%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : LCL856-1 : 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 : n015.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 10:30:58 AM UTC 2026
% Result : Unsatisfiable 13.79s 2.56s
% Output : CNFRefutation 13.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 188
% Syntax : Number of formulae : 1583 (1083 unt; 0 typ; 0 def)
% Number of atoms : 7290 (2709 equ; 0 cnn)
% Maximal formula atoms : 5 ( 4 avg)
% Number of connectives : 23946 (1598 ~;1897 |; 0 &;20451 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 51 ( 48 usr; 13 con; 0-5 aty)
% Number of variables : 5761 ( 0 ^;5761 !; 0 ?;5761 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_c_ATP__Linkup_Osko__Wellfounded__XaccpI__1__1,type,
c_ATP__Linkup_Osko__Wellfounded__XaccpI__1__1: $i > $i > $i > $i ).
thf(tp_c_ATP__Linkup_Osko__Wellfounded__Xaccp__Xintros__1__1,type,
c_ATP__Linkup_Osko__Wellfounded__Xaccp__Xintros__1__1: $i > $i > $i > $i ).
thf(tp_c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__1__1,type,
c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__1__1: $i > $i > $i > $i ).
thf(tp_c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__rule__1__1,type,
c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__rule__1__1: $i > $i > $i > $i ).
thf(tp_c_ATP__Linkup_Osko__Wellfounded__Xnot__accp__down__1__1,type,
c_ATP__Linkup_Osko__Wellfounded__Xnot__accp__down__1__1: $i > $i > $i > $i ).
thf(tp_c_HOL_Ozero__class_Ozero,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
thf(tp_c_InductTermi_OIT,type,
c_InductTermi_OIT: $i ).
thf(tp_c_Lambda_Obeta,type,
c_Lambda_Obeta: $i ).
thf(tp_c_Lambda_OdB_OAbs,type,
c_Lambda_OdB_OAbs: $i > $i ).
thf(tp_c_Lambda_OdB_OApp,type,
c_Lambda_OdB_OApp: $i ).
thf(tp_c_Lambda_OdB_OVar,type,
c_Lambda_OdB_OVar: $i > $i ).
thf(tp_c_Lambda_Olift,type,
c_Lambda_Olift: $i > $i > $i ).
thf(tp_c_Lambda_Osubst,type,
c_Lambda_Osubst: $i > $i > $i > $i ).
thf(tp_c_Lattices_Olower__semilattice__class_Oinf,type,
c_Lattices_Olower__semilattice__class_Oinf: $i > $i > $i > $i ).
thf(tp_c_Lattices_Oupper__semilattice__class_Osup,type,
c_Lattices_Oupper__semilattice__class_Osup: $i > $i > $i > $i ).
thf(tp_c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1,type,
c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1: $i > $i > $i > $i > $i ).
thf(tp_c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1,type,
c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1: $i > $i > $i > $i ).
thf(tp_c_ListOrder_Ostep1,type,
c_ListOrder_Ostep1: $i > $i > $i > $i > $o ).
thf(tp_c_List_Ofoldl,type,
c_List_Ofoldl: $i > $i > $i > $i > $i > $i ).
thf(tp_c_List_Olist_ONil,type,
c_List_Olist_ONil: $i > $i ).
thf(tp_c_List_Olistsp,type,
c_List_Olistsp: $i > $i > $i > $o ).
thf(tp_c_Predicate_Oconversep,type,
c_Predicate_Oconversep: $i > $i > $i > $i ).
thf(tp_c_Predicate_Opred__comp,type,
c_Predicate_Opred__comp: $i > $i > $i > $i > $i > $i ).
thf(tp_c_Transitive__Closure_Ortranclp,type,
c_Transitive__Closure_Ortranclp: $i > $i > $i ).
thf(tp_c_Transitive__Closure_Otranclp,type,
c_Transitive__Closure_Otranclp: $i > $i > $i ).
thf(tp_c_Type_Oshift,type,
c_Type_Oshift: $i > $i > $i > $i > $i ).
thf(tp_c_Type_Otype_OFun,type,
c_Type_Otype_OFun: $i > $i > $i ).
thf(tp_c_Type_Otyping,type,
c_Type_Otyping: $i > $i > $i > $o ).
thf(tp_c_Wellfounded_Oaccp,type,
c_Wellfounded_Oaccp: $i > $i > $i > $o ).
thf(tp_c_Wellfounded_OwfP,type,
c_Wellfounded_OwfP: $i > $i > $o ).
thf(tp_c_fequal,type,
c_fequal: $i > $i ).
thf(tp_class_Lattices_Odistrib__lattice,type,
class_Lattices_Odistrib__lattice: $i > $o ).
thf(tp_class_Lattices_Olattice,type,
class_Lattices_Olattice: $i > $o ).
thf(tp_class_Lattices_Olower__semilattice,type,
class_Lattices_Olower__semilattice: $i > $o ).
thf(tp_class_Lattices_Oupper__semilattice,type,
class_Lattices_Oupper__semilattice: $i > $o ).
thf(tp_hAPP,type,
hAPP: $i > $i > $i ).
thf(tp_hBOOL,type,
hBOOL: $i > $o ).
thf(tp_t_a,type,
t_a: $i ).
thf(tp_tc_Lambda_OdB,type,
tc_Lambda_OdB: $i ).
thf(tp_tc_Type_Otype,type,
tc_Type_Otype: $i ).
thf(tp_tc_bool,type,
tc_bool: $i ).
thf(tp_tc_fun,type,
tc_fun: $i > $i > $i ).
thf(tp_tc_nat,type,
tc_nat: $i ).
thf(tp_v_T,type,
v_T: $i ).
thf(tp_v_e,type,
v_e: $i ).
thf(tp_v_sko__Wellfounded__Xaccp__Xinduct__1,type,
v_sko__Wellfounded__Xaccp__Xinduct__1: $i > $i > $i ).
thf(tp_v_sko__Wellfounded__Xaccp__Xinducts__1,type,
v_sko__Wellfounded__Xaccp__Xinducts__1: $i > $i > $i ).
thf(tp_v_t,type,
v_t: $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_Odistrib__lattice @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Odistrib__lattice) ).
thf(5,axiom,
class_Lattices_Olower__semilattice @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olower__semilattice) ).
thf(6,axiom,
class_Lattices_Oupper__semilattice @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oupper__semilattice) ).
thf(7,axiom,
class_Lattices_Olattice @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olattice) ).
thf(8,axiom,
class_Lattices_Odistrib__lattice @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Lattices_Odistrib__lattice) ).
thf(9,axiom,
class_Lattices_Olower__semilattice @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olower__semilattice) ).
thf(10,axiom,
class_Lattices_Oupper__semilattice @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Lattices_Oupper__semilattice) ).
thf(11,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(12,axiom,
! [T_2: $i,T_1: $i] :
( ( class_Lattices_Odistrib__lattice @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Lattices_Odistrib__lattice @ T_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Odistrib__lattice) ).
thf(13,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(14,axiom,
! [T_2: $i,T_1: $i] :
( ( class_Lattices_Oupper__semilattice @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Lattices_Olattice @ T_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oupper__semilattice) ).
thf(15,axiom,
! [V_s: $i,V_t: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ V_s ) ) @ ( c_Lambda_OdB_OAbs @ V_t ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_s ) @ V_t ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs_0) ).
thf(16,axiom,
! [V_t: $i,V_e: $i,V_T: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_t ) )
| ~ ( c_Type_Otyping @ V_e @ V_t @ V_T ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_type__implies__IT_0) ).
thf(17,axiom,
! [V_r: $i,V_s: $i,T_b: $i,T_c: $i,T_a: $i] :
( ( c_Predicate_Oconversep @ ( c_Predicate_Opred__comp @ V_r @ V_s @ T_b @ T_c @ T_a ) @ T_b @ T_a )
= ( c_Predicate_Opred__comp @ ( c_Predicate_Oconversep @ V_s @ T_c @ T_a ) @ ( c_Predicate_Oconversep @ V_r @ T_b @ T_c ) @ T_a @ T_c @ T_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converse__pred__comp_0) ).
thf(18,axiom,
! [V_P: $i,V_a: $i,V_y: $i,V_r: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ( hBOOL @ ( hAPP @ V_P @ V_y ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__rule__1__1 @ V_P @ V_r @ T_a ) ) )
| ~ ( c_Wellfounded_Oaccp @ V_r @ V_a @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_accp__induct__rule_1) ).
thf(19,axiom,
! [V_P: $i,V_a: $i,V_r: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__rule__1__1 @ V_P @ V_r @ T_a ) ) )
| ~ ( c_Wellfounded_Oaccp @ V_r @ V_a @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_accp__induct__rule_2) ).
thf(20,axiom,
! [V_r: $i,V_i: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Olift @ V_r @ V_i ) ) @ ( c_Lambda_Olift @ V_s @ V_i ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_r ) @ V_s ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift__preserves__beta_0) ).
thf(21,axiom,
! [V_e: $i,V_t_H: $i,V_T: $i,V_t: $i] :
( ( c_Type_Otyping @ V_e @ V_t_H @ V_T )
| ~ ( c_Type_Otyping @ V_e @ V_t @ V_T )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_t ) @ V_t_H ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subject__reduction_H_0) ).
thf(22,axiom,
! [V_P: $i,V_a: $i,V_r: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ( c_Wellfounded_Oaccp @ V_r @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__rule__1__1 @ V_P @ V_r @ T_a ) @ T_a )
| ~ ( c_Wellfounded_Oaccp @ V_r @ V_a @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_accp__induct__rule_0) ).
thf(23,axiom,
! [V_s: $i,V_u: $i,V_t: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_u ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_t ) @ V_u ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_s ) @ V_t ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_appL_0) ).
thf(24,axiom,
! [V_u: $i,V_s: $i,V_t: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_u ) @ V_s ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_u ) @ V_t ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_s ) @ V_t ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_appR_0) ).
thf(25,axiom,
! [V_r: $i,V_x: $i,T_a: $i] :
( ( c_Wellfounded_Oaccp @ V_r @ V_x @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ ( c_ATP__Linkup_Osko__Wellfounded__XaccpI__1__1 @ V_r @ V_x @ T_a ) ) @ V_x ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_accpI_0) ).
thf(26,axiom,
! [V_r: $i,V_x: $i,T_a: $i] :
( ( c_Wellfounded_Oaccp @ V_r @ V_x @ T_a )
| ~ ( c_Wellfounded_Oaccp @ V_r @ ( c_ATP__Linkup_Osko__Wellfounded__XaccpI__1__1 @ V_r @ V_x @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_accpI_1) ).
thf(27,axiom,
! [V_r: $i,V_x: $i,T_a: $i] :
( ( c_Wellfounded_Oaccp @ V_r @ V_x @ T_a )
| ~ ( c_Wellfounded_Oaccp @ V_r @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__Xintros__1__1 @ V_r @ V_x @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_accp_OaccI_1) ).
thf(28,axiom,
! [V_r: $i,V_s: $i,T_b: $i,T_a: $i] :
( ( c_Predicate_Oconversep @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_r @ V_s @ ( tc_fun @ T_b @ ( tc_fun @ T_a @ tc_bool ) ) ) @ T_b @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Predicate_Oconversep @ V_r @ T_b @ T_a ) @ ( c_Predicate_Oconversep @ V_s @ T_b @ T_a ) @ ( tc_fun @ T_a @ ( tc_fun @ T_b @ tc_bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converse__meet_0) ).
thf(29,axiom,
! [V_env: $i,V_x: $i] : ( c_Type_Otyping @ V_env @ ( c_Lambda_OdB_OVar @ V_x ) @ ( hAPP @ V_env @ V_x ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_typing_OVar_0) ).
thf(30,axiom,
! [V_P: $i,V_a: $i,V_r: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ( c_Wellfounded_Oaccp @ V_r @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__1__1 @ V_P @ V_r @ T_a ) @ T_a )
| ~ ( c_Wellfounded_Oaccp @ V_r @ V_a @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_accp__induct_0) ).
thf(31,axiom,
! [V_r: $i,T_a: $i,V_x: $i,V_y: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ V_r @ T_a @ T_a ) @ T_a ) @ V_x ) @ V_y ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_y ) @ V_x ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtranclp__converseI_0) ).
thf(32,axiom,
! [V_r: $i,T_a: $i,V_y: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_y ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ V_r @ T_a @ T_a ) @ T_a ) @ V_x ) @ V_y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtranclp__converseD_0) ).
thf(33,axiom,
! [V_r: $i,V_s: $i,T_b: $i,T_a: $i] :
( ( c_Predicate_Oconversep @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_r @ V_s @ ( tc_fun @ T_b @ ( tc_fun @ T_a @ tc_bool ) ) ) @ T_b @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Predicate_Oconversep @ V_r @ T_b @ T_a ) @ ( c_Predicate_Oconversep @ V_s @ T_b @ T_a ) @ ( tc_fun @ T_a @ ( tc_fun @ T_b @ tc_bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converse__join_0) ).
thf(34,axiom,
! [V_P: $i,V_x: $i,V_r: $i,V_ya: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ( c_Wellfounded_Oaccp @ V_r @ V_ya @ t_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_ya ) @ ( v_sko__Wellfounded__Xaccp__Xinduct__1 @ V_P @ V_r ) ) )
| ~ ( c_Wellfounded_Oaccp @ V_r @ V_x @ t_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_accp_Oinduct_0) ).
thf(35,axiom,
! [V_P: $i,V_x: $i,V_r: $i,V_ya: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ( c_Wellfounded_Oaccp @ V_r @ V_ya @ t_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_ya ) @ ( v_sko__Wellfounded__Xaccp__Xinducts__1 @ V_P @ V_r ) ) )
| ~ ( c_Wellfounded_Oaccp @ V_r @ V_x @ t_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_accp_Oinducts_0) ).
thf(36,axiom,
! [V_r: $i,V_b: $i,V_a: $i,T_a: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_b ) @ V_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ V_r @ T_a @ T_b ) @ V_a ) @ V_b ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conversepD_0) ).
thf(37,axiom,
! [V_r: $i,T_a: $i,T_b: $i,V_a: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ V_r @ T_a @ T_b ) @ V_a ) @ V_b ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_b ) @ V_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conversep__iff_1) ).
thf(38,axiom,
! [V_r: $i,V_a2: $i,V_a1: $i,T_a: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_a2 ) @ V_a1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ V_r @ T_a @ T_b ) @ V_a1 ) @ V_a2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conversep_Ocases_0) ).
thf(39,axiom,
! [V_r: $i,T_a: $i,T_b: $i,V_b: $i,V_a: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ V_r @ T_a @ T_b ) @ V_b ) @ V_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_a ) @ V_b ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conversep_Ointros_0) ).
thf(40,axiom,
! [V_P: $i,V_x: $i,V_y: $i,V_r: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ( hBOOL @ ( hAPP @ V_P @ V_y ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ ( v_sko__Wellfounded__Xaccp__Xinduct__1 @ V_P @ V_r ) ) )
| ~ ( c_Wellfounded_Oaccp @ V_r @ V_x @ t_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_accp_Oinduct_1) ).
thf(41,axiom,
! [V_P: $i,V_x: $i,V_r: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( v_sko__Wellfounded__Xaccp__Xinduct__1 @ V_P @ V_r ) ) )
| ~ ( c_Wellfounded_Oaccp @ V_r @ V_x @ t_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_accp_Oinduct_2) ).
thf(42,axiom,
! [V_r: $i,V_s: $i,V_ss: $i] :
( ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ V_r @ V_s @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
| ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_s @ tc_Lambda_OdB )
| ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_r ) ) @ V_s ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__induction__lemma_0) ).
thf(43,axiom,
! [V_P: $i,V_x: $i,V_y: $i,V_r: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ( hBOOL @ ( hAPP @ V_P @ V_y ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ ( v_sko__Wellfounded__Xaccp__Xinducts__1 @ V_P @ V_r ) ) )
| ~ ( c_Wellfounded_Oaccp @ V_r @ V_x @ t_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_accp_Oinducts_1) ).
thf(44,axiom,
! [V_P: $i,V_x: $i,V_r: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( v_sko__Wellfounded__Xaccp__Xinducts__1 @ V_P @ V_r ) ) )
| ~ ( c_Wellfounded_Oaccp @ V_r @ V_x @ t_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_accp_Oinducts_2) ).
thf(45,axiom,
! [V_r: $i,V_t: $i,V_i: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Osubst @ V_r @ V_t @ V_i ) ) @ ( c_Lambda_Osubst @ V_s @ V_t @ V_i ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_r ) @ V_s ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__preserves__beta_0) ).
thf(46,axiom,
! [V_r: $i,V_b: $i,T_a: $i,V_a: $i] :
( ( c_Wellfounded_Oaccp @ V_r @ V_b @ T_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_b ) @ V_a ) )
| ~ ( c_Wellfounded_Oaccp @ V_r @ V_a @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_accp__downwards_0) ).
thf(47,axiom,
! [V_r: $i,V_b: $i,T_a: $i,V_a: $i] :
( ( c_Wellfounded_Oaccp @ V_r @ V_b @ T_a )
| ~ ( c_Wellfounded_Oaccp @ V_r @ V_a @ T_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_b ) @ V_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_accp__downwards__aux_0) ).
thf(48,axiom,
! [V_t: $i] :
( ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_t @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_t ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IT__implies__termi_0) ).
thf(49,axiom,
! [V_r: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_r ) )
| ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_r @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_termi__implies__IT_0) ).
thf(50,axiom,
! [V_r: $i,T_a: $i] :
( ( c_Transitive__Closure_Otranclp @ ( c_Predicate_Oconversep @ V_r @ T_a @ T_a ) @ T_a )
= ( c_Predicate_Oconversep @ ( c_Transitive__Closure_Otranclp @ V_r @ T_a ) @ T_a @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_tranclp__converse_0) ).
thf(51,axiom,
! [V_R: $i,V_x: $i,T_a: $i] :
( ~ ( c_Wellfounded_Oaccp @ V_R @ ( c_ATP__Linkup_Osko__Wellfounded__Xnot__accp__down__1__1 @ V_R @ V_x @ T_a ) @ T_a )
| ( c_Wellfounded_Oaccp @ V_R @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__accp__down_1) ).
thf(52,axiom,
! [V_e: $i,V_i: $i,V_T: $i] :
( ( ( hAPP @ V_e @ V_i )
= V_T )
| ~ ( c_Type_Otyping @ V_e @ ( c_Lambda_OdB_OVar @ V_i ) @ V_T ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_typing__elims_I1_J_0) ).
thf(53,axiom,
! [V_r: $i,T_a: $i,V_x: $i,V_y: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ ( c_Predicate_Oconversep @ V_r @ T_a @ T_a ) @ T_a ) @ V_x ) @ V_y ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ ( c_Transitive__Closure_Otranclp @ V_r @ T_a ) @ T_a @ T_a ) @ V_x ) @ V_y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_tranclp__converseI_0) ).
thf(54,axiom,
! [V_r: $i,T_a: $i,V_x: $i,V_y: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ ( c_Transitive__Closure_Otranclp @ V_r @ T_a ) @ T_a @ T_a ) @ V_x ) @ V_y ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ ( c_Predicate_Oconversep @ V_r @ T_a @ T_a ) @ T_a ) @ V_x ) @ V_y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_tranclp__converseD_0) ).
thf(55,axiom,
! [T_a: $i] :
( ( c_Predicate_Oconversep @ ( c_fequal @ T_a ) @ T_a @ T_a )
= ( c_fequal @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conversep__eq_0) ).
thf(56,axiom,
! [V_r: $i,V_x: $i,T_a: $i] :
( ( c_Wellfounded_Oaccp @ V_r @ V_x @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__Xintros__1__1 @ V_r @ V_x @ T_a ) ) @ V_x ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_accp_OaccI_0) ).
thf(57,axiom,
! [V_i: $i,V_t: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OVar @ V_i ) ) @ V_t ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_beta__cases_I1_J_0) ).
thf(58,axiom,
! [V_r: $i,T_a: $i,T_b: $i] :
( ( c_Predicate_Oconversep @ ( c_Predicate_Oconversep @ V_r @ T_a @ T_b ) @ T_b @ T_a )
= V_r ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conversep__conversep_0) ).
thf(59,axiom,
! [V_r: $i,V_x: $i,T_a: $i] :
( ( c_Wellfounded_Oaccp @ V_r @ V_x @ T_a )
| ~ ( c_Wellfounded_OwfP @ V_r @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_accp__wfPD_0) ).
thf(60,axiom,
! [V_e: $i,V_t_H: $i,V_T: $i,V_t: $i] :
( ( c_Type_Otyping @ V_e @ V_t_H @ V_T )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_t ) @ V_t_H ) )
| ~ ( c_Type_Otyping @ V_e @ V_t @ V_T ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subject__reduction_0) ).
thf(61,axiom,
! [V_R: $i,V_x: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_R @ ( c_ATP__Linkup_Osko__Wellfounded__Xnot__accp__down__1__1 @ V_R @ V_x @ T_a ) ) @ V_x ) )
| ( c_Wellfounded_Oaccp @ V_R @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__accp__down_0) ).
thf(62,axiom,
! [V_P: $i,V_a: $i,V_y: $i,V_r: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ( hBOOL @ ( hAPP @ V_P @ V_y ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__1__1 @ V_P @ V_r @ T_a ) ) )
| ~ ( c_Wellfounded_Oaccp @ V_r @ V_a @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_accp__induct_1) ).
thf(63,axiom,
! [V_P: $i,V_a: $i,V_r: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__1__1 @ V_P @ V_r @ T_a ) ) )
| ~ ( c_Wellfounded_Oaccp @ V_r @ V_a @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_accp__induct_2) ).
thf(64,axiom,
! [V_r: $i,V_y: $i,T_a: $i,V_a: $i] :
( ( c_Wellfounded_Oaccp @ V_r @ V_y @ T_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ V_a ) )
| ~ ( c_Wellfounded_Oaccp @ V_r @ V_a @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_accp_Ocases_0) ).
thf(65,axiom,
! [V_r: $i,V_a: $i,T_a: $i,V_b: $i] :
( ( c_Wellfounded_Oaccp @ V_r @ V_a @ T_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_a ) @ V_b ) )
| ~ ( c_Wellfounded_Oaccp @ V_r @ V_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_accp__downward_0) ).
thf(66,axiom,
! [V_r: $i,T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ V_r @ T_a ) @ V_a ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ V_r @ T_a ) @ V_b ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_a ) @ V_b ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_tranclp__into__tranclp2_0) ).
thf(67,axiom,
! [V_r: $i,T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ V_r @ T_a ) @ V_a ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_b ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ V_r @ T_a ) @ V_a ) @ V_b ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_tranclp_Otrancl__into__trancl_0) ).
thf(68,axiom,
! [V_r: $i,T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_a ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_b ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_a ) @ V_b ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtranclp_Ortrancl__into__rtrancl_0) ).
thf(69,axiom,
! [V_r: $i,T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_a ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_b ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_a ) @ V_b ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converse__rtranclp__into__rtranclp_0) ).
thf(70,axiom,
! [V_A: $i,V_B: $i,T_a: $i,T_b: $i,V_x: $i,V_y: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ ( tc_fun @ T_b @ tc_bool ) ) ) @ V_x ) @ V_y ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_B @ V_x ) @ V_y ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_A @ V_x ) @ V_y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf2I_0) ).
thf(71,axiom,
! [V_t: $i,V_u: $i,V_s: $i,V_k: $i] :
( ( c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_t ) @ V_u ) @ V_s @ V_k )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ V_t @ V_s @ V_k ) ) @ ( c_Lambda_Osubst @ V_u @ V_s @ V_k ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__App_0) ).
thf(72,axiom,
! [V_dB_H: $i,V_nat: $i] :
( ( c_Lambda_OdB_OAbs @ V_dB_H )
!= ( c_Lambda_OdB_OVar @ V_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I7_J_0) ).
thf(73,axiom,
! [V_dB1: $i,V_dB2: $i,V_dB_H: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1 ) @ V_dB2 )
!= ( c_Lambda_OdB_OAbs @ V_dB_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I8_J_0) ).
thf(74,axiom,
! [V_nat: $i,V_nat_H: $i] :
( ( ( c_Lambda_OdB_OVar @ V_nat )
!= ( c_Lambda_OdB_OVar @ V_nat_H ) )
| ( V_nat = V_nat_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I1_J_0) ).
thf(75,axiom,
! [V_r: $i,T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ V_r @ T_a ) @ V_x ) @ V_z ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ V_r @ T_a ) @ V_y ) @ V_z ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ V_r @ T_a ) @ V_x ) @ V_y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_tranclp__trans_0) ).
thf(76,axiom,
! [V_dB_H: $i,V_dB1: $i,V_dB2: $i] :
( ( c_Lambda_OdB_OAbs @ V_dB_H )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1 ) @ V_dB2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I9_J_0) ).
thf(77,axiom,
! [V_m: $i,V_rs: $i,V_n: $i,V_ss: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_m ) @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_m = V_n ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Var__apps__eq__Var__apps__conv_0) ).
thf(78,axiom,
! [V_m: $i,V_rs: $i,V_n: $i,V_ss: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_m ) @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_rs = V_ss ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Var__apps__eq__Var__apps__conv_1) ).
thf(79,axiom,
! [V_k: $i,V_u: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ V_k ) @ V_u @ V_k )
= V_u ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__eq_0) ).
thf(80,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(81,axiom,
! [V_r: $i,T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Otranclp @ V_r @ T_a ) @ ( c_fequal @ T_a ) @ ( tc_fun @ T_a @ ( tc_fun @ T_a @ tc_bool ) ) )
= ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_reflcl__tranclp_0) ).
thf(82,axiom,
! [V_r: $i,V_i: $i,V_j: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ V_r @ ( c_Lambda_OdB_OVar @ V_i ) @ V_j ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_r ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__Var__IT_0) ).
thf(83,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(84,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(85,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_z @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__inf__distrib1_0) ).
thf(86,axiom,
! [T_a: $i,V_y: $i,V_z: $i,V_x: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ V_x @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_x @ T_a ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_z @ V_x @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__inf__distrib2_0) ).
thf(87,axiom,
! [V_R: $i,T_a: $i,V_S: $i] :
( ( c_Transitive__Closure_Ortranclp @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Ortranclp @ V_R @ T_a ) @ ( c_Transitive__Closure_Ortranclp @ V_S @ T_a ) @ ( tc_fun @ T_a @ ( tc_fun @ T_a @ tc_bool ) ) ) @ T_a )
= ( c_Transitive__Closure_Ortranclp @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_R @ V_S @ ( tc_fun @ T_a @ ( tc_fun @ T_a @ tc_bool ) ) ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtranclp__sup__rtranclp_0) ).
thf(88,axiom,
! [V_r: $i,V_ss: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_r @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_r ) @ V_s ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_apps__preserves__beta2_0) ).
thf(89,axiom,
! [V_R: $i,T_a: $i,V_a: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ V_R @ T_a ) @ V_a ) @ V_b ) )
| ( V_a = V_b )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_R @ T_a ) @ V_a ) @ V_b ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtranclpD_0) ).
thf(90,axiom,
! [V_r: $i,T_a: $i,V_a: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ V_r @ T_a ) @ V_a ) @ V_b ) )
| ( V_a = V_b )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_a ) @ V_b ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nitpick_Ortranclp__def_0) ).
thf(91,axiom,
! [V_R: $i,T_a: $i] :
( ( c_Transitive__Closure_Ortranclp @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_R @ ( c_fequal @ T_a ) @ ( tc_fun @ T_a @ ( tc_fun @ T_a @ tc_bool ) ) ) @ T_a )
= ( c_Transitive__Closure_Ortranclp @ V_R @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtranclp__reflcl_0) ).
thf(92,axiom,
! [V_s: $i,V_ss: $i,V_r: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ V_r ) )
| ( V_s
= ( c_Lambda_OdB_OAbs @ V_r ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_apps__eq__Abs__conv_0) ).
thf(93,axiom,
! [V_r: $i,V_rs: $i,V_s: $i,V_ss: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_r ) @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_s ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_r = V_s ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Abs__apps__eq__Abs__apps__conv_0) ).
thf(94,axiom,
! [V_r: $i,V_rs: $i,V_s: $i,V_ss: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_r ) @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_s ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_rs = V_ss ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Abs__apps__eq__Abs__apps__conv_1) ).
thf(95,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_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ T_a )
= V_x ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__absorb_0) ).
thf(96,axiom,
! [V_dB1: $i,V_dB2: $i,V_dB1_H: $i,V_dB2_H: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1 ) @ V_dB2 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1_H ) @ V_dB2_H ) )
| ( V_dB1 = V_dB1_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I2_J_0) ).
thf(97,axiom,
! [V_dB1: $i,V_dB2: $i,V_dB1_H: $i,V_dB2_H: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1 ) @ V_dB2 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1_H ) @ V_dB2_H ) )
| ( V_dB2 = V_dB2_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I2_J_1) ).
thf(98,axiom,
! [V_T: $i,V_U: $i,V_e: $i,V_i: $i,V_ts: $i] :
( ( V_T = V_U )
| ~ ( c_Type_Otyping @ V_e @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_i ) @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_U )
| ~ ( c_Type_Otyping @ V_e @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_i ) @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_T ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_var__app__type__eq_0) ).
thf(99,axiom,
! [V_r: $i,V_i: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Olift @ V_r @ V_i ) ) @ ( c_Lambda_Olift @ V_s @ V_i ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_r ) @ V_s ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift__preserves__beta_H_0) ).
thf(100,axiom,
! [V_s: $i,V_t: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_s ) ) @ V_t ) ) @ ( c_Lambda_Osubst @ V_s @ V_t @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_beta_0) ).
thf(101,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ T_a )
= V_x ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__inf__absorb_0) ).
thf(102,axiom,
! [V_r: $i,V_ss: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_r @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_r ) @ V_s ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_apps__preserves__beta_0) ).
thf(103,axiom,
! [V_m: $i,V_s: $i,V_ss: $i] :
( ( ( c_Lambda_OdB_OVar @ V_m )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OVar @ V_m )
= V_s ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Var__eq__apps__conv_0) ).
thf(104,axiom,
! [V_nat: $i,V_dB1_H: $i,V_dB2_H: $i] :
( ( c_Lambda_OdB_OVar @ V_nat )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1_H ) @ V_dB2_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I4_J_0) ).
thf(105,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(106,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(107,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(108,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(109,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(110,axiom,
! [V_n: $i,V_ts: $i,V_r: $i,V_ss: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_r ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Var__apps__neq__Abs__apps_0) ).
thf(111,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(112,axiom,
! [V_r: $i,V_s: $i,V_ss: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_r ) ) @ V_s ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_s ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ V_r @ V_s @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Beta_0) ).
thf(113,axiom,
! [V_A: $i,V_B: $i,T_a: $i,T_b: $i,V_x: $i,V_y: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ ( tc_fun @ T_b @ tc_bool ) ) ) @ V_x ) @ V_y ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_A @ V_x ) @ V_y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup2CI_1) ).
thf(114,axiom,
! [V_A: $i,V_B: $i,T_a: $i,T_b: $i,V_x: $i,V_y: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ ( tc_fun @ T_b @ tc_bool ) ) ) @ V_x ) @ V_y ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_B @ V_x ) @ V_y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup2CI_0) ).
thf(115,axiom,
! [V_B: $i,V_x: $i,V_y: $i,V_A: $i,T_a: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_B @ V_x ) @ V_y ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ V_A @ V_x ) @ V_y ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ ( tc_fun @ T_b @ tc_bool ) ) ) @ V_x ) @ V_y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup2E_0) ).
thf(116,axiom,
! [V_r: $i,T_a: $i,V_x: $i,V_y: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_x ) @ V_y ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_x ) @ V_y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_r__into__rtranclp_0) ).
thf(117,axiom,
! [V_nat: $i,V_dB_H: $i] :
( ( c_Lambda_OdB_OVar @ V_nat )
!= ( c_Lambda_OdB_OAbs @ V_dB_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I6_J_0) ).
thf(118,axiom,
! [V_n: $i] : ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OVar @ V_n ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Var__IT_0) ).
thf(119,axiom,
! [V_t: $i,V_r: $i,V_i: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ V_t @ V_r @ V_i ) ) @ ( c_Lambda_Osubst @ V_t @ V_s @ V_i ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_r ) @ V_s ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__preserves__beta2_H_0) ).
thf(120,axiom,
! [V_r: $i,V_t: $i,V_i: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ V_r @ V_t @ V_i ) ) @ ( c_Lambda_Osubst @ V_s @ V_t @ V_i ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_r ) @ V_s ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__preserves__beta_H_0) ).
thf(121,axiom,
! [V_r: $i,T_a: $i,V_a: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_a ) @ V_b ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ V_r @ T_a ) @ V_a ) @ V_b ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nitpick_Ortranclp__def_2) ).
thf(122,axiom,
! [V_r: $i,T_a: $i] :
( ( c_Wellfounded_OwfP @ ( c_Transitive__Closure_Otranclp @ V_r @ T_a ) @ T_a )
| ~ ( c_Wellfounded_OwfP @ V_r @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wfP__trancl_0) ).
thf(123,axiom,
! [V_s: $i,V_t: $i,V_k: $i] :
( ( c_Lambda_Olift @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_t ) @ V_k )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Olift @ V_s @ V_k ) ) @ ( c_Lambda_Olift @ V_t @ V_k ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift_Osimps_I2_J_0) ).
thf(124,axiom,
! [V_r: $i,T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ V_r @ T_a ) @ V_a ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_b ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_a ) @ V_b ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtranclp__into__tranclp1_0) ).
thf(125,axiom,
! [V_r: $i,T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ V_r @ T_a ) @ V_a ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_b ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_a ) @ V_b ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtranclp__into__tranclp2_0) ).
thf(126,axiom,
! [V_t: $i,V_r: $i,V_i: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ V_t @ V_r @ V_i ) ) @ ( c_Lambda_Osubst @ V_t @ V_s @ V_i ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_r ) @ V_s ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__preserves__beta2_0) ).
thf(127,axiom,
! [V_r: $i,T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_x ) @ V_z ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_y ) @ V_z ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_x ) @ V_y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtranclp__trans_0) ).
thf(128,axiom,
! [V_r: $i,T_a: $i,V_x: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_x ) @ V_x ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nitpick_Ortranclp__def_1) ).
thf(129,axiom,
! [V_r: $i,T_a: $i,V_a: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_a ) @ V_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtranclp_Ortrancl__refl_0) ).
thf(130,axiom,
! [V_r: $i,T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ V_r @ T_a ) @ V_x ) @ V_z ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ V_r @ T_a ) @ V_y ) @ V_z ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_x ) @ V_y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtranclp__tranclp__tranclp_0) ).
thf(131,axiom,
! [V_r: $i,T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ V_r @ T_a ) @ V_a ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_b ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ V_r @ T_a ) @ V_a ) @ V_b ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_tranclp__rtranclp__tranclp_0) ).
thf(132,axiom,
! [V_r: $i,V_s: $i,T_a: $i,T_b: $i,T_c: $i,V_a: $i,V_c: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ V_r @ V_s @ T_a @ T_b @ T_c ) @ V_a ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_s @ V_b ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_a ) @ V_b ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pred__comp_Ointros_0) ).
thf(133,axiom,
! [V_s: $i,V_s_H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_OdB_OAbs @ V_s ) ) @ ( c_Lambda_OdB_OAbs @ V_s_H ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_s ) @ V_s_H ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__beta__Abs_0) ).
thf(134,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_z @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__distrib1_0) ).
thf(135,axiom,
! [T_a: $i,V_y: $i,V_z: $i,V_x: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) @ V_x @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_x @ T_a ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_z @ V_x @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__distrib2_0) ).
thf(136,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_x @ T_a )
= V_x ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__idem_0) ).
thf(137,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ V_z @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__assoc_0) ).
thf(138,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_z @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__left__commute_0) ).
thf(139,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_z @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I7_J_0) ).
thf(140,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ V_z @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I6_J_0) ).
thf(141,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(142,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(143,axiom,
! [V_r: $i,V_s: $i,V_ss: $i] :
( ( ( c_Lambda_OdB_OAbs @ V_r )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OAbs @ V_r )
= V_s ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Abs__eq__apps__conv_0) ).
thf(144,axiom,
! [V_s: $i,V_t: $i,V_t_H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_t ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_t_H ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_t ) @ V_t_H ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__beta__AppR_0) ).
thf(145,axiom,
! [V_s: $i,V_t: $i,V_s_H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_t ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s_H ) @ V_t ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_s ) @ V_s_H ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__beta__AppL_0) ).
thf(146,axiom,
! [V_r: $i,V_ts: $i,V_s: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_r @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_r = V_s ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_apps__eq__tail__conv_0) ).
thf(147,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(148,axiom,
! [V_s: $i,V_t: $i,V_s_H: $i,V_t_H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_t ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s_H ) @ V_t_H ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_t ) @ V_t_H ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_s ) @ V_s_H ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__beta__App_0) ).
thf(149,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_x @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__commute_0) ).
thf(150,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_x @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I5_J_0) ).
thf(151,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__left__idem_0) ).
thf(152,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I8_J_0) ).
thf(153,axiom,
! [V_r: $i,T_a: $i,V_a: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ V_r @ T_a ) @ V_a ) @ V_b ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_a ) @ V_b ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_tranclp_Or__into__trancl_0) ).
thf(154,axiom,
! [V_t: $i,V_k: $i,V_s: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_Olift @ V_t @ V_k ) @ V_s @ V_k )
= V_t ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__lift_0) ).
thf(155,axiom,
! [V_t: $i,V_i: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_t ) @ ( c_Lambda_OdB_OVar @ V_i ) ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_t ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_app__Var__IT_0) ).
thf(156,axiom,
! [V_B: $i,V_x: $i,V_y: $i,V_A: $i,T_a: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_B @ V_x ) @ V_y ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ ( tc_fun @ T_b @ tc_bool ) ) ) @ V_x ) @ V_y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf2E_1) ).
thf(157,axiom,
! [V_A: $i,V_x: $i,V_y: $i,V_B: $i,T_a: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_A @ V_x ) @ V_y ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ ( tc_fun @ T_b @ tc_bool ) ) ) @ V_x ) @ V_y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf2E_0) ).
thf(158,axiom,
! [V_s: $i,V_t: $i,V_n: $i,V_ss: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_s ) ) @ V_t )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Abs__App__neq__Var__apps_0) ).
thf(159,axiom,
! [V_r: $i,T_a: $i] :
( ( c_Transitive__Closure_Ortranclp @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ T_a )
= ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtranclp__idemp_0) ).
thf(160,axiom,
! [V_dB1_H: $i,V_dB2_H: $i,V_nat: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1_H ) @ V_dB2_H )
!= ( c_Lambda_OdB_OVar @ V_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I5_J_0) ).
thf(161,axiom,
! [V_n: $i,V_rs: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( c_List_Olistsp @ c_InductTermi_OIT @ V_rs @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IT_OVar_0) ).
thf(162,axiom,
! [V_v: $i,V_n: $i,V_rs: $i] :
( ( V_v
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ V_n @ V_rs @ V_v ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ V_v ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_head__Var__reduction_1) ).
thf(163,axiom,
! [V_t: $i,V_u: $i,V_i: $i,V_e: $i,V_U: $i,V_T: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ V_t @ V_u @ V_i ) ) )
| ~ ( c_Type_Otyping @ V_e @ V_u @ V_U )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_u ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ V_e @ V_i @ V_U @ tc_Type_Otype ) @ V_t @ V_T )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_t ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__type__IT_0) ).
thf(164,axiom,
! [V_m: $i] :
( ( c_Lambda_OdB_OVar @ V_m )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_m ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Var__eq__apps__conv_2) ).
thf(165,axiom,
! [V_m: $i,V_s: $i,V_ss: $i] :
( ( ( c_Lambda_OdB_OVar @ V_m )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_ss
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Var__eq__apps__conv_1) ).
thf(166,axiom,
! [V_r: $i,V_s: $i,V_t: $i,V_ts: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_r ) @ V_s )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_r
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ V_r @ V_s @ V_t @ V_ts ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_ts
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_App__eq__foldl__conv_2) ).
thf(167,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(168,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(169,axiom,
! [V_e: $i,V_x: $i,V_T: $i,T_a: $i] :
( ( hAPP @ ( c_Type_Oshift @ V_e @ V_x @ V_T @ T_a ) @ V_x )
= V_T ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_shift__eq_0) ).
thf(170,axiom,
! [V_env: $i,V_t: $i,V_T: $i,V_U: $i] :
( ( c_Type_Otyping @ V_env @ ( c_Lambda_OdB_OAbs @ V_t ) @ ( c_Type_Otype_OFun @ V_T @ V_U ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ V_env @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_T @ tc_Type_Otype ) @ V_t @ V_U ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Abs_0) ).
thf(171,axiom,
! [V_r: $i,V_s: $i,V_t: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_r ) @ V_s )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_r ) @ V_s )
= V_t ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_App__eq__foldl__conv_0) ).
thf(172,axiom,
! [V_r: $i,V_s: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_r ) @ V_s )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_r ) @ V_s ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_App__eq__foldl__conv_4) ).
thf(173,axiom,
! [V_rs: $i,V_n: $i,V_v: $i] :
( ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ V_rs @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ V_n @ V_rs @ V_v ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ V_v ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_head__Var__reduction_0) ).
thf(174,axiom,
! [V_e_H: $i,V_u: $i,V_U: $i,V_i: $i,V_t: $i,V_T: $i] :
( ~ ( c_Type_Otyping @ V_e_H @ V_u @ V_U )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ V_e_H @ V_i @ V_U @ tc_Type_Otype ) @ V_t @ V_T )
| ( c_Type_Otyping @ V_e_H @ ( c_Lambda_Osubst @ V_t @ V_u @ V_i ) @ V_T ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__lemma_0) ).
thf(175,axiom,
! [V_e: $i,V_i: $i,V_U: $i,V_t: $i,V_T: $i] :
( ( c_Type_Otyping @ ( c_Type_Oshift @ V_e @ V_i @ V_U @ tc_Type_Otype ) @ ( c_Lambda_Olift @ V_t @ V_i ) @ V_T )
| ~ ( c_Type_Otyping @ V_e @ V_t @ V_T ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift__type_0) ).
thf(176,axiom,
! [V_r: $i,V_rs: $i,V_ss: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_r @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_r @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ V_rs @ V_ss @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_apps__preserves__betas_0) ).
thf(177,axiom,
! [V_r: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_r ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_Lambda_OdB_OAbs @ V_r ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_apps__eq__Abs__conv_2) ).
thf(178,axiom,
! [V_s: $i,V_ss: $i,V_r: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ V_r ) )
| ( V_ss
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_apps__eq__Abs__conv_1) ).
thf(179,axiom,
! [V_r: $i] :
( ( c_Lambda_OdB_OAbs @ V_r )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_r ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Abs__eq__apps__conv_2) ).
thf(180,axiom,
! [V_r: $i,V_s: $i,V_ss: $i] :
( ( ( c_Lambda_OdB_OAbs @ V_r )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_ss
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Abs__eq__apps__conv_1) ).
thf(181,axiom,
! [V_env: $i,V_s: $i,V_t: $i,V_U: $i,V_T: $i] :
( ( c_Type_Otyping @ V_env @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_t ) @ V_U )
| ~ ( c_Type_Otyping @ V_env @ V_t @ V_T )
| ~ ( c_Type_Otyping @ V_env @ V_s @ ( c_Type_Otype_OFun @ V_T @ V_U ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_App_0) ).
thf(182,axiom,
! [V_type1: $i,V_type2: $i,V_type1_H: $i,V_type2_H: $i] :
( ( ( c_Type_Otype_OFun @ V_type1 @ V_type2 )
!= ( c_Type_Otype_OFun @ V_type1_H @ V_type2_H ) )
| ( V_type1 = V_type1_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_type_Osimps_I2_J_0) ).
thf(183,axiom,
! [V_type1: $i,V_type2: $i,V_type1_H: $i,V_type2_H: $i] :
( ( ( c_Type_Otype_OFun @ V_type1 @ V_type2 )
!= ( c_Type_Otype_OFun @ V_type1_H @ V_type2_H ) )
| ( V_type2 = V_type2_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_type_Osimps_I2_J_1) ).
thf(184,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(185,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(186,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(187,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[186]) ).
thf(188,negated_conjecture,
~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ v_t @ tc_Lambda_OdB ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(189,negated_conjecture,
c_Type_Otyping @ v_e @ v_t @ v_T,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(190,plain,
$false = $false,
inference(unfold_def,[status(thm)],[187]) ).
thf(191,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(192,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(193,plain,
( ( class_Lattices_Olattice @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(194,plain,
( ( class_Lattices_Odistrib__lattice @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(195,plain,
( ( class_Lattices_Olower__semilattice @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(196,plain,
( ( class_Lattices_Oupper__semilattice @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(197,plain,
( ( class_Lattices_Olattice @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(198,plain,
( ( class_Lattices_Odistrib__lattice @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(199,plain,
( ( class_Lattices_Olower__semilattice @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(200,plain,
( ( class_Lattices_Oupper__semilattice @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(201,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)],[11]) ).
thf(202,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Lattices_Odistrib__lattice @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Lattices_Odistrib__lattice @ T_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(203,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)],[13]) ).
thf(204,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Lattices_Oupper__semilattice @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Lattices_Olattice @ T_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(205,plain,
( ( ! [V_s: $i,V_t: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ V_s ) ) @ ( c_Lambda_OdB_OAbs @ V_t ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_s ) @ V_t ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(206,plain,
( ( ! [V_t: $i,V_e: $i,V_T: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_t ) )
| ~ ( c_Type_Otyping @ V_e @ V_t @ V_T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(207,plain,
( ( ! [V_r: $i,V_s: $i,T_b: $i,T_c: $i,T_a: $i] :
( ( c_Predicate_Oconversep @ ( c_Predicate_Opred__comp @ V_r @ V_s @ T_b @ T_c @ T_a ) @ T_b @ T_a )
= ( c_Predicate_Opred__comp @ ( c_Predicate_Oconversep @ V_s @ T_c @ T_a ) @ ( c_Predicate_Oconversep @ V_r @ T_b @ T_c ) @ T_a @ T_c @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(208,plain,
( ( ! [V_P: $i,V_a: $i,V_y: $i,V_r: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ( hBOOL @ ( hAPP @ V_P @ V_y ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__rule__1__1 @ V_P @ V_r @ T_a ) ) )
| ~ ( c_Wellfounded_Oaccp @ V_r @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(209,plain,
( ( ! [V_P: $i,V_a: $i,V_r: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__rule__1__1 @ V_P @ V_r @ T_a ) ) )
| ~ ( c_Wellfounded_Oaccp @ V_r @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(210,plain,
( ( ! [V_r: $i,V_i: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Olift @ V_r @ V_i ) ) @ ( c_Lambda_Olift @ V_s @ V_i ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_r ) @ V_s ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(211,plain,
( ( ! [V_e: $i,V_t_H: $i,V_T: $i,V_t: $i] :
( ( c_Type_Otyping @ V_e @ V_t_H @ V_T )
| ~ ( c_Type_Otyping @ V_e @ V_t @ V_T )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_t ) @ V_t_H ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(212,plain,
( ( ! [V_P: $i,V_a: $i,V_r: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ( c_Wellfounded_Oaccp @ V_r @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__rule__1__1 @ V_P @ V_r @ T_a ) @ T_a )
| ~ ( c_Wellfounded_Oaccp @ V_r @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(213,plain,
( ( ! [V_s: $i,V_u: $i,V_t: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_u ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_t ) @ V_u ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_s ) @ V_t ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(214,plain,
( ( ! [V_u: $i,V_s: $i,V_t: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_u ) @ V_s ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_u ) @ V_t ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_s ) @ V_t ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(215,plain,
( ( ! [V_r: $i,V_x: $i,T_a: $i] :
( ( c_Wellfounded_Oaccp @ V_r @ V_x @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ ( c_ATP__Linkup_Osko__Wellfounded__XaccpI__1__1 @ V_r @ V_x @ T_a ) ) @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(216,plain,
( ( ! [V_r: $i,V_x: $i,T_a: $i] :
( ( c_Wellfounded_Oaccp @ V_r @ V_x @ T_a )
| ~ ( c_Wellfounded_Oaccp @ V_r @ ( c_ATP__Linkup_Osko__Wellfounded__XaccpI__1__1 @ V_r @ V_x @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(217,plain,
( ( ! [V_r: $i,V_x: $i,T_a: $i] :
( ( c_Wellfounded_Oaccp @ V_r @ V_x @ T_a )
| ~ ( c_Wellfounded_Oaccp @ V_r @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__Xintros__1__1 @ V_r @ V_x @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(218,plain,
( ( ! [V_r: $i,V_s: $i,T_b: $i,T_a: $i] :
( ( c_Predicate_Oconversep @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_r @ V_s @ ( tc_fun @ T_b @ ( tc_fun @ T_a @ tc_bool ) ) ) @ T_b @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Predicate_Oconversep @ V_r @ T_b @ T_a ) @ ( c_Predicate_Oconversep @ V_s @ T_b @ T_a ) @ ( tc_fun @ T_a @ ( tc_fun @ T_b @ tc_bool ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(219,plain,
( ( ! [V_env: $i,V_x: $i] : ( c_Type_Otyping @ V_env @ ( c_Lambda_OdB_OVar @ V_x ) @ ( hAPP @ V_env @ V_x ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(220,plain,
( ( ! [V_P: $i,V_a: $i,V_r: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ( c_Wellfounded_Oaccp @ V_r @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__1__1 @ V_P @ V_r @ T_a ) @ T_a )
| ~ ( c_Wellfounded_Oaccp @ V_r @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(221,plain,
( ( ! [V_r: $i,T_a: $i,V_x: $i,V_y: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ V_r @ T_a @ T_a ) @ T_a ) @ V_x ) @ V_y ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_y ) @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(222,plain,
( ( ! [V_r: $i,T_a: $i,V_y: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_y ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ V_r @ T_a @ T_a ) @ T_a ) @ V_x ) @ V_y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(223,plain,
( ( ! [V_r: $i,V_s: $i,T_b: $i,T_a: $i] :
( ( c_Predicate_Oconversep @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_r @ V_s @ ( tc_fun @ T_b @ ( tc_fun @ T_a @ tc_bool ) ) ) @ T_b @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Predicate_Oconversep @ V_r @ T_b @ T_a ) @ ( c_Predicate_Oconversep @ V_s @ T_b @ T_a ) @ ( tc_fun @ T_a @ ( tc_fun @ T_b @ tc_bool ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(224,plain,
( ( ! [V_P: $i,V_x: $i,V_r: $i,V_ya: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ( c_Wellfounded_Oaccp @ V_r @ V_ya @ t_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_ya ) @ ( v_sko__Wellfounded__Xaccp__Xinduct__1 @ V_P @ V_r ) ) )
| ~ ( c_Wellfounded_Oaccp @ V_r @ V_x @ t_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(225,plain,
( ( ! [V_P: $i,V_x: $i,V_r: $i,V_ya: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ( c_Wellfounded_Oaccp @ V_r @ V_ya @ t_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_ya ) @ ( v_sko__Wellfounded__Xaccp__Xinducts__1 @ V_P @ V_r ) ) )
| ~ ( c_Wellfounded_Oaccp @ V_r @ V_x @ t_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(226,plain,
( ( ! [V_r: $i,V_b: $i,V_a: $i,T_a: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_b ) @ V_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ V_r @ T_a @ T_b ) @ V_a ) @ V_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(227,plain,
( ( ! [V_r: $i,T_a: $i,T_b: $i,V_a: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ V_r @ T_a @ T_b ) @ V_a ) @ V_b ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_b ) @ V_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(228,plain,
( ( ! [V_r: $i,V_a2: $i,V_a1: $i,T_a: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_a2 ) @ V_a1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ V_r @ T_a @ T_b ) @ V_a1 ) @ V_a2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(229,plain,
( ( ! [V_r: $i,T_a: $i,T_b: $i,V_b: $i,V_a: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ V_r @ T_a @ T_b ) @ V_b ) @ V_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_a ) @ V_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(230,plain,
( ( ! [V_P: $i,V_x: $i,V_y: $i,V_r: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ( hBOOL @ ( hAPP @ V_P @ V_y ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ ( v_sko__Wellfounded__Xaccp__Xinduct__1 @ V_P @ V_r ) ) )
| ~ ( c_Wellfounded_Oaccp @ V_r @ V_x @ t_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(231,plain,
( ( ! [V_P: $i,V_x: $i,V_r: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( v_sko__Wellfounded__Xaccp__Xinduct__1 @ V_P @ V_r ) ) )
| ~ ( c_Wellfounded_Oaccp @ V_r @ V_x @ t_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(232,plain,
( ( ! [V_r: $i,V_s: $i,V_ss: $i] :
( ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ V_r @ V_s @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
| ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_s @ tc_Lambda_OdB )
| ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_r ) ) @ V_s ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(233,plain,
( ( ! [V_P: $i,V_x: $i,V_y: $i,V_r: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ( hBOOL @ ( hAPP @ V_P @ V_y ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ ( v_sko__Wellfounded__Xaccp__Xinducts__1 @ V_P @ V_r ) ) )
| ~ ( c_Wellfounded_Oaccp @ V_r @ V_x @ t_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(234,plain,
( ( ! [V_P: $i,V_x: $i,V_r: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( v_sko__Wellfounded__Xaccp__Xinducts__1 @ V_P @ V_r ) ) )
| ~ ( c_Wellfounded_Oaccp @ V_r @ V_x @ t_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(235,plain,
( ( ! [V_r: $i,V_t: $i,V_i: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Osubst @ V_r @ V_t @ V_i ) ) @ ( c_Lambda_Osubst @ V_s @ V_t @ V_i ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_r ) @ V_s ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(236,plain,
( ( ! [V_r: $i,V_b: $i,T_a: $i,V_a: $i] :
( ( c_Wellfounded_Oaccp @ V_r @ V_b @ T_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_b ) @ V_a ) )
| ~ ( c_Wellfounded_Oaccp @ V_r @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(237,plain,
( ( ! [V_r: $i,V_b: $i,T_a: $i,V_a: $i] :
( ( c_Wellfounded_Oaccp @ V_r @ V_b @ T_a )
| ~ ( c_Wellfounded_Oaccp @ V_r @ V_a @ T_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_b ) @ V_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(238,plain,
( ( ! [V_t: $i] :
( ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_t @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_t ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(239,plain,
( ( ! [V_r: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_r ) )
| ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_r @ tc_Lambda_OdB ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(240,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Transitive__Closure_Otranclp @ ( c_Predicate_Oconversep @ V_r @ T_a @ T_a ) @ T_a )
= ( c_Predicate_Oconversep @ ( c_Transitive__Closure_Otranclp @ V_r @ T_a ) @ T_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(241,plain,
( ( ! [V_R: $i,V_x: $i,T_a: $i] :
( ~ ( c_Wellfounded_Oaccp @ V_R @ ( c_ATP__Linkup_Osko__Wellfounded__Xnot__accp__down__1__1 @ V_R @ V_x @ T_a ) @ T_a )
| ( c_Wellfounded_Oaccp @ V_R @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(242,plain,
( ( ! [V_e: $i,V_i: $i,V_T: $i] :
( ( ( hAPP @ V_e @ V_i )
= V_T )
| ~ ( c_Type_Otyping @ V_e @ ( c_Lambda_OdB_OVar @ V_i ) @ V_T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(243,plain,
( ( ! [V_r: $i,T_a: $i,V_x: $i,V_y: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ ( c_Predicate_Oconversep @ V_r @ T_a @ T_a ) @ T_a ) @ V_x ) @ V_y ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ ( c_Transitive__Closure_Otranclp @ V_r @ T_a ) @ T_a @ T_a ) @ V_x ) @ V_y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(244,plain,
( ( ! [V_r: $i,T_a: $i,V_x: $i,V_y: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ ( c_Transitive__Closure_Otranclp @ V_r @ T_a ) @ T_a @ T_a ) @ V_x ) @ V_y ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ ( c_Predicate_Oconversep @ V_r @ T_a @ T_a ) @ T_a ) @ V_x ) @ V_y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(245,plain,
( ( ! [T_a: $i] :
( ( c_Predicate_Oconversep @ ( c_fequal @ T_a ) @ T_a @ T_a )
= ( c_fequal @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(246,plain,
( ( ! [V_r: $i,V_x: $i,T_a: $i] :
( ( c_Wellfounded_Oaccp @ V_r @ V_x @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__Xintros__1__1 @ V_r @ V_x @ T_a ) ) @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[56]) ).
