%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : LCL858-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:30:58 AM UTC 2026
% Result : Unsatisfiable 17.56s 3.23s
% Output : CNFRefutation 17.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 205
% Syntax : Number of formulae : 1822 (1155 unt; 0 typ; 0 def)
% Number of atoms : 8636 (3286 equ; 0 cnn)
% Maximal formula atoms : 5 ( 4 avg)
% Number of connectives : 28569 (1802 ~;2192 |; 0 &;24575 @)
% ( 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; 11 con; 0-5 aty)
% Number of variables : 6832 ( 0 ^;6832 !; 0 ?;6832 :)
% 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 ).
thf(tp_c_List_Ofoldl,type,
c_List_Ofoldl: $i > $i > $i > $i > $i > $i ).
thf(tp_c_List_Olist_OCons,type,
c_List_Olist_OCons: $i > $i > $i > $i ).
thf(tp_c_List_Olist_ONil,type,
c_List_Olist_ONil: $i > $i ).
thf(tp_c_List_Olistsp,type,
c_List_Olistsp: $i > $i > $i > $o ).
thf(tp_c_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 ).
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_List_Olist,type,
tc_List_Olist: $i > $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_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,
hBOOL @ ( hAPP @ c_InductTermi_OIT @ v_t ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0) ).
thf(16,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(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 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ T_a ) @ V_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 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ T_a ) @ V_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_P: $i,V_a: $i,V_r: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ T_a ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__rule__1__1 @ V_P @ V_r @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ T_a ) @ V_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_accp__induct__rule_0) ).
thf(22,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(23,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(24,axiom,
! [V_r: $i,T_a: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ T_a ) @ V_x ) )
| ( 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(25,axiom,
! [V_r: $i,T_a: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ T_a ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ T_a ) @ ( c_ATP__Linkup_Osko__Wellfounded__XaccpI__1__1 @ V_r @ V_x @ T_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_accpI_1) ).
thf(26,axiom,
! [V_r: $i,T_a: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ T_a ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ T_a ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__Xintros__1__1 @ V_r @ V_x @ T_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_accp_OaccI_1) ).
thf(27,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(28,axiom,
! [V_P: $i,V_a: $i,V_r: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ T_a ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__1__1 @ V_P @ V_r @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ T_a ) @ V_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_accp__induct_0) ).
thf(29,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(30,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(31,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(32,axiom,
! [V_P: $i,V_x: $i,V_r: $i,V_ya: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ t_a ) @ V_ya ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_ya ) @ ( v_sko__Wellfounded__Xaccp__Xinduct__1 @ V_P @ V_r ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ t_a ) @ V_x ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_accp_Oinduct_0) ).
thf(33,axiom,
! [V_P: $i,V_x: $i,V_r: $i,V_ya: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ t_a ) @ V_ya ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_ya ) @ ( v_sko__Wellfounded__Xaccp__Xinducts__1 @ V_P @ V_r ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ t_a ) @ V_x ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_accp_Oinducts_0) ).
thf(34,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(35,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(36,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(37,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(38,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 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ t_a ) @ V_x ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_accp_Oinduct_1) ).
thf(39,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 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ t_a ) @ V_x ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_accp_Oinduct_2) ).
thf(40,axiom,
! [V_r: $i,V_s: $i,V_ss: $i] :
( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ 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 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ V_s ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ 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 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__induction__lemma_0) ).
thf(41,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 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ t_a ) @ V_x ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_accp_Oinducts_1) ).
thf(42,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 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ t_a ) @ V_x ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_accp_Oinducts_2) ).
thf(43,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(44,axiom,
! [V_r: $i,T_a: $i,V_b: $i,V_a: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ T_a ) @ V_b ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_b ) @ V_a ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ T_a ) @ V_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_accp__downwards_0) ).
thf(45,axiom,
! [V_r: $i,T_a: $i,V_b: $i,V_a: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ T_a ) @ V_b ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ T_a ) @ V_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(46,axiom,
! [V_t: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ V_t ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_t ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IT__implies__termi_0) ).
thf(47,axiom,
! [V_r: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_r ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ V_r ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_termi__implies__IT_0) ).
thf(48,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(49,axiom,
! [V_R: $i,T_a: $i,V_x: $i] :
( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_R @ T_a ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xnot__accp__down__1__1 @ V_R @ V_x @ T_a ) ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_R @ T_a ) @ V_x ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__accp__down_1) ).
thf(50,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(51,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(52,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(53,axiom,
! [V_r: $i,T_a: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ T_a ) @ V_x ) )
| ( 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(54,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(55,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(56,axiom,
! [V_r: $i,T_a: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ T_a ) @ V_x ) )
| ~ ( c_Wellfounded_OwfP @ V_r @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_accp__wfPD_0) ).
thf(57,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(58,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 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_R @ T_a ) @ V_x ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__accp__down_0) ).
thf(59,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 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ T_a ) @ V_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_accp__induct_1) ).
thf(60,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 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ T_a ) @ V_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_accp__induct_2) ).
thf(61,axiom,
! [V_r: $i,T_a: $i,V_y: $i,V_a: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ T_a ) @ V_y ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ V_a ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ T_a ) @ V_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_accp_Ocases_0) ).
thf(62,axiom,
! [V_r: $i,T_a: $i,V_a: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ T_a ) @ V_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_a ) @ V_b ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ T_a ) @ V_b ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_accp__downward_0) ).
thf(63,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(64,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(65,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(66,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(67,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(68,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(69,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(70,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(71,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(72,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(73,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(74,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(75,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(76,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(77,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(78,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(79,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(80,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(81,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(82,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(83,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(84,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(85,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(86,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(87,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(88,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(89,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(90,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(91,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(92,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(93,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(94,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(95,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(96,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(97,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(98,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(99,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(100,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(101,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(102,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(103,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(104,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(105,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(106,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(107,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(108,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(109,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(110,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(111,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(112,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(113,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(114,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(115,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(116,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(117,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(118,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(119,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(120,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(121,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(122,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(123,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(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 @ ( 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(125,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(126,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(127,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(128,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(129,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(130,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(131,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(132,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(133,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(134,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(135,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(136,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(137,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(138,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(139,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(140,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(141,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(142,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(143,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(144,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(145,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(146,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(147,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(148,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(149,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(150,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(151,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(152,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(153,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(154,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(155,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(156,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(157,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(158,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(159,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(160,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(161,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(162,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 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_rs ) @ V_ss ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_apps__preserves__betas_0) ).
thf(163,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(164,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(165,axiom,
! [V_r: $i,T_a: $i,V_xs: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ V_r @ T_a ) @ ( c_List_Olist_ONil @ T_a ) ) @ V_xs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__Nil__step1_0) ).
thf(166,axiom,
! [V_r: $i,T_a: $i,V_xs: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ V_r @ T_a ) @ V_xs ) @ ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__step1__Nil_0) ).
thf(167,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(168,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(169,axiom,
! [V_r: $i,T_a: $i,V_xs: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( c_ListOrder_Ostep1 @ V_r @ T_a ) @ ( tc_List_Olist @ T_a ) ) @ V_xs ) )
| ~ ( c_List_Olistsp @ ( c_Wellfounded_Oaccp @ V_r @ T_a ) @ V_xs @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lists__accD_0) ).
thf(170,axiom,
! [V_r: $i,T_a: $i,V_xs: $i] :
( ( c_List_Olistsp @ ( c_Wellfounded_Oaccp @ V_r @ T_a ) @ V_xs @ T_a )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( c_ListOrder_Ostep1 @ V_r @ T_a ) @ ( tc_List_Olist @ T_a ) ) @ V_xs ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lists__accI_0) ).
thf(171,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(172,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(173,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(174,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(175,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(176,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(177,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(178,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(179,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(180,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(181,axiom,
! [V_rs: $i,V_n: $i,V_v: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_rs ) @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ V_n @ V_rs @ V_v ) ) )
| ~ ( 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(182,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(183,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(184,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(185,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(186,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(187,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(188,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(189,axiom,
! [V_r: $i,T_a: $i,V_x: $i,V_xs: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( c_ListOrder_Ostep1 @ V_r @ T_a ) @ ( tc_List_Olist @ T_a ) ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( c_ListOrder_Ostep1 @ V_r @ T_a ) @ ( tc_List_Olist @ T_a ) ) @ V_xs ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ T_a ) @ V_x ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__acc__step1I_0) ).
thf(190,axiom,
! [V_xs: $i,V_x: $i,T_a: $i] :
( V_xs
!= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__Cons__self_0) ).
thf(191,axiom,
! [V_x: $i,V_t: $i,T_a: $i] :
( ( c_List_Olist_OCons @ V_x @ V_t @ T_a )
!= V_t ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__Cons__self2_0) ).
thf(192,axiom,
! [V_x: $i,V_y: $i,V_r: $i,T_a: $i,V_ys: $i,V_xs: $i] :
( ( V_x = V_y )
| ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ V_r @ T_a ) @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__step1__Cons_0) ).
thf(193,axiom,
! [V_a_H: $i,V_list_H: $i,T_a: $i] :
( ( c_List_Olist_OCons @ V_a_H @ V_list_H @ T_a )
!= ( c_List_Olist_ONil @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Osimps_I3_J_0) ).
thf(194,axiom,
! [V_x: $i,V_xa: $i,T_a: $i] :
( ( c_List_Olist_OCons @ V_x @ V_xa @ T_a )
!= ( c_List_Olist_ONil @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neq__Nil__conv_1) ).
thf(195,axiom,
! [V_f: $i,V_a: $i,V_x: $i,V_xs: $i,T_b: $i,T_a: $i] :
( ( c_List_Ofoldl @ V_f @ V_a @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_b ) @ T_a @ T_b )
= ( c_List_Ofoldl @ V_f @ ( hAPP @ ( hAPP @ V_f @ V_a ) @ V_x ) @ V_xs @ T_a @ T_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldl__Cons_0) ).
thf(196,axiom,
! [V_x: $i,V_y: $i,V_xs: $i,V_ys: $i,V_r: $i,T_a: $i] :
( ( V_x = V_y )
| ( V_xs = V_ys )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ V_r @ T_a ) @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__step1__Cons_2) ).
thf(197,axiom,
! [V_r: $i,V_y: $i,V_xa: $i,T_a: $i,V_x: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ V_xa ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ V_r @ T_a ) @ ( c_List_Olist_OCons @ V_y @ V_x @ T_a ) ) @ ( c_List_Olist_OCons @ V_xa @ V_x @ T_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__step1__Cons_4) ).
thf(198,axiom,
! [V_r: $i,T_a: $i,V_ys: $i,V_xs: $i,V_y: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ V_r @ T_a ) @ V_ys ) @ V_xs ) )
| ( V_xs = V_ys )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ V_r @ T_a ) @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__step1__Cons_3) ).
thf(199,axiom,
! [T_a: $i,V_a_H: $i,V_list_H: $i] :
( ( c_List_Olist_ONil @ T_a )
!= ( c_List_Olist_OCons @ V_a_H @ V_list_H @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Osimps_I2_J_0) ).
thf(200,axiom,
! [V_a: $i,V_list: $i,T_a: $i,V_a_H: $i,V_list_H: $i] :
( ( ( c_List_Olist_OCons @ V_a @ V_list @ T_a )
!= ( c_List_Olist_OCons @ V_a_H @ V_list_H @ T_a ) )
| ( V_a = V_a_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Oinject_0) ).
thf(201,axiom,
! [V_a: $i,V_list: $i,T_a: $i,V_a_H: $i,V_list_H: $i] :
( ( ( c_List_Olist_OCons @ V_a @ V_list @ T_a )
!= ( c_List_Olist_OCons @ V_a_H @ V_list_H @ T_a ) )
| ( V_list = V_list_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Oinject_1) ).
thf(202,axiom,
! [V_r: $i,T_a: $i,V_ys: $i,V_xs: $i,V_y: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ V_r @ T_a ) @ V_ys ) @ V_xs ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ V_r @ T_a ) @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__step1__Cons_1) ).
thf(203,axiom,
! [V_r: $i,T_a: $i,V_x: $i,V_ys: $i,V_xs: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ V_r @ T_a ) @ ( c_List_Olist_OCons @ V_x @ V_ys @ T_a ) ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ V_r @ T_a ) @ V_ys ) @ V_xs ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__step1__Cons_5) ).
thf(204,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(205,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[204]) ).
thf(206,negated_conjecture,
~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ v_t ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(207,plain,
$false = $false,
inference(unfold_def,[status(thm)],[205]) ).
thf(208,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(209,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(210,plain,
( ( class_Lattices_Olattice @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(211,plain,
( ( class_Lattices_Odistrib__lattice @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(212,plain,
( ( class_Lattices_Olower__semilattice @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(213,plain,
( ( class_Lattices_Oupper__semilattice @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(214,plain,
( ( class_Lattices_Olattice @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(215,plain,
( ( class_Lattices_Odistrib__lattice @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(216,plain,
( ( class_Lattices_Olower__semilattice @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(217,plain,
( ( class_Lattices_Oupper__semilattice @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(218,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(219,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(220,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(221,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(222,plain,
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ v_t ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(223,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)],[16]) ).
thf(224,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(225,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 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ T_a ) @ V_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(226,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 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ T_a ) @ V_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(227,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(228,plain,
( ( ! [V_P: $i,V_a: $i,V_r: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ T_a ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__rule__1__1 @ V_P @ V_r @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ T_a ) @ V_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(229,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)],[22]) ).
thf(230,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)],[23]) ).
thf(231,plain,
( ( ! [V_r: $i,T_a: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ T_a ) @ V_x ) )
| ( 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)],[24]) ).
thf(232,plain,
( ( ! [V_r: $i,T_a: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ T_a ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ T_a ) @ ( c_ATP__Linkup_Osko__Wellfounded__XaccpI__1__1 @ V_r @ V_x @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(233,plain,
( ( ! [V_r: $i,T_a: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ T_a ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ T_a ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__Xintros__1__1 @ V_r @ V_x @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(234,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)],[27]) ).
thf(235,plain,
( ( ! [V_P: $i,V_a: $i,V_r: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ T_a ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__1__1 @ V_P @ V_r @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ T_a ) @ V_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(236,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)],[29]) ).
thf(237,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)],[30]) ).
thf(238,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)],[31]) ).
thf(239,plain,
( ( ! [V_P: $i,V_x: $i,V_r: $i,V_ya: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ t_a ) @ V_ya ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_ya ) @ ( v_sko__Wellfounded__Xaccp__Xinduct__1 @ V_P @ V_r ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ t_a ) @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(240,plain,
( ( ! [V_P: $i,V_x: $i,V_r: $i,V_ya: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ t_a ) @ V_ya ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_ya ) @ ( v_sko__Wellfounded__Xaccp__Xinducts__1 @ V_P @ V_r ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ t_a ) @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(241,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)],[34]) ).
thf(242,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)],[35]) ).
thf(243,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)],[36]) ).
thf(244,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)],[37]) ).
thf(245,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 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ t_a ) @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(246,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 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ t_a ) @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(247,plain,
( ( ! [V_r: $i,V_s: $i,V_ss: $i] :
( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ 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 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ V_s ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ 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 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(248,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 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ t_a ) @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(249,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 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ t_a ) @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(250,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)],[43]) ).
thf(251,plain,
( ( ! [V_r: $i,T_a: $i,V_b: $i,V_a: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ T_a ) @ V_b ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_b ) @ V_a ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ T_a ) @ V_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(252,plain,
( ( ! [V_r: $i,T_a: $i,V_b: $i,V_a: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ T_a ) @ V_b ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ T_a ) @ V_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_b ) @ V_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(253,plain,
( ( ! [V_t: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ V_t ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_t ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(254,plain,
( ( ! [V_r: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_r ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ V_r ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(255,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)],[48]) ).
thf(256,plain,
( ( ! [V_R: $i,T_a: $i,V_x: $i] :
( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_R @ T_a ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xnot__accp__down__1__1 @ V_R @ V_x @ T_a ) ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_R @ T_a ) @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(257,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)],[50]) ).
thf(258,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)],[51]) ).
thf(259,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)],[52]) ).
thf(260,plain,
( ( ! [V_r: $i,T_a: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ T_a ) @ V_x ) )
| ( 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)],[53]) ).
thf(261,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)],[54]) ).
thf(262,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)],[55]) ).
thf(263,plain,
( ( ! [V_r: $i,T_a: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ T_a ) @ V_x ) )
| ~ ( c_Wellfounded_OwfP @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[56]) ).
thf(264,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)],[57]) ).
thf(265,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 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_R @ T_a ) @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[58]) ).
thf(266,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 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ T_a ) @ V_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[59]) ).
thf(267,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 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ T_a ) @ V_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(268,plain,
( ( ! [V_r: $i,T_a: $i,V_y: $i,V_a: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ T_a ) @ V_y ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ V_a ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ T_a ) @ V_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(269,plain,
( ( ! [V_r: $i,T_a: $i,V_a: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ T_a ) @ V_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_a ) @ V_b ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ T_a ) @ V_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[62]) ).
thf(270,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)],[63]) ).
thf(271,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)],[64]) ).
thf(272,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)],[65]) ).
thf(273,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)],[66]) ).
thf(274,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)],[67]) ).
thf(275,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)],[68]) ).
thf(276,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)],[69]) ).
thf(277,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)],[70]) ).
thf(278,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)],[71]) ).
thf(279,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)],[72]) ).
thf(280,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)],[73]) ).
thf(281,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)],[74]) ).
thf(282,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)],[75]) ).
thf(283,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)],[76]) ).
thf(284,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)],[77]) ).
thf(285,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)],[78]) ).
thf(286,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)],[79]) ).
thf(287,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)],[80]) ).
thf(288,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)],[81]) ).
thf(289,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)],[82]) ).
thf(290,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)],[83]) ).
thf(291,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)],[84]) ).
thf(292,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)],[85]) ).
thf(293,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)],[86]) ).
thf(294,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)],[87]) ).
thf(295,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)],[88]) ).
thf(296,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)],[89]) ).
thf(297,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)],[90]) ).
thf(298,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)],[91]) ).
thf(299,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)],[92]) ).
thf(300,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)],[93]) ).
thf(301,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)],[94]) ).
thf(302,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)],[95]) ).
thf(303,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)],[96]) ).
thf(304,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)],[97]) ).
thf(305,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)],[98]) ).
thf(306,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)],[99]) ).
thf(307,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)],[100]) ).
thf(308,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)],[101]) ).
thf(309,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)],[102]) ).
thf(310,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)],[103]) ).
thf(311,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)],[104]) ).
thf(312,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)],[105]) ).
thf(313,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)],[106]) ).
thf(314,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)],[107]) ).
thf(315,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)],[108]) ).
thf(316,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)],[109]) ).
thf(317,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)],[110]) ).
thf(318,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)],[111]) ).
thf(319,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)],[112]) ).
thf(320,plain,
( ( ! [V_n: $i] : ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OVar @ V_n ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[113]) ).
thf(321,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)],[114]) ).
thf(322,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)],[115]) ).
thf(323,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)],[116]) ).
thf(324,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)],[117]) ).
thf(325,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)],[118]) ).
thf(326,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)],[119]) ).
thf(327,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)],[120]) ).
thf(328,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)],[121]) ).
thf(329,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)],[122]) ).
thf(330,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)],[123]) ).
thf(331,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)],[124]) ).
thf(332,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)],[125]) ).
thf(333,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)],[126]) ).
thf(334,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)],[127]) ).
thf(335,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)],[128]) ).
thf(336,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)],[129]) ).
thf(337,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)],[130]) ).
thf(338,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)],[131]) ).
thf(339,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)],[132]) ).
thf(340,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)],[133]) ).
thf(341,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)],[134]) ).
thf(342,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)],[135]) ).
thf(343,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)],[136]) ).
thf(344,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)],[137]) ).
thf(345,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)],[138]) ).
thf(346,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)],[139]) ).
thf(347,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)],[140]) ).
thf(348,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)],[141]) ).
thf(349,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)],[142]) ).
thf(350,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)],[143]) ).
thf(351,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)],[144]) ).
thf(352,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)],[145]) ).
thf(353,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)],[146]) ).
thf(354,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)],[147]) ).
thf(355,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)],[148]) ).
thf(356,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)],[149]) ).
thf(357,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)],[150]) ).
thf(358,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)],[151]) ).
thf(359,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)],[152]) ).
thf(360,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)],[153]) ).
thf(361,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)],[154]) ).
thf(362,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)],[155]) ).
thf(363,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)],[156]) ).
thf(364,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)],[157]) ).
thf(365,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)],[158]) ).
thf(366,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)],[159]) ).
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)],[160]) ).
thf(368,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)],[161]) ).
thf(369,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 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_rs ) @ V_ss ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[162]) ).
thf(370,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)],[163]) ).
thf(371,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)],[164]) ).
thf(372,plain,
( ( ! [V_r: $i,T_a: $i,V_xs: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ V_r @ T_a ) @ ( c_List_Olist_ONil @ T_a ) ) @ V_xs ) ) )
= $true ),
inference(unfold_def,[status(thm)],[165]) ).
thf(373,plain,
( ( ! [V_r: $i,T_a: $i,V_xs: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ V_r @ T_a ) @ V_xs ) @ ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[166]) ).
thf(374,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)],[167]) ).
thf(375,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)],[168]) ).
thf(376,plain,
( ( ! [V_r: $i,T_a: $i,V_xs: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( c_ListOrder_Ostep1 @ V_r @ T_a ) @ ( tc_List_Olist @ T_a ) ) @ V_xs ) )
| ~ ( c_List_Olistsp @ ( c_Wellfounded_Oaccp @ V_r @ T_a ) @ V_xs @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[169]) ).
thf(377,plain,
( ( ! [V_r: $i,T_a: $i,V_xs: $i] :
( ( c_List_Olistsp @ ( c_Wellfounded_Oaccp @ V_r @ T_a ) @ V_xs @ T_a )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( c_ListOrder_Ostep1 @ V_r @ T_a ) @ ( tc_List_Olist @ T_a ) ) @ V_xs ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[170]) ).
thf(378,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)],[171]) ).
thf(379,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)],[172]) ).
thf(380,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)],[173]) ).
thf(381,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)],[174]) ).
thf(382,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)],[175]) ).
thf(383,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)],[176]) ).
thf(384,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)],[177]) ).
thf(385,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)],[178]) ).
thf(386,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)],[179]) ).
thf(387,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)],[180]) ).
thf(388,plain,
( ( ! [V_rs: $i,V_n: $i,V_v: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_rs ) @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ V_n @ V_rs @ V_v ) ) )
| ~ ( 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)],[181]) ).
thf(389,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)],[182]) ).
thf(390,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)],[183]) ).
thf(391,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)],[184]) ).
thf(392,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)],[185]) ).
thf(393,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)],[186]) ).
thf(394,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)],[187]) ).
thf(395,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)],[188]) ).
thf(396,plain,
( ( ! [V_r: $i,T_a: $i,V_x: $i,V_xs: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( c_ListOrder_Ostep1 @ V_r @ T_a ) @ ( tc_List_Olist @ T_a ) ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( c_ListOrder_Ostep1 @ V_r @ T_a ) @ ( tc_List_Olist @ T_a ) ) @ V_xs ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ T_a ) @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[189]) ).
thf(397,plain,
( ( ! [V_xs: $i,V_x: $i,T_a: $i] :
( V_xs
!= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[190]) ).
thf(398,plain,
( ( ! [V_x: $i,V_t: $i,T_a: $i] :
( ( c_List_Olist_OCons @ V_x @ V_t @ T_a )
!= V_t ) )
= $true ),
inference(unfold_def,[status(thm)],[191]) ).
thf(399,plain,
( ( ! [V_x: $i,V_y: $i,V_r: $i,T_a: $i,V_ys: $i,V_xs: $i] :
( ( V_x = V_y )
| ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ V_r @ T_a ) @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[192]) ).
thf(400,plain,
( ( ! [V_a_H: $i,V_list_H: $i,T_a: $i] :
( ( c_List_Olist_OCons @ V_a_H @ V_list_H @ T_a )
!= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[193]) ).
thf(401,plain,
( ( ! [V_x: $i,V_xa: $i,T_a: $i] :
( ( c_List_Olist_OCons @ V_x @ V_xa @ T_a )
!= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[194]) ).
thf(402,plain,
( ( ! [V_f: $i,V_a: $i,V_x: $i,V_xs: $i,T_b: $i,T_a: $i] :
( ( c_List_Ofoldl @ V_f @ V_a @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_b ) @ T_a @ T_b )
= ( c_List_Ofoldl @ V_f @ ( hAPP @ ( hAPP @ V_f @ V_a ) @ V_x ) @ V_xs @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[195]) ).
thf(403,plain,
( ( ! [V_x: $i,V_y: $i,V_xs: $i,V_ys: $i,V_r: $i,T_a: $i] :
( ( V_x = V_y )
| ( V_xs = V_ys )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ V_r @ T_a ) @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[196]) ).
thf(404,plain,
( ( ! [V_r: $i,V_y: $i,V_xa: $i,T_a: $i,V_x: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ V_xa ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ V_r @ T_a ) @ ( c_List_Olist_OCons @ V_y @ V_x @ T_a ) ) @ ( c_List_Olist_OCons @ V_xa @ V_x @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[197]) ).
thf(405,plain,
( ( ! [V_r: $i,T_a: $i,V_ys: $i,V_xs: $i,V_y: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ V_r @ T_a ) @ V_ys ) @ V_xs ) )
| ( V_xs = V_ys )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ V_r @ T_a ) @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[198]) ).
thf(406,plain,
( ( ! [T_a: $i,V_a_H: $i,V_list_H: $i] :
( ( c_List_Olist_ONil @ T_a )
!= ( c_List_Olist_OCons @ V_a_H @ V_list_H @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[199]) ).
thf(407,plain,
( ( ! [V_a: $i,V_list: $i,T_a: $i,V_a_H: $i,V_list_H: $i] :
( ( ( c_List_Olist_OCons @ V_a @ V_list @ T_a )
!= ( c_List_Olist_OCons @ V_a_H @ V_list_H @ T_a ) )
| ( V_a = V_a_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[200]) ).
thf(408,plain,
( ( ! [V_a: $i,V_list: $i,T_a: $i,V_a_H: $i,V_list_H: $i] :
( ( ( c_List_Olist_OCons @ V_a @ V_list @ T_a )
!= ( c_List_Olist_OCons @ V_a_H @ V_list_H @ T_a ) )
| ( V_list = V_list_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[201]) ).
thf(409,plain,
( ( ! [V_r: $i,T_a: $i,V_ys: $i,V_xs: $i,V_y: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ V_r @ T_a ) @ V_ys ) @ V_xs ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ V_r @ T_a ) @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[202]) ).
thf(410,plain,
( ( ! [V_r: $i,T_a: $i,V_x: $i,V_ys: $i,V_xs: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ V_r @ T_a ) @ ( c_List_Olist_OCons @ V_x @ V_ys @ T_a ) ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ V_r @ T_a ) @ V_ys ) @ V_xs ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[203]) ).
thf(411,plain,
( ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ v_t ) ) )
= $true ),
inference(unfold_def,[status(thm)],[206]) ).
thf(412,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[207]) ).
thf(413,plain,
( ( ! [V_X: $i,V_Y: $i] :
( ( V_X = V_Y )
| ! [T_a: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ T_a ) @ V_X ) @ V_Y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[208]) ).
thf(414,plain,
( ( ! [V_P: $i,V_a: $i,V_y: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ( hBOOL @ ( hAPP @ V_P @ V_y ) )
| ! [V_r: $i,T_a: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__rule__1__1 @ V_P @ V_r @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ T_a ) @ V_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[225]) ).
thf(415,plain,
( ( ! [V_P: $i,V_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ! [V_r: $i,T_a: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__rule__1__1 @ V_P @ V_r @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ T_a ) @ V_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[226]) ).
thf(416,plain,
( ( ! [V_P: $i,V_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ! [V_r: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ T_a ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__rule__1__1 @ V_P @ V_r @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ T_a ) @ V_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[228]) ).
thf(417,plain,
( ( ! [V_P: $i,V_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ! [V_r: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ T_a ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__1__1 @ V_P @ V_r @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ T_a ) @ V_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[235]) ).
thf(418,plain,
( ( ! [V_P: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ! [V_r: $i,V_ya: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ t_a ) @ V_ya ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_ya ) @ ( v_sko__Wellfounded__Xaccp__Xinduct__1 @ V_P @ V_r ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ t_a ) @ V_x ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[239]) ).
thf(419,plain,
( ( ! [V_P: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ! [V_r: $i,V_ya: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ t_a ) @ V_ya ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_ya ) @ ( v_sko__Wellfounded__Xaccp__Xinducts__1 @ V_P @ V_r ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ t_a ) @ V_x ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[240]) ).
thf(420,plain,
( ( ! [V_r: $i,V_b: $i,V_a: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_b ) @ V_a ) )
| ! [T_a: $i,T_b: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ V_r @ T_a @ T_b ) @ V_a ) @ V_b ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[241]) ).
thf(421,plain,
( ( ! [V_r: $i,V_a2: $i,V_a1: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_a2 ) @ V_a1 ) )
| ! [T_a: $i,T_b: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ V_r @ T_a @ T_b ) @ V_a1 ) @ V_a2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[243]) ).
thf(422,plain,
( ( ! [V_P: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ! [V_y: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_y ) )
| ! [V_r: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ ( v_sko__Wellfounded__Xaccp__Xinduct__1 @ V_P @ V_r ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ t_a ) @ V_x ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[245]) ).
thf(423,plain,
( ( ! [V_P: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ! [V_r: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( v_sko__Wellfounded__Xaccp__Xinduct__1 @ V_P @ V_r ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ t_a ) @ V_x ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[246]) ).
thf(424,plain,
( ( ! [V_P: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ! [V_y: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_y ) )
| ! [V_r: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ ( v_sko__Wellfounded__Xaccp__Xinducts__1 @ V_P @ V_r ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ t_a ) @ V_x ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[248]) ).
thf(425,plain,
( ( ! [V_P: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ! [V_r: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( v_sko__Wellfounded__Xaccp__Xinducts__1 @ V_P @ V_r ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ t_a ) @ V_x ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[249]) ).
thf(426,plain,
( ( ! [V_r: $i,T_a: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ T_a ) @ V_b ) )
| ! [V_a: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_b ) @ V_a ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ T_a ) @ V_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[251]) ).
thf(427,plain,
( ( ! [V_r: $i,T_a: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ T_a ) @ V_b ) )
| ! [V_a: $i] :
( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ T_a ) @ V_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_b ) @ V_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[252]) ).
thf(428,plain,
( ( ! [V_r: $i,T_a: $i] :
( ! [V_x: $i] : ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ T_a ) @ V_x ) )
| ~ ( c_Wellfounded_OwfP @ V_r @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[263]) ).
thf(429,plain,
( ( ! [V_e: $i,V_t_H: $i,V_T: $i] :
( ( c_Type_Otyping @ V_e @ V_t_H @ V_T )
| ! [V_t: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_t ) @ V_t_H ) )
| ~ ( c_Type_Otyping @ V_e @ V_t @ V_T ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[264]) ).
thf(430,plain,
( ( ! [V_P: $i,V_a: $i,V_y: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ( hBOOL @ ( hAPP @ V_P @ V_y ) )
| ! [V_r: $i,T_a: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__1__1 @ V_P @ V_r @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ T_a ) @ V_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[266]) ).
thf(431,plain,
( ( ! [V_P: $i,V_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ! [V_r: $i,T_a: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__1__1 @ V_P @ V_r @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ T_a ) @ V_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[267]) ).
thf(432,plain,
( ( ! [V_r: $i,T_a: $i,V_y: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ T_a ) @ V_y ) )
| ! [V_a: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ V_a ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ T_a ) @ V_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[268]) ).
thf(433,plain,
( ( ! [V_r: $i,T_a: $i,V_a: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ T_a ) @ V_a ) )
| ! [V_b: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_a ) @ V_b ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ T_a ) @ V_b ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[269]) ).
thf(434,plain,
( ( ! [V_r: $i,T_a: $i,V_a: $i,V_c: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ V_r @ T_a ) @ V_a ) @ V_c ) )
| ! [V_b: $i] :
( ~ ( 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(extcnf_combined,[status(esa)],[270]) ).
thf(435,plain,
( ( ! [V_r: $i,T_a: $i,V_a: $i,V_c: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ V_r @ T_a ) @ V_a ) @ V_c ) )
| ! [V_b: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_b ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ V_r @ T_a ) @ V_a ) @ V_b ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[271]) ).
thf(436,plain,
( ( ! [V_r: $i,T_a: $i,V_a: $i,V_c: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_a ) @ V_c ) )
| ! [V_b: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_b ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_a ) @ V_b ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[272]) ).
thf(437,plain,
( ( ! [V_r: $i,T_a: $i,V_a: $i,V_c: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_a ) @ V_c ) )
| ! [V_b: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_b ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_a ) @ V_b ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[273]) ).
thf(438,plain,
( ( ! [V_dB_H: $i,V_nat: $i] :
( ( c_Lambda_OdB_OAbs @ V_dB_H )
!= ( c_Lambda_OdB_OVar @ V_nat ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[276]) ).
thf(439,plain,
( ( ! [V_dB1: $i,V_dB2: $i,V_dB_H: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1 ) @ V_dB2 )
!= ( c_Lambda_OdB_OAbs @ V_dB_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[277]) ).
thf(440,plain,
( ( ! [V_nat: $i,V_nat_H: $i] :
( ( ( c_Lambda_OdB_OVar @ V_nat )
!= ( c_Lambda_OdB_OVar @ V_nat_H ) )
| ( V_nat = V_nat_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[278]) ).
thf(441,plain,
( ( ! [V_r: $i,T_a: $i,V_x: $i,V_z: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ V_r @ T_a ) @ V_x ) @ V_z ) )
| ! [V_y: $i] :
( ~ ( 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(extcnf_combined,[status(esa)],[279]) ).
thf(442,plain,
( ( ! [V_dB_H: $i,V_dB1: $i,V_dB2: $i] :
( ( c_Lambda_OdB_OAbs @ V_dB_H )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1 ) @ V_dB2 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[280]) ).
thf(443,plain,
( ( ! [V_m: $i,V_rs: $i,V_n: $i] :
( ! [V_ss: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_m ) @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_m = V_n ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[281]) ).
thf(444,plain,
( ( ! [V_m: $i,V_rs: $i,V_n: $i,V_ss: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_m ) @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_rs = V_ss ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[282]) ).
thf(445,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_x: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_x @ T_a )
= V_x ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[284]) ).
thf(446,plain,
( ( ! [V_r: $i] :
( ! [V_i: $i,V_j: $i] : ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ V_r @ ( c_Lambda_OdB_OVar @ V_i ) @ V_j ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_r ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[286]) ).
thf(447,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[287]) ).
thf(448,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[288]) ).
thf(449,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ T_a )
| ! [V_y: $i,V_z: $i] :
( ( 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(extcnf_combined,[status(esa)],[289]) ).
thf(450,plain,
( ( ! [T_a: $i,V_y: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ T_a )
| ! [V_z: $i,V_x: $i] :
( ( 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(extcnf_combined,[status(esa)],[290]) ).
thf(451,plain,
( ( ! [V_s: $i,V_ss: $i,V_r: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ V_r ) )
| ( V_s
= ( c_Lambda_OdB_OAbs @ V_r ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[295]) ).
thf(452,plain,
( ( ! [V_r: $i,V_rs: $i,V_s: $i] :
( ! [V_ss: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_r ) @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_s ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_r = V_s ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[296]) ).
thf(453,plain,
( ( ! [V_r: $i,V_rs: $i,V_s: $i,V_ss: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_r ) @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_s ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_rs = V_ss ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[297]) ).
thf(454,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ T_a )
= V_x ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[298]) ).
thf(455,plain,
( ( ! [V_dB1: $i,V_dB2: $i,V_dB1_H: $i] :
( ! [V_dB2_H: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1 ) @ V_dB2 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1_H ) @ V_dB2_H ) )
| ( V_dB1 = V_dB1_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[299]) ).
thf(456,plain,
( ( ! [V_dB1: $i,V_dB2: $i,V_dB1_H: $i,V_dB2_H: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1 ) @ V_dB2 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1_H ) @ V_dB2_H ) )
| ( V_dB2 = V_dB2_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[300]) ).
thf(457,plain,
( ( ! [V_T: $i,V_U: $i,V_e: $i] :
( ( V_T = V_U )
| ! [V_i: $i,V_ts: $i] :
( ~ ( c_Type_Otyping @ V_e @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_i ) @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_U )
| ~ ( c_Type_Otyping @ V_e @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_i ) @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_T ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[301]) ).
thf(458,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( 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(extcnf_combined,[status(esa)],[303]) ).
thf(459,plain,
( ( ! [V_m: $i,V_s: $i] :
( ! [V_ss: $i] :
( ( c_Lambda_OdB_OVar @ V_m )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OVar @ V_m )
= V_s ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[305]) ).
thf(460,plain,
( ( ! [V_nat: $i,V_dB1_H: $i,V_dB2_H: $i] :
( ( c_Lambda_OdB_OVar @ V_nat )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1_H ) @ V_dB2_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[306]) ).
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(extcnf_combined,[status(esa)],[307]) ).
thf(462,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_y: $i,V_z: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ V_z @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[308]) ).
thf(463,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_y: $i,V_z: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[309]) ).
thf(464,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_y: $i,V_z: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[310]) ).
thf(465,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_y: $i,V_z: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ V_z @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[311]) ).
thf(466,plain,
( ( ! [V_n: $i,V_ts: $i,V_r: $i,V_ss: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_r ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[312]) ).
thf(467,plain,
( ( ! [V_t: $i] :
( ! [V_i: $i] : ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Olift @ V_t @ V_i ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_t ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[313]) ).
thf(468,plain,
( ( ! [V_B: $i,V_x: $i,V_y: $i,V_A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_B @ V_x ) @ V_y ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ V_A @ V_x ) @ V_y ) )
| ! [T_a: $i,T_b: $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 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[317]) ).
thf(469,plain,
( ( ! [V_nat: $i,V_dB_H: $i] :
( ( c_Lambda_OdB_OVar @ V_nat )
!= ( c_Lambda_OdB_OAbs @ V_dB_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[319]) ).
thf(470,plain,
( ( ! [V_r: $i,T_a: $i,V_a: $i,V_c: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ V_r @ T_a ) @ V_a ) @ V_c ) )
| ! [V_b: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_b ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_a ) @ V_b ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[325]) ).
thf(471,plain,
( ( ! [V_r: $i,T_a: $i,V_a: $i,V_c: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ V_r @ T_a ) @ V_a ) @ V_c ) )
| ! [V_b: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_b ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_a ) @ V_b ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[326]) ).
thf(472,plain,
( ( ! [V_r: $i,T_a: $i,V_x: $i,V_z: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_x ) @ V_z ) )
| ! [V_y: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_y ) @ V_z ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_x ) @ V_y ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[327]) ).
thf(473,plain,
( ( ! [V_r: $i,T_a: $i,V_x: $i,V_z: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ V_r @ T_a ) @ V_x ) @ V_z ) )
| ! [V_y: $i] :
( ~ ( 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(extcnf_combined,[status(esa)],[330]) ).
thf(474,plain,
( ( ! [V_r: $i,T_a: $i,V_a: $i,V_c: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ V_r @ T_a ) @ V_a ) @ V_c ) )
| ! [V_b: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_b ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ V_r @ T_a ) @ V_a ) @ V_b ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[331]) ).
thf(475,plain,
( ( ! [V_r: $i,V_s: $i,T_a: $i,T_b: $i,T_c: $i,V_a: $i,V_c: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ V_r @ V_s @ T_a @ T_b @ T_c ) @ V_a ) @ V_c ) )
| ! [V_b: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_s @ V_b ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_a ) @ V_b ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[332]) ).
thf(476,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ T_a )
| ! [V_y: $i,V_z: $i] :
( ( 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(extcnf_combined,[status(esa)],[333]) ).
thf(477,plain,
( ( ! [T_a: $i,V_y: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ T_a )
| ! [V_z: $i,V_x: $i] :
( ( 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(extcnf_combined,[status(esa)],[334]) ).
thf(478,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_x: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_x @ T_a )
= V_x ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[335]) ).
thf(479,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_y: $i,V_z: $i] :
( ( 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(extcnf_combined,[status(esa)],[336]) ).
thf(480,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_y: $i,V_z: $i] :
( ( 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(extcnf_combined,[status(esa)],[337]) ).
thf(481,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_y: $i,V_z: $i] :
( ( 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(extcnf_combined,[status(esa)],[338]) ).
thf(482,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_y: $i,V_z: $i] :
( ( 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(extcnf_combined,[status(esa)],[339]) ).
thf(483,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[340]) ).
thf(484,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[341]) ).
thf(485,plain,
( ( ! [V_r: $i,V_s: $i] :
( ! [V_ss: $i] :
( ( c_Lambda_OdB_OAbs @ V_r )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OAbs @ V_r )
= V_s ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[343]) ).
thf(486,plain,
( ( ! [V_r: $i,V_ts: $i,V_s: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_r @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_r = V_s ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[344]) ).
thf(487,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( 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(extcnf_combined,[status(esa)],[346]) ).
thf(488,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( 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(extcnf_combined,[status(esa)],[347]) ).
thf(489,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( 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(extcnf_combined,[status(esa)],[348]) ).
thf(490,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( 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(extcnf_combined,[status(esa)],[349]) ).
thf(491,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(extcnf_combined,[status(esa)],[352]) ).
thf(492,plain,
( ( ! [V_B: $i,V_x: $i,V_y: $i,V_A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_B @ V_x ) @ V_y ) )
| ! [T_a: $i,T_b: $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 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[353]) ).
thf(493,plain,
( ( ! [V_A: $i,V_x: $i,V_y: $i,V_B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_A @ V_x ) @ V_y ) )
| ! [T_a: $i,T_b: $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 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[354]) ).
thf(494,plain,
( ( ! [V_s: $i,V_t: $i,V_n: $i,V_ss: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_s ) ) @ V_t )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[355]) ).
thf(495,plain,
( ( ! [V_t: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_t ) )
| ! [V_e: $i,V_T: $i] :
~ ( c_Type_Otyping @ V_e @ V_t @ V_T ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[356]) ).
thf(496,plain,
( ( ! [V_dB1_H: $i,V_dB2_H: $i,V_nat: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1_H ) @ V_dB2_H )
!= ( c_Lambda_OdB_OVar @ V_nat ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[358]) ).
thf(497,plain,
( ( ! [V_t: $i,V_u: $i,V_i: $i,V_e: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ V_t @ V_u @ V_i ) ) )
| ! [V_U: $i] :
( ~ ( c_Type_Otyping @ V_e @ V_u @ V_U )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_u ) )
| ! [V_T: $i] :
~ ( 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(extcnf_combined,[status(esa)],[361]) ).
thf(498,plain,
( ( ! [V_m: $i,V_s: $i,V_ss: $i] :
( ( ( c_Lambda_OdB_OVar @ V_m )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_ss
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[363]) ).
thf(499,plain,
( ( ! [V_r: $i,V_s: $i,V_ss: $i] :
( ( ( c_Lambda_OdB_OAbs @ V_r )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_ss
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[364]) ).
thf(500,plain,
( ( ! [V_s: $i,V_ss: $i] :
( ! [V_r: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ V_r ) )
| ( V_ss
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[366]) ).
thf(501,plain,
( ( ! [V_r: $i,V_s: $i,V_t: $i,V_ts: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_r ) @ V_s )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_r
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ V_r @ V_s @ V_t @ V_ts ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_ts
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[370]) ).
thf(502,plain,
( ( ! [V_r: $i,V_s: $i,V_t: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_r ) @ V_s )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_r ) @ V_s )
= V_t ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[383]) ).
thf(503,plain,
( ( ! [V_e: $i,V_t_H: $i,V_T: $i] :
( ( c_Type_Otyping @ V_e @ V_t_H @ V_T )
| ! [V_t: $i] :
( ~ ( c_Type_Otyping @ V_e @ V_t @ V_T )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_t ) @ V_t_H ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[389]) ).
thf(504,plain,
( ( ! [V_e_H: $i,V_u: $i,V_U: $i,V_i: $i] :
( ~ ( c_Type_Otyping @ V_e_H @ V_u @ V_U )
| ! [V_t: $i,V_T: $i] :
( ~ ( 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(extcnf_combined,[status(esa)],[390]) ).
thf(505,plain,
( ( ! [V_env: $i,V_s: $i,V_t: $i,V_U: $i] :
( ( c_Type_Otyping @ V_env @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_t ) @ V_U )
| ! [V_T: $i] :
( ~ ( 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(extcnf_combined,[status(esa)],[393]) ).
thf(506,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(extcnf_combined,[status(esa)],[394]) ).
thf(507,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(extcnf_combined,[status(esa)],[395]) ).
thf(508,plain,
( ( ! [V_xs: $i,V_x: $i,T_a: $i] :
( V_xs
!= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[397]) ).
thf(509,plain,
( ( ! [V_x: $i,V_t: $i,T_a: $i] :
( ( c_List_Olist_OCons @ V_x @ V_t @ T_a )
!= V_t ) )
= $true ),
inference(extcnf_combined,[status(esa)],[398]) ).
thf(510,plain,
( ( ! [V_x: $i,V_y: $i,V_r: $i,T_a: $i] :
( ( V_x = V_y )
| ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ V_x ) )
| ! [V_ys: $i,V_xs: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ V_r @ T_a ) @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[399]) ).
thf(511,plain,
( ( ! [V_a_H: $i,V_list_H: $i,T_a: $i] :
( ( c_List_Olist_OCons @ V_a_H @ V_list_H @ T_a )
!= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[400]) ).
thf(512,plain,
( ( ! [V_x: $i,V_xa: $i,T_a: $i] :
( ( c_List_Olist_OCons @ V_x @ V_xa @ T_a )
!= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[401]) ).
thf(513,plain,
( ( ! [V_x: $i,V_y: $i,V_xs: $i,V_ys: $i] :
( ( V_x = V_y )
| ( V_xs = V_ys )
| ! [V_r: $i,T_a: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ V_r @ T_a ) @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[403]) ).
thf(514,plain,
( ( ! [V_r: $i,V_y: $i,V_xa: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ V_xa ) )
| ! [T_a: $i,V_x: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ V_r @ T_a ) @ ( c_List_Olist_OCons @ V_y @ V_x @ T_a ) ) @ ( c_List_Olist_OCons @ V_xa @ V_x @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[404]) ).
thf(515,plain,
( ( ! [V_r: $i,T_a: $i,V_ys: $i,V_xs: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ V_r @ T_a ) @ V_ys ) @ V_xs ) )
| ( V_xs = V_ys )
| ! [V_y: $i,V_x: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ V_r @ T_a ) @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[405]) ).
thf(516,plain,
( ( ! [T_a: $i,V_a_H: $i,V_list_H: $i] :
( ( c_List_Olist_ONil @ T_a )
!= ( c_List_Olist_OCons @ V_a_H @ V_list_H @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[406]) ).
thf(517,plain,
( ( ! [V_a: $i,V_list: $i,T_a: $i,V_a_H: $i] :
( ! [V_list_H: $i] :
( ( c_List_Olist_OCons @ V_a @ V_list @ T_a )
!= ( c_List_Olist_OCons @ V_a_H @ V_list_H @ T_a ) )
| ( V_a = V_a_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[407]) ).
thf(518,plain,
( ( ! [V_a: $i,V_list: $i,T_a: $i,V_a_H: $i,V_list_H: $i] :
( ( ( c_List_Olist_OCons @ V_a @ V_list @ T_a )
!= ( c_List_Olist_OCons @ V_a_H @ V_list_H @ T_a ) )
| ( V_list = V_list_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[408]) ).
thf(519,plain,
( ( ! [V_r: $i,T_a: $i,V_ys: $i,V_xs: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ V_r @ T_a ) @ V_ys ) @ V_xs ) )
| ! [V_y: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ V_r @ T_a ) @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[409]) ).
thf(520,plain,
( ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ v_t ) ) )
= $true ),
inference(copy,[status(thm)],[411]) ).
thf(521,plain,
( ( ! [V_r: $i,T_a: $i,V_x: $i,V_ys: $i,V_xs: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ V_r @ T_a ) @ ( c_List_Olist_OCons @ V_x @ V_ys @ T_a ) ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ V_r @ T_a ) @ V_ys ) @ V_xs ) ) ) )
= $true ),
inference(copy,[status(thm)],[410]) ).
thf(522,plain,
( ( ! [V_r: $i,T_a: $i,V_ys: $i,V_xs: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ V_r @ T_a ) @ V_ys ) @ V_xs ) )
| ! [V_y: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ V_r @ T_a ) @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[519]) ).
thf(523,plain,
( ( ! [V_a: $i,V_list: $i,T_a: $i,V_a_H: $i,V_list_H: $i] :
( ( ( c_List_Olist_OCons @ V_a @ V_list @ T_a )
!= ( c_List_Olist_OCons @ V_a_H @ V_list_H @ T_a ) )
| ( V_list = V_list_H ) ) )
= $true ),
inference(copy,[status(thm)],[518]) ).
thf(524,plain,
( ( ! [V_a: $i,V_list: $i,T_a: $i,V_a_H: $i] :
( ! [V_list_H: $i] :
( ( c_List_Olist_OCons @ V_a @ V_list @ T_a )
!= ( c_List_Olist_OCons @ V_a_H @ V_list_H @ T_a ) )
| ( V_a = V_a_H ) ) )
= $true ),
inference(copy,[status(thm)],[517]) ).
thf(525,plain,
( ( ! [T_a: $i,V_a_H: $i,V_list_H: $i] :
( ( c_List_Olist_ONil @ T_a )
!= ( c_List_Olist_OCons @ V_a_H @ V_list_H @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[516]) ).
thf(526,plain,
( ( ! [V_r: $i,T_a: $i,V_ys: $i,V_xs: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ V_r @ T_a ) @ V_ys ) @ V_xs ) )
| ( V_xs = V_ys )
| ! [V_y: $i,V_x: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ V_r @ T_a ) @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[515]) ).
thf(527,plain,
( ( ! [V_r: $i,V_y: $i,V_xa: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ V_xa ) )
| ! [T_a: $i,V_x: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ V_r @ T_a ) @ ( c_List_Olist_OCons @ V_y @ V_x @ T_a ) ) @ ( c_List_Olist_OCons @ V_xa @ V_x @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[514]) ).
thf(528,plain,
( ( ! [V_x: $i,V_y: $i,V_xs: $i,V_ys: $i] :
( ( V_x = V_y )
| ( V_xs = V_ys )
| ! [V_r: $i,T_a: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ V_r @ T_a ) @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[513]) ).
thf(529,plain,
( ( ! [V_f: $i,V_a: $i,V_x: $i,V_xs: $i,T_b: $i,T_a: $i] :
( ( c_List_Ofoldl @ V_f @ V_a @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_b ) @ T_a @ T_b )
= ( c_List_Ofoldl @ V_f @ ( hAPP @ ( hAPP @ V_f @ V_a ) @ V_x ) @ V_xs @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[402]) ).
thf(530,plain,
( ( ! [V_x: $i,V_xa: $i,T_a: $i] :
( ( c_List_Olist_OCons @ V_x @ V_xa @ T_a )
!= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[512]) ).
thf(531,plain,
( ( ! [V_a_H: $i,V_list_H: $i,T_a: $i] :
( ( c_List_Olist_OCons @ V_a_H @ V_list_H @ T_a )
!= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[511]) ).
thf(532,plain,
( ( ! [V_x: $i,V_y: $i,V_r: $i,T_a: $i] :
( ( V_x = V_y )
| ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ V_x ) )
| ! [V_ys: $i,V_xs: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ V_r @ T_a ) @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[510]) ).
