%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SCT100-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:38:26 AM UTC 2026
% Result : Unsatisfiable 223.21s 45.22s
% Output : CNFRefutation 223.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 678
% Syntax : Number of formulae : 6137 (3855 unt; 0 typ; 0 def)
% Number of atoms : 31049 (10970 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 121174 (6601 ~;8562 |; 0 &;106011 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 37 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 127 ( 124 usr; 19 con; 0-7 aty)
% Number of variables : 23826 ( 0 ^;23826 !; 0 ?;23826 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_c_ATP__Linkup_Osko__Product__Type__XSigmaE__1__1,type,
c_ATP__Linkup_Osko__Product__Type__XSigmaE__1__1: $i > $i > $i > $i > $i > $i ).
thf(tp_c_ATP__Linkup_Osko__Relation__XDomainE__1__1,type,
c_ATP__Linkup_Osko__Relation__XDomainE__1__1: $i > $i > $i > $i > $i ).
thf(tp_c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1,type,
c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1: $i > $i > $i > $i > $i ).
thf(tp_c_ATP__Linkup_Osko__Relation__XIdE__1__1,type,
c_ATP__Linkup_Osko__Relation__XIdE__1__1: $i > $i > $i ).
thf(tp_c_ATP__Linkup_Osko__Relation__XId__onE__1__1,type,
c_ATP__Linkup_Osko__Relation__XId__onE__1__1: $i > $i > $i > $i ).
thf(tp_c_ATP__Linkup_Osko__Relation__XImageE__1__1,type,
c_ATP__Linkup_Osko__Relation__XImageE__1__1: $i > $i > $i > $i > $i > $i ).
thf(tp_c_ATP__Linkup_Osko__Relation__XImage__iff__1__1,type,
c_ATP__Linkup_Osko__Relation__XImage__iff__1__1: $i > $i > $i > $i > $i > $i ).
thf(tp_c_ATP__Linkup_Osko__Relation__XRangeE__1__1,type,
c_ATP__Linkup_Osko__Relation__XRangeE__1__1: $i > $i > $i > $i > $i ).
thf(tp_c_ATP__Linkup_Osko__Relation__XRange__iff__1__1,type,
c_ATP__Linkup_Osko__Relation__XRange__iff__1__1: $i > $i > $i > $i > $i ).
thf(tp_c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1,type,
c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1: $i > $i > $i ).
thf(tp_c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1,type,
c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1: $i > $i > $i > $i > $i > $i > $i > $i ).
thf(tp_c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1,type,
c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1: $i > $i > $i > $i > $i ).
thf(tp_c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1,type,
c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1: $i > $i > $i > $i > $i ).
thf(tp_c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2,type,
c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2: $i > $i > $i > $i > $i ).
thf(tp_c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1,type,
c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1: $i > $i > $i > $i > $i ).
thf(tp_c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1,type,
c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1: $i > $i > $i ).
thf(tp_c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1,type,
c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1: $i > $i > $i > $i > $i ).
thf(tp_c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1,type,
c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1: $i > $i > $i > $i > $i ).
thf(tp_c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2,type,
c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2: $i > $i > $i > $i > $i ).
thf(tp_c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1,type,
c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1: $i > $i > $i > $i > $i ).
thf(tp_c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1,type,
c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1: $i > $i > $i > $i > $i ).
thf(tp_c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1,type,
c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1: $i > $i > $i > $i > $i ).
thf(tp_c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1,type,
c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1: $i > $i > $i > $i ).
thf(tp_c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1,type,
c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1: $i > $i > $i > $i ).
thf(tp_c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1,type,
c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1: $i > $i > $i > $i ).
thf(tp_c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1,type,
c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1: $i > $i > $i ).
thf(tp_c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1,type,
c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1: $i > $i > $i > $i ).
thf(tp_c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1,type,
c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1: $i > $i > $i > $i ).
thf(tp_c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1,type,
c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1: $i > $i > $i ).
thf(tp_c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1,type,
c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1: $i > $i > $i > $i ).
thf(tp_c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1,type,
c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1: $i > $i > $i > $i ).
thf(tp_c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1,type,
c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1: $i > $i > $i > $i ).
thf(tp_c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1,type,
c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1: $i > $i > $i > $i ).
thf(tp_c_Arrow__Order__Mirabelle_OIIA,type,
c_Arrow__Order__Mirabelle_OIIA: $i > $o ).
thf(tp_c_Arrow__Order__Mirabelle_Oabove,type,
c_Arrow__Order__Mirabelle_Oabove: $i ).
thf(tp_c_Arrow__Order__Mirabelle_Omkbot,type,
c_Arrow__Order__Mirabelle_Omkbot: $i ).
thf(tp_c_Arrow__Order__Mirabelle_Omktop,type,
c_Arrow__Order__Mirabelle_Omktop: $i ).
thf(tp_c_Arrow__Order__Mirabelle_Ounanimity,type,
c_Arrow__Order__Mirabelle_Ounanimity: $i > $o ).
thf(tp_c_COMBB,type,
c_COMBB: $i > $i > $i > $i > $i > $i ).
thf(tp_c_COMBC,type,
c_COMBC: $i > $i > $i > $i > $i > $i ).
thf(tp_c_COMBK,type,
c_COMBK: $i > $i > $i > $i ).
thf(tp_c_COMBS,type,
c_COMBS: $i > $i > $i > $i > $i > $i ).
thf(tp_c_Equiv__Relations_Ocongruent,type,
c_Equiv__Relations_Ocongruent: $i > $i > $i > $i > $o ).
thf(tp_c_Equiv__Relations_Ocongruent2,type,
c_Equiv__Relations_Ocongruent2: $i > $i > $i > $i > $i > $i > $o ).
thf(tp_c_Equiv__Relations_Oequiv,type,
c_Equiv__Relations_Oequiv: $i > $i > $i > $o ).
thf(tp_c_FunDef_Oin__rel,type,
c_FunDef_Oin__rel: $i > $i > $i > $i ).
thf(tp_c_HOL_OIf,type,
c_HOL_OIf: $i > $i ).
thf(tp_c_HOL_Ominus__class_Ominus,type,
c_HOL_Ominus__class_Ominus: $i > $i > $i > $i ).
thf(tp_c_HOL_Oord__class_Oless,type,
c_HOL_Oord__class_Oless: $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_List_Osko__Recdef__Xcuts__eq__1__1,type,
c_List_Osko__Recdef__Xcuts__eq__1__1: $i > $i > $i > $i > $i > $i > $i ).
thf(tp_c_List_Osko__Recdef__Xtfl__wf__induct__1__1,type,
c_List_Osko__Recdef__Xtfl__wf__induct__1__1: $i > $i > $i > $i ).
thf(tp_c_Nitpick_Orefl_H,type,
c_Nitpick_Orefl_H: $i > $i > $o ).
thf(tp_c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1,type,
c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1: $i > $i > $i ).
thf(tp_c_Order__Relation_Ostrict__linear__order__on,type,
c_Order__Relation_Ostrict__linear__order__on: $i > $i > $i > $o ).
thf(tp_c_Orderings_Obot__class_Obot,type,
c_Orderings_Obot__class_Obot: $i > $i ).
thf(tp_c_Pair,type,
c_Pair: $i > $i > $i > $i > $i ).
thf(tp_c_Product__Type_OSigma,type,
c_Product__Type_OSigma: $i > $i > $i > $i > $i ).
thf(tp_c_Recdef_Ocut,type,
c_Recdef_Ocut: $i > $i > $i > $i > $i > $i ).
thf(tp_c_Relation_ODomain,type,
c_Relation_ODomain: $i > $i > $i > $i ).
thf(tp_c_Relation_OId,type,
c_Relation_OId: $i > $i ).
thf(tp_c_Relation_OId__on,type,
c_Relation_OId__on: $i > $i > $i ).
thf(tp_c_Relation_OImage,type,
c_Relation_OImage: $i > $i > $i > $i > $i ).
thf(tp_c_Relation_ORange,type,
c_Relation_ORange: $i > $i > $i > $i ).
thf(tp_c_Relation_Oantisym,type,
c_Relation_Oantisym: $i > $i > $o ).
thf(tp_c_Relation_Oconverse,type,
c_Relation_Oconverse: $i > $i > $i > $i ).
thf(tp_c_Relation_Oinv__image,type,
c_Relation_Oinv__image: $i > $i > $i > $i > $i ).
thf(tp_c_Relation_Oirrefl,type,
c_Relation_Oirrefl: $i > $i > $o ).
thf(tp_c_Relation_Orefl__on,type,
c_Relation_Orefl__on: $i > $i > $i > $o ).
thf(tp_c_Relation_Orel__comp,type,
c_Relation_Orel__comp: $i > $i > $i > $i > $i > $i ).
thf(tp_c_Relation_Osingle__valued,type,
c_Relation_Osingle__valued: $i > $i > $i > $o ).
thf(tp_c_Relation_Osym,type,
c_Relation_Osym: $i > $i > $o ).
thf(tp_c_Relation_Ototal__on,type,
c_Relation_Ototal__on: $i > $i > $i > $o ).
thf(tp_c_Relation_Otrans,type,
c_Relation_Otrans: $i > $i > $o ).
thf(tp_c_Set_Oimage,type,
c_Set_Oimage: $i > $i > $i > $i > $i ).
thf(tp_c_Set_Oinsert,type,
c_Set_Oinsert: $i > $i > $i > $i ).
thf(tp_c_Transitive__Closure_Ortrancl,type,
c_Transitive__Closure_Ortrancl: $i > $i > $i ).
thf(tp_c_Transitive__Closure_Otrancl,type,
c_Transitive__Closure_Otrancl: $i > $i > $i ).
thf(tp_c_Wellfounded_Oacc,type,
c_Wellfounded_Oacc: $i > $i > $i ).
thf(tp_c_Wellfounded_Oacyclic,type,
c_Wellfounded_Oacyclic: $i > $i > $o ).
thf(tp_c_Wellfounded_Owf,type,
c_Wellfounded_Owf: $i > $i > $o ).
thf(tp_c_Wellfounded_OwfP,type,
c_Wellfounded_OwfP: $i > $i > $o ).
thf(tp_c_fequal,type,
c_fequal: $i > $i ).
thf(tp_c_fst,type,
c_fst: $i > $i > $i ).
thf(tp_c_in,type,
c_in: $i > $i > $i > $o ).
thf(tp_c_lessequals,type,
c_lessequals: $i > $i > $i > $o ).
thf(tp_c_snd,type,
c_snd: $i > $i > $i ).
thf(tp_c_split,type,
c_split: $i > $i > $i > $i > $i ).
thf(tp_class_HOL_Oord,type,
class_HOL_Oord: $i > $o ).
thf(tp_class_Lattices_Obounded__lattice,type,
class_Lattices_Obounded__lattice: $i > $o ).
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_class_OrderedGroup_Oab__group__add,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
thf(tp_class_OrderedGroup_Opordered__ab__group__add,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
thf(tp_class_Orderings_Obot,type,
class_Orderings_Obot: $i > $o ).
thf(tp_class_Orderings_Olinorder,type,
class_Orderings_Olinorder: $i > $o ).
thf(tp_class_Orderings_Oorder,type,
class_Orderings_Oorder: $i > $o ).
thf(tp_class_Orderings_Opreorder,type,
class_Orderings_Opreorder: $i > $o ).
thf(tp_hAPP,type,
hAPP: $i > $i > $i ).
thf(tp_hBOOL,type,
hBOOL: $i > $o ).
thf(tp_t_a,type,
t_a: $i ).
thf(tp_t_b,type,
t_b: $i ).
thf(tp_tc_Arrow__Order__Mirabelle_Oalt,type,
tc_Arrow__Order__Mirabelle_Oalt: $i ).
thf(tp_tc_Arrow__Order__Mirabelle_Oindi,type,
tc_Arrow__Order__Mirabelle_Oindi: $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_tc_prod,type,
tc_prod: $i > $i > $i ).
thf(tp_v_F,type,
v_F: $i ).
thf(tp_v_P____,type,
v_P____: $i ).
thf(tp_v_c____,type,
v_c____: $i ).
thf(tp_v_d____,type,
v_d____: $i ).
thf(tp_v_e____,type,
v_e____: $i ).
thf(tp_v_h____,type,
v_h____: $i ).
thf(tp_v_n____,type,
v_n____: $i ).
thf(tp_v_r,type,
v_r: $i ).
thf(tp_v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1,type,
v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1: $i > $i > $i ).
thf(tp_v_sko__Transitive__Closure__Xrtrancl__Xcases__1,type,
v_sko__Transitive__Closure__Xrtrancl__Xcases__1: $i > $i > $i > $i ).
thf(tp_v_sko__Transitive__Closure__Xtrancl__Xcases__1,type,
v_sko__Transitive__Closure__Xtrancl__Xcases__1: $i > $i > $i > $i ).
thf(tp_v_sko__Wellfounded__Xacc__Xinduct__1,type,
v_sko__Wellfounded__Xacc__Xinduct__1: $i > $i > $i ).
thf(tp_v_sko__Wellfounded__Xacc__Xinducts__1,type,
v_sko__Wellfounded__Xacc__Xinducts__1: $i > $i > $i ).
thf(1,axiom,
! [V_X: $i,V_Y: $i,T_a: $i] :
( ( V_X = V_Y )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ T_a ) @ V_X ) @ V_Y ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).
thf(3,axiom,
class_HOL_Oord @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__HOL_Oord) ).
thf(4,axiom,
class_Orderings_Obot @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Obot) ).
thf(5,axiom,
class_Orderings_Oorder @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).
thf(6,axiom,
class_Lattices_Olattice @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olattice) ).
thf(7,axiom,
class_Orderings_Opreorder @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).
thf(8,axiom,
class_Lattices_Obounded__lattice @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Obounded__lattice) ).
thf(9,axiom,
class_Lattices_Odistrib__lattice @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Odistrib__lattice) ).
thf(10,axiom,
class_Lattices_Olower__semilattice @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olower__semilattice) ).
thf(11,axiom,
class_Lattices_Oupper__semilattice @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oupper__semilattice) ).
thf(12,axiom,
class_HOL_Oord @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__HOL_Oord) ).
thf(13,axiom,
class_Orderings_Obot @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Obot) ).
thf(14,axiom,
class_Orderings_Oorder @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
thf(15,axiom,
class_Lattices_Olattice @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olattice) ).
thf(16,axiom,
class_Orderings_Olinorder @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
thf(17,axiom,
class_Orderings_Opreorder @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
thf(18,axiom,
class_Lattices_Odistrib__lattice @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Odistrib__lattice) ).
thf(19,axiom,
class_Lattices_Olower__semilattice @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olower__semilattice) ).
thf(20,axiom,
class_Lattices_Oupper__semilattice @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Oupper__semilattice) ).
thf(21,axiom,
! [T_2: $i,T_1: $i] :
( ( class_HOL_Oord @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_HOL_Oord @ T_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__HOL_Oord) ).
thf(22,axiom,
! [T_2: $i,T_1: $i] :
( ( class_Orderings_Obot @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Orderings_Obot @ T_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Obot) ).
thf(23,axiom,
! [T_2: $i,T_1: $i] :
( ( class_Orderings_Oorder @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Orderings_Oorder @ T_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).
thf(24,axiom,
! [T_2: $i,T_1: $i] :
( ( class_Lattices_Olattice @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Lattices_Olattice @ T_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olattice) ).
thf(25,axiom,
! [T_2: $i,T_1: $i] :
( ( class_Orderings_Opreorder @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Orderings_Opreorder @ T_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).
thf(26,axiom,
! [T_2: $i,T_1: $i] :
( ( class_Lattices_Obounded__lattice @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Lattices_Obounded__lattice @ T_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Obounded__lattice) ).
thf(27,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/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Odistrib__lattice) ).
thf(28,axiom,
! [T_2: $i,T_1: $i] :
( ( class_Lattices_Olower__semilattice @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Lattices_Olattice @ T_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olower__semilattice) ).
thf(29,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/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oupper__semilattice) ).
thf(30,axiom,
c_in @ ( c_Pair @ v_c____ @ v_d____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_HOL_OIf @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ v_h____ @ tc_nat @ ( tc_fun @ tc_nat @ tc_bool ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ v_n____ @ tc_Arrow__Order__Mirabelle_Oindi @ tc_nat @ tc_bool ) @ tc_bool @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ ( c_COMBC @ ( c_COMBB @ c_Arrow__Order__Mirabelle_Omktop @ v_P____ @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ v_e____ @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_HOL_OIf @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ ( c_COMBC @ ( c_COMBB @ ( c_fequal @ tc_nat ) @ v_h____ @ tc_nat @ ( tc_fun @ tc_nat @ tc_bool ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ v_n____ @ tc_Arrow__Order__Mirabelle_Oindi @ tc_nat @ tc_bool ) @ tc_bool @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ ( c_COMBC @ ( c_COMBC @ ( c_COMBB @ c_Arrow__Order__Mirabelle_Oabove @ v_P____ @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ v_c____ @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ v_e____ @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ ( c_COMBC @ ( c_COMBB @ c_Arrow__Order__Mirabelle_Omkbot @ v_P____ @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ v_e____ @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0_01) ).
thf(31,axiom,
( ( c_in @ ( c_Pair @ v_c____ @ v_d____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_HOL_OIf @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ v_h____ @ tc_nat @ ( tc_fun @ tc_nat @ tc_bool ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ v_n____ @ tc_Arrow__Order__Mirabelle_Oindi @ tc_nat @ tc_bool ) @ tc_bool @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ ( c_COMBC @ ( c_COMBB @ c_Arrow__Order__Mirabelle_Omktop @ v_P____ @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ v_e____ @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_HOL_OIf @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ ( c_COMBC @ ( c_COMBB @ ( c_fequal @ tc_nat ) @ v_h____ @ tc_nat @ ( tc_fun @ tc_nat @ tc_bool ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ v_n____ @ tc_Arrow__Order__Mirabelle_Oindi @ tc_nat @ tc_bool ) @ tc_bool @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ ( c_COMBC @ ( c_COMBC @ ( c_COMBB @ c_Arrow__Order__Mirabelle_Oabove @ v_P____ @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ v_c____ @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ v_e____ @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ ( c_COMBC @ ( c_COMBB @ c_Arrow__Order__Mirabelle_Omkbot @ v_P____ @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ v_e____ @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ v_c____ @ v_d____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ v_P____ ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0) ).
thf(32,axiom,
( ( c_in @ ( c_Pair @ v_c____ @ v_d____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ v_P____ ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ v_c____ @ v_d____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_HOL_OIf @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ v_h____ @ tc_nat @ ( tc_fun @ tc_nat @ tc_bool ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ v_n____ @ tc_Arrow__Order__Mirabelle_Oindi @ tc_nat @ tc_bool ) @ tc_bool @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ ( c_COMBC @ ( c_COMBB @ c_Arrow__Order__Mirabelle_Omktop @ v_P____ @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ v_e____ @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_HOL_OIf @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ ( c_COMBC @ ( c_COMBB @ ( c_fequal @ tc_nat ) @ v_h____ @ tc_nat @ ( tc_fun @ tc_nat @ tc_bool ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ v_n____ @ tc_Arrow__Order__Mirabelle_Oindi @ tc_nat @ tc_bool ) @ tc_bool @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ ( c_COMBC @ ( c_COMBC @ ( c_COMBB @ c_Arrow__Order__Mirabelle_Oabove @ v_P____ @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ v_c____ @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ v_e____ @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ ( c_COMBC @ ( c_COMBB @ c_Arrow__Order__Mirabelle_Omkbot @ v_P____ @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ v_e____ @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_1) ).
thf(33,axiom,
! [V_S: $i,V_x: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_S @ V_x ) )
| ~ ( c_in @ V_x @ V_S @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_0) ).
thf(34,axiom,
! [V_x: $i,V_S: $i,T_a: $i] :
( ( c_in @ V_x @ V_S @ T_a )
| ~ ( hBOOL @ ( hAPP @ V_S @ V_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_1) ).
thf(35,axiom,
! [V_a: $i,V_b: $i,T_a: $i,T_b: $i,V_a_H: $i,V_b_H: $i] :
( ( ( c_Pair @ V_a @ V_b @ T_a @ T_b )
!= ( c_Pair @ V_a_H @ V_b_H @ T_a @ T_b ) )
| ( V_a = V_a_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Pair__eq_0) ).
thf(36,axiom,
! [V_a: $i,V_b: $i,T_a: $i,T_b: $i,V_a_H: $i,V_b_H: $i] :
( ( ( c_Pair @ V_a @ V_b @ T_a @ T_b )
!= ( c_Pair @ V_a_H @ V_b_H @ T_a @ T_b ) )
| ( V_b = V_b_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Pair__eq_1) ).
thf(37,axiom,
! [V_a: $i,T_a: $i,V_r: $i,V_A: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_a @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_a @ V_A @ T_a )
| ~ ( c_Relation_Orefl__on @ V_A @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__onD_0) ).
thf(38,axiom,
! [V_x: $i,V_A: $i,T_a: $i,V_y: $i,V_r: $i] :
( ( c_in @ V_x @ V_A @ T_a )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Relation_Orefl__on @ V_A @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__onD1_0) ).
thf(39,axiom,
! [V_y: $i,V_A: $i,T_a: $i,V_x: $i,V_r: $i] :
( ( c_in @ V_y @ V_A @ T_a )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Relation_Orefl__on @ V_A @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__onD2_0) ).
thf(40,axiom,
! [V_x: $i,T_a: $i,V_r: $i,V_A: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_x @ V_A @ T_a )
| ~ ( c_Relation_Orefl__on @ V_A @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__def_1) ).
thf(41,axiom,
! [V_xa: $i,V_x: $i,T_a: $i,V_r: $i,V_A: $i] :
( ( c_in @ ( c_Pair @ V_xa @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ( c_in @ ( c_Pair @ V_x @ V_xa @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ( V_x = V_xa )
| ~ ( c_in @ V_xa @ V_A @ T_a )
| ~ ( c_in @ V_x @ V_A @ T_a )
| ~ ( c_Relation_Ototal__on @ V_A @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_total__on__def_0) ).
thf(42,axiom,
! [V_a: $i,V_A: $i,T_a: $i,V_b: $i,T_b: $i,V_B: $i] :
( ( c_in @ V_a @ V_A @ T_a )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ ( c_Product__Type_OSigma @ V_A @ V_B @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SigmaD1_0) ).
thf(43,axiom,
! [V_b: $i,V_B: $i,V_a: $i,T_b: $i,T_a: $i,V_A: $i] :
( ( c_in @ V_b @ ( hAPP @ V_B @ V_a ) @ T_b )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ ( c_Product__Type_OSigma @ V_A @ V_B @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SigmaD2_0) ).
thf(44,axiom,
! [V_a: $i,V_r: $i,T_a: $i,T_b: $i,V_b: $i] :
( ( c_in @ V_a @ ( c_Relation_ODomain @ V_r @ T_a @ T_b ) @ T_a )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ V_r @ ( tc_prod @ T_a @ T_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DomainI_0) ).
thf(45,axiom,
! [V_a: $i,V_r: $i,T_a: $i,T_b: $i,V_x: $i] :
( ( c_in @ V_a @ ( c_Relation_ODomain @ V_r @ T_a @ T_b ) @ T_a )
| ~ ( c_in @ ( c_Pair @ V_a @ V_x @ T_a @ T_b ) @ V_r @ ( tc_prod @ T_a @ T_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__iff_1) ).
thf(46,axiom,
! [V_b: $i,V_r: $i,T_a: $i,T_b: $i,V_a: $i] :
( ( c_in @ V_b @ ( c_Relation_ORange @ V_r @ T_a @ T_b ) @ T_b )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ V_r @ ( tc_prod @ T_a @ T_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_RangeI_0) ).
thf(47,axiom,
! [V_a: $i,V_r: $i,T_b: $i,T_a: $i,V_x: $i] :
( ( c_in @ V_a @ ( c_Relation_ORange @ V_r @ T_b @ T_a ) @ T_a )
| ~ ( c_in @ ( c_Pair @ V_x @ V_a @ T_b @ T_a ) @ V_r @ ( tc_prod @ T_b @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__iff_1) ).
thf(48,axiom,
! [V_x: $i,V_A: $i,T_a: $i,V_y: $i,V_r: $i] :
( ( c_in @ V_x @ V_A @ T_a )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__eq__iff_1) ).
thf(49,axiom,
! [V_y: $i,V_A: $i,T_a: $i,V_x: $i,V_r: $i] :
( ( c_in @ V_y @ V_A @ T_a )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__eq__iff_2) ).
thf(50,axiom,
! [V_x: $i,T_a: $i,V_A: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_x @ T_a @ T_a ) @ ( c_Relation_OId__on @ V_A @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_x @ V_A @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__on__eqI_0) ).
thf(51,axiom,
! [V_x: $i,V_A: $i,T_a: $i,V_y: $i] :
( ( c_in @ V_x @ V_A @ T_a )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Relation_OId__on @ V_A @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__on__iff_1) ).
thf(52,axiom,
! [V_b: $i,V_r: $i,V_A: $i,T_b: $i,T_a: $i,V_x: $i] :
( ( c_in @ V_b @ ( c_Relation_OImage @ V_r @ V_A @ T_b @ T_a ) @ T_a )
| ~ ( c_in @ ( c_Pair @ V_x @ V_b @ T_b @ T_a ) @ V_r @ ( tc_prod @ T_b @ T_a ) )
| ~ ( c_in @ V_x @ V_A @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__iff_2) ).
thf(53,axiom,
! [V_b: $i,V_r: $i,V_A: $i,T_a: $i,T_b: $i,V_a: $i] :
( ( c_in @ V_b @ ( c_Relation_OImage @ V_r @ V_A @ T_a @ T_b ) @ T_b )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ V_r @ ( tc_prod @ T_a @ T_b ) )
| ~ ( c_in @ V_a @ V_A @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__ImageI_0) ).
thf(54,axiom,
! [V_y: $i,V_r: $i,T_a: $i,V_a: $i] :
( ( c_in @ V_y @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a )
| ~ ( c_in @ ( c_Pair @ V_y @ V_a @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_a @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_Ocases_0) ).
thf(55,axiom,
! [V_a: $i,V_r: $i,T_a: $i,V_b: $i] :
( ( c_in @ V_a @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_b @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__downward_0) ).
thf(56,axiom,
! [V_a: $i,V_b: $i,T_a: $i,T_b: $i,V_A: $i,V_B: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ ( c_Product__Type_OSigma @ V_A @ V_B @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) )
| ~ ( c_in @ V_b @ ( hAPP @ V_B @ V_a ) @ T_b )
| ~ ( c_in @ V_a @ V_A @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SigmaI_0) ).
thf(57,axiom,
! [V_a: $i,V_b: $i,T_a: $i,T_b: $i,V_A: $i,V_B: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ ( c_Product__Type_OSigma @ V_A @ V_B @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) )
| ~ ( c_in @ V_b @ ( hAPP @ V_B @ V_a ) @ T_b )
| ~ ( c_in @ V_a @ V_A @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__Sigma__iff_2) ).
thf(58,axiom,
! [V_a: $i,V_b: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_b @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1 @ V_a @ V_b ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( V_a = V_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__Lin_1) ).
thf(59,axiom,
! [V_x: $i,V_y: $i,V_L: $i,V_z: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ V_L @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( V_x = V_z )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omkbot @ V_L ) @ V_z ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mkbot_2) ).
thf(60,axiom,
! [V_xa: $i,V_x: $i,V_L: $i] :
( ( V_xa = V_x )
| ( V_xa = V_x )
| ( c_in @ ( c_Pair @ V_xa @ V_x @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omktop @ V_L ) @ V_x ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mktop_4) ).
thf(61,axiom,
! [V_x: $i,V_y: $i,V_L: $i,V_z: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omkbot @ V_L ) @ V_z ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ V_L @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( V_x = V_z )
| ( V_y = V_z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mkbot_3) ).
thf(62,axiom,
! [V_x: $i,V_y: $i,V_L: $i,V_z: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omkbot @ V_L ) @ V_z ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ V_L @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( V_x = V_y )
| ( V_y = V_z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mkbot_5) ).
thf(63,axiom,
! [V_xa: $i,V_x: $i,V_L: $i] :
~ ( c_in @ ( c_Pair @ V_xa @ V_x @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omkbot @ V_L ) @ V_x ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mkbot_0) ).
thf(64,axiom,
! [V_x: $i,V_L: $i] :
~ ( c_in @ ( c_Pair @ V_x @ V_x @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omkbot @ V_L ) @ V_x ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mkbot_1) ).
thf(65,axiom,
! [V_x: $i,V_y: $i,V_L: $i] :
( ( V_x = V_y )
| ( V_y = V_x )
| ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omkbot @ V_L ) @ V_x ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mkbot_4) ).
thf(66,axiom,
! [V_x: $i,V_y: $i,V_L: $i,V_z: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ V_L @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( V_y = V_z )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omktop @ V_L ) @ V_z ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mktop_2) ).
thf(67,axiom,
! [V_x: $i,V_y: $i,V_L: $i] :
~ ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omktop @ V_L ) @ V_x ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mktop_0) ).
thf(68,axiom,
! [V_x: $i,V_L: $i] :
~ ( c_in @ ( c_Pair @ V_x @ V_x @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omktop @ V_L ) @ V_x ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mktop_1) ).
thf(69,axiom,
! [V_x: $i,V_y: $i,V_L: $i,V_z: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omktop @ V_L ) @ V_z ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ V_L @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( V_y = V_z )
| ( V_x = V_z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mktop_3) ).
thf(70,axiom,
! [V_x: $i,V_y: $i,V_L: $i,V_z: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omktop @ V_L ) @ V_z ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ V_L @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( V_x = V_y )
| ( V_x = V_z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mktop_5) ).
thf(71,axiom,
! [V_a: $i,T_a: $i] : ( c_in @ ( c_Pair @ V_a @ V_a @ T_a @ T_a ) @ ( c_Relation_OId @ T_a ) @ ( tc_prod @ T_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IdI_0) ).
thf(72,axiom,
! [V_x: $i,T_a: $i] : ( c_in @ ( c_Pair @ V_x @ V_x @ T_a @ T_a ) @ ( c_Relation_OId @ T_a ) @ ( tc_prod @ T_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pair__in__Id__conv_1) ).
thf(73,axiom,
! [V_a: $i,V_c: $i,T_a: $i,V_r: $i,V_b: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_b @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__trans_0) ).
thf(74,axiom,
! [V_a: $i,V_c: $i,T_a: $i,V_R: $i,V_b: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_b @ V_c @ T_a @ T_a ) @ V_R @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_R @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_r__r__into__trancl_0) ).
thf(75,axiom,
! [V_a: $i,V_c: $i,T_a: $i,T_c: $i,V_r: $i,V_s: $i,T_b: $i,V_b: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_c ) @ ( c_Relation_Orel__comp @ V_r @ V_s @ T_a @ T_b @ T_c ) @ ( tc_prod @ T_a @ T_c ) )
| ~ ( c_in @ ( c_Pair @ V_b @ V_c @ T_b @ T_c ) @ V_s @ ( tc_prod @ T_b @ T_c ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ V_r @ ( tc_prod @ T_a @ T_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__compI_0) ).
thf(76,axiom,
! [V_b: $i,V_a: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_b @ V_a @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Relation_Osym @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_symD_0) ).
thf(77,axiom,
! [V_y: $i,V_x: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_y @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Relation_Osym @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__def_0) ).
thf(78,axiom,
! [V_f: $i,V_x: $i,V_y: $i,T_b: $i,V_r: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ ( hAPP @ V_f @ V_x ) @ ( hAPP @ V_f @ V_y ) @ T_b @ T_b ) @ V_r @ ( tc_prod @ T_b @ T_b ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Relation_Oinv__image @ V_r @ V_f @ T_b @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__inv__image_0) ).
thf(79,axiom,
! [V_x: $i,V_y: $i,T_a: $i,V_r: $i,V_f: $i,T_b: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Relation_Oinv__image @ V_r @ V_f @ T_b @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ ( hAPP @ V_f @ V_x ) @ ( hAPP @ V_f @ V_y ) @ T_b @ T_b ) @ V_r @ ( tc_prod @ T_b @ T_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__inv__image_1) ).
thf(80,axiom,
! [V_a: $i,T_a: $i,V_r: $i] :
( ~ ( c_in @ ( c_Pair @ V_a @ V_a @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__irrefl_0) ).
thf(81,axiom,
! [V_x: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Nitpick_Orefl_H @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nitpick_Orefl_H__def_0) ).
thf(82,axiom,
! [V_a: $i,V_b: $i,T_a: $i] :
( ( V_a = V_b )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Relation_OId @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pair__in__Id__conv_0) ).
thf(83,axiom,
! [V_f: $i,V_r: $i,V_x: $i,T_a: $i,T_b: $i,V_g: $i,V_y: $i] :
( ( ( c_Recdef_Ocut @ V_f @ V_r @ V_x @ T_a @ T_b )
!= ( c_Recdef_Ocut @ V_g @ V_r @ V_x @ T_a @ T_b ) )
| ( ( hAPP @ V_f @ V_y )
= ( hAPP @ V_g @ V_y ) )
| ~ ( c_in @ ( c_Pair @ V_y @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cuts__eq_0) ).
thf(84,axiom,
! [V_x: $i,V_y: $i,T_a: $i,V_A: $i] :
( ( V_x = V_y )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Relation_OId__on @ V_A @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__on__iff_0) ).
thf(85,axiom,
! [V_f: $i,V_y: $i,V_z: $i,T_a: $i,V_r: $i,T_b: $i] :
( ( ( hAPP @ V_f @ V_y )
= ( hAPP @ V_f @ V_z ) )
| ~ ( c_in @ ( c_Pair @ V_y @ V_z @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Equiv__Relations_Ocongruent @ V_r @ V_f @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_congruent_Ocongruent_0) ).
thf(86,axiom,
! [V_a: $i,V_b: $i,T_a: $i,V_r: $i] :
( ( V_a = V_b )
| ~ ( c_in @ ( c_Pair @ V_b @ V_a @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Relation_Oantisym @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisymD_0) ).
thf(87,axiom,
! [V_x: $i,V_y: $i,T_a: $i,V_r: $i] :
( ( V_x = V_y )
| ~ ( c_in @ ( c_Pair @ V_y @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Relation_Oantisym @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__def_0) ).
thf(88,axiom,
! [V_x: $i,V_a: $i,T_a: $i,V_r: $i] :
( ~ ( c_in @ ( c_Pair @ V_x @ V_a @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__asym_0) ).
thf(89,axiom,
! [V_x: $i,T_a: $i,V_R: $i] : ( c_in @ ( c_Pair @ V_x @ V_x @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__eq__or__trancl_1) ).
thf(90,axiom,
! [V_a: $i,T_a: $i,V_r: $i] : ( c_in @ ( c_Pair @ V_a @ V_a @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl_Ortrancl__refl_0) ).
thf(91,axiom,
! [V_a: $i,V_c: $i,T_a: $i,V_r: $i,V_b: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_b @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__trans_0) ).
thf(92,axiom,
! [V_a: $i,V_b: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl_Or__into__trancl_0) ).
thf(93,axiom,
! [V_a: $i,V_c: $i,T_a: $i,V_r: $i,V_b: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_b @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rtrancl__into__rtrancl_0) ).
thf(94,axiom,
! [V_a: $i,V_c: $i,T_a: $i,V_r: $i,V_b: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_b @ V_c @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl_Ortrancl__into__rtrancl_0) ).
thf(95,axiom,
! [V_a: $i,V_c: $i,T_a: $i,V_r: $i,V_b: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_b @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__into__trancl2_0) ).
thf(96,axiom,
! [V_a: $i,V_c: $i,T_a: $i,V_r: $i,V_b: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_b @ V_c @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__into__trancl_0) ).
thf(97,axiom,
! [V_x: $i,T_a: $i,V_r: $i] :
( ~ ( c_in @ ( c_Pair @ V_x @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Relation_Oirrefl @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_irrefl__def_0) ).
thf(98,axiom,
! [V_b: $i,V_a: $i,T_b: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_b @ V_a @ T_b @ T_a ) @ V_r @ ( tc_prod @ T_b @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ ( c_Relation_Oconverse @ V_r @ T_b @ T_a ) @ ( tc_prod @ T_a @ T_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converseD_0) ).
thf(99,axiom,
! [V_b: $i,V_a: $i,T_b: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_b @ V_a @ T_b @ T_a ) @ ( c_Relation_Oconverse @ V_r @ T_a @ T_b ) @ ( tc_prod @ T_b @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ V_r @ ( tc_prod @ T_a @ T_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converseI_0) ).
thf(100,axiom,
! [V_a: $i,V_b: $i,T_a: $i,T_b: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ ( c_Relation_Oconverse @ V_r @ T_b @ T_a ) @ ( tc_prod @ T_a @ T_b ) )
| ~ ( c_in @ ( c_Pair @ V_b @ V_a @ T_b @ T_a ) @ V_r @ ( tc_prod @ T_b @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__iff_1) ).
thf(101,axiom,
! [V_a: $i,V_c: $i,T_a: $i,V_r: $i,V_b: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_b @ V_c @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Relation_Otrans @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_transD_0) ).
thf(102,axiom,
! [V_x: $i,V_z: $i,T_a: $i,V_r: $i,V_y: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_z @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_y @ V_z @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Relation_Otrans @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__def_0) ).
thf(103,axiom,
! [V_x: $i,V_y: $i,T_a: $i,T_b: $i,V_R: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_b ) @ V_R @ ( tc_prod @ T_a @ T_b ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_FunDef_Oin__rel @ V_R @ T_a @ T_b ) @ V_x ) @ V_y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__rel__def_0) ).
thf(104,axiom,
! [V_R: $i,T_a: $i,T_b: $i,V_x: $i,V_y: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_FunDef_Oin__rel @ V_R @ T_a @ T_b ) @ V_x ) @ V_y ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_b ) @ V_R @ ( tc_prod @ T_a @ T_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__rel__def_1) ).
thf(105,axiom,
! [V_f: $i,V_r: $i,V_a: $i,T_a: $i,T_b: $i,V_x: $i] :
( ( ( hAPP @ ( c_Recdef_Ocut @ V_f @ V_r @ V_a @ T_a @ T_b ) @ V_x )
= ( hAPP @ V_f @ V_x ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_a @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cut__apply_0) ).
thf(106,axiom,
! [V_f: $i,V_R: $i,V_a: $i,T_a: $i,T_b: $i,V_x: $i] :
( ( ( hAPP @ ( c_Recdef_Ocut @ V_f @ V_R @ V_a @ T_a @ T_b ) @ V_x )
= ( hAPP @ V_f @ V_x ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_a @ T_a @ T_a ) @ V_R @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tfl__cut__apply_0) ).
thf(107,axiom,
! [V_y: $i,V_z: $i,V_x: $i,T_a: $i,T_b: $i,V_r: $i] :
( ( V_y = V_z )
| ~ ( c_in @ ( c_Pair @ V_x @ V_z @ T_a @ T_b ) @ V_r @ ( tc_prod @ T_a @ T_b ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_b ) @ V_r @ ( tc_prod @ T_a @ T_b ) )
| ~ ( c_Relation_Osingle__valued @ V_r @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_single__valuedD_0) ).
thf(108,axiom,
! [V_f: $i,V_y1: $i,V_y2: $i,V_z1: $i,V_z2: $i,T_b: $i,V_r2: $i,T_a: $i,V_r1: $i,T_c: $i] :
( ( ( hAPP @ ( hAPP @ V_f @ V_y1 ) @ V_y2 )
= ( hAPP @ ( hAPP @ V_f @ V_z1 ) @ V_z2 ) )
| ~ ( c_in @ ( c_Pair @ V_y2 @ V_z2 @ T_b @ T_b ) @ V_r2 @ ( tc_prod @ T_b @ T_b ) )
| ~ ( c_in @ ( c_Pair @ V_y1 @ V_z1 @ T_a @ T_a ) @ V_r1 @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Equiv__Relations_Ocongruent2 @ V_r1 @ V_r2 @ V_f @ T_a @ T_b @ T_c ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_congruent2_Ocongruent2_0) ).
thf(109,axiom,
! [V_z: $i,V_c: $i,T_b: $i,T_c: $i,T_a: $i,V_a: $i,V_b: $i] :
( ( c_in @ V_z @ ( hAPP @ ( c_split @ V_c @ T_b @ T_c @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Pair @ V_a @ V_b @ T_b @ T_c ) ) @ T_a )
| ~ ( c_in @ V_z @ ( hAPP @ ( hAPP @ V_c @ V_a ) @ V_b ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__splitI_0) ).
thf(110,axiom,
! [V_a: $i,V_r: $i,T_a: $i,T_b: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XRange__iff__1__1 @ V_a @ V_r @ T_a @ T_b ) @ V_a @ T_b @ T_a ) @ V_r @ ( tc_prod @ T_b @ T_a ) )
| ~ ( c_in @ V_a @ ( c_Relation_ORange @ V_r @ T_b @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__iff_0) ).
thf(111,axiom,
! [V_x: $i,V_y: $i,T_a: $i,V_R: $i] :
( ( V_x = V_y )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ( c_in @ V_x @ ( c_Relation_ODomain @ V_R @ T_a @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Not__Domain__rtrancl_0) ).
thf(112,axiom,
! [V_A: $i,V_b: $i,V_r: $i,T_b: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XImage__iff__1__1 @ V_A @ V_b @ V_r @ T_b @ T_a ) @ V_b @ T_b @ T_a ) @ V_r @ ( tc_prod @ T_b @ T_a ) )
| ~ ( c_in @ V_b @ ( c_Relation_OImage @ V_r @ V_A @ T_b @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__iff_1) ).
thf(113,axiom,
! [V_a: $i,V_r: $i,T_a: $i,T_b: $i] :
( ( c_in @ ( c_Pair @ V_a @ ( c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1 @ V_a @ V_r @ T_a @ T_b ) @ T_a @ T_b ) @ V_r @ ( tc_prod @ T_a @ T_b ) )
| ~ ( c_in @ V_a @ ( c_Relation_ODomain @ V_r @ T_a @ T_b ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__iff_0) ).
thf(114,axiom,
! [V_y: $i,V_Q: $i,T_a: $i,V_r: $i,V_xa: $i] :
( ~ ( c_in @ V_y @ V_Q @ T_a )
| ~ ( c_in @ ( c_Pair @ V_y @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 @ V_Q @ V_r @ T_a ) @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_xa @ V_Q @ T_a )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__eq__minimal_1) ).
thf(115,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 ) )
| ~ ( c_in @ ( c_Pair @ V_y @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ V_P @ V_r @ T_a ) @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_a @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__induct_1) ).
thf(116,axiom,
! [V_P: $i,V_x: $i,V_ya: $i,V_r: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ( c_in @ V_ya @ ( c_Wellfounded_Oacc @ V_r @ t_a ) @ t_a )
| ~ ( c_in @ ( c_Pair @ V_ya @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ V_P @ V_r ) @ t_a @ t_a ) @ V_r @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ V_x @ ( c_Wellfounded_Oacc @ V_r @ t_a ) @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_Oinduct_0) ).
thf(117,axiom,
! [V_a: $i,V_r: $i,T_a: $i,T_b: $i] :
( ( c_in @ ( c_Pair @ V_a @ ( c_ATP__Linkup_Osko__Relation__XDomainE__1__1 @ V_a @ V_r @ T_a @ T_b ) @ T_a @ T_b ) @ V_r @ ( tc_prod @ T_a @ T_b ) )
| ~ ( c_in @ V_a @ ( c_Relation_ODomain @ V_r @ T_a @ T_b ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DomainE_0) ).
thf(118,axiom,
! [V_f: $i,V_a: $i,V_b: $i,T_a: $i,T_b: $i,T_c: $i,V_A: $i] :
( ( c_in @ ( hAPP @ ( hAPP @ V_f @ V_a ) @ V_b ) @ ( c_Set_Oimage @ ( c_split @ V_f @ T_a @ T_b @ T_c ) @ V_A @ ( tc_prod @ T_a @ T_b ) @ T_c ) @ T_c )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ V_A @ ( tc_prod @ T_a @ T_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pair__imageI_0) ).
thf(119,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 ) )
| ~ ( c_in @ ( c_Pair @ V_y @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ V_P @ V_r ) @ t_a @ t_a ) @ V_r @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ V_x @ ( c_Wellfounded_Oacc @ V_r @ t_a ) @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_Oinducts_1) ).
thf(120,axiom,
! [V_x: $i,V_R: $i,T_a: $i] :
( ( c_in @ V_x @ ( c_Relation_ODomain @ V_R @ T_a @ T_a ) @ T_a )
| ( c_in @ ( c_Pair @ V_x @ V_x @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Not__Domain__rtrancl_1) ).
thf(121,axiom,
! [V_P: $i,V_x: $i,V_ya: $i,V_r: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ( c_in @ V_ya @ ( c_Wellfounded_Oacc @ V_r @ t_a ) @ t_a )
| ~ ( c_in @ ( c_Pair @ V_ya @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ V_P @ V_r ) @ t_a @ t_a ) @ V_r @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ V_x @ ( c_Wellfounded_Oacc @ V_r @ t_a ) @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_Oinducts_0) ).
thf(122,axiom,
! [V_b: $i,V_r: $i,T_a: $i,V_a: $i] :
( ( c_in @ V_b @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a )
| ~ ( c_in @ ( c_Pair @ V_b @ V_a @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_a @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__downwards_0) ).
thf(123,axiom,
! [V_b: $i,V_r: $i,T_a: $i,V_a: $i] :
( ( c_in @ V_b @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a )
| ~ ( c_in @ V_a @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a )
| ~ ( c_in @ ( c_Pair @ V_b @ V_a @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__downwards__aux_0) ).
thf(124,axiom,
! [V_x: $i,V_r: $i,T_a: $i] :
( ( c_in @ V_x @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a )
| ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1 @ V_r @ V_x @ T_a ) @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_OaccI_0) ).
thf(125,axiom,
! [V_b: $i,V_r: $i,T_a: $i,T_b: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XRangeE__1__1 @ V_b @ V_r @ T_a @ T_b ) @ V_b @ T_b @ T_a ) @ V_r @ ( tc_prod @ T_b @ T_a ) )
| ~ ( c_in @ V_b @ ( c_Relation_ORange @ V_r @ T_b @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_RangeE_0) ).
thf(126,axiom,
! [V_y: $i,V_Q: $i,T_a: $i,V_R: $i,V_x: $i] :
( ~ ( c_in @ V_y @ V_Q @ T_a )
| ~ ( c_in @ ( c_Pair @ V_y @ ( c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 @ V_Q @ V_R @ T_a ) @ T_a @ T_a ) @ V_R @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_x @ V_Q @ T_a )
| ~ ( c_Wellfounded_Owf @ V_R @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wfE__min_1) ).
thf(127,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 ) )
| ~ ( c_in @ ( c_Pair @ V_y @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ V_P @ V_r ) @ t_a @ t_a ) @ V_r @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ V_x @ ( c_Wellfounded_Oacc @ V_r @ t_a ) @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_Oinduct_1) ).
thf(128,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 ) )
| ~ ( c_in @ ( c_Pair @ V_y @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ V_P @ V_r @ T_a ) @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_a @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__induct__rule_1) ).
thf(129,axiom,
! [V_R: $i,V_x: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1 @ V_R @ V_x @ T_a ) @ V_x @ T_a @ T_a ) @ V_R @ ( tc_prod @ T_a @ T_a ) )
| ( c_in @ V_x @ ( c_Wellfounded_Oacc @ V_R @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__acc__down_0) ).
thf(130,axiom,
! [V_A: $i,V_b: $i,V_r: $i,T_b: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XImageE__1__1 @ V_A @ V_b @ V_r @ T_b @ T_a ) @ V_b @ T_b @ T_a ) @ V_r @ ( tc_prod @ T_b @ T_a ) )
| ~ ( c_in @ V_b @ ( c_Relation_OImage @ V_r @ V_A @ T_b @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ImageE_0) ).
thf(131,axiom,
c_Arrow__Order__Mirabelle_Ounanimity @ v_F,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_u_0) ).
thf(132,axiom,
c_Arrow__Order__Mirabelle_OIIA @ v_F,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_assms_I3_J_0) ).
thf(133,axiom,
! [V_r: $i,T_a: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ T_a )
= ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__idemp_0) ).
thf(134,axiom,
! [V_R: $i,T_a: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( c_Transitive__Closure_Otrancl @ V_R @ T_a ) @ T_a )
= ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__rtrancl__absorb_0) ).
thf(135,axiom,
! [V_P: $i,V_a: $i,V_r: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ V_P @ V_r @ T_a ) @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a )
| ~ ( c_in @ V_a @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__induct_0) ).
thf(136,axiom,
! [V_r: $i,T_a: $i,V_A: $i] :
( ( c_Relation_Otrans @ V_r @ T_a )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv_Otrans_0) ).
thf(137,axiom,
! [V_A: $i,V_r: $i,T_a: $i] :
( ( c_Relation_Ototal__on @ V_A @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a )
| ~ ( c_Relation_Ototal__on @ V_A @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_total__on__converse_1) ).
thf(138,axiom,
! [V_A: $i,V_r: $i,T_a: $i] :
( ( c_Relation_Ototal__on @ V_A @ V_r @ T_a )
| ~ ( c_Relation_Ototal__on @ V_A @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_total__on__converse_0) ).
thf(139,axiom,
! [V_r: $i,T_b: $i,T_a: $i] :
( ( c_Relation_ORange @ V_r @ T_b @ T_a )
= ( c_Relation_ODomain @ ( c_Relation_Oconverse @ V_r @ T_b @ T_a ) @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__def_0) ).
thf(140,axiom,
! [V_r: $i,T_a: $i] :
( ( c_Transitive__Closure_Otrancl @ V_r @ T_a )
= ( c_Relation_Orel__comp @ V_r @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ T_a @ T_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__unfold__left_0) ).
thf(141,axiom,
! [V_r: $i,T_a: $i] :
( ( c_Transitive__Closure_Otrancl @ V_r @ T_a )
= ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ V_r @ T_a @ T_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__unfold__right_0) ).
thf(142,axiom,
! [V_r: $i,T_b: $i,T_a: $i] :
( ( c_Relation_ODomain @ ( c_Relation_Oconverse @ V_r @ T_b @ T_a ) @ T_a @ T_b )
= ( c_Relation_ORange @ V_r @ T_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__converse_0) ).
thf(143,axiom,
! [V_r2: $i,V_f: $i,V_a: $i,T_b: $i,T_c: $i,V_A: $i,T_a: $i,V_r1: $i] :
( ( c_Equiv__Relations_Ocongruent @ V_r2 @ ( hAPP @ V_f @ V_a ) @ T_b @ T_c )
| ~ ( c_in @ V_a @ V_A @ T_a )
| ~ ( c_Equiv__Relations_Ocongruent2 @ V_r1 @ V_r2 @ V_f @ T_a @ T_b @ T_c )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r1 @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_congruent2__implies__congruent_0) ).
thf(144,axiom,
! [V_x: $i,V_r: $i,T_a: $i] :
( ( c_in @ V_x @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a )
| ~ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1 @ V_r @ V_x @ T_a ) @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_OaccI_1) ).
thf(145,axiom,
! [V_r: $i,T_a: $i,V_A: $i] :
( ( c_Relation_Osym @ V_r @ T_a )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv_Osym_0) ).
thf(146,axiom,
! [V_Q: $i,V_R: $i,T_a: $i,V_x: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 @ V_Q @ V_R @ T_a ) @ V_Q @ T_a )
| ~ ( c_in @ V_x @ V_Q @ T_a )
| ~ ( c_Wellfounded_Owf @ V_R @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wfE__min_0) ).
thf(147,axiom,
! [V_r: $i,T_a: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a )
= ( c_Relation_Oconverse @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ T_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__converse_0) ).
thf(148,axiom,
! [V_A: $i,V_r: $i,T_a: $i] :
( ( c_Relation_Orefl__on @ V_A @ V_r @ T_a )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv_Orefl__on_0) ).
thf(149,axiom,
! [V_P: $i,V_x: $i,V_r: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ V_P @ V_r ) ) )
| ~ ( c_in @ V_x @ ( c_Wellfounded_Oacc @ V_r @ t_a ) @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_Oinduct_2) ).
thf(150,axiom,
! [V_r: $i,T_a: $i] :
( ( c_Relation_Oantisym @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a )
| ~ ( c_Relation_Oantisym @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__converse_1) ).
thf(151,axiom,
! [V_r: $i,T_a: $i] :
( ( c_Relation_Oantisym @ V_r @ T_a )
| ~ ( c_Relation_Oantisym @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__converse_0) ).
thf(152,axiom,
! [V_R: $i,T_a: $i] :
( ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) @ T_a @ T_a @ T_a )
= ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__idemp__self__comp_0) ).
thf(153,axiom,
! [V_r: $i,T_a: $i,V_A: $i] :
( ( ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ V_r @ T_a @ T_a @ T_a )
= V_r )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__comp__eq_0) ).
thf(154,axiom,
! [T_a: $i] : ( c_Relation_Otrans @ ( c_Relation_OId @ T_a ) @ T_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__Id_0) ).
thf(155,axiom,
! [V_r: $i,T_a: $i,T_b: $i] :
( ( c_Relation_Oconverse @ ( c_Relation_Oconverse @ V_r @ T_a @ T_b ) @ T_b @ T_a )
= V_r ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__converse_0) ).
thf(156,axiom,
! [V_r: $i,V_s: $i,T_a: $i,T_b: $i,T_c: $i] :
( ( c_Relation_Osingle__valued @ ( c_Relation_Orel__comp @ V_r @ V_s @ T_a @ T_b @ T_c ) @ T_a @ T_c )
| ~ ( c_Relation_Osingle__valued @ V_s @ T_b @ T_c )
| ~ ( c_Relation_Osingle__valued @ V_r @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_single__valued__rel__comp_0) ).
thf(157,axiom,
! [V_A: $i,T_a: $i] :
( ( c_Relation_ORange @ ( c_Relation_OId__on @ V_A @ T_a ) @ T_a @ T_a )
= V_A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__Id__on_0) ).
thf(158,axiom,
! [V_Q: $i,V_r: $i,T_a: $i,V_xa: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 @ V_Q @ V_r @ T_a ) @ V_Q @ T_a )
| ~ ( c_in @ V_xa @ V_Q @ T_a )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__eq__minimal_0) ).
thf(159,axiom,
! [V_r: $i,T_a: $i,T_b: $i] :
( ( c_Relation_ORange @ ( c_Relation_Oconverse @ V_r @ T_a @ T_b ) @ T_b @ T_a )
= ( c_Relation_ODomain @ V_r @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__converse_0) ).
thf(160,axiom,
! [T_a: $i] : ( c_Relation_Oantisym @ ( c_Relation_OId @ T_a ) @ T_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__Id_0) ).
thf(161,axiom,
! [V_r: $i,T_a: $i] :
( ( ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ V_r @ T_a @ T_a @ T_a )
!= V_r )
| ( c_Equiv__Relations_Oequiv @ ( c_Relation_ODomain @ V_r @ T_a @ T_a ) @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comp__equivI_0) ).
thf(162,axiom,
! [V_A: $i,T_a: $i] :
( ( c_Relation_Oconverse @ ( c_Relation_OId__on @ V_A @ T_a ) @ T_a @ T_a )
= ( c_Relation_OId__on @ V_A @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__Id__on_0) ).
thf(163,axiom,
! [V_r: $i,V_f: $i,T_a: $i,T_b: $i] :
( ( c_Relation_Otrans @ ( c_Relation_Oinv__image @ V_r @ V_f @ T_a @ T_b ) @ T_b )
| ~ ( c_Relation_Otrans @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__inv__image_0) ).
thf(164,axiom,
! [V_r: $i,T_a: $i] :
( ( c_Transitive__Closure_Otrancl @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a )
= ( c_Relation_Oconverse @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ T_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__converse_0) ).
thf(165,axiom,
! [V_R: $i,V_f: $i,T_b: $i,T_a: $i] :
( ( c_Relation_Oconverse @ ( c_Relation_Oinv__image @ V_R @ V_f @ T_b @ T_a ) @ T_a @ T_a )
= ( c_Relation_Oinv__image @ ( c_Relation_Oconverse @ V_R @ T_b @ T_b ) @ V_f @ T_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__inv__image_0) ).
thf(166,axiom,
! [V_R: $i,V_S: $i,T_a: $i,T_d: $i,T_c: $i,V_T: $i,T_b: $i] :
( ( c_Relation_Orel__comp @ ( c_Relation_Orel__comp @ V_R @ V_S @ T_a @ T_d @ T_c ) @ V_T @ T_a @ T_c @ T_b )
= ( c_Relation_Orel__comp @ V_R @ ( c_Relation_Orel__comp @ V_S @ V_T @ T_d @ T_c @ T_b ) @ T_a @ T_d @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_O__assoc_0) ).
thf(167,axiom,
! [V_r: $i,T_a: $i] :
( ( c_Wellfounded_Owf @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ T_a )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__trancl_0) ).
thf(168,axiom,
! [T_a: $i] :
( ( c_Relation_Oconverse @ ( c_Relation_OId @ T_a ) @ T_a @ T_a )
= ( c_Relation_OId @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__Id_0) ).
thf(169,axiom,
! [V_r: $i,T_a: $i] :
( ( c_Relation_Otrans @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a )
| ~ ( c_Relation_Otrans @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__converse_1) ).
thf(170,axiom,
! [V_r: $i,T_a: $i] :
( ( c_Relation_Otrans @ V_r @ T_a )
| ~ ( c_Relation_Otrans @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__converse_0) ).
thf(171,axiom,
! [V_r: $i,T_a: $i] : ( c_Relation_Otrans @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ T_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__rtrancl_0) ).
thf(172,axiom,
! [V_R: $i,T_a: $i] :
( ( c_Transitive__Closure_Otrancl @ ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) @ T_a )
= ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__trancl__absorb_0) ).
thf(173,axiom,
! [V_r: $i,V_f: $i,T_a: $i,T_b: $i] :
( ( c_Relation_Osym @ ( c_Relation_Oinv__image @ V_r @ V_f @ T_a @ T_b ) @ T_b )
| ~ ( c_Relation_Osym @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__inv__image_0) ).
thf(174,axiom,
! [V_r: $i,T_a: $i] :
( ( c_Relation_Orel__comp @ V_r @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ T_a @ T_a @ T_a )
= ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ V_r @ T_a @ T_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_r__comp__rtrancl__eq_0) ).
thf(175,axiom,
! [V_r: $i,V_f: $i,T_a: $i,T_b: $i] :
( ( c_Wellfounded_Owf @ ( c_Relation_Oinv__image @ V_r @ V_f @ T_a @ T_b ) @ T_b )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__inv__image_0) ).
thf(176,axiom,
! [V_A: $i,T_a: $i] : ( c_Relation_Orefl__on @ V_A @ ( c_Relation_OId__on @ V_A @ T_a ) @ T_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__Id__on_0) ).
thf(177,axiom,
! [V_A: $i,T_a: $i] : ( c_Relation_Osym @ ( c_Relation_OId__on @ V_A @ T_a ) @ T_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__Id__on_0) ).
thf(178,axiom,
! [V_r: $i,V_s: $i,T_b: $i,T_c: $i,T_a: $i] :
( ( c_Relation_Oconverse @ ( c_Relation_Orel__comp @ V_r @ V_s @ T_b @ T_c @ T_a ) @ T_b @ T_a )
= ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ V_s @ T_c @ T_a ) @ ( c_Relation_Oconverse @ V_r @ T_b @ T_c ) @ T_a @ T_c @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rel__comp_0) ).
thf(179,axiom,
! [V_r: $i,T_a: $i] : ( c_Relation_Otrans @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ T_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__trancl_0) ).
thf(180,axiom,
! [V_r: $i,T_a: $i] :
( ( c_Relation_ORange @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ T_a @ T_a )
= ( c_Relation_ORange @ V_r @ T_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__range_0) ).
thf(181,axiom,
! [V_r: $i,T_a: $i] :
( ( ( c_Relation_Oconverse @ V_r @ T_a @ T_a )
!= V_r )
| ( c_Relation_Osym @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__conv__converse__eq_1) ).
thf(182,axiom,
! [V_r: $i,T_a: $i] :
( ( ( c_Relation_Oconverse @ V_r @ T_a @ T_a )
= V_r )
| ~ ( c_Relation_Osym @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__conv__converse__eq_0) ).
thf(183,axiom,
! [V_A: $i,T_a: $i] :
( ( c_Relation_ODomain @ ( c_Relation_OId__on @ V_A @ T_a ) @ T_a @ T_a )
= V_A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__Id__on_0) ).
thf(184,axiom,
! [T_a: $i] : ( c_Relation_Osingle__valued @ ( c_Relation_OId @ T_a ) @ T_a @ T_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_single__valued__Id_0) ).
thf(185,axiom,
! [T_a: $i,V_A: $i] :
( ( c_Relation_OImage @ ( c_Relation_OId @ T_a ) @ V_A @ T_a @ T_a )
= V_A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__Id_0) ).
thf(186,axiom,
! [V_R: $i,T_a: $i] :
( ( c_Wellfounded_Owf @ V_R @ T_a )
| ~ ( c_Wellfounded_Owf @ ( c_Relation_Orel__comp @ V_R @ V_R @ T_a @ T_a @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__comp__self_1) ).
thf(187,axiom,
! [V_R: $i,T_a: $i] :
( ( c_Wellfounded_Owf @ ( c_Relation_Orel__comp @ V_R @ V_R @ T_a @ T_a @ T_a ) @ T_a )
| ~ ( c_Wellfounded_Owf @ V_R @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__comp__self_0) ).
thf(188,axiom,
! [V_r: $i,T_a: $i] :
( ( c_Relation_Osym @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ T_a )
| ~ ( c_Relation_Osym @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__rtrancl_0) ).
thf(189,axiom,
! [V_A: $i,V_r: $i,T_a: $i] :
( ( c_Relation_Orefl__on @ V_A @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a )
| ~ ( c_Relation_Orefl__on @ V_A @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__converse_1) ).
thf(190,axiom,
! [V_A: $i,V_r: $i,T_a: $i] :
( ( c_Relation_Orefl__on @ V_A @ V_r @ T_a )
| ~ ( c_Relation_Orefl__on @ V_A @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__converse_0) ).
thf(191,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__Xacc__induct__rule__1__1 @ V_P @ V_r @ T_a ) ) )
| ~ ( c_in @ V_a @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__induct__rule_2) ).
thf(192,axiom,
! [V_r: $i,T_a: $i] :
( ( c_Wellfounded_Owf @ ( c_Relation_Oconverse @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ T_a @ T_a ) @ T_a )
| ~ ( c_Wellfounded_Owf @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__converse__trancl_0) ).
thf(193,axiom,
! [V_A: $i,T_a: $i] : ( c_Relation_Oantisym @ ( c_Relation_OId__on @ V_A @ T_a ) @ T_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__Id__on_0) ).
thf(194,axiom,
! [V_R: $i,T_b: $i,T_a: $i] :
( ( c_Relation_Orel__comp @ V_R @ ( c_Relation_OId @ T_b ) @ T_a @ T_b @ T_b )
= V_R ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_R__O__Id_0) ).
thf(195,axiom,
! [T_a: $i,V_R: $i,T_b: $i] :
( ( c_Relation_Orel__comp @ ( c_Relation_OId @ T_a ) @ V_R @ T_a @ T_a @ T_b )
= V_R ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__O__R_0) ).
thf(196,axiom,
! [V_A: $i,T_a: $i] : ( c_Relation_Otrans @ ( c_Relation_OId__on @ V_A @ T_a ) @ T_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__Id__on_0) ).
thf(197,axiom,
! [T_a: $i] : ( c_Relation_Osym @ ( c_Relation_OId @ T_a ) @ T_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__Id_0) ).
thf(198,axiom,
! [V_R: $i,V_x: $i,T_a: $i] :
( ~ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1 @ V_R @ V_x @ T_a ) @ ( c_Wellfounded_Oacc @ V_R @ T_a ) @ T_a )
| ( c_in @ V_x @ ( c_Wellfounded_Oacc @ V_R @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__acc__down_1) ).
thf(199,axiom,
! [V_A: $i,V_b: $i,V_r: $i,T_b: $i,T_a: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Relation__XImage__iff__1__1 @ V_A @ V_b @ V_r @ T_b @ T_a ) @ V_A @ T_b )
| ~ ( c_in @ V_b @ ( c_Relation_OImage @ V_r @ V_A @ T_b @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__iff_0) ).
thf(200,axiom,
! [V_r: $i,T_a: $i] :
( ( c_Relation_ODomain @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ T_a @ T_a )
= ( c_Relation_ODomain @ V_r @ T_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__domain_0) ).
thf(201,axiom,
! [V_r: $i,T_a: $i] :
( ( c_Relation_Osym @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a )
| ~ ( c_Relation_Osym @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__converse_1) ).
thf(202,axiom,
! [V_r: $i,T_a: $i] :
( ( c_Relation_Osym @ V_r @ T_a )
| ~ ( c_Relation_Osym @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__converse_0) ).
thf(203,axiom,
! [V_P: $i,V_a: $i,V_r: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ V_P @ V_r @ T_a ) @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a )
| ~ ( c_in @ V_a @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__induct__rule_0) ).
thf(204,axiom,
! [V_P: $i,V_x: $i,V_r: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ V_P @ V_r ) ) )
| ~ ( c_in @ V_x @ ( c_Wellfounded_Oacc @ V_r @ t_a ) @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_Oinducts_2) ).
thf(205,axiom,
! [V_r: $i,T_a: $i] :
( ( ( c_Transitive__Closure_Otrancl @ V_r @ T_a )
= V_r )
| ~ ( c_Relation_Otrans @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__id_0) ).
thf(206,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__Xacc__induct__1__1 @ V_P @ V_r @ T_a ) ) )
| ~ ( c_in @ V_a @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__induct_2) ).
thf(207,axiom,
! [V_r: $i,T_a: $i] :
( ( c_Relation_Osym @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ T_a )
| ~ ( c_Relation_Osym @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__trancl_0) ).
thf(208,axiom,
! [V_A: $i,V_b: $i,V_r: $i,T_b: $i,T_a: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Relation__XImageE__1__1 @ V_A @ V_b @ V_r @ T_b @ T_a ) @ V_A @ T_b )
| ~ ( c_in @ V_b @ ( c_Relation_OImage @ V_r @ V_A @ T_b @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ImageE_1) ).
thf(209,axiom,
! [V_A: $i,T_a: $i] : ( c_Relation_Osingle__valued @ ( c_Relation_OId__on @ V_A @ T_a ) @ T_a @ T_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_single__valued__Id__on_0) ).
thf(210,axiom,
! [V_x: $i,V_r: $i,T_a: $i] :
( ( c_in @ V_x @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__wfD_0) ).
thf(211,axiom,
! [V_x: $i,V_A: $i,T_aa: $i,V_f: $i,T_a: $i] :
( ~ ( c_in @ V_x @ V_A @ T_aa )
| ( c_in @ ( hAPP @ V_f @ V_x ) @ ( c_Set_Oimage @ V_f @ V_A @ T_aa @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__image__eqI_0) ).
thf(212,axiom,
! [V_x: $i,V_A: $i,T_b: $i,V_f: $i,T_a: $i] :
( ~ ( c_in @ V_x @ V_A @ T_b )
| ( c_in @ ( hAPP @ V_f @ V_x ) @ ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__iff_2) ).
thf(213,axiom,
! [V_f: $i,V_x: $i,V_A: $i,T_b: $i,T_a: $i] :
( ( c_in @ ( hAPP @ V_f @ V_x ) @ ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a ) @ T_a )
| ~ ( c_in @ V_x @ V_A @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__eqI_0) ).
thf(214,axiom,
! [V_f: $i,V_x: $i,V_A: $i,T_a: $i,T_b: $i] :
( ( c_in @ ( hAPP @ V_f @ V_x ) @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) @ T_b )
| ~ ( c_in @ V_x @ V_A @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_imageI_0) ).
thf(215,axiom,
! [V_R: $i,V_a: $i,V_b: $i,V_c: $i,T_a: $i,T_b: $i,T_c: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ V_R @ V_a ) @ V_b ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_split @ V_R @ T_a @ T_b @ ( tc_fun @ T_c @ tc_bool ) ) @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) ) @ V_c ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_splitD_H_0) ).
thf(216,axiom,
! [V_f: $i,T_a: $i,T_b: $i,T_c: $i,V_a: $i,V_b: $i] :
( ( hAPP @ ( c_split @ V_f @ T_a @ T_b @ T_c ) @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) )
= ( hAPP @ ( hAPP @ V_f @ V_a ) @ V_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__case__cert_0) ).
thf(217,axiom,
! [V_f: $i,T_b: $i,T_c: $i,T_a: $i,V_a: $i,V_b: $i] :
( ( hAPP @ ( c_split @ V_f @ T_b @ T_c @ T_a ) @ ( c_Pair @ V_a @ V_b @ T_b @ T_c ) )
= ( hAPP @ ( hAPP @ V_f @ V_a ) @ V_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Product__Type_Osplit_0) ).
thf(218,axiom,
! [V_x: $i,V_y: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Relation_Oconverse @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ T_a @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__converseI_0) ).
thf(219,axiom,
! [V_x: $i,V_y: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Relation_Oconverse @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ T_a @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__converseD_0) ).
thf(220,axiom,
! [V_x: $i,V_z: $i,T_a: $i,V_r: $i,V_y: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_z @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_y @ V_z @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__trancl__trancl_0) ).
thf(221,axiom,
! [V_a: $i,V_c: $i,T_a: $i,V_r: $i,V_b: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_b @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__rtrancl__trancl_0) ).
thf(222,axiom,
! [V_a: $i,V_b: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__into__rtrancl_0) ).
thf(223,axiom,
! [V_z: $i,V_y: $i,T_a: $i,V_r: $i,V_x: $i] :
( ( c_in @ ( c_Pair @ V_z @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ( c_in @ ( c_Pair @ V_y @ V_z @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_z @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Relation_Osingle__valued @ V_r @ T_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_single__valued__confluent_0) ).
thf(224,axiom,
! [V_y: $i,V_x: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_y @ V_x @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__converseD_0) ).
thf(225,axiom,
! [V_x: $i,V_y: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_y @ V_x @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__converseI_0) ).
thf(226,axiom,
! [V_a: $i,V_b: $i,T_a: $i,V_R: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ( V_a = V_b )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclD_0) ).
thf(227,axiom,
! [V_x: $i,V_y: $i,T_a: $i,V_R: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ( V_x = V_y )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__eq__or__trancl_0) ).
thf(228,axiom,
! [V_x: $i,V_y: $i,T_a: $i,V_R: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ( V_x = V_y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__eq__or__trancl_2) ).
thf(229,axiom,
! [V_a: $i,V_c: $i,T_a: $i,V_r: $i,V_b: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_b @ V_c @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__into__trancl1_0) ).
thf(230,axiom,
! [V_a: $i,V_c: $i,T_a: $i,V_r: $i,V_b: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_b @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__into__trancl2_0) ).
thf(231,axiom,
! [V_p: $i,V_r: $i,T_a: $i] :
( ( c_in @ V_p @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_p @ V_r @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_r__into__trancl_H_0) ).
thf(232,axiom,
! [V_p: $i,V_r: $i,T_a: $i] :
( ( c_in @ V_p @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_p @ V_r @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_r__into__rtrancl_0) ).
thf(233,axiom,
! [T_a: $i,T_b: $i,V_R: $i] :
( ( c_Set_Oimage @ ( c_fst @ T_a @ T_b ) @ V_R @ ( tc_prod @ T_a @ T_b ) @ T_a )
= ( c_Relation_ODomain @ V_R @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fst__eq__Domain_0) ).
thf(234,axiom,
! [V_a: $i,V_A: $i,T_a: $i,V_b: $i,V_r: $i] :
( ( c_in @ V_a @ V_A @ T_a )
| ( V_a = V_b )
| ~ ( c_lessequals @ V_r @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_A @ ( tc_fun @ T_a @ tc_bool ) @ T_a ) @ T_a @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__subset__Sigma__aux_0) ).
thf(235,axiom,
! [T_b: $i,T_a: $i,V_R: $i] :
( ( c_Set_Oimage @ ( c_snd @ T_b @ T_a ) @ V_R @ ( tc_prod @ T_b @ T_a ) @ T_a )
= ( c_Relation_ORange @ V_R @ T_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_snd__eq__Range_0) ).
thf(236,axiom,
! [V_r: $i,V_x: $i,T_a: $i,V_y: $i,V_A: $i] :
( ( ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a )
!= ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_y @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) )
| ~ ( c_in @ V_y @ V_A @ T_a )
| ~ ( c_in @ V_x @ V_A @ T_a )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a )
| ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__equiv__class__iff_0) ).
thf(237,axiom,
! [V_r: $i,V_x: $i,T_a: $i,V_y: $i,V_A: $i] :
( ( ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a )
= ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_y @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_y @ V_A @ T_a )
| ~ ( c_in @ V_x @ V_A @ T_a )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__equiv__class__iff_1) ).
thf(238,axiom,
! [V_r: $i,V_x: $i,T_a: $i,V_y: $i,V_A: $i] :
( ( ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a )
!= ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_y @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a )
| ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_y @ V_A @ T_a )
| ~ ( c_in @ V_x @ V_A @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__eq__iff_3) ).
thf(239,axiom,
! [V_r: $i,V_a: $i,T_a: $i,V_b: $i,V_A: $i] :
( ( ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a )
!= ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) )
| ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_b @ V_A @ T_a )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__equiv__class_0) ).
thf(240,axiom,
! [V_r: $i,T_a: $i,V_x: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_x @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_irrefl__tranclI_0) ).
thf(241,axiom,
! [V_r: $i,T_a: $i] : ( c_Relation_Oirrefl @ ( c_HOL_Ominus__class_Ominus @ V_r @ ( c_Relation_OId @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_irrefl__diff__Id_0) ).
thf(242,axiom,
! [V_R: $i,T_a: $i] :
( ( c_Wellfounded_OwfP @ ( c_FunDef_Oin__rel @ V_R @ T_a @ T_a ) @ T_a )
| ~ ( c_Wellfounded_Owf @ V_R @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__in__rel_0) ).
thf(243,axiom,
! [V_A: $i,V_B: $i,V_c: $i,T_a: $i,T_b: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Product__Type__XSigmaE__1__1 @ V_A @ V_B @ V_c @ T_a @ T_b ) @ V_A @ T_a )
| ~ ( c_in @ V_c @ ( c_Product__Type_OSigma @ V_A @ V_B @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SigmaE_0) ).
thf(244,axiom,
! [V_a: $i,V_b: $i,V_r: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ V_a @ ( c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1 @ V_a @ V_b @ V_r @ T_a ) @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ( V_a = V_b )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclE_0) ).
thf(245,axiom,
! [V_P: $i,V_a: $i,V_b: $i,V_r: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1 @ V_P @ V_b @ V_r @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_b ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rtrancl__induct_3) ).
thf(246,axiom,
! [V_a1: $i,V_a2: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ ( v_sko__Transitive__Closure__Xrtrancl__Xcases__1 @ V_a1 @ V_a2 @ V_r ) @ V_a2 @ t_a @ t_a ) @ V_r @ ( tc_prod @ t_a @ t_a ) )
| ( V_a2 = V_a1 )
| ~ ( c_in @ ( c_Pair @ V_a1 @ V_a2 @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl_Ocases_1) ).
thf(247,axiom,
! [V_P: $i,V_b: $i,V_a: $i,V_r: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_b ) )
| ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 @ V_P @ V_a @ V_r @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__induct_2) ).
thf(248,axiom,
! [V_a1: $i,V_a2: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_a1 @ ( v_sko__Transitive__Closure__Xrtrancl__Xcases__1 @ V_a1 @ V_a2 @ V_r ) @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ t_a ) @ ( tc_prod @ t_a @ t_a ) )
| ( V_a2 = V_a1 )
| ~ ( c_in @ ( c_Pair @ V_a1 @ V_a2 @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl_Ocases_0) ).
thf(249,axiom,
! [V_P: $i,V_b: $i,V_a: $i,V_r: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_b ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2 @ V_P @ V_a @ V_r @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__induct_3) ).
thf(250,axiom,
! [V_P: $i,V_b: $i,V_a: $i,V_r: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_b ) )
| ( c_in @ ( c_Pair @ V_a @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 @ V_P @ V_a @ V_r @ T_a ) @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__induct_0) ).
thf(251,axiom,
! [V_P: $i,V_a: $i,V_b: $i,V_r: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 @ V_P @ V_b @ V_r @ T_a ) @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_b ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rtrancl__induct_1) ).
thf(252,axiom,
! [V_P: $i,V_a: $i,V_b: $i,V_r: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 @ V_P @ V_b @ V_r @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_b ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rtrancl__induct_2) ).
thf(253,axiom,
! [V_x: $i,V_r: $i,V_z: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ V_x @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1 @ V_r @ V_x @ V_z @ T_a ) @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ( V_x = V_z )
| ~ ( c_in @ ( c_Pair @ V_x @ V_z @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rtranclE_0) ).
thf(254,axiom,
! [V_r: $i,V_x: $i,V_z: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1 @ V_r @ V_x @ V_z @ T_a ) @ V_z @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ( V_x = V_z )
| ~ ( c_in @ ( c_Pair @ V_x @ V_z @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rtranclE_1) ).
thf(255,axiom,
! [V_a: $i,V_b: $i,V_r: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1 @ V_a @ V_b @ V_r @ T_a ) @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ( V_a = V_b )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclE_1) ).
thf(256,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 ) )
| ~ ( c_in @ ( c_Pair @ V_y @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1 @ V_P @ V_r @ T_a ) @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__induct_0) ).
thf(257,axiom,
! [V_P: $i,V_Ra: $i,V_y: $i,V_R: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_Ra ) )
| ( hBOOL @ ( hAPP @ V_P @ V_y ) )
| ~ ( c_in @ ( c_Pair @ V_y @ ( c_List_Osko__Recdef__Xtfl__wf__induct__1__1 @ V_P @ V_R @ T_a ) @ T_a @ T_a ) @ V_R @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Wellfounded_Owf @ V_R @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tfl__wf__induct_0) ).
thf(258,axiom,
! [V_P: $i,V_xa: $i,V_y: $i,V_r: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_xa ) )
| ( hBOOL @ ( hAPP @ V_P @ V_y ) )
| ~ ( c_in @ ( c_Pair @ V_y @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1 @ V_P @ V_r @ T_a ) @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__def_0) ).
thf(259,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 ) )
| ~ ( c_in @ ( c_Pair @ V_y @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1 @ V_P @ V_r @ T_a ) @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__induct__rule_0) ).
thf(260,axiom,
! [V_a1: $i,V_a2: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ ( v_sko__Transitive__Closure__Xtrancl__Xcases__1 @ V_a1 @ V_a2 @ V_r ) @ V_a2 @ t_a @ t_a ) @ V_r @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ ( c_Pair @ V_a1 @ V_a2 @ t_a @ t_a ) @ V_r @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ ( c_Pair @ V_a1 @ V_a2 @ t_a @ t_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl_Ocases_1) ).
thf(261,axiom,
! [V_x: $i,V_r: $i,V_z: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ V_x @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1 @ V_r @ V_x @ V_z @ T_a ) @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ( c_in @ ( c_Pair @ V_x @ V_z @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_z @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__tranclE_0) ).
thf(262,axiom,
! [V_R: $i,V_x: $i,V_y: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1 @ V_R @ V_x @ V_y @ T_a ) @ V_y @ T_a @ T_a ) @ V_R @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tranclD2_1) ).
thf(263,axiom,
! [V_a: $i,V_b: $i,V_r: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ V_a @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1 @ V_a @ V_b @ V_r @ T_a ) @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tranclE_0) ).
thf(264,axiom,
! [V_a: $i,V_b: $i,V_r: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1 @ V_a @ V_b @ V_r @ T_a ) @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tranclE_1) ).
thf(265,axiom,
! [V_x: $i,T_a: $i,V_r: $i] :
( ~ ( c_in @ ( c_Pair @ V_x @ V_x @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Wellfounded_Oacyclic @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__def_0) ).
thf(266,axiom,
! [V_a1: $i,V_a2: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_a1 @ ( v_sko__Transitive__Closure__Xtrancl__Xcases__1 @ V_a1 @ V_a2 @ V_r ) @ t_a @ t_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ t_a ) @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ ( c_Pair @ V_a1 @ V_a2 @ t_a @ t_a ) @ V_r @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ ( c_Pair @ V_a1 @ V_a2 @ t_a @ t_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl_Ocases_0) ).
thf(267,axiom,
! [V_x: $i,V_R: $i,V_y: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ V_x @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1 @ V_R @ V_x @ V_y @ T_a ) @ T_a @ T_a ) @ V_R @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tranclD_0) ).
thf(268,axiom,
! [V_r: $i,V_x: $i,V_z: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1 @ V_r @ V_x @ V_z @ T_a ) @ V_z @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ( c_in @ ( c_Pair @ V_x @ V_z @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_z @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__tranclE_1) ).
thf(269,axiom,
! [V_x: $i,T_a: $i,V_r: $i] :
( ~ ( c_in @ ( c_Pair @ V_x @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1 @ V_r @ T_a ) @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1 @ V_r @ T_a ) @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_irrefl__trancl__rD_0) ).
thf(270,axiom,
! [V_a: $i,V_c: $i,V_r: $i,V_s: $i,T_a: $i,T_b: $i,T_c: $i] :
( ( c_in @ ( c_Pair @ V_a @ ( c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 @ V_a @ V_c @ V_r @ V_s @ T_a @ T_b @ T_c ) @ T_a @ T_c ) @ V_r @ ( tc_prod @ T_a @ T_c ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_b ) @ ( c_Relation_Orel__comp @ V_r @ V_s @ T_a @ T_c @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__compEpair_0) ).
thf(271,axiom,
! [V_a: $i,V_c: $i,V_r: $i,V_s: $i,T_a: $i,T_b: $i,T_c: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 @ V_a @ V_c @ V_r @ V_s @ T_a @ T_b @ T_c ) @ V_c @ T_c @ T_b ) @ V_s @ ( tc_prod @ T_c @ T_b ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_b ) @ ( c_Relation_Orel__comp @ V_r @ V_s @ T_a @ T_c @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__compEpair_1) ).
thf(272,axiom,
! [V_p: $i,T_a: $i] :
( ( V_p
= ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XIdE__1__1 @ V_p @ T_a ) @ ( c_ATP__Linkup_Osko__Relation__XIdE__1__1 @ V_p @ T_a ) @ T_a @ T_a ) )
| ~ ( c_in @ V_p @ ( c_Relation_OId @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IdE_0) ).
thf(273,axiom,
! [V_r: $i,T_a: $i] :
( ( c_Wellfounded_Owf @ V_r @ T_a )
| ~ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1 @ V_r @ T_a ) @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__wfI_0) ).
thf(274,axiom,
! [V_r: $i,T_a: $i] :
( ( c_Wellfounded_Owf @ V_r @ T_a )
| ~ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1 @ V_r @ T_a ) @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__acc__iff_1) ).
thf(275,axiom,
! [V_A: $i,V_c: $i,T_a: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Relation__XId__onE__1__1 @ V_A @ V_c @ T_a ) @ V_A @ T_a )
| ~ ( c_in @ V_c @ ( c_Relation_OId__on @ V_A @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__onE_0) ).
thf(276,axiom,
! [V_c: $i,V_A: $i,T_a: $i] :
( ( V_c
= ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XId__onE__1__1 @ V_A @ V_c @ T_a ) @ ( c_ATP__Linkup_Osko__Relation__XId__onE__1__1 @ V_A @ V_c @ T_a ) @ T_a @ T_a ) )
| ~ ( c_in @ V_c @ ( c_Relation_OId__on @ V_A @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__onE_1) ).
thf(277,axiom,
! [V_f: $i,V_r: $i,V_x: $i,T_a: $i,T_b: $i,V_g: $i] :
( ( ( c_Recdef_Ocut @ V_f @ V_r @ V_x @ T_a @ T_b )
= ( c_Recdef_Ocut @ V_g @ V_r @ V_x @ T_a @ T_b ) )
| ( c_in @ ( c_Pair @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ V_f @ V_g @ V_r @ V_x @ T_a @ T_b ) @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cuts__eq_1) ).
thf(278,axiom,
! [V_r: $i,T_a: $i] :
( ( c_Transitive__Closure_Ortrancl @ V_r @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( c_Relation_OId @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nitpick_Ortrancl__def_0) ).
thf(279,axiom,
! [V_r: $i,T_a: $i] :
( ( c_Transitive__Closure_Otrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_r @ ( c_Relation_OId @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
= ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__reflcl_0) ).
thf(280,axiom,
! [V_r: $i,T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( c_Relation_OId @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
= ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_reflcl__trancl_0) ).
thf(281,axiom,
! [V_r: $i,T_a: $i] :
( ( c_Transitive__Closure_Ortrancl @ V_r @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_OId @ T_a ) @ ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ V_r @ T_a @ T_a @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__unfold_0) ).
thf(282,axiom,
! [V_r: $i,T_a: $i,V_A: $i] :
( ( c_lessequals @ V_r @ ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ V_r @ T_a @ T_a @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_Relation_Orefl__on @ V_A @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__comp__subset_0) ).
thf(283,axiom,
( ( c_Relation_ORange @ v_r @ t_a @ t_b )
= ( c_Relation_ODomain @ ( c_Relation_Oconverse @ v_r @ t_a @ t_b ) @ t_b @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__def__raw_0) ).
thf(284,axiom,
! [V_r: $i,T_a: $i] :
( ( c_Relation_Oirrefl @ V_r @ T_a )
| ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1 @ V_r @ T_a ) @ ( c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1 @ V_r @ T_a ) @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_irrefl__def_1) ).
thf(285,axiom,
! [V_R: $i,V_A: $i,V_B: $i,T_b: $i,T_a: $i] :
( ( ( c_Relation_OImage @ V_R @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_OImage @ V_R @ V_A @ T_b @ T_a ) @ ( c_Relation_OImage @ V_R @ V_B @ T_b @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( c_Relation_Osingle__valued @ ( c_Relation_Oconverse @ V_R @ T_b @ T_a ) @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__Int__eq_0) ).
thf(286,axiom,
! [V_r: $i,T_a: $i] :
( ( c_Relation_Otrans @ ( c_HOL_Ominus__class_Ominus @ V_r @ ( c_Relation_OId @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
| ~ ( c_Relation_Oantisym @ V_r @ T_a )
| ~ ( c_Relation_Otrans @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__diff__Id_0) ).
thf(287,axiom,
! [V_r: $i,T_a: $i] :
( ( c_Nitpick_Orefl_H @ V_r @ T_a )
| ~ ( c_in @ ( c_Pair @ ( c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1 @ V_r @ T_a ) @ ( c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1 @ V_r @ T_a ) @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nitpick_Orefl_H__def_1) ).
thf(288,axiom,
! [V_A: $i,V_r: $i,T_a: $i] :
( ( c_Order__Relation_Ostrict__linear__order__on @ V_A @ V_r @ T_a )
| ~ ( c_Relation_Ototal__on @ V_A @ V_r @ T_a )
| ~ ( c_Relation_Oirrefl @ V_r @ T_a )
| ~ ( c_Relation_Otrans @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_strict__linear__order__on__def_3) ).
thf(289,axiom,
! [V_y: $i,V_x: $i,T_a: $i,V_r: $i] :
( ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ V_y @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) @ T_a )
| ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__insert_2) ).
thf(290,axiom,
! [V_x: $i,V_y: $i,T_a: $i,V_r: $i] :
( ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ V_y @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__insert_1) ).
thf(291,axiom,
! [V_R: $i,V_x: $i,V_y: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1 @ V_R @ V_x @ V_y @ T_a ) @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tranclD_1) ).
thf(292,axiom,
! [V_x: $i,V_R: $i,V_y: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ V_x @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1 @ V_R @ V_x @ V_y @ T_a ) @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tranclD2_0) ).
thf(293,axiom,
! [V_r: $i,T_a: $i] :
( ( c_lessequals @ ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ V_r @ T_a @ T_a @ T_a ) @ V_r @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_Relation_Otrans @ V_r @ T_a )
| ~ ( c_Relation_Osym @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__trans__comp__subset_0) ).
thf(294,axiom,
! [V_A: $i,V_r: $i,T_a: $i] :
( ( c_Relation_Ototal__on @ V_A @ ( c_HOL_Ominus__class_Ominus @ V_r @ ( c_Relation_OId @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
| ~ ( c_Relation_Ototal__on @ V_A @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_total__on__diff__Id_1) ).
thf(295,axiom,
! [V_A: $i,V_r: $i,T_a: $i] :
( ( c_Relation_Ototal__on @ V_A @ V_r @ T_a )
| ~ ( c_Relation_Ototal__on @ V_A @ ( c_HOL_Ominus__class_Ominus @ V_r @ ( c_Relation_OId @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_total__on__diff__Id_0) ).
thf(296,axiom,
! [V_r: $i,T_a: $i] :
( ( c_Relation_Oantisym @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_r @ ( c_Relation_OId @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
| ~ ( c_Relation_Oantisym @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__reflcl_1) ).
thf(297,axiom,
! [V_r: $i,T_a: $i] :
( ( c_Relation_Oantisym @ V_r @ T_a )
| ~ ( c_Relation_Oantisym @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_r @ ( c_Relation_OId @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__reflcl_0) ).
thf(298,axiom,
! [V_A: $i,T_a: $i,V_B: $i] :
( ( c_Relation_OImage @ ( c_Relation_OId__on @ V_A @ T_a ) @ V_B @ T_a @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__Id__on_0) ).
thf(299,axiom,
! [V_r: $i,T_a: $i] :
( ( c_Relation_Otrans @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_r @ ( c_Relation_OId @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
| ~ ( c_Relation_Otrans @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__reflclI_0) ).
thf(300,axiom,
! [V_r: $i,T_a: $i] : ( c_Relation_Osym @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_r @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__Int__converse_0) ).
thf(301,axiom,
! [V_r: $i,T_a: $i] : ( c_Relation_Osym @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_r @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__Un__converse_0) ).
thf(302,axiom,
! [V_r: $i,T_a: $i] :
( ( c_lessequals @ ( c_Relation_Orel__comp @ V_r @ V_r @ T_a @ T_a @ T_a ) @ V_r @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_Relation_Otrans @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__O__subset_0) ).
thf(303,axiom,
! [V_r: $i,T_a: $i] :
( ( c_Relation_Oantisym @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ T_a )
| ~ ( c_Wellfounded_Oacyclic @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__impl__antisym__rtrancl_0) ).
thf(304,axiom,
! [V_r: $i,T_a: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( c_HOL_Ominus__class_Ominus @ V_r @ ( c_Relation_OId @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
= ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__r__diff__Id_0) ).
thf(305,axiom,
! [T_a: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
= ( c_Relation_OId @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__empty_0) ).
thf(306,axiom,
! [V_R: $i,T_a: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_R @ ( c_Relation_OId @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
= ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__reflcl_0) ).
thf(307,axiom,
! [V_R: $i,T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) @ ( c_Relation_OId @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
= ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__reflcl__absorb_0) ).
thf(308,axiom,
! [V_r: $i,T_a: $i] :
( ( c_Transitive__Closure_Otrancl @ V_r @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_r @ ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ V_r @ T_a @ T_a @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__unfold_0) ).
thf(309,axiom,
! [V_R: $i,T_a: $i] :
( ( ( c_Relation_Orel__comp @ V_R @ V_R @ T_a @ T_a @ T_a )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) )
| ( c_Wellfounded_Owf @ V_R @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__no__loop_0) ).
thf(310,axiom,
! [V_R: $i,V_S: $i,T_a: $i] :
( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_R @ V_S @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
| ~ ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ V_R @ V_R @ T_a @ T_a @ T_a ) @ ( c_Relation_Orel__comp @ V_S @ V_R @ T_a @ T_a @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ V_S @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__union__merge_1) ).
thf(311,axiom,
! [V_R: $i,T_a: $i,V_S: $i] :
( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ V_R @ V_R @ T_a @ T_a @ T_a ) @ ( c_Relation_Orel__comp @ V_S @ V_R @ T_a @ T_a @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ V_S @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
| ~ ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_R @ V_S @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__union__merge_0) ).
thf(312,axiom,
! [V_r: $i,V_x: $i,T_a: $i,V_y: $i,V_A: $i] :
( ( ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a )
= ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_y @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__eq__iff_0) ).
thf(313,axiom,
! [V_r: $i,V_a: $i,T_a: $i,V_b: $i,V_A: $i] :
( ( ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a )
= ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__eq_0) ).
thf(314,axiom,
! [V_p: $i,V_s: $i,T_a: $i,V_r: $i] :
( ( c_in @ V_p @ ( c_Transitive__Closure_Otrancl @ V_s @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_lessequals @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_in @ V_p @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__mono_0) ).
thf(315,axiom,
! [V_x: $i,V_R: $i,V_S: $i,T_a: $i] :
( ( c_in @ V_x @ ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_R @ V_S @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_x @ ( c_Transitive__Closure_Ortrancl @ V_S @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__rtrancl__UnI_1) ).
thf(316,axiom,
! [V_x: $i,V_R: $i,V_S: $i,T_a: $i] :
( ( c_in @ V_x @ ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_R @ V_S @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_x @ ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__rtrancl__UnI_0) ).
thf(317,axiom,
! [V_r: $i,T_a: $i,V_y: $i,V_x: $i] :
( ( c_Wellfounded_Owf @ V_r @ T_a )
| ~ ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ V_y @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__insert_0) ).
thf(318,axiom,
! [V_A: $i,V_C: $i,T_a: $i,T_b: $i,V_B: $i,V_x: $i] :
( ( ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_C @ ( tc_fun @ T_a @ tc_bool ) @ T_b ) @ T_b @ T_a )
!= ( c_Product__Type_OSigma @ V_B @ ( c_COMBK @ V_C @ ( tc_fun @ T_a @ tc_bool ) @ T_b ) @ T_b @ T_a ) )
| ~ ( c_in @ V_x @ V_C @ T_a )
| ( V_A = V_B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Times__eq__cancel2_0) ).
thf(319,axiom,
! [V_b: $i,V_r: $i,V_a: $i,T_b: $i,T_a: $i] :
( ( c_in @ V_b @ ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b ) @ T_b @ T_a ) @ T_a )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_b @ T_a ) @ V_r @ ( tc_prod @ T_b @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__singleton__iff_1) ).
thf(320,axiom,
! [V_a: $i,V_b: $i,T_b: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_b @ T_b @ T_a ) @ V_r @ ( tc_prod @ T_b @ T_a ) )
| ~ ( c_in @ V_b @ ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b ) @ T_b @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__singleton__iff_0) ).
thf(321,axiom,
! [V_f: $i,V_x: $i,V_B: $i,T_a: $i,V_A: $i,T_b: $i] :
( ( c_in @ ( hAPP @ V_f @ V_x ) @ V_B @ T_a )
| ~ ( c_in @ V_x @ V_A @ T_b )
| ~ ( c_lessequals @ ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__subset__iff_0) ).
thf(322,axiom,
! [V_f: $i,V_x: $i,V_A: $i,T_a: $i,T_b: $i] :
( ( ( c_Set_Oinsert @ ( hAPP @ V_f @ V_x ) @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) @ T_b )
= ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) )
| ~ ( c_in @ V_x @ V_A @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__image_0) ).
thf(323,axiom,
! [V_a: $i,V_b: $i,T_a: $i,V_r: $i,V_A: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_b @ V_A @ T_a )
| ~ ( c_lessequals @ ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) @ ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__equiv__class_0) ).
thf(324,axiom,
! [V_a: $i,V_b: $i,T_a: $i,V_r: $i,V_x: $i,V_A: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) @ ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__nondisjoint_0) ).
thf(325,axiom,
! [V_r: $i,T_a: $i,V_s: $i] :
( ( c_lessequals @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Relation_Orel__comp @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ V_r @ T_a @ T_a @ T_a ) @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Relation_OId @ T_a ) @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__Int__subset_0) ).
thf(326,axiom,
! [V_a: $i,V_r: $i,T_a: $i,V_A: $i] :
( ( c_in @ V_a @ ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) @ T_a )
| ~ ( c_in @ V_a @ V_A @ T_a )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__self_0) ).
thf(327,axiom,
! [V_P: $i,V_b: $i,V_a: $i,V_r: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_b ) )
| ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 @ V_P @ V_a @ V_r @ T_a ) @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2 @ V_P @ V_a @ V_r @ T_a ) @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__induct_1) ).
thf(328,axiom,
! [V_P: $i,V_a: $i,V_b: $i,V_r: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1 @ V_P @ V_b @ V_r @ T_a ) @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 @ V_P @ V_b @ V_r @ T_a ) @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_b ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rtrancl__induct_0) ).
thf(329,axiom,
! [V_x: $i,V_y: $i,T_a: $i,V_r: $i] :
( ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Wellfounded_Oacyclic @ ( c_Set_Oinsert @ ( c_Pair @ V_y @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__insert_1) ).
thf(330,axiom,
! [V_y: $i,V_x: $i,T_a: $i,V_r: $i] :
( ( c_Wellfounded_Oacyclic @ ( c_Set_Oinsert @ ( c_Pair @ V_y @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) @ T_a )
| ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Wellfounded_Oacyclic @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__insert_2) ).
thf(331,axiom,
! [V_r: $i,T_a: $i,V_A: $i] :
( ( c_Relation_Oirrefl @ V_r @ T_a )
| ~ ( c_Order__Relation_Ostrict__linear__order__on @ V_A @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_strict__linear__order__on__def_1) ).
thf(332,axiom,
! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_y @ V_x @ T_a )
| ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__linear_0) ).
thf(333,axiom,
! [V_r: $i,V_A: $i,T_a: $i] :
( ( c_lessequals @ V_r @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_A @ ( tc_fun @ T_a @ tc_bool ) @ T_a ) @ T_a @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__type_0) ).
thf(334,axiom,
! [V_r_H: $i,V_A_H: $i,T_a: $i,T_b: $i,V_r: $i,V_A: $i] :
( ( c_lessequals @ ( c_Relation_OImage @ V_r_H @ V_A_H @ T_a @ T_b ) @ ( c_Relation_OImage @ V_r @ V_A @ T_a @ T_b ) @ ( tc_fun @ T_b @ tc_bool ) )
| ~ ( c_lessequals @ V_A_H @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_r_H @ V_r @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__mono_0) ).
thf(335,axiom,
! [V_r: $i,T_b: $i,T_a: $i] :
( ( ( c_Relation_ORange @ V_r @ T_b @ T_a )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( V_r
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_b @ T_a ) @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__empty__iff_0) ).
thf(336,axiom,
! [V_P: $i,T_b: $i,T_a: $i,V_x: $i,V_y: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_P @ ( hAPP @ ( c_snd @ T_b @ T_a ) @ ( c_Pair @ V_x @ V_y @ T_b @ T_a ) ) ) @ ( hAPP @ ( c_fst @ T_b @ T_a ) @ ( c_Pair @ V_x @ V_y @ T_b @ T_a ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_P @ V_y ) @ V_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exI__realizer_0) ).
thf(337,axiom,
! [T_a: $i] :
( ( c_Transitive__Closure_Otrancl @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__empty_0) ).
thf(338,axiom,
! [V_f: $i,V_A: $i,V_B: $i,T_b: $i,T_a: $i] :
( ( c_Set_Oimage @ V_f @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a ) @ ( c_Set_Oimage @ V_f @ V_B @ T_b @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__Un_0) ).
thf(339,axiom,
! [T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty_2) ).
thf(340,axiom,
! [V_a: $i,V_C: $i,T_a: $i,V_D: $i] :
( ( c_lessequals @ ( c_Set_Oinsert @ V_a @ V_C @ T_a ) @ ( c_Set_Oinsert @ V_a @ V_D @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_C @ V_D @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__mono_0) ).
thf(341,axiom,
! [V_x: $i,V_A: $i,T_b: $i,V_f: $i,T_a: $i] :
( ~ ( c_lessequals @ V_x @ V_A @ ( tc_fun @ T_b @ tc_bool ) )
| ( c_lessequals @ ( c_Set_Oimage @ V_f @ V_x @ T_b @ T_a ) @ ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__image__iff_2) ).
thf(342,axiom,
! [V_f: $i,V_A: $i,T_a: $i,T_b: $i,V_B: $i] :
( ( c_lessequals @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) @ ( c_Set_Oimage @ V_f @ V_B @ T_a @ T_b ) @ ( tc_fun @ T_b @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__mono_0) ).
thf(343,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_x_H: $i,V_y_H: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x_H @ V_y_H @ T_a ) )
| ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_lessequals @ V_y_H @ V_x_H @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eqI_1) ).
thf(344,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_x_H: $i,V_y_H: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x_H @ V_y_H @ T_a ) )
| ( c_lessequals @ V_y_H @ V_x_H @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eqI_0) ).
thf(345,axiom,
! [V_B: $i,V_C: $i,V_A: $i,T_a: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ V_B @ ( c_HOL_Ominus__class_Ominus @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= V_A )
| ~ ( c_lessequals @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__diff_0) ).
thf(346,axiom,
! [V_A: $i,V_B: $i,T_a: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ V_B @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ V_A @ V_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1I_0) ).
thf(347,axiom,
! [V_A: $i,T_b: $i,T_a: $i] :
( ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) @ ( tc_fun @ T_b @ tc_bool ) @ T_a ) @ T_a @ T_b )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sigma__empty2_0) ).
thf(348,axiom,
! [V_A: $i,V_B: $i,V_C: $i,T_a: $i] :
( ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int_0) ).
thf(349,axiom,
! [V_A: $i,V_x: $i,T_a: $i] :
( ( V_A
= ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
| ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__singletonD_0) ).
thf(350,axiom,
! [V_r: $i,T_a: $i,T_b: $i,V_s: $i] :
( ( c_lessequals @ ( c_Relation_ODomain @ V_r @ T_a @ T_b ) @ ( c_Relation_ODomain @ V_s @ T_a @ T_b ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__mono_0) ).
thf(351,axiom,
! [V_x: $i,T_a: $i] : ( c_in @ V_x @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__iff_1) ).
thf(352,axiom,
! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_HOL_Ominus__class_Ominus @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Diff_0) ).
thf(353,axiom,
! [V_A: $i,V_B: $i,V_C: $i,T_a: $i] :
( ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Un_0) ).
thf(354,axiom,
! [V_A: $i,V_B: $i,T_a: $i,V_C: $i,V_D: $i] :
( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_C @ V_D @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_B @ V_D @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__mono_0) ).
thf(355,axiom,
! [V_f: $i,V_A: $i,T_b: $i,T_a: $i] :
( ( ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__is__empty_0) ).
thf(356,axiom,
! [V_r: $i,T_a: $i,T_b: $i,V_s: $i] :
( ( c_Relation_Osingle__valued @ V_r @ T_a @ T_b )
| ~ ( c_Relation_Osingle__valued @ V_s @ T_a @ T_b )
| ~ ( c_lessequals @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_single__valued__subset_0) ).
thf(357,axiom,
! [V_r: $i,T_a: $i,V_s: $i] :
( ( c_Wellfounded_Oacyclic @ V_r @ T_a )
| ~ ( c_lessequals @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_Wellfounded_Oacyclic @ V_s @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__subset_0) ).
thf(358,axiom,
! [V_Q: $i,V_x: $i,V_P: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_Q @ V_x ) )
| ~ ( c_lessequals @ V_P @ V_Q @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__predicate1D_0) ).
thf(359,axiom,
! [V_r: $i,T_a: $i,V_s: $i] :
( ( c_Relation_Oantisym @ V_r @ T_a )
| ~ ( c_Relation_Oantisym @ V_s @ T_a )
| ~ ( c_lessequals @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__subset_0) ).
thf(360,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_lessequals @ V_x @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).
thf(361,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_lessequals @ V_x @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).
thf(362,axiom,
! [V_p: $i,T_a: $i,V_r: $i] :
( ( c_Wellfounded_Owf @ V_p @ T_a )
| ~ ( c_lessequals @ V_p @ V_r @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__subset_0) ).
thf(363,axiom,
! [V_Q: $i,V_x: $i,V_P: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_Q @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( c_lessequals @ V_P @ V_Q @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_predicate1D_0) ).
thf(364,axiom,
! [V_A: $i,V_C: $i,T_a: $i,V_B: $i] :
( ( c_lessequals @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__trans_0) ).
thf(365,axiom,
! [V_A: $i,T_a: $i] : ( c_lessequals @ V_A @ V_A @ ( tc_fun @ T_a @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__refl_0) ).
thf(366,axiom,
! [V_x: $i,T_a: $i] : ( c_lessequals @ V_x @ V_x @ ( tc_fun @ T_a @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equalityE_0) ).
thf(367,axiom,
! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_lessequals @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ V_y @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__trans_0) ).
thf(368,axiom,
! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_lessequals @ V_z @ V_x @ T_a )
| ~ ( c_lessequals @ V_z @ V_y @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).
thf(369,axiom,
! [V_B: $i,V_C: $i,T_a: $i,V_A: $i] :
( ( c_lessequals @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_1) ).
thf(370,axiom,
! [V_A: $i,V_C: $i,T_a: $i,V_B: $i] :
( ( c_lessequals @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_0) ).
thf(371,axiom,
! [T_a: $i,V_a: $i,V_x: $i,V_b: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ V_a @ V_x @ T_a )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supE_0) ).
thf(372,axiom,
! [T_a: $i,V_b: $i,V_x: $i,V_a: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ V_b @ V_x @ T_a )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supE_1) ).
thf(373,axiom,
! [T_a: $i,V_x: $i,V_a: $i,V_b: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI1_0) ).
thf(374,axiom,
! [T_a: $i,V_x: $i,V_a: $i,V_b: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI2_0) ).
thf(375,axiom,
! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ V_z @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__sup__iff_0) ).
thf(376,axiom,
! [T_a: $i,V_y: $i,V_z: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ V_y @ V_z @ T_a )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ V_z @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__sup__iff_1) ).
thf(377,axiom,
! [V_A: $i,T_a: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
= V_A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb_0) ).
thf(378,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_x @ T_a )
= V_x ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__idem_0) ).
thf(379,axiom,
! [V_a: $i,V_A: $i,T_a: $i] :
( ( ( c_Set_Oinsert @ V_a @ ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
= V_A )
| ~ ( c_in @ V_a @ V_A @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff_0) ).
thf(380,axiom,
! [V_r_H: $i,V_r: $i,T_a: $i] :
( ( c_Wellfounded_Owf @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_r_H @ V_r @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__Int2_0) ).
thf(381,axiom,
! [V_r: $i,V_r_H: $i,T_a: $i] :
( ( c_Wellfounded_Owf @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_r @ V_r_H @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__Int1_0) ).
thf(382,axiom,
! [V_A: $i,V_B: $i,T_b: $i,T_a: $i] :
( ( c_Relation_ORange @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ ( tc_prod @ T_b @ T_a ) @ tc_bool ) ) @ T_b @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_ORange @ V_A @ T_b @ T_a ) @ ( c_Relation_ORange @ V_B @ T_b @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__Un__eq_0) ).
thf(383,axiom,
! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__left__absorb_0) ).
thf(384,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__left__idem_0) ).
thf(385,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I4_J_0) ).
thf(386,axiom,
! [V_A: $i,V_B: $i,T_a: $i,V_C: $i,T_b: $i] :
( ( c_Product__Type_OSigma @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_COMBK @ V_C @ ( tc_fun @ T_b @ tc_bool ) @ T_a ) @ T_a @ T_b )
= ( c_HOL_Ominus__class_Ominus @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_C @ ( tc_fun @ T_b @ tc_bool ) @ T_a ) @ T_a @ T_b ) @ ( c_Product__Type_OSigma @ V_B @ ( c_COMBK @ V_C @ ( tc_fun @ T_b @ tc_bool ) @ T_a ) @ T_a @ T_b ) @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Times__Diff__distrib1_0) ).
thf(387,axiom,
! [V_x: $i,V_A: $i,T_a: $i,V_B: $i] :
( ( c_lessequals @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_in @ V_x @ V_B @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_2) ).
thf(388,axiom,
! [V_x: $i,V_A: $i,T_a: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ V_x ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_1) ).
thf(389,axiom,
! [V_r: $i,T_a: $i,V_A: $i] :
( ( c_Relation_Otrans @ V_r @ T_a )
| ~ ( c_Order__Relation_Ostrict__linear__order__on @ V_A @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_strict__linear__order__on__def_0) ).
thf(390,axiom,
! [V_B: $i,V_C: $i,T_a: $i,V_A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__distrib2_0) ).
thf(391,axiom,
! [V_A: $i,V_B: $i,V_C: $i,T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__distrib_0) ).
thf(392,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/sandbox/benchmark/theBenchmark.p',cls_sup__inf__distrib1_0) ).
thf(393,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/sandbox/benchmark/theBenchmark.p',cls_sup__inf__distrib2_0) ).
thf(394,axiom,
! [V_Q: $i,T_a: $i,T_b: $i,V_p: $i,V_q: $i,V_P: $i] :
( ( hBOOL @ ( hAPP @ V_Q @ ( hAPP @ ( c_snd @ T_a @ T_b ) @ ( c_Pair @ V_p @ V_q @ T_a @ T_b ) ) ) )
| ~ ( hBOOL @ ( hAPP @ V_Q @ V_q ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_p ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjI__realizer_1) ).
thf(395,axiom,
! [V_P: $i,T_a: $i,T_b: $i,V_p: $i,V_q: $i,V_Q: $i] :
( ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ ( c_fst @ T_a @ T_b ) @ ( c_Pair @ V_p @ V_q @ T_a @ T_b ) ) ) )
| ~ ( hBOOL @ ( hAPP @ V_Q @ V_q ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_p ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjI__realizer_0) ).
thf(396,axiom,
! [V_y: $i,T_b: $i,T_a: $i,V_x: $i] :
( V_y
= ( hAPP @ ( c_snd @ T_b @ T_a ) @ ( c_Pair @ V_x @ V_y @ T_b @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_snd__eqD_0) ).
thf(397,axiom,
! [T_b: $i,T_a: $i,V_a: $i,V_b: $i] :
( ( hAPP @ ( c_snd @ T_b @ T_a ) @ ( c_Pair @ V_a @ V_b @ T_b @ T_a ) )
= V_b ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_snd__conv_0) ).
thf(398,axiom,
! [V_x: $i,T_a: $i,T_b: $i,V_y: $i] :
( V_x
= ( hAPP @ ( c_fst @ T_a @ T_b ) @ ( c_Pair @ V_x @ V_y @ T_a @ T_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fst__eqD_0) ).
thf(399,axiom,
! [T_a: $i,T_b: $i,V_a: $i,V_b: $i] :
( ( hAPP @ ( c_fst @ T_a @ T_b ) @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) )
= V_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fst__conv_0) ).
thf(400,axiom,
! [V_a: $i,V_A: $i,T_a: $i] :
( ( ( c_Set_Oinsert @ V_a @ V_A @ T_a )
= V_A )
| ~ ( c_in @ V_a @ V_A @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb_0) ).