thf(247,plain,
( ( ! [V_i: $i,V_t: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OVar @ V_i ) ) @ V_t ) ) )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(248,plain,
( ( ! [V_r: $i,T_a: $i,T_b: $i] :
( ( c_Predicate_Oconversep @ ( c_Predicate_Oconversep @ V_r @ T_a @ T_b ) @ T_b @ T_a )
= V_r ) )
= $true ),
inference(unfold_def,[status(thm)],[58]) ).
thf(249,plain,
( ( ! [V_r: $i,V_x: $i,T_a: $i] :
( ( c_Wellfounded_Oaccp @ V_r @ V_x @ T_a )
| ~ ( c_Wellfounded_OwfP @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[59]) ).
thf(250,plain,
( ( ! [V_e: $i,V_t_H: $i,V_T: $i,V_t: $i] :
( ( c_Type_Otyping @ V_e @ V_t_H @ V_T )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_t ) @ V_t_H ) )
| ~ ( c_Type_Otyping @ V_e @ V_t @ V_T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(251,plain,
( ( ! [V_R: $i,V_x: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_R @ ( c_ATP__Linkup_Osko__Wellfounded__Xnot__accp__down__1__1 @ V_R @ V_x @ T_a ) ) @ V_x ) )
| ( c_Wellfounded_Oaccp @ V_R @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(252,plain,
( ( ! [V_P: $i,V_a: $i,V_y: $i,V_r: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ( hBOOL @ ( hAPP @ V_P @ V_y ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__1__1 @ V_P @ V_r @ T_a ) ) )
| ~ ( c_Wellfounded_Oaccp @ V_r @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[62]) ).
thf(253,plain,
( ( ! [V_P: $i,V_a: $i,V_r: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__1__1 @ V_P @ V_r @ T_a ) ) )
| ~ ( c_Wellfounded_Oaccp @ V_r @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[63]) ).
thf(254,plain,
( ( ! [V_r: $i,V_y: $i,T_a: $i,V_a: $i] :
( ( c_Wellfounded_Oaccp @ V_r @ V_y @ T_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ V_a ) )
| ~ ( c_Wellfounded_Oaccp @ V_r @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[64]) ).
thf(255,plain,
( ( ! [V_r: $i,V_a: $i,T_a: $i,V_b: $i] :
( ( c_Wellfounded_Oaccp @ V_r @ V_a @ T_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_a ) @ V_b ) )
| ~ ( c_Wellfounded_Oaccp @ V_r @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[65]) ).
thf(256,plain,
( ( ! [V_r: $i,T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ V_r @ T_a ) @ V_a ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ V_r @ T_a ) @ V_b ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_a ) @ V_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[66]) ).
thf(257,plain,
( ( ! [V_r: $i,T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ V_r @ T_a ) @ V_a ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_b ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ V_r @ T_a ) @ V_a ) @ V_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[67]) ).
thf(258,plain,
( ( ! [V_r: $i,T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_a ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_b ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_a ) @ V_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[68]) ).
thf(259,plain,
( ( ! [V_r: $i,T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_a ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_b ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_a ) @ V_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[69]) ).
thf(260,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,T_b: $i,V_x: $i,V_y: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ ( tc_fun @ T_b @ tc_bool ) ) ) @ V_x ) @ V_y ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_B @ V_x ) @ V_y ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_A @ V_x ) @ V_y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(261,plain,
( ( ! [V_t: $i,V_u: $i,V_s: $i,V_k: $i] :
( ( c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_t ) @ V_u ) @ V_s @ V_k )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ V_t @ V_s @ V_k ) ) @ ( c_Lambda_Osubst @ V_u @ V_s @ V_k ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[71]) ).
thf(262,plain,
( ( ! [V_dB_H: $i,V_nat: $i] :
( ( c_Lambda_OdB_OAbs @ V_dB_H )
!= ( c_Lambda_OdB_OVar @ V_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[72]) ).
thf(263,plain,
( ( ! [V_dB1: $i,V_dB2: $i,V_dB_H: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1 ) @ V_dB2 )
!= ( c_Lambda_OdB_OAbs @ V_dB_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[73]) ).
thf(264,plain,
( ( ! [V_nat: $i,V_nat_H: $i] :
( ( ( c_Lambda_OdB_OVar @ V_nat )
!= ( c_Lambda_OdB_OVar @ V_nat_H ) )
| ( V_nat = V_nat_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[74]) ).
thf(265,plain,
( ( ! [V_r: $i,T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ V_r @ T_a ) @ V_x ) @ V_z ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ V_r @ T_a ) @ V_y ) @ V_z ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ V_r @ T_a ) @ V_x ) @ V_y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[75]) ).
thf(266,plain,
( ( ! [V_dB_H: $i,V_dB1: $i,V_dB2: $i] :
( ( c_Lambda_OdB_OAbs @ V_dB_H )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1 ) @ V_dB2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[76]) ).
thf(267,plain,
( ( ! [V_m: $i,V_rs: $i,V_n: $i,V_ss: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_m ) @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_m = V_n ) ) )
= $true ),
inference(unfold_def,[status(thm)],[77]) ).
thf(268,plain,
( ( ! [V_m: $i,V_rs: $i,V_n: $i,V_ss: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_m ) @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_rs = V_ss ) ) )
= $true ),
inference(unfold_def,[status(thm)],[78]) ).
thf(269,plain,
( ( ! [V_k: $i,V_u: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ V_k ) @ V_u @ V_k )
= V_u ) )
= $true ),
inference(unfold_def,[status(thm)],[79]) ).
thf(270,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)],[80]) ).
thf(271,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Otranclp @ V_r @ T_a ) @ ( c_fequal @ T_a ) @ ( tc_fun @ T_a @ ( tc_fun @ T_a @ tc_bool ) ) )
= ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[81]) ).
thf(272,plain,
( ( ! [V_r: $i,V_i: $i,V_j: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ V_r @ ( c_Lambda_OdB_OVar @ V_i ) @ V_j ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_r ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[82]) ).
thf(273,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)],[83]) ).
thf(274,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)],[84]) ).
thf(275,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[85]) ).
thf(276,plain,
( ( ! [T_a: $i,V_y: $i,V_z: $i,V_x: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ V_x @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_x @ T_a ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_z @ V_x @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[86]) ).
thf(277,plain,
( ( ! [V_R: $i,T_a: $i,V_S: $i] :
( ( c_Transitive__Closure_Ortranclp @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Ortranclp @ V_R @ T_a ) @ ( c_Transitive__Closure_Ortranclp @ V_S @ T_a ) @ ( tc_fun @ T_a @ ( tc_fun @ T_a @ tc_bool ) ) ) @ T_a )
= ( c_Transitive__Closure_Ortranclp @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_R @ V_S @ ( tc_fun @ T_a @ ( tc_fun @ T_a @ tc_bool ) ) ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[87]) ).
thf(278,plain,
( ( ! [V_r: $i,V_ss: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_r @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_r ) @ V_s ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[88]) ).
thf(279,plain,
( ( ! [V_R: $i,T_a: $i,V_a: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ V_R @ T_a ) @ V_a ) @ V_b ) )
| ( V_a = V_b )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_R @ T_a ) @ V_a ) @ V_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[89]) ).
thf(280,plain,
( ( ! [V_r: $i,T_a: $i,V_a: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ V_r @ T_a ) @ V_a ) @ V_b ) )
| ( V_a = V_b )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_a ) @ V_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[90]) ).
thf(281,plain,
( ( ! [V_R: $i,T_a: $i] :
( ( c_Transitive__Closure_Ortranclp @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_R @ ( c_fequal @ T_a ) @ ( tc_fun @ T_a @ ( tc_fun @ T_a @ tc_bool ) ) ) @ T_a )
= ( c_Transitive__Closure_Ortranclp @ V_R @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[91]) ).
thf(282,plain,
( ( ! [V_s: $i,V_ss: $i,V_r: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ V_r ) )
| ( V_s
= ( c_Lambda_OdB_OAbs @ V_r ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[92]) ).
thf(283,plain,
( ( ! [V_r: $i,V_rs: $i,V_s: $i,V_ss: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_r ) @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_s ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_r = V_s ) ) )
= $true ),
inference(unfold_def,[status(thm)],[93]) ).
thf(284,plain,
( ( ! [V_r: $i,V_rs: $i,V_s: $i,V_ss: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_r ) @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_s ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_rs = V_ss ) ) )
= $true ),
inference(unfold_def,[status(thm)],[94]) ).
thf(285,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_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ T_a )
= V_x ) ) )
= $true ),
inference(unfold_def,[status(thm)],[95]) ).
thf(286,plain,
( ( ! [V_dB1: $i,V_dB2: $i,V_dB1_H: $i,V_dB2_H: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1 ) @ V_dB2 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1_H ) @ V_dB2_H ) )
| ( V_dB1 = V_dB1_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[96]) ).
thf(287,plain,
( ( ! [V_dB1: $i,V_dB2: $i,V_dB1_H: $i,V_dB2_H: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1 ) @ V_dB2 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1_H ) @ V_dB2_H ) )
| ( V_dB2 = V_dB2_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[97]) ).
thf(288,plain,
( ( ! [V_T: $i,V_U: $i,V_e: $i,V_i: $i,V_ts: $i] :
( ( V_T = V_U )
| ~ ( c_Type_Otyping @ V_e @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_i ) @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_U )
| ~ ( c_Type_Otyping @ V_e @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_i ) @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[98]) ).
thf(289,plain,
( ( ! [V_r: $i,V_i: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Olift @ V_r @ V_i ) ) @ ( c_Lambda_Olift @ V_s @ V_i ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_r ) @ V_s ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[99]) ).
thf(290,plain,
( ( ! [V_s: $i,V_t: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_s ) ) @ V_t ) ) @ ( c_Lambda_Osubst @ V_s @ V_t @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[100]) ).
thf(291,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ T_a )
= V_x ) ) )
= $true ),
inference(unfold_def,[status(thm)],[101]) ).
thf(292,plain,
( ( ! [V_r: $i,V_ss: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_r @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_r ) @ V_s ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[102]) ).
thf(293,plain,
( ( ! [V_m: $i,V_s: $i,V_ss: $i] :
( ( ( c_Lambda_OdB_OVar @ V_m )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OVar @ V_m )
= V_s ) ) )
= $true ),
inference(unfold_def,[status(thm)],[103]) ).
thf(294,plain,
( ( ! [V_nat: $i,V_dB1_H: $i,V_dB2_H: $i] :
( ( c_Lambda_OdB_OVar @ V_nat )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1_H ) @ V_dB2_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[104]) ).
thf(295,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)],[105]) ).
thf(296,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)],[106]) ).
thf(297,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)],[107]) ).
thf(298,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)],[108]) ).
thf(299,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)],[109]) ).
thf(300,plain,
( ( ! [V_n: $i,V_ts: $i,V_r: $i,V_ss: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_r ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(unfold_def,[status(thm)],[110]) ).
thf(301,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)],[111]) ).
thf(302,plain,
( ( ! [V_r: $i,V_s: $i,V_ss: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_r ) ) @ V_s ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_s ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ V_r @ V_s @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[112]) ).
thf(303,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,T_b: $i,V_x: $i,V_y: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ ( tc_fun @ T_b @ tc_bool ) ) ) @ V_x ) @ V_y ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_A @ V_x ) @ V_y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[113]) ).
thf(304,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,T_b: $i,V_x: $i,V_y: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ ( tc_fun @ T_b @ tc_bool ) ) ) @ V_x ) @ V_y ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_B @ V_x ) @ V_y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[114]) ).
thf(305,plain,
( ( ! [V_B: $i,V_x: $i,V_y: $i,V_A: $i,T_a: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_B @ V_x ) @ V_y ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ V_A @ V_x ) @ V_y ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ ( tc_fun @ T_b @ tc_bool ) ) ) @ V_x ) @ V_y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[115]) ).
thf(306,plain,
( ( ! [V_r: $i,T_a: $i,V_x: $i,V_y: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_x ) @ V_y ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_x ) @ V_y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[116]) ).
thf(307,plain,
( ( ! [V_nat: $i,V_dB_H: $i] :
( ( c_Lambda_OdB_OVar @ V_nat )
!= ( c_Lambda_OdB_OAbs @ V_dB_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[117]) ).
thf(308,plain,
( ( ! [V_n: $i] : ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OVar @ V_n ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[118]) ).
thf(309,plain,
( ( ! [V_t: $i,V_r: $i,V_i: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ V_t @ V_r @ V_i ) ) @ ( c_Lambda_Osubst @ V_t @ V_s @ V_i ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_r ) @ V_s ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[119]) ).
thf(310,plain,
( ( ! [V_r: $i,V_t: $i,V_i: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ V_r @ V_t @ V_i ) ) @ ( c_Lambda_Osubst @ V_s @ V_t @ V_i ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_r ) @ V_s ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[120]) ).
thf(311,plain,
( ( ! [V_r: $i,T_a: $i,V_a: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_a ) @ V_b ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ V_r @ T_a ) @ V_a ) @ V_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[121]) ).
thf(312,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Wellfounded_OwfP @ ( c_Transitive__Closure_Otranclp @ V_r @ T_a ) @ T_a )
| ~ ( c_Wellfounded_OwfP @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[122]) ).
thf(313,plain,
( ( ! [V_s: $i,V_t: $i,V_k: $i] :
( ( c_Lambda_Olift @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_t ) @ V_k )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Olift @ V_s @ V_k ) ) @ ( c_Lambda_Olift @ V_t @ V_k ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[123]) ).
thf(314,plain,
( ( ! [V_r: $i,T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ V_r @ T_a ) @ V_a ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_b ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_a ) @ V_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[124]) ).
thf(315,plain,
( ( ! [V_r: $i,T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ V_r @ T_a ) @ V_a ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_b ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_a ) @ V_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[125]) ).
thf(316,plain,
( ( ! [V_t: $i,V_r: $i,V_i: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ V_t @ V_r @ V_i ) ) @ ( c_Lambda_Osubst @ V_t @ V_s @ V_i ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_r ) @ V_s ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[126]) ).
thf(317,plain,
( ( ! [V_r: $i,T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_x ) @ V_z ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_y ) @ V_z ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_x ) @ V_y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[127]) ).
thf(318,plain,
( ( ! [V_r: $i,T_a: $i,V_x: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_x ) @ V_x ) ) )
= $true ),
inference(unfold_def,[status(thm)],[128]) ).
thf(319,plain,
( ( ! [V_r: $i,T_a: $i,V_a: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_a ) @ V_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[129]) ).
thf(320,plain,
( ( ! [V_r: $i,T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ V_r @ T_a ) @ V_x ) @ V_z ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ V_r @ T_a ) @ V_y ) @ V_z ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_x ) @ V_y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[130]) ).
thf(321,plain,
( ( ! [V_r: $i,T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ V_r @ T_a ) @ V_a ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_b ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ V_r @ T_a ) @ V_a ) @ V_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[131]) ).
thf(322,plain,
( ( ! [V_r: $i,V_s: $i,T_a: $i,T_b: $i,T_c: $i,V_a: $i,V_c: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ V_r @ V_s @ T_a @ T_b @ T_c ) @ V_a ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_s @ V_b ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_a ) @ V_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[132]) ).
thf(323,plain,
( ( ! [V_s: $i,V_s_H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_OdB_OAbs @ V_s ) ) @ ( c_Lambda_OdB_OAbs @ V_s_H ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_s ) @ V_s_H ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[133]) ).
thf(324,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[134]) ).
thf(325,plain,
( ( ! [T_a: $i,V_y: $i,V_z: $i,V_x: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) @ V_x @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_x @ T_a ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_z @ V_x @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[135]) ).
thf(326,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_x @ T_a )
= V_x ) ) )
= $true ),
inference(unfold_def,[status(thm)],[136]) ).
thf(327,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ V_z @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[137]) ).
thf(328,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[138]) ).
thf(329,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[139]) ).
thf(330,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ V_z @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[140]) ).
thf(331,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)],[141]) ).
thf(332,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)],[142]) ).
thf(333,plain,
( ( ! [V_r: $i,V_s: $i,V_ss: $i] :
( ( ( c_Lambda_OdB_OAbs @ V_r )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OAbs @ V_r )
= V_s ) ) )
= $true ),
inference(unfold_def,[status(thm)],[143]) ).
thf(334,plain,
( ( ! [V_s: $i,V_t: $i,V_t_H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_t ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_t_H ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_t ) @ V_t_H ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[144]) ).
thf(335,plain,
( ( ! [V_s: $i,V_t: $i,V_s_H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_t ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s_H ) @ V_t ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_s ) @ V_s_H ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[145]) ).
thf(336,plain,
( ( ! [V_r: $i,V_ts: $i,V_s: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_r @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_r = V_s ) ) )
= $true ),
inference(unfold_def,[status(thm)],[146]) ).
thf(337,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)],[147]) ).
thf(338,plain,
( ( ! [V_s: $i,V_t: $i,V_s_H: $i,V_t_H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_t ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s_H ) @ V_t_H ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_t ) @ V_t_H ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_s ) @ V_s_H ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[148]) ).
thf(339,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[149]) ).
thf(340,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[150]) ).
thf(341,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[151]) ).
thf(342,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[152]) ).
thf(343,plain,
( ( ! [V_r: $i,T_a: $i,V_a: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ V_r @ T_a ) @ V_a ) @ V_b ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_a ) @ V_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[153]) ).
thf(344,plain,
( ( ! [V_t: $i,V_k: $i,V_s: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_Olift @ V_t @ V_k ) @ V_s @ V_k )
= V_t ) )
= $true ),
inference(unfold_def,[status(thm)],[154]) ).
thf(345,plain,
( ( ! [V_t: $i,V_i: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_t ) @ ( c_Lambda_OdB_OVar @ V_i ) ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_t ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[155]) ).
thf(346,plain,
( ( ! [V_B: $i,V_x: $i,V_y: $i,V_A: $i,T_a: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_B @ V_x ) @ V_y ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ ( tc_fun @ T_b @ tc_bool ) ) ) @ V_x ) @ V_y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[156]) ).
thf(347,plain,
( ( ! [V_A: $i,V_x: $i,V_y: $i,V_B: $i,T_a: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_A @ V_x ) @ V_y ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ ( tc_fun @ T_b @ tc_bool ) ) ) @ V_x ) @ V_y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[157]) ).
thf(348,plain,
( ( ! [V_s: $i,V_t: $i,V_n: $i,V_ss: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_s ) ) @ V_t )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(unfold_def,[status(thm)],[158]) ).
thf(349,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Transitive__Closure_Ortranclp @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ T_a )
= ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[159]) ).
thf(350,plain,
( ( ! [V_dB1_H: $i,V_dB2_H: $i,V_nat: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1_H ) @ V_dB2_H )
!= ( c_Lambda_OdB_OVar @ V_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[160]) ).
thf(351,plain,
( ( ! [V_n: $i,V_rs: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( c_List_Olistsp @ c_InductTermi_OIT @ V_rs @ tc_Lambda_OdB ) ) )
= $true ),
inference(unfold_def,[status(thm)],[161]) ).
thf(352,plain,
( ( ! [V_v: $i,V_n: $i,V_rs: $i] :
( ( V_v
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ V_n @ V_rs @ V_v ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ V_v ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[162]) ).
thf(353,plain,
( ( ! [V_t: $i,V_u: $i,V_i: $i,V_e: $i,V_U: $i,V_T: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ V_t @ V_u @ V_i ) ) )
| ~ ( c_Type_Otyping @ V_e @ V_u @ V_U )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_u ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ V_e @ V_i @ V_U @ tc_Type_Otype ) @ V_t @ V_T )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_t ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[163]) ).
thf(354,plain,
( ( ! [V_m: $i] :
( ( c_Lambda_OdB_OVar @ V_m )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_m ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(unfold_def,[status(thm)],[164]) ).
thf(355,plain,
( ( ! [V_m: $i,V_s: $i,V_ss: $i] :
( ( ( c_Lambda_OdB_OVar @ V_m )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_ss
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[165]) ).
thf(356,plain,
( ( ! [V_r: $i,V_s: $i,V_t: $i,V_ts: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_r ) @ V_s )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_r
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ V_r @ V_s @ V_t @ V_ts ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_ts
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[166]) ).
thf(357,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)],[167]) ).
thf(358,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)],[168]) ).
thf(359,plain,
( ( ! [V_e: $i,V_x: $i,V_T: $i,T_a: $i] :
( ( hAPP @ ( c_Type_Oshift @ V_e @ V_x @ V_T @ T_a ) @ V_x )
= V_T ) )
= $true ),
inference(unfold_def,[status(thm)],[169]) ).
thf(360,plain,
( ( ! [V_env: $i,V_t: $i,V_T: $i,V_U: $i] :
( ( c_Type_Otyping @ V_env @ ( c_Lambda_OdB_OAbs @ V_t ) @ ( c_Type_Otype_OFun @ V_T @ V_U ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ V_env @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_T @ tc_Type_Otype ) @ V_t @ V_U ) ) )
= $true ),
inference(unfold_def,[status(thm)],[170]) ).
thf(361,plain,
( ( ! [V_r: $i,V_s: $i,V_t: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_r ) @ V_s )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_r ) @ V_s )
= V_t ) ) )
= $true ),
inference(unfold_def,[status(thm)],[171]) ).
thf(362,plain,
( ( ! [V_r: $i,V_s: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_r ) @ V_s )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_r ) @ V_s ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(unfold_def,[status(thm)],[172]) ).
thf(363,plain,
( ( ! [V_rs: $i,V_n: $i,V_v: $i] :
( ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ V_rs @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ V_n @ V_rs @ V_v ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ V_v ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[173]) ).
thf(364,plain,
( ( ! [V_e_H: $i,V_u: $i,V_U: $i,V_i: $i,V_t: $i,V_T: $i] :
( ~ ( c_Type_Otyping @ V_e_H @ V_u @ V_U )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ V_e_H @ V_i @ V_U @ tc_Type_Otype ) @ V_t @ V_T )
| ( c_Type_Otyping @ V_e_H @ ( c_Lambda_Osubst @ V_t @ V_u @ V_i ) @ V_T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[174]) ).
thf(365,plain,
( ( ! [V_e: $i,V_i: $i,V_U: $i,V_t: $i,V_T: $i] :
( ( c_Type_Otyping @ ( c_Type_Oshift @ V_e @ V_i @ V_U @ tc_Type_Otype ) @ ( c_Lambda_Olift @ V_t @ V_i ) @ V_T )
| ~ ( c_Type_Otyping @ V_e @ V_t @ V_T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[175]) ).
thf(366,plain,
( ( ! [V_r: $i,V_rs: $i,V_ss: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_r @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_r @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ V_rs @ V_ss @ tc_Lambda_OdB ) ) )
= $true ),
inference(unfold_def,[status(thm)],[176]) ).
thf(367,plain,
( ( ! [V_r: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_r ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_Lambda_OdB_OAbs @ V_r ) ) )
= $true ),
inference(unfold_def,[status(thm)],[177]) ).
thf(368,plain,
( ( ! [V_s: $i,V_ss: $i,V_r: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ V_r ) )
| ( V_ss
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[178]) ).
thf(369,plain,
( ( ! [V_r: $i] :
( ( c_Lambda_OdB_OAbs @ V_r )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_r ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(unfold_def,[status(thm)],[179]) ).
thf(370,plain,
( ( ! [V_r: $i,V_s: $i,V_ss: $i] :
( ( ( c_Lambda_OdB_OAbs @ V_r )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_ss
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[180]) ).
thf(371,plain,
( ( ! [V_env: $i,V_s: $i,V_t: $i,V_U: $i,V_T: $i] :
( ( c_Type_Otyping @ V_env @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_t ) @ V_U )
| ~ ( c_Type_Otyping @ V_env @ V_t @ V_T )
| ~ ( c_Type_Otyping @ V_env @ V_s @ ( c_Type_Otype_OFun @ V_T @ V_U ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[181]) ).
thf(372,plain,
( ( ! [V_type1: $i,V_type2: $i,V_type1_H: $i,V_type2_H: $i] :
( ( ( c_Type_Otype_OFun @ V_type1 @ V_type2 )
!= ( c_Type_Otype_OFun @ V_type1_H @ V_type2_H ) )
| ( V_type1 = V_type1_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[182]) ).
thf(373,plain,
( ( ! [V_type1: $i,V_type2: $i,V_type1_H: $i,V_type2_H: $i] :
( ( ( c_Type_Otype_OFun @ V_type1 @ V_type2 )
!= ( c_Type_Otype_OFun @ V_type1_H @ V_type2_H ) )
| ( V_type2 = V_type2_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[183]) ).
thf(374,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)],[184]) ).
thf(375,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)],[185]) ).
thf(376,plain,
( ( ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ v_t @ tc_Lambda_OdB ) )
= $true ),
inference(unfold_def,[status(thm)],[188]) ).
thf(377,plain,
( ( c_Type_Otyping @ v_e @ v_t @ v_T )
= $true ),
inference(unfold_def,[status(thm)],[189]) ).
thf(378,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[190]) ).
thf(379,plain,
( ( c_Type_Otyping @ v_e @ v_t @ v_T )
= $true ),
inference(copy,[status(thm)],[377]) ).
thf(380,plain,
( ( ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ v_t @ tc_Lambda_OdB ) )
= $true ),
inference(copy,[status(thm)],[376]) ).
thf(381,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)],[375]) ).
thf(382,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)],[374]) ).
thf(383,plain,
( ( ! [V_type1: $i,V_type2: $i,V_type1_H: $i,V_type2_H: $i] :
( ( ( c_Type_Otype_OFun @ V_type1 @ V_type2 )
!= ( c_Type_Otype_OFun @ V_type1_H @ V_type2_H ) )
| ( V_type2 = V_type2_H ) ) )
= $true ),
inference(copy,[status(thm)],[373]) ).
thf(384,plain,
( ( ! [V_type1: $i,V_type2: $i,V_type1_H: $i,V_type2_H: $i] :
( ( ( c_Type_Otype_OFun @ V_type1 @ V_type2 )
!= ( c_Type_Otype_OFun @ V_type1_H @ V_type2_H ) )
| ( V_type1 = V_type1_H ) ) )
= $true ),
inference(copy,[status(thm)],[372]) ).
thf(385,plain,
( ( ! [V_env: $i,V_s: $i,V_t: $i,V_U: $i,V_T: $i] :
( ( c_Type_Otyping @ V_env @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_t ) @ V_U )
| ~ ( c_Type_Otyping @ V_env @ V_t @ V_T )
| ~ ( c_Type_Otyping @ V_env @ V_s @ ( c_Type_Otype_OFun @ V_T @ V_U ) ) ) )
= $true ),
inference(copy,[status(thm)],[371]) ).
thf(386,plain,
( ( ! [V_r: $i,V_s: $i,V_ss: $i] :
( ( ( c_Lambda_OdB_OAbs @ V_r )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_ss
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(copy,[status(thm)],[370]) ).
thf(387,plain,
( ( ! [V_r: $i] :
( ( c_Lambda_OdB_OAbs @ V_r )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_r ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(copy,[status(thm)],[369]) ).
thf(388,plain,
( ( ! [V_s: $i,V_ss: $i,V_r: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ V_r ) )
| ( V_ss
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(copy,[status(thm)],[368]) ).
thf(389,plain,
( ( ! [V_r: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_r ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_Lambda_OdB_OAbs @ V_r ) ) )
= $true ),
inference(copy,[status(thm)],[367]) ).
thf(390,plain,
( ( ! [V_r: $i,V_rs: $i,V_ss: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_r @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_r @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ V_rs @ V_ss @ tc_Lambda_OdB ) ) )
= $true ),
inference(copy,[status(thm)],[366]) ).
thf(391,plain,
( ( ! [V_e: $i,V_i: $i,V_U: $i,V_t: $i,V_T: $i] :
( ( c_Type_Otyping @ ( c_Type_Oshift @ V_e @ V_i @ V_U @ tc_Type_Otype ) @ ( c_Lambda_Olift @ V_t @ V_i ) @ V_T )
| ~ ( c_Type_Otyping @ V_e @ V_t @ V_T ) ) )
= $true ),
inference(copy,[status(thm)],[365]) ).
thf(392,plain,
( ( ! [V_e_H: $i,V_u: $i,V_U: $i,V_i: $i,V_t: $i,V_T: $i] :
( ~ ( c_Type_Otyping @ V_e_H @ V_u @ V_U )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ V_e_H @ V_i @ V_U @ tc_Type_Otype ) @ V_t @ V_T )
| ( c_Type_Otyping @ V_e_H @ ( c_Lambda_Osubst @ V_t @ V_u @ V_i ) @ V_T ) ) )
= $true ),
inference(copy,[status(thm)],[364]) ).
thf(393,plain,
( ( ! [V_rs: $i,V_n: $i,V_v: $i] :
( ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ V_rs @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ V_n @ V_rs @ V_v ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ V_v ) ) ) )
= $true ),
inference(copy,[status(thm)],[363]) ).
thf(394,plain,
( ( ! [V_r: $i,V_s: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_r ) @ V_s )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_r ) @ V_s ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(copy,[status(thm)],[362]) ).
thf(395,plain,
( ( ! [V_r: $i,V_s: $i,V_t: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_r ) @ V_s )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_r ) @ V_s )
= V_t ) ) )
= $true ),
inference(copy,[status(thm)],[361]) ).
thf(396,plain,
( ( ! [V_env: $i,V_t: $i,V_T: $i,V_U: $i] :
( ( c_Type_Otyping @ V_env @ ( c_Lambda_OdB_OAbs @ V_t ) @ ( c_Type_Otype_OFun @ V_T @ V_U ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ V_env @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_T @ tc_Type_Otype ) @ V_t @ V_U ) ) )
= $true ),
inference(copy,[status(thm)],[360]) ).
thf(397,plain,
( ( ! [V_e: $i,V_x: $i,V_T: $i,T_a: $i] :
( ( hAPP @ ( c_Type_Oshift @ V_e @ V_x @ V_T @ T_a ) @ V_x )
= V_T ) )
= $true ),
inference(copy,[status(thm)],[359]) ).
thf(398,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)],[358]) ).
thf(399,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)],[357]) ).
thf(400,plain,
( ( ! [V_r: $i,V_s: $i,V_t: $i,V_ts: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_r ) @ V_s )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_r
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ V_r @ V_s @ V_t @ V_ts ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_ts
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(copy,[status(thm)],[356]) ).
thf(401,plain,
( ( ! [V_m: $i,V_s: $i,V_ss: $i] :
( ( ( c_Lambda_OdB_OVar @ V_m )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_ss
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(copy,[status(thm)],[355]) ).
thf(402,plain,
( ( ! [V_m: $i] :
( ( c_Lambda_OdB_OVar @ V_m )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_m ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(copy,[status(thm)],[354]) ).
thf(403,plain,
( ( ! [V_t: $i,V_u: $i,V_i: $i,V_e: $i,V_U: $i,V_T: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ V_t @ V_u @ V_i ) ) )
| ~ ( c_Type_Otyping @ V_e @ V_u @ V_U )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_u ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ V_e @ V_i @ V_U @ tc_Type_Otype ) @ V_t @ V_T )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_t ) ) ) )
= $true ),
inference(copy,[status(thm)],[353]) ).
thf(404,plain,
( ( ! [V_v: $i,V_n: $i,V_rs: $i] :
( ( V_v
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ V_n @ V_rs @ V_v ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ V_v ) ) ) )
= $true ),
inference(copy,[status(thm)],[352]) ).
thf(405,plain,
( ( ! [V_n: $i,V_rs: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( c_List_Olistsp @ c_InductTermi_OIT @ V_rs @ tc_Lambda_OdB ) ) )
= $true ),
inference(copy,[status(thm)],[351]) ).
thf(406,plain,
( ( ! [V_dB1_H: $i,V_dB2_H: $i,V_nat: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1_H ) @ V_dB2_H )
!= ( c_Lambda_OdB_OVar @ V_nat ) ) )
= $true ),
inference(copy,[status(thm)],[350]) ).
thf(407,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Transitive__Closure_Ortranclp @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ T_a )
= ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[349]) ).
thf(408,plain,
( ( ! [V_s: $i,V_t: $i,V_n: $i,V_ss: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_s ) ) @ V_t )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(copy,[status(thm)],[348]) ).
thf(409,plain,
( ( ! [V_A: $i,V_x: $i,V_y: $i,V_B: $i,T_a: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_A @ V_x ) @ V_y ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ ( tc_fun @ T_b @ tc_bool ) ) ) @ V_x ) @ V_y ) ) ) )
= $true ),
inference(copy,[status(thm)],[347]) ).
thf(410,plain,
( ( ! [V_B: $i,V_x: $i,V_y: $i,V_A: $i,T_a: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_B @ V_x ) @ V_y ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ ( tc_fun @ T_b @ tc_bool ) ) ) @ V_x ) @ V_y ) ) ) )
= $true ),
inference(copy,[status(thm)],[346]) ).
thf(411,plain,
( ( ! [V_t: $i,V_i: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_t ) @ ( c_Lambda_OdB_OVar @ V_i ) ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_t ) ) ) )
= $true ),
inference(copy,[status(thm)],[345]) ).
thf(412,plain,
( ( ! [V_t: $i,V_k: $i,V_s: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_Olift @ V_t @ V_k ) @ V_s @ V_k )
= V_t ) )
= $true ),
inference(copy,[status(thm)],[344]) ).
thf(413,plain,
( ( ! [V_r: $i,T_a: $i,V_a: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ V_r @ T_a ) @ V_a ) @ V_b ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_a ) @ V_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[343]) ).
thf(414,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[342]) ).
thf(415,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[341]) ).
thf(416,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[340]) ).
thf(417,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[339]) ).
thf(418,plain,
( ( ! [V_s: $i,V_t: $i,V_s_H: $i,V_t_H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_t ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s_H ) @ V_t_H ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_t ) @ V_t_H ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_s ) @ V_s_H ) ) ) )
= $true ),
inference(copy,[status(thm)],[338]) ).
thf(419,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)],[337]) ).
thf(420,plain,
( ( ! [V_r: $i,V_ts: $i,V_s: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_r @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_r = V_s ) ) )
= $true ),
inference(copy,[status(thm)],[336]) ).
thf(421,plain,
( ( ! [V_s: $i,V_t: $i,V_s_H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_t ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s_H ) @ V_t ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_s ) @ V_s_H ) ) ) )
= $true ),
inference(copy,[status(thm)],[335]) ).
thf(422,plain,
( ( ! [V_s: $i,V_t: $i,V_t_H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_t ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_t_H ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_t ) @ V_t_H ) ) ) )
= $true ),
inference(copy,[status(thm)],[334]) ).
thf(423,plain,
( ( ! [V_r: $i,V_s: $i,V_ss: $i] :
( ( ( c_Lambda_OdB_OAbs @ V_r )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OAbs @ V_r )
= V_s ) ) )
= $true ),
inference(copy,[status(thm)],[333]) ).
thf(424,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)],[332]) ).
thf(425,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)],[331]) ).
thf(426,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ V_z @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[330]) ).
thf(427,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[329]) ).
thf(428,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[328]) ).
thf(429,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ V_z @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[327]) ).
thf(430,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_x @ T_a )
= V_x ) ) )
= $true ),
inference(copy,[status(thm)],[326]) ).
thf(431,plain,
( ( ! [T_a: $i,V_y: $i,V_z: $i,V_x: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) @ V_x @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_x @ T_a ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_z @ V_x @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[325]) ).
thf(432,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[324]) ).
thf(433,plain,
( ( ! [V_s: $i,V_s_H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_OdB_OAbs @ V_s ) ) @ ( c_Lambda_OdB_OAbs @ V_s_H ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_s ) @ V_s_H ) ) ) )
= $true ),
inference(copy,[status(thm)],[323]) ).
thf(434,plain,
( ( ! [V_r: $i,V_s: $i,T_a: $i,T_b: $i,T_c: $i,V_a: $i,V_c: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ V_r @ V_s @ T_a @ T_b @ T_c ) @ V_a ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_s @ V_b ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_a ) @ V_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[322]) ).
thf(435,plain,
( ( ! [V_r: $i,T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ V_r @ T_a ) @ V_a ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_b ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ V_r @ T_a ) @ V_a ) @ V_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[321]) ).
thf(436,plain,
( ( ! [V_r: $i,T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ V_r @ T_a ) @ V_x ) @ V_z ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ V_r @ T_a ) @ V_y ) @ V_z ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_x ) @ V_y ) ) ) )
= $true ),
inference(copy,[status(thm)],[320]) ).
thf(437,plain,
( ( ! [V_r: $i,T_a: $i,V_a: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_a ) @ V_a ) ) )
= $true ),
inference(copy,[status(thm)],[319]) ).
thf(438,plain,
( ( ! [V_r: $i,T_a: $i,V_x: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_x ) @ V_x ) ) )
= $true ),
inference(copy,[status(thm)],[318]) ).
thf(439,plain,
( ( ! [V_r: $i,T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_x ) @ V_z ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_y ) @ V_z ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_x ) @ V_y ) ) ) )
= $true ),
inference(copy,[status(thm)],[317]) ).
thf(440,plain,
( ( ! [V_t: $i,V_r: $i,V_i: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ V_t @ V_r @ V_i ) ) @ ( c_Lambda_Osubst @ V_t @ V_s @ V_i ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_r ) @ V_s ) ) ) )
= $true ),
inference(copy,[status(thm)],[316]) ).
thf(441,plain,
( ( ! [V_r: $i,T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ V_r @ T_a ) @ V_a ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_b ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_a ) @ V_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[315]) ).
thf(442,plain,
( ( ! [V_r: $i,T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ V_r @ T_a ) @ V_a ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_b ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_a ) @ V_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[314]) ).
thf(443,plain,
( ( ! [V_s: $i,V_t: $i,V_k: $i] :
( ( c_Lambda_Olift @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_t ) @ V_k )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Olift @ V_s @ V_k ) ) @ ( c_Lambda_Olift @ V_t @ V_k ) ) ) )
= $true ),
inference(copy,[status(thm)],[313]) ).
thf(444,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Wellfounded_OwfP @ ( c_Transitive__Closure_Otranclp @ V_r @ T_a ) @ T_a )
| ~ ( c_Wellfounded_OwfP @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[312]) ).
thf(445,plain,
( ( ! [V_r: $i,T_a: $i,V_a: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_a ) @ V_b ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ V_r @ T_a ) @ V_a ) @ V_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[311]) ).
thf(446,plain,
( ( ! [V_r: $i,V_t: $i,V_i: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ V_r @ V_t @ V_i ) ) @ ( c_Lambda_Osubst @ V_s @ V_t @ V_i ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_r ) @ V_s ) ) ) )
= $true ),
inference(copy,[status(thm)],[310]) ).
thf(447,plain,
( ( ! [V_t: $i,V_r: $i,V_i: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ V_t @ V_r @ V_i ) ) @ ( c_Lambda_Osubst @ V_t @ V_s @ V_i ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_r ) @ V_s ) ) ) )
= $true ),
inference(copy,[status(thm)],[309]) ).
thf(448,plain,
( ( ! [V_n: $i] : ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OVar @ V_n ) ) ) )
= $true ),
inference(copy,[status(thm)],[308]) ).
thf(449,plain,
( ( ! [V_nat: $i,V_dB_H: $i] :
( ( c_Lambda_OdB_OVar @ V_nat )
!= ( c_Lambda_OdB_OAbs @ V_dB_H ) ) )
= $true ),
inference(copy,[status(thm)],[307]) ).
thf(450,plain,
( ( ! [V_r: $i,T_a: $i,V_x: $i,V_y: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_x ) @ V_y ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_x ) @ V_y ) ) ) )
= $true ),
inference(copy,[status(thm)],[306]) ).
thf(451,plain,
( ( ! [V_B: $i,V_x: $i,V_y: $i,V_A: $i,T_a: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_B @ V_x ) @ V_y ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ V_A @ V_x ) @ V_y ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ ( tc_fun @ T_b @ tc_bool ) ) ) @ V_x ) @ V_y ) ) ) )
= $true ),
inference(copy,[status(thm)],[305]) ).
thf(452,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,T_b: $i,V_x: $i,V_y: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ ( tc_fun @ T_b @ tc_bool ) ) ) @ V_x ) @ V_y ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_B @ V_x ) @ V_y ) ) ) )
= $true ),
inference(copy,[status(thm)],[304]) ).
thf(453,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,T_b: $i,V_x: $i,V_y: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ ( tc_fun @ T_b @ tc_bool ) ) ) @ V_x ) @ V_y ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_A @ V_x ) @ V_y ) ) ) )
= $true ),
inference(copy,[status(thm)],[303]) ).
thf(454,plain,
( ( ! [V_r: $i,V_s: $i,V_ss: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_r ) ) @ V_s ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_s ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ V_r @ V_s @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[302]) ).
thf(455,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)],[301]) ).
thf(456,plain,
( ( ! [V_n: $i,V_ts: $i,V_r: $i,V_ss: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_r ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(copy,[status(thm)],[300]) ).
thf(457,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)],[299]) ).
thf(458,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)],[298]) ).
thf(459,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)],[297]) ).
thf(460,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)],[296]) ).
thf(461,plain,
( ( ! [V_dB: $i,V_dB_H: $i] :
( ( ( c_Lambda_OdB_OAbs @ V_dB )
!= ( c_Lambda_OdB_OAbs @ V_dB_H ) )
| ( V_dB = V_dB_H ) ) )
= $true ),
inference(copy,[status(thm)],[295]) ).
thf(462,plain,
( ( ! [V_nat: $i,V_dB1_H: $i,V_dB2_H: $i] :
( ( c_Lambda_OdB_OVar @ V_nat )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1_H ) @ V_dB2_H ) ) )
= $true ),
inference(copy,[status(thm)],[294]) ).
thf(463,plain,
( ( ! [V_m: $i,V_s: $i,V_ss: $i] :
( ( ( c_Lambda_OdB_OVar @ V_m )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OVar @ V_m )
= V_s ) ) )
= $true ),
inference(copy,[status(thm)],[293]) ).
thf(464,plain,
( ( ! [V_r: $i,V_ss: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_r @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_r ) @ V_s ) ) ) )
= $true ),
inference(copy,[status(thm)],[292]) ).
thf(465,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ T_a )
= V_x ) ) )
= $true ),
inference(copy,[status(thm)],[291]) ).
thf(466,plain,
( ( ! [V_s: $i,V_t: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_s ) ) @ V_t ) ) @ ( c_Lambda_Osubst @ V_s @ V_t @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[290]) ).
thf(467,plain,
( ( ! [V_r: $i,V_i: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Olift @ V_r @ V_i ) ) @ ( c_Lambda_Olift @ V_s @ V_i ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_r ) @ V_s ) ) ) )
= $true ),
inference(copy,[status(thm)],[289]) ).
thf(468,plain,
( ( ! [V_T: $i,V_U: $i,V_e: $i,V_i: $i,V_ts: $i] :
( ( V_T = V_U )
| ~ ( c_Type_Otyping @ V_e @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_i ) @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_U )
| ~ ( c_Type_Otyping @ V_e @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_i ) @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_T ) ) )
= $true ),
inference(copy,[status(thm)],[288]) ).
thf(469,plain,
( ( ! [V_dB1: $i,V_dB2: $i,V_dB1_H: $i,V_dB2_H: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1 ) @ V_dB2 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1_H ) @ V_dB2_H ) )
| ( V_dB2 = V_dB2_H ) ) )
= $true ),
inference(copy,[status(thm)],[287]) ).
thf(470,plain,
( ( ! [V_dB1: $i,V_dB2: $i,V_dB1_H: $i,V_dB2_H: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1 ) @ V_dB2 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1_H ) @ V_dB2_H ) )
| ( V_dB1 = V_dB1_H ) ) )
= $true ),
inference(copy,[status(thm)],[286]) ).
thf(471,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_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ T_a )
= V_x ) ) )
= $true ),
inference(copy,[status(thm)],[285]) ).
thf(472,plain,
( ( ! [V_r: $i,V_rs: $i,V_s: $i,V_ss: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_r ) @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_s ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_rs = V_ss ) ) )
= $true ),
inference(copy,[status(thm)],[284]) ).
thf(473,plain,
( ( ! [V_r: $i,V_rs: $i,V_s: $i,V_ss: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_r ) @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_s ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_r = V_s ) ) )
= $true ),
inference(copy,[status(thm)],[283]) ).
thf(474,plain,
( ( ! [V_s: $i,V_ss: $i,V_r: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ V_r ) )
| ( V_s
= ( c_Lambda_OdB_OAbs @ V_r ) ) ) )
= $true ),
inference(copy,[status(thm)],[282]) ).
thf(475,plain,
( ( ! [V_R: $i,T_a: $i] :
( ( c_Transitive__Closure_Ortranclp @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_R @ ( c_fequal @ T_a ) @ ( tc_fun @ T_a @ ( tc_fun @ T_a @ tc_bool ) ) ) @ T_a )
= ( c_Transitive__Closure_Ortranclp @ V_R @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[281]) ).
thf(476,plain,
( ( ! [V_r: $i,T_a: $i,V_a: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ V_r @ T_a ) @ V_a ) @ V_b ) )
| ( V_a = V_b )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_a ) @ V_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[280]) ).
thf(477,plain,
( ( ! [V_R: $i,T_a: $i,V_a: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ V_R @ T_a ) @ V_a ) @ V_b ) )
| ( V_a = V_b )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_R @ T_a ) @ V_a ) @ V_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[279]) ).
thf(478,plain,
( ( ! [V_r: $i,V_ss: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_r @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_r ) @ V_s ) ) ) )
= $true ),
inference(copy,[status(thm)],[278]) ).
thf(479,plain,
( ( ! [V_R: $i,T_a: $i,V_S: $i] :
( ( c_Transitive__Closure_Ortranclp @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Ortranclp @ V_R @ T_a ) @ ( c_Transitive__Closure_Ortranclp @ V_S @ T_a ) @ ( tc_fun @ T_a @ ( tc_fun @ T_a @ tc_bool ) ) ) @ T_a )
= ( c_Transitive__Closure_Ortranclp @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_R @ V_S @ ( tc_fun @ T_a @ ( tc_fun @ T_a @ tc_bool ) ) ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[277]) ).
thf(480,plain,
( ( ! [T_a: $i,V_y: $i,V_z: $i,V_x: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ V_x @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_x @ T_a ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_z @ V_x @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[276]) ).
thf(481,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[275]) ).
thf(482,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)],[274]) ).
thf(483,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)],[273]) ).
thf(484,plain,
( ( ! [V_r: $i,V_i: $i,V_j: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ V_r @ ( c_Lambda_OdB_OVar @ V_i ) @ V_j ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_r ) ) ) )
= $true ),
inference(copy,[status(thm)],[272]) ).
thf(485,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Otranclp @ V_r @ T_a ) @ ( c_fequal @ T_a ) @ ( tc_fun @ T_a @ ( tc_fun @ T_a @ tc_bool ) ) )
= ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[271]) ).
thf(486,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)],[270]) ).
thf(487,plain,
( ( ! [V_k: $i,V_u: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ V_k ) @ V_u @ V_k )
= V_u ) )
= $true ),
inference(copy,[status(thm)],[269]) ).
thf(488,plain,
( ( ! [V_m: $i,V_rs: $i,V_n: $i,V_ss: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_m ) @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_rs = V_ss ) ) )
= $true ),
inference(copy,[status(thm)],[268]) ).
thf(489,plain,
( ( ! [V_m: $i,V_rs: $i,V_n: $i,V_ss: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_m ) @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_m = V_n ) ) )
= $true ),
inference(copy,[status(thm)],[267]) ).
thf(490,plain,
( ( ! [V_dB_H: $i,V_dB1: $i,V_dB2: $i] :
( ( c_Lambda_OdB_OAbs @ V_dB_H )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1 ) @ V_dB2 ) ) )
= $true ),
inference(copy,[status(thm)],[266]) ).
thf(491,plain,
( ( ! [V_r: $i,T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ V_r @ T_a ) @ V_x ) @ V_z ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ V_r @ T_a ) @ V_y ) @ V_z ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ V_r @ T_a ) @ V_x ) @ V_y ) ) ) )
= $true ),
inference(copy,[status(thm)],[265]) ).
thf(492,plain,
( ( ! [V_nat: $i,V_nat_H: $i] :
( ( ( c_Lambda_OdB_OVar @ V_nat )
!= ( c_Lambda_OdB_OVar @ V_nat_H ) )
| ( V_nat = V_nat_H ) ) )
= $true ),
inference(copy,[status(thm)],[264]) ).
thf(493,plain,
( ( ! [V_dB1: $i,V_dB2: $i,V_dB_H: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1 ) @ V_dB2 )
!= ( c_Lambda_OdB_OAbs @ V_dB_H ) ) )
= $true ),
inference(copy,[status(thm)],[263]) ).
thf(494,plain,
( ( ! [V_dB_H: $i,V_nat: $i] :
( ( c_Lambda_OdB_OAbs @ V_dB_H )
!= ( c_Lambda_OdB_OVar @ V_nat ) ) )
= $true ),
inference(copy,[status(thm)],[262]) ).
thf(495,plain,
( ( ! [V_t: $i,V_u: $i,V_s: $i,V_k: $i] :
( ( c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_t ) @ V_u ) @ V_s @ V_k )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ V_t @ V_s @ V_k ) ) @ ( c_Lambda_Osubst @ V_u @ V_s @ V_k ) ) ) )
= $true ),
inference(copy,[status(thm)],[261]) ).
thf(496,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,T_b: $i,V_x: $i,V_y: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ ( tc_fun @ T_b @ tc_bool ) ) ) @ V_x ) @ V_y ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_B @ V_x ) @ V_y ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_A @ V_x ) @ V_y ) ) ) )
= $true ),
inference(copy,[status(thm)],[260]) ).
thf(497,plain,
( ( ! [V_r: $i,T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_a ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_b ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_a ) @ V_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[259]) ).
thf(498,plain,
( ( ! [V_r: $i,T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_a ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_b ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_a ) @ V_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[258]) ).
thf(499,plain,
( ( ! [V_r: $i,T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ V_r @ T_a ) @ V_a ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_b ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ V_r @ T_a ) @ V_a ) @ V_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[257]) ).
thf(500,plain,
( ( ! [V_r: $i,T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ V_r @ T_a ) @ V_a ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ V_r @ T_a ) @ V_b ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_a ) @ V_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[256]) ).
thf(501,plain,
( ( ! [V_r: $i,V_a: $i,T_a: $i,V_b: $i] :
( ( c_Wellfounded_Oaccp @ V_r @ V_a @ T_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_a ) @ V_b ) )
| ~ ( c_Wellfounded_Oaccp @ V_r @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[255]) ).
thf(502,plain,
( ( ! [V_r: $i,V_y: $i,T_a: $i,V_a: $i] :
( ( c_Wellfounded_Oaccp @ V_r @ V_y @ T_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ V_a ) )
| ~ ( c_Wellfounded_Oaccp @ V_r @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[254]) ).
thf(503,plain,
( ( ! [V_P: $i,V_a: $i,V_r: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__1__1 @ V_P @ V_r @ T_a ) ) )
| ~ ( c_Wellfounded_Oaccp @ V_r @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[253]) ).
thf(504,plain,
( ( ! [V_P: $i,V_a: $i,V_y: $i,V_r: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ( hBOOL @ ( hAPP @ V_P @ V_y ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__1__1 @ V_P @ V_r @ T_a ) ) )
| ~ ( c_Wellfounded_Oaccp @ V_r @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[252]) ).
thf(505,plain,
( ( ! [V_R: $i,V_x: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_R @ ( c_ATP__Linkup_Osko__Wellfounded__Xnot__accp__down__1__1 @ V_R @ V_x @ T_a ) ) @ V_x ) )
| ( c_Wellfounded_Oaccp @ V_R @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[251]) ).
thf(506,plain,
( ( ! [V_e: $i,V_t_H: $i,V_T: $i,V_t: $i] :
( ( c_Type_Otyping @ V_e @ V_t_H @ V_T )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_t ) @ V_t_H ) )
| ~ ( c_Type_Otyping @ V_e @ V_t @ V_T ) ) )
= $true ),
inference(copy,[status(thm)],[250]) ).