thf(533,plain,
( ( ! [V_x: $i,V_t: $i,T_a: $i] :
( ( c_List_Olist_OCons @ V_x @ V_t @ T_a )
!= V_t ) )
= $true ),
inference(copy,[status(thm)],[509]) ).
thf(534,plain,
( ( ! [V_xs: $i,V_x: $i,T_a: $i] :
( V_xs
!= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[508]) ).
thf(535,plain,
( ( ! [V_r: $i,T_a: $i,V_x: $i,V_xs: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( c_ListOrder_Ostep1 @ V_r @ T_a ) @ ( tc_List_Olist @ T_a ) ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( c_ListOrder_Ostep1 @ V_r @ T_a ) @ ( tc_List_Olist @ T_a ) ) @ V_xs ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ T_a ) @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[396]) ).
thf(536,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)],[507]) ).
thf(537,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)],[506]) ).
thf(538,plain,
( ( ! [V_env: $i,V_s: $i,V_t: $i,V_U: $i] :
( ( c_Type_Otyping @ V_env @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_t ) @ V_U )
| ! [V_T: $i] :
( ~ ( 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)],[505]) ).
thf(539,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)],[392]) ).
thf(540,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)],[391]) ).
thf(541,plain,
( ( ! [V_e_H: $i,V_u: $i,V_U: $i,V_i: $i] :
( ~ ( c_Type_Otyping @ V_e_H @ V_u @ V_U )
| ! [V_t: $i,V_T: $i] :
( ~ ( 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)],[504]) ).
thf(542,plain,
( ( ! [V_e: $i,V_t_H: $i,V_T: $i] :
( ( c_Type_Otyping @ V_e @ V_t_H @ V_T )
| ! [V_t: $i] :
( ~ ( c_Type_Otyping @ V_e @ V_t @ V_T )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_t ) @ V_t_H ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[503]) ).
thf(543,plain,
( ( ! [V_rs: $i,V_n: $i,V_v: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_rs ) @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ V_n @ V_rs @ V_v ) ) )
| ~ ( 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)],[388]) ).
thf(544,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)],[387]) ).
thf(545,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)],[386]) ).
thf(546,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)],[385]) ).
thf(547,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)],[384]) ).
thf(548,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)],[502]) ).
thf(549,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)],[382]) ).
thf(550,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)],[381]) ).
thf(551,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)],[380]) ).
thf(552,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)],[379]) ).
thf(553,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)],[378]) ).
thf(554,plain,
( ( ! [V_r: $i,T_a: $i,V_xs: $i] :
( ( c_List_Olistsp @ ( c_Wellfounded_Oaccp @ V_r @ T_a ) @ V_xs @ T_a )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( c_ListOrder_Ostep1 @ V_r @ T_a ) @ ( tc_List_Olist @ T_a ) ) @ V_xs ) ) ) )
= $true ),
inference(copy,[status(thm)],[377]) ).
thf(555,plain,
( ( ! [V_r: $i,T_a: $i,V_xs: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( c_ListOrder_Ostep1 @ V_r @ T_a ) @ ( tc_List_Olist @ T_a ) ) @ V_xs ) )
| ~ ( c_List_Olistsp @ ( c_Wellfounded_Oaccp @ V_r @ T_a ) @ V_xs @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[376]) ).
thf(556,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)],[375]) ).
thf(557,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)],[374]) ).
thf(558,plain,
( ( ! [V_r: $i,T_a: $i,V_xs: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ V_r @ T_a ) @ V_xs ) @ ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[373]) ).
thf(559,plain,
( ( ! [V_r: $i,T_a: $i,V_xs: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ V_r @ T_a ) @ ( c_List_Olist_ONil @ T_a ) ) @ V_xs ) ) )
= $true ),
inference(copy,[status(thm)],[372]) ).
thf(560,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)],[371]) ).
thf(561,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)],[501]) ).
thf(562,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 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_rs ) @ V_ss ) ) ) )
= $true ),
inference(copy,[status(thm)],[369]) ).
thf(563,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)],[368]) ).
thf(564,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(565,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)],[500]) ).
thf(566,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)],[365]) ).
thf(567,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)],[499]) ).
thf(568,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)],[498]) ).
thf(569,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)],[362]) ).
thf(570,plain,
( ( ! [V_t: $i,V_u: $i,V_i: $i,V_e: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ V_t @ V_u @ V_i ) ) )
| ! [V_U: $i] :
( ~ ( c_Type_Otyping @ V_e @ V_u @ V_U )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_u ) )
| ! [V_T: $i] :
~ ( 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)],[497]) ).
thf(571,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)],[360]) ).
thf(572,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)],[359]) ).
thf(573,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)],[496]) ).
thf(574,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)],[357]) ).
thf(575,plain,
( ( ! [V_t: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_t ) )
| ! [V_e: $i,V_T: $i] :
~ ( c_Type_Otyping @ V_e @ V_t @ V_T ) ) )
= $true ),
inference(copy,[status(thm)],[495]) ).
thf(576,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)],[494]) ).
thf(577,plain,
( ( ! [V_A: $i,V_x: $i,V_y: $i,V_B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_A @ V_x ) @ V_y ) )
| ! [T_a: $i,T_b: $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 ) ) ) )
= $true ),
inference(copy,[status(thm)],[493]) ).
thf(578,plain,
( ( ! [V_B: $i,V_x: $i,V_y: $i,V_A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_B @ V_x ) @ V_y ) )
| ! [T_a: $i,T_b: $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 ) ) ) )
= $true ),
inference(copy,[status(thm)],[492]) ).
thf(579,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)],[491]) ).
thf(580,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)],[351]) ).
thf(581,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)],[350]) ).
thf(582,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( 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)],[490]) ).
thf(583,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( 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)],[489]) ).
thf(584,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( 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)],[488]) ).
thf(585,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( 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)],[487]) ).
thf(586,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)],[345]) ).
thf(587,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)],[486]) ).
thf(588,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)],[485]) ).
thf(589,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)],[342]) ).
thf(590,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[484]) ).
thf(591,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[483]) ).
thf(592,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_y: $i,V_z: $i] :
( ( 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)],[482]) ).
thf(593,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_y: $i,V_z: $i] :
( ( 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)],[481]) ).
thf(594,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_y: $i,V_z: $i] :
( ( 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)],[480]) ).
thf(595,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_y: $i,V_z: $i] :
( ( 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)],[479]) ).
thf(596,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_x: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_x @ T_a )
= V_x ) ) )
= $true ),
inference(copy,[status(thm)],[478]) ).
thf(597,plain,
( ( ! [T_a: $i,V_y: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ T_a )
| ! [V_z: $i,V_x: $i] :
( ( 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)],[477]) ).
thf(598,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ T_a )
| ! [V_y: $i,V_z: $i] :
( ( 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)],[476]) ).
thf(599,plain,
( ( ! [V_r: $i,V_s: $i,T_a: $i,T_b: $i,T_c: $i,V_a: $i,V_c: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ V_r @ V_s @ T_a @ T_b @ T_c ) @ V_a ) @ V_c ) )
| ! [V_b: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_s @ V_b ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_a ) @ V_b ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[475]) ).
thf(600,plain,
( ( ! [V_r: $i,T_a: $i,V_a: $i,V_c: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ V_r @ T_a ) @ V_a ) @ V_c ) )
| ! [V_b: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_b ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ V_r @ T_a ) @ V_a ) @ V_b ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[474]) ).
thf(601,plain,
( ( ! [V_r: $i,T_a: $i,V_x: $i,V_z: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ V_r @ T_a ) @ V_x ) @ V_z ) )
| ! [V_y: $i] :
( ~ ( 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)],[473]) ).
thf(602,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)],[329]) ).
thf(603,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)],[328]) ).
thf(604,plain,
( ( ! [V_r: $i,T_a: $i,V_x: $i,V_z: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_x ) @ V_z ) )
| ! [V_y: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_y ) @ V_z ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_x ) @ V_y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[472]) ).
thf(605,plain,
( ( ! [V_r: $i,T_a: $i,V_a: $i,V_c: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ V_r @ T_a ) @ V_a ) @ V_c ) )
| ! [V_b: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_b ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_a ) @ V_b ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[471]) ).
thf(606,plain,
( ( ! [V_r: $i,T_a: $i,V_a: $i,V_c: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ V_r @ T_a ) @ V_a ) @ V_c ) )
| ! [V_b: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_b ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_a ) @ V_b ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[470]) ).
thf(607,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)],[324]) ).
thf(608,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)],[323]) ).
thf(609,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)],[322]) ).
thf(610,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)],[321]) ).
thf(611,plain,
( ( ! [V_n: $i] : ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OVar @ V_n ) ) ) )
= $true ),
inference(copy,[status(thm)],[320]) ).
thf(612,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)],[469]) ).
thf(613,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)],[318]) ).
thf(614,plain,
( ( ! [V_B: $i,V_x: $i,V_y: $i,V_A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_B @ V_x ) @ V_y ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ V_A @ V_x ) @ V_y ) )
| ! [T_a: $i,T_b: $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 ) ) ) )
= $true ),
inference(copy,[status(thm)],[468]) ).
thf(615,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)],[316]) ).
thf(616,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)],[315]) ).
thf(617,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)],[314]) ).
thf(618,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)],[467]) ).
thf(619,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)],[466]) ).
thf(620,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_y: $i,V_z: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ V_z @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[465]) ).
thf(621,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_y: $i,V_z: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[464]) ).
thf(622,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_y: $i,V_z: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[463]) ).
thf(623,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_y: $i,V_z: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ V_z @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[462]) ).
thf(624,plain,
( ( ! [V_dB: $i,V_dB_H: $i] :
( ( ( c_Lambda_OdB_OAbs @ V_dB )
!= ( c_Lambda_OdB_OAbs @ V_dB_H ) )
| ( V_dB = V_dB_H ) ) )
= $true ),
inference(copy,[status(thm)],[461]) ).
thf(625,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)],[460]) ).
thf(626,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)],[459]) ).
thf(627,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)],[304]) ).
thf(628,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( 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)],[458]) ).
thf(629,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)],[302]) ).
thf(630,plain,
( ( ! [V_T: $i,V_U: $i,V_e: $i] :
( ( V_T = V_U )
| ! [V_i: $i,V_ts: $i] :
( ~ ( c_Type_Otyping @ V_e @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_i ) @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_U )
| ~ ( c_Type_Otyping @ V_e @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_i ) @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_T ) ) ) )
= $true ),
inference(copy,[status(thm)],[457]) ).
thf(631,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)],[456]) ).
thf(632,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)],[455]) ).
thf(633,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ T_a )
= V_x ) ) )
= $true ),
inference(copy,[status(thm)],[454]) ).
thf(634,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)],[453]) ).
thf(635,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)],[452]) ).
thf(636,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)],[451]) ).
thf(637,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)],[294]) ).
thf(638,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)],[293]) ).
thf(639,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)],[292]) ).
thf(640,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)],[291]) ).
thf(641,plain,
( ( ! [T_a: $i,V_y: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ T_a )
| ! [V_z: $i,V_x: $i] :
( ( 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)],[450]) ).
thf(642,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ T_a )
| ! [V_y: $i,V_z: $i] :
( ( 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)],[449]) ).
thf(643,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[448]) ).
thf(644,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[447]) ).
thf(645,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)],[446]) ).
thf(646,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)],[285]) ).
thf(647,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_x: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_x @ T_a )
= V_x ) ) )
= $true ),
inference(copy,[status(thm)],[445]) ).
thf(648,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)],[283]) ).
thf(649,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)],[444]) ).
thf(650,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)],[443]) ).
thf(651,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)],[442]) ).
thf(652,plain,
( ( ! [V_r: $i,T_a: $i,V_x: $i,V_z: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ V_r @ T_a ) @ V_x ) @ V_z ) )
| ! [V_y: $i] :
( ~ ( 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)],[441]) ).
thf(653,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)],[440]) ).
thf(654,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)],[439]) ).
thf(655,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)],[438]) ).
thf(656,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)],[275]) ).
thf(657,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)],[274]) ).
thf(658,plain,
( ( ! [V_r: $i,T_a: $i,V_a: $i,V_c: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_a ) @ V_c ) )
| ! [V_b: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_b ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_a ) @ V_b ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[437]) ).
thf(659,plain,
( ( ! [V_r: $i,T_a: $i,V_a: $i,V_c: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_a ) @ V_c ) )
| ! [V_b: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_b ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_a ) @ V_b ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[436]) ).
thf(660,plain,
( ( ! [V_r: $i,T_a: $i,V_a: $i,V_c: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ V_r @ T_a ) @ V_a ) @ V_c ) )
| ! [V_b: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_b ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ V_r @ T_a ) @ V_a ) @ V_b ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[435]) ).
thf(661,plain,
( ( ! [V_r: $i,T_a: $i,V_a: $i,V_c: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ V_r @ T_a ) @ V_a ) @ V_c ) )
| ! [V_b: $i] :
( ~ ( 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)],[434]) ).
thf(662,plain,
( ( ! [V_r: $i,T_a: $i,V_a: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ T_a ) @ V_a ) )
| ! [V_b: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_a ) @ V_b ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ T_a ) @ V_b ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[433]) ).
thf(663,plain,
( ( ! [V_r: $i,T_a: $i,V_y: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ T_a ) @ V_y ) )
| ! [V_a: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ V_a ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ T_a ) @ V_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[432]) ).
thf(664,plain,
( ( ! [V_P: $i,V_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ! [V_r: $i,T_a: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__1__1 @ V_P @ V_r @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ T_a ) @ V_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[431]) ).
thf(665,plain,
( ( ! [V_P: $i,V_a: $i,V_y: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ( hBOOL @ ( hAPP @ V_P @ V_y ) )
| ! [V_r: $i,T_a: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__1__1 @ V_P @ V_r @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ T_a ) @ V_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[430]) ).
thf(666,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 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_R @ T_a ) @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[265]) ).
thf(667,plain,
( ( ! [V_e: $i,V_t_H: $i,V_T: $i] :
( ( c_Type_Otyping @ V_e @ V_t_H @ V_T )
| ! [V_t: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_t ) @ V_t_H ) )
| ~ ( c_Type_Otyping @ V_e @ V_t @ V_T ) ) ) )
= $true ),
inference(copy,[status(thm)],[429]) ).
thf(668,plain,
( ( ! [V_r: $i,T_a: $i] :
( ! [V_x: $i] : ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ T_a ) @ V_x ) )
| ~ ( c_Wellfounded_OwfP @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[428]) ).
thf(669,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)],[262]) ).
thf(670,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)],[261]) ).
thf(671,plain,
( ( ! [V_r: $i,T_a: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ T_a ) @ V_x ) )
| ( 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)],[260]) ).
thf(672,plain,
( ( ! [T_a: $i] :
( ( c_Predicate_Oconversep @ ( c_fequal @ T_a ) @ T_a @ T_a )
= ( c_fequal @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[259]) ).
thf(673,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)],[258]) ).
thf(674,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)],[257]) ).
thf(675,plain,
( ( ! [V_R: $i,T_a: $i,V_x: $i] :
( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_R @ T_a ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xnot__accp__down__1__1 @ V_R @ V_x @ T_a ) ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_R @ T_a ) @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[256]) ).
thf(676,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)],[255]) ).
thf(677,plain,
( ( ! [V_r: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_r ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ V_r ) ) ) )
= $true ),
inference(copy,[status(thm)],[254]) ).
thf(678,plain,
( ( ! [V_t: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ V_t ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_t ) ) ) )
= $true ),
inference(copy,[status(thm)],[253]) ).
thf(679,plain,
( ( ! [V_r: $i,T_a: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ T_a ) @ V_b ) )
| ! [V_a: $i] :
( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ T_a ) @ V_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_b ) @ V_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[427]) ).
thf(680,plain,
( ( ! [V_r: $i,T_a: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ T_a ) @ V_b ) )
| ! [V_a: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_b ) @ V_a ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ T_a ) @ V_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[426]) ).
thf(681,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)],[250]) ).
thf(682,plain,
( ( ! [V_P: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ! [V_r: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( v_sko__Wellfounded__Xaccp__Xinducts__1 @ V_P @ V_r ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ t_a ) @ V_x ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[425]) ).
thf(683,plain,
( ( ! [V_P: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ! [V_y: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_y ) )
| ! [V_r: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ ( v_sko__Wellfounded__Xaccp__Xinducts__1 @ V_P @ V_r ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ t_a ) @ V_x ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[424]) ).
thf(684,plain,
( ( ! [V_r: $i,V_s: $i,V_ss: $i] :
( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ 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 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ V_s ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ 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 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[247]) ).
thf(685,plain,
( ( ! [V_P: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ! [V_r: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( v_sko__Wellfounded__Xaccp__Xinduct__1 @ V_P @ V_r ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ t_a ) @ V_x ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[423]) ).
thf(686,plain,
( ( ! [V_P: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ! [V_y: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_y ) )
| ! [V_r: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ ( v_sko__Wellfounded__Xaccp__Xinduct__1 @ V_P @ V_r ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ t_a ) @ V_x ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[422]) ).
thf(687,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)],[244]) ).
thf(688,plain,
( ( ! [V_r: $i,V_a2: $i,V_a1: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_a2 ) @ V_a1 ) )
| ! [T_a: $i,T_b: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ V_r @ T_a @ T_b ) @ V_a1 ) @ V_a2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[421]) ).
thf(689,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)],[242]) ).
thf(690,plain,
( ( ! [V_r: $i,V_b: $i,V_a: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_b ) @ V_a ) )
| ! [T_a: $i,T_b: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ V_r @ T_a @ T_b ) @ V_a ) @ V_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[420]) ).
thf(691,plain,
( ( ! [V_P: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ! [V_r: $i,V_ya: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ t_a ) @ V_ya ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_ya ) @ ( v_sko__Wellfounded__Xaccp__Xinducts__1 @ V_P @ V_r ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ t_a ) @ V_x ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[419]) ).
thf(692,plain,
( ( ! [V_P: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ! [V_r: $i,V_ya: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ t_a ) @ V_ya ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_ya ) @ ( v_sko__Wellfounded__Xaccp__Xinduct__1 @ V_P @ V_r ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ t_a ) @ V_x ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[418]) ).
thf(693,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)],[238]) ).
thf(694,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)],[237]) ).
thf(695,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)],[236]) ).
thf(696,plain,
( ( ! [V_P: $i,V_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ! [V_r: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ T_a ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__1__1 @ V_P @ V_r @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ T_a ) @ V_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[417]) ).
thf(697,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)],[234]) ).
thf(698,plain,
( ( ! [V_r: $i,T_a: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ T_a ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ T_a ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__Xintros__1__1 @ V_r @ V_x @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[233]) ).
thf(699,plain,
( ( ! [V_r: $i,T_a: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ T_a ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ T_a ) @ ( c_ATP__Linkup_Osko__Wellfounded__XaccpI__1__1 @ V_r @ V_x @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[232]) ).
thf(700,plain,
( ( ! [V_r: $i,T_a: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ T_a ) @ V_x ) )
| ( 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)],[231]) ).
thf(701,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)],[230]) ).
thf(702,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)],[229]) ).
thf(703,plain,
( ( ! [V_P: $i,V_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ! [V_r: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ T_a ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__rule__1__1 @ V_P @ V_r @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ T_a ) @ V_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[416]) ).
thf(704,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)],[227]) ).
thf(705,plain,
( ( ! [V_P: $i,V_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ! [V_r: $i,T_a: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__rule__1__1 @ V_P @ V_r @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ T_a ) @ V_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[415]) ).
thf(706,plain,
( ( ! [V_P: $i,V_a: $i,V_y: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ( hBOOL @ ( hAPP @ V_P @ V_y ) )
| ! [V_r: $i,T_a: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__rule__1__1 @ V_P @ V_r @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ V_r @ T_a ) @ V_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[414]) ).
thf(707,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)],[224]) ).
thf(708,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)],[223]) ).
thf(709,plain,
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ v_t ) )
= $true ),
inference(copy,[status(thm)],[222]) ).
thf(710,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)],[221]) ).
thf(711,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)],[220]) ).
thf(712,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)],[219]) ).
thf(713,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)],[218]) ).
thf(714,plain,
( ( class_Lattices_Oupper__semilattice @ tc_nat )
= $true ),
inference(copy,[status(thm)],[217]) ).
thf(715,plain,
( ( class_Lattices_Olower__semilattice @ tc_nat )
= $true ),
inference(copy,[status(thm)],[216]) ).
thf(716,plain,
( ( class_Lattices_Odistrib__lattice @ tc_nat )
= $true ),
inference(copy,[status(thm)],[215]) ).
thf(717,plain,
( ( class_Lattices_Olattice @ tc_nat )
= $true ),
inference(copy,[status(thm)],[214]) ).
thf(718,plain,
( ( class_Lattices_Oupper__semilattice @ tc_bool )
= $true ),
inference(copy,[status(thm)],[213]) ).
thf(719,plain,
( ( class_Lattices_Olower__semilattice @ tc_bool )
= $true ),
inference(copy,[status(thm)],[212]) ).
thf(720,plain,
( ( class_Lattices_Odistrib__lattice @ tc_bool )
= $true ),
inference(copy,[status(thm)],[211]) ).
thf(721,plain,
( ( class_Lattices_Olattice @ tc_bool )
= $true ),
inference(copy,[status(thm)],[210]) ).
thf(722,plain,
( ( ! [T_a: $i,V_x: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ T_a ) @ V_x ) @ V_x ) ) )
= $true ),
inference(copy,[status(thm)],[209]) ).
thf(723,plain,
( ( ! [V_X: $i,V_Y: $i] :
( ( V_X = V_Y )
| ! [T_a: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ T_a ) @ V_X ) @ V_Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[413]) ).
thf(724,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[412]) ).
thf(725,plain,
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ v_t ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[520]) ).
thf(726,plain,
! [SV1: $i] :
( ( ! [SY689: $i,SY690: $i,SY691: $i,SY692: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ SV1 @ SY689 ) @ ( c_List_Olist_OCons @ SY690 @ SY691 @ SY689 ) ) @ ( c_List_Olist_OCons @ SY690 @ SY692 @ SY689 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ SV1 @ SY689 ) @ SY691 ) @ SY692 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[521]) ).
thf(727,plain,
! [SV2: $i] :
( ( ! [SY693: $i,SY694: $i,SY695: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ SV2 @ SY693 ) @ SY694 ) @ SY695 ) )
| ! [SY696: $i,SY697: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV2 @ SY696 ) @ SY697 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ SV2 @ SY693 ) @ ( c_List_Olist_OCons @ SY696 @ SY694 @ SY693 ) ) @ ( c_List_Olist_OCons @ SY697 @ SY695 @ SY693 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[522]) ).
thf(728,plain,
! [SV3: $i] :
( ( ! [SY698: $i,SY699: $i,SY700: $i,SY701: $i] :
( ( ( c_List_Olist_OCons @ SV3 @ SY698 @ SY699 )
!= ( c_List_Olist_OCons @ SY700 @ SY701 @ SY699 ) )
| ( SY698 = SY701 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[523]) ).
thf(729,plain,
! [SV4: $i] :
( ( ! [SY702: $i,SY703: $i,SY704: $i] :
( ! [SY705: $i] :
( ( c_List_Olist_OCons @ SV4 @ SY702 @ SY703 )
!= ( c_List_Olist_OCons @ SY704 @ SY705 @ SY703 ) )
| ( SV4 = SY704 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[524]) ).
thf(730,plain,
! [SV5: $i] :
( ( ! [SY706: $i,SY707: $i] :
( ( c_List_Olist_ONil @ SV5 )
!= ( c_List_Olist_OCons @ SY706 @ SY707 @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[525]) ).
thf(731,plain,
! [SV6: $i] :
( ( ! [SY708: $i,SY709: $i,SY710: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ SV6 @ SY708 ) @ SY709 ) @ SY710 ) )
| ( SY710 = SY709 )
| ! [SY711: $i,SY712: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ SV6 @ SY708 ) @ ( c_List_Olist_OCons @ SY711 @ SY709 @ SY708 ) ) @ ( c_List_Olist_OCons @ SY712 @ SY710 @ SY708 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[526]) ).
thf(732,plain,
! [SV7: $i] :
( ( ! [SY713: $i,SY714: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV7 @ SY713 ) @ SY714 ) )
| ! [SY715: $i,SY716: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ SV7 @ SY715 ) @ ( c_List_Olist_OCons @ SY713 @ SY716 @ SY715 ) ) @ ( c_List_Olist_OCons @ SY714 @ SY716 @ SY715 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[527]) ).
thf(733,plain,
! [SV8: $i] :
( ( ! [SY717: $i,SY718: $i,SY719: $i] :
( ( SV8 = SY717 )
| ( SY718 = SY719 )
| ! [SY720: $i,SY721: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ SY720 @ SY721 ) @ ( c_List_Olist_OCons @ SY717 @ SY719 @ SY721 ) ) @ ( c_List_Olist_OCons @ SV8 @ SY718 @ SY721 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[528]) ).
thf(734,plain,
! [SV9: $i] :
( ( ! [SY722: $i,SY723: $i,SY724: $i,SY725: $i,SY726: $i] :
( ( c_List_Ofoldl @ SV9 @ SY722 @ ( c_List_Olist_OCons @ SY723 @ SY724 @ SY725 ) @ SY726 @ SY725 )
= ( c_List_Ofoldl @ SV9 @ ( hAPP @ ( hAPP @ SV9 @ SY722 ) @ SY723 ) @ SY724 @ SY726 @ SY725 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[529]) ).
thf(735,plain,
! [SV10: $i] :
( ( ! [SY727: $i,SY728: $i] :
( ( c_List_Olist_OCons @ SV10 @ SY727 @ SY728 )
!= ( c_List_Olist_ONil @ SY728 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[530]) ).
thf(736,plain,
! [SV11: $i] :
( ( ! [SY729: $i,SY730: $i] :
( ( c_List_Olist_OCons @ SV11 @ SY729 @ SY730 )
!= ( c_List_Olist_ONil @ SY730 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[531]) ).
thf(737,plain,
! [SV12: $i] :
( ( ! [SY731: $i,SY732: $i,SY733: $i] :
( ( SV12 = SY731 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY732 @ SY731 ) @ SV12 ) )
| ! [SY734: $i,SY735: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ SY732 @ SY733 ) @ ( c_List_Olist_OCons @ SY731 @ SY734 @ SY733 ) ) @ ( c_List_Olist_OCons @ SV12 @ SY735 @ SY733 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[532]) ).
thf(738,plain,
! [SV13: $i] :
( ( ! [SY736: $i,SY737: $i] :
( ( c_List_Olist_OCons @ SV13 @ SY736 @ SY737 )
!= SY736 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[533]) ).
thf(739,plain,
! [SV14: $i] :
( ( ! [SY738: $i,SY739: $i] :
( SV14
!= ( c_List_Olist_OCons @ SY738 @ SV14 @ SY739 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[534]) ).
thf(740,plain,
! [SV15: $i] :
( ( ! [SY740: $i,SY741: $i,SY742: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( c_ListOrder_Ostep1 @ SV15 @ SY740 ) @ ( tc_List_Olist @ SY740 ) ) @ ( c_List_Olist_OCons @ SY741 @ SY742 @ SY740 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( c_ListOrder_Ostep1 @ SV15 @ SY740 ) @ ( tc_List_Olist @ SY740 ) ) @ SY742 ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV15 @ SY740 ) @ SY741 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[535]) ).
thf(741,plain,
! [SV16: $i] :
( ( ! [SY743: $i,SY744: $i,SY745: $i] :
( ( ( c_Type_Otype_OFun @ SV16 @ SY743 )
!= ( c_Type_Otype_OFun @ SY744 @ SY745 ) )
| ( SY743 = SY745 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[536]) ).
thf(742,plain,
! [SV17: $i] :
( ( ! [SY746: $i,SY747: $i] :
( ! [SY748: $i] :
( ( c_Type_Otype_OFun @ SV17 @ SY746 )
!= ( c_Type_Otype_OFun @ SY747 @ SY748 ) )
| ( SV17 = SY747 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[537]) ).
thf(743,plain,
! [SV18: $i] :
( ( ! [SY749: $i,SY750: $i,SY751: $i] :
( ( c_Type_Otyping @ SV18 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY749 ) @ SY750 ) @ SY751 )
| ! [SY752: $i] :
( ~ ( c_Type_Otyping @ SV18 @ SY750 @ SY752 )
| ~ ( c_Type_Otyping @ SV18 @ SY749 @ ( c_Type_Otype_OFun @ SY752 @ SY751 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[538]) ).
thf(744,plain,
! [SV19: $i] :
( ( ! [SY753: $i,SY754: $i,SY755: $i,SY756: $i] :
( ( c_Type_Otyping @ ( c_Type_Oshift @ SV19 @ SY753 @ SY754 @ tc_Type_Otype ) @ ( c_Lambda_Olift @ SY755 @ SY753 ) @ SY756 )
| ~ ( c_Type_Otyping @ SV19 @ SY755 @ SY756 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[539]) ).
thf(745,plain,
! [SV20: $i] :
( ( ! [SY757: $i,SY758: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Olift @ SV20 @ SY757 ) ) @ ( c_Lambda_Olift @ SY758 @ SY757 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV20 ) @ SY758 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[540]) ).
thf(746,plain,
! [SV21: $i] :
( ( ! [SY759: $i,SY760: $i,SY761: $i] :
( ~ ( c_Type_Otyping @ SV21 @ SY759 @ SY760 )
| ! [SY762: $i,SY763: $i] :
( ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV21 @ SY761 @ SY760 @ tc_Type_Otype ) @ SY762 @ SY763 )
| ( c_Type_Otyping @ SV21 @ ( c_Lambda_Osubst @ SY762 @ SY759 @ SY761 ) @ SY763 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[541]) ).
thf(747,plain,
! [SV22: $i] :
( ( ! [SY764: $i,SY765: $i] :
( ( c_Type_Otyping @ SV22 @ SY764 @ SY765 )
| ! [SY766: $i] :
( ~ ( c_Type_Otyping @ SV22 @ SY766 @ SY765 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SY766 ) @ SY764 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[542]) ).
thf(748,plain,
! [SV23: $i] :
( ( ! [SY767: $i,SY768: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV23 ) @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SY767 @ SV23 @ SY768 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY767 ) @ SV23 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SY768 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[543]) ).
thf(749,plain,
! [SV24: $i] :
( ( ! [SY769: $i,SY770: $i,SY771: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV24 @ SY769 @ SY770 ) ) @ ( c_Lambda_Osubst @ SV24 @ SY771 @ SY770 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SY769 ) @ SY771 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[544]) ).
thf(750,plain,
! [SV25: $i] :
( ( ! [SY772: $i,SY773: $i,SY774: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV25 @ SY772 @ SY773 ) ) @ ( c_Lambda_Osubst @ SY774 @ SY772 @ SY773 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV25 ) @ SY774 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[545]) ).
thf(751,plain,
! [SV26: $i] :
( ( ! [SY775: $i,SY776: $i,SY777: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV26 @ SY775 @ SY776 ) ) @ ( c_Lambda_Osubst @ SV26 @ SY777 @ SY776 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SY775 ) @ SY777 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[546]) ).
thf(752,plain,
! [SV27: $i] :
( ( ! [SY778: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV27 ) @ SY778 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV27 ) @ SY778 ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[547]) ).
thf(753,plain,
! [SV28: $i] :
( ( ! [SY779: $i,SY780: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV28 ) @ SY779 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY780 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV28 ) @ SY779 )
= SY780 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[548]) ).
thf(754,plain,
! [SV29: $i] :
( ( ! [SY781: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_OdB_OAbs @ SV29 ) ) @ ( c_Lambda_OdB_OAbs @ SY781 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV29 ) @ SY781 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[549]) ).
thf(755,plain,
! [SV30: $i] :
( ( ! [SY782: $i,SY783: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV30 ) @ SY782 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV30 ) @ SY783 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SY782 ) @ SY783 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[550]) ).
thf(756,plain,
! [SV31: $i] :
( ( ! [SY784: $i,SY785: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV31 ) @ SY784 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY785 ) @ SY784 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV31 ) @ SY785 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[551]) ).
thf(757,plain,
! [SV32: $i] :
( ( ! [SY786: $i,SY787: $i,SY788: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV32 ) @ SY786 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY787 ) @ SY788 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SY786 ) @ SY788 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV32 ) @ SY787 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[552]) ).
thf(758,plain,
! [SV33: $i] :
( ( ! [SY789: $i,SY790: $i,SY791: $i] :
( ( c_Type_Otyping @ SV33 @ ( c_Lambda_OdB_OAbs @ SY789 ) @ ( c_Type_Otype_OFun @ SY790 @ SY791 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV33 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY790 @ tc_Type_Otype ) @ SY789 @ SY791 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[553]) ).
thf(759,plain,
! [SV34: $i] :
( ( ! [SY792: $i,SY793: $i] :
( ( c_List_Olistsp @ ( c_Wellfounded_Oaccp @ SV34 @ SY792 ) @ SY793 @ SY792 )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( c_ListOrder_Ostep1 @ SV34 @ SY792 ) @ ( tc_List_Olist @ SY792 ) ) @ SY793 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[554]) ).
thf(760,plain,
! [SV35: $i] :
( ( ! [SY794: $i,SY795: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( c_ListOrder_Ostep1 @ SV35 @ SY794 ) @ ( tc_List_Olist @ SY794 ) ) @ SY795 ) )
| ~ ( c_List_Olistsp @ ( c_Wellfounded_Oaccp @ SV35 @ SY794 ) @ SY795 @ SY794 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[555]) ).
thf(761,plain,
! [SV36: $i] :
( ( ! [SY796: $i,SY797: $i,SY798: $i] :
( ( hAPP @ ( c_Type_Oshift @ SV36 @ SY796 @ SY797 @ SY798 ) @ SY796 )
= SY797 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[556]) ).
thf(762,plain,
! [SV37: $i] :
( ( ! [SY799: $i,SY800: $i,SY801: $i] :
( ( c_List_Ofoldl @ SV37 @ SY799 @ ( c_List_Olist_ONil @ SY800 ) @ SY801 @ SY800 )
= SY799 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[557]) ).
thf(763,plain,
! [SV38: $i] :
( ( ! [SY802: $i,SY803: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ SV38 @ SY802 ) @ SY803 ) @ ( c_List_Olist_ONil @ SY802 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[558]) ).
thf(764,plain,
! [SV39: $i] :
( ( ! [SY804: $i,SY805: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ SV39 @ SY804 ) @ ( c_List_Olist_ONil @ SY804 ) ) @ SY805 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[559]) ).
thf(765,plain,
! [SV40: $i] :
( ( ! [SY806: $i] : ( c_List_Olistsp @ SV40 @ ( c_List_Olist_ONil @ SY806 ) @ SY806 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[560]) ).
thf(766,plain,
! [SV41: $i] :
( ( ! [SY807: $i,SY808: $i,SY809: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV41 ) @ SY807 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY808 @ SY809 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV41
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY808 @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ SV41 @ SY807 @ SY808 @ SY809 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY809
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[561]) ).
thf(767,plain,
! [SV42: $i] :
( ( ! [SY810: $i,SY811: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV42 @ SY810 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV42 @ SY811 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SY810 ) @ SY811 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[562]) ).
thf(768,plain,
! [SV43: $i] :
( ( ! [SY812: $i,SY813: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV43 @ SY812 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY813 @ SY812 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV43 ) @ SY813 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[563]) ).
thf(769,plain,
! [SV44: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV44 ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_Lambda_OdB_OAbs @ SV44 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[564]) ).
thf(770,plain,
! [SV45: $i] :
( ( ! [SY814: $i] :
( ! [SY815: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV45 @ SY814 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SY815 ) )
| ( SY814
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[565]) ).
thf(771,plain,
! [SV46: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV46 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV46 ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[566]) ).
thf(772,plain,
! [SV47: $i] :
( ( ! [SY816: $i,SY817: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV47 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY816 @ SY817 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY817
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[567]) ).
thf(773,plain,
! [SV48: $i] :
( ( ! [SY818: $i,SY819: $i] :
( ( ( c_Lambda_OdB_OVar @ SV48 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY818 @ SY819 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY819
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[568]) ).
thf(774,plain,
! [SV49: $i] :
( ( ( c_Lambda_OdB_OVar @ SV49 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV49 ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[569]) ).
thf(775,plain,
! [SV50: $i] :
( ( ! [SY820: $i,SY821: $i,SY822: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV50 @ SY820 @ SY821 ) ) )
| ! [SY823: $i] :
( ~ ( c_Type_Otyping @ SY822 @ SY820 @ SY823 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SY820 ) )
| ! [SY824: $i] :
~ ( c_Type_Otyping @ ( c_Type_Oshift @ SY822 @ SY821 @ SY823 @ tc_Type_Otype ) @ SV50 @ SY824 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV50 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[570]) ).
thf(776,plain,
! [SV51: $i] :
( ( ! [SY825: $i,SY826: $i] :
( ( SV51
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY825 ) @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SY825 @ SY826 @ SV51 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY825 ) @ SY826 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV51 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[571]) ).
thf(777,plain,
! [SV52: $i] :
( ( ! [SY827: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV52 ) @ SY827 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( c_List_Olistsp @ c_InductTermi_OIT @ SY827 @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[572]) ).
thf(778,plain,
! [SV53: $i] :
( ( ! [SY828: $i,SY829: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV53 ) @ SY828 )
!= ( c_Lambda_OdB_OVar @ SY829 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[573]) ).
thf(779,plain,
! [SV54: $i] :
( ( ! [SY830: $i] :
( ( c_Transitive__Closure_Ortranclp @ ( c_Transitive__Closure_Ortranclp @ SV54 @ SY830 ) @ SY830 )
= ( c_Transitive__Closure_Ortranclp @ SV54 @ SY830 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[574]) ).
thf(780,plain,
! [SV55: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV55 ) )
| ! [SY831: $i,SY832: $i] :
~ ( c_Type_Otyping @ SY831 @ SV55 @ SY832 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[575]) ).
thf(781,plain,
! [SV56: $i] :
( ( ! [SY833: $i,SY834: $i,SY835: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV56 ) ) @ SY833 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY834 ) @ SY835 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[576]) ).
thf(782,plain,
! [SV57: $i] :
( ( ! [SY836: $i,SY837: $i,SY838: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV57 @ SY836 ) @ SY837 ) )
| ! [SY839: $i,SY840: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV57 @ SY838 @ ( tc_fun @ SY839 @ ( tc_fun @ SY840 @ tc_bool ) ) ) @ SY836 ) @ SY837 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[577]) ).
thf(783,plain,
! [SV58: $i] :
( ( ! [SY841: $i,SY842: $i,SY843: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV58 @ SY841 ) @ SY842 ) )
| ! [SY844: $i,SY845: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY843 @ SV58 @ ( tc_fun @ SY844 @ ( tc_fun @ SY845 @ tc_bool ) ) ) @ SY841 ) @ SY842 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[578]) ).
thf(784,plain,
! [SV59: $i] :
( ( ! [SY846: $i] : ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV59 ) @ ( c_Lambda_OdB_OVar @ SY846 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV59 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[579]) ).
thf(785,plain,
! [SV60: $i] :
( ( ! [SY847: $i,SY848: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_Olift @ SV60 @ SY847 ) @ SY848 @ SY847 )
= SV60 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[580]) ).
thf(786,plain,
! [SV61: $i] :
( ( ! [SY849: $i,SY850: $i,SY851: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV61 @ SY849 ) @ SY850 ) @ SY851 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV61 @ SY850 ) @ SY851 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[581]) ).
thf(787,plain,
! [SV62: $i] :
( ( ~ ( class_Lattices_Olattice @ SV62 )
| ! [SY852: $i,SY853: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY852 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY852 @ SY853 @ SV62 ) @ SV62 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY852 @ SY853 @ SV62 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[582]) ).
thf(788,plain,
! [SV63: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV63 )
| ! [SY854: $i,SY855: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY854 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY854 @ SY855 @ SV63 ) @ SV63 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY854 @ SY855 @ SV63 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[583]) ).
thf(789,plain,
! [SV64: $i] :
( ( ~ ( class_Lattices_Olattice @ SV64 )
| ! [SY856: $i,SY857: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY856 @ SY857 @ SV64 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY857 @ SY856 @ SV64 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[584]) ).
thf(790,plain,
! [SV65: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV65 )
| ! [SY858: $i,SY859: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY858 @ SY859 @ SV65 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY859 @ SY858 @ SV65 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[585]) ).
thf(791,plain,
! [SV66: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OAbs @ SV66 ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV66 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[586]) ).
thf(792,plain,
! [SV67: $i] :
( ( ! [SY860: $i,SY861: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV67 @ SY860 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY861 @ SY860 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV67 = SY861 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[587]) ).
thf(793,plain,
! [SV68: $i] :
( ( ! [SY862: $i] :
( ! [SY863: $i] :
( ( c_Lambda_OdB_OAbs @ SV68 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY862 @ SY863 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OAbs @ SV68 )
= SY862 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[588]) ).
thf(794,plain,
! [SV69: $i] :
( ( ! [SY864: $i] : ( c_Type_Otyping @ SV69 @ ( c_Lambda_OdB_OVar @ SY864 ) @ ( hAPP @ SV69 @ SY864 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[589]) ).
thf(795,plain,
! [SV70: $i] :
( ( ~ ( class_Lattices_Olattice @ SV70 )
| ! [SY865: $i,SY866: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY865 @ SY866 @ SV70 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY866 @ SY865 @ SV70 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[590]) ).
thf(796,plain,
! [SV71: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV71 )
| ! [SY867: $i,SY868: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY867 @ SY868 @ SV71 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY868 @ SY867 @ SV71 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[591]) ).
thf(797,plain,
! [SV72: $i] :
( ( ! [SY869: $i] :
( ~ ( class_Lattices_Olattice @ SV72 )
| ! [SY870: $i,SY871: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY869 @ SY870 @ SV72 ) @ SY871 @ SV72 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY869 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY870 @ SY871 @ SV72 ) @ SV72 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[592]) ).
thf(798,plain,
! [SV73: $i] :
( ( ! [SY872: $i] :
( ~ ( class_Lattices_Olattice @ SV73 )
| ! [SY873: $i,SY874: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY872 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY873 @ SY874 @ SV73 ) @ SV73 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY873 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY872 @ SY874 @ SV73 ) @ SV73 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[593]) ).
thf(799,plain,
! [SV74: $i] :
( ( ! [SY875: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV74 )
| ! [SY876: $i,SY877: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY875 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY876 @ SY877 @ SV74 ) @ SV74 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY876 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY875 @ SY877 @ SV74 ) @ SV74 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[594]) ).
thf(800,plain,
! [SV75: $i] :
( ( ! [SY878: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV75 )
| ! [SY879: $i,SY880: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY878 @ SY879 @ SV75 ) @ SY880 @ SV75 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY878 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY879 @ SY880 @ SV75 ) @ SV75 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[595]) ).
thf(801,plain,
! [SV76: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV76 )
| ! [SY881: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY881 @ SY881 @ SV76 )
= SY881 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[596]) ).
thf(802,plain,
! [SV77: $i] :
( ( ! [SY882: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ SV77 )
| ! [SY883: $i,SY884: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY882 @ SY883 @ SV77 ) @ SY884 @ SV77 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY882 @ SY884 @ SV77 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY883 @ SY884 @ SV77 ) @ SV77 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[597]) ).
thf(803,plain,
! [SV78: $i] :
( ( ! [SY885: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ SV78 )
| ! [SY886: $i,SY887: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY885 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY886 @ SY887 @ SV78 ) @ SV78 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY885 @ SY886 @ SV78 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY885 @ SY887 @ SV78 ) @ SV78 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[598]) ).
thf(804,plain,
! [SV79: $i] :
( ( ! [SY888: $i,SY889: $i,SY890: $i,SY891: $i,SY892: $i,SY893: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV79 @ SY888 @ SY889 @ SY890 @ SY891 ) @ SY892 ) @ SY893 ) )
| ! [SY894: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY888 @ SY894 ) @ SY893 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV79 @ SY892 ) @ SY894 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[599]) ).
thf(805,plain,
! [SV80: $i] :
( ( ! [SY895: $i,SY896: $i,SY897: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV80 @ SY895 ) @ SY896 ) @ SY897 ) )
| ! [SY898: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV80 @ SY895 ) @ SY898 ) @ SY897 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV80 @ SY895 ) @ SY896 ) @ SY898 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[600]) ).
thf(806,plain,
! [SV81: $i] :
( ( ! [SY899: $i,SY900: $i,SY901: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV81 @ SY899 ) @ SY900 ) @ SY901 ) )
| ! [SY902: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV81 @ SY899 ) @ SY902 ) @ SY901 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV81 @ SY899 ) @ SY900 ) @ SY902 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[601]) ).
thf(807,plain,
! [SV82: $i] :
( ( ! [SY903: $i,SY904: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV82 @ SY903 ) @ SY904 ) @ SY904 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[602]) ).
thf(808,plain,
! [SV83: $i] :
( ( ! [SY905: $i,SY906: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV83 @ SY905 ) @ SY906 ) @ SY906 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[603]) ).
thf(809,plain,
! [SV84: $i] :
( ( ! [SY907: $i,SY908: $i,SY909: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV84 @ SY907 ) @ SY908 ) @ SY909 ) )
| ! [SY910: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV84 @ SY907 ) @ SY910 ) @ SY909 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV84 @ SY907 ) @ SY908 ) @ SY910 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[604]) ).
thf(810,plain,
! [SV85: $i] :
( ( ! [SY911: $i,SY912: $i,SY913: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV85 @ SY911 ) @ SY912 ) @ SY913 ) )
| ! [SY914: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV85 @ SY911 ) @ SY914 ) @ SY913 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV85 @ SY912 ) @ SY914 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[605]) ).
thf(811,plain,
! [SV86: $i] :
( ( ! [SY915: $i,SY916: $i,SY917: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV86 @ SY915 ) @ SY916 ) @ SY917 ) )
| ! [SY918: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV86 @ SY918 ) @ SY917 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV86 @ SY915 ) @ SY916 ) @ SY918 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[606]) ).
thf(812,plain,
! [SV87: $i] :
( ( ! [SY919: $i,SY920: $i] :
( ( c_Lambda_Olift @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV87 ) @ SY919 ) @ SY920 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Olift @ SV87 @ SY920 ) ) @ ( c_Lambda_Olift @ SY919 @ SY920 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[607]) ).
thf(813,plain,
! [SV88: $i] :
( ( ! [SY921: $i] :
( ( c_Wellfounded_OwfP @ ( c_Transitive__Closure_Otranclp @ SV88 @ SY921 ) @ SY921 )
| ~ ( c_Wellfounded_OwfP @ SV88 @ SY921 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[608]) ).
thf(814,plain,
! [SV89: $i] :
( ( ! [SY922: $i,SY923: $i] :
( ( ( hAPP @ SV89 @ SY922 )
= SY923 )
| ~ ( c_Type_Otyping @ SV89 @ ( c_Lambda_OdB_OVar @ SY922 ) @ SY923 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[609]) ).
thf(815,plain,
! [SV90: $i] :
( ( ! [SY924: $i,SY925: $i,SY926: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV90 @ SY924 ) @ SY925 ) @ SY926 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV90 @ SY924 ) @ SY925 ) @ SY926 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[610]) ).
thf(816,plain,
! [SV91: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OVar @ SV91 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[611]) ).
thf(817,plain,
! [SV92: $i] :
( ( ! [SY927: $i] :
( ( c_Lambda_OdB_OVar @ SV92 )
!= ( c_Lambda_OdB_OAbs @ SY927 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[612]) ).
thf(818,plain,
! [SV93: $i] :
( ( ! [SY928: $i,SY929: $i,SY930: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV93 @ SY928 ) @ SY929 ) @ SY930 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV93 @ SY929 ) @ SY930 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[613]) ).
thf(819,plain,
! [SV94: $i] :
( ( ! [SY931: $i,SY932: $i,SY933: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV94 @ SY931 ) @ SY932 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY933 @ SY931 ) @ SY932 ) )
| ! [SY934: $i,SY935: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY933 @ SV94 @ ( tc_fun @ SY934 @ ( tc_fun @ SY935 @ tc_bool ) ) ) @ SY931 ) @ SY932 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[614]) ).
thf(820,plain,
! [SV95: $i] :
( ( ! [SY936: $i,SY937: $i,SY938: $i,SY939: $i,SY940: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV95 @ SY936 @ ( tc_fun @ SY937 @ ( tc_fun @ SY938 @ tc_bool ) ) ) @ SY939 ) @ SY940 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY936 @ SY939 ) @ SY940 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[615]) ).
thf(821,plain,
! [SV96: $i] :
( ( ! [SY941: $i,SY942: $i,SY943: $i,SY944: $i,SY945: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV96 @ SY941 @ ( tc_fun @ SY942 @ ( tc_fun @ SY943 @ tc_bool ) ) ) @ SY944 ) @ SY945 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV96 @ SY944 ) @ SY945 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[616]) ).
thf(822,plain,
! [SV97: $i] :
( ( ! [SY946: $i,SY947: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV97 ) ) @ SY946 ) @ SY947 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SY946 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV97 @ SY946 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SY947 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[617]) ).
thf(823,plain,
! [SV98: $i] :
( ( ! [SY948: $i] : ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Olift @ SV98 @ SY948 ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV98 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[618]) ).
thf(824,plain,
! [SV99: $i] :
( ( ! [SY949: $i,SY950: $i,SY951: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV99 ) @ SY949 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SY950 ) @ SY951 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[619]) ).
thf(825,plain,
! [SV100: $i] :
( ( ! [SY952: $i] :
( ~ ( class_Lattices_Olattice @ SV100 )
| ! [SY953: $i,SY954: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY952 @ SY953 @ SV100 ) @ SY954 @ SV100 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY952 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY953 @ SY954 @ SV100 ) @ SV100 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[620]) ).
thf(826,plain,
! [SV101: $i] :
( ( ! [SY955: $i] :
( ~ ( class_Lattices_Olattice @ SV101 )
| ! [SY956: $i,SY957: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY955 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY956 @ SY957 @ SV101 ) @ SV101 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY956 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY955 @ SY957 @ SV101 ) @ SV101 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[621]) ).
thf(827,plain,
! [SV102: $i] :
( ( ! [SY958: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV102 )
| ! [SY959: $i,SY960: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY958 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY959 @ SY960 @ SV102 ) @ SV102 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY959 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY958 @ SY960 @ SV102 ) @ SV102 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[622]) ).
thf(828,plain,
! [SV103: $i] :
( ( ! [SY961: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV103 )
| ! [SY962: $i,SY963: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY961 @ SY962 @ SV103 ) @ SY963 @ SV103 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY961 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY962 @ SY963 @ SV103 ) @ SV103 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[623]) ).
thf(829,plain,
! [SV104: $i] :
( ( ! [SY964: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV104 )
!= ( c_Lambda_OdB_OAbs @ SY964 ) )
| ( SV104 = SY964 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[624]) ).
thf(830,plain,
! [SV105: $i] :
( ( ! [SY965: $i,SY966: $i] :
( ( c_Lambda_OdB_OVar @ SV105 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY965 ) @ SY966 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[625]) ).
thf(831,plain,
! [SV106: $i] :
( ( ! [SY967: $i] :
( ! [SY968: $i] :
( ( c_Lambda_OdB_OVar @ SV106 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY967 @ SY968 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OVar @ SV106 )
= SY967 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[626]) ).