thf(401,axiom,
! [V_x: $i,V_A: $i,T_a: $i,V_B: $i] :
( ( ( c_Set_Oinsert @ V_x @ V_A @ T_a )
!= ( c_Set_Oinsert @ V_x @ V_B @ T_a ) )
| ( c_in @ V_x @ V_B @ T_a )
| ( c_in @ V_x @ V_A @ T_a )
| ( V_A = V_B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__ident_0) ).
thf(402,axiom,
! [V_c: $i,V_A: $i,V_B: $i,T_a: $i] :
( ( c_in @ V_c @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
| ( c_in @ V_c @ V_B @ T_a )
| ~ ( c_in @ V_c @ V_A @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DiffI_0) ).
thf(403,axiom,
! [V_c: $i,V_A: $i,V_B: $i,T_a: $i] :
( ( c_in @ V_c @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
| ( c_in @ V_c @ V_B @ T_a )
| ~ ( c_in @ V_c @ V_A @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__iff_2) ).
thf(404,axiom,
! [V_P: $i,V_x: $i,T_a: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( c_in @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bex__empty_0) ).
thf(405,axiom,
! [V_c: $i,V_A: $i,T_a: $i,V_B: $i] :
( ( c_in @ V_c @ V_A @ T_a )
| ~ ( c_in @ V_c @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntE_0) ).
thf(406,axiom,
! [V_c: $i,V_B: $i,T_a: $i,V_A: $i] :
( ( c_in @ V_c @ V_B @ T_a )
| ~ ( c_in @ V_c @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntE_1) ).
thf(407,axiom,
! [V_x: $i,V_B: $i,T_a: $i] : ( c_in @ V_x @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ T_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertCI_1) ).
thf(408,axiom,
! [V_a: $i,V_B: $i,T_a: $i] : ( c_in @ V_a @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ T_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertI1_0) ).
thf(409,axiom,
! [V_x: $i,V_A: $i,T_a: $i] : ( c_in @ V_x @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ T_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__iff_1) ).
thf(410,axiom,
! [V_c: $i,V_A: $i,T_a: $i,V_B: $i] :
( ( c_in @ V_c @ V_A @ T_a )
| ~ ( c_in @ V_c @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DiffE_0) ).
thf(411,axiom,
! [V_c: $i,V_B: $i,T_a: $i,V_A: $i] :
( ~ ( c_in @ V_c @ V_B @ T_a )
| ~ ( c_in @ V_c @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DiffE_1) ).
thf(412,axiom,
! [V_c: $i,V_B: $i,T_a: $i,V_A: $i] :
( ( c_in @ V_c @ V_B @ T_a )
| ( c_in @ V_c @ V_A @ T_a )
| ~ ( c_in @ V_c @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnE_0) ).
thf(413,axiom,
! [V_a: $i,V_A: $i,T_a: $i,V_b: $i] :
( ( c_in @ V_a @ V_A @ T_a )
| ( V_a = V_b )
| ~ ( c_in @ V_a @ ( c_Set_Oinsert @ V_b @ V_A @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertE_0) ).
thf(414,axiom,
! [V_a: $i,T_a: $i] :
~ ( c_in @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_emptyE_0) ).
thf(415,axiom,
! [V_c: $i,T_a: $i] :
~ ( c_in @ V_c @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__iff_0) ).
thf(416,axiom,
! [V_P: $i,V_x: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( c_in @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ball__empty_0) ).
thf(417,axiom,
! [V_x: $i,T_a: $i] :
~ ( c_in @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ex__in__conv_0) ).
thf(418,axiom,
! [V_c: $i,V_A: $i,V_B: $i,T_a: $i] :
( ( c_in @ V_c @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
| ~ ( c_in @ V_c @ V_B @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnCI_0) ).
thf(419,axiom,
! [V_c: $i,V_A: $i,V_B: $i,T_a: $i] :
( ( c_in @ V_c @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
| ~ ( c_in @ V_c @ V_A @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnCI_1) ).
thf(420,axiom,
! [V_x: $i,V_B: $i,T_a: $i,V_A: $i] :
( ( c_in @ V_x @ V_B @ T_a )
| ~ ( c_in @ V_x @ V_A @ T_a )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__mp_0) ).
thf(421,axiom,
! [V_c: $i,V_B: $i,T_a: $i,V_A: $i] :
( ( c_in @ V_c @ V_B @ T_a )
| ~ ( c_in @ V_c @ V_A @ T_a )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subsetD_0) ).
thf(422,axiom,
! [V_x: $i,V_B: $i,T_a: $i,V_A: $i] :
( ( c_in @ V_x @ V_B @ T_a )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_in @ V_x @ V_A @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__rev__mp_0) ).
thf(423,axiom,
! [V_t: $i,V_B: $i,T_a: $i,V_A: $i] :
( ( c_in @ V_t @ V_B @ T_a )
| ~ ( c_in @ V_t @ V_A @ T_a )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__iff_0) ).
thf(424,axiom,
! [V_a: $i,V_b: $i,V_B: $i,T_a: $i] :
( ( c_in @ V_a @ ( c_Set_Oinsert @ V_b @ V_B @ T_a ) @ T_a )
| ~ ( c_in @ V_a @ V_B @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertCI_0) ).
thf(425,axiom,
! [V_a: $i,V_b: $i,V_A: $i,T_a: $i] :
( ( c_in @ V_a @ ( c_Set_Oinsert @ V_b @ V_A @ T_a ) @ T_a )
| ~ ( c_in @ V_a @ V_A @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__iff_2) ).
thf(426,axiom,
! [V_c: $i,V_A: $i,V_B: $i,T_a: $i] :
( ( c_in @ V_c @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
| ~ ( c_in @ V_c @ V_B @ T_a )
| ~ ( c_in @ V_c @ V_A @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntI_0) ).
thf(427,axiom,
! [V_c: $i,V_A: $i,V_B: $i,T_a: $i] :
( ( c_in @ V_c @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
| ~ ( c_in @ V_c @ V_B @ T_a )
| ~ ( c_in @ V_c @ V_A @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__iff_2) ).
thf(428,axiom,
! [T_b: $i,V_f: $i,V_x: $i,V_g: $i,T_a: $i] :
( ~ ( class_HOL_Oord @ T_b )
| ( c_lessequals @ ( hAPP @ V_f @ V_x ) @ ( hAPP @ V_g @ V_x ) @ T_b )
| ~ ( c_lessequals @ V_f @ V_g @ ( tc_fun @ T_a @ T_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__funD_0) ).
thf(429,axiom,
! [V_r: $i,T_a: $i,V_y: $i,V_x: $i] :
( ( c_Wellfounded_Oacyclic @ V_r @ T_a )
| ~ ( c_Wellfounded_Oacyclic @ ( c_Set_Oinsert @ ( c_Pair @ V_y @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__insert_0) ).
thf(430,axiom,
! [V_f: $i,V_g: $i,V_r: $i,V_x: $i,T_a: $i,T_b: $i] :
( ( ( hAPP @ V_f @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ V_f @ V_g @ V_r @ V_x @ T_a @ T_b ) )
!= ( hAPP @ V_g @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ V_f @ V_g @ V_r @ V_x @ T_a @ T_b ) ) )
| ( ( c_Recdef_Ocut @ V_f @ V_r @ V_x @ T_a @ T_b )
= ( c_Recdef_Ocut @ V_g @ V_r @ V_x @ T_a @ T_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cuts__eq_2) ).
thf(431,axiom,
! [V_A: $i,V_B: $i,V_C: $i,T_a: $i] :
( ( c_lessequals @ V_A @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__subset__conv_0) ).
thf(432,axiom,
! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__subset__conv_1) ).
thf(433,axiom,
! [V_x: $i,V_A: $i,T_a: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
= V_A )
| ( c_in @ V_x @ V_A @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__insert__absorb_0) ).
thf(434,axiom,
! [V_r: $i,V_s: $i,T_a: $i] :
( ( c_Relation_Osym @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
| ~ ( c_Relation_Osym @ V_s @ T_a )
| ~ ( c_Relation_Osym @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__Int_0) ).
thf(435,axiom,
! [V_a: $i,V_b: $i,T_b: $i,T_a: $i,V_r: $i] :
( ( c_Relation_ORange @ ( c_Set_Oinsert @ ( c_Pair @ V_a @ V_b @ T_b @ T_a ) @ V_r @ ( tc_prod @ T_b @ T_a ) ) @ T_b @ T_a )
= ( c_Set_Oinsert @ V_b @ ( c_Relation_ORange @ V_r @ T_b @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__insert_0) ).
thf(436,axiom,
! [V_A: $i,V_x: $i,V_B: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_A @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1E_0) ).
thf(437,axiom,
! [V_B: $i,V_x: $i,V_A: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_B @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1E_1) ).
thf(438,axiom,
! [V_A: $i,V_x: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_4) ).
thf(439,axiom,
! [V_x: $i,V_A: $i,T_a: $i,V_B: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Set_Oinsert @ V_x @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
| ( c_in @ V_x @ V_B @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff__if_1) ).
thf(440,axiom,
! [V_R: $i,T_a: $i,V_S: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_S @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
= ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_R @ V_S @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__Un__rtrancl_0) ).
thf(441,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__Xwf__induct__rule__1__1 @ V_P @ V_r @ T_a ) ) )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__induct__rule_1) ).
thf(442,axiom,
! [V_A: $i,V_B: $i,T_b: $i,T_a: $i] : ( c_lessequals @ ( c_Relation_ORange @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ ( tc_prod @ T_b @ T_a ) @ tc_bool ) ) @ T_b @ T_a ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_ORange @ V_A @ T_b @ T_a ) @ ( c_Relation_ORange @ V_B @ T_b @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__Int__subset_0) ).
thf(443,axiom,
! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_HOL_Ominus__class_Ominus @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__disjoint_0) ).
thf(444,axiom,
! [T_a: $i,V_f: $i,T_b: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Set_Oimage @ V_f @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__is__image_1) ).
thf(445,axiom,
! [V_r: $i,T_a: $i,T_b: $i] :
( ( ( c_Relation_ODomain @ V_r @ T_a @ T_b )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( V_r
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__empty__iff_0) ).
thf(446,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/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I8_J_0) ).
thf(447,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/sandbox/benchmark/theBenchmark.p',cls_sup__left__idem_0) ).
thf(448,axiom,
! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__left__absorb_0) ).
thf(449,axiom,
! [V_R2: $i,T_a: $i,V_R1: $i] :
( ( c_lessequals @ ( c_Wellfounded_Oacc @ V_R2 @ T_a ) @ ( c_Wellfounded_Oacc @ V_R1 @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_R1 @ V_R2 @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__subset_0) ).
thf(450,axiom,
! [T_a: $i,V_B: $i,T_b: $i] :
( ( c_Product__Type_OSigma @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ T_a @ T_b )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sigma__empty1_0) ).
thf(451,axiom,
! [V_a: $i,V_A: $i,T_a: $i] :
( ( c_Set_Oinsert @ V_a @ V_A @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__is__Un_0) ).
thf(452,axiom,
! [V_A: $i,V_B: $i,T_a: $i,T_b: $i] :
( ( c_Relation_ODomain @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) @ T_a @ T_b )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_ODomain @ V_A @ T_a @ T_b ) @ ( c_Relation_ODomain @ V_B @ T_a @ T_b ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__Un__eq_0) ).
thf(453,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/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I5_J_0) ).
thf(454,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/sandbox/benchmark/theBenchmark.p',cls_sup__commute_0) ).
thf(455,axiom,
! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__commute_0) ).
thf(456,axiom,
! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff_0) ).
thf(457,axiom,
! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_lessequals @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__inf__iff_1) ).
thf(458,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_lessequals @ V_x @ V_y @ T_a )
| ~ ( c_lessequals @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__inf__iff_0) ).
thf(459,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_x: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_a @ V_b @ T_a ) @ V_x @ T_a )
| ~ ( c_lessequals @ V_b @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI2_0) ).
thf(460,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_x: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_a @ V_b @ T_a ) @ V_x @ T_a )
| ~ ( c_lessequals @ V_a @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI1_0) ).
thf(461,axiom,
! [T_a: $i,V_x: $i,V_b: $i,V_a: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_lessequals @ V_x @ V_b @ T_a )
| ~ ( c_lessequals @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_a @ V_b @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infE_1) ).
thf(462,axiom,
! [T_a: $i,V_x: $i,V_a: $i,V_b: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_lessequals @ V_x @ V_a @ T_a )
| ~ ( c_lessequals @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_a @ V_b @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infE_0) ).
thf(463,axiom,
! [V_C: $i,V_A: $i,T_a: $i,V_B: $i] :
( ( c_lessequals @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_C @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__subset__iff_0) ).
thf(464,axiom,
! [V_C: $i,V_B: $i,T_a: $i,V_A: $i] :
( ( c_lessequals @ V_C @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_C @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__subset__iff_1) ).
thf(465,axiom,
! [V_R: $i,V_S: $i,V_T: $i,T_c: $i,T_b: $i,T_a: $i] :
( ( c_Relation_Orel__comp @ V_R @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_S @ V_T @ ( tc_fun @ ( tc_prod @ T_c @ T_b ) @ tc_bool ) ) @ T_a @ T_c @ T_b )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ V_R @ V_S @ T_a @ T_c @ T_b ) @ ( c_Relation_Orel__comp @ V_R @ V_T @ T_a @ T_c @ T_b ) @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__comp__distrib_0) ).
thf(466,axiom,
! [V_S: $i,V_T: $i,T_a: $i,T_c: $i,V_R: $i,T_b: $i] :
( ( c_Relation_Orel__comp @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_S @ V_T @ ( tc_fun @ ( tc_prod @ T_a @ T_c ) @ tc_bool ) ) @ V_R @ T_a @ T_c @ T_b )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ V_S @ V_R @ T_a @ T_c @ T_b ) @ ( c_Relation_Orel__comp @ V_T @ V_R @ T_a @ T_c @ T_b ) @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__comp__distrib2_0) ).
thf(467,axiom,
! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ ( c_HOL_Ominus__class_Ominus @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff__cancel_0) ).
thf(468,axiom,
! [V_B: $i,V_A: $i,T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff__cancel2_0) ).
thf(469,axiom,
! [T_a: $i,V_A: $i,V_B: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ T_a )
!= ( c_Orderings_Obot__class_Obot @ T_a ) )
| ( V_B
= ( c_Orderings_Obot__class_Obot @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__eq__bot__eq2_0) ).
thf(470,axiom,
! [T_a: $i,V_A: $i,V_B: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ T_a )
!= ( c_Orderings_Obot__class_Obot @ T_a ) )
| ( V_A
= ( c_Orderings_Obot__class_Obot @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__eq__bot__eq1_0) ).
thf(471,axiom,
! [V_A: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty_0) ).
thf(472,axiom,
! [V_A: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( V_B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty_1) ).
thf(473,axiom,
! [V_A: $i,V_r: $i,T_a: $i] :
( ( c_Relation_Ototal__on @ V_A @ V_r @ T_a )
| ~ ( c_Order__Relation_Ostrict__linear__order__on @ V_A @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_strict__linear__order__on__def_2) ).
thf(474,axiom,
! [V_a: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( c_in @ V_a @ V_C @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__left_1) ).
thf(475,axiom,
! [V_A: $i,V_a: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( c_in @ V_a @ V_A @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__right_1) ).
thf(476,axiom,
! [V_r: $i,V_s: $i,T_b: $i,T_a: $i] :
( ( c_Relation_Oconverse @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_b @ T_a ) @ tc_bool ) ) @ T_b @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_Oconverse @ V_r @ T_b @ T_a ) @ ( c_Relation_Oconverse @ V_s @ T_b @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__Int_0) ).
thf(477,axiom,
! [V_A: $i,V_B: $i,T_a: $i,V_x: $i] :
( ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ( c_in @ V_x @ V_A @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert_0) ).
thf(478,axiom,
! [V_A: $i,V_x: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ( c_in @ V_x @ V_A @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert_1) ).
thf(479,axiom,
! [V_A: $i,V_B: $i,T_a: $i,V_x: $i] :
( ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ( c_in @ V_x @ V_A @ T_a )
| ~ ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_1) ).
thf(480,axiom,
! [V_A: $i,V_x: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ( c_in @ V_x @ V_A @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_2) ).
thf(481,axiom,
! [V_y: $i,V_A: $i,T_a: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ V_y @ V_A @ T_a ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ V_A @ V_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_2) ).
thf(482,axiom,
! [V_I: $i,V_J: $i,T_a: $i,V_C: $i,T_b: $i] :
( ( c_Product__Type_OSigma @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_I @ V_J @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ T_a @ T_b )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Product__Type_OSigma @ V_I @ V_C @ T_a @ T_b ) @ ( c_Product__Type_OSigma @ V_J @ V_C @ T_a @ T_b ) @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sigma__Un__distrib1_0) ).
thf(483,axiom,
! [V_x: $i,V_B: $i,T_a: $i,V_A: $i] :
( ( c_in @ V_x @ V_B @ T_a )
| ~ ( c_lessequals @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_0) ).
thf(484,axiom,
! [T_a: $i] : ( c_Wellfounded_Owf @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__empty_0) ).
thf(485,axiom,
! [V_x: $i,V_xa: $i,T_a: $i] :
( ( ( c_Set_Oinsert @ V_x @ V_xa @ T_a )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( c_in @ V_x @ V_xa @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Ononempty__iff_2) ).
thf(486,axiom,
! [V_c: $i,T_a: $i,T_b: $i] :
( ( c_Set_Oimage @ ( c_COMBK @ V_c @ T_a @ T_b ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b @ T_a )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__constant__conv_0) ).
thf(487,axiom,
! [T_a: $i] :
( ( c_Relation_OId__on @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__on__empty_0) ).
thf(488,axiom,
! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__crazy_0) ).
thf(489,axiom,
! [V_a: $i,T_a: $i,V_b: $i] :
( ( ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
!= ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
| ( V_a = V_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__inject_0) ).
thf(490,axiom,
! [V_a: $i,V_A: $i,T_a: $i] :
( ( c_Set_Oinsert @ V_a @ ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
= ( c_Set_Oinsert @ V_a @ V_A @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff__single_0) ).
thf(491,axiom,
! [V_A: $i,V_B: $i,T_a: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A @ ( tc_fun @ T_a @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__subset_0) ).
thf(492,axiom,
! [V_S: $i,T_a: $i,V_R: $i] :
( ( ( c_Transitive__Closure_Ortrancl @ V_S @ T_a )
= ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) )
| ~ ( c_lessequals @ V_S @ ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_lessequals @ V_R @ V_S @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__subset_0) ).
thf(493,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( c_lessequals @ ( 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 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distrib__inf__le_0) ).
thf(494,axiom,
! [V_A: $i,V_B: $i,T_a: $i,V_C: $i,T_b: $i] :
( ( c_Product__Type_OSigma @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_COMBK @ V_C @ ( tc_fun @ T_b @ tc_bool ) @ T_a ) @ T_a @ T_b )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_C @ ( tc_fun @ T_b @ tc_bool ) @ T_a ) @ T_a @ T_b ) @ ( c_Product__Type_OSigma @ V_B @ ( c_COMBK @ V_C @ ( tc_fun @ T_b @ tc_bool ) @ T_a ) @ T_a @ T_b ) @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Times__Un__distrib1_0) ).
thf(495,axiom,
! [V_C: $i,V_A: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_C @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_C @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__subset__iff_2) ).
thf(496,axiom,
! [V_C: $i,V_A: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_C @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_C @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__greatest_0) ).
thf(497,axiom,
! [V_A: $i,V_B: $i,T_a: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__lower2_0) ).
thf(498,axiom,
! [V_A: $i,V_B: $i,T_a: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A @ ( tc_fun @ T_a @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__lower1_0) ).
thf(499,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__le1_0) ).
thf(500,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__le2_0) ).
thf(501,axiom,
! [T_a: $i,V_x: $i,V_a: $i,V_b: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_lessequals @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_b @ T_a )
| ~ ( c_lessequals @ V_x @ V_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI_0) ).
thf(502,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_lessequals @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__inf__iff_2) ).
thf(503,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_lessequals @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__greatest_0) ).
thf(504,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I2_J_0) ).
thf(505,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I1_J_0) ).
thf(506,axiom,
! [V_r: $i,V_s: $i,T_b: $i,T_a: $i] :
( ( c_Relation_Oconverse @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_b @ T_a ) @ tc_bool ) ) @ T_b @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Oconverse @ V_r @ T_b @ T_a ) @ ( c_Relation_Oconverse @ V_s @ T_b @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__Un_0) ).
thf(507,axiom,
! [V_A: $i,V_B: $i,T_a: $i,V_C: $i,V_D: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_C @ V_D @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_B @ V_D @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__mono_0) ).
thf(508,axiom,
! [T_a: $i,V_r: $i] : ( c_Relation_Ototal__on @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ V_r @ T_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_total__on__empty_0) ).
thf(509,axiom,
! [V_f: $i,V_a: $i,V_B: $i,T_b: $i,T_a: $i] :
( ( c_Set_Oimage @ V_f @ ( c_Set_Oinsert @ V_a @ V_B @ T_b ) @ T_b @ T_a )
= ( c_Set_Oinsert @ ( hAPP @ V_f @ V_a ) @ ( c_Set_Oimage @ V_f @ V_B @ T_b @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__insert_0) ).
thf(510,axiom,
! [V_A: $i,V_a: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Set_Oinsert @ V_a @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
| ~ ( c_in @ V_a @ V_A @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__right_0) ).
thf(511,axiom,
! [V_a: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Set_Oinsert @ V_a @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
| ~ ( c_in @ V_a @ V_C @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__left_0) ).
thf(512,axiom,
! [T_a: $i] : ( c_Relation_Orefl__on @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__empty_0) ).
thf(513,axiom,
! [T_a: $i,V_a: $i,V_A: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Set_Oinsert @ V_a @ V_A @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__not__insert_0) ).
thf(514,axiom,
! [T_a: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__empty_1) ).
thf(515,axiom,
! [V_A: $i,T_a: $i] :
( ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( c_lessequals @ V_A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__empty_0) ).
thf(516,axiom,
! [V_r: $i,T_a: $i,V_s: $i] :
( ( c_lessequals @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_s @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_lessequals @ V_r @ ( c_Transitive__Closure_Ortrancl @ V_s @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__subset__rtrancl_0) ).
thf(517,axiom,
! [V_r: $i,T_a: $i,V_A: $i] :
( ( c_lessequals @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_A @ ( tc_fun @ T_a @ tc_bool ) @ T_a ) @ T_a @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_lessequals @ V_r @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_A @ ( tc_fun @ T_a @ tc_bool ) @ T_a ) @ T_a @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__subset__Sigma_0) ).
thf(518,axiom,
! [V_a: $i,V_b: $i,T_a: $i,V_c: $i,V_d: $i] :
( ( ( c_Set_Oinsert @ V_a @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a )
!= ( c_Set_Oinsert @ V_c @ ( c_Set_Oinsert @ V_d @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) )
| ( V_b = V_c )
| ( V_b = V_d ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_3) ).
thf(519,axiom,
! [V_a: $i,V_b: $i,T_a: $i,V_c: $i,V_d: $i] :
( ( ( c_Set_Oinsert @ V_a @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a )
!= ( c_Set_Oinsert @ V_c @ ( c_Set_Oinsert @ V_d @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) )
| ( V_a = V_d )
| ( V_b = V_d ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_2) ).
thf(520,axiom,
! [V_a: $i,V_b: $i,T_a: $i,V_c: $i,V_d: $i] :
( ( ( c_Set_Oinsert @ V_a @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a )
!= ( c_Set_Oinsert @ V_c @ ( c_Set_Oinsert @ V_d @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) )
| ( V_b = V_c )
| ( V_a = V_c ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_1) ).
thf(521,axiom,
! [V_a: $i,V_b: $i,T_a: $i,V_c: $i,V_d: $i] :
( ( ( c_Set_Oinsert @ V_a @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a )
!= ( c_Set_Oinsert @ V_c @ ( c_Set_Oinsert @ V_d @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) )
| ( V_a = V_d )
| ( V_a = V_c ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_0) ).
thf(522,axiom,
! [T_b: $i,T_a: $i] :
( ( c_Relation_ORange @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_b @ T_a ) @ tc_bool ) ) @ T_b @ T_a )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__empty_0) ).
thf(523,axiom,
! [T_a: $i] : ( c_Relation_Oantisym @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__empty_0) ).
thf(524,axiom,
! [V_A: $i,V_B: $i,T_a: $i,V_r: $i,V_s: $i] :
( ( c_Relation_Orefl__on @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
| ~ ( c_Relation_Orefl__on @ V_B @ V_s @ T_a )
| ~ ( c_Relation_Orefl__on @ V_A @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__Int_0) ).
thf(525,axiom,
! [V_A: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
!= V_B )
| ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__Un__eq_1) ).
thf(526,axiom,
! [V_A: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= V_A )
| ~ ( c_lessequals @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb2_0) ).
thf(527,axiom,
! [V_A: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= V_B )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb1_0) ).
thf(528,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 )
= V_y )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__sup_0) ).
thf(529,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 )
!= V_y )
| ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__sup_1) ).
thf(530,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 )
= V_x )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__absorb1_0) ).
thf(531,axiom,
! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= V_A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff__Int_0) ).
thf(532,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/sandbox/benchmark/theBenchmark.p',cls_inf__sup__absorb_0) ).
thf(533,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( V_x = V_y )
| ~ ( c_lessequals @ V_x @ V_y @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__antisym__conv_0) ).
thf(534,axiom,
! [V_P: $i,T_b: $i,T_c: $i,T_a: $i,V_z: $i] :
( ( hAPP @ ( c_split @ V_P @ T_b @ T_c @ T_a ) @ V_z )
= ( hAPP @ ( hAPP @ V_P @ ( hAPP @ ( c_fst @ T_b @ T_c ) @ V_z ) ) @ ( hAPP @ ( c_snd @ T_b @ T_c ) @ V_z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__beta_0) ).
thf(535,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( V_x = V_y )
| ~ ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__antisym_0) ).
thf(536,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( V_x = V_y )
| ~ ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_2) ).
thf(537,axiom,
! [V_A: $i,V_B: $i,T_a: $i] :
( ( V_A = V_B )
| ~ ( c_lessequals @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__eq__subset_2) ).
thf(538,axiom,
! [V_A: $i,V_B: $i,T_a: $i] :
( ( V_A = V_B )
| ~ ( c_lessequals @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equalityI_0) ).
thf(539,axiom,
! [V_r: $i,T_a: $i] :
( ( c_Wellfounded_Oacyclic @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a )
| ~ ( c_Wellfounded_Oacyclic @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__converse_1) ).
thf(540,axiom,
! [V_r: $i,T_a: $i] :
( ( c_Wellfounded_Oacyclic @ V_r @ T_a )
| ~ ( c_Wellfounded_Oacyclic @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__converse_0) ).
thf(541,axiom,
! [V_P: $i,V_xb: $i,V_r: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_xb ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1 @ V_P @ V_r @ T_a ) ) )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__def_1) ).
thf(542,axiom,
! [V_A: $i,V_C: $i,T_a: $i,V_B: $i] :
( ( ( c_Relation_Orel__comp @ V_A @ V_C @ T_a @ T_a @ T_a )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) )
| ( ( c_Relation_Orel__comp @ V_A @ V_B @ T_a @ T_a @ T_a )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) )
| ( ( c_Relation_Orel__comp @ V_A @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a @ T_a @ T_a )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_union__comp__emptyR_0) ).
thf(543,axiom,
! [V_B: $i,V_C: $i,T_a: $i,V_A: $i] :
( ( ( c_Relation_Orel__comp @ V_B @ V_C @ T_a @ T_a @ T_a )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) )
| ( ( c_Relation_Orel__comp @ V_A @ V_C @ T_a @ T_a @ T_a )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) )
| ( ( c_Relation_Orel__comp @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ V_C @ T_a @ T_a @ T_a )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_union__comp__emptyL_0) ).
thf(544,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/sandbox/benchmark/theBenchmark.p',cls_sup__inf__absorb_0) ).
thf(545,axiom,
! [V_A: $i,V_C: $i,T_a: $i,V_B: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int2_0) ).
thf(546,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( c_lessequals @ ( 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 ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distrib__sup__le_0) ).
thf(547,axiom,
! [V_r: $i,V_s: $i,T_a: $i] :
( ( c_Relation_Otrans @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
| ~ ( c_Relation_Otrans @ V_s @ T_a )
| ~ ( c_Relation_Otrans @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__Int_0) ).
thf(548,axiom,
! [V_x: $i,V_B: $i,T_a: $i,V_A: $i] :
( ~ ( c_in @ V_x @ V_B @ T_a )
| ~ ( c_in @ V_x @ V_A @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_disjoint__iff__not__equal_0) ).
thf(549,axiom,
! [V_A: $i,V_B: $i,T_a: $i,V_C: $i,V_D: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ V_C @ V_D @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_D @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__mono_0) ).
thf(550,axiom,
! [V_c: $i,T_a: $i,T_b: $i,V_A: $i] :
( ( ( c_Set_Oimage @ ( c_COMBK @ V_c @ T_a @ T_b ) @ V_A @ T_b @ T_a )
= ( c_Set_Oinsert @ V_c @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
| ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__constant__conv_1) ).
thf(551,axiom,
! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int__distrib2_0) ).
thf(552,axiom,
! [V_C: $i,V_A: $i,V_B: $i,T_a: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_C @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_C @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int__distrib_0) ).
thf(553,axiom,
! [T_a: $i,V_x: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ V_x ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot1E_0) ).
thf(554,axiom,
! [V_A: $i,T_a: $i,V_R: $i] :
( ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( c_lessequals @ V_A @ ( c_Relation_OImage @ V_R @ V_A @ T_a @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_Wellfounded_Owf @ V_R @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wfE__pf_0) ).
thf(555,axiom,
! [V_a: $i,V_A: $i,T_a: $i,V_b: $i,V_B: $i,T_b: $i] :
( ( c_Product__Type_OSigma @ ( c_Set_Oinsert @ V_a @ V_A @ T_a ) @ ( c_COMBK @ ( c_Set_Oinsert @ V_b @ V_B @ T_b ) @ ( tc_fun @ T_b @ tc_bool ) @ T_a ) @ T_a @ T_b )
= ( c_Set_Oinsert @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ ( c_Set_Oinsert @ V_b @ V_B @ T_b ) @ ( tc_fun @ T_b @ tc_bool ) @ T_a ) @ T_a @ T_b ) @ ( c_Product__Type_OSigma @ ( c_Set_Oinsert @ V_a @ V_A @ T_a ) @ ( c_COMBK @ V_B @ ( tc_fun @ T_b @ tc_bool ) @ T_a ) @ T_a @ T_b ) @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) @ ( tc_prod @ T_a @ T_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__times__insert_0) ).
thf(556,axiom,
! [T_a: $i,V_A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__Diff_0) ).
thf(557,axiom,
! [V_A: $i,T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= V_A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty__right_0) ).
thf(558,axiom,
! [T_a: $i,V_B: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= V_B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty__left_0) ).
thf(559,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ T_a ) @ V_x @ T_a )
= V_x ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__bot__left_0) ).
thf(560,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Orderings_Obot__class_Obot @ T_a ) @ T_a )
= V_x ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__bot__right_0) ).
thf(561,axiom,
! [V_A: $i,V_B: $i,V_C: $i,T_a: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__left__commute_0) ).
thf(562,axiom,
! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__assoc_0) ).
thf(563,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ V_z @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__assoc_0) ).
thf(564,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_z @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__left__commute_0) ).
thf(565,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_z @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I3_J_0) ).
thf(566,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ V_z @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I2_J_0) ).
thf(567,axiom,
! [V_A: $i,V_B: $i,T_a: $i,V_r: $i,V_s: $i] :
( ( c_Relation_Orefl__on @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
| ~ ( c_Relation_Orefl__on @ V_B @ V_s @ T_a )
| ~ ( c_Relation_Orefl__on @ V_A @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__Un_0) ).
thf(568,axiom,
! [V_A: $i,V_B: $i,T_a: $i,V_C: $i,T_b: $i] :
( ( c_Product__Type_OSigma @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_COMBK @ V_C @ ( tc_fun @ T_b @ tc_bool ) @ T_a ) @ T_a @ T_b )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_C @ ( tc_fun @ T_b @ tc_bool ) @ T_a ) @ T_a @ T_b ) @ ( c_Product__Type_OSigma @ V_B @ ( c_COMBK @ V_C @ ( tc_fun @ T_b @ tc_bool ) @ T_a ) @ T_a @ T_b ) @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Times__Int__distrib1_0) ).
thf(569,axiom,
! [V_r: $i,T_a: $i,V_s: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_ODomain @ V_r @ T_a @ T_a ) @ ( c_Relation_ORange @ V_s @ T_a @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( c_Wellfounded_Owf @ V_s @ T_a )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a )
| ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__Un_0) ).
thf(570,axiom,
! [V_A: $i,V_B: $i,T_a: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ V_A @ V_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1CI_1) ).
thf(571,axiom,
! [V_A: $i,V_B: $i,T_a: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ V_B @ V_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1CI_0) ).
thf(572,axiom,
! [V_B: $i,V_x: $i,V_A: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_B @ V_x ) )
| ( hBOOL @ ( hAPP @ V_A @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1E_0) ).
thf(573,axiom,
! [V_R: $i,V_S: $i,T_a: $i] :
( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_R @ V_S @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
| ~ ( c_lessequals @ ( c_Relation_Orel__comp @ V_R @ V_S @ T_a @ T_a @ T_a ) @ V_R @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_Wellfounded_Owf @ V_S @ T_a )
| ~ ( c_Wellfounded_Owf @ V_R @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__union__compatible_0) ).
thf(574,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] :
( ( c_lessequals @ ( c_Relation_Orel__comp @ V_r @ V_s @ T_a @ T_b @ T_c ) @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_C @ ( tc_fun @ T_c @ tc_bool ) @ T_a ) @ T_a @ T_c ) @ ( tc_fun @ ( tc_prod @ T_a @ T_c ) @ tc_bool ) )
| ~ ( c_lessequals @ V_s @ ( c_Product__Type_OSigma @ V_B @ ( c_COMBK @ V_C @ ( tc_fun @ T_c @ tc_bool ) @ T_b ) @ T_b @ T_c ) @ ( tc_fun @ ( tc_prod @ T_b @ T_c ) @ tc_bool ) )
| ~ ( c_lessequals @ V_r @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_B @ ( tc_fun @ T_b @ tc_bool ) @ T_a ) @ T_a @ T_b ) @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__comp__subset__Sigma_0) ).
thf(575,axiom,
! [V_A: $i,T_a: $i] :
( ( c_HOL_Ominus__class_Ominus @ V_A @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__cancel_0) ).
thf(576,axiom,
! [V_A: $i,T_a: $i] :
( ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= V_A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__empty_0) ).
thf(577,axiom,
! [V_I: $i,V_J: $i,T_a: $i,V_C: $i,T_b: $i] :
( ( c_Product__Type_OSigma @ ( c_HOL_Ominus__class_Ominus @ V_I @ V_J @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ T_a @ T_b )
= ( c_HOL_Ominus__class_Ominus @ ( c_Product__Type_OSigma @ V_I @ V_C @ T_a @ T_b ) @ ( c_Product__Type_OSigma @ V_J @ V_C @ T_a @ T_b ) @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sigma__Diff__distrib1_0) ).
thf(578,axiom,
! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( c_lessequals @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__assoc__eq_1) ).
thf(579,axiom,
! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( c_lessequals @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__assoc__eq_0) ).
thf(580,axiom,
! [V_R: $i,V_A: $i,V_B: $i,T_b: $i,T_a: $i] : ( c_lessequals @ ( c_Relation_OImage @ V_R @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b @ T_a ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_OImage @ V_R @ V_A @ T_b @ T_a ) @ ( c_Relation_OImage @ V_R @ V_B @ T_b @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__Int__subset_0) ).
thf(581,axiom,
! [V_f: $i,V_A: $i,V_B: $i,T_b: $i,T_a: $i] : ( c_lessequals @ ( c_Set_Oimage @ V_f @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b @ T_a ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a ) @ ( c_Set_Oimage @ V_f @ V_B @ T_b @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__Int__subset_0) ).
thf(582,axiom,
! [V_B: $i,V_a: $i,T_a: $i] : ( c_lessequals @ V_B @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insertI_0) ).
thf(583,axiom,
! [V_A: $i,T_a: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__empty__right_0) ).
thf(584,axiom,
! [T_a: $i,V_B: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__empty__left_0) ).
thf(585,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Orderings_Obot__class_Obot @ T_a ) @ V_x @ T_a )
= ( c_Orderings_Obot__class_Obot @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__bot__left_0) ).
thf(586,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Orderings_Obot__class_Obot @ T_a ) @ T_a )
= ( c_Orderings_Obot__class_Obot @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__bot__right_0) ).
thf(587,axiom,
! [V_A: $i,V_B: $i,T_a: $i,T_b: $i] : ( c_lessequals @ ( c_Relation_ODomain @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) @ T_a @ T_b ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_ODomain @ V_A @ T_a @ T_b ) @ ( c_Relation_ODomain @ V_B @ T_a @ T_b ) @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__Int__subset_0) ).
thf(588,axiom,
! [V_r: $i,T_a: $i,V_s: $i] :
( ( c_lessequals @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_s @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_lessequals @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__mono_0) ).
thf(589,axiom,
! [V_r: $i,V_s: $i,T_a: $i] :
( ( c_Relation_Osym @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
| ~ ( c_Relation_Osym @ V_s @ T_a )
| ~ ( c_Relation_Osym @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__Un_0) ).
thf(590,axiom,
! [V_a: $i,V_b: $i,T_a: $i,T_b: $i,V_r: $i] :
( ( c_Relation_ODomain @ ( c_Set_Oinsert @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ V_r @ ( tc_prod @ T_a @ T_b ) ) @ T_a @ T_b )
= ( c_Set_Oinsert @ V_a @ ( c_Relation_ODomain @ V_r @ T_a @ T_b ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__insert_0) ).
thf(591,axiom,
! [V_A: $i,V_x: $i,V_y: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_A @ V_x ) )
| ( V_y = V_x )
| ~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ V_y @ V_A @ T_a ) @ V_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_0) ).
thf(592,axiom,
! [V_x: $i,V_A: $i,T_a: $i] :
( ( c_Set_Oinsert @ V_x @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ T_a )
= ( c_Set_Oinsert @ V_x @ V_A @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb2_0) ).
thf(593,axiom,
! [V_R: $i,T_b: $i,T_a: $i] :
( ( c_Relation_OImage @ V_R @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b @ T_a )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__empty_0) ).
thf(594,axiom,
! [V_r: $i,V_a: $i,T_a: $i,V_b: $i,V_A: $i] :
( ( c_lessequals @ ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) @ ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__subset_0) ).
thf(595,axiom,
! [V_A: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ ( c_HOL_Ominus__class_Ominus @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= V_B )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__partition_0) ).
thf(596,axiom,
! [V_r: $i,T_a: $i] :
( ( c_Wellfounded_Oacyclic @ V_r @ T_a )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__acyclic_0) ).
thf(597,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_x @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I1_J_0) ).
thf(598,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_x @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__commute_0) ).
thf(599,axiom,
! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__commute_0) ).
thf(600,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( c_lessequals @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I3_J_0) ).
thf(601,axiom,
! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( c_lessequals @ V_y @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I4_J_0) ).
thf(602,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ V_z @ T_a )
| ~ ( c_lessequals @ V_y @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_z @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__sup__iff_2) ).
thf(603,axiom,
! [T_a: $i,V_y: $i,V_z: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) @ V_x @ T_a )
| ~ ( c_lessequals @ V_z @ V_x @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__least_0) ).
thf(604,axiom,
! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ V_y @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__ge2_0) ).
thf(605,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__ge1_0) ).
thf(606,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) @ V_x @ T_a )
| ~ ( c_lessequals @ V_b @ V_x @ T_a )
| ~ ( c_lessequals @ V_a @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI_0) ).
thf(607,axiom,
! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__least_0) ).
thf(608,axiom,
! [V_A: $i,V_B: $i,T_a: $i] : ( c_lessequals @ V_A @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__upper1_0) ).
thf(609,axiom,
! [V_B: $i,V_A: $i,T_a: $i] : ( c_lessequals @ V_B @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__upper2_0) ).
thf(610,axiom,
! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_2) ).
thf(611,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 )
= V_y )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__absorb2_0) ).
thf(612,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 )
!= V_x )
| ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__inf_1) ).
thf(613,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 )
= V_x )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__inf_0) ).
thf(614,axiom,
! [V_A: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= V_B )
| ~ ( c_lessequals @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb1_0) ).
thf(615,axiom,
! [V_A: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= V_A )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb2_0) ).
thf(616,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/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I6_J_0) ).
thf(617,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/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I7_J_0) ).
thf(618,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/sandbox/benchmark/theBenchmark.p',cls_sup__left__commute_0) ).
thf(619,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/sandbox/benchmark/theBenchmark.p',cls_sup__assoc_0) ).
thf(620,axiom,
! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__assoc_0) ).
thf(621,axiom,
! [V_A: $i,V_B: $i,V_C: $i,T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__left__commute_0) ).
thf(622,axiom,
! [V_f: $i,V_A: $i,T_b: $i,T_a: $i,V_B: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a ) @ ( c_Set_Oimage @ V_f @ V_B @ T_b @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Set_Oimage @ V_f @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__diff__subset_0) ).
thf(623,axiom,
! [V_f: $i,T_b: $i,T_a: $i] :
( ( c_Set_Oimage @ V_f @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b @ T_a )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__empty_0) ).
thf(624,axiom,
! [T_a: $i,V_x: $i,V_x_H: $i,V_y_H: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_x @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x_H @ V_y_H @ T_a ) )
| ( V_x_H = V_y_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__eqI_0) ).
thf(625,axiom,
! [T_a: $i,V_xa: $i,V_y: $i,V_x: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_xa @ V_y @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x @ V_x @ T_a ) )
| ( V_xa = V_y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__eqI_1) ).
thf(626,axiom,
! [V_r: $i,V_C: $i,T_a: $i,T_b: $i,V_B: $i,V_A: $i] :
( ( c_lessequals @ ( c_Relation_OImage @ V_r @ V_C @ T_a @ T_b ) @ V_B @ ( tc_fun @ T_b @ tc_bool ) )
| ~ ( c_lessequals @ V_r @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_B @ ( tc_fun @ T_b @ tc_bool ) @ T_a ) @ T_a @ T_b ) @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__subset_0) ).
thf(627,axiom,
! [V_xa: $i,V_x: $i,T_a: $i] :
( ( c_Set_Oinsert @ V_xa @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a )
= ( c_Set_Oinsert @ V_x @ ( c_Set_Oinsert @ V_xa @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_4) ).
thf(628,axiom,
! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__idemp_0) ).
thf(629,axiom,
! [V_P: $i,T_a: $i,T_b: $i,V_Q: $i] :
( ( hAPP @ ( c_COMBK @ V_P @ T_a @ T_b ) @ V_Q )
= V_P ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBK__def_0) ).
thf(630,axiom,
! [T_a: $i,T_b: $i,V_p: $i] :
( ( c_Pair @ ( hAPP @ ( c_fst @ T_a @ T_b ) @ V_p ) @ ( hAPP @ ( c_snd @ T_a @ T_b ) @ V_p ) @ T_a @ T_b )
= V_p ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pair__collapse_0) ).
thf(631,axiom,
! [V_t: $i,T_a: $i,T_b: $i] :
( V_t
= ( c_Pair @ ( hAPP @ ( c_fst @ T_a @ T_b ) @ V_t ) @ ( hAPP @ ( c_snd @ T_a @ T_b ) @ V_t ) @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_surjective__pairing_0) ).
thf(632,axiom,
! [V_x: $i,V_y: $i,V_A: $i,T_a: $i] :
( ( c_Set_Oinsert @ V_x @ ( c_Set_Oinsert @ V_y @ V_A @ T_a ) @ T_a )
= ( c_Set_Oinsert @ V_y @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__commute_0) ).
thf(633,axiom,
! [T_a: $i,T_b: $i] :
( ( c_Relation_ODomain @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) @ T_a @ T_b )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__empty_0) ).
thf(634,axiom,
! [V_P: $i,V_Rb: $i,V_R: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_Rb ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Osko__Recdef__Xtfl__wf__induct__1__1 @ V_P @ V_R @ T_a ) ) )
| ~ ( c_Wellfounded_Owf @ V_R @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tfl__wf__induct_1) ).
thf(635,axiom,
! [V_R: $i,V_A: $i,V_B: $i,T_b: $i,T_a: $i] :
( ( c_Relation_OImage @ V_R @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_OImage @ V_R @ V_A @ T_b @ T_a ) @ ( c_Relation_OImage @ V_R @ V_B @ T_b @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__Un_0) ).
thf(636,axiom,
! [V_R: $i,V_S: $i,T_b: $i,T_a: $i,V_A: $i] :
( ( c_Relation_OImage @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_R @ V_S @ ( tc_fun @ ( tc_prod @ T_b @ T_a ) @ tc_bool ) ) @ V_A @ T_b @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_OImage @ V_R @ V_A @ T_b @ T_a ) @ ( c_Relation_OImage @ V_S @ V_A @ T_b @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Image_0) ).
thf(637,axiom,
! [V_r_H: $i,V_s_H: $i,T_a: $i,T_b: $i,T_c: $i,V_r: $i,V_s: $i] :
( ( c_lessequals @ ( c_Relation_Orel__comp @ V_r_H @ V_s_H @ T_a @ T_b @ T_c ) @ ( c_Relation_Orel__comp @ V_r @ V_s @ T_a @ T_b @ T_c ) @ ( tc_fun @ ( tc_prod @ T_a @ T_c ) @ tc_bool ) )
| ~ ( c_lessequals @ V_s_H @ V_s @ ( tc_fun @ ( tc_prod @ T_b @ T_c ) @ tc_bool ) )
| ~ ( c_lessequals @ V_r_H @ V_r @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__comp__mono_0) ).
thf(638,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/sandbox/benchmark/theBenchmark.p',cls_sup__idem_0) ).
thf(639,axiom,
! [V_A: $i,T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
= V_A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb_0) ).
thf(640,axiom,
! [V_r: $i,V_A: $i,T_a: $i] :
( ( c_lessequals @ V_r @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_A @ ( tc_fun @ T_a @ tc_bool ) @ T_a ) @ T_a @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_Relation_Orefl__on @ V_A @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__def_0) ).
thf(641,axiom,
! [V_A: $i,T_a: $i] : ( c_lessequals @ ( c_Relation_OId__on @ V_A @ T_a ) @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_A @ ( tc_fun @ T_a @ tc_bool ) @ T_a ) @ T_a @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__on__subset__Times_0) ).
thf(642,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/sandbox/benchmark/theBenchmark.p',cls_inf__sup__distrib2_0) ).
thf(643,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/sandbox/benchmark/theBenchmark.p',cls_inf__sup__distrib1_0) ).
thf(644,axiom,
! [V_A: $i,V_B: $i,V_C: $i,T_a: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Un__distrib_0) ).
thf(645,axiom,
! [V_B: $i,V_C: $i,T_a: $i,V_A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Un__distrib2_0) ).
thf(646,axiom,
! [V_A: $i,T_a: $i,T_b: $i,V_B: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ ( c_Relation_ODomain @ V_A @ T_a @ T_b ) @ ( c_Relation_ODomain @ V_B @ T_a @ T_b ) @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Relation_ODomain @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) @ T_a @ T_b ) @ ( tc_fun @ T_a @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__Diff__subset_0) ).
thf(647,axiom,
! [V_A: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= V_A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__triv_0) ).
thf(648,axiom,
! [V_b: $i,V_a: $i,T_a: $i] :
( ( V_b = V_a )
| ~ ( c_in @ V_b @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singletonE_0) ).
thf(649,axiom,
! [V_I: $i,V_J: $i,T_a: $i,V_C: $i,T_b: $i] :
( ( c_Product__Type_OSigma @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_I @ V_J @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ T_a @ T_b )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Product__Type_OSigma @ V_I @ V_C @ T_a @ T_b ) @ ( c_Product__Type_OSigma @ V_J @ V_C @ T_a @ T_b ) @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sigma__Int__distrib1_0) ).
thf(650,axiom,
! [V_r: $i,T_a: $i,V_s: $i] :
( ( c_lessequals @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Relation_Orel__comp @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ V_r @ T_a @ T_a @ T_a ) @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_lessequals @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__Int__subset_0) ).
thf(651,axiom,
! [V_c: $i,T_b: $i,T_a: $i,V_A: $i,V_x: $i] :
( ( ( c_Set_Oimage @ ( c_COMBK @ V_c @ T_b @ T_a ) @ V_A @ T_a @ T_b )
= ( c_Set_Oinsert @ V_c @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b ) )
| ~ ( c_in @ V_x @ V_A @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__constant_0) ).
thf(652,axiom,
! [V_A: $i,V_x: $i,T_a: $i,V_B: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_in @ V_x @ V_A @ T_a )
| ~ ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_0) ).
thf(653,axiom,
! [V_A: $i,V_x: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_in @ V_x @ V_A @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_3) ).
thf(654,axiom,
! [V_A: $i,V_x: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_in @ V_x @ V_A @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__single__insert_0) ).
thf(655,axiom,
! [V_A: $i,V_B: $i,T_b: $i,V_C: $i,T_a: $i,V_x: $i] :
( ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_b @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_C @ ( tc_fun @ T_a @ tc_bool ) @ T_b ) @ T_b @ T_a ) @ ( c_Product__Type_OSigma @ V_B @ ( c_COMBK @ V_C @ ( tc_fun @ T_a @ tc_bool ) @ T_b ) @ T_b @ T_a ) @ ( tc_fun @ ( tc_prod @ T_b @ T_a ) @ tc_bool ) )
| ~ ( c_in @ V_x @ V_C @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Times__subset__cancel2_0) ).
thf(656,axiom,
! [V_A: $i,V_C: $i,T_a: $i,T_b: $i,V_B: $i,V_x: $i] :
( ( c_lessequals @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_C @ ( tc_fun @ T_a @ tc_bool ) @ T_b ) @ T_b @ T_a ) @ ( c_Product__Type_OSigma @ V_B @ ( c_COMBK @ V_C @ ( tc_fun @ T_a @ tc_bool ) @ T_b ) @ T_b @ T_a ) @ ( tc_fun @ ( tc_prod @ T_b @ T_a ) @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_b @ tc_bool ) )
| ~ ( c_in @ V_x @ V_C @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Times__subset__cancel2_1) ).
thf(657,axiom,
! [V_x: $i,V_A: $i,T_a: $i,V_B: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( c_in @ V_x @ V_B @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff1_0) ).
thf(658,axiom,
! [V_A: $i,V_B: $i,T_a: $i,V_x: $i] :
( ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_1) ).
thf(659,axiom,
! [V_A: $i,V_b: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_b @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insertI2_0) ).
thf(660,axiom,
! [V_A: $i,T_b: $i,T_a: $i,V_B: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ ( c_Relation_ORange @ V_A @ T_b @ T_a ) @ ( c_Relation_ORange @ V_B @ T_b @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Relation_ORange @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ ( tc_prod @ T_b @ T_a ) @ tc_bool ) ) @ T_b @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__Diff__subset_0) ).
thf(661,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__Xwf__induct__1__1 @ V_P @ V_r @ T_a ) ) )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__induct_1) ).
thf(662,axiom,
! [T_a: $i,T_b: $i,V_p: $i,V_q: $i] :
( ( ( hAPP @ ( c_snd @ T_a @ T_b ) @ V_p )
!= ( hAPP @ ( c_snd @ T_a @ T_b ) @ V_q ) )
| ( ( hAPP @ ( c_fst @ T_a @ T_b ) @ V_p )
!= ( hAPP @ ( c_fst @ T_a @ T_b ) @ V_q ) )
| ( V_p = V_q ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_prod__eqI_0) ).
thf(663,axiom,
! [T_a: $i,T_b: $i,V_s: $i,V_t: $i] :
( ( ( hAPP @ ( c_snd @ T_a @ T_b ) @ V_s )
!= ( hAPP @ ( c_snd @ T_a @ T_b ) @ V_t ) )
| ( ( hAPP @ ( c_fst @ T_a @ T_b ) @ V_s )
!= ( hAPP @ ( c_fst @ T_a @ T_b ) @ V_t ) )
| ( V_s = V_t ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Pair__fst__snd__eq_0) ).
thf(664,axiom,
! [V_R: $i,T_a: $i,V_S: $i] : ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_S @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_R @ V_S @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__Un__subset_0) ).
thf(665,axiom,
! [T_a: $i,V_f: $i,V_A: $i,T_b: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a ) )
| ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__is__image_0) ).
thf(666,axiom,
! [V_a: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Set_Oinsert @ V_a @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__insert__left_0) ).
thf(667,axiom,
! [V_A: $i,V_a: $i,V_B: $i,T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Set_Oinsert @ V_a @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__insert__right_0) ).
thf(668,axiom,
! [T_a: $i,T_c: $i,V_R: $i,T_b: $i] :
( ( c_Relation_Orel__comp @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_c ) @ tc_bool ) ) @ V_R @ T_a @ T_c @ T_b )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__comp__empty1_0) ).
thf(669,axiom,
! [V_R: $i,T_c: $i,T_b: $i,T_a: $i] :
( ( c_Relation_Orel__comp @ V_R @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_c @ T_b ) @ tc_bool ) ) @ T_a @ T_c @ T_b )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__comp__empty2_0) ).
thf(670,axiom,
! [T_a: $i,V_A: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A @ ( tc_fun @ T_a @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__subsetI_0) ).
thf(671,axiom,
! [T_a: $i,V_B: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ V_B @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__by__empty_0) ).
thf(672,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Obot @ T_a )
| ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ T_a ) @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__least_0) ).
thf(673,axiom,
! [V_A: $i,V_a: $i,V_B: $i,T_a: $i] :
( ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__insert_0) ).
thf(674,axiom,
! [V_A: $i,V_a: $i,V_B: $i,T_a: $i] :
( ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__insert2_0) ).
thf(675,axiom,
! [V_a: $i,V_A: $i,T_a: $i] :
( ( c_Set_Oinsert @ V_a @ V_A @ T_a )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__not__empty_0) ).
thf(676,axiom,
! [V_a: $i,V_A: $i,T_a: $i,V_B: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ V_a @ V_A @ T_a ) @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Set_Oinsert @ V_a @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__inter__insert_0) ).
thf(677,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(678,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[677]) ).
thf(679,negated_conjecture,
~ ( c_in @ ( c_Pair @ v_c____ @ v_d____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ v_P____ ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(680,plain,
$false = $false,
inference(unfold_def,[status(thm)],[678]) ).
thf(681,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(682,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(683,plain,
( ( class_HOL_Oord @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(684,plain,
( ( class_Orderings_Obot @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(685,plain,
( ( class_Orderings_Oorder @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(686,plain,
( ( class_Lattices_Olattice @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(687,plain,
( ( class_Orderings_Opreorder @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(688,plain,
( ( class_Lattices_Obounded__lattice @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(689,plain,
( ( class_Lattices_Odistrib__lattice @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(690,plain,
( ( class_Lattices_Olower__semilattice @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(691,plain,
( ( class_Lattices_Oupper__semilattice @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(692,plain,
( ( class_HOL_Oord @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(693,plain,
( ( class_Orderings_Obot @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(694,plain,
( ( class_Orderings_Oorder @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(695,plain,
( ( class_Lattices_Olattice @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(696,plain,
( ( class_Orderings_Olinorder @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(697,plain,
( ( class_Orderings_Opreorder @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(698,plain,
( ( class_Lattices_Odistrib__lattice @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(699,plain,
( ( class_Lattices_Olower__semilattice @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(700,plain,
( ( class_Lattices_Oupper__semilattice @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(701,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_HOL_Oord @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_HOL_Oord @ T_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(702,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Orderings_Obot @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Orderings_Obot @ T_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(703,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Orderings_Oorder @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Orderings_Oorder @ T_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(704,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)],[24]) ).
thf(705,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Orderings_Opreorder @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Orderings_Opreorder @ T_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(706,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Lattices_Obounded__lattice @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Lattices_Obounded__lattice @ T_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(707,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)],[27]) ).
thf(708,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)],[28]) ).
thf(709,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)],[29]) ).
thf(710,plain,
( ( c_in @ ( c_Pair @ v_c____ @ v_d____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_HOL_OIf @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ v_h____ @ tc_nat @ ( tc_fun @ tc_nat @ tc_bool ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ v_n____ @ tc_Arrow__Order__Mirabelle_Oindi @ tc_nat @ tc_bool ) @ tc_bool @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ ( c_COMBC @ ( c_COMBB @ c_Arrow__Order__Mirabelle_Omktop @ v_P____ @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ v_e____ @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_HOL_OIf @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ ( c_COMBC @ ( c_COMBB @ ( c_fequal @ tc_nat ) @ v_h____ @ tc_nat @ ( tc_fun @ tc_nat @ tc_bool ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ v_n____ @ tc_Arrow__Order__Mirabelle_Oindi @ tc_nat @ tc_bool ) @ tc_bool @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ ( c_COMBC @ ( c_COMBC @ ( c_COMBB @ c_Arrow__Order__Mirabelle_Oabove @ v_P____ @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ v_c____ @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ v_e____ @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ ( c_COMBC @ ( c_COMBB @ c_Arrow__Order__Mirabelle_Omkbot @ v_P____ @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ v_e____ @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(711,plain,
( ( ( c_in @ ( c_Pair @ v_c____ @ v_d____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_HOL_OIf @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ v_h____ @ tc_nat @ ( tc_fun @ tc_nat @ tc_bool ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ v_n____ @ tc_Arrow__Order__Mirabelle_Oindi @ tc_nat @ tc_bool ) @ tc_bool @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ ( c_COMBC @ ( c_COMBB @ c_Arrow__Order__Mirabelle_Omktop @ v_P____ @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ v_e____ @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_HOL_OIf @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ ( c_COMBC @ ( c_COMBB @ ( c_fequal @ tc_nat ) @ v_h____ @ tc_nat @ ( tc_fun @ tc_nat @ tc_bool ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ v_n____ @ tc_Arrow__Order__Mirabelle_Oindi @ tc_nat @ tc_bool ) @ tc_bool @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ ( c_COMBC @ ( c_COMBC @ ( c_COMBB @ c_Arrow__Order__Mirabelle_Oabove @ v_P____ @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ v_c____ @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ v_e____ @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ ( c_COMBC @ ( c_COMBB @ c_Arrow__Order__Mirabelle_Omkbot @ v_P____ @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ v_e____ @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ v_c____ @ v_d____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ v_P____ ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(712,plain,
( ( ( c_in @ ( c_Pair @ v_c____ @ v_d____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ v_P____ ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ v_c____ @ v_d____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_HOL_OIf @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ v_h____ @ tc_nat @ ( tc_fun @ tc_nat @ tc_bool ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ v_n____ @ tc_Arrow__Order__Mirabelle_Oindi @ tc_nat @ tc_bool ) @ tc_bool @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ ( c_COMBC @ ( c_COMBB @ c_Arrow__Order__Mirabelle_Omktop @ v_P____ @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ v_e____ @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_HOL_OIf @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ ( c_COMBC @ ( c_COMBB @ ( c_fequal @ tc_nat ) @ v_h____ @ tc_nat @ ( tc_fun @ tc_nat @ tc_bool ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ v_n____ @ tc_Arrow__Order__Mirabelle_Oindi @ tc_nat @ tc_bool ) @ tc_bool @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ ( c_COMBC @ ( c_COMBC @ ( c_COMBB @ c_Arrow__Order__Mirabelle_Oabove @ v_P____ @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ v_c____ @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ v_e____ @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ ( c_COMBC @ ( c_COMBB @ c_Arrow__Order__Mirabelle_Omkbot @ v_P____ @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ v_e____ @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(713,plain,
( ( ! [V_S: $i,V_x: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_S @ V_x ) )
| ~ ( c_in @ V_x @ V_S @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(714,plain,
( ( ! [V_x: $i,V_S: $i,T_a: $i] :
( ( c_in @ V_x @ V_S @ T_a )
| ~ ( hBOOL @ ( hAPP @ V_S @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(715,plain,
( ( ! [V_a: $i,V_b: $i,T_a: $i,T_b: $i,V_a_H: $i,V_b_H: $i] :
( ( ( c_Pair @ V_a @ V_b @ T_a @ T_b )
!= ( c_Pair @ V_a_H @ V_b_H @ T_a @ T_b ) )
| ( V_a = V_a_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(716,plain,
( ( ! [V_a: $i,V_b: $i,T_a: $i,T_b: $i,V_a_H: $i,V_b_H: $i] :
( ( ( c_Pair @ V_a @ V_b @ T_a @ T_b )
!= ( c_Pair @ V_a_H @ V_b_H @ T_a @ T_b ) )
| ( V_b = V_b_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(717,plain,
( ( ! [V_a: $i,T_a: $i,V_r: $i,V_A: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_a @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_a @ V_A @ T_a )
| ~ ( c_Relation_Orefl__on @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(718,plain,
( ( ! [V_x: $i,V_A: $i,T_a: $i,V_y: $i,V_r: $i] :
( ( c_in @ V_x @ V_A @ T_a )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Relation_Orefl__on @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(719,plain,
( ( ! [V_y: $i,V_A: $i,T_a: $i,V_x: $i,V_r: $i] :
( ( c_in @ V_y @ V_A @ T_a )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Relation_Orefl__on @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(720,plain,
( ( ! [V_x: $i,T_a: $i,V_r: $i,V_A: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_x @ V_A @ T_a )
| ~ ( c_Relation_Orefl__on @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(721,plain,
( ( ! [V_xa: $i,V_x: $i,T_a: $i,V_r: $i,V_A: $i] :
( ( c_in @ ( c_Pair @ V_xa @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ( c_in @ ( c_Pair @ V_x @ V_xa @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ( V_x = V_xa )
| ~ ( c_in @ V_xa @ V_A @ T_a )
| ~ ( c_in @ V_x @ V_A @ T_a )
| ~ ( c_Relation_Ototal__on @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(722,plain,
( ( ! [V_a: $i,V_A: $i,T_a: $i,V_b: $i,T_b: $i,V_B: $i] :
( ( c_in @ V_a @ V_A @ T_a )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ ( c_Product__Type_OSigma @ V_A @ V_B @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(723,plain,
( ( ! [V_b: $i,V_B: $i,V_a: $i,T_b: $i,T_a: $i,V_A: $i] :
( ( c_in @ V_b @ ( hAPP @ V_B @ V_a ) @ T_b )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ ( c_Product__Type_OSigma @ V_A @ V_B @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(724,plain,
( ( ! [V_a: $i,V_r: $i,T_a: $i,T_b: $i,V_b: $i] :
( ( c_in @ V_a @ ( c_Relation_ODomain @ V_r @ T_a @ T_b ) @ T_a )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ V_r @ ( tc_prod @ T_a @ T_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(725,plain,
( ( ! [V_a: $i,V_r: $i,T_a: $i,T_b: $i,V_x: $i] :
( ( c_in @ V_a @ ( c_Relation_ODomain @ V_r @ T_a @ T_b ) @ T_a )
| ~ ( c_in @ ( c_Pair @ V_a @ V_x @ T_a @ T_b ) @ V_r @ ( tc_prod @ T_a @ T_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(726,plain,
( ( ! [V_b: $i,V_r: $i,T_a: $i,T_b: $i,V_a: $i] :
( ( c_in @ V_b @ ( c_Relation_ORange @ V_r @ T_a @ T_b ) @ T_b )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ V_r @ ( tc_prod @ T_a @ T_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(727,plain,
( ( ! [V_a: $i,V_r: $i,T_b: $i,T_a: $i,V_x: $i] :
( ( c_in @ V_a @ ( c_Relation_ORange @ V_r @ T_b @ T_a ) @ T_a )
| ~ ( c_in @ ( c_Pair @ V_x @ V_a @ T_b @ T_a ) @ V_r @ ( tc_prod @ T_b @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(728,plain,
( ( ! [V_x: $i,V_A: $i,T_a: $i,V_y: $i,V_r: $i] :
( ( c_in @ V_x @ V_A @ T_a )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(729,plain,
( ( ! [V_y: $i,V_A: $i,T_a: $i,V_x: $i,V_r: $i] :
( ( c_in @ V_y @ V_A @ T_a )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(730,plain,
( ( ! [V_x: $i,T_a: $i,V_A: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_x @ T_a @ T_a ) @ ( c_Relation_OId__on @ V_A @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_x @ V_A @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(731,plain,
( ( ! [V_x: $i,V_A: $i,T_a: $i,V_y: $i] :
( ( c_in @ V_x @ V_A @ T_a )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Relation_OId__on @ V_A @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(732,plain,
( ( ! [V_b: $i,V_r: $i,V_A: $i,T_b: $i,T_a: $i,V_x: $i] :
( ( c_in @ V_b @ ( c_Relation_OImage @ V_r @ V_A @ T_b @ T_a ) @ T_a )
| ~ ( c_in @ ( c_Pair @ V_x @ V_b @ T_b @ T_a ) @ V_r @ ( tc_prod @ T_b @ T_a ) )
| ~ ( c_in @ V_x @ V_A @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(733,plain,
( ( ! [V_b: $i,V_r: $i,V_A: $i,T_a: $i,T_b: $i,V_a: $i] :
( ( c_in @ V_b @ ( c_Relation_OImage @ V_r @ V_A @ T_a @ T_b ) @ T_b )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ V_r @ ( tc_prod @ T_a @ T_b ) )
| ~ ( c_in @ V_a @ V_A @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(734,plain,
( ( ! [V_y: $i,V_r: $i,T_a: $i,V_a: $i] :
( ( c_in @ V_y @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a )
| ~ ( c_in @ ( c_Pair @ V_y @ V_a @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_a @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(735,plain,
( ( ! [V_a: $i,V_r: $i,T_a: $i,V_b: $i] :
( ( c_in @ V_a @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_b @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(736,plain,
( ( ! [V_a: $i,V_b: $i,T_a: $i,T_b: $i,V_A: $i,V_B: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ ( c_Product__Type_OSigma @ V_A @ V_B @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) )
| ~ ( c_in @ V_b @ ( hAPP @ V_B @ V_a ) @ T_b )
| ~ ( c_in @ V_a @ V_A @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[56]) ).
thf(737,plain,
( ( ! [V_a: $i,V_b: $i,T_a: $i,T_b: $i,V_A: $i,V_B: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ ( c_Product__Type_OSigma @ V_A @ V_B @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) )
| ~ ( c_in @ V_b @ ( hAPP @ V_B @ V_a ) @ T_b )
| ~ ( c_in @ V_a @ V_A @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(738,plain,
( ( ! [V_a: $i,V_b: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_b @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1 @ V_a @ V_b ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( V_a = V_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[58]) ).
thf(739,plain,
( ( ! [V_x: $i,V_y: $i,V_L: $i,V_z: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ V_L @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( V_x = V_z )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omkbot @ V_L ) @ V_z ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[59]) ).
thf(740,plain,
( ( ! [V_xa: $i,V_x: $i,V_L: $i] :
( ( V_xa = V_x )
| ( V_xa = V_x )
| ( c_in @ ( c_Pair @ V_xa @ V_x @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omktop @ V_L ) @ V_x ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(741,plain,
( ( ! [V_x: $i,V_y: $i,V_L: $i,V_z: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omkbot @ V_L ) @ V_z ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ V_L @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( V_x = V_z )
| ( V_y = V_z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(742,plain,
( ( ! [V_x: $i,V_y: $i,V_L: $i,V_z: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omkbot @ V_L ) @ V_z ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ V_L @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( V_x = V_y )
| ( V_y = V_z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[62]) ).
thf(743,plain,
( ( ! [V_xa: $i,V_x: $i,V_L: $i] :
~ ( c_in @ ( c_Pair @ V_xa @ V_x @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omkbot @ V_L ) @ V_x ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ),
inference(unfold_def,[status(thm)],[63]) ).
thf(744,plain,
( ( ! [V_x: $i,V_L: $i] :
~ ( c_in @ ( c_Pair @ V_x @ V_x @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omkbot @ V_L ) @ V_x ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ),
inference(unfold_def,[status(thm)],[64]) ).
thf(745,plain,
( ( ! [V_x: $i,V_y: $i,V_L: $i] :
( ( V_x = V_y )
| ( V_y = V_x )
| ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omkbot @ V_L ) @ V_x ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[65]) ).
thf(746,plain,
( ( ! [V_x: $i,V_y: $i,V_L: $i,V_z: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ V_L @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( V_y = V_z )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omktop @ V_L ) @ V_z ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[66]) ).
thf(747,plain,
( ( ! [V_x: $i,V_y: $i,V_L: $i] :
~ ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omktop @ V_L ) @ V_x ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ),
inference(unfold_def,[status(thm)],[67]) ).
thf(748,plain,
( ( ! [V_x: $i,V_L: $i] :
~ ( c_in @ ( c_Pair @ V_x @ V_x @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omktop @ V_L ) @ V_x ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ),
inference(unfold_def,[status(thm)],[68]) ).
thf(749,plain,
( ( ! [V_x: $i,V_y: $i,V_L: $i,V_z: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omktop @ V_L ) @ V_z ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ V_L @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( V_y = V_z )
| ( V_x = V_z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[69]) ).
thf(750,plain,
( ( ! [V_x: $i,V_y: $i,V_L: $i,V_z: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omktop @ V_L ) @ V_z ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ V_L @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( V_x = V_y )
| ( V_x = V_z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(751,plain,
( ( ! [V_a: $i,T_a: $i] : ( c_in @ ( c_Pair @ V_a @ V_a @ T_a @ T_a ) @ ( c_Relation_OId @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[71]) ).
thf(752,plain,
( ( ! [V_x: $i,T_a: $i] : ( c_in @ ( c_Pair @ V_x @ V_x @ T_a @ T_a ) @ ( c_Relation_OId @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[72]) ).
thf(753,plain,
( ( ! [V_a: $i,V_c: $i,T_a: $i,V_r: $i,V_b: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_b @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[73]) ).
thf(754,plain,
( ( ! [V_a: $i,V_c: $i,T_a: $i,V_R: $i,V_b: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_b @ V_c @ T_a @ T_a ) @ V_R @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_R @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[74]) ).
thf(755,plain,
( ( ! [V_a: $i,V_c: $i,T_a: $i,T_c: $i,V_r: $i,V_s: $i,T_b: $i,V_b: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_c ) @ ( c_Relation_Orel__comp @ V_r @ V_s @ T_a @ T_b @ T_c ) @ ( tc_prod @ T_a @ T_c ) )
| ~ ( c_in @ ( c_Pair @ V_b @ V_c @ T_b @ T_c ) @ V_s @ ( tc_prod @ T_b @ T_c ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ V_r @ ( tc_prod @ T_a @ T_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[75]) ).
thf(756,plain,
( ( ! [V_b: $i,V_a: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_b @ V_a @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Relation_Osym @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[76]) ).
thf(757,plain,
( ( ! [V_y: $i,V_x: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_y @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Relation_Osym @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[77]) ).
thf(758,plain,
( ( ! [V_f: $i,V_x: $i,V_y: $i,T_b: $i,V_r: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ ( hAPP @ V_f @ V_x ) @ ( hAPP @ V_f @ V_y ) @ T_b @ T_b ) @ V_r @ ( tc_prod @ T_b @ T_b ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Relation_Oinv__image @ V_r @ V_f @ T_b @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[78]) ).
thf(759,plain,
( ( ! [V_x: $i,V_y: $i,T_a: $i,V_r: $i,V_f: $i,T_b: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Relation_Oinv__image @ V_r @ V_f @ T_b @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ ( hAPP @ V_f @ V_x ) @ ( hAPP @ V_f @ V_y ) @ T_b @ T_b ) @ V_r @ ( tc_prod @ T_b @ T_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[79]) ).
thf(760,plain,
( ( ! [V_a: $i,T_a: $i,V_r: $i] :
( ~ ( c_in @ ( c_Pair @ V_a @ V_a @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[80]) ).
thf(761,plain,
( ( ! [V_x: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Nitpick_Orefl_H @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[81]) ).
thf(762,plain,
( ( ! [V_a: $i,V_b: $i,T_a: $i] :
( ( V_a = V_b )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Relation_OId @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[82]) ).
thf(763,plain,
( ( ! [V_f: $i,V_r: $i,V_x: $i,T_a: $i,T_b: $i,V_g: $i,V_y: $i] :
( ( ( c_Recdef_Ocut @ V_f @ V_r @ V_x @ T_a @ T_b )
!= ( c_Recdef_Ocut @ V_g @ V_r @ V_x @ T_a @ T_b ) )
| ( ( hAPP @ V_f @ V_y )
= ( hAPP @ V_g @ V_y ) )
| ~ ( c_in @ ( c_Pair @ V_y @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[83]) ).
thf(764,plain,
( ( ! [V_x: $i,V_y: $i,T_a: $i,V_A: $i] :
( ( V_x = V_y )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Relation_OId__on @ V_A @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[84]) ).
thf(765,plain,
( ( ! [V_f: $i,V_y: $i,V_z: $i,T_a: $i,V_r: $i,T_b: $i] :
( ( ( hAPP @ V_f @ V_y )
= ( hAPP @ V_f @ V_z ) )
| ~ ( c_in @ ( c_Pair @ V_y @ V_z @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Equiv__Relations_Ocongruent @ V_r @ V_f @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[85]) ).
thf(766,plain,
( ( ! [V_a: $i,V_b: $i,T_a: $i,V_r: $i] :
( ( V_a = V_b )
| ~ ( c_in @ ( c_Pair @ V_b @ V_a @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Relation_Oantisym @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[86]) ).
thf(767,plain,
( ( ! [V_x: $i,V_y: $i,T_a: $i,V_r: $i] :
( ( V_x = V_y )
| ~ ( c_in @ ( c_Pair @ V_y @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Relation_Oantisym @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[87]) ).
thf(768,plain,
( ( ! [V_x: $i,V_a: $i,T_a: $i,V_r: $i] :
( ~ ( c_in @ ( c_Pair @ V_x @ V_a @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[88]) ).
thf(769,plain,
( ( ! [V_x: $i,T_a: $i,V_R: $i] : ( c_in @ ( c_Pair @ V_x @ V_x @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[89]) ).
thf(770,plain,
( ( ! [V_a: $i,T_a: $i,V_r: $i] : ( c_in @ ( c_Pair @ V_a @ V_a @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[90]) ).
thf(771,plain,
( ( ! [V_a: $i,V_c: $i,T_a: $i,V_r: $i,V_b: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_b @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[91]) ).
thf(772,plain,
( ( ! [V_a: $i,V_b: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[92]) ).
thf(773,plain,
( ( ! [V_a: $i,V_c: $i,T_a: $i,V_r: $i,V_b: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_b @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[93]) ).
thf(774,plain,
( ( ! [V_a: $i,V_c: $i,T_a: $i,V_r: $i,V_b: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_b @ V_c @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[94]) ).
thf(775,plain,
( ( ! [V_a: $i,V_c: $i,T_a: $i,V_r: $i,V_b: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_b @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[95]) ).
thf(776,plain,
( ( ! [V_a: $i,V_c: $i,T_a: $i,V_r: $i,V_b: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_b @ V_c @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[96]) ).
thf(777,plain,
( ( ! [V_x: $i,T_a: $i,V_r: $i] :
( ~ ( c_in @ ( c_Pair @ V_x @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Relation_Oirrefl @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[97]) ).
thf(778,plain,
( ( ! [V_b: $i,V_a: $i,T_b: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_b @ V_a @ T_b @ T_a ) @ V_r @ ( tc_prod @ T_b @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ ( c_Relation_Oconverse @ V_r @ T_b @ T_a ) @ ( tc_prod @ T_a @ T_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[98]) ).
thf(779,plain,
( ( ! [V_b: $i,V_a: $i,T_b: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_b @ V_a @ T_b @ T_a ) @ ( c_Relation_Oconverse @ V_r @ T_a @ T_b ) @ ( tc_prod @ T_b @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ V_r @ ( tc_prod @ T_a @ T_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[99]) ).
thf(780,plain,
( ( ! [V_a: $i,V_b: $i,T_a: $i,T_b: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ ( c_Relation_Oconverse @ V_r @ T_b @ T_a ) @ ( tc_prod @ T_a @ T_b ) )
| ~ ( c_in @ ( c_Pair @ V_b @ V_a @ T_b @ T_a ) @ V_r @ ( tc_prod @ T_b @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[100]) ).
thf(781,plain,
( ( ! [V_a: $i,V_c: $i,T_a: $i,V_r: $i,V_b: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_b @ V_c @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Relation_Otrans @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[101]) ).
thf(782,plain,
( ( ! [V_x: $i,V_z: $i,T_a: $i,V_r: $i,V_y: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_z @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_y @ V_z @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Relation_Otrans @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[102]) ).
thf(783,plain,
( ( ! [V_x: $i,V_y: $i,T_a: $i,T_b: $i,V_R: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_b ) @ V_R @ ( tc_prod @ T_a @ T_b ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_FunDef_Oin__rel @ V_R @ T_a @ T_b ) @ V_x ) @ V_y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[103]) ).
thf(784,plain,
( ( ! [V_R: $i,T_a: $i,T_b: $i,V_x: $i,V_y: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_FunDef_Oin__rel @ V_R @ T_a @ T_b ) @ V_x ) @ V_y ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_b ) @ V_R @ ( tc_prod @ T_a @ T_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[104]) ).
thf(785,plain,
( ( ! [V_f: $i,V_r: $i,V_a: $i,T_a: $i,T_b: $i,V_x: $i] :
( ( ( hAPP @ ( c_Recdef_Ocut @ V_f @ V_r @ V_a @ T_a @ T_b ) @ V_x )
= ( hAPP @ V_f @ V_x ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_a @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[105]) ).
thf(786,plain,
( ( ! [V_f: $i,V_R: $i,V_a: $i,T_a: $i,T_b: $i,V_x: $i] :
( ( ( hAPP @ ( c_Recdef_Ocut @ V_f @ V_R @ V_a @ T_a @ T_b ) @ V_x )
= ( hAPP @ V_f @ V_x ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_a @ T_a @ T_a ) @ V_R @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[106]) ).
thf(787,plain,
( ( ! [V_y: $i,V_z: $i,V_x: $i,T_a: $i,T_b: $i,V_r: $i] :
( ( V_y = V_z )
| ~ ( c_in @ ( c_Pair @ V_x @ V_z @ T_a @ T_b ) @ V_r @ ( tc_prod @ T_a @ T_b ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_b ) @ V_r @ ( tc_prod @ T_a @ T_b ) )
| ~ ( c_Relation_Osingle__valued @ V_r @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[107]) ).
thf(788,plain,
( ( ! [V_f: $i,V_y1: $i,V_y2: $i,V_z1: $i,V_z2: $i,T_b: $i,V_r2: $i,T_a: $i,V_r1: $i,T_c: $i] :
( ( ( hAPP @ ( hAPP @ V_f @ V_y1 ) @ V_y2 )
= ( hAPP @ ( hAPP @ V_f @ V_z1 ) @ V_z2 ) )
| ~ ( c_in @ ( c_Pair @ V_y2 @ V_z2 @ T_b @ T_b ) @ V_r2 @ ( tc_prod @ T_b @ T_b ) )
| ~ ( c_in @ ( c_Pair @ V_y1 @ V_z1 @ T_a @ T_a ) @ V_r1 @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Equiv__Relations_Ocongruent2 @ V_r1 @ V_r2 @ V_f @ T_a @ T_b @ T_c ) ) )
= $true ),
inference(unfold_def,[status(thm)],[108]) ).
thf(789,plain,
( ( ! [V_z: $i,V_c: $i,T_b: $i,T_c: $i,T_a: $i,V_a: $i,V_b: $i] :
( ( c_in @ V_z @ ( hAPP @ ( c_split @ V_c @ T_b @ T_c @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Pair @ V_a @ V_b @ T_b @ T_c ) ) @ T_a )
| ~ ( c_in @ V_z @ ( hAPP @ ( hAPP @ V_c @ V_a ) @ V_b ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[109]) ).
thf(790,plain,
( ( ! [V_a: $i,V_r: $i,T_a: $i,T_b: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XRange__iff__1__1 @ V_a @ V_r @ T_a @ T_b ) @ V_a @ T_b @ T_a ) @ V_r @ ( tc_prod @ T_b @ T_a ) )
| ~ ( c_in @ V_a @ ( c_Relation_ORange @ V_r @ T_b @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[110]) ).
thf(791,plain,
( ( ! [V_x: $i,V_y: $i,T_a: $i,V_R: $i] :
( ( V_x = V_y )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ( c_in @ V_x @ ( c_Relation_ODomain @ V_R @ T_a @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[111]) ).
thf(792,plain,
( ( ! [V_A: $i,V_b: $i,V_r: $i,T_b: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XImage__iff__1__1 @ V_A @ V_b @ V_r @ T_b @ T_a ) @ V_b @ T_b @ T_a ) @ V_r @ ( tc_prod @ T_b @ T_a ) )
| ~ ( c_in @ V_b @ ( c_Relation_OImage @ V_r @ V_A @ T_b @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[112]) ).
thf(793,plain,
( ( ! [V_a: $i,V_r: $i,T_a: $i,T_b: $i] :
( ( c_in @ ( c_Pair @ V_a @ ( c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1 @ V_a @ V_r @ T_a @ T_b ) @ T_a @ T_b ) @ V_r @ ( tc_prod @ T_a @ T_b ) )
| ~ ( c_in @ V_a @ ( c_Relation_ODomain @ V_r @ T_a @ T_b ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[113]) ).
thf(794,plain,
( ( ! [V_y: $i,V_Q: $i,T_a: $i,V_r: $i,V_xa: $i] :
( ~ ( c_in @ V_y @ V_Q @ T_a )
| ~ ( c_in @ ( c_Pair @ V_y @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 @ V_Q @ V_r @ T_a ) @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_xa @ V_Q @ T_a )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[114]) ).
thf(795,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 ) )
| ~ ( c_in @ ( c_Pair @ V_y @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ V_P @ V_r @ T_a ) @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_a @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[115]) ).
thf(796,plain,
( ( ! [V_P: $i,V_x: $i,V_ya: $i,V_r: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ( c_in @ V_ya @ ( c_Wellfounded_Oacc @ V_r @ t_a ) @ t_a )
| ~ ( c_in @ ( c_Pair @ V_ya @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ V_P @ V_r ) @ t_a @ t_a ) @ V_r @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ V_x @ ( c_Wellfounded_Oacc @ V_r @ t_a ) @ t_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[116]) ).
thf(797,plain,
( ( ! [V_a: $i,V_r: $i,T_a: $i,T_b: $i] :
( ( c_in @ ( c_Pair @ V_a @ ( c_ATP__Linkup_Osko__Relation__XDomainE__1__1 @ V_a @ V_r @ T_a @ T_b ) @ T_a @ T_b ) @ V_r @ ( tc_prod @ T_a @ T_b ) )
| ~ ( c_in @ V_a @ ( c_Relation_ODomain @ V_r @ T_a @ T_b ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[117]) ).
thf(798,plain,
( ( ! [V_f: $i,V_a: $i,V_b: $i,T_a: $i,T_b: $i,T_c: $i,V_A: $i] :
( ( c_in @ ( hAPP @ ( hAPP @ V_f @ V_a ) @ V_b ) @ ( c_Set_Oimage @ ( c_split @ V_f @ T_a @ T_b @ T_c ) @ V_A @ ( tc_prod @ T_a @ T_b ) @ T_c ) @ T_c )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ V_A @ ( tc_prod @ T_a @ T_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[118]) ).
thf(799,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 ) )
| ~ ( c_in @ ( c_Pair @ V_y @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ V_P @ V_r ) @ t_a @ t_a ) @ V_r @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ V_x @ ( c_Wellfounded_Oacc @ V_r @ t_a ) @ t_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[119]) ).
thf(800,plain,
( ( ! [V_x: $i,V_R: $i,T_a: $i] :
( ( c_in @ V_x @ ( c_Relation_ODomain @ V_R @ T_a @ T_a ) @ T_a )
| ( c_in @ ( c_Pair @ V_x @ V_x @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[120]) ).
thf(801,plain,
( ( ! [V_P: $i,V_x: $i,V_ya: $i,V_r: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ( c_in @ V_ya @ ( c_Wellfounded_Oacc @ V_r @ t_a ) @ t_a )
| ~ ( c_in @ ( c_Pair @ V_ya @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ V_P @ V_r ) @ t_a @ t_a ) @ V_r @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ V_x @ ( c_Wellfounded_Oacc @ V_r @ t_a ) @ t_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[121]) ).
thf(802,plain,
( ( ! [V_b: $i,V_r: $i,T_a: $i,V_a: $i] :
( ( c_in @ V_b @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a )
| ~ ( c_in @ ( c_Pair @ V_b @ V_a @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_a @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[122]) ).
thf(803,plain,
( ( ! [V_b: $i,V_r: $i,T_a: $i,V_a: $i] :
( ( c_in @ V_b @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a )
| ~ ( c_in @ V_a @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a )
| ~ ( c_in @ ( c_Pair @ V_b @ V_a @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[123]) ).
thf(804,plain,
( ( ! [V_x: $i,V_r: $i,T_a: $i] :
( ( c_in @ V_x @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a )
| ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1 @ V_r @ V_x @ T_a ) @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[124]) ).
thf(805,plain,
( ( ! [V_b: $i,V_r: $i,T_a: $i,T_b: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XRangeE__1__1 @ V_b @ V_r @ T_a @ T_b ) @ V_b @ T_b @ T_a ) @ V_r @ ( tc_prod @ T_b @ T_a ) )
| ~ ( c_in @ V_b @ ( c_Relation_ORange @ V_r @ T_b @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[125]) ).
thf(806,plain,
( ( ! [V_y: $i,V_Q: $i,T_a: $i,V_R: $i,V_x: $i] :
( ~ ( c_in @ V_y @ V_Q @ T_a )
| ~ ( c_in @ ( c_Pair @ V_y @ ( c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 @ V_Q @ V_R @ T_a ) @ T_a @ T_a ) @ V_R @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_x @ V_Q @ T_a )
| ~ ( c_Wellfounded_Owf @ V_R @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[126]) ).
thf(807,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 ) )
| ~ ( c_in @ ( c_Pair @ V_y @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ V_P @ V_r ) @ t_a @ t_a ) @ V_r @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ V_x @ ( c_Wellfounded_Oacc @ V_r @ t_a ) @ t_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[127]) ).
thf(808,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 ) )
| ~ ( c_in @ ( c_Pair @ V_y @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ V_P @ V_r @ T_a ) @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_a @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[128]) ).
thf(809,plain,
( ( ! [V_R: $i,V_x: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1 @ V_R @ V_x @ T_a ) @ V_x @ T_a @ T_a ) @ V_R @ ( tc_prod @ T_a @ T_a ) )
| ( c_in @ V_x @ ( c_Wellfounded_Oacc @ V_R @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[129]) ).
thf(810,plain,
( ( ! [V_A: $i,V_b: $i,V_r: $i,T_b: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XImageE__1__1 @ V_A @ V_b @ V_r @ T_b @ T_a ) @ V_b @ T_b @ T_a ) @ V_r @ ( tc_prod @ T_b @ T_a ) )
| ~ ( c_in @ V_b @ ( c_Relation_OImage @ V_r @ V_A @ T_b @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[130]) ).
thf(811,plain,
( ( c_Arrow__Order__Mirabelle_Ounanimity @ v_F )
= $true ),
inference(unfold_def,[status(thm)],[131]) ).
thf(812,plain,
( ( c_Arrow__Order__Mirabelle_OIIA @ v_F )
= $true ),
inference(unfold_def,[status(thm)],[132]) ).
thf(813,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ T_a )
= ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[133]) ).
thf(814,plain,
( ( ! [V_R: $i,T_a: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( c_Transitive__Closure_Otrancl @ V_R @ T_a ) @ T_a )
= ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[134]) ).
thf(815,plain,
( ( ! [V_P: $i,V_a: $i,V_r: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ V_P @ V_r @ T_a ) @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a )
| ~ ( c_in @ V_a @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[135]) ).
thf(816,plain,
( ( ! [V_r: $i,T_a: $i,V_A: $i] :
( ( c_Relation_Otrans @ V_r @ T_a )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[136]) ).
thf(817,plain,
( ( ! [V_A: $i,V_r: $i,T_a: $i] :
( ( c_Relation_Ototal__on @ V_A @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a )
| ~ ( c_Relation_Ototal__on @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[137]) ).
thf(818,plain,
( ( ! [V_A: $i,V_r: $i,T_a: $i] :
( ( c_Relation_Ototal__on @ V_A @ V_r @ T_a )
| ~ ( c_Relation_Ototal__on @ V_A @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[138]) ).
thf(819,plain,
( ( ! [V_r: $i,T_b: $i,T_a: $i] :
( ( c_Relation_ORange @ V_r @ T_b @ T_a )
= ( c_Relation_ODomain @ ( c_Relation_Oconverse @ V_r @ T_b @ T_a ) @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[139]) ).
thf(820,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Transitive__Closure_Otrancl @ V_r @ T_a )
= ( c_Relation_Orel__comp @ V_r @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ T_a @ T_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[140]) ).
thf(821,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Transitive__Closure_Otrancl @ V_r @ T_a )
= ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ V_r @ T_a @ T_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[141]) ).
thf(822,plain,
( ( ! [V_r: $i,T_b: $i,T_a: $i] :
( ( c_Relation_ODomain @ ( c_Relation_Oconverse @ V_r @ T_b @ T_a ) @ T_a @ T_b )
= ( c_Relation_ORange @ V_r @ T_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[142]) ).
thf(823,plain,
( ( ! [V_r2: $i,V_f: $i,V_a: $i,T_b: $i,T_c: $i,V_A: $i,T_a: $i,V_r1: $i] :
( ( c_Equiv__Relations_Ocongruent @ V_r2 @ ( hAPP @ V_f @ V_a ) @ T_b @ T_c )
| ~ ( c_in @ V_a @ V_A @ T_a )
| ~ ( c_Equiv__Relations_Ocongruent2 @ V_r1 @ V_r2 @ V_f @ T_a @ T_b @ T_c )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r1 @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[143]) ).
thf(824,plain,
( ( ! [V_x: $i,V_r: $i,T_a: $i] :
( ( c_in @ V_x @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a )
| ~ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1 @ V_r @ V_x @ T_a ) @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[144]) ).
thf(825,plain,
( ( ! [V_r: $i,T_a: $i,V_A: $i] :
( ( c_Relation_Osym @ V_r @ T_a )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[145]) ).
thf(826,plain,
( ( ! [V_Q: $i,V_R: $i,T_a: $i,V_x: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 @ V_Q @ V_R @ T_a ) @ V_Q @ T_a )
| ~ ( c_in @ V_x @ V_Q @ T_a )
| ~ ( c_Wellfounded_Owf @ V_R @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[146]) ).
thf(827,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a )
= ( c_Relation_Oconverse @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ T_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[147]) ).
thf(828,plain,
( ( ! [V_A: $i,V_r: $i,T_a: $i] :
( ( c_Relation_Orefl__on @ V_A @ V_r @ T_a )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[148]) ).
thf(829,plain,
( ( ! [V_P: $i,V_x: $i,V_r: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ V_P @ V_r ) ) )
| ~ ( c_in @ V_x @ ( c_Wellfounded_Oacc @ V_r @ t_a ) @ t_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[149]) ).
thf(830,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Relation_Oantisym @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a )
| ~ ( c_Relation_Oantisym @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[150]) ).
thf(831,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Relation_Oantisym @ V_r @ T_a )
| ~ ( c_Relation_Oantisym @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[151]) ).
thf(832,plain,
( ( ! [V_R: $i,T_a: $i] :
( ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) @ T_a @ T_a @ T_a )
= ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[152]) ).
thf(833,plain,
( ( ! [V_r: $i,T_a: $i,V_A: $i] :
( ( ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ V_r @ T_a @ T_a @ T_a )
= V_r )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[153]) ).
thf(834,plain,
( ( ! [T_a: $i] : ( c_Relation_Otrans @ ( c_Relation_OId @ T_a ) @ T_a ) )
= $true ),
inference(unfold_def,[status(thm)],[154]) ).
thf(835,plain,
( ( ! [V_r: $i,T_a: $i,T_b: $i] :
( ( c_Relation_Oconverse @ ( c_Relation_Oconverse @ V_r @ T_a @ T_b ) @ T_b @ T_a )
= V_r ) )
= $true ),
inference(unfold_def,[status(thm)],[155]) ).
thf(836,plain,
( ( ! [V_r: $i,V_s: $i,T_a: $i,T_b: $i,T_c: $i] :
( ( c_Relation_Osingle__valued @ ( c_Relation_Orel__comp @ V_r @ V_s @ T_a @ T_b @ T_c ) @ T_a @ T_c )
| ~ ( c_Relation_Osingle__valued @ V_s @ T_b @ T_c )
| ~ ( c_Relation_Osingle__valued @ V_r @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[156]) ).
thf(837,plain,
( ( ! [V_A: $i,T_a: $i] :
( ( c_Relation_ORange @ ( c_Relation_OId__on @ V_A @ T_a ) @ T_a @ T_a )
= V_A ) )
= $true ),
inference(unfold_def,[status(thm)],[157]) ).
thf(838,plain,
( ( ! [V_Q: $i,V_r: $i,T_a: $i,V_xa: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 @ V_Q @ V_r @ T_a ) @ V_Q @ T_a )
| ~ ( c_in @ V_xa @ V_Q @ T_a )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[158]) ).
thf(839,plain,
( ( ! [V_r: $i,T_a: $i,T_b: $i] :
( ( c_Relation_ORange @ ( c_Relation_Oconverse @ V_r @ T_a @ T_b ) @ T_b @ T_a )
= ( c_Relation_ODomain @ V_r @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[159]) ).
thf(840,plain,
( ( ! [T_a: $i] : ( c_Relation_Oantisym @ ( c_Relation_OId @ T_a ) @ T_a ) )
= $true ),
inference(unfold_def,[status(thm)],[160]) ).
thf(841,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ V_r @ T_a @ T_a @ T_a )
!= V_r )
| ( c_Equiv__Relations_Oequiv @ ( c_Relation_ODomain @ V_r @ T_a @ T_a ) @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[161]) ).
thf(842,plain,
( ( ! [V_A: $i,T_a: $i] :
( ( c_Relation_Oconverse @ ( c_Relation_OId__on @ V_A @ T_a ) @ T_a @ T_a )
= ( c_Relation_OId__on @ V_A @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[162]) ).
thf(843,plain,
( ( ! [V_r: $i,V_f: $i,T_a: $i,T_b: $i] :
( ( c_Relation_Otrans @ ( c_Relation_Oinv__image @ V_r @ V_f @ T_a @ T_b ) @ T_b )
| ~ ( c_Relation_Otrans @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[163]) ).
thf(844,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Transitive__Closure_Otrancl @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a )
= ( c_Relation_Oconverse @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ T_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[164]) ).
thf(845,plain,
( ( ! [V_R: $i,V_f: $i,T_b: $i,T_a: $i] :
( ( c_Relation_Oconverse @ ( c_Relation_Oinv__image @ V_R @ V_f @ T_b @ T_a ) @ T_a @ T_a )
= ( c_Relation_Oinv__image @ ( c_Relation_Oconverse @ V_R @ T_b @ T_b ) @ V_f @ T_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[165]) ).
thf(846,plain,
( ( ! [V_R: $i,V_S: $i,T_a: $i,T_d: $i,T_c: $i,V_T: $i,T_b: $i] :
( ( c_Relation_Orel__comp @ ( c_Relation_Orel__comp @ V_R @ V_S @ T_a @ T_d @ T_c ) @ V_T @ T_a @ T_c @ T_b )
= ( c_Relation_Orel__comp @ V_R @ ( c_Relation_Orel__comp @ V_S @ V_T @ T_d @ T_c @ T_b ) @ T_a @ T_d @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[166]) ).
thf(847,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Wellfounded_Owf @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ T_a )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[167]) ).
thf(848,plain,
( ( ! [T_a: $i] :
( ( c_Relation_Oconverse @ ( c_Relation_OId @ T_a ) @ T_a @ T_a )
= ( c_Relation_OId @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[168]) ).
thf(849,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Relation_Otrans @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a )
| ~ ( c_Relation_Otrans @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[169]) ).
thf(850,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Relation_Otrans @ V_r @ T_a )
| ~ ( c_Relation_Otrans @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[170]) ).
thf(851,plain,
( ( ! [V_r: $i,T_a: $i] : ( c_Relation_Otrans @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ T_a ) )
= $true ),
inference(unfold_def,[status(thm)],[171]) ).
thf(852,plain,
( ( ! [V_R: $i,T_a: $i] :
( ( c_Transitive__Closure_Otrancl @ ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) @ T_a )
= ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[172]) ).
thf(853,plain,
( ( ! [V_r: $i,V_f: $i,T_a: $i,T_b: $i] :
( ( c_Relation_Osym @ ( c_Relation_Oinv__image @ V_r @ V_f @ T_a @ T_b ) @ T_b )
| ~ ( c_Relation_Osym @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[173]) ).
thf(854,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Relation_Orel__comp @ V_r @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ T_a @ T_a @ T_a )
= ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ V_r @ T_a @ T_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[174]) ).
thf(855,plain,
( ( ! [V_r: $i,V_f: $i,T_a: $i,T_b: $i] :
( ( c_Wellfounded_Owf @ ( c_Relation_Oinv__image @ V_r @ V_f @ T_a @ T_b ) @ T_b )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[175]) ).
thf(856,plain,
( ( ! [V_A: $i,T_a: $i] : ( c_Relation_Orefl__on @ V_A @ ( c_Relation_OId__on @ V_A @ T_a ) @ T_a ) )
= $true ),
inference(unfold_def,[status(thm)],[176]) ).
thf(857,plain,
( ( ! [V_A: $i,T_a: $i] : ( c_Relation_Osym @ ( c_Relation_OId__on @ V_A @ T_a ) @ T_a ) )
= $true ),
inference(unfold_def,[status(thm)],[177]) ).
thf(858,plain,
( ( ! [V_r: $i,V_s: $i,T_b: $i,T_c: $i,T_a: $i] :
( ( c_Relation_Oconverse @ ( c_Relation_Orel__comp @ V_r @ V_s @ T_b @ T_c @ T_a ) @ T_b @ T_a )
= ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ V_s @ T_c @ T_a ) @ ( c_Relation_Oconverse @ V_r @ T_b @ T_c ) @ T_a @ T_c @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[178]) ).
thf(859,plain,
( ( ! [V_r: $i,T_a: $i] : ( c_Relation_Otrans @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ T_a ) )
= $true ),
inference(unfold_def,[status(thm)],[179]) ).
thf(860,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Relation_ORange @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ T_a @ T_a )
= ( c_Relation_ORange @ V_r @ T_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[180]) ).
thf(861,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( ( c_Relation_Oconverse @ V_r @ T_a @ T_a )
!= V_r )
| ( c_Relation_Osym @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[181]) ).
thf(862,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( ( c_Relation_Oconverse @ V_r @ T_a @ T_a )
= V_r )
| ~ ( c_Relation_Osym @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[182]) ).
thf(863,plain,
( ( ! [V_A: $i,T_a: $i] :
( ( c_Relation_ODomain @ ( c_Relation_OId__on @ V_A @ T_a ) @ T_a @ T_a )
= V_A ) )
= $true ),
inference(unfold_def,[status(thm)],[183]) ).
thf(864,plain,
( ( ! [T_a: $i] : ( c_Relation_Osingle__valued @ ( c_Relation_OId @ T_a ) @ T_a @ T_a ) )
= $true ),
inference(unfold_def,[status(thm)],[184]) ).
thf(865,plain,
( ( ! [T_a: $i,V_A: $i] :
( ( c_Relation_OImage @ ( c_Relation_OId @ T_a ) @ V_A @ T_a @ T_a )
= V_A ) )
= $true ),
inference(unfold_def,[status(thm)],[185]) ).
thf(866,plain,
( ( ! [V_R: $i,T_a: $i] :
( ( c_Wellfounded_Owf @ V_R @ T_a )
| ~ ( c_Wellfounded_Owf @ ( c_Relation_Orel__comp @ V_R @ V_R @ T_a @ T_a @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[186]) ).
thf(867,plain,
( ( ! [V_R: $i,T_a: $i] :
( ( c_Wellfounded_Owf @ ( c_Relation_Orel__comp @ V_R @ V_R @ T_a @ T_a @ T_a ) @ T_a )
| ~ ( c_Wellfounded_Owf @ V_R @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[187]) ).
thf(868,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Relation_Osym @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ T_a )
| ~ ( c_Relation_Osym @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[188]) ).
thf(869,plain,
( ( ! [V_A: $i,V_r: $i,T_a: $i] :
( ( c_Relation_Orefl__on @ V_A @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a )
| ~ ( c_Relation_Orefl__on @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[189]) ).
thf(870,plain,
( ( ! [V_A: $i,V_r: $i,T_a: $i] :
( ( c_Relation_Orefl__on @ V_A @ V_r @ T_a )
| ~ ( c_Relation_Orefl__on @ V_A @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[190]) ).
thf(871,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__Xacc__induct__rule__1__1 @ V_P @ V_r @ T_a ) ) )
| ~ ( c_in @ V_a @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[191]) ).
thf(872,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Wellfounded_Owf @ ( c_Relation_Oconverse @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ T_a @ T_a ) @ T_a )
| ~ ( c_Wellfounded_Owf @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[192]) ).
thf(873,plain,
( ( ! [V_A: $i,T_a: $i] : ( c_Relation_Oantisym @ ( c_Relation_OId__on @ V_A @ T_a ) @ T_a ) )
= $true ),
inference(unfold_def,[status(thm)],[193]) ).
thf(874,plain,
( ( ! [V_R: $i,T_b: $i,T_a: $i] :
( ( c_Relation_Orel__comp @ V_R @ ( c_Relation_OId @ T_b ) @ T_a @ T_b @ T_b )
= V_R ) )
= $true ),
inference(unfold_def,[status(thm)],[194]) ).
thf(875,plain,
( ( ! [T_a: $i,V_R: $i,T_b: $i] :
( ( c_Relation_Orel__comp @ ( c_Relation_OId @ T_a ) @ V_R @ T_a @ T_a @ T_b )
= V_R ) )
= $true ),
inference(unfold_def,[status(thm)],[195]) ).
thf(876,plain,
( ( ! [V_A: $i,T_a: $i] : ( c_Relation_Otrans @ ( c_Relation_OId__on @ V_A @ T_a ) @ T_a ) )
= $true ),
inference(unfold_def,[status(thm)],[196]) ).
thf(877,plain,
( ( ! [T_a: $i] : ( c_Relation_Osym @ ( c_Relation_OId @ T_a ) @ T_a ) )
= $true ),
inference(unfold_def,[status(thm)],[197]) ).
thf(878,plain,
( ( ! [V_R: $i,V_x: $i,T_a: $i] :
( ~ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1 @ V_R @ V_x @ T_a ) @ ( c_Wellfounded_Oacc @ V_R @ T_a ) @ T_a )
| ( c_in @ V_x @ ( c_Wellfounded_Oacc @ V_R @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[198]) ).
thf(879,plain,
( ( ! [V_A: $i,V_b: $i,V_r: $i,T_b: $i,T_a: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Relation__XImage__iff__1__1 @ V_A @ V_b @ V_r @ T_b @ T_a ) @ V_A @ T_b )
| ~ ( c_in @ V_b @ ( c_Relation_OImage @ V_r @ V_A @ T_b @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[199]) ).
thf(880,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Relation_ODomain @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ T_a @ T_a )
= ( c_Relation_ODomain @ V_r @ T_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[200]) ).
thf(881,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Relation_Osym @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a )
| ~ ( c_Relation_Osym @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[201]) ).
thf(882,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Relation_Osym @ V_r @ T_a )
| ~ ( c_Relation_Osym @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[202]) ).
thf(883,plain,
( ( ! [V_P: $i,V_a: $i,V_r: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ V_P @ V_r @ T_a ) @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a )
| ~ ( c_in @ V_a @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[203]) ).
thf(884,plain,
( ( ! [V_P: $i,V_x: $i,V_r: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ V_P @ V_r ) ) )
| ~ ( c_in @ V_x @ ( c_Wellfounded_Oacc @ V_r @ t_a ) @ t_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[204]) ).
thf(885,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( ( c_Transitive__Closure_Otrancl @ V_r @ T_a )
= V_r )
| ~ ( c_Relation_Otrans @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[205]) ).
thf(886,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__Xacc__induct__1__1 @ V_P @ V_r @ T_a ) ) )
| ~ ( c_in @ V_a @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[206]) ).
thf(887,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Relation_Osym @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ T_a )
| ~ ( c_Relation_Osym @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[207]) ).
thf(888,plain,
( ( ! [V_A: $i,V_b: $i,V_r: $i,T_b: $i,T_a: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Relation__XImageE__1__1 @ V_A @ V_b @ V_r @ T_b @ T_a ) @ V_A @ T_b )
| ~ ( c_in @ V_b @ ( c_Relation_OImage @ V_r @ V_A @ T_b @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[208]) ).
thf(889,plain,
( ( ! [V_A: $i,T_a: $i] : ( c_Relation_Osingle__valued @ ( c_Relation_OId__on @ V_A @ T_a ) @ T_a @ T_a ) )
= $true ),
inference(unfold_def,[status(thm)],[209]) ).
thf(890,plain,
( ( ! [V_x: $i,V_r: $i,T_a: $i] :
( ( c_in @ V_x @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[210]) ).
thf(891,plain,
( ( ! [V_x: $i,V_A: $i,T_aa: $i,V_f: $i,T_a: $i] :
( ~ ( c_in @ V_x @ V_A @ T_aa )
| ( c_in @ ( hAPP @ V_f @ V_x ) @ ( c_Set_Oimage @ V_f @ V_A @ T_aa @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[211]) ).
thf(892,plain,
( ( ! [V_x: $i,V_A: $i,T_b: $i,V_f: $i,T_a: $i] :
( ~ ( c_in @ V_x @ V_A @ T_b )
| ( c_in @ ( hAPP @ V_f @ V_x ) @ ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[212]) ).
thf(893,plain,
( ( ! [V_f: $i,V_x: $i,V_A: $i,T_b: $i,T_a: $i] :
( ( c_in @ ( hAPP @ V_f @ V_x ) @ ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a ) @ T_a )
| ~ ( c_in @ V_x @ V_A @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[213]) ).
thf(894,plain,
( ( ! [V_f: $i,V_x: $i,V_A: $i,T_a: $i,T_b: $i] :
( ( c_in @ ( hAPP @ V_f @ V_x ) @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) @ T_b )
| ~ ( c_in @ V_x @ V_A @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[214]) ).
thf(895,plain,
( ( ! [V_R: $i,V_a: $i,V_b: $i,V_c: $i,T_a: $i,T_b: $i,T_c: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ V_R @ V_a ) @ V_b ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_split @ V_R @ T_a @ T_b @ ( tc_fun @ T_c @ tc_bool ) ) @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) ) @ V_c ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[215]) ).
thf(896,plain,
( ( ! [V_f: $i,T_a: $i,T_b: $i,T_c: $i,V_a: $i,V_b: $i] :
( ( hAPP @ ( c_split @ V_f @ T_a @ T_b @ T_c ) @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) )
= ( hAPP @ ( hAPP @ V_f @ V_a ) @ V_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[216]) ).
thf(897,plain,
( ( ! [V_f: $i,T_b: $i,T_c: $i,T_a: $i,V_a: $i,V_b: $i] :
( ( hAPP @ ( c_split @ V_f @ T_b @ T_c @ T_a ) @ ( c_Pair @ V_a @ V_b @ T_b @ T_c ) )
= ( hAPP @ ( hAPP @ V_f @ V_a ) @ V_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[217]) ).
thf(898,plain,
( ( ! [V_x: $i,V_y: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Relation_Oconverse @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ T_a @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[218]) ).
thf(899,plain,
( ( ! [V_x: $i,V_y: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Relation_Oconverse @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ T_a @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[219]) ).
thf(900,plain,
( ( ! [V_x: $i,V_z: $i,T_a: $i,V_r: $i,V_y: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_z @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_y @ V_z @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[220]) ).
thf(901,plain,
( ( ! [V_a: $i,V_c: $i,T_a: $i,V_r: $i,V_b: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_b @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[221]) ).
thf(902,plain,
( ( ! [V_a: $i,V_b: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[222]) ).
thf(903,plain,
( ( ! [V_z: $i,V_y: $i,T_a: $i,V_r: $i,V_x: $i] :
( ( c_in @ ( c_Pair @ V_z @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ( c_in @ ( c_Pair @ V_y @ V_z @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_z @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Relation_Osingle__valued @ V_r @ T_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[223]) ).
thf(904,plain,
( ( ! [V_y: $i,V_x: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_y @ V_x @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[224]) ).
thf(905,plain,
( ( ! [V_x: $i,V_y: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_y @ V_x @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[225]) ).
thf(906,plain,
( ( ! [V_a: $i,V_b: $i,T_a: $i,V_R: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ( V_a = V_b )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[226]) ).
thf(907,plain,
( ( ! [V_x: $i,V_y: $i,T_a: $i,V_R: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ( V_x = V_y )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[227]) ).
thf(908,plain,
( ( ! [V_x: $i,V_y: $i,T_a: $i,V_R: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ( V_x = V_y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[228]) ).
thf(909,plain,
( ( ! [V_a: $i,V_c: $i,T_a: $i,V_r: $i,V_b: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_b @ V_c @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[229]) ).
thf(910,plain,
( ( ! [V_a: $i,V_c: $i,T_a: $i,V_r: $i,V_b: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_b @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[230]) ).
thf(911,plain,
( ( ! [V_p: $i,V_r: $i,T_a: $i] :
( ( c_in @ V_p @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_p @ V_r @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[231]) ).
thf(912,plain,
( ( ! [V_p: $i,V_r: $i,T_a: $i] :
( ( c_in @ V_p @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_p @ V_r @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[232]) ).
thf(913,plain,
( ( ! [T_a: $i,T_b: $i,V_R: $i] :
( ( c_Set_Oimage @ ( c_fst @ T_a @ T_b ) @ V_R @ ( tc_prod @ T_a @ T_b ) @ T_a )
= ( c_Relation_ODomain @ V_R @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[233]) ).
thf(914,plain,
( ( ! [V_a: $i,V_A: $i,T_a: $i,V_b: $i,V_r: $i] :
( ( c_in @ V_a @ V_A @ T_a )
| ( V_a = V_b )
| ~ ( c_lessequals @ V_r @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_A @ ( tc_fun @ T_a @ tc_bool ) @ T_a ) @ T_a @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[234]) ).
thf(915,plain,
( ( ! [T_b: $i,T_a: $i,V_R: $i] :
( ( c_Set_Oimage @ ( c_snd @ T_b @ T_a ) @ V_R @ ( tc_prod @ T_b @ T_a ) @ T_a )
= ( c_Relation_ORange @ V_R @ T_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[235]) ).
thf(916,plain,
( ( ! [V_r: $i,V_x: $i,T_a: $i,V_y: $i,V_A: $i] :
( ( ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a )
!= ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_y @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) )
| ~ ( c_in @ V_y @ V_A @ T_a )
| ~ ( c_in @ V_x @ V_A @ T_a )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a )
| ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[236]) ).