thf(507,plain,
( ( ! [V_r: $i,V_x: $i,T_a: $i] :
( ( c_Wellfounded_Oaccp @ V_r @ V_x @ T_a )
| ~ ( c_Wellfounded_OwfP @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[249]) ).
thf(508,plain,
( ( ! [V_r: $i,T_a: $i,T_b: $i] :
( ( c_Predicate_Oconversep @ ( c_Predicate_Oconversep @ V_r @ T_a @ T_b ) @ T_b @ T_a )
= V_r ) )
= $true ),
inference(copy,[status(thm)],[248]) ).
thf(509,plain,
( ( ! [V_i: $i,V_t: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OVar @ V_i ) ) @ V_t ) ) )
= $true ),
inference(copy,[status(thm)],[247]) ).
thf(510,plain,
( ( ! [V_r: $i,V_x: $i,T_a: $i] :
( ( c_Wellfounded_Oaccp @ V_r @ V_x @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__Xintros__1__1 @ V_r @ V_x @ T_a ) ) @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[246]) ).
thf(511,plain,
( ( ! [T_a: $i] :
( ( c_Predicate_Oconversep @ ( c_fequal @ T_a ) @ T_a @ T_a )
= ( c_fequal @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[245]) ).
thf(512,plain,
( ( ! [V_r: $i,T_a: $i,V_x: $i,V_y: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ ( c_Transitive__Closure_Otranclp @ V_r @ T_a ) @ T_a @ T_a ) @ V_x ) @ V_y ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ ( c_Predicate_Oconversep @ V_r @ T_a @ T_a ) @ T_a ) @ V_x ) @ V_y ) ) ) )
= $true ),
inference(copy,[status(thm)],[244]) ).
thf(513,plain,
( ( ! [V_r: $i,T_a: $i,V_x: $i,V_y: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ ( c_Predicate_Oconversep @ V_r @ T_a @ T_a ) @ T_a ) @ V_x ) @ V_y ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ ( c_Transitive__Closure_Otranclp @ V_r @ T_a ) @ T_a @ T_a ) @ V_x ) @ V_y ) ) ) )
= $true ),
inference(copy,[status(thm)],[243]) ).
thf(514,plain,
( ( ! [V_e: $i,V_i: $i,V_T: $i] :
( ( ( hAPP @ V_e @ V_i )
= V_T )
| ~ ( c_Type_Otyping @ V_e @ ( c_Lambda_OdB_OVar @ V_i ) @ V_T ) ) )
= $true ),
inference(copy,[status(thm)],[242]) ).
thf(515,plain,
( ( ! [V_R: $i,V_x: $i,T_a: $i] :
( ~ ( c_Wellfounded_Oaccp @ V_R @ ( c_ATP__Linkup_Osko__Wellfounded__Xnot__accp__down__1__1 @ V_R @ V_x @ T_a ) @ T_a )
| ( c_Wellfounded_Oaccp @ V_R @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[241]) ).
thf(516,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Transitive__Closure_Otranclp @ ( c_Predicate_Oconversep @ V_r @ T_a @ T_a ) @ T_a )
= ( c_Predicate_Oconversep @ ( c_Transitive__Closure_Otranclp @ V_r @ T_a ) @ T_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[240]) ).
thf(517,plain,
( ( ! [V_r: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_r ) )
| ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_r @ tc_Lambda_OdB ) ) )
= $true ),
inference(copy,[status(thm)],[239]) ).
thf(518,plain,
( ( ! [V_t: $i] :
( ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_t @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_t ) ) ) )
= $true ),
inference(copy,[status(thm)],[238]) ).
thf(519,plain,
( ( ! [V_r: $i,V_b: $i,T_a: $i,V_a: $i] :
( ( c_Wellfounded_Oaccp @ V_r @ V_b @ T_a )
| ~ ( c_Wellfounded_Oaccp @ V_r @ V_a @ T_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_b ) @ V_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[237]) ).
thf(520,plain,
( ( ! [V_r: $i,V_b: $i,T_a: $i,V_a: $i] :
( ( c_Wellfounded_Oaccp @ V_r @ V_b @ T_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_b ) @ V_a ) )
| ~ ( c_Wellfounded_Oaccp @ V_r @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[236]) ).
thf(521,plain,
( ( ! [V_r: $i,V_t: $i,V_i: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Osubst @ V_r @ V_t @ V_i ) ) @ ( c_Lambda_Osubst @ V_s @ V_t @ V_i ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_r ) @ V_s ) ) ) )
= $true ),
inference(copy,[status(thm)],[235]) ).
thf(522,plain,
( ( ! [V_P: $i,V_x: $i,V_r: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( v_sko__Wellfounded__Xaccp__Xinducts__1 @ V_P @ V_r ) ) )
| ~ ( c_Wellfounded_Oaccp @ V_r @ V_x @ t_a ) ) )
= $true ),
inference(copy,[status(thm)],[234]) ).
thf(523,plain,
( ( ! [V_P: $i,V_x: $i,V_y: $i,V_r: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ( hBOOL @ ( hAPP @ V_P @ V_y ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ ( v_sko__Wellfounded__Xaccp__Xinducts__1 @ V_P @ V_r ) ) )
| ~ ( c_Wellfounded_Oaccp @ V_r @ V_x @ t_a ) ) )
= $true ),
inference(copy,[status(thm)],[233]) ).
thf(524,plain,
( ( ! [V_r: $i,V_s: $i,V_ss: $i] :
( ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ V_r @ V_s @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
| ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_s @ tc_Lambda_OdB )
| ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_r ) ) @ V_s ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) ) )
= $true ),
inference(copy,[status(thm)],[232]) ).
thf(525,plain,
( ( ! [V_P: $i,V_x: $i,V_r: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( v_sko__Wellfounded__Xaccp__Xinduct__1 @ V_P @ V_r ) ) )
| ~ ( c_Wellfounded_Oaccp @ V_r @ V_x @ t_a ) ) )
= $true ),
inference(copy,[status(thm)],[231]) ).
thf(526,plain,
( ( ! [V_P: $i,V_x: $i,V_y: $i,V_r: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ( hBOOL @ ( hAPP @ V_P @ V_y ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ ( v_sko__Wellfounded__Xaccp__Xinduct__1 @ V_P @ V_r ) ) )
| ~ ( c_Wellfounded_Oaccp @ V_r @ V_x @ t_a ) ) )
= $true ),
inference(copy,[status(thm)],[230]) ).
thf(527,plain,
( ( ! [V_r: $i,T_a: $i,T_b: $i,V_b: $i,V_a: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ V_r @ T_a @ T_b ) @ V_b ) @ V_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_a ) @ V_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[229]) ).
thf(528,plain,
( ( ! [V_r: $i,V_a2: $i,V_a1: $i,T_a: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_a2 ) @ V_a1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ V_r @ T_a @ T_b ) @ V_a1 ) @ V_a2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[228]) ).
thf(529,plain,
( ( ! [V_r: $i,T_a: $i,T_b: $i,V_a: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ V_r @ T_a @ T_b ) @ V_a ) @ V_b ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_b ) @ V_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[227]) ).
thf(530,plain,
( ( ! [V_r: $i,V_b: $i,V_a: $i,T_a: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_b ) @ V_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ V_r @ T_a @ T_b ) @ V_a ) @ V_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[226]) ).
thf(531,plain,
( ( ! [V_P: $i,V_x: $i,V_r: $i,V_ya: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ( c_Wellfounded_Oaccp @ V_r @ V_ya @ t_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_ya ) @ ( v_sko__Wellfounded__Xaccp__Xinducts__1 @ V_P @ V_r ) ) )
| ~ ( c_Wellfounded_Oaccp @ V_r @ V_x @ t_a ) ) )
= $true ),
inference(copy,[status(thm)],[225]) ).
thf(532,plain,
( ( ! [V_P: $i,V_x: $i,V_r: $i,V_ya: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ( c_Wellfounded_Oaccp @ V_r @ V_ya @ t_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_ya ) @ ( v_sko__Wellfounded__Xaccp__Xinduct__1 @ V_P @ V_r ) ) )
| ~ ( c_Wellfounded_Oaccp @ V_r @ V_x @ t_a ) ) )
= $true ),
inference(copy,[status(thm)],[224]) ).
thf(533,plain,
( ( ! [V_r: $i,V_s: $i,T_b: $i,T_a: $i] :
( ( c_Predicate_Oconversep @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_r @ V_s @ ( tc_fun @ T_b @ ( tc_fun @ T_a @ tc_bool ) ) ) @ T_b @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Predicate_Oconversep @ V_r @ T_b @ T_a ) @ ( c_Predicate_Oconversep @ V_s @ T_b @ T_a ) @ ( tc_fun @ T_a @ ( tc_fun @ T_b @ tc_bool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[223]) ).
thf(534,plain,
( ( ! [V_r: $i,T_a: $i,V_y: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_y ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ V_r @ T_a @ T_a ) @ T_a ) @ V_x ) @ V_y ) ) ) )
= $true ),
inference(copy,[status(thm)],[222]) ).
thf(535,plain,
( ( ! [V_r: $i,T_a: $i,V_x: $i,V_y: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ V_r @ T_a @ T_a ) @ T_a ) @ V_x ) @ V_y ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_y ) @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[221]) ).
thf(536,plain,
( ( ! [V_P: $i,V_a: $i,V_r: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ( c_Wellfounded_Oaccp @ V_r @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__1__1 @ V_P @ V_r @ T_a ) @ T_a )
| ~ ( c_Wellfounded_Oaccp @ V_r @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[220]) ).
thf(537,plain,
( ( ! [V_env: $i,V_x: $i] : ( c_Type_Otyping @ V_env @ ( c_Lambda_OdB_OVar @ V_x ) @ ( hAPP @ V_env @ V_x ) ) )
= $true ),
inference(copy,[status(thm)],[219]) ).
thf(538,plain,
( ( ! [V_r: $i,V_s: $i,T_b: $i,T_a: $i] :
( ( c_Predicate_Oconversep @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_r @ V_s @ ( tc_fun @ T_b @ ( tc_fun @ T_a @ tc_bool ) ) ) @ T_b @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Predicate_Oconversep @ V_r @ T_b @ T_a ) @ ( c_Predicate_Oconversep @ V_s @ T_b @ T_a ) @ ( tc_fun @ T_a @ ( tc_fun @ T_b @ tc_bool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[218]) ).
thf(539,plain,
( ( ! [V_r: $i,V_x: $i,T_a: $i] :
( ( c_Wellfounded_Oaccp @ V_r @ V_x @ T_a )
| ~ ( c_Wellfounded_Oaccp @ V_r @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__Xintros__1__1 @ V_r @ V_x @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[217]) ).
thf(540,plain,
( ( ! [V_r: $i,V_x: $i,T_a: $i] :
( ( c_Wellfounded_Oaccp @ V_r @ V_x @ T_a )
| ~ ( c_Wellfounded_Oaccp @ V_r @ ( c_ATP__Linkup_Osko__Wellfounded__XaccpI__1__1 @ V_r @ V_x @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[216]) ).
thf(541,plain,
( ( ! [V_r: $i,V_x: $i,T_a: $i] :
( ( c_Wellfounded_Oaccp @ V_r @ V_x @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ ( c_ATP__Linkup_Osko__Wellfounded__XaccpI__1__1 @ V_r @ V_x @ T_a ) ) @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[215]) ).
thf(542,plain,
( ( ! [V_u: $i,V_s: $i,V_t: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_u ) @ V_s ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_u ) @ V_t ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_s ) @ V_t ) ) ) )
= $true ),
inference(copy,[status(thm)],[214]) ).
thf(543,plain,
( ( ! [V_s: $i,V_u: $i,V_t: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_u ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_t ) @ V_u ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_s ) @ V_t ) ) ) )
= $true ),
inference(copy,[status(thm)],[213]) ).
thf(544,plain,
( ( ! [V_P: $i,V_a: $i,V_r: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ( c_Wellfounded_Oaccp @ V_r @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__rule__1__1 @ V_P @ V_r @ T_a ) @ T_a )
| ~ ( c_Wellfounded_Oaccp @ V_r @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[212]) ).
thf(545,plain,
( ( ! [V_e: $i,V_t_H: $i,V_T: $i,V_t: $i] :
( ( c_Type_Otyping @ V_e @ V_t_H @ V_T )
| ~ ( c_Type_Otyping @ V_e @ V_t @ V_T )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_t ) @ V_t_H ) ) ) )
= $true ),
inference(copy,[status(thm)],[211]) ).
thf(546,plain,
( ( ! [V_r: $i,V_i: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Olift @ V_r @ V_i ) ) @ ( c_Lambda_Olift @ V_s @ V_i ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_r ) @ V_s ) ) ) )
= $true ),
inference(copy,[status(thm)],[210]) ).
thf(547,plain,
( ( ! [V_P: $i,V_a: $i,V_r: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__rule__1__1 @ V_P @ V_r @ T_a ) ) )
| ~ ( c_Wellfounded_Oaccp @ V_r @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[209]) ).
thf(548,plain,
( ( ! [V_P: $i,V_a: $i,V_y: $i,V_r: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ( hBOOL @ ( hAPP @ V_P @ V_y ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__rule__1__1 @ V_P @ V_r @ T_a ) ) )
| ~ ( c_Wellfounded_Oaccp @ V_r @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[208]) ).
thf(549,plain,
( ( ! [V_r: $i,V_s: $i,T_b: $i,T_c: $i,T_a: $i] :
( ( c_Predicate_Oconversep @ ( c_Predicate_Opred__comp @ V_r @ V_s @ T_b @ T_c @ T_a ) @ T_b @ T_a )
= ( c_Predicate_Opred__comp @ ( c_Predicate_Oconversep @ V_s @ T_c @ T_a ) @ ( c_Predicate_Oconversep @ V_r @ T_b @ T_c ) @ T_a @ T_c @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[207]) ).
thf(550,plain,
( ( ! [V_t: $i,V_e: $i,V_T: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_t ) )
| ~ ( c_Type_Otyping @ V_e @ V_t @ V_T ) ) )
= $true ),
inference(copy,[status(thm)],[206]) ).
thf(551,plain,
( ( ! [V_s: $i,V_t: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ V_s ) ) @ ( c_Lambda_OdB_OAbs @ V_t ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_s ) @ V_t ) ) ) )
= $true ),
inference(copy,[status(thm)],[205]) ).
thf(552,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Lattices_Oupper__semilattice @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Lattices_Olattice @ T_1 ) ) )
= $true ),
inference(copy,[status(thm)],[204]) ).
thf(553,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)],[203]) ).
thf(554,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Lattices_Odistrib__lattice @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Lattices_Odistrib__lattice @ T_1 ) ) )
= $true ),
inference(copy,[status(thm)],[202]) ).
thf(555,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)],[201]) ).
thf(556,plain,
( ( class_Lattices_Oupper__semilattice @ tc_nat )
= $true ),
inference(copy,[status(thm)],[200]) ).
thf(557,plain,
( ( class_Lattices_Olower__semilattice @ tc_nat )
= $true ),
inference(copy,[status(thm)],[199]) ).
thf(558,plain,
( ( class_Lattices_Odistrib__lattice @ tc_nat )
= $true ),
inference(copy,[status(thm)],[198]) ).
thf(559,plain,
( ( class_Lattices_Olattice @ tc_nat )
= $true ),
inference(copy,[status(thm)],[197]) ).
thf(560,plain,
( ( class_Lattices_Oupper__semilattice @ tc_bool )
= $true ),
inference(copy,[status(thm)],[196]) ).
thf(561,plain,
( ( class_Lattices_Olower__semilattice @ tc_bool )
= $true ),
inference(copy,[status(thm)],[195]) ).
thf(562,plain,
( ( class_Lattices_Odistrib__lattice @ tc_bool )
= $true ),
inference(copy,[status(thm)],[194]) ).
thf(563,plain,
( ( class_Lattices_Olattice @ tc_bool )
= $true ),
inference(copy,[status(thm)],[193]) ).
thf(564,plain,
( ( ! [T_a: $i,V_x: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ T_a ) @ V_x ) @ V_x ) ) )
= $true ),
inference(copy,[status(thm)],[192]) ).
thf(565,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)],[191]) ).
thf(566,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[378]) ).
thf(567,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SX0 ) @ SX1 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SX2 ) @ SX3 ) )
| ( SX1 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[469]) ).
thf(568,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( c_Lambda_OdB_OVar @ SX0 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SX1 ) @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[462]) ).
thf(569,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( c_Lambda_OdB_OAbs @ SX0 )
!= ( c_Lambda_OdB_OVar @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[494]) ).
thf(570,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SX0 ) @ SX1 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SX2 ) @ SX3 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SX1 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[472]) ).
thf(571,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SX0 ) @ SX1 )
!= ( c_Lambda_OdB_OVar @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[406]) ).
thf(572,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( c_Type_Otype_OFun @ SX0 @ SX1 )
!= ( c_Type_Otype_OFun @ SX2 @ SX3 ) )
| ( SX1 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[383]) ).
thf(573,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SX0 ) @ SX1 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SX2 ) @ SX3 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SX0 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[473]) ).
thf(574,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_Lambda_OdB_OAbs @ SX0 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SX1 @ SX2 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OAbs @ SX0 )
= SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[423]) ).
thf(575,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SX0 ) @ SX1 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SX2 ) @ SX3 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SX0 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[489]) ).
thf(576,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SX0 @ SX1 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SX2 ) )
| ( SX1
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[388]) ).
thf(577,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SX0 @ SX1 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SX2 @ SX1 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SX0 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[420]) ).
thf(578,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SX0 ) @ SX1 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SX2 ) @ SX3 ) )
| ( SX0 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[470]) ).
thf(579,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( c_Lambda_OdB_OAbs @ SX0 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SX1 ) @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[490]) ).
thf(580,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( c_Lambda_OdB_OVar @ SX0 )
!= ( c_Lambda_OdB_OAbs @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[449]) ).
thf(581,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SX0 ) ) @ SX1 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SX2 ) @ SX3 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(unfold_def,[status(thm)],[408]) ).
thf(582,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_Lambda_OdB_OVar @ SX0 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SX1 @ SX2 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SX2
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[401]) ).
thf(583,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SX0 ) @ SX1 )
!= ( c_Lambda_OdB_OAbs @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[493]) ).
thf(584,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SX0 ) @ SX1 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SX2 ) @ SX3 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(unfold_def,[status(thm)],[456]) ).
thf(585,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_Lambda_OdB_OVar @ SX0 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SX1 @ SX2 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OVar @ SX0 )
= SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[463]) ).
thf(586,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SX0 @ SX1 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SX2 ) )
| ( SX0
= ( c_Lambda_OdB_OAbs @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[474]) ).
thf(587,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SX0 ) @ SX1 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SX2 @ SX3 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SX0
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SX2 @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ SX0 @ SX1 @ SX2 @ SX3 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SX3
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[400]) ).
thf(588,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_Lambda_OdB_OAbs @ SX0 )
!= ( c_Lambda_OdB_OAbs @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[461]) ).
thf(589,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( c_Type_Otype_OFun @ SX0 @ SX1 )
!= ( c_Type_Otype_OFun @ SX2 @ SX3 ) )
| ( SX0 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[384]) ).
thf(590,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_Lambda_OdB_OVar @ SX0 )
!= ( c_Lambda_OdB_OVar @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[492]) ).
thf(591,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SX0 ) @ SX1 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SX2 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SX0 ) @ SX1 )
= SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[395]) ).
thf(592,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SX0 ) @ SX1 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SX2 ) @ SX3 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SX1 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[488]) ).
thf(593,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_Lambda_OdB_OAbs @ SX0 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SX1 @ SX2 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SX2
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[386]) ).
thf(594,plain,
( ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ v_t @ tc_Lambda_OdB )
= $false ),
inference(extcnf_not_pos,[status(thm)],[380]) ).
thf(595,plain,
! [SV1: $i] :
( ( ! [SY614: $i,SY615: $i] :
~ ( c_ListOrder_Ostep1 @ SV1 @ ( c_List_Olist_ONil @ SY614 ) @ SY615 @ SY614 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[381]) ).
thf(596,plain,
! [SV2: $i] :
( ( ! [SY616: $i,SY617: $i] :
~ ( c_ListOrder_Ostep1 @ SV2 @ SY616 @ ( c_List_Olist_ONil @ SY617 ) @ SY617 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[382]) ).
thf(597,plain,
! [SV3: $i] :
( ( ! [SY618: $i,SY619: $i,SY620: $i,SY621: $i] :
( ( c_Type_Otyping @ SV3 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY618 ) @ SY619 ) @ SY620 )
| ~ ( c_Type_Otyping @ SV3 @ SY619 @ SY621 )
| ~ ( c_Type_Otyping @ SV3 @ SY618 @ ( c_Type_Otype_OFun @ SY621 @ SY620 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[385]) ).
thf(598,plain,
! [SV4: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV4 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV4 ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[387]) ).
thf(599,plain,
! [SV5: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV5 ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_Lambda_OdB_OAbs @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[389]) ).
thf(600,plain,
! [SV6: $i] :
( ( ! [SY622: $i,SY623: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV6 @ SY622 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV6 @ SY623 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ SY622 @ SY623 @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[390]) ).
thf(601,plain,
! [SV7: $i] :
( ( ! [SY624: $i,SY625: $i,SY626: $i,SY627: $i] :
( ( c_Type_Otyping @ ( c_Type_Oshift @ SV7 @ SY624 @ SY625 @ tc_Type_Otype ) @ ( c_Lambda_Olift @ SY626 @ SY624 ) @ SY627 )
| ~ ( c_Type_Otyping @ SV7 @ SY626 @ SY627 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[391]) ).
thf(602,plain,
! [SV8: $i] :
( ( ! [SY628: $i,SY629: $i,SY630: $i,SY631: $i,SY632: $i] :
( ~ ( c_Type_Otyping @ SV8 @ SY628 @ SY629 )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV8 @ SY630 @ SY629 @ tc_Type_Otype ) @ SY631 @ SY632 )
| ( c_Type_Otyping @ SV8 @ ( c_Lambda_Osubst @ SY631 @ SY628 @ SY630 ) @ SY632 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[392]) ).
thf(603,plain,
! [SV9: $i] :
( ( ! [SY633: $i,SY634: $i] :
( ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ SV9 @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SY633 @ SV9 @ SY634 ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY633 ) @ SV9 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SY634 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[393]) ).
thf(604,plain,
! [SV10: $i] :
( ( ! [SY635: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV10 ) @ SY635 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV10 ) @ SY635 ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[394]) ).
thf(605,plain,
! [SV11: $i] :
( ( ! [SY636: $i,SY637: $i,SY638: $i] :
( ( c_Type_Otyping @ SV11 @ ( c_Lambda_OdB_OAbs @ SY636 ) @ ( c_Type_Otype_OFun @ SY637 @ SY638 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV11 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY637 @ tc_Type_Otype ) @ SY636 @ SY638 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[396]) ).
thf(606,plain,
! [SV12: $i] :
( ( ! [SY639: $i,SY640: $i,SY641: $i] :
( ( hAPP @ ( c_Type_Oshift @ SV12 @ SY639 @ SY640 @ SY641 ) @ SY639 )
= SY640 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[397]) ).
thf(607,plain,
! [SV13: $i] :
( ( ! [SY642: $i,SY643: $i,SY644: $i] :
( ( c_List_Ofoldl @ SV13 @ SY642 @ ( c_List_Olist_ONil @ SY643 ) @ SY644 @ SY643 )
= SY642 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[398]) ).
thf(608,plain,
! [SV14: $i] :
( ( ! [SY645: $i] : ( c_List_Olistsp @ SV14 @ ( c_List_Olist_ONil @ SY645 ) @ SY645 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[399]) ).
thf(609,plain,
! [SV15: $i] :
( ( ( c_Lambda_OdB_OVar @ SV15 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV15 ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[402]) ).
thf(610,plain,
! [SV16: $i] :
( ( ! [SY646: $i,SY647: $i,SY648: $i,SY649: $i,SY650: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV16 @ SY646 @ SY647 ) ) )
| ~ ( c_Type_Otyping @ SY648 @ SY646 @ SY649 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SY646 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SY648 @ SY647 @ SY649 @ tc_Type_Otype ) @ SV16 @ SY650 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV16 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[403]) ).
thf(611,plain,
! [SV17: $i] :
( ( ! [SY651: $i,SY652: $i] :
( ( SV17
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY651 ) @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SY651 @ SY652 @ SV17 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY651 ) @ SY652 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV17 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[404]) ).
thf(612,plain,
! [SV18: $i] :
( ( ! [SY653: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV18 ) @ SY653 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( c_List_Olistsp @ c_InductTermi_OIT @ SY653 @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[405]) ).
thf(613,plain,
! [SV19: $i] :
( ( ! [SY654: $i] :
( ( c_Transitive__Closure_Ortranclp @ ( c_Transitive__Closure_Ortranclp @ SV19 @ SY654 ) @ SY654 )
= ( c_Transitive__Closure_Ortranclp @ SV19 @ SY654 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[407]) ).
thf(614,plain,
! [SV20: $i] :
( ( ! [SY655: $i,SY656: $i,SY657: $i,SY658: $i,SY659: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV20 @ SY655 ) @ SY656 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV20 @ SY657 @ ( tc_fun @ SY658 @ ( tc_fun @ SY659 @ tc_bool ) ) ) @ SY655 ) @ SY656 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[409]) ).
thf(615,plain,
! [SV21: $i] :
( ( ! [SY660: $i,SY661: $i,SY662: $i,SY663: $i,SY664: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV21 @ SY660 ) @ SY661 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY662 @ SV21 @ ( tc_fun @ SY663 @ ( tc_fun @ SY664 @ tc_bool ) ) ) @ SY660 ) @ SY661 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[410]) ).
thf(616,plain,
! [SV22: $i] :
( ( ! [SY665: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV22 ) @ ( c_Lambda_OdB_OVar @ SY665 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV22 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[411]) ).
thf(617,plain,
! [SV23: $i] :
( ( ! [SY666: $i,SY667: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_Olift @ SV23 @ SY666 ) @ SY667 @ SY666 )
= SV23 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[412]) ).
thf(618,plain,
! [SV24: $i] :
( ( ! [SY668: $i,SY669: $i,SY670: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV24 @ SY668 ) @ SY669 ) @ SY670 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV24 @ SY669 ) @ SY670 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[413]) ).
thf(619,plain,
! [SV25: $i] :
( ( ! [SY671: $i,SY672: $i] :
( ~ ( class_Lattices_Olattice @ SV25 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SY671 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY671 @ SY672 @ SV25 ) @ SV25 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY671 @ SY672 @ SV25 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[414]) ).
thf(620,plain,
! [SV26: $i] :
( ( ! [SY673: $i,SY674: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV26 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SY673 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY673 @ SY674 @ SV26 ) @ SV26 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY673 @ SY674 @ SV26 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[415]) ).
thf(621,plain,
! [SV27: $i] :
( ( ! [SY675: $i,SY676: $i] :
( ~ ( class_Lattices_Olattice @ SV27 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SY675 @ SY676 @ SV27 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY676 @ SY675 @ SV27 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[416]) ).
thf(622,plain,
! [SV28: $i] :
( ( ! [SY677: $i,SY678: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV28 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SY677 @ SY678 @ SV28 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY678 @ SY677 @ SV28 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[417]) ).
thf(623,plain,
! [SV29: $i] :
( ( ! [SY679: $i,SY680: $i,SY681: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV29 ) @ SY679 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY680 ) @ SY681 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SY679 ) @ SY681 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV29 ) @ SY680 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[418]) ).
thf(624,plain,
! [SV30: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OAbs @ SV30 ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV30 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[419]) ).
thf(625,plain,
! [SV31: $i] :
( ( ! [SY682: $i,SY683: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV31 ) @ SY682 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY683 ) @ SY682 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV31 ) @ SY683 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[421]) ).
thf(626,plain,
! [SV32: $i] :
( ( ! [SY684: $i,SY685: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV32 ) @ SY684 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV32 ) @ SY685 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SY684 ) @ SY685 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[422]) ).
thf(627,plain,
! [SV33: $i] :
( ( ! [SY686: $i,SY687: $i] :
( ~ ( class_Lattices_Olattice @ SV33 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SY686 @ SY687 @ SV33 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY687 @ SY686 @ SV33 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[424]) ).
thf(628,plain,
! [SV34: $i] :
( ( ! [SY688: $i,SY689: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV34 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SY688 @ SY689 @ SV34 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY689 @ SY688 @ SV34 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[425]) ).
thf(629,plain,
! [SV35: $i] :
( ( ! [SY690: $i,SY691: $i,SY692: $i] :
( ~ ( class_Lattices_Olattice @ SV35 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY690 @ SY691 @ SV35 ) @ SY692 @ SV35 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY690 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY691 @ SY692 @ SV35 ) @ SV35 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[426]) ).
thf(630,plain,
! [SV36: $i] :
( ( ! [SY693: $i,SY694: $i,SY695: $i] :
( ~ ( class_Lattices_Olattice @ SV36 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SY693 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY694 @ SY695 @ SV36 ) @ SV36 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY694 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY693 @ SY695 @ SV36 ) @ SV36 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[427]) ).
thf(631,plain,
! [SV37: $i] :
( ( ! [SY696: $i,SY697: $i,SY698: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV37 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SY696 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY697 @ SY698 @ SV37 ) @ SV37 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY697 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY696 @ SY698 @ SV37 ) @ SV37 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[428]) ).
thf(632,plain,
! [SV38: $i] :
( ( ! [SY699: $i,SY700: $i,SY701: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV38 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY699 @ SY700 @ SV38 ) @ SY701 @ SV38 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY699 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY700 @ SY701 @ SV38 ) @ SV38 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[429]) ).
thf(633,plain,
! [SV39: $i] :
( ( ! [SY702: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV39 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SY702 @ SY702 @ SV39 )
= SY702 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[430]) ).
thf(634,plain,
! [SV40: $i] :
( ( ! [SY703: $i,SY704: $i,SY705: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ SV40 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY703 @ SY704 @ SV40 ) @ SY705 @ SV40 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY703 @ SY705 @ SV40 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY704 @ SY705 @ SV40 ) @ SV40 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[431]) ).
thf(635,plain,
! [SV41: $i] :
( ( ! [SY706: $i,SY707: $i,SY708: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ SV41 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SY706 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY707 @ SY708 @ SV41 ) @ SV41 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY706 @ SY707 @ SV41 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY706 @ SY708 @ SV41 ) @ SV41 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[432]) ).
thf(636,plain,
! [SV42: $i] :
( ( ! [SY709: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_OdB_OAbs @ SV42 ) ) @ ( c_Lambda_OdB_OAbs @ SY709 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV42 ) @ SY709 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[433]) ).
thf(637,plain,
! [SV43: $i] :
( ( ! [SY710: $i,SY711: $i,SY712: $i,SY713: $i,SY714: $i,SY715: $i,SY716: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV43 @ SY710 @ SY711 @ SY712 @ SY713 ) @ SY714 ) @ SY715 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY710 @ SY716 ) @ SY715 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV43 @ SY714 ) @ SY716 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[434]) ).
thf(638,plain,
! [SV44: $i] :
( ( ! [SY717: $i,SY718: $i,SY719: $i,SY720: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV44 @ SY717 ) @ SY718 ) @ SY719 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV44 @ SY717 ) @ SY720 ) @ SY719 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV44 @ SY717 ) @ SY718 ) @ SY720 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[435]) ).
thf(639,plain,
! [SV45: $i] :
( ( ! [SY721: $i,SY722: $i,SY723: $i,SY724: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV45 @ SY721 ) @ SY722 ) @ SY723 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV45 @ SY721 ) @ SY724 ) @ SY723 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV45 @ SY721 ) @ SY722 ) @ SY724 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[436]) ).
thf(640,plain,
! [SV46: $i] :
( ( ! [SY725: $i,SY726: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV46 @ SY725 ) @ SY726 ) @ SY726 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[437]) ).
thf(641,plain,
! [SV47: $i] :
( ( ! [SY727: $i,SY728: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV47 @ SY727 ) @ SY728 ) @ SY728 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[438]) ).
thf(642,plain,
! [SV48: $i] :
( ( ! [SY729: $i,SY730: $i,SY731: $i,SY732: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV48 @ SY729 ) @ SY730 ) @ SY731 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV48 @ SY729 ) @ SY732 ) @ SY731 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV48 @ SY729 ) @ SY730 ) @ SY732 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[439]) ).
thf(643,plain,
! [SV49: $i] :
( ( ! [SY733: $i,SY734: $i,SY735: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV49 @ SY733 @ SY734 ) ) @ ( c_Lambda_Osubst @ SV49 @ SY735 @ SY734 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SY733 ) @ SY735 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[440]) ).
thf(644,plain,
! [SV50: $i] :
( ( ! [SY736: $i,SY737: $i,SY738: $i,SY739: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV50 @ SY736 ) @ SY737 ) @ SY738 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV50 @ SY736 ) @ SY739 ) @ SY738 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV50 @ SY737 ) @ SY739 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[441]) ).
thf(645,plain,
! [SV51: $i] :
( ( ! [SY740: $i,SY741: $i,SY742: $i,SY743: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV51 @ SY740 ) @ SY741 ) @ SY742 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV51 @ SY743 ) @ SY742 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV51 @ SY740 ) @ SY741 ) @ SY743 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[442]) ).
thf(646,plain,
! [SV52: $i] :
( ( ! [SY744: $i,SY745: $i] :
( ( c_Lambda_Olift @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV52 ) @ SY744 ) @ SY745 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Olift @ SV52 @ SY745 ) ) @ ( c_Lambda_Olift @ SY744 @ SY745 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[443]) ).
thf(647,plain,
! [SV53: $i] :
( ( ! [SY746: $i] :
( ( c_Wellfounded_OwfP @ ( c_Transitive__Closure_Otranclp @ SV53 @ SY746 ) @ SY746 )
| ~ ( c_Wellfounded_OwfP @ SV53 @ SY746 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[444]) ).
thf(648,plain,
! [SV54: $i] :
( ( ! [SY747: $i,SY748: $i,SY749: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV54 @ SY747 ) @ SY748 ) @ SY749 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV54 @ SY747 ) @ SY748 ) @ SY749 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[445]) ).
thf(649,plain,
! [SV55: $i] :
( ( ! [SY750: $i,SY751: $i,SY752: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV55 @ SY750 @ SY751 ) ) @ ( c_Lambda_Osubst @ SY752 @ SY750 @ SY751 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV55 ) @ SY752 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[446]) ).
thf(650,plain,
! [SV56: $i] :
( ( ! [SY753: $i,SY754: $i,SY755: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV56 @ SY753 @ SY754 ) ) @ ( c_Lambda_Osubst @ SV56 @ SY755 @ SY754 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SY753 ) @ SY755 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[447]) ).
thf(651,plain,
! [SV57: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OVar @ SV57 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[448]) ).
thf(652,plain,
! [SV58: $i] :
( ( ! [SY756: $i,SY757: $i,SY758: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV58 @ SY756 ) @ SY757 ) @ SY758 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV58 @ SY757 ) @ SY758 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[450]) ).
thf(653,plain,
! [SV59: $i] :
( ( ! [SY759: $i,SY760: $i,SY761: $i,SY762: $i,SY763: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV59 @ SY759 ) @ SY760 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY761 @ SY759 ) @ SY760 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY761 @ SV59 @ ( tc_fun @ SY762 @ ( tc_fun @ SY763 @ tc_bool ) ) ) @ SY759 ) @ SY760 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[451]) ).
thf(654,plain,
! [SV60: $i] :
( ( ! [SY764: $i,SY765: $i,SY766: $i,SY767: $i,SY768: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV60 @ SY764 @ ( tc_fun @ SY765 @ ( tc_fun @ SY766 @ tc_bool ) ) ) @ SY767 ) @ SY768 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY764 @ SY767 ) @ SY768 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[452]) ).
thf(655,plain,
! [SV61: $i] :
( ( ! [SY769: $i,SY770: $i,SY771: $i,SY772: $i,SY773: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV61 @ SY769 @ ( tc_fun @ SY770 @ ( tc_fun @ SY771 @ tc_bool ) ) ) @ SY772 ) @ SY773 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV61 @ SY772 ) @ SY773 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[453]) ).
thf(656,plain,
! [SV62: $i] :
( ( ! [SY774: $i,SY775: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV62 ) ) @ SY774 ) @ SY775 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SY774 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV62 @ SY774 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SY775 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[454]) ).
thf(657,plain,
! [SV63: $i] :
( ( ! [SY776: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Olift @ SV63 @ SY776 ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV63 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[455]) ).
thf(658,plain,
! [SV64: $i] :
( ( ! [SY777: $i,SY778: $i,SY779: $i] :
( ~ ( class_Lattices_Olattice @ SV64 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY777 @ SY778 @ SV64 ) @ SY779 @ SV64 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY777 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY778 @ SY779 @ SV64 ) @ SV64 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[457]) ).
thf(659,plain,
! [SV65: $i] :
( ( ! [SY780: $i,SY781: $i,SY782: $i] :
( ~ ( class_Lattices_Olattice @ SV65 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SY780 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY781 @ SY782 @ SV65 ) @ SV65 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY781 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY780 @ SY782 @ SV65 ) @ SV65 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[458]) ).
thf(660,plain,
! [SV66: $i] :
( ( ! [SY783: $i,SY784: $i,SY785: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV66 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SY783 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY784 @ SY785 @ SV66 ) @ SV66 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY784 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY783 @ SY785 @ SV66 ) @ SV66 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[459]) ).
thf(661,plain,
! [SV67: $i] :
( ( ! [SY786: $i,SY787: $i,SY788: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV67 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY786 @ SY787 @ SV67 ) @ SY788 @ SV67 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY786 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY787 @ SY788 @ SV67 ) @ SV67 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[460]) ).
thf(662,plain,
! [SV68: $i] :
( ( ! [SY789: $i,SY790: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV68 @ SY789 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY790 @ SY789 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV68 ) @ SY790 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[464]) ).
thf(663,plain,
! [SV69: $i] :
( ( ! [SY791: $i,SY792: $i] :
( ~ ( class_Lattices_Olattice @ SV69 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SY791 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY791 @ SY792 @ SV69 ) @ SV69 )
= SY791 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[465]) ).
thf(664,plain,
! [SV70: $i] :
( ( ! [SY793: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV70 ) ) @ SY793 ) ) @ ( c_Lambda_Osubst @ SV70 @ SY793 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[466]) ).
thf(665,plain,
! [SV71: $i] :
( ( ! [SY794: $i,SY795: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Olift @ SV71 @ SY794 ) ) @ ( c_Lambda_Olift @ SY795 @ SY794 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV71 ) @ SY795 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[467]) ).
thf(666,plain,
! [SV72: $i] :
( ( ! [SY796: $i,SY797: $i,SY798: $i,SY799: $i] :
( ( SV72 = SY796 )
| ~ ( c_Type_Otyping @ SY797 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY798 ) @ SY799 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY796 )
| ~ ( c_Type_Otyping @ SY797 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY798 ) @ SY799 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV72 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[468]) ).
thf(667,plain,
! [SV73: $i] :
( ( ! [SY800: $i,SY801: $i] :
( ~ ( class_Lattices_Olattice @ SV73 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SY800 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY800 @ SY801 @ SV73 ) @ SV73 )
= SY800 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[471]) ).
thf(668,plain,
! [SV74: $i] :
( ( ! [SY802: $i] :
( ( c_Transitive__Closure_Ortranclp @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV74 @ ( c_fequal @ SY802 ) @ ( tc_fun @ SY802 @ ( tc_fun @ SY802 @ tc_bool ) ) ) @ SY802 )
= ( c_Transitive__Closure_Ortranclp @ SV74 @ SY802 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[475]) ).
thf(669,plain,
! [SV75: $i] :
( ( ! [SY803: $i,SY804: $i,SY805: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV75 @ SY803 ) @ SY804 ) @ SY805 ) )
| ( SY804 = SY805 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV75 @ SY803 ) @ SY804 ) @ SY805 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[476]) ).
thf(670,plain,
! [SV76: $i] :
( ( ! [SY806: $i,SY807: $i,SY808: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV76 @ SY806 ) @ SY807 ) @ SY808 ) )
| ( SY807 = SY808 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV76 @ SY806 ) @ SY807 ) @ SY808 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[477]) ).
thf(671,plain,
! [SV77: $i] :
( ( ! [SY809: $i,SY810: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV77 @ SY809 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY810 @ SY809 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV77 ) @ SY810 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[478]) ).
thf(672,plain,
! [SV78: $i] :
( ( ! [SY811: $i,SY812: $i] :
( ( c_Transitive__Closure_Ortranclp @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Ortranclp @ SV78 @ SY811 ) @ ( c_Transitive__Closure_Ortranclp @ SY812 @ SY811 ) @ ( tc_fun @ SY811 @ ( tc_fun @ SY811 @ tc_bool ) ) ) @ SY811 )
= ( c_Transitive__Closure_Ortranclp @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV78 @ SY812 @ ( tc_fun @ SY811 @ ( tc_fun @ SY811 @ tc_bool ) ) ) @ SY811 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[479]) ).
thf(673,plain,
! [SV79: $i] :
( ( ! [SY813: $i,SY814: $i,SY815: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ SV79 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY813 @ SY814 @ SV79 ) @ SY815 @ SV79 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY813 @ SY815 @ SV79 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY814 @ SY815 @ SV79 ) @ SV79 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[480]) ).
thf(674,plain,
! [SV80: $i] :
( ( ! [SY816: $i,SY817: $i,SY818: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ SV80 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SY816 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY817 @ SY818 @ SV80 ) @ SV80 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY816 @ SY817 @ SV80 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY816 @ SY818 @ SV80 ) @ SV80 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[481]) ).
thf(675,plain,
! [SV81: $i] :
( ( ! [SY819: $i,SY820: $i] :
( ~ ( class_Lattices_Olattice @ SV81 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SY819 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY819 @ SY820 @ SV81 ) @ SV81 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY819 @ SY820 @ SV81 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[482]) ).
thf(676,plain,
! [SV82: $i] :
( ( ! [SY821: $i,SY822: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV82 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SY821 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY821 @ SY822 @ SV82 ) @ SV82 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY821 @ SY822 @ SV82 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[483]) ).
thf(677,plain,
! [SV83: $i] :
( ( ! [SY823: $i,SY824: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV83 @ ( c_Lambda_OdB_OVar @ SY823 ) @ SY824 ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV83 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[484]) ).
thf(678,plain,
! [SV84: $i] :
( ( ! [SY825: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Otranclp @ SV84 @ SY825 ) @ ( c_fequal @ SY825 ) @ ( tc_fun @ SY825 @ ( tc_fun @ SY825 @ tc_bool ) ) )
= ( c_Transitive__Closure_Ortranclp @ SV84 @ SY825 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[485]) ).
thf(679,plain,
! [SV85: $i] :
( ( ! [SY826: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV85 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SY826 @ SY826 @ SV85 )
= SY826 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[486]) ).
thf(680,plain,
! [SV86: $i] :
( ( ! [SY827: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV86 ) @ SY827 @ SV86 )
= SY827 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[487]) ).
thf(681,plain,
! [SV87: $i] :
( ( ! [SY828: $i,SY829: $i,SY830: $i,SY831: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV87 @ SY828 ) @ SY829 ) @ SY830 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV87 @ SY828 ) @ SY831 ) @ SY830 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV87 @ SY828 ) @ SY829 ) @ SY831 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[491]) ).
thf(682,plain,
! [SV88: $i] :
( ( ! [SY832: $i,SY833: $i,SY834: $i] :
( ( c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV88 ) @ SY832 ) @ SY833 @ SY834 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV88 @ SY833 @ SY834 ) ) @ ( c_Lambda_Osubst @ SY832 @ SY833 @ SY834 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[495]) ).
thf(683,plain,
! [SV89: $i] :
( ( ! [SY835: $i,SY836: $i,SY837: $i,SY838: $i,SY839: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV89 @ SY835 @ ( tc_fun @ SY836 @ ( tc_fun @ SY837 @ tc_bool ) ) ) @ SY838 ) @ SY839 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY835 @ SY838 ) @ SY839 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV89 @ SY838 ) @ SY839 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[496]) ).
thf(684,plain,
! [SV90: $i] :
( ( ! [SY840: $i,SY841: $i,SY842: $i,SY843: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV90 @ SY840 ) @ SY841 ) @ SY842 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV90 @ SY840 ) @ SY843 ) @ SY842 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV90 @ SY841 ) @ SY843 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[497]) ).
thf(685,plain,
! [SV91: $i] :
( ( ! [SY844: $i,SY845: $i,SY846: $i,SY847: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV91 @ SY844 ) @ SY845 ) @ SY846 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV91 @ SY847 ) @ SY846 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV91 @ SY844 ) @ SY845 ) @ SY847 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[498]) ).
thf(686,plain,
! [SV92: $i] :
( ( ! [SY848: $i,SY849: $i,SY850: $i,SY851: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV92 @ SY848 ) @ SY849 ) @ SY850 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV92 @ SY851 ) @ SY850 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV92 @ SY848 ) @ SY849 ) @ SY851 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[499]) ).
thf(687,plain,
! [SV93: $i] :
( ( ! [SY852: $i,SY853: $i,SY854: $i,SY855: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV93 @ SY852 ) @ SY853 ) @ SY854 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV93 @ SY852 ) @ SY855 ) @ SY854 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV93 @ SY853 ) @ SY855 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[500]) ).
thf(688,plain,
! [SV94: $i] :
( ( ! [SY856: $i,SY857: $i,SY858: $i] :
( ( c_Wellfounded_Oaccp @ SV94 @ SY856 @ SY857 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV94 @ SY856 ) @ SY858 ) )
| ~ ( c_Wellfounded_Oaccp @ SV94 @ SY858 @ SY857 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[501]) ).
thf(689,plain,
! [SV95: $i] :
( ( ! [SY859: $i,SY860: $i,SY861: $i] :
( ( c_Wellfounded_Oaccp @ SV95 @ SY859 @ SY860 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV95 @ SY859 ) @ SY861 ) )
| ~ ( c_Wellfounded_Oaccp @ SV95 @ SY861 @ SY860 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[502]) ).
thf(690,plain,
! [SV96: $i] :
( ( ! [SY862: $i,SY863: $i,SY864: $i] :
( ( hBOOL @ ( hAPP @ SV96 @ SY862 ) )
| ~ ( hBOOL @ ( hAPP @ SV96 @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__1__1 @ SV96 @ SY863 @ SY864 ) ) )
| ~ ( c_Wellfounded_Oaccp @ SY863 @ SY862 @ SY864 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[503]) ).
thf(691,plain,
! [SV97: $i] :
( ( ! [SY865: $i,SY866: $i,SY867: $i,SY868: $i] :
( ( hBOOL @ ( hAPP @ SV97 @ SY865 ) )
| ( hBOOL @ ( hAPP @ SV97 @ SY866 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY867 @ SY866 ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__1__1 @ SV97 @ SY867 @ SY868 ) ) )
| ~ ( c_Wellfounded_Oaccp @ SY867 @ SY865 @ SY868 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[504]) ).
thf(692,plain,
! [SV98: $i] :
( ( ! [SY869: $i,SY870: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV98 @ ( c_ATP__Linkup_Osko__Wellfounded__Xnot__accp__down__1__1 @ SV98 @ SY869 @ SY870 ) ) @ SY869 ) )
| ( c_Wellfounded_Oaccp @ SV98 @ SY869 @ SY870 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[505]) ).
thf(693,plain,
! [SV99: $i] :
( ( ! [SY871: $i,SY872: $i,SY873: $i] :
( ( c_Type_Otyping @ SV99 @ SY871 @ SY872 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SY873 ) @ SY871 ) )
| ~ ( c_Type_Otyping @ SV99 @ SY873 @ SY872 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[506]) ).
thf(694,plain,
! [SV100: $i] :
( ( ! [SY874: $i,SY875: $i] :
( ( c_Wellfounded_Oaccp @ SV100 @ SY874 @ SY875 )
| ~ ( c_Wellfounded_OwfP @ SV100 @ SY875 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[507]) ).
thf(695,plain,
! [SV101: $i] :
( ( ! [SY876: $i,SY877: $i] :
( ( c_Predicate_Oconversep @ ( c_Predicate_Oconversep @ SV101 @ SY876 @ SY877 ) @ SY877 @ SY876 )
= SV101 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[508]) ).
thf(696,plain,
! [SV102: $i] :
( ( ! [SY878: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OVar @ SV102 ) ) @ SY878 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[509]) ).
thf(697,plain,
! [SV103: $i] :
( ( ! [SY879: $i,SY880: $i] :
( ( c_Wellfounded_Oaccp @ SV103 @ SY879 @ SY880 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV103 @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__Xintros__1__1 @ SV103 @ SY879 @ SY880 ) ) @ SY879 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[510]) ).
thf(698,plain,
! [SV104: $i] :
( ( ( c_Predicate_Oconversep @ ( c_fequal @ SV104 ) @ SV104 @ SV104 )
= ( c_fequal @ SV104 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[511]) ).
thf(699,plain,
! [SV105: $i] :
( ( ! [SY881: $i,SY882: $i,SY883: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ ( c_Transitive__Closure_Otranclp @ SV105 @ SY881 ) @ SY881 @ SY881 ) @ SY882 ) @ SY883 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ ( c_Predicate_Oconversep @ SV105 @ SY881 @ SY881 ) @ SY881 ) @ SY882 ) @ SY883 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[512]) ).
thf(700,plain,
! [SV106: $i] :
( ( ! [SY884: $i,SY885: $i,SY886: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ ( c_Predicate_Oconversep @ SV106 @ SY884 @ SY884 ) @ SY884 ) @ SY885 ) @ SY886 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ ( c_Transitive__Closure_Otranclp @ SV106 @ SY884 ) @ SY884 @ SY884 ) @ SY885 ) @ SY886 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[513]) ).
thf(701,plain,
! [SV107: $i] :
( ( ! [SY887: $i,SY888: $i] :
( ( ( hAPP @ SV107 @ SY887 )
= SY888 )
| ~ ( c_Type_Otyping @ SV107 @ ( c_Lambda_OdB_OVar @ SY887 ) @ SY888 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[514]) ).
thf(702,plain,
! [SV108: $i] :
( ( ! [SY889: $i,SY890: $i] :
( ~ ( c_Wellfounded_Oaccp @ SV108 @ ( c_ATP__Linkup_Osko__Wellfounded__Xnot__accp__down__1__1 @ SV108 @ SY889 @ SY890 ) @ SY890 )
| ( c_Wellfounded_Oaccp @ SV108 @ SY889 @ SY890 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[515]) ).
thf(703,plain,
! [SV109: $i] :
( ( ! [SY891: $i] :
( ( c_Transitive__Closure_Otranclp @ ( c_Predicate_Oconversep @ SV109 @ SY891 @ SY891 ) @ SY891 )
= ( c_Predicate_Oconversep @ ( c_Transitive__Closure_Otranclp @ SV109 @ SY891 ) @ SY891 @ SY891 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[516]) ).
thf(704,plain,
! [SV110: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV110 ) )
| ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV110 @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[517]) ).
thf(705,plain,
! [SV111: $i] :
( ( ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV111 @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV111 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[518]) ).
thf(706,plain,
! [SV112: $i] :
( ( ! [SY892: $i,SY893: $i,SY894: $i] :
( ( c_Wellfounded_Oaccp @ SV112 @ SY892 @ SY893 )
| ~ ( c_Wellfounded_Oaccp @ SV112 @ SY894 @ SY893 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV112 @ SY893 ) @ SY892 ) @ SY894 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[519]) ).
thf(707,plain,
! [SV113: $i] :
( ( ! [SY895: $i,SY896: $i,SY897: $i] :
( ( c_Wellfounded_Oaccp @ SV113 @ SY895 @ SY896 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV113 @ SY896 ) @ SY895 ) @ SY897 ) )
| ~ ( c_Wellfounded_Oaccp @ SV113 @ SY897 @ SY896 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[520]) ).
thf(708,plain,
! [SV114: $i] :
( ( ! [SY898: $i,SY899: $i,SY900: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Osubst @ SV114 @ SY898 @ SY899 ) ) @ ( c_Lambda_Osubst @ SY900 @ SY898 @ SY899 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV114 ) @ SY900 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[521]) ).
thf(709,plain,
! [SV115: $i] :
( ( ! [SY901: $i,SY902: $i] :
( ( hBOOL @ ( hAPP @ SV115 @ SY901 ) )
| ~ ( hBOOL @ ( hAPP @ SV115 @ ( v_sko__Wellfounded__Xaccp__Xinducts__1 @ SV115 @ SY902 ) ) )
| ~ ( c_Wellfounded_Oaccp @ SY902 @ SY901 @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[522]) ).
thf(710,plain,
! [SV116: $i] :
( ( ! [SY903: $i,SY904: $i,SY905: $i] :
( ( hBOOL @ ( hAPP @ SV116 @ SY903 ) )
| ( hBOOL @ ( hAPP @ SV116 @ SY904 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY905 @ SY904 ) @ ( v_sko__Wellfounded__Xaccp__Xinducts__1 @ SV116 @ SY905 ) ) )
| ~ ( c_Wellfounded_Oaccp @ SY905 @ SY903 @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[523]) ).
thf(711,plain,
! [SV117: $i] :
( ( ! [SY906: $i,SY907: $i] :
( ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV117 @ SY906 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SY907 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
| ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY906 @ tc_Lambda_OdB )
| ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV117 ) ) @ SY906 ) @ SY907 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[524]) ).
thf(712,plain,
! [SV118: $i] :
( ( ! [SY908: $i,SY909: $i] :
( ( hBOOL @ ( hAPP @ SV118 @ SY908 ) )
| ~ ( hBOOL @ ( hAPP @ SV118 @ ( v_sko__Wellfounded__Xaccp__Xinduct__1 @ SV118 @ SY909 ) ) )
| ~ ( c_Wellfounded_Oaccp @ SY909 @ SY908 @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[525]) ).