thf(832,plain,
! [SV107: $i] :
( ( ! [SY969: $i,SY970: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV107 @ SY969 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY970 @ SY969 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV107 ) @ SY970 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[627]) ).
thf(833,plain,
! [SV108: $i] :
( ( ~ ( class_Lattices_Olattice @ SV108 )
| ! [SY971: $i,SY972: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY971 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY971 @ SY972 @ SV108 ) @ SV108 )
= SY971 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[628]) ).
thf(834,plain,
! [SV109: $i] :
( ( ! [SY973: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV109 ) ) @ SY973 ) ) @ ( c_Lambda_Osubst @ SV109 @ SY973 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[629]) ).
thf(835,plain,
! [SV110: $i] :
( ( ! [SY974: $i,SY975: $i] :
( ( SV110 = SY974 )
| ! [SY976: $i,SY977: $i] :
( ~ ( c_Type_Otyping @ SY975 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY976 ) @ SY977 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY974 )
| ~ ( c_Type_Otyping @ SY975 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY976 ) @ SY977 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV110 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[630]) ).
thf(836,plain,
! [SV111: $i] :
( ( ! [SY978: $i,SY979: $i,SY980: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV111 ) @ SY978 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY979 ) @ SY980 ) )
| ( SY978 = SY980 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[631]) ).
thf(837,plain,
! [SV112: $i] :
( ( ! [SY981: $i,SY982: $i] :
( ! [SY983: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV112 ) @ SY981 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY982 ) @ SY983 ) )
| ( SV112 = SY982 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[632]) ).
thf(838,plain,
! [SV113: $i] :
( ( ~ ( class_Lattices_Olattice @ SV113 )
| ! [SY984: $i,SY985: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY984 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY984 @ SY985 @ SV113 ) @ SV113 )
= SY984 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[633]) ).
thf(839,plain,
! [SV114: $i] :
( ( ! [SY986: $i,SY987: $i,SY988: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV114 ) @ SY986 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SY987 ) @ SY988 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY986 = SY988 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[634]) ).
thf(840,plain,
! [SV115: $i] :
( ( ! [SY989: $i,SY990: $i] :
( ! [SY991: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV115 ) @ SY989 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SY990 ) @ SY991 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV115 = SY990 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[635]) ).
thf(841,plain,
! [SV116: $i] :
( ( ! [SY992: $i,SY993: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV116 @ SY992 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SY993 ) )
| ( SV116
= ( c_Lambda_OdB_OAbs @ SY993 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[636]) ).
thf(842,plain,
! [SV117: $i] :
( ( ! [SY994: $i] :
( ( c_Transitive__Closure_Ortranclp @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV117 @ ( c_fequal @ SY994 ) @ ( tc_fun @ SY994 @ ( tc_fun @ SY994 @ tc_bool ) ) ) @ SY994 )
= ( c_Transitive__Closure_Ortranclp @ SV117 @ SY994 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[637]) ).
thf(843,plain,
! [SV118: $i] :
( ( ! [SY995: $i,SY996: $i,SY997: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV118 @ SY995 ) @ SY996 ) @ SY997 ) )
| ( SY996 = SY997 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV118 @ SY995 ) @ SY996 ) @ SY997 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[638]) ).
thf(844,plain,
! [SV119: $i] :
( ( ! [SY998: $i,SY999: $i,SY1000: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV119 @ SY998 ) @ SY999 ) @ SY1000 ) )
| ( SY999 = SY1000 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV119 @ SY998 ) @ SY999 ) @ SY1000 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[639]) ).
thf(845,plain,
! [SV120: $i] :
( ( ! [SY1001: $i,SY1002: $i] :
( ( c_Transitive__Closure_Ortranclp @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Ortranclp @ SV120 @ SY1001 ) @ ( c_Transitive__Closure_Ortranclp @ SY1002 @ SY1001 ) @ ( tc_fun @ SY1001 @ ( tc_fun @ SY1001 @ tc_bool ) ) ) @ SY1001 )
= ( c_Transitive__Closure_Ortranclp @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV120 @ SY1002 @ ( tc_fun @ SY1001 @ ( tc_fun @ SY1001 @ tc_bool ) ) ) @ SY1001 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[640]) ).
thf(846,plain,
! [SV121: $i] :
( ( ! [SY1003: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ SV121 )
| ! [SY1004: $i,SY1005: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY1003 @ SY1004 @ SV121 ) @ SY1005 @ SV121 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY1003 @ SY1005 @ SV121 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY1004 @ SY1005 @ SV121 ) @ SV121 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[641]) ).
thf(847,plain,
! [SV122: $i] :
( ( ! [SY1006: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ SV122 )
| ! [SY1007: $i,SY1008: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY1006 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY1007 @ SY1008 @ SV122 ) @ SV122 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY1006 @ SY1007 @ SV122 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY1006 @ SY1008 @ SV122 ) @ SV122 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[642]) ).
thf(848,plain,
! [SV123: $i] :
( ( ~ ( class_Lattices_Olattice @ SV123 )
| ! [SY1009: $i,SY1010: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY1009 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY1009 @ SY1010 @ SV123 ) @ SV123 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY1009 @ SY1010 @ SV123 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[643]) ).
thf(849,plain,
! [SV124: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV124 )
| ! [SY1011: $i,SY1012: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY1011 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY1011 @ SY1012 @ SV124 ) @ SV124 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY1011 @ SY1012 @ SV124 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[644]) ).
thf(850,plain,
! [SV125: $i] :
( ( ! [SY1013: $i,SY1014: $i] : ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV125 @ ( c_Lambda_OdB_OVar @ SY1013 ) @ SY1014 ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV125 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[645]) ).
thf(851,plain,
! [SV126: $i] :
( ( ! [SY1015: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Otranclp @ SV126 @ SY1015 ) @ ( c_fequal @ SY1015 ) @ ( tc_fun @ SY1015 @ ( tc_fun @ SY1015 @ tc_bool ) ) )
= ( c_Transitive__Closure_Ortranclp @ SV126 @ SY1015 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[646]) ).
thf(852,plain,
! [SV127: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV127 )
| ! [SY1016: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY1016 @ SY1016 @ SV127 )
= SY1016 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[647]) ).
thf(853,plain,
! [SV128: $i] :
( ( ! [SY1017: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV128 ) @ SY1017 @ SV128 )
= SY1017 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[648]) ).
thf(854,plain,
! [SV129: $i] :
( ( ! [SY1018: $i,SY1019: $i,SY1020: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV129 ) @ SY1018 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1019 ) @ SY1020 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY1018 = SY1020 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[649]) ).
thf(855,plain,
! [SV130: $i] :
( ( ! [SY1021: $i,SY1022: $i] :
( ! [SY1023: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV130 ) @ SY1021 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1022 ) @ SY1023 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV130 = SY1022 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[650]) ).
thf(856,plain,
! [SV131: $i] :
( ( ! [SY1024: $i,SY1025: $i] :
( ( c_Lambda_OdB_OAbs @ SV131 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1024 ) @ SY1025 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[651]) ).
thf(857,plain,
! [SV132: $i] :
( ( ! [SY1026: $i,SY1027: $i,SY1028: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV132 @ SY1026 ) @ SY1027 ) @ SY1028 ) )
| ! [SY1029: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV132 @ SY1026 ) @ SY1029 ) @ SY1028 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV132 @ SY1026 ) @ SY1027 ) @ SY1029 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[652]) ).
thf(858,plain,
! [SV133: $i] :
( ( ! [SY1030: $i] :
( ( ( c_Lambda_OdB_OVar @ SV133 )
!= ( c_Lambda_OdB_OVar @ SY1030 ) )
| ( SV133 = SY1030 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[653]) ).
thf(859,plain,
! [SV134: $i] :
( ( ! [SY1031: $i,SY1032: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV134 ) @ SY1031 )
!= ( c_Lambda_OdB_OAbs @ SY1032 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[654]) ).
thf(860,plain,
! [SV135: $i] :
( ( ! [SY1033: $i] :
( ( c_Lambda_OdB_OAbs @ SV135 )
!= ( c_Lambda_OdB_OVar @ SY1033 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[655]) ).
thf(861,plain,
! [SV136: $i] :
( ( ! [SY1034: $i,SY1035: $i,SY1036: $i] :
( ( c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV136 ) @ SY1034 ) @ SY1035 @ SY1036 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV136 @ SY1035 @ SY1036 ) ) @ ( c_Lambda_Osubst @ SY1034 @ SY1035 @ SY1036 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[656]) ).
thf(862,plain,
! [SV137: $i] :
( ( ! [SY1037: $i,SY1038: $i,SY1039: $i,SY1040: $i,SY1041: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV137 @ SY1037 @ ( tc_fun @ SY1038 @ ( tc_fun @ SY1039 @ tc_bool ) ) ) @ SY1040 ) @ SY1041 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1037 @ SY1040 ) @ SY1041 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ SY1040 ) @ SY1041 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[657]) ).
thf(863,plain,
! [SV138: $i] :
( ( ! [SY1042: $i,SY1043: $i,SY1044: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV138 @ SY1042 ) @ SY1043 ) @ SY1044 ) )
| ! [SY1045: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV138 @ SY1042 ) @ SY1045 ) @ SY1044 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV138 @ SY1043 ) @ SY1045 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[658]) ).
thf(864,plain,
! [SV139: $i] :
( ( ! [SY1046: $i,SY1047: $i,SY1048: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV139 @ SY1046 ) @ SY1047 ) @ SY1048 ) )
| ! [SY1049: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV139 @ SY1049 ) @ SY1048 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV139 @ SY1046 ) @ SY1047 ) @ SY1049 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[659]) ).
thf(865,plain,
! [SV140: $i] :
( ( ! [SY1050: $i,SY1051: $i,SY1052: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV140 @ SY1050 ) @ SY1051 ) @ SY1052 ) )
| ! [SY1053: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV140 @ SY1053 ) @ SY1052 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV140 @ SY1050 ) @ SY1051 ) @ SY1053 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[660]) ).
thf(866,plain,
! [SV141: $i] :
( ( ! [SY1054: $i,SY1055: $i,SY1056: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV141 @ SY1054 ) @ SY1055 ) @ SY1056 ) )
| ! [SY1057: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV141 @ SY1054 ) @ SY1057 ) @ SY1056 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV141 @ SY1055 ) @ SY1057 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[661]) ).
thf(867,plain,
! [SV142: $i] :
( ( ! [SY1058: $i,SY1059: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV142 @ SY1058 ) @ SY1059 ) )
| ! [SY1060: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV142 @ SY1059 ) @ SY1060 ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV142 @ SY1058 ) @ SY1060 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[662]) ).
thf(868,plain,
! [SV143: $i] :
( ( ! [SY1061: $i,SY1062: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV143 @ SY1061 ) @ SY1062 ) )
| ! [SY1063: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1062 ) @ SY1063 ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV143 @ SY1061 ) @ SY1063 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[663]) ).
thf(869,plain,
! [SV144: $i] :
( ( ! [SY1064: $i] :
( ( hBOOL @ ( hAPP @ SV144 @ SY1064 ) )
| ! [SY1065: $i,SY1066: $i] :
( ~ ( hBOOL @ ( hAPP @ SV144 @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__1__1 @ SV144 @ SY1065 @ SY1066 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1065 @ SY1066 ) @ SY1064 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[664]) ).
thf(870,plain,
! [SV145: $i] :
( ( ! [SY1067: $i,SY1068: $i] :
( ( hBOOL @ ( hAPP @ SV145 @ SY1067 ) )
| ( hBOOL @ ( hAPP @ SV145 @ SY1068 ) )
| ! [SY1069: $i,SY1070: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1069 @ SY1068 ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__1__1 @ SV145 @ SY1069 @ SY1070 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1069 @ SY1070 ) @ SY1067 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[665]) ).
thf(871,plain,
! [SV146: $i] :
( ( ! [SY1071: $i,SY1072: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV146 @ ( c_ATP__Linkup_Osko__Wellfounded__Xnot__accp__down__1__1 @ SV146 @ SY1071 @ SY1072 ) ) @ SY1071 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV146 @ SY1072 ) @ SY1071 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[666]) ).
thf(872,plain,
! [SV147: $i] :
( ( ! [SY1073: $i,SY1074: $i] :
( ( c_Type_Otyping @ SV147 @ SY1073 @ SY1074 )
| ! [SY1075: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SY1075 ) @ SY1073 ) )
| ~ ( c_Type_Otyping @ SV147 @ SY1075 @ SY1074 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[667]) ).
thf(873,plain,
! [SV148: $i] :
( ( ! [SY1076: $i] :
( ! [SY1077: $i] : ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV148 @ SY1076 ) @ SY1077 ) )
| ~ ( c_Wellfounded_OwfP @ SV148 @ SY1076 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[668]) ).
thf(874,plain,
! [SV149: $i] :
( ( ! [SY1078: $i,SY1079: $i] :
( ( c_Predicate_Oconversep @ ( c_Predicate_Oconversep @ SV149 @ SY1078 @ SY1079 ) @ SY1079 @ SY1078 )
= SV149 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[669]) ).
thf(875,plain,
! [SV150: $i] :
( ( ! [SY1080: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OVar @ SV150 ) ) @ SY1080 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[670]) ).
thf(876,plain,
! [SV151: $i] :
( ( ! [SY1081: $i,SY1082: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV151 @ SY1081 ) @ SY1082 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV151 @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__Xintros__1__1 @ SV151 @ SY1082 @ SY1081 ) ) @ SY1082 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[671]) ).
thf(877,plain,
! [SV152: $i] :
( ( ( c_Predicate_Oconversep @ ( c_fequal @ SV152 ) @ SV152 @ SV152 )
= ( c_fequal @ SV152 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[672]) ).
thf(878,plain,
! [SV153: $i] :
( ( ! [SY1083: $i,SY1084: $i,SY1085: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ ( c_Transitive__Closure_Otranclp @ SV153 @ SY1083 ) @ SY1083 @ SY1083 ) @ SY1084 ) @ SY1085 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ ( c_Predicate_Oconversep @ SV153 @ SY1083 @ SY1083 ) @ SY1083 ) @ SY1084 ) @ SY1085 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[673]) ).
thf(879,plain,
! [SV154: $i] :
( ( ! [SY1086: $i,SY1087: $i,SY1088: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ ( c_Predicate_Oconversep @ SV154 @ SY1086 @ SY1086 ) @ SY1086 ) @ SY1087 ) @ SY1088 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ ( c_Transitive__Closure_Otranclp @ SV154 @ SY1086 ) @ SY1086 @ SY1086 ) @ SY1087 ) @ SY1088 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[674]) ).
thf(880,plain,
! [SV155: $i] :
( ( ! [SY1089: $i,SY1090: $i] :
( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV155 @ SY1089 ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xnot__accp__down__1__1 @ SV155 @ SY1090 @ SY1089 ) ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV155 @ SY1089 ) @ SY1090 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[675]) ).
thf(881,plain,
! [SV156: $i] :
( ( ! [SY1091: $i] :
( ( c_Transitive__Closure_Otranclp @ ( c_Predicate_Oconversep @ SV156 @ SY1091 @ SY1091 ) @ SY1091 )
= ( c_Predicate_Oconversep @ ( c_Transitive__Closure_Otranclp @ SV156 @ SY1091 ) @ SY1091 @ SY1091 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[676]) ).
thf(882,plain,
! [SV157: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV157 ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ SV157 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[677]) ).
thf(883,plain,
! [SV158: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ SV158 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV158 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[678]) ).
thf(884,plain,
! [SV159: $i] :
( ( ! [SY1092: $i,SY1093: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV159 @ SY1092 ) @ SY1093 ) )
| ! [SY1094: $i] :
( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV159 @ SY1092 ) @ SY1094 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV159 @ SY1092 ) @ SY1093 ) @ SY1094 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[679]) ).
thf(885,plain,
! [SV160: $i] :
( ( ! [SY1095: $i,SY1096: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV160 @ SY1095 ) @ SY1096 ) )
| ! [SY1097: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV160 @ SY1095 ) @ SY1096 ) @ SY1097 ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV160 @ SY1095 ) @ SY1097 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[680]) ).
thf(886,plain,
! [SV161: $i] :
( ( ! [SY1098: $i,SY1099: $i,SY1100: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Osubst @ SV161 @ SY1098 @ SY1099 ) ) @ ( c_Lambda_Osubst @ SY1100 @ SY1098 @ SY1099 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV161 ) @ SY1100 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[681]) ).
thf(887,plain,
! [SV162: $i] :
( ( ! [SY1101: $i] :
( ( hBOOL @ ( hAPP @ SV162 @ SY1101 ) )
| ! [SY1102: $i] :
( ~ ( hBOOL @ ( hAPP @ SV162 @ ( v_sko__Wellfounded__Xaccp__Xinducts__1 @ SV162 @ SY1102 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1102 @ t_a ) @ SY1101 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[682]) ).
thf(888,plain,
! [SV163: $i] :
( ( ! [SY1103: $i] :
( ( hBOOL @ ( hAPP @ SV163 @ SY1103 ) )
| ! [SY1104: $i] :
( ( hBOOL @ ( hAPP @ SV163 @ SY1104 ) )
| ! [SY1105: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1105 @ SY1104 ) @ ( v_sko__Wellfounded__Xaccp__Xinducts__1 @ SV163 @ SY1105 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1105 @ t_a ) @ SY1103 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[683]) ).
thf(889,plain,
! [SV164: $i] :
( ( ! [SY1106: $i,SY1107: $i] :
( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV164 @ SY1106 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SY1107 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ SY1106 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV164 ) ) @ SY1106 ) @ SY1107 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[684]) ).
thf(890,plain,
! [SV165: $i] :
( ( ! [SY1108: $i] :
( ( hBOOL @ ( hAPP @ SV165 @ SY1108 ) )
| ! [SY1109: $i] :
( ~ ( hBOOL @ ( hAPP @ SV165 @ ( v_sko__Wellfounded__Xaccp__Xinduct__1 @ SV165 @ SY1109 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1109 @ t_a ) @ SY1108 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[685]) ).
thf(891,plain,
! [SV166: $i] :
( ( ! [SY1110: $i] :
( ( hBOOL @ ( hAPP @ SV166 @ SY1110 ) )
| ! [SY1111: $i] :
( ( hBOOL @ ( hAPP @ SV166 @ SY1111 ) )
| ! [SY1112: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1112 @ SY1111 ) @ ( v_sko__Wellfounded__Xaccp__Xinduct__1 @ SV166 @ SY1112 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1112 @ t_a ) @ SY1110 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[686]) ).
thf(892,plain,
! [SV167: $i] :
( ( ! [SY1113: $i,SY1114: $i,SY1115: $i,SY1116: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV167 @ SY1113 @ SY1114 ) @ SY1115 ) @ SY1116 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV167 @ SY1116 ) @ SY1115 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[687]) ).
thf(893,plain,
! [SV168: $i] :
( ( ! [SY1117: $i,SY1118: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV168 @ SY1117 ) @ SY1118 ) )
| ! [SY1119: $i,SY1120: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV168 @ SY1119 @ SY1120 ) @ SY1118 ) @ SY1117 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[688]) ).
thf(894,plain,
! [SV169: $i] :
( ( ! [SY1121: $i,SY1122: $i,SY1123: $i,SY1124: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV169 @ SY1121 @ SY1122 ) @ SY1123 ) @ SY1124 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV169 @ SY1124 ) @ SY1123 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[689]) ).
thf(895,plain,
! [SV170: $i] :
( ( ! [SY1125: $i,SY1126: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV170 @ SY1125 ) @ SY1126 ) )
| ! [SY1127: $i,SY1128: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV170 @ SY1127 @ SY1128 ) @ SY1126 ) @ SY1125 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[690]) ).
thf(896,plain,
! [SV171: $i] :
( ( ! [SY1129: $i] :
( ( hBOOL @ ( hAPP @ SV171 @ SY1129 ) )
| ! [SY1130: $i,SY1131: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1130 @ t_a ) @ SY1131 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1130 @ SY1131 ) @ ( v_sko__Wellfounded__Xaccp__Xinducts__1 @ SV171 @ SY1130 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1130 @ t_a ) @ SY1129 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[691]) ).
thf(897,plain,
! [SV172: $i] :
( ( ! [SY1132: $i] :
( ( hBOOL @ ( hAPP @ SV172 @ SY1132 ) )
| ! [SY1133: $i,SY1134: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1133 @ t_a ) @ SY1134 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1133 @ SY1134 ) @ ( v_sko__Wellfounded__Xaccp__Xinduct__1 @ SV172 @ SY1133 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1133 @ t_a ) @ SY1132 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[692]) ).
thf(898,plain,
! [SV173: $i] :
( ( ! [SY1135: $i,SY1136: $i,SY1137: $i] :
( ( c_Predicate_Oconversep @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV173 @ SY1135 @ ( tc_fun @ SY1136 @ ( tc_fun @ SY1137 @ tc_bool ) ) ) @ SY1136 @ SY1137 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Predicate_Oconversep @ SV173 @ SY1136 @ SY1137 ) @ ( c_Predicate_Oconversep @ SY1135 @ SY1136 @ SY1137 ) @ ( tc_fun @ SY1137 @ ( tc_fun @ SY1136 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[693]) ).
thf(899,plain,
! [SV174: $i] :
( ( ! [SY1138: $i,SY1139: $i,SY1140: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV174 @ SY1138 ) @ SY1139 ) @ SY1140 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ SV174 @ SY1138 @ SY1138 ) @ SY1138 ) @ SY1140 ) @ SY1139 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[694]) ).
thf(900,plain,
! [SV175: $i] :
( ( ! [SY1141: $i,SY1142: $i,SY1143: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ SV175 @ SY1141 @ SY1141 ) @ SY1141 ) @ SY1142 ) @ SY1143 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV175 @ SY1141 ) @ SY1143 ) @ SY1142 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[695]) ).
thf(901,plain,
! [SV176: $i] :
( ( ! [SY1144: $i] :
( ( hBOOL @ ( hAPP @ SV176 @ SY1144 ) )
| ! [SY1145: $i,SY1146: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1145 @ SY1146 ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__1__1 @ SV176 @ SY1145 @ SY1146 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1145 @ SY1146 ) @ SY1144 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[696]) ).
thf(902,plain,
! [SV177: $i] :
( ( ! [SY1147: $i,SY1148: $i,SY1149: $i] :
( ( c_Predicate_Oconversep @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV177 @ SY1147 @ ( tc_fun @ SY1148 @ ( tc_fun @ SY1149 @ tc_bool ) ) ) @ SY1148 @ SY1149 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Predicate_Oconversep @ SV177 @ SY1148 @ SY1149 ) @ ( c_Predicate_Oconversep @ SY1147 @ SY1148 @ SY1149 ) @ ( tc_fun @ SY1149 @ ( tc_fun @ SY1148 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[697]) ).
thf(903,plain,
! [SV178: $i] :
( ( ! [SY1150: $i,SY1151: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV178 @ SY1150 ) @ SY1151 ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV178 @ SY1150 ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__Xintros__1__1 @ SV178 @ SY1151 @ SY1150 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[698]) ).
thf(904,plain,
! [SV179: $i] :
( ( ! [SY1152: $i,SY1153: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV179 @ SY1152 ) @ SY1153 ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV179 @ SY1152 ) @ ( c_ATP__Linkup_Osko__Wellfounded__XaccpI__1__1 @ SV179 @ SY1153 @ SY1152 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[699]) ).
thf(905,plain,
! [SV180: $i] :
( ( ! [SY1154: $i,SY1155: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV180 @ SY1154 ) @ SY1155 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV180 @ ( c_ATP__Linkup_Osko__Wellfounded__XaccpI__1__1 @ SV180 @ SY1155 @ SY1154 ) ) @ SY1155 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[700]) ).
thf(906,plain,
! [SV181: $i] :
( ( ! [SY1156: $i,SY1157: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV181 ) @ SY1156 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV181 ) @ SY1157 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SY1156 ) @ SY1157 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[701]) ).
thf(907,plain,
! [SV182: $i] :
( ( ! [SY1158: $i,SY1159: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV182 ) @ SY1158 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1159 ) @ SY1158 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV182 ) @ SY1159 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[702]) ).
thf(908,plain,
! [SV183: $i] :
( ( ! [SY1160: $i] :
( ( hBOOL @ ( hAPP @ SV183 @ SY1160 ) )
| ! [SY1161: $i,SY1162: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1161 @ SY1162 ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__rule__1__1 @ SV183 @ SY1161 @ SY1162 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1161 @ SY1162 ) @ SY1160 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[703]) ).
thf(909,plain,
! [SV184: $i] :
( ( ! [SY1163: $i,SY1164: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Olift @ SV184 @ SY1163 ) ) @ ( c_Lambda_Olift @ SY1164 @ SY1163 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV184 ) @ SY1164 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[704]) ).
thf(910,plain,
! [SV185: $i] :
( ( ! [SY1165: $i] :
( ( hBOOL @ ( hAPP @ SV185 @ SY1165 ) )
| ! [SY1166: $i,SY1167: $i] :
( ~ ( hBOOL @ ( hAPP @ SV185 @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__rule__1__1 @ SV185 @ SY1166 @ SY1167 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1166 @ SY1167 ) @ SY1165 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[705]) ).
thf(911,plain,
! [SV186: $i] :
( ( ! [SY1168: $i,SY1169: $i] :
( ( hBOOL @ ( hAPP @ SV186 @ SY1168 ) )
| ( hBOOL @ ( hAPP @ SV186 @ SY1169 ) )
| ! [SY1170: $i,SY1171: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1170 @ SY1169 ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__rule__1__1 @ SV186 @ SY1170 @ SY1171 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1170 @ SY1171 ) @ SY1168 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[706]) ).
thf(912,plain,
! [SV187: $i] :
( ( ! [SY1172: $i,SY1173: $i,SY1174: $i,SY1175: $i] :
( ( c_Predicate_Oconversep @ ( c_Predicate_Opred__comp @ SV187 @ SY1172 @ SY1173 @ SY1174 @ SY1175 ) @ SY1173 @ SY1175 )
= ( c_Predicate_Opred__comp @ ( c_Predicate_Oconversep @ SY1172 @ SY1174 @ SY1175 ) @ ( c_Predicate_Oconversep @ SV187 @ SY1173 @ SY1174 ) @ SY1175 @ SY1174 @ SY1173 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[707]) ).
thf(913,plain,
! [SV188: $i] :
( ( ! [SY1176: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ SV188 ) ) @ ( c_Lambda_OdB_OAbs @ SY1176 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV188 ) @ SY1176 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[708]) ).
thf(914,plain,
! [SV189: $i] :
( ( ! [SY1177: $i] :
( ( class_Lattices_Oupper__semilattice @ ( tc_fun @ SV189 @ SY1177 ) )
| ~ ( class_Lattices_Olattice @ SY1177 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[710]) ).
thf(915,plain,
! [SV190: $i] :
( ( ! [SY1178: $i] :
( ( class_Lattices_Olower__semilattice @ ( tc_fun @ SV190 @ SY1178 ) )
| ~ ( class_Lattices_Olattice @ SY1178 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[711]) ).
thf(916,plain,
! [SV191: $i] :
( ( ! [SY1179: $i] :
( ( class_Lattices_Odistrib__lattice @ ( tc_fun @ SV191 @ SY1179 ) )
| ~ ( class_Lattices_Odistrib__lattice @ SY1179 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[712]) ).
thf(917,plain,
! [SV192: $i] :
( ( ! [SY1180: $i] :
( ( class_Lattices_Olattice @ ( tc_fun @ SV192 @ SY1180 ) )
| ~ ( class_Lattices_Olattice @ SY1180 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[713]) ).
thf(918,plain,
! [SV193: $i] :
( ( ! [SY1181: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ SV193 ) @ SY1181 ) @ SY1181 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[722]) ).
thf(919,plain,
! [SV194: $i] :
( ( ! [SY1182: $i] :
( ( SV194 = SY1182 )
| ! [SY1183: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ SY1183 ) @ SV194 ) @ SY1182 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[723]) ).
thf(920,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[724]) ).
thf(921,plain,
! [SV195: $i,SV1: $i] :
( ( ! [SY1184: $i,SY1185: $i,SY1186: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ SV1 @ SV195 ) @ ( c_List_Olist_OCons @ SY1184 @ SY1185 @ SV195 ) ) @ ( c_List_Olist_OCons @ SY1184 @ SY1186 @ SV195 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ SV1 @ SV195 ) @ SY1185 ) @ SY1186 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[726]) ).
thf(922,plain,
! [SV196: $i,SV2: $i] :
( ( ! [SY1187: $i,SY1188: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ SV2 @ SV196 ) @ SY1187 ) @ SY1188 ) )
| ! [SY1189: $i,SY1190: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV2 @ SY1189 ) @ SY1190 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ SV2 @ SV196 ) @ ( c_List_Olist_OCons @ SY1189 @ SY1187 @ SV196 ) ) @ ( c_List_Olist_OCons @ SY1190 @ SY1188 @ SV196 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[727]) ).
thf(923,plain,
! [SV197: $i,SV3: $i] :
( ( ! [SY1191: $i,SY1192: $i,SY1193: $i] :
( ( ( c_List_Olist_OCons @ SV3 @ SV197 @ SY1191 )
!= ( c_List_Olist_OCons @ SY1192 @ SY1193 @ SY1191 ) )
| ( SV197 = SY1193 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[728]) ).
thf(924,plain,
! [SV198: $i,SV4: $i] :
( ( ! [SY1194: $i,SY1195: $i] :
( ! [SY1196: $i] :
( ( c_List_Olist_OCons @ SV4 @ SV198 @ SY1194 )
!= ( c_List_Olist_OCons @ SY1195 @ SY1196 @ SY1194 ) )
| ( SV4 = SY1195 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[729]) ).
thf(925,plain,
! [SV199: $i,SV5: $i] :
( ( ! [SY1197: $i] :
( ( c_List_Olist_ONil @ SV5 )
!= ( c_List_Olist_OCons @ SV199 @ SY1197 @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[730]) ).
thf(926,plain,
! [SV200: $i,SV6: $i] :
( ( ! [SY1198: $i,SY1199: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ SV6 @ SV200 ) @ SY1198 ) @ SY1199 ) )
| ( SY1199 = SY1198 )
| ! [SY1200: $i,SY1201: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ SV6 @ SV200 ) @ ( c_List_Olist_OCons @ SY1200 @ SY1198 @ SV200 ) ) @ ( c_List_Olist_OCons @ SY1201 @ SY1199 @ SV200 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[731]) ).
thf(927,plain,
! [SV201: $i,SV7: $i] :
( ( ! [SY1202: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV7 @ SV201 ) @ SY1202 ) )
| ! [SY1203: $i,SY1204: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ SV7 @ SY1203 ) @ ( c_List_Olist_OCons @ SV201 @ SY1204 @ SY1203 ) ) @ ( c_List_Olist_OCons @ SY1202 @ SY1204 @ SY1203 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[732]) ).
thf(928,plain,
! [SV202: $i,SV8: $i] :
( ( ! [SY1205: $i,SY1206: $i] :
( ( SV8 = SV202 )
| ( SY1205 = SY1206 )
| ! [SY1207: $i,SY1208: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ SY1207 @ SY1208 ) @ ( c_List_Olist_OCons @ SV202 @ SY1206 @ SY1208 ) ) @ ( c_List_Olist_OCons @ SV8 @ SY1205 @ SY1208 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[733]) ).
thf(929,plain,
! [SV203: $i,SV9: $i] :
( ( ! [SY1209: $i,SY1210: $i,SY1211: $i,SY1212: $i] :
( ( c_List_Ofoldl @ SV9 @ SV203 @ ( c_List_Olist_OCons @ SY1209 @ SY1210 @ SY1211 ) @ SY1212 @ SY1211 )
= ( c_List_Ofoldl @ SV9 @ ( hAPP @ ( hAPP @ SV9 @ SV203 ) @ SY1209 ) @ SY1210 @ SY1212 @ SY1211 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[734]) ).
thf(930,plain,
! [SV204: $i,SV10: $i] :
( ( ! [SY1213: $i] :
( ( c_List_Olist_OCons @ SV10 @ SV204 @ SY1213 )
!= ( c_List_Olist_ONil @ SY1213 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[735]) ).
thf(931,plain,
! [SV205: $i,SV11: $i] :
( ( ! [SY1214: $i] :
( ( c_List_Olist_OCons @ SV11 @ SV205 @ SY1214 )
!= ( c_List_Olist_ONil @ SY1214 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[736]) ).
thf(932,plain,
! [SV206: $i,SV12: $i] :
( ( ! [SY1215: $i,SY1216: $i] :
( ( SV12 = SV206 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY1215 @ SV206 ) @ SV12 ) )
| ! [SY1217: $i,SY1218: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ SY1215 @ SY1216 ) @ ( c_List_Olist_OCons @ SV206 @ SY1217 @ SY1216 ) ) @ ( c_List_Olist_OCons @ SV12 @ SY1218 @ SY1216 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[737]) ).
thf(933,plain,
! [SV207: $i,SV13: $i] :
( ( ! [SY1219: $i] :
( ( c_List_Olist_OCons @ SV13 @ SV207 @ SY1219 )
!= SV207 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[738]) ).
thf(934,plain,
! [SV208: $i,SV14: $i] :
( ( ! [SY1220: $i] :
( SV14
!= ( c_List_Olist_OCons @ SV208 @ SV14 @ SY1220 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[739]) ).
thf(935,plain,
! [SV209: $i,SV15: $i] :
( ( ! [SY1221: $i,SY1222: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( c_ListOrder_Ostep1 @ SV15 @ SV209 ) @ ( tc_List_Olist @ SV209 ) ) @ ( c_List_Olist_OCons @ SY1221 @ SY1222 @ SV209 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( c_ListOrder_Ostep1 @ SV15 @ SV209 ) @ ( tc_List_Olist @ SV209 ) ) @ SY1222 ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV15 @ SV209 ) @ SY1221 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[740]) ).
thf(936,plain,
! [SV210: $i,SV16: $i] :
( ( ! [SY1223: $i,SY1224: $i] :
( ( ( c_Type_Otype_OFun @ SV16 @ SV210 )
!= ( c_Type_Otype_OFun @ SY1223 @ SY1224 ) )
| ( SV210 = SY1224 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[741]) ).
thf(937,plain,
! [SV211: $i,SV17: $i] :
( ( ! [SY1225: $i] :
( ! [SY1226: $i] :
( ( c_Type_Otype_OFun @ SV17 @ SV211 )
!= ( c_Type_Otype_OFun @ SY1225 @ SY1226 ) )
| ( SV17 = SY1225 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[742]) ).
thf(938,plain,
! [SV212: $i,SV18: $i] :
( ( ! [SY1227: $i,SY1228: $i] :
( ( c_Type_Otyping @ SV18 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV212 ) @ SY1227 ) @ SY1228 )
| ! [SY1229: $i] :
( ~ ( c_Type_Otyping @ SV18 @ SY1227 @ SY1229 )
| ~ ( c_Type_Otyping @ SV18 @ SV212 @ ( c_Type_Otype_OFun @ SY1229 @ SY1228 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[743]) ).
thf(939,plain,
! [SV213: $i,SV19: $i] :
( ( ! [SY1230: $i,SY1231: $i,SY1232: $i] :
( ( c_Type_Otyping @ ( c_Type_Oshift @ SV19 @ SV213 @ SY1230 @ tc_Type_Otype ) @ ( c_Lambda_Olift @ SY1231 @ SV213 ) @ SY1232 )
| ~ ( c_Type_Otyping @ SV19 @ SY1231 @ SY1232 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[744]) ).
thf(940,plain,
! [SV214: $i,SV20: $i] :
( ( ! [SY1233: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Olift @ SV20 @ SV214 ) ) @ ( c_Lambda_Olift @ SY1233 @ SV214 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV20 ) @ SY1233 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[745]) ).
thf(941,plain,
! [SV215: $i,SV21: $i] :
( ( ! [SY1234: $i,SY1235: $i] :
( ~ ( c_Type_Otyping @ SV21 @ SV215 @ SY1234 )
| ! [SY1236: $i,SY1237: $i] :
( ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV21 @ SY1235 @ SY1234 @ tc_Type_Otype ) @ SY1236 @ SY1237 )
| ( c_Type_Otyping @ SV21 @ ( c_Lambda_Osubst @ SY1236 @ SV215 @ SY1235 ) @ SY1237 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[746]) ).
thf(942,plain,
! [SV216: $i,SV22: $i] :
( ( ! [SY1238: $i] :
( ( c_Type_Otyping @ SV22 @ SV216 @ SY1238 )
| ! [SY1239: $i] :
( ~ ( c_Type_Otyping @ SV22 @ SY1239 @ SY1238 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SY1239 ) @ SV216 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[747]) ).
thf(943,plain,
! [SV217: $i,SV23: $i] :
( ( ! [SY1240: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV23 ) @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SV217 @ SV23 @ SY1240 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV217 ) @ SV23 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SY1240 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[748]) ).
thf(944,plain,
! [SV218: $i,SV24: $i] :
( ( ! [SY1241: $i,SY1242: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV24 @ SV218 @ SY1241 ) ) @ ( c_Lambda_Osubst @ SV24 @ SY1242 @ SY1241 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV218 ) @ SY1242 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[749]) ).
thf(945,plain,
! [SV219: $i,SV25: $i] :
( ( ! [SY1243: $i,SY1244: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV25 @ SV219 @ SY1243 ) ) @ ( c_Lambda_Osubst @ SY1244 @ SV219 @ SY1243 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV25 ) @ SY1244 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[750]) ).
thf(946,plain,
! [SV220: $i,SV26: $i] :
( ( ! [SY1245: $i,SY1246: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV26 @ SV220 @ SY1245 ) ) @ ( c_Lambda_Osubst @ SV26 @ SY1246 @ SY1245 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV220 ) @ SY1246 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[751]) ).
thf(947,plain,
! [SV221: $i,SV27: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV27 ) @ SV221 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV27 ) @ SV221 ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[752]) ).
thf(948,plain,
! [SV222: $i,SV28: $i] :
( ( ! [SY1247: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV28 ) @ SV222 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1247 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV28 ) @ SV222 )
= SY1247 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[753]) ).
thf(949,plain,
! [SV223: $i,SV29: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_OdB_OAbs @ SV29 ) ) @ ( c_Lambda_OdB_OAbs @ SV223 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV29 ) @ SV223 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[754]) ).
thf(950,plain,
! [SV224: $i,SV30: $i] :
( ( ! [SY1248: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV30 ) @ SV224 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV30 ) @ SY1248 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV224 ) @ SY1248 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[755]) ).
thf(951,plain,
! [SV225: $i,SV31: $i] :
( ( ! [SY1249: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV31 ) @ SV225 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1249 ) @ SV225 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV31 ) @ SY1249 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[756]) ).
thf(952,plain,
! [SV226: $i,SV32: $i] :
( ( ! [SY1250: $i,SY1251: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV32 ) @ SV226 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1250 ) @ SY1251 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV226 ) @ SY1251 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV32 ) @ SY1250 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[757]) ).
thf(953,plain,
! [SV227: $i,SV33: $i] :
( ( ! [SY1252: $i,SY1253: $i] :
( ( c_Type_Otyping @ SV33 @ ( c_Lambda_OdB_OAbs @ SV227 ) @ ( c_Type_Otype_OFun @ SY1252 @ SY1253 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV33 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY1252 @ tc_Type_Otype ) @ SV227 @ SY1253 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[758]) ).
thf(954,plain,
! [SV228: $i,SV34: $i] :
( ( ! [SY1254: $i] :
( ( c_List_Olistsp @ ( c_Wellfounded_Oaccp @ SV34 @ SV228 ) @ SY1254 @ SV228 )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( c_ListOrder_Ostep1 @ SV34 @ SV228 ) @ ( tc_List_Olist @ SV228 ) ) @ SY1254 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[759]) ).
thf(955,plain,
! [SV229: $i,SV35: $i] :
( ( ! [SY1255: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( c_ListOrder_Ostep1 @ SV35 @ SV229 ) @ ( tc_List_Olist @ SV229 ) ) @ SY1255 ) )
| ~ ( c_List_Olistsp @ ( c_Wellfounded_Oaccp @ SV35 @ SV229 ) @ SY1255 @ SV229 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[760]) ).
thf(956,plain,
! [SV230: $i,SV36: $i] :
( ( ! [SY1256: $i,SY1257: $i] :
( ( hAPP @ ( c_Type_Oshift @ SV36 @ SV230 @ SY1256 @ SY1257 ) @ SV230 )
= SY1256 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[761]) ).
thf(957,plain,
! [SV231: $i,SV37: $i] :
( ( ! [SY1258: $i,SY1259: $i] :
( ( c_List_Ofoldl @ SV37 @ SV231 @ ( c_List_Olist_ONil @ SY1258 ) @ SY1259 @ SY1258 )
= SV231 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[762]) ).
thf(958,plain,
! [SV232: $i,SV38: $i] :
( ( ! [SY1260: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ SV38 @ SV232 ) @ SY1260 ) @ ( c_List_Olist_ONil @ SV232 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[763]) ).
thf(959,plain,
! [SV233: $i,SV39: $i] :
( ( ! [SY1261: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ SV39 @ SV233 ) @ ( c_List_Olist_ONil @ SV233 ) ) @ SY1261 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[764]) ).
thf(960,plain,
! [SV234: $i,SV40: $i] :
( ( c_List_Olistsp @ SV40 @ ( c_List_Olist_ONil @ SV234 ) @ SV234 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[765]) ).
thf(961,plain,
! [SV235: $i,SV41: $i] :
( ( ! [SY1262: $i,SY1263: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV41 ) @ SV235 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1262 @ SY1263 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV41
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1262 @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ SV41 @ SV235 @ SY1262 @ SY1263 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY1263
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[766]) ).
thf(962,plain,
! [SV236: $i,SV42: $i] :
( ( ! [SY1264: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV42 @ SV236 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV42 @ SY1264 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV236 ) @ SY1264 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[767]) ).
thf(963,plain,
! [SV237: $i,SV43: $i] :
( ( ! [SY1265: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV43 @ SV237 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1265 @ SV237 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV43 ) @ SY1265 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[768]) ).
thf(964,plain,
! [SV238: $i,SV45: $i] :
( ( ! [SY1266: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV45 @ SV238 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SY1266 ) )
| ( SV238
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[770]) ).
thf(965,plain,
! [SV239: $i,SV47: $i] :
( ( ! [SY1267: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV47 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV239 @ SY1267 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY1267
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[772]) ).
thf(966,plain,
! [SV240: $i,SV48: $i] :
( ( ! [SY1268: $i] :
( ( ( c_Lambda_OdB_OVar @ SV48 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV240 @ SY1268 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY1268
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[773]) ).
thf(967,plain,
! [SV241: $i,SV50: $i] :
( ( ! [SY1269: $i,SY1270: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV50 @ SV241 @ SY1269 ) ) )
| ! [SY1271: $i] :
( ~ ( c_Type_Otyping @ SY1270 @ SV241 @ SY1271 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV241 ) )
| ! [SY824: $i] :
~ ( c_Type_Otyping @ ( c_Type_Oshift @ SY1270 @ SY1269 @ SY1271 @ tc_Type_Otype ) @ SV50 @ SY824 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV50 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[775]) ).
thf(968,plain,
! [SV242: $i,SV51: $i] :
( ( ! [SY1273: $i] :
( ( SV51
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV242 ) @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SV242 @ SY1273 @ SV51 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV242 ) @ SY1273 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV51 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[776]) ).
thf(969,plain,
! [SV243: $i,SV52: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV52 ) @ SV243 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( c_List_Olistsp @ c_InductTermi_OIT @ SV243 @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[777]) ).
thf(970,plain,
! [SV244: $i,SV53: $i] :
( ( ! [SY1274: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV53 ) @ SV244 )
!= ( c_Lambda_OdB_OVar @ SY1274 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[778]) ).
thf(971,plain,
! [SV245: $i,SV54: $i] :
( ( ( c_Transitive__Closure_Ortranclp @ ( c_Transitive__Closure_Ortranclp @ SV54 @ SV245 ) @ SV245 )
= ( c_Transitive__Closure_Ortranclp @ SV54 @ SV245 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[779]) ).
thf(972,plain,
! [SV55: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV55 ) )
= $true )
| ( ( ! [SY831: $i,SY832: $i] :
~ ( c_Type_Otyping @ SY831 @ SV55 @ SY832 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[780]) ).
thf(973,plain,
! [SV246: $i,SV56: $i] :
( ( ! [SY1275: $i,SY1276: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV56 ) ) @ SV246 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1275 ) @ SY1276 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[781]) ).
thf(974,plain,
! [SV247: $i,SV57: $i] :
( ( ! [SY1277: $i,SY1278: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV57 @ SV247 ) @ SY1277 ) )
| ! [SY1279: $i,SY1280: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV57 @ SY1278 @ ( tc_fun @ SY1279 @ ( tc_fun @ SY1280 @ tc_bool ) ) ) @ SV247 ) @ SY1277 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[782]) ).
thf(975,plain,
! [SV248: $i,SV58: $i] :
( ( ! [SY1281: $i,SY1282: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV58 @ SV248 ) @ SY1281 ) )
| ! [SY1283: $i,SY1284: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY1282 @ SV58 @ ( tc_fun @ SY1283 @ ( tc_fun @ SY1284 @ tc_bool ) ) ) @ SV248 ) @ SY1281 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[783]) ).
thf(976,plain,
! [SV59: $i] :
( ( ( ! [SY846: $i] : ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV59 ) @ ( c_Lambda_OdB_OVar @ SY846 ) ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV59 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[784]) ).
thf(977,plain,
! [SV249: $i,SV60: $i] :
( ( ! [SY1285: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_Olift @ SV60 @ SV249 ) @ SY1285 @ SV249 )
= SV60 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[785]) ).
thf(978,plain,
! [SV250: $i,SV61: $i] :
( ( ! [SY1286: $i,SY1287: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV61 @ SV250 ) @ SY1286 ) @ SY1287 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV61 @ SY1286 ) @ SY1287 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[786]) ).
thf(979,plain,
! [SV62: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV62 ) )
= $true )
| ( ( ! [SY852: $i,SY853: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY852 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY852 @ SY853 @ SV62 ) @ SV62 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY852 @ SY853 @ SV62 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[787]) ).
thf(980,plain,
! [SV63: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV63 ) )
= $true )
| ( ( ! [SY854: $i,SY855: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY854 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY854 @ SY855 @ SV63 ) @ SV63 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY854 @ SY855 @ SV63 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[788]) ).
thf(981,plain,
! [SV64: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV64 ) )
= $true )
| ( ( ! [SY856: $i,SY857: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY856 @ SY857 @ SV64 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY857 @ SY856 @ SV64 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[789]) ).
thf(982,plain,
! [SV65: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV65 ) )
= $true )
| ( ( ! [SY858: $i,SY859: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY858 @ SY859 @ SV65 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY859 @ SY858 @ SV65 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[790]) ).
thf(983,plain,
! [SV66: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OAbs @ SV66 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV66 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[791]) ).
thf(984,plain,
! [SV251: $i,SV67: $i] :
( ( ! [SY1288: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV67 @ SV251 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1288 @ SV251 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV67 = SY1288 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[792]) ).
thf(985,plain,
! [SV252: $i,SV68: $i] :
( ( ! [SY1289: $i] :
( ( c_Lambda_OdB_OAbs @ SV68 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV252 @ SY1289 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OAbs @ SV68 )
= SV252 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[793]) ).
thf(986,plain,
! [SV253: $i,SV69: $i] :
( ( c_Type_Otyping @ SV69 @ ( c_Lambda_OdB_OVar @ SV253 ) @ ( hAPP @ SV69 @ SV253 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[794]) ).
thf(987,plain,
! [SV70: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV70 ) )
= $true )
| ( ( ! [SY865: $i,SY866: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY865 @ SY866 @ SV70 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY866 @ SY865 @ SV70 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[795]) ).
thf(988,plain,
! [SV71: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV71 ) )
= $true )
| ( ( ! [SY867: $i,SY868: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY867 @ SY868 @ SV71 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY868 @ SY867 @ SV71 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[796]) ).
thf(989,plain,
! [SV254: $i,SV72: $i] :
( ( ~ ( class_Lattices_Olattice @ SV72 )
| ! [SY1290: $i,SY1291: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV254 @ SY1290 @ SV72 ) @ SY1291 @ SV72 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV254 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY1290 @ SY1291 @ SV72 ) @ SV72 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[797]) ).
thf(990,plain,
! [SV255: $i,SV73: $i] :
( ( ~ ( class_Lattices_Olattice @ SV73 )
| ! [SY1292: $i,SY1293: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV255 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY1292 @ SY1293 @ SV73 ) @ SV73 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY1292 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV255 @ SY1293 @ SV73 ) @ SV73 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[798]) ).
thf(991,plain,
! [SV256: $i,SV74: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV74 )
| ! [SY1294: $i,SY1295: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV256 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY1294 @ SY1295 @ SV74 ) @ SV74 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY1294 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV256 @ SY1295 @ SV74 ) @ SV74 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[799]) ).
thf(992,plain,
! [SV257: $i,SV75: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV75 )
| ! [SY1296: $i,SY1297: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV257 @ SY1296 @ SV75 ) @ SY1297 @ SV75 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV257 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY1296 @ SY1297 @ SV75 ) @ SV75 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[800]) ).
thf(993,plain,
! [SV76: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV76 ) )
= $true )
| ( ( ! [SY881: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY881 @ SY881 @ SV76 )
= SY881 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[801]) ).
thf(994,plain,
! [SV258: $i,SV77: $i] :
( ( ~ ( class_Lattices_Odistrib__lattice @ SV77 )
| ! [SY1298: $i,SY1299: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV258 @ SY1298 @ SV77 ) @ SY1299 @ SV77 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV258 @ SY1299 @ SV77 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY1298 @ SY1299 @ SV77 ) @ SV77 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[802]) ).
thf(995,plain,
! [SV259: $i,SV78: $i] :
( ( ~ ( class_Lattices_Odistrib__lattice @ SV78 )
| ! [SY1300: $i,SY1301: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV259 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY1300 @ SY1301 @ SV78 ) @ SV78 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV259 @ SY1300 @ SV78 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV259 @ SY1301 @ SV78 ) @ SV78 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[803]) ).
thf(996,plain,
! [SV260: $i,SV79: $i] :
( ( ! [SY1302: $i,SY1303: $i,SY1304: $i,SY1305: $i,SY1306: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV79 @ SV260 @ SY1302 @ SY1303 @ SY1304 ) @ SY1305 ) @ SY1306 ) )
| ! [SY1307: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV260 @ SY1307 ) @ SY1306 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV79 @ SY1305 ) @ SY1307 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[804]) ).
thf(997,plain,
! [SV261: $i,SV80: $i] :
( ( ! [SY1308: $i,SY1309: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV80 @ SV261 ) @ SY1308 ) @ SY1309 ) )
| ! [SY1310: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV80 @ SV261 ) @ SY1310 ) @ SY1309 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV80 @ SV261 ) @ SY1308 ) @ SY1310 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[805]) ).
thf(998,plain,
! [SV262: $i,SV81: $i] :
( ( ! [SY1311: $i,SY1312: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV81 @ SV262 ) @ SY1311 ) @ SY1312 ) )
| ! [SY1313: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV81 @ SV262 ) @ SY1313 ) @ SY1312 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV81 @ SV262 ) @ SY1311 ) @ SY1313 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[806]) ).