thf(917,plain,
( ( ! [V_r: $i,V_x: $i,T_a: $i,V_y: $i,V_A: $i] :
( ( ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a )
= ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_y @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_y @ V_A @ T_a )
| ~ ( c_in @ V_x @ V_A @ T_a )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[237]) ).
thf(918,plain,
( ( ! [V_r: $i,V_x: $i,T_a: $i,V_y: $i,V_A: $i] :
( ( ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a )
!= ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_y @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a )
| ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_y @ V_A @ T_a )
| ~ ( c_in @ V_x @ V_A @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[238]) ).
thf(919,plain,
( ( ! [V_r: $i,V_a: $i,T_a: $i,V_b: $i,V_A: $i] :
( ( ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a )
!= ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) )
| ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_b @ V_A @ T_a )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[239]) ).
thf(920,plain,
( ( ! [V_r: $i,T_a: $i,V_x: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_x @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[240]) ).
thf(921,plain,
( ( ! [V_r: $i,T_a: $i] : ( c_Relation_Oirrefl @ ( c_HOL_Ominus__class_Ominus @ V_r @ ( c_Relation_OId @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a ) )
= $true ),
inference(unfold_def,[status(thm)],[241]) ).
thf(922,plain,
( ( ! [V_R: $i,T_a: $i] :
( ( c_Wellfounded_OwfP @ ( c_FunDef_Oin__rel @ V_R @ T_a @ T_a ) @ T_a )
| ~ ( c_Wellfounded_Owf @ V_R @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[242]) ).
thf(923,plain,
( ( ! [V_A: $i,V_B: $i,V_c: $i,T_a: $i,T_b: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Product__Type__XSigmaE__1__1 @ V_A @ V_B @ V_c @ T_a @ T_b ) @ V_A @ T_a )
| ~ ( c_in @ V_c @ ( c_Product__Type_OSigma @ V_A @ V_B @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[243]) ).
thf(924,plain,
( ( ! [V_a: $i,V_b: $i,V_r: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ V_a @ ( c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1 @ V_a @ V_b @ V_r @ T_a ) @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ( V_a = V_b )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[244]) ).
thf(925,plain,
( ( ! [V_P: $i,V_a: $i,V_b: $i,V_r: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1 @ V_P @ V_b @ V_r @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_b ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[245]) ).
thf(926,plain,
( ( ! [V_a1: $i,V_a2: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ ( v_sko__Transitive__Closure__Xrtrancl__Xcases__1 @ V_a1 @ V_a2 @ V_r ) @ V_a2 @ t_a @ t_a ) @ V_r @ ( tc_prod @ t_a @ t_a ) )
| ( V_a2 = V_a1 )
| ~ ( c_in @ ( c_Pair @ V_a1 @ V_a2 @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[246]) ).
thf(927,plain,
( ( ! [V_P: $i,V_b: $i,V_a: $i,V_r: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_b ) )
| ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 @ V_P @ V_a @ V_r @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[247]) ).
thf(928,plain,
( ( ! [V_a1: $i,V_a2: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_a1 @ ( v_sko__Transitive__Closure__Xrtrancl__Xcases__1 @ V_a1 @ V_a2 @ V_r ) @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ t_a ) @ ( tc_prod @ t_a @ t_a ) )
| ( V_a2 = V_a1 )
| ~ ( c_in @ ( c_Pair @ V_a1 @ V_a2 @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[248]) ).
thf(929,plain,
( ( ! [V_P: $i,V_b: $i,V_a: $i,V_r: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_b ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2 @ V_P @ V_a @ V_r @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[249]) ).
thf(930,plain,
( ( ! [V_P: $i,V_b: $i,V_a: $i,V_r: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_b ) )
| ( c_in @ ( c_Pair @ V_a @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 @ V_P @ V_a @ V_r @ T_a ) @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[250]) ).
thf(931,plain,
( ( ! [V_P: $i,V_a: $i,V_b: $i,V_r: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 @ V_P @ V_b @ V_r @ T_a ) @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_b ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[251]) ).
thf(932,plain,
( ( ! [V_P: $i,V_a: $i,V_b: $i,V_r: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 @ V_P @ V_b @ V_r @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_b ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[252]) ).
thf(933,plain,
( ( ! [V_x: $i,V_r: $i,V_z: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ V_x @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1 @ V_r @ V_x @ V_z @ T_a ) @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ( V_x = V_z )
| ~ ( c_in @ ( c_Pair @ V_x @ V_z @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[253]) ).
thf(934,plain,
( ( ! [V_r: $i,V_x: $i,V_z: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1 @ V_r @ V_x @ V_z @ T_a ) @ V_z @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ( V_x = V_z )
| ~ ( c_in @ ( c_Pair @ V_x @ V_z @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[254]) ).
thf(935,plain,
( ( ! [V_a: $i,V_b: $i,V_r: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1 @ V_a @ V_b @ V_r @ T_a ) @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ( V_a = V_b )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[255]) ).
thf(936,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 ) )
| ~ ( c_in @ ( c_Pair @ V_y @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1 @ V_P @ V_r @ T_a ) @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[256]) ).
thf(937,plain,
( ( ! [V_P: $i,V_Ra: $i,V_y: $i,V_R: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_Ra ) )
| ( hBOOL @ ( hAPP @ V_P @ V_y ) )
| ~ ( c_in @ ( c_Pair @ V_y @ ( c_List_Osko__Recdef__Xtfl__wf__induct__1__1 @ V_P @ V_R @ T_a ) @ T_a @ T_a ) @ V_R @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Wellfounded_Owf @ V_R @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[257]) ).
thf(938,plain,
( ( ! [V_P: $i,V_xa: $i,V_y: $i,V_r: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_xa ) )
| ( hBOOL @ ( hAPP @ V_P @ V_y ) )
| ~ ( c_in @ ( c_Pair @ V_y @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1 @ V_P @ V_r @ T_a ) @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[258]) ).
thf(939,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 ) )
| ~ ( c_in @ ( c_Pair @ V_y @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1 @ V_P @ V_r @ T_a ) @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[259]) ).
thf(940,plain,
( ( ! [V_a1: $i,V_a2: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ ( v_sko__Transitive__Closure__Xtrancl__Xcases__1 @ V_a1 @ V_a2 @ V_r ) @ V_a2 @ t_a @ t_a ) @ V_r @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ ( c_Pair @ V_a1 @ V_a2 @ t_a @ t_a ) @ V_r @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ ( c_Pair @ V_a1 @ V_a2 @ t_a @ t_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[260]) ).
thf(941,plain,
( ( ! [V_x: $i,V_r: $i,V_z: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ V_x @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1 @ V_r @ V_x @ V_z @ T_a ) @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ( c_in @ ( c_Pair @ V_x @ V_z @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_z @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[261]) ).
thf(942,plain,
( ( ! [V_R: $i,V_x: $i,V_y: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1 @ V_R @ V_x @ V_y @ T_a ) @ V_y @ T_a @ T_a ) @ V_R @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[262]) ).
thf(943,plain,
( ( ! [V_a: $i,V_b: $i,V_r: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ V_a @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1 @ V_a @ V_b @ V_r @ T_a ) @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[263]) ).
thf(944,plain,
( ( ! [V_a: $i,V_b: $i,V_r: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1 @ V_a @ V_b @ V_r @ T_a ) @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[264]) ).
thf(945,plain,
( ( ! [V_x: $i,T_a: $i,V_r: $i] :
( ~ ( c_in @ ( c_Pair @ V_x @ V_x @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Wellfounded_Oacyclic @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[265]) ).
thf(946,plain,
( ( ! [V_a1: $i,V_a2: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_a1 @ ( v_sko__Transitive__Closure__Xtrancl__Xcases__1 @ V_a1 @ V_a2 @ V_r ) @ t_a @ t_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ t_a ) @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ ( c_Pair @ V_a1 @ V_a2 @ t_a @ t_a ) @ V_r @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ ( c_Pair @ V_a1 @ V_a2 @ t_a @ t_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[266]) ).
thf(947,plain,
( ( ! [V_x: $i,V_R: $i,V_y: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ V_x @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1 @ V_R @ V_x @ V_y @ T_a ) @ T_a @ T_a ) @ V_R @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[267]) ).
thf(948,plain,
( ( ! [V_r: $i,V_x: $i,V_z: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1 @ V_r @ V_x @ V_z @ T_a ) @ V_z @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ( c_in @ ( c_Pair @ V_x @ V_z @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_z @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[268]) ).
thf(949,plain,
( ( ! [V_x: $i,T_a: $i,V_r: $i] :
( ~ ( c_in @ ( c_Pair @ V_x @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1 @ V_r @ T_a ) @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1 @ V_r @ T_a ) @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[269]) ).
thf(950,plain,
( ( ! [V_a: $i,V_c: $i,V_r: $i,V_s: $i,T_a: $i,T_b: $i,T_c: $i] :
( ( c_in @ ( c_Pair @ V_a @ ( c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 @ V_a @ V_c @ V_r @ V_s @ T_a @ T_b @ T_c ) @ T_a @ T_c ) @ V_r @ ( tc_prod @ T_a @ T_c ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_b ) @ ( c_Relation_Orel__comp @ V_r @ V_s @ T_a @ T_c @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[270]) ).
thf(951,plain,
( ( ! [V_a: $i,V_c: $i,V_r: $i,V_s: $i,T_a: $i,T_b: $i,T_c: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 @ V_a @ V_c @ V_r @ V_s @ T_a @ T_b @ T_c ) @ V_c @ T_c @ T_b ) @ V_s @ ( tc_prod @ T_c @ T_b ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_b ) @ ( c_Relation_Orel__comp @ V_r @ V_s @ T_a @ T_c @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[271]) ).
thf(952,plain,
( ( ! [V_p: $i,T_a: $i] :
( ( V_p
= ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XIdE__1__1 @ V_p @ T_a ) @ ( c_ATP__Linkup_Osko__Relation__XIdE__1__1 @ V_p @ T_a ) @ T_a @ T_a ) )
| ~ ( c_in @ V_p @ ( c_Relation_OId @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[272]) ).
thf(953,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Wellfounded_Owf @ V_r @ T_a )
| ~ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1 @ V_r @ T_a ) @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[273]) ).
thf(954,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Wellfounded_Owf @ V_r @ T_a )
| ~ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1 @ V_r @ T_a ) @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[274]) ).
thf(955,plain,
( ( ! [V_A: $i,V_c: $i,T_a: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Relation__XId__onE__1__1 @ V_A @ V_c @ T_a ) @ V_A @ T_a )
| ~ ( c_in @ V_c @ ( c_Relation_OId__on @ V_A @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[275]) ).
thf(956,plain,
( ( ! [V_c: $i,V_A: $i,T_a: $i] :
( ( V_c
= ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XId__onE__1__1 @ V_A @ V_c @ T_a ) @ ( c_ATP__Linkup_Osko__Relation__XId__onE__1__1 @ V_A @ V_c @ T_a ) @ T_a @ T_a ) )
| ~ ( c_in @ V_c @ ( c_Relation_OId__on @ V_A @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[276]) ).
thf(957,plain,
( ( ! [V_f: $i,V_r: $i,V_x: $i,T_a: $i,T_b: $i,V_g: $i] :
( ( ( c_Recdef_Ocut @ V_f @ V_r @ V_x @ T_a @ T_b )
= ( c_Recdef_Ocut @ V_g @ V_r @ V_x @ T_a @ T_b ) )
| ( c_in @ ( c_Pair @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ V_f @ V_g @ V_r @ V_x @ T_a @ T_b ) @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[277]) ).
thf(958,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Transitive__Closure_Ortrancl @ V_r @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( c_Relation_OId @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[278]) ).
thf(959,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Transitive__Closure_Otrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_r @ ( c_Relation_OId @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
= ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[279]) ).
thf(960,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( c_Relation_OId @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
= ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[280]) ).
thf(961,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Transitive__Closure_Ortrancl @ V_r @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_OId @ T_a ) @ ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ V_r @ T_a @ T_a @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[281]) ).
thf(962,plain,
( ( ! [V_r: $i,T_a: $i,V_A: $i] :
( ( c_lessequals @ V_r @ ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ V_r @ T_a @ T_a @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_Relation_Orefl__on @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[282]) ).
thf(963,plain,
( ( ( c_Relation_ORange @ v_r @ t_a @ t_b )
= ( c_Relation_ODomain @ ( c_Relation_Oconverse @ v_r @ t_a @ t_b ) @ t_b @ t_a ) )
= $true ),
inference(unfold_def,[status(thm)],[283]) ).
thf(964,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Relation_Oirrefl @ V_r @ T_a )
| ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1 @ V_r @ T_a ) @ ( c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1 @ V_r @ T_a ) @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[284]) ).
thf(965,plain,
( ( ! [V_R: $i,V_A: $i,V_B: $i,T_b: $i,T_a: $i] :
( ( ( c_Relation_OImage @ V_R @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_OImage @ V_R @ V_A @ T_b @ T_a ) @ ( c_Relation_OImage @ V_R @ V_B @ T_b @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( c_Relation_Osingle__valued @ ( c_Relation_Oconverse @ V_R @ T_b @ T_a ) @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[285]) ).
thf(966,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Relation_Otrans @ ( c_HOL_Ominus__class_Ominus @ V_r @ ( c_Relation_OId @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
| ~ ( c_Relation_Oantisym @ V_r @ T_a )
| ~ ( c_Relation_Otrans @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[286]) ).
thf(967,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Nitpick_Orefl_H @ V_r @ T_a )
| ~ ( c_in @ ( c_Pair @ ( c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1 @ V_r @ T_a ) @ ( c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1 @ V_r @ T_a ) @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[287]) ).
thf(968,plain,
( ( ! [V_A: $i,V_r: $i,T_a: $i] :
( ( c_Order__Relation_Ostrict__linear__order__on @ V_A @ V_r @ T_a )
| ~ ( c_Relation_Ototal__on @ V_A @ V_r @ T_a )
| ~ ( c_Relation_Oirrefl @ V_r @ T_a )
| ~ ( c_Relation_Otrans @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[288]) ).
thf(969,plain,
( ( ! [V_y: $i,V_x: $i,T_a: $i,V_r: $i] :
( ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ V_y @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) @ T_a )
| ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[289]) ).
thf(970,plain,
( ( ! [V_x: $i,V_y: $i,T_a: $i,V_r: $i] :
( ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ V_y @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[290]) ).
thf(971,plain,
( ( ! [V_R: $i,V_x: $i,V_y: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1 @ V_R @ V_x @ V_y @ T_a ) @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[291]) ).
thf(972,plain,
( ( ! [V_x: $i,V_R: $i,V_y: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ V_x @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1 @ V_R @ V_x @ V_y @ T_a ) @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[292]) ).
thf(973,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_lessequals @ ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ V_r @ T_a @ T_a @ T_a ) @ V_r @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_Relation_Otrans @ V_r @ T_a )
| ~ ( c_Relation_Osym @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[293]) ).
thf(974,plain,
( ( ! [V_A: $i,V_r: $i,T_a: $i] :
( ( c_Relation_Ototal__on @ V_A @ ( c_HOL_Ominus__class_Ominus @ V_r @ ( c_Relation_OId @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
| ~ ( c_Relation_Ototal__on @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[294]) ).
thf(975,plain,
( ( ! [V_A: $i,V_r: $i,T_a: $i] :
( ( c_Relation_Ototal__on @ V_A @ V_r @ T_a )
| ~ ( c_Relation_Ototal__on @ V_A @ ( c_HOL_Ominus__class_Ominus @ V_r @ ( c_Relation_OId @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[295]) ).
thf(976,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Relation_Oantisym @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_r @ ( c_Relation_OId @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
| ~ ( c_Relation_Oantisym @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[296]) ).
thf(977,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Relation_Oantisym @ V_r @ T_a )
| ~ ( c_Relation_Oantisym @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_r @ ( c_Relation_OId @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[297]) ).
thf(978,plain,
( ( ! [V_A: $i,T_a: $i,V_B: $i] :
( ( c_Relation_OImage @ ( c_Relation_OId__on @ V_A @ T_a ) @ V_B @ T_a @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[298]) ).
thf(979,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Relation_Otrans @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_r @ ( c_Relation_OId @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
| ~ ( c_Relation_Otrans @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[299]) ).
thf(980,plain,
( ( ! [V_r: $i,T_a: $i] : ( c_Relation_Osym @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_r @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a ) )
= $true ),
inference(unfold_def,[status(thm)],[300]) ).
thf(981,plain,
( ( ! [V_r: $i,T_a: $i] : ( c_Relation_Osym @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_r @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a ) )
= $true ),
inference(unfold_def,[status(thm)],[301]) ).
thf(982,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_lessequals @ ( c_Relation_Orel__comp @ V_r @ V_r @ T_a @ T_a @ T_a ) @ V_r @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_Relation_Otrans @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[302]) ).
thf(983,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Relation_Oantisym @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ T_a )
| ~ ( c_Wellfounded_Oacyclic @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[303]) ).
thf(984,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( c_HOL_Ominus__class_Ominus @ V_r @ ( c_Relation_OId @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
= ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[304]) ).
thf(985,plain,
( ( ! [T_a: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
= ( c_Relation_OId @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[305]) ).
thf(986,plain,
( ( ! [V_R: $i,T_a: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_R @ ( c_Relation_OId @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
= ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[306]) ).
thf(987,plain,
( ( ! [V_R: $i,T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) @ ( c_Relation_OId @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
= ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[307]) ).
thf(988,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Transitive__Closure_Otrancl @ V_r @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_r @ ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ V_r @ T_a @ T_a @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[308]) ).
thf(989,plain,
( ( ! [V_R: $i,T_a: $i] :
( ( ( c_Relation_Orel__comp @ V_R @ V_R @ T_a @ T_a @ T_a )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) )
| ( c_Wellfounded_Owf @ V_R @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[309]) ).
thf(990,plain,
( ( ! [V_R: $i,V_S: $i,T_a: $i] :
( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_R @ V_S @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
| ~ ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ V_R @ V_R @ T_a @ T_a @ T_a ) @ ( c_Relation_Orel__comp @ V_S @ V_R @ T_a @ T_a @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ V_S @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[310]) ).
thf(991,plain,
( ( ! [V_R: $i,T_a: $i,V_S: $i] :
( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ V_R @ V_R @ T_a @ T_a @ T_a ) @ ( c_Relation_Orel__comp @ V_S @ V_R @ T_a @ T_a @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ V_S @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
| ~ ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_R @ V_S @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[311]) ).
thf(992,plain,
( ( ! [V_r: $i,V_x: $i,T_a: $i,V_y: $i,V_A: $i] :
( ( ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a )
= ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_y @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[312]) ).
thf(993,plain,
( ( ! [V_r: $i,V_a: $i,T_a: $i,V_b: $i,V_A: $i] :
( ( ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a )
= ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[313]) ).
thf(994,plain,
( ( ! [V_p: $i,V_s: $i,T_a: $i,V_r: $i] :
( ( c_in @ V_p @ ( c_Transitive__Closure_Otrancl @ V_s @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_lessequals @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_in @ V_p @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[314]) ).
thf(995,plain,
( ( ! [V_x: $i,V_R: $i,V_S: $i,T_a: $i] :
( ( c_in @ V_x @ ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_R @ V_S @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_x @ ( c_Transitive__Closure_Ortrancl @ V_S @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[315]) ).
thf(996,plain,
( ( ! [V_x: $i,V_R: $i,V_S: $i,T_a: $i] :
( ( c_in @ V_x @ ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_R @ V_S @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_x @ ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[316]) ).
thf(997,plain,
( ( ! [V_r: $i,T_a: $i,V_y: $i,V_x: $i] :
( ( c_Wellfounded_Owf @ V_r @ T_a )
| ~ ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ V_y @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[317]) ).
thf(998,plain,
( ( ! [V_A: $i,V_C: $i,T_a: $i,T_b: $i,V_B: $i,V_x: $i] :
( ( ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_C @ ( tc_fun @ T_a @ tc_bool ) @ T_b ) @ T_b @ T_a )
!= ( c_Product__Type_OSigma @ V_B @ ( c_COMBK @ V_C @ ( tc_fun @ T_a @ tc_bool ) @ T_b ) @ T_b @ T_a ) )
| ~ ( c_in @ V_x @ V_C @ T_a )
| ( V_A = V_B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[318]) ).
thf(999,plain,
( ( ! [V_b: $i,V_r: $i,V_a: $i,T_b: $i,T_a: $i] :
( ( c_in @ V_b @ ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b ) @ T_b @ T_a ) @ T_a )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_b @ T_a ) @ V_r @ ( tc_prod @ T_b @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[319]) ).
thf(1000,plain,
( ( ! [V_a: $i,V_b: $i,T_b: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_b @ T_b @ T_a ) @ V_r @ ( tc_prod @ T_b @ T_a ) )
| ~ ( c_in @ V_b @ ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b ) @ T_b @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[320]) ).
thf(1001,plain,
( ( ! [V_f: $i,V_x: $i,V_B: $i,T_a: $i,V_A: $i,T_b: $i] :
( ( c_in @ ( hAPP @ V_f @ V_x ) @ V_B @ T_a )
| ~ ( c_in @ V_x @ V_A @ T_b )
| ~ ( c_lessequals @ ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[321]) ).
thf(1002,plain,
( ( ! [V_f: $i,V_x: $i,V_A: $i,T_a: $i,T_b: $i] :
( ( ( c_Set_Oinsert @ ( hAPP @ V_f @ V_x ) @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) @ T_b )
= ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) )
| ~ ( c_in @ V_x @ V_A @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[322]) ).
thf(1003,plain,
( ( ! [V_a: $i,V_b: $i,T_a: $i,V_r: $i,V_A: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_b @ V_A @ T_a )
| ~ ( c_lessequals @ ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) @ ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[323]) ).
thf(1004,plain,
( ( ! [V_a: $i,V_b: $i,T_a: $i,V_r: $i,V_x: $i,V_A: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) @ ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[324]) ).
thf(1005,plain,
( ( ! [V_r: $i,T_a: $i,V_s: $i] :
( ( c_lessequals @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Relation_Orel__comp @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ V_r @ T_a @ T_a @ T_a ) @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Relation_OId @ T_a ) @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[325]) ).
thf(1006,plain,
( ( ! [V_a: $i,V_r: $i,T_a: $i,V_A: $i] :
( ( c_in @ V_a @ ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) @ T_a )
| ~ ( c_in @ V_a @ V_A @ T_a )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[326]) ).
thf(1007,plain,
( ( ! [V_P: $i,V_b: $i,V_a: $i,V_r: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_b ) )
| ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 @ V_P @ V_a @ V_r @ T_a ) @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2 @ V_P @ V_a @ V_r @ T_a ) @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[327]) ).
thf(1008,plain,
( ( ! [V_P: $i,V_a: $i,V_b: $i,V_r: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1 @ V_P @ V_b @ V_r @ T_a ) @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 @ V_P @ V_b @ V_r @ T_a ) @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_b ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[328]) ).
thf(1009,plain,
( ( ! [V_x: $i,V_y: $i,T_a: $i,V_r: $i] :
( ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Wellfounded_Oacyclic @ ( c_Set_Oinsert @ ( c_Pair @ V_y @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[329]) ).
thf(1010,plain,
( ( ! [V_y: $i,V_x: $i,T_a: $i,V_r: $i] :
( ( c_Wellfounded_Oacyclic @ ( c_Set_Oinsert @ ( c_Pair @ V_y @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) @ T_a )
| ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Wellfounded_Oacyclic @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[330]) ).
thf(1011,plain,
( ( ! [V_r: $i,T_a: $i,V_A: $i] :
( ( c_Relation_Oirrefl @ V_r @ T_a )
| ~ ( c_Order__Relation_Ostrict__linear__order__on @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[331]) ).
thf(1012,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_y @ V_x @ T_a )
| ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[332]) ).
thf(1013,plain,
( ( ! [V_r: $i,V_A: $i,T_a: $i] :
( ( c_lessequals @ V_r @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_A @ ( tc_fun @ T_a @ tc_bool ) @ T_a ) @ T_a @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[333]) ).
thf(1014,plain,
( ( ! [V_r_H: $i,V_A_H: $i,T_a: $i,T_b: $i,V_r: $i,V_A: $i] :
( ( c_lessequals @ ( c_Relation_OImage @ V_r_H @ V_A_H @ T_a @ T_b ) @ ( c_Relation_OImage @ V_r @ V_A @ T_a @ T_b ) @ ( tc_fun @ T_b @ tc_bool ) )
| ~ ( c_lessequals @ V_A_H @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_r_H @ V_r @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[334]) ).
thf(1015,plain,
( ( ! [V_r: $i,T_b: $i,T_a: $i] :
( ( ( c_Relation_ORange @ V_r @ T_b @ T_a )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( V_r
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_b @ T_a ) @ tc_bool ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[335]) ).
thf(1016,plain,
( ( ! [V_P: $i,T_b: $i,T_a: $i,V_x: $i,V_y: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_P @ ( hAPP @ ( c_snd @ T_b @ T_a ) @ ( c_Pair @ V_x @ V_y @ T_b @ T_a ) ) ) @ ( hAPP @ ( c_fst @ T_b @ T_a ) @ ( c_Pair @ V_x @ V_y @ T_b @ T_a ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_P @ V_y ) @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[336]) ).
thf(1017,plain,
( ( ! [T_a: $i] :
( ( c_Transitive__Closure_Otrancl @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[337]) ).
thf(1018,plain,
( ( ! [V_f: $i,V_A: $i,V_B: $i,T_b: $i,T_a: $i] :
( ( c_Set_Oimage @ V_f @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a ) @ ( c_Set_Oimage @ V_f @ V_B @ T_b @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[338]) ).
thf(1019,plain,
( ( ! [T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[339]) ).
thf(1020,plain,
( ( ! [V_a: $i,V_C: $i,T_a: $i,V_D: $i] :
( ( c_lessequals @ ( c_Set_Oinsert @ V_a @ V_C @ T_a ) @ ( c_Set_Oinsert @ V_a @ V_D @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_C @ V_D @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[340]) ).
thf(1021,plain,
( ( ! [V_x: $i,V_A: $i,T_b: $i,V_f: $i,T_a: $i] :
( ~ ( c_lessequals @ V_x @ V_A @ ( tc_fun @ T_b @ tc_bool ) )
| ( c_lessequals @ ( c_Set_Oimage @ V_f @ V_x @ T_b @ T_a ) @ ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[341]) ).
thf(1022,plain,
( ( ! [V_f: $i,V_A: $i,T_a: $i,T_b: $i,V_B: $i] :
( ( c_lessequals @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) @ ( c_Set_Oimage @ V_f @ V_B @ T_a @ T_b ) @ ( tc_fun @ T_b @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[342]) ).
thf(1023,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_x_H: $i,V_y_H: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x_H @ V_y_H @ T_a ) )
| ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_lessequals @ V_y_H @ V_x_H @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[343]) ).
thf(1024,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_x_H: $i,V_y_H: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x_H @ V_y_H @ T_a ) )
| ( c_lessequals @ V_y_H @ V_x_H @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[344]) ).
thf(1025,plain,
( ( ! [V_B: $i,V_C: $i,V_A: $i,T_a: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ V_B @ ( c_HOL_Ominus__class_Ominus @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= V_A )
| ~ ( c_lessequals @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[345]) ).
thf(1026,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ V_B @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ V_A @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[346]) ).
thf(1027,plain,
( ( ! [V_A: $i,T_b: $i,T_a: $i] :
( ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) @ ( tc_fun @ T_b @ tc_bool ) @ T_a ) @ T_a @ T_b )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[347]) ).
thf(1028,plain,
( ( ! [V_A: $i,V_B: $i,V_C: $i,T_a: $i] :
( ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[348]) ).
thf(1029,plain,
( ( ! [V_A: $i,V_x: $i,T_a: $i] :
( ( V_A
= ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
| ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[349]) ).
thf(1030,plain,
( ( ! [V_r: $i,T_a: $i,T_b: $i,V_s: $i] :
( ( c_lessequals @ ( c_Relation_ODomain @ V_r @ T_a @ T_b ) @ ( c_Relation_ODomain @ V_s @ T_a @ T_b ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[350]) ).
thf(1031,plain,
( ( ! [V_x: $i,T_a: $i] : ( c_in @ V_x @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) )
= $true ),
inference(unfold_def,[status(thm)],[351]) ).
thf(1032,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_HOL_Ominus__class_Ominus @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[352]) ).
thf(1033,plain,
( ( ! [V_A: $i,V_B: $i,V_C: $i,T_a: $i] :
( ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[353]) ).
thf(1034,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i,V_D: $i] :
( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_C @ V_D @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_B @ V_D @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[354]) ).
thf(1035,plain,
( ( ! [V_f: $i,V_A: $i,T_b: $i,T_a: $i] :
( ( ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[355]) ).
thf(1036,plain,
( ( ! [V_r: $i,T_a: $i,T_b: $i,V_s: $i] :
( ( c_Relation_Osingle__valued @ V_r @ T_a @ T_b )
| ~ ( c_Relation_Osingle__valued @ V_s @ T_a @ T_b )
| ~ ( c_lessequals @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[356]) ).
thf(1037,plain,
( ( ! [V_r: $i,T_a: $i,V_s: $i] :
( ( c_Wellfounded_Oacyclic @ V_r @ T_a )
| ~ ( c_lessequals @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_Wellfounded_Oacyclic @ V_s @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[357]) ).
thf(1038,plain,
( ( ! [V_Q: $i,V_x: $i,V_P: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_Q @ V_x ) )
| ~ ( c_lessequals @ V_P @ V_Q @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[358]) ).
thf(1039,plain,
( ( ! [V_r: $i,T_a: $i,V_s: $i] :
( ( c_Relation_Oantisym @ V_r @ T_a )
| ~ ( c_Relation_Oantisym @ V_s @ T_a )
| ~ ( c_lessequals @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[359]) ).
thf(1040,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_lessequals @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[360]) ).
thf(1041,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_lessequals @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[361]) ).
thf(1042,plain,
( ( ! [V_p: $i,T_a: $i,V_r: $i] :
( ( c_Wellfounded_Owf @ V_p @ T_a )
| ~ ( c_lessequals @ V_p @ V_r @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[362]) ).
thf(1043,plain,
( ( ! [V_Q: $i,V_x: $i,V_P: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_Q @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( c_lessequals @ V_P @ V_Q @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[363]) ).
thf(1044,plain,
( ( ! [V_A: $i,V_C: $i,T_a: $i,V_B: $i] :
( ( c_lessequals @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[364]) ).
thf(1045,plain,
( ( ! [V_A: $i,T_a: $i] : ( c_lessequals @ V_A @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(unfold_def,[status(thm)],[365]) ).
thf(1046,plain,
( ( ! [V_x: $i,T_a: $i] : ( c_lessequals @ V_x @ V_x @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(unfold_def,[status(thm)],[366]) ).
thf(1047,plain,
( ( ! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_lessequals @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ V_y @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[367]) ).
thf(1048,plain,
( ( ! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_lessequals @ V_z @ V_x @ T_a )
| ~ ( c_lessequals @ V_z @ V_y @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[368]) ).
thf(1049,plain,
( ( ! [V_B: $i,V_C: $i,T_a: $i,V_A: $i] :
( ( c_lessequals @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[369]) ).
thf(1050,plain,
( ( ! [V_A: $i,V_C: $i,T_a: $i,V_B: $i] :
( ( c_lessequals @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[370]) ).
thf(1051,plain,
( ( ! [T_a: $i,V_a: $i,V_x: $i,V_b: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ V_a @ V_x @ T_a )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[371]) ).
thf(1052,plain,
( ( ! [T_a: $i,V_b: $i,V_x: $i,V_a: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ V_b @ V_x @ T_a )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[372]) ).
thf(1053,plain,
( ( ! [T_a: $i,V_x: $i,V_a: $i,V_b: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[373]) ).
thf(1054,plain,
( ( ! [T_a: $i,V_x: $i,V_a: $i,V_b: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[374]) ).
thf(1055,plain,
( ( ! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ V_z @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[375]) ).
thf(1056,plain,
( ( ! [T_a: $i,V_y: $i,V_z: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ V_y @ V_z @ T_a )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ V_z @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[376]) ).
thf(1057,plain,
( ( ! [V_A: $i,T_a: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
= V_A ) )
= $true ),
inference(unfold_def,[status(thm)],[377]) ).
thf(1058,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)],[378]) ).
thf(1059,plain,
( ( ! [V_a: $i,V_A: $i,T_a: $i] :
( ( ( c_Set_Oinsert @ V_a @ ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
= V_A )
| ~ ( c_in @ V_a @ V_A @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[379]) ).
thf(1060,plain,
( ( ! [V_r_H: $i,V_r: $i,T_a: $i] :
( ( c_Wellfounded_Owf @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_r_H @ V_r @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[380]) ).
thf(1061,plain,
( ( ! [V_r: $i,V_r_H: $i,T_a: $i] :
( ( c_Wellfounded_Owf @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_r @ V_r_H @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[381]) ).
thf(1062,plain,
( ( ! [V_A: $i,V_B: $i,T_b: $i,T_a: $i] :
( ( c_Relation_ORange @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ ( tc_prod @ T_b @ T_a ) @ tc_bool ) ) @ T_b @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_ORange @ V_A @ T_b @ T_a ) @ ( c_Relation_ORange @ V_B @ T_b @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[382]) ).
thf(1063,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[383]) ).
thf(1064,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)],[384]) ).
thf(1065,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)],[385]) ).
thf(1066,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i,T_b: $i] :
( ( c_Product__Type_OSigma @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_COMBK @ V_C @ ( tc_fun @ T_b @ tc_bool ) @ T_a ) @ T_a @ T_b )
= ( c_HOL_Ominus__class_Ominus @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_C @ ( tc_fun @ T_b @ tc_bool ) @ T_a ) @ T_a @ T_b ) @ ( c_Product__Type_OSigma @ V_B @ ( c_COMBK @ V_C @ ( tc_fun @ T_b @ tc_bool ) @ T_a ) @ T_a @ T_b ) @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[386]) ).
thf(1067,plain,
( ( ! [V_x: $i,V_A: $i,T_a: $i,V_B: $i] :
( ( c_lessequals @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_in @ V_x @ V_B @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[387]) ).
thf(1068,plain,
( ( ! [V_x: $i,V_A: $i,T_a: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ V_x ) ) )
= $true ),
inference(unfold_def,[status(thm)],[388]) ).
thf(1069,plain,
( ( ! [V_r: $i,T_a: $i,V_A: $i] :
( ( c_Relation_Otrans @ V_r @ T_a )
| ~ ( c_Order__Relation_Ostrict__linear__order__on @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[389]) ).
thf(1070,plain,
( ( ! [V_B: $i,V_C: $i,T_a: $i,V_A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[390]) ).
thf(1071,plain,
( ( ! [V_A: $i,V_B: $i,V_C: $i,T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[391]) ).
thf(1072,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)],[392]) ).
thf(1073,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)],[393]) ).
thf(1074,plain,
( ( ! [V_Q: $i,T_a: $i,T_b: $i,V_p: $i,V_q: $i,V_P: $i] :
( ( hBOOL @ ( hAPP @ V_Q @ ( hAPP @ ( c_snd @ T_a @ T_b ) @ ( c_Pair @ V_p @ V_q @ T_a @ T_b ) ) ) )
| ~ ( hBOOL @ ( hAPP @ V_Q @ V_q ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_p ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[394]) ).
thf(1075,plain,
( ( ! [V_P: $i,T_a: $i,T_b: $i,V_p: $i,V_q: $i,V_Q: $i] :
( ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ ( c_fst @ T_a @ T_b ) @ ( c_Pair @ V_p @ V_q @ T_a @ T_b ) ) ) )
| ~ ( hBOOL @ ( hAPP @ V_Q @ V_q ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_p ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[395]) ).
thf(1076,plain,
( ( ! [V_y: $i,T_b: $i,T_a: $i,V_x: $i] :
( V_y
= ( hAPP @ ( c_snd @ T_b @ T_a ) @ ( c_Pair @ V_x @ V_y @ T_b @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[396]) ).
thf(1077,plain,
( ( ! [T_b: $i,T_a: $i,V_a: $i,V_b: $i] :
( ( hAPP @ ( c_snd @ T_b @ T_a ) @ ( c_Pair @ V_a @ V_b @ T_b @ T_a ) )
= V_b ) )
= $true ),
inference(unfold_def,[status(thm)],[397]) ).
thf(1078,plain,
( ( ! [V_x: $i,T_a: $i,T_b: $i,V_y: $i] :
( V_x
= ( hAPP @ ( c_fst @ T_a @ T_b ) @ ( c_Pair @ V_x @ V_y @ T_a @ T_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[398]) ).
thf(1079,plain,
( ( ! [T_a: $i,T_b: $i,V_a: $i,V_b: $i] :
( ( hAPP @ ( c_fst @ T_a @ T_b ) @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) )
= V_a ) )
= $true ),
inference(unfold_def,[status(thm)],[399]) ).
thf(1080,plain,
( ( ! [V_a: $i,V_A: $i,T_a: $i] :
( ( ( c_Set_Oinsert @ V_a @ V_A @ T_a )
= V_A )
| ~ ( c_in @ V_a @ V_A @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[400]) ).
thf(1081,plain,
( ( ! [V_x: $i,V_A: $i,T_a: $i,V_B: $i] :
( ( ( c_Set_Oinsert @ V_x @ V_A @ T_a )
!= ( c_Set_Oinsert @ V_x @ V_B @ T_a ) )
| ( c_in @ V_x @ V_B @ T_a )
| ( c_in @ V_x @ V_A @ T_a )
| ( V_A = V_B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[401]) ).
thf(1082,plain,
( ( ! [V_c: $i,V_A: $i,V_B: $i,T_a: $i] :
( ( c_in @ V_c @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
| ( c_in @ V_c @ V_B @ T_a )
| ~ ( c_in @ V_c @ V_A @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[402]) ).
thf(1083,plain,
( ( ! [V_c: $i,V_A: $i,V_B: $i,T_a: $i] :
( ( c_in @ V_c @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
| ( c_in @ V_c @ V_B @ T_a )
| ~ ( c_in @ V_c @ V_A @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[403]) ).
thf(1084,plain,
( ( ! [V_P: $i,V_x: $i,T_a: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( c_in @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[404]) ).
thf(1085,plain,
( ( ! [V_c: $i,V_A: $i,T_a: $i,V_B: $i] :
( ( c_in @ V_c @ V_A @ T_a )
| ~ ( c_in @ V_c @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[405]) ).
thf(1086,plain,
( ( ! [V_c: $i,V_B: $i,T_a: $i,V_A: $i] :
( ( c_in @ V_c @ V_B @ T_a )
| ~ ( c_in @ V_c @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[406]) ).
thf(1087,plain,
( ( ! [V_x: $i,V_B: $i,T_a: $i] : ( c_in @ V_x @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ T_a ) )
= $true ),
inference(unfold_def,[status(thm)],[407]) ).
thf(1088,plain,
( ( ! [V_a: $i,V_B: $i,T_a: $i] : ( c_in @ V_a @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ T_a ) )
= $true ),
inference(unfold_def,[status(thm)],[408]) ).
thf(1089,plain,
( ( ! [V_x: $i,V_A: $i,T_a: $i] : ( c_in @ V_x @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ T_a ) )
= $true ),
inference(unfold_def,[status(thm)],[409]) ).
thf(1090,plain,
( ( ! [V_c: $i,V_A: $i,T_a: $i,V_B: $i] :
( ( c_in @ V_c @ V_A @ T_a )
| ~ ( c_in @ V_c @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[410]) ).
thf(1091,plain,
( ( ! [V_c: $i,V_B: $i,T_a: $i,V_A: $i] :
( ~ ( c_in @ V_c @ V_B @ T_a )
| ~ ( c_in @ V_c @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[411]) ).
thf(1092,plain,
( ( ! [V_c: $i,V_B: $i,T_a: $i,V_A: $i] :
( ( c_in @ V_c @ V_B @ T_a )
| ( c_in @ V_c @ V_A @ T_a )
| ~ ( c_in @ V_c @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[412]) ).
thf(1093,plain,
( ( ! [V_a: $i,V_A: $i,T_a: $i,V_b: $i] :
( ( c_in @ V_a @ V_A @ T_a )
| ( V_a = V_b )
| ~ ( c_in @ V_a @ ( c_Set_Oinsert @ V_b @ V_A @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[413]) ).
thf(1094,plain,
( ( ! [V_a: $i,T_a: $i] :
~ ( c_in @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
= $true ),
inference(unfold_def,[status(thm)],[414]) ).
thf(1095,plain,
( ( ! [V_c: $i,T_a: $i] :
~ ( c_in @ V_c @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
= $true ),
inference(unfold_def,[status(thm)],[415]) ).
thf(1096,plain,
( ( ! [V_P: $i,V_x: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( c_in @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[416]) ).
thf(1097,plain,
( ( ! [V_x: $i,T_a: $i] :
~ ( c_in @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
= $true ),
inference(unfold_def,[status(thm)],[417]) ).
thf(1098,plain,
( ( ! [V_c: $i,V_A: $i,V_B: $i,T_a: $i] :
( ( c_in @ V_c @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
| ~ ( c_in @ V_c @ V_B @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[418]) ).
thf(1099,plain,
( ( ! [V_c: $i,V_A: $i,V_B: $i,T_a: $i] :
( ( c_in @ V_c @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
| ~ ( c_in @ V_c @ V_A @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[419]) ).
thf(1100,plain,
( ( ! [V_x: $i,V_B: $i,T_a: $i,V_A: $i] :
( ( c_in @ V_x @ V_B @ T_a )
| ~ ( c_in @ V_x @ V_A @ T_a )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[420]) ).
thf(1101,plain,
( ( ! [V_c: $i,V_B: $i,T_a: $i,V_A: $i] :
( ( c_in @ V_c @ V_B @ T_a )
| ~ ( c_in @ V_c @ V_A @ T_a )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[421]) ).
thf(1102,plain,
( ( ! [V_x: $i,V_B: $i,T_a: $i,V_A: $i] :
( ( c_in @ V_x @ V_B @ T_a )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_in @ V_x @ V_A @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[422]) ).
thf(1103,plain,
( ( ! [V_t: $i,V_B: $i,T_a: $i,V_A: $i] :
( ( c_in @ V_t @ V_B @ T_a )
| ~ ( c_in @ V_t @ V_A @ T_a )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[423]) ).
thf(1104,plain,
( ( ! [V_a: $i,V_b: $i,V_B: $i,T_a: $i] :
( ( c_in @ V_a @ ( c_Set_Oinsert @ V_b @ V_B @ T_a ) @ T_a )
| ~ ( c_in @ V_a @ V_B @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[424]) ).
thf(1105,plain,
( ( ! [V_a: $i,V_b: $i,V_A: $i,T_a: $i] :
( ( c_in @ V_a @ ( c_Set_Oinsert @ V_b @ V_A @ T_a ) @ T_a )
| ~ ( c_in @ V_a @ V_A @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[425]) ).
thf(1106,plain,
( ( ! [V_c: $i,V_A: $i,V_B: $i,T_a: $i] :
( ( c_in @ V_c @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
| ~ ( c_in @ V_c @ V_B @ T_a )
| ~ ( c_in @ V_c @ V_A @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[426]) ).
thf(1107,plain,
( ( ! [V_c: $i,V_A: $i,V_B: $i,T_a: $i] :
( ( c_in @ V_c @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
| ~ ( c_in @ V_c @ V_B @ T_a )
| ~ ( c_in @ V_c @ V_A @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[427]) ).
thf(1108,plain,
( ( ! [T_b: $i,V_f: $i,V_x: $i,V_g: $i,T_a: $i] :
( ~ ( class_HOL_Oord @ T_b )
| ( c_lessequals @ ( hAPP @ V_f @ V_x ) @ ( hAPP @ V_g @ V_x ) @ T_b )
| ~ ( c_lessequals @ V_f @ V_g @ ( tc_fun @ T_a @ T_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[428]) ).
thf(1109,plain,
( ( ! [V_r: $i,T_a: $i,V_y: $i,V_x: $i] :
( ( c_Wellfounded_Oacyclic @ V_r @ T_a )
| ~ ( c_Wellfounded_Oacyclic @ ( c_Set_Oinsert @ ( c_Pair @ V_y @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[429]) ).
thf(1110,plain,
( ( ! [V_f: $i,V_g: $i,V_r: $i,V_x: $i,T_a: $i,T_b: $i] :
( ( ( hAPP @ V_f @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ V_f @ V_g @ V_r @ V_x @ T_a @ T_b ) )
!= ( hAPP @ V_g @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ V_f @ V_g @ V_r @ V_x @ T_a @ T_b ) ) )
| ( ( c_Recdef_Ocut @ V_f @ V_r @ V_x @ T_a @ T_b )
= ( c_Recdef_Ocut @ V_g @ V_r @ V_x @ T_a @ T_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[430]) ).
thf(1111,plain,
( ( ! [V_A: $i,V_B: $i,V_C: $i,T_a: $i] :
( ( c_lessequals @ V_A @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[431]) ).
thf(1112,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[432]) ).
thf(1113,plain,
( ( ! [V_x: $i,V_A: $i,T_a: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
= V_A )
| ( c_in @ V_x @ V_A @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[433]) ).
thf(1114,plain,
( ( ! [V_r: $i,V_s: $i,T_a: $i] :
( ( c_Relation_Osym @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
| ~ ( c_Relation_Osym @ V_s @ T_a )
| ~ ( c_Relation_Osym @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[434]) ).
thf(1115,plain,
( ( ! [V_a: $i,V_b: $i,T_b: $i,T_a: $i,V_r: $i] :
( ( c_Relation_ORange @ ( c_Set_Oinsert @ ( c_Pair @ V_a @ V_b @ T_b @ T_a ) @ V_r @ ( tc_prod @ T_b @ T_a ) ) @ T_b @ T_a )
= ( c_Set_Oinsert @ V_b @ ( c_Relation_ORange @ V_r @ T_b @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[435]) ).
thf(1116,plain,
( ( ! [V_A: $i,V_x: $i,V_B: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_A @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[436]) ).
thf(1117,plain,
( ( ! [V_B: $i,V_x: $i,V_A: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_B @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[437]) ).
thf(1118,plain,
( ( ! [V_A: $i,V_x: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[438]) ).
thf(1119,plain,
( ( ! [V_x: $i,V_A: $i,T_a: $i,V_B: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Set_Oinsert @ V_x @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
| ( c_in @ V_x @ V_B @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[439]) ).
thf(1120,plain,
( ( ! [V_R: $i,T_a: $i,V_S: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_S @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
= ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_R @ V_S @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[440]) ).
thf(1121,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__Xwf__induct__rule__1__1 @ V_P @ V_r @ T_a ) ) )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[441]) ).
thf(1122,plain,
( ( ! [V_A: $i,V_B: $i,T_b: $i,T_a: $i] : ( c_lessequals @ ( c_Relation_ORange @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ ( tc_prod @ T_b @ T_a ) @ tc_bool ) ) @ T_b @ T_a ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_ORange @ V_A @ T_b @ T_a ) @ ( c_Relation_ORange @ V_B @ T_b @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(unfold_def,[status(thm)],[442]) ).
thf(1123,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_HOL_Ominus__class_Ominus @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[443]) ).
thf(1124,plain,
( ( ! [T_a: $i,V_f: $i,T_b: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Set_Oimage @ V_f @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[444]) ).
thf(1125,plain,
( ( ! [V_r: $i,T_a: $i,T_b: $i] :
( ( ( c_Relation_ODomain @ V_r @ T_a @ T_b )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( V_r
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[445]) ).
thf(1126,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)],[446]) ).
thf(1127,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)],[447]) ).
thf(1128,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[448]) ).
thf(1129,plain,
( ( ! [V_R2: $i,T_a: $i,V_R1: $i] :
( ( c_lessequals @ ( c_Wellfounded_Oacc @ V_R2 @ T_a ) @ ( c_Wellfounded_Oacc @ V_R1 @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_R1 @ V_R2 @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[449]) ).
thf(1130,plain,
( ( ! [T_a: $i,V_B: $i,T_b: $i] :
( ( c_Product__Type_OSigma @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ T_a @ T_b )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[450]) ).
thf(1131,plain,
( ( ! [V_a: $i,V_A: $i,T_a: $i] :
( ( c_Set_Oinsert @ V_a @ V_A @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[451]) ).
thf(1132,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,T_b: $i] :
( ( c_Relation_ODomain @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) @ T_a @ T_b )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_ODomain @ V_A @ T_a @ T_b ) @ ( c_Relation_ODomain @ V_B @ T_a @ T_b ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[452]) ).
thf(1133,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)],[453]) ).
thf(1134,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)],[454]) ).
thf(1135,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[455]) ).
thf(1136,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[456]) ).
thf(1137,plain,
( ( ! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_lessequals @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[457]) ).
thf(1138,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_lessequals @ V_x @ V_y @ T_a )
| ~ ( c_lessequals @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[458]) ).
thf(1139,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_x: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_a @ V_b @ T_a ) @ V_x @ T_a )
| ~ ( c_lessequals @ V_b @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[459]) ).
thf(1140,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_x: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_a @ V_b @ T_a ) @ V_x @ T_a )
| ~ ( c_lessequals @ V_a @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[460]) ).
thf(1141,plain,
( ( ! [T_a: $i,V_x: $i,V_b: $i,V_a: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_lessequals @ V_x @ V_b @ T_a )
| ~ ( c_lessequals @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_a @ V_b @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[461]) ).
thf(1142,plain,
( ( ! [T_a: $i,V_x: $i,V_a: $i,V_b: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_lessequals @ V_x @ V_a @ T_a )
| ~ ( c_lessequals @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_a @ V_b @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[462]) ).
thf(1143,plain,
( ( ! [V_C: $i,V_A: $i,T_a: $i,V_B: $i] :
( ( c_lessequals @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_C @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[463]) ).
thf(1144,plain,
( ( ! [V_C: $i,V_B: $i,T_a: $i,V_A: $i] :
( ( c_lessequals @ V_C @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_C @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[464]) ).
thf(1145,plain,
( ( ! [V_R: $i,V_S: $i,V_T: $i,T_c: $i,T_b: $i,T_a: $i] :
( ( c_Relation_Orel__comp @ V_R @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_S @ V_T @ ( tc_fun @ ( tc_prod @ T_c @ T_b ) @ tc_bool ) ) @ T_a @ T_c @ T_b )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ V_R @ V_S @ T_a @ T_c @ T_b ) @ ( c_Relation_Orel__comp @ V_R @ V_T @ T_a @ T_c @ T_b ) @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[465]) ).
thf(1146,plain,
( ( ! [V_S: $i,V_T: $i,T_a: $i,T_c: $i,V_R: $i,T_b: $i] :
( ( c_Relation_Orel__comp @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_S @ V_T @ ( tc_fun @ ( tc_prod @ T_a @ T_c ) @ tc_bool ) ) @ V_R @ T_a @ T_c @ T_b )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ V_S @ V_R @ T_a @ T_c @ T_b ) @ ( c_Relation_Orel__comp @ V_T @ V_R @ T_a @ T_c @ T_b ) @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[466]) ).
thf(1147,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ ( c_HOL_Ominus__class_Ominus @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[467]) ).
thf(1148,plain,
( ( ! [V_B: $i,V_A: $i,T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[468]) ).
thf(1149,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ T_a )
!= ( c_Orderings_Obot__class_Obot @ T_a ) )
| ( V_B
= ( c_Orderings_Obot__class_Obot @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[469]) ).
thf(1150,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ T_a )
!= ( c_Orderings_Obot__class_Obot @ T_a ) )
| ( V_A
= ( c_Orderings_Obot__class_Obot @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[470]) ).
thf(1151,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[471]) ).
thf(1152,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( V_B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[472]) ).
thf(1153,plain,
( ( ! [V_A: $i,V_r: $i,T_a: $i] :
( ( c_Relation_Ototal__on @ V_A @ V_r @ T_a )
| ~ ( c_Order__Relation_Ostrict__linear__order__on @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[473]) ).
thf(1154,plain,
( ( ! [V_a: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( c_in @ V_a @ V_C @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[474]) ).
thf(1155,plain,
( ( ! [V_A: $i,V_a: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( c_in @ V_a @ V_A @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[475]) ).
thf(1156,plain,
( ( ! [V_r: $i,V_s: $i,T_b: $i,T_a: $i] :
( ( c_Relation_Oconverse @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_b @ T_a ) @ tc_bool ) ) @ T_b @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_Oconverse @ V_r @ T_b @ T_a ) @ ( c_Relation_Oconverse @ V_s @ T_b @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[476]) ).
thf(1157,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_x: $i] :
( ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ( c_in @ V_x @ V_A @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[477]) ).
thf(1158,plain,
( ( ! [V_A: $i,V_x: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ( c_in @ V_x @ V_A @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[478]) ).
thf(1159,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_x: $i] :
( ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ( c_in @ V_x @ V_A @ T_a )
| ~ ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[479]) ).
thf(1160,plain,
( ( ! [V_A: $i,V_x: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ( c_in @ V_x @ V_A @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[480]) ).
thf(1161,plain,
( ( ! [V_y: $i,V_A: $i,T_a: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ V_y @ V_A @ T_a ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ V_A @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[481]) ).
thf(1162,plain,
( ( ! [V_I: $i,V_J: $i,T_a: $i,V_C: $i,T_b: $i] :
( ( c_Product__Type_OSigma @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_I @ V_J @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ T_a @ T_b )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Product__Type_OSigma @ V_I @ V_C @ T_a @ T_b ) @ ( c_Product__Type_OSigma @ V_J @ V_C @ T_a @ T_b ) @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[482]) ).
thf(1163,plain,
( ( ! [V_x: $i,V_B: $i,T_a: $i,V_A: $i] :
( ( c_in @ V_x @ V_B @ T_a )
| ~ ( c_lessequals @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[483]) ).
thf(1164,plain,
( ( ! [T_a: $i] : ( c_Wellfounded_Owf @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a ) )
= $true ),
inference(unfold_def,[status(thm)],[484]) ).
thf(1165,plain,
( ( ! [V_x: $i,V_xa: $i,T_a: $i] :
( ( ( c_Set_Oinsert @ V_x @ V_xa @ T_a )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( c_in @ V_x @ V_xa @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[485]) ).
thf(1166,plain,
( ( ! [V_c: $i,T_a: $i,T_b: $i] :
( ( c_Set_Oimage @ ( c_COMBK @ V_c @ T_a @ T_b ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b @ T_a )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[486]) ).
thf(1167,plain,
( ( ! [T_a: $i] :
( ( c_Relation_OId__on @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[487]) ).
thf(1168,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[488]) ).
thf(1169,plain,
( ( ! [V_a: $i,T_a: $i,V_b: $i] :
( ( ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
!= ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
| ( V_a = V_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[489]) ).
thf(1170,plain,
( ( ! [V_a: $i,V_A: $i,T_a: $i] :
( ( c_Set_Oinsert @ V_a @ ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
= ( c_Set_Oinsert @ V_a @ V_A @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[490]) ).
thf(1171,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(unfold_def,[status(thm)],[491]) ).
thf(1172,plain,
( ( ! [V_S: $i,T_a: $i,V_R: $i] :
( ( ( c_Transitive__Closure_Ortrancl @ V_S @ T_a )
= ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) )
| ~ ( c_lessequals @ V_S @ ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_lessequals @ V_R @ V_S @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[492]) ).
thf(1173,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( c_lessequals @ ( 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 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[493]) ).
thf(1174,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i,T_b: $i] :
( ( c_Product__Type_OSigma @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_COMBK @ V_C @ ( tc_fun @ T_b @ tc_bool ) @ T_a ) @ T_a @ T_b )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_C @ ( tc_fun @ T_b @ tc_bool ) @ T_a ) @ T_a @ T_b ) @ ( c_Product__Type_OSigma @ V_B @ ( c_COMBK @ V_C @ ( tc_fun @ T_b @ tc_bool ) @ T_a ) @ T_a @ T_b ) @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[494]) ).
thf(1175,plain,
( ( ! [V_C: $i,V_A: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_C @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_C @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[495]) ).
thf(1176,plain,
( ( ! [V_C: $i,V_A: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_C @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_C @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[496]) ).
thf(1177,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(unfold_def,[status(thm)],[497]) ).
thf(1178,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(unfold_def,[status(thm)],[498]) ).
thf(1179,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[499]) ).
thf(1180,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[500]) ).
thf(1181,plain,
( ( ! [T_a: $i,V_x: $i,V_a: $i,V_b: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_lessequals @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_b @ T_a )
| ~ ( c_lessequals @ V_x @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[501]) ).
thf(1182,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_lessequals @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[502]) ).
thf(1183,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_lessequals @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[503]) ).
thf(1184,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[504]) ).
thf(1185,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[505]) ).
thf(1186,plain,
( ( ! [V_r: $i,V_s: $i,T_b: $i,T_a: $i] :
( ( c_Relation_Oconverse @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_b @ T_a ) @ tc_bool ) ) @ T_b @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Oconverse @ V_r @ T_b @ T_a ) @ ( c_Relation_Oconverse @ V_s @ T_b @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[506]) ).
thf(1187,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i,V_D: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_C @ V_D @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_B @ V_D @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[507]) ).
thf(1188,plain,
( ( ! [T_a: $i,V_r: $i] : ( c_Relation_Ototal__on @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ V_r @ T_a ) )
= $true ),
inference(unfold_def,[status(thm)],[508]) ).
thf(1189,plain,
( ( ! [V_f: $i,V_a: $i,V_B: $i,T_b: $i,T_a: $i] :
( ( c_Set_Oimage @ V_f @ ( c_Set_Oinsert @ V_a @ V_B @ T_b ) @ T_b @ T_a )
= ( c_Set_Oinsert @ ( hAPP @ V_f @ V_a ) @ ( c_Set_Oimage @ V_f @ V_B @ T_b @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[509]) ).
thf(1190,plain,
( ( ! [V_A: $i,V_a: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Set_Oinsert @ V_a @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
| ~ ( c_in @ V_a @ V_A @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[510]) ).
thf(1191,plain,
( ( ! [V_a: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Set_Oinsert @ V_a @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
| ~ ( c_in @ V_a @ V_C @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[511]) ).
thf(1192,plain,
( ( ! [T_a: $i] : ( c_Relation_Orefl__on @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a ) )
= $true ),
inference(unfold_def,[status(thm)],[512]) ).
thf(1193,plain,
( ( ! [T_a: $i,V_a: $i,V_A: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Set_Oinsert @ V_a @ V_A @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[513]) ).
thf(1194,plain,
( ( ! [T_a: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(unfold_def,[status(thm)],[514]) ).
thf(1195,plain,
( ( ! [V_A: $i,T_a: $i] :
( ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( c_lessequals @ V_A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[515]) ).
thf(1196,plain,
( ( ! [V_r: $i,T_a: $i,V_s: $i] :
( ( c_lessequals @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_s @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_lessequals @ V_r @ ( c_Transitive__Closure_Ortrancl @ V_s @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[516]) ).
thf(1197,plain,
( ( ! [V_r: $i,T_a: $i,V_A: $i] :
( ( c_lessequals @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_A @ ( tc_fun @ T_a @ tc_bool ) @ T_a ) @ T_a @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_lessequals @ V_r @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_A @ ( tc_fun @ T_a @ tc_bool ) @ T_a ) @ T_a @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[517]) ).
thf(1198,plain,
( ( ! [V_a: $i,V_b: $i,T_a: $i,V_c: $i,V_d: $i] :
( ( ( c_Set_Oinsert @ V_a @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a )
!= ( c_Set_Oinsert @ V_c @ ( c_Set_Oinsert @ V_d @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) )
| ( V_b = V_c )
| ( V_b = V_d ) ) )
= $true ),
inference(unfold_def,[status(thm)],[518]) ).
thf(1199,plain,
( ( ! [V_a: $i,V_b: $i,T_a: $i,V_c: $i,V_d: $i] :
( ( ( c_Set_Oinsert @ V_a @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a )
!= ( c_Set_Oinsert @ V_c @ ( c_Set_Oinsert @ V_d @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) )
| ( V_a = V_d )
| ( V_b = V_d ) ) )
= $true ),
inference(unfold_def,[status(thm)],[519]) ).
thf(1200,plain,
( ( ! [V_a: $i,V_b: $i,T_a: $i,V_c: $i,V_d: $i] :
( ( ( c_Set_Oinsert @ V_a @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a )
!= ( c_Set_Oinsert @ V_c @ ( c_Set_Oinsert @ V_d @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) )
| ( V_b = V_c )
| ( V_a = V_c ) ) )
= $true ),
inference(unfold_def,[status(thm)],[520]) ).
thf(1201,plain,
( ( ! [V_a: $i,V_b: $i,T_a: $i,V_c: $i,V_d: $i] :
( ( ( c_Set_Oinsert @ V_a @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a )
!= ( c_Set_Oinsert @ V_c @ ( c_Set_Oinsert @ V_d @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) )
| ( V_a = V_d )
| ( V_a = V_c ) ) )
= $true ),
inference(unfold_def,[status(thm)],[521]) ).
thf(1202,plain,
( ( ! [T_b: $i,T_a: $i] :
( ( c_Relation_ORange @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_b @ T_a ) @ tc_bool ) ) @ T_b @ T_a )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[522]) ).
thf(1203,plain,
( ( ! [T_a: $i] : ( c_Relation_Oantisym @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a ) )
= $true ),
inference(unfold_def,[status(thm)],[523]) ).
thf(1204,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_r: $i,V_s: $i] :
( ( c_Relation_Orefl__on @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
| ~ ( c_Relation_Orefl__on @ V_B @ V_s @ T_a )
| ~ ( c_Relation_Orefl__on @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[524]) ).
thf(1205,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
!= V_B )
| ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[525]) ).
thf(1206,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= V_A )
| ~ ( c_lessequals @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[526]) ).
thf(1207,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= V_B )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[527]) ).
thf(1208,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 )
= V_y )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[528]) ).
thf(1209,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 )
!= V_y )
| ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[529]) ).
thf(1210,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 )
= V_x )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[530]) ).
thf(1211,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= V_A ) )
= $true ),
inference(unfold_def,[status(thm)],[531]) ).
thf(1212,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)],[532]) ).
thf(1213,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( V_x = V_y )
| ~ ( c_lessequals @ V_x @ V_y @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[533]) ).
thf(1214,plain,
( ( ! [V_P: $i,T_b: $i,T_c: $i,T_a: $i,V_z: $i] :
( ( hAPP @ ( c_split @ V_P @ T_b @ T_c @ T_a ) @ V_z )
= ( hAPP @ ( hAPP @ V_P @ ( hAPP @ ( c_fst @ T_b @ T_c ) @ V_z ) ) @ ( hAPP @ ( c_snd @ T_b @ T_c ) @ V_z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[534]) ).
thf(1215,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( V_x = V_y )
| ~ ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[535]) ).
thf(1216,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( V_x = V_y )
| ~ ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[536]) ).
thf(1217,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( V_A = V_B )
| ~ ( c_lessequals @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[537]) ).
thf(1218,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( V_A = V_B )
| ~ ( c_lessequals @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[538]) ).
thf(1219,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Wellfounded_Oacyclic @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a )
| ~ ( c_Wellfounded_Oacyclic @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[539]) ).
thf(1220,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Wellfounded_Oacyclic @ V_r @ T_a )
| ~ ( c_Wellfounded_Oacyclic @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[540]) ).
thf(1221,plain,
( ( ! [V_P: $i,V_xb: $i,V_r: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_xb ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1 @ V_P @ V_r @ T_a ) ) )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[541]) ).
thf(1222,plain,
( ( ! [V_A: $i,V_C: $i,T_a: $i,V_B: $i] :
( ( ( c_Relation_Orel__comp @ V_A @ V_C @ T_a @ T_a @ T_a )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) )
| ( ( c_Relation_Orel__comp @ V_A @ V_B @ T_a @ T_a @ T_a )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) )
| ( ( c_Relation_Orel__comp @ V_A @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a @ T_a @ T_a )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[542]) ).
thf(1223,plain,
( ( ! [V_B: $i,V_C: $i,T_a: $i,V_A: $i] :
( ( ( c_Relation_Orel__comp @ V_B @ V_C @ T_a @ T_a @ T_a )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) )
| ( ( c_Relation_Orel__comp @ V_A @ V_C @ T_a @ T_a @ T_a )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) )
| ( ( c_Relation_Orel__comp @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ V_C @ T_a @ T_a @ T_a )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[543]) ).
thf(1224,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)],[544]) ).
thf(1225,plain,
( ( ! [V_A: $i,V_C: $i,T_a: $i,V_B: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[545]) ).
thf(1226,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( c_lessequals @ ( 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 ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[546]) ).
thf(1227,plain,
( ( ! [V_r: $i,V_s: $i,T_a: $i] :
( ( c_Relation_Otrans @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
| ~ ( c_Relation_Otrans @ V_s @ T_a )
| ~ ( c_Relation_Otrans @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[547]) ).
thf(1228,plain,
( ( ! [V_x: $i,V_B: $i,T_a: $i,V_A: $i] :
( ~ ( c_in @ V_x @ V_B @ T_a )
| ~ ( c_in @ V_x @ V_A @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[548]) ).
thf(1229,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i,V_D: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ V_C @ V_D @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_D @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[549]) ).
thf(1230,plain,
( ( ! [V_c: $i,T_a: $i,T_b: $i,V_A: $i] :
( ( ( c_Set_Oimage @ ( c_COMBK @ V_c @ T_a @ T_b ) @ V_A @ T_b @ T_a )
= ( c_Set_Oinsert @ V_c @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
| ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[550]) ).
thf(1231,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[551]) ).
thf(1232,plain,
( ( ! [V_C: $i,V_A: $i,V_B: $i,T_a: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_C @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_C @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[552]) ).
thf(1233,plain,
( ( ! [T_a: $i,V_x: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ V_x ) ) )
= $true ),
inference(unfold_def,[status(thm)],[553]) ).
thf(1234,plain,
( ( ! [V_A: $i,T_a: $i,V_R: $i] :
( ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( c_lessequals @ V_A @ ( c_Relation_OImage @ V_R @ V_A @ T_a @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_Wellfounded_Owf @ V_R @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[554]) ).
thf(1235,plain,
( ( ! [V_a: $i,V_A: $i,T_a: $i,V_b: $i,V_B: $i,T_b: $i] :
( ( c_Product__Type_OSigma @ ( c_Set_Oinsert @ V_a @ V_A @ T_a ) @ ( c_COMBK @ ( c_Set_Oinsert @ V_b @ V_B @ T_b ) @ ( tc_fun @ T_b @ tc_bool ) @ T_a ) @ T_a @ T_b )
= ( c_Set_Oinsert @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ ( c_Set_Oinsert @ V_b @ V_B @ T_b ) @ ( tc_fun @ T_b @ tc_bool ) @ T_a ) @ T_a @ T_b ) @ ( c_Product__Type_OSigma @ ( c_Set_Oinsert @ V_a @ V_A @ T_a ) @ ( c_COMBK @ V_B @ ( tc_fun @ T_b @ tc_bool ) @ T_a ) @ T_a @ T_b ) @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) @ ( tc_prod @ T_a @ T_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[555]) ).
thf(1236,plain,
( ( ! [T_a: $i,V_A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[556]) ).
thf(1237,plain,
( ( ! [V_A: $i,T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= V_A ) )
= $true ),
inference(unfold_def,[status(thm)],[557]) ).
thf(1238,plain,
( ( ! [T_a: $i,V_B: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= V_B ) )
= $true ),
inference(unfold_def,[status(thm)],[558]) ).
thf(1239,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ T_a ) @ V_x @ T_a )
= V_x ) ) )
= $true ),
inference(unfold_def,[status(thm)],[559]) ).
thf(1240,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Orderings_Obot__class_Obot @ T_a ) @ T_a )
= V_x ) ) )
= $true ),
inference(unfold_def,[status(thm)],[560]) ).
thf(1241,plain,
( ( ! [V_A: $i,V_B: $i,V_C: $i,T_a: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[561]) ).
thf(1242,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[562]) ).
thf(1243,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)],[563]) ).
thf(1244,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)],[564]) ).
thf(1245,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)],[565]) ).
thf(1246,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)],[566]) ).
thf(1247,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_r: $i,V_s: $i] :
( ( c_Relation_Orefl__on @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
| ~ ( c_Relation_Orefl__on @ V_B @ V_s @ T_a )
| ~ ( c_Relation_Orefl__on @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[567]) ).
thf(1248,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i,T_b: $i] :
( ( c_Product__Type_OSigma @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_COMBK @ V_C @ ( tc_fun @ T_b @ tc_bool ) @ T_a ) @ T_a @ T_b )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_C @ ( tc_fun @ T_b @ tc_bool ) @ T_a ) @ T_a @ T_b ) @ ( c_Product__Type_OSigma @ V_B @ ( c_COMBK @ V_C @ ( tc_fun @ T_b @ tc_bool ) @ T_a ) @ T_a @ T_b ) @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[568]) ).
thf(1249,plain,
( ( ! [V_r: $i,T_a: $i,V_s: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_ODomain @ V_r @ T_a @ T_a ) @ ( c_Relation_ORange @ V_s @ T_a @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( c_Wellfounded_Owf @ V_s @ T_a )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a )
| ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[569]) ).
thf(1250,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ V_A @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[570]) ).
thf(1251,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ V_B @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[571]) ).
thf(1252,plain,
( ( ! [V_B: $i,V_x: $i,V_A: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_B @ V_x ) )
| ( hBOOL @ ( hAPP @ V_A @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[572]) ).
thf(1253,plain,
( ( ! [V_R: $i,V_S: $i,T_a: $i] :
( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_R @ V_S @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
| ~ ( c_lessequals @ ( c_Relation_Orel__comp @ V_R @ V_S @ T_a @ T_a @ T_a ) @ V_R @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_Wellfounded_Owf @ V_S @ T_a )
| ~ ( c_Wellfounded_Owf @ V_R @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[573]) ).
thf(1254,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] :
( ( c_lessequals @ ( c_Relation_Orel__comp @ V_r @ V_s @ T_a @ T_b @ T_c ) @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_C @ ( tc_fun @ T_c @ tc_bool ) @ T_a ) @ T_a @ T_c ) @ ( tc_fun @ ( tc_prod @ T_a @ T_c ) @ tc_bool ) )
| ~ ( c_lessequals @ V_s @ ( c_Product__Type_OSigma @ V_B @ ( c_COMBK @ V_C @ ( tc_fun @ T_c @ tc_bool ) @ T_b ) @ T_b @ T_c ) @ ( tc_fun @ ( tc_prod @ T_b @ T_c ) @ tc_bool ) )
| ~ ( c_lessequals @ V_r @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_B @ ( tc_fun @ T_b @ tc_bool ) @ T_a ) @ T_a @ T_b ) @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[574]) ).
thf(1255,plain,
( ( ! [V_A: $i,T_a: $i] :
( ( c_HOL_Ominus__class_Ominus @ V_A @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[575]) ).
thf(1256,plain,
( ( ! [V_A: $i,T_a: $i] :
( ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= V_A ) )
= $true ),
inference(unfold_def,[status(thm)],[576]) ).
thf(1257,plain,
( ( ! [V_I: $i,V_J: $i,T_a: $i,V_C: $i,T_b: $i] :
( ( c_Product__Type_OSigma @ ( c_HOL_Ominus__class_Ominus @ V_I @ V_J @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ T_a @ T_b )
= ( c_HOL_Ominus__class_Ominus @ ( c_Product__Type_OSigma @ V_I @ V_C @ T_a @ T_b ) @ ( c_Product__Type_OSigma @ V_J @ V_C @ T_a @ T_b ) @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[577]) ).
thf(1258,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( c_lessequals @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[578]) ).
thf(1259,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( c_lessequals @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[579]) ).
thf(1260,plain,
( ( ! [V_R: $i,V_A: $i,V_B: $i,T_b: $i,T_a: $i] : ( c_lessequals @ ( c_Relation_OImage @ V_R @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b @ T_a ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_OImage @ V_R @ V_A @ T_b @ T_a ) @ ( c_Relation_OImage @ V_R @ V_B @ T_b @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(unfold_def,[status(thm)],[580]) ).
thf(1261,plain,
( ( ! [V_f: $i,V_A: $i,V_B: $i,T_b: $i,T_a: $i] : ( c_lessequals @ ( c_Set_Oimage @ V_f @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b @ T_a ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a ) @ ( c_Set_Oimage @ V_f @ V_B @ T_b @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(unfold_def,[status(thm)],[581]) ).
thf(1262,plain,
( ( ! [V_B: $i,V_a: $i,T_a: $i] : ( c_lessequals @ V_B @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(unfold_def,[status(thm)],[582]) ).
thf(1263,plain,
( ( ! [V_A: $i,T_a: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[583]) ).
thf(1264,plain,
( ( ! [T_a: $i,V_B: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[584]) ).
thf(1265,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Orderings_Obot__class_Obot @ T_a ) @ V_x @ T_a )
= ( c_Orderings_Obot__class_Obot @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[585]) ).
thf(1266,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Orderings_Obot__class_Obot @ T_a ) @ T_a )
= ( c_Orderings_Obot__class_Obot @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[586]) ).
thf(1267,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,T_b: $i] : ( c_lessequals @ ( c_Relation_ODomain @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) @ T_a @ T_b ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_ODomain @ V_A @ T_a @ T_b ) @ ( c_Relation_ODomain @ V_B @ T_a @ T_b ) @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(unfold_def,[status(thm)],[587]) ).
thf(1268,plain,
( ( ! [V_r: $i,T_a: $i,V_s: $i] :
( ( c_lessequals @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_s @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_lessequals @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[588]) ).
thf(1269,plain,
( ( ! [V_r: $i,V_s: $i,T_a: $i] :
( ( c_Relation_Osym @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
| ~ ( c_Relation_Osym @ V_s @ T_a )
| ~ ( c_Relation_Osym @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[589]) ).
thf(1270,plain,
( ( ! [V_a: $i,V_b: $i,T_a: $i,T_b: $i,V_r: $i] :
( ( c_Relation_ODomain @ ( c_Set_Oinsert @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ V_r @ ( tc_prod @ T_a @ T_b ) ) @ T_a @ T_b )
= ( c_Set_Oinsert @ V_a @ ( c_Relation_ODomain @ V_r @ T_a @ T_b ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[590]) ).
thf(1271,plain,
( ( ! [V_A: $i,V_x: $i,V_y: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_A @ V_x ) )
| ( V_y = V_x )
| ~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ V_y @ V_A @ T_a ) @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[591]) ).
thf(1272,plain,
( ( ! [V_x: $i,V_A: $i,T_a: $i] :
( ( c_Set_Oinsert @ V_x @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ T_a )
= ( c_Set_Oinsert @ V_x @ V_A @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[592]) ).
thf(1273,plain,
( ( ! [V_R: $i,T_b: $i,T_a: $i] :
( ( c_Relation_OImage @ V_R @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b @ T_a )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[593]) ).
thf(1274,plain,
( ( ! [V_r: $i,V_a: $i,T_a: $i,V_b: $i,V_A: $i] :
( ( c_lessequals @ ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) @ ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[594]) ).
thf(1275,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ ( c_HOL_Ominus__class_Ominus @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= V_B )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[595]) ).
thf(1276,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Wellfounded_Oacyclic @ V_r @ T_a )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[596]) ).
thf(1277,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)],[597]) ).
thf(1278,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)],[598]) ).
thf(1279,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[599]) ).
thf(1280,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( c_lessequals @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[600]) ).
thf(1281,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( c_lessequals @ V_y @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[601]) ).
thf(1282,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ V_z @ T_a )
| ~ ( c_lessequals @ V_y @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_z @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[602]) ).
thf(1283,plain,
( ( ! [T_a: $i,V_y: $i,V_z: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) @ V_x @ T_a )
| ~ ( c_lessequals @ V_z @ V_x @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[603]) ).
thf(1284,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ V_y @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[604]) ).
thf(1285,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[605]) ).
thf(1286,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) @ V_x @ T_a )
| ~ ( c_lessequals @ V_b @ V_x @ T_a )
| ~ ( c_lessequals @ V_a @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[606]) ).
thf(1287,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[607]) ).
thf(1288,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] : ( c_lessequals @ V_A @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(unfold_def,[status(thm)],[608]) ).
thf(1289,plain,
( ( ! [V_B: $i,V_A: $i,T_a: $i] : ( c_lessequals @ V_B @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(unfold_def,[status(thm)],[609]) ).
thf(1290,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[610]) ).
thf(1291,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 )
= V_y )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[611]) ).
thf(1292,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 )
!= V_x )
| ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[612]) ).
thf(1293,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 )
= V_x )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[613]) ).
thf(1294,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= V_B )
| ~ ( c_lessequals @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[614]) ).
thf(1295,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= V_A )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[615]) ).
thf(1296,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)],[616]) ).
thf(1297,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)],[617]) ).
thf(1298,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)],[618]) ).
thf(1299,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)],[619]) ).
thf(1300,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[620]) ).
thf(1301,plain,
( ( ! [V_A: $i,V_B: $i,V_C: $i,T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[621]) ).
thf(1302,plain,
( ( ! [V_f: $i,V_A: $i,T_b: $i,T_a: $i,V_B: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a ) @ ( c_Set_Oimage @ V_f @ V_B @ T_b @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Set_Oimage @ V_f @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(unfold_def,[status(thm)],[622]) ).
thf(1303,plain,
( ( ! [V_f: $i,T_b: $i,T_a: $i] :
( ( c_Set_Oimage @ V_f @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b @ T_a )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[623]) ).
thf(1304,plain,
( ( ! [T_a: $i,V_x: $i,V_x_H: $i,V_y_H: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_x @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x_H @ V_y_H @ T_a ) )
| ( V_x_H = V_y_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[624]) ).
thf(1305,plain,
( ( ! [T_a: $i,V_xa: $i,V_y: $i,V_x: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_xa @ V_y @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x @ V_x @ T_a ) )
| ( V_xa = V_y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[625]) ).
thf(1306,plain,
( ( ! [V_r: $i,V_C: $i,T_a: $i,T_b: $i,V_B: $i,V_A: $i] :
( ( c_lessequals @ ( c_Relation_OImage @ V_r @ V_C @ T_a @ T_b ) @ V_B @ ( tc_fun @ T_b @ tc_bool ) )
| ~ ( c_lessequals @ V_r @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_B @ ( tc_fun @ T_b @ tc_bool ) @ T_a ) @ T_a @ T_b ) @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[626]) ).
thf(1307,plain,
( ( ! [V_xa: $i,V_x: $i,T_a: $i] :
( ( c_Set_Oinsert @ V_xa @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a )
= ( c_Set_Oinsert @ V_x @ ( c_Set_Oinsert @ V_xa @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[627]) ).
thf(1308,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[628]) ).
thf(1309,plain,
( ( ! [V_P: $i,T_a: $i,T_b: $i,V_Q: $i] :
( ( hAPP @ ( c_COMBK @ V_P @ T_a @ T_b ) @ V_Q )
= V_P ) )
= $true ),
inference(unfold_def,[status(thm)],[629]) ).
thf(1310,plain,
( ( ! [T_a: $i,T_b: $i,V_p: $i] :
( ( c_Pair @ ( hAPP @ ( c_fst @ T_a @ T_b ) @ V_p ) @ ( hAPP @ ( c_snd @ T_a @ T_b ) @ V_p ) @ T_a @ T_b )
= V_p ) )
= $true ),
inference(unfold_def,[status(thm)],[630]) ).
thf(1311,plain,
( ( ! [V_t: $i,T_a: $i,T_b: $i] :
( V_t
= ( c_Pair @ ( hAPP @ ( c_fst @ T_a @ T_b ) @ V_t ) @ ( hAPP @ ( c_snd @ T_a @ T_b ) @ V_t ) @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[631]) ).
thf(1312,plain,
( ( ! [V_x: $i,V_y: $i,V_A: $i,T_a: $i] :
( ( c_Set_Oinsert @ V_x @ ( c_Set_Oinsert @ V_y @ V_A @ T_a ) @ T_a )
= ( c_Set_Oinsert @ V_y @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[632]) ).
thf(1313,plain,
( ( ! [T_a: $i,T_b: $i] :
( ( c_Relation_ODomain @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) @ T_a @ T_b )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[633]) ).
thf(1314,plain,
( ( ! [V_P: $i,V_Rb: $i,V_R: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_Rb ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Osko__Recdef__Xtfl__wf__induct__1__1 @ V_P @ V_R @ T_a ) ) )
| ~ ( c_Wellfounded_Owf @ V_R @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[634]) ).
thf(1315,plain,
( ( ! [V_R: $i,V_A: $i,V_B: $i,T_b: $i,T_a: $i] :
( ( c_Relation_OImage @ V_R @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_OImage @ V_R @ V_A @ T_b @ T_a ) @ ( c_Relation_OImage @ V_R @ V_B @ T_b @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[635]) ).
thf(1316,plain,
( ( ! [V_R: $i,V_S: $i,T_b: $i,T_a: $i,V_A: $i] :
( ( c_Relation_OImage @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_R @ V_S @ ( tc_fun @ ( tc_prod @ T_b @ T_a ) @ tc_bool ) ) @ V_A @ T_b @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_OImage @ V_R @ V_A @ T_b @ T_a ) @ ( c_Relation_OImage @ V_S @ V_A @ T_b @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[636]) ).
thf(1317,plain,
( ( ! [V_r_H: $i,V_s_H: $i,T_a: $i,T_b: $i,T_c: $i,V_r: $i,V_s: $i] :
( ( c_lessequals @ ( c_Relation_Orel__comp @ V_r_H @ V_s_H @ T_a @ T_b @ T_c ) @ ( c_Relation_Orel__comp @ V_r @ V_s @ T_a @ T_b @ T_c ) @ ( tc_fun @ ( tc_prod @ T_a @ T_c ) @ tc_bool ) )
| ~ ( c_lessequals @ V_s_H @ V_s @ ( tc_fun @ ( tc_prod @ T_b @ T_c ) @ tc_bool ) )
| ~ ( c_lessequals @ V_r_H @ V_r @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[637]) ).
thf(1318,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)],[638]) ).
thf(1319,plain,
( ( ! [V_A: $i,T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
= V_A ) )
= $true ),
inference(unfold_def,[status(thm)],[639]) ).
thf(1320,plain,
( ( ! [V_r: $i,V_A: $i,T_a: $i] :
( ( c_lessequals @ V_r @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_A @ ( tc_fun @ T_a @ tc_bool ) @ T_a ) @ T_a @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_Relation_Orefl__on @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[640]) ).
thf(1321,plain,
( ( ! [V_A: $i,T_a: $i] : ( c_lessequals @ ( c_Relation_OId__on @ V_A @ T_a ) @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_A @ ( tc_fun @ T_a @ tc_bool ) @ T_a ) @ T_a @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) )
= $true ),
inference(unfold_def,[status(thm)],[641]) ).
thf(1322,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)],[642]) ).
thf(1323,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)],[643]) ).
thf(1324,plain,
( ( ! [V_A: $i,V_B: $i,V_C: $i,T_a: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[644]) ).
thf(1325,plain,
( ( ! [V_B: $i,V_C: $i,T_a: $i,V_A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[645]) ).
thf(1326,plain,
( ( ! [V_A: $i,T_a: $i,T_b: $i,V_B: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ ( c_Relation_ODomain @ V_A @ T_a @ T_b ) @ ( c_Relation_ODomain @ V_B @ T_a @ T_b ) @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Relation_ODomain @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) @ T_a @ T_b ) @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(unfold_def,[status(thm)],[646]) ).
thf(1327,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= V_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[647]) ).
thf(1328,plain,
( ( ! [V_b: $i,V_a: $i,T_a: $i] :
( ( V_b = V_a )
| ~ ( c_in @ V_b @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[648]) ).
thf(1329,plain,
( ( ! [V_I: $i,V_J: $i,T_a: $i,V_C: $i,T_b: $i] :
( ( c_Product__Type_OSigma @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_I @ V_J @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ T_a @ T_b )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Product__Type_OSigma @ V_I @ V_C @ T_a @ T_b ) @ ( c_Product__Type_OSigma @ V_J @ V_C @ T_a @ T_b ) @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[649]) ).
thf(1330,plain,
( ( ! [V_r: $i,T_a: $i,V_s: $i] :
( ( c_lessequals @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Relation_Orel__comp @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ V_r @ T_a @ T_a @ T_a ) @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_lessequals @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[650]) ).
thf(1331,plain,
( ( ! [V_c: $i,T_b: $i,T_a: $i,V_A: $i,V_x: $i] :
( ( ( c_Set_Oimage @ ( c_COMBK @ V_c @ T_b @ T_a ) @ V_A @ T_a @ T_b )
= ( c_Set_Oinsert @ V_c @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b ) )
| ~ ( c_in @ V_x @ V_A @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[651]) ).
thf(1332,plain,
( ( ! [V_A: $i,V_x: $i,T_a: $i,V_B: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_in @ V_x @ V_A @ T_a )
| ~ ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[652]) ).
thf(1333,plain,
( ( ! [V_A: $i,V_x: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_in @ V_x @ V_A @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[653]) ).
thf(1334,plain,
( ( ! [V_A: $i,V_x: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_in @ V_x @ V_A @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[654]) ).
thf(1335,plain,
( ( ! [V_A: $i,V_B: $i,T_b: $i,V_C: $i,T_a: $i,V_x: $i] :
( ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_b @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_C @ ( tc_fun @ T_a @ tc_bool ) @ T_b ) @ T_b @ T_a ) @ ( c_Product__Type_OSigma @ V_B @ ( c_COMBK @ V_C @ ( tc_fun @ T_a @ tc_bool ) @ T_b ) @ T_b @ T_a ) @ ( tc_fun @ ( tc_prod @ T_b @ T_a ) @ tc_bool ) )
| ~ ( c_in @ V_x @ V_C @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[655]) ).
thf(1336,plain,
( ( ! [V_A: $i,V_C: $i,T_a: $i,T_b: $i,V_B: $i,V_x: $i] :
( ( c_lessequals @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_C @ ( tc_fun @ T_a @ tc_bool ) @ T_b ) @ T_b @ T_a ) @ ( c_Product__Type_OSigma @ V_B @ ( c_COMBK @ V_C @ ( tc_fun @ T_a @ tc_bool ) @ T_b ) @ T_b @ T_a ) @ ( tc_fun @ ( tc_prod @ T_b @ T_a ) @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_b @ tc_bool ) )
| ~ ( c_in @ V_x @ V_C @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[656]) ).
thf(1337,plain,
( ( ! [V_x: $i,V_A: $i,T_a: $i,V_B: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( c_in @ V_x @ V_B @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[657]) ).
thf(1338,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_x: $i] :
( ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[658]) ).
thf(1339,plain,
( ( ! [V_A: $i,V_b: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_b @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[659]) ).
thf(1340,plain,
( ( ! [V_A: $i,T_b: $i,T_a: $i,V_B: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ ( c_Relation_ORange @ V_A @ T_b @ T_a ) @ ( c_Relation_ORange @ V_B @ T_b @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Relation_ORange @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ ( tc_prod @ T_b @ T_a ) @ tc_bool ) ) @ T_b @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(unfold_def,[status(thm)],[660]) ).
thf(1341,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__Xwf__induct__1__1 @ V_P @ V_r @ T_a ) ) )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[661]) ).
thf(1342,plain,
( ( ! [T_a: $i,T_b: $i,V_p: $i,V_q: $i] :
( ( ( hAPP @ ( c_snd @ T_a @ T_b ) @ V_p )
!= ( hAPP @ ( c_snd @ T_a @ T_b ) @ V_q ) )
| ( ( hAPP @ ( c_fst @ T_a @ T_b ) @ V_p )
!= ( hAPP @ ( c_fst @ T_a @ T_b ) @ V_q ) )
| ( V_p = V_q ) ) )
= $true ),
inference(unfold_def,[status(thm)],[662]) ).
thf(1343,plain,
( ( ! [T_a: $i,T_b: $i,V_s: $i,V_t: $i] :
( ( ( hAPP @ ( c_snd @ T_a @ T_b ) @ V_s )
!= ( hAPP @ ( c_snd @ T_a @ T_b ) @ V_t ) )
| ( ( hAPP @ ( c_fst @ T_a @ T_b ) @ V_s )
!= ( hAPP @ ( c_fst @ T_a @ T_b ) @ V_t ) )
| ( V_s = V_t ) ) )
= $true ),
inference(unfold_def,[status(thm)],[663]) ).
thf(1344,plain,
( ( ! [V_R: $i,T_a: $i,V_S: $i] : ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_S @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_R @ V_S @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) )
= $true ),
inference(unfold_def,[status(thm)],[664]) ).
thf(1345,plain,
( ( ! [T_a: $i,V_f: $i,V_A: $i,T_b: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a ) )
| ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[665]) ).
thf(1346,plain,
( ( ! [V_a: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Set_Oinsert @ V_a @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[666]) ).
thf(1347,plain,
( ( ! [V_A: $i,V_a: $i,V_B: $i,T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Set_Oinsert @ V_a @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[667]) ).
thf(1348,plain,
( ( ! [T_a: $i,T_c: $i,V_R: $i,T_b: $i] :
( ( c_Relation_Orel__comp @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_c ) @ tc_bool ) ) @ V_R @ T_a @ T_c @ T_b )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[668]) ).
thf(1349,plain,
( ( ! [V_R: $i,T_c: $i,T_b: $i,T_a: $i] :
( ( c_Relation_Orel__comp @ V_R @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_c @ T_b ) @ tc_bool ) ) @ T_a @ T_c @ T_b )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[669]) ).
thf(1350,plain,
( ( ! [T_a: $i,V_A: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(unfold_def,[status(thm)],[670]) ).
thf(1351,plain,
( ( ! [T_a: $i,V_B: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ V_B @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) )
= $true ),
inference(unfold_def,[status(thm)],[671]) ).
thf(1352,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Obot @ T_a )
| ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ T_a ) @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[672]) ).
thf(1353,plain,
( ( ! [V_A: $i,V_a: $i,V_B: $i,T_a: $i] :
( ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[673]) ).
thf(1354,plain,
( ( ! [V_A: $i,V_a: $i,V_B: $i,T_a: $i] :
( ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[674]) ).
thf(1355,plain,
( ( ! [V_a: $i,V_A: $i,T_a: $i] :
( ( c_Set_Oinsert @ V_a @ V_A @ T_a )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[675]) ).
thf(1356,plain,
( ( ! [V_a: $i,V_A: $i,T_a: $i,V_B: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ V_a @ V_A @ T_a ) @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Set_Oinsert @ V_a @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[676]) ).
thf(1357,plain,
( ( ~ ( c_in @ ( c_Pair @ v_c____ @ v_d____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ v_P____ ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ),
inference(unfold_def,[status(thm)],[679]) ).
thf(1358,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[680]) ).
thf(1359,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)],[681]) ).
thf(1360,plain,
( ( ! [V_S: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_S @ V_x ) )
| ! [T_a: $i] :
~ ( c_in @ V_x @ V_S @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[713]) ).
thf(1361,plain,
( ( ! [V_x: $i,V_S: $i] :
( ! [T_a: $i] : ( c_in @ V_x @ V_S @ T_a )
| ~ ( hBOOL @ ( hAPP @ V_S @ V_x ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[714]) ).
thf(1362,plain,
( ( ! [V_a: $i,V_b: $i,T_a: $i,T_b: $i,V_a_H: $i] :
( ! [V_b_H: $i] :
( ( c_Pair @ V_a @ V_b @ T_a @ T_b )
!= ( c_Pair @ V_a_H @ V_b_H @ T_a @ T_b ) )
| ( V_a = V_a_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[715]) ).
thf(1363,plain,
( ( ! [V_a: $i,V_b: $i,T_a: $i,T_b: $i,V_a_H: $i,V_b_H: $i] :
( ( ( c_Pair @ V_a @ V_b @ T_a @ T_b )
!= ( c_Pair @ V_a_H @ V_b_H @ T_a @ T_b ) )
| ( V_b = V_b_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[716]) ).
thf(1364,plain,
( ( ! [V_a: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_a @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ! [V_A: $i] :
( ~ ( c_in @ V_a @ V_A @ T_a )
| ~ ( c_Relation_Orefl__on @ V_A @ V_r @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[717]) ).
thf(1365,plain,
( ( ! [V_x: $i,V_A: $i,T_a: $i] :
( ( c_in @ V_x @ V_A @ T_a )
| ! [V_y: $i,V_r: $i] :
( ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Relation_Orefl__on @ V_A @ V_r @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[718]) ).
thf(1366,plain,
( ( ! [V_y: $i,V_A: $i,T_a: $i] :
( ( c_in @ V_y @ V_A @ T_a )
| ! [V_x: $i,V_r: $i] :
( ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Relation_Orefl__on @ V_A @ V_r @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[719]) ).
thf(1367,plain,
( ( ! [V_x: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ! [V_A: $i] :
( ~ ( c_in @ V_x @ V_A @ T_a )
| ~ ( c_Relation_Orefl__on @ V_A @ V_r @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[720]) ).
thf(1368,plain,
( ( ! [V_xa: $i,V_x: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_xa @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ( c_in @ ( c_Pair @ V_x @ V_xa @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ( V_x = V_xa )
| ! [V_A: $i] :
( ~ ( c_in @ V_xa @ V_A @ T_a )
| ~ ( c_in @ V_x @ V_A @ T_a )
| ~ ( c_Relation_Ototal__on @ V_A @ V_r @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[721]) ).
thf(1369,plain,
( ( ! [V_a: $i,V_A: $i,T_a: $i,V_b: $i] :
( ( c_in @ V_a @ V_A @ T_a )
| ! [T_b: $i,V_B: $i] :
~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ ( c_Product__Type_OSigma @ V_A @ V_B @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[722]) ).
thf(1370,plain,
( ( ! [V_b: $i,V_B: $i,V_a: $i,T_b: $i] :
( ( c_in @ V_b @ ( hAPP @ V_B @ V_a ) @ T_b )
| ! [T_a: $i,V_A: $i] :
~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ ( c_Product__Type_OSigma @ V_A @ V_B @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[723]) ).
thf(1371,plain,
( ( ! [V_a: $i,V_r: $i,T_a: $i,T_b: $i] :
( ( c_in @ V_a @ ( c_Relation_ODomain @ V_r @ T_a @ T_b ) @ T_a )
| ! [V_b: $i] :
~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ V_r @ ( tc_prod @ T_a @ T_b ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[724]) ).
thf(1372,plain,
( ( ! [V_a: $i,V_r: $i,T_a: $i,T_b: $i] :
( ( c_in @ V_a @ ( c_Relation_ODomain @ V_r @ T_a @ T_b ) @ T_a )
| ! [V_x: $i] :
~ ( c_in @ ( c_Pair @ V_a @ V_x @ T_a @ T_b ) @ V_r @ ( tc_prod @ T_a @ T_b ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[725]) ).
thf(1373,plain,
( ( ! [V_b: $i,V_r: $i,T_a: $i,T_b: $i] :
( ( c_in @ V_b @ ( c_Relation_ORange @ V_r @ T_a @ T_b ) @ T_b )
| ! [V_a: $i] :
~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ V_r @ ( tc_prod @ T_a @ T_b ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[726]) ).
thf(1374,plain,
( ( ! [V_a: $i,V_r: $i,T_b: $i,T_a: $i] :
( ( c_in @ V_a @ ( c_Relation_ORange @ V_r @ T_b @ T_a ) @ T_a )
| ! [V_x: $i] :
~ ( c_in @ ( c_Pair @ V_x @ V_a @ T_b @ T_a ) @ V_r @ ( tc_prod @ T_b @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[727]) ).
thf(1375,plain,
( ( ! [V_x: $i,V_A: $i,T_a: $i] :
( ( c_in @ V_x @ V_A @ T_a )
| ! [V_y: $i,V_r: $i] :
( ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[728]) ).
thf(1376,plain,
( ( ! [V_y: $i,V_A: $i,T_a: $i] :
( ( c_in @ V_y @ V_A @ T_a )
| ! [V_x: $i,V_r: $i] :
( ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[729]) ).
thf(1377,plain,
( ( ! [V_x: $i,V_A: $i,T_a: $i] :
( ( c_in @ V_x @ V_A @ T_a )
| ! [V_y: $i] :
~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Relation_OId__on @ V_A @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[731]) ).
thf(1378,plain,
( ( ! [V_b: $i,V_r: $i,V_A: $i,T_b: $i,T_a: $i] :
( ( c_in @ V_b @ ( c_Relation_OImage @ V_r @ V_A @ T_b @ T_a ) @ T_a )
| ! [V_x: $i] :
( ~ ( c_in @ ( c_Pair @ V_x @ V_b @ T_b @ T_a ) @ V_r @ ( tc_prod @ T_b @ T_a ) )
| ~ ( c_in @ V_x @ V_A @ T_b ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[732]) ).
thf(1379,plain,
( ( ! [V_b: $i,V_r: $i,V_A: $i,T_a: $i,T_b: $i] :
( ( c_in @ V_b @ ( c_Relation_OImage @ V_r @ V_A @ T_a @ T_b ) @ T_b )
| ! [V_a: $i] :
( ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ V_r @ ( tc_prod @ T_a @ T_b ) )
| ~ ( c_in @ V_a @ V_A @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[733]) ).
thf(1380,plain,
( ( ! [V_y: $i,V_r: $i,T_a: $i] :
( ( c_in @ V_y @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a )
| ! [V_a: $i] :
( ~ ( c_in @ ( c_Pair @ V_y @ V_a @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_a @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[734]) ).
thf(1381,plain,
( ( ! [V_a: $i,V_r: $i,T_a: $i] :
( ( c_in @ V_a @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a )
| ! [V_b: $i] :
( ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_b @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[735]) ).
thf(1382,plain,
( ( ! [V_a: $i,V_b: $i] :
( ( V_a = V_b )
| ( c_in @ ( c_Pair @ V_a @ V_b @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1 @ V_a @ V_b ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[738]) ).
thf(1383,plain,
( ( ! [V_x: $i,V_y: $i,V_L: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ V_L @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ! [V_z: $i] :
( ( V_x = V_z )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omkbot @ V_L ) @ V_z ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[739]) ).
thf(1384,plain,
( ( ! [V_xa: $i,V_x: $i] :
( ( V_xa = V_x )
| ( V_xa = V_x )
| ! [V_L: $i] : ( c_in @ ( c_Pair @ V_xa @ V_x @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omktop @ V_L ) @ V_x ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[740]) ).
thf(1385,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( V_x = V_y )
| ( V_y = V_x )
| ! [V_L: $i] : ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omkbot @ V_L ) @ V_x ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[745]) ).
thf(1386,plain,
( ( ! [V_x: $i,V_y: $i,V_L: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ V_L @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ! [V_z: $i] :
( ( V_y = V_z )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omktop @ V_L ) @ V_z ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[746]) ).
thf(1387,plain,
( ( ! [V_a: $i,V_c: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ! [V_b: $i] :
( ~ ( c_in @ ( c_Pair @ V_b @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[753]) ).
thf(1388,plain,
( ( ! [V_a: $i,V_c: $i,T_a: $i,V_R: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ! [V_b: $i] :
( ~ ( c_in @ ( c_Pair @ V_b @ V_c @ T_a @ T_a ) @ V_R @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_R @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[754]) ).
thf(1389,plain,
( ( ! [V_a: $i,V_c: $i,T_a: $i,T_c: $i,V_r: $i,V_s: $i,T_b: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_c ) @ ( c_Relation_Orel__comp @ V_r @ V_s @ T_a @ T_b @ T_c ) @ ( tc_prod @ T_a @ T_c ) )
| ! [V_b: $i] :
( ~ ( c_in @ ( c_Pair @ V_b @ V_c @ T_b @ T_c ) @ V_s @ ( tc_prod @ T_b @ T_c ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ V_r @ ( tc_prod @ T_a @ T_b ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[755]) ).
thf(1390,plain,
( ( ! [V_f: $i,V_x: $i,V_y: $i,T_b: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ ( hAPP @ V_f @ V_x ) @ ( hAPP @ V_f @ V_y ) @ T_b @ T_b ) @ V_r @ ( tc_prod @ T_b @ T_b ) )
| ! [T_a: $i] :
~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Relation_Oinv__image @ V_r @ V_f @ T_b @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[758]) ).
thf(1391,plain,
( ( ! [V_a: $i,V_b: $i] :
( ( V_a = V_b )
| ! [T_a: $i] :
~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Relation_OId @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[762]) ).
thf(1392,plain,
( ( ! [V_f: $i,V_r: $i,V_x: $i,T_a: $i,T_b: $i,V_g: $i] :
( ( ( c_Recdef_Ocut @ V_f @ V_r @ V_x @ T_a @ T_b )
!= ( c_Recdef_Ocut @ V_g @ V_r @ V_x @ T_a @ T_b ) )
| ! [V_y: $i] :
( ( ( hAPP @ V_f @ V_y )
= ( hAPP @ V_g @ V_y ) )
| ~ ( c_in @ ( c_Pair @ V_y @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[763]) ).
thf(1393,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( V_x = V_y )
| ! [T_a: $i,V_A: $i] :
~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Relation_OId__on @ V_A @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[764]) ).
thf(1394,plain,
( ( ! [V_f: $i,V_y: $i,V_z: $i,T_a: $i] :
( ( ( hAPP @ V_f @ V_y )
= ( hAPP @ V_f @ V_z ) )
| ! [V_r: $i] :
( ~ ( c_in @ ( c_Pair @ V_y @ V_z @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ! [T_b: $i] :
~ ( c_Equiv__Relations_Ocongruent @ V_r @ V_f @ T_a @ T_b ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[765]) ).
thf(1395,plain,
( ( ! [V_a: $i,V_b: $i] :
( ( V_a = V_b )
| ! [T_a: $i,V_r: $i] :
( ~ ( c_in @ ( c_Pair @ V_b @ V_a @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Relation_Oantisym @ V_r @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[766]) ).
thf(1396,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( V_x = V_y )
| ! [T_a: $i,V_r: $i] :
( ~ ( c_in @ ( c_Pair @ V_y @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Relation_Oantisym @ V_r @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[767]) ).
thf(1397,plain,
( ( ! [V_a: $i,V_c: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ! [V_b: $i] :
( ~ ( c_in @ ( c_Pair @ V_b @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[771]) ).
thf(1398,plain,
( ( ! [V_a: $i,V_c: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ! [V_b: $i] :
( ~ ( c_in @ ( c_Pair @ V_b @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[773]) ).
thf(1399,plain,
( ( ! [V_a: $i,V_c: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ! [V_b: $i] :
( ~ ( c_in @ ( c_Pair @ V_b @ V_c @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[774]) ).
thf(1400,plain,
( ( ! [V_a: $i,V_c: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ! [V_b: $i] :
( ~ ( c_in @ ( c_Pair @ V_b @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[775]) ).
thf(1401,plain,
( ( ! [V_a: $i,V_c: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ! [V_b: $i] :
( ~ ( c_in @ ( c_Pair @ V_b @ V_c @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[776]) ).
thf(1402,plain,
( ( ! [V_a: $i,V_c: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ! [V_b: $i] :
( ~ ( c_in @ ( c_Pair @ V_b @ V_c @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Relation_Otrans @ V_r @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[781]) ).
thf(1403,plain,
( ( ! [V_x: $i,V_z: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_z @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ! [V_y: $i] :
( ~ ( c_in @ ( c_Pair @ V_y @ V_z @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Relation_Otrans @ V_r @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[782]) ).
thf(1404,plain,
( ( ! [V_y: $i,V_z: $i,V_x: $i,T_a: $i] :
( ( V_y = V_z )
| ! [T_b: $i,V_r: $i] :
( ~ ( c_in @ ( c_Pair @ V_x @ V_z @ T_a @ T_b ) @ V_r @ ( tc_prod @ T_a @ T_b ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_b ) @ V_r @ ( tc_prod @ T_a @ T_b ) )
| ~ ( c_Relation_Osingle__valued @ V_r @ T_a @ T_b ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[787]) ).
thf(1405,plain,
( ( ! [V_f: $i,V_y1: $i,V_y2: $i,V_z1: $i,V_z2: $i,T_b: $i,V_r2: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_f @ V_y1 ) @ V_y2 )
= ( hAPP @ ( hAPP @ V_f @ V_z1 ) @ V_z2 ) )
| ~ ( c_in @ ( c_Pair @ V_y2 @ V_z2 @ T_b @ T_b ) @ V_r2 @ ( tc_prod @ T_b @ T_b ) )
| ! [V_r1: $i] :
( ~ ( c_in @ ( c_Pair @ V_y1 @ V_z1 @ T_a @ T_a ) @ V_r1 @ ( tc_prod @ T_a @ T_a ) )
| ! [T_c: $i] :
~ ( c_Equiv__Relations_Ocongruent2 @ V_r1 @ V_r2 @ V_f @ T_a @ T_b @ T_c ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[788]) ).
thf(1406,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( V_x = V_y )
| ! [T_a: $i,V_R: $i] :
( ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ( c_in @ V_x @ ( c_Relation_ODomain @ V_R @ T_a @ T_a ) @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[791]) ).
thf(1407,plain,
( ( ! [V_y: $i,V_Q: $i,T_a: $i] :
( ~ ( c_in @ V_y @ V_Q @ T_a )
| ! [V_r: $i] :
( ~ ( c_in @ ( c_Pair @ V_y @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 @ V_Q @ V_r @ T_a ) @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ! [V_xa: $i] :
~ ( c_in @ V_xa @ V_Q @ T_a )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[794]) ).
thf(1408,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] :
( ~ ( c_in @ ( c_Pair @ V_y @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ V_P @ V_r @ T_a ) @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_a @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[795]) ).
thf(1409,plain,
( ( ! [V_P: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ! [V_ya: $i,V_r: $i] :
( ( c_in @ V_ya @ ( c_Wellfounded_Oacc @ V_r @ t_a ) @ t_a )
| ~ ( c_in @ ( c_Pair @ V_ya @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ V_P @ V_r ) @ t_a @ t_a ) @ V_r @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ V_x @ ( c_Wellfounded_Oacc @ V_r @ t_a ) @ t_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[796]) ).
thf(1410,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] :
( ~ ( c_in @ ( c_Pair @ V_y @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ V_P @ V_r ) @ t_a @ t_a ) @ V_r @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ V_x @ ( c_Wellfounded_Oacc @ V_r @ t_a ) @ t_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[799]) ).
thf(1411,plain,
( ( ! [V_P: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ! [V_ya: $i,V_r: $i] :
( ( c_in @ V_ya @ ( c_Wellfounded_Oacc @ V_r @ t_a ) @ t_a )
| ~ ( c_in @ ( c_Pair @ V_ya @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ V_P @ V_r ) @ t_a @ t_a ) @ V_r @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ V_x @ ( c_Wellfounded_Oacc @ V_r @ t_a ) @ t_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[801]) ).
thf(1412,plain,
( ( ! [V_b: $i,V_r: $i,T_a: $i] :
( ( c_in @ V_b @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a )
| ! [V_a: $i] :
( ~ ( c_in @ ( c_Pair @ V_b @ V_a @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_a @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[802]) ).
thf(1413,plain,
( ( ! [V_b: $i,V_r: $i,T_a: $i] :
( ( c_in @ V_b @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a )
| ! [V_a: $i] :
( ~ ( c_in @ V_a @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a )
| ~ ( c_in @ ( c_Pair @ V_b @ V_a @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[803]) ).
thf(1414,plain,
( ( ! [V_y: $i,V_Q: $i,T_a: $i] :
( ~ ( c_in @ V_y @ V_Q @ T_a )
| ! [V_R: $i] :
( ~ ( c_in @ ( c_Pair @ V_y @ ( c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 @ V_Q @ V_R @ T_a ) @ T_a @ T_a ) @ V_R @ ( tc_prod @ T_a @ T_a ) )
| ! [V_x: $i] :
~ ( c_in @ V_x @ V_Q @ T_a )
| ~ ( c_Wellfounded_Owf @ V_R @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[806]) ).
thf(1415,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] :
( ~ ( c_in @ ( c_Pair @ V_y @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ V_P @ V_r ) @ t_a @ t_a ) @ V_r @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ V_x @ ( c_Wellfounded_Oacc @ V_r @ t_a ) @ t_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[807]) ).
thf(1416,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] :
( ~ ( c_in @ ( c_Pair @ V_y @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ V_P @ V_r @ T_a ) @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_a @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[808]) ).
thf(1417,plain,
( ( ! [V_P: $i,V_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ! [V_r: $i,T_a: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ V_P @ V_r @ T_a ) @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a )
| ~ ( c_in @ V_a @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[815]) ).
thf(1418,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Relation_Otrans @ V_r @ T_a )
| ! [V_A: $i] :
~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[816]) ).
thf(1419,plain,
( ( ! [V_r2: $i,V_f: $i,V_a: $i,T_b: $i,T_c: $i,V_A: $i] :
( ( c_Equiv__Relations_Ocongruent @ V_r2 @ ( hAPP @ V_f @ V_a ) @ T_b @ T_c )
| ! [T_a: $i] :
( ~ ( c_in @ V_a @ V_A @ T_a )
| ! [V_r1: $i] :
( ~ ( c_Equiv__Relations_Ocongruent2 @ V_r1 @ V_r2 @ V_f @ T_a @ T_b @ T_c )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r1 @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[823]) ).
thf(1420,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Relation_Osym @ V_r @ T_a )
| ! [V_A: $i] :
~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[825]) ).
thf(1421,plain,
( ( ! [V_Q: $i,V_R: $i,T_a: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 @ V_Q @ V_R @ T_a ) @ V_Q @ T_a )
| ! [V_x: $i] :
~ ( c_in @ V_x @ V_Q @ T_a )
| ~ ( c_Wellfounded_Owf @ V_R @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[826]) ).
thf(1422,plain,
( ( ! [V_P: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ! [V_r: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ V_P @ V_r ) ) )
| ~ ( c_in @ V_x @ ( c_Wellfounded_Oacc @ V_r @ t_a ) @ t_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[829]) ).
thf(1423,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ V_r @ T_a @ T_a @ T_a )
= V_r )
| ! [V_A: $i] :
~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[833]) ).
thf(1424,plain,
( ( ! [V_Q: $i,V_r: $i,T_a: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 @ V_Q @ V_r @ T_a ) @ V_Q @ T_a )
| ! [V_xa: $i] :
~ ( c_in @ V_xa @ V_Q @ T_a )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[838]) ).
thf(1425,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ V_r @ T_a @ T_a @ T_a )
!= V_r )
| ( c_Equiv__Relations_Oequiv @ ( c_Relation_ODomain @ V_r @ T_a @ T_a ) @ V_r @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[841]) ).
thf(1426,plain,
( ( ! [V_r: $i,V_f: $i,T_a: $i] :
( ! [T_b: $i] : ( c_Relation_Otrans @ ( c_Relation_Oinv__image @ V_r @ V_f @ T_a @ T_b ) @ T_b )
| ~ ( c_Relation_Otrans @ V_r @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[843]) ).
thf(1427,plain,
( ( ! [V_r: $i,V_f: $i,T_a: $i] :
( ! [T_b: $i] : ( c_Relation_Osym @ ( c_Relation_Oinv__image @ V_r @ V_f @ T_a @ T_b ) @ T_b )
| ~ ( c_Relation_Osym @ V_r @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[853]) ).