thf(713,plain,
! [SV119: $i] :
( ( ! [SY910: $i,SY911: $i,SY912: $i] :
( ( hBOOL @ ( hAPP @ SV119 @ SY910 ) )
| ( hBOOL @ ( hAPP @ SV119 @ SY911 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY912 @ SY911 ) @ ( v_sko__Wellfounded__Xaccp__Xinduct__1 @ SV119 @ SY912 ) ) )
| ~ ( c_Wellfounded_Oaccp @ SY912 @ SY910 @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[526]) ).
thf(714,plain,
! [SV120: $i] :
( ( ! [SY913: $i,SY914: $i,SY915: $i,SY916: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV120 @ SY913 @ SY914 ) @ SY915 ) @ SY916 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV120 @ SY916 ) @ SY915 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[527]) ).
thf(715,plain,
! [SV121: $i] :
( ( ! [SY917: $i,SY918: $i,SY919: $i,SY920: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV121 @ SY917 ) @ SY918 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV121 @ SY919 @ SY920 ) @ SY918 ) @ SY917 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[528]) ).
thf(716,plain,
! [SV122: $i] :
( ( ! [SY921: $i,SY922: $i,SY923: $i,SY924: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV122 @ SY921 @ SY922 ) @ SY923 ) @ SY924 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV122 @ SY924 ) @ SY923 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[529]) ).
thf(717,plain,
! [SV123: $i] :
( ( ! [SY925: $i,SY926: $i,SY927: $i,SY928: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV123 @ SY925 ) @ SY926 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV123 @ SY927 @ SY928 ) @ SY926 ) @ SY925 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[530]) ).
thf(718,plain,
! [SV124: $i] :
( ( ! [SY929: $i,SY930: $i,SY931: $i] :
( ( hBOOL @ ( hAPP @ SV124 @ SY929 ) )
| ( c_Wellfounded_Oaccp @ SY930 @ SY931 @ t_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY930 @ SY931 ) @ ( v_sko__Wellfounded__Xaccp__Xinducts__1 @ SV124 @ SY930 ) ) )
| ~ ( c_Wellfounded_Oaccp @ SY930 @ SY929 @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[531]) ).
thf(719,plain,
! [SV125: $i] :
( ( ! [SY932: $i,SY933: $i,SY934: $i] :
( ( hBOOL @ ( hAPP @ SV125 @ SY932 ) )
| ( c_Wellfounded_Oaccp @ SY933 @ SY934 @ t_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY933 @ SY934 ) @ ( v_sko__Wellfounded__Xaccp__Xinduct__1 @ SV125 @ SY933 ) ) )
| ~ ( c_Wellfounded_Oaccp @ SY933 @ SY932 @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[532]) ).
thf(720,plain,
! [SV126: $i] :
( ( ! [SY935: $i,SY936: $i,SY937: $i] :
( ( c_Predicate_Oconversep @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV126 @ SY935 @ ( tc_fun @ SY936 @ ( tc_fun @ SY937 @ tc_bool ) ) ) @ SY936 @ SY937 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Predicate_Oconversep @ SV126 @ SY936 @ SY937 ) @ ( c_Predicate_Oconversep @ SY935 @ SY936 @ SY937 ) @ ( tc_fun @ SY937 @ ( tc_fun @ SY936 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[533]) ).
thf(721,plain,
! [SV127: $i] :
( ( ! [SY938: $i,SY939: $i,SY940: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV127 @ SY938 ) @ SY939 ) @ SY940 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ SV127 @ SY938 @ SY938 ) @ SY938 ) @ SY940 ) @ SY939 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[534]) ).
thf(722,plain,
! [SV128: $i] :
( ( ! [SY941: $i,SY942: $i,SY943: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ SV128 @ SY941 @ SY941 ) @ SY941 ) @ SY942 ) @ SY943 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV128 @ SY941 ) @ SY943 ) @ SY942 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[535]) ).
thf(723,plain,
! [SV129: $i] :
( ( ! [SY944: $i,SY945: $i,SY946: $i] :
( ( hBOOL @ ( hAPP @ SV129 @ SY944 ) )
| ( c_Wellfounded_Oaccp @ SY945 @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__1__1 @ SV129 @ SY945 @ SY946 ) @ SY946 )
| ~ ( c_Wellfounded_Oaccp @ SY945 @ SY944 @ SY946 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[536]) ).
thf(724,plain,
! [SV130: $i] :
( ( ! [SY947: $i] : ( c_Type_Otyping @ SV130 @ ( c_Lambda_OdB_OVar @ SY947 ) @ ( hAPP @ SV130 @ SY947 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[537]) ).
thf(725,plain,
! [SV131: $i] :
( ( ! [SY948: $i,SY949: $i,SY950: $i] :
( ( c_Predicate_Oconversep @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV131 @ SY948 @ ( tc_fun @ SY949 @ ( tc_fun @ SY950 @ tc_bool ) ) ) @ SY949 @ SY950 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Predicate_Oconversep @ SV131 @ SY949 @ SY950 ) @ ( c_Predicate_Oconversep @ SY948 @ SY949 @ SY950 ) @ ( tc_fun @ SY950 @ ( tc_fun @ SY949 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[538]) ).
thf(726,plain,
! [SV132: $i] :
( ( ! [SY951: $i,SY952: $i] :
( ( c_Wellfounded_Oaccp @ SV132 @ SY951 @ SY952 )
| ~ ( c_Wellfounded_Oaccp @ SV132 @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__Xintros__1__1 @ SV132 @ SY951 @ SY952 ) @ SY952 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[539]) ).
thf(727,plain,
! [SV133: $i] :
( ( ! [SY953: $i,SY954: $i] :
( ( c_Wellfounded_Oaccp @ SV133 @ SY953 @ SY954 )
| ~ ( c_Wellfounded_Oaccp @ SV133 @ ( c_ATP__Linkup_Osko__Wellfounded__XaccpI__1__1 @ SV133 @ SY953 @ SY954 ) @ SY954 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[540]) ).
thf(728,plain,
! [SV134: $i] :
( ( ! [SY955: $i,SY956: $i] :
( ( c_Wellfounded_Oaccp @ SV134 @ SY955 @ SY956 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV134 @ ( c_ATP__Linkup_Osko__Wellfounded__XaccpI__1__1 @ SV134 @ SY955 @ SY956 ) ) @ SY955 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[541]) ).
thf(729,plain,
! [SV135: $i] :
( ( ! [SY957: $i,SY958: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV135 ) @ SY957 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV135 ) @ SY958 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SY957 ) @ SY958 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[542]) ).
thf(730,plain,
! [SV136: $i] :
( ( ! [SY959: $i,SY960: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV136 ) @ SY959 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY960 ) @ SY959 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV136 ) @ SY960 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[543]) ).
thf(731,plain,
! [SV137: $i] :
( ( ! [SY961: $i,SY962: $i,SY963: $i] :
( ( hBOOL @ ( hAPP @ SV137 @ SY961 ) )
| ( c_Wellfounded_Oaccp @ SY962 @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__rule__1__1 @ SV137 @ SY962 @ SY963 ) @ SY963 )
| ~ ( c_Wellfounded_Oaccp @ SY962 @ SY961 @ SY963 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[544]) ).
thf(732,plain,
! [SV138: $i] :
( ( ! [SY964: $i,SY965: $i,SY966: $i] :
( ( c_Type_Otyping @ SV138 @ SY964 @ SY965 )
| ~ ( c_Type_Otyping @ SV138 @ SY966 @ SY965 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SY966 ) @ SY964 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[545]) ).
thf(733,plain,
! [SV139: $i] :
( ( ! [SY967: $i,SY968: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Olift @ SV139 @ SY967 ) ) @ ( c_Lambda_Olift @ SY968 @ SY967 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV139 ) @ SY968 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[546]) ).
thf(734,plain,
! [SV140: $i] :
( ( ! [SY969: $i,SY970: $i,SY971: $i] :
( ( hBOOL @ ( hAPP @ SV140 @ SY969 ) )
| ~ ( hBOOL @ ( hAPP @ SV140 @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__rule__1__1 @ SV140 @ SY970 @ SY971 ) ) )
| ~ ( c_Wellfounded_Oaccp @ SY970 @ SY969 @ SY971 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[547]) ).
thf(735,plain,
! [SV141: $i] :
( ( ! [SY972: $i,SY973: $i,SY974: $i,SY975: $i] :
( ( hBOOL @ ( hAPP @ SV141 @ SY972 ) )
| ( hBOOL @ ( hAPP @ SV141 @ SY973 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY974 @ SY973 ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__rule__1__1 @ SV141 @ SY974 @ SY975 ) ) )
| ~ ( c_Wellfounded_Oaccp @ SY974 @ SY972 @ SY975 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[548]) ).
thf(736,plain,
! [SV142: $i] :
( ( ! [SY976: $i,SY977: $i,SY978: $i,SY979: $i] :
( ( c_Predicate_Oconversep @ ( c_Predicate_Opred__comp @ SV142 @ SY976 @ SY977 @ SY978 @ SY979 ) @ SY977 @ SY979 )
= ( c_Predicate_Opred__comp @ ( c_Predicate_Oconversep @ SY976 @ SY978 @ SY979 ) @ ( c_Predicate_Oconversep @ SV142 @ SY977 @ SY978 ) @ SY979 @ SY978 @ SY977 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[549]) ).
thf(737,plain,
! [SV143: $i] :
( ( ! [SY980: $i,SY981: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV143 ) )
| ~ ( c_Type_Otyping @ SY980 @ SV143 @ SY981 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[550]) ).
thf(738,plain,
! [SV144: $i] :
( ( ! [SY982: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ SV144 ) ) @ ( c_Lambda_OdB_OAbs @ SY982 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV144 ) @ SY982 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[551]) ).
thf(739,plain,
! [SV145: $i] :
( ( ! [SY983: $i] :
( ( class_Lattices_Oupper__semilattice @ ( tc_fun @ SV145 @ SY983 ) )
| ~ ( class_Lattices_Olattice @ SY983 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[552]) ).
thf(740,plain,
! [SV146: $i] :
( ( ! [SY984: $i] :
( ( class_Lattices_Olower__semilattice @ ( tc_fun @ SV146 @ SY984 ) )
| ~ ( class_Lattices_Olattice @ SY984 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[553]) ).
thf(741,plain,
! [SV147: $i] :
( ( ! [SY985: $i] :
( ( class_Lattices_Odistrib__lattice @ ( tc_fun @ SV147 @ SY985 ) )
| ~ ( class_Lattices_Odistrib__lattice @ SY985 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[554]) ).
thf(742,plain,
! [SV148: $i] :
( ( ! [SY986: $i] :
( ( class_Lattices_Olattice @ ( tc_fun @ SV148 @ SY986 ) )
| ~ ( class_Lattices_Olattice @ SY986 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[555]) ).
thf(743,plain,
! [SV149: $i] :
( ( ! [SY987: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ SV149 ) @ SY987 ) @ SY987 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[564]) ).
thf(744,plain,
! [SV150: $i] :
( ( ! [SY988: $i,SY989: $i] :
( ( SV150 = SY988 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ SY989 ) @ SV150 ) @ SY988 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[565]) ).
thf(745,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[566]) ).
thf(746,plain,
! [SV151: $i] :
( ( ! [SY990: $i,SY991: $i,SY992: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV151 ) @ SY990 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY991 ) @ SY992 ) )
| ( SY990 = SY992 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[567]) ).
thf(747,plain,
! [SV152: $i] :
( ( ! [SY993: $i,SY994: $i] :
( ( c_Lambda_OdB_OVar @ SV152 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY993 ) @ SY994 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[568]) ).
thf(748,plain,
! [SV153: $i] :
( ( ! [SY995: $i] :
( ( c_Lambda_OdB_OAbs @ SV153 )
!= ( c_Lambda_OdB_OVar @ SY995 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[569]) ).
thf(749,plain,
! [SV154: $i] :
( ( ! [SY996: $i,SY997: $i,SY998: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV154 ) @ SY996 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SY997 ) @ SY998 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY996 = SY998 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[570]) ).
thf(750,plain,
! [SV155: $i] :
( ( ! [SY999: $i,SY1000: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV155 ) @ SY999 )
!= ( c_Lambda_OdB_OVar @ SY1000 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[571]) ).
thf(751,plain,
! [SV156: $i] :
( ( ! [SY1001: $i,SY1002: $i,SY1003: $i] :
( ( ( c_Type_Otype_OFun @ SV156 @ SY1001 )
!= ( c_Type_Otype_OFun @ SY1002 @ SY1003 ) )
| ( SY1001 = SY1003 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[572]) ).
thf(752,plain,
! [SV157: $i] :
( ( ! [SY1004: $i,SY1005: $i,SY1006: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV157 ) @ SY1004 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SY1005 ) @ SY1006 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV157 = SY1005 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[573]) ).
thf(753,plain,
! [SV158: $i] :
( ( ! [SY1007: $i,SY1008: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV158 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1007 @ SY1008 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OAbs @ SV158 )
= SY1007 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[574]) ).
thf(754,plain,
! [SV159: $i] :
( ( ! [SY1009: $i,SY1010: $i,SY1011: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV159 ) @ SY1009 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1010 ) @ SY1011 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV159 = SY1010 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[575]) ).
thf(755,plain,
! [SV160: $i] :
( ( ! [SY1012: $i,SY1013: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV160 @ SY1012 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SY1013 ) )
| ( SY1012
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[576]) ).
thf(756,plain,
! [SV161: $i] :
( ( ! [SY1014: $i,SY1015: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV161 @ SY1014 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1015 @ SY1014 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV161 = SY1015 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[577]) ).
thf(757,plain,
! [SV162: $i] :
( ( ! [SY1016: $i,SY1017: $i,SY1018: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV162 ) @ SY1016 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1017 ) @ SY1018 ) )
| ( SV162 = SY1017 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[578]) ).
thf(758,plain,
! [SV163: $i] :
( ( ! [SY1019: $i,SY1020: $i] :
( ( c_Lambda_OdB_OAbs @ SV163 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1019 ) @ SY1020 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[579]) ).
thf(759,plain,
! [SV164: $i] :
( ( ! [SY1021: $i] :
( ( c_Lambda_OdB_OVar @ SV164 )
!= ( c_Lambda_OdB_OAbs @ SY1021 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[580]) ).
thf(760,plain,
! [SV165: $i] :
( ( ! [SY1022: $i,SY1023: $i,SY1024: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV165 ) ) @ SY1022 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1023 ) @ SY1024 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[581]) ).
thf(761,plain,
! [SV166: $i] :
( ( ! [SY1025: $i,SY1026: $i] :
( ( ( c_Lambda_OdB_OVar @ SV166 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1025 @ SY1026 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY1026
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[582]) ).
thf(762,plain,
! [SV167: $i] :
( ( ! [SY1027: $i,SY1028: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV167 ) @ SY1027 )
!= ( c_Lambda_OdB_OAbs @ SY1028 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[583]) ).
thf(763,plain,
! [SV168: $i] :
( ( ! [SY1029: $i,SY1030: $i,SY1031: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV168 ) @ SY1029 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SY1030 ) @ SY1031 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[584]) ).
thf(764,plain,
! [SV169: $i] :
( ( ! [SY1032: $i,SY1033: $i] :
( ( ( c_Lambda_OdB_OVar @ SV169 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1032 @ SY1033 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OVar @ SV169 )
= SY1032 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[585]) ).
thf(765,plain,
! [SV170: $i] :
( ( ! [SY1034: $i,SY1035: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV170 @ SY1034 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SY1035 ) )
| ( SV170
= ( c_Lambda_OdB_OAbs @ SY1035 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[586]) ).
thf(766,plain,
! [SV171: $i] :
( ( ! [SY1036: $i,SY1037: $i,SY1038: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV171 ) @ SY1036 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1037 @ SY1038 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV171
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1037 @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ SV171 @ SY1036 @ SY1037 @ SY1038 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY1038
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[587]) ).
thf(767,plain,
! [SV172: $i] :
( ( ! [SY1039: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV172 )
!= ( c_Lambda_OdB_OAbs @ SY1039 ) )
| ( SV172 = SY1039 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[588]) ).
thf(768,plain,
! [SV173: $i] :
( ( ! [SY1040: $i,SY1041: $i,SY1042: $i] :
( ( ( c_Type_Otype_OFun @ SV173 @ SY1040 )
!= ( c_Type_Otype_OFun @ SY1041 @ SY1042 ) )
| ( SV173 = SY1041 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[589]) ).
thf(769,plain,
! [SV174: $i] :
( ( ! [SY1043: $i] :
( ( ( c_Lambda_OdB_OVar @ SV174 )
!= ( c_Lambda_OdB_OVar @ SY1043 ) )
| ( SV174 = SY1043 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[590]) ).
thf(770,plain,
! [SV175: $i] :
( ( ! [SY1044: $i,SY1045: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV175 ) @ SY1044 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1045 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV175 ) @ SY1044 )
= SY1045 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[591]) ).
thf(771,plain,
! [SV176: $i] :
( ( ! [SY1046: $i,SY1047: $i,SY1048: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV176 ) @ SY1046 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1047 ) @ SY1048 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY1046 = SY1048 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[592]) ).
thf(772,plain,
! [SV177: $i] :
( ( ! [SY1049: $i,SY1050: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV177 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1049 @ SY1050 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY1050
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[593]) ).
thf(773,plain,
! [SV178: $i,SV1: $i] :
( ( ! [SY1051: $i] :
~ ( c_ListOrder_Ostep1 @ SV1 @ ( c_List_Olist_ONil @ SV178 ) @ SY1051 @ SV178 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[595]) ).
thf(774,plain,
! [SV179: $i,SV2: $i] :
( ( ! [SY1052: $i] :
~ ( c_ListOrder_Ostep1 @ SV2 @ SV179 @ ( c_List_Olist_ONil @ SY1052 ) @ SY1052 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[596]) ).
thf(775,plain,
! [SV180: $i,SV3: $i] :
( ( ! [SY1053: $i,SY1054: $i,SY1055: $i] :
( ( c_Type_Otyping @ SV3 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV180 ) @ SY1053 ) @ SY1054 )
| ~ ( c_Type_Otyping @ SV3 @ SY1053 @ SY1055 )
| ~ ( c_Type_Otyping @ SV3 @ SV180 @ ( c_Type_Otype_OFun @ SY1055 @ SY1054 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[597]) ).
thf(776,plain,
! [SV181: $i,SV6: $i] :
( ( ! [SY1056: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV6 @ SV181 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV6 @ SY1056 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ SV181 @ SY1056 @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[600]) ).
thf(777,plain,
! [SV182: $i,SV7: $i] :
( ( ! [SY1057: $i,SY1058: $i,SY1059: $i] :
( ( c_Type_Otyping @ ( c_Type_Oshift @ SV7 @ SV182 @ SY1057 @ tc_Type_Otype ) @ ( c_Lambda_Olift @ SY1058 @ SV182 ) @ SY1059 )
| ~ ( c_Type_Otyping @ SV7 @ SY1058 @ SY1059 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[601]) ).
thf(778,plain,
! [SV183: $i,SV8: $i] :
( ( ! [SY1060: $i,SY1061: $i,SY1062: $i,SY1063: $i] :
( ~ ( c_Type_Otyping @ SV8 @ SV183 @ SY1060 )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV8 @ SY1061 @ SY1060 @ tc_Type_Otype ) @ SY1062 @ SY1063 )
| ( c_Type_Otyping @ SV8 @ ( c_Lambda_Osubst @ SY1062 @ SV183 @ SY1061 ) @ SY1063 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[602]) ).
thf(779,plain,
! [SV184: $i,SV9: $i] :
( ( ! [SY1064: $i] :
( ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ SV9 @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SV184 @ SV9 @ SY1064 ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV184 ) @ SV9 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SY1064 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[603]) ).
thf(780,plain,
! [SV185: $i,SV10: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV10 ) @ SV185 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV10 ) @ SV185 ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[604]) ).
thf(781,plain,
! [SV186: $i,SV11: $i] :
( ( ! [SY1065: $i,SY1066: $i] :
( ( c_Type_Otyping @ SV11 @ ( c_Lambda_OdB_OAbs @ SV186 ) @ ( c_Type_Otype_OFun @ SY1065 @ SY1066 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV11 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY1065 @ tc_Type_Otype ) @ SV186 @ SY1066 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[605]) ).
thf(782,plain,
! [SV187: $i,SV12: $i] :
( ( ! [SY1067: $i,SY1068: $i] :
( ( hAPP @ ( c_Type_Oshift @ SV12 @ SV187 @ SY1067 @ SY1068 ) @ SV187 )
= SY1067 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[606]) ).
thf(783,plain,
! [SV188: $i,SV13: $i] :
( ( ! [SY1069: $i,SY1070: $i] :
( ( c_List_Ofoldl @ SV13 @ SV188 @ ( c_List_Olist_ONil @ SY1069 ) @ SY1070 @ SY1069 )
= SV188 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[607]) ).
thf(784,plain,
! [SV189: $i,SV14: $i] :
( ( c_List_Olistsp @ SV14 @ ( c_List_Olist_ONil @ SV189 ) @ SV189 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[608]) ).
thf(785,plain,
! [SV190: $i,SV16: $i] :
( ( ! [SY1071: $i,SY1072: $i,SY1073: $i,SY1074: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV16 @ SV190 @ SY1071 ) ) )
| ~ ( c_Type_Otyping @ SY1072 @ SV190 @ SY1073 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV190 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SY1072 @ SY1071 @ SY1073 @ tc_Type_Otype ) @ SV16 @ SY1074 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV16 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[610]) ).
thf(786,plain,
! [SV191: $i,SV17: $i] :
( ( ! [SY1075: $i] :
( ( SV17
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV191 ) @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SV191 @ SY1075 @ SV17 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV191 ) @ SY1075 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV17 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[611]) ).
thf(787,plain,
! [SV192: $i,SV18: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV18 ) @ SV192 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( c_List_Olistsp @ c_InductTermi_OIT @ SV192 @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[612]) ).
thf(788,plain,
! [SV193: $i,SV19: $i] :
( ( ( c_Transitive__Closure_Ortranclp @ ( c_Transitive__Closure_Ortranclp @ SV19 @ SV193 ) @ SV193 )
= ( c_Transitive__Closure_Ortranclp @ SV19 @ SV193 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[613]) ).
thf(789,plain,
! [SV194: $i,SV20: $i] :
( ( ! [SY1076: $i,SY1077: $i,SY1078: $i,SY1079: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV20 @ SV194 ) @ SY1076 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV20 @ SY1077 @ ( tc_fun @ SY1078 @ ( tc_fun @ SY1079 @ tc_bool ) ) ) @ SV194 ) @ SY1076 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[614]) ).
thf(790,plain,
! [SV195: $i,SV21: $i] :
( ( ! [SY1080: $i,SY1081: $i,SY1082: $i,SY1083: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV21 @ SV195 ) @ SY1080 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY1081 @ SV21 @ ( tc_fun @ SY1082 @ ( tc_fun @ SY1083 @ tc_bool ) ) ) @ SV195 ) @ SY1080 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[615]) ).
thf(791,plain,
! [SV196: $i,SV22: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV22 ) @ ( c_Lambda_OdB_OVar @ SV196 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[616]) ).
thf(792,plain,
! [SV197: $i,SV23: $i] :
( ( ! [SY1084: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_Olift @ SV23 @ SV197 ) @ SY1084 @ SV197 )
= SV23 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[617]) ).
thf(793,plain,
! [SV198: $i,SV24: $i] :
( ( ! [SY1085: $i,SY1086: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV24 @ SV198 ) @ SY1085 ) @ SY1086 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV24 @ SY1085 ) @ SY1086 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[618]) ).
thf(794,plain,
! [SV199: $i,SV25: $i] :
( ( ! [SY1087: $i] :
( ~ ( class_Lattices_Olattice @ SV25 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV199 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV199 @ SY1087 @ SV25 ) @ SV25 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV199 @ SY1087 @ SV25 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[619]) ).
thf(795,plain,
! [SV200: $i,SV26: $i] :
( ( ! [SY1088: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV26 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV200 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV200 @ SY1088 @ SV26 ) @ SV26 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV200 @ SY1088 @ SV26 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[620]) ).
thf(796,plain,
! [SV201: $i,SV27: $i] :
( ( ! [SY1089: $i] :
( ~ ( class_Lattices_Olattice @ SV27 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV201 @ SY1089 @ SV27 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY1089 @ SV201 @ SV27 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[621]) ).
thf(797,plain,
! [SV202: $i,SV28: $i] :
( ( ! [SY1090: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV28 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV202 @ SY1090 @ SV28 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY1090 @ SV202 @ SV28 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[622]) ).
thf(798,plain,
! [SV203: $i,SV29: $i] :
( ( ! [SY1091: $i,SY1092: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV29 ) @ SV203 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1091 ) @ SY1092 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV203 ) @ SY1092 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV29 ) @ SY1091 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[623]) ).
thf(799,plain,
! [SV30: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OAbs @ SV30 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV30 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[624]) ).
thf(800,plain,
! [SV204: $i,SV31: $i] :
( ( ! [SY1093: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV31 ) @ SV204 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1093 ) @ SV204 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV31 ) @ SY1093 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[625]) ).
thf(801,plain,
! [SV205: $i,SV32: $i] :
( ( ! [SY1094: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV32 ) @ SV205 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV32 ) @ SY1094 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV205 ) @ SY1094 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[626]) ).
thf(802,plain,
! [SV206: $i,SV33: $i] :
( ( ! [SY1095: $i] :
( ~ ( class_Lattices_Olattice @ SV33 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV206 @ SY1095 @ SV33 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY1095 @ SV206 @ SV33 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[627]) ).
thf(803,plain,
! [SV207: $i,SV34: $i] :
( ( ! [SY1096: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV34 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV207 @ SY1096 @ SV34 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY1096 @ SV207 @ SV34 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[628]) ).
thf(804,plain,
! [SV208: $i,SV35: $i] :
( ( ! [SY1097: $i,SY1098: $i] :
( ~ ( class_Lattices_Olattice @ SV35 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV208 @ SY1097 @ SV35 ) @ SY1098 @ SV35 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV208 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY1097 @ SY1098 @ SV35 ) @ SV35 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[629]) ).
thf(805,plain,
! [SV209: $i,SV36: $i] :
( ( ! [SY1099: $i,SY1100: $i] :
( ~ ( class_Lattices_Olattice @ SV36 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV209 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY1099 @ SY1100 @ SV36 ) @ SV36 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY1099 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV209 @ SY1100 @ SV36 ) @ SV36 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[630]) ).
thf(806,plain,
! [SV210: $i,SV37: $i] :
( ( ! [SY1101: $i,SY1102: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV37 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV210 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY1101 @ SY1102 @ SV37 ) @ SV37 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY1101 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV210 @ SY1102 @ SV37 ) @ SV37 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[631]) ).
thf(807,plain,
! [SV211: $i,SV38: $i] :
( ( ! [SY1103: $i,SY1104: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV38 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV211 @ SY1103 @ SV38 ) @ SY1104 @ SV38 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV211 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY1103 @ SY1104 @ SV38 ) @ SV38 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[632]) ).
thf(808,plain,
! [SV212: $i,SV39: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV39 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV212 @ SV212 @ SV39 )
= SV212 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[633]) ).
thf(809,plain,
! [SV213: $i,SV40: $i] :
( ( ! [SY1105: $i,SY1106: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ SV40 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV213 @ SY1105 @ SV40 ) @ SY1106 @ SV40 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV213 @ SY1106 @ SV40 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY1105 @ SY1106 @ SV40 ) @ SV40 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[634]) ).
thf(810,plain,
! [SV214: $i,SV41: $i] :
( ( ! [SY1107: $i,SY1108: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ SV41 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV214 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY1107 @ SY1108 @ SV41 ) @ SV41 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV214 @ SY1107 @ SV41 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV214 @ SY1108 @ SV41 ) @ SV41 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[635]) ).
thf(811,plain,
! [SV215: $i,SV42: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_OdB_OAbs @ SV42 ) ) @ ( c_Lambda_OdB_OAbs @ SV215 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV42 ) @ SV215 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[636]) ).
thf(812,plain,
! [SV216: $i,SV43: $i] :
( ( ! [SY1109: $i,SY1110: $i,SY1111: $i,SY1112: $i,SY1113: $i,SY1114: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV43 @ SV216 @ SY1109 @ SY1110 @ SY1111 ) @ SY1112 ) @ SY1113 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV216 @ SY1114 ) @ SY1113 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV43 @ SY1112 ) @ SY1114 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[637]) ).
thf(813,plain,
! [SV217: $i,SV44: $i] :
( ( ! [SY1115: $i,SY1116: $i,SY1117: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV44 @ SV217 ) @ SY1115 ) @ SY1116 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV44 @ SV217 ) @ SY1117 ) @ SY1116 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV44 @ SV217 ) @ SY1115 ) @ SY1117 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[638]) ).
thf(814,plain,
! [SV218: $i,SV45: $i] :
( ( ! [SY1118: $i,SY1119: $i,SY1120: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV45 @ SV218 ) @ SY1118 ) @ SY1119 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV45 @ SV218 ) @ SY1120 ) @ SY1119 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV45 @ SV218 ) @ SY1118 ) @ SY1120 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[639]) ).
thf(815,plain,
! [SV219: $i,SV46: $i] :
( ( ! [SY1121: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV46 @ SV219 ) @ SY1121 ) @ SY1121 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[640]) ).
thf(816,plain,
! [SV220: $i,SV47: $i] :
( ( ! [SY1122: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV47 @ SV220 ) @ SY1122 ) @ SY1122 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[641]) ).
thf(817,plain,
! [SV221: $i,SV48: $i] :
( ( ! [SY1123: $i,SY1124: $i,SY1125: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV48 @ SV221 ) @ SY1123 ) @ SY1124 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV48 @ SV221 ) @ SY1125 ) @ SY1124 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV48 @ SV221 ) @ SY1123 ) @ SY1125 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[642]) ).
thf(818,plain,
! [SV222: $i,SV49: $i] :
( ( ! [SY1126: $i,SY1127: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV49 @ SV222 @ SY1126 ) ) @ ( c_Lambda_Osubst @ SV49 @ SY1127 @ SY1126 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV222 ) @ SY1127 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[643]) ).
thf(819,plain,
! [SV223: $i,SV50: $i] :
( ( ! [SY1128: $i,SY1129: $i,SY1130: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV50 @ SV223 ) @ SY1128 ) @ SY1129 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV50 @ SV223 ) @ SY1130 ) @ SY1129 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV50 @ SY1128 ) @ SY1130 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[644]) ).
thf(820,plain,
! [SV224: $i,SV51: $i] :
( ( ! [SY1131: $i,SY1132: $i,SY1133: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV51 @ SV224 ) @ SY1131 ) @ SY1132 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV51 @ SY1133 ) @ SY1132 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV51 @ SV224 ) @ SY1131 ) @ SY1133 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[645]) ).
thf(821,plain,
! [SV225: $i,SV52: $i] :
( ( ! [SY1134: $i] :
( ( c_Lambda_Olift @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV52 ) @ SV225 ) @ SY1134 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Olift @ SV52 @ SY1134 ) ) @ ( c_Lambda_Olift @ SV225 @ SY1134 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[646]) ).
thf(822,plain,
! [SV226: $i,SV53: $i] :
( ( ( c_Wellfounded_OwfP @ ( c_Transitive__Closure_Otranclp @ SV53 @ SV226 ) @ SV226 )
| ~ ( c_Wellfounded_OwfP @ SV53 @ SV226 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[647]) ).
thf(823,plain,
! [SV227: $i,SV54: $i] :
( ( ! [SY1135: $i,SY1136: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV54 @ SV227 ) @ SY1135 ) @ SY1136 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV54 @ SV227 ) @ SY1135 ) @ SY1136 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[648]) ).
thf(824,plain,
! [SV228: $i,SV55: $i] :
( ( ! [SY1137: $i,SY1138: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV55 @ SV228 @ SY1137 ) ) @ ( c_Lambda_Osubst @ SY1138 @ SV228 @ SY1137 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV55 ) @ SY1138 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[649]) ).
thf(825,plain,
! [SV229: $i,SV56: $i] :
( ( ! [SY1139: $i,SY1140: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV56 @ SV229 @ SY1139 ) ) @ ( c_Lambda_Osubst @ SV56 @ SY1140 @ SY1139 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV229 ) @ SY1140 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[650]) ).
thf(826,plain,
! [SV230: $i,SV58: $i] :
( ( ! [SY1141: $i,SY1142: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV58 @ SV230 ) @ SY1141 ) @ SY1142 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV58 @ SY1141 ) @ SY1142 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[652]) ).
thf(827,plain,
! [SV231: $i,SV59: $i] :
( ( ! [SY1143: $i,SY1144: $i,SY1145: $i,SY1146: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV59 @ SV231 ) @ SY1143 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY1144 @ SV231 ) @ SY1143 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY1144 @ SV59 @ ( tc_fun @ SY1145 @ ( tc_fun @ SY1146 @ tc_bool ) ) ) @ SV231 ) @ SY1143 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[653]) ).
thf(828,plain,
! [SV232: $i,SV60: $i] :
( ( ! [SY1147: $i,SY1148: $i,SY1149: $i,SY1150: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV60 @ SV232 @ ( tc_fun @ SY1147 @ ( tc_fun @ SY1148 @ tc_bool ) ) ) @ SY1149 ) @ SY1150 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV232 @ SY1149 ) @ SY1150 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[654]) ).
thf(829,plain,
! [SV233: $i,SV61: $i] :
( ( ! [SY1151: $i,SY1152: $i,SY1153: $i,SY1154: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV61 @ SV233 @ ( tc_fun @ SY1151 @ ( tc_fun @ SY1152 @ tc_bool ) ) ) @ SY1153 ) @ SY1154 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV61 @ SY1153 ) @ SY1154 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[655]) ).
thf(830,plain,
! [SV234: $i,SV62: $i] :
( ( ! [SY1155: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV62 ) ) @ SV234 ) @ SY1155 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV234 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV62 @ SV234 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SY1155 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[656]) ).
thf(831,plain,
! [SV235: $i,SV63: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Olift @ SV63 @ SV235 ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV63 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[657]) ).
thf(832,plain,
! [SV236: $i,SV64: $i] :
( ( ! [SY1156: $i,SY1157: $i] :
( ~ ( class_Lattices_Olattice @ SV64 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV236 @ SY1156 @ SV64 ) @ SY1157 @ SV64 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV236 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY1156 @ SY1157 @ SV64 ) @ SV64 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[658]) ).
thf(833,plain,
! [SV237: $i,SV65: $i] :
( ( ! [SY1158: $i,SY1159: $i] :
( ~ ( class_Lattices_Olattice @ SV65 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV237 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY1158 @ SY1159 @ SV65 ) @ SV65 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY1158 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV237 @ SY1159 @ SV65 ) @ SV65 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[659]) ).
thf(834,plain,
! [SV238: $i,SV66: $i] :
( ( ! [SY1160: $i,SY1161: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV66 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV238 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY1160 @ SY1161 @ SV66 ) @ SV66 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY1160 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV238 @ SY1161 @ SV66 ) @ SV66 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[660]) ).
thf(835,plain,
! [SV239: $i,SV67: $i] :
( ( ! [SY1162: $i,SY1163: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV67 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV239 @ SY1162 @ SV67 ) @ SY1163 @ SV67 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV239 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY1162 @ SY1163 @ SV67 ) @ SV67 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[661]) ).
thf(836,plain,
! [SV240: $i,SV68: $i] :
( ( ! [SY1164: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV68 @ SV240 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1164 @ SV240 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV68 ) @ SY1164 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[662]) ).
thf(837,plain,
! [SV241: $i,SV69: $i] :
( ( ! [SY1165: $i] :
( ~ ( class_Lattices_Olattice @ SV69 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV241 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV241 @ SY1165 @ SV69 ) @ SV69 )
= SV241 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[663]) ).
thf(838,plain,
! [SV242: $i,SV70: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV70 ) ) @ SV242 ) ) @ ( c_Lambda_Osubst @ SV70 @ SV242 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[664]) ).
thf(839,plain,
! [SV243: $i,SV71: $i] :
( ( ! [SY1166: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Olift @ SV71 @ SV243 ) ) @ ( c_Lambda_Olift @ SY1166 @ SV243 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV71 ) @ SY1166 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[665]) ).
thf(840,plain,
! [SV244: $i,SV72: $i] :
( ( ! [SY1167: $i,SY1168: $i,SY1169: $i] :
( ( SV72 = SV244 )
| ~ ( c_Type_Otyping @ SY1167 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1168 ) @ SY1169 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV244 )
| ~ ( c_Type_Otyping @ SY1167 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1168 ) @ SY1169 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV72 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[666]) ).
thf(841,plain,
! [SV245: $i,SV73: $i] :
( ( ! [SY1170: $i] :
( ~ ( class_Lattices_Olattice @ SV73 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV245 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV245 @ SY1170 @ SV73 ) @ SV73 )
= SV245 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[667]) ).
thf(842,plain,
! [SV246: $i,SV74: $i] :
( ( ( c_Transitive__Closure_Ortranclp @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV74 @ ( c_fequal @ SV246 ) @ ( tc_fun @ SV246 @ ( tc_fun @ SV246 @ tc_bool ) ) ) @ SV246 )
= ( c_Transitive__Closure_Ortranclp @ SV74 @ SV246 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[668]) ).
thf(843,plain,
! [SV247: $i,SV75: $i] :
( ( ! [SY1171: $i,SY1172: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV75 @ SV247 ) @ SY1171 ) @ SY1172 ) )
| ( SY1171 = SY1172 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV75 @ SV247 ) @ SY1171 ) @ SY1172 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[669]) ).
thf(844,plain,
! [SV248: $i,SV76: $i] :
( ( ! [SY1173: $i,SY1174: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV76 @ SV248 ) @ SY1173 ) @ SY1174 ) )
| ( SY1173 = SY1174 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV76 @ SV248 ) @ SY1173 ) @ SY1174 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[670]) ).
thf(845,plain,
! [SV249: $i,SV77: $i] :
( ( ! [SY1175: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV77 @ SV249 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1175 @ SV249 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV77 ) @ SY1175 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[671]) ).
thf(846,plain,
! [SV250: $i,SV78: $i] :
( ( ! [SY1176: $i] :
( ( c_Transitive__Closure_Ortranclp @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Ortranclp @ SV78 @ SV250 ) @ ( c_Transitive__Closure_Ortranclp @ SY1176 @ SV250 ) @ ( tc_fun @ SV250 @ ( tc_fun @ SV250 @ tc_bool ) ) ) @ SV250 )
= ( c_Transitive__Closure_Ortranclp @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV78 @ SY1176 @ ( tc_fun @ SV250 @ ( tc_fun @ SV250 @ tc_bool ) ) ) @ SV250 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[672]) ).
thf(847,plain,
! [SV251: $i,SV79: $i] :
( ( ! [SY1177: $i,SY1178: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ SV79 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV251 @ SY1177 @ SV79 ) @ SY1178 @ SV79 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV251 @ SY1178 @ SV79 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY1177 @ SY1178 @ SV79 ) @ SV79 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[673]) ).
thf(848,plain,
! [SV252: $i,SV80: $i] :
( ( ! [SY1179: $i,SY1180: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ SV80 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV252 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY1179 @ SY1180 @ SV80 ) @ SV80 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV252 @ SY1179 @ SV80 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV252 @ SY1180 @ SV80 ) @ SV80 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[674]) ).
thf(849,plain,
! [SV253: $i,SV81: $i] :
( ( ! [SY1181: $i] :
( ~ ( class_Lattices_Olattice @ SV81 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV253 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV253 @ SY1181 @ SV81 ) @ SV81 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV253 @ SY1181 @ SV81 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[675]) ).
thf(850,plain,
! [SV254: $i,SV82: $i] :
( ( ! [SY1182: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV82 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV254 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV254 @ SY1182 @ SV82 ) @ SV82 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV254 @ SY1182 @ SV82 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[676]) ).
thf(851,plain,
! [SV255: $i,SV83: $i] :
( ( ! [SY1183: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV83 @ ( c_Lambda_OdB_OVar @ SV255 ) @ SY1183 ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV83 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[677]) ).
thf(852,plain,
! [SV256: $i,SV84: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Otranclp @ SV84 @ SV256 ) @ ( c_fequal @ SV256 ) @ ( tc_fun @ SV256 @ ( tc_fun @ SV256 @ tc_bool ) ) )
= ( c_Transitive__Closure_Ortranclp @ SV84 @ SV256 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[678]) ).
thf(853,plain,
! [SV257: $i,SV85: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV85 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV257 @ SV257 @ SV85 )
= SV257 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[679]) ).
thf(854,plain,
! [SV258: $i,SV86: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV86 ) @ SV258 @ SV86 )
= SV258 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[680]) ).
thf(855,plain,
! [SV259: $i,SV87: $i] :
( ( ! [SY1184: $i,SY1185: $i,SY1186: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV87 @ SV259 ) @ SY1184 ) @ SY1185 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV87 @ SV259 ) @ SY1186 ) @ SY1185 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV87 @ SV259 ) @ SY1184 ) @ SY1186 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[681]) ).
thf(856,plain,
! [SV260: $i,SV88: $i] :
( ( ! [SY1187: $i,SY1188: $i] :
( ( c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV88 ) @ SV260 ) @ SY1187 @ SY1188 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV88 @ SY1187 @ SY1188 ) ) @ ( c_Lambda_Osubst @ SV260 @ SY1187 @ SY1188 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[682]) ).
thf(857,plain,
! [SV261: $i,SV89: $i] :
( ( ! [SY1189: $i,SY1190: $i,SY1191: $i,SY1192: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV89 @ SV261 @ ( tc_fun @ SY1189 @ ( tc_fun @ SY1190 @ tc_bool ) ) ) @ SY1191 ) @ SY1192 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV261 @ SY1191 ) @ SY1192 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV89 @ SY1191 ) @ SY1192 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[683]) ).
thf(858,plain,
! [SV262: $i,SV90: $i] :
( ( ! [SY1193: $i,SY1194: $i,SY1195: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV90 @ SV262 ) @ SY1193 ) @ SY1194 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV90 @ SV262 ) @ SY1195 ) @ SY1194 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV90 @ SY1193 ) @ SY1195 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[684]) ).
thf(859,plain,
! [SV263: $i,SV91: $i] :
( ( ! [SY1196: $i,SY1197: $i,SY1198: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV91 @ SV263 ) @ SY1196 ) @ SY1197 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV91 @ SY1198 ) @ SY1197 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV91 @ SV263 ) @ SY1196 ) @ SY1198 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[685]) ).
thf(860,plain,
! [SV264: $i,SV92: $i] :
( ( ! [SY1199: $i,SY1200: $i,SY1201: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV92 @ SV264 ) @ SY1199 ) @ SY1200 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV92 @ SY1201 ) @ SY1200 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV92 @ SV264 ) @ SY1199 ) @ SY1201 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[686]) ).
thf(861,plain,
! [SV265: $i,SV93: $i] :
( ( ! [SY1202: $i,SY1203: $i,SY1204: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV93 @ SV265 ) @ SY1202 ) @ SY1203 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV93 @ SV265 ) @ SY1204 ) @ SY1203 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV93 @ SY1202 ) @ SY1204 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[687]) ).
thf(862,plain,
! [SV266: $i,SV94: $i] :
( ( ! [SY1205: $i,SY1206: $i] :
( ( c_Wellfounded_Oaccp @ SV94 @ SV266 @ SY1205 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV94 @ SV266 ) @ SY1206 ) )
| ~ ( c_Wellfounded_Oaccp @ SV94 @ SY1206 @ SY1205 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[688]) ).
thf(863,plain,
! [SV267: $i,SV95: $i] :
( ( ! [SY1207: $i,SY1208: $i] :
( ( c_Wellfounded_Oaccp @ SV95 @ SV267 @ SY1207 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV95 @ SV267 ) @ SY1208 ) )
| ~ ( c_Wellfounded_Oaccp @ SV95 @ SY1208 @ SY1207 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[689]) ).
thf(864,plain,
! [SV268: $i,SV96: $i] :
( ( ! [SY1209: $i,SY1210: $i] :
( ( hBOOL @ ( hAPP @ SV96 @ SV268 ) )
| ~ ( hBOOL @ ( hAPP @ SV96 @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__1__1 @ SV96 @ SY1209 @ SY1210 ) ) )
| ~ ( c_Wellfounded_Oaccp @ SY1209 @ SV268 @ SY1210 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[690]) ).
thf(865,plain,
! [SV269: $i,SV97: $i] :
( ( ! [SY1211: $i,SY1212: $i,SY1213: $i] :
( ( hBOOL @ ( hAPP @ SV97 @ SV269 ) )
| ( hBOOL @ ( hAPP @ SV97 @ SY1211 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1212 @ SY1211 ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__1__1 @ SV97 @ SY1212 @ SY1213 ) ) )
| ~ ( c_Wellfounded_Oaccp @ SY1212 @ SV269 @ SY1213 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[691]) ).
thf(866,plain,
! [SV270: $i,SV98: $i] :
( ( ! [SY1214: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV98 @ ( c_ATP__Linkup_Osko__Wellfounded__Xnot__accp__down__1__1 @ SV98 @ SV270 @ SY1214 ) ) @ SV270 ) )
| ( c_Wellfounded_Oaccp @ SV98 @ SV270 @ SY1214 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[692]) ).
thf(867,plain,
! [SV271: $i,SV99: $i] :
( ( ! [SY1215: $i,SY1216: $i] :
( ( c_Type_Otyping @ SV99 @ SV271 @ SY1215 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SY1216 ) @ SV271 ) )
| ~ ( c_Type_Otyping @ SV99 @ SY1216 @ SY1215 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[693]) ).
thf(868,plain,
! [SV272: $i,SV100: $i] :
( ( ! [SY1217: $i] :
( ( c_Wellfounded_Oaccp @ SV100 @ SV272 @ SY1217 )
| ~ ( c_Wellfounded_OwfP @ SV100 @ SY1217 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[694]) ).
thf(869,plain,
! [SV273: $i,SV101: $i] :
( ( ! [SY1218: $i] :
( ( c_Predicate_Oconversep @ ( c_Predicate_Oconversep @ SV101 @ SV273 @ SY1218 ) @ SY1218 @ SV273 )
= SV101 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[695]) ).
thf(870,plain,
! [SV274: $i,SV102: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OVar @ SV102 ) ) @ SV274 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[696]) ).
thf(871,plain,
! [SV275: $i,SV103: $i] :
( ( ! [SY1219: $i] :
( ( c_Wellfounded_Oaccp @ SV103 @ SV275 @ SY1219 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV103 @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__Xintros__1__1 @ SV103 @ SV275 @ SY1219 ) ) @ SV275 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[697]) ).
thf(872,plain,
! [SV276: $i,SV105: $i] :
( ( ! [SY1220: $i,SY1221: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ ( c_Transitive__Closure_Otranclp @ SV105 @ SV276 ) @ SV276 @ SV276 ) @ SY1220 ) @ SY1221 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ ( c_Predicate_Oconversep @ SV105 @ SV276 @ SV276 ) @ SV276 ) @ SY1220 ) @ SY1221 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[699]) ).
thf(873,plain,
! [SV277: $i,SV106: $i] :
( ( ! [SY1222: $i,SY1223: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ ( c_Predicate_Oconversep @ SV106 @ SV277 @ SV277 ) @ SV277 ) @ SY1222 ) @ SY1223 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ ( c_Transitive__Closure_Otranclp @ SV106 @ SV277 ) @ SV277 @ SV277 ) @ SY1222 ) @ SY1223 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[700]) ).
thf(874,plain,
! [SV278: $i,SV107: $i] :
( ( ! [SY1224: $i] :
( ( ( hAPP @ SV107 @ SV278 )
= SY1224 )
| ~ ( c_Type_Otyping @ SV107 @ ( c_Lambda_OdB_OVar @ SV278 ) @ SY1224 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[701]) ).
thf(875,plain,
! [SV279: $i,SV108: $i] :
( ( ! [SY1225: $i] :
( ~ ( c_Wellfounded_Oaccp @ SV108 @ ( c_ATP__Linkup_Osko__Wellfounded__Xnot__accp__down__1__1 @ SV108 @ SV279 @ SY1225 ) @ SY1225 )
| ( c_Wellfounded_Oaccp @ SV108 @ SV279 @ SY1225 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[702]) ).
thf(876,plain,
! [SV280: $i,SV109: $i] :
( ( ( c_Transitive__Closure_Otranclp @ ( c_Predicate_Oconversep @ SV109 @ SV280 @ SV280 ) @ SV280 )
= ( c_Predicate_Oconversep @ ( c_Transitive__Closure_Otranclp @ SV109 @ SV280 ) @ SV280 @ SV280 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[703]) ).
thf(877,plain,
! [SV110: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV110 ) )
= $true )
| ( ( ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV110 @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[704]) ).
thf(878,plain,
! [SV111: $i] :
( ( ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV111 @ tc_Lambda_OdB )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV111 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[705]) ).
thf(879,plain,
! [SV281: $i,SV112: $i] :
( ( ! [SY1226: $i,SY1227: $i] :
( ( c_Wellfounded_Oaccp @ SV112 @ SV281 @ SY1226 )
| ~ ( c_Wellfounded_Oaccp @ SV112 @ SY1227 @ SY1226 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV112 @ SY1226 ) @ SV281 ) @ SY1227 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[706]) ).
thf(880,plain,
! [SV282: $i,SV113: $i] :
( ( ! [SY1228: $i,SY1229: $i] :
( ( c_Wellfounded_Oaccp @ SV113 @ SV282 @ SY1228 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV113 @ SY1228 ) @ SV282 ) @ SY1229 ) )
| ~ ( c_Wellfounded_Oaccp @ SV113 @ SY1229 @ SY1228 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[707]) ).
thf(881,plain,
! [SV283: $i,SV114: $i] :
( ( ! [SY1230: $i,SY1231: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Osubst @ SV114 @ SV283 @ SY1230 ) ) @ ( c_Lambda_Osubst @ SY1231 @ SV283 @ SY1230 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV114 ) @ SY1231 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[708]) ).
thf(882,plain,
! [SV284: $i,SV115: $i] :
( ( ! [SY1232: $i] :
( ( hBOOL @ ( hAPP @ SV115 @ SV284 ) )
| ~ ( hBOOL @ ( hAPP @ SV115 @ ( v_sko__Wellfounded__Xaccp__Xinducts__1 @ SV115 @ SY1232 ) ) )
| ~ ( c_Wellfounded_Oaccp @ SY1232 @ SV284 @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[709]) ).
thf(883,plain,
! [SV285: $i,SV116: $i] :
( ( ! [SY1233: $i,SY1234: $i] :
( ( hBOOL @ ( hAPP @ SV116 @ SV285 ) )
| ( hBOOL @ ( hAPP @ SV116 @ SY1233 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1234 @ SY1233 ) @ ( v_sko__Wellfounded__Xaccp__Xinducts__1 @ SV116 @ SY1234 ) ) )
| ~ ( c_Wellfounded_Oaccp @ SY1234 @ SV285 @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[710]) ).
thf(884,plain,
! [SV286: $i,SV117: $i] :
( ( ! [SY1235: $i] :
( ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV117 @ SV286 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SY1235 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
| ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV286 @ tc_Lambda_OdB )
| ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV117 ) ) @ SV286 ) @ SY1235 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[711]) ).
thf(885,plain,
! [SV287: $i,SV118: $i] :
( ( ! [SY1236: $i] :
( ( hBOOL @ ( hAPP @ SV118 @ SV287 ) )
| ~ ( hBOOL @ ( hAPP @ SV118 @ ( v_sko__Wellfounded__Xaccp__Xinduct__1 @ SV118 @ SY1236 ) ) )
| ~ ( c_Wellfounded_Oaccp @ SY1236 @ SV287 @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[712]) ).
thf(886,plain,
! [SV288: $i,SV119: $i] :
( ( ! [SY1237: $i,SY1238: $i] :
( ( hBOOL @ ( hAPP @ SV119 @ SV288 ) )
| ( hBOOL @ ( hAPP @ SV119 @ SY1237 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1238 @ SY1237 ) @ ( v_sko__Wellfounded__Xaccp__Xinduct__1 @ SV119 @ SY1238 ) ) )
| ~ ( c_Wellfounded_Oaccp @ SY1238 @ SV288 @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[713]) ).
thf(887,plain,
! [SV289: $i,SV120: $i] :
( ( ! [SY1239: $i,SY1240: $i,SY1241: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV120 @ SV289 @ SY1239 ) @ SY1240 ) @ SY1241 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV120 @ SY1241 ) @ SY1240 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[714]) ).
thf(888,plain,
! [SV290: $i,SV121: $i] :
( ( ! [SY1242: $i,SY1243: $i,SY1244: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV121 @ SV290 ) @ SY1242 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV121 @ SY1243 @ SY1244 ) @ SY1242 ) @ SV290 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[715]) ).
thf(889,plain,
! [SV291: $i,SV122: $i] :
( ( ! [SY1245: $i,SY1246: $i,SY1247: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV122 @ SV291 @ SY1245 ) @ SY1246 ) @ SY1247 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV122 @ SY1247 ) @ SY1246 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[716]) ).
thf(890,plain,
! [SV292: $i,SV123: $i] :
( ( ! [SY1248: $i,SY1249: $i,SY1250: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV123 @ SV292 ) @ SY1248 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV123 @ SY1249 @ SY1250 ) @ SY1248 ) @ SV292 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[717]) ).
thf(891,plain,
! [SV293: $i,SV124: $i] :
( ( ! [SY1251: $i,SY1252: $i] :
( ( hBOOL @ ( hAPP @ SV124 @ SV293 ) )
| ( c_Wellfounded_Oaccp @ SY1251 @ SY1252 @ t_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1251 @ SY1252 ) @ ( v_sko__Wellfounded__Xaccp__Xinducts__1 @ SV124 @ SY1251 ) ) )
| ~ ( c_Wellfounded_Oaccp @ SY1251 @ SV293 @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[718]) ).