thf(999,plain,
! [SV263: $i,SV82: $i] :
( ( ! [SY1314: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV82 @ SV263 ) @ SY1314 ) @ SY1314 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[807]) ).
thf(1000,plain,
! [SV264: $i,SV83: $i] :
( ( ! [SY1315: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV83 @ SV264 ) @ SY1315 ) @ SY1315 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[808]) ).
thf(1001,plain,
! [SV265: $i,SV84: $i] :
( ( ! [SY1316: $i,SY1317: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV84 @ SV265 ) @ SY1316 ) @ SY1317 ) )
| ! [SY1318: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV84 @ SV265 ) @ SY1318 ) @ SY1317 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV84 @ SV265 ) @ SY1316 ) @ SY1318 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[809]) ).
thf(1002,plain,
! [SV266: $i,SV85: $i] :
( ( ! [SY1319: $i,SY1320: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV85 @ SV266 ) @ SY1319 ) @ SY1320 ) )
| ! [SY1321: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV85 @ SV266 ) @ SY1321 ) @ SY1320 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV85 @ SY1319 ) @ SY1321 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[810]) ).
thf(1003,plain,
! [SV267: $i,SV86: $i] :
( ( ! [SY1322: $i,SY1323: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV86 @ SV267 ) @ SY1322 ) @ SY1323 ) )
| ! [SY1324: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV86 @ SY1324 ) @ SY1323 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV86 @ SV267 ) @ SY1322 ) @ SY1324 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[811]) ).
thf(1004,plain,
! [SV268: $i,SV87: $i] :
( ( ! [SY1325: $i] :
( ( c_Lambda_Olift @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV87 ) @ SV268 ) @ SY1325 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Olift @ SV87 @ SY1325 ) ) @ ( c_Lambda_Olift @ SV268 @ SY1325 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[812]) ).
thf(1005,plain,
! [SV269: $i,SV88: $i] :
( ( ( c_Wellfounded_OwfP @ ( c_Transitive__Closure_Otranclp @ SV88 @ SV269 ) @ SV269 )
| ~ ( c_Wellfounded_OwfP @ SV88 @ SV269 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[813]) ).
thf(1006,plain,
! [SV270: $i,SV89: $i] :
( ( ! [SY1326: $i] :
( ( ( hAPP @ SV89 @ SV270 )
= SY1326 )
| ~ ( c_Type_Otyping @ SV89 @ ( c_Lambda_OdB_OVar @ SV270 ) @ SY1326 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[814]) ).
thf(1007,plain,
! [SV271: $i,SV90: $i] :
( ( ! [SY1327: $i,SY1328: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV90 @ SV271 ) @ SY1327 ) @ SY1328 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV90 @ SV271 ) @ SY1327 ) @ SY1328 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[815]) ).
thf(1008,plain,
! [SV272: $i,SV92: $i] :
( ( ( c_Lambda_OdB_OVar @ SV92 )
!= ( c_Lambda_OdB_OAbs @ SV272 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[817]) ).
thf(1009,plain,
! [SV273: $i,SV93: $i] :
( ( ! [SY1329: $i,SY1330: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV93 @ SV273 ) @ SY1329 ) @ SY1330 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV93 @ SY1329 ) @ SY1330 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[818]) ).
thf(1010,plain,
! [SV274: $i,SV94: $i] :
( ( ! [SY1331: $i,SY1332: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV94 @ SV274 ) @ SY1331 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY1332 @ SV274 ) @ SY1331 ) )
| ! [SY1333: $i,SY1334: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY1332 @ SV94 @ ( tc_fun @ SY1333 @ ( tc_fun @ SY1334 @ tc_bool ) ) ) @ SV274 ) @ SY1331 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[819]) ).
thf(1011,plain,
! [SV275: $i,SV95: $i] :
( ( ! [SY1335: $i,SY1336: $i,SY1337: $i,SY1338: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV95 @ SV275 @ ( tc_fun @ SY1335 @ ( tc_fun @ SY1336 @ tc_bool ) ) ) @ SY1337 ) @ SY1338 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV275 @ SY1337 ) @ SY1338 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[820]) ).
thf(1012,plain,
! [SV276: $i,SV96: $i] :
( ( ! [SY1339: $i,SY1340: $i,SY1341: $i,SY1342: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV96 @ SV276 @ ( tc_fun @ SY1339 @ ( tc_fun @ SY1340 @ tc_bool ) ) ) @ SY1341 ) @ SY1342 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV96 @ SY1341 ) @ SY1342 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[821]) ).
thf(1013,plain,
! [SV277: $i,SV97: $i] :
( ( ! [SY1343: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV97 ) ) @ SV277 ) @ SY1343 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV277 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV97 @ SV277 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SY1343 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[822]) ).
thf(1014,plain,
! [SV98: $i] :
( ( ( ! [SY948: $i] : ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Olift @ SV98 @ SY948 ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV98 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[823]) ).
thf(1015,plain,
! [SV278: $i,SV99: $i] :
( ( ! [SY1344: $i,SY1345: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV99 ) @ SV278 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SY1344 ) @ SY1345 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[824]) ).
thf(1016,plain,
! [SV279: $i,SV100: $i] :
( ( ~ ( class_Lattices_Olattice @ SV100 )
| ! [SY1346: $i,SY1347: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV279 @ SY1346 @ SV100 ) @ SY1347 @ SV100 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV279 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY1346 @ SY1347 @ SV100 ) @ SV100 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[825]) ).
thf(1017,plain,
! [SV280: $i,SV101: $i] :
( ( ~ ( class_Lattices_Olattice @ SV101 )
| ! [SY1348: $i,SY1349: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV280 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY1348 @ SY1349 @ SV101 ) @ SV101 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY1348 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV280 @ SY1349 @ SV101 ) @ SV101 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[826]) ).
thf(1018,plain,
! [SV281: $i,SV102: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV102 )
| ! [SY1350: $i,SY1351: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV281 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY1350 @ SY1351 @ SV102 ) @ SV102 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY1350 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV281 @ SY1351 @ SV102 ) @ SV102 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[827]) ).
thf(1019,plain,
! [SV282: $i,SV103: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV103 )
| ! [SY1352: $i,SY1353: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV282 @ SY1352 @ SV103 ) @ SY1353 @ SV103 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV282 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY1352 @ SY1353 @ SV103 ) @ SV103 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[828]) ).
thf(1020,plain,
! [SV283: $i,SV104: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV104 )
!= ( c_Lambda_OdB_OAbs @ SV283 ) )
| ( SV104 = SV283 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[829]) ).
thf(1021,plain,
! [SV284: $i,SV105: $i] :
( ( ! [SY1354: $i] :
( ( c_Lambda_OdB_OVar @ SV105 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV284 ) @ SY1354 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[830]) ).
thf(1022,plain,
! [SV285: $i,SV106: $i] :
( ( ! [SY1355: $i] :
( ( c_Lambda_OdB_OVar @ SV106 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV285 @ SY1355 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OVar @ SV106 )
= SV285 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[831]) ).
thf(1023,plain,
! [SV286: $i,SV107: $i] :
( ( ! [SY1356: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV107 @ SV286 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY1356 @ SV286 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV107 ) @ SY1356 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[832]) ).
thf(1024,plain,
! [SV108: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV108 ) )
= $true )
| ( ( ! [SY971: $i,SY972: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY971 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY971 @ SY972 @ SV108 ) @ SV108 )
= SY971 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[833]) ).
thf(1025,plain,
! [SV287: $i,SV109: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV109 ) ) @ SV287 ) ) @ ( c_Lambda_Osubst @ SV109 @ SV287 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[834]) ).
thf(1026,plain,
! [SV288: $i,SV110: $i] :
( ( ! [SY1357: $i] :
( ( SV110 = SV288 )
| ! [SY1358: $i,SY1359: $i] :
( ~ ( c_Type_Otyping @ SY1357 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1358 ) @ SY1359 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV288 )
| ~ ( c_Type_Otyping @ SY1357 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1358 ) @ SY1359 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV110 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[835]) ).
thf(1027,plain,
! [SV289: $i,SV111: $i] :
( ( ! [SY1360: $i,SY1361: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV111 ) @ SV289 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1360 ) @ SY1361 ) )
| ( SV289 = SY1361 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[836]) ).
thf(1028,plain,
! [SV290: $i,SV112: $i] :
( ( ! [SY1362: $i] :
( ! [SY1363: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV112 ) @ SV290 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1362 ) @ SY1363 ) )
| ( SV112 = SY1362 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[837]) ).
thf(1029,plain,
! [SV113: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV113 ) )
= $true )
| ( ( ! [SY984: $i,SY985: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY984 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY984 @ SY985 @ SV113 ) @ SV113 )
= SY984 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[838]) ).
thf(1030,plain,
! [SV291: $i,SV114: $i] :
( ( ! [SY1364: $i,SY1365: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV114 ) @ SV291 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SY1364 ) @ SY1365 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV291 = SY1365 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[839]) ).
thf(1031,plain,
! [SV292: $i,SV115: $i] :
( ( ! [SY1366: $i] :
( ! [SY1367: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV115 ) @ SV292 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SY1366 ) @ SY1367 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV115 = SY1366 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[840]) ).
thf(1032,plain,
! [SV293: $i,SV116: $i] :
( ( ! [SY1368: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV116 @ SV293 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SY1368 ) )
| ( SV116
= ( c_Lambda_OdB_OAbs @ SY1368 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[841]) ).
thf(1033,plain,
! [SV294: $i,SV117: $i] :
( ( ( c_Transitive__Closure_Ortranclp @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV117 @ ( c_fequal @ SV294 ) @ ( tc_fun @ SV294 @ ( tc_fun @ SV294 @ tc_bool ) ) ) @ SV294 )
= ( c_Transitive__Closure_Ortranclp @ SV117 @ SV294 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[842]) ).
thf(1034,plain,
! [SV295: $i,SV118: $i] :
( ( ! [SY1369: $i,SY1370: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV118 @ SV295 ) @ SY1369 ) @ SY1370 ) )
| ( SY1369 = SY1370 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV118 @ SV295 ) @ SY1369 ) @ SY1370 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[843]) ).
thf(1035,plain,
! [SV296: $i,SV119: $i] :
( ( ! [SY1371: $i,SY1372: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV119 @ SV296 ) @ SY1371 ) @ SY1372 ) )
| ( SY1371 = SY1372 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV119 @ SV296 ) @ SY1371 ) @ SY1372 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[844]) ).
thf(1036,plain,
! [SV297: $i,SV120: $i] :
( ( ! [SY1373: $i] :
( ( c_Transitive__Closure_Ortranclp @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Ortranclp @ SV120 @ SV297 ) @ ( c_Transitive__Closure_Ortranclp @ SY1373 @ SV297 ) @ ( tc_fun @ SV297 @ ( tc_fun @ SV297 @ tc_bool ) ) ) @ SV297 )
= ( c_Transitive__Closure_Ortranclp @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV120 @ SY1373 @ ( tc_fun @ SV297 @ ( tc_fun @ SV297 @ tc_bool ) ) ) @ SV297 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[845]) ).
thf(1037,plain,
! [SV298: $i,SV121: $i] :
( ( ~ ( class_Lattices_Odistrib__lattice @ SV121 )
| ! [SY1374: $i,SY1375: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV298 @ SY1374 @ SV121 ) @ SY1375 @ SV121 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV298 @ SY1375 @ SV121 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY1374 @ SY1375 @ SV121 ) @ SV121 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[846]) ).
thf(1038,plain,
! [SV299: $i,SV122: $i] :
( ( ~ ( class_Lattices_Odistrib__lattice @ SV122 )
| ! [SY1376: $i,SY1377: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV299 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY1376 @ SY1377 @ SV122 ) @ SV122 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV299 @ SY1376 @ SV122 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV299 @ SY1377 @ SV122 ) @ SV122 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[847]) ).
thf(1039,plain,
! [SV123: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV123 ) )
= $true )
| ( ( ! [SY1009: $i,SY1010: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY1009 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY1009 @ SY1010 @ SV123 ) @ SV123 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY1009 @ SY1010 @ SV123 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[848]) ).
thf(1040,plain,
! [SV124: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV124 ) )
= $true )
| ( ( ! [SY1011: $i,SY1012: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY1011 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY1011 @ SY1012 @ SV124 ) @ SV124 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY1011 @ SY1012 @ SV124 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[849]) ).
thf(1041,plain,
! [SV125: $i] :
( ( ( ! [SY1013: $i,SY1014: $i] : ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV125 @ ( c_Lambda_OdB_OVar @ SY1013 ) @ SY1014 ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV125 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[850]) ).
thf(1042,plain,
! [SV300: $i,SV126: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Otranclp @ SV126 @ SV300 ) @ ( c_fequal @ SV300 ) @ ( tc_fun @ SV300 @ ( tc_fun @ SV300 @ tc_bool ) ) )
= ( c_Transitive__Closure_Ortranclp @ SV126 @ SV300 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[851]) ).
thf(1043,plain,
! [SV127: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV127 ) )
= $true )
| ( ( ! [SY1016: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY1016 @ SY1016 @ SV127 )
= SY1016 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[852]) ).
thf(1044,plain,
! [SV301: $i,SV128: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV128 ) @ SV301 @ SV128 )
= SV301 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[853]) ).
thf(1045,plain,
! [SV302: $i,SV129: $i] :
( ( ! [SY1378: $i,SY1379: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV129 ) @ SV302 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1378 ) @ SY1379 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV302 = SY1379 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[854]) ).
thf(1046,plain,
! [SV303: $i,SV130: $i] :
( ( ! [SY1380: $i] :
( ! [SY1381: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV130 ) @ SV303 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1380 ) @ SY1381 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV130 = SY1380 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[855]) ).
thf(1047,plain,
! [SV304: $i,SV131: $i] :
( ( ! [SY1382: $i] :
( ( c_Lambda_OdB_OAbs @ SV131 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV304 ) @ SY1382 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[856]) ).
thf(1048,plain,
! [SV305: $i,SV132: $i] :
( ( ! [SY1383: $i,SY1384: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV132 @ SV305 ) @ SY1383 ) @ SY1384 ) )
| ! [SY1385: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV132 @ SV305 ) @ SY1385 ) @ SY1384 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV132 @ SV305 ) @ SY1383 ) @ SY1385 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[857]) ).
thf(1049,plain,
! [SV306: $i,SV133: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV133 )
!= ( c_Lambda_OdB_OVar @ SV306 ) )
| ( SV133 = SV306 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[858]) ).
thf(1050,plain,
! [SV307: $i,SV134: $i] :
( ( ! [SY1386: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV134 ) @ SV307 )
!= ( c_Lambda_OdB_OAbs @ SY1386 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[859]) ).
thf(1051,plain,
! [SV308: $i,SV135: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV135 )
!= ( c_Lambda_OdB_OVar @ SV308 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[860]) ).
thf(1052,plain,
! [SV309: $i,SV136: $i] :
( ( ! [SY1387: $i,SY1388: $i] :
( ( c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV136 ) @ SV309 ) @ SY1387 @ SY1388 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV136 @ SY1387 @ SY1388 ) ) @ ( c_Lambda_Osubst @ SV309 @ SY1387 @ SY1388 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[861]) ).
thf(1053,plain,
! [SV310: $i,SV137: $i] :
( ( ! [SY1389: $i,SY1390: $i,SY1391: $i,SY1392: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV137 @ SV310 @ ( tc_fun @ SY1389 @ ( tc_fun @ SY1390 @ tc_bool ) ) ) @ SY1391 ) @ SY1392 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV310 @ SY1391 ) @ SY1392 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ SY1391 ) @ SY1392 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[862]) ).
thf(1054,plain,
! [SV311: $i,SV138: $i] :
( ( ! [SY1393: $i,SY1394: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV138 @ SV311 ) @ SY1393 ) @ SY1394 ) )
| ! [SY1395: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV138 @ SV311 ) @ SY1395 ) @ SY1394 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV138 @ SY1393 ) @ SY1395 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[863]) ).
thf(1055,plain,
! [SV312: $i,SV139: $i] :
( ( ! [SY1396: $i,SY1397: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV139 @ SV312 ) @ SY1396 ) @ SY1397 ) )
| ! [SY1398: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV139 @ SY1398 ) @ SY1397 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV139 @ SV312 ) @ SY1396 ) @ SY1398 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[864]) ).
thf(1056,plain,
! [SV313: $i,SV140: $i] :
( ( ! [SY1399: $i,SY1400: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV140 @ SV313 ) @ SY1399 ) @ SY1400 ) )
| ! [SY1401: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV140 @ SY1401 ) @ SY1400 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV140 @ SV313 ) @ SY1399 ) @ SY1401 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[865]) ).
thf(1057,plain,
! [SV314: $i,SV141: $i] :
( ( ! [SY1402: $i,SY1403: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV141 @ SV314 ) @ SY1402 ) @ SY1403 ) )
| ! [SY1404: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV141 @ SV314 ) @ SY1404 ) @ SY1403 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV141 @ SY1402 ) @ SY1404 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[866]) ).
thf(1058,plain,
! [SV315: $i,SV142: $i] :
( ( ! [SY1405: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV142 @ SV315 ) @ SY1405 ) )
| ! [SY1406: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV142 @ SY1405 ) @ SY1406 ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV142 @ SV315 ) @ SY1406 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[867]) ).
thf(1059,plain,
! [SV316: $i,SV143: $i] :
( ( ! [SY1407: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV143 @ SV316 ) @ SY1407 ) )
| ! [SY1408: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SY1407 ) @ SY1408 ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV143 @ SV316 ) @ SY1408 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[868]) ).
thf(1060,plain,
! [SV317: $i,SV144: $i] :
( ( ( hBOOL @ ( hAPP @ SV144 @ SV317 ) )
| ! [SY1409: $i,SY1410: $i] :
( ~ ( hBOOL @ ( hAPP @ SV144 @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__1__1 @ SV144 @ SY1409 @ SY1410 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1409 @ SY1410 ) @ SV317 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[869]) ).
thf(1061,plain,
! [SV318: $i,SV145: $i] :
( ( ! [SY1411: $i] :
( ( hBOOL @ ( hAPP @ SV145 @ SV318 ) )
| ( hBOOL @ ( hAPP @ SV145 @ SY1411 ) )
| ! [SY1412: $i,SY1413: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1412 @ SY1411 ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__1__1 @ SV145 @ SY1412 @ SY1413 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1412 @ SY1413 ) @ SV318 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[870]) ).
thf(1062,plain,
! [SV319: $i,SV146: $i] :
( ( ! [SY1414: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV146 @ ( c_ATP__Linkup_Osko__Wellfounded__Xnot__accp__down__1__1 @ SV146 @ SV319 @ SY1414 ) ) @ SV319 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV146 @ SY1414 ) @ SV319 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[871]) ).
thf(1063,plain,
! [SV320: $i,SV147: $i] :
( ( ! [SY1415: $i] :
( ( c_Type_Otyping @ SV147 @ SV320 @ SY1415 )
| ! [SY1416: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SY1416 ) @ SV320 ) )
| ~ ( c_Type_Otyping @ SV147 @ SY1416 @ SY1415 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[872]) ).
thf(1064,plain,
! [SV321: $i,SV148: $i] :
( ( ! [SY1417: $i] : ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV148 @ SV321 ) @ SY1417 ) )
| ~ ( c_Wellfounded_OwfP @ SV148 @ SV321 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[873]) ).
thf(1065,plain,
! [SV322: $i,SV149: $i] :
( ( ! [SY1418: $i] :
( ( c_Predicate_Oconversep @ ( c_Predicate_Oconversep @ SV149 @ SV322 @ SY1418 ) @ SY1418 @ SV322 )
= SV149 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[874]) ).
thf(1066,plain,
! [SV323: $i,SV150: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OVar @ SV150 ) ) @ SV323 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[875]) ).
thf(1067,plain,
! [SV324: $i,SV151: $i] :
( ( ! [SY1419: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV151 @ SV324 ) @ SY1419 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV151 @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__Xintros__1__1 @ SV151 @ SY1419 @ SV324 ) ) @ SY1419 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[876]) ).
thf(1068,plain,
! [SV325: $i,SV153: $i] :
( ( ! [SY1420: $i,SY1421: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ ( c_Transitive__Closure_Otranclp @ SV153 @ SV325 ) @ SV325 @ SV325 ) @ SY1420 ) @ SY1421 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ ( c_Predicate_Oconversep @ SV153 @ SV325 @ SV325 ) @ SV325 ) @ SY1420 ) @ SY1421 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[878]) ).
thf(1069,plain,
! [SV326: $i,SV154: $i] :
( ( ! [SY1422: $i,SY1423: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ ( c_Predicate_Oconversep @ SV154 @ SV326 @ SV326 ) @ SV326 ) @ SY1422 ) @ SY1423 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ ( c_Transitive__Closure_Otranclp @ SV154 @ SV326 ) @ SV326 @ SV326 ) @ SY1422 ) @ SY1423 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[879]) ).
thf(1070,plain,
! [SV327: $i,SV155: $i] :
( ( ! [SY1424: $i] :
( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV155 @ SV327 ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xnot__accp__down__1__1 @ SV155 @ SY1424 @ SV327 ) ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV155 @ SV327 ) @ SY1424 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[880]) ).
thf(1071,plain,
! [SV328: $i,SV156: $i] :
( ( ( c_Transitive__Closure_Otranclp @ ( c_Predicate_Oconversep @ SV156 @ SV328 @ SV328 ) @ SV328 )
= ( c_Predicate_Oconversep @ ( c_Transitive__Closure_Otranclp @ SV156 @ SV328 ) @ SV328 @ SV328 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[881]) ).
thf(1072,plain,
! [SV157: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV157 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ SV157 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[882]) ).
thf(1073,plain,
! [SV158: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ SV158 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV158 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[883]) ).
thf(1074,plain,
! [SV329: $i,SV159: $i] :
( ( ! [SY1425: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV159 @ SV329 ) @ SY1425 ) )
| ! [SY1426: $i] :
( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV159 @ SV329 ) @ SY1426 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV159 @ SV329 ) @ SY1425 ) @ SY1426 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[884]) ).
thf(1075,plain,
! [SV330: $i,SV160: $i] :
( ( ! [SY1427: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV160 @ SV330 ) @ SY1427 ) )
| ! [SY1428: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV160 @ SV330 ) @ SY1427 ) @ SY1428 ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV160 @ SV330 ) @ SY1428 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[885]) ).
thf(1076,plain,
! [SV331: $i,SV161: $i] :
( ( ! [SY1429: $i,SY1430: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Osubst @ SV161 @ SV331 @ SY1429 ) ) @ ( c_Lambda_Osubst @ SY1430 @ SV331 @ SY1429 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV161 ) @ SY1430 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[886]) ).
thf(1077,plain,
! [SV332: $i,SV162: $i] :
( ( ( hBOOL @ ( hAPP @ SV162 @ SV332 ) )
| ! [SY1431: $i] :
( ~ ( hBOOL @ ( hAPP @ SV162 @ ( v_sko__Wellfounded__Xaccp__Xinducts__1 @ SV162 @ SY1431 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1431 @ t_a ) @ SV332 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[887]) ).
thf(1078,plain,
! [SV333: $i,SV163: $i] :
( ( ( hBOOL @ ( hAPP @ SV163 @ SV333 ) )
| ! [SY1432: $i] :
( ( hBOOL @ ( hAPP @ SV163 @ SY1432 ) )
| ! [SY1433: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1433 @ SY1432 ) @ ( v_sko__Wellfounded__Xaccp__Xinducts__1 @ SV163 @ SY1433 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1433 @ t_a ) @ SV333 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[888]) ).
thf(1079,plain,
! [SV334: $i,SV164: $i] :
( ( ! [SY1434: $i] :
( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV164 @ SV334 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SY1434 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ SV334 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV164 ) ) @ SV334 ) @ SY1434 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[889]) ).
thf(1080,plain,
! [SV335: $i,SV165: $i] :
( ( ( hBOOL @ ( hAPP @ SV165 @ SV335 ) )
| ! [SY1435: $i] :
( ~ ( hBOOL @ ( hAPP @ SV165 @ ( v_sko__Wellfounded__Xaccp__Xinduct__1 @ SV165 @ SY1435 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1435 @ t_a ) @ SV335 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[890]) ).
thf(1081,plain,
! [SV336: $i,SV166: $i] :
( ( ( hBOOL @ ( hAPP @ SV166 @ SV336 ) )
| ! [SY1436: $i] :
( ( hBOOL @ ( hAPP @ SV166 @ SY1436 ) )
| ! [SY1437: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1437 @ SY1436 ) @ ( v_sko__Wellfounded__Xaccp__Xinduct__1 @ SV166 @ SY1437 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1437 @ t_a ) @ SV336 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[891]) ).
thf(1082,plain,
! [SV337: $i,SV167: $i] :
( ( ! [SY1438: $i,SY1439: $i,SY1440: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV167 @ SV337 @ SY1438 ) @ SY1439 ) @ SY1440 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV167 @ SY1440 ) @ SY1439 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[892]) ).
thf(1083,plain,
! [SV338: $i,SV168: $i] :
( ( ! [SY1441: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV168 @ SV338 ) @ SY1441 ) )
| ! [SY1442: $i,SY1443: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV168 @ SY1442 @ SY1443 ) @ SY1441 ) @ SV338 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[893]) ).
thf(1084,plain,
! [SV339: $i,SV169: $i] :
( ( ! [SY1444: $i,SY1445: $i,SY1446: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV169 @ SV339 @ SY1444 ) @ SY1445 ) @ SY1446 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV169 @ SY1446 ) @ SY1445 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[894]) ).
thf(1085,plain,
! [SV340: $i,SV170: $i] :
( ( ! [SY1447: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV170 @ SV340 ) @ SY1447 ) )
| ! [SY1448: $i,SY1449: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV170 @ SY1448 @ SY1449 ) @ SY1447 ) @ SV340 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[895]) ).
thf(1086,plain,
! [SV341: $i,SV171: $i] :
( ( ( hBOOL @ ( hAPP @ SV171 @ SV341 ) )
| ! [SY1450: $i,SY1451: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1450 @ t_a ) @ SY1451 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1450 @ SY1451 ) @ ( v_sko__Wellfounded__Xaccp__Xinducts__1 @ SV171 @ SY1450 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1450 @ t_a ) @ SV341 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[896]) ).
thf(1087,plain,
! [SV342: $i,SV172: $i] :
( ( ( hBOOL @ ( hAPP @ SV172 @ SV342 ) )
| ! [SY1452: $i,SY1453: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1452 @ t_a ) @ SY1453 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1452 @ SY1453 ) @ ( v_sko__Wellfounded__Xaccp__Xinduct__1 @ SV172 @ SY1452 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1452 @ t_a ) @ SV342 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[897]) ).
thf(1088,plain,
! [SV343: $i,SV173: $i] :
( ( ! [SY1454: $i,SY1455: $i] :
( ( c_Predicate_Oconversep @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV173 @ SV343 @ ( tc_fun @ SY1454 @ ( tc_fun @ SY1455 @ tc_bool ) ) ) @ SY1454 @ SY1455 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Predicate_Oconversep @ SV173 @ SY1454 @ SY1455 ) @ ( c_Predicate_Oconversep @ SV343 @ SY1454 @ SY1455 ) @ ( tc_fun @ SY1455 @ ( tc_fun @ SY1454 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[898]) ).
thf(1089,plain,
! [SV344: $i,SV174: $i] :
( ( ! [SY1456: $i,SY1457: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV174 @ SV344 ) @ SY1456 ) @ SY1457 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ SV174 @ SV344 @ SV344 ) @ SV344 ) @ SY1457 ) @ SY1456 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[899]) ).
thf(1090,plain,
! [SV345: $i,SV175: $i] :
( ( ! [SY1458: $i,SY1459: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ SV175 @ SV345 @ SV345 ) @ SV345 ) @ SY1458 ) @ SY1459 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV175 @ SV345 ) @ SY1459 ) @ SY1458 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[900]) ).
thf(1091,plain,
! [SV346: $i,SV176: $i] :
( ( ( hBOOL @ ( hAPP @ SV176 @ SV346 ) )
| ! [SY1460: $i,SY1461: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1460 @ SY1461 ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__1__1 @ SV176 @ SY1460 @ SY1461 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1460 @ SY1461 ) @ SV346 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[901]) ).
thf(1092,plain,
! [SV347: $i,SV177: $i] :
( ( ! [SY1462: $i,SY1463: $i] :
( ( c_Predicate_Oconversep @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV177 @ SV347 @ ( tc_fun @ SY1462 @ ( tc_fun @ SY1463 @ tc_bool ) ) ) @ SY1462 @ SY1463 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Predicate_Oconversep @ SV177 @ SY1462 @ SY1463 ) @ ( c_Predicate_Oconversep @ SV347 @ SY1462 @ SY1463 ) @ ( tc_fun @ SY1463 @ ( tc_fun @ SY1462 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[902]) ).
thf(1093,plain,
! [SV348: $i,SV178: $i] :
( ( ! [SY1464: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV178 @ SV348 ) @ SY1464 ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV178 @ SV348 ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__Xintros__1__1 @ SV178 @ SY1464 @ SV348 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[903]) ).
thf(1094,plain,
! [SV349: $i,SV179: $i] :
( ( ! [SY1465: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV179 @ SV349 ) @ SY1465 ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV179 @ SV349 ) @ ( c_ATP__Linkup_Osko__Wellfounded__XaccpI__1__1 @ SV179 @ SY1465 @ SV349 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[904]) ).
thf(1095,plain,
! [SV350: $i,SV180: $i] :
( ( ! [SY1466: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV180 @ SV350 ) @ SY1466 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV180 @ ( c_ATP__Linkup_Osko__Wellfounded__XaccpI__1__1 @ SV180 @ SY1466 @ SV350 ) ) @ SY1466 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[905]) ).
thf(1096,plain,
! [SV351: $i,SV181: $i] :
( ( ! [SY1467: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV181 ) @ SV351 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV181 ) @ SY1467 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV351 ) @ SY1467 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[906]) ).
thf(1097,plain,
! [SV352: $i,SV182: $i] :
( ( ! [SY1468: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV182 ) @ SV352 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY1468 ) @ SV352 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV182 ) @ SY1468 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[907]) ).
thf(1098,plain,
! [SV353: $i,SV183: $i] :
( ( ( hBOOL @ ( hAPP @ SV183 @ SV353 ) )
| ! [SY1469: $i,SY1470: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1469 @ SY1470 ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__rule__1__1 @ SV183 @ SY1469 @ SY1470 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1469 @ SY1470 ) @ SV353 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[908]) ).
thf(1099,plain,
! [SV354: $i,SV184: $i] :
( ( ! [SY1471: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Olift @ SV184 @ SV354 ) ) @ ( c_Lambda_Olift @ SY1471 @ SV354 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV184 ) @ SY1471 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[909]) ).
thf(1100,plain,
! [SV355: $i,SV185: $i] :
( ( ( hBOOL @ ( hAPP @ SV185 @ SV355 ) )
| ! [SY1472: $i,SY1473: $i] :
( ~ ( hBOOL @ ( hAPP @ SV185 @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__rule__1__1 @ SV185 @ SY1472 @ SY1473 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1472 @ SY1473 ) @ SV355 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[910]) ).
thf(1101,plain,
! [SV356: $i,SV186: $i] :
( ( ! [SY1474: $i] :
( ( hBOOL @ ( hAPP @ SV186 @ SV356 ) )
| ( hBOOL @ ( hAPP @ SV186 @ SY1474 ) )
| ! [SY1475: $i,SY1476: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1475 @ SY1474 ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__rule__1__1 @ SV186 @ SY1475 @ SY1476 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1475 @ SY1476 ) @ SV356 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[911]) ).
thf(1102,plain,
! [SV357: $i,SV187: $i] :
( ( ! [SY1477: $i,SY1478: $i,SY1479: $i] :
( ( c_Predicate_Oconversep @ ( c_Predicate_Opred__comp @ SV187 @ SV357 @ SY1477 @ SY1478 @ SY1479 ) @ SY1477 @ SY1479 )
= ( c_Predicate_Opred__comp @ ( c_Predicate_Oconversep @ SV357 @ SY1478 @ SY1479 ) @ ( c_Predicate_Oconversep @ SV187 @ SY1477 @ SY1478 ) @ SY1479 @ SY1478 @ SY1477 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[912]) ).
thf(1103,plain,
! [SV358: $i,SV188: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ SV188 ) ) @ ( c_Lambda_OdB_OAbs @ SV358 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV188 ) @ SV358 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[913]) ).
thf(1104,plain,
! [SV359: $i,SV189: $i] :
( ( ( class_Lattices_Oupper__semilattice @ ( tc_fun @ SV189 @ SV359 ) )
| ~ ( class_Lattices_Olattice @ SV359 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[914]) ).
thf(1105,plain,
! [SV360: $i,SV190: $i] :
( ( ( class_Lattices_Olower__semilattice @ ( tc_fun @ SV190 @ SV360 ) )
| ~ ( class_Lattices_Olattice @ SV360 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[915]) ).
thf(1106,plain,
! [SV361: $i,SV191: $i] :
( ( ( class_Lattices_Odistrib__lattice @ ( tc_fun @ SV191 @ SV361 ) )
| ~ ( class_Lattices_Odistrib__lattice @ SV361 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[916]) ).
thf(1107,plain,
! [SV362: $i,SV192: $i] :
( ( ( class_Lattices_Olattice @ ( tc_fun @ SV192 @ SV362 ) )
| ~ ( class_Lattices_Olattice @ SV362 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[917]) ).
thf(1108,plain,
! [SV363: $i,SV193: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ SV193 ) @ SV363 ) @ SV363 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[918]) ).
thf(1109,plain,
! [SV364: $i,SV194: $i] :
( ( ( SV194 = SV364 )
| ! [SY1480: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ SY1480 ) @ SV194 ) @ SV364 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[919]) ).
thf(1110,plain,
! [SV365: $i,SV195: $i,SV1: $i] :
( ( ! [SY1481: $i,SY1482: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ SV1 @ SV195 ) @ ( c_List_Olist_OCons @ SV365 @ SY1481 @ SV195 ) ) @ ( c_List_Olist_OCons @ SV365 @ SY1482 @ SV195 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ SV1 @ SV195 ) @ SY1481 ) @ SY1482 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[921]) ).
thf(1111,plain,
! [SV366: $i,SV196: $i,SV2: $i] :
( ( ! [SY1483: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ SV2 @ SV196 ) @ SV366 ) @ SY1483 ) )
| ! [SY1484: $i,SY1485: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV2 @ SY1484 ) @ SY1485 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ SV2 @ SV196 ) @ ( c_List_Olist_OCons @ SY1484 @ SV366 @ SV196 ) ) @ ( c_List_Olist_OCons @ SY1485 @ SY1483 @ SV196 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[922]) ).
thf(1112,plain,
! [SV367: $i,SV197: $i,SV3: $i] :
( ( ! [SY1486: $i,SY1487: $i] :
( ( ( c_List_Olist_OCons @ SV3 @ SV197 @ SV367 )
!= ( c_List_Olist_OCons @ SY1486 @ SY1487 @ SV367 ) )
| ( SV197 = SY1487 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[923]) ).
thf(1113,plain,
! [SV368: $i,SV198: $i,SV4: $i] :
( ( ! [SY1488: $i] :
( ! [SY1489: $i] :
( ( c_List_Olist_OCons @ SV4 @ SV198 @ SV368 )
!= ( c_List_Olist_OCons @ SY1488 @ SY1489 @ SV368 ) )
| ( SV4 = SY1488 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[924]) ).
thf(1114,plain,
! [SV369: $i,SV199: $i,SV5: $i] :
( ( ( c_List_Olist_ONil @ SV5 )
!= ( c_List_Olist_OCons @ SV199 @ SV369 @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[925]) ).
thf(1115,plain,
! [SV370: $i,SV200: $i,SV6: $i] :
( ( ! [SY1490: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ SV6 @ SV200 ) @ SV370 ) @ SY1490 ) )
| ( SY1490 = SV370 )
| ! [SY1491: $i,SY1492: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ SV6 @ SV200 ) @ ( c_List_Olist_OCons @ SY1491 @ SV370 @ SV200 ) ) @ ( c_List_Olist_OCons @ SY1492 @ SY1490 @ SV200 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[926]) ).
thf(1116,plain,
! [SV371: $i,SV201: $i,SV7: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV7 @ SV201 ) @ SV371 ) )
| ! [SY1493: $i,SY1494: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ SV7 @ SY1493 ) @ ( c_List_Olist_OCons @ SV201 @ SY1494 @ SY1493 ) ) @ ( c_List_Olist_OCons @ SV371 @ SY1494 @ SY1493 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[927]) ).
thf(1117,plain,
! [SV372: $i,SV202: $i,SV8: $i] :
( ( ! [SY1495: $i] :
( ( SV8 = SV202 )
| ( SV372 = SY1495 )
| ! [SY1496: $i,SY1497: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ SY1496 @ SY1497 ) @ ( c_List_Olist_OCons @ SV202 @ SY1495 @ SY1497 ) ) @ ( c_List_Olist_OCons @ SV8 @ SV372 @ SY1497 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[928]) ).
thf(1118,plain,
! [SV373: $i,SV203: $i,SV9: $i] :
( ( ! [SY1498: $i,SY1499: $i,SY1500: $i] :
( ( c_List_Ofoldl @ SV9 @ SV203 @ ( c_List_Olist_OCons @ SV373 @ SY1498 @ SY1499 ) @ SY1500 @ SY1499 )
= ( c_List_Ofoldl @ SV9 @ ( hAPP @ ( hAPP @ SV9 @ SV203 ) @ SV373 ) @ SY1498 @ SY1500 @ SY1499 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[929]) ).
thf(1119,plain,
! [SV374: $i,SV204: $i,SV10: $i] :
( ( ( c_List_Olist_OCons @ SV10 @ SV204 @ SV374 )
!= ( c_List_Olist_ONil @ SV374 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[930]) ).
thf(1120,plain,
! [SV375: $i,SV205: $i,SV11: $i] :
( ( ( c_List_Olist_OCons @ SV11 @ SV205 @ SV375 )
!= ( c_List_Olist_ONil @ SV375 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[931]) ).
thf(1121,plain,
! [SV376: $i,SV206: $i,SV12: $i] :
( ( ! [SY1501: $i] :
( ( SV12 = SV206 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV376 @ SV206 ) @ SV12 ) )
| ! [SY1502: $i,SY1503: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ SV376 @ SY1501 ) @ ( c_List_Olist_OCons @ SV206 @ SY1502 @ SY1501 ) ) @ ( c_List_Olist_OCons @ SV12 @ SY1503 @ SY1501 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[932]) ).
thf(1122,plain,
! [SV377: $i,SV207: $i,SV13: $i] :
( ( ( c_List_Olist_OCons @ SV13 @ SV207 @ SV377 )
!= SV207 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[933]) ).
thf(1123,plain,
! [SV378: $i,SV208: $i,SV14: $i] :
( ( SV14
!= ( c_List_Olist_OCons @ SV208 @ SV14 @ SV378 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[934]) ).
thf(1124,plain,
! [SV379: $i,SV209: $i,SV15: $i] :
( ( ! [SY1504: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( c_ListOrder_Ostep1 @ SV15 @ SV209 ) @ ( tc_List_Olist @ SV209 ) ) @ ( c_List_Olist_OCons @ SV379 @ SY1504 @ SV209 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( c_ListOrder_Ostep1 @ SV15 @ SV209 ) @ ( tc_List_Olist @ SV209 ) ) @ SY1504 ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV15 @ SV209 ) @ SV379 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[935]) ).
thf(1125,plain,
! [SV380: $i,SV210: $i,SV16: $i] :
( ( ! [SY1505: $i] :
( ( ( c_Type_Otype_OFun @ SV16 @ SV210 )
!= ( c_Type_Otype_OFun @ SV380 @ SY1505 ) )
| ( SV210 = SY1505 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[936]) ).
thf(1126,plain,
! [SV381: $i,SV211: $i,SV17: $i] :
( ( ! [SY1506: $i] :
( ( c_Type_Otype_OFun @ SV17 @ SV211 )
!= ( c_Type_Otype_OFun @ SV381 @ SY1506 ) )
| ( SV17 = SV381 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[937]) ).
thf(1127,plain,
! [SV382: $i,SV212: $i,SV18: $i] :
( ( ! [SY1507: $i] :
( ( c_Type_Otyping @ SV18 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV212 ) @ SV382 ) @ SY1507 )
| ! [SY1508: $i] :
( ~ ( c_Type_Otyping @ SV18 @ SV382 @ SY1508 )
| ~ ( c_Type_Otyping @ SV18 @ SV212 @ ( c_Type_Otype_OFun @ SY1508 @ SY1507 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[938]) ).
thf(1128,plain,
! [SV383: $i,SV213: $i,SV19: $i] :
( ( ! [SY1509: $i,SY1510: $i] :
( ( c_Type_Otyping @ ( c_Type_Oshift @ SV19 @ SV213 @ SV383 @ tc_Type_Otype ) @ ( c_Lambda_Olift @ SY1509 @ SV213 ) @ SY1510 )
| ~ ( c_Type_Otyping @ SV19 @ SY1509 @ SY1510 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[939]) ).
thf(1129,plain,
! [SV384: $i,SV214: $i,SV20: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Olift @ SV20 @ SV214 ) ) @ ( c_Lambda_Olift @ SV384 @ SV214 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV20 ) @ SV384 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[940]) ).
thf(1130,plain,
! [SV385: $i,SV215: $i,SV21: $i] :
( ( ! [SY1511: $i] :
( ~ ( c_Type_Otyping @ SV21 @ SV215 @ SV385 )
| ! [SY1512: $i,SY1513: $i] :
( ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV21 @ SY1511 @ SV385 @ tc_Type_Otype ) @ SY1512 @ SY1513 )
| ( c_Type_Otyping @ SV21 @ ( c_Lambda_Osubst @ SY1512 @ SV215 @ SY1511 ) @ SY1513 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[941]) ).
thf(1131,plain,
! [SV386: $i,SV216: $i,SV22: $i] :
( ( ( c_Type_Otyping @ SV22 @ SV216 @ SV386 )
| ! [SY1514: $i] :
( ~ ( c_Type_Otyping @ SV22 @ SY1514 @ SV386 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SY1514 ) @ SV216 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[942]) ).
thf(1132,plain,
! [SV387: $i,SV217: $i,SV23: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV23 ) @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SV217 @ SV23 @ SV387 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV217 ) @ SV23 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV387 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[943]) ).
thf(1133,plain,
! [SV388: $i,SV218: $i,SV24: $i] :
( ( ! [SY1515: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV24 @ SV218 @ SV388 ) ) @ ( c_Lambda_Osubst @ SV24 @ SY1515 @ SV388 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV218 ) @ SY1515 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[944]) ).
thf(1134,plain,
! [SV389: $i,SV219: $i,SV25: $i] :
( ( ! [SY1516: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV25 @ SV219 @ SV389 ) ) @ ( c_Lambda_Osubst @ SY1516 @ SV219 @ SV389 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV25 ) @ SY1516 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[945]) ).
thf(1135,plain,
! [SV390: $i,SV220: $i,SV26: $i] :
( ( ! [SY1517: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV26 @ SV220 @ SV390 ) ) @ ( c_Lambda_Osubst @ SV26 @ SY1517 @ SV390 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV220 ) @ SY1517 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[946]) ).
thf(1136,plain,
! [SV391: $i,SV222: $i,SV28: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV28 ) @ SV222 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV391 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV28 ) @ SV222 )
= SV391 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[948]) ).
thf(1137,plain,
! [SV223: $i,SV29: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_OdB_OAbs @ SV29 ) ) @ ( c_Lambda_OdB_OAbs @ SV223 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV29 ) @ SV223 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[949]) ).
thf(1138,plain,
! [SV392: $i,SV224: $i,SV30: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV30 ) @ SV224 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV30 ) @ SV392 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV224 ) @ SV392 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[950]) ).
thf(1139,plain,
! [SV393: $i,SV225: $i,SV31: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV31 ) @ SV225 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV393 ) @ SV225 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV31 ) @ SV393 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[951]) ).
thf(1140,plain,
! [SV394: $i,SV226: $i,SV32: $i] :
( ( ! [SY1518: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV32 ) @ SV226 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV394 ) @ SY1518 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV226 ) @ SY1518 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV32 ) @ SV394 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[952]) ).
thf(1141,plain,
! [SV395: $i,SV227: $i,SV33: $i] :
( ( ! [SY1519: $i] :
( ( c_Type_Otyping @ SV33 @ ( c_Lambda_OdB_OAbs @ SV227 ) @ ( c_Type_Otype_OFun @ SV395 @ SY1519 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV33 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV395 @ tc_Type_Otype ) @ SV227 @ SY1519 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[953]) ).
thf(1142,plain,
! [SV396: $i,SV228: $i,SV34: $i] :
( ( ( c_List_Olistsp @ ( c_Wellfounded_Oaccp @ SV34 @ SV228 ) @ SV396 @ SV228 )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( c_ListOrder_Ostep1 @ SV34 @ SV228 ) @ ( tc_List_Olist @ SV228 ) ) @ SV396 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[954]) ).
thf(1143,plain,
! [SV397: $i,SV229: $i,SV35: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( c_ListOrder_Ostep1 @ SV35 @ SV229 ) @ ( tc_List_Olist @ SV229 ) ) @ SV397 ) )
| ~ ( c_List_Olistsp @ ( c_Wellfounded_Oaccp @ SV35 @ SV229 ) @ SV397 @ SV229 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[955]) ).
thf(1144,plain,
! [SV398: $i,SV230: $i,SV36: $i] :
( ( ! [SY1520: $i] :
( ( hAPP @ ( c_Type_Oshift @ SV36 @ SV230 @ SV398 @ SY1520 ) @ SV230 )
= SV398 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[956]) ).
thf(1145,plain,
! [SV399: $i,SV231: $i,SV37: $i] :
( ( ! [SY1521: $i] :
( ( c_List_Ofoldl @ SV37 @ SV231 @ ( c_List_Olist_ONil @ SV399 ) @ SY1521 @ SV399 )
= SV231 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[957]) ).
thf(1146,plain,
! [SV400: $i,SV232: $i,SV38: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ SV38 @ SV232 ) @ SV400 ) @ ( c_List_Olist_ONil @ SV232 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[958]) ).
thf(1147,plain,
! [SV401: $i,SV233: $i,SV39: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ SV39 @ SV233 ) @ ( c_List_Olist_ONil @ SV233 ) ) @ SV401 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[959]) ).
thf(1148,plain,
! [SV402: $i,SV235: $i,SV41: $i] :
( ( ! [SY1522: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV41 ) @ SV235 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV402 @ SY1522 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV41
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV402 @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ SV41 @ SV235 @ SV402 @ SY1522 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY1522
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[961]) ).
thf(1149,plain,
! [SV403: $i,SV236: $i,SV42: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV42 @ SV236 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV42 @ SV403 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV236 ) @ SV403 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[962]) ).
thf(1150,plain,
! [SV404: $i,SV237: $i,SV43: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV43 @ SV237 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV404 @ SV237 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV43 ) @ SV404 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[963]) ).
thf(1151,plain,
! [SV238: $i,SV45: $i] :
( ( ( ! [SY1266: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV45 @ SV238 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SY1266 ) ) )
= $true )
| ( ( SV238
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[964]) ).
thf(1152,plain,
! [SV405: $i,SV239: $i,SV47: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV47 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV239 @ SV405 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV405
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[965]) ).
thf(1153,plain,
! [SV406: $i,SV240: $i,SV48: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV48 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV240 @ SV406 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV406
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[966]) ).
thf(1154,plain,
! [SV407: $i,SV241: $i,SV50: $i] :
( ( ! [SY1523: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV50 @ SV241 @ SV407 ) ) )
| ! [SY1524: $i] :
( ~ ( c_Type_Otyping @ SY1523 @ SV241 @ SY1524 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV241 ) )
| ! [SY1525: $i] :
~ ( c_Type_Otyping @ ( c_Type_Oshift @ SY1523 @ SV407 @ SY1524 @ tc_Type_Otype ) @ SV50 @ SY1525 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV50 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[967]) ).
thf(1155,plain,
! [SV408: $i,SV242: $i,SV51: $i] :
( ( ( SV51
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV242 ) @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SV242 @ SV408 @ SV51 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV242 ) @ SV408 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV51 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[968]) ).
thf(1156,plain,
! [SV243: $i,SV52: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV52 ) @ SV243 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true )
| ( ( ~ ( c_List_Olistsp @ c_InductTermi_OIT @ SV243 @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[969]) ).
thf(1157,plain,
! [SV409: $i,SV244: $i,SV53: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV53 ) @ SV244 )
!= ( c_Lambda_OdB_OVar @ SV409 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[970]) ).
thf(1158,plain,
! [SV55: $i,SV410: $i] :
( ( ( ! [SY1526: $i] :
~ ( c_Type_Otyping @ SV410 @ SV55 @ SY1526 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV55 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[972]) ).
thf(1159,plain,
! [SV411: $i,SV246: $i,SV56: $i] :
( ( ! [SY1527: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV56 ) ) @ SV246 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV411 ) @ SY1527 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[973]) ).
thf(1160,plain,
! [SV412: $i,SV247: $i,SV57: $i] :
( ( ! [SY1528: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV57 @ SV247 ) @ SV412 ) )
| ! [SY1529: $i,SY1530: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV57 @ SY1528 @ ( tc_fun @ SY1529 @ ( tc_fun @ SY1530 @ tc_bool ) ) ) @ SV247 ) @ SV412 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[974]) ).
thf(1161,plain,
! [SV413: $i,SV248: $i,SV58: $i] :
( ( ! [SY1531: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV58 @ SV248 ) @ SV413 ) )
| ! [SY1532: $i,SY1533: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY1531 @ SV58 @ ( tc_fun @ SY1532 @ ( tc_fun @ SY1533 @ tc_bool ) ) ) @ SV248 ) @ SV413 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[975]) ).
thf(1162,plain,
! [SV414: $i,SV59: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV59 ) @ ( c_Lambda_OdB_OVar @ SV414 ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV59 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[976]) ).
thf(1163,plain,
! [SV415: $i,SV249: $i,SV60: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_Olift @ SV60 @ SV249 ) @ SV415 @ SV249 )
= SV60 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[977]) ).
thf(1164,plain,
! [SV416: $i,SV250: $i,SV61: $i] :
( ( ! [SY1534: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV61 @ SV250 ) @ SV416 ) @ SY1534 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV61 @ SV416 ) @ SY1534 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[978]) ).
thf(1165,plain,
! [SV62: $i] :
( ( ( class_Lattices_Olattice @ SV62 )
= $false )
| ( ( ! [SY852: $i,SY853: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY852 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY852 @ SY853 @ SV62 ) @ SV62 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY852 @ SY853 @ SV62 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[979]) ).
thf(1166,plain,
! [SV63: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV63 )
= $false )
| ( ( ! [SY854: $i,SY855: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY854 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY854 @ SY855 @ SV63 ) @ SV63 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY854 @ SY855 @ SV63 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[980]) ).
thf(1167,plain,
! [SV64: $i] :
( ( ( class_Lattices_Olattice @ SV64 )
= $false )
| ( ( ! [SY856: $i,SY857: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY856 @ SY857 @ SV64 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY857 @ SY856 @ SV64 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[981]) ).
thf(1168,plain,
! [SV65: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV65 )
= $false )
| ( ( ! [SY858: $i,SY859: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY858 @ SY859 @ SV65 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY859 @ SY858 @ SV65 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[982]) ).
thf(1169,plain,
! [SV66: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV66 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OAbs @ SV66 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[983]) ).