thf(1428,plain,
( ( ! [V_r: $i,V_f: $i,T_a: $i] :
( ! [T_b: $i] : ( c_Wellfounded_Owf @ ( c_Relation_Oinv__image @ V_r @ V_f @ T_a @ T_b ) @ T_b )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[855]) ).
thf(1429,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( ( c_Relation_Oconverse @ V_r @ T_a @ T_a )
!= V_r )
| ( c_Relation_Osym @ V_r @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[861]) ).
thf(1430,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__Xacc__induct__rule__1__1 @ V_P @ V_r @ T_a ) ) )
| ~ ( c_in @ V_a @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[871]) ).
thf(1431,plain,
( ( ! [V_P: $i,V_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ! [V_r: $i,T_a: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ V_P @ V_r @ T_a ) @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a )
| ~ ( c_in @ V_a @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[883]) ).
thf(1432,plain,
( ( ! [V_P: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ! [V_r: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ V_P @ V_r ) ) )
| ~ ( c_in @ V_x @ ( c_Wellfounded_Oacc @ V_r @ t_a ) @ t_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[884]) ).
thf(1433,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__Xacc__induct__1__1 @ V_P @ V_r @ T_a ) ) )
| ~ ( c_in @ V_a @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[886]) ).
thf(1434,plain,
( ( ! [V_x: $i,V_A: $i,T_aa: $i] :
( ~ ( c_in @ V_x @ V_A @ T_aa )
| ! [V_f: $i,T_a: $i] : ( c_in @ ( hAPP @ V_f @ V_x ) @ ( c_Set_Oimage @ V_f @ V_A @ T_aa @ T_a ) @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[891]) ).
thf(1435,plain,
( ( ! [V_x: $i,V_A: $i,T_b: $i] :
( ~ ( c_in @ V_x @ V_A @ T_b )
| ! [V_f: $i,T_a: $i] : ( c_in @ ( hAPP @ V_f @ V_x ) @ ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a ) @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[892]) ).
thf(1436,plain,
( ( ! [V_f: $i,V_x: $i,V_A: $i,T_b: $i] :
( ! [T_a: $i] : ( c_in @ ( hAPP @ V_f @ V_x ) @ ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a ) @ T_a )
| ~ ( c_in @ V_x @ V_A @ T_b ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[893]) ).
thf(1437,plain,
( ( ! [V_f: $i,V_x: $i,V_A: $i,T_a: $i] :
( ! [T_b: $i] : ( c_in @ ( hAPP @ V_f @ V_x ) @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) @ T_b )
| ~ ( c_in @ V_x @ V_A @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[894]) ).
thf(1438,plain,
( ( ! [V_R: $i,V_a: $i,V_b: $i,V_c: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ V_R @ V_a ) @ V_b ) @ V_c ) )
| ! [T_b: $i,T_c: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_split @ V_R @ T_a @ T_b @ ( tc_fun @ T_c @ tc_bool ) ) @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) ) @ V_c ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[895]) ).
thf(1439,plain,
( ( ! [V_x: $i,V_z: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_z @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ! [V_y: $i] :
( ~ ( c_in @ ( c_Pair @ V_y @ V_z @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[900]) ).
thf(1440,plain,
( ( ! [V_a: $i,V_c: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ! [V_b: $i] :
( ~ ( c_in @ ( c_Pair @ V_b @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[901]) ).
thf(1441,plain,
( ( ! [V_z: $i,V_y: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_z @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ( c_in @ ( c_Pair @ V_y @ V_z @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ! [V_x: $i] :
( ~ ( c_in @ ( c_Pair @ V_x @ V_z @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Relation_Osingle__valued @ V_r @ T_a @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[903]) ).
thf(1442,plain,
( ( ! [V_a: $i,V_c: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ! [V_b: $i] :
( ~ ( c_in @ ( c_Pair @ V_b @ V_c @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[909]) ).
thf(1443,plain,
( ( ! [V_a: $i,V_c: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ! [V_b: $i] :
( ~ ( c_in @ ( c_Pair @ V_b @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[910]) ).
thf(1444,plain,
( ( ! [V_a: $i,V_A: $i,T_a: $i] :
( ( c_in @ V_a @ V_A @ T_a )
| ! [V_b: $i] :
( ( V_a = V_b )
| ! [V_r: $i] :
( ~ ( c_lessequals @ V_r @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_A @ ( tc_fun @ T_a @ tc_bool ) @ T_a ) @ T_a @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[914]) ).
thf(1445,plain,
( ( ! [V_r: $i,V_x: $i,T_a: $i,V_y: $i] :
( ( ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a )
!= ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_y @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) )
| ! [V_A: $i] :
( ~ ( c_in @ V_y @ V_A @ T_a )
| ~ ( c_in @ V_x @ V_A @ T_a )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a )
| ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[916]) ).
thf(1446,plain,
( ( ! [V_r: $i,V_x: $i,T_a: $i,V_y: $i] :
( ( ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a )
= ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_y @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ! [V_A: $i] :
( ~ ( c_in @ V_y @ V_A @ T_a )
| ~ ( c_in @ V_x @ V_A @ T_a )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[917]) ).
thf(1447,plain,
( ( ! [V_r: $i,V_x: $i,T_a: $i,V_y: $i] :
( ( ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a )
!= ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_y @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) )
| ! [V_A: $i] :
( ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a )
| ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_y @ V_A @ T_a )
| ~ ( c_in @ V_x @ V_A @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[918]) ).
thf(1448,plain,
( ( ! [V_r: $i,V_a: $i,T_a: $i,V_b: $i] :
( ( ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a )
!= ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) )
| ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ! [V_A: $i] :
( ~ ( c_in @ V_b @ V_A @ T_a )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[919]) ).
thf(1449,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) )
| ! [V_x: $i] :
~ ( c_in @ ( c_Pair @ V_x @ V_x @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[920]) ).
thf(1450,plain,
( ( ! [V_P: $i,V_a: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ! [V_r: $i,T_a: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1 @ V_P @ V_b @ V_r @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_b ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[925]) ).
thf(1451,plain,
( ( ! [V_P: $i,V_b: $i,V_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_b ) )
| ! [V_r: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 @ V_P @ V_a @ V_r @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[927]) ).
thf(1452,plain,
( ( ! [V_P: $i,V_b: $i,V_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_b ) )
| ! [V_r: $i,T_a: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2 @ V_P @ V_a @ V_r @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[929]) ).
thf(1453,plain,
( ( ! [V_P: $i,V_b: $i,V_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_b ) )
| ! [V_r: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ V_a @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 @ V_P @ V_a @ V_r @ T_a ) @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[930]) ).
thf(1454,plain,
( ( ! [V_P: $i,V_a: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ! [V_r: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 @ V_P @ V_b @ V_r @ T_a ) @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_b ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[931]) ).
thf(1455,plain,
( ( ! [V_P: $i,V_a: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ! [V_r: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 @ V_P @ V_b @ V_r @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_b ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[932]) ).
thf(1456,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] :
( ~ ( c_in @ ( c_Pair @ V_y @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1 @ V_P @ V_r @ T_a ) @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[936]) ).
thf(1457,plain,
( ( ! [V_P: $i,V_Ra: $i,V_y: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_Ra ) )
| ( hBOOL @ ( hAPP @ V_P @ V_y ) )
| ! [V_R: $i,T_a: $i] :
( ~ ( c_in @ ( c_Pair @ V_y @ ( c_List_Osko__Recdef__Xtfl__wf__induct__1__1 @ V_P @ V_R @ T_a ) @ T_a @ T_a ) @ V_R @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Wellfounded_Owf @ V_R @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[937]) ).
thf(1458,plain,
( ( ! [V_P: $i,V_xa: $i,V_y: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_xa ) )
| ( hBOOL @ ( hAPP @ V_P @ V_y ) )
| ! [V_r: $i,T_a: $i] :
( ~ ( c_in @ ( c_Pair @ V_y @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1 @ V_P @ V_r @ T_a ) @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[938]) ).
thf(1459,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] :
( ~ ( c_in @ ( c_Pair @ V_y @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1 @ V_P @ V_r @ T_a ) @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[939]) ).
thf(1460,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_lessequals @ V_r @ ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ V_r @ T_a @ T_a @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ! [V_A: $i] :
~ ( c_Relation_Orefl__on @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[962]) ).
thf(1461,plain,
( ( ! [V_R: $i,T_a: $i] :
( ( ( c_Relation_Orel__comp @ V_R @ V_R @ T_a @ T_a @ T_a )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) )
| ( c_Wellfounded_Owf @ V_R @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[989]) ).
thf(1462,plain,
( ( ! [V_r: $i,V_x: $i,T_a: $i,V_y: $i] :
( ( ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a )
= ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_y @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ! [V_A: $i] :
~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[992]) ).
thf(1463,plain,
( ( ! [V_r: $i,V_a: $i,T_a: $i,V_b: $i] :
( ( ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a )
= ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ! [V_A: $i] :
~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[993]) ).
thf(1464,plain,
( ( ! [V_p: $i,V_s: $i,T_a: $i] :
( ( c_in @ V_p @ ( c_Transitive__Closure_Otrancl @ V_s @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ! [V_r: $i] :
( ~ ( c_lessequals @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_in @ V_p @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[994]) ).
thf(1465,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Wellfounded_Owf @ V_r @ T_a )
| ! [V_y: $i,V_x: $i] :
~ ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ V_y @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[997]) ).
thf(1466,plain,
( ( ! [V_A: $i,V_C: $i,T_a: $i,T_b: $i,V_B: $i] :
( ( ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_C @ ( tc_fun @ T_a @ tc_bool ) @ T_b ) @ T_b @ T_a )
!= ( c_Product__Type_OSigma @ V_B @ ( c_COMBK @ V_C @ ( tc_fun @ T_a @ tc_bool ) @ T_b ) @ T_b @ T_a ) )
| ! [V_x: $i] :
~ ( c_in @ V_x @ V_C @ T_a )
| ( V_A = V_B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[998]) ).
thf(1467,plain,
( ( ! [V_f: $i,V_x: $i,V_B: $i,T_a: $i] :
( ( c_in @ ( hAPP @ V_f @ V_x ) @ V_B @ T_a )
| ! [V_A: $i,T_b: $i] :
( ~ ( c_in @ V_x @ V_A @ T_b )
| ~ ( c_lessequals @ ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1001]) ).
thf(1468,plain,
( ( ! [V_f: $i,V_x: $i,V_A: $i,T_a: $i] :
( ! [T_b: $i] :
( ( c_Set_Oinsert @ ( hAPP @ V_f @ V_x ) @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) @ T_b )
= ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) )
| ~ ( c_in @ V_x @ V_A @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1002]) ).
thf(1469,plain,
( ( ! [V_a: $i,V_b: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ! [V_A: $i] :
( ~ ( c_in @ V_b @ V_A @ T_a )
| ~ ( c_lessequals @ ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) @ ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1003]) ).
thf(1470,plain,
( ( ! [V_a: $i,V_b: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ! [V_x: $i] :
~ ( c_in @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) @ ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
| ! [V_A: $i] :
~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1004]) ).
thf(1471,plain,
( ( ! [V_a: $i,V_r: $i,T_a: $i] :
( ( c_in @ V_a @ ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) @ T_a )
| ! [V_A: $i] :
( ~ ( c_in @ V_a @ V_A @ T_a )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1006]) ).
thf(1472,plain,
( ( ! [V_P: $i,V_b: $i,V_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_b ) )
| ! [V_r: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 @ V_P @ V_a @ V_r @ T_a ) @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2 @ V_P @ V_a @ V_r @ T_a ) @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1007]) ).
thf(1473,plain,
( ( ! [V_P: $i,V_a: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ! [V_r: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1 @ V_P @ V_b @ V_r @ T_a ) @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 @ V_P @ V_b @ V_r @ T_a ) @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_b ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1008]) ).
thf(1474,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Relation_Oirrefl @ V_r @ T_a )
| ! [V_A: $i] :
~ ( c_Order__Relation_Ostrict__linear__order__on @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1011]) ).
thf(1475,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ! [V_y: $i,V_x: $i] :
( ( c_lessequals @ V_y @ V_x @ T_a )
| ( c_lessequals @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1012]) ).
thf(1476,plain,
( ( ! [V_r: $i,T_b: $i,T_a: $i] :
( ( ( c_Relation_ORange @ V_r @ T_b @ T_a )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( V_r
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_b @ T_a ) @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1015]) ).
thf(1477,plain,
( ( ! [V_x: $i,V_A: $i,T_b: $i] :
( ~ ( c_lessequals @ V_x @ V_A @ ( tc_fun @ T_b @ tc_bool ) )
| ! [V_f: $i,T_a: $i] : ( c_lessequals @ ( c_Set_Oimage @ V_f @ V_x @ T_b @ T_a ) @ ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1021]) ).
thf(1478,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ! [V_x_H: $i,V_y_H: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x_H @ V_y_H @ T_a ) )
| ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_lessequals @ V_y_H @ V_x_H @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1023]) ).
thf(1479,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ! [V_x_H: $i,V_y_H: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x_H @ V_y_H @ T_a ) )
| ( c_lessequals @ V_y_H @ V_x_H @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1024]) ).
thf(1480,plain,
( ( ! [V_f: $i,V_A: $i,T_b: $i] :
( ! [T_a: $i] :
( ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1035]) ).
thf(1481,plain,
( ( ! [V_r: $i,T_a: $i,T_b: $i] :
( ( c_Relation_Osingle__valued @ V_r @ T_a @ T_b )
| ! [V_s: $i] :
( ~ ( c_Relation_Osingle__valued @ V_s @ T_a @ T_b )
| ~ ( c_lessequals @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1036]) ).
thf(1482,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Wellfounded_Oacyclic @ V_r @ T_a )
| ! [V_s: $i] :
( ~ ( c_lessequals @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_Wellfounded_Oacyclic @ V_s @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1037]) ).
thf(1483,plain,
( ( ! [V_Q: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_Q @ V_x ) )
| ! [V_P: $i] :
( ! [T_a: $i] :
~ ( c_lessequals @ V_P @ V_Q @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1038]) ).
thf(1484,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Relation_Oantisym @ V_r @ T_a )
| ! [V_s: $i] :
( ~ ( c_Relation_Oantisym @ V_s @ T_a )
| ~ ( c_lessequals @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1039]) ).
thf(1485,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ! [V_x: $i] : ( c_lessequals @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1040]) ).
thf(1486,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_x: $i] : ( c_lessequals @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1041]) ).
thf(1487,plain,
( ( ! [V_p: $i,T_a: $i] :
( ( c_Wellfounded_Owf @ V_p @ T_a )
| ! [V_r: $i] :
( ~ ( c_lessequals @ V_p @ V_r @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1042]) ).
thf(1488,plain,
( ( ! [V_Q: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_Q @ V_x ) )
| ! [V_P: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ! [T_a: $i] :
~ ( c_lessequals @ V_P @ V_Q @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1043]) ).
thf(1489,plain,
( ( ! [V_A: $i,V_C: $i,T_a: $i] :
( ( c_lessequals @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ! [V_B: $i] :
( ~ ( c_lessequals @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1044]) ).
thf(1490,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ! [V_z: $i] :
( ( c_lessequals @ V_x @ V_z @ T_a )
| ! [V_y: $i] :
( ~ ( c_lessequals @ V_y @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1047]) ).
thf(1491,plain,
( ( ! [T_a: $i,V_z: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_x: $i] :
( ( c_lessequals @ V_z @ V_x @ T_a )
| ! [V_y: $i] :
( ~ ( c_lessequals @ V_z @ V_y @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1048]) ).
thf(1492,plain,
( ( ! [V_B: $i,V_C: $i,T_a: $i] :
( ( c_lessequals @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ! [V_A: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1049]) ).
thf(1493,plain,
( ( ! [V_A: $i,V_C: $i,T_a: $i] :
( ( c_lessequals @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ! [V_B: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1050]) ).
thf(1494,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_x: $i] :
( ( c_lessequals @ V_a @ V_x @ T_a )
| ! [V_b: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) @ V_x @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1051]) ).
thf(1495,plain,
( ( ! [T_a: $i,V_b: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_x: $i] :
( ( c_lessequals @ V_b @ V_x @ T_a )
| ! [V_a: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) @ V_x @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1052]) ).
thf(1496,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_a: $i] :
( ! [V_b: $i] : ( c_lessequals @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_a @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1053]) ).
thf(1497,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_a: $i,V_b: $i] :
( ( c_lessequals @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_b @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1054]) ).
thf(1498,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_z: $i] :
( ( c_lessequals @ V_x @ V_z @ T_a )
| ! [V_y: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ V_z @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1055]) ).
thf(1499,plain,
( ( ! [T_a: $i,V_y: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_z: $i] :
( ( c_lessequals @ V_y @ V_z @ T_a )
| ! [V_x: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ V_z @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1056]) ).
thf(1500,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)],[1058]) ).
thf(1501,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)],[1064]) ).
thf(1502,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)],[1065]) ).
thf(1503,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Relation_Otrans @ V_r @ T_a )
| ! [V_A: $i] :
~ ( c_Order__Relation_Ostrict__linear__order__on @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1069]) ).
thf(1504,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)],[1072]) ).
thf(1505,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)],[1073]) ).
thf(1506,plain,
( ( ! [V_Q: $i,T_a: $i,T_b: $i,V_p: $i,V_q: $i] :
( ( hBOOL @ ( hAPP @ V_Q @ ( hAPP @ ( c_snd @ T_a @ T_b ) @ ( c_Pair @ V_p @ V_q @ T_a @ T_b ) ) ) )
| ~ ( hBOOL @ ( hAPP @ V_Q @ V_q ) )
| ! [V_P: $i] :
~ ( hBOOL @ ( hAPP @ V_P @ V_p ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1074]) ).
thf(1507,plain,
( ( ! [V_P: $i,T_a: $i,T_b: $i,V_p: $i,V_q: $i] :
( ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ ( c_fst @ T_a @ T_b ) @ ( c_Pair @ V_p @ V_q @ T_a @ T_b ) ) ) )
| ! [V_Q: $i] :
~ ( hBOOL @ ( hAPP @ V_Q @ V_q ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_p ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1075]) ).
thf(1508,plain,
( ( ! [V_x: $i,V_A: $i,T_a: $i,V_B: $i] :
( ( ( c_Set_Oinsert @ V_x @ V_A @ T_a )
!= ( c_Set_Oinsert @ V_x @ V_B @ T_a ) )
| ( c_in @ V_x @ V_B @ T_a )
| ( V_A = V_B )
| ( c_in @ V_x @ V_A @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1081]) ).
thf(1509,plain,
( ( ! [V_P: $i,V_x: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ! [T_a: $i] :
~ ( c_in @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1084]) ).
thf(1510,plain,
( ( ! [V_c: $i,V_A: $i,T_a: $i] :
( ( c_in @ V_c @ V_A @ T_a )
| ! [V_B: $i] :
~ ( c_in @ V_c @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1085]) ).
thf(1511,plain,
( ( ! [V_c: $i,V_B: $i,T_a: $i] :
( ( c_in @ V_c @ V_B @ T_a )
| ! [V_A: $i] :
~ ( c_in @ V_c @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1086]) ).
thf(1512,plain,
( ( ! [V_c: $i,V_A: $i,T_a: $i] :
( ( c_in @ V_c @ V_A @ T_a )
| ! [V_B: $i] :
~ ( c_in @ V_c @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1090]) ).
thf(1513,plain,
( ( ! [V_c: $i,V_B: $i,T_a: $i] :
( ~ ( c_in @ V_c @ V_B @ T_a )
| ! [V_A: $i] :
~ ( c_in @ V_c @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1091]) ).
thf(1514,plain,
( ( ! [V_c: $i,V_B: $i,T_a: $i] :
( ( c_in @ V_c @ V_B @ T_a )
| ! [V_A: $i] :
( ( c_in @ V_c @ V_A @ T_a )
| ~ ( c_in @ V_c @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1092]) ).
thf(1515,plain,
( ( ! [V_a: $i,V_A: $i,T_a: $i] :
( ( c_in @ V_a @ V_A @ T_a )
| ! [V_b: $i] :
( ( V_a = V_b )
| ~ ( c_in @ V_a @ ( c_Set_Oinsert @ V_b @ V_A @ T_a ) @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1093]) ).
thf(1516,plain,
( ( ! [V_P: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ! [T_a: $i] :
~ ( c_in @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1096]) ).
thf(1517,plain,
( ( ! [V_x: $i,V_B: $i,T_a: $i] :
( ( c_in @ V_x @ V_B @ T_a )
| ! [V_A: $i] :
( ~ ( c_in @ V_x @ V_A @ T_a )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1100]) ).
thf(1518,plain,
( ( ! [V_c: $i,V_B: $i,T_a: $i] :
( ( c_in @ V_c @ V_B @ T_a )
| ! [V_A: $i] :
( ~ ( c_in @ V_c @ V_A @ T_a )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1101]) ).
thf(1519,plain,
( ( ! [V_x: $i,V_B: $i,T_a: $i] :
( ( c_in @ V_x @ V_B @ T_a )
| ! [V_A: $i] :
( ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_in @ V_x @ V_A @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1102]) ).
thf(1520,plain,
( ( ! [V_t: $i,V_B: $i,T_a: $i] :
( ( c_in @ V_t @ V_B @ T_a )
| ! [V_A: $i] :
( ~ ( c_in @ V_t @ V_A @ T_a )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1103]) ).
thf(1521,plain,
( ( ! [T_b: $i,V_f: $i,V_x: $i] :
( ~ ( class_HOL_Oord @ T_b )
| ! [V_g: $i] :
( ( c_lessequals @ ( hAPP @ V_f @ V_x ) @ ( hAPP @ V_g @ V_x ) @ T_b )
| ! [T_a: $i] :
~ ( c_lessequals @ V_f @ V_g @ ( tc_fun @ T_a @ T_b ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1108]) ).
thf(1522,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Wellfounded_Oacyclic @ V_r @ T_a )
| ! [V_y: $i,V_x: $i] :
~ ( c_Wellfounded_Oacyclic @ ( c_Set_Oinsert @ ( c_Pair @ V_y @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1109]) ).
thf(1523,plain,
( ( ! [V_f: $i,V_g: $i,V_r: $i,V_x: $i,T_a: $i,T_b: $i] :
( ( ( hAPP @ V_f @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ V_f @ V_g @ V_r @ V_x @ T_a @ T_b ) )
!= ( hAPP @ V_g @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ V_f @ V_g @ V_r @ V_x @ T_a @ T_b ) ) )
| ( ( c_Recdef_Ocut @ V_f @ V_r @ V_x @ T_a @ T_b )
= ( c_Recdef_Ocut @ V_g @ V_r @ V_x @ T_a @ T_b ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1110]) ).
thf(1524,plain,
( ( ! [V_A: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_A @ V_x ) )
| ! [V_B: $i,T_a: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_x ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1116]) ).
thf(1525,plain,
( ( ! [V_B: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_B @ V_x ) )
| ! [V_A: $i,T_a: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_x ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1117]) ).
thf(1526,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__Xwf__induct__rule__1__1 @ V_P @ V_r @ T_a ) ) )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1121]) ).
thf(1527,plain,
( ( ! [V_r: $i,T_a: $i,T_b: $i] :
( ( ( c_Relation_ODomain @ V_r @ T_a @ T_b )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( V_r
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1125]) ).
thf(1528,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)],[1126]) ).
thf(1529,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)],[1127]) ).
thf(1530,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)],[1133]) ).
thf(1531,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)],[1134]) ).
thf(1532,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_z: $i] :
( ( c_lessequals @ V_x @ V_z @ T_a )
| ! [V_y: $i] :
~ ( c_lessequals @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1137]) ).
thf(1533,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_y: $i] :
( ( c_lessequals @ V_x @ V_y @ T_a )
| ! [V_z: $i] :
~ ( c_lessequals @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1138]) ).
thf(1534,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_b: $i,V_x: $i] :
( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_a @ V_b @ T_a ) @ V_x @ T_a )
| ~ ( c_lessequals @ V_b @ V_x @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1139]) ).
thf(1535,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_b: $i,V_x: $i] :
( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_a @ V_b @ T_a ) @ V_x @ T_a )
| ~ ( c_lessequals @ V_a @ V_x @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1140]) ).
thf(1536,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_b: $i] :
( ( c_lessequals @ V_x @ V_b @ T_a )
| ! [V_a: $i] :
~ ( c_lessequals @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_a @ V_b @ T_a ) @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1141]) ).
thf(1537,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_a: $i] :
( ( c_lessequals @ V_x @ V_a @ T_a )
| ! [V_b: $i] :
~ ( c_lessequals @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_a @ V_b @ T_a ) @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1142]) ).
thf(1538,plain,
( ( ! [V_C: $i,V_A: $i,T_a: $i] :
( ( c_lessequals @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
| ! [V_B: $i] :
~ ( c_lessequals @ V_C @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1143]) ).
thf(1539,plain,
( ( ! [V_C: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_C @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ! [V_A: $i] :
~ ( c_lessequals @ V_C @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1144]) ).
thf(1540,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ! [V_A: $i,V_B: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ T_a )
!= ( c_Orderings_Obot__class_Obot @ T_a ) )
| ( V_B
= ( c_Orderings_Obot__class_Obot @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1149]) ).
thf(1541,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ! [V_A: $i] :
( ! [V_B: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ T_a )
!= ( c_Orderings_Obot__class_Obot @ T_a ) )
| ( V_A
= ( c_Orderings_Obot__class_Obot @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1150]) ).
thf(1542,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1151]) ).
thf(1543,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( V_B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1152]) ).
thf(1544,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ! [V_x: $i] :
( ~ ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ( c_in @ V_x @ V_A @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1157]) ).
thf(1545,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ! [V_x: $i] :
( ( c_in @ V_x @ V_A @ T_a )
| ~ ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1159]) ).
thf(1546,plain,
( ( ! [V_x: $i,V_B: $i,T_a: $i] :
( ( c_in @ V_x @ V_B @ T_a )
| ! [V_A: $i] :
~ ( c_lessequals @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1163]) ).
thf(1547,plain,
( ( ! [V_x: $i,V_xa: $i,T_a: $i] :
( ( ( c_Set_Oinsert @ V_x @ V_xa @ T_a )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( c_in @ V_x @ V_xa @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1165]) ).
thf(1548,plain,
( ( ! [V_a: $i,T_a: $i,V_b: $i] :
( ( ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
!= ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
| ( V_a = V_b ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1169]) ).
thf(1549,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_y: $i,V_z: $i] : ( c_lessequals @ ( 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 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1173]) ).
thf(1550,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_x: $i,V_y: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ V_x @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1179]) ).
thf(1551,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_x: $i,V_y: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ V_y @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1180]) ).
thf(1552,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_a: $i,V_b: $i] :
( ( c_lessequals @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_b @ T_a )
| ~ ( c_lessequals @ V_x @ V_a @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1181]) ).
thf(1553,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_y: $i,V_z: $i] :
( ( c_lessequals @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1182]) ).
thf(1554,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_y: $i,V_z: $i] :
( ( c_lessequals @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1183]) ).
thf(1555,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_x: $i,V_y: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ V_y @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1184]) ).
thf(1556,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_x: $i,V_y: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ V_x @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1185]) ).
thf(1557,plain,
( ( ! [T_a: $i,V_a: $i,V_A: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Set_Oinsert @ V_a @ V_A @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1193]) ).
thf(1558,plain,
( ( ! [V_a: $i,V_b: $i,T_a: $i,V_c: $i,V_d: $i] :
( ( ( c_Set_Oinsert @ V_a @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a )
!= ( c_Set_Oinsert @ V_c @ ( c_Set_Oinsert @ V_d @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) )
| ( V_b = V_c )
| ( V_b = V_d ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1198]) ).
thf(1559,plain,
( ( ! [V_a: $i,V_b: $i,T_a: $i,V_c: $i,V_d: $i] :
( ( ( c_Set_Oinsert @ V_a @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a )
!= ( c_Set_Oinsert @ V_c @ ( c_Set_Oinsert @ V_d @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) )
| ( V_a = V_d )
| ( V_b = V_d ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1199]) ).
thf(1560,plain,
( ( ! [V_a: $i,V_b: $i,T_a: $i,V_c: $i] :
( ! [V_d: $i] :
( ( c_Set_Oinsert @ V_a @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a )
!= ( c_Set_Oinsert @ V_c @ ( c_Set_Oinsert @ V_d @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) )
| ( V_b = V_c )
| ( V_a = V_c ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1200]) ).
thf(1561,plain,
( ( ! [V_a: $i,V_b: $i,T_a: $i,V_c: $i,V_d: $i] :
( ( ( c_Set_Oinsert @ V_a @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a )
!= ( c_Set_Oinsert @ V_c @ ( c_Set_Oinsert @ V_d @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) )
| ( V_a = V_d )
| ( V_a = V_c ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1201]) ).
thf(1562,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
!= V_B )
| ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1205]) ).
thf(1563,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 )
= V_y )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1208]) ).
thf(1564,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 )
!= V_y )
| ( c_lessequals @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1209]) ).
thf(1565,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 )
= V_x )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1210]) ).
thf(1566,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)],[1212]) ).
thf(1567,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( V_x = V_y )
| ~ ( c_lessequals @ V_x @ V_y @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1213]) ).
thf(1568,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( V_x = V_y )
| ~ ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1215]) ).
thf(1569,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( V_x = V_y )
| ~ ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1216]) ).
thf(1570,plain,
( ( ! [V_A: $i,V_B: $i] :
( ( V_A = V_B )
| ! [T_a: $i] :
( ~ ( c_lessequals @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1217]) ).
thf(1571,plain,
( ( ! [V_A: $i,V_B: $i] :
( ( V_A = V_B )
| ! [T_a: $i] :
( ~ ( c_lessequals @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1218]) ).
thf(1572,plain,
( ( ! [V_P: $i,V_xb: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_xb ) )
| ! [V_r: $i,T_a: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1 @ V_P @ V_r @ T_a ) ) )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1221]) ).
thf(1573,plain,
( ( ! [V_A: $i,V_C: $i,T_a: $i] :
( ( ( c_Relation_Orel__comp @ V_A @ V_C @ T_a @ T_a @ T_a )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) )
| ! [V_B: $i] :
( ( ( c_Relation_Orel__comp @ V_A @ V_B @ T_a @ T_a @ T_a )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) )
| ( ( c_Relation_Orel__comp @ V_A @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a @ T_a @ T_a )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1222]) ).
thf(1574,plain,
( ( ! [V_B: $i,V_C: $i,T_a: $i] :
( ( ( c_Relation_Orel__comp @ V_B @ V_C @ T_a @ T_a @ T_a )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) )
| ! [V_A: $i] :
( ( ( c_Relation_Orel__comp @ V_A @ V_C @ T_a @ T_a @ T_a )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) )
| ( ( c_Relation_Orel__comp @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ V_C @ T_a @ T_a @ T_a )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1223]) ).
thf(1575,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)],[1224]) ).
thf(1576,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_y: $i,V_z: $i] : ( c_lessequals @ ( 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 ) @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1226]) ).
thf(1577,plain,
( ( ! [V_x: $i,V_B: $i,T_a: $i] :
( ~ ( c_in @ V_x @ V_B @ T_a )
| ! [V_A: $i] :
( ~ ( c_in @ V_x @ V_A @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1228]) ).
thf(1578,plain,
( ( ! [V_A: $i,T_a: $i] :
( ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ! [V_R: $i] :
( ~ ( c_lessequals @ V_A @ ( c_Relation_OImage @ V_R @ V_A @ T_a @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_Wellfounded_Owf @ V_R @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1234]) ).
thf(1579,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ! [V_x: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ T_a ) @ V_x @ T_a )
= V_x ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1239]) ).
thf(1580,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ! [V_x: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Orderings_Obot__class_Obot @ T_a ) @ T_a )
= V_x ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1240]) ).
thf(1581,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)],[1243]) ).
thf(1582,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)],[1244]) ).
thf(1583,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)],[1245]) ).
thf(1584,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)],[1246]) ).
thf(1585,plain,
( ( ! [V_r: $i,T_a: $i,V_s: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_ODomain @ V_r @ T_a @ T_a ) @ ( c_Relation_ORange @ V_s @ T_a @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( c_Wellfounded_Owf @ V_s @ T_a )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a )
| ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1249]) ).
thf(1586,plain,
( ( ! [V_B: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_B @ V_x ) )
| ! [V_A: $i] :
( ( hBOOL @ ( hAPP @ V_A @ V_x ) )
| ! [T_a: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_x ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1252]) ).
thf(1587,plain,
( ( ! [V_r: $i,V_s: $i,T_a: $i,T_b: $i,T_c: $i,V_A: $i,V_C: $i] :
( ( c_lessequals @ ( c_Relation_Orel__comp @ V_r @ V_s @ T_a @ T_b @ T_c ) @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_C @ ( tc_fun @ T_c @ tc_bool ) @ T_a ) @ T_a @ T_c ) @ ( tc_fun @ ( tc_prod @ T_a @ T_c ) @ tc_bool ) )
| ! [V_B: $i] :
( ~ ( c_lessequals @ V_s @ ( c_Product__Type_OSigma @ V_B @ ( c_COMBK @ V_C @ ( tc_fun @ T_c @ tc_bool ) @ T_b ) @ T_b @ T_c ) @ ( tc_fun @ ( tc_prod @ T_b @ T_c ) @ tc_bool ) )
| ~ ( c_lessequals @ V_r @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_B @ ( tc_fun @ T_b @ tc_bool ) @ T_a ) @ T_a @ T_b ) @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1254]) ).
thf(1588,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( c_lessequals @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1259]) ).
thf(1589,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ! [V_x: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Orderings_Obot__class_Obot @ T_a ) @ V_x @ T_a )
= ( c_Orderings_Obot__class_Obot @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1265]) ).
thf(1590,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ! [V_x: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Orderings_Obot__class_Obot @ T_a ) @ T_a )
= ( c_Orderings_Obot__class_Obot @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1266]) ).
thf(1591,plain,
( ( ! [V_A: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_A @ V_x ) )
| ! [V_y: $i] :
( ( V_y = V_x )
| ! [T_a: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ V_y @ V_A @ T_a ) @ V_x ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1271]) ).
thf(1592,plain,
( ( ! [V_r: $i,V_a: $i,T_a: $i,V_b: $i] :
( ( c_lessequals @ ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) @ ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ! [V_A: $i] :
~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1274]) ).
thf(1593,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)],[1277]) ).
thf(1594,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)],[1278]) ).
thf(1595,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_x: $i,V_y: $i] : ( c_lessequals @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1280]) ).
thf(1596,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_y: $i,V_x: $i] : ( c_lessequals @ V_y @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1281]) ).
thf(1597,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_y: $i,V_z: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ V_z @ T_a )
| ~ ( c_lessequals @ V_y @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_z @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1282]) ).
thf(1598,plain,
( ( ! [T_a: $i,V_y: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_z: $i,V_x: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) @ V_x @ T_a )
| ~ ( c_lessequals @ V_z @ V_x @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1283]) ).
thf(1599,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_y: $i,V_x: $i] : ( c_lessequals @ V_y @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1284]) ).
thf(1600,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_x: $i,V_y: $i] : ( c_lessequals @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1285]) ).
thf(1601,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_b: $i,V_x: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) @ V_x @ T_a )
| ~ ( c_lessequals @ V_b @ V_x @ T_a )
| ~ ( c_lessequals @ V_a @ V_x @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1286]) ).
thf(1602,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 )
= V_y )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1291]) ).
thf(1603,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 )
!= V_x )
| ( c_lessequals @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1292]) ).
thf(1604,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 )
= V_x )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1293]) ).
thf(1605,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)],[1296]) ).
thf(1606,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)],[1297]) ).
thf(1607,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)],[1298]) ).
thf(1608,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)],[1299]) ).
thf(1609,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ! [V_x_H: $i,V_y_H: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_x @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x_H @ V_y_H @ T_a ) )
| ( V_x_H = V_y_H ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1304]) ).
thf(1610,plain,
( ( ! [T_a: $i,V_xa: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ! [V_y: $i] :
( ! [V_x: $i] :
( ( c_HOL_Ominus__class_Ominus @ V_xa @ V_y @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x @ V_x @ T_a ) )
| ( V_xa = V_y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1305]) ).
thf(1611,plain,
( ( ! [V_r: $i,V_C: $i,T_a: $i,T_b: $i,V_B: $i] :
( ( c_lessequals @ ( c_Relation_OImage @ V_r @ V_C @ T_a @ T_b ) @ V_B @ ( tc_fun @ T_b @ tc_bool ) )
| ! [V_A: $i] :
~ ( c_lessequals @ V_r @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_B @ ( tc_fun @ T_b @ tc_bool ) @ T_a ) @ T_a @ T_b ) @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1306]) ).
thf(1612,plain,
( ( ! [V_P: $i,V_Rb: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_Rb ) )
| ! [V_R: $i,T_a: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Osko__Recdef__Xtfl__wf__induct__1__1 @ V_P @ V_R @ T_a ) ) )
| ~ ( c_Wellfounded_Owf @ V_R @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1314]) ).
thf(1613,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)],[1318]) ).
thf(1614,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)],[1322]) ).
thf(1615,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)],[1323]) ).
thf(1616,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= V_A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1327]) ).
thf(1617,plain,
( ( ! [V_b: $i,V_a: $i] :
( ( V_b = V_a )
| ! [T_a: $i] :
~ ( c_in @ V_b @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1328]) ).
thf(1618,plain,
( ( ! [V_c: $i,T_b: $i,T_a: $i,V_A: $i] :
( ( ( c_Set_Oimage @ ( c_COMBK @ V_c @ T_b @ T_a ) @ V_A @ T_a @ T_b )
= ( c_Set_Oinsert @ V_c @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b ) )
| ! [V_x: $i] :
~ ( c_in @ V_x @ V_A @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1331]) ).
thf(1619,plain,
( ( ! [V_A: $i,V_B: $i,T_b: $i,V_C: $i] :
( ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_b @ tc_bool ) )
| ! [T_a: $i] :
( ~ ( c_lessequals @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_C @ ( tc_fun @ T_a @ tc_bool ) @ T_b ) @ T_b @ T_a ) @ ( c_Product__Type_OSigma @ V_B @ ( c_COMBK @ V_C @ ( tc_fun @ T_a @ tc_bool ) @ T_b ) @ T_b @ T_a ) @ ( tc_fun @ ( tc_prod @ T_b @ T_a ) @ tc_bool ) )
| ! [V_x: $i] :
~ ( c_in @ V_x @ V_C @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1335]) ).
thf(1620,plain,
( ( ! [V_A: $i,V_C: $i,T_a: $i,T_b: $i,V_B: $i] :
( ( c_lessequals @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_C @ ( tc_fun @ T_a @ tc_bool ) @ T_b ) @ T_b @ T_a ) @ ( c_Product__Type_OSigma @ V_B @ ( c_COMBK @ V_C @ ( tc_fun @ T_a @ tc_bool ) @ T_b ) @ T_b @ T_a ) @ ( tc_fun @ ( tc_prod @ T_b @ T_a ) @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_b @ tc_bool ) )
| ! [V_x: $i] :
~ ( c_in @ V_x @ V_C @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1336]) ).
thf(1621,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ! [V_x: $i] :
~ ( c_lessequals @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1338]) ).
thf(1622,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__Xwf__induct__1__1 @ V_P @ V_r @ T_a ) ) )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1341]) ).
thf(1623,plain,
( ( ! [T_a: $i,T_b: $i,V_p: $i,V_q: $i] :
( ( ( hAPP @ ( c_snd @ T_a @ T_b ) @ V_p )
!= ( hAPP @ ( c_snd @ T_a @ T_b ) @ V_q ) )
| ( ( hAPP @ ( c_fst @ T_a @ T_b ) @ V_p )
!= ( hAPP @ ( c_fst @ T_a @ T_b ) @ V_q ) )
| ( V_p = V_q ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1342]) ).
thf(1624,plain,
( ( ! [T_a: $i,T_b: $i,V_s: $i,V_t: $i] :
( ( ( hAPP @ ( c_snd @ T_a @ T_b ) @ V_s )
!= ( hAPP @ ( c_snd @ T_a @ T_b ) @ V_t ) )
| ( ( hAPP @ ( c_fst @ T_a @ T_b ) @ V_s )
!= ( hAPP @ ( c_fst @ T_a @ T_b ) @ V_t ) )
| ( V_s = V_t ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1343]) ).
thf(1625,plain,
( ( ! [T_a: $i,V_f: $i,V_A: $i,T_b: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a ) )
| ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1345]) ).
thf(1626,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Obot @ T_a )
| ! [V_x: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ T_a ) @ V_x @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1352]) ).
thf(1627,plain,
( ( ! [V_a: $i,V_A: $i,T_a: $i] :
( ( c_Set_Oinsert @ V_a @ V_A @ T_a )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1355]) ).
thf(1628,plain,
( ( ~ ( c_in @ ( c_Pair @ v_c____ @ v_d____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ v_P____ ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ),
inference(copy,[status(thm)],[1357]) ).
thf(1629,plain,
( ( ! [V_a: $i,V_A: $i,T_a: $i,V_B: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ V_a @ V_A @ T_a ) @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Set_Oinsert @ V_a @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1356]) ).
thf(1630,plain,
( ( ! [V_a: $i,V_A: $i,T_a: $i] :
( ( c_Set_Oinsert @ V_a @ V_A @ T_a )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1627]) ).
thf(1631,plain,
( ( ! [V_A: $i,V_a: $i,V_B: $i,T_a: $i] :
( ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1354]) ).
thf(1632,plain,
( ( ! [V_A: $i,V_a: $i,V_B: $i,T_a: $i] :
( ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1353]) ).
thf(1633,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Obot @ T_a )
| ! [V_x: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ T_a ) @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1626]) ).
thf(1634,plain,
( ( ! [T_a: $i,V_B: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ V_B @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) )
= $true ),
inference(copy,[status(thm)],[1351]) ).
thf(1635,plain,
( ( ! [T_a: $i,V_A: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(copy,[status(thm)],[1350]) ).
thf(1636,plain,
( ( ! [V_R: $i,T_c: $i,T_b: $i,T_a: $i] :
( ( c_Relation_Orel__comp @ V_R @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_c @ T_b ) @ tc_bool ) ) @ T_a @ T_c @ T_b )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1349]) ).
thf(1637,plain,
( ( ! [T_a: $i,T_c: $i,V_R: $i,T_b: $i] :
( ( c_Relation_Orel__comp @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_c ) @ tc_bool ) ) @ V_R @ T_a @ T_c @ T_b )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1348]) ).
thf(1638,plain,
( ( ! [V_A: $i,V_a: $i,V_B: $i,T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Set_Oinsert @ V_a @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1347]) ).
thf(1639,plain,
( ( ! [V_a: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Set_Oinsert @ V_a @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1346]) ).
thf(1640,plain,
( ( ! [T_a: $i,V_f: $i,V_A: $i,T_b: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a ) )
| ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1625]) ).
thf(1641,plain,
( ( ! [V_R: $i,T_a: $i,V_S: $i] : ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_S @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_R @ V_S @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) )
= $true ),
inference(copy,[status(thm)],[1344]) ).
thf(1642,plain,
( ( ! [T_a: $i,T_b: $i,V_s: $i,V_t: $i] :
( ( ( hAPP @ ( c_snd @ T_a @ T_b ) @ V_s )
!= ( hAPP @ ( c_snd @ T_a @ T_b ) @ V_t ) )
| ( ( hAPP @ ( c_fst @ T_a @ T_b ) @ V_s )
!= ( hAPP @ ( c_fst @ T_a @ T_b ) @ V_t ) )
| ( V_s = V_t ) ) )
= $true ),
inference(copy,[status(thm)],[1624]) ).
thf(1643,plain,
( ( ! [T_a: $i,T_b: $i,V_p: $i,V_q: $i] :
( ( ( hAPP @ ( c_snd @ T_a @ T_b ) @ V_p )
!= ( hAPP @ ( c_snd @ T_a @ T_b ) @ V_q ) )
| ( ( hAPP @ ( c_fst @ T_a @ T_b ) @ V_p )
!= ( hAPP @ ( c_fst @ T_a @ T_b ) @ V_q ) )
| ( V_p = V_q ) ) )
= $true ),
inference(copy,[status(thm)],[1623]) ).
thf(1644,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__Xwf__induct__1__1 @ V_P @ V_r @ T_a ) ) )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1622]) ).
thf(1645,plain,
( ( ! [V_A: $i,T_b: $i,T_a: $i,V_B: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ ( c_Relation_ORange @ V_A @ T_b @ T_a ) @ ( c_Relation_ORange @ V_B @ T_b @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Relation_ORange @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ ( tc_prod @ T_b @ T_a ) @ tc_bool ) ) @ T_b @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(copy,[status(thm)],[1340]) ).
thf(1646,plain,
( ( ! [V_A: $i,V_b: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_b @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1339]) ).
thf(1647,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ! [V_x: $i] :
~ ( c_lessequals @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1621]) ).
thf(1648,plain,
( ( ! [V_x: $i,V_A: $i,T_a: $i,V_B: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( c_in @ V_x @ V_B @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1337]) ).
thf(1649,plain,
( ( ! [V_A: $i,V_C: $i,T_a: $i,T_b: $i,V_B: $i] :
( ( c_lessequals @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_C @ ( tc_fun @ T_a @ tc_bool ) @ T_b ) @ T_b @ T_a ) @ ( c_Product__Type_OSigma @ V_B @ ( c_COMBK @ V_C @ ( tc_fun @ T_a @ tc_bool ) @ T_b ) @ T_b @ T_a ) @ ( tc_fun @ ( tc_prod @ T_b @ T_a ) @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_b @ tc_bool ) )
| ! [V_x: $i] :
~ ( c_in @ V_x @ V_C @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1620]) ).
thf(1650,plain,
( ( ! [V_A: $i,V_B: $i,T_b: $i,V_C: $i] :
( ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_b @ tc_bool ) )
| ! [T_a: $i] :
( ~ ( c_lessequals @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_C @ ( tc_fun @ T_a @ tc_bool ) @ T_b ) @ T_b @ T_a ) @ ( c_Product__Type_OSigma @ V_B @ ( c_COMBK @ V_C @ ( tc_fun @ T_a @ tc_bool ) @ T_b ) @ T_b @ T_a ) @ ( tc_fun @ ( tc_prod @ T_b @ T_a ) @ tc_bool ) )
| ! [V_x: $i] :
~ ( c_in @ V_x @ V_C @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1619]) ).
thf(1651,plain,
( ( ! [V_A: $i,V_x: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_in @ V_x @ V_A @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1334]) ).
thf(1652,plain,
( ( ! [V_A: $i,V_x: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_in @ V_x @ V_A @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1333]) ).
thf(1653,plain,
( ( ! [V_A: $i,V_x: $i,T_a: $i,V_B: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_in @ V_x @ V_A @ T_a )
| ~ ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1332]) ).
thf(1654,plain,
( ( ! [V_c: $i,T_b: $i,T_a: $i,V_A: $i] :
( ( ( c_Set_Oimage @ ( c_COMBK @ V_c @ T_b @ T_a ) @ V_A @ T_a @ T_b )
= ( c_Set_Oinsert @ V_c @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b ) )
| ! [V_x: $i] :
~ ( c_in @ V_x @ V_A @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1618]) ).
thf(1655,plain,
( ( ! [V_r: $i,T_a: $i,V_s: $i] :
( ( c_lessequals @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Relation_Orel__comp @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ V_r @ T_a @ T_a @ T_a ) @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_lessequals @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1330]) ).
thf(1656,plain,
( ( ! [V_I: $i,V_J: $i,T_a: $i,V_C: $i,T_b: $i] :
( ( c_Product__Type_OSigma @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_I @ V_J @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ T_a @ T_b )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Product__Type_OSigma @ V_I @ V_C @ T_a @ T_b ) @ ( c_Product__Type_OSigma @ V_J @ V_C @ T_a @ T_b ) @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1329]) ).
thf(1657,plain,
( ( ! [V_b: $i,V_a: $i] :
( ( V_b = V_a )
| ! [T_a: $i] :
~ ( c_in @ V_b @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1617]) ).
thf(1658,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= V_A ) ) )
= $true ),
inference(copy,[status(thm)],[1616]) ).
thf(1659,plain,
( ( ! [V_A: $i,T_a: $i,T_b: $i,V_B: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ ( c_Relation_ODomain @ V_A @ T_a @ T_b ) @ ( c_Relation_ODomain @ V_B @ T_a @ T_b ) @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Relation_ODomain @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) @ T_a @ T_b ) @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(copy,[status(thm)],[1326]) ).
thf(1660,plain,
( ( ! [V_B: $i,V_C: $i,T_a: $i,V_A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1325]) ).
thf(1661,plain,
( ( ! [V_A: $i,V_B: $i,V_C: $i,T_a: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1324]) ).
thf(1662,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)],[1615]) ).
thf(1663,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)],[1614]) ).
thf(1664,plain,
( ( ! [V_A: $i,T_a: $i] : ( c_lessequals @ ( c_Relation_OId__on @ V_A @ T_a ) @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_A @ ( tc_fun @ T_a @ tc_bool ) @ T_a ) @ T_a @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) )
= $true ),
inference(copy,[status(thm)],[1321]) ).
thf(1665,plain,
( ( ! [V_r: $i,V_A: $i,T_a: $i] :
( ( c_lessequals @ V_r @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_A @ ( tc_fun @ T_a @ tc_bool ) @ T_a ) @ T_a @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_Relation_Orefl__on @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1320]) ).
thf(1666,plain,
( ( ! [V_A: $i,T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
= V_A ) )
= $true ),
inference(copy,[status(thm)],[1319]) ).
thf(1667,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)],[1613]) ).
thf(1668,plain,
( ( ! [V_r_H: $i,V_s_H: $i,T_a: $i,T_b: $i,T_c: $i,V_r: $i,V_s: $i] :
( ( c_lessequals @ ( c_Relation_Orel__comp @ V_r_H @ V_s_H @ T_a @ T_b @ T_c ) @ ( c_Relation_Orel__comp @ V_r @ V_s @ T_a @ T_b @ T_c ) @ ( tc_fun @ ( tc_prod @ T_a @ T_c ) @ tc_bool ) )
| ~ ( c_lessequals @ V_s_H @ V_s @ ( tc_fun @ ( tc_prod @ T_b @ T_c ) @ tc_bool ) )
| ~ ( c_lessequals @ V_r_H @ V_r @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1317]) ).
thf(1669,plain,
( ( ! [V_R: $i,V_S: $i,T_b: $i,T_a: $i,V_A: $i] :
( ( c_Relation_OImage @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_R @ V_S @ ( tc_fun @ ( tc_prod @ T_b @ T_a ) @ tc_bool ) ) @ V_A @ T_b @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_OImage @ V_R @ V_A @ T_b @ T_a ) @ ( c_Relation_OImage @ V_S @ V_A @ T_b @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1316]) ).
thf(1670,plain,
( ( ! [V_R: $i,V_A: $i,V_B: $i,T_b: $i,T_a: $i] :
( ( c_Relation_OImage @ V_R @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_OImage @ V_R @ V_A @ T_b @ T_a ) @ ( c_Relation_OImage @ V_R @ V_B @ T_b @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1315]) ).
thf(1671,plain,
( ( ! [V_P: $i,V_Rb: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_Rb ) )
| ! [V_R: $i,T_a: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Osko__Recdef__Xtfl__wf__induct__1__1 @ V_P @ V_R @ T_a ) ) )
| ~ ( c_Wellfounded_Owf @ V_R @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1612]) ).
thf(1672,plain,
( ( ! [T_a: $i,T_b: $i] :
( ( c_Relation_ODomain @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) @ T_a @ T_b )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1313]) ).
thf(1673,plain,
( ( ! [V_x: $i,V_y: $i,V_A: $i,T_a: $i] :
( ( c_Set_Oinsert @ V_x @ ( c_Set_Oinsert @ V_y @ V_A @ T_a ) @ T_a )
= ( c_Set_Oinsert @ V_y @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1312]) ).
thf(1674,plain,
( ( ! [V_t: $i,T_a: $i,T_b: $i] :
( V_t
= ( c_Pair @ ( hAPP @ ( c_fst @ T_a @ T_b ) @ V_t ) @ ( hAPP @ ( c_snd @ T_a @ T_b ) @ V_t ) @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[1311]) ).
thf(1675,plain,
( ( ! [T_a: $i,T_b: $i,V_p: $i] :
( ( c_Pair @ ( hAPP @ ( c_fst @ T_a @ T_b ) @ V_p ) @ ( hAPP @ ( c_snd @ T_a @ T_b ) @ V_p ) @ T_a @ T_b )
= V_p ) )
= $true ),
inference(copy,[status(thm)],[1310]) ).
thf(1676,plain,
( ( ! [V_P: $i,T_a: $i,T_b: $i,V_Q: $i] :
( ( hAPP @ ( c_COMBK @ V_P @ T_a @ T_b ) @ V_Q )
= V_P ) )
= $true ),
inference(copy,[status(thm)],[1309]) ).
thf(1677,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1308]) ).
thf(1678,plain,
( ( ! [V_xa: $i,V_x: $i,T_a: $i] :
( ( c_Set_Oinsert @ V_xa @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a )
= ( c_Set_Oinsert @ V_x @ ( c_Set_Oinsert @ V_xa @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1307]) ).
thf(1679,plain,
( ( ! [V_r: $i,V_C: $i,T_a: $i,T_b: $i,V_B: $i] :
( ( c_lessequals @ ( c_Relation_OImage @ V_r @ V_C @ T_a @ T_b ) @ V_B @ ( tc_fun @ T_b @ tc_bool ) )
| ! [V_A: $i] :
~ ( c_lessequals @ V_r @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_B @ ( tc_fun @ T_b @ tc_bool ) @ T_a ) @ T_a @ T_b ) @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1611]) ).
thf(1680,plain,
( ( ! [T_a: $i,V_xa: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ! [V_y: $i] :
( ! [V_x: $i] :
( ( c_HOL_Ominus__class_Ominus @ V_xa @ V_y @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x @ V_x @ T_a ) )
| ( V_xa = V_y ) ) ) )
= $true ),
inference(copy,[status(thm)],[1610]) ).
thf(1681,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ! [V_x_H: $i,V_y_H: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_x @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x_H @ V_y_H @ T_a ) )
| ( V_x_H = V_y_H ) ) ) )
= $true ),
inference(copy,[status(thm)],[1609]) ).
thf(1682,plain,
( ( ! [V_f: $i,T_b: $i,T_a: $i] :
( ( c_Set_Oimage @ V_f @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b @ T_a )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1303]) ).
thf(1683,plain,
( ( ! [V_f: $i,V_A: $i,T_b: $i,T_a: $i,V_B: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a ) @ ( c_Set_Oimage @ V_f @ V_B @ T_b @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Set_Oimage @ V_f @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(copy,[status(thm)],[1302]) ).
thf(1684,plain,
( ( ! [V_A: $i,V_B: $i,V_C: $i,T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1301]) ).
thf(1685,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1300]) ).
thf(1686,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)],[1608]) ).
thf(1687,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)],[1607]) ).
thf(1688,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)],[1606]) ).
thf(1689,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)],[1605]) ).
thf(1690,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= V_A )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1295]) ).
thf(1691,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= V_B )
| ~ ( c_lessequals @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1294]) ).
thf(1692,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 )
= V_x )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1604]) ).
thf(1693,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 )
!= V_x )
| ( c_lessequals @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1603]) ).
thf(1694,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 )
= V_y )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1602]) ).
thf(1695,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1290]) ).
thf(1696,plain,
( ( ! [V_B: $i,V_A: $i,T_a: $i] : ( c_lessequals @ V_B @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(copy,[status(thm)],[1289]) ).
thf(1697,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] : ( c_lessequals @ V_A @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(copy,[status(thm)],[1288]) ).
thf(1698,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1287]) ).
thf(1699,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_b: $i,V_x: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) @ V_x @ T_a )
| ~ ( c_lessequals @ V_b @ V_x @ T_a )
| ~ ( c_lessequals @ V_a @ V_x @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1601]) ).
thf(1700,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_x: $i,V_y: $i] : ( c_lessequals @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1600]) ).
thf(1701,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_y: $i,V_x: $i] : ( c_lessequals @ V_y @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1599]) ).
thf(1702,plain,
( ( ! [T_a: $i,V_y: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_z: $i,V_x: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) @ V_x @ T_a )
| ~ ( c_lessequals @ V_z @ V_x @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1598]) ).
thf(1703,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_y: $i,V_z: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ V_z @ T_a )
| ~ ( c_lessequals @ V_y @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_z @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1597]) ).
thf(1704,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_y: $i,V_x: $i] : ( c_lessequals @ V_y @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1596]) ).
thf(1705,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_x: $i,V_y: $i] : ( c_lessequals @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1595]) ).
thf(1706,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1279]) ).
thf(1707,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)],[1594]) ).
thf(1708,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)],[1593]) ).
thf(1709,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Wellfounded_Oacyclic @ V_r @ T_a )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1276]) ).
thf(1710,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ ( c_HOL_Ominus__class_Ominus @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= V_B )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1275]) ).
thf(1711,plain,
( ( ! [V_r: $i,V_a: $i,T_a: $i,V_b: $i] :
( ( c_lessequals @ ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) @ ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ! [V_A: $i] :
~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1592]) ).
thf(1712,plain,
( ( ! [V_R: $i,T_b: $i,T_a: $i] :
( ( c_Relation_OImage @ V_R @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b @ T_a )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1273]) ).
thf(1713,plain,
( ( ! [V_x: $i,V_A: $i,T_a: $i] :
( ( c_Set_Oinsert @ V_x @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ T_a )
= ( c_Set_Oinsert @ V_x @ V_A @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1272]) ).
thf(1714,plain,
( ( ! [V_A: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_A @ V_x ) )
| ! [V_y: $i] :
( ( V_y = V_x )
| ! [T_a: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ V_y @ V_A @ T_a ) @ V_x ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1591]) ).
thf(1715,plain,
( ( ! [V_a: $i,V_b: $i,T_a: $i,T_b: $i,V_r: $i] :
( ( c_Relation_ODomain @ ( c_Set_Oinsert @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ V_r @ ( tc_prod @ T_a @ T_b ) ) @ T_a @ T_b )
= ( c_Set_Oinsert @ V_a @ ( c_Relation_ODomain @ V_r @ T_a @ T_b ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1270]) ).
thf(1716,plain,
( ( ! [V_r: $i,V_s: $i,T_a: $i] :
( ( c_Relation_Osym @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
| ~ ( c_Relation_Osym @ V_s @ T_a )
| ~ ( c_Relation_Osym @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1269]) ).
thf(1717,plain,
( ( ! [V_r: $i,T_a: $i,V_s: $i] :
( ( c_lessequals @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_s @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_lessequals @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1268]) ).
thf(1718,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,T_b: $i] : ( c_lessequals @ ( c_Relation_ODomain @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) @ T_a @ T_b ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_ODomain @ V_A @ T_a @ T_b ) @ ( c_Relation_ODomain @ V_B @ T_a @ T_b ) @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(copy,[status(thm)],[1267]) ).
thf(1719,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ! [V_x: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Orderings_Obot__class_Obot @ T_a ) @ T_a )
= ( c_Orderings_Obot__class_Obot @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1590]) ).
thf(1720,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ! [V_x: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Orderings_Obot__class_Obot @ T_a ) @ V_x @ T_a )
= ( c_Orderings_Obot__class_Obot @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1589]) ).
thf(1721,plain,
( ( ! [T_a: $i,V_B: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1264]) ).
thf(1722,plain,
( ( ! [V_A: $i,T_a: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1263]) ).
thf(1723,plain,
( ( ! [V_B: $i,V_a: $i,T_a: $i] : ( c_lessequals @ V_B @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(copy,[status(thm)],[1262]) ).
thf(1724,plain,
( ( ! [V_f: $i,V_A: $i,V_B: $i,T_b: $i,T_a: $i] : ( c_lessequals @ ( c_Set_Oimage @ V_f @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b @ T_a ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a ) @ ( c_Set_Oimage @ V_f @ V_B @ T_b @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(copy,[status(thm)],[1261]) ).
thf(1725,plain,
( ( ! [V_R: $i,V_A: $i,V_B: $i,T_b: $i,T_a: $i] : ( c_lessequals @ ( c_Relation_OImage @ V_R @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b @ T_a ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_OImage @ V_R @ V_A @ T_b @ T_a ) @ ( c_Relation_OImage @ V_R @ V_B @ T_b @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(copy,[status(thm)],[1260]) ).
thf(1726,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( c_lessequals @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1588]) ).
thf(1727,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( c_lessequals @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1258]) ).
thf(1728,plain,
( ( ! [V_I: $i,V_J: $i,T_a: $i,V_C: $i,T_b: $i] :
( ( c_Product__Type_OSigma @ ( c_HOL_Ominus__class_Ominus @ V_I @ V_J @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ T_a @ T_b )
= ( c_HOL_Ominus__class_Ominus @ ( c_Product__Type_OSigma @ V_I @ V_C @ T_a @ T_b ) @ ( c_Product__Type_OSigma @ V_J @ V_C @ T_a @ T_b ) @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1257]) ).
thf(1729,plain,
( ( ! [V_A: $i,T_a: $i] :
( ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= V_A ) )
= $true ),
inference(copy,[status(thm)],[1256]) ).
thf(1730,plain,
( ( ! [V_A: $i,T_a: $i] :
( ( c_HOL_Ominus__class_Ominus @ V_A @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1255]) ).
thf(1731,plain,
( ( ! [V_r: $i,V_s: $i,T_a: $i,T_b: $i,T_c: $i,V_A: $i,V_C: $i] :
( ( c_lessequals @ ( c_Relation_Orel__comp @ V_r @ V_s @ T_a @ T_b @ T_c ) @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_C @ ( tc_fun @ T_c @ tc_bool ) @ T_a ) @ T_a @ T_c ) @ ( tc_fun @ ( tc_prod @ T_a @ T_c ) @ tc_bool ) )
| ! [V_B: $i] :
( ~ ( c_lessequals @ V_s @ ( c_Product__Type_OSigma @ V_B @ ( c_COMBK @ V_C @ ( tc_fun @ T_c @ tc_bool ) @ T_b ) @ T_b @ T_c ) @ ( tc_fun @ ( tc_prod @ T_b @ T_c ) @ tc_bool ) )
| ~ ( c_lessequals @ V_r @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_B @ ( tc_fun @ T_b @ tc_bool ) @ T_a ) @ T_a @ T_b ) @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1587]) ).
thf(1732,plain,
( ( ! [V_R: $i,V_S: $i,T_a: $i] :
( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_R @ V_S @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
| ~ ( c_lessequals @ ( c_Relation_Orel__comp @ V_R @ V_S @ T_a @ T_a @ T_a ) @ V_R @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_Wellfounded_Owf @ V_S @ T_a )
| ~ ( c_Wellfounded_Owf @ V_R @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1253]) ).
thf(1733,plain,
( ( ! [V_B: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_B @ V_x ) )
| ! [V_A: $i] :
( ( hBOOL @ ( hAPP @ V_A @ V_x ) )
| ! [T_a: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_x ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1586]) ).
thf(1734,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ V_B @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[1251]) ).
thf(1735,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ V_A @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[1250]) ).
thf(1736,plain,
( ( ! [V_r: $i,T_a: $i,V_s: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_ODomain @ V_r @ T_a @ T_a ) @ ( c_Relation_ORange @ V_s @ T_a @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( c_Wellfounded_Owf @ V_s @ T_a )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a )
| ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1585]) ).
thf(1737,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i,T_b: $i] :
( ( c_Product__Type_OSigma @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_COMBK @ V_C @ ( tc_fun @ T_b @ tc_bool ) @ T_a ) @ T_a @ T_b )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_C @ ( tc_fun @ T_b @ tc_bool ) @ T_a ) @ T_a @ T_b ) @ ( c_Product__Type_OSigma @ V_B @ ( c_COMBK @ V_C @ ( tc_fun @ T_b @ tc_bool ) @ T_a ) @ T_a @ T_b ) @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1248]) ).
thf(1738,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_r: $i,V_s: $i] :
( ( c_Relation_Orefl__on @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
| ~ ( c_Relation_Orefl__on @ V_B @ V_s @ T_a )
| ~ ( c_Relation_Orefl__on @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1247]) ).
thf(1739,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)],[1584]) ).
thf(1740,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)],[1583]) ).
thf(1741,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)],[1582]) ).
thf(1742,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)],[1581]) ).
thf(1743,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1242]) ).
thf(1744,plain,
( ( ! [V_A: $i,V_B: $i,V_C: $i,T_a: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1241]) ).
thf(1745,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ! [V_x: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Orderings_Obot__class_Obot @ T_a ) @ T_a )
= V_x ) ) )
= $true ),
inference(copy,[status(thm)],[1580]) ).
thf(1746,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ! [V_x: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ T_a ) @ V_x @ T_a )
= V_x ) ) )
= $true ),
inference(copy,[status(thm)],[1579]) ).
thf(1747,plain,
( ( ! [T_a: $i,V_B: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= V_B ) )
= $true ),
inference(copy,[status(thm)],[1238]) ).
thf(1748,plain,
( ( ! [V_A: $i,T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= V_A ) )
= $true ),
inference(copy,[status(thm)],[1237]) ).
thf(1749,plain,
( ( ! [T_a: $i,V_A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1236]) ).
thf(1750,plain,
( ( ! [V_a: $i,V_A: $i,T_a: $i,V_b: $i,V_B: $i,T_b: $i] :
( ( c_Product__Type_OSigma @ ( c_Set_Oinsert @ V_a @ V_A @ T_a ) @ ( c_COMBK @ ( c_Set_Oinsert @ V_b @ V_B @ T_b ) @ ( tc_fun @ T_b @ tc_bool ) @ T_a ) @ T_a @ T_b )
= ( c_Set_Oinsert @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ ( c_Set_Oinsert @ V_b @ V_B @ T_b ) @ ( tc_fun @ T_b @ tc_bool ) @ T_a ) @ T_a @ T_b ) @ ( c_Product__Type_OSigma @ ( c_Set_Oinsert @ V_a @ V_A @ T_a ) @ ( c_COMBK @ V_B @ ( tc_fun @ T_b @ tc_bool ) @ T_a ) @ T_a @ T_b ) @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) @ ( tc_prod @ T_a @ T_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[1235]) ).
thf(1751,plain,
( ( ! [V_A: $i,T_a: $i] :
( ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ! [V_R: $i] :
( ~ ( c_lessequals @ V_A @ ( c_Relation_OImage @ V_R @ V_A @ T_a @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_Wellfounded_Owf @ V_R @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1578]) ).
thf(1752,plain,
( ( ! [T_a: $i,V_x: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ V_x ) ) )
= $true ),
inference(copy,[status(thm)],[1233]) ).
thf(1753,plain,
( ( ! [V_C: $i,V_A: $i,V_B: $i,T_a: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_C @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_C @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1232]) ).
thf(1754,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1231]) ).
thf(1755,plain,
( ( ! [V_c: $i,T_a: $i,T_b: $i,V_A: $i] :
( ( ( c_Set_Oimage @ ( c_COMBK @ V_c @ T_a @ T_b ) @ V_A @ T_b @ T_a )
= ( c_Set_Oinsert @ V_c @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
| ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1230]) ).
thf(1756,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i,V_D: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ V_C @ V_D @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_D @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1229]) ).
thf(1757,plain,
( ( ! [V_x: $i,V_B: $i,T_a: $i] :
( ~ ( c_in @ V_x @ V_B @ T_a )
| ! [V_A: $i] :
( ~ ( c_in @ V_x @ V_A @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1577]) ).
thf(1758,plain,
( ( ! [V_r: $i,V_s: $i,T_a: $i] :
( ( c_Relation_Otrans @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
| ~ ( c_Relation_Otrans @ V_s @ T_a )
| ~ ( c_Relation_Otrans @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1227]) ).
thf(1759,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_y: $i,V_z: $i] : ( c_lessequals @ ( 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 ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1576]) ).
thf(1760,plain,
( ( ! [V_A: $i,V_C: $i,T_a: $i,V_B: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1225]) ).
thf(1761,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)],[1575]) ).
thf(1762,plain,
( ( ! [V_B: $i,V_C: $i,T_a: $i] :
( ( ( c_Relation_Orel__comp @ V_B @ V_C @ T_a @ T_a @ T_a )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) )
| ! [V_A: $i] :
( ( ( c_Relation_Orel__comp @ V_A @ V_C @ T_a @ T_a @ T_a )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) )
| ( ( c_Relation_Orel__comp @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ V_C @ T_a @ T_a @ T_a )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1574]) ).
thf(1763,plain,
( ( ! [V_A: $i,V_C: $i,T_a: $i] :
( ( ( c_Relation_Orel__comp @ V_A @ V_C @ T_a @ T_a @ T_a )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) )
| ! [V_B: $i] :
( ( ( c_Relation_Orel__comp @ V_A @ V_B @ T_a @ T_a @ T_a )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) )
| ( ( c_Relation_Orel__comp @ V_A @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a @ T_a @ T_a )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1573]) ).
thf(1764,plain,
( ( ! [V_P: $i,V_xb: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_xb ) )
| ! [V_r: $i,T_a: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1 @ V_P @ V_r @ T_a ) ) )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1572]) ).
thf(1765,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Wellfounded_Oacyclic @ V_r @ T_a )
| ~ ( c_Wellfounded_Oacyclic @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1220]) ).
thf(1766,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Wellfounded_Oacyclic @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a )
| ~ ( c_Wellfounded_Oacyclic @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1219]) ).
thf(1767,plain,
( ( ! [V_A: $i,V_B: $i] :
( ( V_A = V_B )
| ! [T_a: $i] :
( ~ ( c_lessequals @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1571]) ).
thf(1768,plain,
( ( ! [V_A: $i,V_B: $i] :
( ( V_A = V_B )
| ! [T_a: $i] :
( ~ ( c_lessequals @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1570]) ).
thf(1769,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( V_x = V_y )
| ~ ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1569]) ).
thf(1770,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( V_x = V_y )
| ~ ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1568]) ).
thf(1771,plain,
( ( ! [V_P: $i,T_b: $i,T_c: $i,T_a: $i,V_z: $i] :
( ( hAPP @ ( c_split @ V_P @ T_b @ T_c @ T_a ) @ V_z )
= ( hAPP @ ( hAPP @ V_P @ ( hAPP @ ( c_fst @ T_b @ T_c ) @ V_z ) ) @ ( hAPP @ ( c_snd @ T_b @ T_c ) @ V_z ) ) ) )
= $true ),
inference(copy,[status(thm)],[1214]) ).
thf(1772,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( V_x = V_y )
| ~ ( c_lessequals @ V_x @ V_y @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1567]) ).
thf(1773,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)],[1566]) ).
thf(1774,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= V_A ) )
= $true ),
inference(copy,[status(thm)],[1211]) ).
thf(1775,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 )
= V_x )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1565]) ).
thf(1776,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 )
!= V_y )
| ( c_lessequals @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1564]) ).
thf(1777,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 )
= V_y )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1563]) ).
thf(1778,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= V_B )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1207]) ).
thf(1779,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= V_A )
| ~ ( c_lessequals @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1206]) ).
thf(1780,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
!= V_B )
| ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1562]) ).
thf(1781,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_r: $i,V_s: $i] :
( ( c_Relation_Orefl__on @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
| ~ ( c_Relation_Orefl__on @ V_B @ V_s @ T_a )
| ~ ( c_Relation_Orefl__on @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1204]) ).
thf(1782,plain,
( ( ! [T_a: $i] : ( c_Relation_Oantisym @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a ) )
= $true ),
inference(copy,[status(thm)],[1203]) ).
thf(1783,plain,
( ( ! [T_b: $i,T_a: $i] :
( ( c_Relation_ORange @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_b @ T_a ) @ tc_bool ) ) @ T_b @ T_a )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1202]) ).
thf(1784,plain,
( ( ! [V_a: $i,V_b: $i,T_a: $i,V_c: $i,V_d: $i] :
( ( ( c_Set_Oinsert @ V_a @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a )
!= ( c_Set_Oinsert @ V_c @ ( c_Set_Oinsert @ V_d @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) )
| ( V_a = V_d )
| ( V_a = V_c ) ) )
= $true ),
inference(copy,[status(thm)],[1561]) ).
thf(1785,plain,
( ( ! [V_a: $i,V_b: $i,T_a: $i,V_c: $i] :
( ! [V_d: $i] :
( ( c_Set_Oinsert @ V_a @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a )
!= ( c_Set_Oinsert @ V_c @ ( c_Set_Oinsert @ V_d @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) )
| ( V_b = V_c )
| ( V_a = V_c ) ) )
= $true ),
inference(copy,[status(thm)],[1560]) ).
thf(1786,plain,
( ( ! [V_a: $i,V_b: $i,T_a: $i,V_c: $i,V_d: $i] :
( ( ( c_Set_Oinsert @ V_a @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a )
!= ( c_Set_Oinsert @ V_c @ ( c_Set_Oinsert @ V_d @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) )
| ( V_a = V_d )
| ( V_b = V_d ) ) )
= $true ),
inference(copy,[status(thm)],[1559]) ).
thf(1787,plain,
( ( ! [V_a: $i,V_b: $i,T_a: $i,V_c: $i,V_d: $i] :
( ( ( c_Set_Oinsert @ V_a @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a )
!= ( c_Set_Oinsert @ V_c @ ( c_Set_Oinsert @ V_d @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) )
| ( V_b = V_c )
| ( V_b = V_d ) ) )
= $true ),
inference(copy,[status(thm)],[1558]) ).
thf(1788,plain,
( ( ! [V_r: $i,T_a: $i,V_A: $i] :
( ( c_lessequals @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_A @ ( tc_fun @ T_a @ tc_bool ) @ T_a ) @ T_a @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_lessequals @ V_r @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_A @ ( tc_fun @ T_a @ tc_bool ) @ T_a ) @ T_a @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1197]) ).
thf(1789,plain,
( ( ! [V_r: $i,T_a: $i,V_s: $i] :
( ( c_lessequals @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_s @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_lessequals @ V_r @ ( c_Transitive__Closure_Ortrancl @ V_s @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1196]) ).
thf(1790,plain,
( ( ! [V_A: $i,T_a: $i] :
( ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( c_lessequals @ V_A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1195]) ).
thf(1791,plain,
( ( ! [T_a: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(copy,[status(thm)],[1194]) ).
thf(1792,plain,
( ( ! [T_a: $i,V_a: $i,V_A: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Set_Oinsert @ V_a @ V_A @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1557]) ).
thf(1793,plain,
( ( ! [T_a: $i] : ( c_Relation_Orefl__on @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a ) )
= $true ),
inference(copy,[status(thm)],[1192]) ).
thf(1794,plain,
( ( ! [V_a: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Set_Oinsert @ V_a @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
| ~ ( c_in @ V_a @ V_C @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1191]) ).
thf(1795,plain,
( ( ! [V_A: $i,V_a: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Set_Oinsert @ V_a @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
| ~ ( c_in @ V_a @ V_A @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1190]) ).
thf(1796,plain,
( ( ! [V_f: $i,V_a: $i,V_B: $i,T_b: $i,T_a: $i] :
( ( c_Set_Oimage @ V_f @ ( c_Set_Oinsert @ V_a @ V_B @ T_b ) @ T_b @ T_a )
= ( c_Set_Oinsert @ ( hAPP @ V_f @ V_a ) @ ( c_Set_Oimage @ V_f @ V_B @ T_b @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1189]) ).
thf(1797,plain,
( ( ! [T_a: $i,V_r: $i] : ( c_Relation_Ototal__on @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ V_r @ T_a ) )
= $true ),
inference(copy,[status(thm)],[1188]) ).
thf(1798,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i,V_D: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_C @ V_D @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_B @ V_D @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1187]) ).
thf(1799,plain,
( ( ! [V_r: $i,V_s: $i,T_b: $i,T_a: $i] :
( ( c_Relation_Oconverse @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_b @ T_a ) @ tc_bool ) ) @ T_b @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Oconverse @ V_r @ T_b @ T_a ) @ ( c_Relation_Oconverse @ V_s @ T_b @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1186]) ).
thf(1800,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_x: $i,V_y: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1556]) ).
thf(1801,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_x: $i,V_y: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1555]) ).
thf(1802,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_y: $i,V_z: $i] :
( ( c_lessequals @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1554]) ).
thf(1803,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_y: $i,V_z: $i] :
( ( c_lessequals @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1553]) ).
thf(1804,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_a: $i,V_b: $i] :
( ( c_lessequals @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_b @ T_a )
| ~ ( c_lessequals @ V_x @ V_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1552]) ).
thf(1805,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_x: $i,V_y: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1551]) ).
thf(1806,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_x: $i,V_y: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1550]) ).
thf(1807,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(copy,[status(thm)],[1178]) ).
thf(1808,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(copy,[status(thm)],[1177]) ).
thf(1809,plain,
( ( ! [V_C: $i,V_A: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_C @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_C @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1176]) ).
thf(1810,plain,
( ( ! [V_C: $i,V_A: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_C @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_C @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1175]) ).
thf(1811,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i,T_b: $i] :
( ( c_Product__Type_OSigma @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_COMBK @ V_C @ ( tc_fun @ T_b @ tc_bool ) @ T_a ) @ T_a @ T_b )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_C @ ( tc_fun @ T_b @ tc_bool ) @ T_a ) @ T_a @ T_b ) @ ( c_Product__Type_OSigma @ V_B @ ( c_COMBK @ V_C @ ( tc_fun @ T_b @ tc_bool ) @ T_a ) @ T_a @ T_b ) @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1174]) ).
thf(1812,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_y: $i,V_z: $i] : ( c_lessequals @ ( 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 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1549]) ).
thf(1813,plain,
( ( ! [V_S: $i,T_a: $i,V_R: $i] :
( ( ( c_Transitive__Closure_Ortrancl @ V_S @ T_a )
= ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) )
| ~ ( c_lessequals @ V_S @ ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_lessequals @ V_R @ V_S @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1172]) ).
thf(1814,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(copy,[status(thm)],[1171]) ).
thf(1815,plain,
( ( ! [V_a: $i,V_A: $i,T_a: $i] :
( ( c_Set_Oinsert @ V_a @ ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
= ( c_Set_Oinsert @ V_a @ V_A @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1170]) ).
thf(1816,plain,
( ( ! [V_a: $i,T_a: $i,V_b: $i] :
( ( ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
!= ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
| ( V_a = V_b ) ) )
= $true ),
inference(copy,[status(thm)],[1548]) ).
thf(1817,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1168]) ).
thf(1818,plain,
( ( ! [T_a: $i] :
( ( c_Relation_OId__on @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1167]) ).
thf(1819,plain,
( ( ! [V_c: $i,T_a: $i,T_b: $i] :
( ( c_Set_Oimage @ ( c_COMBK @ V_c @ T_a @ T_b ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b @ T_a )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1166]) ).
thf(1820,plain,
( ( ! [V_x: $i,V_xa: $i,T_a: $i] :
( ( ( c_Set_Oinsert @ V_x @ V_xa @ T_a )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( c_in @ V_x @ V_xa @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1547]) ).
thf(1821,plain,
( ( ! [T_a: $i] : ( c_Wellfounded_Owf @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a ) )
= $true ),
inference(copy,[status(thm)],[1164]) ).
thf(1822,plain,
( ( ! [V_x: $i,V_B: $i,T_a: $i] :
( ( c_in @ V_x @ V_B @ T_a )
| ! [V_A: $i] :
~ ( c_lessequals @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1546]) ).
thf(1823,plain,
( ( ! [V_I: $i,V_J: $i,T_a: $i,V_C: $i,T_b: $i] :
( ( c_Product__Type_OSigma @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_I @ V_J @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ T_a @ T_b )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Product__Type_OSigma @ V_I @ V_C @ T_a @ T_b ) @ ( c_Product__Type_OSigma @ V_J @ V_C @ T_a @ T_b ) @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1162]) ).
thf(1824,plain,
( ( ! [V_y: $i,V_A: $i,T_a: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ V_y @ V_A @ T_a ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ V_A @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[1161]) ).
thf(1825,plain,
( ( ! [V_A: $i,V_x: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ( c_in @ V_x @ V_A @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1160]) ).
thf(1826,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ! [V_x: $i] :
( ( c_in @ V_x @ V_A @ T_a )
| ~ ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1545]) ).
thf(1827,plain,
( ( ! [V_A: $i,V_x: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ( c_in @ V_x @ V_A @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1158]) ).
thf(1828,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ! [V_x: $i] :
( ~ ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ( c_in @ V_x @ V_A @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1544]) ).
thf(1829,plain,
( ( ! [V_r: $i,V_s: $i,T_b: $i,T_a: $i] :
( ( c_Relation_Oconverse @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_b @ T_a ) @ tc_bool ) ) @ T_b @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_Oconverse @ V_r @ T_b @ T_a ) @ ( c_Relation_Oconverse @ V_s @ T_b @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1156]) ).
thf(1830,plain,
( ( ! [V_A: $i,V_a: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( c_in @ V_a @ V_A @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1155]) ).
thf(1831,plain,
( ( ! [V_a: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( c_in @ V_a @ V_C @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1154]) ).
thf(1832,plain,
( ( ! [V_A: $i,V_r: $i,T_a: $i] :
( ( c_Relation_Ototal__on @ V_A @ V_r @ T_a )
| ~ ( c_Order__Relation_Ostrict__linear__order__on @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1153]) ).
thf(1833,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( V_B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1543]) ).
thf(1834,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1542]) ).
thf(1835,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ! [V_A: $i] :
( ! [V_B: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ T_a )
!= ( c_Orderings_Obot__class_Obot @ T_a ) )
| ( V_A
= ( c_Orderings_Obot__class_Obot @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1541]) ).
thf(1836,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ! [V_A: $i,V_B: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ T_a )
!= ( c_Orderings_Obot__class_Obot @ T_a ) )
| ( V_B
= ( c_Orderings_Obot__class_Obot @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1540]) ).
thf(1837,plain,
( ( ! [V_B: $i,V_A: $i,T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1148]) ).
thf(1838,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ ( c_HOL_Ominus__class_Ominus @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1147]) ).
thf(1839,plain,
( ( ! [V_S: $i,V_T: $i,T_a: $i,T_c: $i,V_R: $i,T_b: $i] :
( ( c_Relation_Orel__comp @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_S @ V_T @ ( tc_fun @ ( tc_prod @ T_a @ T_c ) @ tc_bool ) ) @ V_R @ T_a @ T_c @ T_b )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ V_S @ V_R @ T_a @ T_c @ T_b ) @ ( c_Relation_Orel__comp @ V_T @ V_R @ T_a @ T_c @ T_b ) @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1146]) ).
thf(1840,plain,
( ( ! [V_R: $i,V_S: $i,V_T: $i,T_c: $i,T_b: $i,T_a: $i] :
( ( c_Relation_Orel__comp @ V_R @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_S @ V_T @ ( tc_fun @ ( tc_prod @ T_c @ T_b ) @ tc_bool ) ) @ T_a @ T_c @ T_b )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ V_R @ V_S @ T_a @ T_c @ T_b ) @ ( c_Relation_Orel__comp @ V_R @ V_T @ T_a @ T_c @ T_b ) @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1145]) ).
thf(1841,plain,
( ( ! [V_C: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_C @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ! [V_A: $i] :
~ ( c_lessequals @ V_C @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1539]) ).
thf(1842,plain,
( ( ! [V_C: $i,V_A: $i,T_a: $i] :
( ( c_lessequals @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
| ! [V_B: $i] :
~ ( c_lessequals @ V_C @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1538]) ).
thf(1843,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_a: $i] :
( ( c_lessequals @ V_x @ V_a @ T_a )
| ! [V_b: $i] :
~ ( c_lessequals @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_a @ V_b @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1537]) ).
thf(1844,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_b: $i] :
( ( c_lessequals @ V_x @ V_b @ T_a )
| ! [V_a: $i] :
~ ( c_lessequals @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_a @ V_b @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1536]) ).
thf(1845,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_b: $i,V_x: $i] :
( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_a @ V_b @ T_a ) @ V_x @ T_a )
| ~ ( c_lessequals @ V_a @ V_x @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1535]) ).
thf(1846,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_b: $i,V_x: $i] :
( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_a @ V_b @ T_a ) @ V_x @ T_a )
| ~ ( c_lessequals @ V_b @ V_x @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1534]) ).
thf(1847,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_y: $i] :
( ( c_lessequals @ V_x @ V_y @ T_a )
| ! [V_z: $i] :
~ ( c_lessequals @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1533]) ).
thf(1848,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_z: $i] :
( ( c_lessequals @ V_x @ V_z @ T_a )
| ! [V_y: $i] :
~ ( c_lessequals @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1532]) ).
thf(1849,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1136]) ).
thf(1850,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1135]) ).
thf(1851,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)],[1531]) ).
thf(1852,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)],[1530]) ).
thf(1853,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,T_b: $i] :
( ( c_Relation_ODomain @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) @ T_a @ T_b )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_ODomain @ V_A @ T_a @ T_b ) @ ( c_Relation_ODomain @ V_B @ T_a @ T_b ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1132]) ).
thf(1854,plain,
( ( ! [V_a: $i,V_A: $i,T_a: $i] :
( ( c_Set_Oinsert @ V_a @ V_A @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1131]) ).
thf(1855,plain,
( ( ! [T_a: $i,V_B: $i,T_b: $i] :
( ( c_Product__Type_OSigma @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ T_a @ T_b )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1130]) ).
thf(1856,plain,
( ( ! [V_R2: $i,T_a: $i,V_R1: $i] :
( ( c_lessequals @ ( c_Wellfounded_Oacc @ V_R2 @ T_a ) @ ( c_Wellfounded_Oacc @ V_R1 @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_R1 @ V_R2 @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1129]) ).
thf(1857,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1128]) ).
thf(1858,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)],[1529]) ).
thf(1859,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)],[1528]) ).
thf(1860,plain,
( ( ! [V_r: $i,T_a: $i,T_b: $i] :
( ( ( c_Relation_ODomain @ V_r @ T_a @ T_b )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( V_r
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1527]) ).
thf(1861,plain,
( ( ! [T_a: $i,V_f: $i,T_b: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Set_Oimage @ V_f @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1124]) ).
thf(1862,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_HOL_Ominus__class_Ominus @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1123]) ).
thf(1863,plain,
( ( ! [V_A: $i,V_B: $i,T_b: $i,T_a: $i] : ( c_lessequals @ ( c_Relation_ORange @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ ( tc_prod @ T_b @ T_a ) @ tc_bool ) ) @ T_b @ T_a ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_ORange @ V_A @ T_b @ T_a ) @ ( c_Relation_ORange @ V_B @ T_b @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(copy,[status(thm)],[1122]) ).
thf(1864,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__Xwf__induct__rule__1__1 @ V_P @ V_r @ T_a ) ) )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1526]) ).
thf(1865,plain,
( ( ! [V_R: $i,T_a: $i,V_S: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_S @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
= ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_R @ V_S @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1120]) ).
thf(1866,plain,
( ( ! [V_x: $i,V_A: $i,T_a: $i,V_B: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Set_Oinsert @ V_x @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
| ( c_in @ V_x @ V_B @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1119]) ).
thf(1867,plain,
( ( ! [V_A: $i,V_x: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1118]) ).
thf(1868,plain,
( ( ! [V_B: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_B @ V_x ) )
| ! [V_A: $i,T_a: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[1525]) ).
thf(1869,plain,
( ( ! [V_A: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_A @ V_x ) )
| ! [V_B: $i,T_a: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[1524]) ).
thf(1870,plain,
( ( ! [V_a: $i,V_b: $i,T_b: $i,T_a: $i,V_r: $i] :
( ( c_Relation_ORange @ ( c_Set_Oinsert @ ( c_Pair @ V_a @ V_b @ T_b @ T_a ) @ V_r @ ( tc_prod @ T_b @ T_a ) ) @ T_b @ T_a )
= ( c_Set_Oinsert @ V_b @ ( c_Relation_ORange @ V_r @ T_b @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1115]) ).
thf(1871,plain,
( ( ! [V_r: $i,V_s: $i,T_a: $i] :
( ( c_Relation_Osym @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
| ~ ( c_Relation_Osym @ V_s @ T_a )
| ~ ( c_Relation_Osym @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1114]) ).
thf(1872,plain,
( ( ! [V_x: $i,V_A: $i,T_a: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
= V_A )
| ( c_in @ V_x @ V_A @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1113]) ).
thf(1873,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1112]) ).
thf(1874,plain,
( ( ! [V_A: $i,V_B: $i,V_C: $i,T_a: $i] :
( ( c_lessequals @ V_A @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1111]) ).
thf(1875,plain,
( ( ! [V_f: $i,V_g: $i,V_r: $i,V_x: $i,T_a: $i,T_b: $i] :
( ( ( hAPP @ V_f @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ V_f @ V_g @ V_r @ V_x @ T_a @ T_b ) )
!= ( hAPP @ V_g @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ V_f @ V_g @ V_r @ V_x @ T_a @ T_b ) ) )
| ( ( c_Recdef_Ocut @ V_f @ V_r @ V_x @ T_a @ T_b )
= ( c_Recdef_Ocut @ V_g @ V_r @ V_x @ T_a @ T_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[1523]) ).
thf(1876,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Wellfounded_Oacyclic @ V_r @ T_a )
| ! [V_y: $i,V_x: $i] :
~ ( c_Wellfounded_Oacyclic @ ( c_Set_Oinsert @ ( c_Pair @ V_y @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1522]) ).
thf(1877,plain,
( ( ! [T_b: $i,V_f: $i,V_x: $i] :
( ~ ( class_HOL_Oord @ T_b )
| ! [V_g: $i] :
( ( c_lessequals @ ( hAPP @ V_f @ V_x ) @ ( hAPP @ V_g @ V_x ) @ T_b )
| ! [T_a: $i] :
~ ( c_lessequals @ V_f @ V_g @ ( tc_fun @ T_a @ T_b ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1521]) ).
thf(1878,plain,
( ( ! [V_c: $i,V_A: $i,V_B: $i,T_a: $i] :
( ( c_in @ V_c @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
| ~ ( c_in @ V_c @ V_B @ T_a )
| ~ ( c_in @ V_c @ V_A @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1107]) ).
thf(1879,plain,
( ( ! [V_c: $i,V_A: $i,V_B: $i,T_a: $i] :
( ( c_in @ V_c @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
| ~ ( c_in @ V_c @ V_B @ T_a )
| ~ ( c_in @ V_c @ V_A @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1106]) ).
thf(1880,plain,
( ( ! [V_a: $i,V_b: $i,V_A: $i,T_a: $i] :
( ( c_in @ V_a @ ( c_Set_Oinsert @ V_b @ V_A @ T_a ) @ T_a )
| ~ ( c_in @ V_a @ V_A @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1105]) ).
thf(1881,plain,
( ( ! [V_a: $i,V_b: $i,V_B: $i,T_a: $i] :
( ( c_in @ V_a @ ( c_Set_Oinsert @ V_b @ V_B @ T_a ) @ T_a )
| ~ ( c_in @ V_a @ V_B @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1104]) ).
thf(1882,plain,
( ( ! [V_t: $i,V_B: $i,T_a: $i] :
( ( c_in @ V_t @ V_B @ T_a )
| ! [V_A: $i] :
( ~ ( c_in @ V_t @ V_A @ T_a )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1520]) ).
thf(1883,plain,
( ( ! [V_x: $i,V_B: $i,T_a: $i] :
( ( c_in @ V_x @ V_B @ T_a )
| ! [V_A: $i] :
( ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_in @ V_x @ V_A @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1519]) ).
thf(1884,plain,
( ( ! [V_c: $i,V_B: $i,T_a: $i] :
( ( c_in @ V_c @ V_B @ T_a )
| ! [V_A: $i] :
( ~ ( c_in @ V_c @ V_A @ T_a )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1518]) ).
thf(1885,plain,
( ( ! [V_x: $i,V_B: $i,T_a: $i] :
( ( c_in @ V_x @ V_B @ T_a )
| ! [V_A: $i] :
( ~ ( c_in @ V_x @ V_A @ T_a )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1517]) ).
thf(1886,plain,
( ( ! [V_c: $i,V_A: $i,V_B: $i,T_a: $i] :
( ( c_in @ V_c @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
| ~ ( c_in @ V_c @ V_A @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1099]) ).
thf(1887,plain,
( ( ! [V_c: $i,V_A: $i,V_B: $i,T_a: $i] :
( ( c_in @ V_c @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
| ~ ( c_in @ V_c @ V_B @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1098]) ).
thf(1888,plain,
( ( ! [V_x: $i,T_a: $i] :
~ ( c_in @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
= $true ),
inference(copy,[status(thm)],[1097]) ).
thf(1889,plain,
( ( ! [V_P: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ! [T_a: $i] :
~ ( c_in @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1516]) ).
thf(1890,plain,
( ( ! [V_c: $i,T_a: $i] :
~ ( c_in @ V_c @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
= $true ),
inference(copy,[status(thm)],[1095]) ).
thf(1891,plain,
( ( ! [V_a: $i,T_a: $i] :
~ ( c_in @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
= $true ),
inference(copy,[status(thm)],[1094]) ).
thf(1892,plain,
( ( ! [V_a: $i,V_A: $i,T_a: $i] :
( ( c_in @ V_a @ V_A @ T_a )
| ! [V_b: $i] :
( ( V_a = V_b )
| ~ ( c_in @ V_a @ ( c_Set_Oinsert @ V_b @ V_A @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1515]) ).
thf(1893,plain,
( ( ! [V_c: $i,V_B: $i,T_a: $i] :
( ( c_in @ V_c @ V_B @ T_a )
| ! [V_A: $i] :
( ( c_in @ V_c @ V_A @ T_a )
| ~ ( c_in @ V_c @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1514]) ).
thf(1894,plain,
( ( ! [V_c: $i,V_B: $i,T_a: $i] :
( ~ ( c_in @ V_c @ V_B @ T_a )
| ! [V_A: $i] :
~ ( c_in @ V_c @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1513]) ).
thf(1895,plain,
( ( ! [V_c: $i,V_A: $i,T_a: $i] :
( ( c_in @ V_c @ V_A @ T_a )
| ! [V_B: $i] :
~ ( c_in @ V_c @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1512]) ).
thf(1896,plain,
( ( ! [V_x: $i,V_A: $i,T_a: $i] : ( c_in @ V_x @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ T_a ) )
= $true ),
inference(copy,[status(thm)],[1089]) ).
thf(1897,plain,
( ( ! [V_a: $i,V_B: $i,T_a: $i] : ( c_in @ V_a @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ T_a ) )
= $true ),
inference(copy,[status(thm)],[1088]) ).
thf(1898,plain,
( ( ! [V_x: $i,V_B: $i,T_a: $i] : ( c_in @ V_x @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ T_a ) )
= $true ),
inference(copy,[status(thm)],[1087]) ).
thf(1899,plain,
( ( ! [V_c: $i,V_B: $i,T_a: $i] :
( ( c_in @ V_c @ V_B @ T_a )
| ! [V_A: $i] :
~ ( c_in @ V_c @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1511]) ).
thf(1900,plain,
( ( ! [V_c: $i,V_A: $i,T_a: $i] :
( ( c_in @ V_c @ V_A @ T_a )
| ! [V_B: $i] :
~ ( c_in @ V_c @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1510]) ).
thf(1901,plain,
( ( ! [V_P: $i,V_x: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ! [T_a: $i] :
~ ( c_in @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1509]) ).
thf(1902,plain,
( ( ! [V_c: $i,V_A: $i,V_B: $i,T_a: $i] :
( ( c_in @ V_c @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
| ( c_in @ V_c @ V_B @ T_a )
| ~ ( c_in @ V_c @ V_A @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1083]) ).
thf(1903,plain,
( ( ! [V_c: $i,V_A: $i,V_B: $i,T_a: $i] :
( ( c_in @ V_c @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
| ( c_in @ V_c @ V_B @ T_a )
| ~ ( c_in @ V_c @ V_A @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1082]) ).
thf(1904,plain,
( ( ! [V_x: $i,V_A: $i,T_a: $i,V_B: $i] :
( ( ( c_Set_Oinsert @ V_x @ V_A @ T_a )
!= ( c_Set_Oinsert @ V_x @ V_B @ T_a ) )
| ( c_in @ V_x @ V_B @ T_a )
| ( V_A = V_B )
| ( c_in @ V_x @ V_A @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1508]) ).
thf(1905,plain,
( ( ! [V_a: $i,V_A: $i,T_a: $i] :
( ( ( c_Set_Oinsert @ V_a @ V_A @ T_a )
= V_A )
| ~ ( c_in @ V_a @ V_A @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1080]) ).
thf(1906,plain,
( ( ! [T_a: $i,T_b: $i,V_a: $i,V_b: $i] :
( ( hAPP @ ( c_fst @ T_a @ T_b ) @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) )
= V_a ) )
= $true ),
inference(copy,[status(thm)],[1079]) ).
thf(1907,plain,
( ( ! [V_x: $i,T_a: $i,T_b: $i,V_y: $i] :
( V_x
= ( hAPP @ ( c_fst @ T_a @ T_b ) @ ( c_Pair @ V_x @ V_y @ T_a @ T_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[1078]) ).
thf(1908,plain,
( ( ! [T_b: $i,T_a: $i,V_a: $i,V_b: $i] :
( ( hAPP @ ( c_snd @ T_b @ T_a ) @ ( c_Pair @ V_a @ V_b @ T_b @ T_a ) )
= V_b ) )
= $true ),
inference(copy,[status(thm)],[1077]) ).
thf(1909,plain,
( ( ! [V_y: $i,T_b: $i,T_a: $i,V_x: $i] :
( V_y
= ( hAPP @ ( c_snd @ T_b @ T_a ) @ ( c_Pair @ V_x @ V_y @ T_b @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1076]) ).
thf(1910,plain,
( ( ! [V_P: $i,T_a: $i,T_b: $i,V_p: $i,V_q: $i] :
( ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ ( c_fst @ T_a @ T_b ) @ ( c_Pair @ V_p @ V_q @ T_a @ T_b ) ) ) )
| ! [V_Q: $i] :
~ ( hBOOL @ ( hAPP @ V_Q @ V_q ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_p ) ) ) )
= $true ),
inference(copy,[status(thm)],[1507]) ).
thf(1911,plain,
( ( ! [V_Q: $i,T_a: $i,T_b: $i,V_p: $i,V_q: $i] :
( ( hBOOL @ ( hAPP @ V_Q @ ( hAPP @ ( c_snd @ T_a @ T_b ) @ ( c_Pair @ V_p @ V_q @ T_a @ T_b ) ) ) )
| ~ ( hBOOL @ ( hAPP @ V_Q @ V_q ) )
| ! [V_P: $i] :
~ ( hBOOL @ ( hAPP @ V_P @ V_p ) ) ) )
= $true ),
inference(copy,[status(thm)],[1506]) ).
thf(1912,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)],[1505]) ).
thf(1913,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)],[1504]) ).
thf(1914,plain,
( ( ! [V_A: $i,V_B: $i,V_C: $i,T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1071]) ).
thf(1915,plain,
( ( ! [V_B: $i,V_C: $i,T_a: $i,V_A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1070]) ).
thf(1916,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Relation_Otrans @ V_r @ T_a )
| ! [V_A: $i] :
~ ( c_Order__Relation_Ostrict__linear__order__on @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1503]) ).
thf(1917,plain,
( ( ! [V_x: $i,V_A: $i,T_a: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ V_x ) ) )
= $true ),
inference(copy,[status(thm)],[1068]) ).
thf(1918,plain,
( ( ! [V_x: $i,V_A: $i,T_a: $i,V_B: $i] :
( ( c_lessequals @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_in @ V_x @ V_B @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1067]) ).
thf(1919,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i,T_b: $i] :
( ( c_Product__Type_OSigma @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_COMBK @ V_C @ ( tc_fun @ T_b @ tc_bool ) @ T_a ) @ T_a @ T_b )
= ( c_HOL_Ominus__class_Ominus @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_C @ ( tc_fun @ T_b @ tc_bool ) @ T_a ) @ T_a @ T_b ) @ ( c_Product__Type_OSigma @ V_B @ ( c_COMBK @ V_C @ ( tc_fun @ T_b @ tc_bool ) @ T_a ) @ T_a @ T_b ) @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1066]) ).
thf(1920,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)],[1502]) ).
thf(1921,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)],[1501]) ).
thf(1922,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1063]) ).
thf(1923,plain,
( ( ! [V_A: $i,V_B: $i,T_b: $i,T_a: $i] :
( ( c_Relation_ORange @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ ( tc_prod @ T_b @ T_a ) @ tc_bool ) ) @ T_b @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_ORange @ V_A @ T_b @ T_a ) @ ( c_Relation_ORange @ V_B @ T_b @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1062]) ).
thf(1924,plain,
( ( ! [V_r: $i,V_r_H: $i,T_a: $i] :
( ( c_Wellfounded_Owf @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_r @ V_r_H @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1061]) ).
thf(1925,plain,
( ( ! [V_r_H: $i,V_r: $i,T_a: $i] :
( ( c_Wellfounded_Owf @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_r_H @ V_r @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1060]) ).
thf(1926,plain,
( ( ! [V_a: $i,V_A: $i,T_a: $i] :
( ( ( c_Set_Oinsert @ V_a @ ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
= V_A )
| ~ ( c_in @ V_a @ V_A @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1059]) ).
thf(1927,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)],[1500]) ).
thf(1928,plain,
( ( ! [V_A: $i,T_a: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
= V_A ) )
= $true ),
inference(copy,[status(thm)],[1057]) ).
thf(1929,plain,
( ( ! [T_a: $i,V_y: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_z: $i] :
( ( c_lessequals @ V_y @ V_z @ T_a )
| ! [V_x: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ V_z @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1499]) ).
thf(1930,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_z: $i] :
( ( c_lessequals @ V_x @ V_z @ T_a )
| ! [V_y: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ V_z @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1498]) ).
thf(1931,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_a: $i,V_b: $i] :
( ( c_lessequals @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_b @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1497]) ).
thf(1932,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_a: $i] :
( ! [V_b: $i] : ( c_lessequals @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1496]) ).
thf(1933,plain,
( ( ! [T_a: $i,V_b: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_x: $i] :
( ( c_lessequals @ V_b @ V_x @ T_a )
| ! [V_a: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) @ V_x @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1495]) ).
thf(1934,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_x: $i] :
( ( c_lessequals @ V_a @ V_x @ T_a )
| ! [V_b: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) @ V_x @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1494]) ).
thf(1935,plain,
( ( ! [V_A: $i,V_C: $i,T_a: $i] :
( ( c_lessequals @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ! [V_B: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1493]) ).
thf(1936,plain,
( ( ! [V_B: $i,V_C: $i,T_a: $i] :
( ( c_lessequals @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ! [V_A: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1492]) ).
thf(1937,plain,
( ( ! [T_a: $i,V_z: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_x: $i] :
( ( c_lessequals @ V_z @ V_x @ T_a )
| ! [V_y: $i] :
( ~ ( c_lessequals @ V_z @ V_y @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1491]) ).
thf(1938,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ! [V_z: $i] :
( ( c_lessequals @ V_x @ V_z @ T_a )
| ! [V_y: $i] :
( ~ ( c_lessequals @ V_y @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1490]) ).
thf(1939,plain,
( ( ! [V_x: $i,T_a: $i] : ( c_lessequals @ V_x @ V_x @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(copy,[status(thm)],[1046]) ).
thf(1940,plain,
( ( ! [V_A: $i,T_a: $i] : ( c_lessequals @ V_A @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(copy,[status(thm)],[1045]) ).
thf(1941,plain,
( ( ! [V_A: $i,V_C: $i,T_a: $i] :
( ( c_lessequals @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ! [V_B: $i] :
( ~ ( c_lessequals @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1489]) ).
thf(1942,plain,
( ( ! [V_Q: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_Q @ V_x ) )
| ! [V_P: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ! [T_a: $i] :
~ ( c_lessequals @ V_P @ V_Q @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1488]) ).
thf(1943,plain,
( ( ! [V_p: $i,T_a: $i] :
( ( c_Wellfounded_Owf @ V_p @ T_a )
| ! [V_r: $i] :
( ~ ( c_lessequals @ V_p @ V_r @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1487]) ).
thf(1944,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_x: $i] : ( c_lessequals @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1486]) ).
thf(1945,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ! [V_x: $i] : ( c_lessequals @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1485]) ).
thf(1946,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Relation_Oantisym @ V_r @ T_a )
| ! [V_s: $i] :
( ~ ( c_Relation_Oantisym @ V_s @ T_a )
| ~ ( c_lessequals @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1484]) ).
thf(1947,plain,
( ( ! [V_Q: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_Q @ V_x ) )
| ! [V_P: $i] :
( ! [T_a: $i] :
~ ( c_lessequals @ V_P @ V_Q @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1483]) ).
thf(1948,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Wellfounded_Oacyclic @ V_r @ T_a )
| ! [V_s: $i] :
( ~ ( c_lessequals @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_Wellfounded_Oacyclic @ V_s @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1482]) ).
thf(1949,plain,
( ( ! [V_r: $i,T_a: $i,T_b: $i] :
( ( c_Relation_Osingle__valued @ V_r @ T_a @ T_b )
| ! [V_s: $i] :
( ~ ( c_Relation_Osingle__valued @ V_s @ T_a @ T_b )
| ~ ( c_lessequals @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1481]) ).
thf(1950,plain,
( ( ! [V_f: $i,V_A: $i,T_b: $i] :
( ! [T_a: $i] :
( ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1480]) ).
thf(1951,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i,V_D: $i] :
( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_C @ V_D @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_B @ V_D @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1034]) ).
thf(1952,plain,
( ( ! [V_A: $i,V_B: $i,V_C: $i,T_a: $i] :
( ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1033]) ).
thf(1953,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_HOL_Ominus__class_Ominus @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1032]) ).
thf(1954,plain,
( ( ! [V_x: $i,T_a: $i] : ( c_in @ V_x @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) )
= $true ),
inference(copy,[status(thm)],[1031]) ).
thf(1955,plain,
( ( ! [V_r: $i,T_a: $i,T_b: $i,V_s: $i] :
( ( c_lessequals @ ( c_Relation_ODomain @ V_r @ T_a @ T_b ) @ ( c_Relation_ODomain @ V_s @ T_a @ T_b ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1030]) ).
thf(1956,plain,
( ( ! [V_A: $i,V_x: $i,T_a: $i] :
( ( V_A
= ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
| ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1029]) ).
thf(1957,plain,
( ( ! [V_A: $i,V_B: $i,V_C: $i,T_a: $i] :
( ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1028]) ).
thf(1958,plain,
( ( ! [V_A: $i,T_b: $i,T_a: $i] :
( ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) @ ( tc_fun @ T_b @ tc_bool ) @ T_a ) @ T_a @ T_b )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1027]) ).
thf(1959,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ V_B @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ V_A @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[1026]) ).
thf(1960,plain,
( ( ! [V_B: $i,V_C: $i,V_A: $i,T_a: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ V_B @ ( c_HOL_Ominus__class_Ominus @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= V_A )
| ~ ( c_lessequals @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1025]) ).
thf(1961,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ! [V_x_H: $i,V_y_H: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x_H @ V_y_H @ T_a ) )
| ( c_lessequals @ V_y_H @ V_x_H @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1479]) ).
thf(1962,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ! [V_x_H: $i,V_y_H: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x_H @ V_y_H @ T_a ) )
| ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_lessequals @ V_y_H @ V_x_H @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1478]) ).
thf(1963,plain,
( ( ! [V_f: $i,V_A: $i,T_a: $i,T_b: $i,V_B: $i] :
( ( c_lessequals @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) @ ( c_Set_Oimage @ V_f @ V_B @ T_a @ T_b ) @ ( tc_fun @ T_b @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1022]) ).
thf(1964,plain,
( ( ! [V_x: $i,V_A: $i,T_b: $i] :
( ~ ( c_lessequals @ V_x @ V_A @ ( tc_fun @ T_b @ tc_bool ) )
| ! [V_f: $i,T_a: $i] : ( c_lessequals @ ( c_Set_Oimage @ V_f @ V_x @ T_b @ T_a ) @ ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1477]) ).
thf(1965,plain,
( ( ! [V_a: $i,V_C: $i,T_a: $i,V_D: $i] :
( ( c_lessequals @ ( c_Set_Oinsert @ V_a @ V_C @ T_a ) @ ( c_Set_Oinsert @ V_a @ V_D @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_C @ V_D @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1020]) ).
thf(1966,plain,
( ( ! [T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1019]) ).
thf(1967,plain,
( ( ! [V_f: $i,V_A: $i,V_B: $i,T_b: $i,T_a: $i] :
( ( c_Set_Oimage @ V_f @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a ) @ ( c_Set_Oimage @ V_f @ V_B @ T_b @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1018]) ).
thf(1968,plain,
( ( ! [T_a: $i] :
( ( c_Transitive__Closure_Otrancl @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1017]) ).
thf(1969,plain,
( ( ! [V_P: $i,T_b: $i,T_a: $i,V_x: $i,V_y: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_P @ ( hAPP @ ( c_snd @ T_b @ T_a ) @ ( c_Pair @ V_x @ V_y @ T_b @ T_a ) ) ) @ ( hAPP @ ( c_fst @ T_b @ T_a ) @ ( c_Pair @ V_x @ V_y @ T_b @ T_a ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_P @ V_y ) @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[1016]) ).
thf(1970,plain,
( ( ! [V_r: $i,T_b: $i,T_a: $i] :
( ( ( c_Relation_ORange @ V_r @ T_b @ T_a )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( V_r
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_b @ T_a ) @ tc_bool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1476]) ).
thf(1971,plain,
( ( ! [V_r_H: $i,V_A_H: $i,T_a: $i,T_b: $i,V_r: $i,V_A: $i] :
( ( c_lessequals @ ( c_Relation_OImage @ V_r_H @ V_A_H @ T_a @ T_b ) @ ( c_Relation_OImage @ V_r @ V_A @ T_a @ T_b ) @ ( tc_fun @ T_b @ tc_bool ) )
| ~ ( c_lessequals @ V_A_H @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_r_H @ V_r @ ( tc_fun @ ( tc_prod @ T_a @ T_b ) @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1014]) ).
thf(1972,plain,
( ( ! [V_r: $i,V_A: $i,T_a: $i] :
( ( c_lessequals @ V_r @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_A @ ( tc_fun @ T_a @ tc_bool ) @ T_a ) @ T_a @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1013]) ).
thf(1973,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ! [V_y: $i,V_x: $i] :
( ( c_lessequals @ V_y @ V_x @ T_a )
| ( c_lessequals @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1475]) ).
thf(1974,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Relation_Oirrefl @ V_r @ T_a )
| ! [V_A: $i] :
~ ( c_Order__Relation_Ostrict__linear__order__on @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1474]) ).
thf(1975,plain,
( ( ! [V_y: $i,V_x: $i,T_a: $i,V_r: $i] :
( ( c_Wellfounded_Oacyclic @ ( c_Set_Oinsert @ ( c_Pair @ V_y @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) @ T_a )
| ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Wellfounded_Oacyclic @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1010]) ).