thf(892,plain,
! [SV294: $i,SV125: $i] :
( ( ! [SY1253: $i,SY1254: $i] :
( ( hBOOL @ ( hAPP @ SV125 @ SV294 ) )
| ( c_Wellfounded_Oaccp @ SY1253 @ SY1254 @ t_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1253 @ SY1254 ) @ ( v_sko__Wellfounded__Xaccp__Xinduct__1 @ SV125 @ SY1253 ) ) )
| ~ ( c_Wellfounded_Oaccp @ SY1253 @ SV294 @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[719]) ).
thf(893,plain,
! [SV295: $i,SV126: $i] :
( ( ! [SY1255: $i,SY1256: $i] :
( ( c_Predicate_Oconversep @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV126 @ SV295 @ ( tc_fun @ SY1255 @ ( tc_fun @ SY1256 @ tc_bool ) ) ) @ SY1255 @ SY1256 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Predicate_Oconversep @ SV126 @ SY1255 @ SY1256 ) @ ( c_Predicate_Oconversep @ SV295 @ SY1255 @ SY1256 ) @ ( tc_fun @ SY1256 @ ( tc_fun @ SY1255 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[720]) ).
thf(894,plain,
! [SV296: $i,SV127: $i] :
( ( ! [SY1257: $i,SY1258: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV127 @ SV296 ) @ SY1257 ) @ SY1258 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ SV127 @ SV296 @ SV296 ) @ SV296 ) @ SY1258 ) @ SY1257 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[721]) ).
thf(895,plain,
! [SV297: $i,SV128: $i] :
( ( ! [SY1259: $i,SY1260: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ SV128 @ SV297 @ SV297 ) @ SV297 ) @ SY1259 ) @ SY1260 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV128 @ SV297 ) @ SY1260 ) @ SY1259 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[722]) ).
thf(896,plain,
! [SV298: $i,SV129: $i] :
( ( ! [SY1261: $i,SY1262: $i] :
( ( hBOOL @ ( hAPP @ SV129 @ SV298 ) )
| ( c_Wellfounded_Oaccp @ SY1261 @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__1__1 @ SV129 @ SY1261 @ SY1262 ) @ SY1262 )
| ~ ( c_Wellfounded_Oaccp @ SY1261 @ SV298 @ SY1262 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[723]) ).
thf(897,plain,
! [SV299: $i,SV130: $i] :
( ( c_Type_Otyping @ SV130 @ ( c_Lambda_OdB_OVar @ SV299 ) @ ( hAPP @ SV130 @ SV299 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[724]) ).
thf(898,plain,
! [SV300: $i,SV131: $i] :
( ( ! [SY1263: $i,SY1264: $i] :
( ( c_Predicate_Oconversep @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV131 @ SV300 @ ( tc_fun @ SY1263 @ ( tc_fun @ SY1264 @ tc_bool ) ) ) @ SY1263 @ SY1264 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Predicate_Oconversep @ SV131 @ SY1263 @ SY1264 ) @ ( c_Predicate_Oconversep @ SV300 @ SY1263 @ SY1264 ) @ ( tc_fun @ SY1264 @ ( tc_fun @ SY1263 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[725]) ).
thf(899,plain,
! [SV301: $i,SV132: $i] :
( ( ! [SY1265: $i] :
( ( c_Wellfounded_Oaccp @ SV132 @ SV301 @ SY1265 )
| ~ ( c_Wellfounded_Oaccp @ SV132 @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__Xintros__1__1 @ SV132 @ SV301 @ SY1265 ) @ SY1265 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[726]) ).
thf(900,plain,
! [SV302: $i,SV133: $i] :
( ( ! [SY1266: $i] :
( ( c_Wellfounded_Oaccp @ SV133 @ SV302 @ SY1266 )
| ~ ( c_Wellfounded_Oaccp @ SV133 @ ( c_ATP__Linkup_Osko__Wellfounded__XaccpI__1__1 @ SV133 @ SV302 @ SY1266 ) @ SY1266 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[727]) ).
thf(901,plain,
! [SV303: $i,SV134: $i] :
( ( ! [SY1267: $i] :
( ( c_Wellfounded_Oaccp @ SV134 @ SV303 @ SY1267 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV134 @ ( c_ATP__Linkup_Osko__Wellfounded__XaccpI__1__1 @ SV134 @ SV303 @ SY1267 ) ) @ SV303 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[728]) ).
thf(902,plain,
! [SV304: $i,SV135: $i] :
( ( ! [SY1268: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV135 ) @ SV304 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV135 ) @ SY1268 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV304 ) @ SY1268 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[729]) ).
thf(903,plain,
! [SV305: $i,SV136: $i] :
( ( ! [SY1269: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV136 ) @ SV305 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1269 ) @ SV305 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV136 ) @ SY1269 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[730]) ).
thf(904,plain,
! [SV306: $i,SV137: $i] :
( ( ! [SY1270: $i,SY1271: $i] :
( ( hBOOL @ ( hAPP @ SV137 @ SV306 ) )
| ( c_Wellfounded_Oaccp @ SY1270 @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__rule__1__1 @ SV137 @ SY1270 @ SY1271 ) @ SY1271 )
| ~ ( c_Wellfounded_Oaccp @ SY1270 @ SV306 @ SY1271 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[731]) ).
thf(905,plain,
! [SV307: $i,SV138: $i] :
( ( ! [SY1272: $i,SY1273: $i] :
( ( c_Type_Otyping @ SV138 @ SV307 @ SY1272 )
| ~ ( c_Type_Otyping @ SV138 @ SY1273 @ SY1272 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SY1273 ) @ SV307 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[732]) ).
thf(906,plain,
! [SV308: $i,SV139: $i] :
( ( ! [SY1274: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Olift @ SV139 @ SV308 ) ) @ ( c_Lambda_Olift @ SY1274 @ SV308 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV139 ) @ SY1274 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[733]) ).
thf(907,plain,
! [SV309: $i,SV140: $i] :
( ( ! [SY1275: $i,SY1276: $i] :
( ( hBOOL @ ( hAPP @ SV140 @ SV309 ) )
| ~ ( hBOOL @ ( hAPP @ SV140 @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__rule__1__1 @ SV140 @ SY1275 @ SY1276 ) ) )
| ~ ( c_Wellfounded_Oaccp @ SY1275 @ SV309 @ SY1276 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[734]) ).
thf(908,plain,
! [SV310: $i,SV141: $i] :
( ( ! [SY1277: $i,SY1278: $i,SY1279: $i] :
( ( hBOOL @ ( hAPP @ SV141 @ SV310 ) )
| ( hBOOL @ ( hAPP @ SV141 @ SY1277 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1278 @ SY1277 ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__rule__1__1 @ SV141 @ SY1278 @ SY1279 ) ) )
| ~ ( c_Wellfounded_Oaccp @ SY1278 @ SV310 @ SY1279 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[735]) ).
thf(909,plain,
! [SV311: $i,SV142: $i] :
( ( ! [SY1280: $i,SY1281: $i,SY1282: $i] :
( ( c_Predicate_Oconversep @ ( c_Predicate_Opred__comp @ SV142 @ SV311 @ SY1280 @ SY1281 @ SY1282 ) @ SY1280 @ SY1282 )
= ( c_Predicate_Opred__comp @ ( c_Predicate_Oconversep @ SV311 @ SY1281 @ SY1282 ) @ ( c_Predicate_Oconversep @ SV142 @ SY1280 @ SY1281 ) @ SY1282 @ SY1281 @ SY1280 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[736]) ).
thf(910,plain,
! [SV312: $i,SV143: $i] :
( ( ! [SY1283: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV143 ) )
| ~ ( c_Type_Otyping @ SV312 @ SV143 @ SY1283 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[737]) ).
thf(911,plain,
! [SV313: $i,SV144: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ SV144 ) ) @ ( c_Lambda_OdB_OAbs @ SV313 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV144 ) @ SV313 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[738]) ).
thf(912,plain,
! [SV314: $i,SV145: $i] :
( ( ( class_Lattices_Oupper__semilattice @ ( tc_fun @ SV145 @ SV314 ) )
| ~ ( class_Lattices_Olattice @ SV314 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[739]) ).
thf(913,plain,
! [SV315: $i,SV146: $i] :
( ( ( class_Lattices_Olower__semilattice @ ( tc_fun @ SV146 @ SV315 ) )
| ~ ( class_Lattices_Olattice @ SV315 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[740]) ).
thf(914,plain,
! [SV316: $i,SV147: $i] :
( ( ( class_Lattices_Odistrib__lattice @ ( tc_fun @ SV147 @ SV316 ) )
| ~ ( class_Lattices_Odistrib__lattice @ SV316 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[741]) ).
thf(915,plain,
! [SV317: $i,SV148: $i] :
( ( ( class_Lattices_Olattice @ ( tc_fun @ SV148 @ SV317 ) )
| ~ ( class_Lattices_Olattice @ SV317 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[742]) ).
thf(916,plain,
! [SV318: $i,SV149: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ SV149 ) @ SV318 ) @ SV318 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[743]) ).
thf(917,plain,
! [SV319: $i,SV150: $i] :
( ( ! [SY1284: $i] :
( ( SV150 = SV319 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ SY1284 ) @ SV150 ) @ SV319 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[744]) ).
thf(918,plain,
! [SV320: $i,SV151: $i] :
( ( ! [SY1285: $i,SY1286: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV151 ) @ SV320 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1285 ) @ SY1286 ) )
| ( SV320 = SY1286 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[746]) ).
thf(919,plain,
! [SV321: $i,SV152: $i] :
( ( ! [SY1287: $i] :
( ( c_Lambda_OdB_OVar @ SV152 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV321 ) @ SY1287 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[747]) ).
thf(920,plain,
! [SV322: $i,SV153: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV153 )
!= ( c_Lambda_OdB_OVar @ SV322 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[748]) ).
thf(921,plain,
! [SV323: $i,SV154: $i] :
( ( ! [SY1288: $i,SY1289: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV154 ) @ SV323 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SY1288 ) @ SY1289 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV323 = SY1289 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[749]) ).
thf(922,plain,
! [SV324: $i,SV155: $i] :
( ( ! [SY1290: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV155 ) @ SV324 )
!= ( c_Lambda_OdB_OVar @ SY1290 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[750]) ).
thf(923,plain,
! [SV325: $i,SV156: $i] :
( ( ! [SY1291: $i,SY1292: $i] :
( ( ( c_Type_Otype_OFun @ SV156 @ SV325 )
!= ( c_Type_Otype_OFun @ SY1291 @ SY1292 ) )
| ( SV325 = SY1292 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[751]) ).
thf(924,plain,
! [SV326: $i,SV157: $i] :
( ( ! [SY1293: $i,SY1294: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV157 ) @ SV326 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SY1293 ) @ SY1294 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV157 = SY1293 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[752]) ).
thf(925,plain,
! [SV327: $i,SV158: $i] :
( ( ! [SY1295: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV158 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV327 @ SY1295 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OAbs @ SV158 )
= SV327 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[753]) ).
thf(926,plain,
! [SV328: $i,SV159: $i] :
( ( ! [SY1296: $i,SY1297: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV159 ) @ SV328 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1296 ) @ SY1297 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV159 = SY1296 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[754]) ).
thf(927,plain,
! [SV329: $i,SV160: $i] :
( ( ! [SY1298: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV160 @ SV329 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SY1298 ) )
| ( SV329
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[755]) ).
thf(928,plain,
! [SV330: $i,SV161: $i] :
( ( ! [SY1299: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV161 @ SV330 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1299 @ SV330 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV161 = SY1299 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[756]) ).
thf(929,plain,
! [SV331: $i,SV162: $i] :
( ( ! [SY1300: $i,SY1301: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV162 ) @ SV331 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1300 ) @ SY1301 ) )
| ( SV162 = SY1300 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[757]) ).
thf(930,plain,
! [SV332: $i,SV163: $i] :
( ( ! [SY1302: $i] :
( ( c_Lambda_OdB_OAbs @ SV163 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV332 ) @ SY1302 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[758]) ).
thf(931,plain,
! [SV333: $i,SV164: $i] :
( ( ( c_Lambda_OdB_OVar @ SV164 )
!= ( c_Lambda_OdB_OAbs @ SV333 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[759]) ).
thf(932,plain,
! [SV334: $i,SV165: $i] :
( ( ! [SY1303: $i,SY1304: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV165 ) ) @ SV334 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1303 ) @ SY1304 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[760]) ).
thf(933,plain,
! [SV335: $i,SV166: $i] :
( ( ! [SY1305: $i] :
( ( ( c_Lambda_OdB_OVar @ SV166 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV335 @ SY1305 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY1305
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[761]) ).
thf(934,plain,
! [SV336: $i,SV167: $i] :
( ( ! [SY1306: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV167 ) @ SV336 )
!= ( c_Lambda_OdB_OAbs @ SY1306 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[762]) ).
thf(935,plain,
! [SV337: $i,SV168: $i] :
( ( ! [SY1307: $i,SY1308: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV168 ) @ SV337 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SY1307 ) @ SY1308 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[763]) ).
thf(936,plain,
! [SV338: $i,SV169: $i] :
( ( ! [SY1309: $i] :
( ( ( c_Lambda_OdB_OVar @ SV169 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV338 @ SY1309 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OVar @ SV169 )
= SV338 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[764]) ).
thf(937,plain,
! [SV339: $i,SV170: $i] :
( ( ! [SY1310: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV170 @ SV339 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SY1310 ) )
| ( SV170
= ( c_Lambda_OdB_OAbs @ SY1310 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[765]) ).
thf(938,plain,
! [SV340: $i,SV171: $i] :
( ( ! [SY1311: $i,SY1312: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV171 ) @ SV340 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1311 @ SY1312 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV171
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1311 @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ SV171 @ SV340 @ SY1311 @ SY1312 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY1312
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[766]) ).
thf(939,plain,
! [SV341: $i,SV172: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV172 )
!= ( c_Lambda_OdB_OAbs @ SV341 ) )
| ( SV172 = SV341 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[767]) ).
thf(940,plain,
! [SV342: $i,SV173: $i] :
( ( ! [SY1313: $i,SY1314: $i] :
( ( ( c_Type_Otype_OFun @ SV173 @ SV342 )
!= ( c_Type_Otype_OFun @ SY1313 @ SY1314 ) )
| ( SV173 = SY1313 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[768]) ).
thf(941,plain,
! [SV343: $i,SV174: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV174 )
!= ( c_Lambda_OdB_OVar @ SV343 ) )
| ( SV174 = SV343 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[769]) ).
thf(942,plain,
! [SV344: $i,SV175: $i] :
( ( ! [SY1315: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV175 ) @ SV344 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1315 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV175 ) @ SV344 )
= SY1315 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[770]) ).
thf(943,plain,
! [SV345: $i,SV176: $i] :
( ( ! [SY1316: $i,SY1317: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV176 ) @ SV345 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1316 ) @ SY1317 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV345 = SY1317 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[771]) ).
thf(944,plain,
! [SV346: $i,SV177: $i] :
( ( ! [SY1318: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV177 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV346 @ SY1318 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY1318
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[772]) ).
thf(945,plain,
! [SV347: $i,SV178: $i,SV1: $i] :
( ( ~ ( c_ListOrder_Ostep1 @ SV1 @ ( c_List_Olist_ONil @ SV178 ) @ SV347 @ SV178 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[773]) ).
thf(946,plain,
! [SV348: $i,SV179: $i,SV2: $i] :
( ( ~ ( c_ListOrder_Ostep1 @ SV2 @ SV179 @ ( c_List_Olist_ONil @ SV348 ) @ SV348 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[774]) ).
thf(947,plain,
! [SV349: $i,SV180: $i,SV3: $i] :
( ( ! [SY1319: $i,SY1320: $i] :
( ( c_Type_Otyping @ SV3 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV180 ) @ SV349 ) @ SY1319 )
| ~ ( c_Type_Otyping @ SV3 @ SV349 @ SY1320 )
| ~ ( c_Type_Otyping @ SV3 @ SV180 @ ( c_Type_Otype_OFun @ SY1320 @ SY1319 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[775]) ).
thf(948,plain,
! [SV350: $i,SV181: $i,SV6: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV6 @ SV181 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV6 @ SV350 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ SV181 @ SV350 @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[776]) ).
thf(949,plain,
! [SV351: $i,SV182: $i,SV7: $i] :
( ( ! [SY1321: $i,SY1322: $i] :
( ( c_Type_Otyping @ ( c_Type_Oshift @ SV7 @ SV182 @ SV351 @ tc_Type_Otype ) @ ( c_Lambda_Olift @ SY1321 @ SV182 ) @ SY1322 )
| ~ ( c_Type_Otyping @ SV7 @ SY1321 @ SY1322 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[777]) ).
thf(950,plain,
! [SV352: $i,SV183: $i,SV8: $i] :
( ( ! [SY1323: $i,SY1324: $i,SY1325: $i] :
( ~ ( c_Type_Otyping @ SV8 @ SV183 @ SV352 )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV8 @ SY1323 @ SV352 @ tc_Type_Otype ) @ SY1324 @ SY1325 )
| ( c_Type_Otyping @ SV8 @ ( c_Lambda_Osubst @ SY1324 @ SV183 @ SY1323 ) @ SY1325 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[778]) ).
thf(951,plain,
! [SV353: $i,SV184: $i,SV9: $i] :
( ( ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ SV9 @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SV184 @ SV9 @ SV353 ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV184 ) @ SV9 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV353 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[779]) ).
thf(952,plain,
! [SV354: $i,SV186: $i,SV11: $i] :
( ( ! [SY1326: $i] :
( ( c_Type_Otyping @ SV11 @ ( c_Lambda_OdB_OAbs @ SV186 ) @ ( c_Type_Otype_OFun @ SV354 @ SY1326 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV11 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV354 @ tc_Type_Otype ) @ SV186 @ SY1326 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[781]) ).
thf(953,plain,
! [SV355: $i,SV187: $i,SV12: $i] :
( ( ! [SY1327: $i] :
( ( hAPP @ ( c_Type_Oshift @ SV12 @ SV187 @ SV355 @ SY1327 ) @ SV187 )
= SV355 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[782]) ).
thf(954,plain,
! [SV356: $i,SV188: $i,SV13: $i] :
( ( ! [SY1328: $i] :
( ( c_List_Ofoldl @ SV13 @ SV188 @ ( c_List_Olist_ONil @ SV356 ) @ SY1328 @ SV356 )
= SV188 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[783]) ).
thf(955,plain,
! [SV357: $i,SV190: $i,SV16: $i] :
( ( ! [SY1329: $i,SY1330: $i,SY1331: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV16 @ SV190 @ SV357 ) ) )
| ~ ( c_Type_Otyping @ SY1329 @ SV190 @ SY1330 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV190 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SY1329 @ SV357 @ SY1330 @ tc_Type_Otype ) @ SV16 @ SY1331 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV16 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[785]) ).
thf(956,plain,
! [SV358: $i,SV191: $i,SV17: $i] :
( ( ( SV17
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV191 ) @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SV191 @ SV358 @ SV17 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV191 ) @ SV358 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV17 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[786]) ).
thf(957,plain,
! [SV192: $i,SV18: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV18 ) @ SV192 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true )
| ( ( ~ ( c_List_Olistsp @ c_InductTermi_OIT @ SV192 @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[787]) ).
thf(958,plain,
! [SV359: $i,SV194: $i,SV20: $i] :
( ( ! [SY1332: $i,SY1333: $i,SY1334: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV20 @ SV194 ) @ SV359 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV20 @ SY1332 @ ( tc_fun @ SY1333 @ ( tc_fun @ SY1334 @ tc_bool ) ) ) @ SV194 ) @ SV359 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[789]) ).
thf(959,plain,
! [SV360: $i,SV195: $i,SV21: $i] :
( ( ! [SY1335: $i,SY1336: $i,SY1337: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV21 @ SV195 ) @ SV360 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY1335 @ SV21 @ ( tc_fun @ SY1336 @ ( tc_fun @ SY1337 @ tc_bool ) ) ) @ SV195 ) @ SV360 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[790]) ).
thf(960,plain,
! [SV196: $i,SV22: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV22 ) @ ( c_Lambda_OdB_OVar @ SV196 ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV22 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[791]) ).
thf(961,plain,
! [SV361: $i,SV197: $i,SV23: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_Olift @ SV23 @ SV197 ) @ SV361 @ SV197 )
= SV23 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[792]) ).
thf(962,plain,
! [SV362: $i,SV198: $i,SV24: $i] :
( ( ! [SY1338: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV24 @ SV198 ) @ SV362 ) @ SY1338 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV24 @ SV362 ) @ SY1338 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[793]) ).
thf(963,plain,
! [SV363: $i,SV199: $i,SV25: $i] :
( ( ~ ( class_Lattices_Olattice @ SV25 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV199 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV199 @ SV363 @ SV25 ) @ SV25 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV199 @ SV363 @ SV25 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[794]) ).
thf(964,plain,
! [SV364: $i,SV200: $i,SV26: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV26 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV200 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV200 @ SV364 @ SV26 ) @ SV26 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV200 @ SV364 @ SV26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[795]) ).
thf(965,plain,
! [SV365: $i,SV201: $i,SV27: $i] :
( ( ~ ( class_Lattices_Olattice @ SV27 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV201 @ SV365 @ SV27 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV365 @ SV201 @ SV27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[796]) ).
thf(966,plain,
! [SV366: $i,SV202: $i,SV28: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV28 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV202 @ SV366 @ SV28 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV366 @ SV202 @ SV28 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[797]) ).
thf(967,plain,
! [SV367: $i,SV203: $i,SV29: $i] :
( ( ! [SY1339: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV29 ) @ SV203 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV367 ) @ SY1339 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV203 ) @ SY1339 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV29 ) @ SV367 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[798]) ).
thf(968,plain,
! [SV30: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV30 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OAbs @ SV30 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[799]) ).
thf(969,plain,
! [SV368: $i,SV204: $i,SV31: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV31 ) @ SV204 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV368 ) @ SV204 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV31 ) @ SV368 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[800]) ).
thf(970,plain,
! [SV369: $i,SV205: $i,SV32: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV32 ) @ SV205 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV32 ) @ SV369 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV205 ) @ SV369 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[801]) ).
thf(971,plain,
! [SV370: $i,SV206: $i,SV33: $i] :
( ( ~ ( class_Lattices_Olattice @ SV33 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV206 @ SV370 @ SV33 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV370 @ SV206 @ SV33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[802]) ).
thf(972,plain,
! [SV371: $i,SV207: $i,SV34: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV34 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV207 @ SV371 @ SV34 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV371 @ SV207 @ SV34 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[803]) ).
thf(973,plain,
! [SV372: $i,SV208: $i,SV35: $i] :
( ( ! [SY1340: $i] :
( ~ ( class_Lattices_Olattice @ SV35 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV208 @ SV372 @ SV35 ) @ SY1340 @ SV35 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV208 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV372 @ SY1340 @ SV35 ) @ SV35 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[804]) ).
thf(974,plain,
! [SV373: $i,SV209: $i,SV36: $i] :
( ( ! [SY1341: $i] :
( ~ ( class_Lattices_Olattice @ SV36 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV209 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV373 @ SY1341 @ SV36 ) @ SV36 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV373 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV209 @ SY1341 @ SV36 ) @ SV36 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[805]) ).
thf(975,plain,
! [SV374: $i,SV210: $i,SV37: $i] :
( ( ! [SY1342: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV37 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV210 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV374 @ SY1342 @ SV37 ) @ SV37 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV374 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV210 @ SY1342 @ SV37 ) @ SV37 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[806]) ).
thf(976,plain,
! [SV375: $i,SV211: $i,SV38: $i] :
( ( ! [SY1343: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV38 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV211 @ SV375 @ SV38 ) @ SY1343 @ SV38 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV211 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV375 @ SY1343 @ SV38 ) @ SV38 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[807]) ).
thf(977,plain,
! [SV212: $i,SV39: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV39 ) )
= $true )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV212 @ SV212 @ SV39 )
= SV212 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[808]) ).
thf(978,plain,
! [SV376: $i,SV213: $i,SV40: $i] :
( ( ! [SY1344: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ SV40 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV213 @ SV376 @ SV40 ) @ SY1344 @ SV40 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV213 @ SY1344 @ SV40 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV376 @ SY1344 @ SV40 ) @ SV40 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[809]) ).
thf(979,plain,
! [SV377: $i,SV214: $i,SV41: $i] :
( ( ! [SY1345: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ SV41 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV214 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV377 @ SY1345 @ SV41 ) @ SV41 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV214 @ SV377 @ SV41 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV214 @ SY1345 @ SV41 ) @ SV41 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[810]) ).
thf(980,plain,
! [SV215: $i,SV42: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_OdB_OAbs @ SV42 ) ) @ ( c_Lambda_OdB_OAbs @ SV215 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV42 ) @ SV215 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[811]) ).
thf(981,plain,
! [SV378: $i,SV216: $i,SV43: $i] :
( ( ! [SY1346: $i,SY1347: $i,SY1348: $i,SY1349: $i,SY1350: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV43 @ SV216 @ SV378 @ SY1346 @ SY1347 ) @ SY1348 ) @ SY1349 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV216 @ SY1350 ) @ SY1349 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV43 @ SY1348 ) @ SY1350 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[812]) ).
thf(982,plain,
! [SV379: $i,SV217: $i,SV44: $i] :
( ( ! [SY1351: $i,SY1352: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV44 @ SV217 ) @ SV379 ) @ SY1351 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV44 @ SV217 ) @ SY1352 ) @ SY1351 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV44 @ SV217 ) @ SV379 ) @ SY1352 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[813]) ).
thf(983,plain,
! [SV380: $i,SV218: $i,SV45: $i] :
( ( ! [SY1353: $i,SY1354: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV45 @ SV218 ) @ SV380 ) @ SY1353 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV45 @ SV218 ) @ SY1354 ) @ SY1353 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV45 @ SV218 ) @ SV380 ) @ SY1354 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[814]) ).
thf(984,plain,
! [SV381: $i,SV219: $i,SV46: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV46 @ SV219 ) @ SV381 ) @ SV381 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[815]) ).
thf(985,plain,
! [SV382: $i,SV220: $i,SV47: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV47 @ SV220 ) @ SV382 ) @ SV382 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[816]) ).
thf(986,plain,
! [SV383: $i,SV221: $i,SV48: $i] :
( ( ! [SY1355: $i,SY1356: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV48 @ SV221 ) @ SV383 ) @ SY1355 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV48 @ SV221 ) @ SY1356 ) @ SY1355 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV48 @ SV221 ) @ SV383 ) @ SY1356 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[817]) ).
thf(987,plain,
! [SV384: $i,SV222: $i,SV49: $i] :
( ( ! [SY1357: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV49 @ SV222 @ SV384 ) ) @ ( c_Lambda_Osubst @ SV49 @ SY1357 @ SV384 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV222 ) @ SY1357 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[818]) ).
thf(988,plain,
! [SV385: $i,SV223: $i,SV50: $i] :
( ( ! [SY1358: $i,SY1359: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV50 @ SV223 ) @ SV385 ) @ SY1358 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV50 @ SV223 ) @ SY1359 ) @ SY1358 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV50 @ SV385 ) @ SY1359 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[819]) ).
thf(989,plain,
! [SV386: $i,SV224: $i,SV51: $i] :
( ( ! [SY1360: $i,SY1361: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV51 @ SV224 ) @ SV386 ) @ SY1360 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV51 @ SY1361 ) @ SY1360 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV51 @ SV224 ) @ SV386 ) @ SY1361 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[820]) ).
thf(990,plain,
! [SV387: $i,SV225: $i,SV52: $i] :
( ( ( c_Lambda_Olift @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV52 ) @ SV225 ) @ SV387 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Olift @ SV52 @ SV387 ) ) @ ( c_Lambda_Olift @ SV225 @ SV387 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[821]) ).
thf(991,plain,
! [SV226: $i,SV53: $i] :
( ( ( c_Wellfounded_OwfP @ ( c_Transitive__Closure_Otranclp @ SV53 @ SV226 ) @ SV226 )
= $true )
| ( ( ~ ( c_Wellfounded_OwfP @ SV53 @ SV226 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[822]) ).
thf(992,plain,
! [SV388: $i,SV227: $i,SV54: $i] :
( ( ! [SY1362: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV54 @ SV227 ) @ SV388 ) @ SY1362 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV54 @ SV227 ) @ SV388 ) @ SY1362 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[823]) ).
thf(993,plain,
! [SV389: $i,SV228: $i,SV55: $i] :
( ( ! [SY1363: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV55 @ SV228 @ SV389 ) ) @ ( c_Lambda_Osubst @ SY1363 @ SV228 @ SV389 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV55 ) @ SY1363 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[824]) ).
thf(994,plain,
! [SV390: $i,SV229: $i,SV56: $i] :
( ( ! [SY1364: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV56 @ SV229 @ SV390 ) ) @ ( c_Lambda_Osubst @ SV56 @ SY1364 @ SV390 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV229 ) @ SY1364 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[825]) ).
thf(995,plain,
! [SV391: $i,SV230: $i,SV58: $i] :
( ( ! [SY1365: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV58 @ SV230 ) @ SV391 ) @ SY1365 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV58 @ SV391 ) @ SY1365 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[826]) ).
thf(996,plain,
! [SV392: $i,SV231: $i,SV59: $i] :
( ( ! [SY1366: $i,SY1367: $i,SY1368: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV59 @ SV231 ) @ SV392 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY1366 @ SV231 ) @ SV392 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY1366 @ SV59 @ ( tc_fun @ SY1367 @ ( tc_fun @ SY1368 @ tc_bool ) ) ) @ SV231 ) @ SV392 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[827]) ).
thf(997,plain,
! [SV393: $i,SV232: $i,SV60: $i] :
( ( ! [SY1369: $i,SY1370: $i,SY1371: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV60 @ SV232 @ ( tc_fun @ SV393 @ ( tc_fun @ SY1369 @ tc_bool ) ) ) @ SY1370 ) @ SY1371 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV232 @ SY1370 ) @ SY1371 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[828]) ).
thf(998,plain,
! [SV394: $i,SV233: $i,SV61: $i] :
( ( ! [SY1372: $i,SY1373: $i,SY1374: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV61 @ SV233 @ ( tc_fun @ SV394 @ ( tc_fun @ SY1372 @ tc_bool ) ) ) @ SY1373 ) @ SY1374 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV61 @ SY1373 ) @ SY1374 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[829]) ).
thf(999,plain,
! [SV395: $i,SV234: $i,SV62: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV62 ) ) @ SV234 ) @ SV395 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV234 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV62 @ SV234 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV395 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[830]) ).
thf(1000,plain,
! [SV235: $i,SV63: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Olift @ SV63 @ SV235 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV63 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[831]) ).
thf(1001,plain,
! [SV396: $i,SV236: $i,SV64: $i] :
( ( ! [SY1375: $i] :
( ~ ( class_Lattices_Olattice @ SV64 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV236 @ SV396 @ SV64 ) @ SY1375 @ SV64 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV236 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV396 @ SY1375 @ SV64 ) @ SV64 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[832]) ).
thf(1002,plain,
! [SV397: $i,SV237: $i,SV65: $i] :
( ( ! [SY1376: $i] :
( ~ ( class_Lattices_Olattice @ SV65 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV237 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV397 @ SY1376 @ SV65 ) @ SV65 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV397 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV237 @ SY1376 @ SV65 ) @ SV65 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[833]) ).
thf(1003,plain,
! [SV398: $i,SV238: $i,SV66: $i] :
( ( ! [SY1377: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV66 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV238 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV398 @ SY1377 @ SV66 ) @ SV66 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV398 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV238 @ SY1377 @ SV66 ) @ SV66 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[834]) ).
thf(1004,plain,
! [SV399: $i,SV239: $i,SV67: $i] :
( ( ! [SY1378: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV67 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV239 @ SV399 @ SV67 ) @ SY1378 @ SV67 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV239 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV399 @ SY1378 @ SV67 ) @ SV67 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[835]) ).
thf(1005,plain,
! [SV400: $i,SV240: $i,SV68: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV68 @ SV240 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV400 @ SV240 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV68 ) @ SV400 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[836]) ).
thf(1006,plain,
! [SV401: $i,SV241: $i,SV69: $i] :
( ( ~ ( class_Lattices_Olattice @ SV69 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV241 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV241 @ SV401 @ SV69 ) @ SV69 )
= SV241 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[837]) ).
thf(1007,plain,
! [SV402: $i,SV243: $i,SV71: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Olift @ SV71 @ SV243 ) ) @ ( c_Lambda_Olift @ SV402 @ SV243 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV71 ) @ SV402 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[839]) ).
thf(1008,plain,
! [SV403: $i,SV244: $i,SV72: $i] :
( ( ! [SY1379: $i,SY1380: $i] :
( ( SV72 = SV244 )
| ~ ( c_Type_Otyping @ SV403 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1379 ) @ SY1380 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV244 )
| ~ ( c_Type_Otyping @ SV403 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1379 ) @ SY1380 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV72 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[840]) ).
thf(1009,plain,
! [SV404: $i,SV245: $i,SV73: $i] :
( ( ~ ( class_Lattices_Olattice @ SV73 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV245 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV245 @ SV404 @ SV73 ) @ SV73 )
= SV245 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[841]) ).
thf(1010,plain,
! [SV405: $i,SV247: $i,SV75: $i] :
( ( ! [SY1381: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV75 @ SV247 ) @ SV405 ) @ SY1381 ) )
| ( SV405 = SY1381 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV75 @ SV247 ) @ SV405 ) @ SY1381 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[843]) ).
thf(1011,plain,
! [SV406: $i,SV248: $i,SV76: $i] :
( ( ! [SY1382: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV76 @ SV248 ) @ SV406 ) @ SY1382 ) )
| ( SV406 = SY1382 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV76 @ SV248 ) @ SV406 ) @ SY1382 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[844]) ).
thf(1012,plain,
! [SV407: $i,SV249: $i,SV77: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV77 @ SV249 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV407 @ SV249 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV77 ) @ SV407 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[845]) ).
thf(1013,plain,
! [SV408: $i,SV250: $i,SV78: $i] :
( ( ( c_Transitive__Closure_Ortranclp @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Ortranclp @ SV78 @ SV250 ) @ ( c_Transitive__Closure_Ortranclp @ SV408 @ SV250 ) @ ( tc_fun @ SV250 @ ( tc_fun @ SV250 @ tc_bool ) ) ) @ SV250 )
= ( c_Transitive__Closure_Ortranclp @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV78 @ SV408 @ ( tc_fun @ SV250 @ ( tc_fun @ SV250 @ tc_bool ) ) ) @ SV250 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[846]) ).
thf(1014,plain,
! [SV409: $i,SV251: $i,SV79: $i] :
( ( ! [SY1383: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ SV79 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV251 @ SV409 @ SV79 ) @ SY1383 @ SV79 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV251 @ SY1383 @ SV79 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV409 @ SY1383 @ SV79 ) @ SV79 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[847]) ).
thf(1015,plain,
! [SV410: $i,SV252: $i,SV80: $i] :
( ( ! [SY1384: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ SV80 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV252 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV410 @ SY1384 @ SV80 ) @ SV80 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV252 @ SV410 @ SV80 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV252 @ SY1384 @ SV80 ) @ SV80 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[848]) ).
thf(1016,plain,
! [SV411: $i,SV253: $i,SV81: $i] :
( ( ~ ( class_Lattices_Olattice @ SV81 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV253 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV253 @ SV411 @ SV81 ) @ SV81 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV253 @ SV411 @ SV81 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[849]) ).
thf(1017,plain,
! [SV412: $i,SV254: $i,SV82: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV82 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV254 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV254 @ SV412 @ SV82 ) @ SV82 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV254 @ SV412 @ SV82 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[850]) ).
thf(1018,plain,
! [SV413: $i,SV255: $i,SV83: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV83 @ ( c_Lambda_OdB_OVar @ SV255 ) @ SV413 ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV83 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[851]) ).
thf(1019,plain,
! [SV257: $i,SV85: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV85 ) )
= $true )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV257 @ SV257 @ SV85 )
= SV257 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[853]) ).
thf(1020,plain,
! [SV414: $i,SV259: $i,SV87: $i] :
( ( ! [SY1385: $i,SY1386: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV87 @ SV259 ) @ SV414 ) @ SY1385 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV87 @ SV259 ) @ SY1386 ) @ SY1385 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV87 @ SV259 ) @ SV414 ) @ SY1386 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[855]) ).
thf(1021,plain,
! [SV415: $i,SV260: $i,SV88: $i] :
( ( ! [SY1387: $i] :
( ( c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV88 ) @ SV260 ) @ SV415 @ SY1387 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV88 @ SV415 @ SY1387 ) ) @ ( c_Lambda_Osubst @ SV260 @ SV415 @ SY1387 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[856]) ).
thf(1022,plain,
! [SV416: $i,SV261: $i,SV89: $i] :
( ( ! [SY1388: $i,SY1389: $i,SY1390: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV89 @ SV261 @ ( tc_fun @ SV416 @ ( tc_fun @ SY1388 @ tc_bool ) ) ) @ SY1389 ) @ SY1390 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV261 @ SY1389 ) @ SY1390 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV89 @ SY1389 ) @ SY1390 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[857]) ).
thf(1023,plain,
! [SV417: $i,SV262: $i,SV90: $i] :
( ( ! [SY1391: $i,SY1392: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV90 @ SV262 ) @ SV417 ) @ SY1391 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV90 @ SV262 ) @ SY1392 ) @ SY1391 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV90 @ SV417 ) @ SY1392 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[858]) ).
thf(1024,plain,
! [SV418: $i,SV263: $i,SV91: $i] :
( ( ! [SY1393: $i,SY1394: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV91 @ SV263 ) @ SV418 ) @ SY1393 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV91 @ SY1394 ) @ SY1393 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV91 @ SV263 ) @ SV418 ) @ SY1394 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[859]) ).
thf(1025,plain,
! [SV419: $i,SV264: $i,SV92: $i] :
( ( ! [SY1395: $i,SY1396: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV92 @ SV264 ) @ SV419 ) @ SY1395 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV92 @ SY1396 ) @ SY1395 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV92 @ SV264 ) @ SV419 ) @ SY1396 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[860]) ).
thf(1026,plain,
! [SV420: $i,SV265: $i,SV93: $i] :
( ( ! [SY1397: $i,SY1398: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV93 @ SV265 ) @ SV420 ) @ SY1397 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV93 @ SV265 ) @ SY1398 ) @ SY1397 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV93 @ SV420 ) @ SY1398 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[861]) ).
thf(1027,plain,
! [SV421: $i,SV266: $i,SV94: $i] :
( ( ! [SY1399: $i] :
( ( c_Wellfounded_Oaccp @ SV94 @ SV266 @ SV421 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV94 @ SV266 ) @ SY1399 ) )
| ~ ( c_Wellfounded_Oaccp @ SV94 @ SY1399 @ SV421 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[862]) ).
thf(1028,plain,
! [SV422: $i,SV267: $i,SV95: $i] :
( ( ! [SY1400: $i] :
( ( c_Wellfounded_Oaccp @ SV95 @ SV267 @ SV422 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV95 @ SV267 ) @ SY1400 ) )
| ~ ( c_Wellfounded_Oaccp @ SV95 @ SY1400 @ SV422 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[863]) ).
thf(1029,plain,
! [SV423: $i,SV268: $i,SV96: $i] :
( ( ! [SY1401: $i] :
( ( hBOOL @ ( hAPP @ SV96 @ SV268 ) )
| ~ ( hBOOL @ ( hAPP @ SV96 @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__1__1 @ SV96 @ SV423 @ SY1401 ) ) )
| ~ ( c_Wellfounded_Oaccp @ SV423 @ SV268 @ SY1401 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[864]) ).
thf(1030,plain,
! [SV424: $i,SV269: $i,SV97: $i] :
( ( ! [SY1402: $i,SY1403: $i] :
( ( hBOOL @ ( hAPP @ SV97 @ SV269 ) )
| ( hBOOL @ ( hAPP @ SV97 @ SV424 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1402 @ SV424 ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__1__1 @ SV97 @ SY1402 @ SY1403 ) ) )
| ~ ( c_Wellfounded_Oaccp @ SY1402 @ SV269 @ SY1403 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[865]) ).
thf(1031,plain,
! [SV425: $i,SV270: $i,SV98: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV98 @ ( c_ATP__Linkup_Osko__Wellfounded__Xnot__accp__down__1__1 @ SV98 @ SV270 @ SV425 ) ) @ SV270 ) )
| ( c_Wellfounded_Oaccp @ SV98 @ SV270 @ SV425 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[866]) ).
thf(1032,plain,
! [SV426: $i,SV271: $i,SV99: $i] :
( ( ! [SY1404: $i] :
( ( c_Type_Otyping @ SV99 @ SV271 @ SV426 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SY1404 ) @ SV271 ) )
| ~ ( c_Type_Otyping @ SV99 @ SY1404 @ SV426 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[867]) ).
thf(1033,plain,
! [SV427: $i,SV272: $i,SV100: $i] :
( ( ( c_Wellfounded_Oaccp @ SV100 @ SV272 @ SV427 )
| ~ ( c_Wellfounded_OwfP @ SV100 @ SV427 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[868]) ).
thf(1034,plain,
! [SV428: $i,SV273: $i,SV101: $i] :
( ( ( c_Predicate_Oconversep @ ( c_Predicate_Oconversep @ SV101 @ SV273 @ SV428 ) @ SV428 @ SV273 )
= SV101 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[869]) ).
thf(1035,plain,
! [SV274: $i,SV102: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OVar @ SV102 ) ) @ SV274 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[870]) ).
thf(1036,plain,
! [SV429: $i,SV275: $i,SV103: $i] :
( ( ( c_Wellfounded_Oaccp @ SV103 @ SV275 @ SV429 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV103 @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__Xintros__1__1 @ SV103 @ SV275 @ SV429 ) ) @ SV275 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[871]) ).
thf(1037,plain,
! [SV430: $i,SV276: $i,SV105: $i] :
( ( ! [SY1405: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ ( c_Transitive__Closure_Otranclp @ SV105 @ SV276 ) @ SV276 @ SV276 ) @ SV430 ) @ SY1405 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ ( c_Predicate_Oconversep @ SV105 @ SV276 @ SV276 ) @ SV276 ) @ SV430 ) @ SY1405 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[872]) ).
thf(1038,plain,
! [SV431: $i,SV277: $i,SV106: $i] :
( ( ! [SY1406: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ ( c_Predicate_Oconversep @ SV106 @ SV277 @ SV277 ) @ SV277 ) @ SV431 ) @ SY1406 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ ( c_Transitive__Closure_Otranclp @ SV106 @ SV277 ) @ SV277 @ SV277 ) @ SV431 ) @ SY1406 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[873]) ).
thf(1039,plain,
! [SV432: $i,SV278: $i,SV107: $i] :
( ( ( ( hAPP @ SV107 @ SV278 )
= SV432 )
| ~ ( c_Type_Otyping @ SV107 @ ( c_Lambda_OdB_OVar @ SV278 ) @ SV432 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[874]) ).
thf(1040,plain,
! [SV433: $i,SV279: $i,SV108: $i] :
( ( ~ ( c_Wellfounded_Oaccp @ SV108 @ ( c_ATP__Linkup_Osko__Wellfounded__Xnot__accp__down__1__1 @ SV108 @ SV279 @ SV433 ) @ SV433 )
| ( c_Wellfounded_Oaccp @ SV108 @ SV279 @ SV433 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[875]) ).
thf(1041,plain,
! [SV110: $i] :
( ( ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV110 @ tc_Lambda_OdB )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV110 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[877]) ).
thf(1042,plain,
! [SV111: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV111 ) )
= $false )
| ( ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV111 @ tc_Lambda_OdB )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[878]) ).
thf(1043,plain,
! [SV434: $i,SV281: $i,SV112: $i] :
( ( ! [SY1407: $i] :
( ( c_Wellfounded_Oaccp @ SV112 @ SV281 @ SV434 )
| ~ ( c_Wellfounded_Oaccp @ SV112 @ SY1407 @ SV434 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV112 @ SV434 ) @ SV281 ) @ SY1407 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[879]) ).
thf(1044,plain,
! [SV435: $i,SV282: $i,SV113: $i] :
( ( ! [SY1408: $i] :
( ( c_Wellfounded_Oaccp @ SV113 @ SV282 @ SV435 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV113 @ SV435 ) @ SV282 ) @ SY1408 ) )
| ~ ( c_Wellfounded_Oaccp @ SV113 @ SY1408 @ SV435 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[880]) ).
thf(1045,plain,
! [SV436: $i,SV283: $i,SV114: $i] :
( ( ! [SY1409: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Osubst @ SV114 @ SV283 @ SV436 ) ) @ ( c_Lambda_Osubst @ SY1409 @ SV283 @ SV436 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV114 ) @ SY1409 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[881]) ).
thf(1046,plain,
! [SV437: $i,SV284: $i,SV115: $i] :
( ( ( hBOOL @ ( hAPP @ SV115 @ SV284 ) )
| ~ ( hBOOL @ ( hAPP @ SV115 @ ( v_sko__Wellfounded__Xaccp__Xinducts__1 @ SV115 @ SV437 ) ) )
| ~ ( c_Wellfounded_Oaccp @ SV437 @ SV284 @ t_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[882]) ).
thf(1047,plain,
! [SV438: $i,SV285: $i,SV116: $i] :
( ( ! [SY1410: $i] :
( ( hBOOL @ ( hAPP @ SV116 @ SV285 ) )
| ( hBOOL @ ( hAPP @ SV116 @ SV438 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1410 @ SV438 ) @ ( v_sko__Wellfounded__Xaccp__Xinducts__1 @ SV116 @ SY1410 ) ) )
| ~ ( c_Wellfounded_Oaccp @ SY1410 @ SV285 @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[883]) ).
thf(1048,plain,
! [SV439: $i,SV286: $i,SV117: $i] :
( ( ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV117 @ SV286 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV439 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
| ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV286 @ tc_Lambda_OdB )
| ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV117 ) ) @ SV286 ) @ SV439 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[884]) ).
thf(1049,plain,
! [SV440: $i,SV287: $i,SV118: $i] :
( ( ( hBOOL @ ( hAPP @ SV118 @ SV287 ) )
| ~ ( hBOOL @ ( hAPP @ SV118 @ ( v_sko__Wellfounded__Xaccp__Xinduct__1 @ SV118 @ SV440 ) ) )
| ~ ( c_Wellfounded_Oaccp @ SV440 @ SV287 @ t_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[885]) ).
thf(1050,plain,
! [SV441: $i,SV288: $i,SV119: $i] :
( ( ! [SY1411: $i] :
( ( hBOOL @ ( hAPP @ SV119 @ SV288 ) )
| ( hBOOL @ ( hAPP @ SV119 @ SV441 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1411 @ SV441 ) @ ( v_sko__Wellfounded__Xaccp__Xinduct__1 @ SV119 @ SY1411 ) ) )
| ~ ( c_Wellfounded_Oaccp @ SY1411 @ SV288 @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[886]) ).
thf(1051,plain,
! [SV442: $i,SV289: $i,SV120: $i] :
( ( ! [SY1412: $i,SY1413: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV120 @ SV289 @ SV442 ) @ SY1412 ) @ SY1413 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV120 @ SY1413 ) @ SY1412 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[887]) ).
thf(1052,plain,
! [SV443: $i,SV290: $i,SV121: $i] :
( ( ! [SY1414: $i,SY1415: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV121 @ SV290 ) @ SV443 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV121 @ SY1414 @ SY1415 ) @ SV443 ) @ SV290 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[888]) ).
thf(1053,plain,
! [SV444: $i,SV291: $i,SV122: $i] :
( ( ! [SY1416: $i,SY1417: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV122 @ SV291 @ SV444 ) @ SY1416 ) @ SY1417 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV122 @ SY1417 ) @ SY1416 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[889]) ).
thf(1054,plain,
! [SV445: $i,SV292: $i,SV123: $i] :
( ( ! [SY1418: $i,SY1419: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV123 @ SV292 ) @ SV445 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV123 @ SY1418 @ SY1419 ) @ SV445 ) @ SV292 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[890]) ).
thf(1055,plain,
! [SV446: $i,SV293: $i,SV124: $i] :
( ( ! [SY1420: $i] :
( ( hBOOL @ ( hAPP @ SV124 @ SV293 ) )
| ( c_Wellfounded_Oaccp @ SV446 @ SY1420 @ t_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV446 @ SY1420 ) @ ( v_sko__Wellfounded__Xaccp__Xinducts__1 @ SV124 @ SV446 ) ) )
| ~ ( c_Wellfounded_Oaccp @ SV446 @ SV293 @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[891]) ).
thf(1056,plain,
! [SV447: $i,SV294: $i,SV125: $i] :
( ( ! [SY1421: $i] :
( ( hBOOL @ ( hAPP @ SV125 @ SV294 ) )
| ( c_Wellfounded_Oaccp @ SV447 @ SY1421 @ t_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV447 @ SY1421 ) @ ( v_sko__Wellfounded__Xaccp__Xinduct__1 @ SV125 @ SV447 ) ) )
| ~ ( c_Wellfounded_Oaccp @ SV447 @ SV294 @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[892]) ).
thf(1057,plain,
! [SV448: $i,SV295: $i,SV126: $i] :
( ( ! [SY1422: $i] :
( ( c_Predicate_Oconversep @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV126 @ SV295 @ ( tc_fun @ SV448 @ ( tc_fun @ SY1422 @ tc_bool ) ) ) @ SV448 @ SY1422 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Predicate_Oconversep @ SV126 @ SV448 @ SY1422 ) @ ( c_Predicate_Oconversep @ SV295 @ SV448 @ SY1422 ) @ ( tc_fun @ SY1422 @ ( tc_fun @ SV448 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[893]) ).
thf(1058,plain,
! [SV449: $i,SV296: $i,SV127: $i] :
( ( ! [SY1423: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV127 @ SV296 ) @ SV449 ) @ SY1423 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ SV127 @ SV296 @ SV296 ) @ SV296 ) @ SY1423 ) @ SV449 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[894]) ).
thf(1059,plain,
! [SV450: $i,SV297: $i,SV128: $i] :
( ( ! [SY1424: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ SV128 @ SV297 @ SV297 ) @ SV297 ) @ SV450 ) @ SY1424 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV128 @ SV297 ) @ SY1424 ) @ SV450 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[895]) ).
thf(1060,plain,
! [SV451: $i,SV298: $i,SV129: $i] :
( ( ! [SY1425: $i] :
( ( hBOOL @ ( hAPP @ SV129 @ SV298 ) )
| ( c_Wellfounded_Oaccp @ SV451 @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__1__1 @ SV129 @ SV451 @ SY1425 ) @ SY1425 )
| ~ ( c_Wellfounded_Oaccp @ SV451 @ SV298 @ SY1425 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[896]) ).
thf(1061,plain,
! [SV452: $i,SV300: $i,SV131: $i] :
( ( ! [SY1426: $i] :
( ( c_Predicate_Oconversep @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV131 @ SV300 @ ( tc_fun @ SV452 @ ( tc_fun @ SY1426 @ tc_bool ) ) ) @ SV452 @ SY1426 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Predicate_Oconversep @ SV131 @ SV452 @ SY1426 ) @ ( c_Predicate_Oconversep @ SV300 @ SV452 @ SY1426 ) @ ( tc_fun @ SY1426 @ ( tc_fun @ SV452 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[898]) ).
thf(1062,plain,
! [SV453: $i,SV301: $i,SV132: $i] :
( ( ( c_Wellfounded_Oaccp @ SV132 @ SV301 @ SV453 )
| ~ ( c_Wellfounded_Oaccp @ SV132 @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__Xintros__1__1 @ SV132 @ SV301 @ SV453 ) @ SV453 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[899]) ).
thf(1063,plain,
! [SV454: $i,SV302: $i,SV133: $i] :
( ( ( c_Wellfounded_Oaccp @ SV133 @ SV302 @ SV454 )
| ~ ( c_Wellfounded_Oaccp @ SV133 @ ( c_ATP__Linkup_Osko__Wellfounded__XaccpI__1__1 @ SV133 @ SV302 @ SV454 ) @ SV454 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[900]) ).
thf(1064,plain,
! [SV455: $i,SV303: $i,SV134: $i] :
( ( ( c_Wellfounded_Oaccp @ SV134 @ SV303 @ SV455 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV134 @ ( c_ATP__Linkup_Osko__Wellfounded__XaccpI__1__1 @ SV134 @ SV303 @ SV455 ) ) @ SV303 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[901]) ).
thf(1065,plain,
! [SV456: $i,SV304: $i,SV135: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV135 ) @ SV304 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV135 ) @ SV456 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV304 ) @ SV456 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[902]) ).
thf(1066,plain,
! [SV457: $i,SV305: $i,SV136: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV136 ) @ SV305 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV457 ) @ SV305 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV136 ) @ SV457 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[903]) ).
thf(1067,plain,
! [SV458: $i,SV306: $i,SV137: $i] :
( ( ! [SY1427: $i] :
( ( hBOOL @ ( hAPP @ SV137 @ SV306 ) )
| ( c_Wellfounded_Oaccp @ SV458 @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__rule__1__1 @ SV137 @ SV458 @ SY1427 ) @ SY1427 )
| ~ ( c_Wellfounded_Oaccp @ SV458 @ SV306 @ SY1427 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[904]) ).
thf(1068,plain,
! [SV459: $i,SV307: $i,SV138: $i] :
( ( ! [SY1428: $i] :
( ( c_Type_Otyping @ SV138 @ SV307 @ SV459 )
| ~ ( c_Type_Otyping @ SV138 @ SY1428 @ SV459 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SY1428 ) @ SV307 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[905]) ).
thf(1069,plain,
! [SV460: $i,SV308: $i,SV139: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Olift @ SV139 @ SV308 ) ) @ ( c_Lambda_Olift @ SV460 @ SV308 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV139 ) @ SV460 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[906]) ).
thf(1070,plain,
! [SV461: $i,SV309: $i,SV140: $i] :
( ( ! [SY1429: $i] :
( ( hBOOL @ ( hAPP @ SV140 @ SV309 ) )
| ~ ( hBOOL @ ( hAPP @ SV140 @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__rule__1__1 @ SV140 @ SV461 @ SY1429 ) ) )
| ~ ( c_Wellfounded_Oaccp @ SV461 @ SV309 @ SY1429 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[907]) ).