thf(1170,plain,
! [SV417: $i,SV251: $i,SV67: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV67 @ SV251 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV417 @ SV251 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV67 = SV417 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[984]) ).
thf(1171,plain,
! [SV252: $i,SV68: $i] :
( ( ( ! [SY1289: $i] :
( ( c_Lambda_OdB_OAbs @ SV68 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV252 @ SY1289 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true )
| ( ( ( c_Lambda_OdB_OAbs @ SV68 )
= SV252 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[985]) ).
thf(1172,plain,
! [SV70: $i] :
( ( ( class_Lattices_Olattice @ SV70 )
= $false )
| ( ( ! [SY865: $i,SY866: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY865 @ SY866 @ SV70 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY866 @ SY865 @ SV70 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[987]) ).
thf(1173,plain,
! [SV71: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV71 )
= $false )
| ( ( ! [SY867: $i,SY868: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY867 @ SY868 @ SV71 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY868 @ SY867 @ SV71 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[988]) ).
thf(1174,plain,
! [SV254: $i,SV72: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV72 ) )
= $true )
| ( ( ! [SY1290: $i,SY1291: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV254 @ SY1290 @ SV72 ) @ SY1291 @ SV72 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV254 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY1290 @ SY1291 @ SV72 ) @ SV72 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[989]) ).
thf(1175,plain,
! [SV255: $i,SV73: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV73 ) )
= $true )
| ( ( ! [SY1292: $i,SY1293: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV255 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY1292 @ SY1293 @ SV73 ) @ SV73 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY1292 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV255 @ SY1293 @ SV73 ) @ SV73 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[990]) ).
thf(1176,plain,
! [SV256: $i,SV74: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV74 ) )
= $true )
| ( ( ! [SY1294: $i,SY1295: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV256 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY1294 @ SY1295 @ SV74 ) @ SV74 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY1294 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV256 @ SY1295 @ SV74 ) @ SV74 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[991]) ).
thf(1177,plain,
! [SV257: $i,SV75: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV75 ) )
= $true )
| ( ( ! [SY1296: $i,SY1297: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV257 @ SY1296 @ SV75 ) @ SY1297 @ SV75 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV257 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY1296 @ SY1297 @ SV75 ) @ SV75 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[992]) ).
thf(1178,plain,
! [SV76: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV76 )
= $false )
| ( ( ! [SY881: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY881 @ SY881 @ SV76 )
= SY881 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[993]) ).
thf(1179,plain,
! [SV258: $i,SV77: $i] :
( ( ( ~ ( class_Lattices_Odistrib__lattice @ SV77 ) )
= $true )
| ( ( ! [SY1298: $i,SY1299: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV258 @ SY1298 @ SV77 ) @ SY1299 @ SV77 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV258 @ SY1299 @ SV77 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY1298 @ SY1299 @ SV77 ) @ SV77 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[994]) ).
thf(1180,plain,
! [SV259: $i,SV78: $i] :
( ( ( ~ ( class_Lattices_Odistrib__lattice @ SV78 ) )
= $true )
| ( ( ! [SY1300: $i,SY1301: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV259 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY1300 @ SY1301 @ SV78 ) @ SV78 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV259 @ SY1300 @ SV78 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV259 @ SY1301 @ SV78 ) @ SV78 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[995]) ).
thf(1181,plain,
! [SV418: $i,SV260: $i,SV79: $i] :
( ( ! [SY1535: $i,SY1536: $i,SY1537: $i,SY1538: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV79 @ SV260 @ SV418 @ SY1535 @ SY1536 ) @ SY1537 ) @ SY1538 ) )
| ! [SY1307: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV260 @ SY1307 ) @ SY1538 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV79 @ SY1537 ) @ SY1307 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[996]) ).
thf(1182,plain,
! [SV419: $i,SV261: $i,SV80: $i] :
( ( ! [SY1540: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV80 @ SV261 ) @ SV419 ) @ SY1540 ) )
| ! [SY1541: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV80 @ SV261 ) @ SY1541 ) @ SY1540 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV80 @ SV261 ) @ SV419 ) @ SY1541 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[997]) ).
thf(1183,plain,
! [SV420: $i,SV262: $i,SV81: $i] :
( ( ! [SY1542: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV81 @ SV262 ) @ SV420 ) @ SY1542 ) )
| ! [SY1543: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV81 @ SV262 ) @ SY1543 ) @ SY1542 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV81 @ SV262 ) @ SV420 ) @ SY1543 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[998]) ).
thf(1184,plain,
! [SV421: $i,SV263: $i,SV82: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV82 @ SV263 ) @ SV421 ) @ SV421 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[999]) ).
thf(1185,plain,
! [SV422: $i,SV264: $i,SV83: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV83 @ SV264 ) @ SV422 ) @ SV422 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1000]) ).
thf(1186,plain,
! [SV423: $i,SV265: $i,SV84: $i] :
( ( ! [SY1544: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV84 @ SV265 ) @ SV423 ) @ SY1544 ) )
| ! [SY1545: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV84 @ SV265 ) @ SY1545 ) @ SY1544 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV84 @ SV265 ) @ SV423 ) @ SY1545 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1001]) ).
thf(1187,plain,
! [SV424: $i,SV266: $i,SV85: $i] :
( ( ! [SY1546: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV85 @ SV266 ) @ SV424 ) @ SY1546 ) )
| ! [SY1547: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV85 @ SV266 ) @ SY1547 ) @ SY1546 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV85 @ SV424 ) @ SY1547 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1002]) ).
thf(1188,plain,
! [SV425: $i,SV267: $i,SV86: $i] :
( ( ! [SY1548: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV86 @ SV267 ) @ SV425 ) @ SY1548 ) )
| ! [SY1549: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV86 @ SY1549 ) @ SY1548 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV86 @ SV267 ) @ SV425 ) @ SY1549 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1003]) ).
thf(1189,plain,
! [SV426: $i,SV268: $i,SV87: $i] :
( ( ( c_Lambda_Olift @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV87 ) @ SV268 ) @ SV426 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Olift @ SV87 @ SV426 ) ) @ ( c_Lambda_Olift @ SV268 @ SV426 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1004]) ).
thf(1190,plain,
! [SV269: $i,SV88: $i] :
( ( ( c_Wellfounded_OwfP @ ( c_Transitive__Closure_Otranclp @ SV88 @ SV269 ) @ SV269 )
= $true )
| ( ( ~ ( c_Wellfounded_OwfP @ SV88 @ SV269 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1005]) ).
thf(1191,plain,
! [SV427: $i,SV270: $i,SV89: $i] :
( ( ( ( hAPP @ SV89 @ SV270 )
= SV427 )
| ~ ( c_Type_Otyping @ SV89 @ ( c_Lambda_OdB_OVar @ SV270 ) @ SV427 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1006]) ).
thf(1192,plain,
! [SV428: $i,SV271: $i,SV90: $i] :
( ( ! [SY1550: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV90 @ SV271 ) @ SV428 ) @ SY1550 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV90 @ SV271 ) @ SV428 ) @ SY1550 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1007]) ).
thf(1193,plain,
! [SV272: $i,SV92: $i] :
( ( ( c_Lambda_OdB_OVar @ SV92 )
= ( c_Lambda_OdB_OAbs @ SV272 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1008]) ).
thf(1194,plain,
! [SV429: $i,SV273: $i,SV93: $i] :
( ( ! [SY1551: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV93 @ SV273 ) @ SV429 ) @ SY1551 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV93 @ SV429 ) @ SY1551 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1009]) ).
thf(1195,plain,
! [SV430: $i,SV274: $i,SV94: $i] :
( ( ! [SY1552: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV94 @ SV274 ) @ SV430 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY1552 @ SV274 ) @ SV430 ) )
| ! [SY1553: $i,SY1554: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY1552 @ SV94 @ ( tc_fun @ SY1553 @ ( tc_fun @ SY1554 @ tc_bool ) ) ) @ SV274 ) @ SV430 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1010]) ).
thf(1196,plain,
! [SV431: $i,SV275: $i,SV95: $i] :
( ( ! [SY1555: $i,SY1556: $i,SY1557: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV95 @ SV275 @ ( tc_fun @ SV431 @ ( tc_fun @ SY1555 @ tc_bool ) ) ) @ SY1556 ) @ SY1557 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV275 @ SY1556 ) @ SY1557 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1011]) ).
thf(1197,plain,
! [SV432: $i,SV276: $i,SV96: $i] :
( ( ! [SY1558: $i,SY1559: $i,SY1560: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV96 @ SV276 @ ( tc_fun @ SV432 @ ( tc_fun @ SY1558 @ tc_bool ) ) ) @ SY1559 ) @ SY1560 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV96 @ SY1559 ) @ SY1560 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1012]) ).
thf(1198,plain,
! [SV433: $i,SV277: $i,SV97: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV97 ) ) @ SV277 ) @ SV433 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV277 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV97 @ SV277 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV433 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1013]) ).
thf(1199,plain,
! [SV434: $i,SV98: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Olift @ SV98 @ SV434 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV98 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1014]) ).
thf(1200,plain,
! [SV435: $i,SV278: $i,SV99: $i] :
( ( ! [SY1561: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV99 ) @ SV278 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV435 ) @ SY1561 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1015]) ).
thf(1201,plain,
! [SV279: $i,SV100: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV100 ) )
= $true )
| ( ( ! [SY1346: $i,SY1347: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV279 @ SY1346 @ SV100 ) @ SY1347 @ SV100 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV279 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY1346 @ SY1347 @ SV100 ) @ SV100 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1016]) ).
thf(1202,plain,
! [SV280: $i,SV101: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV101 ) )
= $true )
| ( ( ! [SY1348: $i,SY1349: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV280 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY1348 @ SY1349 @ SV101 ) @ SV101 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY1348 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV280 @ SY1349 @ SV101 ) @ SV101 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1017]) ).
thf(1203,plain,
! [SV281: $i,SV102: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV102 ) )
= $true )
| ( ( ! [SY1350: $i,SY1351: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV281 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY1350 @ SY1351 @ SV102 ) @ SV102 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY1350 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV281 @ SY1351 @ SV102 ) @ SV102 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1018]) ).
thf(1204,plain,
! [SV282: $i,SV103: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV103 ) )
= $true )
| ( ( ! [SY1352: $i,SY1353: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV282 @ SY1352 @ SV103 ) @ SY1353 @ SV103 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV282 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY1352 @ SY1353 @ SV103 ) @ SV103 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1019]) ).
thf(1205,plain,
! [SV283: $i,SV104: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV104 )
!= ( c_Lambda_OdB_OAbs @ SV283 ) )
= $true )
| ( ( SV104 = SV283 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1020]) ).
thf(1206,plain,
! [SV436: $i,SV284: $i,SV105: $i] :
( ( ( c_Lambda_OdB_OVar @ SV105 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV284 ) @ SV436 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1021]) ).
thf(1207,plain,
! [SV285: $i,SV106: $i] :
( ( ( ! [SY1355: $i] :
( ( c_Lambda_OdB_OVar @ SV106 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV285 @ SY1355 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true )
| ( ( ( c_Lambda_OdB_OVar @ SV106 )
= SV285 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1022]) ).
thf(1208,plain,
! [SV437: $i,SV286: $i,SV107: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV107 @ SV286 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV437 @ SV286 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV107 ) @ SV437 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1023]) ).
thf(1209,plain,
! [SV108: $i] :
( ( ( class_Lattices_Olattice @ SV108 )
= $false )
| ( ( ! [SY971: $i,SY972: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY971 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY971 @ SY972 @ SV108 ) @ SV108 )
= SY971 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1024]) ).
thf(1210,plain,
! [SV438: $i,SV288: $i,SV110: $i] :
( ( ( SV110 = SV288 )
| ! [SY1562: $i,SY1563: $i] :
( ~ ( c_Type_Otyping @ SV438 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1562 ) @ SY1563 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV288 )
| ~ ( c_Type_Otyping @ SV438 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1562 ) @ SY1563 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV110 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1026]) ).
thf(1211,plain,
! [SV439: $i,SV289: $i,SV111: $i] :
( ( ! [SY1564: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV111 ) @ SV289 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV439 ) @ SY1564 ) )
| ( SV289 = SY1564 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1027]) ).
thf(1212,plain,
! [SV440: $i,SV290: $i,SV112: $i] :
( ( ! [SY1565: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV112 ) @ SV290 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV440 ) @ SY1565 ) )
| ( SV112 = SV440 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1028]) ).
thf(1213,plain,
! [SV113: $i] :
( ( ( class_Lattices_Olattice @ SV113 )
= $false )
| ( ( ! [SY984: $i,SY985: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY984 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY984 @ SY985 @ SV113 ) @ SV113 )
= SY984 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1029]) ).
thf(1214,plain,
! [SV441: $i,SV291: $i,SV114: $i] :
( ( ! [SY1566: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV114 ) @ SV291 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV441 ) @ SY1566 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV291 = SY1566 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1030]) ).
thf(1215,plain,
! [SV442: $i,SV292: $i,SV115: $i] :
( ( ! [SY1567: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV115 ) @ SV292 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV442 ) @ SY1567 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV115 = SV442 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1031]) ).
thf(1216,plain,
! [SV443: $i,SV293: $i,SV116: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV116 @ SV293 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SV443 ) )
| ( SV116
= ( c_Lambda_OdB_OAbs @ SV443 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1032]) ).
thf(1217,plain,
! [SV444: $i,SV295: $i,SV118: $i] :
( ( ! [SY1568: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV118 @ SV295 ) @ SV444 ) @ SY1568 ) )
| ( SV444 = SY1568 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV118 @ SV295 ) @ SV444 ) @ SY1568 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1034]) ).
thf(1218,plain,
! [SV445: $i,SV296: $i,SV119: $i] :
( ( ! [SY1569: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV119 @ SV296 ) @ SV445 ) @ SY1569 ) )
| ( SV445 = SY1569 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV119 @ SV296 ) @ SV445 ) @ SY1569 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1035]) ).
thf(1219,plain,
! [SV446: $i,SV297: $i,SV120: $i] :
( ( ( c_Transitive__Closure_Ortranclp @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Ortranclp @ SV120 @ SV297 ) @ ( c_Transitive__Closure_Ortranclp @ SV446 @ SV297 ) @ ( tc_fun @ SV297 @ ( tc_fun @ SV297 @ tc_bool ) ) ) @ SV297 )
= ( c_Transitive__Closure_Ortranclp @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV120 @ SV446 @ ( tc_fun @ SV297 @ ( tc_fun @ SV297 @ tc_bool ) ) ) @ SV297 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1036]) ).
thf(1220,plain,
! [SV298: $i,SV121: $i] :
( ( ( ~ ( class_Lattices_Odistrib__lattice @ SV121 ) )
= $true )
| ( ( ! [SY1374: $i,SY1375: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV298 @ SY1374 @ SV121 ) @ SY1375 @ SV121 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV298 @ SY1375 @ SV121 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY1374 @ SY1375 @ SV121 ) @ SV121 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1037]) ).
thf(1221,plain,
! [SV299: $i,SV122: $i] :
( ( ( ~ ( class_Lattices_Odistrib__lattice @ SV122 ) )
= $true )
| ( ( ! [SY1376: $i,SY1377: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV299 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY1376 @ SY1377 @ SV122 ) @ SV122 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV299 @ SY1376 @ SV122 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV299 @ SY1377 @ SV122 ) @ SV122 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1038]) ).
thf(1222,plain,
! [SV123: $i] :
( ( ( class_Lattices_Olattice @ SV123 )
= $false )
| ( ( ! [SY1009: $i,SY1010: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY1009 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY1009 @ SY1010 @ SV123 ) @ SV123 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY1009 @ SY1010 @ SV123 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1039]) ).
thf(1223,plain,
! [SV124: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV124 )
= $false )
| ( ( ! [SY1011: $i,SY1012: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY1011 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY1011 @ SY1012 @ SV124 ) @ SV124 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY1011 @ SY1012 @ SV124 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1040]) ).
thf(1224,plain,
! [SV447: $i,SV125: $i] :
( ( ( ! [SY1570: $i] : ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV125 @ ( c_Lambda_OdB_OVar @ SV447 ) @ SY1570 ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV125 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1041]) ).
thf(1225,plain,
! [SV127: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV127 )
= $false )
| ( ( ! [SY1016: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY1016 @ SY1016 @ SV127 )
= SY1016 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1043]) ).
thf(1226,plain,
! [SV448: $i,SV302: $i,SV129: $i] :
( ( ! [SY1571: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV129 ) @ SV302 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV448 ) @ SY1571 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV302 = SY1571 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1045]) ).
thf(1227,plain,
! [SV449: $i,SV303: $i,SV130: $i] :
( ( ! [SY1572: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV130 ) @ SV303 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV449 ) @ SY1572 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV130 = SV449 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1046]) ).
thf(1228,plain,
! [SV450: $i,SV304: $i,SV131: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV131 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV304 ) @ SV450 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1047]) ).
thf(1229,plain,
! [SV451: $i,SV305: $i,SV132: $i] :
( ( ! [SY1573: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV132 @ SV305 ) @ SV451 ) @ SY1573 ) )
| ! [SY1574: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV132 @ SV305 ) @ SY1574 ) @ SY1573 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV132 @ SV305 ) @ SV451 ) @ SY1574 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1048]) ).
thf(1230,plain,
! [SV306: $i,SV133: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV133 )
!= ( c_Lambda_OdB_OVar @ SV306 ) )
= $true )
| ( ( SV133 = SV306 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1049]) ).
thf(1231,plain,
! [SV452: $i,SV307: $i,SV134: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV134 ) @ SV307 )
!= ( c_Lambda_OdB_OAbs @ SV452 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1050]) ).
thf(1232,plain,
! [SV308: $i,SV135: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV135 )
= ( c_Lambda_OdB_OVar @ SV308 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1051]) ).
thf(1233,plain,
! [SV453: $i,SV309: $i,SV136: $i] :
( ( ! [SY1575: $i] :
( ( c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV136 ) @ SV309 ) @ SV453 @ SY1575 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV136 @ SV453 @ SY1575 ) ) @ ( c_Lambda_Osubst @ SV309 @ SV453 @ SY1575 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1052]) ).
thf(1234,plain,
! [SV454: $i,SV310: $i,SV137: $i] :
( ( ! [SY1576: $i,SY1577: $i,SY1578: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV137 @ SV310 @ ( tc_fun @ SV454 @ ( tc_fun @ SY1576 @ tc_bool ) ) ) @ SY1577 ) @ SY1578 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV310 @ SY1577 ) @ SY1578 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ SY1577 ) @ SY1578 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1053]) ).
thf(1235,plain,
! [SV455: $i,SV311: $i,SV138: $i] :
( ( ! [SY1579: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV138 @ SV311 ) @ SV455 ) @ SY1579 ) )
| ! [SY1580: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV138 @ SV311 ) @ SY1580 ) @ SY1579 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV138 @ SV455 ) @ SY1580 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1054]) ).
thf(1236,plain,
! [SV456: $i,SV312: $i,SV139: $i] :
( ( ! [SY1581: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV139 @ SV312 ) @ SV456 ) @ SY1581 ) )
| ! [SY1582: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV139 @ SY1582 ) @ SY1581 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV139 @ SV312 ) @ SV456 ) @ SY1582 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1055]) ).
thf(1237,plain,
! [SV457: $i,SV313: $i,SV140: $i] :
( ( ! [SY1583: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV140 @ SV313 ) @ SV457 ) @ SY1583 ) )
| ! [SY1584: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV140 @ SY1584 ) @ SY1583 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV140 @ SV313 ) @ SV457 ) @ SY1584 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1056]) ).
thf(1238,plain,
! [SV458: $i,SV314: $i,SV141: $i] :
( ( ! [SY1585: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV141 @ SV314 ) @ SV458 ) @ SY1585 ) )
| ! [SY1586: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV141 @ SV314 ) @ SY1586 ) @ SY1585 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV141 @ SV458 ) @ SY1586 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1057]) ).
thf(1239,plain,
! [SV459: $i,SV315: $i,SV142: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV142 @ SV315 ) @ SV459 ) )
| ! [SY1587: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV142 @ SV459 ) @ SY1587 ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV142 @ SV315 ) @ SY1587 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1058]) ).
thf(1240,plain,
! [SV460: $i,SV316: $i,SV143: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV143 @ SV316 ) @ SV460 ) )
| ! [SY1588: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV460 ) @ SY1588 ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV143 @ SV316 ) @ SY1588 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1059]) ).
thf(1241,plain,
! [SV317: $i,SV144: $i] :
( ( ( hBOOL @ ( hAPP @ SV144 @ SV317 ) )
= $true )
| ( ( ! [SY1409: $i,SY1410: $i] :
( ~ ( hBOOL @ ( hAPP @ SV144 @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__1__1 @ SV144 @ SY1409 @ SY1410 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1409 @ SY1410 ) @ SV317 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1060]) ).
thf(1242,plain,
! [SV461: $i,SV318: $i,SV145: $i] :
( ( ( hBOOL @ ( hAPP @ SV145 @ SV318 ) )
| ( hBOOL @ ( hAPP @ SV145 @ SV461 ) )
| ! [SY1589: $i,SY1590: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1589 @ SV461 ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__1__1 @ SV145 @ SY1589 @ SY1590 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1589 @ SY1590 ) @ SV318 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1061]) ).
thf(1243,plain,
! [SV462: $i,SV319: $i,SV146: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV146 @ ( c_ATP__Linkup_Osko__Wellfounded__Xnot__accp__down__1__1 @ SV146 @ SV319 @ SV462 ) ) @ SV319 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV146 @ SV462 ) @ SV319 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1062]) ).
thf(1244,plain,
! [SV463: $i,SV320: $i,SV147: $i] :
( ( ( c_Type_Otyping @ SV147 @ SV320 @ SV463 )
| ! [SY1591: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SY1591 ) @ SV320 ) )
| ~ ( c_Type_Otyping @ SV147 @ SY1591 @ SV463 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1063]) ).
thf(1245,plain,
! [SV321: $i,SV148: $i] :
( ( ( ! [SY1417: $i] : ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV148 @ SV321 ) @ SY1417 ) ) )
= $true )
| ( ( ~ ( c_Wellfounded_OwfP @ SV148 @ SV321 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1064]) ).
thf(1246,plain,
! [SV464: $i,SV322: $i,SV149: $i] :
( ( ( c_Predicate_Oconversep @ ( c_Predicate_Oconversep @ SV149 @ SV322 @ SV464 ) @ SV464 @ SV322 )
= SV149 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1065]) ).
thf(1247,plain,
! [SV323: $i,SV150: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OVar @ SV150 ) ) @ SV323 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1066]) ).
thf(1248,plain,
! [SV465: $i,SV324: $i,SV151: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV151 @ SV324 ) @ SV465 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV151 @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__Xintros__1__1 @ SV151 @ SV465 @ SV324 ) ) @ SV465 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1067]) ).
thf(1249,plain,
! [SV466: $i,SV325: $i,SV153: $i] :
( ( ! [SY1592: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ ( c_Transitive__Closure_Otranclp @ SV153 @ SV325 ) @ SV325 @ SV325 ) @ SV466 ) @ SY1592 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ ( c_Predicate_Oconversep @ SV153 @ SV325 @ SV325 ) @ SV325 ) @ SV466 ) @ SY1592 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1068]) ).
thf(1250,plain,
! [SV467: $i,SV326: $i,SV154: $i] :
( ( ! [SY1593: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ ( c_Predicate_Oconversep @ SV154 @ SV326 @ SV326 ) @ SV326 ) @ SV467 ) @ SY1593 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ ( c_Transitive__Closure_Otranclp @ SV154 @ SV326 ) @ SV326 @ SV326 ) @ SV467 ) @ SY1593 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1069]) ).
thf(1251,plain,
! [SV468: $i,SV327: $i,SV155: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV155 @ SV327 ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xnot__accp__down__1__1 @ SV155 @ SV468 @ SV327 ) ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV155 @ SV327 ) @ SV468 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1070]) ).
thf(1252,plain,
! [SV157: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ SV157 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV157 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1072]) ).
thf(1253,plain,
! [SV158: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV158 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ SV158 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1073]) ).
thf(1254,plain,
! [SV469: $i,SV329: $i,SV159: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV159 @ SV329 ) @ SV469 ) )
| ! [SY1594: $i] :
( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV159 @ SV329 ) @ SY1594 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV159 @ SV329 ) @ SV469 ) @ SY1594 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1074]) ).
thf(1255,plain,
! [SV470: $i,SV330: $i,SV160: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV160 @ SV330 ) @ SV470 ) )
| ! [SY1595: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV160 @ SV330 ) @ SV470 ) @ SY1595 ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV160 @ SV330 ) @ SY1595 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1075]) ).
thf(1256,plain,
! [SV471: $i,SV331: $i,SV161: $i] :
( ( ! [SY1596: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Osubst @ SV161 @ SV331 @ SV471 ) ) @ ( c_Lambda_Osubst @ SY1596 @ SV331 @ SV471 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV161 ) @ SY1596 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1076]) ).
thf(1257,plain,
! [SV332: $i,SV162: $i] :
( ( ( hBOOL @ ( hAPP @ SV162 @ SV332 ) )
= $true )
| ( ( ! [SY1431: $i] :
( ~ ( hBOOL @ ( hAPP @ SV162 @ ( v_sko__Wellfounded__Xaccp__Xinducts__1 @ SV162 @ SY1431 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1431 @ t_a ) @ SV332 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1077]) ).
thf(1258,plain,
! [SV333: $i,SV163: $i] :
( ( ( hBOOL @ ( hAPP @ SV163 @ SV333 ) )
= $true )
| ( ( ! [SY1432: $i] :
( ( hBOOL @ ( hAPP @ SV163 @ SY1432 ) )
| ! [SY1433: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1433 @ SY1432 ) @ ( v_sko__Wellfounded__Xaccp__Xinducts__1 @ SV163 @ SY1433 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1433 @ t_a ) @ SV333 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1078]) ).
thf(1259,plain,
! [SV472: $i,SV334: $i,SV164: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV164 @ SV334 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV472 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ SV334 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV164 ) ) @ SV334 ) @ SV472 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1079]) ).
thf(1260,plain,
! [SV335: $i,SV165: $i] :
( ( ( hBOOL @ ( hAPP @ SV165 @ SV335 ) )
= $true )
| ( ( ! [SY1435: $i] :
( ~ ( hBOOL @ ( hAPP @ SV165 @ ( v_sko__Wellfounded__Xaccp__Xinduct__1 @ SV165 @ SY1435 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1435 @ t_a ) @ SV335 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1080]) ).
thf(1261,plain,
! [SV336: $i,SV166: $i] :
( ( ( hBOOL @ ( hAPP @ SV166 @ SV336 ) )
= $true )
| ( ( ! [SY1436: $i] :
( ( hBOOL @ ( hAPP @ SV166 @ SY1436 ) )
| ! [SY1437: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1437 @ SY1436 ) @ ( v_sko__Wellfounded__Xaccp__Xinduct__1 @ SV166 @ SY1437 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1437 @ t_a ) @ SV336 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1081]) ).
thf(1262,plain,
! [SV473: $i,SV337: $i,SV167: $i] :
( ( ! [SY1597: $i,SY1598: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV167 @ SV337 @ SV473 ) @ SY1597 ) @ SY1598 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV167 @ SY1598 ) @ SY1597 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1082]) ).
thf(1263,plain,
! [SV474: $i,SV338: $i,SV168: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV168 @ SV338 ) @ SV474 ) )
| ! [SY1599: $i,SY1600: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV168 @ SY1599 @ SY1600 ) @ SV474 ) @ SV338 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1083]) ).
thf(1264,plain,
! [SV475: $i,SV339: $i,SV169: $i] :
( ( ! [SY1601: $i,SY1602: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV169 @ SV339 @ SV475 ) @ SY1601 ) @ SY1602 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV169 @ SY1602 ) @ SY1601 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1084]) ).
thf(1265,plain,
! [SV476: $i,SV340: $i,SV170: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV170 @ SV340 ) @ SV476 ) )
| ! [SY1603: $i,SY1604: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV170 @ SY1603 @ SY1604 ) @ SV476 ) @ SV340 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1085]) ).
thf(1266,plain,
! [SV341: $i,SV171: $i] :
( ( ( hBOOL @ ( hAPP @ SV171 @ SV341 ) )
= $true )
| ( ( ! [SY1450: $i,SY1451: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1450 @ t_a ) @ SY1451 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1450 @ SY1451 ) @ ( v_sko__Wellfounded__Xaccp__Xinducts__1 @ SV171 @ SY1450 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1450 @ t_a ) @ SV341 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1086]) ).
thf(1267,plain,
! [SV342: $i,SV172: $i] :
( ( ( hBOOL @ ( hAPP @ SV172 @ SV342 ) )
= $true )
| ( ( ! [SY1452: $i,SY1453: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1452 @ t_a ) @ SY1453 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1452 @ SY1453 ) @ ( v_sko__Wellfounded__Xaccp__Xinduct__1 @ SV172 @ SY1452 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1452 @ t_a ) @ SV342 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1087]) ).
thf(1268,plain,
! [SV477: $i,SV343: $i,SV173: $i] :
( ( ! [SY1605: $i] :
( ( c_Predicate_Oconversep @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV173 @ SV343 @ ( tc_fun @ SV477 @ ( tc_fun @ SY1605 @ tc_bool ) ) ) @ SV477 @ SY1605 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Predicate_Oconversep @ SV173 @ SV477 @ SY1605 ) @ ( c_Predicate_Oconversep @ SV343 @ SV477 @ SY1605 ) @ ( tc_fun @ SY1605 @ ( tc_fun @ SV477 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1088]) ).
thf(1269,plain,
! [SV478: $i,SV344: $i,SV174: $i] :
( ( ! [SY1606: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV174 @ SV344 ) @ SV478 ) @ SY1606 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ SV174 @ SV344 @ SV344 ) @ SV344 ) @ SY1606 ) @ SV478 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1089]) ).
thf(1270,plain,
! [SV479: $i,SV345: $i,SV175: $i] :
( ( ! [SY1607: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ SV175 @ SV345 @ SV345 ) @ SV345 ) @ SV479 ) @ SY1607 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV175 @ SV345 ) @ SY1607 ) @ SV479 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1090]) ).
thf(1271,plain,
! [SV346: $i,SV176: $i] :
( ( ( hBOOL @ ( hAPP @ SV176 @ SV346 ) )
= $true )
| ( ( ! [SY1460: $i,SY1461: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1460 @ SY1461 ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__1__1 @ SV176 @ SY1460 @ SY1461 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1460 @ SY1461 ) @ SV346 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1091]) ).
thf(1272,plain,
! [SV480: $i,SV347: $i,SV177: $i] :
( ( ! [SY1608: $i] :
( ( c_Predicate_Oconversep @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV177 @ SV347 @ ( tc_fun @ SV480 @ ( tc_fun @ SY1608 @ tc_bool ) ) ) @ SV480 @ SY1608 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Predicate_Oconversep @ SV177 @ SV480 @ SY1608 ) @ ( c_Predicate_Oconversep @ SV347 @ SV480 @ SY1608 ) @ ( tc_fun @ SY1608 @ ( tc_fun @ SV480 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1092]) ).
thf(1273,plain,
! [SV481: $i,SV348: $i,SV178: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV178 @ SV348 ) @ SV481 ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV178 @ SV348 ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__Xintros__1__1 @ SV178 @ SV481 @ SV348 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1093]) ).
thf(1274,plain,
! [SV482: $i,SV349: $i,SV179: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV179 @ SV349 ) @ SV482 ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV179 @ SV349 ) @ ( c_ATP__Linkup_Osko__Wellfounded__XaccpI__1__1 @ SV179 @ SV482 @ SV349 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1094]) ).
thf(1275,plain,
! [SV483: $i,SV350: $i,SV180: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV180 @ SV350 ) @ SV483 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV180 @ ( c_ATP__Linkup_Osko__Wellfounded__XaccpI__1__1 @ SV180 @ SV483 @ SV350 ) ) @ SV483 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1095]) ).
thf(1276,plain,
! [SV484: $i,SV351: $i,SV181: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV181 ) @ SV351 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV181 ) @ SV484 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV351 ) @ SV484 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1096]) ).
thf(1277,plain,
! [SV485: $i,SV352: $i,SV182: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV182 ) @ SV352 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV485 ) @ SV352 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV182 ) @ SV485 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1097]) ).
thf(1278,plain,
! [SV353: $i,SV183: $i] :
( ( ( hBOOL @ ( hAPP @ SV183 @ SV353 ) )
= $true )
| ( ( ! [SY1469: $i,SY1470: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1469 @ SY1470 ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__rule__1__1 @ SV183 @ SY1469 @ SY1470 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1469 @ SY1470 ) @ SV353 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1098]) ).
thf(1279,plain,
! [SV486: $i,SV354: $i,SV184: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Olift @ SV184 @ SV354 ) ) @ ( c_Lambda_Olift @ SV486 @ SV354 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV184 ) @ SV486 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1099]) ).
thf(1280,plain,
! [SV355: $i,SV185: $i] :
( ( ( hBOOL @ ( hAPP @ SV185 @ SV355 ) )
= $true )
| ( ( ! [SY1472: $i,SY1473: $i] :
( ~ ( hBOOL @ ( hAPP @ SV185 @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__rule__1__1 @ SV185 @ SY1472 @ SY1473 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1472 @ SY1473 ) @ SV355 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1100]) ).
thf(1281,plain,
! [SV487: $i,SV356: $i,SV186: $i] :
( ( ( hBOOL @ ( hAPP @ SV186 @ SV356 ) )
| ( hBOOL @ ( hAPP @ SV186 @ SV487 ) )
| ! [SY1609: $i,SY1610: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1609 @ SV487 ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__rule__1__1 @ SV186 @ SY1609 @ SY1610 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1609 @ SY1610 ) @ SV356 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1101]) ).
thf(1282,plain,
! [SV488: $i,SV357: $i,SV187: $i] :
( ( ! [SY1611: $i,SY1612: $i] :
( ( c_Predicate_Oconversep @ ( c_Predicate_Opred__comp @ SV187 @ SV357 @ SV488 @ SY1611 @ SY1612 ) @ SV488 @ SY1612 )
= ( c_Predicate_Opred__comp @ ( c_Predicate_Oconversep @ SV357 @ SY1611 @ SY1612 ) @ ( c_Predicate_Oconversep @ SV187 @ SV488 @ SY1611 ) @ SY1612 @ SY1611 @ SV488 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1102]) ).
thf(1283,plain,
! [SV358: $i,SV188: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ SV188 ) ) @ ( c_Lambda_OdB_OAbs @ SV358 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV188 ) @ SV358 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1103]) ).
thf(1284,plain,
! [SV359: $i,SV189: $i] :
( ( ( class_Lattices_Oupper__semilattice @ ( tc_fun @ SV189 @ SV359 ) )
= $true )
| ( ( ~ ( class_Lattices_Olattice @ SV359 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1104]) ).
thf(1285,plain,
! [SV360: $i,SV190: $i] :
( ( ( class_Lattices_Olower__semilattice @ ( tc_fun @ SV190 @ SV360 ) )
= $true )
| ( ( ~ ( class_Lattices_Olattice @ SV360 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1105]) ).
thf(1286,plain,
! [SV361: $i,SV191: $i] :
( ( ( class_Lattices_Odistrib__lattice @ ( tc_fun @ SV191 @ SV361 ) )
= $true )
| ( ( ~ ( class_Lattices_Odistrib__lattice @ SV361 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1106]) ).
thf(1287,plain,
! [SV362: $i,SV192: $i] :
( ( ( class_Lattices_Olattice @ ( tc_fun @ SV192 @ SV362 ) )
= $true )
| ( ( ~ ( class_Lattices_Olattice @ SV362 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1107]) ).
thf(1288,plain,
! [SV364: $i,SV194: $i] :
( ( ( SV194 = SV364 )
= $true )
| ( ( ! [SY1480: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ SY1480 ) @ SV194 ) @ SV364 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1109]) ).
thf(1289,plain,
! [SV489: $i,SV365: $i,SV195: $i,SV1: $i] :
( ( ! [SY1613: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ SV1 @ SV195 ) @ ( c_List_Olist_OCons @ SV365 @ SV489 @ SV195 ) ) @ ( c_List_Olist_OCons @ SV365 @ SY1613 @ SV195 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ SV1 @ SV195 ) @ SV489 ) @ SY1613 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1110]) ).
thf(1290,plain,
! [SV490: $i,SV366: $i,SV196: $i,SV2: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ SV2 @ SV196 ) @ SV366 ) @ SV490 ) )
| ! [SY1614: $i,SY1615: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV2 @ SY1614 ) @ SY1615 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ SV2 @ SV196 ) @ ( c_List_Olist_OCons @ SY1614 @ SV366 @ SV196 ) ) @ ( c_List_Olist_OCons @ SY1615 @ SV490 @ SV196 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1111]) ).
thf(1291,plain,
! [SV491: $i,SV367: $i,SV197: $i,SV3: $i] :
( ( ! [SY1616: $i] :
( ( ( c_List_Olist_OCons @ SV3 @ SV197 @ SV367 )
!= ( c_List_Olist_OCons @ SV491 @ SY1616 @ SV367 ) )
| ( SV197 = SY1616 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1112]) ).
thf(1292,plain,
! [SV492: $i,SV368: $i,SV198: $i,SV4: $i] :
( ( ! [SY1617: $i] :
( ( c_List_Olist_OCons @ SV4 @ SV198 @ SV368 )
!= ( c_List_Olist_OCons @ SV492 @ SY1617 @ SV368 ) )
| ( SV4 = SV492 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1113]) ).
thf(1293,plain,
! [SV369: $i,SV199: $i,SV5: $i] :
( ( ( c_List_Olist_ONil @ SV5 )
= ( c_List_Olist_OCons @ SV199 @ SV369 @ SV5 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1114]) ).
thf(1294,plain,
! [SV493: $i,SV370: $i,SV200: $i,SV6: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ SV6 @ SV200 ) @ SV370 ) @ SV493 ) )
| ( SV493 = SV370 )
| ! [SY1618: $i,SY1619: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ SV6 @ SV200 ) @ ( c_List_Olist_OCons @ SY1618 @ SV370 @ SV200 ) ) @ ( c_List_Olist_OCons @ SY1619 @ SV493 @ SV200 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1115]) ).
thf(1295,plain,
! [SV371: $i,SV201: $i,SV7: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV7 @ SV201 ) @ SV371 ) ) )
= $true )
| ( ( ! [SY1493: $i,SY1494: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ SV7 @ SY1493 ) @ ( c_List_Olist_OCons @ SV201 @ SY1494 @ SY1493 ) ) @ ( c_List_Olist_OCons @ SV371 @ SY1494 @ SY1493 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1116]) ).
thf(1296,plain,
! [SV494: $i,SV372: $i,SV202: $i,SV8: $i] :
( ( ( SV8 = SV202 )
| ( SV372 = SV494 )
| ! [SY1620: $i,SY1621: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ SY1620 @ SY1621 ) @ ( c_List_Olist_OCons @ SV202 @ SV494 @ SY1621 ) ) @ ( c_List_Olist_OCons @ SV8 @ SV372 @ SY1621 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1117]) ).
thf(1297,plain,
! [SV495: $i,SV373: $i,SV203: $i,SV9: $i] :
( ( ! [SY1622: $i,SY1623: $i] :
( ( c_List_Ofoldl @ SV9 @ SV203 @ ( c_List_Olist_OCons @ SV373 @ SV495 @ SY1622 ) @ SY1623 @ SY1622 )
= ( c_List_Ofoldl @ SV9 @ ( hAPP @ ( hAPP @ SV9 @ SV203 ) @ SV373 ) @ SV495 @ SY1623 @ SY1622 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1118]) ).
thf(1298,plain,
! [SV374: $i,SV204: $i,SV10: $i] :
( ( ( c_List_Olist_OCons @ SV10 @ SV204 @ SV374 )
= ( c_List_Olist_ONil @ SV374 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1119]) ).
thf(1299,plain,
! [SV375: $i,SV205: $i,SV11: $i] :
( ( ( c_List_Olist_OCons @ SV11 @ SV205 @ SV375 )
= ( c_List_Olist_ONil @ SV375 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1120]) ).
thf(1300,plain,
! [SV496: $i,SV376: $i,SV206: $i,SV12: $i] :
( ( ( SV12 = SV206 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV376 @ SV206 ) @ SV12 ) )
| ! [SY1624: $i,SY1625: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ SV376 @ SV496 ) @ ( c_List_Olist_OCons @ SV206 @ SY1624 @ SV496 ) ) @ ( c_List_Olist_OCons @ SV12 @ SY1625 @ SV496 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1121]) ).
thf(1301,plain,
! [SV377: $i,SV207: $i,SV13: $i] :
( ( ( c_List_Olist_OCons @ SV13 @ SV207 @ SV377 )
= SV207 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1122]) ).
thf(1302,plain,
! [SV378: $i,SV208: $i,SV14: $i] :
( ( SV14
= ( c_List_Olist_OCons @ SV208 @ SV14 @ SV378 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1123]) ).
thf(1303,plain,
! [SV497: $i,SV379: $i,SV209: $i,SV15: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( c_ListOrder_Ostep1 @ SV15 @ SV209 ) @ ( tc_List_Olist @ SV209 ) ) @ ( c_List_Olist_OCons @ SV379 @ SV497 @ SV209 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( c_ListOrder_Ostep1 @ SV15 @ SV209 ) @ ( tc_List_Olist @ SV209 ) ) @ SV497 ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV15 @ SV209 ) @ SV379 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1124]) ).
thf(1304,plain,
! [SV498: $i,SV380: $i,SV210: $i,SV16: $i] :
( ( ( ( c_Type_Otype_OFun @ SV16 @ SV210 )
!= ( c_Type_Otype_OFun @ SV380 @ SV498 ) )
| ( SV210 = SV498 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1125]) ).
thf(1305,plain,
! [SV381: $i,SV211: $i,SV17: $i] :
( ( ( ! [SY1506: $i] :
( ( c_Type_Otype_OFun @ SV17 @ SV211 )
!= ( c_Type_Otype_OFun @ SV381 @ SY1506 ) ) )
= $true )
| ( ( SV17 = SV381 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1126]) ).
thf(1306,plain,
! [SV499: $i,SV382: $i,SV212: $i,SV18: $i] :
( ( ( c_Type_Otyping @ SV18 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV212 ) @ SV382 ) @ SV499 )
| ! [SY1626: $i] :
( ~ ( c_Type_Otyping @ SV18 @ SV382 @ SY1626 )
| ~ ( c_Type_Otyping @ SV18 @ SV212 @ ( c_Type_Otype_OFun @ SY1626 @ SV499 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1127]) ).
thf(1307,plain,
! [SV500: $i,SV383: $i,SV213: $i,SV19: $i] :
( ( ! [SY1627: $i] :
( ( c_Type_Otyping @ ( c_Type_Oshift @ SV19 @ SV213 @ SV383 @ tc_Type_Otype ) @ ( c_Lambda_Olift @ SV500 @ SV213 ) @ SY1627 )
| ~ ( c_Type_Otyping @ SV19 @ SV500 @ SY1627 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1128]) ).
thf(1308,plain,
! [SV384: $i,SV214: $i,SV20: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Olift @ SV20 @ SV214 ) ) @ ( c_Lambda_Olift @ SV384 @ SV214 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV20 ) @ SV384 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1129]) ).
thf(1309,plain,
! [SV501: $i,SV385: $i,SV215: $i,SV21: $i] :
( ( ~ ( c_Type_Otyping @ SV21 @ SV215 @ SV385 )
| ! [SY1628: $i,SY1629: $i] :
( ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV21 @ SV501 @ SV385 @ tc_Type_Otype ) @ SY1628 @ SY1629 )
| ( c_Type_Otyping @ SV21 @ ( c_Lambda_Osubst @ SY1628 @ SV215 @ SV501 ) @ SY1629 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1130]) ).
thf(1310,plain,
! [SV386: $i,SV216: $i,SV22: $i] :
( ( ( c_Type_Otyping @ SV22 @ SV216 @ SV386 )
= $true )
| ( ( ! [SY1514: $i] :
( ~ ( c_Type_Otyping @ SV22 @ SY1514 @ SV386 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SY1514 ) @ SV216 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1131]) ).
thf(1311,plain,
! [SV387: $i,SV217: $i,SV23: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV23 ) @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SV217 @ SV23 @ SV387 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV217 ) @ SV23 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV387 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1132]) ).
thf(1312,plain,
! [SV502: $i,SV388: $i,SV218: $i,SV24: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV24 @ SV218 @ SV388 ) ) @ ( c_Lambda_Osubst @ SV24 @ SV502 @ SV388 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV218 ) @ SV502 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1133]) ).
thf(1313,plain,
! [SV503: $i,SV389: $i,SV219: $i,SV25: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV25 @ SV219 @ SV389 ) ) @ ( c_Lambda_Osubst @ SV503 @ SV219 @ SV389 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV25 ) @ SV503 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1134]) ).
thf(1314,plain,
! [SV504: $i,SV390: $i,SV220: $i,SV26: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV26 @ SV220 @ SV390 ) ) @ ( c_Lambda_Osubst @ SV26 @ SV504 @ SV390 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV220 ) @ SV504 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1135]) ).
thf(1315,plain,
! [SV391: $i,SV222: $i,SV28: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV28 ) @ SV222 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV391 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV28 ) @ SV222 )
= SV391 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1136]) ).
thf(1316,plain,
! [SV223: $i,SV29: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV29 ) @ SV223 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_OdB_OAbs @ SV29 ) ) @ ( c_Lambda_OdB_OAbs @ SV223 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1137]) ).
thf(1317,plain,
! [SV392: $i,SV224: $i,SV30: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV30 ) @ SV224 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV30 ) @ SV392 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV224 ) @ SV392 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1138]) ).
thf(1318,plain,
! [SV393: $i,SV225: $i,SV31: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV31 ) @ SV225 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV393 ) @ SV225 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV31 ) @ SV393 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1139]) ).
thf(1319,plain,
! [SV505: $i,SV394: $i,SV226: $i,SV32: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV32 ) @ SV226 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV394 ) @ SV505 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV226 ) @ SV505 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV32 ) @ SV394 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1140]) ).
thf(1320,plain,
! [SV506: $i,SV395: $i,SV227: $i,SV33: $i] :
( ( ( c_Type_Otyping @ SV33 @ ( c_Lambda_OdB_OAbs @ SV227 ) @ ( c_Type_Otype_OFun @ SV395 @ SV506 ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV33 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV395 @ tc_Type_Otype ) @ SV227 @ SV506 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1141]) ).
thf(1321,plain,
! [SV396: $i,SV228: $i,SV34: $i] :
( ( ( c_List_Olistsp @ ( c_Wellfounded_Oaccp @ SV34 @ SV228 ) @ SV396 @ SV228 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( c_ListOrder_Ostep1 @ SV34 @ SV228 ) @ ( tc_List_Olist @ SV228 ) ) @ SV396 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1142]) ).
thf(1322,plain,
! [SV397: $i,SV229: $i,SV35: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( c_ListOrder_Ostep1 @ SV35 @ SV229 ) @ ( tc_List_Olist @ SV229 ) ) @ SV397 ) )
= $true )
| ( ( ~ ( c_List_Olistsp @ ( c_Wellfounded_Oaccp @ SV35 @ SV229 ) @ SV397 @ SV229 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1143]) ).
thf(1323,plain,
! [SV507: $i,SV398: $i,SV230: $i,SV36: $i] :
( ( ( hAPP @ ( c_Type_Oshift @ SV36 @ SV230 @ SV398 @ SV507 ) @ SV230 )
= SV398 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1144]) ).
thf(1324,plain,
! [SV508: $i,SV399: $i,SV231: $i,SV37: $i] :
( ( ( c_List_Ofoldl @ SV37 @ SV231 @ ( c_List_Olist_ONil @ SV399 ) @ SV508 @ SV399 )
= SV231 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1145]) ).
thf(1325,plain,
! [SV400: $i,SV232: $i,SV38: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ SV38 @ SV232 ) @ SV400 ) @ ( c_List_Olist_ONil @ SV232 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1146]) ).
thf(1326,plain,
! [SV401: $i,SV233: $i,SV39: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ SV39 @ SV233 ) @ ( c_List_Olist_ONil @ SV233 ) ) @ SV401 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1147]) ).
thf(1327,plain,
! [SV509: $i,SV402: $i,SV235: $i,SV41: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV41 ) @ SV235 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV402 @ SV509 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV41
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV402 @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ SV41 @ SV235 @ SV402 @ SV509 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV509
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1148]) ).
thf(1328,plain,
! [SV403: $i,SV236: $i,SV42: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV42 @ SV236 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV42 @ SV403 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV236 ) @ SV403 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1149]) ).
thf(1329,plain,
! [SV404: $i,SV237: $i,SV43: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV43 @ SV237 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV404 @ SV237 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV43 ) @ SV404 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1150]) ).
thf(1330,plain,
! [SV510: $i,SV238: $i,SV45: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV45 @ SV238 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SV510 ) )
= $true )
| ( ( SV238
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1151]) ).
thf(1331,plain,
! [SV405: $i,SV239: $i,SV47: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV47 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV239 @ SV405 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV405
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1152]) ).
thf(1332,plain,
! [SV406: $i,SV240: $i,SV48: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV48 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV240 @ SV406 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV406
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1153]) ).
thf(1333,plain,
! [SV511: $i,SV407: $i,SV241: $i,SV50: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV50 @ SV241 @ SV407 ) ) )
| ! [SY1630: $i] :
( ~ ( c_Type_Otyping @ SV511 @ SV241 @ SY1630 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV241 ) )
| ! [SY1631: $i] :
~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV511 @ SV407 @ SY1630 @ tc_Type_Otype ) @ SV50 @ SY1631 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV50 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1154]) ).
thf(1334,plain,
! [SV408: $i,SV242: $i,SV51: $i] :
( ( ( SV51
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV242 ) @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SV242 @ SV408 @ SV51 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV242 ) @ SV408 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV51 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1155]) ).
thf(1335,plain,
! [SV52: $i,SV243: $i] :
( ( ( c_List_Olistsp @ c_InductTermi_OIT @ SV243 @ tc_Lambda_OdB )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV52 ) @ SV243 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1156]) ).
thf(1336,plain,
! [SV409: $i,SV244: $i,SV53: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV53 ) @ SV244 )
= ( c_Lambda_OdB_OVar @ SV409 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1157]) ).
thf(1337,plain,
! [SV512: $i,SV55: $i,SV410: $i] :
( ( ( ~ ( c_Type_Otyping @ SV410 @ SV55 @ SV512 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV55 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1158]) ).
thf(1338,plain,
! [SV513: $i,SV411: $i,SV246: $i,SV56: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV56 ) ) @ SV246 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV411 ) @ SV513 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1159]) ).
thf(1339,plain,
! [SV514: $i,SV412: $i,SV247: $i,SV57: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV57 @ SV247 ) @ SV412 ) )
| ! [SY1632: $i,SY1633: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV57 @ SV514 @ ( tc_fun @ SY1632 @ ( tc_fun @ SY1633 @ tc_bool ) ) ) @ SV247 ) @ SV412 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1160]) ).
thf(1340,plain,
! [SV515: $i,SV413: $i,SV248: $i,SV58: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV58 @ SV248 ) @ SV413 ) )
| ! [SY1634: $i,SY1635: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV515 @ SV58 @ ( tc_fun @ SY1634 @ ( tc_fun @ SY1635 @ tc_bool ) ) ) @ SV248 ) @ SV413 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1161]) ).