thf(1976,plain,
( ( ! [V_x: $i,V_y: $i,T_a: $i,V_r: $i] :
( ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Wellfounded_Oacyclic @ ( c_Set_Oinsert @ ( c_Pair @ V_y @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1009]) ).
thf(1977,plain,
( ( ! [V_P: $i,V_a: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ! [V_r: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1 @ V_P @ V_b @ V_r @ T_a ) @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 @ V_P @ V_b @ V_r @ T_a ) @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_b ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1473]) ).
thf(1978,plain,
( ( ! [V_P: $i,V_b: $i,V_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_b ) )
| ! [V_r: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 @ V_P @ V_a @ V_r @ T_a ) @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2 @ V_P @ V_a @ V_r @ T_a ) @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1472]) ).
thf(1979,plain,
( ( ! [V_a: $i,V_r: $i,T_a: $i] :
( ( c_in @ V_a @ ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) @ T_a )
| ! [V_A: $i] :
( ~ ( c_in @ V_a @ V_A @ T_a )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1471]) ).
thf(1980,plain,
( ( ! [V_r: $i,T_a: $i,V_s: $i] :
( ( c_lessequals @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Relation_Orel__comp @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ V_r @ T_a @ T_a @ T_a ) @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Relation_OId @ T_a ) @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1005]) ).
thf(1981,plain,
( ( ! [V_a: $i,V_b: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ! [V_x: $i] :
~ ( c_in @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) @ ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
| ! [V_A: $i] :
~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1470]) ).
thf(1982,plain,
( ( ! [V_a: $i,V_b: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ! [V_A: $i] :
( ~ ( c_in @ V_b @ V_A @ T_a )
| ~ ( c_lessequals @ ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) @ ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1469]) ).
thf(1983,plain,
( ( ! [V_f: $i,V_x: $i,V_A: $i,T_a: $i] :
( ! [T_b: $i] :
( ( c_Set_Oinsert @ ( hAPP @ V_f @ V_x ) @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) @ T_b )
= ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) )
| ~ ( c_in @ V_x @ V_A @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1468]) ).
thf(1984,plain,
( ( ! [V_f: $i,V_x: $i,V_B: $i,T_a: $i] :
( ( c_in @ ( hAPP @ V_f @ V_x ) @ V_B @ T_a )
| ! [V_A: $i,T_b: $i] :
( ~ ( c_in @ V_x @ V_A @ T_b )
| ~ ( c_lessequals @ ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1467]) ).
thf(1985,plain,
( ( ! [V_a: $i,V_b: $i,T_b: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_b @ T_b @ T_a ) @ V_r @ ( tc_prod @ T_b @ T_a ) )
| ~ ( c_in @ V_b @ ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b ) @ T_b @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1000]) ).
thf(1986,plain,
( ( ! [V_b: $i,V_r: $i,V_a: $i,T_b: $i,T_a: $i] :
( ( c_in @ V_b @ ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b ) @ T_b @ T_a ) @ T_a )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_b @ T_a ) @ V_r @ ( tc_prod @ T_b @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[999]) ).
thf(1987,plain,
( ( ! [V_A: $i,V_C: $i,T_a: $i,T_b: $i,V_B: $i] :
( ( ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_C @ ( tc_fun @ T_a @ tc_bool ) @ T_b ) @ T_b @ T_a )
!= ( c_Product__Type_OSigma @ V_B @ ( c_COMBK @ V_C @ ( tc_fun @ T_a @ tc_bool ) @ T_b ) @ T_b @ T_a ) )
| ! [V_x: $i] :
~ ( c_in @ V_x @ V_C @ T_a )
| ( V_A = V_B ) ) )
= $true ),
inference(copy,[status(thm)],[1466]) ).
thf(1988,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Wellfounded_Owf @ V_r @ T_a )
| ! [V_y: $i,V_x: $i] :
~ ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ V_y @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1465]) ).
thf(1989,plain,
( ( ! [V_x: $i,V_R: $i,V_S: $i,T_a: $i] :
( ( c_in @ V_x @ ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_R @ V_S @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_x @ ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[996]) ).
thf(1990,plain,
( ( ! [V_x: $i,V_R: $i,V_S: $i,T_a: $i] :
( ( c_in @ V_x @ ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_R @ V_S @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_x @ ( c_Transitive__Closure_Ortrancl @ V_S @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[995]) ).
thf(1991,plain,
( ( ! [V_p: $i,V_s: $i,T_a: $i] :
( ( c_in @ V_p @ ( c_Transitive__Closure_Otrancl @ V_s @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ! [V_r: $i] :
( ~ ( c_lessequals @ V_r @ V_s @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_in @ V_p @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1464]) ).
thf(1992,plain,
( ( ! [V_r: $i,V_a: $i,T_a: $i,V_b: $i] :
( ( ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a )
= ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ! [V_A: $i] :
~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1463]) ).
thf(1993,plain,
( ( ! [V_r: $i,V_x: $i,T_a: $i,V_y: $i] :
( ( ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a )
= ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_y @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ! [V_A: $i] :
~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1462]) ).
thf(1994,plain,
( ( ! [V_R: $i,T_a: $i,V_S: $i] :
( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ V_R @ V_R @ T_a @ T_a @ T_a ) @ ( c_Relation_Orel__comp @ V_S @ V_R @ T_a @ T_a @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ V_S @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
| ~ ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_R @ V_S @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[991]) ).
thf(1995,plain,
( ( ! [V_R: $i,V_S: $i,T_a: $i] :
( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_R @ V_S @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
| ~ ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ V_R @ V_R @ T_a @ T_a @ T_a ) @ ( c_Relation_Orel__comp @ V_S @ V_R @ T_a @ T_a @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ V_S @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[990]) ).
thf(1996,plain,
( ( ! [V_R: $i,T_a: $i] :
( ( ( c_Relation_Orel__comp @ V_R @ V_R @ T_a @ T_a @ T_a )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) )
| ( c_Wellfounded_Owf @ V_R @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1461]) ).
thf(1997,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Transitive__Closure_Otrancl @ V_r @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_r @ ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ V_r @ T_a @ T_a @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[988]) ).
thf(1998,plain,
( ( ! [V_R: $i,T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) @ ( c_Relation_OId @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
= ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[987]) ).
thf(1999,plain,
( ( ! [V_R: $i,T_a: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_R @ ( c_Relation_OId @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
= ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[986]) ).
thf(2000,plain,
( ( ! [T_a: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
= ( c_Relation_OId @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[985]) ).
thf(2001,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( c_HOL_Ominus__class_Ominus @ V_r @ ( c_Relation_OId @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
= ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[984]) ).
thf(2002,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Relation_Oantisym @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ T_a )
| ~ ( c_Wellfounded_Oacyclic @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[983]) ).
thf(2003,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_lessequals @ ( c_Relation_Orel__comp @ V_r @ V_r @ T_a @ T_a @ T_a ) @ V_r @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_Relation_Otrans @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[982]) ).
thf(2004,plain,
( ( ! [V_r: $i,T_a: $i] : ( c_Relation_Osym @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_r @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a ) )
= $true ),
inference(copy,[status(thm)],[981]) ).
thf(2005,plain,
( ( ! [V_r: $i,T_a: $i] : ( c_Relation_Osym @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_r @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a ) )
= $true ),
inference(copy,[status(thm)],[980]) ).
thf(2006,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Relation_Otrans @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_r @ ( c_Relation_OId @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
| ~ ( c_Relation_Otrans @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[979]) ).
thf(2007,plain,
( ( ! [V_A: $i,T_a: $i,V_B: $i] :
( ( c_Relation_OImage @ ( c_Relation_OId__on @ V_A @ T_a ) @ V_B @ T_a @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[978]) ).
thf(2008,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Relation_Oantisym @ V_r @ T_a )
| ~ ( c_Relation_Oantisym @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_r @ ( c_Relation_OId @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[977]) ).
thf(2009,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Relation_Oantisym @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_r @ ( c_Relation_OId @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
| ~ ( c_Relation_Oantisym @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[976]) ).
thf(2010,plain,
( ( ! [V_A: $i,V_r: $i,T_a: $i] :
( ( c_Relation_Ototal__on @ V_A @ V_r @ T_a )
| ~ ( c_Relation_Ototal__on @ V_A @ ( c_HOL_Ominus__class_Ominus @ V_r @ ( c_Relation_OId @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[975]) ).
thf(2011,plain,
( ( ! [V_A: $i,V_r: $i,T_a: $i] :
( ( c_Relation_Ototal__on @ V_A @ ( c_HOL_Ominus__class_Ominus @ V_r @ ( c_Relation_OId @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
| ~ ( c_Relation_Ototal__on @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[974]) ).
thf(2012,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_lessequals @ ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ V_r @ T_a @ T_a @ T_a ) @ V_r @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_Relation_Otrans @ V_r @ T_a )
| ~ ( c_Relation_Osym @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[973]) ).
thf(2013,plain,
( ( ! [V_x: $i,V_R: $i,V_y: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ V_x @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1 @ V_R @ V_x @ V_y @ T_a ) @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[972]) ).
thf(2014,plain,
( ( ! [V_R: $i,V_x: $i,V_y: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1 @ V_R @ V_x @ V_y @ T_a ) @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[971]) ).
thf(2015,plain,
( ( ! [V_x: $i,V_y: $i,T_a: $i,V_r: $i] :
( ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ V_y @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[970]) ).
thf(2016,plain,
( ( ! [V_y: $i,V_x: $i,T_a: $i,V_r: $i] :
( ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ V_y @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) @ T_a )
| ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[969]) ).
thf(2017,plain,
( ( ! [V_A: $i,V_r: $i,T_a: $i] :
( ( c_Order__Relation_Ostrict__linear__order__on @ V_A @ V_r @ T_a )
| ~ ( c_Relation_Ototal__on @ V_A @ V_r @ T_a )
| ~ ( c_Relation_Oirrefl @ V_r @ T_a )
| ~ ( c_Relation_Otrans @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[968]) ).
thf(2018,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Nitpick_Orefl_H @ V_r @ T_a )
| ~ ( c_in @ ( c_Pair @ ( c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1 @ V_r @ T_a ) @ ( c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1 @ V_r @ T_a ) @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[967]) ).
thf(2019,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Relation_Otrans @ ( c_HOL_Ominus__class_Ominus @ V_r @ ( c_Relation_OId @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
| ~ ( c_Relation_Oantisym @ V_r @ T_a )
| ~ ( c_Relation_Otrans @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[966]) ).
thf(2020,plain,
( ( ! [V_R: $i,V_A: $i,V_B: $i,T_b: $i,T_a: $i] :
( ( ( c_Relation_OImage @ V_R @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_OImage @ V_R @ V_A @ T_b @ T_a ) @ ( c_Relation_OImage @ V_R @ V_B @ T_b @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( c_Relation_Osingle__valued @ ( c_Relation_Oconverse @ V_R @ T_b @ T_a ) @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[965]) ).
thf(2021,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Relation_Oirrefl @ V_r @ T_a )
| ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1 @ V_r @ T_a ) @ ( c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1 @ V_r @ T_a ) @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[964]) ).
thf(2022,plain,
( ( ( c_Relation_ORange @ v_r @ t_a @ t_b )
= ( c_Relation_ODomain @ ( c_Relation_Oconverse @ v_r @ t_a @ t_b ) @ t_b @ t_a ) )
= $true ),
inference(copy,[status(thm)],[963]) ).
thf(2023,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_lessequals @ V_r @ ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ V_r @ T_a @ T_a @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ! [V_A: $i] :
~ ( c_Relation_Orefl__on @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1460]) ).
thf(2024,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Transitive__Closure_Ortrancl @ V_r @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_OId @ T_a ) @ ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ V_r @ T_a @ T_a @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[961]) ).
thf(2025,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( c_Relation_OId @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
= ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[960]) ).
thf(2026,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Transitive__Closure_Otrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_r @ ( c_Relation_OId @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a )
= ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[959]) ).
thf(2027,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Transitive__Closure_Ortrancl @ V_r @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( c_Relation_OId @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[958]) ).
thf(2028,plain,
( ( ! [V_f: $i,V_r: $i,V_x: $i,T_a: $i,T_b: $i,V_g: $i] :
( ( ( c_Recdef_Ocut @ V_f @ V_r @ V_x @ T_a @ T_b )
= ( c_Recdef_Ocut @ V_g @ V_r @ V_x @ T_a @ T_b ) )
| ( c_in @ ( c_Pair @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ V_f @ V_g @ V_r @ V_x @ T_a @ T_b ) @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[957]) ).
thf(2029,plain,
( ( ! [V_c: $i,V_A: $i,T_a: $i] :
( ( V_c
= ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XId__onE__1__1 @ V_A @ V_c @ T_a ) @ ( c_ATP__Linkup_Osko__Relation__XId__onE__1__1 @ V_A @ V_c @ T_a ) @ T_a @ T_a ) )
| ~ ( c_in @ V_c @ ( c_Relation_OId__on @ V_A @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[956]) ).
thf(2030,plain,
( ( ! [V_A: $i,V_c: $i,T_a: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Relation__XId__onE__1__1 @ V_A @ V_c @ T_a ) @ V_A @ T_a )
| ~ ( c_in @ V_c @ ( c_Relation_OId__on @ V_A @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[955]) ).
thf(2031,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Wellfounded_Owf @ V_r @ T_a )
| ~ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1 @ V_r @ T_a ) @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[954]) ).
thf(2032,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Wellfounded_Owf @ V_r @ T_a )
| ~ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1 @ V_r @ T_a ) @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[953]) ).
thf(2033,plain,
( ( ! [V_p: $i,T_a: $i] :
( ( V_p
= ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XIdE__1__1 @ V_p @ T_a ) @ ( c_ATP__Linkup_Osko__Relation__XIdE__1__1 @ V_p @ T_a ) @ T_a @ T_a ) )
| ~ ( c_in @ V_p @ ( c_Relation_OId @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[952]) ).
thf(2034,plain,
( ( ! [V_a: $i,V_c: $i,V_r: $i,V_s: $i,T_a: $i,T_b: $i,T_c: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 @ V_a @ V_c @ V_r @ V_s @ T_a @ T_b @ T_c ) @ V_c @ T_c @ T_b ) @ V_s @ ( tc_prod @ T_c @ T_b ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_b ) @ ( c_Relation_Orel__comp @ V_r @ V_s @ T_a @ T_c @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[951]) ).
thf(2035,plain,
( ( ! [V_a: $i,V_c: $i,V_r: $i,V_s: $i,T_a: $i,T_b: $i,T_c: $i] :
( ( c_in @ ( c_Pair @ V_a @ ( c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 @ V_a @ V_c @ V_r @ V_s @ T_a @ T_b @ T_c ) @ T_a @ T_c ) @ V_r @ ( tc_prod @ T_a @ T_c ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_b ) @ ( c_Relation_Orel__comp @ V_r @ V_s @ T_a @ T_c @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[950]) ).
thf(2036,plain,
( ( ! [V_x: $i,T_a: $i,V_r: $i] :
( ~ ( c_in @ ( c_Pair @ V_x @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1 @ V_r @ T_a ) @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1 @ V_r @ T_a ) @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[949]) ).
thf(2037,plain,
( ( ! [V_r: $i,V_x: $i,V_z: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1 @ V_r @ V_x @ V_z @ T_a ) @ V_z @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ( c_in @ ( c_Pair @ V_x @ V_z @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_z @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[948]) ).
thf(2038,plain,
( ( ! [V_x: $i,V_R: $i,V_y: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ V_x @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1 @ V_R @ V_x @ V_y @ T_a ) @ T_a @ T_a ) @ V_R @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[947]) ).
thf(2039,plain,
( ( ! [V_a1: $i,V_a2: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_a1 @ ( v_sko__Transitive__Closure__Xtrancl__Xcases__1 @ V_a1 @ V_a2 @ V_r ) @ t_a @ t_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ t_a ) @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ ( c_Pair @ V_a1 @ V_a2 @ t_a @ t_a ) @ V_r @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ ( c_Pair @ V_a1 @ V_a2 @ t_a @ t_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[946]) ).
thf(2040,plain,
( ( ! [V_x: $i,T_a: $i,V_r: $i] :
( ~ ( c_in @ ( c_Pair @ V_x @ V_x @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Wellfounded_Oacyclic @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[945]) ).
thf(2041,plain,
( ( ! [V_a: $i,V_b: $i,V_r: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1 @ V_a @ V_b @ V_r @ T_a ) @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[944]) ).
thf(2042,plain,
( ( ! [V_a: $i,V_b: $i,V_r: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ V_a @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1 @ V_a @ V_b @ V_r @ T_a ) @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[943]) ).
thf(2043,plain,
( ( ! [V_R: $i,V_x: $i,V_y: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1 @ V_R @ V_x @ V_y @ T_a ) @ V_y @ T_a @ T_a ) @ V_R @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[942]) ).
thf(2044,plain,
( ( ! [V_x: $i,V_r: $i,V_z: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ V_x @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1 @ V_r @ V_x @ V_z @ T_a ) @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ( c_in @ ( c_Pair @ V_x @ V_z @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_z @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[941]) ).
thf(2045,plain,
( ( ! [V_a1: $i,V_a2: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ ( v_sko__Transitive__Closure__Xtrancl__Xcases__1 @ V_a1 @ V_a2 @ V_r ) @ V_a2 @ t_a @ t_a ) @ V_r @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ ( c_Pair @ V_a1 @ V_a2 @ t_a @ t_a ) @ V_r @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ ( c_Pair @ V_a1 @ V_a2 @ t_a @ t_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[940]) ).
thf(2046,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] :
( ~ ( c_in @ ( c_Pair @ V_y @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1 @ V_P @ V_r @ T_a ) @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1459]) ).
thf(2047,plain,
( ( ! [V_P: $i,V_xa: $i,V_y: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_xa ) )
| ( hBOOL @ ( hAPP @ V_P @ V_y ) )
| ! [V_r: $i,T_a: $i] :
( ~ ( c_in @ ( c_Pair @ V_y @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1 @ V_P @ V_r @ T_a ) @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1458]) ).
thf(2048,plain,
( ( ! [V_P: $i,V_Ra: $i,V_y: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_Ra ) )
| ( hBOOL @ ( hAPP @ V_P @ V_y ) )
| ! [V_R: $i,T_a: $i] :
( ~ ( c_in @ ( c_Pair @ V_y @ ( c_List_Osko__Recdef__Xtfl__wf__induct__1__1 @ V_P @ V_R @ T_a ) @ T_a @ T_a ) @ V_R @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Wellfounded_Owf @ V_R @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1457]) ).
thf(2049,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] :
( ~ ( c_in @ ( c_Pair @ V_y @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1 @ V_P @ V_r @ T_a ) @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1456]) ).
thf(2050,plain,
( ( ! [V_a: $i,V_b: $i,V_r: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1 @ V_a @ V_b @ V_r @ T_a ) @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ( V_a = V_b )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[935]) ).
thf(2051,plain,
( ( ! [V_r: $i,V_x: $i,V_z: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1 @ V_r @ V_x @ V_z @ T_a ) @ V_z @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ( V_x = V_z )
| ~ ( c_in @ ( c_Pair @ V_x @ V_z @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[934]) ).
thf(2052,plain,
( ( ! [V_x: $i,V_r: $i,V_z: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ V_x @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1 @ V_r @ V_x @ V_z @ T_a ) @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ( V_x = V_z )
| ~ ( c_in @ ( c_Pair @ V_x @ V_z @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[933]) ).
thf(2053,plain,
( ( ! [V_P: $i,V_a: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ! [V_r: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 @ V_P @ V_b @ V_r @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_b ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1455]) ).
thf(2054,plain,
( ( ! [V_P: $i,V_a: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ! [V_r: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 @ V_P @ V_b @ V_r @ T_a ) @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_b ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1454]) ).
thf(2055,plain,
( ( ! [V_P: $i,V_b: $i,V_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_b ) )
| ! [V_r: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ V_a @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 @ V_P @ V_a @ V_r @ T_a ) @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1453]) ).
thf(2056,plain,
( ( ! [V_P: $i,V_b: $i,V_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_b ) )
| ! [V_r: $i,T_a: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2 @ V_P @ V_a @ V_r @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1452]) ).
thf(2057,plain,
( ( ! [V_a1: $i,V_a2: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_a1 @ ( v_sko__Transitive__Closure__Xrtrancl__Xcases__1 @ V_a1 @ V_a2 @ V_r ) @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ t_a ) @ ( tc_prod @ t_a @ t_a ) )
| ( V_a2 = V_a1 )
| ~ ( c_in @ ( c_Pair @ V_a1 @ V_a2 @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[928]) ).
thf(2058,plain,
( ( ! [V_P: $i,V_b: $i,V_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_b ) )
| ! [V_r: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 @ V_P @ V_a @ V_r @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1451]) ).
thf(2059,plain,
( ( ! [V_a1: $i,V_a2: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ ( v_sko__Transitive__Closure__Xrtrancl__Xcases__1 @ V_a1 @ V_a2 @ V_r ) @ V_a2 @ t_a @ t_a ) @ V_r @ ( tc_prod @ t_a @ t_a ) )
| ( V_a2 = V_a1 )
| ~ ( c_in @ ( c_Pair @ V_a1 @ V_a2 @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[926]) ).
thf(2060,plain,
( ( ! [V_P: $i,V_a: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ! [V_r: $i,T_a: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1 @ V_P @ V_b @ V_r @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_b ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1450]) ).
thf(2061,plain,
( ( ! [V_a: $i,V_b: $i,V_r: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ V_a @ ( c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1 @ V_a @ V_b @ V_r @ T_a ) @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ( V_a = V_b )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[924]) ).
thf(2062,plain,
( ( ! [V_A: $i,V_B: $i,V_c: $i,T_a: $i,T_b: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Product__Type__XSigmaE__1__1 @ V_A @ V_B @ V_c @ T_a @ T_b ) @ V_A @ T_a )
| ~ ( c_in @ V_c @ ( c_Product__Type_OSigma @ V_A @ V_B @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[923]) ).
thf(2063,plain,
( ( ! [V_R: $i,T_a: $i] :
( ( c_Wellfounded_OwfP @ ( c_FunDef_Oin__rel @ V_R @ T_a @ T_a ) @ T_a )
| ~ ( c_Wellfounded_Owf @ V_R @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[922]) ).
thf(2064,plain,
( ( ! [V_r: $i,T_a: $i] : ( c_Relation_Oirrefl @ ( c_HOL_Ominus__class_Ominus @ V_r @ ( c_Relation_OId @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) @ T_a ) )
= $true ),
inference(copy,[status(thm)],[921]) ).
thf(2065,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) ) )
| ! [V_x: $i] :
~ ( c_in @ ( c_Pair @ V_x @ V_x @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1449]) ).
thf(2066,plain,
( ( ! [V_r: $i,V_a: $i,T_a: $i,V_b: $i] :
( ( ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a )
!= ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) )
| ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ! [V_A: $i] :
( ~ ( c_in @ V_b @ V_A @ T_a )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1448]) ).
thf(2067,plain,
( ( ! [V_r: $i,V_x: $i,T_a: $i,V_y: $i] :
( ( ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a )
!= ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_y @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) )
| ! [V_A: $i] :
( ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a )
| ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_y @ V_A @ T_a )
| ~ ( c_in @ V_x @ V_A @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1447]) ).
thf(2068,plain,
( ( ! [V_r: $i,V_x: $i,T_a: $i,V_y: $i] :
( ( ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a )
= ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_y @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ! [V_A: $i] :
( ~ ( c_in @ V_y @ V_A @ T_a )
| ~ ( c_in @ V_x @ V_A @ T_a )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1446]) ).
thf(2069,plain,
( ( ! [V_r: $i,V_x: $i,T_a: $i,V_y: $i] :
( ( ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a )
!= ( c_Relation_OImage @ V_r @ ( c_Set_Oinsert @ V_y @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a @ T_a ) )
| ! [V_A: $i] :
( ~ ( c_in @ V_y @ V_A @ T_a )
| ~ ( c_in @ V_x @ V_A @ T_a )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a )
| ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1445]) ).
thf(2070,plain,
( ( ! [T_b: $i,T_a: $i,V_R: $i] :
( ( c_Set_Oimage @ ( c_snd @ T_b @ T_a ) @ V_R @ ( tc_prod @ T_b @ T_a ) @ T_a )
= ( c_Relation_ORange @ V_R @ T_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[915]) ).
thf(2071,plain,
( ( ! [V_a: $i,V_A: $i,T_a: $i] :
( ( c_in @ V_a @ V_A @ T_a )
| ! [V_b: $i] :
( ( V_a = V_b )
| ! [V_r: $i] :
( ~ ( c_lessequals @ V_r @ ( c_Product__Type_OSigma @ V_A @ ( c_COMBK @ V_A @ ( tc_fun @ T_a @ tc_bool ) @ T_a ) @ T_a @ T_a ) @ ( tc_fun @ ( tc_prod @ T_a @ T_a ) @ tc_bool ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1444]) ).
thf(2072,plain,
( ( ! [T_a: $i,T_b: $i,V_R: $i] :
( ( c_Set_Oimage @ ( c_fst @ T_a @ T_b ) @ V_R @ ( tc_prod @ T_a @ T_b ) @ T_a )
= ( c_Relation_ODomain @ V_R @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[913]) ).
thf(2073,plain,
( ( ! [V_p: $i,V_r: $i,T_a: $i] :
( ( c_in @ V_p @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_p @ V_r @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[912]) ).
thf(2074,plain,
( ( ! [V_p: $i,V_r: $i,T_a: $i] :
( ( c_in @ V_p @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_p @ V_r @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[911]) ).
thf(2075,plain,
( ( ! [V_a: $i,V_c: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ! [V_b: $i] :
( ~ ( c_in @ ( c_Pair @ V_b @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1443]) ).
thf(2076,plain,
( ( ! [V_a: $i,V_c: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ! [V_b: $i] :
( ~ ( c_in @ ( c_Pair @ V_b @ V_c @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1442]) ).
thf(2077,plain,
( ( ! [V_x: $i,V_y: $i,T_a: $i,V_R: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ( V_x = V_y ) ) )
= $true ),
inference(copy,[status(thm)],[908]) ).
thf(2078,plain,
( ( ! [V_x: $i,V_y: $i,T_a: $i,V_R: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ( V_x = V_y )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[907]) ).
thf(2079,plain,
( ( ! [V_a: $i,V_b: $i,T_a: $i,V_R: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ( V_a = V_b )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[906]) ).
thf(2080,plain,
( ( ! [V_x: $i,V_y: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_y @ V_x @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[905]) ).
thf(2081,plain,
( ( ! [V_y: $i,V_x: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_y @ V_x @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[904]) ).
thf(2082,plain,
( ( ! [V_z: $i,V_y: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_z @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ( c_in @ ( c_Pair @ V_y @ V_z @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ! [V_x: $i] :
( ~ ( c_in @ ( c_Pair @ V_x @ V_z @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Relation_Osingle__valued @ V_r @ T_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1441]) ).
thf(2083,plain,
( ( ! [V_a: $i,V_b: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[902]) ).
thf(2084,plain,
( ( ! [V_a: $i,V_c: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ! [V_b: $i] :
( ~ ( c_in @ ( c_Pair @ V_b @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1440]) ).
thf(2085,plain,
( ( ! [V_x: $i,V_z: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_z @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ! [V_y: $i] :
( ~ ( c_in @ ( c_Pair @ V_y @ V_z @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1439]) ).
thf(2086,plain,
( ( ! [V_x: $i,V_y: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Relation_Oconverse @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ T_a @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[899]) ).
thf(2087,plain,
( ( ! [V_x: $i,V_y: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Relation_Oconverse @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ T_a @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[898]) ).
thf(2088,plain,
( ( ! [V_f: $i,T_b: $i,T_c: $i,T_a: $i,V_a: $i,V_b: $i] :
( ( hAPP @ ( c_split @ V_f @ T_b @ T_c @ T_a ) @ ( c_Pair @ V_a @ V_b @ T_b @ T_c ) )
= ( hAPP @ ( hAPP @ V_f @ V_a ) @ V_b ) ) )
= $true ),
inference(copy,[status(thm)],[897]) ).
thf(2089,plain,
( ( ! [V_f: $i,T_a: $i,T_b: $i,T_c: $i,V_a: $i,V_b: $i] :
( ( hAPP @ ( c_split @ V_f @ T_a @ T_b @ T_c ) @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) )
= ( hAPP @ ( hAPP @ V_f @ V_a ) @ V_b ) ) )
= $true ),
inference(copy,[status(thm)],[896]) ).
thf(2090,plain,
( ( ! [V_R: $i,V_a: $i,V_b: $i,V_c: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ V_R @ V_a ) @ V_b ) @ V_c ) )
| ! [T_b: $i,T_c: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_split @ V_R @ T_a @ T_b @ ( tc_fun @ T_c @ tc_bool ) ) @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) ) @ V_c ) ) ) )
= $true ),
inference(copy,[status(thm)],[1438]) ).
thf(2091,plain,
( ( ! [V_f: $i,V_x: $i,V_A: $i,T_a: $i] :
( ! [T_b: $i] : ( c_in @ ( hAPP @ V_f @ V_x ) @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) @ T_b )
| ~ ( c_in @ V_x @ V_A @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1437]) ).
thf(2092,plain,
( ( ! [V_f: $i,V_x: $i,V_A: $i,T_b: $i] :
( ! [T_a: $i] : ( c_in @ ( hAPP @ V_f @ V_x ) @ ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a ) @ T_a )
| ~ ( c_in @ V_x @ V_A @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[1436]) ).
thf(2093,plain,
( ( ! [V_x: $i,V_A: $i,T_b: $i] :
( ~ ( c_in @ V_x @ V_A @ T_b )
| ! [V_f: $i,T_a: $i] : ( c_in @ ( hAPP @ V_f @ V_x ) @ ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1435]) ).
thf(2094,plain,
( ( ! [V_x: $i,V_A: $i,T_aa: $i] :
( ~ ( c_in @ V_x @ V_A @ T_aa )
| ! [V_f: $i,T_a: $i] : ( c_in @ ( hAPP @ V_f @ V_x ) @ ( c_Set_Oimage @ V_f @ V_A @ T_aa @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1434]) ).
thf(2095,plain,
( ( ! [V_x: $i,V_r: $i,T_a: $i] :
( ( c_in @ V_x @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[890]) ).
thf(2096,plain,
( ( ! [V_A: $i,T_a: $i] : ( c_Relation_Osingle__valued @ ( c_Relation_OId__on @ V_A @ T_a ) @ T_a @ T_a ) )
= $true ),
inference(copy,[status(thm)],[889]) ).
thf(2097,plain,
( ( ! [V_A: $i,V_b: $i,V_r: $i,T_b: $i,T_a: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Relation__XImageE__1__1 @ V_A @ V_b @ V_r @ T_b @ T_a ) @ V_A @ T_b )
| ~ ( c_in @ V_b @ ( c_Relation_OImage @ V_r @ V_A @ T_b @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[888]) ).
thf(2098,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Relation_Osym @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ T_a )
| ~ ( c_Relation_Osym @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[887]) ).
thf(2099,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__Xacc__induct__1__1 @ V_P @ V_r @ T_a ) ) )
| ~ ( c_in @ V_a @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1433]) ).
thf(2100,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( ( c_Transitive__Closure_Otrancl @ V_r @ T_a )
= V_r )
| ~ ( c_Relation_Otrans @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[885]) ).
thf(2101,plain,
( ( ! [V_P: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ! [V_r: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ V_P @ V_r ) ) )
| ~ ( c_in @ V_x @ ( c_Wellfounded_Oacc @ V_r @ t_a ) @ t_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1432]) ).
thf(2102,plain,
( ( ! [V_P: $i,V_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ! [V_r: $i,T_a: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ V_P @ V_r @ T_a ) @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a )
| ~ ( c_in @ V_a @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1431]) ).
thf(2103,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Relation_Osym @ V_r @ T_a )
| ~ ( c_Relation_Osym @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[882]) ).
thf(2104,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Relation_Osym @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a )
| ~ ( c_Relation_Osym @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[881]) ).
thf(2105,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Relation_ODomain @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ T_a @ T_a )
= ( c_Relation_ODomain @ V_r @ T_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[880]) ).
thf(2106,plain,
( ( ! [V_A: $i,V_b: $i,V_r: $i,T_b: $i,T_a: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Relation__XImage__iff__1__1 @ V_A @ V_b @ V_r @ T_b @ T_a ) @ V_A @ T_b )
| ~ ( c_in @ V_b @ ( c_Relation_OImage @ V_r @ V_A @ T_b @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[879]) ).
thf(2107,plain,
( ( ! [V_R: $i,V_x: $i,T_a: $i] :
( ~ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1 @ V_R @ V_x @ T_a ) @ ( c_Wellfounded_Oacc @ V_R @ T_a ) @ T_a )
| ( c_in @ V_x @ ( c_Wellfounded_Oacc @ V_R @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[878]) ).
thf(2108,plain,
( ( ! [T_a: $i] : ( c_Relation_Osym @ ( c_Relation_OId @ T_a ) @ T_a ) )
= $true ),
inference(copy,[status(thm)],[877]) ).
thf(2109,plain,
( ( ! [V_A: $i,T_a: $i] : ( c_Relation_Otrans @ ( c_Relation_OId__on @ V_A @ T_a ) @ T_a ) )
= $true ),
inference(copy,[status(thm)],[876]) ).
thf(2110,plain,
( ( ! [T_a: $i,V_R: $i,T_b: $i] :
( ( c_Relation_Orel__comp @ ( c_Relation_OId @ T_a ) @ V_R @ T_a @ T_a @ T_b )
= V_R ) )
= $true ),
inference(copy,[status(thm)],[875]) ).
thf(2111,plain,
( ( ! [V_R: $i,T_b: $i,T_a: $i] :
( ( c_Relation_Orel__comp @ V_R @ ( c_Relation_OId @ T_b ) @ T_a @ T_b @ T_b )
= V_R ) )
= $true ),
inference(copy,[status(thm)],[874]) ).
thf(2112,plain,
( ( ! [V_A: $i,T_a: $i] : ( c_Relation_Oantisym @ ( c_Relation_OId__on @ V_A @ T_a ) @ T_a ) )
= $true ),
inference(copy,[status(thm)],[873]) ).
thf(2113,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Wellfounded_Owf @ ( c_Relation_Oconverse @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ T_a @ T_a ) @ T_a )
| ~ ( c_Wellfounded_Owf @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[872]) ).
thf(2114,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__Xacc__induct__rule__1__1 @ V_P @ V_r @ T_a ) ) )
| ~ ( c_in @ V_a @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1430]) ).
thf(2115,plain,
( ( ! [V_A: $i,V_r: $i,T_a: $i] :
( ( c_Relation_Orefl__on @ V_A @ V_r @ T_a )
| ~ ( c_Relation_Orefl__on @ V_A @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[870]) ).
thf(2116,plain,
( ( ! [V_A: $i,V_r: $i,T_a: $i] :
( ( c_Relation_Orefl__on @ V_A @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a )
| ~ ( c_Relation_Orefl__on @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[869]) ).
thf(2117,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Relation_Osym @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ T_a )
| ~ ( c_Relation_Osym @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[868]) ).
thf(2118,plain,
( ( ! [V_R: $i,T_a: $i] :
( ( c_Wellfounded_Owf @ ( c_Relation_Orel__comp @ V_R @ V_R @ T_a @ T_a @ T_a ) @ T_a )
| ~ ( c_Wellfounded_Owf @ V_R @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[867]) ).
thf(2119,plain,
( ( ! [V_R: $i,T_a: $i] :
( ( c_Wellfounded_Owf @ V_R @ T_a )
| ~ ( c_Wellfounded_Owf @ ( c_Relation_Orel__comp @ V_R @ V_R @ T_a @ T_a @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[866]) ).
thf(2120,plain,
( ( ! [T_a: $i,V_A: $i] :
( ( c_Relation_OImage @ ( c_Relation_OId @ T_a ) @ V_A @ T_a @ T_a )
= V_A ) )
= $true ),
inference(copy,[status(thm)],[865]) ).
thf(2121,plain,
( ( ! [T_a: $i] : ( c_Relation_Osingle__valued @ ( c_Relation_OId @ T_a ) @ T_a @ T_a ) )
= $true ),
inference(copy,[status(thm)],[864]) ).
thf(2122,plain,
( ( ! [V_A: $i,T_a: $i] :
( ( c_Relation_ODomain @ ( c_Relation_OId__on @ V_A @ T_a ) @ T_a @ T_a )
= V_A ) )
= $true ),
inference(copy,[status(thm)],[863]) ).
thf(2123,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( ( c_Relation_Oconverse @ V_r @ T_a @ T_a )
= V_r )
| ~ ( c_Relation_Osym @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[862]) ).
thf(2124,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( ( c_Relation_Oconverse @ V_r @ T_a @ T_a )
!= V_r )
| ( c_Relation_Osym @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1429]) ).
thf(2125,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Relation_ORange @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ T_a @ T_a )
= ( c_Relation_ORange @ V_r @ T_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[860]) ).
thf(2126,plain,
( ( ! [V_r: $i,T_a: $i] : ( c_Relation_Otrans @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ T_a ) )
= $true ),
inference(copy,[status(thm)],[859]) ).
thf(2127,plain,
( ( ! [V_r: $i,V_s: $i,T_b: $i,T_c: $i,T_a: $i] :
( ( c_Relation_Oconverse @ ( c_Relation_Orel__comp @ V_r @ V_s @ T_b @ T_c @ T_a ) @ T_b @ T_a )
= ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ V_s @ T_c @ T_a ) @ ( c_Relation_Oconverse @ V_r @ T_b @ T_c ) @ T_a @ T_c @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[858]) ).
thf(2128,plain,
( ( ! [V_A: $i,T_a: $i] : ( c_Relation_Osym @ ( c_Relation_OId__on @ V_A @ T_a ) @ T_a ) )
= $true ),
inference(copy,[status(thm)],[857]) ).
thf(2129,plain,
( ( ! [V_A: $i,T_a: $i] : ( c_Relation_Orefl__on @ V_A @ ( c_Relation_OId__on @ V_A @ T_a ) @ T_a ) )
= $true ),
inference(copy,[status(thm)],[856]) ).
thf(2130,plain,
( ( ! [V_r: $i,V_f: $i,T_a: $i] :
( ! [T_b: $i] : ( c_Wellfounded_Owf @ ( c_Relation_Oinv__image @ V_r @ V_f @ T_a @ T_b ) @ T_b )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1428]) ).
thf(2131,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Relation_Orel__comp @ V_r @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ T_a @ T_a @ T_a )
= ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ V_r @ T_a @ T_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[854]) ).
thf(2132,plain,
( ( ! [V_r: $i,V_f: $i,T_a: $i] :
( ! [T_b: $i] : ( c_Relation_Osym @ ( c_Relation_Oinv__image @ V_r @ V_f @ T_a @ T_b ) @ T_b )
| ~ ( c_Relation_Osym @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1427]) ).
thf(2133,plain,
( ( ! [V_R: $i,T_a: $i] :
( ( c_Transitive__Closure_Otrancl @ ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) @ T_a )
= ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[852]) ).
thf(2134,plain,
( ( ! [V_r: $i,T_a: $i] : ( c_Relation_Otrans @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ T_a ) )
= $true ),
inference(copy,[status(thm)],[851]) ).
thf(2135,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Relation_Otrans @ V_r @ T_a )
| ~ ( c_Relation_Otrans @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[850]) ).
thf(2136,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Relation_Otrans @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a )
| ~ ( c_Relation_Otrans @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[849]) ).
thf(2137,plain,
( ( ! [T_a: $i] :
( ( c_Relation_Oconverse @ ( c_Relation_OId @ T_a ) @ T_a @ T_a )
= ( c_Relation_OId @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[848]) ).
thf(2138,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Wellfounded_Owf @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ T_a )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[847]) ).
thf(2139,plain,
( ( ! [V_R: $i,V_S: $i,T_a: $i,T_d: $i,T_c: $i,V_T: $i,T_b: $i] :
( ( c_Relation_Orel__comp @ ( c_Relation_Orel__comp @ V_R @ V_S @ T_a @ T_d @ T_c ) @ V_T @ T_a @ T_c @ T_b )
= ( c_Relation_Orel__comp @ V_R @ ( c_Relation_Orel__comp @ V_S @ V_T @ T_d @ T_c @ T_b ) @ T_a @ T_d @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[846]) ).
thf(2140,plain,
( ( ! [V_R: $i,V_f: $i,T_b: $i,T_a: $i] :
( ( c_Relation_Oconverse @ ( c_Relation_Oinv__image @ V_R @ V_f @ T_b @ T_a ) @ T_a @ T_a )
= ( c_Relation_Oinv__image @ ( c_Relation_Oconverse @ V_R @ T_b @ T_b ) @ V_f @ T_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[845]) ).
thf(2141,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Transitive__Closure_Otrancl @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a )
= ( c_Relation_Oconverse @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ T_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[844]) ).
thf(2142,plain,
( ( ! [V_r: $i,V_f: $i,T_a: $i] :
( ! [T_b: $i] : ( c_Relation_Otrans @ ( c_Relation_Oinv__image @ V_r @ V_f @ T_a @ T_b ) @ T_b )
| ~ ( c_Relation_Otrans @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1426]) ).
thf(2143,plain,
( ( ! [V_A: $i,T_a: $i] :
( ( c_Relation_Oconverse @ ( c_Relation_OId__on @ V_A @ T_a ) @ T_a @ T_a )
= ( c_Relation_OId__on @ V_A @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[842]) ).
thf(2144,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ V_r @ T_a @ T_a @ T_a )
!= V_r )
| ( c_Equiv__Relations_Oequiv @ ( c_Relation_ODomain @ V_r @ T_a @ T_a ) @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1425]) ).
thf(2145,plain,
( ( ! [T_a: $i] : ( c_Relation_Oantisym @ ( c_Relation_OId @ T_a ) @ T_a ) )
= $true ),
inference(copy,[status(thm)],[840]) ).
thf(2146,plain,
( ( ! [V_r: $i,T_a: $i,T_b: $i] :
( ( c_Relation_ORange @ ( c_Relation_Oconverse @ V_r @ T_a @ T_b ) @ T_b @ T_a )
= ( c_Relation_ODomain @ V_r @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[839]) ).
thf(2147,plain,
( ( ! [V_Q: $i,V_r: $i,T_a: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 @ V_Q @ V_r @ T_a ) @ V_Q @ T_a )
| ! [V_xa: $i] :
~ ( c_in @ V_xa @ V_Q @ T_a )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1424]) ).
thf(2148,plain,
( ( ! [V_A: $i,T_a: $i] :
( ( c_Relation_ORange @ ( c_Relation_OId__on @ V_A @ T_a ) @ T_a @ T_a )
= V_A ) )
= $true ),
inference(copy,[status(thm)],[837]) ).
thf(2149,plain,
( ( ! [V_r: $i,V_s: $i,T_a: $i,T_b: $i,T_c: $i] :
( ( c_Relation_Osingle__valued @ ( c_Relation_Orel__comp @ V_r @ V_s @ T_a @ T_b @ T_c ) @ T_a @ T_c )
| ~ ( c_Relation_Osingle__valued @ V_s @ T_b @ T_c )
| ~ ( c_Relation_Osingle__valued @ V_r @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[836]) ).
thf(2150,plain,
( ( ! [V_r: $i,T_a: $i,T_b: $i] :
( ( c_Relation_Oconverse @ ( c_Relation_Oconverse @ V_r @ T_a @ T_b ) @ T_b @ T_a )
= V_r ) )
= $true ),
inference(copy,[status(thm)],[835]) ).
thf(2151,plain,
( ( ! [T_a: $i] : ( c_Relation_Otrans @ ( c_Relation_OId @ T_a ) @ T_a ) )
= $true ),
inference(copy,[status(thm)],[834]) ).
thf(2152,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ V_r @ T_a @ T_a @ T_a )
= V_r )
| ! [V_A: $i] :
~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1423]) ).
thf(2153,plain,
( ( ! [V_R: $i,T_a: $i] :
( ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) @ T_a @ T_a @ T_a )
= ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[832]) ).
thf(2154,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Relation_Oantisym @ V_r @ T_a )
| ~ ( c_Relation_Oantisym @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[831]) ).
thf(2155,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Relation_Oantisym @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a )
| ~ ( c_Relation_Oantisym @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[830]) ).
thf(2156,plain,
( ( ! [V_P: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ! [V_r: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ V_P @ V_r ) ) )
| ~ ( c_in @ V_x @ ( c_Wellfounded_Oacc @ V_r @ t_a ) @ t_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1422]) ).
thf(2157,plain,
( ( ! [V_A: $i,V_r: $i,T_a: $i] :
( ( c_Relation_Orefl__on @ V_A @ V_r @ T_a )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[828]) ).
thf(2158,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a )
= ( c_Relation_Oconverse @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ T_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[827]) ).
thf(2159,plain,
( ( ! [V_Q: $i,V_R: $i,T_a: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 @ V_Q @ V_R @ T_a ) @ V_Q @ T_a )
| ! [V_x: $i] :
~ ( c_in @ V_x @ V_Q @ T_a )
| ~ ( c_Wellfounded_Owf @ V_R @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1421]) ).
thf(2160,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Relation_Osym @ V_r @ T_a )
| ! [V_A: $i] :
~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1420]) ).
thf(2161,plain,
( ( ! [V_x: $i,V_r: $i,T_a: $i] :
( ( c_in @ V_x @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a )
| ~ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1 @ V_r @ V_x @ T_a ) @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[824]) ).
thf(2162,plain,
( ( ! [V_r2: $i,V_f: $i,V_a: $i,T_b: $i,T_c: $i,V_A: $i] :
( ( c_Equiv__Relations_Ocongruent @ V_r2 @ ( hAPP @ V_f @ V_a ) @ T_b @ T_c )
| ! [T_a: $i] :
( ~ ( c_in @ V_a @ V_A @ T_a )
| ! [V_r1: $i] :
( ~ ( c_Equiv__Relations_Ocongruent2 @ V_r1 @ V_r2 @ V_f @ T_a @ T_b @ T_c )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r1 @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1419]) ).
thf(2163,plain,
( ( ! [V_r: $i,T_b: $i,T_a: $i] :
( ( c_Relation_ODomain @ ( c_Relation_Oconverse @ V_r @ T_b @ T_a ) @ T_a @ T_b )
= ( c_Relation_ORange @ V_r @ T_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[822]) ).
thf(2164,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Transitive__Closure_Otrancl @ V_r @ T_a )
= ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ V_r @ T_a @ T_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[821]) ).
thf(2165,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Transitive__Closure_Otrancl @ V_r @ T_a )
= ( c_Relation_Orel__comp @ V_r @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ T_a @ T_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[820]) ).
thf(2166,plain,
( ( ! [V_r: $i,T_b: $i,T_a: $i] :
( ( c_Relation_ORange @ V_r @ T_b @ T_a )
= ( c_Relation_ODomain @ ( c_Relation_Oconverse @ V_r @ T_b @ T_a ) @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[819]) ).
thf(2167,plain,
( ( ! [V_A: $i,V_r: $i,T_a: $i] :
( ( c_Relation_Ototal__on @ V_A @ V_r @ T_a )
| ~ ( c_Relation_Ototal__on @ V_A @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[818]) ).
thf(2168,plain,
( ( ! [V_A: $i,V_r: $i,T_a: $i] :
( ( c_Relation_Ototal__on @ V_A @ ( c_Relation_Oconverse @ V_r @ T_a @ T_a ) @ T_a )
| ~ ( c_Relation_Ototal__on @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[817]) ).
thf(2169,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Relation_Otrans @ V_r @ T_a )
| ! [V_A: $i] :
~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1418]) ).
thf(2170,plain,
( ( ! [V_P: $i,V_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ! [V_r: $i,T_a: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ V_P @ V_r @ T_a ) @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a )
| ~ ( c_in @ V_a @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1417]) ).
thf(2171,plain,
( ( ! [V_R: $i,T_a: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( c_Transitive__Closure_Otrancl @ V_R @ T_a ) @ T_a )
= ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[814]) ).
thf(2172,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ T_a )
= ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[813]) ).
thf(2173,plain,
( ( c_Arrow__Order__Mirabelle_OIIA @ v_F )
= $true ),
inference(copy,[status(thm)],[812]) ).
thf(2174,plain,
( ( c_Arrow__Order__Mirabelle_Ounanimity @ v_F )
= $true ),
inference(copy,[status(thm)],[811]) ).
thf(2175,plain,
( ( ! [V_A: $i,V_b: $i,V_r: $i,T_b: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XImageE__1__1 @ V_A @ V_b @ V_r @ T_b @ T_a ) @ V_b @ T_b @ T_a ) @ V_r @ ( tc_prod @ T_b @ T_a ) )
| ~ ( c_in @ V_b @ ( c_Relation_OImage @ V_r @ V_A @ T_b @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[810]) ).
thf(2176,plain,
( ( ! [V_R: $i,V_x: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1 @ V_R @ V_x @ T_a ) @ V_x @ T_a @ T_a ) @ V_R @ ( tc_prod @ T_a @ T_a ) )
| ( c_in @ V_x @ ( c_Wellfounded_Oacc @ V_R @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[809]) ).
thf(2177,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] :
( ~ ( c_in @ ( c_Pair @ V_y @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ V_P @ V_r @ T_a ) @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_a @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1416]) ).
thf(2178,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] :
( ~ ( c_in @ ( c_Pair @ V_y @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ V_P @ V_r ) @ t_a @ t_a ) @ V_r @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ V_x @ ( c_Wellfounded_Oacc @ V_r @ t_a ) @ t_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1415]) ).
thf(2179,plain,
( ( ! [V_y: $i,V_Q: $i,T_a: $i] :
( ~ ( c_in @ V_y @ V_Q @ T_a )
| ! [V_R: $i] :
( ~ ( c_in @ ( c_Pair @ V_y @ ( c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 @ V_Q @ V_R @ T_a ) @ T_a @ T_a ) @ V_R @ ( tc_prod @ T_a @ T_a ) )
| ! [V_x: $i] :
~ ( c_in @ V_x @ V_Q @ T_a )
| ~ ( c_Wellfounded_Owf @ V_R @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1414]) ).
thf(2180,plain,
( ( ! [V_b: $i,V_r: $i,T_a: $i,T_b: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XRangeE__1__1 @ V_b @ V_r @ T_a @ T_b ) @ V_b @ T_b @ T_a ) @ V_r @ ( tc_prod @ T_b @ T_a ) )
| ~ ( c_in @ V_b @ ( c_Relation_ORange @ V_r @ T_b @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[805]) ).
thf(2181,plain,
( ( ! [V_x: $i,V_r: $i,T_a: $i] :
( ( c_in @ V_x @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a )
| ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1 @ V_r @ V_x @ T_a ) @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[804]) ).
thf(2182,plain,
( ( ! [V_b: $i,V_r: $i,T_a: $i] :
( ( c_in @ V_b @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a )
| ! [V_a: $i] :
( ~ ( c_in @ V_a @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a )
| ~ ( c_in @ ( c_Pair @ V_b @ V_a @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1413]) ).
thf(2183,plain,
( ( ! [V_b: $i,V_r: $i,T_a: $i] :
( ( c_in @ V_b @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a )
| ! [V_a: $i] :
( ~ ( c_in @ ( c_Pair @ V_b @ V_a @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_a @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1412]) ).
thf(2184,plain,
( ( ! [V_P: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ! [V_ya: $i,V_r: $i] :
( ( c_in @ V_ya @ ( c_Wellfounded_Oacc @ V_r @ t_a ) @ t_a )
| ~ ( c_in @ ( c_Pair @ V_ya @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ V_P @ V_r ) @ t_a @ t_a ) @ V_r @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ V_x @ ( c_Wellfounded_Oacc @ V_r @ t_a ) @ t_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1411]) ).
thf(2185,plain,
( ( ! [V_x: $i,V_R: $i,T_a: $i] :
( ( c_in @ V_x @ ( c_Relation_ODomain @ V_R @ T_a @ T_a ) @ T_a )
| ( c_in @ ( c_Pair @ V_x @ V_x @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[800]) ).
thf(2186,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] :
( ~ ( c_in @ ( c_Pair @ V_y @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ V_P @ V_r ) @ t_a @ t_a ) @ V_r @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ V_x @ ( c_Wellfounded_Oacc @ V_r @ t_a ) @ t_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1410]) ).
thf(2187,plain,
( ( ! [V_f: $i,V_a: $i,V_b: $i,T_a: $i,T_b: $i,T_c: $i,V_A: $i] :
( ( c_in @ ( hAPP @ ( hAPP @ V_f @ V_a ) @ V_b ) @ ( c_Set_Oimage @ ( c_split @ V_f @ T_a @ T_b @ T_c ) @ V_A @ ( tc_prod @ T_a @ T_b ) @ T_c ) @ T_c )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ V_A @ ( tc_prod @ T_a @ T_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[798]) ).
thf(2188,plain,
( ( ! [V_a: $i,V_r: $i,T_a: $i,T_b: $i] :
( ( c_in @ ( c_Pair @ V_a @ ( c_ATP__Linkup_Osko__Relation__XDomainE__1__1 @ V_a @ V_r @ T_a @ T_b ) @ T_a @ T_b ) @ V_r @ ( tc_prod @ T_a @ T_b ) )
| ~ ( c_in @ V_a @ ( c_Relation_ODomain @ V_r @ T_a @ T_b ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[797]) ).
thf(2189,plain,
( ( ! [V_P: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ! [V_ya: $i,V_r: $i] :
( ( c_in @ V_ya @ ( c_Wellfounded_Oacc @ V_r @ t_a ) @ t_a )
| ~ ( c_in @ ( c_Pair @ V_ya @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ V_P @ V_r ) @ t_a @ t_a ) @ V_r @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ V_x @ ( c_Wellfounded_Oacc @ V_r @ t_a ) @ t_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1409]) ).
thf(2190,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] :
( ~ ( c_in @ ( c_Pair @ V_y @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ V_P @ V_r @ T_a ) @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_a @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1408]) ).
thf(2191,plain,
( ( ! [V_y: $i,V_Q: $i,T_a: $i] :
( ~ ( c_in @ V_y @ V_Q @ T_a )
| ! [V_r: $i] :
( ~ ( c_in @ ( c_Pair @ V_y @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 @ V_Q @ V_r @ T_a ) @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ! [V_xa: $i] :
~ ( c_in @ V_xa @ V_Q @ T_a )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1407]) ).
thf(2192,plain,
( ( ! [V_a: $i,V_r: $i,T_a: $i,T_b: $i] :
( ( c_in @ ( c_Pair @ V_a @ ( c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1 @ V_a @ V_r @ T_a @ T_b ) @ T_a @ T_b ) @ V_r @ ( tc_prod @ T_a @ T_b ) )
| ~ ( c_in @ V_a @ ( c_Relation_ODomain @ V_r @ T_a @ T_b ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[793]) ).
thf(2193,plain,
( ( ! [V_A: $i,V_b: $i,V_r: $i,T_b: $i,T_a: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XImage__iff__1__1 @ V_A @ V_b @ V_r @ T_b @ T_a ) @ V_b @ T_b @ T_a ) @ V_r @ ( tc_prod @ T_b @ T_a ) )
| ~ ( c_in @ V_b @ ( c_Relation_OImage @ V_r @ V_A @ T_b @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[792]) ).
thf(2194,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( V_x = V_y )
| ! [T_a: $i,V_R: $i] :
( ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ( c_in @ V_x @ ( c_Relation_ODomain @ V_R @ T_a @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1406]) ).
thf(2195,plain,
( ( ! [V_a: $i,V_r: $i,T_a: $i,T_b: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XRange__iff__1__1 @ V_a @ V_r @ T_a @ T_b ) @ V_a @ T_b @ T_a ) @ V_r @ ( tc_prod @ T_b @ T_a ) )
| ~ ( c_in @ V_a @ ( c_Relation_ORange @ V_r @ T_b @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[790]) ).
thf(2196,plain,
( ( ! [V_z: $i,V_c: $i,T_b: $i,T_c: $i,T_a: $i,V_a: $i,V_b: $i] :
( ( c_in @ V_z @ ( hAPP @ ( c_split @ V_c @ T_b @ T_c @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Pair @ V_a @ V_b @ T_b @ T_c ) ) @ T_a )
| ~ ( c_in @ V_z @ ( hAPP @ ( hAPP @ V_c @ V_a ) @ V_b ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[789]) ).
thf(2197,plain,
( ( ! [V_f: $i,V_y1: $i,V_y2: $i,V_z1: $i,V_z2: $i,T_b: $i,V_r2: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_f @ V_y1 ) @ V_y2 )
= ( hAPP @ ( hAPP @ V_f @ V_z1 ) @ V_z2 ) )
| ~ ( c_in @ ( c_Pair @ V_y2 @ V_z2 @ T_b @ T_b ) @ V_r2 @ ( tc_prod @ T_b @ T_b ) )
| ! [V_r1: $i] :
( ~ ( c_in @ ( c_Pair @ V_y1 @ V_z1 @ T_a @ T_a ) @ V_r1 @ ( tc_prod @ T_a @ T_a ) )
| ! [T_c: $i] :
~ ( c_Equiv__Relations_Ocongruent2 @ V_r1 @ V_r2 @ V_f @ T_a @ T_b @ T_c ) ) ) )
= $true ),
inference(copy,[status(thm)],[1405]) ).
thf(2198,plain,
( ( ! [V_y: $i,V_z: $i,V_x: $i,T_a: $i] :
( ( V_y = V_z )
| ! [T_b: $i,V_r: $i] :
( ~ ( c_in @ ( c_Pair @ V_x @ V_z @ T_a @ T_b ) @ V_r @ ( tc_prod @ T_a @ T_b ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_b ) @ V_r @ ( tc_prod @ T_a @ T_b ) )
| ~ ( c_Relation_Osingle__valued @ V_r @ T_a @ T_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[1404]) ).
thf(2199,plain,
( ( ! [V_f: $i,V_R: $i,V_a: $i,T_a: $i,T_b: $i,V_x: $i] :
( ( ( hAPP @ ( c_Recdef_Ocut @ V_f @ V_R @ V_a @ T_a @ T_b ) @ V_x )
= ( hAPP @ V_f @ V_x ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_a @ T_a @ T_a ) @ V_R @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[786]) ).
thf(2200,plain,
( ( ! [V_f: $i,V_r: $i,V_a: $i,T_a: $i,T_b: $i,V_x: $i] :
( ( ( hAPP @ ( c_Recdef_Ocut @ V_f @ V_r @ V_a @ T_a @ T_b ) @ V_x )
= ( hAPP @ V_f @ V_x ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_a @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[785]) ).
thf(2201,plain,
( ( ! [V_R: $i,T_a: $i,T_b: $i,V_x: $i,V_y: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_FunDef_Oin__rel @ V_R @ T_a @ T_b ) @ V_x ) @ V_y ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_b ) @ V_R @ ( tc_prod @ T_a @ T_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[784]) ).
thf(2202,plain,
( ( ! [V_x: $i,V_y: $i,T_a: $i,T_b: $i,V_R: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_b ) @ V_R @ ( tc_prod @ T_a @ T_b ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_FunDef_Oin__rel @ V_R @ T_a @ T_b ) @ V_x ) @ V_y ) ) ) )
= $true ),
inference(copy,[status(thm)],[783]) ).
thf(2203,plain,
( ( ! [V_x: $i,V_z: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_z @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ! [V_y: $i] :
( ~ ( c_in @ ( c_Pair @ V_y @ V_z @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Relation_Otrans @ V_r @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1403]) ).
thf(2204,plain,
( ( ! [V_a: $i,V_c: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ! [V_b: $i] :
( ~ ( c_in @ ( c_Pair @ V_b @ V_c @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Relation_Otrans @ V_r @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1402]) ).
thf(2205,plain,
( ( ! [V_a: $i,V_b: $i,T_a: $i,T_b: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ ( c_Relation_Oconverse @ V_r @ T_b @ T_a ) @ ( tc_prod @ T_a @ T_b ) )
| ~ ( c_in @ ( c_Pair @ V_b @ V_a @ T_b @ T_a ) @ V_r @ ( tc_prod @ T_b @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[780]) ).
thf(2206,plain,
( ( ! [V_b: $i,V_a: $i,T_b: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_b @ V_a @ T_b @ T_a ) @ ( c_Relation_Oconverse @ V_r @ T_a @ T_b ) @ ( tc_prod @ T_b @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ V_r @ ( tc_prod @ T_a @ T_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[779]) ).
thf(2207,plain,
( ( ! [V_b: $i,V_a: $i,T_b: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_b @ V_a @ T_b @ T_a ) @ V_r @ ( tc_prod @ T_b @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ ( c_Relation_Oconverse @ V_r @ T_b @ T_a ) @ ( tc_prod @ T_a @ T_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[778]) ).
thf(2208,plain,
( ( ! [V_x: $i,T_a: $i,V_r: $i] :
( ~ ( c_in @ ( c_Pair @ V_x @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Relation_Oirrefl @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[777]) ).
thf(2209,plain,
( ( ! [V_a: $i,V_c: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ! [V_b: $i] :
( ~ ( c_in @ ( c_Pair @ V_b @ V_c @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1401]) ).
thf(2210,plain,
( ( ! [V_a: $i,V_c: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ! [V_b: $i] :
( ~ ( c_in @ ( c_Pair @ V_b @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1400]) ).
thf(2211,plain,
( ( ! [V_a: $i,V_c: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ! [V_b: $i] :
( ~ ( c_in @ ( c_Pair @ V_b @ V_c @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1399]) ).
thf(2212,plain,
( ( ! [V_a: $i,V_c: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ! [V_b: $i] :
( ~ ( c_in @ ( c_Pair @ V_b @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1398]) ).
thf(2213,plain,
( ( ! [V_a: $i,V_b: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[772]) ).
thf(2214,plain,
( ( ! [V_a: $i,V_c: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ! [V_b: $i] :
( ~ ( c_in @ ( c_Pair @ V_b @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1397]) ).
thf(2215,plain,
( ( ! [V_a: $i,T_a: $i,V_r: $i] : ( c_in @ ( c_Pair @ V_a @ V_a @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[770]) ).
thf(2216,plain,
( ( ! [V_x: $i,T_a: $i,V_R: $i] : ( c_in @ ( c_Pair @ V_x @ V_x @ T_a @ T_a ) @ ( c_Transitive__Closure_Ortrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[769]) ).
thf(2217,plain,
( ( ! [V_x: $i,V_a: $i,T_a: $i,V_r: $i] :
( ~ ( c_in @ ( c_Pair @ V_x @ V_a @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[768]) ).
thf(2218,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( V_x = V_y )
| ! [T_a: $i,V_r: $i] :
( ~ ( c_in @ ( c_Pair @ V_y @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Relation_Oantisym @ V_r @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1396]) ).
thf(2219,plain,
( ( ! [V_a: $i,V_b: $i] :
( ( V_a = V_b )
| ! [T_a: $i,V_r: $i] :
( ~ ( c_in @ ( c_Pair @ V_b @ V_a @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Relation_Oantisym @ V_r @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1395]) ).
thf(2220,plain,
( ( ! [V_f: $i,V_y: $i,V_z: $i,T_a: $i] :
( ( ( hAPP @ V_f @ V_y )
= ( hAPP @ V_f @ V_z ) )
| ! [V_r: $i] :
( ~ ( c_in @ ( c_Pair @ V_y @ V_z @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ! [T_b: $i] :
~ ( c_Equiv__Relations_Ocongruent @ V_r @ V_f @ T_a @ T_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[1394]) ).
thf(2221,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( V_x = V_y )
| ! [T_a: $i,V_A: $i] :
~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Relation_OId__on @ V_A @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1393]) ).
thf(2222,plain,
( ( ! [V_f: $i,V_r: $i,V_x: $i,T_a: $i,T_b: $i,V_g: $i] :
( ( ( c_Recdef_Ocut @ V_f @ V_r @ V_x @ T_a @ T_b )
!= ( c_Recdef_Ocut @ V_g @ V_r @ V_x @ T_a @ T_b ) )
| ! [V_y: $i] :
( ( ( hAPP @ V_f @ V_y )
= ( hAPP @ V_g @ V_y ) )
| ~ ( c_in @ ( c_Pair @ V_y @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1392]) ).
thf(2223,plain,
( ( ! [V_a: $i,V_b: $i] :
( ( V_a = V_b )
| ! [T_a: $i] :
~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Relation_OId @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1391]) ).
thf(2224,plain,
( ( ! [V_x: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Nitpick_Orefl_H @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[761]) ).
thf(2225,plain,
( ( ! [V_a: $i,T_a: $i,V_r: $i] :
( ~ ( c_in @ ( c_Pair @ V_a @ V_a @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Wellfounded_Owf @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[760]) ).
thf(2226,plain,
( ( ! [V_x: $i,V_y: $i,T_a: $i,V_r: $i,V_f: $i,T_b: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Relation_Oinv__image @ V_r @ V_f @ T_b @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ ( hAPP @ V_f @ V_x ) @ ( hAPP @ V_f @ V_y ) @ T_b @ T_b ) @ V_r @ ( tc_prod @ T_b @ T_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[759]) ).
thf(2227,plain,
( ( ! [V_f: $i,V_x: $i,V_y: $i,T_b: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ ( hAPP @ V_f @ V_x ) @ ( hAPP @ V_f @ V_y ) @ T_b @ T_b ) @ V_r @ ( tc_prod @ T_b @ T_b ) )
| ! [T_a: $i] :
~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Relation_Oinv__image @ V_r @ V_f @ T_b @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1390]) ).
thf(2228,plain,
( ( ! [V_y: $i,V_x: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_y @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Relation_Osym @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[757]) ).
thf(2229,plain,
( ( ! [V_b: $i,V_a: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_b @ V_a @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Relation_Osym @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[756]) ).
thf(2230,plain,
( ( ! [V_a: $i,V_c: $i,T_a: $i,T_c: $i,V_r: $i,V_s: $i,T_b: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_c ) @ ( c_Relation_Orel__comp @ V_r @ V_s @ T_a @ T_b @ T_c ) @ ( tc_prod @ T_a @ T_c ) )
| ! [V_b: $i] :
( ~ ( c_in @ ( c_Pair @ V_b @ V_c @ T_b @ T_c ) @ V_s @ ( tc_prod @ T_b @ T_c ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ V_r @ ( tc_prod @ T_a @ T_b ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1389]) ).
thf(2231,plain,
( ( ! [V_a: $i,V_c: $i,T_a: $i,V_R: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_R @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ! [V_b: $i] :
( ~ ( c_in @ ( c_Pair @ V_b @ V_c @ T_a @ T_a ) @ V_R @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_R @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1388]) ).
thf(2232,plain,
( ( ! [V_a: $i,V_c: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ! [V_b: $i] :
( ~ ( c_in @ ( c_Pair @ V_b @ V_c @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ ( c_Transitive__Closure_Otrancl @ V_r @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1387]) ).
thf(2233,plain,
( ( ! [V_x: $i,T_a: $i] : ( c_in @ ( c_Pair @ V_x @ V_x @ T_a @ T_a ) @ ( c_Relation_OId @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[752]) ).
thf(2234,plain,
( ( ! [V_a: $i,T_a: $i] : ( c_in @ ( c_Pair @ V_a @ V_a @ T_a @ T_a ) @ ( c_Relation_OId @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[751]) ).
thf(2235,plain,
( ( ! [V_x: $i,V_y: $i,V_L: $i,V_z: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omktop @ V_L ) @ V_z ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ V_L @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( V_x = V_y )
| ( V_x = V_z ) ) )
= $true ),
inference(copy,[status(thm)],[750]) ).
thf(2236,plain,
( ( ! [V_x: $i,V_y: $i,V_L: $i,V_z: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omktop @ V_L ) @ V_z ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ V_L @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( V_y = V_z )
| ( V_x = V_z ) ) )
= $true ),
inference(copy,[status(thm)],[749]) ).
thf(2237,plain,
( ( ! [V_x: $i,V_L: $i] :
~ ( c_in @ ( c_Pair @ V_x @ V_x @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omktop @ V_L ) @ V_x ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ),
inference(copy,[status(thm)],[748]) ).
thf(2238,plain,
( ( ! [V_x: $i,V_y: $i,V_L: $i] :
~ ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omktop @ V_L ) @ V_x ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ),
inference(copy,[status(thm)],[747]) ).
thf(2239,plain,
( ( ! [V_x: $i,V_y: $i,V_L: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ V_L @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ! [V_z: $i] :
( ( V_y = V_z )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omktop @ V_L ) @ V_z ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1386]) ).
thf(2240,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( V_x = V_y )
| ( V_y = V_x )
| ! [V_L: $i] : ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omkbot @ V_L ) @ V_x ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(copy,[status(thm)],[1385]) ).
thf(2241,plain,
( ( ! [V_x: $i,V_L: $i] :
~ ( c_in @ ( c_Pair @ V_x @ V_x @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omkbot @ V_L ) @ V_x ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ),
inference(copy,[status(thm)],[744]) ).
thf(2242,plain,
( ( ! [V_xa: $i,V_x: $i,V_L: $i] :
~ ( c_in @ ( c_Pair @ V_xa @ V_x @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omkbot @ V_L ) @ V_x ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ),
inference(copy,[status(thm)],[743]) ).
thf(2243,plain,
( ( ! [V_x: $i,V_y: $i,V_L: $i,V_z: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omkbot @ V_L ) @ V_z ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ V_L @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( V_x = V_y )
| ( V_y = V_z ) ) )
= $true ),
inference(copy,[status(thm)],[742]) ).
thf(2244,plain,
( ( ! [V_x: $i,V_y: $i,V_L: $i,V_z: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omkbot @ V_L ) @ V_z ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ V_L @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( V_x = V_z )
| ( V_y = V_z ) ) )
= $true ),
inference(copy,[status(thm)],[741]) ).
thf(2245,plain,
( ( ! [V_xa: $i,V_x: $i] :
( ( V_xa = V_x )
| ( V_xa = V_x )
| ! [V_L: $i] : ( c_in @ ( c_Pair @ V_xa @ V_x @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omktop @ V_L ) @ V_x ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(copy,[status(thm)],[1384]) ).
thf(2246,plain,
( ( ! [V_x: $i,V_y: $i,V_L: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ V_L @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ! [V_z: $i] :
( ( V_x = V_z )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omkbot @ V_L ) @ V_z ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1383]) ).
thf(2247,plain,
( ( ! [V_a: $i,V_b: $i] :
( ( V_a = V_b )
| ( c_in @ ( c_Pair @ V_a @ V_b @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1 @ V_a @ V_b ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(copy,[status(thm)],[1382]) ).
thf(2248,plain,
( ( ! [V_a: $i,V_b: $i,T_a: $i,T_b: $i,V_A: $i,V_B: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ ( c_Product__Type_OSigma @ V_A @ V_B @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) )
| ~ ( c_in @ V_b @ ( hAPP @ V_B @ V_a ) @ T_b )
| ~ ( c_in @ V_a @ V_A @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[737]) ).
thf(2249,plain,
( ( ! [V_a: $i,V_b: $i,T_a: $i,T_b: $i,V_A: $i,V_B: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ ( c_Product__Type_OSigma @ V_A @ V_B @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) )
| ~ ( c_in @ V_b @ ( hAPP @ V_B @ V_a ) @ T_b )
| ~ ( c_in @ V_a @ V_A @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[736]) ).
thf(2250,plain,
( ( ! [V_a: $i,V_r: $i,T_a: $i] :
( ( c_in @ V_a @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a )
| ! [V_b: $i] :
( ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_b @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1381]) ).
thf(2251,plain,
( ( ! [V_y: $i,V_r: $i,T_a: $i] :
( ( c_in @ V_y @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a )
| ! [V_a: $i] :
( ~ ( c_in @ ( c_Pair @ V_y @ V_a @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_a @ ( c_Wellfounded_Oacc @ V_r @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1380]) ).
thf(2252,plain,
( ( ! [V_b: $i,V_r: $i,V_A: $i,T_a: $i,T_b: $i] :
( ( c_in @ V_b @ ( c_Relation_OImage @ V_r @ V_A @ T_a @ T_b ) @ T_b )
| ! [V_a: $i] :
( ~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ V_r @ ( tc_prod @ T_a @ T_b ) )
| ~ ( c_in @ V_a @ V_A @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1379]) ).
thf(2253,plain,
( ( ! [V_b: $i,V_r: $i,V_A: $i,T_b: $i,T_a: $i] :
( ( c_in @ V_b @ ( c_Relation_OImage @ V_r @ V_A @ T_b @ T_a ) @ T_a )
| ! [V_x: $i] :
( ~ ( c_in @ ( c_Pair @ V_x @ V_b @ T_b @ T_a ) @ V_r @ ( tc_prod @ T_b @ T_a ) )
| ~ ( c_in @ V_x @ V_A @ T_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[1378]) ).
thf(2254,plain,
( ( ! [V_x: $i,V_A: $i,T_a: $i] :
( ( c_in @ V_x @ V_A @ T_a )
| ! [V_y: $i] :
~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ ( c_Relation_OId__on @ V_A @ T_a ) @ ( tc_prod @ T_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1377]) ).
thf(2255,plain,
( ( ! [V_x: $i,T_a: $i,V_A: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_x @ T_a @ T_a ) @ ( c_Relation_OId__on @ V_A @ T_a ) @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_in @ V_x @ V_A @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[730]) ).
thf(2256,plain,
( ( ! [V_y: $i,V_A: $i,T_a: $i] :
( ( c_in @ V_y @ V_A @ T_a )
| ! [V_x: $i,V_r: $i] :
( ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1376]) ).
thf(2257,plain,
( ( ! [V_x: $i,V_A: $i,T_a: $i] :
( ( c_in @ V_x @ V_A @ T_a )
| ! [V_y: $i,V_r: $i] :
( ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Equiv__Relations_Oequiv @ V_A @ V_r @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1375]) ).
thf(2258,plain,
( ( ! [V_a: $i,V_r: $i,T_b: $i,T_a: $i] :
( ( c_in @ V_a @ ( c_Relation_ORange @ V_r @ T_b @ T_a ) @ T_a )
| ! [V_x: $i] :
~ ( c_in @ ( c_Pair @ V_x @ V_a @ T_b @ T_a ) @ V_r @ ( tc_prod @ T_b @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1374]) ).
thf(2259,plain,
( ( ! [V_b: $i,V_r: $i,T_a: $i,T_b: $i] :
( ( c_in @ V_b @ ( c_Relation_ORange @ V_r @ T_a @ T_b ) @ T_b )
| ! [V_a: $i] :
~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ V_r @ ( tc_prod @ T_a @ T_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[1373]) ).
thf(2260,plain,
( ( ! [V_a: $i,V_r: $i,T_a: $i,T_b: $i] :
( ( c_in @ V_a @ ( c_Relation_ODomain @ V_r @ T_a @ T_b ) @ T_a )
| ! [V_x: $i] :
~ ( c_in @ ( c_Pair @ V_a @ V_x @ T_a @ T_b ) @ V_r @ ( tc_prod @ T_a @ T_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[1372]) ).
thf(2261,plain,
( ( ! [V_a: $i,V_r: $i,T_a: $i,T_b: $i] :
( ( c_in @ V_a @ ( c_Relation_ODomain @ V_r @ T_a @ T_b ) @ T_a )
| ! [V_b: $i] :
~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ V_r @ ( tc_prod @ T_a @ T_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[1371]) ).
thf(2262,plain,
( ( ! [V_b: $i,V_B: $i,V_a: $i,T_b: $i] :
( ( c_in @ V_b @ ( hAPP @ V_B @ V_a ) @ T_b )
| ! [T_a: $i,V_A: $i] :
~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ ( c_Product__Type_OSigma @ V_A @ V_B @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[1370]) ).
thf(2263,plain,
( ( ! [V_a: $i,V_A: $i,T_a: $i,V_b: $i] :
( ( c_in @ V_a @ V_A @ T_a )
| ! [T_b: $i,V_B: $i] :
~ ( c_in @ ( c_Pair @ V_a @ V_b @ T_a @ T_b ) @ ( c_Product__Type_OSigma @ V_A @ V_B @ T_a @ T_b ) @ ( tc_prod @ T_a @ T_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[1369]) ).
thf(2264,plain,
( ( ! [V_xa: $i,V_x: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_xa @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ( c_in @ ( c_Pair @ V_x @ V_xa @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ( V_x = V_xa )
| ! [V_A: $i] :
( ~ ( c_in @ V_xa @ V_A @ T_a )
| ~ ( c_in @ V_x @ V_A @ T_a )
| ~ ( c_Relation_Ototal__on @ V_A @ V_r @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1368]) ).
thf(2265,plain,
( ( ! [V_x: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_x @ V_x @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ! [V_A: $i] :
( ~ ( c_in @ V_x @ V_A @ T_a )
| ~ ( c_Relation_Orefl__on @ V_A @ V_r @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1367]) ).
thf(2266,plain,
( ( ! [V_y: $i,V_A: $i,T_a: $i] :
( ( c_in @ V_y @ V_A @ T_a )
| ! [V_x: $i,V_r: $i] :
( ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Relation_Orefl__on @ V_A @ V_r @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1366]) ).
thf(2267,plain,
( ( ! [V_x: $i,V_A: $i,T_a: $i] :
( ( c_in @ V_x @ V_A @ T_a )
| ! [V_y: $i,V_r: $i] :
( ~ ( c_in @ ( c_Pair @ V_x @ V_y @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ~ ( c_Relation_Orefl__on @ V_A @ V_r @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1365]) ).
thf(2268,plain,
( ( ! [V_a: $i,T_a: $i,V_r: $i] :
( ( c_in @ ( c_Pair @ V_a @ V_a @ T_a @ T_a ) @ V_r @ ( tc_prod @ T_a @ T_a ) )
| ! [V_A: $i] :
( ~ ( c_in @ V_a @ V_A @ T_a )
| ~ ( c_Relation_Orefl__on @ V_A @ V_r @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1364]) ).
thf(2269,plain,
( ( ! [V_a: $i,V_b: $i,T_a: $i,T_b: $i,V_a_H: $i,V_b_H: $i] :
( ( ( c_Pair @ V_a @ V_b @ T_a @ T_b )
!= ( c_Pair @ V_a_H @ V_b_H @ T_a @ T_b ) )
| ( V_b = V_b_H ) ) )
= $true ),
inference(copy,[status(thm)],[1363]) ).
thf(2270,plain,
( ( ! [V_a: $i,V_b: $i,T_a: $i,T_b: $i,V_a_H: $i] :
( ! [V_b_H: $i] :
( ( c_Pair @ V_a @ V_b @ T_a @ T_b )
!= ( c_Pair @ V_a_H @ V_b_H @ T_a @ T_b ) )
| ( V_a = V_a_H ) ) )
= $true ),
inference(copy,[status(thm)],[1362]) ).
thf(2271,plain,
( ( ! [V_x: $i,V_S: $i] :
( ! [T_a: $i] : ( c_in @ V_x @ V_S @ T_a )
| ~ ( hBOOL @ ( hAPP @ V_S @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[1361]) ).
thf(2272,plain,
( ( ! [V_S: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_S @ V_x ) )
| ! [T_a: $i] :
~ ( c_in @ V_x @ V_S @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1360]) ).
thf(2273,plain,
( ( ( c_in @ ( c_Pair @ v_c____ @ v_d____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ v_P____ ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ v_c____ @ v_d____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_HOL_OIf @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ v_h____ @ tc_nat @ ( tc_fun @ tc_nat @ tc_bool ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ v_n____ @ tc_Arrow__Order__Mirabelle_Oindi @ tc_nat @ tc_bool ) @ tc_bool @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ ( c_COMBC @ ( c_COMBB @ c_Arrow__Order__Mirabelle_Omktop @ v_P____ @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ v_e____ @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_HOL_OIf @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ ( c_COMBC @ ( c_COMBB @ ( c_fequal @ tc_nat ) @ v_h____ @ tc_nat @ ( tc_fun @ tc_nat @ tc_bool ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ v_n____ @ tc_Arrow__Order__Mirabelle_Oindi @ tc_nat @ tc_bool ) @ tc_bool @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ ( c_COMBC @ ( c_COMBC @ ( c_COMBB @ c_Arrow__Order__Mirabelle_Oabove @ v_P____ @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ v_c____ @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ v_e____ @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ ( c_COMBC @ ( c_COMBB @ c_Arrow__Order__Mirabelle_Omkbot @ v_P____ @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ v_e____ @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ),
inference(copy,[status(thm)],[712]) ).
thf(2274,plain,
( ( ( c_in @ ( c_Pair @ v_c____ @ v_d____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_HOL_OIf @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ v_h____ @ tc_nat @ ( tc_fun @ tc_nat @ tc_bool ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ v_n____ @ tc_Arrow__Order__Mirabelle_Oindi @ tc_nat @ tc_bool ) @ tc_bool @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ ( c_COMBC @ ( c_COMBB @ c_Arrow__Order__Mirabelle_Omktop @ v_P____ @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ v_e____ @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_HOL_OIf @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ ( c_COMBC @ ( c_COMBB @ ( c_fequal @ tc_nat ) @ v_h____ @ tc_nat @ ( tc_fun @ tc_nat @ tc_bool ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ v_n____ @ tc_Arrow__Order__Mirabelle_Oindi @ tc_nat @ tc_bool ) @ tc_bool @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ ( c_COMBC @ ( c_COMBC @ ( c_COMBB @ c_Arrow__Order__Mirabelle_Oabove @ v_P____ @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ v_c____ @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ v_e____ @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ ( c_COMBC @ ( c_COMBB @ c_Arrow__Order__Mirabelle_Omkbot @ v_P____ @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ v_e____ @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ v_c____ @ v_d____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ v_P____ ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ),
inference(copy,[status(thm)],[711]) ).
thf(2275,plain,
( ( c_in @ ( c_Pair @ v_c____ @ v_d____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_HOL_OIf @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ v_h____ @ tc_nat @ ( tc_fun @ tc_nat @ tc_bool ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ v_n____ @ tc_Arrow__Order__Mirabelle_Oindi @ tc_nat @ tc_bool ) @ tc_bool @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ ( c_COMBC @ ( c_COMBB @ c_Arrow__Order__Mirabelle_Omktop @ v_P____ @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ v_e____ @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_HOL_OIf @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ ( c_COMBC @ ( c_COMBB @ ( c_fequal @ tc_nat ) @ v_h____ @ tc_nat @ ( tc_fun @ tc_nat @ tc_bool ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ v_n____ @ tc_Arrow__Order__Mirabelle_Oindi @ tc_nat @ tc_bool ) @ tc_bool @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ ( c_COMBC @ ( c_COMBC @ ( c_COMBB @ c_Arrow__Order__Mirabelle_Oabove @ v_P____ @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ v_c____ @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ v_e____ @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ ( c_COMBC @ ( c_COMBB @ c_Arrow__Order__Mirabelle_Omkbot @ v_P____ @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ v_e____ @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ),
inference(copy,[status(thm)],[710]) ).
thf(2276,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)],[709]) ).
thf(2277,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)],[708]) ).
thf(2278,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)],[707]) ).
thf(2279,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Lattices_Obounded__lattice @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Lattices_Obounded__lattice @ T_1 ) ) )
= $true ),
inference(copy,[status(thm)],[706]) ).
thf(2280,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Orderings_Opreorder @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Orderings_Opreorder @ T_1 ) ) )
= $true ),
inference(copy,[status(thm)],[705]) ).
thf(2281,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)],[704]) ).
thf(2282,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Orderings_Oorder @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Orderings_Oorder @ T_1 ) ) )
= $true ),
inference(copy,[status(thm)],[703]) ).
thf(2283,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Orderings_Obot @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Orderings_Obot @ T_1 ) ) )
= $true ),
inference(copy,[status(thm)],[702]) ).
thf(2284,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_HOL_Oord @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_HOL_Oord @ T_1 ) ) )
= $true ),
inference(copy,[status(thm)],[701]) ).
thf(2285,plain,
( ( class_Lattices_Oupper__semilattice @ tc_nat )
= $true ),
inference(copy,[status(thm)],[700]) ).
thf(2286,plain,
( ( class_Lattices_Olower__semilattice @ tc_nat )
= $true ),
inference(copy,[status(thm)],[699]) ).
thf(2287,plain,
( ( class_Lattices_Odistrib__lattice @ tc_nat )
= $true ),
inference(copy,[status(thm)],[698]) ).
thf(2288,plain,
( ( class_Orderings_Opreorder @ tc_nat )
= $true ),
inference(copy,[status(thm)],[697]) ).
thf(2289,plain,
( ( class_Orderings_Olinorder @ tc_nat )
= $true ),
inference(copy,[status(thm)],[696]) ).
thf(2290,plain,
( ( class_Lattices_Olattice @ tc_nat )
= $true ),
inference(copy,[status(thm)],[695]) ).
thf(2291,plain,
( ( class_Orderings_Oorder @ tc_nat )
= $true ),
inference(copy,[status(thm)],[694]) ).
thf(2292,plain,
( ( class_Orderings_Obot @ tc_nat )
= $true ),
inference(copy,[status(thm)],[693]) ).
thf(2293,plain,
( ( class_HOL_Oord @ tc_nat )
= $true ),
inference(copy,[status(thm)],[692]) ).
thf(2294,plain,
( ( class_Lattices_Oupper__semilattice @ tc_bool )
= $true ),
inference(copy,[status(thm)],[691]) ).
thf(2295,plain,
( ( class_Lattices_Olower__semilattice @ tc_bool )
= $true ),
inference(copy,[status(thm)],[690]) ).
thf(2296,plain,
( ( class_Lattices_Odistrib__lattice @ tc_bool )
= $true ),
inference(copy,[status(thm)],[689]) ).
thf(2297,plain,
( ( class_Lattices_Obounded__lattice @ tc_bool )
= $true ),
inference(copy,[status(thm)],[688]) ).
thf(2298,plain,
( ( class_Orderings_Opreorder @ tc_bool )
= $true ),
inference(copy,[status(thm)],[687]) ).
thf(2299,plain,
( ( class_Lattices_Olattice @ tc_bool )
= $true ),
inference(copy,[status(thm)],[686]) ).
thf(2300,plain,
( ( class_Orderings_Oorder @ tc_bool )
= $true ),
inference(copy,[status(thm)],[685]) ).
thf(2301,plain,
( ( class_Orderings_Obot @ tc_bool )
= $true ),
inference(copy,[status(thm)],[684]) ).
thf(2302,plain,
( ( class_HOL_Oord @ tc_bool )
= $true ),
inference(copy,[status(thm)],[683]) ).
thf(2303,plain,
( ( ! [T_a: $i,V_x: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ T_a ) @ V_x ) @ V_x ) ) )
= $true ),
inference(copy,[status(thm)],[682]) ).
thf(2304,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)],[1359]) ).
thf(2305,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[1358]) ).
thf(2306,plain,
( ( c_in @ ( c_Pair @ v_c____ @ v_d____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ v_P____ ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1628]) ).
thf(2307,plain,
! [SV1: $i] :
( ( ! [SY2379: $i,SY2380: $i,SY2381: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ SV1 @ SY2379 @ SY2380 ) @ ( c_Set_Oinsert @ SV1 @ SY2381 @ SY2380 ) @ ( tc_fun @ SY2380 @ tc_bool ) )
= ( c_Set_Oinsert @ SV1 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2379 @ SY2381 @ ( tc_fun @ SY2380 @ tc_bool ) ) @ SY2380 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1629]) ).
thf(2308,plain,
! [SV2: $i] :
( ( ! [SY2382: $i,SY2383: $i] :
( ( c_Set_Oinsert @ SV2 @ SY2382 @ SY2383 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2383 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1630]) ).
thf(2309,plain,
! [SV3: $i] :
( ( ! [SY2384: $i,SY2385: $i,SY2386: $i] :
( ( c_HOL_Ominus__class_Ominus @ SV3 @ ( c_Set_Oinsert @ SY2384 @ SY2385 @ SY2386 ) @ ( tc_fun @ SY2386 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV3 @ ( c_Set_Oinsert @ SY2384 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2386 @ tc_bool ) ) @ SY2386 ) @ ( tc_fun @ SY2386 @ tc_bool ) ) @ SY2385 @ ( tc_fun @ SY2386 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1631]) ).
thf(2310,plain,
! [SV4: $i] :
( ( ! [SY2387: $i,SY2388: $i,SY2389: $i] :
( ( c_HOL_Ominus__class_Ominus @ SV4 @ ( c_Set_Oinsert @ SY2387 @ SY2388 @ SY2389 ) @ ( tc_fun @ SY2389 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV4 @ SY2388 @ ( tc_fun @ SY2389 @ tc_bool ) ) @ ( c_Set_Oinsert @ SY2387 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2389 @ tc_bool ) ) @ SY2389 ) @ ( tc_fun @ SY2389 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1632]) ).
thf(2311,plain,
! [SV5: $i] :
( ( ~ ( class_Orderings_Obot @ SV5 )
| ! [SY2390: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ SV5 ) @ SY2390 @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1633]) ).
thf(2312,plain,
! [SV6: $i] :
( ( ! [SY2391: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV6 @ SV6 ) @ tc_bool ) ) @ SY2391 @ ( tc_fun @ ( tc_prod @ SV6 @ SV6 ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1634]) ).
thf(2313,plain,
! [SV7: $i] :
( ( ! [SY2392: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV7 @ tc_bool ) ) @ SY2392 @ ( tc_fun @ SV7 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1635]) ).
thf(2314,plain,
! [SV8: $i] :
( ( ! [SY2393: $i,SY2394: $i,SY2395: $i] :
( ( c_Relation_Orel__comp @ SV8 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SY2393 @ SY2394 ) @ tc_bool ) ) @ SY2395 @ SY2393 @ SY2394 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SY2395 @ SY2394 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1636]) ).
thf(2315,plain,
! [SV9: $i] :
( ( ! [SY2396: $i,SY2397: $i,SY2398: $i] :
( ( c_Relation_Orel__comp @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV9 @ SY2396 ) @ tc_bool ) ) @ SY2397 @ SV9 @ SY2396 @ SY2398 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV9 @ SY2398 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1637]) ).
thf(2316,plain,
! [SV10: $i] :
( ( ! [SY2399: $i,SY2400: $i,SY2401: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV10 @ ( c_Set_Oinsert @ SY2399 @ SY2400 @ SY2401 ) @ ( tc_fun @ SY2401 @ tc_bool ) )
= ( c_Set_Oinsert @ SY2399 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV10 @ SY2400 @ ( tc_fun @ SY2401 @ tc_bool ) ) @ SY2401 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1638]) ).
thf(2317,plain,
! [SV11: $i] :
( ( ! [SY2402: $i,SY2403: $i,SY2404: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ SV11 @ SY2402 @ SY2403 ) @ SY2404 @ ( tc_fun @ SY2403 @ tc_bool ) )
= ( c_Set_Oinsert @ SV11 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2402 @ SY2404 @ ( tc_fun @ SY2403 @ tc_bool ) ) @ SY2403 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1639]) ).
thf(2318,plain,
! [SV12: $i] :
( ( ! [SY2405: $i,SY2406: $i,SY2407: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV12 @ tc_bool ) )
!= ( c_Set_Oimage @ SY2405 @ SY2406 @ SY2407 @ SV12 ) )
| ( SY2406
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2407 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1640]) ).
thf(2319,plain,
! [SV13: $i] :
( ( ! [SY2408: $i,SY2409: $i] : ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Ortrancl @ SV13 @ SY2408 ) @ ( c_Transitive__Closure_Ortrancl @ SY2409 @ SY2408 ) @ ( tc_fun @ ( tc_prod @ SY2408 @ SY2408 ) @ tc_bool ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV13 @ SY2409 @ ( tc_fun @ ( tc_prod @ SY2408 @ SY2408 ) @ tc_bool ) ) @ SY2408 ) @ ( tc_fun @ ( tc_prod @ SY2408 @ SY2408 ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1641]) ).
thf(2320,plain,
! [SV14: $i] :
( ( ! [SY2410: $i,SY2411: $i,SY2412: $i] :
( ( ( hAPP @ ( c_snd @ SV14 @ SY2410 ) @ SY2411 )
!= ( hAPP @ ( c_snd @ SV14 @ SY2410 ) @ SY2412 ) )
| ( ( hAPP @ ( c_fst @ SV14 @ SY2410 ) @ SY2411 )
!= ( hAPP @ ( c_fst @ SV14 @ SY2410 ) @ SY2412 ) )
| ( SY2411 = SY2412 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1642]) ).
thf(2321,plain,
! [SV15: $i] :
( ( ! [SY2413: $i,SY2414: $i,SY2415: $i] :
( ( ( hAPP @ ( c_snd @ SV15 @ SY2413 ) @ SY2414 )
!= ( hAPP @ ( c_snd @ SV15 @ SY2413 ) @ SY2415 ) )
| ( ( hAPP @ ( c_fst @ SV15 @ SY2413 ) @ SY2414 )
!= ( hAPP @ ( c_fst @ SV15 @ SY2413 ) @ SY2415 ) )
| ( SY2414 = SY2415 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1643]) ).
thf(2322,plain,
! [SV16: $i] :
( ( ! [SY2416: $i] :
( ( hBOOL @ ( hAPP @ SV16 @ SY2416 ) )
| ! [SY2417: $i,SY2418: $i] :
( ~ ( hBOOL @ ( hAPP @ SV16 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1 @ SV16 @ SY2417 @ SY2418 ) ) )
| ~ ( c_Wellfounded_Owf @ SY2417 @ SY2418 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1644]) ).
thf(2323,plain,
! [SV17: $i] :
( ( ! [SY2419: $i,SY2420: $i,SY2421: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ ( c_Relation_ORange @ SV17 @ SY2419 @ SY2420 ) @ ( c_Relation_ORange @ SY2421 @ SY2419 @ SY2420 ) @ ( tc_fun @ SY2420 @ tc_bool ) ) @ ( c_Relation_ORange @ ( c_HOL_Ominus__class_Ominus @ SV17 @ SY2421 @ ( tc_fun @ ( tc_prod @ SY2419 @ SY2420 ) @ tc_bool ) ) @ SY2419 @ SY2420 ) @ ( tc_fun @ SY2420 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1645]) ).
thf(2324,plain,
! [SV18: $i] :
( ( ! [SY2422: $i,SY2423: $i,SY2424: $i] :
( ( c_lessequals @ SV18 @ ( c_Set_Oinsert @ SY2422 @ SY2423 @ SY2424 ) @ ( tc_fun @ SY2424 @ tc_bool ) )
| ~ ( c_lessequals @ SV18 @ SY2423 @ ( tc_fun @ SY2424 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1646]) ).
thf(2325,plain,
! [SV19: $i] :
( ( ! [SY2425: $i,SY2426: $i] :
( ( c_lessequals @ SV19 @ SY2425 @ ( tc_fun @ SY2426 @ tc_bool ) )
| ! [SY2427: $i] :
~ ( c_lessequals @ ( c_Set_Oinsert @ SY2427 @ SV19 @ SY2426 ) @ SY2425 @ ( tc_fun @ SY2426 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1647]) ).
thf(2326,plain,
! [SV20: $i] :
( ( ! [SY2428: $i,SY2429: $i,SY2430: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ SV20 @ SY2428 @ SY2429 ) @ SY2430 @ ( tc_fun @ SY2429 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ SY2428 @ SY2430 @ ( tc_fun @ SY2429 @ tc_bool ) ) )
| ~ ( c_in @ SV20 @ SY2430 @ SY2429 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1648]) ).
thf(2327,plain,
! [SV21: $i] :
( ( ! [SY2431: $i,SY2432: $i,SY2433: $i,SY2434: $i] :
( ( c_lessequals @ ( c_Product__Type_OSigma @ SV21 @ ( c_COMBK @ SY2431 @ ( tc_fun @ SY2432 @ tc_bool ) @ SY2433 ) @ SY2433 @ SY2432 ) @ ( c_Product__Type_OSigma @ SY2434 @ ( c_COMBK @ SY2431 @ ( tc_fun @ SY2432 @ tc_bool ) @ SY2433 ) @ SY2433 @ SY2432 ) @ ( tc_fun @ ( tc_prod @ SY2433 @ SY2432 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV21 @ SY2434 @ ( tc_fun @ SY2433 @ tc_bool ) )
| ! [V_x: $i] :
~ ( c_in @ V_x @ SY2431 @ SY2432 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1649]) ).
thf(2328,plain,
! [SV22: $i] :
( ( ! [SY2436: $i,SY2437: $i,SY2438: $i] :
( ( c_lessequals @ SV22 @ SY2436 @ ( tc_fun @ SY2437 @ tc_bool ) )
| ! [SY2439: $i] :
( ~ ( c_lessequals @ ( c_Product__Type_OSigma @ SV22 @ ( c_COMBK @ SY2438 @ ( tc_fun @ SY2439 @ tc_bool ) @ SY2437 ) @ SY2437 @ SY2439 ) @ ( c_Product__Type_OSigma @ SY2436 @ ( c_COMBK @ SY2438 @ ( tc_fun @ SY2439 @ tc_bool ) @ SY2437 ) @ SY2437 @ SY2439 ) @ ( tc_fun @ ( tc_prod @ SY2437 @ SY2439 ) @ tc_bool ) )
| ! [V_x: $i] :
~ ( c_in @ V_x @ SY2438 @ SY2439 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1650]) ).
thf(2329,plain,
! [SV23: $i] :
( ( ! [SY2441: $i,SY2442: $i,SY2443: $i] :
( ( c_lessequals @ SV23 @ ( c_Set_Oinsert @ SY2441 @ SY2442 @ SY2443 ) @ ( tc_fun @ SY2443 @ tc_bool ) )
| ~ ( c_in @ SY2441 @ SV23 @ SY2443 )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV23 @ ( c_Set_Oinsert @ SY2441 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2443 @ tc_bool ) ) @ SY2443 ) @ ( tc_fun @ SY2443 @ tc_bool ) ) @ SY2442 @ ( tc_fun @ SY2443 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1651]) ).
thf(2330,plain,
! [SV24: $i] :
( ( ! [SY2444: $i,SY2445: $i,SY2446: $i] :
( ( c_lessequals @ SV24 @ ( c_Set_Oinsert @ SY2444 @ SY2445 @ SY2446 ) @ ( tc_fun @ SY2446 @ tc_bool ) )
| ~ ( c_in @ SY2444 @ SV24 @ SY2446 )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV24 @ ( c_Set_Oinsert @ SY2444 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2446 @ tc_bool ) ) @ SY2446 ) @ ( tc_fun @ SY2446 @ tc_bool ) ) @ SY2445 @ ( tc_fun @ SY2446 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1652]) ).
thf(2331,plain,
! [SV25: $i] :
( ( ! [SY2447: $i,SY2448: $i,SY2449: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV25 @ ( c_Set_Oinsert @ SY2447 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2448 @ tc_bool ) ) @ SY2448 ) @ ( tc_fun @ SY2448 @ tc_bool ) ) @ SY2449 @ ( tc_fun @ SY2448 @ tc_bool ) )
| ~ ( c_in @ SY2447 @ SV25 @ SY2448 )
| ~ ( c_lessequals @ SV25 @ ( c_Set_Oinsert @ SY2447 @ SY2449 @ SY2448 ) @ ( tc_fun @ SY2448 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1653]) ).
thf(2332,plain,
! [SV26: $i] :
( ( ! [SY2450: $i,SY2451: $i,SY2452: $i] :
( ( ( c_Set_Oimage @ ( c_COMBK @ SV26 @ SY2450 @ SY2451 ) @ SY2452 @ SY2451 @ SY2450 )
= ( c_Set_Oinsert @ SV26 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2450 @ tc_bool ) ) @ SY2450 ) )
| ! [V_x: $i] :
~ ( c_in @ V_x @ SY2452 @ SY2451 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1654]) ).
thf(2333,plain,
! [SV27: $i] :
( ( ! [SY2454: $i,SY2455: $i] :
( ( c_lessequals @ ( c_Transitive__Closure_Otrancl @ SV27 @ SY2454 ) @ SY2455 @ ( tc_fun @ ( tc_prod @ SY2454 @ SY2454 ) @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Relation_Orel__comp @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Transitive__Closure_Otrancl @ SV27 @ SY2454 ) @ SY2455 @ ( tc_fun @ ( tc_prod @ SY2454 @ SY2454 ) @ tc_bool ) ) @ SV27 @ SY2454 @ SY2454 @ SY2454 ) @ SY2455 @ ( tc_fun @ ( tc_prod @ SY2454 @ SY2454 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV27 @ SY2455 @ ( tc_fun @ ( tc_prod @ SY2454 @ SY2454 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1655]) ).
thf(2334,plain,
! [SV28: $i] :
( ( ! [SY2456: $i,SY2457: $i,SY2458: $i,SY2459: $i] :
( ( c_Product__Type_OSigma @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV28 @ SY2456 @ ( tc_fun @ SY2457 @ tc_bool ) ) @ SY2458 @ SY2457 @ SY2459 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Product__Type_OSigma @ SV28 @ SY2458 @ SY2457 @ SY2459 ) @ ( c_Product__Type_OSigma @ SY2456 @ SY2458 @ SY2457 @ SY2459 ) @ ( tc_fun @ ( tc_prod @ SY2457 @ SY2459 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1656]) ).
thf(2335,plain,
! [SV29: $i] :
( ( ! [SY2460: $i] :
( ( SV29 = SY2460 )
| ! [SY2461: $i] :
~ ( c_in @ SV29 @ ( c_Set_Oinsert @ SY2460 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2461 @ tc_bool ) ) @ SY2461 ) @ SY2461 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1657]) ).
thf(2336,plain,
! [SV30: $i] :
( ( ! [SY2462: $i,SY2463: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV30 @ SY2462 @ ( tc_fun @ SY2463 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2463 @ tc_bool ) ) )
| ( ( c_HOL_Ominus__class_Ominus @ SV30 @ SY2462 @ ( tc_fun @ SY2463 @ tc_bool ) )
= SV30 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1658]) ).
thf(2337,plain,
! [SV31: $i] :
( ( ! [SY2464: $i,SY2465: $i,SY2466: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ ( c_Relation_ODomain @ SV31 @ SY2464 @ SY2465 ) @ ( c_Relation_ODomain @ SY2466 @ SY2464 @ SY2465 ) @ ( tc_fun @ SY2464 @ tc_bool ) ) @ ( c_Relation_ODomain @ ( c_HOL_Ominus__class_Ominus @ SV31 @ SY2466 @ ( tc_fun @ ( tc_prod @ SY2464 @ SY2465 ) @ tc_bool ) ) @ SY2464 @ SY2465 ) @ ( tc_fun @ SY2464 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1659]) ).
thf(2338,plain,
! [SV32: $i] :
( ( ! [SY2467: $i,SY2468: $i,SY2469: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV32 @ SY2467 @ ( tc_fun @ SY2468 @ tc_bool ) ) @ SY2469 @ ( tc_fun @ SY2468 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV32 @ SY2469 @ ( tc_fun @ SY2468 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2467 @ SY2469 @ ( tc_fun @ SY2468 @ tc_bool ) ) @ ( tc_fun @ SY2468 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1660]) ).
thf(2339,plain,
! [SV33: $i] :
( ( ! [SY2470: $i,SY2471: $i,SY2472: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV33 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2470 @ SY2471 @ ( tc_fun @ SY2472 @ tc_bool ) ) @ ( tc_fun @ SY2472 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV33 @ SY2470 @ ( tc_fun @ SY2472 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV33 @ SY2471 @ ( tc_fun @ SY2472 @ tc_bool ) ) @ ( tc_fun @ SY2472 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1661]) ).
thf(2340,plain,
! [SV34: $i] :
( ( ! [SY2473: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ SV34 )
| ! [SY2474: $i,SY2475: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY2473 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2474 @ SY2475 @ SV34 ) @ SV34 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2473 @ SY2474 @ SV34 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2473 @ SY2475 @ SV34 ) @ SV34 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1662]) ).
thf(2341,plain,
! [SV35: $i] :
( ( ! [SY2476: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ SV35 )
| ! [SY2477: $i,SY2478: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2476 @ SY2477 @ SV35 ) @ SY2478 @ SV35 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2476 @ SY2478 @ SV35 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2477 @ SY2478 @ SV35 ) @ SV35 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1663]) ).
thf(2342,plain,
! [SV36: $i] :
( ( ! [SY2479: $i] : ( c_lessequals @ ( c_Relation_OId__on @ SV36 @ SY2479 ) @ ( c_Product__Type_OSigma @ SV36 @ ( c_COMBK @ SV36 @ ( tc_fun @ SY2479 @ tc_bool ) @ SY2479 ) @ SY2479 @ SY2479 ) @ ( tc_fun @ ( tc_prod @ SY2479 @ SY2479 ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1664]) ).
thf(2343,plain,
! [SV37: $i] :
( ( ! [SY2480: $i,SY2481: $i] :
( ( c_lessequals @ SV37 @ ( c_Product__Type_OSigma @ SY2480 @ ( c_COMBK @ SY2480 @ ( tc_fun @ SY2481 @ tc_bool ) @ SY2481 ) @ SY2481 @ SY2481 ) @ ( tc_fun @ ( tc_prod @ SY2481 @ SY2481 ) @ tc_bool ) )
| ~ ( c_Relation_Orefl__on @ SY2480 @ SV37 @ SY2481 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1665]) ).
thf(2344,plain,
! [SV38: $i] :
( ( ! [SY2482: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV38 @ SV38 @ ( tc_fun @ SY2482 @ tc_bool ) )
= SV38 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1666]) ).
thf(2345,plain,
! [SV39: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV39 )
| ! [SY2483: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2483 @ SY2483 @ SV39 )
= SY2483 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1667]) ).
thf(2346,plain,
! [SV40: $i] :
( ( ! [SY2484: $i,SY2485: $i,SY2486: $i,SY2487: $i,SY2488: $i,SY2489: $i] :
( ( c_lessequals @ ( c_Relation_Orel__comp @ SV40 @ SY2484 @ SY2485 @ SY2486 @ SY2487 ) @ ( c_Relation_Orel__comp @ SY2488 @ SY2489 @ SY2485 @ SY2486 @ SY2487 ) @ ( tc_fun @ ( tc_prod @ SY2485 @ SY2487 ) @ tc_bool ) )
| ~ ( c_lessequals @ SY2484 @ SY2489 @ ( tc_fun @ ( tc_prod @ SY2486 @ SY2487 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV40 @ SY2488 @ ( tc_fun @ ( tc_prod @ SY2485 @ SY2486 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1668]) ).
thf(2347,plain,
! [SV41: $i] :
( ( ! [SY2490: $i,SY2491: $i,SY2492: $i,SY2493: $i] :
( ( c_Relation_OImage @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV41 @ SY2490 @ ( tc_fun @ ( tc_prod @ SY2491 @ SY2492 ) @ tc_bool ) ) @ SY2493 @ SY2491 @ SY2492 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_OImage @ SV41 @ SY2493 @ SY2491 @ SY2492 ) @ ( c_Relation_OImage @ SY2490 @ SY2493 @ SY2491 @ SY2492 ) @ ( tc_fun @ SY2492 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1669]) ).
thf(2348,plain,
! [SV42: $i] :
( ( ! [SY2494: $i,SY2495: $i,SY2496: $i,SY2497: $i] :
( ( c_Relation_OImage @ SV42 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2494 @ SY2495 @ ( tc_fun @ SY2496 @ tc_bool ) ) @ SY2496 @ SY2497 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_OImage @ SV42 @ SY2494 @ SY2496 @ SY2497 ) @ ( c_Relation_OImage @ SV42 @ SY2495 @ SY2496 @ SY2497 ) @ ( tc_fun @ SY2497 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1670]) ).
thf(2349,plain,
! [SV43: $i] :
( ( ! [SY2498: $i] :
( ( hBOOL @ ( hAPP @ SV43 @ SY2498 ) )
| ! [SY2499: $i,SY2500: $i] :
( ~ ( hBOOL @ ( hAPP @ SV43 @ ( c_List_Osko__Recdef__Xtfl__wf__induct__1__1 @ SV43 @ SY2499 @ SY2500 ) ) )
| ~ ( c_Wellfounded_Owf @ SY2499 @ SY2500 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1671]) ).
thf(2350,plain,
! [SV44: $i] :
( ( ! [SY2501: $i] :
( ( c_Relation_ODomain @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV44 @ SY2501 ) @ tc_bool ) ) @ SV44 @ SY2501 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV44 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1672]) ).
thf(2351,plain,
! [SV45: $i] :
( ( ! [SY2502: $i,SY2503: $i,SY2504: $i] :
( ( c_Set_Oinsert @ SV45 @ ( c_Set_Oinsert @ SY2502 @ SY2503 @ SY2504 ) @ SY2504 )
= ( c_Set_Oinsert @ SY2502 @ ( c_Set_Oinsert @ SV45 @ SY2503 @ SY2504 ) @ SY2504 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1673]) ).
thf(2352,plain,
! [SV46: $i] :
( ( ! [SY2505: $i,SY2506: $i] :
( SV46
= ( c_Pair @ ( hAPP @ ( c_fst @ SY2505 @ SY2506 ) @ SV46 ) @ ( hAPP @ ( c_snd @ SY2505 @ SY2506 ) @ SV46 ) @ SY2505 @ SY2506 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1674]) ).
thf(2353,plain,
! [SV47: $i] :
( ( ! [SY2507: $i,SY2508: $i] :
( ( c_Pair @ ( hAPP @ ( c_fst @ SV47 @ SY2507 ) @ SY2508 ) @ ( hAPP @ ( c_snd @ SV47 @ SY2507 ) @ SY2508 ) @ SV47 @ SY2507 )
= SY2508 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1675]) ).
thf(2354,plain,
! [SV48: $i] :
( ( ! [SY2509: $i,SY2510: $i,SY2511: $i] :
( ( hAPP @ ( c_COMBK @ SV48 @ SY2509 @ SY2510 ) @ SY2511 )
= SV48 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1676]) ).
thf(2355,plain,
! [SV49: $i] :
( ( ! [SY2512: $i,SY2513: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV49 @ SY2512 @ ( tc_fun @ SY2513 @ tc_bool ) ) @ SY2512 @ ( tc_fun @ SY2513 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ SV49 @ SY2512 @ ( tc_fun @ SY2513 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1677]) ).
thf(2356,plain,
! [SV50: $i] :
( ( ! [SY2514: $i,SY2515: $i] :
( ( c_Set_Oinsert @ SV50 @ ( c_Set_Oinsert @ SY2514 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2515 @ tc_bool ) ) @ SY2515 ) @ SY2515 )
= ( c_Set_Oinsert @ SY2514 @ ( c_Set_Oinsert @ SV50 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2515 @ tc_bool ) ) @ SY2515 ) @ SY2515 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1678]) ).
thf(2357,plain,
! [SV51: $i] :
( ( ! [SY2516: $i,SY2517: $i,SY2518: $i,SY2519: $i] :
( ( c_lessequals @ ( c_Relation_OImage @ SV51 @ SY2516 @ SY2517 @ SY2518 ) @ SY2519 @ ( tc_fun @ SY2518 @ tc_bool ) )
| ! [SY2520: $i] :
~ ( c_lessequals @ SV51 @ ( c_Product__Type_OSigma @ SY2520 @ ( c_COMBK @ SY2519 @ ( tc_fun @ SY2518 @ tc_bool ) @ SY2517 ) @ SY2517 @ SY2518 ) @ ( tc_fun @ ( tc_prod @ SY2517 @ SY2518 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1679]) ).