thf(1071,plain,
! [SV462: $i,SV310: $i,SV141: $i] :
( ( ! [SY1430: $i,SY1431: $i] :
( ( hBOOL @ ( hAPP @ SV141 @ SV310 ) )
| ( hBOOL @ ( hAPP @ SV141 @ SV462 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1430 @ SV462 ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__rule__1__1 @ SV141 @ SY1430 @ SY1431 ) ) )
| ~ ( c_Wellfounded_Oaccp @ SY1430 @ SV310 @ SY1431 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[908]) ).
thf(1072,plain,
! [SV463: $i,SV311: $i,SV142: $i] :
( ( ! [SY1432: $i,SY1433: $i] :
( ( c_Predicate_Oconversep @ ( c_Predicate_Opred__comp @ SV142 @ SV311 @ SV463 @ SY1432 @ SY1433 ) @ SV463 @ SY1433 )
= ( c_Predicate_Opred__comp @ ( c_Predicate_Oconversep @ SV311 @ SY1432 @ SY1433 ) @ ( c_Predicate_Oconversep @ SV142 @ SV463 @ SY1432 ) @ SY1433 @ SY1432 @ SV463 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[909]) ).
thf(1073,plain,
! [SV464: $i,SV312: $i,SV143: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV143 ) )
| ~ ( c_Type_Otyping @ SV312 @ SV143 @ SV464 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[910]) ).
thf(1074,plain,
! [SV313: $i,SV144: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ SV144 ) ) @ ( c_Lambda_OdB_OAbs @ SV313 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV144 ) @ SV313 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[911]) ).
thf(1075,plain,
! [SV314: $i,SV145: $i] :
( ( ( class_Lattices_Oupper__semilattice @ ( tc_fun @ SV145 @ SV314 ) )
= $true )
| ( ( ~ ( class_Lattices_Olattice @ SV314 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[912]) ).
thf(1076,plain,
! [SV315: $i,SV146: $i] :
( ( ( class_Lattices_Olower__semilattice @ ( tc_fun @ SV146 @ SV315 ) )
= $true )
| ( ( ~ ( class_Lattices_Olattice @ SV315 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[913]) ).
thf(1077,plain,
! [SV316: $i,SV147: $i] :
( ( ( class_Lattices_Odistrib__lattice @ ( tc_fun @ SV147 @ SV316 ) )
= $true )
| ( ( ~ ( class_Lattices_Odistrib__lattice @ SV316 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[914]) ).
thf(1078,plain,
! [SV317: $i,SV148: $i] :
( ( ( class_Lattices_Olattice @ ( tc_fun @ SV148 @ SV317 ) )
= $true )
| ( ( ~ ( class_Lattices_Olattice @ SV317 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[915]) ).
thf(1079,plain,
! [SV465: $i,SV319: $i,SV150: $i] :
( ( ( SV150 = SV319 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ SV465 ) @ SV150 ) @ SV319 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[917]) ).
thf(1080,plain,
! [SV466: $i,SV320: $i,SV151: $i] :
( ( ! [SY1434: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV151 ) @ SV320 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV466 ) @ SY1434 ) )
| ( SV320 = SY1434 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[918]) ).
thf(1081,plain,
! [SV467: $i,SV321: $i,SV152: $i] :
( ( ( c_Lambda_OdB_OVar @ SV152 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV321 ) @ SV467 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[919]) ).
thf(1082,plain,
! [SV322: $i,SV153: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV153 )
= ( c_Lambda_OdB_OVar @ SV322 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[920]) ).
thf(1083,plain,
! [SV468: $i,SV323: $i,SV154: $i] :
( ( ! [SY1435: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV154 ) @ SV323 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV468 ) @ SY1435 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV323 = SY1435 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[921]) ).
thf(1084,plain,
! [SV469: $i,SV324: $i,SV155: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV155 ) @ SV324 )
!= ( c_Lambda_OdB_OVar @ SV469 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[922]) ).
thf(1085,plain,
! [SV470: $i,SV325: $i,SV156: $i] :
( ( ! [SY1436: $i] :
( ( ( c_Type_Otype_OFun @ SV156 @ SV325 )
!= ( c_Type_Otype_OFun @ SV470 @ SY1436 ) )
| ( SV325 = SY1436 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[923]) ).
thf(1086,plain,
! [SV471: $i,SV326: $i,SV157: $i] :
( ( ! [SY1437: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV157 ) @ SV326 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV471 ) @ SY1437 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV157 = SV471 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[924]) ).
thf(1087,plain,
! [SV472: $i,SV327: $i,SV158: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV158 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV327 @ SV472 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OAbs @ SV158 )
= SV327 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[925]) ).
thf(1088,plain,
! [SV473: $i,SV328: $i,SV159: $i] :
( ( ! [SY1438: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV159 ) @ SV328 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV473 ) @ SY1438 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV159 = SV473 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[926]) ).
thf(1089,plain,
! [SV474: $i,SV329: $i,SV160: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV160 @ SV329 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SV474 ) )
| ( SV329
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[927]) ).
thf(1090,plain,
! [SV475: $i,SV330: $i,SV161: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV161 @ SV330 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV475 @ SV330 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV161 = SV475 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[928]) ).
thf(1091,plain,
! [SV476: $i,SV331: $i,SV162: $i] :
( ( ! [SY1439: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV162 ) @ SV331 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV476 ) @ SY1439 ) )
| ( SV162 = SV476 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[929]) ).
thf(1092,plain,
! [SV477: $i,SV332: $i,SV163: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV163 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV332 ) @ SV477 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[930]) ).
thf(1093,plain,
! [SV333: $i,SV164: $i] :
( ( ( c_Lambda_OdB_OVar @ SV164 )
= ( c_Lambda_OdB_OAbs @ SV333 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[931]) ).
thf(1094,plain,
! [SV478: $i,SV334: $i,SV165: $i] :
( ( ! [SY1440: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV165 ) ) @ SV334 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV478 ) @ SY1440 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[932]) ).
thf(1095,plain,
! [SV479: $i,SV335: $i,SV166: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV166 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV335 @ SV479 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV479
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[933]) ).
thf(1096,plain,
! [SV480: $i,SV336: $i,SV167: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV167 ) @ SV336 )
!= ( c_Lambda_OdB_OAbs @ SV480 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[934]) ).
thf(1097,plain,
! [SV481: $i,SV337: $i,SV168: $i] :
( ( ! [SY1441: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV168 ) @ SV337 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV481 ) @ SY1441 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[935]) ).
thf(1098,plain,
! [SV482: $i,SV338: $i,SV169: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV169 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV338 @ SV482 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OVar @ SV169 )
= SV338 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[936]) ).
thf(1099,plain,
! [SV483: $i,SV339: $i,SV170: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV170 @ SV339 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SV483 ) )
| ( SV170
= ( c_Lambda_OdB_OAbs @ SV483 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[937]) ).
thf(1100,plain,
! [SV484: $i,SV340: $i,SV171: $i] :
( ( ! [SY1442: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV171 ) @ SV340 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV484 @ SY1442 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV171
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV484 @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ SV171 @ SV340 @ SV484 @ SY1442 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY1442
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[938]) ).
thf(1101,plain,
! [SV341: $i,SV172: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV172 )
!= ( c_Lambda_OdB_OAbs @ SV341 ) )
= $true )
| ( ( SV172 = SV341 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[939]) ).
thf(1102,plain,
! [SV485: $i,SV342: $i,SV173: $i] :
( ( ! [SY1443: $i] :
( ( ( c_Type_Otype_OFun @ SV173 @ SV342 )
!= ( c_Type_Otype_OFun @ SV485 @ SY1443 ) )
| ( SV173 = SV485 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[940]) ).
thf(1103,plain,
! [SV343: $i,SV174: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV174 )
!= ( c_Lambda_OdB_OVar @ SV343 ) )
= $true )
| ( ( SV174 = SV343 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[941]) ).
thf(1104,plain,
! [SV486: $i,SV344: $i,SV175: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV175 ) @ SV344 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV486 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV175 ) @ SV344 )
= SV486 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[942]) ).
thf(1105,plain,
! [SV487: $i,SV345: $i,SV176: $i] :
( ( ! [SY1444: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV176 ) @ SV345 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV487 ) @ SY1444 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV345 = SY1444 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[943]) ).
thf(1106,plain,
! [SV488: $i,SV346: $i,SV177: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV177 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV346 @ SV488 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV488
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[944]) ).
thf(1107,plain,
! [SV347: $i,SV178: $i,SV1: $i] :
( ( c_ListOrder_Ostep1 @ SV1 @ ( c_List_Olist_ONil @ SV178 ) @ SV347 @ SV178 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[945]) ).
thf(1108,plain,
! [SV348: $i,SV179: $i,SV2: $i] :
( ( c_ListOrder_Ostep1 @ SV2 @ SV179 @ ( c_List_Olist_ONil @ SV348 ) @ SV348 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[946]) ).
thf(1109,plain,
! [SV489: $i,SV349: $i,SV180: $i,SV3: $i] :
( ( ! [SY1445: $i] :
( ( c_Type_Otyping @ SV3 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV180 ) @ SV349 ) @ SV489 )
| ~ ( c_Type_Otyping @ SV3 @ SV349 @ SY1445 )
| ~ ( c_Type_Otyping @ SV3 @ SV180 @ ( c_Type_Otype_OFun @ SY1445 @ SV489 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[947]) ).
thf(1110,plain,
! [SV350: $i,SV181: $i,SV6: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV6 @ SV181 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV6 @ SV350 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true )
| ( ( ~ ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ SV181 @ SV350 @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[948]) ).
thf(1111,plain,
! [SV490: $i,SV351: $i,SV182: $i,SV7: $i] :
( ( ! [SY1446: $i] :
( ( c_Type_Otyping @ ( c_Type_Oshift @ SV7 @ SV182 @ SV351 @ tc_Type_Otype ) @ ( c_Lambda_Olift @ SV490 @ SV182 ) @ SY1446 )
| ~ ( c_Type_Otyping @ SV7 @ SV490 @ SY1446 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[949]) ).
thf(1112,plain,
! [SV491: $i,SV352: $i,SV183: $i,SV8: $i] :
( ( ! [SY1447: $i,SY1448: $i] :
( ~ ( c_Type_Otyping @ SV8 @ SV183 @ SV352 )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV8 @ SV491 @ SV352 @ tc_Type_Otype ) @ SY1447 @ SY1448 )
| ( c_Type_Otyping @ SV8 @ ( c_Lambda_Osubst @ SY1447 @ SV183 @ SV491 ) @ SY1448 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[950]) ).
thf(1113,plain,
! [SV353: $i,SV184: $i,SV9: $i] :
( ( ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ SV9 @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SV184 @ SV9 @ SV353 ) @ tc_Lambda_OdB )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV184 ) @ SV9 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV353 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[951]) ).
thf(1114,plain,
! [SV492: $i,SV354: $i,SV186: $i,SV11: $i] :
( ( ( c_Type_Otyping @ SV11 @ ( c_Lambda_OdB_OAbs @ SV186 ) @ ( c_Type_Otype_OFun @ SV354 @ SV492 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV11 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV354 @ tc_Type_Otype ) @ SV186 @ SV492 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[952]) ).
thf(1115,plain,
! [SV493: $i,SV355: $i,SV187: $i,SV12: $i] :
( ( ( hAPP @ ( c_Type_Oshift @ SV12 @ SV187 @ SV355 @ SV493 ) @ SV187 )
= SV355 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[953]) ).
thf(1116,plain,
! [SV494: $i,SV356: $i,SV188: $i,SV13: $i] :
( ( ( c_List_Ofoldl @ SV13 @ SV188 @ ( c_List_Olist_ONil @ SV356 ) @ SV494 @ SV356 )
= SV188 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[954]) ).
thf(1117,plain,
! [SV495: $i,SV357: $i,SV190: $i,SV16: $i] :
( ( ! [SY1449: $i,SY1450: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV16 @ SV190 @ SV357 ) ) )
| ~ ( c_Type_Otyping @ SV495 @ SV190 @ SY1449 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV190 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV495 @ SV357 @ SY1449 @ tc_Type_Otype ) @ SV16 @ SY1450 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV16 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[955]) ).
thf(1118,plain,
! [SV358: $i,SV191: $i,SV17: $i] :
( ( ( SV17
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV191 ) @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SV191 @ SV358 @ SV17 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV191 ) @ SV358 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV17 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[956]) ).
thf(1119,plain,
! [SV18: $i,SV192: $i] :
( ( ( c_List_Olistsp @ c_InductTermi_OIT @ SV192 @ tc_Lambda_OdB )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV18 ) @ SV192 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[957]) ).
thf(1120,plain,
! [SV496: $i,SV359: $i,SV194: $i,SV20: $i] :
( ( ! [SY1451: $i,SY1452: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV20 @ SV194 ) @ SV359 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV20 @ SV496 @ ( tc_fun @ SY1451 @ ( tc_fun @ SY1452 @ tc_bool ) ) ) @ SV194 ) @ SV359 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[958]) ).
thf(1121,plain,
! [SV497: $i,SV360: $i,SV195: $i,SV21: $i] :
( ( ! [SY1453: $i,SY1454: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV21 @ SV195 ) @ SV360 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV497 @ SV21 @ ( tc_fun @ SY1453 @ ( tc_fun @ SY1454 @ tc_bool ) ) ) @ SV195 ) @ SV360 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[959]) ).
thf(1122,plain,
! [SV196: $i,SV22: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV22 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV22 ) @ ( c_Lambda_OdB_OVar @ SV196 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[960]) ).
thf(1123,plain,
! [SV498: $i,SV362: $i,SV198: $i,SV24: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV24 @ SV198 ) @ SV362 ) @ SV498 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV24 @ SV362 ) @ SV498 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[962]) ).
thf(1124,plain,
! [SV363: $i,SV199: $i,SV25: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV25 ) )
= $true )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV199 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV199 @ SV363 @ SV25 ) @ SV25 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV199 @ SV363 @ SV25 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[963]) ).
thf(1125,plain,
! [SV364: $i,SV200: $i,SV26: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV26 ) )
= $true )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV200 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV200 @ SV364 @ SV26 ) @ SV26 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV200 @ SV364 @ SV26 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[964]) ).
thf(1126,plain,
! [SV365: $i,SV201: $i,SV27: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV27 ) )
= $true )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV201 @ SV365 @ SV27 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV365 @ SV201 @ SV27 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[965]) ).
thf(1127,plain,
! [SV366: $i,SV202: $i,SV28: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV28 ) )
= $true )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV202 @ SV366 @ SV28 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV366 @ SV202 @ SV28 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[966]) ).
thf(1128,plain,
! [SV499: $i,SV367: $i,SV203: $i,SV29: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV29 ) @ SV203 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV367 ) @ SV499 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV203 ) @ SV499 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV29 ) @ SV367 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[967]) ).
thf(1129,plain,
! [SV368: $i,SV204: $i,SV31: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV31 ) @ SV204 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV368 ) @ SV204 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV31 ) @ SV368 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[969]) ).
thf(1130,plain,
! [SV369: $i,SV205: $i,SV32: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV32 ) @ SV205 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV32 ) @ SV369 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV205 ) @ SV369 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[970]) ).
thf(1131,plain,
! [SV370: $i,SV206: $i,SV33: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV33 ) )
= $true )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV206 @ SV370 @ SV33 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV370 @ SV206 @ SV33 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[971]) ).
thf(1132,plain,
! [SV371: $i,SV207: $i,SV34: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV34 ) )
= $true )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV207 @ SV371 @ SV34 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV371 @ SV207 @ SV34 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[972]) ).
thf(1133,plain,
! [SV500: $i,SV372: $i,SV208: $i,SV35: $i] :
( ( ~ ( class_Lattices_Olattice @ SV35 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV208 @ SV372 @ SV35 ) @ SV500 @ SV35 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV208 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV372 @ SV500 @ SV35 ) @ SV35 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[973]) ).
thf(1134,plain,
! [SV501: $i,SV373: $i,SV209: $i,SV36: $i] :
( ( ~ ( class_Lattices_Olattice @ SV36 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV209 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV373 @ SV501 @ SV36 ) @ SV36 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV373 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV209 @ SV501 @ SV36 ) @ SV36 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[974]) ).
thf(1135,plain,
! [SV502: $i,SV374: $i,SV210: $i,SV37: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV37 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV210 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV374 @ SV502 @ SV37 ) @ SV37 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV374 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV210 @ SV502 @ SV37 ) @ SV37 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[975]) ).
thf(1136,plain,
! [SV503: $i,SV375: $i,SV211: $i,SV38: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV38 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV211 @ SV375 @ SV38 ) @ SV503 @ SV38 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV211 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV375 @ SV503 @ SV38 ) @ SV38 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[976]) ).
thf(1137,plain,
! [SV212: $i,SV39: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV39 )
= $false )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV212 @ SV212 @ SV39 )
= SV212 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[977]) ).
thf(1138,plain,
! [SV504: $i,SV376: $i,SV213: $i,SV40: $i] :
( ( ~ ( class_Lattices_Odistrib__lattice @ SV40 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV213 @ SV376 @ SV40 ) @ SV504 @ SV40 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV213 @ SV504 @ SV40 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV376 @ SV504 @ SV40 ) @ SV40 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[978]) ).
thf(1139,plain,
! [SV505: $i,SV377: $i,SV214: $i,SV41: $i] :
( ( ~ ( class_Lattices_Odistrib__lattice @ SV41 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV214 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV377 @ SV505 @ SV41 ) @ SV41 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV214 @ SV377 @ SV41 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV214 @ SV505 @ SV41 ) @ SV41 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[979]) ).
thf(1140,plain,
! [SV215: $i,SV42: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV42 ) @ SV215 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_OdB_OAbs @ SV42 ) ) @ ( c_Lambda_OdB_OAbs @ SV215 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[980]) ).
thf(1141,plain,
! [SV506: $i,SV378: $i,SV216: $i,SV43: $i] :
( ( ! [SY1455: $i,SY1456: $i,SY1457: $i,SY1458: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV43 @ SV216 @ SV378 @ SV506 @ SY1455 ) @ SY1456 ) @ SY1457 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV216 @ SY1458 ) @ SY1457 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV43 @ SY1456 ) @ SY1458 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[981]) ).
thf(1142,plain,
! [SV507: $i,SV379: $i,SV217: $i,SV44: $i] :
( ( ! [SY1459: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV44 @ SV217 ) @ SV379 ) @ SV507 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV44 @ SV217 ) @ SY1459 ) @ SV507 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV44 @ SV217 ) @ SV379 ) @ SY1459 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[982]) ).
thf(1143,plain,
! [SV508: $i,SV380: $i,SV218: $i,SV45: $i] :
( ( ! [SY1460: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV45 @ SV218 ) @ SV380 ) @ SV508 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV45 @ SV218 ) @ SY1460 ) @ SV508 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV45 @ SV218 ) @ SV380 ) @ SY1460 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[983]) ).
thf(1144,plain,
! [SV509: $i,SV383: $i,SV221: $i,SV48: $i] :
( ( ! [SY1461: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV48 @ SV221 ) @ SV383 ) @ SV509 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV48 @ SV221 ) @ SY1461 ) @ SV509 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV48 @ SV221 ) @ SV383 ) @ SY1461 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[986]) ).
thf(1145,plain,
! [SV510: $i,SV384: $i,SV222: $i,SV49: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV49 @ SV222 @ SV384 ) ) @ ( c_Lambda_Osubst @ SV49 @ SV510 @ SV384 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV222 ) @ SV510 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[987]) ).
thf(1146,plain,
! [SV511: $i,SV385: $i,SV223: $i,SV50: $i] :
( ( ! [SY1462: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV50 @ SV223 ) @ SV385 ) @ SV511 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV50 @ SV223 ) @ SY1462 ) @ SV511 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV50 @ SV385 ) @ SY1462 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[988]) ).
thf(1147,plain,
! [SV512: $i,SV386: $i,SV224: $i,SV51: $i] :
( ( ! [SY1463: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV51 @ SV224 ) @ SV386 ) @ SV512 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV51 @ SY1463 ) @ SV512 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV51 @ SV224 ) @ SV386 ) @ SY1463 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[989]) ).
thf(1148,plain,
! [SV226: $i,SV53: $i] :
( ( ( c_Wellfounded_OwfP @ SV53 @ SV226 )
= $false )
| ( ( c_Wellfounded_OwfP @ ( c_Transitive__Closure_Otranclp @ SV53 @ SV226 ) @ SV226 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[991]) ).
thf(1149,plain,
! [SV513: $i,SV388: $i,SV227: $i,SV54: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV54 @ SV227 ) @ SV388 ) @ SV513 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV54 @ SV227 ) @ SV388 ) @ SV513 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[992]) ).
thf(1150,plain,
! [SV514: $i,SV389: $i,SV228: $i,SV55: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV55 @ SV228 @ SV389 ) ) @ ( c_Lambda_Osubst @ SV514 @ SV228 @ SV389 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV55 ) @ SV514 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[993]) ).
thf(1151,plain,
! [SV515: $i,SV390: $i,SV229: $i,SV56: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV56 @ SV229 @ SV390 ) ) @ ( c_Lambda_Osubst @ SV56 @ SV515 @ SV390 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV229 ) @ SV515 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[994]) ).
thf(1152,plain,
! [SV516: $i,SV391: $i,SV230: $i,SV58: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV58 @ SV230 ) @ SV391 ) @ SV516 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV58 @ SV391 ) @ SV516 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[995]) ).
thf(1153,plain,
! [SV517: $i,SV392: $i,SV231: $i,SV59: $i] :
( ( ! [SY1464: $i,SY1465: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV59 @ SV231 ) @ SV392 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV517 @ SV231 ) @ SV392 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV517 @ SV59 @ ( tc_fun @ SY1464 @ ( tc_fun @ SY1465 @ tc_bool ) ) ) @ SV231 ) @ SV392 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[996]) ).
thf(1154,plain,
! [SV518: $i,SV393: $i,SV232: $i,SV60: $i] :
( ( ! [SY1466: $i,SY1467: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV60 @ SV232 @ ( tc_fun @ SV393 @ ( tc_fun @ SV518 @ tc_bool ) ) ) @ SY1466 ) @ SY1467 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV232 @ SY1466 ) @ SY1467 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[997]) ).
thf(1155,plain,
! [SV519: $i,SV394: $i,SV233: $i,SV61: $i] :
( ( ! [SY1468: $i,SY1469: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV61 @ SV233 @ ( tc_fun @ SV394 @ ( tc_fun @ SV519 @ tc_bool ) ) ) @ SY1468 ) @ SY1469 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV61 @ SY1468 ) @ SY1469 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[998]) ).
thf(1156,plain,
! [SV395: $i,SV234: $i,SV62: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV62 ) ) @ SV234 ) @ SV395 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV234 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV62 @ SV234 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV395 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[999]) ).
thf(1157,plain,
! [SV235: $i,SV63: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV63 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Olift @ SV63 @ SV235 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1000]) ).
thf(1158,plain,
! [SV520: $i,SV396: $i,SV236: $i,SV64: $i] :
( ( ~ ( class_Lattices_Olattice @ SV64 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV236 @ SV396 @ SV64 ) @ SV520 @ SV64 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV236 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV396 @ SV520 @ SV64 ) @ SV64 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1001]) ).
thf(1159,plain,
! [SV521: $i,SV397: $i,SV237: $i,SV65: $i] :
( ( ~ ( class_Lattices_Olattice @ SV65 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV237 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV397 @ SV521 @ SV65 ) @ SV65 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV397 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV237 @ SV521 @ SV65 ) @ SV65 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1002]) ).
thf(1160,plain,
! [SV522: $i,SV398: $i,SV238: $i,SV66: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV66 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV238 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV398 @ SV522 @ SV66 ) @ SV66 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV398 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV238 @ SV522 @ SV66 ) @ SV66 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1003]) ).
thf(1161,plain,
! [SV523: $i,SV399: $i,SV239: $i,SV67: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV67 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV239 @ SV399 @ SV67 ) @ SV523 @ SV67 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV239 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV399 @ SV523 @ SV67 ) @ SV67 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1004]) ).
thf(1162,plain,
! [SV400: $i,SV240: $i,SV68: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV68 @ SV240 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV400 @ SV240 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV68 ) @ SV400 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1005]) ).
thf(1163,plain,
! [SV401: $i,SV241: $i,SV69: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV69 ) )
= $true )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV241 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV241 @ SV401 @ SV69 ) @ SV69 )
= SV241 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1006]) ).
thf(1164,plain,
! [SV402: $i,SV243: $i,SV71: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Olift @ SV71 @ SV243 ) ) @ ( c_Lambda_Olift @ SV402 @ SV243 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV71 ) @ SV402 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1007]) ).
thf(1165,plain,
! [SV524: $i,SV403: $i,SV244: $i,SV72: $i] :
( ( ! [SY1470: $i] :
( ( SV72 = SV244 )
| ~ ( c_Type_Otyping @ SV403 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV524 ) @ SY1470 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV244 )
| ~ ( c_Type_Otyping @ SV403 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV524 ) @ SY1470 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV72 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1008]) ).
thf(1166,plain,
! [SV404: $i,SV245: $i,SV73: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV73 ) )
= $true )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV245 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV245 @ SV404 @ SV73 ) @ SV73 )
= SV245 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1009]) ).
thf(1167,plain,
! [SV525: $i,SV405: $i,SV247: $i,SV75: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV75 @ SV247 ) @ SV405 ) @ SV525 ) )
| ( SV405 = SV525 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV75 @ SV247 ) @ SV405 ) @ SV525 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1010]) ).
thf(1168,plain,
! [SV526: $i,SV406: $i,SV248: $i,SV76: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV76 @ SV248 ) @ SV406 ) @ SV526 ) )
| ( SV406 = SV526 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV76 @ SV248 ) @ SV406 ) @ SV526 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1011]) ).
thf(1169,plain,
! [SV407: $i,SV249: $i,SV77: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV77 @ SV249 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV407 @ SV249 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV77 ) @ SV407 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1012]) ).
thf(1170,plain,
! [SV527: $i,SV409: $i,SV251: $i,SV79: $i] :
( ( ~ ( class_Lattices_Odistrib__lattice @ SV79 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV251 @ SV409 @ SV79 ) @ SV527 @ SV79 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV251 @ SV527 @ SV79 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV409 @ SV527 @ SV79 ) @ SV79 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1014]) ).
thf(1171,plain,
! [SV528: $i,SV410: $i,SV252: $i,SV80: $i] :
( ( ~ ( class_Lattices_Odistrib__lattice @ SV80 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV252 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV410 @ SV528 @ SV80 ) @ SV80 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV252 @ SV410 @ SV80 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV252 @ SV528 @ SV80 ) @ SV80 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1015]) ).
thf(1172,plain,
! [SV411: $i,SV253: $i,SV81: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV81 ) )
= $true )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV253 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV253 @ SV411 @ SV81 ) @ SV81 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV253 @ SV411 @ SV81 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1016]) ).
thf(1173,plain,
! [SV412: $i,SV254: $i,SV82: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV82 ) )
= $true )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV254 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV254 @ SV412 @ SV82 ) @ SV82 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV254 @ SV412 @ SV82 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1017]) ).
thf(1174,plain,
! [SV413: $i,SV255: $i,SV83: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV83 @ ( c_Lambda_OdB_OVar @ SV255 ) @ SV413 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV83 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1018]) ).
thf(1175,plain,
! [SV257: $i,SV85: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV85 )
= $false )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV257 @ SV257 @ SV85 )
= SV257 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1019]) ).
thf(1176,plain,
! [SV529: $i,SV414: $i,SV259: $i,SV87: $i] :
( ( ! [SY1471: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV87 @ SV259 ) @ SV414 ) @ SV529 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV87 @ SV259 ) @ SY1471 ) @ SV529 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV87 @ SV259 ) @ SV414 ) @ SY1471 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1020]) ).
thf(1177,plain,
! [SV530: $i,SV415: $i,SV260: $i,SV88: $i] :
( ( ( c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV88 ) @ SV260 ) @ SV415 @ SV530 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV88 @ SV415 @ SV530 ) ) @ ( c_Lambda_Osubst @ SV260 @ SV415 @ SV530 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1021]) ).
thf(1178,plain,
! [SV531: $i,SV416: $i,SV261: $i,SV89: $i] :
( ( ! [SY1472: $i,SY1473: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV89 @ SV261 @ ( tc_fun @ SV416 @ ( tc_fun @ SV531 @ tc_bool ) ) ) @ SY1472 ) @ SY1473 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV261 @ SY1472 ) @ SY1473 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV89 @ SY1472 ) @ SY1473 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1022]) ).
thf(1179,plain,
! [SV532: $i,SV417: $i,SV262: $i,SV90: $i] :
( ( ! [SY1474: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV90 @ SV262 ) @ SV417 ) @ SV532 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV90 @ SV262 ) @ SY1474 ) @ SV532 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV90 @ SV417 ) @ SY1474 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1023]) ).
thf(1180,plain,
! [SV533: $i,SV418: $i,SV263: $i,SV91: $i] :
( ( ! [SY1475: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV91 @ SV263 ) @ SV418 ) @ SV533 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV91 @ SY1475 ) @ SV533 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV91 @ SV263 ) @ SV418 ) @ SY1475 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1024]) ).
thf(1181,plain,
! [SV534: $i,SV419: $i,SV264: $i,SV92: $i] :
( ( ! [SY1476: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV92 @ SV264 ) @ SV419 ) @ SV534 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV92 @ SY1476 ) @ SV534 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV92 @ SV264 ) @ SV419 ) @ SY1476 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1025]) ).
thf(1182,plain,
! [SV535: $i,SV420: $i,SV265: $i,SV93: $i] :
( ( ! [SY1477: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV93 @ SV265 ) @ SV420 ) @ SV535 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV93 @ SV265 ) @ SY1477 ) @ SV535 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV93 @ SV420 ) @ SY1477 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1026]) ).
thf(1183,plain,
! [SV536: $i,SV421: $i,SV266: $i,SV94: $i] :
( ( ( c_Wellfounded_Oaccp @ SV94 @ SV266 @ SV421 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV94 @ SV266 ) @ SV536 ) )
| ~ ( c_Wellfounded_Oaccp @ SV94 @ SV536 @ SV421 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1027]) ).
thf(1184,plain,
! [SV537: $i,SV422: $i,SV267: $i,SV95: $i] :
( ( ( c_Wellfounded_Oaccp @ SV95 @ SV267 @ SV422 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV95 @ SV267 ) @ SV537 ) )
| ~ ( c_Wellfounded_Oaccp @ SV95 @ SV537 @ SV422 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1028]) ).
thf(1185,plain,
! [SV538: $i,SV423: $i,SV268: $i,SV96: $i] :
( ( ( hBOOL @ ( hAPP @ SV96 @ SV268 ) )
| ~ ( hBOOL @ ( hAPP @ SV96 @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__1__1 @ SV96 @ SV423 @ SV538 ) ) )
| ~ ( c_Wellfounded_Oaccp @ SV423 @ SV268 @ SV538 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1029]) ).
thf(1186,plain,
! [SV539: $i,SV424: $i,SV269: $i,SV97: $i] :
( ( ! [SY1478: $i] :
( ( hBOOL @ ( hAPP @ SV97 @ SV269 ) )
| ( hBOOL @ ( hAPP @ SV97 @ SV424 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV539 @ SV424 ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__1__1 @ SV97 @ SV539 @ SY1478 ) ) )
| ~ ( c_Wellfounded_Oaccp @ SV539 @ SV269 @ SY1478 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1030]) ).
thf(1187,plain,
! [SV425: $i,SV270: $i,SV98: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV98 @ ( c_ATP__Linkup_Osko__Wellfounded__Xnot__accp__down__1__1 @ SV98 @ SV270 @ SV425 ) ) @ SV270 ) )
= $true )
| ( ( c_Wellfounded_Oaccp @ SV98 @ SV270 @ SV425 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1031]) ).
thf(1188,plain,
! [SV540: $i,SV426: $i,SV271: $i,SV99: $i] :
( ( ( c_Type_Otyping @ SV99 @ SV271 @ SV426 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV540 ) @ SV271 ) )
| ~ ( c_Type_Otyping @ SV99 @ SV540 @ SV426 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1032]) ).
thf(1189,plain,
! [SV427: $i,SV272: $i,SV100: $i] :
( ( ( c_Wellfounded_Oaccp @ SV100 @ SV272 @ SV427 )
= $true )
| ( ( ~ ( c_Wellfounded_OwfP @ SV100 @ SV427 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1033]) ).
thf(1190,plain,
! [SV429: $i,SV275: $i,SV103: $i] :
( ( ( c_Wellfounded_Oaccp @ SV103 @ SV275 @ SV429 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV103 @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__Xintros__1__1 @ SV103 @ SV275 @ SV429 ) ) @ SV275 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1036]) ).
thf(1191,plain,
! [SV541: $i,SV430: $i,SV276: $i,SV105: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ ( c_Transitive__Closure_Otranclp @ SV105 @ SV276 ) @ SV276 @ SV276 ) @ SV430 ) @ SV541 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ ( c_Predicate_Oconversep @ SV105 @ SV276 @ SV276 ) @ SV276 ) @ SV430 ) @ SV541 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1037]) ).
thf(1192,plain,
! [SV542: $i,SV431: $i,SV277: $i,SV106: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ ( c_Predicate_Oconversep @ SV106 @ SV277 @ SV277 ) @ SV277 ) @ SV431 ) @ SV542 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ ( c_Transitive__Closure_Otranclp @ SV106 @ SV277 ) @ SV277 @ SV277 ) @ SV431 ) @ SV542 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1038]) ).
thf(1193,plain,
! [SV432: $i,SV278: $i,SV107: $i] :
( ( ( ( hAPP @ SV107 @ SV278 )
= SV432 )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV107 @ ( c_Lambda_OdB_OVar @ SV278 ) @ SV432 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1039]) ).
thf(1194,plain,
! [SV433: $i,SV279: $i,SV108: $i] :
( ( ( ~ ( c_Wellfounded_Oaccp @ SV108 @ ( c_ATP__Linkup_Osko__Wellfounded__Xnot__accp__down__1__1 @ SV108 @ SV279 @ SV433 ) @ SV433 ) )
= $true )
| ( ( c_Wellfounded_Oaccp @ SV108 @ SV279 @ SV433 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1040]) ).
thf(1195,plain,
! [SV543: $i,SV434: $i,SV281: $i,SV112: $i] :
( ( ( c_Wellfounded_Oaccp @ SV112 @ SV281 @ SV434 )
| ~ ( c_Wellfounded_Oaccp @ SV112 @ SV543 @ SV434 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV112 @ SV434 ) @ SV281 ) @ SV543 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1043]) ).
thf(1196,plain,
! [SV544: $i,SV435: $i,SV282: $i,SV113: $i] :
( ( ( c_Wellfounded_Oaccp @ SV113 @ SV282 @ SV435 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV113 @ SV435 ) @ SV282 ) @ SV544 ) )
| ~ ( c_Wellfounded_Oaccp @ SV113 @ SV544 @ SV435 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1044]) ).
thf(1197,plain,
! [SV545: $i,SV436: $i,SV283: $i,SV114: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Osubst @ SV114 @ SV283 @ SV436 ) ) @ ( c_Lambda_Osubst @ SV545 @ SV283 @ SV436 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV114 ) @ SV545 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1045]) ).
thf(1198,plain,
! [SV437: $i,SV284: $i,SV115: $i] :
( ( ( hBOOL @ ( hAPP @ SV115 @ SV284 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV115 @ ( v_sko__Wellfounded__Xaccp__Xinducts__1 @ SV115 @ SV437 ) ) )
| ~ ( c_Wellfounded_Oaccp @ SV437 @ SV284 @ t_a ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1046]) ).
thf(1199,plain,
! [SV546: $i,SV438: $i,SV285: $i,SV116: $i] :
( ( ( hBOOL @ ( hAPP @ SV116 @ SV285 ) )
| ( hBOOL @ ( hAPP @ SV116 @ SV438 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV546 @ SV438 ) @ ( v_sko__Wellfounded__Xaccp__Xinducts__1 @ SV116 @ SV546 ) ) )
| ~ ( c_Wellfounded_Oaccp @ SV546 @ SV285 @ t_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1047]) ).
thf(1200,plain,
! [SV439: $i,SV286: $i,SV117: $i] :
( ( ( ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV117 @ SV286 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV439 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) )
= $true )
| ( ( ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV286 @ tc_Lambda_OdB )
| ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV117 ) ) @ SV286 ) @ SV439 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1048]) ).
thf(1201,plain,
! [SV440: $i,SV287: $i,SV118: $i] :
( ( ( hBOOL @ ( hAPP @ SV118 @ SV287 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV118 @ ( v_sko__Wellfounded__Xaccp__Xinduct__1 @ SV118 @ SV440 ) ) )
| ~ ( c_Wellfounded_Oaccp @ SV440 @ SV287 @ t_a ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1049]) ).
thf(1202,plain,
! [SV547: $i,SV441: $i,SV288: $i,SV119: $i] :
( ( ( hBOOL @ ( hAPP @ SV119 @ SV288 ) )
| ( hBOOL @ ( hAPP @ SV119 @ SV441 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV547 @ SV441 ) @ ( v_sko__Wellfounded__Xaccp__Xinduct__1 @ SV119 @ SV547 ) ) )
| ~ ( c_Wellfounded_Oaccp @ SV547 @ SV288 @ t_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1050]) ).
thf(1203,plain,
! [SV548: $i,SV442: $i,SV289: $i,SV120: $i] :
( ( ! [SY1479: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV120 @ SV289 @ SV442 ) @ SV548 ) @ SY1479 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV120 @ SY1479 ) @ SV548 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1051]) ).
thf(1204,plain,
! [SV549: $i,SV443: $i,SV290: $i,SV121: $i] :
( ( ! [SY1480: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV121 @ SV290 ) @ SV443 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV121 @ SV549 @ SY1480 ) @ SV443 ) @ SV290 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1052]) ).
thf(1205,plain,
! [SV550: $i,SV444: $i,SV291: $i,SV122: $i] :
( ( ! [SY1481: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV122 @ SV291 @ SV444 ) @ SV550 ) @ SY1481 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV122 @ SY1481 ) @ SV550 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1053]) ).
thf(1206,plain,
! [SV551: $i,SV445: $i,SV292: $i,SV123: $i] :
( ( ! [SY1482: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV123 @ SV292 ) @ SV445 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV123 @ SV551 @ SY1482 ) @ SV445 ) @ SV292 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1054]) ).
thf(1207,plain,
! [SV552: $i,SV446: $i,SV293: $i,SV124: $i] :
( ( ( hBOOL @ ( hAPP @ SV124 @ SV293 ) )
| ( c_Wellfounded_Oaccp @ SV446 @ SV552 @ t_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV446 @ SV552 ) @ ( v_sko__Wellfounded__Xaccp__Xinducts__1 @ SV124 @ SV446 ) ) )
| ~ ( c_Wellfounded_Oaccp @ SV446 @ SV293 @ t_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1055]) ).
thf(1208,plain,
! [SV553: $i,SV447: $i,SV294: $i,SV125: $i] :
( ( ( hBOOL @ ( hAPP @ SV125 @ SV294 ) )
| ( c_Wellfounded_Oaccp @ SV447 @ SV553 @ t_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV447 @ SV553 ) @ ( v_sko__Wellfounded__Xaccp__Xinduct__1 @ SV125 @ SV447 ) ) )
| ~ ( c_Wellfounded_Oaccp @ SV447 @ SV294 @ t_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1056]) ).
thf(1209,plain,
! [SV554: $i,SV448: $i,SV295: $i,SV126: $i] :
( ( ( c_Predicate_Oconversep @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV126 @ SV295 @ ( tc_fun @ SV448 @ ( tc_fun @ SV554 @ tc_bool ) ) ) @ SV448 @ SV554 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Predicate_Oconversep @ SV126 @ SV448 @ SV554 ) @ ( c_Predicate_Oconversep @ SV295 @ SV448 @ SV554 ) @ ( tc_fun @ SV554 @ ( tc_fun @ SV448 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1057]) ).
thf(1210,plain,
! [SV555: $i,SV449: $i,SV296: $i,SV127: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV127 @ SV296 ) @ SV449 ) @ SV555 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ SV127 @ SV296 @ SV296 ) @ SV296 ) @ SV555 ) @ SV449 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1058]) ).
thf(1211,plain,
! [SV556: $i,SV450: $i,SV297: $i,SV128: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ SV128 @ SV297 @ SV297 ) @ SV297 ) @ SV450 ) @ SV556 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV128 @ SV297 ) @ SV556 ) @ SV450 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1059]) ).
thf(1212,plain,
! [SV557: $i,SV451: $i,SV298: $i,SV129: $i] :
( ( ( hBOOL @ ( hAPP @ SV129 @ SV298 ) )
| ( c_Wellfounded_Oaccp @ SV451 @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__1__1 @ SV129 @ SV451 @ SV557 ) @ SV557 )
| ~ ( c_Wellfounded_Oaccp @ SV451 @ SV298 @ SV557 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1060]) ).
thf(1213,plain,
! [SV558: $i,SV452: $i,SV300: $i,SV131: $i] :
( ( ( c_Predicate_Oconversep @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV131 @ SV300 @ ( tc_fun @ SV452 @ ( tc_fun @ SV558 @ tc_bool ) ) ) @ SV452 @ SV558 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Predicate_Oconversep @ SV131 @ SV452 @ SV558 ) @ ( c_Predicate_Oconversep @ SV300 @ SV452 @ SV558 ) @ ( tc_fun @ SV558 @ ( tc_fun @ SV452 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1061]) ).
thf(1214,plain,
! [SV453: $i,SV301: $i,SV132: $i] :
( ( ( c_Wellfounded_Oaccp @ SV132 @ SV301 @ SV453 )
= $true )
| ( ( ~ ( c_Wellfounded_Oaccp @ SV132 @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__Xintros__1__1 @ SV132 @ SV301 @ SV453 ) @ SV453 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1062]) ).
thf(1215,plain,
! [SV454: $i,SV302: $i,SV133: $i] :
( ( ( c_Wellfounded_Oaccp @ SV133 @ SV302 @ SV454 )
= $true )
| ( ( ~ ( c_Wellfounded_Oaccp @ SV133 @ ( c_ATP__Linkup_Osko__Wellfounded__XaccpI__1__1 @ SV133 @ SV302 @ SV454 ) @ SV454 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1063]) ).
thf(1216,plain,
! [SV455: $i,SV303: $i,SV134: $i] :
( ( ( c_Wellfounded_Oaccp @ SV134 @ SV303 @ SV455 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV134 @ ( c_ATP__Linkup_Osko__Wellfounded__XaccpI__1__1 @ SV134 @ SV303 @ SV455 ) ) @ SV303 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1064]) ).
thf(1217,plain,
! [SV456: $i,SV304: $i,SV135: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV135 ) @ SV304 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV135 ) @ SV456 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV304 ) @ SV456 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1065]) ).
thf(1218,plain,
! [SV457: $i,SV305: $i,SV136: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV136 ) @ SV305 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV457 ) @ SV305 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV136 ) @ SV457 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1066]) ).
thf(1219,plain,
! [SV559: $i,SV458: $i,SV306: $i,SV137: $i] :
( ( ( hBOOL @ ( hAPP @ SV137 @ SV306 ) )
| ( c_Wellfounded_Oaccp @ SV458 @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__rule__1__1 @ SV137 @ SV458 @ SV559 ) @ SV559 )
| ~ ( c_Wellfounded_Oaccp @ SV458 @ SV306 @ SV559 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1067]) ).
thf(1220,plain,
! [SV560: $i,SV459: $i,SV307: $i,SV138: $i] :
( ( ( c_Type_Otyping @ SV138 @ SV307 @ SV459 )
| ~ ( c_Type_Otyping @ SV138 @ SV560 @ SV459 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV560 ) @ SV307 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1068]) ).
thf(1221,plain,
! [SV460: $i,SV308: $i,SV139: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Olift @ SV139 @ SV308 ) ) @ ( c_Lambda_Olift @ SV460 @ SV308 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV139 ) @ SV460 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1069]) ).
thf(1222,plain,
! [SV561: $i,SV461: $i,SV309: $i,SV140: $i] :
( ( ( hBOOL @ ( hAPP @ SV140 @ SV309 ) )
| ~ ( hBOOL @ ( hAPP @ SV140 @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__rule__1__1 @ SV140 @ SV461 @ SV561 ) ) )
| ~ ( c_Wellfounded_Oaccp @ SV461 @ SV309 @ SV561 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1070]) ).
thf(1223,plain,
! [SV562: $i,SV462: $i,SV310: $i,SV141: $i] :
( ( ! [SY1483: $i] :
( ( hBOOL @ ( hAPP @ SV141 @ SV310 ) )
| ( hBOOL @ ( hAPP @ SV141 @ SV462 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV562 @ SV462 ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__rule__1__1 @ SV141 @ SV562 @ SY1483 ) ) )
| ~ ( c_Wellfounded_Oaccp @ SV562 @ SV310 @ SY1483 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1071]) ).
thf(1224,plain,
! [SV563: $i,SV463: $i,SV311: $i,SV142: $i] :
( ( ! [SY1484: $i] :
( ( c_Predicate_Oconversep @ ( c_Predicate_Opred__comp @ SV142 @ SV311 @ SV463 @ SV563 @ SY1484 ) @ SV463 @ SY1484 )
= ( c_Predicate_Opred__comp @ ( c_Predicate_Oconversep @ SV311 @ SV563 @ SY1484 ) @ ( c_Predicate_Oconversep @ SV142 @ SV463 @ SV563 ) @ SY1484 @ SV563 @ SV463 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1072]) ).
thf(1225,plain,
! [SV464: $i,SV312: $i,SV143: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV143 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV312 @ SV143 @ SV464 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1073]) ).
thf(1226,plain,
! [SV313: $i,SV144: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV144 ) @ SV313 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ SV144 ) ) @ ( c_Lambda_OdB_OAbs @ SV313 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1074]) ).
thf(1227,plain,
! [SV145: $i,SV314: $i] :
( ( ( class_Lattices_Olattice @ SV314 )
= $false )
| ( ( class_Lattices_Oupper__semilattice @ ( tc_fun @ SV145 @ SV314 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1075]) ).
thf(1228,plain,
! [SV146: $i,SV315: $i] :
( ( ( class_Lattices_Olattice @ SV315 )
= $false )
| ( ( class_Lattices_Olower__semilattice @ ( tc_fun @ SV146 @ SV315 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1076]) ).
thf(1229,plain,
! [SV147: $i,SV316: $i] :
( ( ( class_Lattices_Odistrib__lattice @ SV316 )
= $false )
| ( ( class_Lattices_Odistrib__lattice @ ( tc_fun @ SV147 @ SV316 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1077]) ).
thf(1230,plain,
! [SV148: $i,SV317: $i] :
( ( ( class_Lattices_Olattice @ SV317 )
= $false )
| ( ( class_Lattices_Olattice @ ( tc_fun @ SV148 @ SV317 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1078]) ).
thf(1231,plain,
! [SV465: $i,SV319: $i,SV150: $i] :
( ( ( SV150 = SV319 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ SV465 ) @ SV150 ) @ SV319 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1079]) ).
thf(1232,plain,
! [SV564: $i,SV466: $i,SV320: $i,SV151: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV151 ) @ SV320 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV466 ) @ SV564 ) )
| ( SV320 = SV564 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1080]) ).
thf(1233,plain,
! [SV467: $i,SV321: $i,SV152: $i] :
( ( ( c_Lambda_OdB_OVar @ SV152 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV321 ) @ SV467 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1081]) ).
thf(1234,plain,
! [SV565: $i,SV468: $i,SV323: $i,SV154: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV154 ) @ SV323 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV468 ) @ SV565 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV323 = SV565 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1083]) ).
thf(1235,plain,
! [SV469: $i,SV324: $i,SV155: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV155 ) @ SV324 )
= ( c_Lambda_OdB_OVar @ SV469 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1084]) ).
thf(1236,plain,
! [SV566: $i,SV470: $i,SV325: $i,SV156: $i] :
( ( ( ( c_Type_Otype_OFun @ SV156 @ SV325 )
!= ( c_Type_Otype_OFun @ SV470 @ SV566 ) )
| ( SV325 = SV566 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1085]) ).
thf(1237,plain,
! [SV567: $i,SV471: $i,SV326: $i,SV157: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV157 ) @ SV326 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV471 ) @ SV567 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV157 = SV471 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1086]) ).
thf(1238,plain,
! [SV472: $i,SV327: $i,SV158: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV158 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV327 @ SV472 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( ( c_Lambda_OdB_OAbs @ SV158 )
= SV327 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1087]) ).
thf(1239,plain,
! [SV568: $i,SV473: $i,SV328: $i,SV159: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV159 ) @ SV328 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV473 ) @ SV568 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV159 = SV473 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1088]) ).
thf(1240,plain,
! [SV474: $i,SV329: $i,SV160: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV160 @ SV329 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SV474 ) )
= $true )
| ( ( SV329
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1089]) ).
thf(1241,plain,
! [SV475: $i,SV330: $i,SV161: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV161 @ SV330 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV475 @ SV330 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV161 = SV475 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1090]) ).
thf(1242,plain,
! [SV569: $i,SV476: $i,SV331: $i,SV162: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV162 ) @ SV331 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV476 ) @ SV569 ) )
| ( SV162 = SV476 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1091]) ).
thf(1243,plain,
! [SV477: $i,SV332: $i,SV163: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV163 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV332 ) @ SV477 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1092]) ).
thf(1244,plain,
! [SV570: $i,SV478: $i,SV334: $i,SV165: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV165 ) ) @ SV334 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV478 ) @ SV570 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1094]) ).
thf(1245,plain,
! [SV479: $i,SV335: $i,SV166: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV166 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV335 @ SV479 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV479
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1095]) ).
thf(1246,plain,
! [SV480: $i,SV336: $i,SV167: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV167 ) @ SV336 )
= ( c_Lambda_OdB_OAbs @ SV480 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1096]) ).
thf(1247,plain,
! [SV571: $i,SV481: $i,SV337: $i,SV168: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV168 ) @ SV337 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV481 ) @ SV571 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1097]) ).
thf(1248,plain,
! [SV482: $i,SV338: $i,SV169: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV169 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV338 @ SV482 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( ( c_Lambda_OdB_OVar @ SV169 )
= SV338 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1098]) ).
thf(1249,plain,
! [SV483: $i,SV339: $i,SV170: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV170 @ SV339 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SV483 ) )
= $true )
| ( ( SV170
= ( c_Lambda_OdB_OAbs @ SV483 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1099]) ).
thf(1250,plain,
! [SV572: $i,SV484: $i,SV340: $i,SV171: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV171 ) @ SV340 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV484 @ SV572 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV171
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV484 @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ SV171 @ SV340 @ SV484 @ SV572 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV572
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1100]) ).
thf(1251,plain,
! [SV341: $i,SV172: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV172 )
= ( c_Lambda_OdB_OAbs @ SV341 ) )
= $false )
| ( ( SV172 = SV341 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1101]) ).
thf(1252,plain,
! [SV573: $i,SV485: $i,SV342: $i,SV173: $i] :
( ( ( ( c_Type_Otype_OFun @ SV173 @ SV342 )
!= ( c_Type_Otype_OFun @ SV485 @ SV573 ) )
| ( SV173 = SV485 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1102]) ).
thf(1253,plain,
! [SV343: $i,SV174: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV174 )
= ( c_Lambda_OdB_OVar @ SV343 ) )
= $false )
| ( ( SV174 = SV343 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1103]) ).
thf(1254,plain,
! [SV486: $i,SV344: $i,SV175: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV175 ) @ SV344 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV486 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV175 ) @ SV344 )
= SV486 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1104]) ).
thf(1255,plain,
! [SV574: $i,SV487: $i,SV345: $i,SV176: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV176 ) @ SV345 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV487 ) @ SV574 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV345 = SV574 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1105]) ).
thf(1256,plain,
! [SV488: $i,SV346: $i,SV177: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV177 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV346 @ SV488 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV488
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1106]) ).
thf(1257,plain,
! [SV575: $i,SV489: $i,SV349: $i,SV180: $i,SV3: $i] :
( ( ( c_Type_Otyping @ SV3 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV180 ) @ SV349 ) @ SV489 )
| ~ ( c_Type_Otyping @ SV3 @ SV349 @ SV575 )
| ~ ( c_Type_Otyping @ SV3 @ SV180 @ ( c_Type_Otype_OFun @ SV575 @ SV489 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1109]) ).
thf(1258,plain,
! [SV6: $i,SV350: $i,SV181: $i] :
( ( ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ SV181 @ SV350 @ tc_Lambda_OdB )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV6 @ SV181 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV6 @ SV350 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1110]) ).
thf(1259,plain,
! [SV576: $i,SV490: $i,SV351: $i,SV182: $i,SV7: $i] :
( ( ( c_Type_Otyping @ ( c_Type_Oshift @ SV7 @ SV182 @ SV351 @ tc_Type_Otype ) @ ( c_Lambda_Olift @ SV490 @ SV182 ) @ SV576 )
| ~ ( c_Type_Otyping @ SV7 @ SV490 @ SV576 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1111]) ).
thf(1260,plain,
! [SV577: $i,SV491: $i,SV352: $i,SV183: $i,SV8: $i] :
( ( ! [SY1485: $i] :
( ~ ( c_Type_Otyping @ SV8 @ SV183 @ SV352 )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV8 @ SV491 @ SV352 @ tc_Type_Otype ) @ SV577 @ SY1485 )
| ( c_Type_Otyping @ SV8 @ ( c_Lambda_Osubst @ SV577 @ SV183 @ SV491 ) @ SY1485 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1112]) ).
thf(1261,plain,
! [SV353: $i,SV9: $i,SV184: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV184 ) @ SV9 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV353 ) )
= $false )
| ( ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ SV9 @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SV184 @ SV9 @ SV353 ) @ tc_Lambda_OdB )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1113]) ).
thf(1262,plain,
! [SV492: $i,SV354: $i,SV186: $i,SV11: $i] :
( ( ( c_Type_Otyping @ SV11 @ ( c_Lambda_OdB_OAbs @ SV186 ) @ ( c_Type_Otype_OFun @ SV354 @ SV492 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV11 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV354 @ tc_Type_Otype ) @ SV186 @ SV492 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1114]) ).