thf(1341,plain,
! [SV414: $i,SV59: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV59 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV59 ) @ ( c_Lambda_OdB_OVar @ SV414 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1162]) ).
thf(1342,plain,
! [SV516: $i,SV416: $i,SV250: $i,SV61: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV61 @ SV250 ) @ SV416 ) @ SV516 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV61 @ SV416 ) @ SV516 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1164]) ).
thf(1343,plain,
! [SV62: $i,SV517: $i] :
( ( ( ! [SY1636: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV517 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV517 @ SY1636 @ SV62 ) @ SV62 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV517 @ SY1636 @ SV62 ) ) )
= $true )
| ( ( class_Lattices_Olattice @ SV62 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1165]) ).
thf(1344,plain,
! [SV63: $i,SV518: $i] :
( ( ( ! [SY1637: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV518 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV518 @ SY1637 @ SV63 ) @ SV63 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV518 @ SY1637 @ SV63 ) ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV63 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1166]) ).
thf(1345,plain,
! [SV64: $i,SV519: $i] :
( ( ( ! [SY1638: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV519 @ SY1638 @ SV64 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY1638 @ SV519 @ SV64 ) ) )
= $true )
| ( ( class_Lattices_Olattice @ SV64 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1167]) ).
thf(1346,plain,
! [SV65: $i,SV520: $i] :
( ( ( ! [SY1639: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV520 @ SY1639 @ SV65 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY1639 @ SV520 @ SV65 ) ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV65 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1168]) ).
thf(1347,plain,
! [SV417: $i,SV251: $i,SV67: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV67 @ SV251 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV417 @ SV251 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV67 = SV417 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1170]) ).
thf(1348,plain,
! [SV521: $i,SV252: $i,SV68: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV68 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV252 @ SV521 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( ( c_Lambda_OdB_OAbs @ SV68 )
= SV252 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1171]) ).
thf(1349,plain,
! [SV70: $i,SV522: $i] :
( ( ( ! [SY1640: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV522 @ SY1640 @ SV70 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY1640 @ SV522 @ SV70 ) ) )
= $true )
| ( ( class_Lattices_Olattice @ SV70 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1172]) ).
thf(1350,plain,
! [SV71: $i,SV523: $i] :
( ( ( ! [SY1641: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV523 @ SY1641 @ SV71 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY1641 @ SV523 @ SV71 ) ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV71 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1173]) ).
thf(1351,plain,
! [SV254: $i,SV72: $i] :
( ( ( class_Lattices_Olattice @ SV72 )
= $false )
| ( ( ! [SY1290: $i,SY1291: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV254 @ SY1290 @ SV72 ) @ SY1291 @ SV72 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV254 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY1290 @ SY1291 @ SV72 ) @ SV72 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1174]) ).
thf(1352,plain,
! [SV255: $i,SV73: $i] :
( ( ( class_Lattices_Olattice @ SV73 )
= $false )
| ( ( ! [SY1292: $i,SY1293: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV255 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY1292 @ SY1293 @ SV73 ) @ SV73 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY1292 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV255 @ SY1293 @ SV73 ) @ SV73 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1175]) ).
thf(1353,plain,
! [SV256: $i,SV74: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV74 )
= $false )
| ( ( ! [SY1294: $i,SY1295: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV256 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY1294 @ SY1295 @ SV74 ) @ SV74 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY1294 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV256 @ SY1295 @ SV74 ) @ SV74 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1176]) ).
thf(1354,plain,
! [SV257: $i,SV75: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV75 )
= $false )
| ( ( ! [SY1296: $i,SY1297: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV257 @ SY1296 @ SV75 ) @ SY1297 @ SV75 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV257 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY1296 @ SY1297 @ SV75 ) @ SV75 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1177]) ).
thf(1355,plain,
! [SV76: $i,SV524: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV524 @ SV524 @ SV76 )
= SV524 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV76 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1178]) ).
thf(1356,plain,
! [SV258: $i,SV77: $i] :
( ( ( class_Lattices_Odistrib__lattice @ SV77 )
= $false )
| ( ( ! [SY1298: $i,SY1299: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV258 @ SY1298 @ SV77 ) @ SY1299 @ SV77 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV258 @ SY1299 @ SV77 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY1298 @ SY1299 @ SV77 ) @ SV77 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1179]) ).
thf(1357,plain,
! [SV259: $i,SV78: $i] :
( ( ( class_Lattices_Odistrib__lattice @ SV78 )
= $false )
| ( ( ! [SY1300: $i,SY1301: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV259 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY1300 @ SY1301 @ SV78 ) @ SV78 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV259 @ SY1300 @ SV78 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV259 @ SY1301 @ SV78 ) @ SV78 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1180]) ).
thf(1358,plain,
! [SV525: $i,SV418: $i,SV260: $i,SV79: $i] :
( ( ! [SY1642: $i,SY1643: $i,SY1644: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV79 @ SV260 @ SV418 @ SV525 @ SY1642 ) @ SY1643 ) @ SY1644 ) )
| ! [SY1307: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV260 @ SY1307 ) @ SY1644 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV79 @ SY1643 ) @ SY1307 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1181]) ).
thf(1359,plain,
! [SV526: $i,SV419: $i,SV261: $i,SV80: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV80 @ SV261 ) @ SV419 ) @ SV526 ) )
| ! [SY1646: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV80 @ SV261 ) @ SY1646 ) @ SV526 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV80 @ SV261 ) @ SV419 ) @ SY1646 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1182]) ).
thf(1360,plain,
! [SV527: $i,SV420: $i,SV262: $i,SV81: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV81 @ SV262 ) @ SV420 ) @ SV527 ) )
| ! [SY1647: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV81 @ SV262 ) @ SY1647 ) @ SV527 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV81 @ SV262 ) @ SV420 ) @ SY1647 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1183]) ).
thf(1361,plain,
! [SV528: $i,SV423: $i,SV265: $i,SV84: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV84 @ SV265 ) @ SV423 ) @ SV528 ) )
| ! [SY1648: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV84 @ SV265 ) @ SY1648 ) @ SV528 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV84 @ SV265 ) @ SV423 ) @ SY1648 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1186]) ).
thf(1362,plain,
! [SV529: $i,SV424: $i,SV266: $i,SV85: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV85 @ SV266 ) @ SV424 ) @ SV529 ) )
| ! [SY1649: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV85 @ SV266 ) @ SY1649 ) @ SV529 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV85 @ SV424 ) @ SY1649 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1187]) ).
thf(1363,plain,
! [SV530: $i,SV425: $i,SV267: $i,SV86: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV86 @ SV267 ) @ SV425 ) @ SV530 ) )
| ! [SY1650: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV86 @ SY1650 ) @ SV530 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV86 @ SV267 ) @ SV425 ) @ SY1650 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1188]) ).
thf(1364,plain,
! [SV269: $i,SV88: $i] :
( ( ( c_Wellfounded_OwfP @ SV88 @ SV269 )
= $false )
| ( ( c_Wellfounded_OwfP @ ( c_Transitive__Closure_Otranclp @ SV88 @ SV269 ) @ SV269 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1190]) ).
thf(1365,plain,
! [SV427: $i,SV270: $i,SV89: $i] :
( ( ( ( hAPP @ SV89 @ SV270 )
= SV427 )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV89 @ ( c_Lambda_OdB_OVar @ SV270 ) @ SV427 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1191]) ).
thf(1366,plain,
! [SV531: $i,SV428: $i,SV271: $i,SV90: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV90 @ SV271 ) @ SV428 ) @ SV531 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV90 @ SV271 ) @ SV428 ) @ SV531 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1192]) ).
thf(1367,plain,
! [SV532: $i,SV429: $i,SV273: $i,SV93: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV93 @ SV273 ) @ SV429 ) @ SV532 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV93 @ SV429 ) @ SV532 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1194]) ).
thf(1368,plain,
! [SV533: $i,SV430: $i,SV274: $i,SV94: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV94 @ SV274 ) @ SV430 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV533 @ SV274 ) @ SV430 ) )
| ! [SY1651: $i,SY1652: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV533 @ SV94 @ ( tc_fun @ SY1651 @ ( tc_fun @ SY1652 @ tc_bool ) ) ) @ SV274 ) @ SV430 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1195]) ).
thf(1369,plain,
! [SV534: $i,SV431: $i,SV275: $i,SV95: $i] :
( ( ! [SY1653: $i,SY1654: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV95 @ SV275 @ ( tc_fun @ SV431 @ ( tc_fun @ SV534 @ tc_bool ) ) ) @ SY1653 ) @ SY1654 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV275 @ SY1653 ) @ SY1654 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1196]) ).
thf(1370,plain,
! [SV535: $i,SV432: $i,SV276: $i,SV96: $i] :
( ( ! [SY1655: $i,SY1656: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV96 @ SV276 @ ( tc_fun @ SV432 @ ( tc_fun @ SV535 @ tc_bool ) ) ) @ SY1655 ) @ SY1656 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV96 @ SY1655 ) @ SY1656 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1197]) ).
thf(1371,plain,
! [SV433: $i,SV277: $i,SV97: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV97 ) ) @ SV277 ) @ SV433 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV277 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV97 @ SV277 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV433 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1198]) ).
thf(1372,plain,
! [SV434: $i,SV98: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV98 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Olift @ SV98 @ SV434 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1199]) ).
thf(1373,plain,
! [SV536: $i,SV435: $i,SV278: $i,SV99: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV99 ) @ SV278 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV435 ) @ SV536 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1200]) ).
thf(1374,plain,
! [SV279: $i,SV100: $i] :
( ( ( class_Lattices_Olattice @ SV100 )
= $false )
| ( ( ! [SY1346: $i,SY1347: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV279 @ SY1346 @ SV100 ) @ SY1347 @ SV100 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV279 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY1346 @ SY1347 @ SV100 ) @ SV100 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1201]) ).
thf(1375,plain,
! [SV280: $i,SV101: $i] :
( ( ( class_Lattices_Olattice @ SV101 )
= $false )
| ( ( ! [SY1348: $i,SY1349: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV280 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY1348 @ SY1349 @ SV101 ) @ SV101 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY1348 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV280 @ SY1349 @ SV101 ) @ SV101 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1202]) ).
thf(1376,plain,
! [SV281: $i,SV102: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV102 )
= $false )
| ( ( ! [SY1350: $i,SY1351: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV281 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY1350 @ SY1351 @ SV102 ) @ SV102 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY1350 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV281 @ SY1351 @ SV102 ) @ SV102 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1203]) ).
thf(1377,plain,
! [SV282: $i,SV103: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV103 )
= $false )
| ( ( ! [SY1352: $i,SY1353: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV282 @ SY1352 @ SV103 ) @ SY1353 @ SV103 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV282 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY1352 @ SY1353 @ SV103 ) @ SV103 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1204]) ).
thf(1378,plain,
! [SV283: $i,SV104: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV104 )
= ( c_Lambda_OdB_OAbs @ SV283 ) )
= $false )
| ( ( SV104 = SV283 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1205]) ).
thf(1379,plain,
! [SV436: $i,SV284: $i,SV105: $i] :
( ( ( c_Lambda_OdB_OVar @ SV105 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV284 ) @ SV436 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1206]) ).
thf(1380,plain,
! [SV537: $i,SV285: $i,SV106: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV106 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV285 @ SV537 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( ( c_Lambda_OdB_OVar @ SV106 )
= SV285 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1207]) ).
thf(1381,plain,
! [SV437: $i,SV286: $i,SV107: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV107 @ SV286 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV437 @ SV286 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV107 ) @ SV437 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1208]) ).
thf(1382,plain,
! [SV108: $i,SV538: $i] :
( ( ( ! [SY1657: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV538 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV538 @ SY1657 @ SV108 ) @ SV108 )
= SV538 ) )
= $true )
| ( ( class_Lattices_Olattice @ SV108 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1209]) ).
thf(1383,plain,
! [SV438: $i,SV288: $i,SV110: $i] :
( ( ( SV110 = SV288 )
= $true )
| ( ( ! [SY1562: $i,SY1563: $i] :
( ~ ( c_Type_Otyping @ SV438 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1562 ) @ SY1563 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV288 )
| ~ ( c_Type_Otyping @ SV438 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY1562 ) @ SY1563 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV110 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1210]) ).
thf(1384,plain,
! [SV539: $i,SV439: $i,SV289: $i,SV111: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV111 ) @ SV289 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV439 ) @ SV539 ) )
| ( SV289 = SV539 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1211]) ).
thf(1385,plain,
! [SV440: $i,SV290: $i,SV112: $i] :
( ( ( ! [SY1565: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV112 ) @ SV290 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV440 ) @ SY1565 ) ) )
= $true )
| ( ( SV112 = SV440 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1212]) ).
thf(1386,plain,
! [SV113: $i,SV540: $i] :
( ( ( ! [SY1658: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV540 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV540 @ SY1658 @ SV113 ) @ SV113 )
= SV540 ) )
= $true )
| ( ( class_Lattices_Olattice @ SV113 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1213]) ).
thf(1387,plain,
! [SV541: $i,SV441: $i,SV291: $i,SV114: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV114 ) @ SV291 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV441 ) @ SV541 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV291 = SV541 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1214]) ).
thf(1388,plain,
! [SV442: $i,SV292: $i,SV115: $i] :
( ( ( ! [SY1567: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV115 ) @ SV292 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV442 ) @ SY1567 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true )
| ( ( SV115 = SV442 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1215]) ).
thf(1389,plain,
! [SV443: $i,SV293: $i,SV116: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV116 @ SV293 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SV443 ) )
= $true )
| ( ( SV116
= ( c_Lambda_OdB_OAbs @ SV443 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1216]) ).
thf(1390,plain,
! [SV542: $i,SV444: $i,SV295: $i,SV118: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV118 @ SV295 ) @ SV444 ) @ SV542 ) )
| ( SV444 = SV542 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV118 @ SV295 ) @ SV444 ) @ SV542 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1217]) ).
thf(1391,plain,
! [SV543: $i,SV445: $i,SV296: $i,SV119: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV119 @ SV296 ) @ SV445 ) @ SV543 ) )
| ( SV445 = SV543 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV119 @ SV296 ) @ SV445 ) @ SV543 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1218]) ).
thf(1392,plain,
! [SV298: $i,SV121: $i] :
( ( ( class_Lattices_Odistrib__lattice @ SV121 )
= $false )
| ( ( ! [SY1374: $i,SY1375: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV298 @ SY1374 @ SV121 ) @ SY1375 @ SV121 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV298 @ SY1375 @ SV121 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY1374 @ SY1375 @ SV121 ) @ SV121 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1220]) ).
thf(1393,plain,
! [SV299: $i,SV122: $i] :
( ( ( class_Lattices_Odistrib__lattice @ SV122 )
= $false )
| ( ( ! [SY1376: $i,SY1377: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV299 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY1376 @ SY1377 @ SV122 ) @ SV122 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV299 @ SY1376 @ SV122 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV299 @ SY1377 @ SV122 ) @ SV122 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1221]) ).
thf(1394,plain,
! [SV123: $i,SV544: $i] :
( ( ( ! [SY1659: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV544 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV544 @ SY1659 @ SV123 ) @ SV123 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV544 @ SY1659 @ SV123 ) ) )
= $true )
| ( ( class_Lattices_Olattice @ SV123 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1222]) ).
thf(1395,plain,
! [SV124: $i,SV545: $i] :
( ( ( ! [SY1660: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV545 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV545 @ SY1660 @ SV124 ) @ SV124 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV545 @ SY1660 @ SV124 ) ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV124 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1223]) ).
thf(1396,plain,
! [SV546: $i,SV447: $i,SV125: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV125 @ ( c_Lambda_OdB_OVar @ SV447 ) @ SV546 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV125 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1224]) ).
thf(1397,plain,
! [SV127: $i,SV547: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV547 @ SV547 @ SV127 )
= SV547 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV127 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1225]) ).
thf(1398,plain,
! [SV548: $i,SV448: $i,SV302: $i,SV129: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV129 ) @ SV302 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV448 ) @ SV548 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV302 = SV548 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1226]) ).
thf(1399,plain,
! [SV449: $i,SV303: $i,SV130: $i] :
( ( ( ! [SY1572: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV130 ) @ SV303 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV449 ) @ SY1572 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true )
| ( ( SV130 = SV449 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1227]) ).
thf(1400,plain,
! [SV450: $i,SV304: $i,SV131: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV131 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV304 ) @ SV450 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1228]) ).
thf(1401,plain,
! [SV549: $i,SV451: $i,SV305: $i,SV132: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV132 @ SV305 ) @ SV451 ) @ SV549 ) )
| ! [SY1661: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV132 @ SV305 ) @ SY1661 ) @ SV549 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV132 @ SV305 ) @ SV451 ) @ SY1661 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1229]) ).
thf(1402,plain,
! [SV306: $i,SV133: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV133 )
= ( c_Lambda_OdB_OVar @ SV306 ) )
= $false )
| ( ( SV133 = SV306 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1230]) ).
thf(1403,plain,
! [SV452: $i,SV307: $i,SV134: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV134 ) @ SV307 )
= ( c_Lambda_OdB_OAbs @ SV452 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1231]) ).
thf(1404,plain,
! [SV550: $i,SV453: $i,SV309: $i,SV136: $i] :
( ( ( c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV136 ) @ SV309 ) @ SV453 @ SV550 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV136 @ SV453 @ SV550 ) ) @ ( c_Lambda_Osubst @ SV309 @ SV453 @ SV550 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1233]) ).
thf(1405,plain,
! [SV551: $i,SV454: $i,SV310: $i,SV137: $i] :
( ( ! [SY1662: $i,SY1663: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV137 @ SV310 @ ( tc_fun @ SV454 @ ( tc_fun @ SV551 @ tc_bool ) ) ) @ SY1662 ) @ SY1663 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV310 @ SY1662 ) @ SY1663 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ SY1662 ) @ SY1663 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1234]) ).
thf(1406,plain,
! [SV552: $i,SV455: $i,SV311: $i,SV138: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV138 @ SV311 ) @ SV455 ) @ SV552 ) )
| ! [SY1664: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV138 @ SV311 ) @ SY1664 ) @ SV552 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV138 @ SV455 ) @ SY1664 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1235]) ).
thf(1407,plain,
! [SV553: $i,SV456: $i,SV312: $i,SV139: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV139 @ SV312 ) @ SV456 ) @ SV553 ) )
| ! [SY1665: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV139 @ SY1665 ) @ SV553 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV139 @ SV312 ) @ SV456 ) @ SY1665 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1236]) ).
thf(1408,plain,
! [SV554: $i,SV457: $i,SV313: $i,SV140: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV140 @ SV313 ) @ SV457 ) @ SV554 ) )
| ! [SY1666: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV140 @ SY1666 ) @ SV554 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV140 @ SV313 ) @ SV457 ) @ SY1666 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1237]) ).
thf(1409,plain,
! [SV555: $i,SV458: $i,SV314: $i,SV141: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV141 @ SV314 ) @ SV458 ) @ SV555 ) )
| ! [SY1667: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV141 @ SV314 ) @ SY1667 ) @ SV555 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV141 @ SV458 ) @ SY1667 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1238]) ).
thf(1410,plain,
! [SV459: $i,SV315: $i,SV142: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV142 @ SV315 ) @ SV459 ) )
= $true )
| ( ( ! [SY1587: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV142 @ SV459 ) @ SY1587 ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV142 @ SV315 ) @ SY1587 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1239]) ).
thf(1411,plain,
! [SV460: $i,SV316: $i,SV143: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV143 @ SV316 ) @ SV460 ) )
= $true )
| ( ( ! [SY1588: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV460 ) @ SY1588 ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV143 @ SV316 ) @ SY1588 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1240]) ).
thf(1412,plain,
! [SV317: $i,SV556: $i,SV144: $i] :
( ( ( ! [SY1668: $i] :
( ~ ( hBOOL @ ( hAPP @ SV144 @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__1__1 @ SV144 @ SV556 @ SY1668 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV556 @ SY1668 ) @ SV317 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV144 @ SV317 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1241]) ).
thf(1413,plain,
! [SV461: $i,SV318: $i,SV145: $i] :
( ( ( hBOOL @ ( hAPP @ SV145 @ SV318 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ SV145 @ SV461 ) )
| ! [SY1589: $i,SY1590: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1589 @ SV461 ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__1__1 @ SV145 @ SY1589 @ SY1590 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1589 @ SY1590 ) @ SV318 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1242]) ).
thf(1414,plain,
! [SV462: $i,SV319: $i,SV146: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV146 @ ( c_ATP__Linkup_Osko__Wellfounded__Xnot__accp__down__1__1 @ SV146 @ SV319 @ SV462 ) ) @ SV319 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV146 @ SV462 ) @ SV319 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1243]) ).
thf(1415,plain,
! [SV463: $i,SV320: $i,SV147: $i] :
( ( ( c_Type_Otyping @ SV147 @ SV320 @ SV463 )
= $true )
| ( ( ! [SY1591: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SY1591 ) @ SV320 ) )
| ~ ( c_Type_Otyping @ SV147 @ SY1591 @ SV463 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1244]) ).
thf(1416,plain,
! [SV557: $i,SV321: $i,SV148: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV148 @ SV321 ) @ SV557 ) )
= $true )
| ( ( ~ ( c_Wellfounded_OwfP @ SV148 @ SV321 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1245]) ).
thf(1417,plain,
! [SV465: $i,SV324: $i,SV151: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV151 @ SV324 ) @ SV465 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV151 @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__Xintros__1__1 @ SV151 @ SV465 @ SV324 ) ) @ SV465 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1248]) ).
thf(1418,plain,
! [SV558: $i,SV466: $i,SV325: $i,SV153: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ ( c_Transitive__Closure_Otranclp @ SV153 @ SV325 ) @ SV325 @ SV325 ) @ SV466 ) @ SV558 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ ( c_Predicate_Oconversep @ SV153 @ SV325 @ SV325 ) @ SV325 ) @ SV466 ) @ SV558 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1249]) ).
thf(1419,plain,
! [SV559: $i,SV467: $i,SV326: $i,SV154: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ ( c_Predicate_Oconversep @ SV154 @ SV326 @ SV326 ) @ SV326 ) @ SV467 ) @ SV559 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ ( c_Transitive__Closure_Otranclp @ SV154 @ SV326 ) @ SV326 @ SV326 ) @ SV467 ) @ SV559 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1250]) ).
thf(1420,plain,
! [SV468: $i,SV327: $i,SV155: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV155 @ SV327 ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xnot__accp__down__1__1 @ SV155 @ SV468 @ SV327 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV155 @ SV327 ) @ SV468 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1251]) ).
thf(1421,plain,
! [SV469: $i,SV329: $i,SV159: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV159 @ SV329 ) @ SV469 ) )
= $true )
| ( ( ! [SY1594: $i] :
( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV159 @ SV329 ) @ SY1594 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV159 @ SV329 ) @ SV469 ) @ SY1594 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1254]) ).
thf(1422,plain,
! [SV470: $i,SV330: $i,SV160: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV160 @ SV330 ) @ SV470 ) )
= $true )
| ( ( ! [SY1595: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV160 @ SV330 ) @ SV470 ) @ SY1595 ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV160 @ SV330 ) @ SY1595 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1255]) ).
thf(1423,plain,
! [SV560: $i,SV471: $i,SV331: $i,SV161: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Osubst @ SV161 @ SV331 @ SV471 ) ) @ ( c_Lambda_Osubst @ SV560 @ SV331 @ SV471 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV161 ) @ SV560 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1256]) ).
thf(1424,plain,
! [SV332: $i,SV561: $i,SV162: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV162 @ ( v_sko__Wellfounded__Xaccp__Xinducts__1 @ SV162 @ SV561 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV561 @ t_a ) @ SV332 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV162 @ SV332 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1257]) ).
thf(1425,plain,
! [SV333: $i,SV562: $i,SV163: $i] :
( ( ( ( hBOOL @ ( hAPP @ SV163 @ SV562 ) )
| ! [SY1669: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1669 @ SV562 ) @ ( v_sko__Wellfounded__Xaccp__Xinducts__1 @ SV163 @ SY1669 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1669 @ t_a ) @ SV333 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV163 @ SV333 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1258]) ).
thf(1426,plain,
! [SV472: $i,SV334: $i,SV164: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV164 @ SV334 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV472 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ SV334 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV164 ) ) @ SV334 ) @ SV472 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1259]) ).
thf(1427,plain,
! [SV335: $i,SV563: $i,SV165: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV165 @ ( v_sko__Wellfounded__Xaccp__Xinduct__1 @ SV165 @ SV563 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV563 @ t_a ) @ SV335 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV165 @ SV335 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1260]) ).
thf(1428,plain,
! [SV336: $i,SV564: $i,SV166: $i] :
( ( ( ( hBOOL @ ( hAPP @ SV166 @ SV564 ) )
| ! [SY1670: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1670 @ SV564 ) @ ( v_sko__Wellfounded__Xaccp__Xinduct__1 @ SV166 @ SY1670 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1670 @ t_a ) @ SV336 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV166 @ SV336 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1261]) ).
thf(1429,plain,
! [SV565: $i,SV473: $i,SV337: $i,SV167: $i] :
( ( ! [SY1671: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV167 @ SV337 @ SV473 ) @ SV565 ) @ SY1671 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV167 @ SY1671 ) @ SV565 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1262]) ).
thf(1430,plain,
! [SV474: $i,SV338: $i,SV168: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV168 @ SV338 ) @ SV474 ) )
= $true )
| ( ( ! [SY1599: $i,SY1600: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV168 @ SY1599 @ SY1600 ) @ SV474 ) @ SV338 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1263]) ).
thf(1431,plain,
! [SV566: $i,SV475: $i,SV339: $i,SV169: $i] :
( ( ! [SY1672: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV169 @ SV339 @ SV475 ) @ SV566 ) @ SY1672 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV169 @ SY1672 ) @ SV566 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1264]) ).
thf(1432,plain,
! [SV476: $i,SV340: $i,SV170: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV170 @ SV340 ) @ SV476 ) )
= $true )
| ( ( ! [SY1603: $i,SY1604: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV170 @ SY1603 @ SY1604 ) @ SV476 ) @ SV340 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1265]) ).
thf(1433,plain,
! [SV341: $i,SV171: $i,SV567: $i] :
( ( ( ! [SY1673: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV567 @ t_a ) @ SY1673 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV567 @ SY1673 ) @ ( v_sko__Wellfounded__Xaccp__Xinducts__1 @ SV171 @ SV567 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV567 @ t_a ) @ SV341 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV171 @ SV341 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1266]) ).
thf(1434,plain,
! [SV342: $i,SV172: $i,SV568: $i] :
( ( ( ! [SY1674: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV568 @ t_a ) @ SY1674 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV568 @ SY1674 ) @ ( v_sko__Wellfounded__Xaccp__Xinduct__1 @ SV172 @ SV568 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV568 @ t_a ) @ SV342 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV172 @ SV342 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1267]) ).
thf(1435,plain,
! [SV569: $i,SV477: $i,SV343: $i,SV173: $i] :
( ( ( c_Predicate_Oconversep @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV173 @ SV343 @ ( tc_fun @ SV477 @ ( tc_fun @ SV569 @ tc_bool ) ) ) @ SV477 @ SV569 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Predicate_Oconversep @ SV173 @ SV477 @ SV569 ) @ ( c_Predicate_Oconversep @ SV343 @ SV477 @ SV569 ) @ ( tc_fun @ SV569 @ ( tc_fun @ SV477 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1268]) ).
thf(1436,plain,
! [SV570: $i,SV478: $i,SV344: $i,SV174: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV174 @ SV344 ) @ SV478 ) @ SV570 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ SV174 @ SV344 @ SV344 ) @ SV344 ) @ SV570 ) @ SV478 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1269]) ).
thf(1437,plain,
! [SV571: $i,SV479: $i,SV345: $i,SV175: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ SV175 @ SV345 @ SV345 ) @ SV345 ) @ SV479 ) @ SV571 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV175 @ SV345 ) @ SV571 ) @ SV479 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1270]) ).
thf(1438,plain,
! [SV346: $i,SV176: $i,SV572: $i] :
( ( ( ! [SY1675: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV572 @ SY1675 ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__1__1 @ SV176 @ SV572 @ SY1675 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV572 @ SY1675 ) @ SV346 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV176 @ SV346 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1271]) ).
thf(1439,plain,
! [SV573: $i,SV480: $i,SV347: $i,SV177: $i] :
( ( ( c_Predicate_Oconversep @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV177 @ SV347 @ ( tc_fun @ SV480 @ ( tc_fun @ SV573 @ tc_bool ) ) ) @ SV480 @ SV573 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Predicate_Oconversep @ SV177 @ SV480 @ SV573 ) @ ( c_Predicate_Oconversep @ SV347 @ SV480 @ SV573 ) @ ( tc_fun @ SV573 @ ( tc_fun @ SV480 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1272]) ).
thf(1440,plain,
! [SV481: $i,SV348: $i,SV178: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV178 @ SV348 ) @ SV481 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV178 @ SV348 ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__Xintros__1__1 @ SV178 @ SV481 @ SV348 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1273]) ).
thf(1441,plain,
! [SV482: $i,SV349: $i,SV179: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV179 @ SV349 ) @ SV482 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV179 @ SV349 ) @ ( c_ATP__Linkup_Osko__Wellfounded__XaccpI__1__1 @ SV179 @ SV482 @ SV349 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1274]) ).
thf(1442,plain,
! [SV483: $i,SV350: $i,SV180: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV180 @ SV350 ) @ SV483 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV180 @ ( c_ATP__Linkup_Osko__Wellfounded__XaccpI__1__1 @ SV180 @ SV483 @ SV350 ) ) @ SV483 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1275]) ).
thf(1443,plain,
! [SV484: $i,SV351: $i,SV181: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV181 ) @ SV351 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV181 ) @ SV484 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV351 ) @ SV484 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1276]) ).
thf(1444,plain,
! [SV485: $i,SV352: $i,SV182: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV182 ) @ SV352 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV485 ) @ SV352 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV182 ) @ SV485 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1277]) ).
thf(1445,plain,
! [SV353: $i,SV183: $i,SV574: $i] :
( ( ( ! [SY1676: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV574 @ SY1676 ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__rule__1__1 @ SV183 @ SV574 @ SY1676 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV574 @ SY1676 ) @ SV353 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV183 @ SV353 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1278]) ).
thf(1446,plain,
! [SV486: $i,SV354: $i,SV184: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Olift @ SV184 @ SV354 ) ) @ ( c_Lambda_Olift @ SV486 @ SV354 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV184 ) @ SV486 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1279]) ).
thf(1447,plain,
! [SV355: $i,SV575: $i,SV185: $i] :
( ( ( ! [SY1677: $i] :
( ~ ( hBOOL @ ( hAPP @ SV185 @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__rule__1__1 @ SV185 @ SV575 @ SY1677 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV575 @ SY1677 ) @ SV355 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV185 @ SV355 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1280]) ).
thf(1448,plain,
! [SV487: $i,SV356: $i,SV186: $i] :
( ( ( hBOOL @ ( hAPP @ SV186 @ SV356 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ SV186 @ SV487 ) )
| ! [SY1609: $i,SY1610: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1609 @ SV487 ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__rule__1__1 @ SV186 @ SY1609 @ SY1610 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1609 @ SY1610 ) @ SV356 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1281]) ).
thf(1449,plain,
! [SV576: $i,SV488: $i,SV357: $i,SV187: $i] :
( ( ! [SY1678: $i] :
( ( c_Predicate_Oconversep @ ( c_Predicate_Opred__comp @ SV187 @ SV357 @ SV488 @ SV576 @ SY1678 ) @ SV488 @ SY1678 )
= ( c_Predicate_Opred__comp @ ( c_Predicate_Oconversep @ SV357 @ SV576 @ SY1678 ) @ ( c_Predicate_Oconversep @ SV187 @ SV488 @ SV576 ) @ SY1678 @ SV576 @ SV488 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1282]) ).
thf(1450,plain,
! [SV358: $i,SV188: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV188 ) @ SV358 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ SV188 ) ) @ ( c_Lambda_OdB_OAbs @ SV358 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1283]) ).
thf(1451,plain,
! [SV189: $i,SV359: $i] :
( ( ( class_Lattices_Olattice @ SV359 )
= $false )
| ( ( class_Lattices_Oupper__semilattice @ ( tc_fun @ SV189 @ SV359 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1284]) ).
thf(1452,plain,
! [SV190: $i,SV360: $i] :
( ( ( class_Lattices_Olattice @ SV360 )
= $false )
| ( ( class_Lattices_Olower__semilattice @ ( tc_fun @ SV190 @ SV360 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1285]) ).
thf(1453,plain,
! [SV191: $i,SV361: $i] :
( ( ( class_Lattices_Odistrib__lattice @ SV361 )
= $false )
| ( ( class_Lattices_Odistrib__lattice @ ( tc_fun @ SV191 @ SV361 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1286]) ).
thf(1454,plain,
! [SV192: $i,SV362: $i] :
( ( ( class_Lattices_Olattice @ SV362 )
= $false )
| ( ( class_Lattices_Olattice @ ( tc_fun @ SV192 @ SV362 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1287]) ).
thf(1455,plain,
! [SV364: $i,SV194: $i,SV577: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ SV577 ) @ SV194 ) @ SV364 ) ) )
= $true )
| ( ( SV194 = SV364 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1288]) ).
thf(1456,plain,
! [SV578: $i,SV489: $i,SV365: $i,SV195: $i,SV1: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ SV1 @ SV195 ) @ ( c_List_Olist_OCons @ SV365 @ SV489 @ SV195 ) ) @ ( c_List_Olist_OCons @ SV365 @ SV578 @ SV195 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ SV1 @ SV195 ) @ SV489 ) @ SV578 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1289]) ).
thf(1457,plain,
! [SV490: $i,SV366: $i,SV196: $i,SV2: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ SV2 @ SV196 ) @ SV366 ) @ SV490 ) )
= $true )
| ( ( ! [SY1614: $i,SY1615: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV2 @ SY1614 ) @ SY1615 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ SV2 @ SV196 ) @ ( c_List_Olist_OCons @ SY1614 @ SV366 @ SV196 ) ) @ ( c_List_Olist_OCons @ SY1615 @ SV490 @ SV196 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1290]) ).
thf(1458,plain,
! [SV579: $i,SV491: $i,SV367: $i,SV197: $i,SV3: $i] :
( ( ( ( c_List_Olist_OCons @ SV3 @ SV197 @ SV367 )
!= ( c_List_Olist_OCons @ SV491 @ SV579 @ SV367 ) )
| ( SV197 = SV579 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1291]) ).
thf(1459,plain,
! [SV492: $i,SV368: $i,SV198: $i,SV4: $i] :
( ( ( ! [SY1617: $i] :
( ( c_List_Olist_OCons @ SV4 @ SV198 @ SV368 )
!= ( c_List_Olist_OCons @ SV492 @ SY1617 @ SV368 ) ) )
= $true )
| ( ( SV4 = SV492 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1292]) ).
thf(1460,plain,
! [SV493: $i,SV370: $i,SV200: $i,SV6: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ SV6 @ SV200 ) @ SV370 ) @ SV493 ) )
= $true )
| ( ( ( SV493 = SV370 )
| ! [SY1618: $i,SY1619: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ SV6 @ SV200 ) @ ( c_List_Olist_OCons @ SY1618 @ SV370 @ SV200 ) ) @ ( c_List_Olist_OCons @ SY1619 @ SV493 @ SV200 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1294]) ).
thf(1461,plain,
! [SV371: $i,SV201: $i,SV7: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV7 @ SV201 ) @ SV371 ) )
= $false )
| ( ( ! [SY1493: $i,SY1494: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ SV7 @ SY1493 ) @ ( c_List_Olist_OCons @ SV201 @ SY1494 @ SY1493 ) ) @ ( c_List_Olist_OCons @ SV371 @ SY1494 @ SY1493 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1295]) ).
thf(1462,plain,
! [SV494: $i,SV372: $i,SV202: $i,SV8: $i] :
( ( ( SV8 = SV202 )
= $true )
| ( ( ( SV372 = SV494 )
| ! [SY1620: $i,SY1621: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ SY1620 @ SY1621 ) @ ( c_List_Olist_OCons @ SV202 @ SV494 @ SY1621 ) ) @ ( c_List_Olist_OCons @ SV8 @ SV372 @ SY1621 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1296]) ).
thf(1463,plain,
! [SV580: $i,SV495: $i,SV373: $i,SV203: $i,SV9: $i] :
( ( ! [SY1679: $i] :
( ( c_List_Ofoldl @ SV9 @ SV203 @ ( c_List_Olist_OCons @ SV373 @ SV495 @ SV580 ) @ SY1679 @ SV580 )
= ( c_List_Ofoldl @ SV9 @ ( hAPP @ ( hAPP @ SV9 @ SV203 ) @ SV373 ) @ SV495 @ SY1679 @ SV580 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1297]) ).
thf(1464,plain,
! [SV496: $i,SV376: $i,SV206: $i,SV12: $i] :
( ( ( SV12 = SV206 )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV376 @ SV206 ) @ SV12 ) )
| ! [SY1624: $i,SY1625: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ SV376 @ SV496 ) @ ( c_List_Olist_OCons @ SV206 @ SY1624 @ SV496 ) ) @ ( c_List_Olist_OCons @ SV12 @ SY1625 @ SV496 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1300]) ).
thf(1465,plain,
! [SV497: $i,SV379: $i,SV209: $i,SV15: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( c_ListOrder_Ostep1 @ SV15 @ SV209 ) @ ( tc_List_Olist @ SV209 ) ) @ ( c_List_Olist_OCons @ SV379 @ SV497 @ SV209 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( c_ListOrder_Ostep1 @ SV15 @ SV209 ) @ ( tc_List_Olist @ SV209 ) ) @ SV497 ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV15 @ SV209 ) @ SV379 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1303]) ).
thf(1466,plain,
! [SV498: $i,SV380: $i,SV210: $i,SV16: $i] :
( ( ( ( c_Type_Otype_OFun @ SV16 @ SV210 )
!= ( c_Type_Otype_OFun @ SV380 @ SV498 ) )
= $true )
| ( ( SV210 = SV498 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1304]) ).
thf(1467,plain,
! [SV581: $i,SV381: $i,SV211: $i,SV17: $i] :
( ( ( ( c_Type_Otype_OFun @ SV17 @ SV211 )
!= ( c_Type_Otype_OFun @ SV381 @ SV581 ) )
= $true )
| ( ( SV17 = SV381 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1305]) ).
thf(1468,plain,
! [SV499: $i,SV382: $i,SV212: $i,SV18: $i] :
( ( ( c_Type_Otyping @ SV18 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV212 ) @ SV382 ) @ SV499 )
= $true )
| ( ( ! [SY1626: $i] :
( ~ ( c_Type_Otyping @ SV18 @ SV382 @ SY1626 )
| ~ ( c_Type_Otyping @ SV18 @ SV212 @ ( c_Type_Otype_OFun @ SY1626 @ SV499 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1306]) ).
thf(1469,plain,
! [SV582: $i,SV500: $i,SV383: $i,SV213: $i,SV19: $i] :
( ( ( c_Type_Otyping @ ( c_Type_Oshift @ SV19 @ SV213 @ SV383 @ tc_Type_Otype ) @ ( c_Lambda_Olift @ SV500 @ SV213 ) @ SV582 )
| ~ ( c_Type_Otyping @ SV19 @ SV500 @ SV582 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1307]) ).
thf(1470,plain,
! [SV214: $i,SV384: $i,SV20: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV20 ) @ SV384 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Olift @ SV20 @ SV214 ) ) @ ( c_Lambda_Olift @ SV384 @ SV214 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1308]) ).
thf(1471,plain,
! [SV501: $i,SV385: $i,SV215: $i,SV21: $i] :
( ( ( ~ ( c_Type_Otyping @ SV21 @ SV215 @ SV385 ) )
= $true )
| ( ( ! [SY1628: $i,SY1629: $i] :
( ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV21 @ SV501 @ SV385 @ tc_Type_Otype ) @ SY1628 @ SY1629 )
| ( c_Type_Otyping @ SV21 @ ( c_Lambda_Osubst @ SY1628 @ SV215 @ SV501 ) @ SY1629 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1309]) ).
thf(1472,plain,
! [SV216: $i,SV386: $i,SV583: $i,SV22: $i] :
( ( ( ~ ( c_Type_Otyping @ SV22 @ SV583 @ SV386 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV583 ) @ SV216 ) ) )
= $true )
| ( ( c_Type_Otyping @ SV22 @ SV216 @ SV386 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1310]) ).
thf(1473,plain,
! [SV387: $i,SV23: $i,SV217: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV217 ) @ SV23 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV387 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV23 ) @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SV217 @ SV23 @ SV387 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1311]) ).
thf(1474,plain,
! [SV502: $i,SV388: $i,SV218: $i,SV24: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV24 @ SV218 @ SV388 ) ) @ ( c_Lambda_Osubst @ SV24 @ SV502 @ SV388 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV218 ) @ SV502 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1312]) ).
thf(1475,plain,
! [SV503: $i,SV389: $i,SV219: $i,SV25: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV25 @ SV219 @ SV389 ) ) @ ( c_Lambda_Osubst @ SV503 @ SV219 @ SV389 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV25 ) @ SV503 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1313]) ).
thf(1476,plain,
! [SV504: $i,SV390: $i,SV220: $i,SV26: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV26 @ SV220 @ SV390 ) ) @ ( c_Lambda_Osubst @ SV26 @ SV504 @ SV390 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV220 ) @ SV504 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1314]) ).
thf(1477,plain,
! [SV391: $i,SV222: $i,SV28: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV28 ) @ SV222 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV391 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV28 ) @ SV222 )
= SV391 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1315]) ).
thf(1478,plain,
! [SV30: $i,SV392: $i,SV224: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV224 ) @ SV392 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV30 ) @ SV224 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV30 ) @ SV392 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1317]) ).
thf(1479,plain,
! [SV225: $i,SV393: $i,SV31: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV31 ) @ SV393 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV31 ) @ SV225 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV393 ) @ SV225 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1318]) ).
thf(1480,plain,
! [SV505: $i,SV394: $i,SV226: $i,SV32: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV32 ) @ SV226 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV394 ) @ SV505 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV226 ) @ SV505 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV32 ) @ SV394 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1319]) ).
thf(1481,plain,
! [SV506: $i,SV395: $i,SV227: $i,SV33: $i] :
( ( ( c_Type_Otyping @ SV33 @ ( c_Lambda_OdB_OAbs @ SV227 ) @ ( c_Type_Otype_OFun @ SV395 @ SV506 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV33 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV395 @ tc_Type_Otype ) @ SV227 @ SV506 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1320]) ).
thf(1482,plain,
! [SV396: $i,SV228: $i,SV34: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( c_ListOrder_Ostep1 @ SV34 @ SV228 ) @ ( tc_List_Olist @ SV228 ) ) @ SV396 ) )
= $false )
| ( ( c_List_Olistsp @ ( c_Wellfounded_Oaccp @ SV34 @ SV228 ) @ SV396 @ SV228 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1321]) ).
thf(1483,plain,
! [SV397: $i,SV229: $i,SV35: $i] :
( ( ( c_List_Olistsp @ ( c_Wellfounded_Oaccp @ SV35 @ SV229 ) @ SV397 @ SV229 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( c_ListOrder_Ostep1 @ SV35 @ SV229 ) @ ( tc_List_Olist @ SV229 ) ) @ SV397 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1322]) ).
thf(1484,plain,
! [SV509: $i,SV402: $i,SV235: $i,SV41: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV41 ) @ SV235 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV402 @ SV509 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( ( SV41
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV402 @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ SV41 @ SV235 @ SV402 @ SV509 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV509
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1327]) ).
thf(1485,plain,
! [SV42: $i,SV403: $i,SV236: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV236 ) @ SV403 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV42 @ SV236 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV42 @ SV403 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1328]) ).
thf(1486,plain,
! [SV237: $i,SV404: $i,SV43: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV43 ) @ SV404 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV43 @ SV237 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV404 @ SV237 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1329]) ).
thf(1487,plain,
! [SV510: $i,SV238: $i,SV45: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV45 @ SV238 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_Lambda_OdB_OAbs @ SV510 ) )
= $false )
| ( ( SV238
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1330]) ).
thf(1488,plain,
! [SV405: $i,SV239: $i,SV47: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV47 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV239 @ SV405 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( SV405
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1331]) ).
thf(1489,plain,
! [SV406: $i,SV240: $i,SV48: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV48 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV240 @ SV406 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( SV406
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1332]) ).
thf(1490,plain,
! [SV511: $i,SV407: $i,SV241: $i,SV50: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV50 @ SV241 @ SV407 ) ) )
= $true )
| ( ( ! [SY1630: $i] :
( ~ ( c_Type_Otyping @ SV511 @ SV241 @ SY1630 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV241 ) )
| ! [SY1631: $i] :
~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV511 @ SV407 @ SY1630 @ tc_Type_Otype ) @ SV50 @ SY1631 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV50 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1333]) ).
thf(1491,plain,
! [SV51: $i,SV408: $i,SV242: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV242 ) @ SV408 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV51 ) )
= $false )
| ( ( SV51
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV242 ) @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SV242 @ SV408 @ SV51 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1334]) ).
thf(1492,plain,
! [SV512: $i,SV55: $i,SV410: $i] :
( ( ( c_Type_Otyping @ SV410 @ SV55 @ SV512 )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV55 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1337]) ).
thf(1493,plain,
! [SV513: $i,SV411: $i,SV246: $i,SV56: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV56 ) ) @ SV246 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV411 ) @ SV513 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1338]) ).
thf(1494,plain,
! [SV514: $i,SV412: $i,SV247: $i,SV57: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV57 @ SV247 ) @ SV412 ) )
= $true )
| ( ( ! [SY1632: $i,SY1633: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV57 @ SV514 @ ( tc_fun @ SY1632 @ ( tc_fun @ SY1633 @ tc_bool ) ) ) @ SV247 ) @ SV412 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1339]) ).
thf(1495,plain,
! [SV515: $i,SV413: $i,SV248: $i,SV58: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV58 @ SV248 ) @ SV413 ) )
= $true )
| ( ( ! [SY1634: $i,SY1635: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV515 @ SV58 @ ( tc_fun @ SY1634 @ ( tc_fun @ SY1635 @ tc_bool ) ) ) @ SV248 ) @ SV413 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1340]) ).
thf(1496,plain,
! [SV516: $i,SV416: $i,SV250: $i,SV61: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV61 @ SV250 ) @ SV416 ) @ SV516 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV61 @ SV416 ) @ SV516 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1342]) ).
thf(1497,plain,
! [SV62: $i,SV584: $i,SV517: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV517 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV517 @ SV584 @ SV62 ) @ SV62 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV517 @ SV584 @ SV62 ) )
= $true )
| ( ( class_Lattices_Olattice @ SV62 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1343]) ).
thf(1498,plain,
! [SV63: $i,SV585: $i,SV518: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV518 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV518 @ SV585 @ SV63 ) @ SV63 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV518 @ SV585 @ SV63 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV63 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1344]) ).
thf(1499,plain,
! [SV64: $i,SV586: $i,SV519: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV519 @ SV586 @ SV64 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV586 @ SV519 @ SV64 ) )
= $true )
| ( ( class_Lattices_Olattice @ SV64 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1345]) ).
thf(1500,plain,
! [SV65: $i,SV587: $i,SV520: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV520 @ SV587 @ SV65 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV587 @ SV520 @ SV65 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV65 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1346]) ).
thf(1501,plain,
! [SV417: $i,SV251: $i,SV67: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV67 @ SV251 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV417 @ SV251 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( SV67 = SV417 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1347]) ).
thf(1502,plain,
! [SV521: $i,SV252: $i,SV68: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV68 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV252 @ SV521 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( ( c_Lambda_OdB_OAbs @ SV68 )
= SV252 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1348]) ).
thf(1503,plain,
! [SV70: $i,SV588: $i,SV522: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV522 @ SV588 @ SV70 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV588 @ SV522 @ SV70 ) )
= $true )
| ( ( class_Lattices_Olattice @ SV70 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1349]) ).
thf(1504,plain,
! [SV71: $i,SV589: $i,SV523: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV523 @ SV589 @ SV71 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV589 @ SV523 @ SV71 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV71 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1350]) ).
thf(1505,plain,
! [SV72: $i,SV590: $i,SV254: $i] :
( ( ( ! [SY1680: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV254 @ SV590 @ SV72 ) @ SY1680 @ SV72 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV254 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV590 @ SY1680 @ SV72 ) @ SV72 ) ) )
= $true )
| ( ( class_Lattices_Olattice @ SV72 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1351]) ).
thf(1506,plain,
! [SV73: $i,SV591: $i,SV255: $i] :
( ( ( ! [SY1681: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV255 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV591 @ SY1681 @ SV73 ) @ SV73 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV591 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV255 @ SY1681 @ SV73 ) @ SV73 ) ) )
= $true )
| ( ( class_Lattices_Olattice @ SV73 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1352]) ).
thf(1507,plain,
! [SV74: $i,SV592: $i,SV256: $i] :
( ( ( ! [SY1682: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV256 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV592 @ SY1682 @ SV74 ) @ SV74 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV592 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV256 @ SY1682 @ SV74 ) @ SV74 ) ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV74 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1353]) ).
thf(1508,plain,
! [SV75: $i,SV593: $i,SV257: $i] :
( ( ( ! [SY1683: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV257 @ SV593 @ SV75 ) @ SY1683 @ SV75 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV257 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV593 @ SY1683 @ SV75 ) @ SV75 ) ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV75 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1354]) ).
thf(1509,plain,
! [SV77: $i,SV594: $i,SV258: $i] :
( ( ( ! [SY1684: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV258 @ SV594 @ SV77 ) @ SY1684 @ SV77 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV258 @ SY1684 @ SV77 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV594 @ SY1684 @ SV77 ) @ SV77 ) ) )
= $true )
| ( ( class_Lattices_Odistrib__lattice @ SV77 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1356]) ).
thf(1510,plain,
! [SV78: $i,SV595: $i,SV259: $i] :
( ( ( ! [SY1685: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV259 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV595 @ SY1685 @ SV78 ) @ SV78 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV259 @ SV595 @ SV78 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV259 @ SY1685 @ SV78 ) @ SV78 ) ) )
= $true )
| ( ( class_Lattices_Odistrib__lattice @ SV78 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1357]) ).
thf(1511,plain,
! [SV596: $i,SV525: $i,SV418: $i,SV260: $i,SV79: $i] :
( ( ! [SY1686: $i,SY1687: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV79 @ SV260 @ SV418 @ SV525 @ SV596 ) @ SY1686 ) @ SY1687 ) )
| ! [SY1307: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV260 @ SY1307 ) @ SY1687 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV79 @ SY1686 ) @ SY1307 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1358]) ).
thf(1512,plain,
! [SV526: $i,SV419: $i,SV261: $i,SV80: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV80 @ SV261 ) @ SV419 ) @ SV526 ) )
= $true )
| ( ( ! [SY1646: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV80 @ SV261 ) @ SY1646 ) @ SV526 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV80 @ SV261 ) @ SV419 ) @ SY1646 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1359]) ).
thf(1513,plain,
! [SV527: $i,SV420: $i,SV262: $i,SV81: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV81 @ SV262 ) @ SV420 ) @ SV527 ) )
= $true )
| ( ( ! [SY1647: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV81 @ SV262 ) @ SY1647 ) @ SV527 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV81 @ SV262 ) @ SV420 ) @ SY1647 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1360]) ).