thf(2358,plain,
! [SV52: $i] :
( ( ! [SY2521: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV52 )
| ! [SY2522: $i] :
( ! [SY2523: $i] :
( ( c_HOL_Ominus__class_Ominus @ SY2521 @ SY2522 @ SV52 )
!= ( c_HOL_Ominus__class_Ominus @ SY2523 @ SY2523 @ SV52 ) )
| ( SY2521 = SY2522 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1680]) ).
thf(2359,plain,
! [SV53: $i] :
( ( ! [SY2524: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV53 )
| ! [SY2525: $i,SY2526: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SY2524 @ SY2524 @ SV53 )
!= ( c_HOL_Ominus__class_Ominus @ SY2525 @ SY2526 @ SV53 ) )
| ( SY2525 = SY2526 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1681]) ).
thf(2360,plain,
! [SV54: $i] :
( ( ! [SY2527: $i,SY2528: $i] :
( ( c_Set_Oimage @ SV54 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2527 @ tc_bool ) ) @ SY2527 @ SY2528 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2528 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1682]) ).
thf(2361,plain,
! [SV55: $i] :
( ( ! [SY2529: $i,SY2530: $i,SY2531: $i,SY2532: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oimage @ SV55 @ SY2529 @ SY2530 @ SY2531 ) @ ( c_Set_Oimage @ SV55 @ SY2532 @ SY2530 @ SY2531 ) @ ( tc_fun @ SY2531 @ tc_bool ) ) @ ( c_Set_Oimage @ SV55 @ ( c_HOL_Ominus__class_Ominus @ SY2529 @ SY2532 @ ( tc_fun @ SY2530 @ tc_bool ) ) @ SY2530 @ SY2531 ) @ ( tc_fun @ SY2531 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1683]) ).
thf(2362,plain,
! [SV56: $i] :
( ( ! [SY2533: $i,SY2534: $i,SY2535: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV56 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2533 @ SY2534 @ ( tc_fun @ SY2535 @ tc_bool ) ) @ ( tc_fun @ SY2535 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY2533 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV56 @ SY2534 @ ( tc_fun @ SY2535 @ tc_bool ) ) @ ( tc_fun @ SY2535 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1684]) ).
thf(2363,plain,
! [SV57: $i] :
( ( ! [SY2536: $i,SY2537: $i,SY2538: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV57 @ SY2536 @ ( tc_fun @ SY2537 @ tc_bool ) ) @ SY2538 @ ( tc_fun @ SY2537 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV57 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2536 @ SY2538 @ ( tc_fun @ SY2537 @ tc_bool ) ) @ ( tc_fun @ SY2537 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1685]) ).
thf(2364,plain,
! [SV58: $i] :
( ( ! [SY2539: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV58 )
| ! [SY2540: $i,SY2541: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2539 @ SY2540 @ SV58 ) @ SY2541 @ SV58 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY2539 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2540 @ SY2541 @ SV58 ) @ SV58 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1686]) ).
thf(2365,plain,
! [SV59: $i] :
( ( ! [SY2542: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV59 )
| ! [SY2543: $i,SY2544: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2542 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2543 @ SY2544 @ SV59 ) @ SV59 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY2543 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2542 @ SY2544 @ SV59 ) @ SV59 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1687]) ).
thf(2366,plain,
! [SV60: $i] :
( ( ! [SY2545: $i] :
( ~ ( class_Lattices_Olattice @ SV60 )
| ! [SY2546: $i,SY2547: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2545 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2546 @ SY2547 @ SV60 ) @ SV60 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY2546 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2545 @ SY2547 @ SV60 ) @ SV60 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1688]) ).
thf(2367,plain,
! [SV61: $i] :
( ( ! [SY2548: $i] :
( ~ ( class_Lattices_Olattice @ SV61 )
| ! [SY2549: $i,SY2550: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2548 @ SY2549 @ SV61 ) @ SY2550 @ SV61 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY2548 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2549 @ SY2550 @ SV61 ) @ SV61 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1689]) ).
thf(2368,plain,
! [SV62: $i] :
( ( ! [SY2551: $i,SY2552: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV62 @ SY2551 @ ( tc_fun @ SY2552 @ tc_bool ) )
= SV62 )
| ~ ( c_lessequals @ SV62 @ SY2551 @ ( tc_fun @ SY2552 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1690]) ).
thf(2369,plain,
! [SV63: $i] :
( ( ! [SY2553: $i,SY2554: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV63 @ SY2553 @ ( tc_fun @ SY2554 @ tc_bool ) )
= SY2553 )
| ~ ( c_lessequals @ SY2553 @ SV63 @ ( tc_fun @ SY2554 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1691]) ).
thf(2370,plain,
! [SV64: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV64 )
| ! [SY2555: $i,SY2556: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SY2555 @ SY2556 @ SV64 )
= SY2555 )
| ~ ( c_lessequals @ SY2555 @ SY2556 @ SV64 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1692]) ).
thf(2371,plain,
! [SV65: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV65 )
| ! [SY2557: $i,SY2558: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SY2557 @ SY2558 @ SV65 )
!= SY2557 )
| ( c_lessequals @ SY2557 @ SY2558 @ SV65 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1693]) ).
thf(2372,plain,
! [SV66: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV66 )
| ! [SY2559: $i,SY2560: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SY2559 @ SY2560 @ SV66 )
= SY2560 )
| ~ ( c_lessequals @ SY2560 @ SY2559 @ SV66 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1694]) ).
thf(2373,plain,
! [SV67: $i] :
( ( ! [SY2561: $i,SY2562: $i,SY2563: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV67 @ SY2561 @ ( tc_fun @ SY2562 @ tc_bool ) ) @ SY2563 @ ( tc_fun @ SY2562 @ tc_bool ) )
| ~ ( c_lessequals @ SY2561 @ SY2563 @ ( tc_fun @ SY2562 @ tc_bool ) )
| ~ ( c_lessequals @ SV67 @ SY2563 @ ( tc_fun @ SY2562 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1695]) ).
thf(2374,plain,
! [SV68: $i] :
( ( ! [SY2564: $i,SY2565: $i] : ( c_lessequals @ SV68 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2564 @ SV68 @ ( tc_fun @ SY2565 @ tc_bool ) ) @ ( tc_fun @ SY2565 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1696]) ).
thf(2375,plain,
! [SV69: $i] :
( ( ! [SY2566: $i,SY2567: $i] : ( c_lessequals @ SV69 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV69 @ SY2566 @ ( tc_fun @ SY2567 @ tc_bool ) ) @ ( tc_fun @ SY2567 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1697]) ).
thf(2376,plain,
! [SV70: $i] :
( ( ! [SY2568: $i,SY2569: $i,SY2570: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV70 @ SY2568 @ ( tc_fun @ SY2569 @ tc_bool ) ) @ SY2570 @ ( tc_fun @ SY2569 @ tc_bool ) )
| ~ ( c_lessequals @ SY2568 @ SY2570 @ ( tc_fun @ SY2569 @ tc_bool ) )
| ~ ( c_lessequals @ SV70 @ SY2570 @ ( tc_fun @ SY2569 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1698]) ).
thf(2377,plain,
! [SV71: $i] :
( ( ! [SY2571: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV71 )
| ! [SY2572: $i,SY2573: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2571 @ SY2572 @ SV71 ) @ SY2573 @ SV71 )
| ~ ( c_lessequals @ SY2572 @ SY2573 @ SV71 )
| ~ ( c_lessequals @ SY2571 @ SY2573 @ SV71 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1699]) ).
thf(2378,plain,
! [SV72: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV72 )
| ! [SY2574: $i,SY2575: $i] : ( c_lessequals @ SY2574 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2574 @ SY2575 @ SV72 ) @ SV72 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1700]) ).
thf(2379,plain,
! [SV73: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV73 )
| ! [SY2576: $i,SY2577: $i] : ( c_lessequals @ SY2576 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2577 @ SY2576 @ SV73 ) @ SV73 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1701]) ).
thf(2380,plain,
! [SV74: $i] :
( ( ! [SY2578: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV74 )
| ! [SY2579: $i,SY2580: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2578 @ SY2579 @ SV74 ) @ SY2580 @ SV74 )
| ~ ( c_lessequals @ SY2579 @ SY2580 @ SV74 )
| ~ ( c_lessequals @ SY2578 @ SY2580 @ SV74 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1702]) ).
thf(2381,plain,
! [SV75: $i] :
( ( ! [SY2581: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV75 )
| ! [SY2582: $i,SY2583: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2581 @ SY2582 @ SV75 ) @ SY2583 @ SV75 )
| ~ ( c_lessequals @ SY2582 @ SY2583 @ SV75 )
| ~ ( c_lessequals @ SY2581 @ SY2583 @ SV75 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1703]) ).
thf(2382,plain,
! [SV76: $i] :
( ( ~ ( class_Lattices_Olattice @ SV76 )
| ! [SY2584: $i,SY2585: $i] : ( c_lessequals @ SY2584 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2585 @ SY2584 @ SV76 ) @ SV76 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1704]) ).
thf(2383,plain,
! [SV77: $i] :
( ( ~ ( class_Lattices_Olattice @ SV77 )
| ! [SY2586: $i,SY2587: $i] : ( c_lessequals @ SY2586 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2586 @ SY2587 @ SV77 ) @ SV77 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1705]) ).
thf(2384,plain,
! [SV78: $i] :
( ( ! [SY2588: $i,SY2589: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV78 @ SY2588 @ ( tc_fun @ SY2589 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY2588 @ SV78 @ ( tc_fun @ SY2589 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1706]) ).
thf(2385,plain,
! [SV79: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV79 )
| ! [SY2590: $i,SY2591: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY2590 @ SY2591 @ SV79 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY2591 @ SY2590 @ SV79 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1707]) ).
thf(2386,plain,
! [SV80: $i] :
( ( ~ ( class_Lattices_Olattice @ SV80 )
| ! [SY2592: $i,SY2593: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY2592 @ SY2593 @ SV80 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY2593 @ SY2592 @ SV80 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1708]) ).
thf(2387,plain,
! [SV81: $i] :
( ( ! [SY2594: $i] :
( ( c_Wellfounded_Oacyclic @ SV81 @ SY2594 )
| ~ ( c_Wellfounded_Owf @ SV81 @ SY2594 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1709]) ).
thf(2388,plain,
! [SV82: $i] :
( ( ! [SY2595: $i,SY2596: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV82 @ ( c_HOL_Ominus__class_Ominus @ SY2595 @ SV82 @ ( tc_fun @ SY2596 @ tc_bool ) ) @ ( tc_fun @ SY2596 @ tc_bool ) )
= SY2595 )
| ~ ( c_lessequals @ SV82 @ SY2595 @ ( tc_fun @ SY2596 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1710]) ).
thf(2389,plain,
! [SV83: $i] :
( ( ! [SY2597: $i,SY2598: $i,SY2599: $i] :
( ( c_lessequals @ ( c_Relation_OImage @ SV83 @ ( c_Set_Oinsert @ SY2597 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2598 @ tc_bool ) ) @ SY2598 ) @ SY2598 @ SY2598 ) @ ( c_Relation_OImage @ SV83 @ ( c_Set_Oinsert @ SY2599 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2598 @ tc_bool ) ) @ SY2598 ) @ SY2598 @ SY2598 ) @ ( tc_fun @ SY2598 @ tc_bool ) )
| ~ ( c_in @ ( c_Pair @ SY2597 @ SY2599 @ SY2598 @ SY2598 ) @ SV83 @ ( tc_prod @ SY2598 @ SY2598 ) )
| ! [SY2600: $i] :
~ ( c_Equiv__Relations_Oequiv @ SY2600 @ SV83 @ SY2598 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1711]) ).
thf(2390,plain,
! [SV84: $i] :
( ( ! [SY2601: $i,SY2602: $i] :
( ( c_Relation_OImage @ SV84 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2601 @ tc_bool ) ) @ SY2601 @ SY2602 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2602 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1712]) ).
thf(2391,plain,
! [SV85: $i] :
( ( ! [SY2603: $i,SY2604: $i] :
( ( c_Set_Oinsert @ SV85 @ ( c_Set_Oinsert @ SV85 @ SY2603 @ SY2604 ) @ SY2604 )
= ( c_Set_Oinsert @ SV85 @ SY2603 @ SY2604 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1713]) ).
thf(2392,plain,
! [SV86: $i] :
( ( ! [SY2605: $i] :
( ( hBOOL @ ( hAPP @ SV86 @ SY2605 ) )
| ! [SY2606: $i] :
( ( SY2606 = SY2605 )
| ! [SY2607: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SY2606 @ SV86 @ SY2607 ) @ SY2605 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1714]) ).
thf(2393,plain,
! [SV87: $i] :
( ( ! [SY2608: $i,SY2609: $i,SY2610: $i,SY2611: $i] :
( ( c_Relation_ODomain @ ( c_Set_Oinsert @ ( c_Pair @ SV87 @ SY2608 @ SY2609 @ SY2610 ) @ SY2611 @ ( tc_prod @ SY2609 @ SY2610 ) ) @ SY2609 @ SY2610 )
= ( c_Set_Oinsert @ SV87 @ ( c_Relation_ODomain @ SY2611 @ SY2609 @ SY2610 ) @ SY2609 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1715]) ).
thf(2394,plain,
! [SV88: $i] :
( ( ! [SY2612: $i,SY2613: $i] :
( ( c_Relation_Osym @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV88 @ SY2612 @ ( tc_fun @ ( tc_prod @ SY2613 @ SY2613 ) @ tc_bool ) ) @ SY2613 )
| ~ ( c_Relation_Osym @ SY2612 @ SY2613 )
| ~ ( c_Relation_Osym @ SV88 @ SY2613 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1716]) ).
thf(2395,plain,
! [SV89: $i] :
( ( ! [SY2614: $i,SY2615: $i] :
( ( c_lessequals @ ( c_Transitive__Closure_Ortrancl @ SV89 @ SY2614 ) @ ( c_Transitive__Closure_Ortrancl @ SY2615 @ SY2614 ) @ ( tc_fun @ ( tc_prod @ SY2614 @ SY2614 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV89 @ SY2615 @ ( tc_fun @ ( tc_prod @ SY2614 @ SY2614 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1717]) ).
thf(2396,plain,
! [SV90: $i] :
( ( ! [SY2616: $i,SY2617: $i,SY2618: $i] : ( c_lessequals @ ( c_Relation_ODomain @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV90 @ SY2616 @ ( tc_fun @ ( tc_prod @ SY2617 @ SY2618 ) @ tc_bool ) ) @ SY2617 @ SY2618 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_ODomain @ SV90 @ SY2617 @ SY2618 ) @ ( c_Relation_ODomain @ SY2616 @ SY2617 @ SY2618 ) @ ( tc_fun @ SY2617 @ tc_bool ) ) @ ( tc_fun @ SY2617 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1718]) ).
thf(2397,plain,
! [SV91: $i] :
( ( ~ ( class_Lattices_Obounded__lattice @ SV91 )
| ! [SY2619: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY2619 @ ( c_Orderings_Obot__class_Obot @ SV91 ) @ SV91 )
= ( c_Orderings_Obot__class_Obot @ SV91 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1719]) ).
thf(2398,plain,
! [SV92: $i] :
( ( ~ ( class_Lattices_Obounded__lattice @ SV92 )
| ! [SY2620: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Orderings_Obot__class_Obot @ SV92 ) @ SY2620 @ SV92 )
= ( c_Orderings_Obot__class_Obot @ SV92 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1720]) ).
thf(2399,plain,
! [SV93: $i] :
( ( ! [SY2621: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV93 @ tc_bool ) ) @ SY2621 @ ( tc_fun @ SV93 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV93 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1721]) ).
thf(2400,plain,
! [SV94: $i] :
( ( ! [SY2622: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV94 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2622 @ tc_bool ) ) @ ( tc_fun @ SY2622 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2622 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1722]) ).
thf(2401,plain,
! [SV95: $i] :
( ( ! [SY2623: $i,SY2624: $i] : ( c_lessequals @ SV95 @ ( c_Set_Oinsert @ SY2623 @ SV95 @ SY2624 ) @ ( tc_fun @ SY2624 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1723]) ).
thf(2402,plain,
! [SV96: $i] :
( ( ! [SY2625: $i,SY2626: $i,SY2627: $i,SY2628: $i] : ( c_lessequals @ ( c_Set_Oimage @ SV96 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2625 @ SY2626 @ ( tc_fun @ SY2627 @ tc_bool ) ) @ SY2627 @ SY2628 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oimage @ SV96 @ SY2625 @ SY2627 @ SY2628 ) @ ( c_Set_Oimage @ SV96 @ SY2626 @ SY2627 @ SY2628 ) @ ( tc_fun @ SY2628 @ tc_bool ) ) @ ( tc_fun @ SY2628 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1724]) ).
thf(2403,plain,
! [SV97: $i] :
( ( ! [SY2629: $i,SY2630: $i,SY2631: $i,SY2632: $i] : ( c_lessequals @ ( c_Relation_OImage @ SV97 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2629 @ SY2630 @ ( tc_fun @ SY2631 @ tc_bool ) ) @ SY2631 @ SY2632 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_OImage @ SV97 @ SY2629 @ SY2631 @ SY2632 ) @ ( c_Relation_OImage @ SV97 @ SY2630 @ SY2631 @ SY2632 ) @ ( tc_fun @ SY2632 @ tc_bool ) ) @ ( tc_fun @ SY2632 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1725]) ).
thf(2404,plain,
! [SV98: $i] :
( ( ! [SY2633: $i,SY2634: $i,SY2635: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV98 @ SY2633 @ ( tc_fun @ SY2634 @ tc_bool ) ) @ SY2635 @ ( tc_fun @ SY2634 @ tc_bool ) )
!= ( c_Lattices_Olower__semilattice__class_Oinf @ SV98 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2633 @ SY2635 @ ( tc_fun @ SY2634 @ tc_bool ) ) @ ( tc_fun @ SY2634 @ tc_bool ) ) )
| ( c_lessequals @ SY2635 @ SV98 @ ( tc_fun @ SY2634 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1726]) ).
thf(2405,plain,
! [SV99: $i] :
( ( ! [SY2636: $i,SY2637: $i,SY2638: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV99 @ SY2636 @ ( tc_fun @ SY2637 @ tc_bool ) ) @ SY2638 @ ( tc_fun @ SY2637 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV99 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2636 @ SY2638 @ ( tc_fun @ SY2637 @ tc_bool ) ) @ ( tc_fun @ SY2637 @ tc_bool ) ) )
| ~ ( c_lessequals @ SY2638 @ SV99 @ ( tc_fun @ SY2637 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1727]) ).
thf(2406,plain,
! [SV100: $i] :
( ( ! [SY2639: $i,SY2640: $i,SY2641: $i,SY2642: $i] :
( ( c_Product__Type_OSigma @ ( c_HOL_Ominus__class_Ominus @ SV100 @ SY2639 @ ( tc_fun @ SY2640 @ tc_bool ) ) @ SY2641 @ SY2640 @ SY2642 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Product__Type_OSigma @ SV100 @ SY2641 @ SY2640 @ SY2642 ) @ ( c_Product__Type_OSigma @ SY2639 @ SY2641 @ SY2640 @ SY2642 ) @ ( tc_fun @ ( tc_prod @ SY2640 @ SY2642 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1728]) ).
thf(2407,plain,
! [SV101: $i] :
( ( ! [SY2643: $i] :
( ( c_HOL_Ominus__class_Ominus @ SV101 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2643 @ tc_bool ) ) @ ( tc_fun @ SY2643 @ tc_bool ) )
= SV101 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1729]) ).
thf(2408,plain,
! [SV102: $i] :
( ( ! [SY2644: $i] :
( ( c_HOL_Ominus__class_Ominus @ SV102 @ SV102 @ ( tc_fun @ SY2644 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2644 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1730]) ).
thf(2409,plain,
! [SV103: $i] :
( ( ! [SY2645: $i,SY2646: $i,SY2647: $i,SY2648: $i,SY2649: $i,SY2650: $i] :
( ( c_lessequals @ ( c_Relation_Orel__comp @ SV103 @ SY2645 @ SY2646 @ SY2647 @ SY2648 ) @ ( c_Product__Type_OSigma @ SY2649 @ ( c_COMBK @ SY2650 @ ( tc_fun @ SY2648 @ tc_bool ) @ SY2646 ) @ SY2646 @ SY2648 ) @ ( tc_fun @ ( tc_prod @ SY2646 @ SY2648 ) @ tc_bool ) )
| ! [SY2651: $i] :
( ~ ( c_lessequals @ SY2645 @ ( c_Product__Type_OSigma @ SY2651 @ ( c_COMBK @ SY2650 @ ( tc_fun @ SY2648 @ tc_bool ) @ SY2647 ) @ SY2647 @ SY2648 ) @ ( tc_fun @ ( tc_prod @ SY2647 @ SY2648 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV103 @ ( c_Product__Type_OSigma @ SY2649 @ ( c_COMBK @ SY2651 @ ( tc_fun @ SY2647 @ tc_bool ) @ SY2646 ) @ SY2646 @ SY2647 ) @ ( tc_fun @ ( tc_prod @ SY2646 @ SY2647 ) @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1731]) ).
thf(2410,plain,
! [SV104: $i] :
( ( ! [SY2652: $i,SY2653: $i] :
( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV104 @ SY2652 @ ( tc_fun @ ( tc_prod @ SY2653 @ SY2653 ) @ tc_bool ) ) @ SY2653 )
| ~ ( c_lessequals @ ( c_Relation_Orel__comp @ SV104 @ SY2652 @ SY2653 @ SY2653 @ SY2653 ) @ SV104 @ ( tc_fun @ ( tc_prod @ SY2653 @ SY2653 ) @ tc_bool ) )
| ~ ( c_Wellfounded_Owf @ SY2652 @ SY2653 )
| ~ ( c_Wellfounded_Owf @ SV104 @ SY2653 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1732]) ).
thf(2411,plain,
! [SV105: $i] :
( ( ! [SY2654: $i] :
( ( hBOOL @ ( hAPP @ SV105 @ SY2654 ) )
| ! [SY2655: $i] :
( ( hBOOL @ ( hAPP @ SY2655 @ SY2654 ) )
| ! [SY2656: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2655 @ SV105 @ ( tc_fun @ SY2656 @ tc_bool ) ) @ SY2654 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1733]) ).
thf(2412,plain,
! [SV106: $i] :
( ( ! [SY2657: $i,SY2658: $i,SY2659: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV106 @ SY2657 @ ( tc_fun @ SY2658 @ tc_bool ) ) @ SY2659 ) )
| ~ ( hBOOL @ ( hAPP @ SY2657 @ SY2659 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1734]) ).
thf(2413,plain,
! [SV107: $i] :
( ( ! [SY2660: $i,SY2661: $i,SY2662: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV107 @ SY2660 @ ( tc_fun @ SY2661 @ tc_bool ) ) @ SY2662 ) )
| ~ ( hBOOL @ ( hAPP @ SV107 @ SY2662 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1735]) ).
thf(2414,plain,
! [SV108: $i] :
( ( ! [SY2663: $i,SY2664: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_ODomain @ SV108 @ SY2663 @ SY2663 ) @ ( c_Relation_ORange @ SY2664 @ SY2663 @ SY2663 ) @ ( tc_fun @ SY2663 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2663 @ tc_bool ) ) )
| ~ ( c_Wellfounded_Owf @ SY2664 @ SY2663 )
| ~ ( c_Wellfounded_Owf @ SV108 @ SY2663 )
| ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV108 @ SY2664 @ ( tc_fun @ ( tc_prod @ SY2663 @ SY2663 ) @ tc_bool ) ) @ SY2663 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1736]) ).
thf(2415,plain,
! [SV109: $i] :
( ( ! [SY2665: $i,SY2666: $i,SY2667: $i,SY2668: $i] :
( ( c_Product__Type_OSigma @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV109 @ SY2665 @ ( tc_fun @ SY2666 @ tc_bool ) ) @ ( c_COMBK @ SY2667 @ ( tc_fun @ SY2668 @ tc_bool ) @ SY2666 ) @ SY2666 @ SY2668 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Product__Type_OSigma @ SV109 @ ( c_COMBK @ SY2667 @ ( tc_fun @ SY2668 @ tc_bool ) @ SY2666 ) @ SY2666 @ SY2668 ) @ ( c_Product__Type_OSigma @ SY2665 @ ( c_COMBK @ SY2667 @ ( tc_fun @ SY2668 @ tc_bool ) @ SY2666 ) @ SY2666 @ SY2668 ) @ ( tc_fun @ ( tc_prod @ SY2666 @ SY2668 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1737]) ).
thf(2416,plain,
! [SV110: $i] :
( ( ! [SY2669: $i,SY2670: $i,SY2671: $i,SY2672: $i] :
( ( c_Relation_Orefl__on @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV110 @ SY2669 @ ( tc_fun @ SY2670 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2671 @ SY2672 @ ( tc_fun @ ( tc_prod @ SY2670 @ SY2670 ) @ tc_bool ) ) @ SY2670 )
| ~ ( c_Relation_Orefl__on @ SY2669 @ SY2672 @ SY2670 )
| ~ ( c_Relation_Orefl__on @ SV110 @ SY2671 @ SY2670 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1738]) ).
thf(2417,plain,
! [SV111: $i] :
( ( ! [SY2673: $i] :
( ~ ( class_Lattices_Olattice @ SV111 )
| ! [SY2674: $i,SY2675: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2673 @ SY2674 @ SV111 ) @ SY2675 @ SV111 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY2673 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2674 @ SY2675 @ SV111 ) @ SV111 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1739]) ).
thf(2418,plain,
! [SV112: $i] :
( ( ! [SY2676: $i] :
( ~ ( class_Lattices_Olattice @ SV112 )
| ! [SY2677: $i,SY2678: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY2676 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2677 @ SY2678 @ SV112 ) @ SV112 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY2677 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2676 @ SY2678 @ SV112 ) @ SV112 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1740]) ).
thf(2419,plain,
! [SV113: $i] :
( ( ! [SY2679: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV113 )
| ! [SY2680: $i,SY2681: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY2679 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2680 @ SY2681 @ SV113 ) @ SV113 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY2680 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2679 @ SY2681 @ SV113 ) @ SV113 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1741]) ).
thf(2420,plain,
! [SV114: $i] :
( ( ! [SY2682: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV114 )
| ! [SY2683: $i,SY2684: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2682 @ SY2683 @ SV114 ) @ SY2684 @ SV114 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY2682 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2683 @ SY2684 @ SV114 ) @ SV114 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1742]) ).
thf(2421,plain,
! [SV115: $i] :
( ( ! [SY2685: $i,SY2686: $i,SY2687: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV115 @ SY2685 @ ( tc_fun @ SY2686 @ tc_bool ) ) @ SY2687 @ ( tc_fun @ SY2686 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV115 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2685 @ SY2687 @ ( tc_fun @ SY2686 @ tc_bool ) ) @ ( tc_fun @ SY2686 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1743]) ).
thf(2422,plain,
! [SV116: $i] :
( ( ! [SY2688: $i,SY2689: $i,SY2690: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV116 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2688 @ SY2689 @ ( tc_fun @ SY2690 @ tc_bool ) ) @ ( tc_fun @ SY2690 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY2688 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV116 @ SY2689 @ ( tc_fun @ SY2690 @ tc_bool ) ) @ ( tc_fun @ SY2690 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1744]) ).
thf(2423,plain,
! [SV117: $i] :
( ( ~ ( class_Lattices_Obounded__lattice @ SV117 )
| ! [SY2691: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2691 @ ( c_Orderings_Obot__class_Obot @ SV117 ) @ SV117 )
= SY2691 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1745]) ).
thf(2424,plain,
! [SV118: $i] :
( ( ~ ( class_Lattices_Obounded__lattice @ SV118 )
| ! [SY2692: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ SV118 ) @ SY2692 @ SV118 )
= SY2692 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1746]) ).
thf(2425,plain,
! [SV119: $i] :
( ( ! [SY2693: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV119 @ tc_bool ) ) @ SY2693 @ ( tc_fun @ SV119 @ tc_bool ) )
= SY2693 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1747]) ).
thf(2426,plain,
! [SV120: $i] :
( ( ! [SY2694: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV120 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2694 @ tc_bool ) ) @ ( tc_fun @ SY2694 @ tc_bool ) )
= SV120 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1748]) ).
thf(2427,plain,
! [SV121: $i] :
( ( ! [SY2695: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV121 @ tc_bool ) ) @ SY2695 @ ( tc_fun @ SV121 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV121 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1749]) ).
thf(2428,plain,
! [SV122: $i] :
( ( ! [SY2696: $i,SY2697: $i,SY2698: $i,SY2699: $i,SY2700: $i] :
( ( c_Product__Type_OSigma @ ( c_Set_Oinsert @ SV122 @ SY2696 @ SY2697 ) @ ( c_COMBK @ ( c_Set_Oinsert @ SY2698 @ SY2699 @ SY2700 ) @ ( tc_fun @ SY2700 @ tc_bool ) @ SY2697 ) @ SY2697 @ SY2700 )
= ( c_Set_Oinsert @ ( c_Pair @ SV122 @ SY2698 @ SY2697 @ SY2700 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Product__Type_OSigma @ SY2696 @ ( c_COMBK @ ( c_Set_Oinsert @ SY2698 @ SY2699 @ SY2700 ) @ ( tc_fun @ SY2700 @ tc_bool ) @ SY2697 ) @ SY2697 @ SY2700 ) @ ( c_Product__Type_OSigma @ ( c_Set_Oinsert @ SV122 @ SY2696 @ SY2697 ) @ ( c_COMBK @ SY2699 @ ( tc_fun @ SY2700 @ tc_bool ) @ SY2697 ) @ SY2697 @ SY2700 ) @ ( tc_fun @ ( tc_prod @ SY2697 @ SY2700 ) @ tc_bool ) ) @ ( tc_prod @ SY2697 @ SY2700 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1750]) ).
thf(2429,plain,
! [SV123: $i] :
( ( ! [SY2701: $i] :
( ( SV123
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2701 @ tc_bool ) ) )
| ! [SY2702: $i] :
( ~ ( c_lessequals @ SV123 @ ( c_Relation_OImage @ SY2702 @ SV123 @ SY2701 @ SY2701 ) @ ( tc_fun @ SY2701 @ tc_bool ) )
| ~ ( c_Wellfounded_Owf @ SY2702 @ SY2701 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1751]) ).
thf(2430,plain,
! [SV124: $i] :
( ( ! [SY2703: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV124 @ tc_bool ) ) @ SY2703 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1752]) ).
thf(2431,plain,
! [SV125: $i] :
( ( ! [SY2704: $i,SY2705: $i,SY2706: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV125 @ ( c_HOL_Ominus__class_Ominus @ SY2704 @ SY2705 @ ( tc_fun @ SY2706 @ tc_bool ) ) @ ( tc_fun @ SY2706 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV125 @ SY2704 @ ( tc_fun @ SY2706 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV125 @ SY2705 @ ( tc_fun @ SY2706 @ tc_bool ) ) @ ( tc_fun @ SY2706 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1753]) ).
thf(2432,plain,
! [SV126: $i] :
( ( ! [SY2707: $i,SY2708: $i,SY2709: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_HOL_Ominus__class_Ominus @ SV126 @ SY2707 @ ( tc_fun @ SY2708 @ tc_bool ) ) @ SY2709 @ ( tc_fun @ SY2708 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV126 @ SY2709 @ ( tc_fun @ SY2708 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2707 @ SY2709 @ ( tc_fun @ SY2708 @ tc_bool ) ) @ ( tc_fun @ SY2708 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1754]) ).
thf(2433,plain,
! [SV127: $i] :
( ( ! [SY2710: $i,SY2711: $i,SY2712: $i] :
( ( ( c_Set_Oimage @ ( c_COMBK @ SV127 @ SY2710 @ SY2711 ) @ SY2712 @ SY2711 @ SY2710 )
= ( c_Set_Oinsert @ SV127 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2710 @ tc_bool ) ) @ SY2710 ) )
| ( SY2712
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2711 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1755]) ).
thf(2434,plain,
! [SV128: $i] :
( ( ! [SY2713: $i,SY2714: $i,SY2715: $i,SY2716: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV128 @ SY2713 @ ( tc_fun @ SY2714 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SY2715 @ SY2716 @ ( tc_fun @ SY2714 @ tc_bool ) ) @ ( tc_fun @ SY2714 @ tc_bool ) )
| ~ ( c_lessequals @ SY2716 @ SY2713 @ ( tc_fun @ SY2714 @ tc_bool ) )
| ~ ( c_lessequals @ SV128 @ SY2715 @ ( tc_fun @ SY2714 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1756]) ).
thf(2435,plain,
! [SV129: $i] :
( ( ! [SY2717: $i,SY2718: $i] :
( ~ ( c_in @ SV129 @ SY2717 @ SY2718 )
| ! [SY2719: $i] :
( ~ ( c_in @ SV129 @ SY2719 @ SY2718 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SY2719 @ SY2717 @ ( tc_fun @ SY2718 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2718 @ tc_bool ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1757]) ).
thf(2436,plain,
! [SV130: $i] :
( ( ! [SY2720: $i,SY2721: $i] :
( ( c_Relation_Otrans @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV130 @ SY2720 @ ( tc_fun @ ( tc_prod @ SY2721 @ SY2721 ) @ tc_bool ) ) @ SY2721 )
| ~ ( c_Relation_Otrans @ SY2720 @ SY2721 )
| ~ ( c_Relation_Otrans @ SV130 @ SY2721 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1758]) ).
thf(2437,plain,
! [SV131: $i] :
( ( ! [SY2722: $i] :
( ~ ( class_Lattices_Olattice @ SV131 )
| ! [SY2723: $i,SY2724: $i] : ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2722 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2723 @ SY2724 @ SV131 ) @ SV131 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2722 @ SY2723 @ SV131 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2722 @ SY2724 @ SV131 ) @ SV131 ) @ SV131 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1759]) ).
thf(2438,plain,
! [SV132: $i] :
( ( ! [SY2725: $i,SY2726: $i,SY2727: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV132 @ SY2725 @ ( tc_fun @ SY2726 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2727 @ SY2725 @ ( tc_fun @ SY2726 @ tc_bool ) ) @ ( tc_fun @ SY2726 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV132 @ SY2725 @ ( tc_fun @ SY2726 @ tc_bool ) ) @ SY2727 @ ( tc_fun @ SY2726 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1760]) ).
thf(2439,plain,
! [SV133: $i] :
( ( ~ ( class_Lattices_Olattice @ SV133 )
| ! [SY2728: $i,SY2729: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2728 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2728 @ SY2729 @ SV133 ) @ SV133 )
= SY2728 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1761]) ).
thf(2440,plain,
! [SV134: $i] :
( ( ! [SY2730: $i,SY2731: $i] :
( ( ( c_Relation_Orel__comp @ SV134 @ SY2730 @ SY2731 @ SY2731 @ SY2731 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SY2731 @ SY2731 ) @ tc_bool ) ) )
| ! [SY2732: $i] :
( ( ( c_Relation_Orel__comp @ SY2732 @ SY2730 @ SY2731 @ SY2731 @ SY2731 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SY2731 @ SY2731 ) @ tc_bool ) ) )
| ( ( c_Relation_Orel__comp @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2732 @ SV134 @ ( tc_fun @ ( tc_prod @ SY2731 @ SY2731 ) @ tc_bool ) ) @ SY2730 @ SY2731 @ SY2731 @ SY2731 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SY2731 @ SY2731 ) @ tc_bool ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1762]) ).
thf(2441,plain,
! [SV135: $i] :
( ( ! [SY2733: $i,SY2734: $i] :
( ( ( c_Relation_Orel__comp @ SV135 @ SY2733 @ SY2734 @ SY2734 @ SY2734 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SY2734 @ SY2734 ) @ tc_bool ) ) )
| ! [SY2735: $i] :
( ( ( c_Relation_Orel__comp @ SV135 @ SY2735 @ SY2734 @ SY2734 @ SY2734 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SY2734 @ SY2734 ) @ tc_bool ) ) )
| ( ( c_Relation_Orel__comp @ SV135 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2735 @ SY2733 @ ( tc_fun @ ( tc_prod @ SY2734 @ SY2734 ) @ tc_bool ) ) @ SY2734 @ SY2734 @ SY2734 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SY2734 @ SY2734 ) @ tc_bool ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1763]) ).
thf(2442,plain,
! [SV136: $i] :
( ( ! [SY2736: $i] :
( ( hBOOL @ ( hAPP @ SV136 @ SY2736 ) )
| ! [SY2737: $i,SY2738: $i] :
( ~ ( hBOOL @ ( hAPP @ SV136 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1 @ SV136 @ SY2737 @ SY2738 ) ) )
| ~ ( c_Wellfounded_Owf @ SY2737 @ SY2738 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1764]) ).
thf(2443,plain,
! [SV137: $i] :
( ( ! [SY2739: $i] :
( ( c_Wellfounded_Oacyclic @ SV137 @ SY2739 )
| ~ ( c_Wellfounded_Oacyclic @ ( c_Relation_Oconverse @ SV137 @ SY2739 @ SY2739 ) @ SY2739 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1765]) ).
thf(2444,plain,
! [SV138: $i] :
( ( ! [SY2740: $i] :
( ( c_Wellfounded_Oacyclic @ ( c_Relation_Oconverse @ SV138 @ SY2740 @ SY2740 ) @ SY2740 )
| ~ ( c_Wellfounded_Oacyclic @ SV138 @ SY2740 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1766]) ).
thf(2445,plain,
! [SV139: $i] :
( ( ! [SY2741: $i] :
( ( SV139 = SY2741 )
| ! [SY2742: $i] :
( ~ ( c_lessequals @ SY2741 @ SV139 @ ( tc_fun @ SY2742 @ tc_bool ) )
| ~ ( c_lessequals @ SV139 @ SY2741 @ ( tc_fun @ SY2742 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1767]) ).
thf(2446,plain,
! [SV140: $i] :
( ( ! [SY2743: $i] :
( ( SV140 = SY2743 )
| ! [SY2744: $i] :
( ~ ( c_lessequals @ SY2743 @ SV140 @ ( tc_fun @ SY2744 @ tc_bool ) )
| ~ ( c_lessequals @ SV140 @ SY2743 @ ( tc_fun @ SY2744 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1768]) ).
thf(2447,plain,
! [SV141: $i] :
( ( ~ ( class_Orderings_Oorder @ SV141 )
| ! [SY2745: $i,SY2746: $i] :
( ( SY2745 = SY2746 )
| ~ ( c_lessequals @ SY2746 @ SY2745 @ SV141 )
| ~ ( c_lessequals @ SY2745 @ SY2746 @ SV141 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1769]) ).
thf(2448,plain,
! [SV142: $i] :
( ( ~ ( class_Orderings_Oorder @ SV142 )
| ! [SY2747: $i,SY2748: $i] :
( ( SY2747 = SY2748 )
| ~ ( c_lessequals @ SY2748 @ SY2747 @ SV142 )
| ~ ( c_lessequals @ SY2747 @ SY2748 @ SV142 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1770]) ).
thf(2449,plain,
! [SV143: $i] :
( ( ! [SY2749: $i,SY2750: $i,SY2751: $i,SY2752: $i] :
( ( hAPP @ ( c_split @ SV143 @ SY2749 @ SY2750 @ SY2751 ) @ SY2752 )
= ( hAPP @ ( hAPP @ SV143 @ ( hAPP @ ( c_fst @ SY2749 @ SY2750 ) @ SY2752 ) ) @ ( hAPP @ ( c_snd @ SY2749 @ SY2750 ) @ SY2752 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1771]) ).
thf(2450,plain,
! [SV144: $i] :
( ( ~ ( class_Orderings_Oorder @ SV144 )
| ! [SY2753: $i,SY2754: $i] :
( ( SY2753 = SY2754 )
| ~ ( c_lessequals @ SY2753 @ SY2754 @ SV144 )
| ~ ( c_lessequals @ SY2754 @ SY2753 @ SV144 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1772]) ).
thf(2451,plain,
! [SV145: $i] :
( ( ~ ( class_Lattices_Olattice @ SV145 )
| ! [SY2755: $i,SY2756: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY2755 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2755 @ SY2756 @ SV145 ) @ SV145 )
= SY2755 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1773]) ).
thf(2452,plain,
! [SV146: $i] :
( ( ! [SY2757: $i,SY2758: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ SV146 @ SY2757 @ ( tc_fun @ SY2758 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV146 @ SY2757 @ ( tc_fun @ SY2758 @ tc_bool ) ) @ ( tc_fun @ SY2758 @ tc_bool ) )
= SV146 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1774]) ).
thf(2453,plain,
! [SV147: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV147 )
| ! [SY2759: $i,SY2760: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2759 @ SY2760 @ SV147 )
= SY2759 )
| ~ ( c_lessequals @ SY2760 @ SY2759 @ SV147 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1775]) ).
thf(2454,plain,
! [SV148: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV148 )
| ! [SY2761: $i,SY2762: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2761 @ SY2762 @ SV148 )
!= SY2762 )
| ( c_lessequals @ SY2761 @ SY2762 @ SV148 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1776]) ).
thf(2455,plain,
! [SV149: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV149 )
| ! [SY2763: $i,SY2764: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2763 @ SY2764 @ SV149 )
= SY2764 )
| ~ ( c_lessequals @ SY2763 @ SY2764 @ SV149 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1777]) ).
thf(2456,plain,
! [SV150: $i] :
( ( ! [SY2765: $i,SY2766: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV150 @ SY2765 @ ( tc_fun @ SY2766 @ tc_bool ) )
= SY2765 )
| ~ ( c_lessequals @ SV150 @ SY2765 @ ( tc_fun @ SY2766 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1778]) ).
thf(2457,plain,
! [SV151: $i] :
( ( ! [SY2767: $i,SY2768: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV151 @ SY2767 @ ( tc_fun @ SY2768 @ tc_bool ) )
= SV151 )
| ~ ( c_lessequals @ SY2767 @ SV151 @ ( tc_fun @ SY2768 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1779]) ).
thf(2458,plain,
! [SV152: $i] :
( ( ! [SY2769: $i,SY2770: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV152 @ SY2769 @ ( tc_fun @ SY2770 @ tc_bool ) )
!= SY2769 )
| ( c_lessequals @ SV152 @ SY2769 @ ( tc_fun @ SY2770 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1780]) ).
thf(2459,plain,
! [SV153: $i] :
( ( ! [SY2771: $i,SY2772: $i,SY2773: $i,SY2774: $i] :
( ( c_Relation_Orefl__on @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV153 @ SY2771 @ ( tc_fun @ SY2772 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2773 @ SY2774 @ ( tc_fun @ ( tc_prod @ SY2772 @ SY2772 ) @ tc_bool ) ) @ SY2772 )
| ~ ( c_Relation_Orefl__on @ SY2771 @ SY2774 @ SY2772 )
| ~ ( c_Relation_Orefl__on @ SV153 @ SY2773 @ SY2772 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1781]) ).
thf(2460,plain,
! [SV154: $i] :
( ( c_Relation_Oantisym @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV154 @ SV154 ) @ tc_bool ) ) @ SV154 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1782]) ).
thf(2461,plain,
! [SV155: $i] :
( ( ! [SY2775: $i] :
( ( c_Relation_ORange @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV155 @ SY2775 ) @ tc_bool ) ) @ SV155 @ SY2775 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2775 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1783]) ).
thf(2462,plain,
! [SV156: $i] :
( ( ! [SY2776: $i,SY2777: $i,SY2778: $i,SY2779: $i] :
( ( ( c_Set_Oinsert @ SV156 @ ( c_Set_Oinsert @ SY2776 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2777 @ tc_bool ) ) @ SY2777 ) @ SY2777 )
!= ( c_Set_Oinsert @ SY2778 @ ( c_Set_Oinsert @ SY2779 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2777 @ tc_bool ) ) @ SY2777 ) @ SY2777 ) )
| ( SV156 = SY2779 )
| ( SV156 = SY2778 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1784]) ).
thf(2463,plain,
! [SV157: $i] :
( ( ! [SY2780: $i,SY2781: $i,SY2782: $i] :
( ! [SY2783: $i] :
( ( c_Set_Oinsert @ SV157 @ ( c_Set_Oinsert @ SY2780 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2781 @ tc_bool ) ) @ SY2781 ) @ SY2781 )
!= ( c_Set_Oinsert @ SY2782 @ ( c_Set_Oinsert @ SY2783 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2781 @ tc_bool ) ) @ SY2781 ) @ SY2781 ) )
| ( SY2780 = SY2782 )
| ( SV157 = SY2782 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1785]) ).
thf(2464,plain,
! [SV158: $i] :
( ( ! [SY2784: $i,SY2785: $i,SY2786: $i,SY2787: $i] :
( ( ( c_Set_Oinsert @ SV158 @ ( c_Set_Oinsert @ SY2784 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2785 @ tc_bool ) ) @ SY2785 ) @ SY2785 )
!= ( c_Set_Oinsert @ SY2786 @ ( c_Set_Oinsert @ SY2787 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2785 @ tc_bool ) ) @ SY2785 ) @ SY2785 ) )
| ( SV158 = SY2787 )
| ( SY2784 = SY2787 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1786]) ).
thf(2465,plain,
! [SV159: $i] :
( ( ! [SY2788: $i,SY2789: $i,SY2790: $i,SY2791: $i] :
( ( ( c_Set_Oinsert @ SV159 @ ( c_Set_Oinsert @ SY2788 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2789 @ tc_bool ) ) @ SY2789 ) @ SY2789 )
!= ( c_Set_Oinsert @ SY2790 @ ( c_Set_Oinsert @ SY2791 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2789 @ tc_bool ) ) @ SY2789 ) @ SY2789 ) )
| ( SY2788 = SY2790 )
| ( SY2788 = SY2791 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1787]) ).
thf(2466,plain,
! [SV160: $i] :
( ( ! [SY2792: $i,SY2793: $i] :
( ( c_lessequals @ ( c_Transitive__Closure_Otrancl @ SV160 @ SY2792 ) @ ( c_Product__Type_OSigma @ SY2793 @ ( c_COMBK @ SY2793 @ ( tc_fun @ SY2792 @ tc_bool ) @ SY2792 ) @ SY2792 @ SY2792 ) @ ( tc_fun @ ( tc_prod @ SY2792 @ SY2792 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV160 @ ( c_Product__Type_OSigma @ SY2793 @ ( c_COMBK @ SY2793 @ ( tc_fun @ SY2792 @ tc_bool ) @ SY2792 ) @ SY2792 @ SY2792 ) @ ( tc_fun @ ( tc_prod @ SY2792 @ SY2792 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1788]) ).
thf(2467,plain,
! [SV161: $i] :
( ( ! [SY2794: $i,SY2795: $i] :
( ( c_lessequals @ ( c_Transitive__Closure_Ortrancl @ SV161 @ SY2794 ) @ ( c_Transitive__Closure_Ortrancl @ SY2795 @ SY2794 ) @ ( tc_fun @ ( tc_prod @ SY2794 @ SY2794 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV161 @ ( c_Transitive__Closure_Ortrancl @ SY2795 @ SY2794 ) @ ( tc_fun @ ( tc_prod @ SY2794 @ SY2794 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1789]) ).
thf(2468,plain,
! [SV162: $i] :
( ( ! [SY2796: $i] :
( ( SV162
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2796 @ tc_bool ) ) )
| ~ ( c_lessequals @ SV162 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2796 @ tc_bool ) ) @ ( tc_fun @ SY2796 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1790]) ).
thf(2469,plain,
! [SV163: $i] :
( ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV163 @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV163 @ tc_bool ) ) @ ( tc_fun @ SV163 @ tc_bool ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1791]) ).
thf(2470,plain,
! [SV164: $i] :
( ( ! [SY2797: $i,SY2798: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV164 @ tc_bool ) )
!= ( c_Set_Oinsert @ SY2797 @ SY2798 @ SV164 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1792]) ).
thf(2471,plain,
! [SV165: $i] :
( ( c_Relation_Orefl__on @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV165 @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV165 @ SV165 ) @ tc_bool ) ) @ SV165 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1793]) ).
thf(2472,plain,
! [SV166: $i] :
( ( ! [SY2799: $i,SY2800: $i,SY2801: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ SV166 @ SY2799 @ SY2800 ) @ SY2801 @ ( tc_fun @ SY2800 @ tc_bool ) )
= ( c_Set_Oinsert @ SV166 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2799 @ SY2801 @ ( tc_fun @ SY2800 @ tc_bool ) ) @ SY2800 ) )
| ~ ( c_in @ SV166 @ SY2801 @ SY2800 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1794]) ).
thf(2473,plain,
! [SV167: $i] :
( ( ! [SY2802: $i,SY2803: $i,SY2804: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV167 @ ( c_Set_Oinsert @ SY2802 @ SY2803 @ SY2804 ) @ ( tc_fun @ SY2804 @ tc_bool ) )
= ( c_Set_Oinsert @ SY2802 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV167 @ SY2803 @ ( tc_fun @ SY2804 @ tc_bool ) ) @ SY2804 ) )
| ~ ( c_in @ SY2802 @ SV167 @ SY2804 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1795]) ).
thf(2474,plain,
! [SV168: $i] :
( ( ! [SY2805: $i,SY2806: $i,SY2807: $i,SY2808: $i] :
( ( c_Set_Oimage @ SV168 @ ( c_Set_Oinsert @ SY2805 @ SY2806 @ SY2807 ) @ SY2807 @ SY2808 )
= ( c_Set_Oinsert @ ( hAPP @ SV168 @ SY2805 ) @ ( c_Set_Oimage @ SV168 @ SY2806 @ SY2807 @ SY2808 ) @ SY2808 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1796]) ).
thf(2475,plain,
! [SV169: $i] :
( ( ! [SY2809: $i] : ( c_Relation_Ototal__on @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV169 @ tc_bool ) ) @ SY2809 @ SV169 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1797]) ).
thf(2476,plain,
! [SV170: $i] :
( ( ! [SY2810: $i,SY2811: $i,SY2812: $i,SY2813: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV170 @ SY2810 @ ( tc_fun @ SY2811 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2812 @ SY2813 @ ( tc_fun @ SY2811 @ tc_bool ) ) @ ( tc_fun @ SY2811 @ tc_bool ) )
| ~ ( c_lessequals @ SY2810 @ SY2813 @ ( tc_fun @ SY2811 @ tc_bool ) )
| ~ ( c_lessequals @ SV170 @ SY2812 @ ( tc_fun @ SY2811 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1798]) ).
thf(2477,plain,
! [SV171: $i] :
( ( ! [SY2814: $i,SY2815: $i,SY2816: $i] :
( ( c_Relation_Oconverse @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV171 @ SY2814 @ ( tc_fun @ ( tc_prod @ SY2815 @ SY2816 ) @ tc_bool ) ) @ SY2815 @ SY2816 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Oconverse @ SV171 @ SY2815 @ SY2816 ) @ ( c_Relation_Oconverse @ SY2814 @ SY2815 @ SY2816 ) @ ( tc_fun @ ( tc_prod @ SY2816 @ SY2815 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1799]) ).
thf(2478,plain,
! [SV172: $i] :
( ( ~ ( class_Lattices_Olattice @ SV172 )
| ! [SY2817: $i,SY2818: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2817 @ SY2818 @ SV172 ) @ SY2817 @ SV172 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1800]) ).
thf(2479,plain,
! [SV173: $i] :
( ( ~ ( class_Lattices_Olattice @ SV173 )
| ! [SY2819: $i,SY2820: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2819 @ SY2820 @ SV173 ) @ SY2820 @ SV173 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1801]) ).
thf(2480,plain,
! [SV174: $i] :
( ( ! [SY2821: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV174 )
| ! [SY2822: $i,SY2823: $i] :
( ( c_lessequals @ SY2821 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2822 @ SY2823 @ SV174 ) @ SV174 )
| ~ ( c_lessequals @ SY2821 @ SY2823 @ SV174 )
| ~ ( c_lessequals @ SY2821 @ SY2822 @ SV174 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1802]) ).
thf(2481,plain,
! [SV175: $i] :
( ( ! [SY2824: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV175 )
| ! [SY2825: $i,SY2826: $i] :
( ( c_lessequals @ SY2824 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2825 @ SY2826 @ SV175 ) @ SV175 )
| ~ ( c_lessequals @ SY2824 @ SY2826 @ SV175 )
| ~ ( c_lessequals @ SY2824 @ SY2825 @ SV175 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1803]) ).
thf(2482,plain,
! [SV176: $i] :
( ( ! [SY2827: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV176 )
| ! [SY2828: $i,SY2829: $i] :
( ( c_lessequals @ SY2827 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2828 @ SY2829 @ SV176 ) @ SV176 )
| ~ ( c_lessequals @ SY2827 @ SY2829 @ SV176 )
| ~ ( c_lessequals @ SY2827 @ SY2828 @ SV176 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1804]) ).
thf(2483,plain,
! [SV177: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV177 )
| ! [SY2830: $i,SY2831: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2830 @ SY2831 @ SV177 ) @ SY2831 @ SV177 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1805]) ).
thf(2484,plain,
! [SV178: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV178 )
| ! [SY2832: $i,SY2833: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2832 @ SY2833 @ SV178 ) @ SY2832 @ SV178 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1806]) ).
thf(2485,plain,
! [SV179: $i] :
( ( ! [SY2834: $i,SY2835: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV179 @ SY2834 @ ( tc_fun @ SY2835 @ tc_bool ) ) @ SV179 @ ( tc_fun @ SY2835 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1807]) ).
thf(2486,plain,
! [SV180: $i] :
( ( ! [SY2836: $i,SY2837: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV180 @ SY2836 @ ( tc_fun @ SY2837 @ tc_bool ) ) @ SY2836 @ ( tc_fun @ SY2837 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1808]) ).
thf(2487,plain,
! [SV181: $i] :
( ( ! [SY2838: $i,SY2839: $i,SY2840: $i] :
( ( c_lessequals @ SV181 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2838 @ SY2839 @ ( tc_fun @ SY2840 @ tc_bool ) ) @ ( tc_fun @ SY2840 @ tc_bool ) )
| ~ ( c_lessequals @ SV181 @ SY2839 @ ( tc_fun @ SY2840 @ tc_bool ) )
| ~ ( c_lessequals @ SV181 @ SY2838 @ ( tc_fun @ SY2840 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1809]) ).
thf(2488,plain,
! [SV182: $i] :
( ( ! [SY2841: $i,SY2842: $i,SY2843: $i] :
( ( c_lessequals @ SV182 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2841 @ SY2842 @ ( tc_fun @ SY2843 @ tc_bool ) ) @ ( tc_fun @ SY2843 @ tc_bool ) )
| ~ ( c_lessequals @ SV182 @ SY2842 @ ( tc_fun @ SY2843 @ tc_bool ) )
| ~ ( c_lessequals @ SV182 @ SY2841 @ ( tc_fun @ SY2843 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1810]) ).
thf(2489,plain,
! [SV183: $i] :
( ( ! [SY2844: $i,SY2845: $i,SY2846: $i,SY2847: $i] :
( ( c_Product__Type_OSigma @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV183 @ SY2844 @ ( tc_fun @ SY2845 @ tc_bool ) ) @ ( c_COMBK @ SY2846 @ ( tc_fun @ SY2847 @ tc_bool ) @ SY2845 ) @ SY2845 @ SY2847 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Product__Type_OSigma @ SV183 @ ( c_COMBK @ SY2846 @ ( tc_fun @ SY2847 @ tc_bool ) @ SY2845 ) @ SY2845 @ SY2847 ) @ ( c_Product__Type_OSigma @ SY2844 @ ( c_COMBK @ SY2846 @ ( tc_fun @ SY2847 @ tc_bool ) @ SY2845 ) @ SY2845 @ SY2847 ) @ ( tc_fun @ ( tc_prod @ SY2845 @ SY2847 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1811]) ).
thf(2490,plain,
! [SV184: $i] :
( ( ! [SY2848: $i] :
( ~ ( class_Lattices_Olattice @ SV184 )
| ! [SY2849: $i,SY2850: $i] : ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2848 @ SY2849 @ SV184 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2848 @ SY2850 @ SV184 ) @ SV184 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2848 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2849 @ SY2850 @ SV184 ) @ SV184 ) @ SV184 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1812]) ).
thf(2491,plain,
! [SV185: $i] :
( ( ! [SY2851: $i,SY2852: $i] :
( ( ( c_Transitive__Closure_Ortrancl @ SV185 @ SY2851 )
= ( c_Transitive__Closure_Ortrancl @ SY2852 @ SY2851 ) )
| ~ ( c_lessequals @ SV185 @ ( c_Transitive__Closure_Ortrancl @ SY2852 @ SY2851 ) @ ( tc_fun @ ( tc_prod @ SY2851 @ SY2851 ) @ tc_bool ) )
| ~ ( c_lessequals @ SY2852 @ SV185 @ ( tc_fun @ ( tc_prod @ SY2851 @ SY2851 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1813]) ).
thf(2492,plain,
! [SV186: $i] :
( ( ! [SY2853: $i,SY2854: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV186 @ SY2853 @ ( tc_fun @ SY2854 @ tc_bool ) ) @ SV186 @ ( tc_fun @ SY2854 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1814]) ).
thf(2493,plain,
! [SV187: $i] :
( ( ! [SY2855: $i,SY2856: $i] :
( ( c_Set_Oinsert @ SV187 @ ( c_HOL_Ominus__class_Ominus @ SY2855 @ ( c_Set_Oinsert @ SV187 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2856 @ tc_bool ) ) @ SY2856 ) @ ( tc_fun @ SY2856 @ tc_bool ) ) @ SY2856 )
= ( c_Set_Oinsert @ SV187 @ SY2855 @ SY2856 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1815]) ).
thf(2494,plain,
! [SV188: $i] :
( ( ! [SY2857: $i,SY2858: $i] :
( ( ( c_Set_Oinsert @ SV188 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2857 @ tc_bool ) ) @ SY2857 )
!= ( c_Set_Oinsert @ SY2858 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2857 @ tc_bool ) ) @ SY2857 ) )
| ( SV188 = SY2858 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1816]) ).
thf(2495,plain,
! [SV189: $i] :
( ( ! [SY2859: $i,SY2860: $i,SY2861: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV189 @ SY2859 @ ( tc_fun @ SY2860 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2859 @ SY2861 @ ( tc_fun @ SY2860 @ tc_bool ) ) @ ( tc_fun @ SY2860 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2861 @ SV189 @ ( tc_fun @ SY2860 @ tc_bool ) ) @ ( tc_fun @ SY2860 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV189 @ SY2859 @ ( tc_fun @ SY2860 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2859 @ SY2861 @ ( tc_fun @ SY2860 @ tc_bool ) ) @ ( tc_fun @ SY2860 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2861 @ SV189 @ ( tc_fun @ SY2860 @ tc_bool ) ) @ ( tc_fun @ SY2860 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1817]) ).
thf(2496,plain,
! [SV190: $i] :
( ( ( c_Relation_OId__on @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV190 @ tc_bool ) ) @ SV190 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV190 @ SV190 ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1818]) ).
thf(2497,plain,
! [SV191: $i] :
( ( ! [SY2862: $i,SY2863: $i] :
( ( c_Set_Oimage @ ( c_COMBK @ SV191 @ SY2862 @ SY2863 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2863 @ tc_bool ) ) @ SY2863 @ SY2862 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2862 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1819]) ).
thf(2498,plain,
! [SV192: $i] :
( ( ! [SY2864: $i,SY2865: $i] :
( ( ( c_Set_Oinsert @ SV192 @ SY2864 @ SY2865 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2865 @ tc_bool ) ) )
| ( c_in @ SV192 @ SY2864 @ SY2865 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1820]) ).
thf(2499,plain,
! [SV193: $i] :
( ( c_Wellfounded_Owf @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV193 @ SV193 ) @ tc_bool ) ) @ SV193 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1821]) ).
thf(2500,plain,
! [SV194: $i] :
( ( ! [SY2866: $i,SY2867: $i] :
( ( c_in @ SV194 @ SY2866 @ SY2867 )
| ! [SY2868: $i] :
~ ( c_lessequals @ ( c_Set_Oinsert @ SV194 @ SY2868 @ SY2867 ) @ SY2866 @ ( tc_fun @ SY2867 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1822]) ).
thf(2501,plain,
! [SV195: $i] :
( ( ! [SY2869: $i,SY2870: $i,SY2871: $i,SY2872: $i] :
( ( c_Product__Type_OSigma @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV195 @ SY2869 @ ( tc_fun @ SY2870 @ tc_bool ) ) @ SY2871 @ SY2870 @ SY2872 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Product__Type_OSigma @ SV195 @ SY2871 @ SY2870 @ SY2872 ) @ ( c_Product__Type_OSigma @ SY2869 @ SY2871 @ SY2870 @ SY2872 ) @ ( tc_fun @ ( tc_prod @ SY2870 @ SY2872 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1823]) ).
thf(2502,plain,
! [SV196: $i] :
( ( ! [SY2873: $i,SY2874: $i,SY2875: $i] :
( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV196 @ SY2873 @ SY2874 ) @ SY2875 ) )
| ~ ( hBOOL @ ( hAPP @ SY2873 @ SY2875 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1824]) ).
thf(2503,plain,
! [SV197: $i] :
( ( ! [SY2876: $i,SY2877: $i,SY2878: $i] :
( ( c_lessequals @ SV197 @ ( c_Set_Oinsert @ SY2876 @ SY2877 @ SY2878 ) @ ( tc_fun @ SY2878 @ tc_bool ) )
| ~ ( c_lessequals @ SV197 @ SY2877 @ ( tc_fun @ SY2878 @ tc_bool ) )
| ( c_in @ SY2876 @ SV197 @ SY2878 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1825]) ).
thf(2504,plain,
! [SV198: $i] :
( ( ! [SY2879: $i,SY2880: $i] :
( ( c_lessequals @ SV198 @ SY2879 @ ( tc_fun @ SY2880 @ tc_bool ) )
| ! [SY2881: $i] :
( ( c_in @ SY2881 @ SV198 @ SY2880 )
| ~ ( c_lessequals @ SV198 @ ( c_Set_Oinsert @ SY2881 @ SY2879 @ SY2880 ) @ ( tc_fun @ SY2880 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1826]) ).
thf(2505,plain,
! [SV199: $i] :
( ( ! [SY2882: $i,SY2883: $i,SY2884: $i] :
( ( c_lessequals @ SV199 @ ( c_Set_Oinsert @ SY2882 @ SY2883 @ SY2884 ) @ ( tc_fun @ SY2884 @ tc_bool ) )
| ~ ( c_lessequals @ SV199 @ SY2883 @ ( tc_fun @ SY2884 @ tc_bool ) )
| ( c_in @ SY2882 @ SV199 @ SY2884 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1827]) ).
thf(2506,plain,
! [SV200: $i] :
( ( ! [SY2885: $i,SY2886: $i] :
( ( c_lessequals @ SV200 @ SY2885 @ ( tc_fun @ SY2886 @ tc_bool ) )
| ! [SY2887: $i] :
( ~ ( c_lessequals @ SV200 @ ( c_Set_Oinsert @ SY2887 @ SY2885 @ SY2886 ) @ ( tc_fun @ SY2886 @ tc_bool ) )
| ( c_in @ SY2887 @ SV200 @ SY2886 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1828]) ).
thf(2507,plain,
! [SV201: $i] :
( ( ! [SY2888: $i,SY2889: $i,SY2890: $i] :
( ( c_Relation_Oconverse @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV201 @ SY2888 @ ( tc_fun @ ( tc_prod @ SY2889 @ SY2890 ) @ tc_bool ) ) @ SY2889 @ SY2890 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_Oconverse @ SV201 @ SY2889 @ SY2890 ) @ ( c_Relation_Oconverse @ SY2888 @ SY2889 @ SY2890 ) @ ( tc_fun @ ( tc_prod @ SY2890 @ SY2889 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1829]) ).
thf(2508,plain,
! [SV202: $i] :
( ( ! [SY2891: $i,SY2892: $i,SY2893: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV202 @ ( c_Set_Oinsert @ SY2891 @ SY2892 @ SY2893 ) @ ( tc_fun @ SY2893 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV202 @ SY2892 @ ( tc_fun @ SY2893 @ tc_bool ) ) )
| ( c_in @ SY2891 @ SV202 @ SY2893 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1830]) ).
thf(2509,plain,
! [SV203: $i] :
( ( ! [SY2894: $i,SY2895: $i,SY2896: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ SV203 @ SY2894 @ SY2895 ) @ SY2896 @ ( tc_fun @ SY2895 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY2894 @ SY2896 @ ( tc_fun @ SY2895 @ tc_bool ) ) )
| ( c_in @ SV203 @ SY2896 @ SY2895 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1831]) ).
thf(2510,plain,
! [SV204: $i] :
( ( ! [SY2897: $i,SY2898: $i] :
( ( c_Relation_Ototal__on @ SV204 @ SY2897 @ SY2898 )
| ~ ( c_Order__Relation_Ostrict__linear__order__on @ SV204 @ SY2897 @ SY2898 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1832]) ).
thf(2511,plain,
! [SV205: $i] :
( ( ! [SY2899: $i,SY2900: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV205 @ SY2899 @ ( tc_fun @ SY2900 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2900 @ tc_bool ) ) )
| ( SY2899
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2900 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1833]) ).
thf(2512,plain,
! [SV206: $i] :
( ( ! [SY2901: $i,SY2902: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV206 @ SY2901 @ ( tc_fun @ SY2902 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2902 @ tc_bool ) ) )
| ( SV206
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2902 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1834]) ).
thf(2513,plain,
! [SV207: $i] :
( ( ~ ( class_Lattices_Obounded__lattice @ SV207 )
| ! [SY2903: $i] :
( ! [SY2904: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2903 @ SY2904 @ SV207 )
!= ( c_Orderings_Obot__class_Obot @ SV207 ) )
| ( SY2903
= ( c_Orderings_Obot__class_Obot @ SV207 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1835]) ).
thf(2514,plain,
! [SV208: $i] :
( ( ~ ( class_Lattices_Obounded__lattice @ SV208 )
| ! [SY2905: $i,SY2906: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2905 @ SY2906 @ SV208 )
!= ( c_Orderings_Obot__class_Obot @ SV208 ) )
| ( SY2906
= ( c_Orderings_Obot__class_Obot @ SV208 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1836]) ).
thf(2515,plain,
! [SV209: $i] :
( ( ! [SY2907: $i,SY2908: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ SV209 @ SY2907 @ ( tc_fun @ SY2908 @ tc_bool ) ) @ SY2907 @ ( tc_fun @ SY2908 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV209 @ SY2907 @ ( tc_fun @ SY2908 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1837]) ).
thf(2516,plain,
! [SV210: $i] :
( ( ! [SY2909: $i,SY2910: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV210 @ ( c_HOL_Ominus__class_Ominus @ SY2909 @ SV210 @ ( tc_fun @ SY2910 @ tc_bool ) ) @ ( tc_fun @ SY2910 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV210 @ SY2909 @ ( tc_fun @ SY2910 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1838]) ).
thf(2517,plain,
! [SV211: $i] :
( ( ! [SY2911: $i,SY2912: $i,SY2913: $i,SY2914: $i,SY2915: $i] :
( ( c_Relation_Orel__comp @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV211 @ SY2911 @ ( tc_fun @ ( tc_prod @ SY2912 @ SY2913 ) @ tc_bool ) ) @ SY2914 @ SY2912 @ SY2913 @ SY2915 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ SV211 @ SY2914 @ SY2912 @ SY2913 @ SY2915 ) @ ( c_Relation_Orel__comp @ SY2911 @ SY2914 @ SY2912 @ SY2913 @ SY2915 ) @ ( tc_fun @ ( tc_prod @ SY2912 @ SY2915 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1839]) ).
thf(2518,plain,
! [SV212: $i] :
( ( ! [SY2916: $i,SY2917: $i,SY2918: $i,SY2919: $i,SY2920: $i] :
( ( c_Relation_Orel__comp @ SV212 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2916 @ SY2917 @ ( tc_fun @ ( tc_prod @ SY2918 @ SY2919 ) @ tc_bool ) ) @ SY2920 @ SY2918 @ SY2919 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ SV212 @ SY2916 @ SY2920 @ SY2918 @ SY2919 ) @ ( c_Relation_Orel__comp @ SV212 @ SY2917 @ SY2920 @ SY2918 @ SY2919 ) @ ( tc_fun @ ( tc_prod @ SY2920 @ SY2919 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1840]) ).
thf(2519,plain,
! [SV213: $i] :
( ( ! [SY2921: $i,SY2922: $i] :
( ( c_lessequals @ SV213 @ SY2921 @ ( tc_fun @ SY2922 @ tc_bool ) )
| ! [SY2923: $i] :
~ ( c_lessequals @ SV213 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2923 @ SY2921 @ ( tc_fun @ SY2922 @ tc_bool ) ) @ ( tc_fun @ SY2922 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1841]) ).
thf(2520,plain,
! [SV214: $i] :
( ( ! [SY2924: $i,SY2925: $i] :
( ( c_lessequals @ SV214 @ SY2924 @ ( tc_fun @ SY2925 @ tc_bool ) )
| ! [SY2926: $i] :
~ ( c_lessequals @ SV214 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2924 @ SY2926 @ ( tc_fun @ SY2925 @ tc_bool ) ) @ ( tc_fun @ SY2925 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1842]) ).
thf(2521,plain,
! [SV215: $i] :
( ( ! [SY2927: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV215 )
| ! [SY2928: $i] :
( ( c_lessequals @ SY2927 @ SY2928 @ SV215 )
| ! [SY2929: $i] :
~ ( c_lessequals @ SY2927 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2928 @ SY2929 @ SV215 ) @ SV215 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1843]) ).
thf(2522,plain,
! [SV216: $i] :
( ( ! [SY2930: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV216 )
| ! [SY2931: $i] :
( ( c_lessequals @ SY2930 @ SY2931 @ SV216 )
| ! [SY2932: $i] :
~ ( c_lessequals @ SY2930 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2932 @ SY2931 @ SV216 ) @ SV216 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1844]) ).
thf(2523,plain,
! [SV217: $i] :
( ( ! [SY2933: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV217 )
| ! [SY2934: $i,SY2935: $i] :
( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2933 @ SY2934 @ SV217 ) @ SY2935 @ SV217 )
| ~ ( c_lessequals @ SY2933 @ SY2935 @ SV217 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1845]) ).
thf(2524,plain,
! [SV218: $i] :
( ( ! [SY2936: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV218 )
| ! [SY2937: $i,SY2938: $i] :
( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2936 @ SY2937 @ SV218 ) @ SY2938 @ SV218 )
| ~ ( c_lessequals @ SY2937 @ SY2938 @ SV218 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1846]) ).
thf(2525,plain,
! [SV219: $i] :
( ( ! [SY2939: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV219 )
| ! [SY2940: $i] :
( ( c_lessequals @ SY2939 @ SY2940 @ SV219 )
| ! [SY2941: $i] :
~ ( c_lessequals @ SY2939 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2940 @ SY2941 @ SV219 ) @ SV219 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1847]) ).
thf(2526,plain,
! [SV220: $i] :
( ( ! [SY2942: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV220 )
| ! [SY2943: $i] :
( ( c_lessequals @ SY2942 @ SY2943 @ SV220 )
| ! [SY2944: $i] :
~ ( c_lessequals @ SY2942 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2944 @ SY2943 @ SV220 ) @ SV220 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1848]) ).
thf(2527,plain,
! [SV221: $i] :
( ( ! [SY2945: $i,SY2946: $i,SY2947: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV221 @ SY2945 @ ( tc_fun @ SY2946 @ tc_bool ) ) @ SY2947 @ ( tc_fun @ SY2946 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ SV221 @ SY2947 @ ( tc_fun @ SY2946 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SY2945 @ SY2947 @ ( tc_fun @ SY2946 @ tc_bool ) ) @ ( tc_fun @ SY2946 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1849]) ).
thf(2528,plain,
! [SV222: $i] :
( ( ! [SY2948: $i,SY2949: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV222 @ SY2948 @ ( tc_fun @ SY2949 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY2948 @ SV222 @ ( tc_fun @ SY2949 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1850]) ).
thf(2529,plain,
! [SV223: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV223 )
| ! [SY2950: $i,SY2951: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2950 @ SY2951 @ SV223 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY2951 @ SY2950 @ SV223 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1851]) ).
thf(2530,plain,
! [SV224: $i] :
( ( ~ ( class_Lattices_Olattice @ SV224 )
| ! [SY2952: $i,SY2953: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2952 @ SY2953 @ SV224 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY2953 @ SY2952 @ SV224 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1852]) ).
thf(2531,plain,
! [SV225: $i] :
( ( ! [SY2954: $i,SY2955: $i,SY2956: $i] :
( ( c_Relation_ODomain @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV225 @ SY2954 @ ( tc_fun @ ( tc_prod @ SY2955 @ SY2956 ) @ tc_bool ) ) @ SY2955 @ SY2956 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_ODomain @ SV225 @ SY2955 @ SY2956 ) @ ( c_Relation_ODomain @ SY2954 @ SY2955 @ SY2956 ) @ ( tc_fun @ SY2955 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1853]) ).
thf(2532,plain,
! [SV226: $i] :
( ( ! [SY2957: $i,SY2958: $i] :
( ( c_Set_Oinsert @ SV226 @ SY2957 @ SY2958 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ SV226 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2958 @ tc_bool ) ) @ SY2958 ) @ SY2957 @ ( tc_fun @ SY2958 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1854]) ).
thf(2533,plain,
! [SV227: $i] :
( ( ! [SY2959: $i,SY2960: $i] :
( ( c_Product__Type_OSigma @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV227 @ tc_bool ) ) @ SY2959 @ SV227 @ SY2960 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV227 @ SY2960 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1855]) ).
thf(2534,plain,
! [SV228: $i] :
( ( ! [SY2961: $i,SY2962: $i] :
( ( c_lessequals @ ( c_Wellfounded_Oacc @ SV228 @ SY2961 ) @ ( c_Wellfounded_Oacc @ SY2962 @ SY2961 ) @ ( tc_fun @ SY2961 @ tc_bool ) )
| ~ ( c_lessequals @ SY2962 @ SV228 @ ( tc_fun @ ( tc_prod @ SY2961 @ SY2961 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1856]) ).
thf(2535,plain,
! [SV229: $i] :
( ( ! [SY2963: $i,SY2964: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV229 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV229 @ SY2963 @ ( tc_fun @ SY2964 @ tc_bool ) ) @ ( tc_fun @ SY2964 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV229 @ SY2963 @ ( tc_fun @ SY2964 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1857]) ).
thf(2536,plain,
! [SV230: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV230 )
| ! [SY2965: $i,SY2966: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2965 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2965 @ SY2966 @ SV230 ) @ SV230 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY2965 @ SY2966 @ SV230 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1858]) ).
thf(2537,plain,
! [SV231: $i] :
( ( ~ ( class_Lattices_Olattice @ SV231 )
| ! [SY2967: $i,SY2968: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2967 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2967 @ SY2968 @ SV231 ) @ SV231 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY2967 @ SY2968 @ SV231 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1859]) ).
thf(2538,plain,
! [SV232: $i] :
( ( ! [SY2969: $i,SY2970: $i] :
( ( ( c_Relation_ODomain @ SV232 @ SY2969 @ SY2970 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2969 @ tc_bool ) ) )
| ( SV232
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SY2969 @ SY2970 ) @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1860]) ).
thf(2539,plain,
! [SV233: $i] :
( ( ! [SY2971: $i,SY2972: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV233 @ tc_bool ) )
= ( c_Set_Oimage @ SY2971 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2972 @ tc_bool ) ) @ SY2972 @ SV233 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1861]) ).
thf(2540,plain,
! [SV234: $i] :
( ( ! [SY2973: $i,SY2974: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV234 @ ( c_HOL_Ominus__class_Ominus @ SY2973 @ SV234 @ ( tc_fun @ SY2974 @ tc_bool ) ) @ ( tc_fun @ SY2974 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2974 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1862]) ).
thf(2541,plain,
! [SV235: $i] :
( ( ! [SY2975: $i,SY2976: $i,SY2977: $i] : ( c_lessequals @ ( c_Relation_ORange @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV235 @ SY2975 @ ( tc_fun @ ( tc_prod @ SY2976 @ SY2977 ) @ tc_bool ) ) @ SY2976 @ SY2977 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_ORange @ SV235 @ SY2976 @ SY2977 ) @ ( c_Relation_ORange @ SY2975 @ SY2976 @ SY2977 ) @ ( tc_fun @ SY2977 @ tc_bool ) ) @ ( tc_fun @ SY2977 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1863]) ).
thf(2542,plain,
! [SV236: $i] :
( ( ! [SY2978: $i] :
( ( hBOOL @ ( hAPP @ SV236 @ SY2978 ) )
| ! [SY2979: $i,SY2980: $i] :
( ~ ( hBOOL @ ( hAPP @ SV236 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1 @ SV236 @ SY2979 @ SY2980 ) ) )
| ~ ( c_Wellfounded_Owf @ SY2979 @ SY2980 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1864]) ).
thf(2543,plain,
! [SV237: $i] :
( ( ! [SY2981: $i,SY2982: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Ortrancl @ SV237 @ SY2981 ) @ ( c_Transitive__Closure_Ortrancl @ SY2982 @ SY2981 ) @ ( tc_fun @ ( tc_prod @ SY2981 @ SY2981 ) @ tc_bool ) ) @ SY2981 )
= ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV237 @ SY2982 @ ( tc_fun @ ( tc_prod @ SY2981 @ SY2981 ) @ tc_bool ) ) @ SY2981 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1865]) ).
thf(2544,plain,
! [SV238: $i] :
( ( ! [SY2983: $i,SY2984: $i,SY2985: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ SV238 @ SY2983 @ SY2984 ) @ SY2985 @ ( tc_fun @ SY2984 @ tc_bool ) )
= ( c_Set_Oinsert @ SV238 @ ( c_HOL_Ominus__class_Ominus @ SY2983 @ SY2985 @ ( tc_fun @ SY2984 @ tc_bool ) ) @ SY2984 ) )
| ( c_in @ SV238 @ SY2985 @ SY2984 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1866]) ).
thf(2545,plain,
! [SV239: $i] :
( ( ! [SY2986: $i,SY2987: $i,SY2988: $i] :
( ( c_lessequals @ SV239 @ ( c_Set_Oinsert @ SY2986 @ SY2987 @ SY2988 ) @ ( tc_fun @ SY2988 @ tc_bool ) )
| ~ ( c_lessequals @ SV239 @ SY2987 @ ( tc_fun @ SY2988 @ tc_bool ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV239 @ ( c_Set_Oinsert @ SY2986 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2988 @ tc_bool ) ) @ SY2988 ) @ ( tc_fun @ SY2988 @ tc_bool ) ) @ SY2987 @ ( tc_fun @ SY2988 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1867]) ).
thf(2546,plain,
! [SV240: $i] :
( ( ! [SY2989: $i] :
( ( hBOOL @ ( hAPP @ SV240 @ SY2989 ) )
| ! [SY2990: $i,SY2991: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2990 @ SV240 @ ( tc_fun @ SY2991 @ tc_bool ) ) @ SY2989 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1868]) ).
thf(2547,plain,
! [SV241: $i] :
( ( ! [SY2992: $i] :
( ( hBOOL @ ( hAPP @ SV241 @ SY2992 ) )
| ! [SY2993: $i,SY2994: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV241 @ SY2993 @ ( tc_fun @ SY2994 @ tc_bool ) ) @ SY2992 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1869]) ).
thf(2548,plain,
! [SV242: $i] :
( ( ! [SY2995: $i,SY2996: $i,SY2997: $i,SY2998: $i] :
( ( c_Relation_ORange @ ( c_Set_Oinsert @ ( c_Pair @ SV242 @ SY2995 @ SY2996 @ SY2997 ) @ SY2998 @ ( tc_prod @ SY2996 @ SY2997 ) ) @ SY2996 @ SY2997 )
= ( c_Set_Oinsert @ SY2995 @ ( c_Relation_ORange @ SY2998 @ SY2996 @ SY2997 ) @ SY2997 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1870]) ).
thf(2549,plain,
! [SV243: $i] :
( ( ! [SY2999: $i,SY3000: $i] :
( ( c_Relation_Osym @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV243 @ SY2999 @ ( tc_fun @ ( tc_prod @ SY3000 @ SY3000 ) @ tc_bool ) ) @ SY3000 )
| ~ ( c_Relation_Osym @ SY2999 @ SY3000 )
| ~ ( c_Relation_Osym @ SV243 @ SY3000 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1871]) ).
thf(2550,plain,
! [SV244: $i] :
( ( ! [SY3001: $i,SY3002: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ SV244 @ SY3001 @ SY3002 ) @ ( c_Set_Oinsert @ SV244 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3002 @ tc_bool ) ) @ SY3002 ) @ ( tc_fun @ SY3002 @ tc_bool ) )
= SY3001 )
| ( c_in @ SV244 @ SY3001 @ SY3002 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1872]) ).
thf(2551,plain,
! [SV245: $i] :
( ( ! [SY3003: $i,SY3004: $i,SY3005: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV245 @ SY3003 @ ( tc_fun @ SY3004 @ tc_bool ) ) @ SY3005 @ ( tc_fun @ SY3004 @ tc_bool ) )
| ~ ( c_lessequals @ SV245 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3003 @ SY3005 @ ( tc_fun @ SY3004 @ tc_bool ) ) @ ( tc_fun @ SY3004 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1873]) ).
thf(2552,plain,
! [SV246: $i] :
( ( ! [SY3006: $i,SY3007: $i,SY3008: $i] :
( ( c_lessequals @ SV246 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3006 @ SY3007 @ ( tc_fun @ SY3008 @ tc_bool ) ) @ ( tc_fun @ SY3008 @ tc_bool ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV246 @ SY3006 @ ( tc_fun @ SY3008 @ tc_bool ) ) @ SY3007 @ ( tc_fun @ SY3008 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1874]) ).
thf(2553,plain,
! [SV247: $i] :
( ( ! [SY3009: $i,SY3010: $i,SY3011: $i,SY3012: $i,SY3013: $i] :
( ( ( hAPP @ SV247 @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ SV247 @ SY3009 @ SY3010 @ SY3011 @ SY3012 @ SY3013 ) )
!= ( hAPP @ SY3009 @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ SV247 @ SY3009 @ SY3010 @ SY3011 @ SY3012 @ SY3013 ) ) )
| ( ( c_Recdef_Ocut @ SV247 @ SY3010 @ SY3011 @ SY3012 @ SY3013 )
= ( c_Recdef_Ocut @ SY3009 @ SY3010 @ SY3011 @ SY3012 @ SY3013 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1875]) ).
thf(2554,plain,
! [SV248: $i] :
( ( ! [SY3014: $i] :
( ( c_Wellfounded_Oacyclic @ SV248 @ SY3014 )
| ! [SY3015: $i,SY3016: $i] :
~ ( c_Wellfounded_Oacyclic @ ( c_Set_Oinsert @ ( c_Pair @ SY3015 @ SY3016 @ SY3014 @ SY3014 ) @ SV248 @ ( tc_prod @ SY3014 @ SY3014 ) ) @ SY3014 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1876]) ).
thf(2555,plain,
! [SV249: $i] :
( ( ! [SY3017: $i,SY3018: $i] :
( ~ ( class_HOL_Oord @ SV249 )
| ! [SY3019: $i] :
( ( c_lessequals @ ( hAPP @ SY3017 @ SY3018 ) @ ( hAPP @ SY3019 @ SY3018 ) @ SV249 )
| ! [SY3020: $i] :
~ ( c_lessequals @ SY3017 @ SY3019 @ ( tc_fun @ SY3020 @ SV249 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1877]) ).
thf(2556,plain,
! [SV250: $i] :
( ( ! [SY3021: $i,SY3022: $i,SY3023: $i] :
( ( c_in @ SV250 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3021 @ SY3022 @ ( tc_fun @ SY3023 @ tc_bool ) ) @ SY3023 )
| ~ ( c_in @ SV250 @ SY3022 @ SY3023 )
| ~ ( c_in @ SV250 @ SY3021 @ SY3023 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1878]) ).
thf(2557,plain,
! [SV251: $i] :
( ( ! [SY3024: $i,SY3025: $i,SY3026: $i] :
( ( c_in @ SV251 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3024 @ SY3025 @ ( tc_fun @ SY3026 @ tc_bool ) ) @ SY3026 )
| ~ ( c_in @ SV251 @ SY3025 @ SY3026 )
| ~ ( c_in @ SV251 @ SY3024 @ SY3026 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1879]) ).
thf(2558,plain,
! [SV252: $i] :
( ( ! [SY3027: $i,SY3028: $i,SY3029: $i] :
( ( c_in @ SV252 @ ( c_Set_Oinsert @ SY3027 @ SY3028 @ SY3029 ) @ SY3029 )
| ~ ( c_in @ SV252 @ SY3028 @ SY3029 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1880]) ).
thf(2559,plain,
! [SV253: $i] :
( ( ! [SY3030: $i,SY3031: $i,SY3032: $i] :
( ( c_in @ SV253 @ ( c_Set_Oinsert @ SY3030 @ SY3031 @ SY3032 ) @ SY3032 )
| ~ ( c_in @ SV253 @ SY3031 @ SY3032 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1881]) ).
thf(2560,plain,
! [SV254: $i] :
( ( ! [SY3033: $i,SY3034: $i] :
( ( c_in @ SV254 @ SY3033 @ SY3034 )
| ! [SY3035: $i] :
( ~ ( c_in @ SV254 @ SY3035 @ SY3034 )
| ~ ( c_lessequals @ SY3035 @ SY3033 @ ( tc_fun @ SY3034 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1882]) ).
thf(2561,plain,
! [SV255: $i] :
( ( ! [SY3036: $i,SY3037: $i] :
( ( c_in @ SV255 @ SY3036 @ SY3037 )
| ! [SY3038: $i] :
( ~ ( c_lessequals @ SY3038 @ SY3036 @ ( tc_fun @ SY3037 @ tc_bool ) )
| ~ ( c_in @ SV255 @ SY3038 @ SY3037 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1883]) ).
thf(2562,plain,
! [SV256: $i] :
( ( ! [SY3039: $i,SY3040: $i] :
( ( c_in @ SV256 @ SY3039 @ SY3040 )
| ! [SY3041: $i] :
( ~ ( c_in @ SV256 @ SY3041 @ SY3040 )
| ~ ( c_lessequals @ SY3041 @ SY3039 @ ( tc_fun @ SY3040 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1884]) ).
thf(2563,plain,
! [SV257: $i] :
( ( ! [SY3042: $i,SY3043: $i] :
( ( c_in @ SV257 @ SY3042 @ SY3043 )
| ! [SY3044: $i] :
( ~ ( c_in @ SV257 @ SY3044 @ SY3043 )
| ~ ( c_lessequals @ SY3044 @ SY3042 @ ( tc_fun @ SY3043 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1885]) ).
thf(2564,plain,
! [SV258: $i] :
( ( ! [SY3045: $i,SY3046: $i,SY3047: $i] :
( ( c_in @ SV258 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3045 @ SY3046 @ ( tc_fun @ SY3047 @ tc_bool ) ) @ SY3047 )
| ~ ( c_in @ SV258 @ SY3045 @ SY3047 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1886]) ).
thf(2565,plain,
! [SV259: $i] :
( ( ! [SY3048: $i,SY3049: $i,SY3050: $i] :
( ( c_in @ SV259 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3048 @ SY3049 @ ( tc_fun @ SY3050 @ tc_bool ) ) @ SY3050 )
| ~ ( c_in @ SV259 @ SY3049 @ SY3050 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1887]) ).
thf(2566,plain,
! [SV260: $i] :
( ( ! [SY3051: $i] :
~ ( c_in @ SV260 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3051 @ tc_bool ) ) @ SY3051 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1888]) ).
thf(2567,plain,
! [SV261: $i] :
( ( ! [SY3052: $i] :
( ( hBOOL @ ( hAPP @ SV261 @ SY3052 ) )
| ! [T_a: $i] :
~ ( c_in @ SY3052 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1889]) ).
thf(2568,plain,
! [SV262: $i] :
( ( ! [SY3054: $i] :
~ ( c_in @ SV262 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3054 @ tc_bool ) ) @ SY3054 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1890]) ).
thf(2569,plain,
! [SV263: $i] :
( ( ! [SY3055: $i] :
~ ( c_in @ SV263 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3055 @ tc_bool ) ) @ SY3055 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1891]) ).
thf(2570,plain,
! [SV264: $i] :
( ( ! [SY3056: $i,SY3057: $i] :
( ( c_in @ SV264 @ SY3056 @ SY3057 )
| ! [SY3058: $i] :
( ( SV264 = SY3058 )
| ~ ( c_in @ SV264 @ ( c_Set_Oinsert @ SY3058 @ SY3056 @ SY3057 ) @ SY3057 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1892]) ).
thf(2571,plain,
! [SV265: $i] :
( ( ! [SY3059: $i,SY3060: $i] :
( ( c_in @ SV265 @ SY3059 @ SY3060 )
| ! [SY3061: $i] :
( ( c_in @ SV265 @ SY3061 @ SY3060 )
| ~ ( c_in @ SV265 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3061 @ SY3059 @ ( tc_fun @ SY3060 @ tc_bool ) ) @ SY3060 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1893]) ).
thf(2572,plain,
! [SV266: $i] :
( ( ! [SY3062: $i,SY3063: $i] :
( ~ ( c_in @ SV266 @ SY3062 @ SY3063 )
| ! [SY3064: $i] :
~ ( c_in @ SV266 @ ( c_HOL_Ominus__class_Ominus @ SY3064 @ SY3062 @ ( tc_fun @ SY3063 @ tc_bool ) ) @ SY3063 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1894]) ).
thf(2573,plain,
! [SV267: $i] :
( ( ! [SY3065: $i,SY3066: $i] :
( ( c_in @ SV267 @ SY3065 @ SY3066 )
| ! [SY3067: $i] :
~ ( c_in @ SV267 @ ( c_HOL_Ominus__class_Ominus @ SY3065 @ SY3067 @ ( tc_fun @ SY3066 @ tc_bool ) ) @ SY3066 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1895]) ).
thf(2574,plain,
! [SV268: $i] :
( ( ! [SY3068: $i,SY3069: $i] : ( c_in @ SV268 @ ( c_Set_Oinsert @ SV268 @ SY3068 @ SY3069 ) @ SY3069 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1896]) ).
thf(2575,plain,
! [SV269: $i] :
( ( ! [SY3070: $i,SY3071: $i] : ( c_in @ SV269 @ ( c_Set_Oinsert @ SV269 @ SY3070 @ SY3071 ) @ SY3071 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1897]) ).
thf(2576,plain,
! [SV270: $i] :
( ( ! [SY3072: $i,SY3073: $i] : ( c_in @ SV270 @ ( c_Set_Oinsert @ SV270 @ SY3072 @ SY3073 ) @ SY3073 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1898]) ).
thf(2577,plain,
! [SV271: $i] :
( ( ! [SY3074: $i,SY3075: $i] :
( ( c_in @ SV271 @ SY3074 @ SY3075 )
| ! [SY3076: $i] :
~ ( c_in @ SV271 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3076 @ SY3074 @ ( tc_fun @ SY3075 @ tc_bool ) ) @ SY3075 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1899]) ).
thf(2578,plain,
! [SV272: $i] :
( ( ! [SY3077: $i,SY3078: $i] :
( ( c_in @ SV272 @ SY3077 @ SY3078 )
| ! [SY3079: $i] :
~ ( c_in @ SV272 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3077 @ SY3079 @ ( tc_fun @ SY3078 @ tc_bool ) ) @ SY3078 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1900]) ).
thf(2579,plain,
! [SV273: $i] :
( ( ! [SY3080: $i] :
( ~ ( hBOOL @ ( hAPP @ SV273 @ SY3080 ) )
| ! [T_a: $i] :
~ ( c_in @ SY3080 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1901]) ).
thf(2580,plain,
! [SV274: $i] :
( ( ! [SY3082: $i,SY3083: $i,SY3084: $i] :
( ( c_in @ SV274 @ ( c_HOL_Ominus__class_Ominus @ SY3082 @ SY3083 @ ( tc_fun @ SY3084 @ tc_bool ) ) @ SY3084 )
| ( c_in @ SV274 @ SY3083 @ SY3084 )
| ~ ( c_in @ SV274 @ SY3082 @ SY3084 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1902]) ).
thf(2581,plain,
! [SV275: $i] :
( ( ! [SY3085: $i,SY3086: $i,SY3087: $i] :
( ( c_in @ SV275 @ ( c_HOL_Ominus__class_Ominus @ SY3085 @ SY3086 @ ( tc_fun @ SY3087 @ tc_bool ) ) @ SY3087 )
| ( c_in @ SV275 @ SY3086 @ SY3087 )
| ~ ( c_in @ SV275 @ SY3085 @ SY3087 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1903]) ).
thf(2582,plain,
! [SV276: $i] :
( ( ! [SY3088: $i,SY3089: $i,SY3090: $i] :
( ( ( c_Set_Oinsert @ SV276 @ SY3088 @ SY3089 )
!= ( c_Set_Oinsert @ SV276 @ SY3090 @ SY3089 ) )
| ( c_in @ SV276 @ SY3090 @ SY3089 )
| ( SY3088 = SY3090 )
| ( c_in @ SV276 @ SY3088 @ SY3089 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1904]) ).
thf(2583,plain,
! [SV277: $i] :
( ( ! [SY3091: $i,SY3092: $i] :
( ( ( c_Set_Oinsert @ SV277 @ SY3091 @ SY3092 )
= SY3091 )
| ~ ( c_in @ SV277 @ SY3091 @ SY3092 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1905]) ).
thf(2584,plain,
! [SV278: $i] :
( ( ! [SY3093: $i,SY3094: $i,SY3095: $i] :
( ( hAPP @ ( c_fst @ SV278 @ SY3093 ) @ ( c_Pair @ SY3094 @ SY3095 @ SV278 @ SY3093 ) )
= SY3094 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1906]) ).
thf(2585,plain,
! [SV279: $i] :
( ( ! [SY3096: $i,SY3097: $i,SY3098: $i] :
( SV279
= ( hAPP @ ( c_fst @ SY3096 @ SY3097 ) @ ( c_Pair @ SV279 @ SY3098 @ SY3096 @ SY3097 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1907]) ).
thf(2586,plain,
! [SV280: $i] :
( ( ! [SY3099: $i,SY3100: $i,SY3101: $i] :
( ( hAPP @ ( c_snd @ SV280 @ SY3099 ) @ ( c_Pair @ SY3100 @ SY3101 @ SV280 @ SY3099 ) )
= SY3101 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1908]) ).
thf(2587,plain,
! [SV281: $i] :
( ( ! [SY3102: $i,SY3103: $i,SY3104: $i] :
( SV281
= ( hAPP @ ( c_snd @ SY3102 @ SY3103 ) @ ( c_Pair @ SY3104 @ SV281 @ SY3102 @ SY3103 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1909]) ).
thf(2588,plain,
! [SV282: $i] :
( ( ! [SY3105: $i,SY3106: $i,SY3107: $i,SY3108: $i] :
( ( hBOOL @ ( hAPP @ SV282 @ ( hAPP @ ( c_fst @ SY3105 @ SY3106 ) @ ( c_Pair @ SY3107 @ SY3108 @ SY3105 @ SY3106 ) ) ) )
| ! [V_Q: $i] :
~ ( hBOOL @ ( hAPP @ V_Q @ SY3108 ) )
| ~ ( hBOOL @ ( hAPP @ SV282 @ SY3107 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1910]) ).
thf(2589,plain,
! [SV283: $i] :
( ( ! [SY3110: $i,SY3111: $i,SY3112: $i,SY3113: $i] :
( ( hBOOL @ ( hAPP @ SV283 @ ( hAPP @ ( c_snd @ SY3110 @ SY3111 ) @ ( c_Pair @ SY3112 @ SY3113 @ SY3110 @ SY3111 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ SV283 @ SY3113 ) )
| ! [V_P: $i] :
~ ( hBOOL @ ( hAPP @ V_P @ SY3112 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1911]) ).
thf(2590,plain,
! [SV284: $i] :
( ( ! [SY3115: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ SV284 )
| ! [SY3116: $i,SY3117: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3115 @ SY3116 @ SV284 ) @ SY3117 @ SV284 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3115 @ SY3117 @ SV284 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3116 @ SY3117 @ SV284 ) @ SV284 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1912]) ).
thf(2591,plain,
! [SV285: $i] :
( ( ! [SY3118: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ SV285 )
| ! [SY3119: $i,SY3120: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY3118 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3119 @ SY3120 @ SV285 ) @ SV285 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3118 @ SY3119 @ SV285 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3118 @ SY3120 @ SV285 ) @ SV285 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1913]) ).
thf(2592,plain,
! [SV286: $i] :
( ( ! [SY3121: $i,SY3122: $i,SY3123: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV286 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3121 @ SY3122 @ ( tc_fun @ SY3123 @ tc_bool ) ) @ ( tc_fun @ SY3123 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV286 @ SY3121 @ ( tc_fun @ SY3123 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV286 @ SY3122 @ ( tc_fun @ SY3123 @ tc_bool ) ) @ ( tc_fun @ SY3123 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1914]) ).
thf(2593,plain,
! [SV287: $i] :
( ( ! [SY3124: $i,SY3125: $i,SY3126: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV287 @ SY3124 @ ( tc_fun @ SY3125 @ tc_bool ) ) @ SY3126 @ ( tc_fun @ SY3125 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV287 @ SY3126 @ ( tc_fun @ SY3125 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3124 @ SY3126 @ ( tc_fun @ SY3125 @ tc_bool ) ) @ ( tc_fun @ SY3125 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1915]) ).
thf(2594,plain,
! [SV288: $i] :
( ( ! [SY3127: $i] :
( ( c_Relation_Otrans @ SV288 @ SY3127 )
| ! [SY3128: $i] :
~ ( c_Order__Relation_Ostrict__linear__order__on @ SY3128 @ SV288 @ SY3127 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1916]) ).
thf(2595,plain,
! [SV289: $i] :
( ( ! [SY3129: $i,SY3130: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV289 @ SY3129 @ SY3130 ) @ SV289 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1917]) ).
thf(2596,plain,
! [SV290: $i] :
( ( ! [SY3131: $i,SY3132: $i,SY3133: $i] :
( ( c_lessequals @ ( c_Set_Oinsert @ SV290 @ SY3131 @ SY3132 ) @ SY3133 @ ( tc_fun @ SY3132 @ tc_bool ) )
| ~ ( c_lessequals @ SY3131 @ SY3133 @ ( tc_fun @ SY3132 @ tc_bool ) )
| ~ ( c_in @ SV290 @ SY3133 @ SY3132 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1918]) ).
thf(2597,plain,
! [SV291: $i] :
( ( ! [SY3134: $i,SY3135: $i,SY3136: $i,SY3137: $i] :
( ( c_Product__Type_OSigma @ ( c_HOL_Ominus__class_Ominus @ SV291 @ SY3134 @ ( tc_fun @ SY3135 @ tc_bool ) ) @ ( c_COMBK @ SY3136 @ ( tc_fun @ SY3137 @ tc_bool ) @ SY3135 ) @ SY3135 @ SY3137 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Product__Type_OSigma @ SV291 @ ( c_COMBK @ SY3136 @ ( tc_fun @ SY3137 @ tc_bool ) @ SY3135 ) @ SY3135 @ SY3137 ) @ ( c_Product__Type_OSigma @ SY3134 @ ( c_COMBK @ SY3136 @ ( tc_fun @ SY3137 @ tc_bool ) @ SY3135 ) @ SY3135 @ SY3137 ) @ ( tc_fun @ ( tc_prod @ SY3135 @ SY3137 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1919]) ).
thf(2598,plain,
! [SV292: $i] :
( ( ~ ( class_Lattices_Olattice @ SV292 )
| ! [SY3138: $i,SY3139: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY3138 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3138 @ SY3139 @ SV292 ) @ SV292 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY3138 @ SY3139 @ SV292 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1920]) ).
thf(2599,plain,
! [SV293: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV293 )
| ! [SY3140: $i,SY3141: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY3140 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3140 @ SY3141 @ SV293 ) @ SV293 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY3140 @ SY3141 @ SV293 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1921]) ).
thf(2600,plain,
! [SV294: $i] :
( ( ! [SY3142: $i,SY3143: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV294 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV294 @ SY3142 @ ( tc_fun @ SY3143 @ tc_bool ) ) @ ( tc_fun @ SY3143 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV294 @ SY3142 @ ( tc_fun @ SY3143 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1922]) ).
thf(2601,plain,
! [SV295: $i] :
( ( ! [SY3144: $i,SY3145: $i,SY3146: $i] :
( ( c_Relation_ORange @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV295 @ SY3144 @ ( tc_fun @ ( tc_prod @ SY3145 @ SY3146 ) @ tc_bool ) ) @ SY3145 @ SY3146 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_ORange @ SV295 @ SY3145 @ SY3146 ) @ ( c_Relation_ORange @ SY3144 @ SY3145 @ SY3146 ) @ ( tc_fun @ SY3146 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1923]) ).
thf(2602,plain,
! [SV296: $i] :
( ( ! [SY3147: $i,SY3148: $i] :
( ( c_Wellfounded_Owf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV296 @ SY3147 @ ( tc_fun @ ( tc_prod @ SY3148 @ SY3148 ) @ tc_bool ) ) @ SY3148 )
| ~ ( c_Wellfounded_Owf @ SV296 @ SY3148 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1924]) ).
thf(2603,plain,
! [SV297: $i] :
( ( ! [SY3149: $i,SY3150: $i] :
( ( c_Wellfounded_Owf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV297 @ SY3149 @ ( tc_fun @ ( tc_prod @ SY3150 @ SY3150 ) @ tc_bool ) ) @ SY3150 )
| ~ ( c_Wellfounded_Owf @ SY3149 @ SY3150 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1925]) ).
thf(2604,plain,
! [SV298: $i] :
( ( ! [SY3151: $i,SY3152: $i] :
( ( ( c_Set_Oinsert @ SV298 @ ( c_HOL_Ominus__class_Ominus @ SY3151 @ ( c_Set_Oinsert @ SV298 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3152 @ tc_bool ) ) @ SY3152 ) @ ( tc_fun @ SY3152 @ tc_bool ) ) @ SY3152 )
= SY3151 )
| ~ ( c_in @ SV298 @ SY3151 @ SY3152 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1926]) ).
thf(2605,plain,
! [SV299: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV299 )
| ! [SY3153: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY3153 @ SY3153 @ SV299 )
= SY3153 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1927]) ).
thf(2606,plain,
! [SV300: $i] :
( ( ! [SY3154: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV300 @ SV300 @ ( tc_fun @ SY3154 @ tc_bool ) )
= SV300 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1928]) ).
thf(2607,plain,
! [SV301: $i] :
( ( ! [SY3155: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV301 )
| ! [SY3156: $i] :
( ( c_lessequals @ SY3155 @ SY3156 @ SV301 )
| ! [SY3157: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3157 @ SY3155 @ SV301 ) @ SY3156 @ SV301 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1929]) ).
thf(2608,plain,
! [SV302: $i] :
( ( ! [SY3158: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV302 )
| ! [SY3159: $i] :
( ( c_lessequals @ SY3158 @ SY3159 @ SV302 )
| ! [SY3160: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3158 @ SY3160 @ SV302 ) @ SY3159 @ SV302 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1930]) ).
thf(2609,plain,
! [SV303: $i] :
( ( ! [SY3161: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV303 )
| ! [SY3162: $i,SY3163: $i] :
( ( c_lessequals @ SY3161 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3162 @ SY3163 @ SV303 ) @ SV303 )
| ~ ( c_lessequals @ SY3161 @ SY3163 @ SV303 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1931]) ).
thf(2610,plain,
! [SV304: $i] :
( ( ! [SY3164: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV304 )
| ! [SY3165: $i] :
( ! [SY3166: $i] : ( c_lessequals @ SY3164 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3165 @ SY3166 @ SV304 ) @ SV304 )
| ~ ( c_lessequals @ SY3164 @ SY3165 @ SV304 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1932]) ).
thf(2611,plain,
! [SV305: $i] :
( ( ! [SY3167: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV305 )
| ! [SY3168: $i] :
( ( c_lessequals @ SY3167 @ SY3168 @ SV305 )
| ! [SY3169: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3169 @ SY3167 @ SV305 ) @ SY3168 @ SV305 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1933]) ).
thf(2612,plain,
! [SV306: $i] :
( ( ! [SY3170: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV306 )
| ! [SY3171: $i] :
( ( c_lessequals @ SY3170 @ SY3171 @ SV306 )
| ! [SY3172: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3170 @ SY3172 @ SV306 ) @ SY3171 @ SV306 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1934]) ).
thf(2613,plain,
! [SV307: $i] :
( ( ! [SY3173: $i,SY3174: $i] :
( ( c_lessequals @ SV307 @ SY3173 @ ( tc_fun @ SY3174 @ tc_bool ) )
| ! [SY3175: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV307 @ SY3175 @ ( tc_fun @ SY3174 @ tc_bool ) ) @ SY3173 @ ( tc_fun @ SY3174 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1935]) ).
thf(2614,plain,
! [SV308: $i] :
( ( ! [SY3176: $i,SY3177: $i] :
( ( c_lessequals @ SV308 @ SY3176 @ ( tc_fun @ SY3177 @ tc_bool ) )
| ! [SY3178: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3178 @ SV308 @ ( tc_fun @ SY3177 @ tc_bool ) ) @ SY3176 @ ( tc_fun @ SY3177 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1936]) ).
thf(2615,plain,
! [SV309: $i] :
( ( ! [SY3179: $i] :
( ~ ( class_Orderings_Oorder @ SV309 )
| ! [SY3180: $i] :
( ( c_lessequals @ SY3179 @ SY3180 @ SV309 )
| ! [SY3181: $i] :
( ~ ( c_lessequals @ SY3179 @ SY3181 @ SV309 )
| ~ ( c_lessequals @ SY3181 @ SY3180 @ SV309 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1937]) ).
thf(2616,plain,
! [SV310: $i] :
( ( ! [SY3182: $i] :
( ~ ( class_Orderings_Opreorder @ SV310 )
| ! [SY3183: $i] :
( ( c_lessequals @ SY3182 @ SY3183 @ SV310 )
| ! [SY3184: $i] :
( ~ ( c_lessequals @ SY3184 @ SY3183 @ SV310 )
| ~ ( c_lessequals @ SY3182 @ SY3184 @ SV310 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1938]) ).
thf(2617,plain,
! [SV311: $i] :
( ( ! [SY3185: $i] : ( c_lessequals @ SV311 @ SV311 @ ( tc_fun @ SY3185 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1939]) ).
thf(2618,plain,
! [SV312: $i] :
( ( ! [SY3186: $i] : ( c_lessequals @ SV312 @ SV312 @ ( tc_fun @ SY3186 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1940]) ).
thf(2619,plain,
! [SV313: $i] :
( ( ! [SY3187: $i,SY3188: $i] :
( ( c_lessequals @ SV313 @ SY3187 @ ( tc_fun @ SY3188 @ tc_bool ) )
| ! [SY3189: $i] :
( ~ ( c_lessequals @ SY3189 @ SY3187 @ ( tc_fun @ SY3188 @ tc_bool ) )
| ~ ( c_lessequals @ SV313 @ SY3189 @ ( tc_fun @ SY3188 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1941]) ).
thf(2620,plain,
! [SV314: $i] :
( ( ! [SY3190: $i] :
( ( hBOOL @ ( hAPP @ SV314 @ SY3190 ) )
| ! [SY3191: $i] :
( ~ ( hBOOL @ ( hAPP @ SY3191 @ SY3190 ) )
| ! [SY3192: $i] :
~ ( c_lessequals @ SY3191 @ SV314 @ ( tc_fun @ SY3192 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1942]) ).
thf(2621,plain,
! [SV315: $i] :
( ( ! [SY3193: $i] :
( ( c_Wellfounded_Owf @ SV315 @ SY3193 )
| ! [SY3194: $i] :
( ~ ( c_lessequals @ SV315 @ SY3194 @ ( tc_fun @ ( tc_prod @ SY3193 @ SY3193 ) @ tc_bool ) )
| ~ ( c_Wellfounded_Owf @ SY3194 @ SY3193 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1943]) ).
thf(2622,plain,
! [SV316: $i] :
( ( ~ ( class_Orderings_Oorder @ SV316 )
| ! [SY3195: $i] : ( c_lessequals @ SY3195 @ SY3195 @ SV316 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1944]) ).
thf(2623,plain,
! [SV317: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV317 )
| ! [SY3196: $i] : ( c_lessequals @ SY3196 @ SY3196 @ SV317 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1945]) ).
thf(2624,plain,
! [SV318: $i] :
( ( ! [SY3197: $i] :
( ( c_Relation_Oantisym @ SV318 @ SY3197 )
| ! [SY3198: $i] :
( ~ ( c_Relation_Oantisym @ SY3198 @ SY3197 )
| ~ ( c_lessequals @ SV318 @ SY3198 @ ( tc_fun @ ( tc_prod @ SY3197 @ SY3197 ) @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1946]) ).
thf(2625,plain,
! [SV319: $i] :
( ( ! [SY3199: $i] :
( ( hBOOL @ ( hAPP @ SV319 @ SY3199 ) )
| ! [SY3200: $i] :
( ! [SY3201: $i] :
~ ( c_lessequals @ SY3200 @ SV319 @ ( tc_fun @ SY3201 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ SY3200 @ SY3199 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1947]) ).
thf(2626,plain,
! [SV320: $i] :
( ( ! [SY3202: $i] :
( ( c_Wellfounded_Oacyclic @ SV320 @ SY3202 )
| ! [SY3203: $i] :
( ~ ( c_lessequals @ SV320 @ SY3203 @ ( tc_fun @ ( tc_prod @ SY3202 @ SY3202 ) @ tc_bool ) )
| ~ ( c_Wellfounded_Oacyclic @ SY3203 @ SY3202 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1948]) ).
thf(2627,plain,
! [SV321: $i] :
( ( ! [SY3204: $i,SY3205: $i] :
( ( c_Relation_Osingle__valued @ SV321 @ SY3204 @ SY3205 )
| ! [SY3206: $i] :
( ~ ( c_Relation_Osingle__valued @ SY3206 @ SY3204 @ SY3205 )
| ~ ( c_lessequals @ SV321 @ SY3206 @ ( tc_fun @ ( tc_prod @ SY3204 @ SY3205 ) @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1949]) ).
thf(2628,plain,
! [SV322: $i] :
( ( ! [SY3207: $i,SY3208: $i] :
( ! [SY3209: $i] :
( ( c_Set_Oimage @ SV322 @ SY3207 @ SY3208 @ SY3209 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3209 @ tc_bool ) ) )
| ( SY3207
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3208 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1950]) ).