thf(1263,plain,
! [SV578: $i,SV495: $i,SV357: $i,SV190: $i,SV16: $i] :
( ( ! [SY1486: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV16 @ SV190 @ SV357 ) ) )
| ~ ( c_Type_Otyping @ SV495 @ SV190 @ SV578 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV190 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV495 @ SV357 @ SV578 @ tc_Type_Otype ) @ SV16 @ SY1486 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV16 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1117]) ).
thf(1264,plain,
! [SV17: $i,SV358: $i,SV191: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV191 ) @ SV358 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV17 ) )
= $false )
| ( ( SV17
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV191 ) @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SV191 @ SV358 @ SV17 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1118]) ).
thf(1265,plain,
! [SV579: $i,SV496: $i,SV359: $i,SV194: $i,SV20: $i] :
( ( ! [SY1487: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV20 @ SV194 ) @ SV359 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV20 @ SV496 @ ( tc_fun @ SV579 @ ( tc_fun @ SY1487 @ tc_bool ) ) ) @ SV194 ) @ SV359 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1120]) ).
thf(1266,plain,
! [SV580: $i,SV497: $i,SV360: $i,SV195: $i,SV21: $i] :
( ( ! [SY1488: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV21 @ SV195 ) @ SV360 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV497 @ SV21 @ ( tc_fun @ SV580 @ ( tc_fun @ SY1488 @ tc_bool ) ) ) @ SV195 ) @ SV360 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1121]) ).
thf(1267,plain,
! [SV498: $i,SV362: $i,SV198: $i,SV24: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV24 @ SV198 ) @ SV362 ) @ SV498 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV24 @ SV362 ) @ SV498 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1123]) ).
thf(1268,plain,
! [SV363: $i,SV199: $i,SV25: $i] :
( ( ( class_Lattices_Olattice @ SV25 )
= $false )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV199 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV199 @ SV363 @ SV25 ) @ SV25 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV199 @ SV363 @ SV25 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1124]) ).
thf(1269,plain,
! [SV364: $i,SV200: $i,SV26: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV26 )
= $false )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV200 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV200 @ SV364 @ SV26 ) @ SV26 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV200 @ SV364 @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1125]) ).
thf(1270,plain,
! [SV365: $i,SV201: $i,SV27: $i] :
( ( ( class_Lattices_Olattice @ SV27 )
= $false )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV201 @ SV365 @ SV27 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV365 @ SV201 @ SV27 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1126]) ).
thf(1271,plain,
! [SV366: $i,SV202: $i,SV28: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV28 )
= $false )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV202 @ SV366 @ SV28 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV366 @ SV202 @ SV28 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1127]) ).
thf(1272,plain,
! [SV499: $i,SV367: $i,SV203: $i,SV29: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV29 ) @ SV203 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV367 ) @ SV499 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV203 ) @ SV499 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV29 ) @ SV367 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1128]) ).
thf(1273,plain,
! [SV204: $i,SV368: $i,SV31: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV31 ) @ SV368 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV31 ) @ SV204 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV368 ) @ SV204 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1129]) ).
thf(1274,plain,
! [SV32: $i,SV369: $i,SV205: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV205 ) @ SV369 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV32 ) @ SV205 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV32 ) @ SV369 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1130]) ).
thf(1275,plain,
! [SV370: $i,SV206: $i,SV33: $i] :
( ( ( class_Lattices_Olattice @ SV33 )
= $false )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV206 @ SV370 @ SV33 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV370 @ SV206 @ SV33 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1131]) ).
thf(1276,plain,
! [SV371: $i,SV207: $i,SV34: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV34 )
= $false )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV207 @ SV371 @ SV34 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV371 @ SV207 @ SV34 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1132]) ).
thf(1277,plain,
! [SV500: $i,SV372: $i,SV208: $i,SV35: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV35 ) )
= $true )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV208 @ SV372 @ SV35 ) @ SV500 @ SV35 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV208 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV372 @ SV500 @ SV35 ) @ SV35 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1133]) ).
thf(1278,plain,
! [SV501: $i,SV373: $i,SV209: $i,SV36: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV36 ) )
= $true )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV209 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV373 @ SV501 @ SV36 ) @ SV36 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV373 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV209 @ SV501 @ SV36 ) @ SV36 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1134]) ).
thf(1279,plain,
! [SV502: $i,SV374: $i,SV210: $i,SV37: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV37 ) )
= $true )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV210 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV374 @ SV502 @ SV37 ) @ SV37 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV374 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV210 @ SV502 @ SV37 ) @ SV37 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1135]) ).
thf(1280,plain,
! [SV503: $i,SV375: $i,SV211: $i,SV38: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV38 ) )
= $true )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV211 @ SV375 @ SV38 ) @ SV503 @ SV38 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV211 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV375 @ SV503 @ SV38 ) @ SV38 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1136]) ).
thf(1281,plain,
! [SV504: $i,SV376: $i,SV213: $i,SV40: $i] :
( ( ( ~ ( class_Lattices_Odistrib__lattice @ SV40 ) )
= $true )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV213 @ SV376 @ SV40 ) @ SV504 @ SV40 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV213 @ SV504 @ SV40 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV376 @ SV504 @ SV40 ) @ SV40 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1138]) ).
thf(1282,plain,
! [SV505: $i,SV377: $i,SV214: $i,SV41: $i] :
( ( ( ~ ( class_Lattices_Odistrib__lattice @ SV41 ) )
= $true )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV214 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV377 @ SV505 @ SV41 ) @ SV41 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV214 @ SV377 @ SV41 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV214 @ SV505 @ SV41 ) @ SV41 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1139]) ).
thf(1283,plain,
! [SV581: $i,SV506: $i,SV378: $i,SV216: $i,SV43: $i] :
( ( ! [SY1489: $i,SY1490: $i,SY1491: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV43 @ SV216 @ SV378 @ SV506 @ SV581 ) @ SY1489 ) @ SY1490 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV216 @ SY1491 ) @ SY1490 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV43 @ SY1489 ) @ SY1491 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1141]) ).
thf(1284,plain,
! [SV582: $i,SV507: $i,SV379: $i,SV217: $i,SV44: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV44 @ SV217 ) @ SV379 ) @ SV507 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV44 @ SV217 ) @ SV582 ) @ SV507 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV44 @ SV217 ) @ SV379 ) @ SV582 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1142]) ).
thf(1285,plain,
! [SV583: $i,SV508: $i,SV380: $i,SV218: $i,SV45: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV45 @ SV218 ) @ SV380 ) @ SV508 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV45 @ SV218 ) @ SV583 ) @ SV508 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV45 @ SV218 ) @ SV380 ) @ SV583 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1143]) ).
thf(1286,plain,
! [SV584: $i,SV509: $i,SV383: $i,SV221: $i,SV48: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV48 @ SV221 ) @ SV383 ) @ SV509 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV48 @ SV221 ) @ SV584 ) @ SV509 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV48 @ SV221 ) @ SV383 ) @ SV584 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1144]) ).
thf(1287,plain,
! [SV510: $i,SV384: $i,SV222: $i,SV49: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV49 @ SV222 @ SV384 ) ) @ ( c_Lambda_Osubst @ SV49 @ SV510 @ SV384 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV222 ) @ SV510 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1145]) ).
thf(1288,plain,
! [SV585: $i,SV511: $i,SV385: $i,SV223: $i,SV50: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV50 @ SV223 ) @ SV385 ) @ SV511 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV50 @ SV223 ) @ SV585 ) @ SV511 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV50 @ SV385 ) @ SV585 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1146]) ).
thf(1289,plain,
! [SV586: $i,SV512: $i,SV386: $i,SV224: $i,SV51: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV51 @ SV224 ) @ SV386 ) @ SV512 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV51 @ SV586 ) @ SV512 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV51 @ SV224 ) @ SV386 ) @ SV586 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1147]) ).
thf(1290,plain,
! [SV513: $i,SV388: $i,SV227: $i,SV54: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV54 @ SV227 ) @ SV388 ) @ SV513 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV54 @ SV227 ) @ SV388 ) @ SV513 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1149]) ).
thf(1291,plain,
! [SV514: $i,SV389: $i,SV228: $i,SV55: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV55 @ SV228 @ SV389 ) ) @ ( c_Lambda_Osubst @ SV514 @ SV228 @ SV389 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV55 ) @ SV514 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1150]) ).
thf(1292,plain,
! [SV515: $i,SV390: $i,SV229: $i,SV56: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV56 @ SV229 @ SV390 ) ) @ ( c_Lambda_Osubst @ SV56 @ SV515 @ SV390 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV229 ) @ SV515 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1151]) ).
thf(1293,plain,
! [SV516: $i,SV391: $i,SV230: $i,SV58: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV58 @ SV230 ) @ SV391 ) @ SV516 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV58 @ SV391 ) @ SV516 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1152]) ).
thf(1294,plain,
! [SV587: $i,SV517: $i,SV392: $i,SV231: $i,SV59: $i] :
( ( ! [SY1492: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV59 @ SV231 ) @ SV392 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV517 @ SV231 ) @ SV392 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV517 @ SV59 @ ( tc_fun @ SV587 @ ( tc_fun @ SY1492 @ tc_bool ) ) ) @ SV231 ) @ SV392 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1153]) ).
thf(1295,plain,
! [SV588: $i,SV518: $i,SV393: $i,SV232: $i,SV60: $i] :
( ( ! [SY1493: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV60 @ SV232 @ ( tc_fun @ SV393 @ ( tc_fun @ SV518 @ tc_bool ) ) ) @ SV588 ) @ SY1493 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV232 @ SV588 ) @ SY1493 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1154]) ).
thf(1296,plain,
! [SV589: $i,SV519: $i,SV394: $i,SV233: $i,SV61: $i] :
( ( ! [SY1494: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV61 @ SV233 @ ( tc_fun @ SV394 @ ( tc_fun @ SV519 @ tc_bool ) ) ) @ SV589 ) @ SY1494 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV61 @ SV589 ) @ SY1494 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1155]) ).
thf(1297,plain,
! [SV395: $i,SV62: $i,SV234: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV234 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV62 @ SV234 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV395 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV62 ) ) @ SV234 ) @ SV395 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1156]) ).
thf(1298,plain,
! [SV520: $i,SV396: $i,SV236: $i,SV64: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV64 ) )
= $true )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV236 @ SV396 @ SV64 ) @ SV520 @ SV64 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV236 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV396 @ SV520 @ SV64 ) @ SV64 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1158]) ).
thf(1299,plain,
! [SV521: $i,SV397: $i,SV237: $i,SV65: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV65 ) )
= $true )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV237 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV397 @ SV521 @ SV65 ) @ SV65 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV397 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV237 @ SV521 @ SV65 ) @ SV65 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1159]) ).
thf(1300,plain,
! [SV522: $i,SV398: $i,SV238: $i,SV66: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV66 ) )
= $true )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV238 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV398 @ SV522 @ SV66 ) @ SV66 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV398 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV238 @ SV522 @ SV66 ) @ SV66 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1160]) ).
thf(1301,plain,
! [SV523: $i,SV399: $i,SV239: $i,SV67: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV67 ) )
= $true )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV239 @ SV399 @ SV67 ) @ SV523 @ SV67 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV239 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV399 @ SV523 @ SV67 ) @ SV67 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1161]) ).
thf(1302,plain,
! [SV240: $i,SV400: $i,SV68: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV68 ) @ SV400 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV68 @ SV240 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV400 @ SV240 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1162]) ).
thf(1303,plain,
! [SV401: $i,SV241: $i,SV69: $i] :
( ( ( class_Lattices_Olattice @ SV69 )
= $false )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV241 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV241 @ SV401 @ SV69 ) @ SV69 )
= SV241 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1163]) ).
thf(1304,plain,
! [SV243: $i,SV402: $i,SV71: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV71 ) @ SV402 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Olift @ SV71 @ SV243 ) ) @ ( c_Lambda_Olift @ SV402 @ SV243 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1164]) ).
thf(1305,plain,
! [SV590: $i,SV524: $i,SV403: $i,SV244: $i,SV72: $i] :
( ( ( SV72 = SV244 )
| ~ ( c_Type_Otyping @ SV403 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV524 ) @ SV590 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV244 )
| ~ ( c_Type_Otyping @ SV403 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV524 ) @ SV590 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV72 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1165]) ).
thf(1306,plain,
! [SV404: $i,SV245: $i,SV73: $i] :
( ( ( class_Lattices_Olattice @ SV73 )
= $false )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV245 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV245 @ SV404 @ SV73 ) @ SV73 )
= SV245 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1166]) ).
thf(1307,plain,
! [SV525: $i,SV405: $i,SV247: $i,SV75: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV75 @ SV247 ) @ SV405 ) @ SV525 ) )
= $true )
| ( ( ( SV405 = SV525 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV75 @ SV247 ) @ SV405 ) @ SV525 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1167]) ).
thf(1308,plain,
! [SV526: $i,SV406: $i,SV248: $i,SV76: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV76 @ SV248 ) @ SV406 ) @ SV526 ) )
= $true )
| ( ( ( SV406 = SV526 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV76 @ SV248 ) @ SV406 ) @ SV526 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1168]) ).
thf(1309,plain,
! [SV249: $i,SV407: $i,SV77: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV77 ) @ SV407 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV77 @ SV249 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV407 @ SV249 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1169]) ).
thf(1310,plain,
! [SV527: $i,SV409: $i,SV251: $i,SV79: $i] :
( ( ( ~ ( class_Lattices_Odistrib__lattice @ SV79 ) )
= $true )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV251 @ SV409 @ SV79 ) @ SV527 @ SV79 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV251 @ SV527 @ SV79 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV409 @ SV527 @ SV79 ) @ SV79 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1170]) ).
thf(1311,plain,
! [SV528: $i,SV410: $i,SV252: $i,SV80: $i] :
( ( ( ~ ( class_Lattices_Odistrib__lattice @ SV80 ) )
= $true )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV252 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV410 @ SV528 @ SV80 ) @ SV80 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV252 @ SV410 @ SV80 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV252 @ SV528 @ SV80 ) @ SV80 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1171]) ).
thf(1312,plain,
! [SV411: $i,SV253: $i,SV81: $i] :
( ( ( class_Lattices_Olattice @ SV81 )
= $false )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV253 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV253 @ SV411 @ SV81 ) @ SV81 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV253 @ SV411 @ SV81 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1172]) ).
thf(1313,plain,
! [SV412: $i,SV254: $i,SV82: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV82 )
= $false )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV254 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV254 @ SV412 @ SV82 ) @ SV82 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV254 @ SV412 @ SV82 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1173]) ).
thf(1314,plain,
! [SV413: $i,SV255: $i,SV83: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV83 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV83 @ ( c_Lambda_OdB_OVar @ SV255 ) @ SV413 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1174]) ).
thf(1315,plain,
! [SV591: $i,SV529: $i,SV414: $i,SV259: $i,SV87: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV87 @ SV259 ) @ SV414 ) @ SV529 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV87 @ SV259 ) @ SV591 ) @ SV529 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV87 @ SV259 ) @ SV414 ) @ SV591 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1176]) ).
thf(1316,plain,
! [SV592: $i,SV531: $i,SV416: $i,SV261: $i,SV89: $i] :
( ( ! [SY1495: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV89 @ SV261 @ ( tc_fun @ SV416 @ ( tc_fun @ SV531 @ tc_bool ) ) ) @ SV592 ) @ SY1495 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV261 @ SV592 ) @ SY1495 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV89 @ SV592 ) @ SY1495 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1178]) ).
thf(1317,plain,
! [SV593: $i,SV532: $i,SV417: $i,SV262: $i,SV90: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV90 @ SV262 ) @ SV417 ) @ SV532 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV90 @ SV262 ) @ SV593 ) @ SV532 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV90 @ SV417 ) @ SV593 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1179]) ).
thf(1318,plain,
! [SV594: $i,SV533: $i,SV418: $i,SV263: $i,SV91: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV91 @ SV263 ) @ SV418 ) @ SV533 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV91 @ SV594 ) @ SV533 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV91 @ SV263 ) @ SV418 ) @ SV594 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1180]) ).
thf(1319,plain,
! [SV595: $i,SV534: $i,SV419: $i,SV264: $i,SV92: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV92 @ SV264 ) @ SV419 ) @ SV534 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV92 @ SV595 ) @ SV534 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV92 @ SV264 ) @ SV419 ) @ SV595 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1181]) ).
thf(1320,plain,
! [SV596: $i,SV535: $i,SV420: $i,SV265: $i,SV93: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV93 @ SV265 ) @ SV420 ) @ SV535 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV93 @ SV265 ) @ SV596 ) @ SV535 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV93 @ SV420 ) @ SV596 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1182]) ).
thf(1321,plain,
! [SV536: $i,SV421: $i,SV266: $i,SV94: $i] :
( ( ( c_Wellfounded_Oaccp @ SV94 @ SV266 @ SV421 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV94 @ SV266 ) @ SV536 ) )
| ~ ( c_Wellfounded_Oaccp @ SV94 @ SV536 @ SV421 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1183]) ).
thf(1322,plain,
! [SV537: $i,SV422: $i,SV267: $i,SV95: $i] :
( ( ( c_Wellfounded_Oaccp @ SV95 @ SV267 @ SV422 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV95 @ SV267 ) @ SV537 ) )
| ~ ( c_Wellfounded_Oaccp @ SV95 @ SV537 @ SV422 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1184]) ).
thf(1323,plain,
! [SV538: $i,SV423: $i,SV268: $i,SV96: $i] :
( ( ( hBOOL @ ( hAPP @ SV96 @ SV268 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV96 @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__1__1 @ SV96 @ SV423 @ SV538 ) ) )
| ~ ( c_Wellfounded_Oaccp @ SV423 @ SV268 @ SV538 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1185]) ).
thf(1324,plain,
! [SV597: $i,SV539: $i,SV424: $i,SV269: $i,SV97: $i] :
( ( ( hBOOL @ ( hAPP @ SV97 @ SV269 ) )
| ( hBOOL @ ( hAPP @ SV97 @ SV424 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV539 @ SV424 ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__1__1 @ SV97 @ SV539 @ SV597 ) ) )
| ~ ( c_Wellfounded_Oaccp @ SV539 @ SV269 @ SV597 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1186]) ).
thf(1325,plain,
! [SV540: $i,SV426: $i,SV271: $i,SV99: $i] :
( ( ( c_Type_Otyping @ SV99 @ SV271 @ SV426 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV540 ) @ SV271 ) )
| ~ ( c_Type_Otyping @ SV99 @ SV540 @ SV426 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1188]) ).
thf(1326,plain,
! [SV272: $i,SV427: $i,SV100: $i] :
( ( ( c_Wellfounded_OwfP @ SV100 @ SV427 )
= $false )
| ( ( c_Wellfounded_Oaccp @ SV100 @ SV272 @ SV427 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1189]) ).
thf(1327,plain,
! [SV541: $i,SV430: $i,SV276: $i,SV105: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ ( c_Transitive__Closure_Otranclp @ SV105 @ SV276 ) @ SV276 @ SV276 ) @ SV430 ) @ SV541 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ ( c_Predicate_Oconversep @ SV105 @ SV276 @ SV276 ) @ SV276 ) @ SV430 ) @ SV541 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1191]) ).
thf(1328,plain,
! [SV542: $i,SV431: $i,SV277: $i,SV106: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ ( c_Predicate_Oconversep @ SV106 @ SV277 @ SV277 ) @ SV277 ) @ SV431 ) @ SV542 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ ( c_Transitive__Closure_Otranclp @ SV106 @ SV277 ) @ SV277 @ SV277 ) @ SV431 ) @ SV542 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1192]) ).
thf(1329,plain,
! [SV432: $i,SV278: $i,SV107: $i] :
( ( ( c_Type_Otyping @ SV107 @ ( c_Lambda_OdB_OVar @ SV278 ) @ SV432 )
= $false )
| ( ( ( hAPP @ SV107 @ SV278 )
= SV432 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1193]) ).
thf(1330,plain,
! [SV433: $i,SV279: $i,SV108: $i] :
( ( ( c_Wellfounded_Oaccp @ SV108 @ ( c_ATP__Linkup_Osko__Wellfounded__Xnot__accp__down__1__1 @ SV108 @ SV279 @ SV433 ) @ SV433 )
= $false )
| ( ( c_Wellfounded_Oaccp @ SV108 @ SV279 @ SV433 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1194]) ).
thf(1331,plain,
! [SV543: $i,SV434: $i,SV281: $i,SV112: $i] :
( ( ( c_Wellfounded_Oaccp @ SV112 @ SV281 @ SV434 )
= $true )
| ( ( ~ ( c_Wellfounded_Oaccp @ SV112 @ SV543 @ SV434 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV112 @ SV434 ) @ SV281 ) @ SV543 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1195]) ).
thf(1332,plain,
! [SV544: $i,SV435: $i,SV282: $i,SV113: $i] :
( ( ( c_Wellfounded_Oaccp @ SV113 @ SV282 @ SV435 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV113 @ SV435 ) @ SV282 ) @ SV544 ) )
| ~ ( c_Wellfounded_Oaccp @ SV113 @ SV544 @ SV435 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1196]) ).
thf(1333,plain,
! [SV545: $i,SV436: $i,SV283: $i,SV114: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Osubst @ SV114 @ SV283 @ SV436 ) ) @ ( c_Lambda_Osubst @ SV545 @ SV283 @ SV436 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV114 ) @ SV545 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1197]) ).
thf(1334,plain,
! [SV284: $i,SV437: $i,SV115: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV115 @ ( v_sko__Wellfounded__Xaccp__Xinducts__1 @ SV115 @ SV437 ) ) ) )
= $true )
| ( ( ~ ( c_Wellfounded_Oaccp @ SV437 @ SV284 @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV115 @ SV284 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1198]) ).
thf(1335,plain,
! [SV546: $i,SV438: $i,SV285: $i,SV116: $i] :
( ( ( hBOOL @ ( hAPP @ SV116 @ SV285 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ SV116 @ SV438 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV546 @ SV438 ) @ ( v_sko__Wellfounded__Xaccp__Xinducts__1 @ SV116 @ SV546 ) ) )
| ~ ( c_Wellfounded_Oaccp @ SV546 @ SV285 @ t_a ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1199]) ).
thf(1336,plain,
! [SV439: $i,SV286: $i,SV117: $i] :
( ( ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV117 @ SV286 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV439 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
= $false )
| ( ( ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV286 @ tc_Lambda_OdB )
| ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV117 ) ) @ SV286 ) @ SV439 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1200]) ).
thf(1337,plain,
! [SV287: $i,SV440: $i,SV118: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV118 @ ( v_sko__Wellfounded__Xaccp__Xinduct__1 @ SV118 @ SV440 ) ) ) )
= $true )
| ( ( ~ ( c_Wellfounded_Oaccp @ SV440 @ SV287 @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV118 @ SV287 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1201]) ).
thf(1338,plain,
! [SV547: $i,SV441: $i,SV288: $i,SV119: $i] :
( ( ( hBOOL @ ( hAPP @ SV119 @ SV288 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ SV119 @ SV441 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV547 @ SV441 ) @ ( v_sko__Wellfounded__Xaccp__Xinduct__1 @ SV119 @ SV547 ) ) )
| ~ ( c_Wellfounded_Oaccp @ SV547 @ SV288 @ t_a ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1202]) ).
thf(1339,plain,
! [SV598: $i,SV548: $i,SV442: $i,SV289: $i,SV120: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV120 @ SV289 @ SV442 ) @ SV548 ) @ SV598 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV120 @ SV598 ) @ SV548 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1203]) ).
thf(1340,plain,
! [SV599: $i,SV549: $i,SV443: $i,SV290: $i,SV121: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV121 @ SV290 ) @ SV443 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV121 @ SV549 @ SV599 ) @ SV443 ) @ SV290 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1204]) ).
thf(1341,plain,
! [SV600: $i,SV550: $i,SV444: $i,SV291: $i,SV122: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV122 @ SV291 @ SV444 ) @ SV550 ) @ SV600 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV122 @ SV600 ) @ SV550 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1205]) ).
thf(1342,plain,
! [SV601: $i,SV551: $i,SV445: $i,SV292: $i,SV123: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV123 @ SV292 ) @ SV445 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV123 @ SV551 @ SV601 ) @ SV445 ) @ SV292 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1206]) ).
thf(1343,plain,
! [SV552: $i,SV446: $i,SV293: $i,SV124: $i] :
( ( ( hBOOL @ ( hAPP @ SV124 @ SV293 ) )
= $true )
| ( ( ( c_Wellfounded_Oaccp @ SV446 @ SV552 @ t_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV446 @ SV552 ) @ ( v_sko__Wellfounded__Xaccp__Xinducts__1 @ SV124 @ SV446 ) ) )
| ~ ( c_Wellfounded_Oaccp @ SV446 @ SV293 @ t_a ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1207]) ).
thf(1344,plain,
! [SV553: $i,SV447: $i,SV294: $i,SV125: $i] :
( ( ( hBOOL @ ( hAPP @ SV125 @ SV294 ) )
= $true )
| ( ( ( c_Wellfounded_Oaccp @ SV447 @ SV553 @ t_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV447 @ SV553 ) @ ( v_sko__Wellfounded__Xaccp__Xinduct__1 @ SV125 @ SV447 ) ) )
| ~ ( c_Wellfounded_Oaccp @ SV447 @ SV294 @ t_a ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1208]) ).
thf(1345,plain,
! [SV555: $i,SV449: $i,SV296: $i,SV127: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV127 @ SV296 ) @ SV449 ) @ SV555 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ SV127 @ SV296 @ SV296 ) @ SV296 ) @ SV555 ) @ SV449 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1210]) ).
thf(1346,plain,
! [SV556: $i,SV450: $i,SV297: $i,SV128: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ SV128 @ SV297 @ SV297 ) @ SV297 ) @ SV450 ) @ SV556 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV128 @ SV297 ) @ SV556 ) @ SV450 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1211]) ).
thf(1347,plain,
! [SV557: $i,SV451: $i,SV298: $i,SV129: $i] :
( ( ( hBOOL @ ( hAPP @ SV129 @ SV298 ) )
= $true )
| ( ( ( c_Wellfounded_Oaccp @ SV451 @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__1__1 @ SV129 @ SV451 @ SV557 ) @ SV557 )
| ~ ( c_Wellfounded_Oaccp @ SV451 @ SV298 @ SV557 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1212]) ).
thf(1348,plain,
! [SV453: $i,SV301: $i,SV132: $i] :
( ( ( c_Wellfounded_Oaccp @ SV132 @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__Xintros__1__1 @ SV132 @ SV301 @ SV453 ) @ SV453 )
= $false )
| ( ( c_Wellfounded_Oaccp @ SV132 @ SV301 @ SV453 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1214]) ).
thf(1349,plain,
! [SV454: $i,SV302: $i,SV133: $i] :
( ( ( c_Wellfounded_Oaccp @ SV133 @ ( c_ATP__Linkup_Osko__Wellfounded__XaccpI__1__1 @ SV133 @ SV302 @ SV454 ) @ SV454 )
= $false )
| ( ( c_Wellfounded_Oaccp @ SV133 @ SV302 @ SV454 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1215]) ).
thf(1350,plain,
! [SV135: $i,SV456: $i,SV304: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV304 ) @ SV456 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV135 ) @ SV304 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV135 ) @ SV456 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1217]) ).
thf(1351,plain,
! [SV305: $i,SV457: $i,SV136: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV136 ) @ SV457 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV136 ) @ SV305 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV457 ) @ SV305 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1218]) ).
thf(1352,plain,
! [SV559: $i,SV458: $i,SV306: $i,SV137: $i] :
( ( ( hBOOL @ ( hAPP @ SV137 @ SV306 ) )
= $true )
| ( ( ( c_Wellfounded_Oaccp @ SV458 @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__rule__1__1 @ SV137 @ SV458 @ SV559 ) @ SV559 )
| ~ ( c_Wellfounded_Oaccp @ SV458 @ SV306 @ SV559 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1219]) ).
thf(1353,plain,
! [SV560: $i,SV459: $i,SV307: $i,SV138: $i] :
( ( ( c_Type_Otyping @ SV138 @ SV307 @ SV459 )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV138 @ SV560 @ SV459 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV560 ) @ SV307 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1220]) ).
thf(1354,plain,
! [SV308: $i,SV460: $i,SV139: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV139 ) @ SV460 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Olift @ SV139 @ SV308 ) ) @ ( c_Lambda_Olift @ SV460 @ SV308 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1221]) ).
thf(1355,plain,
! [SV561: $i,SV461: $i,SV309: $i,SV140: $i] :
( ( ( hBOOL @ ( hAPP @ SV140 @ SV309 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV140 @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__rule__1__1 @ SV140 @ SV461 @ SV561 ) ) )
| ~ ( c_Wellfounded_Oaccp @ SV461 @ SV309 @ SV561 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1222]) ).
thf(1356,plain,
! [SV602: $i,SV562: $i,SV462: $i,SV310: $i,SV141: $i] :
( ( ( hBOOL @ ( hAPP @ SV141 @ SV310 ) )
| ( hBOOL @ ( hAPP @ SV141 @ SV462 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV562 @ SV462 ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__rule__1__1 @ SV141 @ SV562 @ SV602 ) ) )
| ~ ( c_Wellfounded_Oaccp @ SV562 @ SV310 @ SV602 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1223]) ).
thf(1357,plain,
! [SV603: $i,SV563: $i,SV463: $i,SV311: $i,SV142: $i] :
( ( ( c_Predicate_Oconversep @ ( c_Predicate_Opred__comp @ SV142 @ SV311 @ SV463 @ SV563 @ SV603 ) @ SV463 @ SV603 )
= ( c_Predicate_Opred__comp @ ( c_Predicate_Oconversep @ SV311 @ SV563 @ SV603 ) @ ( c_Predicate_Oconversep @ SV142 @ SV463 @ SV563 ) @ SV603 @ SV563 @ SV463 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1224]) ).
thf(1358,plain,
! [SV464: $i,SV143: $i,SV312: $i] :
( ( ( c_Type_Otyping @ SV312 @ SV143 @ SV464 )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV143 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1225]) ).
thf(1359,plain,
! [SV319: $i,SV150: $i,SV465: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ SV465 ) @ SV150 ) @ SV319 ) )
= $false )
| ( ( SV150 = SV319 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1231]) ).
thf(1360,plain,
! [SV564: $i,SV466: $i,SV320: $i,SV151: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV151 ) @ SV320 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV466 ) @ SV564 ) )
= $true )
| ( ( SV320 = SV564 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1232]) ).
thf(1361,plain,
! [SV565: $i,SV468: $i,SV323: $i,SV154: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV154 ) @ SV323 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV468 ) @ SV565 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV323 = SV565 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1234]) ).
thf(1362,plain,
! [SV566: $i,SV470: $i,SV325: $i,SV156: $i] :
( ( ( ( c_Type_Otype_OFun @ SV156 @ SV325 )
!= ( c_Type_Otype_OFun @ SV470 @ SV566 ) )
= $true )
| ( ( SV325 = SV566 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1236]) ).
thf(1363,plain,
! [SV567: $i,SV471: $i,SV326: $i,SV157: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV157 ) @ SV326 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV471 ) @ SV567 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV157 = SV471 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1237]) ).
thf(1364,plain,
! [SV472: $i,SV327: $i,SV158: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV158 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV327 @ SV472 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( ( c_Lambda_OdB_OAbs @ SV158 )
= SV327 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1238]) ).
thf(1365,plain,
! [SV568: $i,SV473: $i,SV328: $i,SV159: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV159 ) @ SV328 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV473 ) @ SV568 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV159 = SV473 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1239]) ).
thf(1366,plain,
! [SV474: $i,SV329: $i,SV160: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV160 @ SV329 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_Lambda_OdB_OAbs @ SV474 ) )
= $false )
| ( ( SV329
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1240]) ).
thf(1367,plain,
! [SV475: $i,SV330: $i,SV161: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV161 @ SV330 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV475 @ SV330 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( SV161 = SV475 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1241]) ).
thf(1368,plain,
! [SV569: $i,SV476: $i,SV331: $i,SV162: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV162 ) @ SV331 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV476 ) @ SV569 ) )
= $true )
| ( ( SV162 = SV476 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1242]) ).
thf(1369,plain,
! [SV570: $i,SV478: $i,SV334: $i,SV165: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV165 ) ) @ SV334 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV478 ) @ SV570 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1244]) ).
thf(1370,plain,
! [SV479: $i,SV335: $i,SV166: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV166 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV335 @ SV479 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( SV479
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1245]) ).
thf(1371,plain,
! [SV571: $i,SV481: $i,SV337: $i,SV168: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV168 ) @ SV337 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV481 ) @ SV571 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1247]) ).
thf(1372,plain,
! [SV482: $i,SV338: $i,SV169: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV169 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV338 @ SV482 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( ( c_Lambda_OdB_OVar @ SV169 )
= SV338 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1248]) ).
thf(1373,plain,
! [SV483: $i,SV339: $i,SV170: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV170 @ SV339 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_Lambda_OdB_OAbs @ SV483 ) )
= $false )
| ( ( SV170
= ( c_Lambda_OdB_OAbs @ SV483 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1249]) ).
thf(1374,plain,
! [SV572: $i,SV484: $i,SV340: $i,SV171: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV171 ) @ SV340 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV484 @ SV572 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( ( SV171
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV484 @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ SV171 @ SV340 @ SV484 @ SV572 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV572
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1250]) ).
thf(1375,plain,
! [SV573: $i,SV485: $i,SV342: $i,SV173: $i] :
( ( ( ( c_Type_Otype_OFun @ SV173 @ SV342 )
!= ( c_Type_Otype_OFun @ SV485 @ SV573 ) )
= $true )
| ( ( SV173 = SV485 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1252]) ).
thf(1376,plain,
! [SV486: $i,SV344: $i,SV175: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV175 ) @ SV344 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV486 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV175 ) @ SV344 )
= SV486 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1254]) ).
thf(1377,plain,
! [SV574: $i,SV487: $i,SV345: $i,SV176: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV176 ) @ SV345 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV487 ) @ SV574 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV345 = SV574 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1255]) ).
thf(1378,plain,
! [SV488: $i,SV346: $i,SV177: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV177 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV346 @ SV488 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( SV488
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1256]) ).
thf(1379,plain,
! [SV575: $i,SV489: $i,SV349: $i,SV180: $i,SV3: $i] :
( ( ( c_Type_Otyping @ SV3 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV180 ) @ SV349 ) @ SV489 )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV3 @ SV349 @ SV575 )
| ~ ( c_Type_Otyping @ SV3 @ SV180 @ ( c_Type_Otype_OFun @ SV575 @ SV489 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1257]) ).
thf(1380,plain,
! [SV576: $i,SV490: $i,SV351: $i,SV182: $i,SV7: $i] :
( ( ( c_Type_Otyping @ ( c_Type_Oshift @ SV7 @ SV182 @ SV351 @ tc_Type_Otype ) @ ( c_Lambda_Olift @ SV490 @ SV182 ) @ SV576 )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV7 @ SV490 @ SV576 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1259]) ).
thf(1381,plain,
! [SV604: $i,SV577: $i,SV491: $i,SV352: $i,SV183: $i,SV8: $i] :
( ( ~ ( c_Type_Otyping @ SV8 @ SV183 @ SV352 )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV8 @ SV491 @ SV352 @ tc_Type_Otype ) @ SV577 @ SV604 )
| ( c_Type_Otyping @ SV8 @ ( c_Lambda_Osubst @ SV577 @ SV183 @ SV491 ) @ SV604 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1260]) ).
thf(1382,plain,
! [SV492: $i,SV186: $i,SV354: $i,SV11: $i] :
( ( ( c_Type_Otyping @ ( c_Type_Oshift @ SV11 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV354 @ tc_Type_Otype ) @ SV186 @ SV492 )
= $false )
| ( ( c_Type_Otyping @ SV11 @ ( c_Lambda_OdB_OAbs @ SV186 ) @ ( c_Type_Otype_OFun @ SV354 @ SV492 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1262]) ).
thf(1383,plain,
! [SV605: $i,SV578: $i,SV495: $i,SV357: $i,SV190: $i,SV16: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV16 @ SV190 @ SV357 ) ) )
| ~ ( c_Type_Otyping @ SV495 @ SV190 @ SV578 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV190 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV495 @ SV357 @ SV578 @ tc_Type_Otype ) @ SV16 @ SV605 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1263]) ).
thf(1384,plain,
! [SV606: $i,SV579: $i,SV496: $i,SV359: $i,SV194: $i,SV20: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV20 @ SV194 ) @ SV359 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV20 @ SV496 @ ( tc_fun @ SV579 @ ( tc_fun @ SV606 @ tc_bool ) ) ) @ SV194 ) @ SV359 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1265]) ).
thf(1385,plain,
! [SV607: $i,SV580: $i,SV497: $i,SV360: $i,SV195: $i,SV21: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV21 @ SV195 ) @ SV360 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV497 @ SV21 @ ( tc_fun @ SV580 @ ( tc_fun @ SV607 @ tc_bool ) ) ) @ SV195 ) @ SV360 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1266]) ).
thf(1386,plain,
! [SV198: $i,SV498: $i,SV362: $i,SV24: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV24 @ SV362 ) @ SV498 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV24 @ SV198 ) @ SV362 ) @ SV498 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1267]) ).
thf(1387,plain,
! [SV367: $i,SV29: $i,SV499: $i,SV203: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV203 ) @ SV499 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV29 ) @ SV367 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV29 ) @ SV203 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV367 ) @ SV499 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1272]) ).
thf(1388,plain,
! [SV500: $i,SV372: $i,SV208: $i,SV35: $i] :
( ( ( class_Lattices_Olattice @ SV35 )
= $false )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV208 @ SV372 @ SV35 ) @ SV500 @ SV35 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV208 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV372 @ SV500 @ SV35 ) @ SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1277]) ).
thf(1389,plain,
! [SV501: $i,SV373: $i,SV209: $i,SV36: $i] :
( ( ( class_Lattices_Olattice @ SV36 )
= $false )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV209 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV373 @ SV501 @ SV36 ) @ SV36 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV373 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV209 @ SV501 @ SV36 ) @ SV36 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1278]) ).
thf(1390,plain,
! [SV502: $i,SV374: $i,SV210: $i,SV37: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV37 )
= $false )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV210 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV374 @ SV502 @ SV37 ) @ SV37 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV374 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV210 @ SV502 @ SV37 ) @ SV37 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1279]) ).
thf(1391,plain,
! [SV503: $i,SV375: $i,SV211: $i,SV38: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV38 )
= $false )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV211 @ SV375 @ SV38 ) @ SV503 @ SV38 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV211 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV375 @ SV503 @ SV38 ) @ SV38 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1280]) ).
thf(1392,plain,
! [SV504: $i,SV376: $i,SV213: $i,SV40: $i] :
( ( ( class_Lattices_Odistrib__lattice @ SV40 )
= $false )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV213 @ SV376 @ SV40 ) @ SV504 @ SV40 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV213 @ SV504 @ SV40 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV376 @ SV504 @ SV40 ) @ SV40 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1281]) ).
thf(1393,plain,
! [SV505: $i,SV377: $i,SV214: $i,SV41: $i] :
( ( ( class_Lattices_Odistrib__lattice @ SV41 )
= $false )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV214 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV377 @ SV505 @ SV41 ) @ SV41 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV214 @ SV377 @ SV41 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV214 @ SV505 @ SV41 ) @ SV41 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1282]) ).
thf(1394,plain,
! [SV608: $i,SV581: $i,SV506: $i,SV378: $i,SV216: $i,SV43: $i] :
( ( ! [SY1496: $i,SY1497: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV43 @ SV216 @ SV378 @ SV506 @ SV581 ) @ SV608 ) @ SY1496 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV216 @ SY1497 ) @ SY1496 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV43 @ SV608 ) @ SY1497 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1283]) ).
thf(1395,plain,
! [SV582: $i,SV507: $i,SV379: $i,SV217: $i,SV44: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV44 @ SV217 ) @ SV379 ) @ SV507 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV44 @ SV217 ) @ SV582 ) @ SV507 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV44 @ SV217 ) @ SV379 ) @ SV582 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1284]) ).
thf(1396,plain,
! [SV583: $i,SV508: $i,SV380: $i,SV218: $i,SV45: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV45 @ SV218 ) @ SV380 ) @ SV508 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV45 @ SV218 ) @ SV583 ) @ SV508 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV45 @ SV218 ) @ SV380 ) @ SV583 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1285]) ).
thf(1397,plain,
! [SV584: $i,SV509: $i,SV383: $i,SV221: $i,SV48: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV48 @ SV221 ) @ SV383 ) @ SV509 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV48 @ SV221 ) @ SV584 ) @ SV509 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV48 @ SV221 ) @ SV383 ) @ SV584 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1286]) ).
thf(1398,plain,
! [SV384: $i,SV49: $i,SV510: $i,SV222: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV222 ) @ SV510 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV49 @ SV222 @ SV384 ) ) @ ( c_Lambda_Osubst @ SV49 @ SV510 @ SV384 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1287]) ).
thf(1399,plain,
! [SV585: $i,SV511: $i,SV385: $i,SV223: $i,SV50: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV50 @ SV223 ) @ SV385 ) @ SV511 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV50 @ SV223 ) @ SV585 ) @ SV511 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV50 @ SV385 ) @ SV585 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1288]) ).
thf(1400,plain,
! [SV586: $i,SV512: $i,SV386: $i,SV224: $i,SV51: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV51 @ SV224 ) @ SV386 ) @ SV512 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV51 @ SV586 ) @ SV512 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV51 @ SV224 ) @ SV386 ) @ SV586 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1289]) ).
thf(1401,plain,
! [SV513: $i,SV388: $i,SV227: $i,SV54: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV54 @ SV227 ) @ SV388 ) @ SV513 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV54 @ SV227 ) @ SV388 ) @ SV513 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1290]) ).
thf(1402,plain,
! [SV389: $i,SV228: $i,SV514: $i,SV55: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV55 ) @ SV514 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV55 @ SV228 @ SV389 ) ) @ ( c_Lambda_Osubst @ SV514 @ SV228 @ SV389 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1291]) ).
thf(1403,plain,
! [SV390: $i,SV56: $i,SV515: $i,SV229: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV229 ) @ SV515 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV56 @ SV229 @ SV390 ) ) @ ( c_Lambda_Osubst @ SV56 @ SV515 @ SV390 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1292]) ).
thf(1404,plain,
! [SV230: $i,SV516: $i,SV391: $i,SV58: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV58 @ SV391 ) @ SV516 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV58 @ SV230 ) @ SV391 ) @ SV516 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1293]) ).
thf(1405,plain,
! [SV609: $i,SV587: $i,SV517: $i,SV392: $i,SV231: $i,SV59: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV59 @ SV231 ) @ SV392 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV517 @ SV231 ) @ SV392 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV517 @ SV59 @ ( tc_fun @ SV587 @ ( tc_fun @ SV609 @ tc_bool ) ) ) @ SV231 ) @ SV392 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1294]) ).
thf(1406,plain,
! [SV610: $i,SV588: $i,SV518: $i,SV393: $i,SV232: $i,SV60: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV60 @ SV232 @ ( tc_fun @ SV393 @ ( tc_fun @ SV518 @ tc_bool ) ) ) @ SV588 ) @ SV610 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV232 @ SV588 ) @ SV610 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1295]) ).
thf(1407,plain,
! [SV611: $i,SV589: $i,SV519: $i,SV394: $i,SV233: $i,SV61: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV61 @ SV233 @ ( tc_fun @ SV394 @ ( tc_fun @ SV519 @ tc_bool ) ) ) @ SV589 ) @ SV611 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV61 @ SV589 ) @ SV611 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1296]) ).
thf(1408,plain,
! [SV395: $i,SV62: $i,SV234: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV234 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV62 @ SV234 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV395 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV62 ) ) @ SV234 ) @ SV395 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1297]) ).
thf(1409,plain,
! [SV520: $i,SV396: $i,SV236: $i,SV64: $i] :
( ( ( class_Lattices_Olattice @ SV64 )
= $false )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV236 @ SV396 @ SV64 ) @ SV520 @ SV64 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV236 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV396 @ SV520 @ SV64 ) @ SV64 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1298]) ).
thf(1410,plain,
! [SV521: $i,SV397: $i,SV237: $i,SV65: $i] :
( ( ( class_Lattices_Olattice @ SV65 )
= $false )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV237 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV397 @ SV521 @ SV65 ) @ SV65 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV397 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV237 @ SV521 @ SV65 ) @ SV65 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1299]) ).
thf(1411,plain,
! [SV522: $i,SV398: $i,SV238: $i,SV66: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV66 )
= $false )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV238 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV398 @ SV522 @ SV66 ) @ SV66 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV398 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV238 @ SV522 @ SV66 ) @ SV66 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1300]) ).
thf(1412,plain,
! [SV523: $i,SV399: $i,SV239: $i,SV67: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV67 )
= $false )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV239 @ SV399 @ SV67 ) @ SV523 @ SV67 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV239 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV399 @ SV523 @ SV67 ) @ SV67 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1301]) ).
thf(1413,plain,
! [SV590: $i,SV524: $i,SV403: $i,SV244: $i,SV72: $i] :
( ( ( SV72 = SV244 )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV403 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV524 ) @ SV590 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV244 )
| ~ ( c_Type_Otyping @ SV403 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV524 ) @ SV590 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV72 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1305]) ).
thf(1414,plain,
! [SV247: $i,SV75: $i,SV525: $i,SV405: $i] :
( ( ( SV405 = SV525 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV75 @ SV247 ) @ SV405 ) @ SV525 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV75 @ SV247 ) @ SV405 ) @ SV525 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1307]) ).
thf(1415,plain,
! [SV248: $i,SV76: $i,SV526: $i,SV406: $i] :
( ( ( SV406 = SV526 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV76 @ SV248 ) @ SV406 ) @ SV526 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV76 @ SV248 ) @ SV406 ) @ SV526 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1308]) ).
thf(1416,plain,
! [SV527: $i,SV409: $i,SV251: $i,SV79: $i] :
( ( ( class_Lattices_Odistrib__lattice @ SV79 )
= $false )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV251 @ SV409 @ SV79 ) @ SV527 @ SV79 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV251 @ SV527 @ SV79 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV409 @ SV527 @ SV79 ) @ SV79 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1310]) ).
thf(1417,plain,
! [SV528: $i,SV410: $i,SV252: $i,SV80: $i] :
( ( ( class_Lattices_Odistrib__lattice @ SV80 )
= $false )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV252 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV410 @ SV528 @ SV80 ) @ SV80 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV252 @ SV410 @ SV80 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV252 @ SV528 @ SV80 ) @ SV80 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1311]) ).
thf(1418,plain,
! [SV591: $i,SV529: $i,SV414: $i,SV259: $i,SV87: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV87 @ SV259 ) @ SV414 ) @ SV529 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV87 @ SV259 ) @ SV591 ) @ SV529 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV87 @ SV259 ) @ SV414 ) @ SV591 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1315]) ).
thf(1419,plain,
! [SV612: $i,SV592: $i,SV531: $i,SV416: $i,SV261: $i,SV89: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV89 @ SV261 @ ( tc_fun @ SV416 @ ( tc_fun @ SV531 @ tc_bool ) ) ) @ SV592 ) @ SV612 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV261 @ SV592 ) @ SV612 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV89 @ SV592 ) @ SV612 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1316]) ).
thf(1420,plain,
! [SV593: $i,SV532: $i,SV417: $i,SV262: $i,SV90: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV90 @ SV262 ) @ SV417 ) @ SV532 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV90 @ SV262 ) @ SV593 ) @ SV532 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV90 @ SV417 ) @ SV593 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1317]) ).
thf(1421,plain,
! [SV594: $i,SV533: $i,SV418: $i,SV263: $i,SV91: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV91 @ SV263 ) @ SV418 ) @ SV533 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV91 @ SV594 ) @ SV533 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV91 @ SV263 ) @ SV418 ) @ SV594 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1318]) ).
thf(1422,plain,
! [SV595: $i,SV534: $i,SV419: $i,SV264: $i,SV92: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV92 @ SV264 ) @ SV419 ) @ SV534 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV92 @ SV595 ) @ SV534 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV92 @ SV264 ) @ SV419 ) @ SV595 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1319]) ).
thf(1423,plain,
! [SV596: $i,SV535: $i,SV420: $i,SV265: $i,SV93: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV93 @ SV265 ) @ SV420 ) @ SV535 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV93 @ SV265 ) @ SV596 ) @ SV535 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV93 @ SV420 ) @ SV596 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1320]) ).
thf(1424,plain,
! [SV421: $i,SV536: $i,SV266: $i,SV94: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV94 @ SV266 ) @ SV536 ) ) )
= $true )
| ( ( ~ ( c_Wellfounded_Oaccp @ SV94 @ SV536 @ SV421 ) )
= $true )
| ( ( c_Wellfounded_Oaccp @ SV94 @ SV266 @ SV421 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1321]) ).
thf(1425,plain,
! [SV422: $i,SV537: $i,SV267: $i,SV95: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV95 @ SV267 ) @ SV537 ) ) )
= $true )
| ( ( ~ ( c_Wellfounded_Oaccp @ SV95 @ SV537 @ SV422 ) )
= $true )
| ( ( c_Wellfounded_Oaccp @ SV95 @ SV267 @ SV422 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1322]) ).
thf(1426,plain,
! [SV268: $i,SV538: $i,SV423: $i,SV96: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV96 @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__1__1 @ SV96 @ SV423 @ SV538 ) ) ) )
= $true )
| ( ( ~ ( c_Wellfounded_Oaccp @ SV423 @ SV268 @ SV538 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV96 @ SV268 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1323]) ).
thf(1427,plain,
! [SV597: $i,SV539: $i,SV424: $i,SV269: $i,SV97: $i] :
( ( ( hBOOL @ ( hAPP @ SV97 @ SV269 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ SV97 @ SV424 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV539 @ SV424 ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__1__1 @ SV97 @ SV539 @ SV597 ) ) )
| ~ ( c_Wellfounded_Oaccp @ SV539 @ SV269 @ SV597 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1324]) ).
thf(1428,plain,
! [SV426: $i,SV99: $i,SV271: $i,SV540: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV540 ) @ SV271 ) ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV99 @ SV540 @ SV426 ) )
= $true )
| ( ( c_Type_Otyping @ SV99 @ SV271 @ SV426 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1325]) ).
thf(1429,plain,
! [SV541: $i,SV430: $i,SV276: $i,SV105: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ ( c_Predicate_Oconversep @ SV105 @ SV276 @ SV276 ) @ SV276 ) @ SV430 ) @ SV541 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ ( c_Transitive__Closure_Otranclp @ SV105 @ SV276 ) @ SV276 @ SV276 ) @ SV430 ) @ SV541 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1327]) ).
thf(1430,plain,
! [SV542: $i,SV431: $i,SV277: $i,SV106: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ ( c_Transitive__Closure_Otranclp @ SV106 @ SV277 ) @ SV277 @ SV277 ) @ SV431 ) @ SV542 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ ( c_Predicate_Oconversep @ SV106 @ SV277 @ SV277 ) @ SV277 ) @ SV431 ) @ SV542 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1328]) ).
thf(1431,plain,
! [SV281: $i,SV434: $i,SV543: $i,SV112: $i] :
( ( ( ~ ( c_Wellfounded_Oaccp @ SV112 @ SV543 @ SV434 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV112 @ SV434 ) @ SV281 ) @ SV543 ) ) )
= $true )
| ( ( c_Wellfounded_Oaccp @ SV112 @ SV281 @ SV434 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1331]) ).
thf(1432,plain,
! [SV544: $i,SV282: $i,SV435: $i,SV113: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV113 @ SV435 ) @ SV282 ) @ SV544 ) ) )
= $true )
| ( ( ~ ( c_Wellfounded_Oaccp @ SV113 @ SV544 @ SV435 ) )
= $true )
| ( ( c_Wellfounded_Oaccp @ SV113 @ SV282 @ SV435 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1332]) ).
thf(1433,plain,
! [SV436: $i,SV283: $i,SV545: $i,SV114: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV114 ) @ SV545 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Osubst @ SV114 @ SV283 @ SV436 ) ) @ ( c_Lambda_Osubst @ SV545 @ SV283 @ SV436 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1333]) ).
thf(1434,plain,
! [SV284: $i,SV437: $i,SV115: $i] :
( ( ( hBOOL @ ( hAPP @ SV115 @ ( v_sko__Wellfounded__Xaccp__Xinducts__1 @ SV115 @ SV437 ) ) )
= $false )
| ( ( ~ ( c_Wellfounded_Oaccp @ SV437 @ SV284 @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV115 @ SV284 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1334]) ).
thf(1435,plain,
! [SV285: $i,SV546: $i,SV438: $i,SV116: $i] :
( ( ( hBOOL @ ( hAPP @ SV116 @ SV438 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV546 @ SV438 ) @ ( v_sko__Wellfounded__Xaccp__Xinducts__1 @ SV116 @ SV546 ) ) )
| ~ ( c_Wellfounded_Oaccp @ SV546 @ SV285 @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV116 @ SV285 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1335]) ).
thf(1436,plain,
! [SV439: $i,SV117: $i,SV286: $i] :
( ( ( ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV286 @ tc_Lambda_OdB ) )
= $true )
| ( ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV117 ) ) @ SV286 ) @ SV439 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
= $true )
| ( ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV117 @ SV286 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV439 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1336]) ).
thf(1437,plain,
! [SV287: $i,SV440: $i,SV118: $i] :
( ( ( hBOOL @ ( hAPP @ SV118 @ ( v_sko__Wellfounded__Xaccp__Xinduct__1 @ SV118 @ SV440 ) ) )
= $false )
| ( ( ~ ( c_Wellfounded_Oaccp @ SV440 @ SV287 @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV118 @ SV287 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1337]) ).
thf(1438,plain,
! [SV288: $i,SV547: $i,SV441: $i,SV119: $i] :
( ( ( hBOOL @ ( hAPP @ SV119 @ SV441 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV547 @ SV441 ) @ ( v_sko__Wellfounded__Xaccp__Xinduct__1 @ SV119 @ SV547 ) ) )
| ~ ( c_Wellfounded_Oaccp @ SV547 @ SV288 @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV119 @ SV288 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1338]) ).