thf(1514,plain,
! [SV528: $i,SV423: $i,SV265: $i,SV84: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV84 @ SV265 ) @ SV423 ) @ SV528 ) )
= $true )
| ( ( ! [SY1648: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV84 @ SV265 ) @ SY1648 ) @ SV528 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV84 @ SV265 ) @ SV423 ) @ SY1648 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1361]) ).
thf(1515,plain,
! [SV529: $i,SV424: $i,SV266: $i,SV85: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV85 @ SV266 ) @ SV424 ) @ SV529 ) )
= $true )
| ( ( ! [SY1649: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV85 @ SV266 ) @ SY1649 ) @ SV529 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV85 @ SV424 ) @ SY1649 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1362]) ).
thf(1516,plain,
! [SV530: $i,SV425: $i,SV267: $i,SV86: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV86 @ SV267 ) @ SV425 ) @ SV530 ) )
= $true )
| ( ( ! [SY1650: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV86 @ SY1650 ) @ SV530 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV86 @ SV267 ) @ SV425 ) @ SY1650 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1363]) ).
thf(1517,plain,
! [SV427: $i,SV270: $i,SV89: $i] :
( ( ( c_Type_Otyping @ SV89 @ ( c_Lambda_OdB_OVar @ SV270 ) @ SV427 )
= $false )
| ( ( ( hAPP @ SV89 @ SV270 )
= SV427 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1365]) ).
thf(1518,plain,
! [SV531: $i,SV428: $i,SV271: $i,SV90: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV90 @ SV271 ) @ SV428 ) @ SV531 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV90 @ SV271 ) @ SV428 ) @ SV531 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1366]) ).
thf(1519,plain,
! [SV532: $i,SV429: $i,SV273: $i,SV93: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV93 @ SV273 ) @ SV429 ) @ SV532 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV93 @ SV429 ) @ SV532 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1367]) ).
thf(1520,plain,
! [SV533: $i,SV430: $i,SV274: $i,SV94: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV94 @ SV274 ) @ SV430 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV533 @ SV274 ) @ SV430 ) )
| ! [SY1651: $i,SY1652: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV533 @ SV94 @ ( tc_fun @ SY1651 @ ( tc_fun @ SY1652 @ tc_bool ) ) ) @ SV274 ) @ SV430 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1368]) ).
thf(1521,plain,
! [SV597: $i,SV534: $i,SV431: $i,SV275: $i,SV95: $i] :
( ( ! [SY1689: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV95 @ SV275 @ ( tc_fun @ SV431 @ ( tc_fun @ SV534 @ tc_bool ) ) ) @ SV597 ) @ SY1689 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV275 @ SV597 ) @ SY1689 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1369]) ).
thf(1522,plain,
! [SV598: $i,SV535: $i,SV432: $i,SV276: $i,SV96: $i] :
( ( ! [SY1690: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV96 @ SV276 @ ( tc_fun @ SV432 @ ( tc_fun @ SV535 @ tc_bool ) ) ) @ SV598 ) @ SY1690 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV96 @ SV598 ) @ SY1690 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1370]) ).
thf(1523,plain,
! [SV433: $i,SV97: $i,SV277: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV277 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV97 @ SV277 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV433 @ 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 @ SV97 ) ) @ SV277 ) @ SV433 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1371]) ).
thf(1524,plain,
! [SV536: $i,SV435: $i,SV278: $i,SV99: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV99 ) @ SV278 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV435 ) @ SV536 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1373]) ).
thf(1525,plain,
! [SV100: $i,SV599: $i,SV279: $i] :
( ( ( ! [SY1691: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV279 @ SV599 @ SV100 ) @ SY1691 @ SV100 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV279 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV599 @ SY1691 @ SV100 ) @ SV100 ) ) )
= $true )
| ( ( class_Lattices_Olattice @ SV100 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1374]) ).
thf(1526,plain,
! [SV101: $i,SV600: $i,SV280: $i] :
( ( ( ! [SY1692: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV280 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV600 @ SY1692 @ SV101 ) @ SV101 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV600 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV280 @ SY1692 @ SV101 ) @ SV101 ) ) )
= $true )
| ( ( class_Lattices_Olattice @ SV101 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1375]) ).
thf(1527,plain,
! [SV102: $i,SV601: $i,SV281: $i] :
( ( ( ! [SY1693: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV281 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV601 @ SY1693 @ SV102 ) @ SV102 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV601 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV281 @ SY1693 @ SV102 ) @ SV102 ) ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV102 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1376]) ).
thf(1528,plain,
! [SV103: $i,SV602: $i,SV282: $i] :
( ( ( ! [SY1694: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV282 @ SV602 @ SV103 ) @ SY1694 @ SV103 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV282 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV602 @ SY1694 @ SV103 ) @ SV103 ) ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV103 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1377]) ).
thf(1529,plain,
! [SV537: $i,SV285: $i,SV106: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV106 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV285 @ SV537 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( ( c_Lambda_OdB_OVar @ SV106 )
= SV285 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1380]) ).
thf(1530,plain,
! [SV286: $i,SV437: $i,SV107: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV107 ) @ SV437 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV107 @ SV286 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV437 @ SV286 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1381]) ).
thf(1531,plain,
! [SV108: $i,SV603: $i,SV538: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV538 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV538 @ SV603 @ SV108 ) @ SV108 )
= SV538 )
= $true )
| ( ( class_Lattices_Olattice @ SV108 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1382]) ).
thf(1532,plain,
! [SV110: $i,SV288: $i,SV604: $i,SV438: $i] :
( ( ( ! [SY1695: $i] :
( ~ ( c_Type_Otyping @ SV438 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV604 ) @ SY1695 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV288 )
| ~ ( c_Type_Otyping @ SV438 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV604 ) @ SY1695 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV110 ) ) )
= $true )
| ( ( SV110 = SV288 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1383]) ).
thf(1533,plain,
! [SV539: $i,SV439: $i,SV289: $i,SV111: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV111 ) @ SV289 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV439 ) @ SV539 ) )
= $true )
| ( ( SV289 = SV539 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1384]) ).
thf(1534,plain,
! [SV605: $i,SV440: $i,SV290: $i,SV112: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV112 ) @ SV290 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV440 ) @ SV605 ) )
= $true )
| ( ( SV112 = SV440 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1385]) ).
thf(1535,plain,
! [SV113: $i,SV606: $i,SV540: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV540 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV540 @ SV606 @ SV113 ) @ SV113 )
= SV540 )
= $true )
| ( ( class_Lattices_Olattice @ SV113 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1386]) ).
thf(1536,plain,
! [SV541: $i,SV441: $i,SV291: $i,SV114: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV114 ) @ SV291 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV441 ) @ SV541 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV291 = SV541 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1387]) ).
thf(1537,plain,
! [SV607: $i,SV442: $i,SV292: $i,SV115: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV115 ) @ SV292 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV442 ) @ SV607 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV115 = SV442 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1388]) ).
thf(1538,plain,
! [SV443: $i,SV293: $i,SV116: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV116 @ SV293 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_Lambda_OdB_OAbs @ SV443 ) )
= $false )
| ( ( SV116
= ( c_Lambda_OdB_OAbs @ SV443 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1389]) ).
thf(1539,plain,
! [SV542: $i,SV444: $i,SV295: $i,SV118: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV118 @ SV295 ) @ SV444 ) @ SV542 ) )
= $true )
| ( ( ( SV444 = SV542 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV118 @ SV295 ) @ SV444 ) @ SV542 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1390]) ).
thf(1540,plain,
! [SV543: $i,SV445: $i,SV296: $i,SV119: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV119 @ SV296 ) @ SV445 ) @ SV543 ) )
= $true )
| ( ( ( SV445 = SV543 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV119 @ SV296 ) @ SV445 ) @ SV543 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1391]) ).
thf(1541,plain,
! [SV121: $i,SV608: $i,SV298: $i] :
( ( ( ! [SY1696: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV298 @ SV608 @ SV121 ) @ SY1696 @ SV121 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV298 @ SY1696 @ SV121 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV608 @ SY1696 @ SV121 ) @ SV121 ) ) )
= $true )
| ( ( class_Lattices_Odistrib__lattice @ SV121 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1392]) ).
thf(1542,plain,
! [SV122: $i,SV609: $i,SV299: $i] :
( ( ( ! [SY1697: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV299 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV609 @ SY1697 @ SV122 ) @ SV122 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV299 @ SV609 @ SV122 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV299 @ SY1697 @ SV122 ) @ SV122 ) ) )
= $true )
| ( ( class_Lattices_Odistrib__lattice @ SV122 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1393]) ).
thf(1543,plain,
! [SV123: $i,SV610: $i,SV544: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV544 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV544 @ SV610 @ SV123 ) @ SV123 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV544 @ SV610 @ SV123 ) )
= $true )
| ( ( class_Lattices_Olattice @ SV123 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1394]) ).
thf(1544,plain,
! [SV124: $i,SV611: $i,SV545: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV545 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV545 @ SV611 @ SV124 ) @ SV124 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV545 @ SV611 @ SV124 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV124 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1395]) ).
thf(1545,plain,
! [SV546: $i,SV447: $i,SV125: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV125 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV125 @ ( c_Lambda_OdB_OVar @ SV447 ) @ SV546 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1396]) ).
thf(1546,plain,
! [SV548: $i,SV448: $i,SV302: $i,SV129: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV129 ) @ SV302 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV448 ) @ SV548 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV302 = SV548 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1398]) ).
thf(1547,plain,
! [SV612: $i,SV449: $i,SV303: $i,SV130: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV130 ) @ SV303 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV449 ) @ SV612 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV130 = SV449 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1399]) ).
thf(1548,plain,
! [SV549: $i,SV451: $i,SV305: $i,SV132: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV132 @ SV305 ) @ SV451 ) @ SV549 ) )
= $true )
| ( ( ! [SY1661: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV132 @ SV305 ) @ SY1661 ) @ SV549 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV132 @ SV305 ) @ SV451 ) @ SY1661 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1401]) ).
thf(1549,plain,
! [SV613: $i,SV551: $i,SV454: $i,SV310: $i,SV137: $i] :
( ( ! [SY1698: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV137 @ SV310 @ ( tc_fun @ SV454 @ ( tc_fun @ SV551 @ tc_bool ) ) ) @ SV613 ) @ SY1698 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV310 @ SV613 ) @ SY1698 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ SV613 ) @ SY1698 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1405]) ).
thf(1550,plain,
! [SV552: $i,SV455: $i,SV311: $i,SV138: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV138 @ SV311 ) @ SV455 ) @ SV552 ) )
= $true )
| ( ( ! [SY1664: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV138 @ SV311 ) @ SY1664 ) @ SV552 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV138 @ SV455 ) @ SY1664 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1406]) ).
thf(1551,plain,
! [SV553: $i,SV456: $i,SV312: $i,SV139: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV139 @ SV312 ) @ SV456 ) @ SV553 ) )
= $true )
| ( ( ! [SY1665: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV139 @ SY1665 ) @ SV553 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV139 @ SV312 ) @ SV456 ) @ SY1665 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1407]) ).
thf(1552,plain,
! [SV554: $i,SV457: $i,SV313: $i,SV140: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV140 @ SV313 ) @ SV457 ) @ SV554 ) )
= $true )
| ( ( ! [SY1666: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV140 @ SY1666 ) @ SV554 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV140 @ SV313 ) @ SV457 ) @ SY1666 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1408]) ).
thf(1553,plain,
! [SV555: $i,SV458: $i,SV314: $i,SV141: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV141 @ SV314 ) @ SV458 ) @ SV555 ) )
= $true )
| ( ( ! [SY1667: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV141 @ SV314 ) @ SY1667 ) @ SV555 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV141 @ SV458 ) @ SY1667 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1409]) ).
thf(1554,plain,
! [SV315: $i,SV614: $i,SV459: $i,SV142: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV142 @ SV459 ) @ SV614 ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV142 @ SV315 ) @ SV614 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV142 @ SV315 ) @ SV459 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1410]) ).
thf(1555,plain,
! [SV316: $i,SV615: $i,SV460: $i,SV143: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV460 ) @ SV615 ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV143 @ SV316 ) @ SV615 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV143 @ SV316 ) @ SV460 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1411]) ).
thf(1556,plain,
! [SV317: $i,SV616: $i,SV556: $i,SV144: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV144 @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__1__1 @ SV144 @ SV556 @ SV616 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV556 @ SV616 ) @ SV317 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV144 @ SV317 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1412]) ).
thf(1557,plain,
! [SV318: $i,SV461: $i,SV145: $i] :
( ( ( hBOOL @ ( hAPP @ SV145 @ SV461 ) )
= $true )
| ( ( ! [SY1589: $i,SY1590: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1589 @ SV461 ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__1__1 @ SV145 @ SY1589 @ SY1590 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1589 @ SY1590 ) @ SV318 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV145 @ SV318 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1413]) ).
thf(1558,plain,
! [SV463: $i,SV147: $i,SV320: $i,SV617: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV617 ) @ SV320 ) )
| ~ ( c_Type_Otyping @ SV147 @ SV617 @ SV463 ) )
= $true )
| ( ( c_Type_Otyping @ SV147 @ SV320 @ SV463 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1415]) ).
thf(1559,plain,
! [SV557: $i,SV321: $i,SV148: $i] :
( ( ( c_Wellfounded_OwfP @ SV148 @ SV321 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV148 @ SV321 ) @ SV557 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1416]) ).
thf(1560,plain,
! [SV558: $i,SV466: $i,SV325: $i,SV153: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ ( c_Transitive__Closure_Otranclp @ SV153 @ SV325 ) @ SV325 @ SV325 ) @ SV466 ) @ SV558 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ ( c_Predicate_Oconversep @ SV153 @ SV325 @ SV325 ) @ SV325 ) @ SV466 ) @ SV558 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1418]) ).
thf(1561,plain,
! [SV559: $i,SV467: $i,SV326: $i,SV154: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ ( c_Predicate_Oconversep @ SV154 @ SV326 @ SV326 ) @ SV326 ) @ SV467 ) @ SV559 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ ( c_Transitive__Closure_Otranclp @ SV154 @ SV326 ) @ SV326 @ SV326 ) @ SV467 ) @ SV559 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1419]) ).
thf(1562,plain,
! [SV468: $i,SV327: $i,SV155: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV155 @ SV327 ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xnot__accp__down__1__1 @ SV155 @ SV468 @ SV327 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV155 @ SV327 ) @ SV468 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1420]) ).
thf(1563,plain,
! [SV469: $i,SV618: $i,SV329: $i,SV159: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV159 @ SV329 ) @ SV618 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV159 @ SV329 ) @ SV469 ) @ SV618 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV159 @ SV329 ) @ SV469 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1421]) ).
thf(1564,plain,
! [SV619: $i,SV470: $i,SV330: $i,SV160: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV160 @ SV330 ) @ SV470 ) @ SV619 ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV160 @ SV330 ) @ SV619 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV160 @ SV330 ) @ SV470 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1422]) ).
thf(1565,plain,
! [SV560: $i,SV471: $i,SV331: $i,SV161: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Osubst @ SV161 @ SV331 @ SV471 ) ) @ ( c_Lambda_Osubst @ SV560 @ SV331 @ SV471 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV161 ) @ SV560 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1423]) ).
thf(1566,plain,
! [SV332: $i,SV561: $i,SV162: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV162 @ ( v_sko__Wellfounded__Xaccp__Xinducts__1 @ SV162 @ SV561 ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV561 @ t_a ) @ SV332 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV162 @ SV332 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1424]) ).
thf(1567,plain,
! [SV333: $i,SV562: $i,SV163: $i] :
( ( ( hBOOL @ ( hAPP @ SV163 @ SV562 ) )
= $true )
| ( ( ! [SY1669: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1669 @ SV562 ) @ ( v_sko__Wellfounded__Xaccp__Xinducts__1 @ SV163 @ SY1669 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1669 @ t_a ) @ SV333 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV163 @ SV333 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1425]) ).
thf(1568,plain,
! [SV472: $i,SV334: $i,SV164: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV164 @ SV334 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV472 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ SV334 ) )
| ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV164 ) ) @ SV334 ) @ SV472 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1426]) ).
thf(1569,plain,
! [SV335: $i,SV563: $i,SV165: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV165 @ ( v_sko__Wellfounded__Xaccp__Xinduct__1 @ SV165 @ SV563 ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV563 @ t_a ) @ SV335 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV165 @ SV335 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1427]) ).
thf(1570,plain,
! [SV336: $i,SV564: $i,SV166: $i] :
( ( ( hBOOL @ ( hAPP @ SV166 @ SV564 ) )
= $true )
| ( ( ! [SY1670: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1670 @ SV564 ) @ ( v_sko__Wellfounded__Xaccp__Xinduct__1 @ SV166 @ SY1670 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1670 @ t_a ) @ SV336 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV166 @ SV336 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1428]) ).
thf(1571,plain,
! [SV620: $i,SV565: $i,SV473: $i,SV337: $i,SV167: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV167 @ SV337 @ SV473 ) @ SV565 ) @ SV620 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV167 @ SV620 ) @ SV565 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1429]) ).
thf(1572,plain,
! [SV338: $i,SV474: $i,SV621: $i,SV168: $i] :
( ( ( ! [SY1699: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV168 @ SV621 @ SY1699 ) @ SV474 ) @ SV338 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV168 @ SV338 ) @ SV474 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1430]) ).
thf(1573,plain,
! [SV622: $i,SV566: $i,SV475: $i,SV339: $i,SV169: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV169 @ SV339 @ SV475 ) @ SV566 ) @ SV622 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV169 @ SV622 ) @ SV566 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1431]) ).
thf(1574,plain,
! [SV340: $i,SV476: $i,SV623: $i,SV170: $i] :
( ( ( ! [SY1700: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV170 @ SV623 @ SY1700 ) @ SV476 ) @ SV340 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV170 @ SV340 ) @ SV476 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1432]) ).
thf(1575,plain,
! [SV341: $i,SV171: $i,SV624: $i,SV567: $i] :
( ( ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV567 @ t_a ) @ SV624 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV567 @ SV624 ) @ ( v_sko__Wellfounded__Xaccp__Xinducts__1 @ SV171 @ SV567 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV567 @ t_a ) @ SV341 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV171 @ SV341 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1433]) ).
thf(1576,plain,
! [SV342: $i,SV172: $i,SV625: $i,SV568: $i] :
( ( ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV568 @ t_a ) @ SV625 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV568 @ SV625 ) @ ( v_sko__Wellfounded__Xaccp__Xinduct__1 @ SV172 @ SV568 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV568 @ t_a ) @ SV342 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV172 @ SV342 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1434]) ).
thf(1577,plain,
! [SV570: $i,SV478: $i,SV344: $i,SV174: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV174 @ SV344 ) @ SV478 ) @ SV570 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ SV174 @ SV344 @ SV344 ) @ SV344 ) @ SV570 ) @ SV478 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1436]) ).
thf(1578,plain,
! [SV571: $i,SV479: $i,SV345: $i,SV175: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ SV175 @ SV345 @ SV345 ) @ SV345 ) @ SV479 ) @ SV571 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV175 @ SV345 ) @ SV571 ) @ SV479 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1437]) ).
thf(1579,plain,
! [SV346: $i,SV176: $i,SV626: $i,SV572: $i] :
( ( ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV572 @ SV626 ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__1__1 @ SV176 @ SV572 @ SV626 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV572 @ SV626 ) @ SV346 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV176 @ SV346 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1438]) ).
thf(1580,plain,
! [SV481: $i,SV348: $i,SV178: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV178 @ SV348 ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__Xintros__1__1 @ SV178 @ SV481 @ SV348 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV178 @ SV348 ) @ SV481 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1440]) ).
thf(1581,plain,
! [SV482: $i,SV349: $i,SV179: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV179 @ SV349 ) @ ( c_ATP__Linkup_Osko__Wellfounded__XaccpI__1__1 @ SV179 @ SV482 @ SV349 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV179 @ SV349 ) @ SV482 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1441]) ).
thf(1582,plain,
! [SV181: $i,SV484: $i,SV351: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV351 ) @ SV484 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV181 ) @ SV351 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV181 ) @ SV484 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1443]) ).
thf(1583,plain,
! [SV352: $i,SV485: $i,SV182: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV182 ) @ SV485 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV182 ) @ SV352 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV485 ) @ SV352 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1444]) ).
thf(1584,plain,
! [SV353: $i,SV183: $i,SV627: $i,SV574: $i] :
( ( ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV574 @ SV627 ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__rule__1__1 @ SV183 @ SV574 @ SV627 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV574 @ SV627 ) @ SV353 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV183 @ SV353 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1445]) ).
thf(1585,plain,
! [SV354: $i,SV486: $i,SV184: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV184 ) @ SV486 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Olift @ SV184 @ SV354 ) ) @ ( c_Lambda_Olift @ SV486 @ SV354 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1446]) ).
thf(1586,plain,
! [SV355: $i,SV628: $i,SV575: $i,SV185: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV185 @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__rule__1__1 @ SV185 @ SV575 @ SV628 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV575 @ SV628 ) @ SV355 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV185 @ SV355 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1447]) ).
thf(1587,plain,
! [SV356: $i,SV487: $i,SV186: $i] :
( ( ( hBOOL @ ( hAPP @ SV186 @ SV487 ) )
= $true )
| ( ( ! [SY1609: $i,SY1610: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY1609 @ SV487 ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__rule__1__1 @ SV186 @ SY1609 @ SY1610 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SY1609 @ SY1610 ) @ SV356 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV186 @ SV356 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1448]) ).
thf(1588,plain,
! [SV629: $i,SV576: $i,SV488: $i,SV357: $i,SV187: $i] :
( ( ( c_Predicate_Oconversep @ ( c_Predicate_Opred__comp @ SV187 @ SV357 @ SV488 @ SV576 @ SV629 ) @ SV488 @ SV629 )
= ( c_Predicate_Opred__comp @ ( c_Predicate_Oconversep @ SV357 @ SV576 @ SV629 ) @ ( c_Predicate_Oconversep @ SV187 @ SV488 @ SV576 ) @ SV629 @ SV576 @ SV488 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1449]) ).
thf(1589,plain,
! [SV364: $i,SV194: $i,SV577: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ SV577 ) @ SV194 ) @ SV364 ) )
= $false )
| ( ( SV194 = SV364 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1455]) ).
thf(1590,plain,
! [SV578: $i,SV489: $i,SV365: $i,SV195: $i,SV1: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ SV1 @ SV195 ) @ ( c_List_Olist_OCons @ SV365 @ SV489 @ SV195 ) ) @ ( c_List_Olist_OCons @ SV365 @ SV578 @ SV195 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ SV1 @ SV195 ) @ SV489 ) @ SV578 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1456]) ).
thf(1591,plain,
! [SV490: $i,SV366: $i,SV196: $i,SV630: $i,SV2: $i] :
( ( ( ! [SY1701: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV2 @ SV630 ) @ SY1701 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ SV2 @ SV196 ) @ ( c_List_Olist_OCons @ SV630 @ SV366 @ SV196 ) ) @ ( c_List_Olist_OCons @ SY1701 @ SV490 @ SV196 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ SV2 @ SV196 ) @ SV366 ) @ SV490 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1457]) ).
thf(1592,plain,
! [SV579: $i,SV491: $i,SV367: $i,SV197: $i,SV3: $i] :
( ( ( ( c_List_Olist_OCons @ SV3 @ SV197 @ SV367 )
!= ( c_List_Olist_OCons @ SV491 @ SV579 @ SV367 ) )
= $true )
| ( ( SV197 = SV579 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1458]) ).
thf(1593,plain,
! [SV631: $i,SV492: $i,SV368: $i,SV198: $i,SV4: $i] :
( ( ( ( c_List_Olist_OCons @ SV4 @ SV198 @ SV368 )
!= ( c_List_Olist_OCons @ SV492 @ SV631 @ SV368 ) )
= $true )
| ( ( SV4 = SV492 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1459]) ).
thf(1594,plain,
! [SV200: $i,SV6: $i,SV370: $i,SV493: $i] :
( ( ( SV493 = SV370 )
= $true )
| ( ( ! [SY1618: $i,SY1619: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ SV6 @ SV200 ) @ ( c_List_Olist_OCons @ SY1618 @ SV370 @ SV200 ) ) @ ( c_List_Olist_OCons @ SY1619 @ SV493 @ SV200 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ SV6 @ SV200 ) @ SV370 ) @ SV493 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1460]) ).
thf(1595,plain,
! [SV371: $i,SV201: $i,SV632: $i,SV7: $i] :
( ( ( ! [SY1702: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ SV7 @ SV632 ) @ ( c_List_Olist_OCons @ SV201 @ SY1702 @ SV632 ) ) @ ( c_List_Olist_OCons @ SV371 @ SY1702 @ SV632 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV7 @ SV201 ) @ SV371 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1461]) ).
thf(1596,plain,
! [SV8: $i,SV202: $i,SV494: $i,SV372: $i] :
( ( ( SV372 = SV494 )
= $true )
| ( ( ! [SY1620: $i,SY1621: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ SY1620 @ SY1621 ) @ ( c_List_Olist_OCons @ SV202 @ SV494 @ SY1621 ) ) @ ( c_List_Olist_OCons @ SV8 @ SV372 @ SY1621 ) ) ) )
= $true )
| ( ( SV8 = SV202 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1462]) ).
thf(1597,plain,
! [SV633: $i,SV580: $i,SV495: $i,SV373: $i,SV203: $i,SV9: $i] :
( ( ( c_List_Ofoldl @ SV9 @ SV203 @ ( c_List_Olist_OCons @ SV373 @ SV495 @ SV580 ) @ SV633 @ SV580 )
= ( c_List_Ofoldl @ SV9 @ ( hAPP @ ( hAPP @ SV9 @ SV203 ) @ SV373 ) @ SV495 @ SV633 @ SV580 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1463]) ).
thf(1598,plain,
! [SV496: $i,SV12: $i,SV206: $i,SV376: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV376 @ SV206 ) @ SV12 ) )
= $true )
| ( ( ! [SY1624: $i,SY1625: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ SV376 @ SV496 ) @ ( c_List_Olist_OCons @ SV206 @ SY1624 @ SV496 ) ) @ ( c_List_Olist_OCons @ SV12 @ SY1625 @ SV496 ) ) ) )
= $true )
| ( ( SV12 = SV206 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1464]) ).
thf(1599,plain,
! [SV379: $i,SV497: $i,SV209: $i,SV15: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( c_ListOrder_Ostep1 @ SV15 @ SV209 ) @ ( tc_List_Olist @ SV209 ) ) @ SV497 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV15 @ SV209 ) @ SV379 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( c_ListOrder_Ostep1 @ SV15 @ SV209 ) @ ( tc_List_Olist @ SV209 ) ) @ ( c_List_Olist_OCons @ SV379 @ SV497 @ SV209 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1465]) ).
thf(1600,plain,
! [SV498: $i,SV380: $i,SV210: $i,SV16: $i] :
( ( ( ( c_Type_Otype_OFun @ SV16 @ SV210 )
= ( c_Type_Otype_OFun @ SV380 @ SV498 ) )
= $false )
| ( ( SV210 = SV498 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1466]) ).
thf(1601,plain,
! [SV581: $i,SV381: $i,SV211: $i,SV17: $i] :
( ( ( ( c_Type_Otype_OFun @ SV17 @ SV211 )
= ( c_Type_Otype_OFun @ SV381 @ SV581 ) )
= $false )
| ( ( SV17 = SV381 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1467]) ).
thf(1602,plain,
! [SV499: $i,SV212: $i,SV634: $i,SV382: $i,SV18: $i] :
( ( ( ~ ( c_Type_Otyping @ SV18 @ SV382 @ SV634 )
| ~ ( c_Type_Otyping @ SV18 @ SV212 @ ( c_Type_Otype_OFun @ SV634 @ SV499 ) ) )
= $true )
| ( ( c_Type_Otyping @ SV18 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV212 ) @ SV382 ) @ SV499 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1468]) ).
thf(1603,plain,
! [SV582: $i,SV500: $i,SV383: $i,SV213: $i,SV19: $i] :
( ( ( c_Type_Otyping @ ( c_Type_Oshift @ SV19 @ SV213 @ SV383 @ tc_Type_Otype ) @ ( c_Lambda_Olift @ SV500 @ SV213 ) @ SV582 )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV19 @ SV500 @ SV582 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1469]) ).
thf(1604,plain,
! [SV501: $i,SV385: $i,SV215: $i,SV21: $i] :
( ( ( c_Type_Otyping @ SV21 @ SV215 @ SV385 )
= $false )
| ( ( ! [SY1628: $i,SY1629: $i] :
( ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV21 @ SV501 @ SV385 @ tc_Type_Otype ) @ SY1628 @ SY1629 )
| ( c_Type_Otyping @ SV21 @ ( c_Lambda_Osubst @ SY1628 @ SV215 @ SV501 ) @ SY1629 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1471]) ).
thf(1605,plain,
! [SV216: $i,SV386: $i,SV583: $i,SV22: $i] :
( ( ( ~ ( c_Type_Otyping @ SV22 @ SV583 @ SV386 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV583 ) @ SV216 ) ) )
= $true )
| ( ( c_Type_Otyping @ SV22 @ SV216 @ SV386 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1472]) ).
thf(1606,plain,
! [SV388: $i,SV24: $i,SV502: $i,SV218: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV218 ) @ SV502 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV24 @ SV218 @ SV388 ) ) @ ( c_Lambda_Osubst @ SV24 @ SV502 @ SV388 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1474]) ).
thf(1607,plain,
! [SV389: $i,SV219: $i,SV503: $i,SV25: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV25 ) @ SV503 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV25 @ SV219 @ SV389 ) ) @ ( c_Lambda_Osubst @ SV503 @ SV219 @ SV389 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1475]) ).
thf(1608,plain,
! [SV390: $i,SV26: $i,SV504: $i,SV220: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV220 ) @ SV504 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ SV26 @ SV220 @ SV390 ) ) @ ( c_Lambda_Osubst @ SV26 @ SV504 @ SV390 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1476]) ).
thf(1609,plain,
! [SV394: $i,SV32: $i,SV505: $i,SV226: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV226 ) @ SV505 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV32 ) @ SV394 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV32 ) @ SV226 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV394 ) @ SV505 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1480]) ).
thf(1610,plain,
! [SV506: $i,SV227: $i,SV395: $i,SV33: $i] :
( ( ( c_Type_Otyping @ ( c_Type_Oshift @ SV33 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV395 @ tc_Type_Otype ) @ SV227 @ SV506 )
= $false )
| ( ( c_Type_Otyping @ SV33 @ ( c_Lambda_OdB_OAbs @ SV227 ) @ ( c_Type_Otype_OFun @ SV395 @ SV506 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1481]) ).
thf(1611,plain,
! [SV509: $i,SV402: $i,SV235: $i,SV41: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV41 ) @ SV235 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV402 @ SV509 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( ( SV41
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV402 @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ SV41 @ SV235 @ SV402 @ SV509 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV509
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1484]) ).
thf(1612,plain,
! [SV50: $i,SV407: $i,SV635: $i,SV241: $i,SV511: $i] :
( ( ( ~ ( c_Type_Otyping @ SV511 @ SV241 @ SV635 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV241 ) )
| ! [SY1703: $i] :
~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV511 @ SV407 @ SV635 @ tc_Type_Otype ) @ SV50 @ SY1703 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV50 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV50 @ SV241 @ SV407 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1490]) ).
thf(1613,plain,
! [SV412: $i,SV247: $i,SV636: $i,SV514: $i,SV57: $i] :
( ( ( ! [SY1704: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV57 @ SV514 @ ( tc_fun @ SV636 @ ( tc_fun @ SY1704 @ tc_bool ) ) ) @ SV247 ) @ SV412 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV57 @ SV247 ) @ SV412 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1494]) ).
thf(1614,plain,
! [SV413: $i,SV248: $i,SV637: $i,SV58: $i,SV515: $i] :
( ( ( ! [SY1705: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV515 @ SV58 @ ( tc_fun @ SV637 @ ( tc_fun @ SY1705 @ tc_bool ) ) ) @ SV248 ) @ SV413 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV58 @ SV248 ) @ SV413 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1495]) ).
thf(1615,plain,
! [SV250: $i,SV516: $i,SV416: $i,SV61: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV61 @ SV416 ) @ SV516 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV61 @ SV250 ) @ SV416 ) @ SV516 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1496]) ).
thf(1616,plain,
! [SV638: $i,SV72: $i,SV590: $i,SV254: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV254 @ SV590 @ SV72 ) @ SV638 @ SV72 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV254 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV590 @ SV638 @ SV72 ) @ SV72 ) )
= $true )
| ( ( class_Lattices_Olattice @ SV72 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1505]) ).
thf(1617,plain,
! [SV73: $i,SV639: $i,SV591: $i,SV255: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV255 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV591 @ SV639 @ SV73 ) @ SV73 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV591 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV255 @ SV639 @ SV73 ) @ SV73 ) )
= $true )
| ( ( class_Lattices_Olattice @ SV73 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1506]) ).
thf(1618,plain,
! [SV74: $i,SV640: $i,SV592: $i,SV256: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV256 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV592 @ SV640 @ SV74 ) @ SV74 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV592 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV256 @ SV640 @ SV74 ) @ SV74 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV74 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1507]) ).
thf(1619,plain,
! [SV641: $i,SV75: $i,SV593: $i,SV257: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV257 @ SV593 @ SV75 ) @ SV641 @ SV75 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV257 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV593 @ SV641 @ SV75 ) @ SV75 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV75 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1508]) ).
thf(1620,plain,
! [SV642: $i,SV77: $i,SV594: $i,SV258: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV258 @ SV594 @ SV77 ) @ SV642 @ SV77 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV258 @ SV642 @ SV77 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV594 @ SV642 @ SV77 ) @ SV77 ) )
= $true )
| ( ( class_Lattices_Odistrib__lattice @ SV77 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1509]) ).
thf(1621,plain,
! [SV78: $i,SV643: $i,SV595: $i,SV259: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV259 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV595 @ SV643 @ SV78 ) @ SV78 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV259 @ SV595 @ SV78 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV259 @ SV643 @ SV78 ) @ SV78 ) )
= $true )
| ( ( class_Lattices_Odistrib__lattice @ SV78 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1510]) ).
thf(1622,plain,
! [SV644: $i,SV596: $i,SV525: $i,SV418: $i,SV260: $i,SV79: $i] :
( ( ! [SY1706: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV79 @ SV260 @ SV418 @ SV525 @ SV596 ) @ SV644 ) @ SY1706 ) )
| ! [SY1707: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV260 @ SY1707 ) @ SY1706 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV79 @ SV644 ) @ SY1707 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1511]) ).
thf(1623,plain,
! [SV419: $i,SV526: $i,SV645: $i,SV261: $i,SV80: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV80 @ SV261 ) @ SV645 ) @ SV526 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV80 @ SV261 ) @ SV419 ) @ SV645 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV80 @ SV261 ) @ SV419 ) @ SV526 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1512]) ).
thf(1624,plain,
! [SV420: $i,SV527: $i,SV646: $i,SV262: $i,SV81: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV81 @ SV262 ) @ SV646 ) @ SV527 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV81 @ SV262 ) @ SV420 ) @ SV646 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV81 @ SV262 ) @ SV420 ) @ SV527 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1513]) ).
thf(1625,plain,
! [SV423: $i,SV528: $i,SV647: $i,SV265: $i,SV84: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV84 @ SV265 ) @ SV647 ) @ SV528 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV84 @ SV265 ) @ SV423 ) @ SV647 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV84 @ SV265 ) @ SV423 ) @ SV528 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1514]) ).
thf(1626,plain,
! [SV424: $i,SV529: $i,SV648: $i,SV266: $i,SV85: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV85 @ SV266 ) @ SV648 ) @ SV529 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV85 @ SV424 ) @ SV648 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV85 @ SV266 ) @ SV424 ) @ SV529 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1515]) ).
thf(1627,plain,
! [SV425: $i,SV267: $i,SV530: $i,SV649: $i,SV86: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV86 @ SV649 ) @ SV530 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV86 @ SV267 ) @ SV425 ) @ SV649 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV86 @ SV267 ) @ SV425 ) @ SV530 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1516]) ).
thf(1628,plain,
! [SV531: $i,SV428: $i,SV271: $i,SV90: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV90 @ SV271 ) @ SV428 ) @ SV531 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV90 @ SV271 ) @ SV428 ) @ SV531 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1518]) ).
thf(1629,plain,
! [SV273: $i,SV532: $i,SV429: $i,SV93: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV93 @ SV429 ) @ SV532 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV93 @ SV273 ) @ SV429 ) @ SV532 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1519]) ).
thf(1630,plain,
! [SV94: $i,SV430: $i,SV274: $i,SV533: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV533 @ SV274 ) @ SV430 ) )
= $true )
| ( ( ! [SY1651: $i,SY1652: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV533 @ SV94 @ ( tc_fun @ SY1651 @ ( tc_fun @ SY1652 @ tc_bool ) ) ) @ SV274 ) @ SV430 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV94 @ SV274 ) @ SV430 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1520]) ).
thf(1631,plain,
! [SV650: $i,SV597: $i,SV534: $i,SV431: $i,SV275: $i,SV95: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV95 @ SV275 @ ( tc_fun @ SV431 @ ( tc_fun @ SV534 @ tc_bool ) ) ) @ SV597 ) @ SV650 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV275 @ SV597 ) @ SV650 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1521]) ).
thf(1632,plain,
! [SV651: $i,SV598: $i,SV535: $i,SV432: $i,SV276: $i,SV96: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV96 @ SV276 @ ( tc_fun @ SV432 @ ( tc_fun @ SV535 @ tc_bool ) ) ) @ SV598 ) @ SV651 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV96 @ SV598 ) @ SV651 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1522]) ).
thf(1633,plain,
! [SV433: $i,SV97: $i,SV277: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV277 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV97 @ SV277 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV433 @ 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 @ SV97 ) ) @ SV277 ) @ SV433 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1523]) ).
thf(1634,plain,
! [SV652: $i,SV100: $i,SV599: $i,SV279: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV279 @ SV599 @ SV100 ) @ SV652 @ SV100 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV279 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV599 @ SV652 @ SV100 ) @ SV100 ) )
= $true )
| ( ( class_Lattices_Olattice @ SV100 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1525]) ).
thf(1635,plain,
! [SV101: $i,SV653: $i,SV600: $i,SV280: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV280 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV600 @ SV653 @ SV101 ) @ SV101 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV600 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV280 @ SV653 @ SV101 ) @ SV101 ) )
= $true )
| ( ( class_Lattices_Olattice @ SV101 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1526]) ).
thf(1636,plain,
! [SV102: $i,SV654: $i,SV601: $i,SV281: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV281 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV601 @ SV654 @ SV102 ) @ SV102 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV601 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV281 @ SV654 @ SV102 ) @ SV102 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV102 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1527]) ).
thf(1637,plain,
! [SV655: $i,SV103: $i,SV602: $i,SV282: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV282 @ SV602 @ SV103 ) @ SV655 @ SV103 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV282 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV602 @ SV655 @ SV103 ) @ SV103 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV103 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1528]) ).
thf(1638,plain,
! [SV110: $i,SV288: $i,SV656: $i,SV604: $i,SV438: $i] :
( ( ( ~ ( c_Type_Otyping @ SV438 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV604 ) @ SV656 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV288 )
| ~ ( c_Type_Otyping @ SV438 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV604 ) @ SV656 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV110 ) )
= $true )
| ( ( SV110 = SV288 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1532]) ).
thf(1639,plain,
! [SV539: $i,SV439: $i,SV289: $i,SV111: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV111 ) @ SV289 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV439 ) @ SV539 ) )
= $false )
| ( ( SV289 = SV539 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1533]) ).
thf(1640,plain,
! [SV605: $i,SV440: $i,SV290: $i,SV112: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV112 ) @ SV290 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV440 ) @ SV605 ) )
= $false )
| ( ( SV112 = SV440 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1534]) ).
thf(1641,plain,
! [SV541: $i,SV441: $i,SV291: $i,SV114: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV114 ) @ SV291 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV441 ) @ SV541 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( SV291 = SV541 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1536]) ).
thf(1642,plain,
! [SV607: $i,SV442: $i,SV292: $i,SV115: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV115 ) @ SV292 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV442 ) @ SV607 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( SV115 = SV442 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1537]) ).
thf(1643,plain,
! [SV295: $i,SV118: $i,SV542: $i,SV444: $i] :
( ( ( SV444 = SV542 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV118 @ SV295 ) @ SV444 ) @ SV542 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV118 @ SV295 ) @ SV444 ) @ SV542 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1539]) ).
thf(1644,plain,
! [SV296: $i,SV119: $i,SV543: $i,SV445: $i] :
( ( ( SV445 = SV543 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV119 @ SV296 ) @ SV445 ) @ SV543 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV119 @ SV296 ) @ SV445 ) @ SV543 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1540]) ).
thf(1645,plain,
! [SV657: $i,SV121: $i,SV608: $i,SV298: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV298 @ SV608 @ SV121 ) @ SV657 @ SV121 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV298 @ SV657 @ SV121 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV608 @ SV657 @ SV121 ) @ SV121 ) )
= $true )
| ( ( class_Lattices_Odistrib__lattice @ SV121 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1541]) ).
thf(1646,plain,
! [SV122: $i,SV658: $i,SV609: $i,SV299: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV299 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV609 @ SV658 @ SV122 ) @ SV122 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV299 @ SV609 @ SV122 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV299 @ SV658 @ SV122 ) @ SV122 ) )
= $true )
| ( ( class_Lattices_Odistrib__lattice @ SV122 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1542]) ).
thf(1647,plain,
! [SV548: $i,SV448: $i,SV302: $i,SV129: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV129 ) @ SV302 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV448 ) @ SV548 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( SV302 = SV548 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1546]) ).
thf(1648,plain,
! [SV612: $i,SV449: $i,SV303: $i,SV130: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV130 ) @ SV303 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV449 ) @ SV612 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( SV130 = SV449 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1547]) ).
thf(1649,plain,
! [SV451: $i,SV549: $i,SV659: $i,SV305: $i,SV132: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV132 @ SV305 ) @ SV659 ) @ SV549 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV132 @ SV305 ) @ SV451 ) @ SV659 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV132 @ SV305 ) @ SV451 ) @ SV549 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1548]) ).
thf(1650,plain,
! [SV660: $i,SV613: $i,SV551: $i,SV454: $i,SV310: $i,SV137: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV137 @ SV310 @ ( tc_fun @ SV454 @ ( tc_fun @ SV551 @ tc_bool ) ) ) @ SV613 ) @ SV660 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV310 @ SV613 ) @ SV660 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ SV613 ) @ SV660 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1549]) ).
thf(1651,plain,
! [SV455: $i,SV552: $i,SV661: $i,SV311: $i,SV138: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV138 @ SV311 ) @ SV661 ) @ SV552 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV138 @ SV455 ) @ SV661 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV138 @ SV311 ) @ SV455 ) @ SV552 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1550]) ).
thf(1652,plain,
! [SV456: $i,SV312: $i,SV553: $i,SV662: $i,SV139: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV139 @ SV662 ) @ SV553 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV139 @ SV312 ) @ SV456 ) @ SV662 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV139 @ SV312 ) @ SV456 ) @ SV553 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1551]) ).
thf(1653,plain,
! [SV457: $i,SV313: $i,SV554: $i,SV663: $i,SV140: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV140 @ SV663 ) @ SV554 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV140 @ SV313 ) @ SV457 ) @ SV663 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV140 @ SV313 ) @ SV457 ) @ SV554 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1552]) ).
thf(1654,plain,
! [SV458: $i,SV555: $i,SV664: $i,SV314: $i,SV141: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV141 @ SV314 ) @ SV664 ) @ SV555 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV141 @ SV458 ) @ SV664 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV141 @ SV314 ) @ SV458 ) @ SV555 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1553]) ).
thf(1655,plain,
! [SV315: $i,SV614: $i,SV459: $i,SV142: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV142 @ SV459 ) @ SV614 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV142 @ SV315 ) @ SV614 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV142 @ SV315 ) @ SV459 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1554]) ).
thf(1656,plain,
! [SV316: $i,SV615: $i,SV460: $i,SV143: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV460 ) @ SV615 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV143 @ SV316 ) @ SV615 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV143 @ SV316 ) @ SV460 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1555]) ).
thf(1657,plain,
! [SV317: $i,SV616: $i,SV556: $i,SV144: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV144 @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__1__1 @ SV144 @ SV556 @ SV616 ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV556 @ SV616 ) @ SV317 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV144 @ SV317 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1556]) ).
thf(1658,plain,
! [SV318: $i,SV145: $i,SV461: $i,SV665: $i] :
( ( ( ! [SY1708: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV665 @ SV461 ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__1__1 @ SV145 @ SV665 @ SY1708 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV665 @ SY1708 ) @ SV318 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV145 @ SV461 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV145 @ SV318 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1557]) ).
thf(1659,plain,
! [SV463: $i,SV147: $i,SV320: $i,SV617: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV617 ) @ SV320 ) ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV147 @ SV617 @ SV463 ) )
= $true )
| ( ( c_Type_Otyping @ SV147 @ SV320 @ SV463 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1558]) ).
thf(1660,plain,
! [SV558: $i,SV466: $i,SV325: $i,SV153: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ ( c_Predicate_Oconversep @ SV153 @ SV325 @ SV325 ) @ SV325 ) @ SV466 ) @ SV558 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ ( c_Transitive__Closure_Otranclp @ SV153 @ SV325 ) @ SV325 @ SV325 ) @ SV466 ) @ SV558 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1560]) ).
thf(1661,plain,
! [SV559: $i,SV467: $i,SV326: $i,SV154: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ ( c_Transitive__Closure_Otranclp @ SV154 @ SV326 ) @ SV326 @ SV326 ) @ SV467 ) @ SV559 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ ( c_Predicate_Oconversep @ SV154 @ SV326 @ SV326 ) @ SV326 ) @ SV467 ) @ SV559 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1561]) ).
thf(1662,plain,
! [SV469: $i,SV618: $i,SV329: $i,SV159: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV159 @ SV329 ) @ SV618 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV159 @ SV329 ) @ SV469 ) @ SV618 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV159 @ SV329 ) @ SV469 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1563]) ).
thf(1663,plain,
! [SV619: $i,SV470: $i,SV330: $i,SV160: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV160 @ SV330 ) @ SV470 ) @ SV619 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV160 @ SV330 ) @ SV619 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV160 @ SV330 ) @ SV470 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1564]) ).
thf(1664,plain,
! [SV471: $i,SV331: $i,SV560: $i,SV161: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV161 ) @ SV560 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Osubst @ SV161 @ SV331 @ SV471 ) ) @ ( c_Lambda_Osubst @ SV560 @ SV331 @ SV471 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1565]) ).
thf(1665,plain,
! [SV332: $i,SV561: $i,SV162: $i] :
( ( ( hBOOL @ ( hAPP @ SV162 @ ( v_sko__Wellfounded__Xaccp__Xinducts__1 @ SV162 @ SV561 ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV561 @ t_a ) @ SV332 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV162 @ SV332 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1566]) ).
thf(1666,plain,
! [SV333: $i,SV163: $i,SV562: $i,SV666: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV666 @ SV562 ) @ ( v_sko__Wellfounded__Xaccp__Xinducts__1 @ SV163 @ SV666 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV666 @ t_a ) @ SV333 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV163 @ SV562 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV163 @ SV333 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1567]) ).
thf(1667,plain,
! [SV472: $i,SV164: $i,SV334: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ SV334 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV164 ) ) @ SV334 ) @ SV472 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV164 @ SV334 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV472 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1568]) ).
thf(1668,plain,
! [SV335: $i,SV563: $i,SV165: $i] :
( ( ( hBOOL @ ( hAPP @ SV165 @ ( v_sko__Wellfounded__Xaccp__Xinduct__1 @ SV165 @ SV563 ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV563 @ t_a ) @ SV335 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV165 @ SV335 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1569]) ).
thf(1669,plain,
! [SV336: $i,SV166: $i,SV564: $i,SV667: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV667 @ SV564 ) @ ( v_sko__Wellfounded__Xaccp__Xinduct__1 @ SV166 @ SV667 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV667 @ t_a ) @ SV336 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV166 @ SV564 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV166 @ SV336 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1570]) ).
thf(1670,plain,
! [SV620: $i,SV565: $i,SV473: $i,SV337: $i,SV167: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV167 @ SV337 @ SV473 ) @ SV565 ) @ SV620 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV167 @ SV620 ) @ SV565 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1571]) ).
thf(1671,plain,
! [SV338: $i,SV474: $i,SV668: $i,SV621: $i,SV168: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV168 @ SV621 @ SV668 ) @ SV474 ) @ SV338 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV168 @ SV338 ) @ SV474 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1572]) ).
thf(1672,plain,
! [SV622: $i,SV566: $i,SV475: $i,SV339: $i,SV169: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV169 @ SV339 @ SV475 ) @ SV566 ) @ SV622 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV169 @ SV622 ) @ SV566 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1573]) ).
thf(1673,plain,
! [SV340: $i,SV476: $i,SV669: $i,SV623: $i,SV170: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV170 @ SV623 @ SV669 ) @ SV476 ) @ SV340 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV170 @ SV340 ) @ SV476 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1574]) ).
thf(1674,plain,
! [SV341: $i,SV171: $i,SV624: $i,SV567: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV567 @ t_a ) @ SV624 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV567 @ SV624 ) @ ( v_sko__Wellfounded__Xaccp__Xinducts__1 @ SV171 @ SV567 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV567 @ t_a ) @ SV341 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV171 @ SV341 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1575]) ).
thf(1675,plain,
! [SV342: $i,SV172: $i,SV625: $i,SV568: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV568 @ t_a ) @ SV625 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV568 @ SV625 ) @ ( v_sko__Wellfounded__Xaccp__Xinduct__1 @ SV172 @ SV568 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV568 @ t_a ) @ SV342 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV172 @ SV342 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1576]) ).
thf(1676,plain,
! [SV478: $i,SV570: $i,SV344: $i,SV174: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ SV174 @ SV344 @ SV344 ) @ SV344 ) @ SV570 ) @ SV478 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV174 @ SV344 ) @ SV478 ) @ SV570 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1577]) ).
thf(1677,plain,
! [SV479: $i,SV571: $i,SV345: $i,SV175: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV175 @ SV345 ) @ SV571 ) @ SV479 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ SV175 @ SV345 @ SV345 ) @ SV345 ) @ SV479 ) @ SV571 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1578]) ).
thf(1678,plain,
! [SV346: $i,SV176: $i,SV626: $i,SV572: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV572 @ SV626 ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__1__1 @ SV176 @ SV572 @ SV626 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV572 @ SV626 ) @ SV346 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV176 @ SV346 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1579]) ).
thf(1679,plain,
! [SV353: $i,SV183: $i,SV627: $i,SV574: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV574 @ SV627 ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__rule__1__1 @ SV183 @ SV574 @ SV627 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV574 @ SV627 ) @ SV353 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV183 @ SV353 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1584]) ).
thf(1680,plain,
! [SV355: $i,SV628: $i,SV575: $i,SV185: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV185 @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__rule__1__1 @ SV185 @ SV575 @ SV628 ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV575 @ SV628 ) @ SV355 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV185 @ SV355 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1586]) ).
thf(1681,plain,
! [SV356: $i,SV186: $i,SV487: $i,SV670: $i] :
( ( ( ! [SY1709: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV670 @ SV487 ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__rule__1__1 @ SV186 @ SV670 @ SY1709 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV670 @ SY1709 ) @ SV356 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV186 @ SV487 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV186 @ SV356 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1587]) ).