thf(2629,plain,
! [SV323: $i] :
( ( ! [SY3210: $i,SY3211: $i,SY3212: $i,SY3213: $i] :
( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV323 @ SY3210 @ ( tc_fun @ SY3211 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3212 @ SY3213 @ ( tc_fun @ SY3211 @ tc_bool ) ) @ ( tc_fun @ SY3211 @ tc_bool ) )
| ~ ( c_lessequals @ SY3210 @ SY3213 @ ( tc_fun @ SY3211 @ tc_bool ) )
| ~ ( c_lessequals @ SV323 @ SY3212 @ ( tc_fun @ SY3211 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1951]) ).
thf(2630,plain,
! [SV324: $i] :
( ( ! [SY3214: $i,SY3215: $i,SY3216: $i] :
( ( c_HOL_Ominus__class_Ominus @ SV324 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3214 @ SY3215 @ ( tc_fun @ SY3216 @ tc_bool ) ) @ ( tc_fun @ SY3216 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_HOL_Ominus__class_Ominus @ SV324 @ SY3214 @ ( tc_fun @ SY3216 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV324 @ SY3215 @ ( tc_fun @ SY3216 @ tc_bool ) ) @ ( tc_fun @ SY3216 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1952]) ).
thf(2631,plain,
! [SV325: $i] :
( ( ! [SY3217: $i,SY3218: $i,SY3219: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV325 @ SY3217 @ ( tc_fun @ SY3218 @ tc_bool ) ) @ SY3219 @ ( tc_fun @ SY3218 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV325 @ ( c_HOL_Ominus__class_Ominus @ SY3217 @ SY3219 @ ( tc_fun @ SY3218 @ tc_bool ) ) @ ( tc_fun @ SY3218 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1953]) ).
thf(2632,plain,
! [SV326: $i] :
( ( ! [SY3220: $i] : ( c_in @ SV326 @ ( c_Set_Oinsert @ SV326 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3220 @ tc_bool ) ) @ SY3220 ) @ SY3220 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1954]) ).
thf(2633,plain,
! [SV327: $i] :
( ( ! [SY3221: $i,SY3222: $i,SY3223: $i] :
( ( c_lessequals @ ( c_Relation_ODomain @ SV327 @ SY3221 @ SY3222 ) @ ( c_Relation_ODomain @ SY3223 @ SY3221 @ SY3222 ) @ ( tc_fun @ SY3221 @ tc_bool ) )
| ~ ( c_lessequals @ SV327 @ SY3223 @ ( tc_fun @ ( tc_prod @ SY3221 @ SY3222 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1955]) ).
thf(2634,plain,
! [SV328: $i] :
( ( ! [SY3224: $i,SY3225: $i] :
( ( SV328
= ( c_Set_Oinsert @ SY3224 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3225 @ tc_bool ) ) @ SY3225 ) )
| ( SV328
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3225 @ tc_bool ) ) )
| ~ ( c_lessequals @ SV328 @ ( c_Set_Oinsert @ SY3224 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3225 @ tc_bool ) ) @ SY3225 ) @ ( tc_fun @ SY3225 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1956]) ).
thf(2635,plain,
! [SV329: $i] :
( ( ! [SY3226: $i,SY3227: $i,SY3228: $i] :
( ( c_HOL_Ominus__class_Ominus @ SV329 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3226 @ SY3227 @ ( tc_fun @ SY3228 @ tc_bool ) ) @ ( tc_fun @ SY3228 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ SV329 @ SY3226 @ ( tc_fun @ SY3228 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV329 @ SY3227 @ ( tc_fun @ SY3228 @ tc_bool ) ) @ ( tc_fun @ SY3228 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1957]) ).
thf(2636,plain,
! [SV330: $i] :
( ( ! [SY3229: $i,SY3230: $i] :
( ( c_Product__Type_OSigma @ SV330 @ ( c_COMBK @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3229 @ tc_bool ) ) @ ( tc_fun @ SY3229 @ tc_bool ) @ SY3230 ) @ SY3230 @ SY3229 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SY3230 @ SY3229 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1958]) ).
thf(2637,plain,
! [SV331: $i] :
( ( ! [SY3231: $i,SY3232: $i,SY3233: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV331 @ SY3231 @ ( tc_fun @ SY3232 @ tc_bool ) ) @ SY3233 ) )
| ~ ( hBOOL @ ( hAPP @ SY3231 @ SY3233 ) )
| ~ ( hBOOL @ ( hAPP @ SV331 @ SY3233 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1959]) ).
thf(2638,plain,
! [SV332: $i] :
( ( ! [SY3234: $i,SY3235: $i,SY3236: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV332 @ ( c_HOL_Ominus__class_Ominus @ SY3234 @ SY3235 @ ( tc_fun @ SY3236 @ tc_bool ) ) @ ( tc_fun @ SY3236 @ tc_bool ) )
= SY3235 )
| ~ ( c_lessequals @ SV332 @ SY3234 @ ( tc_fun @ SY3236 @ tc_bool ) )
| ~ ( c_lessequals @ SY3235 @ SV332 @ ( tc_fun @ SY3236 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1960]) ).
thf(2639,plain,
! [SV333: $i] :
( ( ! [SY3237: $i,SY3238: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV333 )
| ! [SY3239: $i,SY3240: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SY3237 @ SY3238 @ SV333 )
!= ( c_HOL_Ominus__class_Ominus @ SY3239 @ SY3240 @ SV333 ) )
| ( c_lessequals @ SY3240 @ SY3239 @ SV333 )
| ~ ( c_lessequals @ SY3238 @ SY3237 @ SV333 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1961]) ).
thf(2640,plain,
! [SV334: $i] :
( ( ! [SY3241: $i,SY3242: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV334 )
| ! [SY3243: $i,SY3244: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SY3241 @ SY3242 @ SV334 )
!= ( c_HOL_Ominus__class_Ominus @ SY3243 @ SY3244 @ SV334 ) )
| ( c_lessequals @ SY3242 @ SY3241 @ SV334 )
| ~ ( c_lessequals @ SY3244 @ SY3243 @ SV334 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1962]) ).
thf(2641,plain,
! [SV335: $i] :
( ( ! [SY3245: $i,SY3246: $i,SY3247: $i,SY3248: $i] :
( ( c_lessequals @ ( c_Set_Oimage @ SV335 @ SY3245 @ SY3246 @ SY3247 ) @ ( c_Set_Oimage @ SV335 @ SY3248 @ SY3246 @ SY3247 ) @ ( tc_fun @ SY3247 @ tc_bool ) )
| ~ ( c_lessequals @ SY3245 @ SY3248 @ ( tc_fun @ SY3246 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1963]) ).
thf(2642,plain,
! [SV336: $i] :
( ( ! [SY3249: $i,SY3250: $i] :
( ~ ( c_lessequals @ SV336 @ SY3249 @ ( tc_fun @ SY3250 @ tc_bool ) )
| ! [SY3251: $i,SY3252: $i] : ( c_lessequals @ ( c_Set_Oimage @ SY3251 @ SV336 @ SY3250 @ SY3252 ) @ ( c_Set_Oimage @ SY3251 @ SY3249 @ SY3250 @ SY3252 ) @ ( tc_fun @ SY3252 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1964]) ).
thf(2643,plain,
! [SV337: $i] :
( ( ! [SY3253: $i,SY3254: $i,SY3255: $i] :
( ( c_lessequals @ ( c_Set_Oinsert @ SV337 @ SY3253 @ SY3254 ) @ ( c_Set_Oinsert @ SV337 @ SY3255 @ SY3254 ) @ ( tc_fun @ SY3254 @ tc_bool ) )
| ~ ( c_lessequals @ SY3253 @ SY3255 @ ( tc_fun @ SY3254 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1965]) ).
thf(2644,plain,
! [SV338: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV338 @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV338 @ tc_bool ) ) @ ( tc_fun @ SV338 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV338 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1966]) ).
thf(2645,plain,
! [SV339: $i] :
( ( ! [SY3256: $i,SY3257: $i,SY3258: $i,SY3259: $i] :
( ( c_Set_Oimage @ SV339 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3256 @ SY3257 @ ( tc_fun @ SY3258 @ tc_bool ) ) @ SY3258 @ SY3259 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ SV339 @ SY3256 @ SY3258 @ SY3259 ) @ ( c_Set_Oimage @ SV339 @ SY3257 @ SY3258 @ SY3259 ) @ ( tc_fun @ SY3259 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1967]) ).
thf(2646,plain,
! [SV340: $i] :
( ( ( c_Transitive__Closure_Otrancl @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV340 @ SV340 ) @ tc_bool ) ) @ SV340 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV340 @ SV340 ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1968]) ).
thf(2647,plain,
! [SV341: $i] :
( ( ! [SY3260: $i,SY3261: $i,SY3262: $i,SY3263: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV341 @ ( hAPP @ ( c_snd @ SY3260 @ SY3261 ) @ ( c_Pair @ SY3262 @ SY3263 @ SY3260 @ SY3261 ) ) ) @ ( hAPP @ ( c_fst @ SY3260 @ SY3261 ) @ ( c_Pair @ SY3262 @ SY3263 @ SY3260 @ SY3261 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV341 @ SY3263 ) @ SY3262 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1969]) ).
thf(2648,plain,
! [SV342: $i] :
( ( ! [SY3264: $i,SY3265: $i] :
( ( ( c_Relation_ORange @ SV342 @ SY3264 @ SY3265 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3265 @ tc_bool ) ) )
| ( SV342
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SY3264 @ SY3265 ) @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1970]) ).
thf(2649,plain,
! [SV343: $i] :
( ( ! [SY3266: $i,SY3267: $i,SY3268: $i,SY3269: $i,SY3270: $i] :
( ( c_lessequals @ ( c_Relation_OImage @ SV343 @ SY3266 @ SY3267 @ SY3268 ) @ ( c_Relation_OImage @ SY3269 @ SY3270 @ SY3267 @ SY3268 ) @ ( tc_fun @ SY3268 @ tc_bool ) )
| ~ ( c_lessequals @ SY3266 @ SY3270 @ ( tc_fun @ SY3267 @ tc_bool ) )
| ~ ( c_lessequals @ SV343 @ SY3269 @ ( tc_fun @ ( tc_prod @ SY3267 @ SY3268 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1971]) ).
thf(2650,plain,
! [SV344: $i] :
( ( ! [SY3271: $i,SY3272: $i] :
( ( c_lessequals @ SV344 @ ( c_Product__Type_OSigma @ SY3271 @ ( c_COMBK @ SY3271 @ ( tc_fun @ SY3272 @ tc_bool ) @ SY3272 ) @ SY3272 @ SY3272 ) @ ( tc_fun @ ( tc_prod @ SY3272 @ SY3272 ) @ tc_bool ) )
| ~ ( c_Equiv__Relations_Oequiv @ SY3271 @ SV344 @ SY3272 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1972]) ).
thf(2651,plain,
! [SV345: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV345 )
| ! [SY3273: $i,SY3274: $i] :
( ( c_lessequals @ SY3273 @ SY3274 @ SV345 )
| ( c_lessequals @ SY3274 @ SY3273 @ SV345 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1973]) ).
thf(2652,plain,
! [SV346: $i] :
( ( ! [SY3275: $i] :
( ( c_Relation_Oirrefl @ SV346 @ SY3275 )
| ! [SY3276: $i] :
~ ( c_Order__Relation_Ostrict__linear__order__on @ SY3276 @ SV346 @ SY3275 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1974]) ).
thf(2653,plain,
! [SV347: $i] :
( ( ! [SY3277: $i,SY3278: $i,SY3279: $i] :
( ( c_Wellfounded_Oacyclic @ ( c_Set_Oinsert @ ( c_Pair @ SV347 @ SY3277 @ SY3278 @ SY3278 ) @ SY3279 @ ( tc_prod @ SY3278 @ SY3278 ) ) @ SY3278 )
| ( c_in @ ( c_Pair @ SY3277 @ SV347 @ SY3278 @ SY3278 ) @ ( c_Transitive__Closure_Ortrancl @ SY3279 @ SY3278 ) @ ( tc_prod @ SY3278 @ SY3278 ) )
| ~ ( c_Wellfounded_Oacyclic @ SY3279 @ SY3278 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1975]) ).
thf(2654,plain,
! [SV348: $i] :
( ( ! [SY3280: $i,SY3281: $i,SY3282: $i] :
( ~ ( c_in @ ( c_Pair @ SV348 @ SY3280 @ SY3281 @ SY3281 ) @ ( c_Transitive__Closure_Ortrancl @ SY3282 @ SY3281 ) @ ( tc_prod @ SY3281 @ SY3281 ) )
| ~ ( c_Wellfounded_Oacyclic @ ( c_Set_Oinsert @ ( c_Pair @ SY3280 @ SV348 @ SY3281 @ SY3281 ) @ SY3282 @ ( tc_prod @ SY3281 @ SY3281 ) ) @ SY3281 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1976]) ).
thf(2655,plain,
! [SV349: $i] :
( ( ! [SY3283: $i,SY3284: $i] :
( ( hBOOL @ ( hAPP @ SV349 @ SY3283 ) )
| ! [SY3285: $i,SY3286: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1 @ SV349 @ SY3284 @ SY3285 @ SY3286 ) @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 @ SV349 @ SY3284 @ SY3285 @ SY3286 ) @ SY3286 @ SY3286 ) @ SY3285 @ ( tc_prod @ SY3286 @ SY3286 ) )
| ~ ( hBOOL @ ( hAPP @ SV349 @ SY3284 ) )
| ~ ( c_in @ ( c_Pair @ SY3283 @ SY3284 @ SY3286 @ SY3286 ) @ ( c_Transitive__Closure_Ortrancl @ SY3285 @ SY3286 ) @ ( tc_prod @ SY3286 @ SY3286 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1977]) ).
thf(2656,plain,
! [SV350: $i] :
( ( ! [SY3287: $i,SY3288: $i] :
( ( hBOOL @ ( hAPP @ SV350 @ SY3287 ) )
| ! [SY3289: $i,SY3290: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 @ SV350 @ SY3288 @ SY3289 @ SY3290 ) @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2 @ SV350 @ SY3288 @ SY3289 @ SY3290 ) @ SY3290 @ SY3290 ) @ SY3289 @ ( tc_prod @ SY3290 @ SY3290 ) )
| ~ ( hBOOL @ ( hAPP @ SV350 @ SY3288 ) )
| ~ ( c_in @ ( c_Pair @ SY3288 @ SY3287 @ SY3290 @ SY3290 ) @ ( c_Transitive__Closure_Ortrancl @ SY3289 @ SY3290 ) @ ( tc_prod @ SY3290 @ SY3290 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1978]) ).
thf(2657,plain,
! [SV351: $i] :
( ( ! [SY3291: $i,SY3292: $i] :
( ( c_in @ SV351 @ ( c_Relation_OImage @ SY3291 @ ( c_Set_Oinsert @ SV351 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3292 @ tc_bool ) ) @ SY3292 ) @ SY3292 @ SY3292 ) @ SY3292 )
| ! [SY3293: $i] :
( ~ ( c_in @ SV351 @ SY3293 @ SY3292 )
| ~ ( c_Equiv__Relations_Oequiv @ SY3293 @ SY3291 @ SY3292 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1979]) ).
thf(2658,plain,
! [SV352: $i] :
( ( ! [SY3294: $i,SY3295: $i] :
( ( c_lessequals @ ( c_Transitive__Closure_Ortrancl @ SV352 @ SY3294 ) @ SY3295 @ ( tc_fun @ ( tc_prod @ SY3294 @ SY3294 ) @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Relation_Orel__comp @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Transitive__Closure_Ortrancl @ SV352 @ SY3294 ) @ SY3295 @ ( tc_fun @ ( tc_prod @ SY3294 @ SY3294 ) @ tc_bool ) ) @ SV352 @ SY3294 @ SY3294 @ SY3294 ) @ SY3295 @ ( tc_fun @ ( tc_prod @ SY3294 @ SY3294 ) @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Relation_OId @ SY3294 ) @ SY3295 @ ( tc_fun @ ( tc_prod @ SY3294 @ SY3294 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1980]) ).
thf(2659,plain,
! [SV353: $i] :
( ( ! [SY3296: $i,SY3297: $i,SY3298: $i] :
( ( c_in @ ( c_Pair @ SV353 @ SY3296 @ SY3297 @ SY3297 ) @ SY3298 @ ( tc_prod @ SY3297 @ SY3297 ) )
| ! [SY3299: $i] :
~ ( c_in @ SY3299 @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_OImage @ SY3298 @ ( c_Set_Oinsert @ SV353 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3297 @ tc_bool ) ) @ SY3297 ) @ SY3297 @ SY3297 ) @ ( c_Relation_OImage @ SY3298 @ ( c_Set_Oinsert @ SY3296 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3297 @ tc_bool ) ) @ SY3297 ) @ SY3297 @ SY3297 ) @ ( tc_fun @ SY3297 @ tc_bool ) ) @ SY3297 )
| ! [V_A: $i] :
~ ( c_Equiv__Relations_Oequiv @ V_A @ SY3298 @ SY3297 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1981]) ).
thf(2660,plain,
! [SV354: $i] :
( ( ! [SY3301: $i,SY3302: $i,SY3303: $i] :
( ( c_in @ ( c_Pair @ SV354 @ SY3301 @ SY3302 @ SY3302 ) @ SY3303 @ ( tc_prod @ SY3302 @ SY3302 ) )
| ! [SY3304: $i] :
( ~ ( c_in @ SY3301 @ SY3304 @ SY3302 )
| ~ ( c_lessequals @ ( c_Relation_OImage @ SY3303 @ ( c_Set_Oinsert @ SY3301 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3302 @ tc_bool ) ) @ SY3302 ) @ SY3302 @ SY3302 ) @ ( c_Relation_OImage @ SY3303 @ ( c_Set_Oinsert @ SV354 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3302 @ tc_bool ) ) @ SY3302 ) @ SY3302 @ SY3302 ) @ ( tc_fun @ SY3302 @ tc_bool ) )
| ~ ( c_Equiv__Relations_Oequiv @ SY3304 @ SY3303 @ SY3302 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1982]) ).
thf(2661,plain,
! [SV355: $i] :
( ( ! [SY3305: $i,SY3306: $i,SY3307: $i] :
( ! [SY3308: $i] :
( ( c_Set_Oinsert @ ( hAPP @ SV355 @ SY3305 ) @ ( c_Set_Oimage @ SV355 @ SY3306 @ SY3307 @ SY3308 ) @ SY3308 )
= ( c_Set_Oimage @ SV355 @ SY3306 @ SY3307 @ SY3308 ) )
| ~ ( c_in @ SY3305 @ SY3306 @ SY3307 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1983]) ).
thf(2662,plain,
! [SV356: $i] :
( ( ! [SY3309: $i,SY3310: $i,SY3311: $i] :
( ( c_in @ ( hAPP @ SV356 @ SY3309 ) @ SY3310 @ SY3311 )
| ! [SY3312: $i,SY3313: $i] :
( ~ ( c_in @ SY3309 @ SY3312 @ SY3313 )
| ~ ( c_lessequals @ ( c_Set_Oimage @ SV356 @ SY3312 @ SY3313 @ SY3311 ) @ SY3310 @ ( tc_fun @ SY3311 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1984]) ).
thf(2663,plain,
! [SV357: $i] :
( ( ! [SY3314: $i,SY3315: $i,SY3316: $i,SY3317: $i] :
( ( c_in @ ( c_Pair @ SV357 @ SY3314 @ SY3315 @ SY3316 ) @ SY3317 @ ( tc_prod @ SY3315 @ SY3316 ) )
| ~ ( c_in @ SY3314 @ ( c_Relation_OImage @ SY3317 @ ( c_Set_Oinsert @ SV357 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3315 @ tc_bool ) ) @ SY3315 ) @ SY3315 @ SY3316 ) @ SY3316 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1985]) ).
thf(2664,plain,
! [SV358: $i] :
( ( ! [SY3318: $i,SY3319: $i,SY3320: $i,SY3321: $i] :
( ( c_in @ SV358 @ ( c_Relation_OImage @ SY3318 @ ( c_Set_Oinsert @ SY3319 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3320 @ tc_bool ) ) @ SY3320 ) @ SY3320 @ SY3321 ) @ SY3321 )
| ~ ( c_in @ ( c_Pair @ SY3319 @ SV358 @ SY3320 @ SY3321 ) @ SY3318 @ ( tc_prod @ SY3320 @ SY3321 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1986]) ).
thf(2665,plain,
! [SV359: $i] :
( ( ! [SY3322: $i,SY3323: $i,SY3324: $i,SY3325: $i] :
( ( ( c_Product__Type_OSigma @ SV359 @ ( c_COMBK @ SY3322 @ ( tc_fun @ SY3323 @ tc_bool ) @ SY3324 ) @ SY3324 @ SY3323 )
!= ( c_Product__Type_OSigma @ SY3325 @ ( c_COMBK @ SY3322 @ ( tc_fun @ SY3323 @ tc_bool ) @ SY3324 ) @ SY3324 @ SY3323 ) )
| ! [V_x: $i] :
~ ( c_in @ V_x @ SY3322 @ SY3323 )
| ( SV359 = SY3325 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1987]) ).
thf(2666,plain,
! [SV360: $i] :
( ( ! [SY3327: $i] :
( ( c_Wellfounded_Owf @ SV360 @ SY3327 )
| ! [SY3328: $i,SY3329: $i] :
~ ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ SY3328 @ SY3329 @ SY3327 @ SY3327 ) @ SV360 @ ( tc_prod @ SY3327 @ SY3327 ) ) @ SY3327 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1988]) ).
thf(2667,plain,
! [SV361: $i] :
( ( ! [SY3330: $i,SY3331: $i,SY3332: $i] :
( ( c_in @ SV361 @ ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3330 @ SY3331 @ ( tc_fun @ ( tc_prod @ SY3332 @ SY3332 ) @ tc_bool ) ) @ SY3332 ) @ ( tc_prod @ SY3332 @ SY3332 ) )
| ~ ( c_in @ SV361 @ ( c_Transitive__Closure_Ortrancl @ SY3330 @ SY3332 ) @ ( tc_prod @ SY3332 @ SY3332 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1989]) ).
thf(2668,plain,
! [SV362: $i] :
( ( ! [SY3333: $i,SY3334: $i,SY3335: $i] :
( ( c_in @ SV362 @ ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3333 @ SY3334 @ ( tc_fun @ ( tc_prod @ SY3335 @ SY3335 ) @ tc_bool ) ) @ SY3335 ) @ ( tc_prod @ SY3335 @ SY3335 ) )
| ~ ( c_in @ SV362 @ ( c_Transitive__Closure_Ortrancl @ SY3334 @ SY3335 ) @ ( tc_prod @ SY3335 @ SY3335 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1990]) ).
thf(2669,plain,
! [SV363: $i] :
( ( ! [SY3336: $i,SY3337: $i] :
( ( c_in @ SV363 @ ( c_Transitive__Closure_Otrancl @ SY3336 @ SY3337 ) @ ( tc_prod @ SY3337 @ SY3337 ) )
| ! [SY3338: $i] :
( ~ ( c_lessequals @ SY3338 @ SY3336 @ ( tc_fun @ ( tc_prod @ SY3337 @ SY3337 ) @ tc_bool ) )
| ~ ( c_in @ SV363 @ ( c_Transitive__Closure_Otrancl @ SY3338 @ SY3337 ) @ ( tc_prod @ SY3337 @ SY3337 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1991]) ).
thf(2670,plain,
! [SV364: $i] :
( ( ! [SY3339: $i,SY3340: $i,SY3341: $i] :
( ( ( c_Relation_OImage @ SV364 @ ( c_Set_Oinsert @ SY3339 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3340 @ tc_bool ) ) @ SY3340 ) @ SY3340 @ SY3340 )
= ( c_Relation_OImage @ SV364 @ ( c_Set_Oinsert @ SY3341 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3340 @ tc_bool ) ) @ SY3340 ) @ SY3340 @ SY3340 ) )
| ~ ( c_in @ ( c_Pair @ SY3339 @ SY3341 @ SY3340 @ SY3340 ) @ SV364 @ ( tc_prod @ SY3340 @ SY3340 ) )
| ! [SY3342: $i] :
~ ( c_Equiv__Relations_Oequiv @ SY3342 @ SV364 @ SY3340 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1992]) ).
thf(2671,plain,
! [SV365: $i] :
( ( ! [SY3343: $i,SY3344: $i,SY3345: $i] :
( ( ( c_Relation_OImage @ SV365 @ ( c_Set_Oinsert @ SY3343 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3344 @ tc_bool ) ) @ SY3344 ) @ SY3344 @ SY3344 )
= ( c_Relation_OImage @ SV365 @ ( c_Set_Oinsert @ SY3345 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3344 @ tc_bool ) ) @ SY3344 ) @ SY3344 @ SY3344 ) )
| ~ ( c_in @ ( c_Pair @ SY3343 @ SY3345 @ SY3344 @ SY3344 ) @ SV365 @ ( tc_prod @ SY3344 @ SY3344 ) )
| ! [SY3346: $i] :
~ ( c_Equiv__Relations_Oequiv @ SY3346 @ SV365 @ SY3344 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1993]) ).
thf(2672,plain,
! [SV366: $i] :
( ( ! [SY3347: $i,SY3348: $i] :
( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ SV366 @ SV366 @ SY3347 @ SY3347 @ SY3347 ) @ ( c_Relation_Orel__comp @ SY3348 @ SV366 @ SY3347 @ SY3347 @ SY3347 ) @ ( tc_fun @ ( tc_prod @ SY3347 @ SY3347 ) @ tc_bool ) ) @ SY3348 @ ( tc_fun @ ( tc_prod @ SY3347 @ SY3347 ) @ tc_bool ) ) @ SY3347 )
| ~ ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV366 @ SY3348 @ ( tc_fun @ ( tc_prod @ SY3347 @ SY3347 ) @ tc_bool ) ) @ SY3347 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1994]) ).
thf(2673,plain,
! [SV367: $i] :
( ( ! [SY3349: $i,SY3350: $i] :
( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV367 @ SY3349 @ ( tc_fun @ ( tc_prod @ SY3350 @ SY3350 ) @ tc_bool ) ) @ SY3350 )
| ~ ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ SV367 @ SV367 @ SY3350 @ SY3350 @ SY3350 ) @ ( c_Relation_Orel__comp @ SY3349 @ SV367 @ SY3350 @ SY3350 @ SY3350 ) @ ( tc_fun @ ( tc_prod @ SY3350 @ SY3350 ) @ tc_bool ) ) @ SY3349 @ ( tc_fun @ ( tc_prod @ SY3350 @ SY3350 ) @ tc_bool ) ) @ SY3350 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1995]) ).
thf(2674,plain,
! [SV368: $i] :
( ( ! [SY3351: $i] :
( ( ( c_Relation_Orel__comp @ SV368 @ SV368 @ SY3351 @ SY3351 @ SY3351 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SY3351 @ SY3351 ) @ tc_bool ) ) )
| ( c_Wellfounded_Owf @ SV368 @ SY3351 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1996]) ).
thf(2675,plain,
! [SV369: $i] :
( ( ! [SY3352: $i] :
( ( c_Transitive__Closure_Otrancl @ SV369 @ SY3352 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV369 @ ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Otrancl @ SV369 @ SY3352 ) @ SV369 @ SY3352 @ SY3352 @ SY3352 ) @ ( tc_fun @ ( tc_prod @ SY3352 @ SY3352 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1997]) ).
thf(2676,plain,
! [SV370: $i] :
( ( ! [SY3353: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Ortrancl @ SV370 @ SY3353 ) @ ( c_Relation_OId @ SY3353 ) @ ( tc_fun @ ( tc_prod @ SY3353 @ SY3353 ) @ tc_bool ) )
= ( c_Transitive__Closure_Ortrancl @ SV370 @ SY3353 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1998]) ).
thf(2677,plain,
! [SV371: $i] :
( ( ! [SY3354: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV371 @ ( c_Relation_OId @ SY3354 ) @ ( tc_fun @ ( tc_prod @ SY3354 @ SY3354 ) @ tc_bool ) ) @ SY3354 )
= ( c_Transitive__Closure_Ortrancl @ SV371 @ SY3354 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1999]) ).
thf(2678,plain,
! [SV372: $i] :
( ( ( c_Transitive__Closure_Ortrancl @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV372 @ SV372 ) @ tc_bool ) ) @ SV372 )
= ( c_Relation_OId @ SV372 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2000]) ).
thf(2679,plain,
! [SV373: $i] :
( ( ! [SY3355: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( c_HOL_Ominus__class_Ominus @ SV373 @ ( c_Relation_OId @ SY3355 ) @ ( tc_fun @ ( tc_prod @ SY3355 @ SY3355 ) @ tc_bool ) ) @ SY3355 )
= ( c_Transitive__Closure_Ortrancl @ SV373 @ SY3355 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2001]) ).
thf(2680,plain,
! [SV374: $i] :
( ( ! [SY3356: $i] :
( ( c_Relation_Oantisym @ ( c_Transitive__Closure_Ortrancl @ SV374 @ SY3356 ) @ SY3356 )
| ~ ( c_Wellfounded_Oacyclic @ SV374 @ SY3356 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2002]) ).
thf(2681,plain,
! [SV375: $i] :
( ( ! [SY3357: $i] :
( ( c_lessequals @ ( c_Relation_Orel__comp @ SV375 @ SV375 @ SY3357 @ SY3357 @ SY3357 ) @ SV375 @ ( tc_fun @ ( tc_prod @ SY3357 @ SY3357 ) @ tc_bool ) )
| ~ ( c_Relation_Otrans @ SV375 @ SY3357 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2003]) ).
thf(2682,plain,
! [SV376: $i] :
( ( ! [SY3358: $i] : ( c_Relation_Osym @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV376 @ ( c_Relation_Oconverse @ SV376 @ SY3358 @ SY3358 ) @ ( tc_fun @ ( tc_prod @ SY3358 @ SY3358 ) @ tc_bool ) ) @ SY3358 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2004]) ).
thf(2683,plain,
! [SV377: $i] :
( ( ! [SY3359: $i] : ( c_Relation_Osym @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV377 @ ( c_Relation_Oconverse @ SV377 @ SY3359 @ SY3359 ) @ ( tc_fun @ ( tc_prod @ SY3359 @ SY3359 ) @ tc_bool ) ) @ SY3359 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2005]) ).
thf(2684,plain,
! [SV378: $i] :
( ( ! [SY3360: $i] :
( ( c_Relation_Otrans @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV378 @ ( c_Relation_OId @ SY3360 ) @ ( tc_fun @ ( tc_prod @ SY3360 @ SY3360 ) @ tc_bool ) ) @ SY3360 )
| ~ ( c_Relation_Otrans @ SV378 @ SY3360 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2006]) ).
thf(2685,plain,
! [SV379: $i] :
( ( ! [SY3361: $i,SY3362: $i] :
( ( c_Relation_OImage @ ( c_Relation_OId__on @ SV379 @ SY3361 ) @ SY3362 @ SY3361 @ SY3361 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV379 @ SY3362 @ ( tc_fun @ SY3361 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2007]) ).
thf(2686,plain,
! [SV380: $i] :
( ( ! [SY3363: $i] :
( ( c_Relation_Oantisym @ SV380 @ SY3363 )
| ~ ( c_Relation_Oantisym @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV380 @ ( c_Relation_OId @ SY3363 ) @ ( tc_fun @ ( tc_prod @ SY3363 @ SY3363 ) @ tc_bool ) ) @ SY3363 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2008]) ).
thf(2687,plain,
! [SV381: $i] :
( ( ! [SY3364: $i] :
( ( c_Relation_Oantisym @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV381 @ ( c_Relation_OId @ SY3364 ) @ ( tc_fun @ ( tc_prod @ SY3364 @ SY3364 ) @ tc_bool ) ) @ SY3364 )
| ~ ( c_Relation_Oantisym @ SV381 @ SY3364 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2009]) ).
thf(2688,plain,
! [SV382: $i] :
( ( ! [SY3365: $i,SY3366: $i] :
( ( c_Relation_Ototal__on @ SV382 @ SY3365 @ SY3366 )
| ~ ( c_Relation_Ototal__on @ SV382 @ ( c_HOL_Ominus__class_Ominus @ SY3365 @ ( c_Relation_OId @ SY3366 ) @ ( tc_fun @ ( tc_prod @ SY3366 @ SY3366 ) @ tc_bool ) ) @ SY3366 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2010]) ).
thf(2689,plain,
! [SV383: $i] :
( ( ! [SY3367: $i,SY3368: $i] :
( ( c_Relation_Ototal__on @ SV383 @ ( c_HOL_Ominus__class_Ominus @ SY3367 @ ( c_Relation_OId @ SY3368 ) @ ( tc_fun @ ( tc_prod @ SY3368 @ SY3368 ) @ tc_bool ) ) @ SY3368 )
| ~ ( c_Relation_Ototal__on @ SV383 @ SY3367 @ SY3368 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2011]) ).
thf(2690,plain,
! [SV384: $i] :
( ( ! [SY3369: $i] :
( ( c_lessequals @ ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ SV384 @ SY3369 @ SY3369 ) @ SV384 @ SY3369 @ SY3369 @ SY3369 ) @ SV384 @ ( tc_fun @ ( tc_prod @ SY3369 @ SY3369 ) @ tc_bool ) )
| ~ ( c_Relation_Otrans @ SV384 @ SY3369 )
| ~ ( c_Relation_Osym @ SV384 @ SY3369 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2012]) ).
thf(2691,plain,
! [SV385: $i] :
( ( ! [SY3370: $i,SY3371: $i,SY3372: $i] :
( ( c_in @ ( c_Pair @ SV385 @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1 @ SY3370 @ SV385 @ SY3371 @ SY3372 ) @ SY3372 @ SY3372 ) @ ( c_Transitive__Closure_Ortrancl @ SY3370 @ SY3372 ) @ ( tc_prod @ SY3372 @ SY3372 ) )
| ~ ( c_in @ ( c_Pair @ SV385 @ SY3371 @ SY3372 @ SY3372 ) @ ( c_Transitive__Closure_Otrancl @ SY3370 @ SY3372 ) @ ( tc_prod @ SY3372 @ SY3372 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2013]) ).
thf(2692,plain,
! [SV386: $i] :
( ( ! [SY3373: $i,SY3374: $i,SY3375: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1 @ SV386 @ SY3373 @ SY3374 @ SY3375 ) @ SY3374 @ SY3375 @ SY3375 ) @ ( c_Transitive__Closure_Ortrancl @ SV386 @ SY3375 ) @ ( tc_prod @ SY3375 @ SY3375 ) )
| ~ ( c_in @ ( c_Pair @ SY3373 @ SY3374 @ SY3375 @ SY3375 ) @ ( c_Transitive__Closure_Otrancl @ SV386 @ SY3375 ) @ ( tc_prod @ SY3375 @ SY3375 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2014]) ).
thf(2693,plain,
! [SV387: $i] :
( ( ! [SY3376: $i,SY3377: $i,SY3378: $i] :
( ~ ( c_in @ ( c_Pair @ SV387 @ SY3376 @ SY3377 @ SY3377 ) @ ( c_Transitive__Closure_Ortrancl @ SY3378 @ SY3377 ) @ ( tc_prod @ SY3377 @ SY3377 ) )
| ~ ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ SY3376 @ SV387 @ SY3377 @ SY3377 ) @ SY3378 @ ( tc_prod @ SY3377 @ SY3377 ) ) @ SY3377 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2015]) ).
thf(2694,plain,
! [SV388: $i] :
( ( ! [SY3379: $i,SY3380: $i,SY3381: $i] :
( ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ SV388 @ SY3379 @ SY3380 @ SY3380 ) @ SY3381 @ ( tc_prod @ SY3380 @ SY3380 ) ) @ SY3380 )
| ( c_in @ ( c_Pair @ SY3379 @ SV388 @ SY3380 @ SY3380 ) @ ( c_Transitive__Closure_Ortrancl @ SY3381 @ SY3380 ) @ ( tc_prod @ SY3380 @ SY3380 ) )
| ~ ( c_Wellfounded_Owf @ SY3381 @ SY3380 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2016]) ).
thf(2695,plain,
! [SV389: $i] :
( ( ! [SY3382: $i,SY3383: $i] :
( ( c_Order__Relation_Ostrict__linear__order__on @ SV389 @ SY3382 @ SY3383 )
| ~ ( c_Relation_Ototal__on @ SV389 @ SY3382 @ SY3383 )
| ~ ( c_Relation_Oirrefl @ SY3382 @ SY3383 )
| ~ ( c_Relation_Otrans @ SY3382 @ SY3383 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2017]) ).
thf(2696,plain,
! [SV390: $i] :
( ( ! [SY3384: $i] :
( ( c_Nitpick_Orefl_H @ SV390 @ SY3384 )
| ~ ( c_in @ ( c_Pair @ ( c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1 @ SV390 @ SY3384 ) @ ( c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1 @ SV390 @ SY3384 ) @ SY3384 @ SY3384 ) @ SV390 @ ( tc_prod @ SY3384 @ SY3384 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2018]) ).
thf(2697,plain,
! [SV391: $i] :
( ( ! [SY3385: $i] :
( ( c_Relation_Otrans @ ( c_HOL_Ominus__class_Ominus @ SV391 @ ( c_Relation_OId @ SY3385 ) @ ( tc_fun @ ( tc_prod @ SY3385 @ SY3385 ) @ tc_bool ) ) @ SY3385 )
| ~ ( c_Relation_Oantisym @ SV391 @ SY3385 )
| ~ ( c_Relation_Otrans @ SV391 @ SY3385 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2019]) ).
thf(2698,plain,
! [SV392: $i] :
( ( ! [SY3386: $i,SY3387: $i,SY3388: $i,SY3389: $i] :
( ( ( c_Relation_OImage @ SV392 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3386 @ SY3387 @ ( tc_fun @ SY3388 @ tc_bool ) ) @ SY3388 @ SY3389 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_OImage @ SV392 @ SY3386 @ SY3388 @ SY3389 ) @ ( c_Relation_OImage @ SV392 @ SY3387 @ SY3388 @ SY3389 ) @ ( tc_fun @ SY3389 @ tc_bool ) ) )
| ~ ( c_Relation_Osingle__valued @ ( c_Relation_Oconverse @ SV392 @ SY3388 @ SY3389 ) @ SY3389 @ SY3388 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2020]) ).
thf(2699,plain,
! [SV393: $i] :
( ( ! [SY3390: $i] :
( ( c_Relation_Oirrefl @ SV393 @ SY3390 )
| ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1 @ SV393 @ SY3390 ) @ ( c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1 @ SV393 @ SY3390 ) @ SY3390 @ SY3390 ) @ SV393 @ ( tc_prod @ SY3390 @ SY3390 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2021]) ).
thf(2700,plain,
! [SV394: $i] :
( ( ! [SY3391: $i] :
( ( c_lessequals @ SV394 @ ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ SV394 @ SY3391 @ SY3391 ) @ SV394 @ SY3391 @ SY3391 @ SY3391 ) @ ( tc_fun @ ( tc_prod @ SY3391 @ SY3391 ) @ tc_bool ) )
| ! [SY3392: $i] :
~ ( c_Relation_Orefl__on @ SY3392 @ SV394 @ SY3391 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2023]) ).
thf(2701,plain,
! [SV395: $i] :
( ( ! [SY3393: $i] :
( ( c_Transitive__Closure_Ortrancl @ SV395 @ SY3393 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_OId @ SY3393 ) @ ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Ortrancl @ SV395 @ SY3393 ) @ SV395 @ SY3393 @ SY3393 @ SY3393 ) @ ( tc_fun @ ( tc_prod @ SY3393 @ SY3393 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2024]) ).
thf(2702,plain,
! [SV396: $i] :
( ( ! [SY3394: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Otrancl @ SV396 @ SY3394 ) @ ( c_Relation_OId @ SY3394 ) @ ( tc_fun @ ( tc_prod @ SY3394 @ SY3394 ) @ tc_bool ) )
= ( c_Transitive__Closure_Ortrancl @ SV396 @ SY3394 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2025]) ).
thf(2703,plain,
! [SV397: $i] :
( ( ! [SY3395: $i] :
( ( c_Transitive__Closure_Otrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV397 @ ( c_Relation_OId @ SY3395 ) @ ( tc_fun @ ( tc_prod @ SY3395 @ SY3395 ) @ tc_bool ) ) @ SY3395 )
= ( c_Transitive__Closure_Ortrancl @ SV397 @ SY3395 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2026]) ).
thf(2704,plain,
! [SV398: $i] :
( ( ! [SY3396: $i] :
( ( c_Transitive__Closure_Ortrancl @ SV398 @ SY3396 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Otrancl @ SV398 @ SY3396 ) @ ( c_Relation_OId @ SY3396 ) @ ( tc_fun @ ( tc_prod @ SY3396 @ SY3396 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2027]) ).
thf(2705,plain,
! [SV399: $i] :
( ( ! [SY3397: $i,SY3398: $i,SY3399: $i,SY3400: $i,SY3401: $i] :
( ( ( c_Recdef_Ocut @ SV399 @ SY3397 @ SY3398 @ SY3399 @ SY3400 )
= ( c_Recdef_Ocut @ SY3401 @ SY3397 @ SY3398 @ SY3399 @ SY3400 ) )
| ( c_in @ ( c_Pair @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ SV399 @ SY3401 @ SY3397 @ SY3398 @ SY3399 @ SY3400 ) @ SY3398 @ SY3399 @ SY3399 ) @ SY3397 @ ( tc_prod @ SY3399 @ SY3399 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2028]) ).
thf(2706,plain,
! [SV400: $i] :
( ( ! [SY3402: $i,SY3403: $i] :
( ( SV400
= ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XId__onE__1__1 @ SY3402 @ SV400 @ SY3403 ) @ ( c_ATP__Linkup_Osko__Relation__XId__onE__1__1 @ SY3402 @ SV400 @ SY3403 ) @ SY3403 @ SY3403 ) )
| ~ ( c_in @ SV400 @ ( c_Relation_OId__on @ SY3402 @ SY3403 ) @ ( tc_prod @ SY3403 @ SY3403 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2029]) ).
thf(2707,plain,
! [SV401: $i] :
( ( ! [SY3404: $i,SY3405: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Relation__XId__onE__1__1 @ SV401 @ SY3404 @ SY3405 ) @ SV401 @ SY3405 )
| ~ ( c_in @ SY3404 @ ( c_Relation_OId__on @ SV401 @ SY3405 ) @ ( tc_prod @ SY3405 @ SY3405 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2030]) ).
thf(2708,plain,
! [SV402: $i] :
( ( ! [SY3406: $i] :
( ( c_Wellfounded_Owf @ SV402 @ SY3406 )
| ~ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1 @ SV402 @ SY3406 ) @ ( c_Wellfounded_Oacc @ SV402 @ SY3406 ) @ SY3406 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2031]) ).
thf(2709,plain,
! [SV403: $i] :
( ( ! [SY3407: $i] :
( ( c_Wellfounded_Owf @ SV403 @ SY3407 )
| ~ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1 @ SV403 @ SY3407 ) @ ( c_Wellfounded_Oacc @ SV403 @ SY3407 ) @ SY3407 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2032]) ).
thf(2710,plain,
! [SV404: $i] :
( ( ! [SY3408: $i] :
( ( SV404
= ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XIdE__1__1 @ SV404 @ SY3408 ) @ ( c_ATP__Linkup_Osko__Relation__XIdE__1__1 @ SV404 @ SY3408 ) @ SY3408 @ SY3408 ) )
| ~ ( c_in @ SV404 @ ( c_Relation_OId @ SY3408 ) @ ( tc_prod @ SY3408 @ SY3408 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2033]) ).
thf(2711,plain,
! [SV405: $i] :
( ( ! [SY3409: $i,SY3410: $i,SY3411: $i,SY3412: $i,SY3413: $i,SY3414: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 @ SV405 @ SY3409 @ SY3410 @ SY3411 @ SY3412 @ SY3413 @ SY3414 ) @ SY3409 @ SY3414 @ SY3413 ) @ SY3411 @ ( tc_prod @ SY3414 @ SY3413 ) )
| ~ ( c_in @ ( c_Pair @ SV405 @ SY3409 @ SY3412 @ SY3413 ) @ ( c_Relation_Orel__comp @ SY3410 @ SY3411 @ SY3412 @ SY3414 @ SY3413 ) @ ( tc_prod @ SY3412 @ SY3413 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2034]) ).
thf(2712,plain,
! [SV406: $i] :
( ( ! [SY3415: $i,SY3416: $i,SY3417: $i,SY3418: $i,SY3419: $i,SY3420: $i] :
( ( c_in @ ( c_Pair @ SV406 @ ( c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 @ SV406 @ SY3415 @ SY3416 @ SY3417 @ SY3418 @ SY3419 @ SY3420 ) @ SY3418 @ SY3420 ) @ SY3416 @ ( tc_prod @ SY3418 @ SY3420 ) )
| ~ ( c_in @ ( c_Pair @ SV406 @ SY3415 @ SY3418 @ SY3419 ) @ ( c_Relation_Orel__comp @ SY3416 @ SY3417 @ SY3418 @ SY3420 @ SY3419 ) @ ( tc_prod @ SY3418 @ SY3419 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2035]) ).
thf(2713,plain,
! [SV407: $i] :
( ( ! [SY3421: $i,SY3422: $i] :
( ~ ( c_in @ ( c_Pair @ SV407 @ SV407 @ SY3421 @ SY3421 ) @ SY3422 @ ( tc_prod @ SY3421 @ SY3421 ) )
| ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1 @ SY3422 @ SY3421 ) @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1 @ SY3422 @ SY3421 ) @ SY3421 @ SY3421 ) @ ( c_Transitive__Closure_Otrancl @ SY3422 @ SY3421 ) @ ( tc_prod @ SY3421 @ SY3421 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2036]) ).
thf(2714,plain,
! [SV408: $i] :
( ( ! [SY3423: $i,SY3424: $i,SY3425: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1 @ SV408 @ SY3423 @ SY3424 @ SY3425 ) @ SY3424 @ SY3425 @ SY3425 ) @ ( c_Transitive__Closure_Otrancl @ SV408 @ SY3425 ) @ ( tc_prod @ SY3425 @ SY3425 ) )
| ( c_in @ ( c_Pair @ SY3423 @ SY3424 @ SY3425 @ SY3425 ) @ SV408 @ ( tc_prod @ SY3425 @ SY3425 ) )
| ~ ( c_in @ ( c_Pair @ SY3423 @ SY3424 @ SY3425 @ SY3425 ) @ ( c_Transitive__Closure_Otrancl @ SV408 @ SY3425 ) @ ( tc_prod @ SY3425 @ SY3425 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2037]) ).
thf(2715,plain,
! [SV409: $i] :
( ( ! [SY3426: $i,SY3427: $i,SY3428: $i] :
( ( c_in @ ( c_Pair @ SV409 @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1 @ SY3426 @ SV409 @ SY3427 @ SY3428 ) @ SY3428 @ SY3428 ) @ SY3426 @ ( tc_prod @ SY3428 @ SY3428 ) )
| ~ ( c_in @ ( c_Pair @ SV409 @ SY3427 @ SY3428 @ SY3428 ) @ ( c_Transitive__Closure_Otrancl @ SY3426 @ SY3428 ) @ ( tc_prod @ SY3428 @ SY3428 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2038]) ).
thf(2716,plain,
! [SV410: $i] :
( ( ! [SY3429: $i,SY3430: $i] :
( ( c_in @ ( c_Pair @ SV410 @ ( v_sko__Transitive__Closure__Xtrancl__Xcases__1 @ SV410 @ SY3429 @ SY3430 ) @ t_a @ t_a ) @ ( c_Transitive__Closure_Otrancl @ SY3430 @ t_a ) @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ ( c_Pair @ SV410 @ SY3429 @ t_a @ t_a ) @ SY3430 @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ ( c_Pair @ SV410 @ SY3429 @ t_a @ t_a ) @ ( c_Transitive__Closure_Otrancl @ SY3430 @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2039]) ).
thf(2717,plain,
! [SV411: $i] :
( ( ! [SY3431: $i,SY3432: $i] :
( ~ ( c_in @ ( c_Pair @ SV411 @ SV411 @ SY3431 @ SY3431 ) @ ( c_Transitive__Closure_Otrancl @ SY3432 @ SY3431 ) @ ( tc_prod @ SY3431 @ SY3431 ) )
| ~ ( c_Wellfounded_Oacyclic @ SY3432 @ SY3431 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2040]) ).
thf(2718,plain,
! [SV412: $i] :
( ( ! [SY3433: $i,SY3434: $i,SY3435: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1 @ SV412 @ SY3433 @ SY3434 @ SY3435 ) @ SY3433 @ SY3435 @ SY3435 ) @ SY3434 @ ( tc_prod @ SY3435 @ SY3435 ) )
| ( c_in @ ( c_Pair @ SV412 @ SY3433 @ SY3435 @ SY3435 ) @ SY3434 @ ( tc_prod @ SY3435 @ SY3435 ) )
| ~ ( c_in @ ( c_Pair @ SV412 @ SY3433 @ SY3435 @ SY3435 ) @ ( c_Transitive__Closure_Otrancl @ SY3434 @ SY3435 ) @ ( tc_prod @ SY3435 @ SY3435 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2041]) ).
thf(2719,plain,
! [SV413: $i] :
( ( ! [SY3436: $i,SY3437: $i,SY3438: $i] :
( ( c_in @ ( c_Pair @ SV413 @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1 @ SV413 @ SY3436 @ SY3437 @ SY3438 ) @ SY3438 @ SY3438 ) @ ( c_Transitive__Closure_Otrancl @ SY3437 @ SY3438 ) @ ( tc_prod @ SY3438 @ SY3438 ) )
| ( c_in @ ( c_Pair @ SV413 @ SY3436 @ SY3438 @ SY3438 ) @ SY3437 @ ( tc_prod @ SY3438 @ SY3438 ) )
| ~ ( c_in @ ( c_Pair @ SV413 @ SY3436 @ SY3438 @ SY3438 ) @ ( c_Transitive__Closure_Otrancl @ SY3437 @ SY3438 ) @ ( tc_prod @ SY3438 @ SY3438 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2042]) ).
thf(2720,plain,
! [SV414: $i] :
( ( ! [SY3439: $i,SY3440: $i,SY3441: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1 @ SV414 @ SY3439 @ SY3440 @ SY3441 ) @ SY3440 @ SY3441 @ SY3441 ) @ SV414 @ ( tc_prod @ SY3441 @ SY3441 ) )
| ~ ( c_in @ ( c_Pair @ SY3439 @ SY3440 @ SY3441 @ SY3441 ) @ ( c_Transitive__Closure_Otrancl @ SV414 @ SY3441 ) @ ( tc_prod @ SY3441 @ SY3441 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2043]) ).
thf(2721,plain,
! [SV415: $i] :
( ( ! [SY3442: $i,SY3443: $i,SY3444: $i] :
( ( c_in @ ( c_Pair @ SV415 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1 @ SY3442 @ SV415 @ SY3443 @ SY3444 ) @ SY3444 @ SY3444 ) @ SY3442 @ ( tc_prod @ SY3444 @ SY3444 ) )
| ( c_in @ ( c_Pair @ SV415 @ SY3443 @ SY3444 @ SY3444 ) @ SY3442 @ ( tc_prod @ SY3444 @ SY3444 ) )
| ~ ( c_in @ ( c_Pair @ SV415 @ SY3443 @ SY3444 @ SY3444 ) @ ( c_Transitive__Closure_Otrancl @ SY3442 @ SY3444 ) @ ( tc_prod @ SY3444 @ SY3444 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2044]) ).
thf(2722,plain,
! [SV416: $i] :
( ( ! [SY3445: $i,SY3446: $i] :
( ( c_in @ ( c_Pair @ ( v_sko__Transitive__Closure__Xtrancl__Xcases__1 @ SV416 @ SY3445 @ SY3446 ) @ SY3445 @ t_a @ t_a ) @ SY3446 @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ ( c_Pair @ SV416 @ SY3445 @ t_a @ t_a ) @ SY3446 @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ ( c_Pair @ SV416 @ SY3445 @ t_a @ t_a ) @ ( c_Transitive__Closure_Otrancl @ SY3446 @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2045]) ).
thf(2723,plain,
! [SV417: $i] :
( ( ! [SY3447: $i,SY3448: $i] :
( ( hBOOL @ ( hAPP @ SV417 @ SY3447 ) )
| ( hBOOL @ ( hAPP @ SV417 @ SY3448 ) )
| ! [SY3449: $i,SY3450: $i] :
( ~ ( c_in @ ( c_Pair @ SY3448 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1 @ SV417 @ SY3449 @ SY3450 ) @ SY3450 @ SY3450 ) @ SY3449 @ ( tc_prod @ SY3450 @ SY3450 ) )
| ~ ( c_Wellfounded_Owf @ SY3449 @ SY3450 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2046]) ).
thf(2724,plain,
! [SV418: $i] :
( ( ! [SY3451: $i,SY3452: $i] :
( ( hBOOL @ ( hAPP @ SV418 @ SY3451 ) )
| ( hBOOL @ ( hAPP @ SV418 @ SY3452 ) )
| ! [SY3453: $i,SY3454: $i] :
( ~ ( c_in @ ( c_Pair @ SY3452 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1 @ SV418 @ SY3453 @ SY3454 ) @ SY3454 @ SY3454 ) @ SY3453 @ ( tc_prod @ SY3454 @ SY3454 ) )
| ~ ( c_Wellfounded_Owf @ SY3453 @ SY3454 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2047]) ).
thf(2725,plain,
! [SV419: $i] :
( ( ! [SY3455: $i,SY3456: $i] :
( ( hBOOL @ ( hAPP @ SV419 @ SY3455 ) )
| ( hBOOL @ ( hAPP @ SV419 @ SY3456 ) )
| ! [SY3457: $i,SY3458: $i] :
( ~ ( c_in @ ( c_Pair @ SY3456 @ ( c_List_Osko__Recdef__Xtfl__wf__induct__1__1 @ SV419 @ SY3457 @ SY3458 ) @ SY3458 @ SY3458 ) @ SY3457 @ ( tc_prod @ SY3458 @ SY3458 ) )
| ~ ( c_Wellfounded_Owf @ SY3457 @ SY3458 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2048]) ).
thf(2726,plain,
! [SV420: $i] :
( ( ! [SY3459: $i,SY3460: $i] :
( ( hBOOL @ ( hAPP @ SV420 @ SY3459 ) )
| ( hBOOL @ ( hAPP @ SV420 @ SY3460 ) )
| ! [SY3461: $i,SY3462: $i] :
( ~ ( c_in @ ( c_Pair @ SY3460 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1 @ SV420 @ SY3461 @ SY3462 ) @ SY3462 @ SY3462 ) @ SY3461 @ ( tc_prod @ SY3462 @ SY3462 ) )
| ~ ( c_Wellfounded_Owf @ SY3461 @ SY3462 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2049]) ).
thf(2727,plain,
! [SV421: $i] :
( ( ! [SY3463: $i,SY3464: $i,SY3465: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1 @ SV421 @ SY3463 @ SY3464 @ SY3465 ) @ SY3463 @ SY3465 @ SY3465 ) @ SY3464 @ ( tc_prod @ SY3465 @ SY3465 ) )
| ( SV421 = SY3463 )
| ~ ( c_in @ ( c_Pair @ SV421 @ SY3463 @ SY3465 @ SY3465 ) @ ( c_Transitive__Closure_Ortrancl @ SY3464 @ SY3465 ) @ ( tc_prod @ SY3465 @ SY3465 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2050]) ).
thf(2728,plain,
! [SV422: $i] :
( ( ! [SY3466: $i,SY3467: $i,SY3468: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1 @ SV422 @ SY3466 @ SY3467 @ SY3468 ) @ SY3467 @ SY3468 @ SY3468 ) @ ( c_Transitive__Closure_Ortrancl @ SV422 @ SY3468 ) @ ( tc_prod @ SY3468 @ SY3468 ) )
| ( SY3466 = SY3467 )
| ~ ( c_in @ ( c_Pair @ SY3466 @ SY3467 @ SY3468 @ SY3468 ) @ ( c_Transitive__Closure_Ortrancl @ SV422 @ SY3468 ) @ ( tc_prod @ SY3468 @ SY3468 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2051]) ).
thf(2729,plain,
! [SV423: $i] :
( ( ! [SY3469: $i,SY3470: $i,SY3471: $i] :
( ( c_in @ ( c_Pair @ SV423 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1 @ SY3469 @ SV423 @ SY3470 @ SY3471 ) @ SY3471 @ SY3471 ) @ SY3469 @ ( tc_prod @ SY3471 @ SY3471 ) )
| ( SV423 = SY3470 )
| ~ ( c_in @ ( c_Pair @ SV423 @ SY3470 @ SY3471 @ SY3471 ) @ ( c_Transitive__Closure_Ortrancl @ SY3469 @ SY3471 ) @ ( tc_prod @ SY3471 @ SY3471 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2052]) ).
thf(2730,plain,
! [SV424: $i] :
( ( ! [SY3472: $i,SY3473: $i] :
( ( hBOOL @ ( hAPP @ SV424 @ SY3472 ) )
| ! [SY3474: $i,SY3475: $i] :
( ( hBOOL @ ( hAPP @ SV424 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 @ SV424 @ SY3473 @ SY3474 @ SY3475 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV424 @ SY3473 ) )
| ~ ( c_in @ ( c_Pair @ SY3472 @ SY3473 @ SY3475 @ SY3475 ) @ ( c_Transitive__Closure_Ortrancl @ SY3474 @ SY3475 ) @ ( tc_prod @ SY3475 @ SY3475 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2053]) ).
thf(2731,plain,
! [SV425: $i] :
( ( ! [SY3476: $i,SY3477: $i] :
( ( hBOOL @ ( hAPP @ SV425 @ SY3476 ) )
| ! [SY3478: $i,SY3479: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 @ SV425 @ SY3477 @ SY3478 @ SY3479 ) @ SY3477 @ SY3479 @ SY3479 ) @ ( c_Transitive__Closure_Ortrancl @ SY3478 @ SY3479 ) @ ( tc_prod @ SY3479 @ SY3479 ) )
| ~ ( hBOOL @ ( hAPP @ SV425 @ SY3477 ) )
| ~ ( c_in @ ( c_Pair @ SY3476 @ SY3477 @ SY3479 @ SY3479 ) @ ( c_Transitive__Closure_Ortrancl @ SY3478 @ SY3479 ) @ ( tc_prod @ SY3479 @ SY3479 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2054]) ).
thf(2732,plain,
! [SV426: $i] :
( ( ! [SY3480: $i,SY3481: $i] :
( ( hBOOL @ ( hAPP @ SV426 @ SY3480 ) )
| ! [SY3482: $i,SY3483: $i] :
( ( c_in @ ( c_Pair @ SY3481 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 @ SV426 @ SY3481 @ SY3482 @ SY3483 ) @ SY3483 @ SY3483 ) @ ( c_Transitive__Closure_Ortrancl @ SY3482 @ SY3483 ) @ ( tc_prod @ SY3483 @ SY3483 ) )
| ~ ( hBOOL @ ( hAPP @ SV426 @ SY3481 ) )
| ~ ( c_in @ ( c_Pair @ SY3481 @ SY3480 @ SY3483 @ SY3483 ) @ ( c_Transitive__Closure_Ortrancl @ SY3482 @ SY3483 ) @ ( tc_prod @ SY3483 @ SY3483 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2055]) ).
thf(2733,plain,
! [SV427: $i] :
( ( ! [SY3484: $i,SY3485: $i] :
( ( hBOOL @ ( hAPP @ SV427 @ SY3484 ) )
| ! [SY3486: $i,SY3487: $i] :
( ~ ( hBOOL @ ( hAPP @ SV427 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2 @ SV427 @ SY3485 @ SY3486 @ SY3487 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV427 @ SY3485 ) )
| ~ ( c_in @ ( c_Pair @ SY3485 @ SY3484 @ SY3487 @ SY3487 ) @ ( c_Transitive__Closure_Ortrancl @ SY3486 @ SY3487 ) @ ( tc_prod @ SY3487 @ SY3487 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2056]) ).
thf(2734,plain,
! [SV428: $i] :
( ( ! [SY3488: $i,SY3489: $i] :
( ( c_in @ ( c_Pair @ SV428 @ ( v_sko__Transitive__Closure__Xrtrancl__Xcases__1 @ SV428 @ SY3488 @ SY3489 ) @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ SY3489 @ t_a ) @ ( tc_prod @ t_a @ t_a ) )
| ( SY3488 = SV428 )
| ~ ( c_in @ ( c_Pair @ SV428 @ SY3488 @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ SY3489 @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2057]) ).
thf(2735,plain,
! [SV429: $i] :
( ( ! [SY3490: $i,SY3491: $i] :
( ( hBOOL @ ( hAPP @ SV429 @ SY3490 ) )
| ! [SY3492: $i,SY3493: $i] :
( ( hBOOL @ ( hAPP @ SV429 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 @ SV429 @ SY3491 @ SY3492 @ SY3493 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV429 @ SY3491 ) )
| ~ ( c_in @ ( c_Pair @ SY3491 @ SY3490 @ SY3493 @ SY3493 ) @ ( c_Transitive__Closure_Ortrancl @ SY3492 @ SY3493 ) @ ( tc_prod @ SY3493 @ SY3493 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2058]) ).
thf(2736,plain,
! [SV430: $i] :
( ( ! [SY3494: $i,SY3495: $i] :
( ( c_in @ ( c_Pair @ ( v_sko__Transitive__Closure__Xrtrancl__Xcases__1 @ SV430 @ SY3494 @ SY3495 ) @ SY3494 @ t_a @ t_a ) @ SY3495 @ ( tc_prod @ t_a @ t_a ) )
| ( SY3494 = SV430 )
| ~ ( c_in @ ( c_Pair @ SV430 @ SY3494 @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ SY3495 @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2059]) ).
thf(2737,plain,
! [SV431: $i] :
( ( ! [SY3496: $i,SY3497: $i] :
( ( hBOOL @ ( hAPP @ SV431 @ SY3496 ) )
| ! [SY3498: $i,SY3499: $i] :
( ~ ( hBOOL @ ( hAPP @ SV431 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1 @ SV431 @ SY3497 @ SY3498 @ SY3499 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV431 @ SY3497 ) )
| ~ ( c_in @ ( c_Pair @ SY3496 @ SY3497 @ SY3499 @ SY3499 ) @ ( c_Transitive__Closure_Ortrancl @ SY3498 @ SY3499 ) @ ( tc_prod @ SY3499 @ SY3499 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2060]) ).
thf(2738,plain,
! [SV432: $i] :
( ( ! [SY3500: $i,SY3501: $i,SY3502: $i] :
( ( c_in @ ( c_Pair @ SV432 @ ( c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1 @ SV432 @ SY3500 @ SY3501 @ SY3502 ) @ SY3502 @ SY3502 ) @ ( c_Transitive__Closure_Ortrancl @ SY3501 @ SY3502 ) @ ( tc_prod @ SY3502 @ SY3502 ) )
| ( SV432 = SY3500 )
| ~ ( c_in @ ( c_Pair @ SV432 @ SY3500 @ SY3502 @ SY3502 ) @ ( c_Transitive__Closure_Ortrancl @ SY3501 @ SY3502 ) @ ( tc_prod @ SY3502 @ SY3502 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2061]) ).
thf(2739,plain,
! [SV433: $i] :
( ( ! [SY3503: $i,SY3504: $i,SY3505: $i,SY3506: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Product__Type__XSigmaE__1__1 @ SV433 @ SY3503 @ SY3504 @ SY3505 @ SY3506 ) @ SV433 @ SY3505 )
| ~ ( c_in @ SY3504 @ ( c_Product__Type_OSigma @ SV433 @ SY3503 @ SY3505 @ SY3506 ) @ ( tc_prod @ SY3505 @ SY3506 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2062]) ).
thf(2740,plain,
! [SV434: $i] :
( ( ! [SY3507: $i] :
( ( c_Wellfounded_OwfP @ ( c_FunDef_Oin__rel @ SV434 @ SY3507 @ SY3507 ) @ SY3507 )
| ~ ( c_Wellfounded_Owf @ SV434 @ SY3507 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2063]) ).
thf(2741,plain,
! [SV435: $i] :
( ( ! [SY3508: $i] : ( c_Relation_Oirrefl @ ( c_HOL_Ominus__class_Ominus @ SV435 @ ( c_Relation_OId @ SY3508 ) @ ( tc_fun @ ( tc_prod @ SY3508 @ SY3508 ) @ tc_bool ) ) @ SY3508 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2064]) ).
thf(2742,plain,
! [SV436: $i] :
( ( ! [SY3509: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_Oconverse @ SV436 @ SY3509 @ SY3509 ) @ ( c_Transitive__Closure_Ortrancl @ SV436 @ SY3509 ) @ ( tc_fun @ ( tc_prod @ SY3509 @ SY3509 ) @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SY3509 @ SY3509 ) @ tc_bool ) ) )
| ! [SY3510: $i] :
~ ( c_in @ ( c_Pair @ SY3510 @ SY3510 @ SY3509 @ SY3509 ) @ ( c_Transitive__Closure_Otrancl @ SV436 @ SY3509 ) @ ( tc_prod @ SY3509 @ SY3509 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2065]) ).
thf(2743,plain,
! [SV437: $i] :
( ( ! [SY3511: $i,SY3512: $i,SY3513: $i] :
( ( ( c_Relation_OImage @ SV437 @ ( c_Set_Oinsert @ SY3511 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3512 @ tc_bool ) ) @ SY3512 ) @ SY3512 @ SY3512 )
!= ( c_Relation_OImage @ SV437 @ ( c_Set_Oinsert @ SY3513 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3512 @ tc_bool ) ) @ SY3512 ) @ SY3512 @ SY3512 ) )
| ( c_in @ ( c_Pair @ SY3511 @ SY3513 @ SY3512 @ SY3512 ) @ SV437 @ ( tc_prod @ SY3512 @ SY3512 ) )
| ! [SY3514: $i] :
( ~ ( c_in @ SY3513 @ SY3514 @ SY3512 )
| ~ ( c_Equiv__Relations_Oequiv @ SY3514 @ SV437 @ SY3512 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2066]) ).
thf(2744,plain,
! [SV438: $i] :
( ( ! [SY3515: $i,SY3516: $i,SY3517: $i] :
( ( ( c_Relation_OImage @ SV438 @ ( c_Set_Oinsert @ SY3515 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3516 @ tc_bool ) ) @ SY3516 ) @ SY3516 @ SY3516 )
!= ( c_Relation_OImage @ SV438 @ ( c_Set_Oinsert @ SY3517 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3516 @ tc_bool ) ) @ SY3516 ) @ SY3516 @ SY3516 ) )
| ! [SY3518: $i] :
( ~ ( c_Equiv__Relations_Oequiv @ SY3518 @ SV438 @ SY3516 )
| ( c_in @ ( c_Pair @ SY3515 @ SY3517 @ SY3516 @ SY3516 ) @ SV438 @ ( tc_prod @ SY3516 @ SY3516 ) )
| ~ ( c_in @ SY3517 @ SY3518 @ SY3516 )
| ~ ( c_in @ SY3515 @ SY3518 @ SY3516 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2067]) ).
thf(2745,plain,
! [SV439: $i] :
( ( ! [SY3519: $i,SY3520: $i,SY3521: $i] :
( ( ( c_Relation_OImage @ SV439 @ ( c_Set_Oinsert @ SY3519 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3520 @ tc_bool ) ) @ SY3520 ) @ SY3520 @ SY3520 )
= ( c_Relation_OImage @ SV439 @ ( c_Set_Oinsert @ SY3521 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3520 @ tc_bool ) ) @ SY3520 ) @ SY3520 @ SY3520 ) )
| ~ ( c_in @ ( c_Pair @ SY3519 @ SY3521 @ SY3520 @ SY3520 ) @ SV439 @ ( tc_prod @ SY3520 @ SY3520 ) )
| ! [SY3522: $i] :
( ~ ( c_in @ SY3521 @ SY3522 @ SY3520 )
| ~ ( c_in @ SY3519 @ SY3522 @ SY3520 )
| ~ ( c_Equiv__Relations_Oequiv @ SY3522 @ SV439 @ SY3520 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2068]) ).
thf(2746,plain,
! [SV440: $i] :
( ( ! [SY3523: $i,SY3524: $i,SY3525: $i] :
( ( ( c_Relation_OImage @ SV440 @ ( c_Set_Oinsert @ SY3523 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3524 @ tc_bool ) ) @ SY3524 ) @ SY3524 @ SY3524 )
!= ( c_Relation_OImage @ SV440 @ ( c_Set_Oinsert @ SY3525 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3524 @ tc_bool ) ) @ SY3524 ) @ SY3524 @ SY3524 ) )
| ! [SY3526: $i] :
( ~ ( c_in @ SY3525 @ SY3526 @ SY3524 )
| ~ ( c_in @ SY3523 @ SY3526 @ SY3524 )
| ~ ( c_Equiv__Relations_Oequiv @ SY3526 @ SV440 @ SY3524 )
| ( c_in @ ( c_Pair @ SY3523 @ SY3525 @ SY3524 @ SY3524 ) @ SV440 @ ( tc_prod @ SY3524 @ SY3524 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2069]) ).
thf(2747,plain,
! [SV441: $i] :
( ( ! [SY3527: $i,SY3528: $i] :
( ( c_Set_Oimage @ ( c_snd @ SV441 @ SY3527 ) @ SY3528 @ ( tc_prod @ SV441 @ SY3527 ) @ SY3527 )
= ( c_Relation_ORange @ SY3528 @ SV441 @ SY3527 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2070]) ).
thf(2748,plain,
! [SV442: $i] :
( ( ! [SY3529: $i,SY3530: $i] :
( ( c_in @ SV442 @ SY3529 @ SY3530 )
| ! [SY3531: $i] :
( ( SV442 = SY3531 )
| ! [SY3532: $i] :
( ~ ( c_lessequals @ SY3532 @ ( c_Product__Type_OSigma @ SY3529 @ ( c_COMBK @ SY3529 @ ( tc_fun @ SY3530 @ tc_bool ) @ SY3530 ) @ SY3530 @ SY3530 ) @ ( tc_fun @ ( tc_prod @ SY3530 @ SY3530 ) @ tc_bool ) )
| ~ ( c_in @ ( c_Pair @ SV442 @ SY3531 @ SY3530 @ SY3530 ) @ ( c_Transitive__Closure_Ortrancl @ SY3532 @ SY3530 ) @ ( tc_prod @ SY3530 @ SY3530 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2071]) ).
thf(2749,plain,
! [SV443: $i] :
( ( ! [SY3533: $i,SY3534: $i] :
( ( c_Set_Oimage @ ( c_fst @ SV443 @ SY3533 ) @ SY3534 @ ( tc_prod @ SV443 @ SY3533 ) @ SV443 )
= ( c_Relation_ODomain @ SY3534 @ SV443 @ SY3533 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2072]) ).
thf(2750,plain,
! [SV444: $i] :
( ( ! [SY3535: $i,SY3536: $i] :
( ( c_in @ SV444 @ ( c_Transitive__Closure_Ortrancl @ SY3535 @ SY3536 ) @ ( tc_prod @ SY3536 @ SY3536 ) )
| ~ ( c_in @ SV444 @ SY3535 @ ( tc_prod @ SY3536 @ SY3536 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2073]) ).
thf(2751,plain,
! [SV445: $i] :
( ( ! [SY3537: $i,SY3538: $i] :
( ( c_in @ SV445 @ ( c_Transitive__Closure_Otrancl @ SY3537 @ SY3538 ) @ ( tc_prod @ SY3538 @ SY3538 ) )
| ~ ( c_in @ SV445 @ SY3537 @ ( tc_prod @ SY3538 @ SY3538 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2074]) ).
thf(2752,plain,
! [SV446: $i] :
( ( ! [SY3539: $i,SY3540: $i,SY3541: $i] :
( ( c_in @ ( c_Pair @ SV446 @ SY3539 @ SY3540 @ SY3540 ) @ ( c_Transitive__Closure_Otrancl @ SY3541 @ SY3540 ) @ ( tc_prod @ SY3540 @ SY3540 ) )
| ! [SY3542: $i] :
( ~ ( c_in @ ( c_Pair @ SY3542 @ SY3539 @ SY3540 @ SY3540 ) @ ( c_Transitive__Closure_Ortrancl @ SY3541 @ SY3540 ) @ ( tc_prod @ SY3540 @ SY3540 ) )
| ~ ( c_in @ ( c_Pair @ SV446 @ SY3542 @ SY3540 @ SY3540 ) @ SY3541 @ ( tc_prod @ SY3540 @ SY3540 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2075]) ).
thf(2753,plain,
! [SV447: $i] :
( ( ! [SY3543: $i,SY3544: $i,SY3545: $i] :
( ( c_in @ ( c_Pair @ SV447 @ SY3543 @ SY3544 @ SY3544 ) @ ( c_Transitive__Closure_Otrancl @ SY3545 @ SY3544 ) @ ( tc_prod @ SY3544 @ SY3544 ) )
| ! [SY3546: $i] :
( ~ ( c_in @ ( c_Pair @ SY3546 @ SY3543 @ SY3544 @ SY3544 ) @ SY3545 @ ( tc_prod @ SY3544 @ SY3544 ) )
| ~ ( c_in @ ( c_Pair @ SV447 @ SY3546 @ SY3544 @ SY3544 ) @ ( c_Transitive__Closure_Ortrancl @ SY3545 @ SY3544 ) @ ( tc_prod @ SY3544 @ SY3544 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2076]) ).
thf(2754,plain,
! [SV448: $i] :
( ( ! [SY3547: $i,SY3548: $i,SY3549: $i] :
( ( c_in @ ( c_Pair @ SV448 @ SY3547 @ SY3548 @ SY3548 ) @ ( c_Transitive__Closure_Ortrancl @ SY3549 @ SY3548 ) @ ( tc_prod @ SY3548 @ SY3548 ) )
| ~ ( c_in @ ( c_Pair @ SV448 @ SY3547 @ SY3548 @ SY3548 ) @ ( c_Transitive__Closure_Otrancl @ SY3549 @ SY3548 ) @ ( tc_prod @ SY3548 @ SY3548 ) )
| ( SV448 = SY3547 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2077]) ).
thf(2755,plain,
! [SV449: $i] :
( ( ! [SY3550: $i,SY3551: $i,SY3552: $i] :
( ( c_in @ ( c_Pair @ SV449 @ SY3550 @ SY3551 @ SY3551 ) @ ( c_Transitive__Closure_Otrancl @ SY3552 @ SY3551 ) @ ( tc_prod @ SY3551 @ SY3551 ) )
| ( SV449 = SY3550 )
| ~ ( c_in @ ( c_Pair @ SV449 @ SY3550 @ SY3551 @ SY3551 ) @ ( c_Transitive__Closure_Ortrancl @ SY3552 @ SY3551 ) @ ( tc_prod @ SY3551 @ SY3551 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2078]) ).
thf(2756,plain,
! [SV450: $i] :
( ( ! [SY3553: $i,SY3554: $i,SY3555: $i] :
( ( c_in @ ( c_Pair @ SV450 @ SY3553 @ SY3554 @ SY3554 ) @ ( c_Transitive__Closure_Otrancl @ SY3555 @ SY3554 ) @ ( tc_prod @ SY3554 @ SY3554 ) )
| ( SV450 = SY3553 )
| ~ ( c_in @ ( c_Pair @ SV450 @ SY3553 @ SY3554 @ SY3554 ) @ ( c_Transitive__Closure_Ortrancl @ SY3555 @ SY3554 ) @ ( tc_prod @ SY3554 @ SY3554 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2079]) ).
thf(2757,plain,
! [SV451: $i] :
( ( ! [SY3556: $i,SY3557: $i,SY3558: $i] :
( ( c_in @ ( c_Pair @ SV451 @ SY3556 @ SY3557 @ SY3557 ) @ ( c_Transitive__Closure_Ortrancl @ ( c_Relation_Oconverse @ SY3558 @ SY3557 @ SY3557 ) @ SY3557 ) @ ( tc_prod @ SY3557 @ SY3557 ) )
| ~ ( c_in @ ( c_Pair @ SY3556 @ SV451 @ SY3557 @ SY3557 ) @ ( c_Transitive__Closure_Ortrancl @ SY3558 @ SY3557 ) @ ( tc_prod @ SY3557 @ SY3557 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2080]) ).
thf(2758,plain,
! [SV452: $i] :
( ( ! [SY3559: $i,SY3560: $i,SY3561: $i] :
( ( c_in @ ( c_Pair @ SV452 @ SY3559 @ SY3560 @ SY3560 ) @ ( c_Transitive__Closure_Ortrancl @ SY3561 @ SY3560 ) @ ( tc_prod @ SY3560 @ SY3560 ) )
| ~ ( c_in @ ( c_Pair @ SY3559 @ SV452 @ SY3560 @ SY3560 ) @ ( c_Transitive__Closure_Ortrancl @ ( c_Relation_Oconverse @ SY3561 @ SY3560 @ SY3560 ) @ SY3560 ) @ ( tc_prod @ SY3560 @ SY3560 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2081]) ).
thf(2759,plain,
! [SV453: $i] :
( ( ! [SY3562: $i,SY3563: $i,SY3564: $i] :
( ( c_in @ ( c_Pair @ SV453 @ SY3562 @ SY3563 @ SY3563 ) @ ( c_Transitive__Closure_Ortrancl @ SY3564 @ SY3563 ) @ ( tc_prod @ SY3563 @ SY3563 ) )
| ( c_in @ ( c_Pair @ SY3562 @ SV453 @ SY3563 @ SY3563 ) @ ( c_Transitive__Closure_Ortrancl @ SY3564 @ SY3563 ) @ ( tc_prod @ SY3563 @ SY3563 ) )
| ! [SY3565: $i] :
( ~ ( c_in @ ( c_Pair @ SY3565 @ SV453 @ SY3563 @ SY3563 ) @ ( c_Transitive__Closure_Ortrancl @ SY3564 @ SY3563 ) @ ( tc_prod @ SY3563 @ SY3563 ) )
| ~ ( c_in @ ( c_Pair @ SY3565 @ SY3562 @ SY3563 @ SY3563 ) @ ( c_Transitive__Closure_Ortrancl @ SY3564 @ SY3563 ) @ ( tc_prod @ SY3563 @ SY3563 ) )
| ~ ( c_Relation_Osingle__valued @ SY3564 @ SY3563 @ SY3563 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2082]) ).
thf(2760,plain,
! [SV454: $i] :
( ( ! [SY3566: $i,SY3567: $i,SY3568: $i] :
( ( c_in @ ( c_Pair @ SV454 @ SY3566 @ SY3567 @ SY3567 ) @ ( c_Transitive__Closure_Ortrancl @ SY3568 @ SY3567 ) @ ( tc_prod @ SY3567 @ SY3567 ) )
| ~ ( c_in @ ( c_Pair @ SV454 @ SY3566 @ SY3567 @ SY3567 ) @ ( c_Transitive__Closure_Otrancl @ SY3568 @ SY3567 ) @ ( tc_prod @ SY3567 @ SY3567 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2083]) ).
thf(2761,plain,
! [SV455: $i] :
( ( ! [SY3569: $i,SY3570: $i,SY3571: $i] :
( ( c_in @ ( c_Pair @ SV455 @ SY3569 @ SY3570 @ SY3570 ) @ ( c_Transitive__Closure_Otrancl @ SY3571 @ SY3570 ) @ ( tc_prod @ SY3570 @ SY3570 ) )
| ! [SY3572: $i] :
( ~ ( c_in @ ( c_Pair @ SY3572 @ SY3569 @ SY3570 @ SY3570 ) @ ( c_Transitive__Closure_Ortrancl @ SY3571 @ SY3570 ) @ ( tc_prod @ SY3570 @ SY3570 ) )
| ~ ( c_in @ ( c_Pair @ SV455 @ SY3572 @ SY3570 @ SY3570 ) @ ( c_Transitive__Closure_Otrancl @ SY3571 @ SY3570 ) @ ( tc_prod @ SY3570 @ SY3570 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2084]) ).
thf(2762,plain,
! [SV456: $i] :
( ( ! [SY3573: $i,SY3574: $i,SY3575: $i] :
( ( c_in @ ( c_Pair @ SV456 @ SY3573 @ SY3574 @ SY3574 ) @ ( c_Transitive__Closure_Otrancl @ SY3575 @ SY3574 ) @ ( tc_prod @ SY3574 @ SY3574 ) )
| ! [SY3576: $i] :
( ~ ( c_in @ ( c_Pair @ SY3576 @ SY3573 @ SY3574 @ SY3574 ) @ ( c_Transitive__Closure_Otrancl @ SY3575 @ SY3574 ) @ ( tc_prod @ SY3574 @ SY3574 ) )
| ~ ( c_in @ ( c_Pair @ SV456 @ SY3576 @ SY3574 @ SY3574 ) @ ( c_Transitive__Closure_Ortrancl @ SY3575 @ SY3574 ) @ ( tc_prod @ SY3574 @ SY3574 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2085]) ).
thf(2763,plain,
! [SV457: $i] :
( ( ! [SY3577: $i,SY3578: $i,SY3579: $i] :
( ( c_in @ ( c_Pair @ SV457 @ SY3577 @ SY3578 @ SY3578 ) @ ( c_Relation_Oconverse @ ( c_Transitive__Closure_Otrancl @ SY3579 @ SY3578 ) @ SY3578 @ SY3578 ) @ ( tc_prod @ SY3578 @ SY3578 ) )
| ~ ( c_in @ ( c_Pair @ SV457 @ SY3577 @ SY3578 @ SY3578 ) @ ( c_Transitive__Closure_Otrancl @ ( c_Relation_Oconverse @ SY3579 @ SY3578 @ SY3578 ) @ SY3578 ) @ ( tc_prod @ SY3578 @ SY3578 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2086]) ).
thf(2764,plain,
! [SV458: $i] :
( ( ! [SY3580: $i,SY3581: $i,SY3582: $i] :
( ( c_in @ ( c_Pair @ SV458 @ SY3580 @ SY3581 @ SY3581 ) @ ( c_Transitive__Closure_Otrancl @ ( c_Relation_Oconverse @ SY3582 @ SY3581 @ SY3581 ) @ SY3581 ) @ ( tc_prod @ SY3581 @ SY3581 ) )
| ~ ( c_in @ ( c_Pair @ SV458 @ SY3580 @ SY3581 @ SY3581 ) @ ( c_Relation_Oconverse @ ( c_Transitive__Closure_Otrancl @ SY3582 @ SY3581 ) @ SY3581 @ SY3581 ) @ ( tc_prod @ SY3581 @ SY3581 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2087]) ).
thf(2765,plain,
! [SV459: $i] :
( ( ! [SY3583: $i,SY3584: $i,SY3585: $i,SY3586: $i,SY3587: $i] :
( ( hAPP @ ( c_split @ SV459 @ SY3583 @ SY3584 @ SY3585 ) @ ( c_Pair @ SY3586 @ SY3587 @ SY3583 @ SY3584 ) )
= ( hAPP @ ( hAPP @ SV459 @ SY3586 ) @ SY3587 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2088]) ).
thf(2766,plain,
! [SV460: $i] :
( ( ! [SY3588: $i,SY3589: $i,SY3590: $i,SY3591: $i,SY3592: $i] :
( ( hAPP @ ( c_split @ SV460 @ SY3588 @ SY3589 @ SY3590 ) @ ( c_Pair @ SY3591 @ SY3592 @ SY3588 @ SY3589 ) )
= ( hAPP @ ( hAPP @ SV460 @ SY3591 ) @ SY3592 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2089]) ).
thf(2767,plain,
! [SV461: $i] :
( ( ! [SY3593: $i,SY3594: $i,SY3595: $i,SY3596: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ SV461 @ SY3593 ) @ SY3594 ) @ SY3595 ) )
| ! [SY3597: $i,SY3598: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_split @ SV461 @ SY3596 @ SY3597 @ ( tc_fun @ SY3598 @ tc_bool ) ) @ ( c_Pair @ SY3593 @ SY3594 @ SY3596 @ SY3597 ) ) @ SY3595 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2090]) ).
thf(2768,plain,
! [SV462: $i] :
( ( ! [SY3599: $i,SY3600: $i,SY3601: $i] :
( ! [SY3602: $i] : ( c_in @ ( hAPP @ SV462 @ SY3599 ) @ ( c_Set_Oimage @ SV462 @ SY3600 @ SY3601 @ SY3602 ) @ SY3602 )
| ~ ( c_in @ SY3599 @ SY3600 @ SY3601 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2091]) ).
thf(2769,plain,
! [SV463: $i] :
( ( ! [SY3603: $i,SY3604: $i,SY3605: $i] :
( ! [SY3606: $i] : ( c_in @ ( hAPP @ SV463 @ SY3603 ) @ ( c_Set_Oimage @ SV463 @ SY3604 @ SY3605 @ SY3606 ) @ SY3606 )
| ~ ( c_in @ SY3603 @ SY3604 @ SY3605 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2092]) ).
thf(2770,plain,
! [SV464: $i] :
( ( ! [SY3607: $i,SY3608: $i] :
( ~ ( c_in @ SV464 @ SY3607 @ SY3608 )
| ! [SY3609: $i,SY3610: $i] : ( c_in @ ( hAPP @ SY3609 @ SV464 ) @ ( c_Set_Oimage @ SY3609 @ SY3607 @ SY3608 @ SY3610 ) @ SY3610 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2093]) ).
thf(2771,plain,
! [SV465: $i] :
( ( ! [SY3611: $i,SY3612: $i] :
( ~ ( c_in @ SV465 @ SY3611 @ SY3612 )
| ! [SY3613: $i,SY3614: $i] : ( c_in @ ( hAPP @ SY3613 @ SV465 ) @ ( c_Set_Oimage @ SY3613 @ SY3611 @ SY3612 @ SY3614 ) @ SY3614 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2094]) ).
thf(2772,plain,
! [SV466: $i] :
( ( ! [SY3615: $i,SY3616: $i] :
( ( c_in @ SV466 @ ( c_Wellfounded_Oacc @ SY3615 @ SY3616 ) @ SY3616 )
| ~ ( c_Wellfounded_Owf @ SY3615 @ SY3616 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2095]) ).
thf(2773,plain,
! [SV467: $i] :
( ( ! [SY3617: $i] : ( c_Relation_Osingle__valued @ ( c_Relation_OId__on @ SV467 @ SY3617 ) @ SY3617 @ SY3617 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2096]) ).
thf(2774,plain,
! [SV468: $i] :
( ( ! [SY3618: $i,SY3619: $i,SY3620: $i,SY3621: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Relation__XImageE__1__1 @ SV468 @ SY3618 @ SY3619 @ SY3620 @ SY3621 ) @ SV468 @ SY3620 )
| ~ ( c_in @ SY3618 @ ( c_Relation_OImage @ SY3619 @ SV468 @ SY3620 @ SY3621 ) @ SY3621 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2097]) ).
thf(2775,plain,
! [SV469: $i] :
( ( ! [SY3622: $i] :
( ( c_Relation_Osym @ ( c_Transitive__Closure_Otrancl @ SV469 @ SY3622 ) @ SY3622 )
| ~ ( c_Relation_Osym @ SV469 @ SY3622 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2098]) ).
thf(2776,plain,
! [SV470: $i] :
( ( ! [SY3623: $i] :
( ( hBOOL @ ( hAPP @ SV470 @ SY3623 ) )
| ! [SY3624: $i,SY3625: $i] :
( ~ ( hBOOL @ ( hAPP @ SV470 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ SV470 @ SY3624 @ SY3625 ) ) )
| ~ ( c_in @ SY3623 @ ( c_Wellfounded_Oacc @ SY3624 @ SY3625 ) @ SY3625 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2099]) ).
thf(2777,plain,
! [SV471: $i] :
( ( ! [SY3626: $i] :
( ( ( c_Transitive__Closure_Otrancl @ SV471 @ SY3626 )
= SV471 )
| ~ ( c_Relation_Otrans @ SV471 @ SY3626 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2100]) ).
thf(2778,plain,
! [SV472: $i] :
( ( ! [SY3627: $i] :
( ( hBOOL @ ( hAPP @ SV472 @ SY3627 ) )
| ! [SY3628: $i] :
( ~ ( hBOOL @ ( hAPP @ SV472 @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ SV472 @ SY3628 ) ) )
| ~ ( c_in @ SY3627 @ ( c_Wellfounded_Oacc @ SY3628 @ t_a ) @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2101]) ).
thf(2779,plain,
! [SV473: $i] :
( ( ! [SY3629: $i] :
( ( hBOOL @ ( hAPP @ SV473 @ SY3629 ) )
| ! [SY3630: $i,SY3631: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ SV473 @ SY3630 @ SY3631 ) @ ( c_Wellfounded_Oacc @ SY3630 @ SY3631 ) @ SY3631 )
| ~ ( c_in @ SY3629 @ ( c_Wellfounded_Oacc @ SY3630 @ SY3631 ) @ SY3631 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2102]) ).
thf(2780,plain,
! [SV474: $i] :
( ( ! [SY3632: $i] :
( ( c_Relation_Osym @ SV474 @ SY3632 )
| ~ ( c_Relation_Osym @ ( c_Relation_Oconverse @ SV474 @ SY3632 @ SY3632 ) @ SY3632 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2103]) ).
thf(2781,plain,
! [SV475: $i] :
( ( ! [SY3633: $i] :
( ( c_Relation_Osym @ ( c_Relation_Oconverse @ SV475 @ SY3633 @ SY3633 ) @ SY3633 )
| ~ ( c_Relation_Osym @ SV475 @ SY3633 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2104]) ).
thf(2782,plain,
! [SV476: $i] :
( ( ! [SY3634: $i] :
( ( c_Relation_ODomain @ ( c_Transitive__Closure_Otrancl @ SV476 @ SY3634 ) @ SY3634 @ SY3634 )
= ( c_Relation_ODomain @ SV476 @ SY3634 @ SY3634 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2105]) ).
thf(2783,plain,
! [SV477: $i] :
( ( ! [SY3635: $i,SY3636: $i,SY3637: $i,SY3638: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Relation__XImage__iff__1__1 @ SV477 @ SY3635 @ SY3636 @ SY3637 @ SY3638 ) @ SV477 @ SY3637 )
| ~ ( c_in @ SY3635 @ ( c_Relation_OImage @ SY3636 @ SV477 @ SY3637 @ SY3638 ) @ SY3638 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2106]) ).
thf(2784,plain,
! [SV478: $i] :
( ( ! [SY3639: $i,SY3640: $i] :
( ~ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1 @ SV478 @ SY3639 @ SY3640 ) @ ( c_Wellfounded_Oacc @ SV478 @ SY3640 ) @ SY3640 )
| ( c_in @ SY3639 @ ( c_Wellfounded_Oacc @ SV478 @ SY3640 ) @ SY3640 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2107]) ).
thf(2785,plain,
! [SV479: $i] :
( ( c_Relation_Osym @ ( c_Relation_OId @ SV479 ) @ SV479 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2108]) ).
thf(2786,plain,
! [SV480: $i] :
( ( ! [SY3641: $i] : ( c_Relation_Otrans @ ( c_Relation_OId__on @ SV480 @ SY3641 ) @ SY3641 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2109]) ).
thf(2787,plain,
! [SV481: $i] :
( ( ! [SY3642: $i,SY3643: $i] :
( ( c_Relation_Orel__comp @ ( c_Relation_OId @ SV481 ) @ SY3642 @ SV481 @ SV481 @ SY3643 )
= SY3642 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2110]) ).
thf(2788,plain,
! [SV482: $i] :
( ( ! [SY3644: $i,SY3645: $i] :
( ( c_Relation_Orel__comp @ SV482 @ ( c_Relation_OId @ SY3644 ) @ SY3645 @ SY3644 @ SY3644 )
= SV482 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2111]) ).
thf(2789,plain,
! [SV483: $i] :
( ( ! [SY3646: $i] : ( c_Relation_Oantisym @ ( c_Relation_OId__on @ SV483 @ SY3646 ) @ SY3646 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2112]) ).
thf(2790,plain,
! [SV484: $i] :
( ( ! [SY3647: $i] :
( ( c_Wellfounded_Owf @ ( c_Relation_Oconverse @ ( c_Transitive__Closure_Otrancl @ SV484 @ SY3647 ) @ SY3647 @ SY3647 ) @ SY3647 )
| ~ ( c_Wellfounded_Owf @ ( c_Relation_Oconverse @ SV484 @ SY3647 @ SY3647 ) @ SY3647 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2113]) ).
thf(2791,plain,
! [SV485: $i] :
( ( ! [SY3648: $i] :
( ( hBOOL @ ( hAPP @ SV485 @ SY3648 ) )
| ! [SY3649: $i,SY3650: $i] :
( ~ ( hBOOL @ ( hAPP @ SV485 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ SV485 @ SY3649 @ SY3650 ) ) )
| ~ ( c_in @ SY3648 @ ( c_Wellfounded_Oacc @ SY3649 @ SY3650 ) @ SY3650 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2114]) ).
thf(2792,plain,
! [SV486: $i] :
( ( ! [SY3651: $i,SY3652: $i] :
( ( c_Relation_Orefl__on @ SV486 @ SY3651 @ SY3652 )
| ~ ( c_Relation_Orefl__on @ SV486 @ ( c_Relation_Oconverse @ SY3651 @ SY3652 @ SY3652 ) @ SY3652 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2115]) ).
thf(2793,plain,
! [SV487: $i] :
( ( ! [SY3653: $i,SY3654: $i] :
( ( c_Relation_Orefl__on @ SV487 @ ( c_Relation_Oconverse @ SY3653 @ SY3654 @ SY3654 ) @ SY3654 )
| ~ ( c_Relation_Orefl__on @ SV487 @ SY3653 @ SY3654 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2116]) ).
thf(2794,plain,
! [SV488: $i] :
( ( ! [SY3655: $i] :
( ( c_Relation_Osym @ ( c_Transitive__Closure_Ortrancl @ SV488 @ SY3655 ) @ SY3655 )
| ~ ( c_Relation_Osym @ SV488 @ SY3655 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2117]) ).
thf(2795,plain,
! [SV489: $i] :
( ( ! [SY3656: $i] :
( ( c_Wellfounded_Owf @ ( c_Relation_Orel__comp @ SV489 @ SV489 @ SY3656 @ SY3656 @ SY3656 ) @ SY3656 )
| ~ ( c_Wellfounded_Owf @ SV489 @ SY3656 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2118]) ).
thf(2796,plain,
! [SV490: $i] :
( ( ! [SY3657: $i] :
( ( c_Wellfounded_Owf @ SV490 @ SY3657 )
| ~ ( c_Wellfounded_Owf @ ( c_Relation_Orel__comp @ SV490 @ SV490 @ SY3657 @ SY3657 @ SY3657 ) @ SY3657 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2119]) ).
thf(2797,plain,
! [SV491: $i] :
( ( ! [SY3658: $i] :
( ( c_Relation_OImage @ ( c_Relation_OId @ SV491 ) @ SY3658 @ SV491 @ SV491 )
= SY3658 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2120]) ).
thf(2798,plain,
! [SV492: $i] :
( ( c_Relation_Osingle__valued @ ( c_Relation_OId @ SV492 ) @ SV492 @ SV492 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2121]) ).
thf(2799,plain,
! [SV493: $i] :
( ( ! [SY3659: $i] :
( ( c_Relation_ODomain @ ( c_Relation_OId__on @ SV493 @ SY3659 ) @ SY3659 @ SY3659 )
= SV493 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2122]) ).
thf(2800,plain,
! [SV494: $i] :
( ( ! [SY3660: $i] :
( ( ( c_Relation_Oconverse @ SV494 @ SY3660 @ SY3660 )
= SV494 )
| ~ ( c_Relation_Osym @ SV494 @ SY3660 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2123]) ).
thf(2801,plain,
! [SV495: $i] :
( ( ! [SY3661: $i] :
( ( ( c_Relation_Oconverse @ SV495 @ SY3661 @ SY3661 )
!= SV495 )
| ( c_Relation_Osym @ SV495 @ SY3661 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2124]) ).
thf(2802,plain,
! [SV496: $i] :
( ( ! [SY3662: $i] :
( ( c_Relation_ORange @ ( c_Transitive__Closure_Otrancl @ SV496 @ SY3662 ) @ SY3662 @ SY3662 )
= ( c_Relation_ORange @ SV496 @ SY3662 @ SY3662 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2125]) ).
thf(2803,plain,
! [SV497: $i] :
( ( ! [SY3663: $i] : ( c_Relation_Otrans @ ( c_Transitive__Closure_Otrancl @ SV497 @ SY3663 ) @ SY3663 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2126]) ).
thf(2804,plain,
! [SV498: $i] :
( ( ! [SY3664: $i,SY3665: $i,SY3666: $i,SY3667: $i] :
( ( c_Relation_Oconverse @ ( c_Relation_Orel__comp @ SV498 @ SY3664 @ SY3665 @ SY3666 @ SY3667 ) @ SY3665 @ SY3667 )
= ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ SY3664 @ SY3666 @ SY3667 ) @ ( c_Relation_Oconverse @ SV498 @ SY3665 @ SY3666 ) @ SY3667 @ SY3666 @ SY3665 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2127]) ).
thf(2805,plain,
! [SV499: $i] :
( ( ! [SY3668: $i] : ( c_Relation_Osym @ ( c_Relation_OId__on @ SV499 @ SY3668 ) @ SY3668 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2128]) ).
thf(2806,plain,
! [SV500: $i] :
( ( ! [SY3669: $i] : ( c_Relation_Orefl__on @ SV500 @ ( c_Relation_OId__on @ SV500 @ SY3669 ) @ SY3669 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2129]) ).
thf(2807,plain,
! [SV501: $i] :
( ( ! [SY3670: $i,SY3671: $i] :
( ! [SY3672: $i] : ( c_Wellfounded_Owf @ ( c_Relation_Oinv__image @ SV501 @ SY3670 @ SY3671 @ SY3672 ) @ SY3672 )
| ~ ( c_Wellfounded_Owf @ SV501 @ SY3671 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2130]) ).
thf(2808,plain,
! [SV502: $i] :
( ( ! [SY3673: $i] :
( ( c_Relation_Orel__comp @ SV502 @ ( c_Transitive__Closure_Ortrancl @ SV502 @ SY3673 ) @ SY3673 @ SY3673 @ SY3673 )
= ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Ortrancl @ SV502 @ SY3673 ) @ SV502 @ SY3673 @ SY3673 @ SY3673 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2131]) ).
thf(2809,plain,
! [SV503: $i] :
( ( ! [SY3674: $i,SY3675: $i] :
( ! [SY3676: $i] : ( c_Relation_Osym @ ( c_Relation_Oinv__image @ SV503 @ SY3674 @ SY3675 @ SY3676 ) @ SY3676 )
| ~ ( c_Relation_Osym @ SV503 @ SY3675 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2132]) ).
thf(2810,plain,
! [SV504: $i] :
( ( ! [SY3677: $i] :
( ( c_Transitive__Closure_Otrancl @ ( c_Transitive__Closure_Ortrancl @ SV504 @ SY3677 ) @ SY3677 )
= ( c_Transitive__Closure_Ortrancl @ SV504 @ SY3677 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2133]) ).
thf(2811,plain,
! [SV505: $i] :
( ( ! [SY3678: $i] : ( c_Relation_Otrans @ ( c_Transitive__Closure_Ortrancl @ SV505 @ SY3678 ) @ SY3678 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2134]) ).
thf(2812,plain,
! [SV506: $i] :
( ( ! [SY3679: $i] :
( ( c_Relation_Otrans @ SV506 @ SY3679 )
| ~ ( c_Relation_Otrans @ ( c_Relation_Oconverse @ SV506 @ SY3679 @ SY3679 ) @ SY3679 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2135]) ).
thf(2813,plain,
! [SV507: $i] :
( ( ! [SY3680: $i] :
( ( c_Relation_Otrans @ ( c_Relation_Oconverse @ SV507 @ SY3680 @ SY3680 ) @ SY3680 )
| ~ ( c_Relation_Otrans @ SV507 @ SY3680 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2136]) ).
thf(2814,plain,
! [SV508: $i] :
( ( ( c_Relation_Oconverse @ ( c_Relation_OId @ SV508 ) @ SV508 @ SV508 )
= ( c_Relation_OId @ SV508 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2137]) ).
thf(2815,plain,
! [SV509: $i] :
( ( ! [SY3681: $i] :
( ( c_Wellfounded_Owf @ ( c_Transitive__Closure_Otrancl @ SV509 @ SY3681 ) @ SY3681 )
| ~ ( c_Wellfounded_Owf @ SV509 @ SY3681 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2138]) ).
thf(2816,plain,
! [SV510: $i] :
( ( ! [SY3682: $i,SY3683: $i,SY3684: $i,SY3685: $i,SY3686: $i,SY3687: $i] :
( ( c_Relation_Orel__comp @ ( c_Relation_Orel__comp @ SV510 @ SY3682 @ SY3683 @ SY3684 @ SY3685 ) @ SY3686 @ SY3683 @ SY3685 @ SY3687 )
= ( c_Relation_Orel__comp @ SV510 @ ( c_Relation_Orel__comp @ SY3682 @ SY3686 @ SY3684 @ SY3685 @ SY3687 ) @ SY3683 @ SY3684 @ SY3687 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2139]) ).
thf(2817,plain,
! [SV511: $i] :
( ( ! [SY3688: $i,SY3689: $i,SY3690: $i] :
( ( c_Relation_Oconverse @ ( c_Relation_Oinv__image @ SV511 @ SY3688 @ SY3689 @ SY3690 ) @ SY3690 @ SY3690 )
= ( c_Relation_Oinv__image @ ( c_Relation_Oconverse @ SV511 @ SY3689 @ SY3689 ) @ SY3688 @ SY3689 @ SY3690 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2140]) ).
thf(2818,plain,
! [SV512: $i] :
( ( ! [SY3691: $i] :
( ( c_Transitive__Closure_Otrancl @ ( c_Relation_Oconverse @ SV512 @ SY3691 @ SY3691 ) @ SY3691 )
= ( c_Relation_Oconverse @ ( c_Transitive__Closure_Otrancl @ SV512 @ SY3691 ) @ SY3691 @ SY3691 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2141]) ).
thf(2819,plain,
! [SV513: $i] :
( ( ! [SY3692: $i,SY3693: $i] :
( ! [SY3694: $i] : ( c_Relation_Otrans @ ( c_Relation_Oinv__image @ SV513 @ SY3692 @ SY3693 @ SY3694 ) @ SY3694 )
| ~ ( c_Relation_Otrans @ SV513 @ SY3693 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2142]) ).
thf(2820,plain,
! [SV514: $i] :
( ( ! [SY3695: $i] :
( ( c_Relation_Oconverse @ ( c_Relation_OId__on @ SV514 @ SY3695 ) @ SY3695 @ SY3695 )
= ( c_Relation_OId__on @ SV514 @ SY3695 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2143]) ).
thf(2821,plain,
! [SV515: $i] :
( ( ! [SY3696: $i] :
( ( ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ SV515 @ SY3696 @ SY3696 ) @ SV515 @ SY3696 @ SY3696 @ SY3696 )
!= SV515 )
| ( c_Equiv__Relations_Oequiv @ ( c_Relation_ODomain @ SV515 @ SY3696 @ SY3696 ) @ SV515 @ SY3696 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2144]) ).
thf(2822,plain,
! [SV516: $i] :
( ( c_Relation_Oantisym @ ( c_Relation_OId @ SV516 ) @ SV516 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2145]) ).
thf(2823,plain,
! [SV517: $i] :
( ( ! [SY3697: $i,SY3698: $i] :
( ( c_Relation_ORange @ ( c_Relation_Oconverse @ SV517 @ SY3697 @ SY3698 ) @ SY3698 @ SY3697 )
= ( c_Relation_ODomain @ SV517 @ SY3697 @ SY3698 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2146]) ).
thf(2824,plain,
! [SV518: $i] :
( ( ! [SY3699: $i,SY3700: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 @ SV518 @ SY3699 @ SY3700 ) @ SV518 @ SY3700 )
| ! [SY3701: $i] :
~ ( c_in @ SY3701 @ SV518 @ SY3700 )
| ~ ( c_Wellfounded_Owf @ SY3699 @ SY3700 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2147]) ).
thf(2825,plain,
! [SV519: $i] :
( ( ! [SY3702: $i] :
( ( c_Relation_ORange @ ( c_Relation_OId__on @ SV519 @ SY3702 ) @ SY3702 @ SY3702 )
= SV519 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2148]) ).
thf(2826,plain,
! [SV520: $i] :
( ( ! [SY3703: $i,SY3704: $i,SY3705: $i,SY3706: $i] :
( ( c_Relation_Osingle__valued @ ( c_Relation_Orel__comp @ SV520 @ SY3703 @ SY3704 @ SY3705 @ SY3706 ) @ SY3704 @ SY3706 )
| ~ ( c_Relation_Osingle__valued @ SY3703 @ SY3705 @ SY3706 )
| ~ ( c_Relation_Osingle__valued @ SV520 @ SY3704 @ SY3705 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2149]) ).
thf(2827,plain,
! [SV521: $i] :
( ( ! [SY3707: $i,SY3708: $i] :
( ( c_Relation_Oconverse @ ( c_Relation_Oconverse @ SV521 @ SY3707 @ SY3708 ) @ SY3708 @ SY3707 )
= SV521 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2150]) ).
thf(2828,plain,
! [SV522: $i] :
( ( c_Relation_Otrans @ ( c_Relation_OId @ SV522 ) @ SV522 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2151]) ).
thf(2829,plain,
! [SV523: $i] :
( ( ! [SY3709: $i] :
( ( ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ SV523 @ SY3709 @ SY3709 ) @ SV523 @ SY3709 @ SY3709 @ SY3709 )
= SV523 )
| ! [SY3710: $i] :
~ ( c_Equiv__Relations_Oequiv @ SY3710 @ SV523 @ SY3709 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2152]) ).
thf(2830,plain,
! [SV524: $i] :
( ( ! [SY3711: $i] :
( ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Ortrancl @ SV524 @ SY3711 ) @ ( c_Transitive__Closure_Ortrancl @ SV524 @ SY3711 ) @ SY3711 @ SY3711 @ SY3711 )
= ( c_Transitive__Closure_Ortrancl @ SV524 @ SY3711 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2153]) ).
thf(2831,plain,
! [SV525: $i] :
( ( ! [SY3712: $i] :
( ( c_Relation_Oantisym @ SV525 @ SY3712 )
| ~ ( c_Relation_Oantisym @ ( c_Relation_Oconverse @ SV525 @ SY3712 @ SY3712 ) @ SY3712 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2154]) ).
thf(2832,plain,
! [SV526: $i] :
( ( ! [SY3713: $i] :
( ( c_Relation_Oantisym @ ( c_Relation_Oconverse @ SV526 @ SY3713 @ SY3713 ) @ SY3713 )
| ~ ( c_Relation_Oantisym @ SV526 @ SY3713 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2155]) ).
thf(2833,plain,
! [SV527: $i] :
( ( ! [SY3714: $i] :
( ( hBOOL @ ( hAPP @ SV527 @ SY3714 ) )
| ! [SY3715: $i] :
( ~ ( hBOOL @ ( hAPP @ SV527 @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ SV527 @ SY3715 ) ) )
| ~ ( c_in @ SY3714 @ ( c_Wellfounded_Oacc @ SY3715 @ t_a ) @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2156]) ).
thf(2834,plain,
! [SV528: $i] :
( ( ! [SY3716: $i,SY3717: $i] :
( ( c_Relation_Orefl__on @ SV528 @ SY3716 @ SY3717 )
| ~ ( c_Equiv__Relations_Oequiv @ SV528 @ SY3716 @ SY3717 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2157]) ).
thf(2835,plain,
! [SV529: $i] :
( ( ! [SY3718: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( c_Relation_Oconverse @ SV529 @ SY3718 @ SY3718 ) @ SY3718 )
= ( c_Relation_Oconverse @ ( c_Transitive__Closure_Ortrancl @ SV529 @ SY3718 ) @ SY3718 @ SY3718 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2158]) ).
thf(2836,plain,
! [SV530: $i] :
( ( ! [SY3719: $i,SY3720: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 @ SV530 @ SY3719 @ SY3720 ) @ SV530 @ SY3720 )
| ! [SY3721: $i] :
~ ( c_in @ SY3721 @ SV530 @ SY3720 )
| ~ ( c_Wellfounded_Owf @ SY3719 @ SY3720 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2159]) ).
thf(2837,plain,
! [SV531: $i] :
( ( ! [SY3722: $i] :
( ( c_Relation_Osym @ SV531 @ SY3722 )
| ! [SY3723: $i] :
~ ( c_Equiv__Relations_Oequiv @ SY3723 @ SV531 @ SY3722 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2160]) ).
thf(2838,plain,
! [SV532: $i] :
( ( ! [SY3724: $i,SY3725: $i] :
( ( c_in @ SV532 @ ( c_Wellfounded_Oacc @ SY3724 @ SY3725 ) @ SY3725 )
| ~ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1 @ SY3724 @ SV532 @ SY3725 ) @ ( c_Wellfounded_Oacc @ SY3724 @ SY3725 ) @ SY3725 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2161]) ).
thf(2839,plain,
! [SV533: $i] :
( ( ! [SY3726: $i,SY3727: $i,SY3728: $i,SY3729: $i,SY3730: $i] :
( ( c_Equiv__Relations_Ocongruent @ SV533 @ ( hAPP @ SY3726 @ SY3727 ) @ SY3728 @ SY3729 )
| ! [SY3731: $i] :
( ~ ( c_in @ SY3727 @ SY3730 @ SY3731 )
| ! [SY3732: $i] :
( ~ ( c_Equiv__Relations_Ocongruent2 @ SY3732 @ SV533 @ SY3726 @ SY3731 @ SY3728 @ SY3729 )
| ~ ( c_Equiv__Relations_Oequiv @ SY3730 @ SY3732 @ SY3731 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2162]) ).
thf(2840,plain,
! [SV534: $i] :
( ( ! [SY3733: $i,SY3734: $i] :
( ( c_Relation_ODomain @ ( c_Relation_Oconverse @ SV534 @ SY3733 @ SY3734 ) @ SY3734 @ SY3733 )
= ( c_Relation_ORange @ SV534 @ SY3733 @ SY3734 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2163]) ).
thf(2841,plain,
! [SV535: $i] :
( ( ! [SY3735: $i] :
( ( c_Transitive__Closure_Otrancl @ SV535 @ SY3735 )
= ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Ortrancl @ SV535 @ SY3735 ) @ SV535 @ SY3735 @ SY3735 @ SY3735 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2164]) ).
thf(2842,plain,
! [SV536: $i] :
( ( ! [SY3736: $i] :
( ( c_Transitive__Closure_Otrancl @ SV536 @ SY3736 )
= ( c_Relation_Orel__comp @ SV536 @ ( c_Transitive__Closure_Ortrancl @ SV536 @ SY3736 ) @ SY3736 @ SY3736 @ SY3736 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2165]) ).
thf(2843,plain,
! [SV537: $i] :
( ( ! [SY3737: $i,SY3738: $i] :
( ( c_Relation_ORange @ SV537 @ SY3737 @ SY3738 )
= ( c_Relation_ODomain @ ( c_Relation_Oconverse @ SV537 @ SY3737 @ SY3738 ) @ SY3738 @ SY3737 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2166]) ).