thf(1439,plain,
! [SV598: $i,SV548: $i,SV442: $i,SV289: $i,SV120: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV120 @ SV289 @ SV442 ) @ SV548 ) @ SV598 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV120 @ SV598 ) @ SV548 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1339]) ).
thf(1440,plain,
! [SV599: $i,SV549: $i,SV443: $i,SV290: $i,SV121: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV121 @ SV290 ) @ SV443 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV121 @ SV549 @ SV599 ) @ SV443 ) @ SV290 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1340]) ).
thf(1441,plain,
! [SV600: $i,SV550: $i,SV444: $i,SV291: $i,SV122: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV122 @ SV291 @ SV444 ) @ SV550 ) @ SV600 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV122 @ SV600 ) @ SV550 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1341]) ).
thf(1442,plain,
! [SV601: $i,SV551: $i,SV445: $i,SV292: $i,SV123: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV123 @ SV292 ) @ SV445 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV123 @ SV551 @ SV601 ) @ SV445 ) @ SV292 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1342]) ).
thf(1443,plain,
! [SV293: $i,SV124: $i,SV552: $i,SV446: $i] :
( ( ( c_Wellfounded_Oaccp @ SV446 @ SV552 @ t_a )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV446 @ SV552 ) @ ( v_sko__Wellfounded__Xaccp__Xinducts__1 @ SV124 @ SV446 ) ) )
| ~ ( c_Wellfounded_Oaccp @ SV446 @ SV293 @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV124 @ SV293 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1343]) ).
thf(1444,plain,
! [SV294: $i,SV125: $i,SV553: $i,SV447: $i] :
( ( ( c_Wellfounded_Oaccp @ SV447 @ SV553 @ t_a )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV447 @ SV553 ) @ ( v_sko__Wellfounded__Xaccp__Xinduct__1 @ SV125 @ SV447 ) ) )
| ~ ( c_Wellfounded_Oaccp @ SV447 @ SV294 @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV125 @ SV294 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1344]) ).
thf(1445,plain,
! [SV449: $i,SV555: $i,SV296: $i,SV127: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ SV127 @ SV296 @ SV296 ) @ SV296 ) @ SV555 ) @ SV449 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV127 @ SV296 ) @ SV449 ) @ SV555 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1345]) ).
thf(1446,plain,
! [SV450: $i,SV556: $i,SV297: $i,SV128: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV128 @ SV297 ) @ SV556 ) @ SV450 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ SV128 @ SV297 @ SV297 ) @ SV297 ) @ SV450 ) @ SV556 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1346]) ).
thf(1447,plain,
! [SV298: $i,SV557: $i,SV129: $i,SV451: $i] :
( ( ( c_Wellfounded_Oaccp @ SV451 @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__1__1 @ SV129 @ SV451 @ SV557 ) @ SV557 )
= $true )
| ( ( ~ ( c_Wellfounded_Oaccp @ SV451 @ SV298 @ SV557 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV129 @ SV298 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1347]) ).
thf(1448,plain,
! [SV306: $i,SV559: $i,SV137: $i,SV458: $i] :
( ( ( c_Wellfounded_Oaccp @ SV458 @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__rule__1__1 @ SV137 @ SV458 @ SV559 ) @ SV559 )
= $true )
| ( ( ~ ( c_Wellfounded_Oaccp @ SV458 @ SV306 @ SV559 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV137 @ SV306 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1352]) ).
thf(1449,plain,
! [SV307: $i,SV459: $i,SV560: $i,SV138: $i] :
( ( ( ~ ( c_Type_Otyping @ SV138 @ SV560 @ SV459 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV560 ) @ SV307 ) ) )
= $true )
| ( ( c_Type_Otyping @ SV138 @ SV307 @ SV459 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1353]) ).
thf(1450,plain,
! [SV309: $i,SV561: $i,SV461: $i,SV140: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV140 @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__rule__1__1 @ SV140 @ SV461 @ SV561 ) ) ) )
= $true )
| ( ( ~ ( c_Wellfounded_Oaccp @ SV461 @ SV309 @ SV561 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV140 @ SV309 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1355]) ).
thf(1451,plain,
! [SV602: $i,SV562: $i,SV462: $i,SV310: $i,SV141: $i] :
( ( ( hBOOL @ ( hAPP @ SV141 @ SV310 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ SV141 @ SV462 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV562 @ SV462 ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__rule__1__1 @ SV141 @ SV562 @ SV602 ) ) )
| ~ ( c_Wellfounded_Oaccp @ SV562 @ SV310 @ SV602 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1356]) ).
thf(1452,plain,
! [SV564: $i,SV466: $i,SV320: $i,SV151: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV151 ) @ SV320 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV466 ) @ SV564 ) )
= $false )
| ( ( SV320 = SV564 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1360]) ).
thf(1453,plain,
! [SV565: $i,SV468: $i,SV323: $i,SV154: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV154 ) @ SV323 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV468 ) @ SV565 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( SV323 = SV565 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1361]) ).
thf(1454,plain,
! [SV566: $i,SV470: $i,SV325: $i,SV156: $i] :
( ( ( ( c_Type_Otype_OFun @ SV156 @ SV325 )
= ( c_Type_Otype_OFun @ SV470 @ SV566 ) )
= $false )
| ( ( SV325 = SV566 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1362]) ).
thf(1455,plain,
! [SV567: $i,SV471: $i,SV326: $i,SV157: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV157 ) @ SV326 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV471 ) @ SV567 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( SV157 = SV471 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1363]) ).
thf(1456,plain,
! [SV568: $i,SV473: $i,SV328: $i,SV159: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV159 ) @ SV328 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV473 ) @ SV568 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( SV159 = SV473 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1365]) ).
thf(1457,plain,
! [SV569: $i,SV476: $i,SV331: $i,SV162: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV162 ) @ SV331 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV476 ) @ SV569 ) )
= $false )
| ( ( SV162 = SV476 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1368]) ).
thf(1458,plain,
! [SV572: $i,SV484: $i,SV340: $i,SV171: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV171 ) @ SV340 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV484 @ SV572 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( ( SV171
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV484 @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ SV171 @ SV340 @ SV484 @ SV572 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV572
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1374]) ).
thf(1459,plain,
! [SV573: $i,SV485: $i,SV342: $i,SV173: $i] :
( ( ( ( c_Type_Otype_OFun @ SV173 @ SV342 )
= ( c_Type_Otype_OFun @ SV485 @ SV573 ) )
= $false )
| ( ( SV173 = SV485 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1375]) ).
thf(1460,plain,
! [SV574: $i,SV487: $i,SV345: $i,SV176: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV176 ) @ SV345 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV487 ) @ SV574 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( SV345 = SV574 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1377]) ).
thf(1461,plain,
! [SV489: $i,SV180: $i,SV575: $i,SV349: $i,SV3: $i] :
( ( ( ~ ( c_Type_Otyping @ SV3 @ SV349 @ SV575 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV3 @ SV180 @ ( c_Type_Otype_OFun @ SV575 @ SV489 ) ) )
= $true )
| ( ( c_Type_Otyping @ SV3 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV180 ) @ SV349 ) @ SV489 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1379]) ).
thf(1462,plain,
! [SV351: $i,SV182: $i,SV576: $i,SV490: $i,SV7: $i] :
( ( ( c_Type_Otyping @ SV7 @ SV490 @ SV576 )
= $false )
| ( ( c_Type_Otyping @ ( c_Type_Oshift @ SV7 @ SV182 @ SV351 @ tc_Type_Otype ) @ ( c_Lambda_Olift @ SV490 @ SV182 ) @ SV576 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1380]) ).
thf(1463,plain,
! [SV604: $i,SV577: $i,SV491: $i,SV352: $i,SV183: $i,SV8: $i] :
( ( ( ~ ( c_Type_Otyping @ SV8 @ SV183 @ SV352 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV8 @ SV491 @ SV352 @ tc_Type_Otype ) @ SV577 @ SV604 )
| ( c_Type_Otyping @ SV8 @ ( c_Lambda_Osubst @ SV577 @ SV183 @ SV491 ) @ SV604 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1381]) ).
thf(1464,plain,
! [SV605: $i,SV578: $i,SV495: $i,SV357: $i,SV190: $i,SV16: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV16 @ SV190 @ SV357 ) ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV495 @ SV190 @ SV578 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV190 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV495 @ SV357 @ SV578 @ tc_Type_Otype ) @ SV16 @ SV605 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV16 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1383]) ).
thf(1465,plain,
! [SV606: $i,SV579: $i,SV496: $i,SV359: $i,SV194: $i,SV20: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV20 @ SV194 ) @ SV359 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV20 @ SV496 @ ( tc_fun @ SV579 @ ( tc_fun @ SV606 @ tc_bool ) ) ) @ SV194 ) @ SV359 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1384]) ).
thf(1466,plain,
! [SV607: $i,SV580: $i,SV497: $i,SV360: $i,SV195: $i,SV21: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV21 @ SV195 ) @ SV360 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV497 @ SV21 @ ( tc_fun @ SV580 @ ( tc_fun @ SV607 @ tc_bool ) ) ) @ SV195 ) @ SV360 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1385]) ).
thf(1467,plain,
! [SV367: $i,SV29: $i,SV499: $i,SV203: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV203 ) @ SV499 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV29 ) @ SV367 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV29 ) @ SV203 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV367 ) @ SV499 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1387]) ).
thf(1468,plain,
! [SV613: $i,SV608: $i,SV581: $i,SV506: $i,SV378: $i,SV216: $i,SV43: $i] :
( ( ! [SY1498: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV43 @ SV216 @ SV378 @ SV506 @ SV581 ) @ SV608 ) @ SV613 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV216 @ SY1498 ) @ SV613 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV43 @ SV608 ) @ SY1498 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1394]) ).
thf(1469,plain,
! [SV379: $i,SV507: $i,SV582: $i,SV217: $i,SV44: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV44 @ SV217 ) @ SV582 ) @ SV507 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV44 @ SV217 ) @ SV379 ) @ SV582 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV44 @ SV217 ) @ SV379 ) @ SV507 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1395]) ).
thf(1470,plain,
! [SV380: $i,SV508: $i,SV583: $i,SV218: $i,SV45: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV45 @ SV218 ) @ SV583 ) @ SV508 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV45 @ SV218 ) @ SV380 ) @ SV583 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV45 @ SV218 ) @ SV380 ) @ SV508 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1396]) ).
thf(1471,plain,
! [SV383: $i,SV509: $i,SV584: $i,SV221: $i,SV48: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV48 @ SV221 ) @ SV584 ) @ SV509 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV48 @ SV221 ) @ SV383 ) @ SV584 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV48 @ SV221 ) @ SV383 ) @ SV509 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1397]) ).
thf(1472,plain,
! [SV385: $i,SV511: $i,SV585: $i,SV223: $i,SV50: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV50 @ SV223 ) @ SV585 ) @ SV511 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV50 @ SV385 ) @ SV585 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV50 @ SV223 ) @ SV385 ) @ SV511 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1399]) ).
thf(1473,plain,
! [SV386: $i,SV224: $i,SV512: $i,SV586: $i,SV51: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV51 @ SV586 ) @ SV512 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV51 @ SV224 ) @ SV386 ) @ SV586 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV51 @ SV224 ) @ SV386 ) @ SV512 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1400]) ).
thf(1474,plain,
! [SV609: $i,SV587: $i,SV517: $i,SV392: $i,SV231: $i,SV59: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV59 @ SV231 ) @ SV392 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV517 @ SV231 ) @ SV392 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV517 @ SV59 @ ( tc_fun @ SV587 @ ( tc_fun @ SV609 @ tc_bool ) ) ) @ SV231 ) @ SV392 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1405]) ).
thf(1475,plain,
! [SV610: $i,SV588: $i,SV518: $i,SV393: $i,SV232: $i,SV60: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV60 @ SV232 @ ( tc_fun @ SV393 @ ( tc_fun @ SV518 @ tc_bool ) ) ) @ SV588 ) @ SV610 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV232 @ SV588 ) @ SV610 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1406]) ).
thf(1476,plain,
! [SV611: $i,SV589: $i,SV519: $i,SV394: $i,SV233: $i,SV61: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV61 @ SV233 @ ( tc_fun @ SV394 @ ( tc_fun @ SV519 @ tc_bool ) ) ) @ SV589 ) @ SV611 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV61 @ SV589 ) @ SV611 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1407]) ).
thf(1477,plain,
! [SV395: $i,SV234: $i,SV62: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV62 @ SV234 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV395 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV234 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV62 ) ) @ SV234 ) @ SV395 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1408]) ).
thf(1478,plain,
! [SV72: $i,SV244: $i,SV590: $i,SV524: $i,SV403: $i] :
( ( ( ~ ( c_Type_Otyping @ SV403 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV524 ) @ SV590 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV244 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV403 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV524 ) @ SV590 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV72 ) )
= $true )
| ( ( SV72 = SV244 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1413]) ).
thf(1479,plain,
! [SV525: $i,SV405: $i,SV247: $i,SV75: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV75 @ SV247 ) @ SV405 ) @ SV525 ) )
= $false )
| ( ( SV405 = SV525 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV75 @ SV247 ) @ SV405 ) @ SV525 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1414]) ).
thf(1480,plain,
! [SV526: $i,SV406: $i,SV248: $i,SV76: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV76 @ SV248 ) @ SV406 ) @ SV526 ) )
= $false )
| ( ( SV406 = SV526 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV76 @ SV248 ) @ SV406 ) @ SV526 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1415]) ).
thf(1481,plain,
! [SV414: $i,SV529: $i,SV591: $i,SV259: $i,SV87: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV87 @ SV259 ) @ SV591 ) @ SV529 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV87 @ SV259 ) @ SV414 ) @ SV591 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV87 @ SV259 ) @ SV414 ) @ SV529 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1418]) ).
thf(1482,plain,
! [SV612: $i,SV592: $i,SV531: $i,SV416: $i,SV261: $i,SV89: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV89 @ SV261 @ ( tc_fun @ SV416 @ ( tc_fun @ SV531 @ tc_bool ) ) ) @ SV592 ) @ SV612 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV261 @ SV592 ) @ SV612 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV89 @ SV592 ) @ SV612 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1419]) ).
thf(1483,plain,
! [SV417: $i,SV532: $i,SV593: $i,SV262: $i,SV90: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV90 @ SV262 ) @ SV593 ) @ SV532 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV90 @ SV417 ) @ SV593 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV90 @ SV262 ) @ SV417 ) @ SV532 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1420]) ).
thf(1484,plain,
! [SV418: $i,SV263: $i,SV533: $i,SV594: $i,SV91: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV91 @ SV594 ) @ SV533 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV91 @ SV263 ) @ SV418 ) @ SV594 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV91 @ SV263 ) @ SV418 ) @ SV533 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1421]) ).
thf(1485,plain,
! [SV419: $i,SV264: $i,SV534: $i,SV595: $i,SV92: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV92 @ SV595 ) @ SV534 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV92 @ SV264 ) @ SV419 ) @ SV595 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV92 @ SV264 ) @ SV419 ) @ SV534 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1422]) ).
thf(1486,plain,
! [SV420: $i,SV535: $i,SV596: $i,SV265: $i,SV93: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV93 @ SV265 ) @ SV596 ) @ SV535 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV93 @ SV420 ) @ SV596 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV93 @ SV265 ) @ SV420 ) @ SV535 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1423]) ).
thf(1487,plain,
! [SV421: $i,SV536: $i,SV266: $i,SV94: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV94 @ SV266 ) @ SV536 ) )
= $false )
| ( ( ~ ( c_Wellfounded_Oaccp @ SV94 @ SV536 @ SV421 ) )
= $true )
| ( ( c_Wellfounded_Oaccp @ SV94 @ SV266 @ SV421 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1424]) ).
thf(1488,plain,
! [SV422: $i,SV537: $i,SV267: $i,SV95: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV95 @ SV267 ) @ SV537 ) )
= $false )
| ( ( ~ ( c_Wellfounded_Oaccp @ SV95 @ SV537 @ SV422 ) )
= $true )
| ( ( c_Wellfounded_Oaccp @ SV95 @ SV267 @ SV422 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1425]) ).
thf(1489,plain,
! [SV268: $i,SV538: $i,SV423: $i,SV96: $i] :
( ( ( hBOOL @ ( hAPP @ SV96 @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__1__1 @ SV96 @ SV423 @ SV538 ) ) )
= $false )
| ( ( ~ ( c_Wellfounded_Oaccp @ SV423 @ SV268 @ SV538 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV96 @ SV268 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1426]) ).
thf(1490,plain,
! [SV269: $i,SV597: $i,SV539: $i,SV424: $i,SV97: $i] :
( ( ( hBOOL @ ( hAPP @ SV97 @ SV424 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV539 @ SV424 ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__1__1 @ SV97 @ SV539 @ SV597 ) ) )
| ~ ( c_Wellfounded_Oaccp @ SV539 @ SV269 @ SV597 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV97 @ SV269 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1427]) ).
thf(1491,plain,
! [SV426: $i,SV99: $i,SV271: $i,SV540: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV540 ) @ SV271 ) )
= $false )
| ( ( ~ ( c_Type_Otyping @ SV99 @ SV540 @ SV426 ) )
= $true )
| ( ( c_Type_Otyping @ SV99 @ SV271 @ SV426 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1428]) ).
thf(1492,plain,
! [SV281: $i,SV434: $i,SV543: $i,SV112: $i] :
( ( ( c_Wellfounded_Oaccp @ SV112 @ SV543 @ SV434 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV112 @ SV434 ) @ SV281 ) @ SV543 ) ) )
= $true )
| ( ( c_Wellfounded_Oaccp @ SV112 @ SV281 @ SV434 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1431]) ).
thf(1493,plain,
! [SV544: $i,SV282: $i,SV435: $i,SV113: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV113 @ SV435 ) @ SV282 ) @ SV544 ) )
= $false )
| ( ( ~ ( c_Wellfounded_Oaccp @ SV113 @ SV544 @ SV435 ) )
= $true )
| ( ( c_Wellfounded_Oaccp @ SV113 @ SV282 @ SV435 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1432]) ).
thf(1494,plain,
! [SV115: $i,SV284: $i,SV437: $i] :
( ( ( c_Wellfounded_Oaccp @ SV437 @ SV284 @ t_a )
= $false )
| ( ( hBOOL @ ( hAPP @ SV115 @ ( v_sko__Wellfounded__Xaccp__Xinducts__1 @ SV115 @ SV437 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV115 @ SV284 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1434]) ).
thf(1495,plain,
! [SV285: $i,SV116: $i,SV438: $i,SV546: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV546 @ SV438 ) @ ( v_sko__Wellfounded__Xaccp__Xinducts__1 @ SV116 @ SV546 ) ) ) )
= $true )
| ( ( ~ ( c_Wellfounded_Oaccp @ SV546 @ SV285 @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV116 @ SV438 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV116 @ SV285 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1435]) ).
thf(1496,plain,
! [SV439: $i,SV117: $i,SV286: $i] :
( ( ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV286 @ tc_Lambda_OdB )
= $false )
| ( ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV117 ) ) @ SV286 ) @ SV439 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
= $true )
| ( ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV117 @ SV286 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV439 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1436]) ).
thf(1497,plain,
! [SV118: $i,SV287: $i,SV440: $i] :
( ( ( c_Wellfounded_Oaccp @ SV440 @ SV287 @ t_a )
= $false )
| ( ( hBOOL @ ( hAPP @ SV118 @ ( v_sko__Wellfounded__Xaccp__Xinduct__1 @ SV118 @ SV440 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV118 @ SV287 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1437]) ).
thf(1498,plain,
! [SV288: $i,SV119: $i,SV441: $i,SV547: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV547 @ SV441 ) @ ( v_sko__Wellfounded__Xaccp__Xinduct__1 @ SV119 @ SV547 ) ) ) )
= $true )
| ( ( ~ ( c_Wellfounded_Oaccp @ SV547 @ SV288 @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV119 @ SV441 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV119 @ SV288 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1438]) ).
thf(1499,plain,
! [SV442: $i,SV289: $i,SV548: $i,SV598: $i,SV120: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV120 @ SV598 ) @ SV548 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV120 @ SV289 @ SV442 ) @ SV548 ) @ SV598 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1439]) ).
thf(1500,plain,
! [SV290: $i,SV443: $i,SV599: $i,SV549: $i,SV121: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV121 @ SV549 @ SV599 ) @ SV443 ) @ SV290 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV121 @ SV290 ) @ SV443 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1440]) ).
thf(1501,plain,
! [SV444: $i,SV291: $i,SV550: $i,SV600: $i,SV122: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV122 @ SV600 ) @ SV550 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV122 @ SV291 @ SV444 ) @ SV550 ) @ SV600 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1441]) ).
thf(1502,plain,
! [SV292: $i,SV445: $i,SV601: $i,SV551: $i,SV123: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV123 @ SV551 @ SV601 ) @ SV445 ) @ SV292 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV123 @ SV292 ) @ SV445 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1442]) ).
thf(1503,plain,
! [SV293: $i,SV124: $i,SV552: $i,SV446: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV446 @ SV552 ) @ ( v_sko__Wellfounded__Xaccp__Xinducts__1 @ SV124 @ SV446 ) ) ) )
= $true )
| ( ( ~ ( c_Wellfounded_Oaccp @ SV446 @ SV293 @ t_a ) )
= $true )
| ( ( c_Wellfounded_Oaccp @ SV446 @ SV552 @ t_a )
= $true )
| ( ( hBOOL @ ( hAPP @ SV124 @ SV293 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1443]) ).
thf(1504,plain,
! [SV294: $i,SV125: $i,SV553: $i,SV447: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV447 @ SV553 ) @ ( v_sko__Wellfounded__Xaccp__Xinduct__1 @ SV125 @ SV447 ) ) ) )
= $true )
| ( ( ~ ( c_Wellfounded_Oaccp @ SV447 @ SV294 @ t_a ) )
= $true )
| ( ( c_Wellfounded_Oaccp @ SV447 @ SV553 @ t_a )
= $true )
| ( ( hBOOL @ ( hAPP @ SV125 @ SV294 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1444]) ).
thf(1505,plain,
! [SV129: $i,SV557: $i,SV298: $i,SV451: $i] :
( ( ( c_Wellfounded_Oaccp @ SV451 @ SV298 @ SV557 )
= $false )
| ( ( c_Wellfounded_Oaccp @ SV451 @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__1__1 @ SV129 @ SV451 @ SV557 ) @ SV557 )
= $true )
| ( ( hBOOL @ ( hAPP @ SV129 @ SV298 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1447]) ).
thf(1506,plain,
! [SV137: $i,SV559: $i,SV306: $i,SV458: $i] :
( ( ( c_Wellfounded_Oaccp @ SV458 @ SV306 @ SV559 )
= $false )
| ( ( c_Wellfounded_Oaccp @ SV458 @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__rule__1__1 @ SV137 @ SV458 @ SV559 ) @ SV559 )
= $true )
| ( ( hBOOL @ ( hAPP @ SV137 @ SV306 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1448]) ).
thf(1507,plain,
! [SV307: $i,SV459: $i,SV560: $i,SV138: $i] :
( ( ( c_Type_Otyping @ SV138 @ SV560 @ SV459 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV560 ) @ SV307 ) ) )
= $true )
| ( ( c_Type_Otyping @ SV138 @ SV307 @ SV459 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1449]) ).
thf(1508,plain,
! [SV309: $i,SV561: $i,SV461: $i,SV140: $i] :
( ( ( hBOOL @ ( hAPP @ SV140 @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__rule__1__1 @ SV140 @ SV461 @ SV561 ) ) )
= $false )
| ( ( ~ ( c_Wellfounded_Oaccp @ SV461 @ SV309 @ SV561 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV140 @ SV309 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1450]) ).
thf(1509,plain,
! [SV310: $i,SV602: $i,SV562: $i,SV462: $i,SV141: $i] :
( ( ( hBOOL @ ( hAPP @ SV141 @ SV462 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV562 @ SV462 ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__rule__1__1 @ SV141 @ SV562 @ SV602 ) ) )
| ~ ( c_Wellfounded_Oaccp @ SV562 @ SV310 @ SV602 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV141 @ SV310 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1451]) ).
thf(1510,plain,
! [SV572: $i,SV340: $i,SV484: $i,SV171: $i] :
( ( ( SV171
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV484 @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ SV171 @ SV340 @ SV484 @ SV572 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV572
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV171 ) @ SV340 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV484 @ SV572 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1458]) ).
thf(1511,plain,
! [SV489: $i,SV180: $i,SV575: $i,SV349: $i,SV3: $i] :
( ( ( c_Type_Otyping @ SV3 @ SV349 @ SV575 )
= $false )
| ( ( ~ ( c_Type_Otyping @ SV3 @ SV180 @ ( c_Type_Otype_OFun @ SV575 @ SV489 ) ) )
= $true )
| ( ( c_Type_Otyping @ SV3 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV180 ) @ SV349 ) @ SV489 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1461]) ).
thf(1512,plain,
! [SV604: $i,SV577: $i,SV491: $i,SV352: $i,SV183: $i,SV8: $i] :
( ( ( c_Type_Otyping @ SV8 @ SV183 @ SV352 )
= $false )
| ( ( ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV8 @ SV491 @ SV352 @ tc_Type_Otype ) @ SV577 @ SV604 )
| ( c_Type_Otyping @ SV8 @ ( c_Lambda_Osubst @ SV577 @ SV183 @ SV491 ) @ SV604 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1463]) ).
thf(1513,plain,
! [SV605: $i,SV16: $i,SV357: $i,SV578: $i,SV190: $i,SV495: $i] :
( ( ( ~ ( c_Type_Otyping @ SV495 @ SV190 @ SV578 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV190 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV495 @ SV357 @ SV578 @ tc_Type_Otype ) @ SV16 @ SV605 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV16 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV16 @ SV190 @ SV357 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1464]) ).
thf(1514,plain,
! [SV359: $i,SV194: $i,SV606: $i,SV579: $i,SV496: $i,SV20: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV20 @ SV496 @ ( tc_fun @ SV579 @ ( tc_fun @ SV606 @ tc_bool ) ) ) @ SV194 ) @ SV359 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV20 @ SV194 ) @ SV359 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1465]) ).
thf(1515,plain,
! [SV360: $i,SV195: $i,SV607: $i,SV580: $i,SV21: $i,SV497: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV497 @ SV21 @ ( tc_fun @ SV580 @ ( tc_fun @ SV607 @ tc_bool ) ) ) @ SV195 ) @ SV360 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV21 @ SV195 ) @ SV360 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1466]) ).
thf(1516,plain,
! [SV499: $i,SV203: $i,SV367: $i,SV29: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV29 ) @ SV367 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV203 ) @ SV499 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV29 ) @ SV203 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV367 ) @ SV499 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1467]) ).
thf(1517,plain,
! [SV614: $i,SV613: $i,SV608: $i,SV581: $i,SV506: $i,SV378: $i,SV216: $i,SV43: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV43 @ SV216 @ SV378 @ SV506 @ SV581 ) @ SV608 ) @ SV613 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV216 @ SV614 ) @ SV613 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV43 @ SV608 ) @ SV614 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1468]) ).
thf(1518,plain,
! [SV379: $i,SV507: $i,SV582: $i,SV217: $i,SV44: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV44 @ SV217 ) @ SV582 ) @ SV507 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV44 @ SV217 ) @ SV379 ) @ SV582 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV44 @ SV217 ) @ SV379 ) @ SV507 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1469]) ).
thf(1519,plain,
! [SV380: $i,SV508: $i,SV583: $i,SV218: $i,SV45: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV45 @ SV218 ) @ SV583 ) @ SV508 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV45 @ SV218 ) @ SV380 ) @ SV583 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV45 @ SV218 ) @ SV380 ) @ SV508 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1470]) ).
thf(1520,plain,
! [SV383: $i,SV509: $i,SV584: $i,SV221: $i,SV48: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV48 @ SV221 ) @ SV584 ) @ SV509 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV48 @ SV221 ) @ SV383 ) @ SV584 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV48 @ SV221 ) @ SV383 ) @ SV509 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1471]) ).
thf(1521,plain,
! [SV385: $i,SV511: $i,SV585: $i,SV223: $i,SV50: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV50 @ SV223 ) @ SV585 ) @ SV511 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV50 @ SV385 ) @ SV585 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV50 @ SV223 ) @ SV385 ) @ SV511 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1472]) ).
thf(1522,plain,
! [SV386: $i,SV224: $i,SV512: $i,SV586: $i,SV51: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV51 @ SV586 ) @ SV512 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV51 @ SV224 ) @ SV386 ) @ SV586 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV51 @ SV224 ) @ SV386 ) @ SV512 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1473]) ).
thf(1523,plain,
! [SV609: $i,SV587: $i,SV59: $i,SV392: $i,SV231: $i,SV517: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV517 @ SV231 ) @ SV392 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV517 @ SV59 @ ( tc_fun @ SV587 @ ( tc_fun @ SV609 @ tc_bool ) ) ) @ SV231 ) @ SV392 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV59 @ SV231 ) @ SV392 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1474]) ).
thf(1524,plain,
! [SV518: $i,SV393: $i,SV60: $i,SV610: $i,SV588: $i,SV232: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV232 @ SV588 ) @ SV610 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV60 @ SV232 @ ( tc_fun @ SV393 @ ( tc_fun @ SV518 @ tc_bool ) ) ) @ SV588 ) @ SV610 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1475]) ).
thf(1525,plain,
! [SV519: $i,SV394: $i,SV233: $i,SV611: $i,SV589: $i,SV61: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV61 @ SV589 ) @ SV611 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV61 @ SV233 @ ( tc_fun @ SV394 @ ( tc_fun @ SV519 @ tc_bool ) ) ) @ SV589 ) @ SV611 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1476]) ).
thf(1526,plain,
! [SV72: $i,SV244: $i,SV590: $i,SV524: $i,SV403: $i] :
( ( ( c_Type_Otyping @ SV403 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV524 ) @ SV590 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV244 )
= $false )
| ( ( ~ ( c_Type_Otyping @ SV403 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV524 ) @ SV590 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV72 ) )
= $true )
| ( ( SV72 = SV244 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1478]) ).
thf(1527,plain,
! [SV414: $i,SV529: $i,SV591: $i,SV259: $i,SV87: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV87 @ SV259 ) @ SV591 ) @ SV529 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV87 @ SV259 ) @ SV414 ) @ SV591 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV87 @ SV259 ) @ SV414 ) @ SV529 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1481]) ).
thf(1528,plain,
! [SV531: $i,SV416: $i,SV89: $i,SV612: $i,SV592: $i,SV261: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV261 @ SV592 ) @ SV612 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV89 @ SV592 ) @ SV612 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV89 @ SV261 @ ( tc_fun @ SV416 @ ( tc_fun @ SV531 @ tc_bool ) ) ) @ SV592 ) @ SV612 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1482]) ).
thf(1529,plain,
! [SV417: $i,SV532: $i,SV593: $i,SV262: $i,SV90: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV90 @ SV262 ) @ SV593 ) @ SV532 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV90 @ SV417 ) @ SV593 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV90 @ SV262 ) @ SV417 ) @ SV532 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1483]) ).
thf(1530,plain,
! [SV418: $i,SV263: $i,SV533: $i,SV594: $i,SV91: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV91 @ SV594 ) @ SV533 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV91 @ SV263 ) @ SV418 ) @ SV594 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV91 @ SV263 ) @ SV418 ) @ SV533 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1484]) ).
thf(1531,plain,
! [SV419: $i,SV264: $i,SV534: $i,SV595: $i,SV92: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV92 @ SV595 ) @ SV534 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV92 @ SV264 ) @ SV419 ) @ SV595 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV92 @ SV264 ) @ SV419 ) @ SV534 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1485]) ).
thf(1532,plain,
! [SV420: $i,SV535: $i,SV596: $i,SV265: $i,SV93: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV93 @ SV265 ) @ SV596 ) @ SV535 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV93 @ SV420 ) @ SV596 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV93 @ SV265 ) @ SV420 ) @ SV535 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1486]) ).
thf(1533,plain,
! [SV266: $i,SV421: $i,SV536: $i,SV94: $i] :
( ( ( c_Wellfounded_Oaccp @ SV94 @ SV536 @ SV421 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV94 @ SV266 ) @ SV536 ) )
= $false )
| ( ( c_Wellfounded_Oaccp @ SV94 @ SV266 @ SV421 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1487]) ).
thf(1534,plain,
! [SV267: $i,SV422: $i,SV537: $i,SV95: $i] :
( ( ( c_Wellfounded_Oaccp @ SV95 @ SV537 @ SV422 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV95 @ SV267 ) @ SV537 ) )
= $false )
| ( ( c_Wellfounded_Oaccp @ SV95 @ SV267 @ SV422 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1488]) ).
thf(1535,plain,
! [SV96: $i,SV538: $i,SV268: $i,SV423: $i] :
( ( ( c_Wellfounded_Oaccp @ SV423 @ SV268 @ SV538 )
= $false )
| ( ( hBOOL @ ( hAPP @ SV96 @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__1__1 @ SV96 @ SV423 @ SV538 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV96 @ SV268 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1489]) ).
thf(1536,plain,
! [SV269: $i,SV597: $i,SV97: $i,SV424: $i,SV539: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV539 @ SV424 ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__1__1 @ SV97 @ SV539 @ SV597 ) ) ) )
= $true )
| ( ( ~ ( c_Wellfounded_Oaccp @ SV539 @ SV269 @ SV597 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV97 @ SV424 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV97 @ SV269 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1490]) ).
thf(1537,plain,
! [SV271: $i,SV426: $i,SV540: $i,SV99: $i] :
( ( ( c_Type_Otyping @ SV99 @ SV540 @ SV426 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV540 ) @ SV271 ) )
= $false )
| ( ( c_Type_Otyping @ SV99 @ SV271 @ SV426 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1491]) ).
thf(1538,plain,
! [SV543: $i,SV281: $i,SV434: $i,SV112: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV112 @ SV434 ) @ SV281 ) @ SV543 ) )
= $false )
| ( ( c_Wellfounded_Oaccp @ SV112 @ SV543 @ SV434 )
= $false )
| ( ( c_Wellfounded_Oaccp @ SV112 @ SV281 @ SV434 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1492]) ).
thf(1539,plain,
! [SV282: $i,SV435: $i,SV544: $i,SV113: $i] :
( ( ( c_Wellfounded_Oaccp @ SV113 @ SV544 @ SV435 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV113 @ SV435 ) @ SV282 ) @ SV544 ) )
= $false )
| ( ( c_Wellfounded_Oaccp @ SV113 @ SV282 @ SV435 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1493]) ).
thf(1540,plain,
! [SV285: $i,SV116: $i,SV438: $i,SV546: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV546 @ SV438 ) @ ( v_sko__Wellfounded__Xaccp__Xinducts__1 @ SV116 @ SV546 ) ) )
= $false )
| ( ( ~ ( c_Wellfounded_Oaccp @ SV546 @ SV285 @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV116 @ SV438 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV116 @ SV285 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1495]) ).
thf(1541,plain,
! [SV288: $i,SV119: $i,SV441: $i,SV547: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV547 @ SV441 ) @ ( v_sko__Wellfounded__Xaccp__Xinduct__1 @ SV119 @ SV547 ) ) )
= $false )
| ( ( ~ ( c_Wellfounded_Oaccp @ SV547 @ SV288 @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV119 @ SV441 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV119 @ SV288 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1498]) ).
thf(1542,plain,
! [SV293: $i,SV124: $i,SV552: $i,SV446: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV446 @ SV552 ) @ ( v_sko__Wellfounded__Xaccp__Xinducts__1 @ SV124 @ SV446 ) ) )
= $false )
| ( ( ~ ( c_Wellfounded_Oaccp @ SV446 @ SV293 @ t_a ) )
= $true )
| ( ( c_Wellfounded_Oaccp @ SV446 @ SV552 @ t_a )
= $true )
| ( ( hBOOL @ ( hAPP @ SV124 @ SV293 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1503]) ).
thf(1543,plain,
! [SV294: $i,SV125: $i,SV553: $i,SV447: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV447 @ SV553 ) @ ( v_sko__Wellfounded__Xaccp__Xinduct__1 @ SV125 @ SV447 ) ) )
= $false )
| ( ( ~ ( c_Wellfounded_Oaccp @ SV447 @ SV294 @ t_a ) )
= $true )
| ( ( c_Wellfounded_Oaccp @ SV447 @ SV553 @ t_a )
= $true )
| ( ( hBOOL @ ( hAPP @ SV125 @ SV294 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1504]) ).
thf(1544,plain,
! [SV459: $i,SV138: $i,SV307: $i,SV560: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV560 ) @ SV307 ) )
= $false )
| ( ( c_Type_Otyping @ SV138 @ SV560 @ SV459 )
= $false )
| ( ( c_Type_Otyping @ SV138 @ SV307 @ SV459 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1507]) ).
thf(1545,plain,
! [SV140: $i,SV561: $i,SV309: $i,SV461: $i] :
( ( ( c_Wellfounded_Oaccp @ SV461 @ SV309 @ SV561 )
= $false )
| ( ( hBOOL @ ( hAPP @ SV140 @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__rule__1__1 @ SV140 @ SV461 @ SV561 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV140 @ SV309 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1508]) ).
thf(1546,plain,
! [SV310: $i,SV602: $i,SV141: $i,SV462: $i,SV562: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV562 @ SV462 ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__rule__1__1 @ SV141 @ SV562 @ SV602 ) ) ) )
= $true )
| ( ( ~ ( c_Wellfounded_Oaccp @ SV562 @ SV310 @ SV602 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV141 @ SV462 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV141 @ SV310 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1509]) ).
thf(1547,plain,
! [SV349: $i,SV489: $i,SV575: $i,SV180: $i,SV3: $i] :
( ( ( c_Type_Otyping @ SV3 @ SV180 @ ( c_Type_Otype_OFun @ SV575 @ SV489 ) )
= $false )
| ( ( c_Type_Otyping @ SV3 @ SV349 @ SV575 )
= $false )
| ( ( c_Type_Otyping @ SV3 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV180 ) @ SV349 ) @ SV489 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1511]) ).
thf(1548,plain,
! [SV183: $i,SV604: $i,SV577: $i,SV352: $i,SV491: $i,SV8: $i] :
( ( ( ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV8 @ SV491 @ SV352 @ tc_Type_Otype ) @ SV577 @ SV604 ) )
= $true )
| ( ( c_Type_Otyping @ SV8 @ ( c_Lambda_Osubst @ SV577 @ SV183 @ SV491 ) @ SV604 )
= $true )
| ( ( c_Type_Otyping @ SV8 @ SV183 @ SV352 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1512]) ).
thf(1549,plain,
! [SV605: $i,SV16: $i,SV357: $i,SV578: $i,SV190: $i,SV495: $i] :
( ( ( c_Type_Otyping @ SV495 @ SV190 @ SV578 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV190 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV495 @ SV357 @ SV578 @ tc_Type_Otype ) @ SV16 @ SV605 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV16 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV16 @ SV190 @ SV357 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1513]) ).
thf(1550,plain,
! [SV614: $i,SV613: $i,SV608: $i,SV581: $i,SV506: $i,SV378: $i,SV216: $i,SV43: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV43 @ SV216 @ SV378 @ SV506 @ SV581 ) @ SV608 ) @ SV613 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV216 @ SV614 ) @ SV613 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV43 @ SV608 ) @ SV614 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1517]) ).
thf(1551,plain,
! [SV507: $i,SV582: $i,SV379: $i,SV217: $i,SV44: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV44 @ SV217 ) @ SV379 ) @ SV582 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV44 @ SV217 ) @ SV582 ) @ SV507 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV44 @ SV217 ) @ SV379 ) @ SV507 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1518]) ).
thf(1552,plain,
! [SV508: $i,SV583: $i,SV380: $i,SV218: $i,SV45: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV45 @ SV218 ) @ SV380 ) @ SV583 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV45 @ SV218 ) @ SV583 ) @ SV508 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV45 @ SV218 ) @ SV380 ) @ SV508 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1519]) ).
thf(1553,plain,
! [SV509: $i,SV584: $i,SV383: $i,SV221: $i,SV48: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV48 @ SV221 ) @ SV383 ) @ SV584 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV48 @ SV221 ) @ SV584 ) @ SV509 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV48 @ SV221 ) @ SV383 ) @ SV509 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1520]) ).
thf(1554,plain,
! [SV511: $i,SV223: $i,SV585: $i,SV385: $i,SV50: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV50 @ SV385 ) @ SV585 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV50 @ SV223 ) @ SV585 ) @ SV511 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV50 @ SV223 ) @ SV385 ) @ SV511 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1521]) ).
thf(1555,plain,
! [SV512: $i,SV586: $i,SV386: $i,SV224: $i,SV51: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV51 @ SV224 ) @ SV386 ) @ SV586 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV51 @ SV586 ) @ SV512 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV51 @ SV224 ) @ SV386 ) @ SV512 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1522]) ).
thf(1556,plain,
! [SV392: $i,SV231: $i,SV609: $i,SV587: $i,SV59: $i,SV517: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV517 @ SV59 @ ( tc_fun @ SV587 @ ( tc_fun @ SV609 @ tc_bool ) ) ) @ SV231 ) @ SV392 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV517 @ SV231 ) @ SV392 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV59 @ SV231 ) @ SV392 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1523]) ).
thf(1557,plain,
! [SV244: $i,SV72: $i,SV590: $i,SV524: $i,SV403: $i] :
( ( ( c_Type_Otyping @ SV403 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV524 ) @ SV590 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV72 )
= $false )
| ( ( c_Type_Otyping @ SV403 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV524 ) @ SV590 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV244 )
= $false )
| ( ( SV72 = SV244 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1526]) ).
thf(1558,plain,
! [SV529: $i,SV591: $i,SV414: $i,SV259: $i,SV87: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV87 @ SV259 ) @ SV414 ) @ SV591 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV87 @ SV259 ) @ SV591 ) @ SV529 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV87 @ SV259 ) @ SV414 ) @ SV529 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1527]) ).
thf(1559,plain,
! [SV531: $i,SV416: $i,SV89: $i,SV612: $i,SV592: $i,SV261: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV261 @ SV592 ) @ SV612 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV89 @ SV592 ) @ SV612 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV89 @ SV261 @ ( tc_fun @ SV416 @ ( tc_fun @ SV531 @ tc_bool ) ) ) @ SV592 ) @ SV612 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1528]) ).
thf(1560,plain,
! [SV532: $i,SV262: $i,SV593: $i,SV417: $i,SV90: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV90 @ SV417 ) @ SV593 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV90 @ SV262 ) @ SV593 ) @ SV532 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV90 @ SV262 ) @ SV417 ) @ SV532 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1529]) ).
thf(1561,plain,
! [SV533: $i,SV594: $i,SV418: $i,SV263: $i,SV91: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV91 @ SV263 ) @ SV418 ) @ SV594 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV91 @ SV594 ) @ SV533 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV91 @ SV263 ) @ SV418 ) @ SV533 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1530]) ).
thf(1562,plain,
! [SV534: $i,SV595: $i,SV419: $i,SV264: $i,SV92: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV92 @ SV264 ) @ SV419 ) @ SV595 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV92 @ SV595 ) @ SV534 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV92 @ SV264 ) @ SV419 ) @ SV534 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1531]) ).
thf(1563,plain,
! [SV535: $i,SV265: $i,SV596: $i,SV420: $i,SV93: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV93 @ SV420 ) @ SV596 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV93 @ SV265 ) @ SV596 ) @ SV535 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV93 @ SV265 ) @ SV420 ) @ SV535 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1532]) ).
thf(1564,plain,
! [SV269: $i,SV597: $i,SV97: $i,SV424: $i,SV539: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV539 @ SV424 ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__1__1 @ SV97 @ SV539 @ SV597 ) ) )
= $false )
| ( ( ~ ( c_Wellfounded_Oaccp @ SV539 @ SV269 @ SV597 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV97 @ SV424 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV97 @ SV269 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1536]) ).
thf(1565,plain,
! [SV116: $i,SV438: $i,SV285: $i,SV546: $i] :
( ( ( c_Wellfounded_Oaccp @ SV546 @ SV285 @ t_a )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV546 @ SV438 ) @ ( v_sko__Wellfounded__Xaccp__Xinducts__1 @ SV116 @ SV546 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV116 @ SV438 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV116 @ SV285 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1540]) ).
thf(1566,plain,
! [SV119: $i,SV441: $i,SV288: $i,SV547: $i] :
( ( ( c_Wellfounded_Oaccp @ SV547 @ SV288 @ t_a )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV547 @ SV441 ) @ ( v_sko__Wellfounded__Xaccp__Xinduct__1 @ SV119 @ SV547 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV119 @ SV441 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV119 @ SV288 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1541]) ).
thf(1567,plain,
! [SV124: $i,SV552: $i,SV293: $i,SV446: $i] :
( ( ( c_Wellfounded_Oaccp @ SV446 @ SV293 @ t_a )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV446 @ SV552 ) @ ( v_sko__Wellfounded__Xaccp__Xinducts__1 @ SV124 @ SV446 ) ) )
= $false )
| ( ( c_Wellfounded_Oaccp @ SV446 @ SV552 @ t_a )
= $true )
| ( ( hBOOL @ ( hAPP @ SV124 @ SV293 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1542]) ).
thf(1568,plain,
! [SV125: $i,SV553: $i,SV294: $i,SV447: $i] :
( ( ( c_Wellfounded_Oaccp @ SV447 @ SV294 @ t_a )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV447 @ SV553 ) @ ( v_sko__Wellfounded__Xaccp__Xinduct__1 @ SV125 @ SV447 ) ) )
= $false )
| ( ( c_Wellfounded_Oaccp @ SV447 @ SV553 @ t_a )
= $true )
| ( ( hBOOL @ ( hAPP @ SV125 @ SV294 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1543]) ).
thf(1569,plain,
! [SV310: $i,SV602: $i,SV141: $i,SV462: $i,SV562: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV562 @ SV462 ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__rule__1__1 @ SV141 @ SV562 @ SV602 ) ) )
= $false )
| ( ( ~ ( c_Wellfounded_Oaccp @ SV562 @ SV310 @ SV602 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV141 @ SV462 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV141 @ SV310 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1546]) ).
thf(1570,plain,
! [SV183: $i,SV604: $i,SV577: $i,SV352: $i,SV491: $i,SV8: $i] :
( ( ( c_Type_Otyping @ ( c_Type_Oshift @ SV8 @ SV491 @ SV352 @ tc_Type_Otype ) @ SV577 @ SV604 )
= $false )
| ( ( c_Type_Otyping @ SV8 @ ( c_Lambda_Osubst @ SV577 @ SV183 @ SV491 ) @ SV604 )
= $true )
| ( ( c_Type_Otyping @ SV8 @ SV183 @ SV352 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1548]) ).
thf(1571,plain,
! [SV605: $i,SV16: $i,SV578: $i,SV357: $i,SV495: $i,SV190: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV190 ) ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV495 @ SV357 @ SV578 @ tc_Type_Otype ) @ SV16 @ SV605 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV16 ) ) )
= $true )
| ( ( c_Type_Otyping @ SV495 @ SV190 @ SV578 )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV16 @ SV190 @ SV357 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1549]) ).
thf(1572,plain,
! [SV581: $i,SV506: $i,SV378: $i,SV608: $i,SV43: $i,SV613: $i,SV614: $i,SV216: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV216 @ SV614 ) @ SV613 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV43 @ SV608 ) @ SV614 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV43 @ SV216 @ SV378 @ SV506 @ SV581 ) @ SV608 ) @ SV613 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1550]) ).
thf(1573,plain,
! [SV531: $i,SV416: $i,SV261: $i,SV612: $i,SV592: $i,SV89: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV89 @ SV592 ) @ SV612 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV261 @ SV592 ) @ SV612 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV89 @ SV261 @ ( tc_fun @ SV416 @ ( tc_fun @ SV531 @ tc_bool ) ) ) @ SV592 ) @ SV612 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1559]) ).
thf(1574,plain,
! [SV97: $i,SV424: $i,SV597: $i,SV269: $i,SV539: $i] :
( ( ( c_Wellfounded_Oaccp @ SV539 @ SV269 @ SV597 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV539 @ SV424 ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__1__1 @ SV97 @ SV539 @ SV597 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV97 @ SV424 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV97 @ SV269 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1564]) ).
thf(1575,plain,
! [SV141: $i,SV462: $i,SV602: $i,SV310: $i,SV562: $i] :
( ( ( c_Wellfounded_Oaccp @ SV562 @ SV310 @ SV602 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV562 @ SV462 ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__rule__1__1 @ SV141 @ SV562 @ SV602 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV141 @ SV462 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV141 @ SV310 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1569]) ).
thf(1576,plain,
! [SV605: $i,SV16: $i,SV578: $i,SV357: $i,SV495: $i,SV190: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV190 ) )
= $false )
| ( ( ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV495 @ SV357 @ SV578 @ tc_Type_Otype ) @ SV16 @ SV605 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV16 ) ) )
= $true )
| ( ( c_Type_Otyping @ SV495 @ SV190 @ SV578 )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV16 @ SV190 @ SV357 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1571]) ).
thf(1577,plain,
! [SV581: $i,SV506: $i,SV378: $i,SV608: $i,SV43: $i,SV613: $i,SV614: $i,SV216: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV216 @ SV614 ) @ SV613 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV43 @ SV608 ) @ SV614 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV43 @ SV216 @ SV378 @ SV506 @ SV581 ) @ SV608 ) @ SV613 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1572]) ).
thf(1578,plain,
! [SV190: $i,SV605: $i,SV16: $i,SV578: $i,SV357: $i,SV495: $i] :
( ( ( ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV495 @ SV357 @ SV578 @ tc_Type_Otype ) @ SV16 @ SV605 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV16 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV190 ) )
= $false )
| ( ( c_Type_Otyping @ SV495 @ SV190 @ SV578 )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV16 @ SV190 @ SV357 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1576]) ).
thf(1579,plain,
! [SV581: $i,SV506: $i,SV378: $i,SV613: $i,SV216: $i,SV614: $i,SV608: $i,SV43: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV43 @ SV608 ) @ SV614 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV216 @ SV614 ) @ SV613 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV43 @ SV216 @ SV378 @ SV506 @ SV581 ) @ SV608 ) @ SV613 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1577]) ).
thf(1580,plain,
! [SV190: $i,SV605: $i,SV16: $i,SV578: $i,SV357: $i,SV495: $i] :
( ( ( c_Type_Otyping @ ( c_Type_Oshift @ SV495 @ SV357 @ SV578 @ tc_Type_Otype ) @ SV16 @ SV605 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV16 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV190 ) )
= $false )
| ( ( c_Type_Otyping @ SV495 @ SV190 @ SV578 )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV16 @ SV190 @ SV357 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1578]) ).
thf(1581,plain,
! [SV190: $i,SV605: $i,SV578: $i,SV357: $i,SV495: $i,SV16: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV16 ) )
= $false )
| ( ( c_Type_Otyping @ ( c_Type_Oshift @ SV495 @ SV357 @ SV578 @ tc_Type_Otype ) @ SV16 @ SV605 )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV190 ) )
= $false )
| ( ( c_Type_Otyping @ SV495 @ SV190 @ SV578 )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV16 @ SV190 @ SV357 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1580]) ).
thf(1582,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[379,1581,1579,1575,1574,1573,1570,1568,1567,1566,1565,1563,1562,1561,1560,1558,1557,1556,1555,1554,1553,1552,1551,1547,1545,1544,1539,1538,1537,1535,1534,1533,1525,1524,1516,1515,1514,1510,1506,1505,1502,1501,1500,1499,1497,1496,1494,1480,1479,1477,1462,1460,1459,1457,1456,1455,1454,1453,1452,1446,1445,1433,1430,1429,1417,1416,1412,1411,1410,1409,1404,1403,1402,1401,1398,1393,1392,1391,1390,1389,1388,1386,1382,1378,1376,1373,1372,1371,1370,1369,1367,1366,1364,1359,1358,1357,1354,1351,1350,1349,1348,1330,1329,1326,1314,1313,1312,1309,1306,1304,1303,1302,1276,1275,1274,1273,1271,1270,1269,1268,1264,1261,1258,1253,1251,1246,1243,1235,1233,1230,1229,1228,1227,1226,1216,1213,1209,1190,1187,1177,1175,1157,1148,1140,1137,1122,1119,1116,1115,1108,1107,1093,1082,1042,1041,1035,1034,1013,990,985,984,968,961,916,897,876,854,852,842,838,788,784,780,745,698,651,609,599,598,594,563,562,561,560,559,558,557,556]) ).
thf(1583,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[1582]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL856-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.18 % Computer : n015.cluster.edu
% 0.11/0.18 % Model : x86_64 x86_64
% 0.11/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.18 % Memory : 8046.5625MB
% 0.11/0.18 % OS : Linux 6.8.0-71-generic
% 0.11/0.18 % CPULimit : 300
% 0.11/0.18 % WCLimit : 300
% 0.11/0.18 % DateTime : Tue Oct 6 12:39:13 UTC 2026
% 0.11/0.18 % CPUTime :
% 0.11/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.79/2.56 .
% 13.79/2.56
% 13.79/2.56 No.of.Axioms: 187
% 13.79/2.56
% 13.79/2.56 Length.of.Defs: 0
% 13.79/2.56
% 13.79/2.56 Contains.Choice.Funs: false
% 13.79/2.56 ........................................................
% 13.79/2.56
% 13.79/2.56 ********************************
% 13.79/2.56 * All subproblems solved! *
% 13.79/2.56 ********************************
% 13.79/2.56 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:187,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:1582,loop_count:0,foatp_calls:1,translation:fof_full)
% 13.79/2.56
% 13.79/2.56 %**** Beginning of derivation protocol ****
% 13.79/2.56 % SZS output start CNFRefutation
% See solution above
% 13.79/2.58
% 13.79/2.58 %**** End of derivation protocol ****
% 13.79/2.58 %**** no. of clauses in derivation: 1583 ****
% 13.79/2.58 %**** clause counter: 1582 ****
% 13.79/2.58
% 13.79/2.58 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:187,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:1582,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------