thf(1682,plain,
! [SV365: $i,SV578: $i,SV489: $i,SV195: $i,SV1: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ SV1 @ SV195 ) @ SV489 ) @ SV578 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ SV1 @ SV195 ) @ ( c_List_Olist_OCons @ SV365 @ SV489 @ SV195 ) ) @ ( c_List_Olist_OCons @ SV365 @ SV578 @ SV195 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1590]) ).
thf(1683,plain,
! [SV490: $i,SV366: $i,SV196: $i,SV671: $i,SV630: $i,SV2: $i] :
( ( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV2 @ SV630 ) @ SV671 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ SV2 @ SV196 ) @ ( c_List_Olist_OCons @ SV630 @ SV366 @ SV196 ) ) @ ( c_List_Olist_OCons @ SV671 @ SV490 @ SV196 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ SV2 @ SV196 ) @ SV366 ) @ SV490 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1591]) ).
thf(1684,plain,
! [SV579: $i,SV491: $i,SV367: $i,SV197: $i,SV3: $i] :
( ( ( ( c_List_Olist_OCons @ SV3 @ SV197 @ SV367 )
= ( c_List_Olist_OCons @ SV491 @ SV579 @ SV367 ) )
= $false )
| ( ( SV197 = SV579 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1592]) ).
thf(1685,plain,
! [SV631: $i,SV492: $i,SV368: $i,SV198: $i,SV4: $i] :
( ( ( ( c_List_Olist_OCons @ SV4 @ SV198 @ SV368 )
= ( c_List_Olist_OCons @ SV492 @ SV631 @ SV368 ) )
= $false )
| ( ( SV4 = SV492 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1593]) ).
thf(1686,plain,
! [SV493: $i,SV370: $i,SV672: $i,SV200: $i,SV6: $i] :
( ( ( ! [SY1710: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ SV6 @ SV200 ) @ ( c_List_Olist_OCons @ SV672 @ SV370 @ SV200 ) ) @ ( c_List_Olist_OCons @ SY1710 @ SV493 @ SV200 ) ) ) )
= $true )
| ( ( SV493 = SV370 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ SV6 @ SV200 ) @ SV370 ) @ SV493 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1594]) ).
thf(1687,plain,
! [SV371: $i,SV673: $i,SV201: $i,SV632: $i,SV7: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ SV7 @ SV632 ) @ ( c_List_Olist_OCons @ SV201 @ SV673 @ SV632 ) ) @ ( c_List_Olist_OCons @ SV371 @ SV673 @ SV632 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV7 @ SV201 ) @ SV371 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1595]) ).
thf(1688,plain,
! [SV372: $i,SV8: $i,SV494: $i,SV202: $i,SV674: $i] :
( ( ( ! [SY1711: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ SV674 @ SY1711 ) @ ( c_List_Olist_OCons @ SV202 @ SV494 @ SY1711 ) ) @ ( c_List_Olist_OCons @ SV8 @ SV372 @ SY1711 ) ) ) )
= $true )
| ( ( SV372 = SV494 )
= $true )
| ( ( SV8 = SV202 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1596]) ).
thf(1689,plain,
! [SV12: $i,SV675: $i,SV206: $i,SV496: $i,SV376: $i] :
( ( ( ! [SY1712: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ SV376 @ SV496 ) @ ( c_List_Olist_OCons @ SV206 @ SV675 @ SV496 ) ) @ ( c_List_Olist_OCons @ SV12 @ SY1712 @ SV496 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV376 @ SV206 ) @ SV12 ) )
= $true )
| ( ( SV12 = SV206 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1598]) ).
thf(1690,plain,
! [SV379: $i,SV497: $i,SV209: $i,SV15: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( c_ListOrder_Ostep1 @ SV15 @ SV209 ) @ ( tc_List_Olist @ SV209 ) ) @ SV497 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV15 @ SV209 ) @ SV379 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( c_ListOrder_Ostep1 @ SV15 @ SV209 ) @ ( tc_List_Olist @ SV209 ) ) @ ( c_List_Olist_OCons @ SV379 @ SV497 @ SV209 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1599]) ).
thf(1691,plain,
! [SV499: $i,SV212: $i,SV634: $i,SV382: $i,SV18: $i] :
( ( ( ~ ( c_Type_Otyping @ SV18 @ SV382 @ SV634 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV18 @ SV212 @ ( c_Type_Otype_OFun @ SV634 @ SV499 ) ) )
= $true )
| ( ( c_Type_Otyping @ SV18 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV212 ) @ SV382 ) @ SV499 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1602]) ).
thf(1692,plain,
! [SV383: $i,SV213: $i,SV582: $i,SV500: $i,SV19: $i] :
( ( ( c_Type_Otyping @ SV19 @ SV500 @ SV582 )
= $false )
| ( ( c_Type_Otyping @ ( c_Type_Oshift @ SV19 @ SV213 @ SV383 @ tc_Type_Otype ) @ ( c_Lambda_Olift @ SV500 @ SV213 ) @ SV582 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1603]) ).
thf(1693,plain,
! [SV215: $i,SV676: $i,SV385: $i,SV501: $i,SV21: $i] :
( ( ( ! [SY1713: $i] :
( ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV21 @ SV501 @ SV385 @ tc_Type_Otype ) @ SV676 @ SY1713 )
| ( c_Type_Otyping @ SV21 @ ( c_Lambda_Osubst @ SV676 @ SV215 @ SV501 ) @ SY1713 ) ) )
= $true )
| ( ( c_Type_Otyping @ SV21 @ SV215 @ SV385 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1604]) ).
thf(1694,plain,
! [SV216: $i,SV386: $i,SV583: $i,SV22: $i] :
( ( ( c_Type_Otyping @ SV22 @ SV583 @ SV386 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV583 ) @ SV216 ) ) )
= $true )
| ( ( c_Type_Otyping @ SV22 @ SV216 @ SV386 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1605]) ).
thf(1695,plain,
! [SV394: $i,SV32: $i,SV505: $i,SV226: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV226 ) @ SV505 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV32 ) @ SV394 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV32 ) @ SV226 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV394 ) @ SV505 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1609]) ).
thf(1696,plain,
! [SV509: $i,SV235: $i,SV402: $i,SV41: $i] :
( ( ( SV41
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV402 @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ SV41 @ SV235 @ SV402 @ SV509 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV509
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV41 ) @ SV235 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV402 @ SV509 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1611]) ).
thf(1697,plain,
! [SV50: $i,SV407: $i,SV635: $i,SV241: $i,SV511: $i] :
( ( ( ~ ( c_Type_Otyping @ SV511 @ SV241 @ SV635 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV241 ) )
| ! [SY1703: $i] :
~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV511 @ SV407 @ SV635 @ tc_Type_Otype ) @ SV50 @ SY1703 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV50 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV50 @ SV241 @ SV407 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1612]) ).
thf(1698,plain,
! [SV412: $i,SV247: $i,SV677: $i,SV636: $i,SV514: $i,SV57: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV57 @ SV514 @ ( tc_fun @ SV636 @ ( tc_fun @ SV677 @ tc_bool ) ) ) @ SV247 ) @ SV412 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV57 @ SV247 ) @ SV412 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1613]) ).
thf(1699,plain,
! [SV413: $i,SV248: $i,SV678: $i,SV637: $i,SV58: $i,SV515: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV515 @ SV58 @ ( tc_fun @ SV637 @ ( tc_fun @ SV678 @ tc_bool ) ) ) @ SV248 ) @ SV413 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV58 @ SV248 ) @ SV413 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1614]) ).
thf(1700,plain,
! [SV679: $i,SV644: $i,SV596: $i,SV525: $i,SV418: $i,SV260: $i,SV79: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV79 @ SV260 @ SV418 @ SV525 @ SV596 ) @ SV644 ) @ SV679 ) )
| ! [SY1714: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV260 @ SY1714 ) @ SV679 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV79 @ SV644 ) @ SY1714 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1622]) ).
thf(1701,plain,
! [SV419: $i,SV526: $i,SV645: $i,SV261: $i,SV80: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV80 @ SV261 ) @ SV645 ) @ SV526 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV80 @ SV261 ) @ SV419 ) @ SV645 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV80 @ SV261 ) @ SV419 ) @ SV526 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1623]) ).
thf(1702,plain,
! [SV420: $i,SV527: $i,SV646: $i,SV262: $i,SV81: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV81 @ SV262 ) @ SV646 ) @ SV527 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV81 @ SV262 ) @ SV420 ) @ SV646 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV81 @ SV262 ) @ SV420 ) @ SV527 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1624]) ).
thf(1703,plain,
! [SV423: $i,SV528: $i,SV647: $i,SV265: $i,SV84: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV84 @ SV265 ) @ SV647 ) @ SV528 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV84 @ SV265 ) @ SV423 ) @ SV647 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV84 @ SV265 ) @ SV423 ) @ SV528 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1625]) ).
thf(1704,plain,
! [SV424: $i,SV529: $i,SV648: $i,SV266: $i,SV85: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV85 @ SV266 ) @ SV648 ) @ SV529 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV85 @ SV424 ) @ SV648 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV85 @ SV266 ) @ SV424 ) @ SV529 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1626]) ).
thf(1705,plain,
! [SV425: $i,SV267: $i,SV530: $i,SV649: $i,SV86: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV86 @ SV649 ) @ SV530 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV86 @ SV267 ) @ SV425 ) @ SV649 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV86 @ SV267 ) @ SV425 ) @ SV530 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1627]) ).
thf(1706,plain,
! [SV430: $i,SV274: $i,SV680: $i,SV94: $i,SV533: $i] :
( ( ( ! [SY1715: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV533 @ SV94 @ ( tc_fun @ SV680 @ ( tc_fun @ SY1715 @ tc_bool ) ) ) @ SV274 ) @ SV430 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV533 @ SV274 ) @ SV430 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV94 @ SV274 ) @ SV430 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1630]) ).
thf(1707,plain,
! [SV650: $i,SV597: $i,SV534: $i,SV431: $i,SV275: $i,SV95: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV95 @ SV275 @ ( tc_fun @ SV431 @ ( tc_fun @ SV534 @ tc_bool ) ) ) @ SV597 ) @ SV650 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV275 @ SV597 ) @ SV650 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1631]) ).
thf(1708,plain,
! [SV651: $i,SV598: $i,SV535: $i,SV432: $i,SV276: $i,SV96: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV96 @ SV276 @ ( tc_fun @ SV432 @ ( tc_fun @ SV535 @ tc_bool ) ) ) @ SV598 ) @ SV651 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV96 @ SV598 ) @ SV651 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1632]) ).
thf(1709,plain,
! [SV433: $i,SV277: $i,SV97: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV97 @ SV277 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV433 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV277 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV97 ) ) @ SV277 ) @ SV433 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1633]) ).
thf(1710,plain,
! [SV110: $i,SV288: $i,SV656: $i,SV604: $i,SV438: $i] :
( ( ( ~ ( c_Type_Otyping @ SV438 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV604 ) @ SV656 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV288 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV438 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV604 ) @ SV656 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV110 ) )
= $true )
| ( ( SV110 = SV288 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1638]) ).
thf(1711,plain,
! [SV542: $i,SV444: $i,SV295: $i,SV118: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV118 @ SV295 ) @ SV444 ) @ SV542 ) )
= $false )
| ( ( SV444 = SV542 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV118 @ SV295 ) @ SV444 ) @ SV542 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1643]) ).
thf(1712,plain,
! [SV543: $i,SV445: $i,SV296: $i,SV119: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV119 @ SV296 ) @ SV445 ) @ SV543 ) )
= $false )
| ( ( SV445 = SV543 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV119 @ SV296 ) @ SV445 ) @ SV543 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1644]) ).
thf(1713,plain,
! [SV451: $i,SV549: $i,SV659: $i,SV305: $i,SV132: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV132 @ SV305 ) @ SV659 ) @ SV549 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV132 @ SV305 ) @ SV451 ) @ SV659 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV132 @ SV305 ) @ SV451 ) @ SV549 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1649]) ).
thf(1714,plain,
! [SV660: $i,SV613: $i,SV551: $i,SV454: $i,SV310: $i,SV137: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV137 @ SV310 @ ( tc_fun @ SV454 @ ( tc_fun @ SV551 @ tc_bool ) ) ) @ SV613 ) @ SV660 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV310 @ SV613 ) @ SV660 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ SV613 ) @ SV660 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1650]) ).
thf(1715,plain,
! [SV455: $i,SV552: $i,SV661: $i,SV311: $i,SV138: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV138 @ SV311 ) @ SV661 ) @ SV552 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV138 @ SV455 ) @ SV661 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV138 @ SV311 ) @ SV455 ) @ SV552 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1651]) ).
thf(1716,plain,
! [SV456: $i,SV312: $i,SV553: $i,SV662: $i,SV139: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV139 @ SV662 ) @ SV553 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV139 @ SV312 ) @ SV456 ) @ SV662 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV139 @ SV312 ) @ SV456 ) @ SV553 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1652]) ).
thf(1717,plain,
! [SV457: $i,SV313: $i,SV554: $i,SV663: $i,SV140: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV140 @ SV663 ) @ SV554 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV140 @ SV313 ) @ SV457 ) @ SV663 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV140 @ SV313 ) @ SV457 ) @ SV554 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1653]) ).
thf(1718,plain,
! [SV458: $i,SV555: $i,SV664: $i,SV314: $i,SV141: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV141 @ SV314 ) @ SV664 ) @ SV555 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV141 @ SV458 ) @ SV664 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV141 @ SV314 ) @ SV458 ) @ SV555 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1654]) ).
thf(1719,plain,
! [SV315: $i,SV614: $i,SV459: $i,SV142: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV142 @ SV459 ) @ SV614 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV142 @ SV315 ) @ SV614 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV142 @ SV315 ) @ SV459 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1655]) ).
thf(1720,plain,
! [SV316: $i,SV615: $i,SV460: $i,SV143: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV460 ) @ SV615 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV143 @ SV316 ) @ SV615 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV143 @ SV316 ) @ SV460 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1656]) ).
thf(1721,plain,
! [SV317: $i,SV616: $i,SV556: $i,SV144: $i] :
( ( ( hBOOL @ ( hAPP @ SV144 @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__1__1 @ SV144 @ SV556 @ SV616 ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV556 @ SV616 ) @ SV317 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV144 @ SV317 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1657]) ).
thf(1722,plain,
! [SV318: $i,SV681: $i,SV145: $i,SV461: $i,SV665: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV665 @ SV461 ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__1__1 @ SV145 @ SV665 @ SV681 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV665 @ SV681 ) @ SV318 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV145 @ SV461 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV145 @ SV318 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1658]) ).
thf(1723,plain,
! [SV463: $i,SV147: $i,SV320: $i,SV617: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV617 ) @ SV320 ) )
= $false )
| ( ( ~ ( c_Type_Otyping @ SV147 @ SV617 @ SV463 ) )
= $true )
| ( ( c_Type_Otyping @ SV147 @ SV320 @ SV463 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1659]) ).
thf(1724,plain,
! [SV469: $i,SV618: $i,SV329: $i,SV159: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV159 @ SV329 ) @ SV618 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV159 @ SV329 ) @ SV469 ) @ SV618 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV159 @ SV329 ) @ SV469 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1662]) ).
thf(1725,plain,
! [SV619: $i,SV470: $i,SV330: $i,SV160: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV160 @ SV330 ) @ SV470 ) @ SV619 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV160 @ SV330 ) @ SV619 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV160 @ SV330 ) @ SV470 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1663]) ).
thf(1726,plain,
! [SV162: $i,SV332: $i,SV561: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV561 @ t_a ) @ SV332 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV162 @ ( v_sko__Wellfounded__Xaccp__Xinducts__1 @ SV162 @ SV561 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV162 @ SV332 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1665]) ).
thf(1727,plain,
! [SV333: $i,SV163: $i,SV562: $i,SV666: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV666 @ SV562 ) @ ( v_sko__Wellfounded__Xaccp__Xinducts__1 @ SV163 @ SV666 ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV666 @ t_a ) @ SV333 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV163 @ SV562 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV163 @ SV333 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1666]) ).
thf(1728,plain,
! [SV472: $i,SV164: $i,SV334: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ SV334 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV164 ) ) @ SV334 ) @ SV472 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV164 @ SV334 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV472 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1667]) ).
thf(1729,plain,
! [SV165: $i,SV335: $i,SV563: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV563 @ t_a ) @ SV335 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV165 @ ( v_sko__Wellfounded__Xaccp__Xinduct__1 @ SV165 @ SV563 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV165 @ SV335 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1668]) ).
thf(1730,plain,
! [SV336: $i,SV166: $i,SV564: $i,SV667: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV667 @ SV564 ) @ ( v_sko__Wellfounded__Xaccp__Xinduct__1 @ SV166 @ SV667 ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV667 @ t_a ) @ SV336 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV166 @ SV564 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV166 @ SV336 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1669]) ).
thf(1731,plain,
! [SV473: $i,SV337: $i,SV565: $i,SV620: $i,SV167: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV167 @ SV620 ) @ SV565 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV167 @ SV337 @ SV473 ) @ SV565 ) @ SV620 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1670]) ).
thf(1732,plain,
! [SV338: $i,SV474: $i,SV668: $i,SV621: $i,SV168: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV168 @ SV621 @ SV668 ) @ SV474 ) @ SV338 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV168 @ SV338 ) @ SV474 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1671]) ).
thf(1733,plain,
! [SV475: $i,SV339: $i,SV566: $i,SV622: $i,SV169: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV169 @ SV622 ) @ SV566 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV169 @ SV339 @ SV475 ) @ SV566 ) @ SV622 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1672]) ).
thf(1734,plain,
! [SV340: $i,SV476: $i,SV669: $i,SV623: $i,SV170: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV170 @ SV623 @ SV669 ) @ SV476 ) @ SV340 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV170 @ SV340 ) @ SV476 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1673]) ).
thf(1735,plain,
! [SV341: $i,SV171: $i,SV624: $i,SV567: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV567 @ SV624 ) @ ( v_sko__Wellfounded__Xaccp__Xinducts__1 @ SV171 @ SV567 ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV567 @ t_a ) @ SV341 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV567 @ t_a ) @ SV624 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV171 @ SV341 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1674]) ).
thf(1736,plain,
! [SV342: $i,SV172: $i,SV625: $i,SV568: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV568 @ SV625 ) @ ( v_sko__Wellfounded__Xaccp__Xinduct__1 @ SV172 @ SV568 ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV568 @ t_a ) @ SV342 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV568 @ t_a ) @ SV625 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV172 @ SV342 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1675]) ).
thf(1737,plain,
! [SV176: $i,SV346: $i,SV626: $i,SV572: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV572 @ SV626 ) @ SV346 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV572 @ SV626 ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__1__1 @ SV176 @ SV572 @ SV626 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV176 @ SV346 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1678]) ).
thf(1738,plain,
! [SV183: $i,SV353: $i,SV627: $i,SV574: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV574 @ SV627 ) @ SV353 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV574 @ SV627 ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__rule__1__1 @ SV183 @ SV574 @ SV627 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV183 @ SV353 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1679]) ).
thf(1739,plain,
! [SV355: $i,SV628: $i,SV575: $i,SV185: $i] :
( ( ( hBOOL @ ( hAPP @ SV185 @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__rule__1__1 @ SV185 @ SV575 @ SV628 ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV575 @ SV628 ) @ SV355 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV185 @ SV355 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1680]) ).
thf(1740,plain,
! [SV356: $i,SV682: $i,SV186: $i,SV487: $i,SV670: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV670 @ SV487 ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__rule__1__1 @ SV186 @ SV670 @ SV682 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV670 @ SV682 ) @ SV356 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV186 @ SV487 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV186 @ SV356 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1681]) ).
thf(1741,plain,
! [SV490: $i,SV366: $i,SV196: $i,SV671: $i,SV630: $i,SV2: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV2 @ SV630 ) @ SV671 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ SV2 @ SV196 ) @ ( c_List_Olist_OCons @ SV630 @ SV366 @ SV196 ) ) @ ( c_List_Olist_OCons @ SV671 @ SV490 @ SV196 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ SV2 @ SV196 ) @ SV366 ) @ SV490 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1683]) ).
thf(1742,plain,
! [SV493: $i,SV683: $i,SV370: $i,SV672: $i,SV200: $i,SV6: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ SV6 @ SV200 ) @ ( c_List_Olist_OCons @ SV672 @ SV370 @ SV200 ) ) @ ( c_List_Olist_OCons @ SV683 @ SV493 @ SV200 ) ) ) )
= $true )
| ( ( SV493 = SV370 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ SV6 @ SV200 ) @ SV370 ) @ SV493 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1686]) ).
thf(1743,plain,
! [SV372: $i,SV8: $i,SV494: $i,SV202: $i,SV684: $i,SV674: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ SV674 @ SV684 ) @ ( c_List_Olist_OCons @ SV202 @ SV494 @ SV684 ) ) @ ( c_List_Olist_OCons @ SV8 @ SV372 @ SV684 ) ) ) )
= $true )
| ( ( SV372 = SV494 )
= $true )
| ( ( SV8 = SV202 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1688]) ).
thf(1744,plain,
! [SV685: $i,SV12: $i,SV675: $i,SV206: $i,SV496: $i,SV376: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ SV376 @ SV496 ) @ ( c_List_Olist_OCons @ SV206 @ SV675 @ SV496 ) ) @ ( c_List_Olist_OCons @ SV12 @ SV685 @ SV496 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV376 @ SV206 ) @ SV12 ) )
= $true )
| ( ( SV12 = SV206 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1689]) ).
thf(1745,plain,
! [SV497: $i,SV379: $i,SV209: $i,SV15: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV15 @ SV209 ) @ SV379 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( c_ListOrder_Ostep1 @ SV15 @ SV209 ) @ ( tc_List_Olist @ SV209 ) ) @ SV497 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ ( c_ListOrder_Ostep1 @ SV15 @ SV209 ) @ ( tc_List_Olist @ SV209 ) ) @ ( c_List_Olist_OCons @ SV379 @ SV497 @ SV209 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1690]) ).
thf(1746,plain,
! [SV499: $i,SV212: $i,SV634: $i,SV382: $i,SV18: $i] :
( ( ( c_Type_Otyping @ SV18 @ SV382 @ SV634 )
= $false )
| ( ( ~ ( c_Type_Otyping @ SV18 @ SV212 @ ( c_Type_Otype_OFun @ SV634 @ SV499 ) ) )
= $true )
| ( ( c_Type_Otyping @ SV18 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV212 ) @ SV382 ) @ SV499 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1691]) ).
thf(1747,plain,
! [SV215: $i,SV686: $i,SV676: $i,SV385: $i,SV501: $i,SV21: $i] :
( ( ( ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV21 @ SV501 @ SV385 @ tc_Type_Otype ) @ SV676 @ SV686 )
| ( c_Type_Otyping @ SV21 @ ( c_Lambda_Osubst @ SV676 @ SV215 @ SV501 ) @ SV686 ) )
= $true )
| ( ( c_Type_Otyping @ SV21 @ SV215 @ SV385 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1693]) ).
thf(1748,plain,
! [SV386: $i,SV22: $i,SV216: $i,SV583: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV583 ) @ SV216 ) )
= $false )
| ( ( c_Type_Otyping @ SV22 @ SV583 @ SV386 )
= $false )
| ( ( c_Type_Otyping @ SV22 @ SV216 @ SV386 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1694]) ).
thf(1749,plain,
! [SV505: $i,SV226: $i,SV394: $i,SV32: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV32 ) @ SV394 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV226 ) @ SV505 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV32 ) @ SV226 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV394 ) @ SV505 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1695]) ).
thf(1750,plain,
! [SV50: $i,SV407: $i,SV635: $i,SV241: $i,SV511: $i] :
( ( ( c_Type_Otyping @ SV511 @ SV241 @ SV635 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV241 ) )
| ! [SY1703: $i] :
~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV511 @ SV407 @ SV635 @ tc_Type_Otype ) @ SV50 @ SY1703 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV50 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV50 @ SV241 @ SV407 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1697]) ).
thf(1751,plain,
! [SV412: $i,SV247: $i,SV677: $i,SV636: $i,SV514: $i,SV57: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV57 @ SV514 @ ( tc_fun @ SV636 @ ( tc_fun @ SV677 @ tc_bool ) ) ) @ SV247 ) @ SV412 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV57 @ SV247 ) @ SV412 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1698]) ).
thf(1752,plain,
! [SV413: $i,SV248: $i,SV678: $i,SV637: $i,SV58: $i,SV515: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV515 @ SV58 @ ( tc_fun @ SV637 @ ( tc_fun @ SV678 @ tc_bool ) ) ) @ SV248 ) @ SV413 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV58 @ SV248 ) @ SV413 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1699]) ).
thf(1753,plain,
! [SV679: $i,SV644: $i,SV596: $i,SV525: $i,SV418: $i,SV260: $i,SV79: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV79 @ SV260 @ SV418 @ SV525 @ SV596 ) @ SV644 ) @ SV679 ) )
= $true )
| ( ( ! [SY1714: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV260 @ SY1714 ) @ SV679 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV79 @ SV644 ) @ SY1714 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1700]) ).
thf(1754,plain,
! [SV419: $i,SV526: $i,SV645: $i,SV261: $i,SV80: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV80 @ SV261 ) @ SV645 ) @ SV526 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV80 @ SV261 ) @ SV419 ) @ SV645 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV80 @ SV261 ) @ SV419 ) @ SV526 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1701]) ).
thf(1755,plain,
! [SV420: $i,SV527: $i,SV646: $i,SV262: $i,SV81: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV81 @ SV262 ) @ SV646 ) @ SV527 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV81 @ SV262 ) @ SV420 ) @ SV646 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV81 @ SV262 ) @ SV420 ) @ SV527 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1702]) ).
thf(1756,plain,
! [SV423: $i,SV528: $i,SV647: $i,SV265: $i,SV84: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV84 @ SV265 ) @ SV647 ) @ SV528 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV84 @ SV265 ) @ SV423 ) @ SV647 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV84 @ SV265 ) @ SV423 ) @ SV528 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1703]) ).
thf(1757,plain,
! [SV424: $i,SV529: $i,SV648: $i,SV266: $i,SV85: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV85 @ SV266 ) @ SV648 ) @ SV529 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV85 @ SV424 ) @ SV648 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV85 @ SV266 ) @ SV424 ) @ SV529 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1704]) ).
thf(1758,plain,
! [SV425: $i,SV267: $i,SV530: $i,SV649: $i,SV86: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV86 @ SV649 ) @ SV530 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV86 @ SV267 ) @ SV425 ) @ SV649 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV86 @ SV267 ) @ SV425 ) @ SV530 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1705]) ).
thf(1759,plain,
! [SV430: $i,SV274: $i,SV687: $i,SV680: $i,SV94: $i,SV533: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV533 @ SV94 @ ( tc_fun @ SV680 @ ( tc_fun @ SV687 @ tc_bool ) ) ) @ SV274 ) @ SV430 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV533 @ SV274 ) @ SV430 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV94 @ SV274 ) @ SV430 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1706]) ).
thf(1760,plain,
! [SV534: $i,SV431: $i,SV95: $i,SV650: $i,SV597: $i,SV275: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV275 @ SV597 ) @ SV650 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV95 @ SV275 @ ( tc_fun @ SV431 @ ( tc_fun @ SV534 @ tc_bool ) ) ) @ SV597 ) @ SV650 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1707]) ).
thf(1761,plain,
! [SV535: $i,SV432: $i,SV276: $i,SV651: $i,SV598: $i,SV96: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV96 @ SV598 ) @ SV651 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV96 @ SV276 @ ( tc_fun @ SV432 @ ( tc_fun @ SV535 @ tc_bool ) ) ) @ SV598 ) @ SV651 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1708]) ).
thf(1762,plain,
! [SV110: $i,SV288: $i,SV656: $i,SV604: $i,SV438: $i] :
( ( ( c_Type_Otyping @ SV438 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV604 ) @ SV656 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV288 )
= $false )
| ( ( ~ ( c_Type_Otyping @ SV438 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV604 ) @ SV656 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV110 ) )
= $true )
| ( ( SV110 = SV288 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1710]) ).
thf(1763,plain,
! [SV451: $i,SV549: $i,SV659: $i,SV305: $i,SV132: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV132 @ SV305 ) @ SV659 ) @ SV549 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV132 @ SV305 ) @ SV451 ) @ SV659 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV132 @ SV305 ) @ SV451 ) @ SV549 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1713]) ).
thf(1764,plain,
! [SV551: $i,SV454: $i,SV137: $i,SV660: $i,SV613: $i,SV310: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV310 @ SV613 ) @ SV660 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ SV613 ) @ SV660 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV137 @ SV310 @ ( tc_fun @ SV454 @ ( tc_fun @ SV551 @ tc_bool ) ) ) @ SV613 ) @ SV660 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1714]) ).
thf(1765,plain,
! [SV455: $i,SV552: $i,SV661: $i,SV311: $i,SV138: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV138 @ SV311 ) @ SV661 ) @ SV552 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV138 @ SV455 ) @ SV661 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV138 @ SV311 ) @ SV455 ) @ SV552 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1715]) ).
thf(1766,plain,
! [SV456: $i,SV312: $i,SV553: $i,SV662: $i,SV139: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV139 @ SV662 ) @ SV553 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV139 @ SV312 ) @ SV456 ) @ SV662 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV139 @ SV312 ) @ SV456 ) @ SV553 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1716]) ).
thf(1767,plain,
! [SV457: $i,SV313: $i,SV554: $i,SV663: $i,SV140: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV140 @ SV663 ) @ SV554 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV140 @ SV313 ) @ SV457 ) @ SV663 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV140 @ SV313 ) @ SV457 ) @ SV554 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1717]) ).
thf(1768,plain,
! [SV458: $i,SV555: $i,SV664: $i,SV314: $i,SV141: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV141 @ SV314 ) @ SV664 ) @ SV555 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV141 @ SV458 ) @ SV664 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV141 @ SV314 ) @ SV458 ) @ SV555 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1718]) ).
thf(1769,plain,
! [SV459: $i,SV614: $i,SV315: $i,SV142: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV142 @ SV315 ) @ SV614 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV142 @ SV459 ) @ SV614 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV142 @ SV315 ) @ SV459 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1719]) ).
thf(1770,plain,
! [SV460: $i,SV615: $i,SV316: $i,SV143: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV143 @ SV316 ) @ SV615 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV143 @ SV460 ) @ SV615 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV143 @ SV316 ) @ SV460 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1720]) ).
thf(1771,plain,
! [SV144: $i,SV317: $i,SV616: $i,SV556: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV556 @ SV616 ) @ SV317 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV144 @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__1__1 @ SV144 @ SV556 @ SV616 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV144 @ SV317 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1721]) ).
thf(1772,plain,
! [SV318: $i,SV681: $i,SV145: $i,SV461: $i,SV665: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV665 @ SV461 ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__1__1 @ SV145 @ SV665 @ SV681 ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV665 @ SV681 ) @ SV318 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV145 @ SV461 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV145 @ SV318 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1722]) ).
thf(1773,plain,
! [SV320: $i,SV463: $i,SV617: $i,SV147: $i] :
( ( ( c_Type_Otyping @ SV147 @ SV617 @ SV463 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV617 ) @ SV320 ) )
= $false )
| ( ( c_Type_Otyping @ SV147 @ SV320 @ SV463 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1723]) ).
thf(1774,plain,
! [SV618: $i,SV469: $i,SV329: $i,SV159: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV159 @ SV329 ) @ SV469 ) @ SV618 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV159 @ SV329 ) @ SV618 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV159 @ SV329 ) @ SV469 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1724]) ).
thf(1775,plain,
! [SV470: $i,SV619: $i,SV330: $i,SV160: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV160 @ SV330 ) @ SV619 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV160 @ SV330 ) @ SV470 ) @ SV619 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV160 @ SV330 ) @ SV470 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1725]) ).
thf(1776,plain,
! [SV333: $i,SV163: $i,SV562: $i,SV666: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV666 @ SV562 ) @ ( v_sko__Wellfounded__Xaccp__Xinducts__1 @ SV163 @ SV666 ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV666 @ t_a ) @ SV333 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV163 @ SV562 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV163 @ SV333 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1727]) ).
thf(1777,plain,
! [SV336: $i,SV166: $i,SV564: $i,SV667: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV667 @ SV564 ) @ ( v_sko__Wellfounded__Xaccp__Xinduct__1 @ SV166 @ SV667 ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV667 @ t_a ) @ SV336 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV166 @ SV564 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV166 @ SV336 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1730]) ).
thf(1778,plain,
! [SV341: $i,SV171: $i,SV624: $i,SV567: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV567 @ SV624 ) @ ( v_sko__Wellfounded__Xaccp__Xinducts__1 @ SV171 @ SV567 ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV567 @ t_a ) @ SV341 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV567 @ t_a ) @ SV624 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV171 @ SV341 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1735]) ).
thf(1779,plain,
! [SV342: $i,SV172: $i,SV625: $i,SV568: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV568 @ SV625 ) @ ( v_sko__Wellfounded__Xaccp__Xinduct__1 @ SV172 @ SV568 ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV568 @ t_a ) @ SV342 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV568 @ t_a ) @ SV625 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV172 @ SV342 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1736]) ).
thf(1780,plain,
! [SV185: $i,SV355: $i,SV628: $i,SV575: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV575 @ SV628 ) @ SV355 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV185 @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__rule__1__1 @ SV185 @ SV575 @ SV628 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV185 @ SV355 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1739]) ).
thf(1781,plain,
! [SV356: $i,SV682: $i,SV186: $i,SV487: $i,SV670: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV670 @ SV487 ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__rule__1__1 @ SV186 @ SV670 @ SV682 ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV670 @ SV682 ) @ SV356 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV186 @ SV487 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV186 @ SV356 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1740]) ).
thf(1782,plain,
! [SV490: $i,SV671: $i,SV366: $i,SV630: $i,SV196: $i,SV2: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ SV2 @ SV196 ) @ ( c_List_Olist_OCons @ SV630 @ SV366 @ SV196 ) ) @ ( c_List_Olist_OCons @ SV671 @ SV490 @ SV196 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV2 @ SV630 ) @ SV671 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ SV2 @ SV196 ) @ SV366 ) @ SV490 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1741]) ).
thf(1783,plain,
! [SV493: $i,SV683: $i,SV370: $i,SV672: $i,SV200: $i,SV6: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ SV6 @ SV200 ) @ ( c_List_Olist_OCons @ SV672 @ SV370 @ SV200 ) ) @ ( c_List_Olist_OCons @ SV683 @ SV493 @ SV200 ) ) )
= $false )
| ( ( SV493 = SV370 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ SV6 @ SV200 ) @ SV370 ) @ SV493 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1742]) ).
thf(1784,plain,
! [SV372: $i,SV8: $i,SV494: $i,SV202: $i,SV684: $i,SV674: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ SV674 @ SV684 ) @ ( c_List_Olist_OCons @ SV202 @ SV494 @ SV684 ) ) @ ( c_List_Olist_OCons @ SV8 @ SV372 @ SV684 ) ) )
= $false )
| ( ( SV372 = SV494 )
= $true )
| ( ( SV8 = SV202 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1743]) ).
thf(1785,plain,
! [SV685: $i,SV12: $i,SV675: $i,SV206: $i,SV496: $i,SV376: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_ListOrder_Ostep1 @ SV376 @ SV496 ) @ ( c_List_Olist_OCons @ SV206 @ SV675 @ SV496 ) ) @ ( c_List_Olist_OCons @ SV12 @ SV685 @ SV496 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV376 @ SV206 ) @ SV12 ) )
= $true )
| ( ( SV12 = SV206 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1744]) ).
thf(1786,plain,
! [SV382: $i,SV499: $i,SV634: $i,SV212: $i,SV18: $i] :
( ( ( c_Type_Otyping @ SV18 @ SV212 @ ( c_Type_Otype_OFun @ SV634 @ SV499 ) )
= $false )
| ( ( c_Type_Otyping @ SV18 @ SV382 @ SV634 )
= $false )
| ( ( c_Type_Otyping @ SV18 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV212 ) @ SV382 ) @ SV499 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1746]) ).
thf(1787,plain,
! [SV215: $i,SV686: $i,SV676: $i,SV385: $i,SV501: $i,SV21: $i] :
( ( ( ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV21 @ SV501 @ SV385 @ tc_Type_Otype ) @ SV676 @ SV686 ) )
= $true )
| ( ( c_Type_Otyping @ SV21 @ ( c_Lambda_Osubst @ SV676 @ SV215 @ SV501 ) @ SV686 )
= $true )
| ( ( c_Type_Otyping @ SV21 @ SV215 @ SV385 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1747]) ).
thf(1788,plain,
! [SV50: $i,SV635: $i,SV407: $i,SV511: $i,SV241: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV241 ) ) )
= $true )
| ( ( ! [SY1703: $i] :
~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV511 @ SV407 @ SV635 @ tc_Type_Otype ) @ SV50 @ SY1703 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV50 ) ) )
= $true )
| ( ( c_Type_Otyping @ SV511 @ SV241 @ SV635 )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV50 @ SV241 @ SV407 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1750]) ).
thf(1789,plain,
! [SV596: $i,SV525: $i,SV418: $i,SV644: $i,SV79: $i,SV679: $i,SV688: $i,SV260: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV260 @ SV688 ) @ SV679 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV79 @ SV644 ) @ SV688 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV79 @ SV260 @ SV418 @ SV525 @ SV596 ) @ SV644 ) @ SV679 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1753]) ).
thf(1790,plain,
! [SV526: $i,SV645: $i,SV419: $i,SV261: $i,SV80: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV80 @ SV261 ) @ SV419 ) @ SV645 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV80 @ SV261 ) @ SV645 ) @ SV526 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV80 @ SV261 ) @ SV419 ) @ SV526 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1754]) ).
thf(1791,plain,
! [SV527: $i,SV646: $i,SV420: $i,SV262: $i,SV81: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV81 @ SV262 ) @ SV420 ) @ SV646 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV81 @ SV262 ) @ SV646 ) @ SV527 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV81 @ SV262 ) @ SV420 ) @ SV527 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1755]) ).
thf(1792,plain,
! [SV528: $i,SV647: $i,SV423: $i,SV265: $i,SV84: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV84 @ SV265 ) @ SV423 ) @ SV647 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV84 @ SV265 ) @ SV647 ) @ SV528 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV84 @ SV265 ) @ SV423 ) @ SV528 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1756]) ).
thf(1793,plain,
! [SV529: $i,SV266: $i,SV648: $i,SV424: $i,SV85: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV85 @ SV424 ) @ SV648 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV85 @ SV266 ) @ SV648 ) @ SV529 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV85 @ SV266 ) @ SV424 ) @ SV529 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1757]) ).
thf(1794,plain,
! [SV530: $i,SV649: $i,SV425: $i,SV267: $i,SV86: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV86 @ SV267 ) @ SV425 ) @ SV649 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV86 @ SV649 ) @ SV530 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV86 @ SV267 ) @ SV425 ) @ SV530 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1758]) ).
thf(1795,plain,
! [SV430: $i,SV274: $i,SV687: $i,SV680: $i,SV94: $i,SV533: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV533 @ SV94 @ ( tc_fun @ SV680 @ ( tc_fun @ SV687 @ tc_bool ) ) ) @ SV274 ) @ SV430 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV533 @ SV274 ) @ SV430 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV94 @ SV274 ) @ SV430 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1759]) ).
thf(1796,plain,
! [SV288: $i,SV110: $i,SV656: $i,SV604: $i,SV438: $i] :
( ( ( c_Type_Otyping @ SV438 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV604 ) @ SV656 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV110 )
= $false )
| ( ( c_Type_Otyping @ SV438 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV604 ) @ SV656 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV288 )
= $false )
| ( ( SV110 = SV288 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1762]) ).
thf(1797,plain,
! [SV549: $i,SV659: $i,SV451: $i,SV305: $i,SV132: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV132 @ SV305 ) @ SV451 ) @ SV659 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV132 @ SV305 ) @ SV659 ) @ SV549 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV132 @ SV305 ) @ SV451 ) @ SV549 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1763]) ).
thf(1798,plain,
! [SV551: $i,SV454: $i,SV137: $i,SV660: $i,SV613: $i,SV310: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV310 @ SV613 ) @ SV660 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ SV613 ) @ SV660 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV137 @ SV310 @ ( tc_fun @ SV454 @ ( tc_fun @ SV551 @ tc_bool ) ) ) @ SV613 ) @ SV660 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1764]) ).
thf(1799,plain,
! [SV552: $i,SV311: $i,SV661: $i,SV455: $i,SV138: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV138 @ SV455 ) @ SV661 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV138 @ SV311 ) @ SV661 ) @ SV552 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV138 @ SV311 ) @ SV455 ) @ SV552 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1765]) ).
thf(1800,plain,
! [SV553: $i,SV662: $i,SV456: $i,SV312: $i,SV139: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV139 @ SV312 ) @ SV456 ) @ SV662 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV139 @ SV662 ) @ SV553 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV139 @ SV312 ) @ SV456 ) @ SV553 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1766]) ).
thf(1801,plain,
! [SV554: $i,SV663: $i,SV457: $i,SV313: $i,SV140: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV140 @ SV313 ) @ SV457 ) @ SV663 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV140 @ SV663 ) @ SV554 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV140 @ SV313 ) @ SV457 ) @ SV554 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1767]) ).
thf(1802,plain,
! [SV555: $i,SV314: $i,SV664: $i,SV458: $i,SV141: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV141 @ SV458 ) @ SV664 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV141 @ SV314 ) @ SV664 ) @ SV555 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ SV141 @ SV314 ) @ SV458 ) @ SV555 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1768]) ).
thf(1803,plain,
! [SV318: $i,SV681: $i,SV145: $i,SV461: $i,SV665: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV665 @ SV461 ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__1__1 @ SV145 @ SV665 @ SV681 ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV665 @ SV681 ) @ SV318 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV145 @ SV461 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV145 @ SV318 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1772]) ).
thf(1804,plain,
! [SV163: $i,SV562: $i,SV333: $i,SV666: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV666 @ t_a ) @ SV333 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV666 @ SV562 ) @ ( v_sko__Wellfounded__Xaccp__Xinducts__1 @ SV163 @ SV666 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV163 @ SV562 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV163 @ SV333 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1776]) ).
thf(1805,plain,
! [SV166: $i,SV564: $i,SV336: $i,SV667: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV667 @ t_a ) @ SV336 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV667 @ SV564 ) @ ( v_sko__Wellfounded__Xaccp__Xinduct__1 @ SV166 @ SV667 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV166 @ SV564 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV166 @ SV336 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1777]) ).
thf(1806,plain,
! [SV171: $i,SV624: $i,SV341: $i,SV567: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV567 @ t_a ) @ SV341 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV567 @ SV624 ) @ ( v_sko__Wellfounded__Xaccp__Xinducts__1 @ SV171 @ SV567 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV567 @ t_a ) @ SV624 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV171 @ SV341 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1778]) ).
thf(1807,plain,
! [SV172: $i,SV625: $i,SV342: $i,SV568: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV568 @ t_a ) @ SV342 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV568 @ SV625 ) @ ( v_sko__Wellfounded__Xaccp__Xinduct__1 @ SV172 @ SV568 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV568 @ t_a ) @ SV625 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV172 @ SV342 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1779]) ).
thf(1808,plain,
! [SV356: $i,SV682: $i,SV186: $i,SV487: $i,SV670: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV670 @ SV487 ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__rule__1__1 @ SV186 @ SV670 @ SV682 ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV670 @ SV682 ) @ SV356 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV186 @ SV487 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV186 @ SV356 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1781]) ).
thf(1809,plain,
! [SV215: $i,SV686: $i,SV676: $i,SV385: $i,SV501: $i,SV21: $i] :
( ( ( c_Type_Otyping @ ( c_Type_Oshift @ SV21 @ SV501 @ SV385 @ tc_Type_Otype ) @ SV676 @ SV686 )
= $false )
| ( ( c_Type_Otyping @ SV21 @ ( c_Lambda_Osubst @ SV676 @ SV215 @ SV501 ) @ SV686 )
= $true )
| ( ( c_Type_Otyping @ SV21 @ SV215 @ SV385 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1787]) ).
thf(1810,plain,
! [SV50: $i,SV635: $i,SV407: $i,SV511: $i,SV241: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV241 ) )
= $false )
| ( ( ! [SY1703: $i] :
~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV511 @ SV407 @ SV635 @ tc_Type_Otype ) @ SV50 @ SY1703 )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV50 ) ) )
= $true )
| ( ( c_Type_Otyping @ SV511 @ SV241 @ SV635 )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV50 @ SV241 @ SV407 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1788]) ).
thf(1811,plain,
! [SV596: $i,SV525: $i,SV418: $i,SV644: $i,SV79: $i,SV679: $i,SV688: $i,SV260: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV260 @ SV688 ) @ SV679 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV79 @ SV644 ) @ SV688 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV79 @ SV260 @ SV418 @ SV525 @ SV596 ) @ SV644 ) @ SV679 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1789]) ).
thf(1812,plain,
! [SV551: $i,SV454: $i,SV310: $i,SV660: $i,SV613: $i,SV137: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ SV613 ) @ SV660 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV310 @ SV613 ) @ SV660 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV137 @ SV310 @ ( tc_fun @ SV454 @ ( tc_fun @ SV551 @ tc_bool ) ) ) @ SV613 ) @ SV660 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1798]) ).
thf(1813,plain,
! [SV145: $i,SV461: $i,SV318: $i,SV681: $i,SV665: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV665 @ SV681 ) @ SV318 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV665 @ SV461 ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__1__1 @ SV145 @ SV665 @ SV681 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV145 @ SV461 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV145 @ SV318 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1803]) ).
thf(1814,plain,
! [SV186: $i,SV487: $i,SV356: $i,SV682: $i,SV670: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ SV670 @ SV682 ) @ SV356 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV670 @ SV487 ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__rule__1__1 @ SV186 @ SV670 @ SV682 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV186 @ SV487 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV186 @ SV356 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1808]) ).
thf(1815,plain,
! [SV241: $i,SV50: $i,SV635: $i,SV407: $i,SV511: $i] :
( ( ( ! [SY1703: $i] :
~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV511 @ SV407 @ SV635 @ tc_Type_Otype ) @ SV50 @ SY1703 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV50 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV241 ) )
= $false )
| ( ( c_Type_Otyping @ SV511 @ SV241 @ SV635 )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV50 @ SV241 @ SV407 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1810]) ).
thf(1816,plain,
! [SV596: $i,SV525: $i,SV418: $i,SV644: $i,SV79: $i,SV679: $i,SV688: $i,SV260: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV260 @ SV688 ) @ SV679 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV79 @ SV644 ) @ SV688 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV79 @ SV260 @ SV418 @ SV525 @ SV596 ) @ SV644 ) @ SV679 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1811]) ).
thf(1817,plain,
! [SV241: $i,SV689: $i,SV50: $i,SV635: $i,SV407: $i,SV511: $i] :
( ( ( ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV511 @ SV407 @ SV635 @ tc_Type_Otype ) @ SV50 @ SV689 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV50 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV241 ) )
= $false )
| ( ( c_Type_Otyping @ SV511 @ SV241 @ SV635 )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV50 @ SV241 @ SV407 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1815]) ).
thf(1818,plain,
! [SV596: $i,SV525: $i,SV418: $i,SV679: $i,SV260: $i,SV688: $i,SV644: $i,SV79: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV79 @ SV644 ) @ SV688 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV260 @ SV688 ) @ SV679 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ SV79 @ SV260 @ SV418 @ SV525 @ SV596 ) @ SV644 ) @ SV679 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1816]) ).
thf(1819,plain,
! [SV241: $i,SV689: $i,SV50: $i,SV635: $i,SV407: $i,SV511: $i] :
( ( ( c_Type_Otyping @ ( c_Type_Oshift @ SV511 @ SV407 @ SV635 @ tc_Type_Otype ) @ SV50 @ SV689 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV50 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV241 ) )
= $false )
| ( ( c_Type_Otyping @ SV511 @ SV241 @ SV635 )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV50 @ SV241 @ SV407 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1817]) ).
thf(1820,plain,
! [SV241: $i,SV689: $i,SV635: $i,SV407: $i,SV511: $i,SV50: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV50 ) )
= $false )
| ( ( c_Type_Otyping @ ( c_Type_Oshift @ SV511 @ SV407 @ SV635 @ tc_Type_Otype ) @ SV50 @ SV689 )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV241 ) )
= $false )
| ( ( c_Type_Otyping @ SV511 @ SV241 @ SV635 )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV50 @ SV241 @ SV407 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1819]) ).
thf(1821,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[709,1820,1818,1814,1813,1812,1809,1807,1806,1805,1804,1802,1801,1800,1799,1797,1796,1795,1794,1793,1792,1791,1790,1786,1785,1784,1783,1782,1780,1775,1774,1773,1771,1770,1769,1761,1760,1752,1751,1749,1748,1745,1738,1737,1734,1733,1732,1731,1729,1728,1726,1712,1711,1709,1696,1692,1687,1685,1684,1682,1677,1676,1664,1661,1660,1648,1647,1646,1645,1642,1641,1640,1639,1637,1636,1635,1634,1629,1628,1621,1620,1619,1618,1617,1616,1615,1610,1608,1607,1606,1601,1600,1597,1589,1588,1585,1583,1582,1581,1580,1562,1559,1545,1544,1543,1538,1535,1531,1530,1529,1524,1517,1504,1503,1502,1501,1500,1499,1498,1497,1493,1492,1491,1489,1488,1487,1486,1485,1483,1482,1479,1478,1477,1473,1470,1454,1453,1452,1451,1450,1442,1439,1435,1417,1414,1404,1403,1402,1400,1397,1379,1378,1372,1364,1355,1341,1336,1335,1326,1325,1324,1323,1316,1302,1301,1299,1298,1293,1253,1252,1247,1246,1232,1219,1193,1189,1185,1184,1169,1163,1108,1071,1044,1042,1033,1025,986,971,960,947,920,877,816,774,771,769,725,721,720,719,718,717,716,715,714]) ).
thf(1822,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[1821]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL858-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.21 % Computer : n018.cluster.edu
% 0.09/0.21 % Model : x86_64 x86_64
% 0.09/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.21 % Memory : 8046.5625MB
% 0.09/0.21 % OS : Linux 6.8.0-71-generic
% 0.09/0.22 % CPULimit : 300
% 0.09/0.22 % WCLimit : 300
% 0.09/0.22 % DateTime : Tue Oct 6 12:38:06 UTC 2026
% 0.09/0.22 % CPUTime :
% 0.09/0.22 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 17.56/3.23 .
% 17.56/3.23
% 17.56/3.23 No.of.Axioms: 204
% 17.56/3.23
% 17.56/3.23 Length.of.Defs: 0
% 17.56/3.23
% 17.56/3.23 Contains.Choice.Funs: false
% 17.56/3.23 ......................................................................................................
% 17.56/3.23
% 17.56/3.23 ********************************
% 17.56/3.23 * All subproblems solved! *
% 17.56/3.23 ********************************
% 17.56/3.23 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:2,axioms:204,ps:3,u:5,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:1821,loop_count:0,foatp_calls:1,translation:fof_experiment)
% 17.56/3.23
% 17.56/3.23 %**** Beginning of derivation protocol ****
% 17.56/3.23 % SZS output start CNFRefutation
% See solution above
% 17.56/3.24
% 17.56/3.24 %**** End of derivation protocol ****
% 17.56/3.24 %**** no. of clauses in derivation: 1822 ****
% 17.56/3.24 %**** clause counter: 1821 ****
% 17.56/3.24
% 17.56/3.24 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:2,axioms:204,ps:3,u:5,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:1821,loop_count:0,foatp_calls:1,translation:fof_experiment)
%------------------------------------------------------------------------------