thf(2844,plain,
! [SV538: $i] :
( ( ! [SY3739: $i,SY3740: $i] :
( ( c_Relation_Ototal__on @ SV538 @ SY3739 @ SY3740 )
| ~ ( c_Relation_Ototal__on @ SV538 @ ( c_Relation_Oconverse @ SY3739 @ SY3740 @ SY3740 ) @ SY3740 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2167]) ).
thf(2845,plain,
! [SV539: $i] :
( ( ! [SY3741: $i,SY3742: $i] :
( ( c_Relation_Ototal__on @ SV539 @ ( c_Relation_Oconverse @ SY3741 @ SY3742 @ SY3742 ) @ SY3742 )
| ~ ( c_Relation_Ototal__on @ SV539 @ SY3741 @ SY3742 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2168]) ).
thf(2846,plain,
! [SV540: $i] :
( ( ! [SY3743: $i] :
( ( c_Relation_Otrans @ SV540 @ SY3743 )
| ! [SY3744: $i] :
~ ( c_Equiv__Relations_Oequiv @ SY3744 @ SV540 @ SY3743 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2169]) ).
thf(2847,plain,
! [SV541: $i] :
( ( ! [SY3745: $i] :
( ( hBOOL @ ( hAPP @ SV541 @ SY3745 ) )
| ! [SY3746: $i,SY3747: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ SV541 @ SY3746 @ SY3747 ) @ ( c_Wellfounded_Oacc @ SY3746 @ SY3747 ) @ SY3747 )
| ~ ( c_in @ SY3745 @ ( c_Wellfounded_Oacc @ SY3746 @ SY3747 ) @ SY3747 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2170]) ).
thf(2848,plain,
! [SV542: $i] :
( ( ! [SY3748: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( c_Transitive__Closure_Otrancl @ SV542 @ SY3748 ) @ SY3748 )
= ( c_Transitive__Closure_Ortrancl @ SV542 @ SY3748 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2171]) ).
thf(2849,plain,
! [SV543: $i] :
( ( ! [SY3749: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( c_Transitive__Closure_Ortrancl @ SV543 @ SY3749 ) @ SY3749 )
= ( c_Transitive__Closure_Ortrancl @ SV543 @ SY3749 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2172]) ).
thf(2850,plain,
! [SV544: $i] :
( ( ! [SY3750: $i,SY3751: $i,SY3752: $i,SY3753: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XImageE__1__1 @ SV544 @ SY3750 @ SY3751 @ SY3752 @ SY3753 ) @ SY3750 @ SY3752 @ SY3753 ) @ SY3751 @ ( tc_prod @ SY3752 @ SY3753 ) )
| ~ ( c_in @ SY3750 @ ( c_Relation_OImage @ SY3751 @ SV544 @ SY3752 @ SY3753 ) @ SY3753 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2175]) ).
thf(2851,plain,
! [SV545: $i] :
( ( ! [SY3754: $i,SY3755: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1 @ SV545 @ SY3754 @ SY3755 ) @ SY3754 @ SY3755 @ SY3755 ) @ SV545 @ ( tc_prod @ SY3755 @ SY3755 ) )
| ( c_in @ SY3754 @ ( c_Wellfounded_Oacc @ SV545 @ SY3755 ) @ SY3755 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2176]) ).
thf(2852,plain,
! [SV546: $i] :
( ( ! [SY3756: $i,SY3757: $i] :
( ( hBOOL @ ( hAPP @ SV546 @ SY3756 ) )
| ( hBOOL @ ( hAPP @ SV546 @ SY3757 ) )
| ! [SY3758: $i,SY3759: $i] :
( ~ ( c_in @ ( c_Pair @ SY3757 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ SV546 @ SY3758 @ SY3759 ) @ SY3759 @ SY3759 ) @ SY3758 @ ( tc_prod @ SY3759 @ SY3759 ) )
| ~ ( c_in @ SY3756 @ ( c_Wellfounded_Oacc @ SY3758 @ SY3759 ) @ SY3759 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2177]) ).
thf(2853,plain,
! [SV547: $i] :
( ( ! [SY3760: $i] :
( ( hBOOL @ ( hAPP @ SV547 @ SY3760 ) )
| ! [SY3761: $i] :
( ( hBOOL @ ( hAPP @ SV547 @ SY3761 ) )
| ! [SY3762: $i] :
( ~ ( c_in @ ( c_Pair @ SY3761 @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ SV547 @ SY3762 ) @ t_a @ t_a ) @ SY3762 @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ SY3760 @ ( c_Wellfounded_Oacc @ SY3762 @ t_a ) @ t_a ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2178]) ).
thf(2854,plain,
! [SV548: $i] :
( ( ! [SY3763: $i,SY3764: $i] :
( ~ ( c_in @ SV548 @ SY3763 @ SY3764 )
| ! [SY3765: $i] :
( ~ ( c_in @ ( c_Pair @ SV548 @ ( c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 @ SY3763 @ SY3765 @ SY3764 ) @ SY3764 @ SY3764 ) @ SY3765 @ ( tc_prod @ SY3764 @ SY3764 ) )
| ! [V_x: $i] :
~ ( c_in @ V_x @ SY3763 @ SY3764 )
| ~ ( c_Wellfounded_Owf @ SY3765 @ SY3764 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2179]) ).
thf(2855,plain,
! [SV549: $i] :
( ( ! [SY3767: $i,SY3768: $i,SY3769: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XRangeE__1__1 @ SV549 @ SY3767 @ SY3768 @ SY3769 ) @ SV549 @ SY3769 @ SY3768 ) @ SY3767 @ ( tc_prod @ SY3769 @ SY3768 ) )
| ~ ( c_in @ SV549 @ ( c_Relation_ORange @ SY3767 @ SY3769 @ SY3768 ) @ SY3768 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2180]) ).
thf(2856,plain,
! [SV550: $i] :
( ( ! [SY3770: $i,SY3771: $i] :
( ( c_in @ SV550 @ ( c_Wellfounded_Oacc @ SY3770 @ SY3771 ) @ SY3771 )
| ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1 @ SY3770 @ SV550 @ SY3771 ) @ SV550 @ SY3771 @ SY3771 ) @ SY3770 @ ( tc_prod @ SY3771 @ SY3771 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2181]) ).
thf(2857,plain,
! [SV551: $i] :
( ( ! [SY3772: $i,SY3773: $i] :
( ( c_in @ SV551 @ ( c_Wellfounded_Oacc @ SY3772 @ SY3773 ) @ SY3773 )
| ! [SY3774: $i] :
( ~ ( c_in @ SY3774 @ ( c_Wellfounded_Oacc @ SY3772 @ SY3773 ) @ SY3773 )
| ~ ( c_in @ ( c_Pair @ SV551 @ SY3774 @ SY3773 @ SY3773 ) @ ( c_Transitive__Closure_Ortrancl @ SY3772 @ SY3773 ) @ ( tc_prod @ SY3773 @ SY3773 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2182]) ).
thf(2858,plain,
! [SV552: $i] :
( ( ! [SY3775: $i,SY3776: $i] :
( ( c_in @ SV552 @ ( c_Wellfounded_Oacc @ SY3775 @ SY3776 ) @ SY3776 )
| ! [SY3777: $i] :
( ~ ( c_in @ ( c_Pair @ SV552 @ SY3777 @ SY3776 @ SY3776 ) @ ( c_Transitive__Closure_Ortrancl @ SY3775 @ SY3776 ) @ ( tc_prod @ SY3776 @ SY3776 ) )
| ~ ( c_in @ SY3777 @ ( c_Wellfounded_Oacc @ SY3775 @ SY3776 ) @ SY3776 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2183]) ).
thf(2859,plain,
! [SV553: $i] :
( ( ! [SY3778: $i] :
( ( hBOOL @ ( hAPP @ SV553 @ SY3778 ) )
| ! [SY3779: $i,SY3780: $i] :
( ( c_in @ SY3779 @ ( c_Wellfounded_Oacc @ SY3780 @ t_a ) @ t_a )
| ~ ( c_in @ ( c_Pair @ SY3779 @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ SV553 @ SY3780 ) @ t_a @ t_a ) @ SY3780 @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ SY3778 @ ( c_Wellfounded_Oacc @ SY3780 @ t_a ) @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2184]) ).
thf(2860,plain,
! [SV554: $i] :
( ( ! [SY3781: $i,SY3782: $i] :
( ( c_in @ SV554 @ ( c_Relation_ODomain @ SY3781 @ SY3782 @ SY3782 ) @ SY3782 )
| ( c_in @ ( c_Pair @ SV554 @ SV554 @ SY3782 @ SY3782 ) @ ( c_Transitive__Closure_Ortrancl @ SY3781 @ SY3782 ) @ ( tc_prod @ SY3782 @ SY3782 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2185]) ).
thf(2861,plain,
! [SV555: $i] :
( ( ! [SY3783: $i] :
( ( hBOOL @ ( hAPP @ SV555 @ SY3783 ) )
| ! [SY3784: $i] :
( ( hBOOL @ ( hAPP @ SV555 @ SY3784 ) )
| ! [SY3785: $i] :
( ~ ( c_in @ ( c_Pair @ SY3784 @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ SV555 @ SY3785 ) @ t_a @ t_a ) @ SY3785 @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ SY3783 @ ( c_Wellfounded_Oacc @ SY3785 @ t_a ) @ t_a ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2186]) ).
thf(2862,plain,
! [SV556: $i] :
( ( ! [SY3786: $i,SY3787: $i,SY3788: $i,SY3789: $i,SY3790: $i,SY3791: $i] :
( ( c_in @ ( hAPP @ ( hAPP @ SV556 @ SY3786 ) @ SY3787 ) @ ( c_Set_Oimage @ ( c_split @ SV556 @ SY3788 @ SY3789 @ SY3790 ) @ SY3791 @ ( tc_prod @ SY3788 @ SY3789 ) @ SY3790 ) @ SY3790 )
| ~ ( c_in @ ( c_Pair @ SY3786 @ SY3787 @ SY3788 @ SY3789 ) @ SY3791 @ ( tc_prod @ SY3788 @ SY3789 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2187]) ).
thf(2863,plain,
! [SV557: $i] :
( ( ! [SY3792: $i,SY3793: $i,SY3794: $i] :
( ( c_in @ ( c_Pair @ SV557 @ ( c_ATP__Linkup_Osko__Relation__XDomainE__1__1 @ SV557 @ SY3792 @ SY3793 @ SY3794 ) @ SY3793 @ SY3794 ) @ SY3792 @ ( tc_prod @ SY3793 @ SY3794 ) )
| ~ ( c_in @ SV557 @ ( c_Relation_ODomain @ SY3792 @ SY3793 @ SY3794 ) @ SY3793 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2188]) ).
thf(2864,plain,
! [SV558: $i] :
( ( ! [SY3795: $i] :
( ( hBOOL @ ( hAPP @ SV558 @ SY3795 ) )
| ! [SY3796: $i,SY3797: $i] :
( ( c_in @ SY3796 @ ( c_Wellfounded_Oacc @ SY3797 @ t_a ) @ t_a )
| ~ ( c_in @ ( c_Pair @ SY3796 @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ SV558 @ SY3797 ) @ t_a @ t_a ) @ SY3797 @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ SY3795 @ ( c_Wellfounded_Oacc @ SY3797 @ t_a ) @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2189]) ).
thf(2865,plain,
! [SV559: $i] :
( ( ! [SY3798: $i,SY3799: $i] :
( ( hBOOL @ ( hAPP @ SV559 @ SY3798 ) )
| ( hBOOL @ ( hAPP @ SV559 @ SY3799 ) )
| ! [SY3800: $i,SY3801: $i] :
( ~ ( c_in @ ( c_Pair @ SY3799 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ SV559 @ SY3800 @ SY3801 ) @ SY3801 @ SY3801 ) @ SY3800 @ ( tc_prod @ SY3801 @ SY3801 ) )
| ~ ( c_in @ SY3798 @ ( c_Wellfounded_Oacc @ SY3800 @ SY3801 ) @ SY3801 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2190]) ).
thf(2866,plain,
! [SV560: $i] :
( ( ! [SY3802: $i,SY3803: $i] :
( ~ ( c_in @ SV560 @ SY3802 @ SY3803 )
| ! [SY3804: $i] :
( ~ ( c_in @ ( c_Pair @ SV560 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 @ SY3802 @ SY3804 @ SY3803 ) @ SY3803 @ SY3803 ) @ SY3804 @ ( tc_prod @ SY3803 @ SY3803 ) )
| ! [V_xa: $i] :
~ ( c_in @ V_xa @ SY3802 @ SY3803 )
| ~ ( c_Wellfounded_Owf @ SY3804 @ SY3803 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2191]) ).
thf(2867,plain,
! [SV561: $i] :
( ( ! [SY3806: $i,SY3807: $i,SY3808: $i] :
( ( c_in @ ( c_Pair @ SV561 @ ( c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1 @ SV561 @ SY3806 @ SY3807 @ SY3808 ) @ SY3807 @ SY3808 ) @ SY3806 @ ( tc_prod @ SY3807 @ SY3808 ) )
| ~ ( c_in @ SV561 @ ( c_Relation_ODomain @ SY3806 @ SY3807 @ SY3808 ) @ SY3807 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2192]) ).
thf(2868,plain,
! [SV562: $i] :
( ( ! [SY3809: $i,SY3810: $i,SY3811: $i,SY3812: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XImage__iff__1__1 @ SV562 @ SY3809 @ SY3810 @ SY3811 @ SY3812 ) @ SY3809 @ SY3811 @ SY3812 ) @ SY3810 @ ( tc_prod @ SY3811 @ SY3812 ) )
| ~ ( c_in @ SY3809 @ ( c_Relation_OImage @ SY3810 @ SV562 @ SY3811 @ SY3812 ) @ SY3812 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2193]) ).
thf(2869,plain,
! [SV563: $i] :
( ( ! [SY3813: $i] :
( ( SV563 = SY3813 )
| ! [SY3814: $i,SY3815: $i] :
( ~ ( c_in @ ( c_Pair @ SV563 @ SY3813 @ SY3814 @ SY3814 ) @ ( c_Transitive__Closure_Ortrancl @ SY3815 @ SY3814 ) @ ( tc_prod @ SY3814 @ SY3814 ) )
| ( c_in @ SV563 @ ( c_Relation_ODomain @ SY3815 @ SY3814 @ SY3814 ) @ SY3814 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2194]) ).
thf(2870,plain,
! [SV564: $i] :
( ( ! [SY3816: $i,SY3817: $i,SY3818: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XRange__iff__1__1 @ SV564 @ SY3816 @ SY3817 @ SY3818 ) @ SV564 @ SY3818 @ SY3817 ) @ SY3816 @ ( tc_prod @ SY3818 @ SY3817 ) )
| ~ ( c_in @ SV564 @ ( c_Relation_ORange @ SY3816 @ SY3818 @ SY3817 ) @ SY3817 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2195]) ).
thf(2871,plain,
! [SV565: $i] :
( ( ! [SY3819: $i,SY3820: $i,SY3821: $i,SY3822: $i,SY3823: $i,SY3824: $i] :
( ( c_in @ SV565 @ ( hAPP @ ( c_split @ SY3819 @ SY3820 @ SY3821 @ ( tc_fun @ SY3822 @ tc_bool ) ) @ ( c_Pair @ SY3823 @ SY3824 @ SY3820 @ SY3821 ) ) @ SY3822 )
| ~ ( c_in @ SV565 @ ( hAPP @ ( hAPP @ SY3819 @ SY3823 ) @ SY3824 ) @ SY3822 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2196]) ).
thf(2872,plain,
! [SV566: $i] :
( ( ! [SY3825: $i,SY3826: $i,SY3827: $i,SY3828: $i,SY3829: $i,SY3830: $i,SY3831: $i] :
( ( ( hAPP @ ( hAPP @ SV566 @ SY3825 ) @ SY3826 )
= ( hAPP @ ( hAPP @ SV566 @ SY3827 ) @ SY3828 ) )
| ~ ( c_in @ ( c_Pair @ SY3826 @ SY3828 @ SY3829 @ SY3829 ) @ SY3830 @ ( tc_prod @ SY3829 @ SY3829 ) )
| ! [SY3832: $i] :
( ~ ( c_in @ ( c_Pair @ SY3825 @ SY3827 @ SY3831 @ SY3831 ) @ SY3832 @ ( tc_prod @ SY3831 @ SY3831 ) )
| ! [SY3833: $i] :
~ ( c_Equiv__Relations_Ocongruent2 @ SY3832 @ SY3830 @ SV566 @ SY3831 @ SY3829 @ SY3833 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2197]) ).
thf(2873,plain,
! [SV567: $i] :
( ( ! [SY3834: $i,SY3835: $i,SY3836: $i] :
( ( SV567 = SY3834 )
| ! [SY3837: $i,SY3838: $i] :
( ~ ( c_in @ ( c_Pair @ SY3835 @ SY3834 @ SY3836 @ SY3837 ) @ SY3838 @ ( tc_prod @ SY3836 @ SY3837 ) )
| ~ ( c_in @ ( c_Pair @ SY3835 @ SV567 @ SY3836 @ SY3837 ) @ SY3838 @ ( tc_prod @ SY3836 @ SY3837 ) )
| ~ ( c_Relation_Osingle__valued @ SY3838 @ SY3836 @ SY3837 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2198]) ).
thf(2874,plain,
! [SV568: $i] :
( ( ! [SY3839: $i,SY3840: $i,SY3841: $i,SY3842: $i,SY3843: $i] :
( ( ( hAPP @ ( c_Recdef_Ocut @ SV568 @ SY3839 @ SY3840 @ SY3841 @ SY3842 ) @ SY3843 )
= ( hAPP @ SV568 @ SY3843 ) )
| ~ ( c_in @ ( c_Pair @ SY3843 @ SY3840 @ SY3841 @ SY3841 ) @ SY3839 @ ( tc_prod @ SY3841 @ SY3841 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2199]) ).
thf(2875,plain,
! [SV569: $i] :
( ( ! [SY3844: $i,SY3845: $i,SY3846: $i,SY3847: $i,SY3848: $i] :
( ( ( hAPP @ ( c_Recdef_Ocut @ SV569 @ SY3844 @ SY3845 @ SY3846 @ SY3847 ) @ SY3848 )
= ( hAPP @ SV569 @ SY3848 ) )
| ~ ( c_in @ ( c_Pair @ SY3848 @ SY3845 @ SY3846 @ SY3846 ) @ SY3844 @ ( tc_prod @ SY3846 @ SY3846 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2200]) ).
thf(2876,plain,
! [SV570: $i] :
( ( ! [SY3849: $i,SY3850: $i,SY3851: $i,SY3852: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_FunDef_Oin__rel @ SV570 @ SY3849 @ SY3850 ) @ SY3851 ) @ SY3852 ) )
| ~ ( c_in @ ( c_Pair @ SY3851 @ SY3852 @ SY3849 @ SY3850 ) @ SV570 @ ( tc_prod @ SY3849 @ SY3850 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2201]) ).
thf(2877,plain,
! [SV571: $i] :
( ( ! [SY3853: $i,SY3854: $i,SY3855: $i,SY3856: $i] :
( ( c_in @ ( c_Pair @ SV571 @ SY3853 @ SY3854 @ SY3855 ) @ SY3856 @ ( tc_prod @ SY3854 @ SY3855 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_FunDef_Oin__rel @ SY3856 @ SY3854 @ SY3855 ) @ SV571 ) @ SY3853 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2202]) ).
thf(2878,plain,
! [SV572: $i] :
( ( ! [SY3857: $i,SY3858: $i,SY3859: $i] :
( ( c_in @ ( c_Pair @ SV572 @ SY3857 @ SY3858 @ SY3858 ) @ SY3859 @ ( tc_prod @ SY3858 @ SY3858 ) )
| ! [SY3860: $i] :
( ~ ( c_in @ ( c_Pair @ SY3860 @ SY3857 @ SY3858 @ SY3858 ) @ SY3859 @ ( tc_prod @ SY3858 @ SY3858 ) )
| ~ ( c_in @ ( c_Pair @ SV572 @ SY3860 @ SY3858 @ SY3858 ) @ SY3859 @ ( tc_prod @ SY3858 @ SY3858 ) )
| ~ ( c_Relation_Otrans @ SY3859 @ SY3858 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2203]) ).
thf(2879,plain,
! [SV573: $i] :
( ( ! [SY3861: $i,SY3862: $i,SY3863: $i] :
( ( c_in @ ( c_Pair @ SV573 @ SY3861 @ SY3862 @ SY3862 ) @ SY3863 @ ( tc_prod @ SY3862 @ SY3862 ) )
| ! [SY3864: $i] :
( ~ ( c_in @ ( c_Pair @ SY3864 @ SY3861 @ SY3862 @ SY3862 ) @ SY3863 @ ( tc_prod @ SY3862 @ SY3862 ) )
| ~ ( c_in @ ( c_Pair @ SV573 @ SY3864 @ SY3862 @ SY3862 ) @ SY3863 @ ( tc_prod @ SY3862 @ SY3862 ) )
| ~ ( c_Relation_Otrans @ SY3863 @ SY3862 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2204]) ).
thf(2880,plain,
! [SV574: $i] :
( ( ! [SY3865: $i,SY3866: $i,SY3867: $i,SY3868: $i] :
( ( c_in @ ( c_Pair @ SV574 @ SY3865 @ SY3866 @ SY3867 ) @ ( c_Relation_Oconverse @ SY3868 @ SY3867 @ SY3866 ) @ ( tc_prod @ SY3866 @ SY3867 ) )
| ~ ( c_in @ ( c_Pair @ SY3865 @ SV574 @ SY3867 @ SY3866 ) @ SY3868 @ ( tc_prod @ SY3867 @ SY3866 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2205]) ).
thf(2881,plain,
! [SV575: $i] :
( ( ! [SY3869: $i,SY3870: $i,SY3871: $i,SY3872: $i] :
( ( c_in @ ( c_Pair @ SV575 @ SY3869 @ SY3870 @ SY3871 ) @ ( c_Relation_Oconverse @ SY3872 @ SY3871 @ SY3870 ) @ ( tc_prod @ SY3870 @ SY3871 ) )
| ~ ( c_in @ ( c_Pair @ SY3869 @ SV575 @ SY3871 @ SY3870 ) @ SY3872 @ ( tc_prod @ SY3871 @ SY3870 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2206]) ).
thf(2882,plain,
! [SV576: $i] :
( ( ! [SY3873: $i,SY3874: $i,SY3875: $i,SY3876: $i] :
( ( c_in @ ( c_Pair @ SV576 @ SY3873 @ SY3874 @ SY3875 ) @ SY3876 @ ( tc_prod @ SY3874 @ SY3875 ) )
| ~ ( c_in @ ( c_Pair @ SY3873 @ SV576 @ SY3875 @ SY3874 ) @ ( c_Relation_Oconverse @ SY3876 @ SY3874 @ SY3875 ) @ ( tc_prod @ SY3875 @ SY3874 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2207]) ).
thf(2883,plain,
! [SV577: $i] :
( ( ! [SY3877: $i,SY3878: $i] :
( ~ ( c_in @ ( c_Pair @ SV577 @ SV577 @ SY3877 @ SY3877 ) @ SY3878 @ ( tc_prod @ SY3877 @ SY3877 ) )
| ~ ( c_Relation_Oirrefl @ SY3878 @ SY3877 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2208]) ).
thf(2884,plain,
! [SV578: $i] :
( ( ! [SY3879: $i,SY3880: $i,SY3881: $i] :
( ( c_in @ ( c_Pair @ SV578 @ SY3879 @ SY3880 @ SY3880 ) @ ( c_Transitive__Closure_Otrancl @ SY3881 @ SY3880 ) @ ( tc_prod @ SY3880 @ SY3880 ) )
| ! [SY3882: $i] :
( ~ ( c_in @ ( c_Pair @ SY3882 @ SY3879 @ SY3880 @ SY3880 ) @ SY3881 @ ( tc_prod @ SY3880 @ SY3880 ) )
| ~ ( c_in @ ( c_Pair @ SV578 @ SY3882 @ SY3880 @ SY3880 ) @ ( c_Transitive__Closure_Otrancl @ SY3881 @ SY3880 ) @ ( tc_prod @ SY3880 @ SY3880 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2209]) ).
thf(2885,plain,
! [SV579: $i] :
( ( ! [SY3883: $i,SY3884: $i,SY3885: $i] :
( ( c_in @ ( c_Pair @ SV579 @ SY3883 @ SY3884 @ SY3884 ) @ ( c_Transitive__Closure_Otrancl @ SY3885 @ SY3884 ) @ ( tc_prod @ SY3884 @ SY3884 ) )
| ! [SY3886: $i] :
( ~ ( c_in @ ( c_Pair @ SY3886 @ SY3883 @ SY3884 @ SY3884 ) @ ( c_Transitive__Closure_Otrancl @ SY3885 @ SY3884 ) @ ( tc_prod @ SY3884 @ SY3884 ) )
| ~ ( c_in @ ( c_Pair @ SV579 @ SY3886 @ SY3884 @ SY3884 ) @ SY3885 @ ( tc_prod @ SY3884 @ SY3884 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2210]) ).
thf(2886,plain,
! [SV580: $i] :
( ( ! [SY3887: $i,SY3888: $i,SY3889: $i] :
( ( c_in @ ( c_Pair @ SV580 @ SY3887 @ SY3888 @ SY3888 ) @ ( c_Transitive__Closure_Ortrancl @ SY3889 @ SY3888 ) @ ( tc_prod @ SY3888 @ SY3888 ) )
| ! [SY3890: $i] :
( ~ ( c_in @ ( c_Pair @ SY3890 @ SY3887 @ SY3888 @ SY3888 ) @ SY3889 @ ( tc_prod @ SY3888 @ SY3888 ) )
| ~ ( c_in @ ( c_Pair @ SV580 @ SY3890 @ SY3888 @ SY3888 ) @ ( c_Transitive__Closure_Ortrancl @ SY3889 @ SY3888 ) @ ( tc_prod @ SY3888 @ SY3888 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2211]) ).
thf(2887,plain,
! [SV581: $i] :
( ( ! [SY3891: $i,SY3892: $i,SY3893: $i] :
( ( c_in @ ( c_Pair @ SV581 @ SY3891 @ SY3892 @ SY3892 ) @ ( c_Transitive__Closure_Ortrancl @ SY3893 @ SY3892 ) @ ( tc_prod @ SY3892 @ SY3892 ) )
| ! [SY3894: $i] :
( ~ ( c_in @ ( c_Pair @ SY3894 @ SY3891 @ SY3892 @ SY3892 ) @ ( c_Transitive__Closure_Ortrancl @ SY3893 @ SY3892 ) @ ( tc_prod @ SY3892 @ SY3892 ) )
| ~ ( c_in @ ( c_Pair @ SV581 @ SY3894 @ SY3892 @ SY3892 ) @ SY3893 @ ( tc_prod @ SY3892 @ SY3892 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2212]) ).
thf(2888,plain,
! [SV582: $i] :
( ( ! [SY3895: $i,SY3896: $i,SY3897: $i] :
( ( c_in @ ( c_Pair @ SV582 @ SY3895 @ SY3896 @ SY3896 ) @ ( c_Transitive__Closure_Otrancl @ SY3897 @ SY3896 ) @ ( tc_prod @ SY3896 @ SY3896 ) )
| ~ ( c_in @ ( c_Pair @ SV582 @ SY3895 @ SY3896 @ SY3896 ) @ SY3897 @ ( tc_prod @ SY3896 @ SY3896 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2213]) ).
thf(2889,plain,
! [SV583: $i] :
( ( ! [SY3898: $i,SY3899: $i,SY3900: $i] :
( ( c_in @ ( c_Pair @ SV583 @ SY3898 @ SY3899 @ SY3899 ) @ ( c_Transitive__Closure_Ortrancl @ SY3900 @ SY3899 ) @ ( tc_prod @ SY3899 @ SY3899 ) )
| ! [SY3901: $i] :
( ~ ( c_in @ ( c_Pair @ SY3901 @ SY3898 @ SY3899 @ SY3899 ) @ ( c_Transitive__Closure_Ortrancl @ SY3900 @ SY3899 ) @ ( tc_prod @ SY3899 @ SY3899 ) )
| ~ ( c_in @ ( c_Pair @ SV583 @ SY3901 @ SY3899 @ SY3899 ) @ ( c_Transitive__Closure_Ortrancl @ SY3900 @ SY3899 ) @ ( tc_prod @ SY3899 @ SY3899 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2214]) ).
thf(2890,plain,
! [SV584: $i] :
( ( ! [SY3902: $i,SY3903: $i] : ( c_in @ ( c_Pair @ SV584 @ SV584 @ SY3902 @ SY3902 ) @ ( c_Transitive__Closure_Ortrancl @ SY3903 @ SY3902 ) @ ( tc_prod @ SY3902 @ SY3902 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2215]) ).
thf(2891,plain,
! [SV585: $i] :
( ( ! [SY3904: $i,SY3905: $i] : ( c_in @ ( c_Pair @ SV585 @ SV585 @ SY3904 @ SY3904 ) @ ( c_Transitive__Closure_Ortrancl @ SY3905 @ SY3904 ) @ ( tc_prod @ SY3904 @ SY3904 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2216]) ).
thf(2892,plain,
! [SV586: $i] :
( ( ! [SY3906: $i,SY3907: $i,SY3908: $i] :
( ~ ( c_in @ ( c_Pair @ SV586 @ SY3906 @ SY3907 @ SY3907 ) @ SY3908 @ ( tc_prod @ SY3907 @ SY3907 ) )
| ~ ( c_in @ ( c_Pair @ SY3906 @ SV586 @ SY3907 @ SY3907 ) @ SY3908 @ ( tc_prod @ SY3907 @ SY3907 ) )
| ~ ( c_Wellfounded_Owf @ SY3908 @ SY3907 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2217]) ).
thf(2893,plain,
! [SV587: $i] :
( ( ! [SY3909: $i] :
( ( SV587 = SY3909 )
| ! [SY3910: $i,SY3911: $i] :
( ~ ( c_in @ ( c_Pair @ SY3909 @ SV587 @ SY3910 @ SY3910 ) @ SY3911 @ ( tc_prod @ SY3910 @ SY3910 ) )
| ~ ( c_in @ ( c_Pair @ SV587 @ SY3909 @ SY3910 @ SY3910 ) @ SY3911 @ ( tc_prod @ SY3910 @ SY3910 ) )
| ~ ( c_Relation_Oantisym @ SY3911 @ SY3910 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2218]) ).
thf(2894,plain,
! [SV588: $i] :
( ( ! [SY3912: $i] :
( ( SV588 = SY3912 )
| ! [SY3913: $i,SY3914: $i] :
( ~ ( c_in @ ( c_Pair @ SY3912 @ SV588 @ SY3913 @ SY3913 ) @ SY3914 @ ( tc_prod @ SY3913 @ SY3913 ) )
| ~ ( c_in @ ( c_Pair @ SV588 @ SY3912 @ SY3913 @ SY3913 ) @ SY3914 @ ( tc_prod @ SY3913 @ SY3913 ) )
| ~ ( c_Relation_Oantisym @ SY3914 @ SY3913 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2219]) ).
thf(2895,plain,
! [SV589: $i] :
( ( ! [SY3915: $i,SY3916: $i,SY3917: $i] :
( ( ( hAPP @ SV589 @ SY3915 )
= ( hAPP @ SV589 @ SY3916 ) )
| ! [SY3918: $i] :
( ~ ( c_in @ ( c_Pair @ SY3915 @ SY3916 @ SY3917 @ SY3917 ) @ SY3918 @ ( tc_prod @ SY3917 @ SY3917 ) )
| ! [SY3919: $i] :
~ ( c_Equiv__Relations_Ocongruent @ SY3918 @ SV589 @ SY3917 @ SY3919 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2220]) ).
thf(2896,plain,
! [SV590: $i] :
( ( ! [SY3920: $i] :
( ( SV590 = SY3920 )
| ! [SY3921: $i,SY3922: $i] :
~ ( c_in @ ( c_Pair @ SV590 @ SY3920 @ SY3921 @ SY3921 ) @ ( c_Relation_OId__on @ SY3922 @ SY3921 ) @ ( tc_prod @ SY3921 @ SY3921 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2221]) ).
thf(2897,plain,
! [SV591: $i] :
( ( ! [SY3923: $i,SY3924: $i,SY3925: $i,SY3926: $i,SY3927: $i] :
( ( ( c_Recdef_Ocut @ SV591 @ SY3923 @ SY3924 @ SY3925 @ SY3926 )
!= ( c_Recdef_Ocut @ SY3927 @ SY3923 @ SY3924 @ SY3925 @ SY3926 ) )
| ! [SY3928: $i] :
( ( ( hAPP @ SV591 @ SY3928 )
= ( hAPP @ SY3927 @ SY3928 ) )
| ~ ( c_in @ ( c_Pair @ SY3928 @ SY3924 @ SY3925 @ SY3925 ) @ SY3923 @ ( tc_prod @ SY3925 @ SY3925 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2222]) ).
thf(2898,plain,
! [SV592: $i] :
( ( ! [SY3929: $i] :
( ( SV592 = SY3929 )
| ! [SY3930: $i] :
~ ( c_in @ ( c_Pair @ SV592 @ SY3929 @ SY3930 @ SY3930 ) @ ( c_Relation_OId @ SY3930 ) @ ( tc_prod @ SY3930 @ SY3930 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2223]) ).
thf(2899,plain,
! [SV593: $i] :
( ( ! [SY3931: $i,SY3932: $i] :
( ( c_in @ ( c_Pair @ SV593 @ SV593 @ SY3931 @ SY3931 ) @ SY3932 @ ( tc_prod @ SY3931 @ SY3931 ) )
| ~ ( c_Nitpick_Orefl_H @ SY3932 @ SY3931 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2224]) ).
thf(2900,plain,
! [SV594: $i] :
( ( ! [SY3933: $i,SY3934: $i] :
( ~ ( c_in @ ( c_Pair @ SV594 @ SV594 @ SY3933 @ SY3933 ) @ SY3934 @ ( tc_prod @ SY3933 @ SY3933 ) )
| ~ ( c_Wellfounded_Owf @ SY3934 @ SY3933 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2225]) ).
thf(2901,plain,
! [SV595: $i] :
( ( ! [SY3935: $i,SY3936: $i,SY3937: $i,SY3938: $i,SY3939: $i] :
( ( c_in @ ( c_Pair @ SV595 @ SY3935 @ SY3936 @ SY3936 ) @ ( c_Relation_Oinv__image @ SY3937 @ SY3938 @ SY3939 @ SY3936 ) @ ( tc_prod @ SY3936 @ SY3936 ) )
| ~ ( c_in @ ( c_Pair @ ( hAPP @ SY3938 @ SV595 ) @ ( hAPP @ SY3938 @ SY3935 ) @ SY3939 @ SY3939 ) @ SY3937 @ ( tc_prod @ SY3939 @ SY3939 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2226]) ).
thf(2902,plain,
! [SV596: $i] :
( ( ! [SY3940: $i,SY3941: $i,SY3942: $i,SY3943: $i] :
( ( c_in @ ( c_Pair @ ( hAPP @ SV596 @ SY3940 ) @ ( hAPP @ SV596 @ SY3941 ) @ SY3942 @ SY3942 ) @ SY3943 @ ( tc_prod @ SY3942 @ SY3942 ) )
| ! [SY3944: $i] :
~ ( c_in @ ( c_Pair @ SY3940 @ SY3941 @ SY3944 @ SY3944 ) @ ( c_Relation_Oinv__image @ SY3943 @ SV596 @ SY3942 @ SY3944 ) @ ( tc_prod @ SY3944 @ SY3944 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2227]) ).
thf(2903,plain,
! [SV597: $i] :
( ( ! [SY3945: $i,SY3946: $i,SY3947: $i] :
( ( c_in @ ( c_Pair @ SV597 @ SY3945 @ SY3946 @ SY3946 ) @ SY3947 @ ( tc_prod @ SY3946 @ SY3946 ) )
| ~ ( c_in @ ( c_Pair @ SY3945 @ SV597 @ SY3946 @ SY3946 ) @ SY3947 @ ( tc_prod @ SY3946 @ SY3946 ) )
| ~ ( c_Relation_Osym @ SY3947 @ SY3946 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2228]) ).
thf(2904,plain,
! [SV598: $i] :
( ( ! [SY3948: $i,SY3949: $i,SY3950: $i] :
( ( c_in @ ( c_Pair @ SV598 @ SY3948 @ SY3949 @ SY3949 ) @ SY3950 @ ( tc_prod @ SY3949 @ SY3949 ) )
| ~ ( c_in @ ( c_Pair @ SY3948 @ SV598 @ SY3949 @ SY3949 ) @ SY3950 @ ( tc_prod @ SY3949 @ SY3949 ) )
| ~ ( c_Relation_Osym @ SY3950 @ SY3949 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2229]) ).
thf(2905,plain,
! [SV599: $i] :
( ( ! [SY3951: $i,SY3952: $i,SY3953: $i,SY3954: $i,SY3955: $i,SY3956: $i] :
( ( c_in @ ( c_Pair @ SV599 @ SY3951 @ SY3952 @ SY3953 ) @ ( c_Relation_Orel__comp @ SY3954 @ SY3955 @ SY3952 @ SY3956 @ SY3953 ) @ ( tc_prod @ SY3952 @ SY3953 ) )
| ! [SY3957: $i] :
( ~ ( c_in @ ( c_Pair @ SY3957 @ SY3951 @ SY3956 @ SY3953 ) @ SY3955 @ ( tc_prod @ SY3956 @ SY3953 ) )
| ~ ( c_in @ ( c_Pair @ SV599 @ SY3957 @ SY3952 @ SY3956 ) @ SY3954 @ ( tc_prod @ SY3952 @ SY3956 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2230]) ).
thf(2906,plain,
! [SV600: $i] :
( ( ! [SY3958: $i,SY3959: $i,SY3960: $i] :
( ( c_in @ ( c_Pair @ SV600 @ SY3958 @ SY3959 @ SY3959 ) @ ( c_Transitive__Closure_Otrancl @ SY3960 @ SY3959 ) @ ( tc_prod @ SY3959 @ SY3959 ) )
| ! [SY3961: $i] :
( ~ ( c_in @ ( c_Pair @ SY3961 @ SY3958 @ SY3959 @ SY3959 ) @ SY3960 @ ( tc_prod @ SY3959 @ SY3959 ) )
| ~ ( c_in @ ( c_Pair @ SV600 @ SY3961 @ SY3959 @ SY3959 ) @ SY3960 @ ( tc_prod @ SY3959 @ SY3959 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2231]) ).
thf(2907,plain,
! [SV601: $i] :
( ( ! [SY3962: $i,SY3963: $i,SY3964: $i] :
( ( c_in @ ( c_Pair @ SV601 @ SY3962 @ SY3963 @ SY3963 ) @ ( c_Transitive__Closure_Otrancl @ SY3964 @ SY3963 ) @ ( tc_prod @ SY3963 @ SY3963 ) )
| ! [SY3965: $i] :
( ~ ( c_in @ ( c_Pair @ SY3965 @ SY3962 @ SY3963 @ SY3963 ) @ ( c_Transitive__Closure_Otrancl @ SY3964 @ SY3963 ) @ ( tc_prod @ SY3963 @ SY3963 ) )
| ~ ( c_in @ ( c_Pair @ SV601 @ SY3965 @ SY3963 @ SY3963 ) @ ( c_Transitive__Closure_Otrancl @ SY3964 @ SY3963 ) @ ( tc_prod @ SY3963 @ SY3963 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2232]) ).
thf(2908,plain,
! [SV602: $i] :
( ( ! [SY3966: $i] : ( c_in @ ( c_Pair @ SV602 @ SV602 @ SY3966 @ SY3966 ) @ ( c_Relation_OId @ SY3966 ) @ ( tc_prod @ SY3966 @ SY3966 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2233]) ).
thf(2909,plain,
! [SV603: $i] :
( ( ! [SY3967: $i] : ( c_in @ ( c_Pair @ SV603 @ SV603 @ SY3967 @ SY3967 ) @ ( c_Relation_OId @ SY3967 ) @ ( tc_prod @ SY3967 @ SY3967 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2234]) ).
thf(2910,plain,
! [SV604: $i] :
( ( ! [SY3968: $i,SY3969: $i,SY3970: $i] :
( ( c_in @ ( c_Pair @ SV604 @ SY3968 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omktop @ SY3969 ) @ SY3970 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV604 @ SY3968 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY3969 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV604 = SY3968 )
| ( SV604 = SY3970 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2235]) ).
thf(2911,plain,
! [SV605: $i] :
( ( ! [SY3971: $i,SY3972: $i,SY3973: $i] :
( ( c_in @ ( c_Pair @ SV605 @ SY3971 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omktop @ SY3972 ) @ SY3973 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV605 @ SY3971 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY3972 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SY3971 = SY3973 )
| ( SV605 = SY3973 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2236]) ).
thf(2912,plain,
! [SV606: $i] :
( ( ! [SY3974: $i] :
~ ( c_in @ ( c_Pair @ SV606 @ SV606 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omktop @ SY3974 ) @ SV606 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2237]) ).
thf(2913,plain,
! [SV607: $i] :
( ( ! [SY3975: $i,SY3976: $i] :
~ ( c_in @ ( c_Pair @ SV607 @ SY3975 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omktop @ SY3976 ) @ SV607 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2238]) ).
thf(2914,plain,
! [SV608: $i] :
( ( ! [SY3977: $i,SY3978: $i] :
( ( c_in @ ( c_Pair @ SV608 @ SY3977 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY3978 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ! [SY3979: $i] :
( ( SY3977 = SY3979 )
| ~ ( c_in @ ( c_Pair @ SV608 @ SY3977 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omktop @ SY3978 ) @ SY3979 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2239]) ).
thf(2915,plain,
! [SV609: $i] :
( ( ! [SY3980: $i] :
( ( SV609 = SY3980 )
| ( SY3980 = SV609 )
| ! [SY3981: $i] : ( c_in @ ( c_Pair @ SV609 @ SY3980 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omkbot @ SY3981 ) @ SV609 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2240]) ).
thf(2916,plain,
! [SV610: $i] :
( ( ! [SY3982: $i] :
~ ( c_in @ ( c_Pair @ SV610 @ SV610 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omkbot @ SY3982 ) @ SV610 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2241]) ).
thf(2917,plain,
! [SV611: $i] :
( ( ! [SY3983: $i,SY3984: $i] :
~ ( c_in @ ( c_Pair @ SV611 @ SY3983 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omkbot @ SY3984 ) @ SY3983 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2242]) ).
thf(2918,plain,
! [SV612: $i] :
( ( ! [SY3985: $i,SY3986: $i,SY3987: $i] :
( ( c_in @ ( c_Pair @ SV612 @ SY3985 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omkbot @ SY3986 ) @ SY3987 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV612 @ SY3985 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY3986 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV612 = SY3985 )
| ( SY3985 = SY3987 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2243]) ).
thf(2919,plain,
! [SV613: $i] :
( ( ! [SY3988: $i,SY3989: $i,SY3990: $i] :
( ( c_in @ ( c_Pair @ SV613 @ SY3988 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omkbot @ SY3989 ) @ SY3990 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV613 @ SY3988 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY3989 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV613 = SY3990 )
| ( SY3988 = SY3990 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2244]) ).
thf(2920,plain,
! [SV614: $i] :
( ( ! [SY3991: $i] :
( ( SV614 = SY3991 )
| ( SV614 = SY3991 )
| ! [SY3992: $i] : ( c_in @ ( c_Pair @ SV614 @ SY3991 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omktop @ SY3992 ) @ SY3991 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2245]) ).
thf(2921,plain,
! [SV615: $i] :
( ( ! [SY3993: $i,SY3994: $i] :
( ( c_in @ ( c_Pair @ SV615 @ SY3993 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY3994 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ! [SY3995: $i] :
( ( SV615 = SY3995 )
| ~ ( c_in @ ( c_Pair @ SV615 @ SY3993 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omkbot @ SY3994 ) @ SY3995 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2246]) ).
thf(2922,plain,
! [SV616: $i] :
( ( ! [SY3996: $i] :
( ( SV616 = SY3996 )
| ( c_in @ ( c_Pair @ SV616 @ SY3996 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1 @ SV616 @ SY3996 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2247]) ).
thf(2923,plain,
! [SV617: $i] :
( ( ! [SY3997: $i,SY3998: $i,SY3999: $i,SY4000: $i,SY4001: $i] :
( ( c_in @ ( c_Pair @ SV617 @ SY3997 @ SY3998 @ SY3999 ) @ ( c_Product__Type_OSigma @ SY4000 @ SY4001 @ SY3998 @ SY3999 ) @ ( tc_prod @ SY3998 @ SY3999 ) )
| ~ ( c_in @ SY3997 @ ( hAPP @ SY4001 @ SV617 ) @ SY3999 )
| ~ ( c_in @ SV617 @ SY4000 @ SY3998 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2248]) ).
thf(2924,plain,
! [SV618: $i] :
( ( ! [SY4002: $i,SY4003: $i,SY4004: $i,SY4005: $i,SY4006: $i] :
( ( c_in @ ( c_Pair @ SV618 @ SY4002 @ SY4003 @ SY4004 ) @ ( c_Product__Type_OSigma @ SY4005 @ SY4006 @ SY4003 @ SY4004 ) @ ( tc_prod @ SY4003 @ SY4004 ) )
| ~ ( c_in @ SY4002 @ ( hAPP @ SY4006 @ SV618 ) @ SY4004 )
| ~ ( c_in @ SV618 @ SY4005 @ SY4003 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2249]) ).
thf(2925,plain,
! [SV619: $i] :
( ( ! [SY4007: $i,SY4008: $i] :
( ( c_in @ SV619 @ ( c_Wellfounded_Oacc @ SY4007 @ SY4008 ) @ SY4008 )
| ! [SY4009: $i] :
( ~ ( c_in @ ( c_Pair @ SV619 @ SY4009 @ SY4008 @ SY4008 ) @ SY4007 @ ( tc_prod @ SY4008 @ SY4008 ) )
| ~ ( c_in @ SY4009 @ ( c_Wellfounded_Oacc @ SY4007 @ SY4008 ) @ SY4008 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2250]) ).
thf(2926,plain,
! [SV620: $i] :
( ( ! [SY4010: $i,SY4011: $i] :
( ( c_in @ SV620 @ ( c_Wellfounded_Oacc @ SY4010 @ SY4011 ) @ SY4011 )
| ! [SY4012: $i] :
( ~ ( c_in @ ( c_Pair @ SV620 @ SY4012 @ SY4011 @ SY4011 ) @ SY4010 @ ( tc_prod @ SY4011 @ SY4011 ) )
| ~ ( c_in @ SY4012 @ ( c_Wellfounded_Oacc @ SY4010 @ SY4011 ) @ SY4011 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2251]) ).
thf(2927,plain,
! [SV621: $i] :
( ( ! [SY4013: $i,SY4014: $i,SY4015: $i,SY4016: $i] :
( ( c_in @ SV621 @ ( c_Relation_OImage @ SY4013 @ SY4014 @ SY4015 @ SY4016 ) @ SY4016 )
| ! [SY4017: $i] :
( ~ ( c_in @ ( c_Pair @ SY4017 @ SV621 @ SY4015 @ SY4016 ) @ SY4013 @ ( tc_prod @ SY4015 @ SY4016 ) )
| ~ ( c_in @ SY4017 @ SY4014 @ SY4015 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2252]) ).
thf(2928,plain,
! [SV622: $i] :
( ( ! [SY4018: $i,SY4019: $i,SY4020: $i,SY4021: $i] :
( ( c_in @ SV622 @ ( c_Relation_OImage @ SY4018 @ SY4019 @ SY4020 @ SY4021 ) @ SY4021 )
| ! [SY4022: $i] :
( ~ ( c_in @ ( c_Pair @ SY4022 @ SV622 @ SY4020 @ SY4021 ) @ SY4018 @ ( tc_prod @ SY4020 @ SY4021 ) )
| ~ ( c_in @ SY4022 @ SY4019 @ SY4020 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2253]) ).
thf(2929,plain,
! [SV623: $i] :
( ( ! [SY4023: $i,SY4024: $i] :
( ( c_in @ SV623 @ SY4023 @ SY4024 )
| ! [SY4025: $i] :
~ ( c_in @ ( c_Pair @ SV623 @ SY4025 @ SY4024 @ SY4024 ) @ ( c_Relation_OId__on @ SY4023 @ SY4024 ) @ ( tc_prod @ SY4024 @ SY4024 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2254]) ).
thf(2930,plain,
! [SV624: $i] :
( ( ! [SY4026: $i,SY4027: $i] :
( ( c_in @ ( c_Pair @ SV624 @ SV624 @ SY4026 @ SY4026 ) @ ( c_Relation_OId__on @ SY4027 @ SY4026 ) @ ( tc_prod @ SY4026 @ SY4026 ) )
| ~ ( c_in @ SV624 @ SY4027 @ SY4026 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2255]) ).
thf(2931,plain,
! [SV625: $i] :
( ( ! [SY4028: $i,SY4029: $i] :
( ( c_in @ SV625 @ SY4028 @ SY4029 )
| ! [SY4030: $i,SY4031: $i] :
( ~ ( c_in @ ( c_Pair @ SY4030 @ SV625 @ SY4029 @ SY4029 ) @ SY4031 @ ( tc_prod @ SY4029 @ SY4029 ) )
| ~ ( c_Equiv__Relations_Oequiv @ SY4028 @ SY4031 @ SY4029 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2256]) ).
thf(2932,plain,
! [SV626: $i] :
( ( ! [SY4032: $i,SY4033: $i] :
( ( c_in @ SV626 @ SY4032 @ SY4033 )
| ! [SY4034: $i,SY4035: $i] :
( ~ ( c_in @ ( c_Pair @ SV626 @ SY4034 @ SY4033 @ SY4033 ) @ SY4035 @ ( tc_prod @ SY4033 @ SY4033 ) )
| ~ ( c_Equiv__Relations_Oequiv @ SY4032 @ SY4035 @ SY4033 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2257]) ).
thf(2933,plain,
! [SV627: $i] :
( ( ! [SY4036: $i,SY4037: $i,SY4038: $i] :
( ( c_in @ SV627 @ ( c_Relation_ORange @ SY4036 @ SY4037 @ SY4038 ) @ SY4038 )
| ! [SY4039: $i] :
~ ( c_in @ ( c_Pair @ SY4039 @ SV627 @ SY4037 @ SY4038 ) @ SY4036 @ ( tc_prod @ SY4037 @ SY4038 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2258]) ).
thf(2934,plain,
! [SV628: $i] :
( ( ! [SY4040: $i,SY4041: $i,SY4042: $i] :
( ( c_in @ SV628 @ ( c_Relation_ORange @ SY4040 @ SY4041 @ SY4042 ) @ SY4042 )
| ! [SY4043: $i] :
~ ( c_in @ ( c_Pair @ SY4043 @ SV628 @ SY4041 @ SY4042 ) @ SY4040 @ ( tc_prod @ SY4041 @ SY4042 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2259]) ).
thf(2935,plain,
! [SV629: $i] :
( ( ! [SY4044: $i,SY4045: $i,SY4046: $i] :
( ( c_in @ SV629 @ ( c_Relation_ODomain @ SY4044 @ SY4045 @ SY4046 ) @ SY4045 )
| ! [SY4047: $i] :
~ ( c_in @ ( c_Pair @ SV629 @ SY4047 @ SY4045 @ SY4046 ) @ SY4044 @ ( tc_prod @ SY4045 @ SY4046 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2260]) ).
thf(2936,plain,
! [SV630: $i] :
( ( ! [SY4048: $i,SY4049: $i,SY4050: $i] :
( ( c_in @ SV630 @ ( c_Relation_ODomain @ SY4048 @ SY4049 @ SY4050 ) @ SY4049 )
| ! [SY4051: $i] :
~ ( c_in @ ( c_Pair @ SV630 @ SY4051 @ SY4049 @ SY4050 ) @ SY4048 @ ( tc_prod @ SY4049 @ SY4050 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2261]) ).
thf(2937,plain,
! [SV631: $i] :
( ( ! [SY4052: $i,SY4053: $i,SY4054: $i] :
( ( c_in @ SV631 @ ( hAPP @ SY4052 @ SY4053 ) @ SY4054 )
| ! [SY4055: $i,SY4056: $i] :
~ ( c_in @ ( c_Pair @ SY4053 @ SV631 @ SY4055 @ SY4054 ) @ ( c_Product__Type_OSigma @ SY4056 @ SY4052 @ SY4055 @ SY4054 ) @ ( tc_prod @ SY4055 @ SY4054 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2262]) ).
thf(2938,plain,
! [SV632: $i] :
( ( ! [SY4057: $i,SY4058: $i,SY4059: $i] :
( ( c_in @ SV632 @ SY4057 @ SY4058 )
| ! [SY4060: $i,SY4061: $i] :
~ ( c_in @ ( c_Pair @ SV632 @ SY4059 @ SY4058 @ SY4060 ) @ ( c_Product__Type_OSigma @ SY4057 @ SY4061 @ SY4058 @ SY4060 ) @ ( tc_prod @ SY4058 @ SY4060 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2263]) ).
thf(2939,plain,
! [SV633: $i] :
( ( ! [SY4062: $i,SY4063: $i,SY4064: $i] :
( ( c_in @ ( c_Pair @ SV633 @ SY4062 @ SY4063 @ SY4063 ) @ SY4064 @ ( tc_prod @ SY4063 @ SY4063 ) )
| ( c_in @ ( c_Pair @ SY4062 @ SV633 @ SY4063 @ SY4063 ) @ SY4064 @ ( tc_prod @ SY4063 @ SY4063 ) )
| ( SY4062 = SV633 )
| ! [SY4065: $i] :
( ~ ( c_in @ SV633 @ SY4065 @ SY4063 )
| ~ ( c_in @ SY4062 @ SY4065 @ SY4063 )
| ~ ( c_Relation_Ototal__on @ SY4065 @ SY4064 @ SY4063 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2264]) ).
thf(2940,plain,
! [SV634: $i] :
( ( ! [SY4066: $i,SY4067: $i] :
( ( c_in @ ( c_Pair @ SV634 @ SV634 @ SY4066 @ SY4066 ) @ SY4067 @ ( tc_prod @ SY4066 @ SY4066 ) )
| ! [SY4068: $i] :
( ~ ( c_in @ SV634 @ SY4068 @ SY4066 )
| ~ ( c_Relation_Orefl__on @ SY4068 @ SY4067 @ SY4066 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2265]) ).
thf(2941,plain,
! [SV635: $i] :
( ( ! [SY4069: $i,SY4070: $i] :
( ( c_in @ SV635 @ SY4069 @ SY4070 )
| ! [SY4071: $i,SY4072: $i] :
( ~ ( c_in @ ( c_Pair @ SY4071 @ SV635 @ SY4070 @ SY4070 ) @ SY4072 @ ( tc_prod @ SY4070 @ SY4070 ) )
| ~ ( c_Relation_Orefl__on @ SY4069 @ SY4072 @ SY4070 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2266]) ).
thf(2942,plain,
! [SV636: $i] :
( ( ! [SY4073: $i,SY4074: $i] :
( ( c_in @ SV636 @ SY4073 @ SY4074 )
| ! [SY4075: $i,SY4076: $i] :
( ~ ( c_in @ ( c_Pair @ SV636 @ SY4075 @ SY4074 @ SY4074 ) @ SY4076 @ ( tc_prod @ SY4074 @ SY4074 ) )
| ~ ( c_Relation_Orefl__on @ SY4073 @ SY4076 @ SY4074 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2267]) ).
thf(2943,plain,
! [SV637: $i] :
( ( ! [SY4077: $i,SY4078: $i] :
( ( c_in @ ( c_Pair @ SV637 @ SV637 @ SY4077 @ SY4077 ) @ SY4078 @ ( tc_prod @ SY4077 @ SY4077 ) )
| ! [SY4079: $i] :
( ~ ( c_in @ SV637 @ SY4079 @ SY4077 )
| ~ ( c_Relation_Orefl__on @ SY4079 @ SY4078 @ SY4077 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2268]) ).
thf(2944,plain,
! [SV638: $i] :
( ( ! [SY4080: $i,SY4081: $i,SY4082: $i,SY4083: $i,SY4084: $i] :
( ( ( c_Pair @ SV638 @ SY4080 @ SY4081 @ SY4082 )
!= ( c_Pair @ SY4083 @ SY4084 @ SY4081 @ SY4082 ) )
| ( SY4080 = SY4084 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2269]) ).
thf(2945,plain,
! [SV639: $i] :
( ( ! [SY4085: $i,SY4086: $i,SY4087: $i,SY4088: $i] :
( ! [SY4089: $i] :
( ( c_Pair @ SV639 @ SY4085 @ SY4086 @ SY4087 )
!= ( c_Pair @ SY4088 @ SY4089 @ SY4086 @ SY4087 ) )
| ( SV639 = SY4088 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2270]) ).
thf(2946,plain,
! [SV640: $i] :
( ( ! [SY4090: $i] :
( ! [SY4091: $i] : ( c_in @ SV640 @ SY4090 @ SY4091 )
| ~ ( hBOOL @ ( hAPP @ SY4090 @ SV640 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2271]) ).
thf(2947,plain,
! [SV641: $i] :
( ( ! [SY4092: $i] :
( ( hBOOL @ ( hAPP @ SV641 @ SY4092 ) )
| ! [SY4093: $i] :
~ ( c_in @ SY4092 @ SV641 @ SY4093 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2272]) ).
thf(2948,plain,
( ( ( c_in @ ( c_Pair @ v_c____ @ v_d____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ v_P____ ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ v_c____ @ v_d____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_HOL_OIf @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ v_h____ @ tc_nat @ ( tc_fun @ tc_nat @ tc_bool ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ v_n____ @ tc_Arrow__Order__Mirabelle_Oindi @ tc_nat @ tc_bool ) @ tc_bool @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ ( c_COMBC @ ( c_COMBB @ c_Arrow__Order__Mirabelle_Omktop @ v_P____ @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ v_e____ @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_HOL_OIf @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ ( c_COMBC @ ( c_COMBB @ ( c_fequal @ tc_nat ) @ v_h____ @ tc_nat @ ( tc_fun @ tc_nat @ tc_bool ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ v_n____ @ tc_Arrow__Order__Mirabelle_Oindi @ tc_nat @ tc_bool ) @ tc_bool @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ ( c_COMBC @ ( c_COMBC @ ( c_COMBB @ c_Arrow__Order__Mirabelle_Oabove @ v_P____ @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ v_c____ @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ v_e____ @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ ( c_COMBC @ ( c_COMBB @ c_Arrow__Order__Mirabelle_Omkbot @ v_P____ @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ v_e____ @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2273]) ).
thf(2949,plain,
( ( ( c_in @ ( c_Pair @ v_c____ @ v_d____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_HOL_OIf @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ v_h____ @ tc_nat @ ( tc_fun @ tc_nat @ tc_bool ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ v_n____ @ tc_Arrow__Order__Mirabelle_Oindi @ tc_nat @ tc_bool ) @ tc_bool @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ ( c_COMBC @ ( c_COMBB @ c_Arrow__Order__Mirabelle_Omktop @ v_P____ @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ v_e____ @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_HOL_OIf @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ ( c_COMBC @ ( c_COMBB @ ( c_fequal @ tc_nat ) @ v_h____ @ tc_nat @ ( tc_fun @ tc_nat @ tc_bool ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ v_n____ @ tc_Arrow__Order__Mirabelle_Oindi @ tc_nat @ tc_bool ) @ tc_bool @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ ( c_COMBC @ ( c_COMBC @ ( c_COMBB @ c_Arrow__Order__Mirabelle_Oabove @ v_P____ @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ v_c____ @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ v_e____ @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ ( c_COMBC @ ( c_COMBB @ c_Arrow__Order__Mirabelle_Omkbot @ v_P____ @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ v_e____ @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ v_c____ @ v_d____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ v_P____ ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2274]) ).
thf(2950,plain,
! [SV642: $i] :
( ( ! [SY4094: $i] :
( ( class_Lattices_Oupper__semilattice @ ( tc_fun @ SV642 @ SY4094 ) )
| ~ ( class_Lattices_Olattice @ SY4094 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2276]) ).
thf(2951,plain,
! [SV643: $i] :
( ( ! [SY4095: $i] :
( ( class_Lattices_Olower__semilattice @ ( tc_fun @ SV643 @ SY4095 ) )
| ~ ( class_Lattices_Olattice @ SY4095 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2277]) ).
thf(2952,plain,
! [SV644: $i] :
( ( ! [SY4096: $i] :
( ( class_Lattices_Odistrib__lattice @ ( tc_fun @ SV644 @ SY4096 ) )
| ~ ( class_Lattices_Odistrib__lattice @ SY4096 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2278]) ).
thf(2953,plain,
! [SV645: $i] :
( ( ! [SY4097: $i] :
( ( class_Lattices_Obounded__lattice @ ( tc_fun @ SV645 @ SY4097 ) )
| ~ ( class_Lattices_Obounded__lattice @ SY4097 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2279]) ).
thf(2954,plain,
! [SV646: $i] :
( ( ! [SY4098: $i] :
( ( class_Orderings_Opreorder @ ( tc_fun @ SV646 @ SY4098 ) )
| ~ ( class_Orderings_Opreorder @ SY4098 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2280]) ).
thf(2955,plain,
! [SV647: $i] :
( ( ! [SY4099: $i] :
( ( class_Lattices_Olattice @ ( tc_fun @ SV647 @ SY4099 ) )
| ~ ( class_Lattices_Olattice @ SY4099 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2281]) ).
thf(2956,plain,
! [SV648: $i] :
( ( ! [SY4100: $i] :
( ( class_Orderings_Oorder @ ( tc_fun @ SV648 @ SY4100 ) )
| ~ ( class_Orderings_Oorder @ SY4100 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2282]) ).
thf(2957,plain,
! [SV649: $i] :
( ( ! [SY4101: $i] :
( ( class_Orderings_Obot @ ( tc_fun @ SV649 @ SY4101 ) )
| ~ ( class_Orderings_Obot @ SY4101 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2283]) ).
thf(2958,plain,
! [SV650: $i] :
( ( ! [SY4102: $i] :
( ( class_HOL_Oord @ ( tc_fun @ SV650 @ SY4102 ) )
| ~ ( class_HOL_Oord @ SY4102 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2284]) ).
thf(2959,plain,
! [SV651: $i] :
( ( ! [SY4103: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ SV651 ) @ SY4103 ) @ SY4103 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2303]) ).
thf(2960,plain,
! [SV652: $i] :
( ( ! [SY4104: $i] :
( ( SV652 = SY4104 )
| ! [SY4105: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ SY4105 ) @ SV652 ) @ SY4104 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2304]) ).
thf(2961,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[2305]) ).
thf(2962,plain,
! [SV653: $i,SV1: $i] :
( ( ! [SY4106: $i,SY4107: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ SV1 @ SV653 @ SY4106 ) @ ( c_Set_Oinsert @ SV1 @ SY4107 @ SY4106 ) @ ( tc_fun @ SY4106 @ tc_bool ) )
= ( c_Set_Oinsert @ SV1 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV653 @ SY4107 @ ( tc_fun @ SY4106 @ tc_bool ) ) @ SY4106 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2307]) ).
thf(2963,plain,
! [SV654: $i,SV2: $i] :
( ( ! [SY4108: $i] :
( ( c_Set_Oinsert @ SV2 @ SV654 @ SY4108 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4108 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2308]) ).
thf(2964,plain,
! [SV655: $i,SV3: $i] :
( ( ! [SY4109: $i,SY4110: $i] :
( ( c_HOL_Ominus__class_Ominus @ SV3 @ ( c_Set_Oinsert @ SV655 @ SY4109 @ SY4110 ) @ ( tc_fun @ SY4110 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV3 @ ( c_Set_Oinsert @ SV655 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4110 @ tc_bool ) ) @ SY4110 ) @ ( tc_fun @ SY4110 @ tc_bool ) ) @ SY4109 @ ( tc_fun @ SY4110 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2309]) ).
thf(2965,plain,
! [SV656: $i,SV4: $i] :
( ( ! [SY4111: $i,SY4112: $i] :
( ( c_HOL_Ominus__class_Ominus @ SV4 @ ( c_Set_Oinsert @ SV656 @ SY4111 @ SY4112 ) @ ( tc_fun @ SY4112 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV4 @ SY4111 @ ( tc_fun @ SY4112 @ tc_bool ) ) @ ( c_Set_Oinsert @ SV656 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4112 @ tc_bool ) ) @ SY4112 ) @ ( tc_fun @ SY4112 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2310]) ).
thf(2966,plain,
! [SV5: $i] :
( ( ( ~ ( class_Orderings_Obot @ SV5 ) )
= $true )
| ( ( ! [SY2390: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ SV5 ) @ SY2390 @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2311]) ).
thf(2967,plain,
! [SV657: $i,SV6: $i] :
( ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV6 @ SV6 ) @ tc_bool ) ) @ SV657 @ ( tc_fun @ ( tc_prod @ SV6 @ SV6 ) @ tc_bool ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2312]) ).
thf(2968,plain,
! [SV658: $i,SV7: $i] :
( ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV7 @ tc_bool ) ) @ SV658 @ ( tc_fun @ SV7 @ tc_bool ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2313]) ).
thf(2969,plain,
! [SV659: $i,SV8: $i] :
( ( ! [SY4113: $i,SY4114: $i] :
( ( c_Relation_Orel__comp @ SV8 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV659 @ SY4113 ) @ tc_bool ) ) @ SY4114 @ SV659 @ SY4113 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SY4114 @ SY4113 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2314]) ).
thf(2970,plain,
! [SV660: $i,SV9: $i] :
( ( ! [SY4115: $i,SY4116: $i] :
( ( c_Relation_Orel__comp @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV9 @ SV660 ) @ tc_bool ) ) @ SY4115 @ SV9 @ SV660 @ SY4116 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV9 @ SY4116 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2315]) ).
thf(2971,plain,
! [SV661: $i,SV10: $i] :
( ( ! [SY4117: $i,SY4118: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV10 @ ( c_Set_Oinsert @ SV661 @ SY4117 @ SY4118 ) @ ( tc_fun @ SY4118 @ tc_bool ) )
= ( c_Set_Oinsert @ SV661 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV10 @ SY4117 @ ( tc_fun @ SY4118 @ tc_bool ) ) @ SY4118 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2316]) ).
thf(2972,plain,
! [SV662: $i,SV11: $i] :
( ( ! [SY4119: $i,SY4120: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ SV11 @ SV662 @ SY4119 ) @ SY4120 @ ( tc_fun @ SY4119 @ tc_bool ) )
= ( c_Set_Oinsert @ SV11 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV662 @ SY4120 @ ( tc_fun @ SY4119 @ tc_bool ) ) @ SY4119 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2317]) ).
thf(2973,plain,
! [SV663: $i,SV12: $i] :
( ( ! [SY4121: $i,SY4122: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV12 @ tc_bool ) )
!= ( c_Set_Oimage @ SV663 @ SY4121 @ SY4122 @ SV12 ) )
| ( SY4121
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4122 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2318]) ).
thf(2974,plain,
! [SV664: $i,SV13: $i] :
( ( ! [SY4123: $i] : ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Ortrancl @ SV13 @ SV664 ) @ ( c_Transitive__Closure_Ortrancl @ SY4123 @ SV664 ) @ ( tc_fun @ ( tc_prod @ SV664 @ SV664 ) @ tc_bool ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV13 @ SY4123 @ ( tc_fun @ ( tc_prod @ SV664 @ SV664 ) @ tc_bool ) ) @ SV664 ) @ ( tc_fun @ ( tc_prod @ SV664 @ SV664 ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2319]) ).
thf(2975,plain,
! [SV665: $i,SV14: $i] :
( ( ! [SY4124: $i,SY4125: $i] :
( ( ( hAPP @ ( c_snd @ SV14 @ SV665 ) @ SY4124 )
!= ( hAPP @ ( c_snd @ SV14 @ SV665 ) @ SY4125 ) )
| ( ( hAPP @ ( c_fst @ SV14 @ SV665 ) @ SY4124 )
!= ( hAPP @ ( c_fst @ SV14 @ SV665 ) @ SY4125 ) )
| ( SY4124 = SY4125 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2320]) ).
thf(2976,plain,
! [SV666: $i,SV15: $i] :
( ( ! [SY4126: $i,SY4127: $i] :
( ( ( hAPP @ ( c_snd @ SV15 @ SV666 ) @ SY4126 )
!= ( hAPP @ ( c_snd @ SV15 @ SV666 ) @ SY4127 ) )
| ( ( hAPP @ ( c_fst @ SV15 @ SV666 ) @ SY4126 )
!= ( hAPP @ ( c_fst @ SV15 @ SV666 ) @ SY4127 ) )
| ( SY4126 = SY4127 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2321]) ).
thf(2977,plain,
! [SV667: $i,SV16: $i] :
( ( ( hBOOL @ ( hAPP @ SV16 @ SV667 ) )
| ! [SY2417: $i,SY2418: $i] :
( ~ ( hBOOL @ ( hAPP @ SV16 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1 @ SV16 @ SY2417 @ SY2418 ) ) )
| ~ ( c_Wellfounded_Owf @ SY2417 @ SY2418 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2322]) ).
thf(2978,plain,
! [SV668: $i,SV17: $i] :
( ( ! [SY4130: $i,SY4131: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ ( c_Relation_ORange @ SV17 @ SV668 @ SY4130 ) @ ( c_Relation_ORange @ SY4131 @ SV668 @ SY4130 ) @ ( tc_fun @ SY4130 @ tc_bool ) ) @ ( c_Relation_ORange @ ( c_HOL_Ominus__class_Ominus @ SV17 @ SY4131 @ ( tc_fun @ ( tc_prod @ SV668 @ SY4130 ) @ tc_bool ) ) @ SV668 @ SY4130 ) @ ( tc_fun @ SY4130 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2323]) ).
thf(2979,plain,
! [SV669: $i,SV18: $i] :
( ( ! [SY4132: $i,SY4133: $i] :
( ( c_lessequals @ SV18 @ ( c_Set_Oinsert @ SV669 @ SY4132 @ SY4133 ) @ ( tc_fun @ SY4133 @ tc_bool ) )
| ~ ( c_lessequals @ SV18 @ SY4132 @ ( tc_fun @ SY4133 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2324]) ).
thf(2980,plain,
! [SV670: $i,SV19: $i] :
( ( ! [SY4134: $i] :
( ( c_lessequals @ SV19 @ SV670 @ ( tc_fun @ SY4134 @ tc_bool ) )
| ! [SY4135: $i] :
~ ( c_lessequals @ ( c_Set_Oinsert @ SY4135 @ SV19 @ SY4134 ) @ SV670 @ ( tc_fun @ SY4134 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2325]) ).
thf(2981,plain,
! [SV671: $i,SV20: $i] :
( ( ! [SY4136: $i,SY4137: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ SV20 @ SV671 @ SY4136 ) @ SY4137 @ ( tc_fun @ SY4136 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ SV671 @ SY4137 @ ( tc_fun @ SY4136 @ tc_bool ) ) )
| ~ ( c_in @ SV20 @ SY4137 @ SY4136 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2326]) ).
thf(2982,plain,
! [SV672: $i,SV21: $i] :
( ( ! [SY4138: $i,SY4139: $i,SY4140: $i] :
( ( c_lessequals @ ( c_Product__Type_OSigma @ SV21 @ ( c_COMBK @ SV672 @ ( tc_fun @ SY4138 @ tc_bool ) @ SY4139 ) @ SY4139 @ SY4138 ) @ ( c_Product__Type_OSigma @ SY4140 @ ( c_COMBK @ SV672 @ ( tc_fun @ SY4138 @ tc_bool ) @ SY4139 ) @ SY4139 @ SY4138 ) @ ( tc_fun @ ( tc_prod @ SY4139 @ SY4138 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV21 @ SY4140 @ ( tc_fun @ SY4139 @ tc_bool ) )
| ! [SY4141: $i] :
~ ( c_in @ SY4141 @ SV672 @ SY4138 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2327]) ).
thf(2983,plain,
! [SV673: $i,SV22: $i] :
( ( ! [SY4142: $i,SY4143: $i] :
( ( c_lessequals @ SV22 @ SV673 @ ( tc_fun @ SY4142 @ tc_bool ) )
| ! [SY4144: $i] :
( ~ ( c_lessequals @ ( c_Product__Type_OSigma @ SV22 @ ( c_COMBK @ SY4143 @ ( tc_fun @ SY4144 @ tc_bool ) @ SY4142 ) @ SY4142 @ SY4144 ) @ ( c_Product__Type_OSigma @ SV673 @ ( c_COMBK @ SY4143 @ ( tc_fun @ SY4144 @ tc_bool ) @ SY4142 ) @ SY4142 @ SY4144 ) @ ( tc_fun @ ( tc_prod @ SY4142 @ SY4144 ) @ tc_bool ) )
| ! [V_x: $i] :
~ ( c_in @ V_x @ SY4143 @ SY4144 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2328]) ).
thf(2984,plain,
! [SV674: $i,SV23: $i] :
( ( ! [SY4146: $i,SY4147: $i] :
( ( c_lessequals @ SV23 @ ( c_Set_Oinsert @ SV674 @ SY4146 @ SY4147 ) @ ( tc_fun @ SY4147 @ tc_bool ) )
| ~ ( c_in @ SV674 @ SV23 @ SY4147 )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV23 @ ( c_Set_Oinsert @ SV674 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4147 @ tc_bool ) ) @ SY4147 ) @ ( tc_fun @ SY4147 @ tc_bool ) ) @ SY4146 @ ( tc_fun @ SY4147 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2329]) ).
thf(2985,plain,
! [SV675: $i,SV24: $i] :
( ( ! [SY4148: $i,SY4149: $i] :
( ( c_lessequals @ SV24 @ ( c_Set_Oinsert @ SV675 @ SY4148 @ SY4149 ) @ ( tc_fun @ SY4149 @ tc_bool ) )
| ~ ( c_in @ SV675 @ SV24 @ SY4149 )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV24 @ ( c_Set_Oinsert @ SV675 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4149 @ tc_bool ) ) @ SY4149 ) @ ( tc_fun @ SY4149 @ tc_bool ) ) @ SY4148 @ ( tc_fun @ SY4149 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2330]) ).
thf(2986,plain,
! [SV676: $i,SV25: $i] :
( ( ! [SY4150: $i,SY4151: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV25 @ ( c_Set_Oinsert @ SV676 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4150 @ tc_bool ) ) @ SY4150 ) @ ( tc_fun @ SY4150 @ tc_bool ) ) @ SY4151 @ ( tc_fun @ SY4150 @ tc_bool ) )
| ~ ( c_in @ SV676 @ SV25 @ SY4150 )
| ~ ( c_lessequals @ SV25 @ ( c_Set_Oinsert @ SV676 @ SY4151 @ SY4150 ) @ ( tc_fun @ SY4150 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2331]) ).
thf(2987,plain,
! [SV677: $i,SV26: $i] :
( ( ! [SY4152: $i,SY4153: $i] :
( ( ( c_Set_Oimage @ ( c_COMBK @ SV26 @ SV677 @ SY4152 ) @ SY4153 @ SY4152 @ SV677 )
= ( c_Set_Oinsert @ SV26 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV677 @ tc_bool ) ) @ SV677 ) )
| ! [V_x: $i] :
~ ( c_in @ V_x @ SY4153 @ SY4152 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2332]) ).
thf(2988,plain,
! [SV678: $i,SV27: $i] :
( ( ! [SY4155: $i] :
( ( c_lessequals @ ( c_Transitive__Closure_Otrancl @ SV27 @ SV678 ) @ SY4155 @ ( tc_fun @ ( tc_prod @ SV678 @ SV678 ) @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Relation_Orel__comp @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Transitive__Closure_Otrancl @ SV27 @ SV678 ) @ SY4155 @ ( tc_fun @ ( tc_prod @ SV678 @ SV678 ) @ tc_bool ) ) @ SV27 @ SV678 @ SV678 @ SV678 ) @ SY4155 @ ( tc_fun @ ( tc_prod @ SV678 @ SV678 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV27 @ SY4155 @ ( tc_fun @ ( tc_prod @ SV678 @ SV678 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2333]) ).
thf(2989,plain,
! [SV679: $i,SV28: $i] :
( ( ! [SY4156: $i,SY4157: $i,SY4158: $i] :
( ( c_Product__Type_OSigma @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV28 @ SV679 @ ( tc_fun @ SY4156 @ tc_bool ) ) @ SY4157 @ SY4156 @ SY4158 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Product__Type_OSigma @ SV28 @ SY4157 @ SY4156 @ SY4158 ) @ ( c_Product__Type_OSigma @ SV679 @ SY4157 @ SY4156 @ SY4158 ) @ ( tc_fun @ ( tc_prod @ SY4156 @ SY4158 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2334]) ).
thf(2990,plain,
! [SV680: $i,SV29: $i] :
( ( ( SV29 = SV680 )
| ! [SY4159: $i] :
~ ( c_in @ SV29 @ ( c_Set_Oinsert @ SV680 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4159 @ tc_bool ) ) @ SY4159 ) @ SY4159 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2335]) ).
thf(2991,plain,
! [SV681: $i,SV30: $i] :
( ( ! [SY4160: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV30 @ SV681 @ ( tc_fun @ SY4160 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4160 @ tc_bool ) ) )
| ( ( c_HOL_Ominus__class_Ominus @ SV30 @ SV681 @ ( tc_fun @ SY4160 @ tc_bool ) )
= SV30 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2336]) ).
thf(2992,plain,
! [SV682: $i,SV31: $i] :
( ( ! [SY4161: $i,SY4162: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ ( c_Relation_ODomain @ SV31 @ SV682 @ SY4161 ) @ ( c_Relation_ODomain @ SY4162 @ SV682 @ SY4161 ) @ ( tc_fun @ SV682 @ tc_bool ) ) @ ( c_Relation_ODomain @ ( c_HOL_Ominus__class_Ominus @ SV31 @ SY4162 @ ( tc_fun @ ( tc_prod @ SV682 @ SY4161 ) @ tc_bool ) ) @ SV682 @ SY4161 ) @ ( tc_fun @ SV682 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2337]) ).
thf(2993,plain,
! [SV683: $i,SV32: $i] :
( ( ! [SY4163: $i,SY4164: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV32 @ SV683 @ ( tc_fun @ SY4163 @ tc_bool ) ) @ SY4164 @ ( tc_fun @ SY4163 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV32 @ SY4164 @ ( tc_fun @ SY4163 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV683 @ SY4164 @ ( tc_fun @ SY4163 @ tc_bool ) ) @ ( tc_fun @ SY4163 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2338]) ).
thf(2994,plain,
! [SV684: $i,SV33: $i] :
( ( ! [SY4165: $i,SY4166: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV33 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV684 @ SY4165 @ ( tc_fun @ SY4166 @ tc_bool ) ) @ ( tc_fun @ SY4166 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV33 @ SV684 @ ( tc_fun @ SY4166 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV33 @ SY4165 @ ( tc_fun @ SY4166 @ tc_bool ) ) @ ( tc_fun @ SY4166 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2339]) ).
thf(2995,plain,
! [SV685: $i,SV34: $i] :
( ( ~ ( class_Lattices_Odistrib__lattice @ SV34 )
| ! [SY4167: $i,SY4168: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV685 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4167 @ SY4168 @ SV34 ) @ SV34 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV685 @ SY4167 @ SV34 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV685 @ SY4168 @ SV34 ) @ SV34 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2340]) ).
thf(2996,plain,
! [SV686: $i,SV35: $i] :
( ( ~ ( class_Lattices_Odistrib__lattice @ SV35 )
| ! [SY4169: $i,SY4170: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV686 @ SY4169 @ SV35 ) @ SY4170 @ SV35 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV686 @ SY4170 @ SV35 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4169 @ SY4170 @ SV35 ) @ SV35 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2341]) ).
thf(2997,plain,
! [SV687: $i,SV36: $i] :
( ( c_lessequals @ ( c_Relation_OId__on @ SV36 @ SV687 ) @ ( c_Product__Type_OSigma @ SV36 @ ( c_COMBK @ SV36 @ ( tc_fun @ SV687 @ tc_bool ) @ SV687 ) @ SV687 @ SV687 ) @ ( tc_fun @ ( tc_prod @ SV687 @ SV687 ) @ tc_bool ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2342]) ).
thf(2998,plain,
! [SV688: $i,SV37: $i] :
( ( ! [SY4171: $i] :
( ( c_lessequals @ SV37 @ ( c_Product__Type_OSigma @ SV688 @ ( c_COMBK @ SV688 @ ( tc_fun @ SY4171 @ tc_bool ) @ SY4171 ) @ SY4171 @ SY4171 ) @ ( tc_fun @ ( tc_prod @ SY4171 @ SY4171 ) @ tc_bool ) )
| ~ ( c_Relation_Orefl__on @ SV688 @ SV37 @ SY4171 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2343]) ).
thf(2999,plain,
! [SV689: $i,SV38: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV38 @ SV38 @ ( tc_fun @ SV689 @ tc_bool ) )
= SV38 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2344]) ).
thf(3000,plain,
! [SV39: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV39 ) )
= $true )
| ( ( ! [SY2483: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2483 @ SY2483 @ SV39 )
= SY2483 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2345]) ).
thf(3001,plain,
! [SV690: $i,SV40: $i] :
( ( ! [SY4172: $i,SY4173: $i,SY4174: $i,SY4175: $i,SY4176: $i] :
( ( c_lessequals @ ( c_Relation_Orel__comp @ SV40 @ SV690 @ SY4172 @ SY4173 @ SY4174 ) @ ( c_Relation_Orel__comp @ SY4175 @ SY4176 @ SY4172 @ SY4173 @ SY4174 ) @ ( tc_fun @ ( tc_prod @ SY4172 @ SY4174 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV690 @ SY4176 @ ( tc_fun @ ( tc_prod @ SY4173 @ SY4174 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV40 @ SY4175 @ ( tc_fun @ ( tc_prod @ SY4172 @ SY4173 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2346]) ).
thf(3002,plain,
! [SV691: $i,SV41: $i] :
( ( ! [SY4177: $i,SY4178: $i,SY4179: $i] :
( ( c_Relation_OImage @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV41 @ SV691 @ ( tc_fun @ ( tc_prod @ SY4177 @ SY4178 ) @ tc_bool ) ) @ SY4179 @ SY4177 @ SY4178 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_OImage @ SV41 @ SY4179 @ SY4177 @ SY4178 ) @ ( c_Relation_OImage @ SV691 @ SY4179 @ SY4177 @ SY4178 ) @ ( tc_fun @ SY4178 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2347]) ).
thf(3003,plain,
! [SV692: $i,SV42: $i] :
( ( ! [SY4180: $i,SY4181: $i,SY4182: $i] :
( ( c_Relation_OImage @ SV42 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV692 @ SY4180 @ ( tc_fun @ SY4181 @ tc_bool ) ) @ SY4181 @ SY4182 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_OImage @ SV42 @ SV692 @ SY4181 @ SY4182 ) @ ( c_Relation_OImage @ SV42 @ SY4180 @ SY4181 @ SY4182 ) @ ( tc_fun @ SY4182 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2348]) ).
thf(3004,plain,
! [SV693: $i,SV43: $i] :
( ( ( hBOOL @ ( hAPP @ SV43 @ SV693 ) )
| ! [SY2499: $i,SY2500: $i] :
( ~ ( hBOOL @ ( hAPP @ SV43 @ ( c_List_Osko__Recdef__Xtfl__wf__induct__1__1 @ SV43 @ SY2499 @ SY2500 ) ) )
| ~ ( c_Wellfounded_Owf @ SY2499 @ SY2500 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2349]) ).
thf(3005,plain,
! [SV694: $i,SV44: $i] :
( ( ( c_Relation_ODomain @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV44 @ SV694 ) @ tc_bool ) ) @ SV44 @ SV694 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV44 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2350]) ).
thf(3006,plain,
! [SV695: $i,SV45: $i] :
( ( ! [SY4185: $i,SY4186: $i] :
( ( c_Set_Oinsert @ SV45 @ ( c_Set_Oinsert @ SV695 @ SY4185 @ SY4186 ) @ SY4186 )
= ( c_Set_Oinsert @ SV695 @ ( c_Set_Oinsert @ SV45 @ SY4185 @ SY4186 ) @ SY4186 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2351]) ).
thf(3007,plain,
! [SV696: $i,SV46: $i] :
( ( ! [SY4187: $i] :
( SV46
= ( c_Pair @ ( hAPP @ ( c_fst @ SV696 @ SY4187 ) @ SV46 ) @ ( hAPP @ ( c_snd @ SV696 @ SY4187 ) @ SV46 ) @ SV696 @ SY4187 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2352]) ).
thf(3008,plain,
! [SV697: $i,SV47: $i] :
( ( ! [SY4188: $i] :
( ( c_Pair @ ( hAPP @ ( c_fst @ SV47 @ SV697 ) @ SY4188 ) @ ( hAPP @ ( c_snd @ SV47 @ SV697 ) @ SY4188 ) @ SV47 @ SV697 )
= SY4188 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2353]) ).
thf(3009,plain,
! [SV698: $i,SV48: $i] :
( ( ! [SY4189: $i,SY4190: $i] :
( ( hAPP @ ( c_COMBK @ SV48 @ SV698 @ SY4189 ) @ SY4190 )
= SV48 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2354]) ).
thf(3010,plain,
! [SV699: $i,SV49: $i] :
( ( ! [SY4191: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV49 @ SV699 @ ( tc_fun @ SY4191 @ tc_bool ) ) @ SV699 @ ( tc_fun @ SY4191 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ SV49 @ SV699 @ ( tc_fun @ SY4191 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2355]) ).
thf(3011,plain,
! [SV700: $i,SV50: $i] :
( ( ! [SY4192: $i] :
( ( c_Set_Oinsert @ SV50 @ ( c_Set_Oinsert @ SV700 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4192 @ tc_bool ) ) @ SY4192 ) @ SY4192 )
= ( c_Set_Oinsert @ SV700 @ ( c_Set_Oinsert @ SV50 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4192 @ tc_bool ) ) @ SY4192 ) @ SY4192 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2356]) ).
thf(3012,plain,
! [SV701: $i,SV51: $i] :
( ( ! [SY4193: $i,SY4194: $i,SY4195: $i] :
( ( c_lessequals @ ( c_Relation_OImage @ SV51 @ SV701 @ SY4193 @ SY4194 ) @ SY4195 @ ( tc_fun @ SY4194 @ tc_bool ) )
| ! [SY2520: $i] :
~ ( c_lessequals @ SV51 @ ( c_Product__Type_OSigma @ SY2520 @ ( c_COMBK @ SY4195 @ ( tc_fun @ SY4194 @ tc_bool ) @ SY4193 ) @ SY4193 @ SY4194 ) @ ( tc_fun @ ( tc_prod @ SY4193 @ SY4194 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2357]) ).
thf(3013,plain,
! [SV702: $i,SV52: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV52 )
| ! [SY4197: $i] :
( ! [SY4198: $i] :
( ( c_HOL_Ominus__class_Ominus @ SV702 @ SY4197 @ SV52 )
!= ( c_HOL_Ominus__class_Ominus @ SY4198 @ SY4198 @ SV52 ) )
| ( SV702 = SY4197 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2358]) ).
thf(3014,plain,
! [SV703: $i,SV53: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV53 )
| ! [SY4199: $i,SY4200: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV703 @ SV703 @ SV53 )
!= ( c_HOL_Ominus__class_Ominus @ SY4199 @ SY4200 @ SV53 ) )
| ( SY4199 = SY4200 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2359]) ).
thf(3015,plain,
! [SV704: $i,SV54: $i] :
( ( ! [SY4201: $i] :
( ( c_Set_Oimage @ SV54 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV704 @ tc_bool ) ) @ SV704 @ SY4201 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4201 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2360]) ).
thf(3016,plain,
! [SV705: $i,SV55: $i] :
( ( ! [SY4202: $i,SY4203: $i,SY4204: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oimage @ SV55 @ SV705 @ SY4202 @ SY4203 ) @ ( c_Set_Oimage @ SV55 @ SY4204 @ SY4202 @ SY4203 ) @ ( tc_fun @ SY4203 @ tc_bool ) ) @ ( c_Set_Oimage @ SV55 @ ( c_HOL_Ominus__class_Ominus @ SV705 @ SY4204 @ ( tc_fun @ SY4202 @ tc_bool ) ) @ SY4202 @ SY4203 ) @ ( tc_fun @ SY4203 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2361]) ).
thf(3017,plain,
! [SV706: $i,SV56: $i] :
( ( ! [SY4205: $i,SY4206: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV56 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV706 @ SY4205 @ ( tc_fun @ SY4206 @ tc_bool ) ) @ ( tc_fun @ SY4206 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV706 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV56 @ SY4205 @ ( tc_fun @ SY4206 @ tc_bool ) ) @ ( tc_fun @ SY4206 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2362]) ).
thf(3018,plain,
! [SV707: $i,SV57: $i] :
( ( ! [SY4207: $i,SY4208: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV57 @ SV707 @ ( tc_fun @ SY4207 @ tc_bool ) ) @ SY4208 @ ( tc_fun @ SY4207 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV57 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV707 @ SY4208 @ ( tc_fun @ SY4207 @ tc_bool ) ) @ ( tc_fun @ SY4207 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2363]) ).
thf(3019,plain,
! [SV708: $i,SV58: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV58 )
| ! [SY4209: $i,SY4210: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV708 @ SY4209 @ SV58 ) @ SY4210 @ SV58 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV708 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4209 @ SY4210 @ SV58 ) @ SV58 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2364]) ).
thf(3020,plain,
! [SV709: $i,SV59: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV59 )
| ! [SY4211: $i,SY4212: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV709 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4211 @ SY4212 @ SV59 ) @ SV59 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY4211 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV709 @ SY4212 @ SV59 ) @ SV59 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2365]) ).
thf(3021,plain,
! [SV710: $i,SV60: $i] :
( ( ~ ( class_Lattices_Olattice @ SV60 )
| ! [SY4213: $i,SY4214: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV710 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4213 @ SY4214 @ SV60 ) @ SV60 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY4213 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV710 @ SY4214 @ SV60 ) @ SV60 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2366]) ).
thf(3022,plain,
! [SV711: $i,SV61: $i] :
( ( ~ ( class_Lattices_Olattice @ SV61 )
| ! [SY4215: $i,SY4216: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV711 @ SY4215 @ SV61 ) @ SY4216 @ SV61 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV711 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4215 @ SY4216 @ SV61 ) @ SV61 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2367]) ).
thf(3023,plain,
! [SV712: $i,SV62: $i] :
( ( ! [SY4217: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV62 @ SV712 @ ( tc_fun @ SY4217 @ tc_bool ) )
= SV62 )
| ~ ( c_lessequals @ SV62 @ SV712 @ ( tc_fun @ SY4217 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2368]) ).
thf(3024,plain,
! [SV713: $i,SV63: $i] :
( ( ! [SY4218: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV63 @ SV713 @ ( tc_fun @ SY4218 @ tc_bool ) )
= SV713 )
| ~ ( c_lessequals @ SV713 @ SV63 @ ( tc_fun @ SY4218 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2369]) ).
thf(3025,plain,
! [SV64: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV64 ) )
= $true )
| ( ( ! [SY2555: $i,SY2556: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SY2555 @ SY2556 @ SV64 )
= SY2555 )
| ~ ( c_lessequals @ SY2555 @ SY2556 @ SV64 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2370]) ).
thf(3026,plain,
! [SV65: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV65 ) )
= $true )
| ( ( ! [SY2557: $i,SY2558: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SY2557 @ SY2558 @ SV65 )
!= SY2557 )
| ( c_lessequals @ SY2557 @ SY2558 @ SV65 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2371]) ).
thf(3027,plain,
! [SV66: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV66 ) )
= $true )
| ( ( ! [SY2559: $i,SY2560: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SY2559 @ SY2560 @ SV66 )
= SY2560 )
| ~ ( c_lessequals @ SY2560 @ SY2559 @ SV66 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2372]) ).
thf(3028,plain,
! [SV714: $i,SV67: $i] :
( ( ! [SY4219: $i,SY4220: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV67 @ SV714 @ ( tc_fun @ SY4219 @ tc_bool ) ) @ SY4220 @ ( tc_fun @ SY4219 @ tc_bool ) )
| ~ ( c_lessequals @ SV714 @ SY4220 @ ( tc_fun @ SY4219 @ tc_bool ) )
| ~ ( c_lessequals @ SV67 @ SY4220 @ ( tc_fun @ SY4219 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2373]) ).
thf(3029,plain,
! [SV715: $i,SV68: $i] :
( ( ! [SY4221: $i] : ( c_lessequals @ SV68 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV715 @ SV68 @ ( tc_fun @ SY4221 @ tc_bool ) ) @ ( tc_fun @ SY4221 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2374]) ).
thf(3030,plain,
! [SV716: $i,SV69: $i] :
( ( ! [SY4222: $i] : ( c_lessequals @ SV69 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV69 @ SV716 @ ( tc_fun @ SY4222 @ tc_bool ) ) @ ( tc_fun @ SY4222 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2375]) ).
thf(3031,plain,
! [SV717: $i,SV70: $i] :
( ( ! [SY4223: $i,SY4224: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV70 @ SV717 @ ( tc_fun @ SY4223 @ tc_bool ) ) @ SY4224 @ ( tc_fun @ SY4223 @ tc_bool ) )
| ~ ( c_lessequals @ SV717 @ SY4224 @ ( tc_fun @ SY4223 @ tc_bool ) )
| ~ ( c_lessequals @ SV70 @ SY4224 @ ( tc_fun @ SY4223 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2376]) ).
thf(3032,plain,
! [SV718: $i,SV71: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV71 )
| ! [SY4225: $i,SY4226: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV718 @ SY4225 @ SV71 ) @ SY4226 @ SV71 )
| ~ ( c_lessequals @ SY4225 @ SY4226 @ SV71 )
| ~ ( c_lessequals @ SV718 @ SY4226 @ SV71 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2377]) ).
thf(3033,plain,
! [SV72: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV72 ) )
= $true )
| ( ( ! [SY2574: $i,SY2575: $i] : ( c_lessequals @ SY2574 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2574 @ SY2575 @ SV72 ) @ SV72 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2378]) ).
thf(3034,plain,
! [SV73: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV73 ) )
= $true )
| ( ( ! [SY2576: $i,SY2577: $i] : ( c_lessequals @ SY2576 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2577 @ SY2576 @ SV73 ) @ SV73 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2379]) ).
thf(3035,plain,
! [SV719: $i,SV74: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV74 )
| ! [SY4227: $i,SY4228: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV719 @ SY4227 @ SV74 ) @ SY4228 @ SV74 )
| ~ ( c_lessequals @ SY4227 @ SY4228 @ SV74 )
| ~ ( c_lessequals @ SV719 @ SY4228 @ SV74 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2380]) ).
thf(3036,plain,
! [SV720: $i,SV75: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV75 )
| ! [SY4229: $i,SY4230: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV720 @ SY4229 @ SV75 ) @ SY4230 @ SV75 )
| ~ ( c_lessequals @ SY4229 @ SY4230 @ SV75 )
| ~ ( c_lessequals @ SV720 @ SY4230 @ SV75 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2381]) ).
thf(3037,plain,
! [SV76: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV76 ) )
= $true )
| ( ( ! [SY2584: $i,SY2585: $i] : ( c_lessequals @ SY2584 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2585 @ SY2584 @ SV76 ) @ SV76 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2382]) ).
thf(3038,plain,
! [SV77: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV77 ) )
= $true )
| ( ( ! [SY2586: $i,SY2587: $i] : ( c_lessequals @ SY2586 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2586 @ SY2587 @ SV77 ) @ SV77 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2383]) ).
thf(3039,plain,
! [SV721: $i,SV78: $i] :
( ( ! [SY4231: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV78 @ SV721 @ ( tc_fun @ SY4231 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV721 @ SV78 @ ( tc_fun @ SY4231 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2384]) ).
thf(3040,plain,
! [SV79: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV79 ) )
= $true )
| ( ( ! [SY2590: $i,SY2591: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY2590 @ SY2591 @ SV79 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY2591 @ SY2590 @ SV79 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2385]) ).
thf(3041,plain,
! [SV80: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV80 ) )
= $true )
| ( ( ! [SY2592: $i,SY2593: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY2592 @ SY2593 @ SV80 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY2593 @ SY2592 @ SV80 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2386]) ).
thf(3042,plain,
! [SV722: $i,SV81: $i] :
( ( ( c_Wellfounded_Oacyclic @ SV81 @ SV722 )
| ~ ( c_Wellfounded_Owf @ SV81 @ SV722 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2387]) ).
thf(3043,plain,
! [SV723: $i,SV82: $i] :
( ( ! [SY4232: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV82 @ ( c_HOL_Ominus__class_Ominus @ SV723 @ SV82 @ ( tc_fun @ SY4232 @ tc_bool ) ) @ ( tc_fun @ SY4232 @ tc_bool ) )
= SV723 )
| ~ ( c_lessequals @ SV82 @ SV723 @ ( tc_fun @ SY4232 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2388]) ).
thf(3044,plain,
! [SV724: $i,SV83: $i] :
( ( ! [SY4233: $i,SY4234: $i] :
( ( c_lessequals @ ( c_Relation_OImage @ SV83 @ ( c_Set_Oinsert @ SV724 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4233 @ tc_bool ) ) @ SY4233 ) @ SY4233 @ SY4233 ) @ ( c_Relation_OImage @ SV83 @ ( c_Set_Oinsert @ SY4234 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4233 @ tc_bool ) ) @ SY4233 ) @ SY4233 @ SY4233 ) @ ( tc_fun @ SY4233 @ tc_bool ) )
| ~ ( c_in @ ( c_Pair @ SV724 @ SY4234 @ SY4233 @ SY4233 ) @ SV83 @ ( tc_prod @ SY4233 @ SY4233 ) )
| ! [SY2600: $i] :
~ ( c_Equiv__Relations_Oequiv @ SY2600 @ SV83 @ SY4233 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2389]) ).
thf(3045,plain,
! [SV725: $i,SV84: $i] :
( ( ! [SY4236: $i] :
( ( c_Relation_OImage @ SV84 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV725 @ tc_bool ) ) @ SV725 @ SY4236 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4236 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2390]) ).
thf(3046,plain,
! [SV726: $i,SV85: $i] :
( ( ! [SY4237: $i] :
( ( c_Set_Oinsert @ SV85 @ ( c_Set_Oinsert @ SV85 @ SV726 @ SY4237 ) @ SY4237 )
= ( c_Set_Oinsert @ SV85 @ SV726 @ SY4237 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2391]) ).
thf(3047,plain,
! [SV727: $i,SV86: $i] :
( ( ( hBOOL @ ( hAPP @ SV86 @ SV727 ) )
| ! [SY4238: $i] :
( ( SY4238 = SV727 )
| ! [SY4239: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SY4238 @ SV86 @ SY4239 ) @ SV727 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2392]) ).
thf(3048,plain,
! [SV728: $i,SV87: $i] :
( ( ! [SY4240: $i,SY4241: $i,SY4242: $i] :
( ( c_Relation_ODomain @ ( c_Set_Oinsert @ ( c_Pair @ SV87 @ SV728 @ SY4240 @ SY4241 ) @ SY4242 @ ( tc_prod @ SY4240 @ SY4241 ) ) @ SY4240 @ SY4241 )
= ( c_Set_Oinsert @ SV87 @ ( c_Relation_ODomain @ SY4242 @ SY4240 @ SY4241 ) @ SY4240 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2393]) ).
thf(3049,plain,
! [SV729: $i,SV88: $i] :
( ( ! [SY4243: $i] :
( ( c_Relation_Osym @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV88 @ SV729 @ ( tc_fun @ ( tc_prod @ SY4243 @ SY4243 ) @ tc_bool ) ) @ SY4243 )
| ~ ( c_Relation_Osym @ SV729 @ SY4243 )
| ~ ( c_Relation_Osym @ SV88 @ SY4243 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2394]) ).
thf(3050,plain,
! [SV730: $i,SV89: $i] :
( ( ! [SY4244: $i] :
( ( c_lessequals @ ( c_Transitive__Closure_Ortrancl @ SV89 @ SV730 ) @ ( c_Transitive__Closure_Ortrancl @ SY4244 @ SV730 ) @ ( tc_fun @ ( tc_prod @ SV730 @ SV730 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV89 @ SY4244 @ ( tc_fun @ ( tc_prod @ SV730 @ SV730 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2395]) ).
thf(3051,plain,
! [SV731: $i,SV90: $i] :
( ( ! [SY4245: $i,SY4246: $i] : ( c_lessequals @ ( c_Relation_ODomain @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV90 @ SV731 @ ( tc_fun @ ( tc_prod @ SY4245 @ SY4246 ) @ tc_bool ) ) @ SY4245 @ SY4246 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_ODomain @ SV90 @ SY4245 @ SY4246 ) @ ( c_Relation_ODomain @ SV731 @ SY4245 @ SY4246 ) @ ( tc_fun @ SY4245 @ tc_bool ) ) @ ( tc_fun @ SY4245 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2396]) ).
thf(3052,plain,
! [SV91: $i] :
( ( ( ~ ( class_Lattices_Obounded__lattice @ SV91 ) )
= $true )
| ( ( ! [SY2619: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY2619 @ ( c_Orderings_Obot__class_Obot @ SV91 ) @ SV91 )
= ( c_Orderings_Obot__class_Obot @ SV91 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2397]) ).
thf(3053,plain,
! [SV92: $i] :
( ( ( ~ ( class_Lattices_Obounded__lattice @ SV92 ) )
= $true )
| ( ( ! [SY2620: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Orderings_Obot__class_Obot @ SV92 ) @ SY2620 @ SV92 )
= ( c_Orderings_Obot__class_Obot @ SV92 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2398]) ).
thf(3054,plain,
! [SV732: $i,SV93: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV93 @ tc_bool ) ) @ SV732 @ ( tc_fun @ SV93 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV93 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2399]) ).
thf(3055,plain,
! [SV733: $i,SV94: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV94 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV733 @ tc_bool ) ) @ ( tc_fun @ SV733 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV733 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2400]) ).
thf(3056,plain,
! [SV734: $i,SV95: $i] :
( ( ! [SY4247: $i] : ( c_lessequals @ SV95 @ ( c_Set_Oinsert @ SV734 @ SV95 @ SY4247 ) @ ( tc_fun @ SY4247 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2401]) ).
thf(3057,plain,
! [SV735: $i,SV96: $i] :
( ( ! [SY4248: $i,SY4249: $i,SY4250: $i] : ( c_lessequals @ ( c_Set_Oimage @ SV96 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV735 @ SY4248 @ ( tc_fun @ SY4249 @ tc_bool ) ) @ SY4249 @ SY4250 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oimage @ SV96 @ SV735 @ SY4249 @ SY4250 ) @ ( c_Set_Oimage @ SV96 @ SY4248 @ SY4249 @ SY4250 ) @ ( tc_fun @ SY4250 @ tc_bool ) ) @ ( tc_fun @ SY4250 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2402]) ).
thf(3058,plain,
! [SV736: $i,SV97: $i] :
( ( ! [SY4251: $i,SY4252: $i,SY4253: $i] : ( c_lessequals @ ( c_Relation_OImage @ SV97 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV736 @ SY4251 @ ( tc_fun @ SY4252 @ tc_bool ) ) @ SY4252 @ SY4253 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_OImage @ SV97 @ SV736 @ SY4252 @ SY4253 ) @ ( c_Relation_OImage @ SV97 @ SY4251 @ SY4252 @ SY4253 ) @ ( tc_fun @ SY4253 @ tc_bool ) ) @ ( tc_fun @ SY4253 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2403]) ).
thf(3059,plain,
! [SV737: $i,SV98: $i] :
( ( ! [SY4254: $i,SY4255: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV98 @ SV737 @ ( tc_fun @ SY4254 @ tc_bool ) ) @ SY4255 @ ( tc_fun @ SY4254 @ tc_bool ) )
!= ( c_Lattices_Olower__semilattice__class_Oinf @ SV98 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV737 @ SY4255 @ ( tc_fun @ SY4254 @ tc_bool ) ) @ ( tc_fun @ SY4254 @ tc_bool ) ) )
| ( c_lessequals @ SY4255 @ SV98 @ ( tc_fun @ SY4254 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2404]) ).
thf(3060,plain,
! [SV738: $i,SV99: $i] :
( ( ! [SY4256: $i,SY4257: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV99 @ SV738 @ ( tc_fun @ SY4256 @ tc_bool ) ) @ SY4257 @ ( tc_fun @ SY4256 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV99 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV738 @ SY4257 @ ( tc_fun @ SY4256 @ tc_bool ) ) @ ( tc_fun @ SY4256 @ tc_bool ) ) )
| ~ ( c_lessequals @ SY4257 @ SV99 @ ( tc_fun @ SY4256 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2405]) ).
thf(3061,plain,
! [SV739: $i,SV100: $i] :
( ( ! [SY4258: $i,SY4259: $i,SY4260: $i] :
( ( c_Product__Type_OSigma @ ( c_HOL_Ominus__class_Ominus @ SV100 @ SV739 @ ( tc_fun @ SY4258 @ tc_bool ) ) @ SY4259 @ SY4258 @ SY4260 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Product__Type_OSigma @ SV100 @ SY4259 @ SY4258 @ SY4260 ) @ ( c_Product__Type_OSigma @ SV739 @ SY4259 @ SY4258 @ SY4260 ) @ ( tc_fun @ ( tc_prod @ SY4258 @ SY4260 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2406]) ).
thf(3062,plain,
! [SV740: $i,SV101: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV101 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV740 @ tc_bool ) ) @ ( tc_fun @ SV740 @ tc_bool ) )
= SV101 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2407]) ).
thf(3063,plain,
! [SV741: $i,SV102: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV102 @ SV102 @ ( tc_fun @ SV741 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV741 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2408]) ).
thf(3064,plain,
! [SV742: $i,SV103: $i] :
( ( ! [SY4261: $i,SY4262: $i,SY4263: $i,SY4264: $i,SY4265: $i] :
( ( c_lessequals @ ( c_Relation_Orel__comp @ SV103 @ SV742 @ SY4261 @ SY4262 @ SY4263 ) @ ( c_Product__Type_OSigma @ SY4264 @ ( c_COMBK @ SY4265 @ ( tc_fun @ SY4263 @ tc_bool ) @ SY4261 ) @ SY4261 @ SY4263 ) @ ( tc_fun @ ( tc_prod @ SY4261 @ SY4263 ) @ tc_bool ) )
| ! [SY4266: $i] :
( ~ ( c_lessequals @ SV742 @ ( c_Product__Type_OSigma @ SY4266 @ ( c_COMBK @ SY4265 @ ( tc_fun @ SY4263 @ tc_bool ) @ SY4262 ) @ SY4262 @ SY4263 ) @ ( tc_fun @ ( tc_prod @ SY4262 @ SY4263 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV103 @ ( c_Product__Type_OSigma @ SY4264 @ ( c_COMBK @ SY4266 @ ( tc_fun @ SY4262 @ tc_bool ) @ SY4261 ) @ SY4261 @ SY4262 ) @ ( tc_fun @ ( tc_prod @ SY4261 @ SY4262 ) @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2409]) ).
thf(3065,plain,
! [SV743: $i,SV104: $i] :
( ( ! [SY4267: $i] :
( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV104 @ SV743 @ ( tc_fun @ ( tc_prod @ SY4267 @ SY4267 ) @ tc_bool ) ) @ SY4267 )
| ~ ( c_lessequals @ ( c_Relation_Orel__comp @ SV104 @ SV743 @ SY4267 @ SY4267 @ SY4267 ) @ SV104 @ ( tc_fun @ ( tc_prod @ SY4267 @ SY4267 ) @ tc_bool ) )
| ~ ( c_Wellfounded_Owf @ SV743 @ SY4267 )
| ~ ( c_Wellfounded_Owf @ SV104 @ SY4267 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2410]) ).
thf(3066,plain,
! [SV744: $i,SV105: $i] :
( ( ( hBOOL @ ( hAPP @ SV105 @ SV744 ) )
| ! [SY4268: $i] :
( ( hBOOL @ ( hAPP @ SY4268 @ SV744 ) )
| ! [SY4269: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4268 @ SV105 @ ( tc_fun @ SY4269 @ tc_bool ) ) @ SV744 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2411]) ).
thf(3067,plain,
! [SV745: $i,SV106: $i] :
( ( ! [SY4270: $i,SY4271: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV106 @ SV745 @ ( tc_fun @ SY4270 @ tc_bool ) ) @ SY4271 ) )
| ~ ( hBOOL @ ( hAPP @ SV745 @ SY4271 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2412]) ).
thf(3068,plain,
! [SV746: $i,SV107: $i] :
( ( ! [SY4272: $i,SY4273: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV107 @ SV746 @ ( tc_fun @ SY4272 @ tc_bool ) ) @ SY4273 ) )
| ~ ( hBOOL @ ( hAPP @ SV107 @ SY4273 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2413]) ).
thf(3069,plain,
! [SV747: $i,SV108: $i] :
( ( ! [SY4274: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_ODomain @ SV108 @ SV747 @ SV747 ) @ ( c_Relation_ORange @ SY4274 @ SV747 @ SV747 ) @ ( tc_fun @ SV747 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV747 @ tc_bool ) ) )
| ~ ( c_Wellfounded_Owf @ SY4274 @ SV747 )
| ~ ( c_Wellfounded_Owf @ SV108 @ SV747 )
| ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV108 @ SY4274 @ ( tc_fun @ ( tc_prod @ SV747 @ SV747 ) @ tc_bool ) ) @ SV747 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2414]) ).
thf(3070,plain,
! [SV748: $i,SV109: $i] :
( ( ! [SY4275: $i,SY4276: $i,SY4277: $i] :
( ( c_Product__Type_OSigma @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV109 @ SV748 @ ( tc_fun @ SY4275 @ tc_bool ) ) @ ( c_COMBK @ SY4276 @ ( tc_fun @ SY4277 @ tc_bool ) @ SY4275 ) @ SY4275 @ SY4277 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Product__Type_OSigma @ SV109 @ ( c_COMBK @ SY4276 @ ( tc_fun @ SY4277 @ tc_bool ) @ SY4275 ) @ SY4275 @ SY4277 ) @ ( c_Product__Type_OSigma @ SV748 @ ( c_COMBK @ SY4276 @ ( tc_fun @ SY4277 @ tc_bool ) @ SY4275 ) @ SY4275 @ SY4277 ) @ ( tc_fun @ ( tc_prod @ SY4275 @ SY4277 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2415]) ).
thf(3071,plain,
! [SV749: $i,SV110: $i] :
( ( ! [SY4278: $i,SY4279: $i,SY4280: $i] :
( ( c_Relation_Orefl__on @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV110 @ SV749 @ ( tc_fun @ SY4278 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4279 @ SY4280 @ ( tc_fun @ ( tc_prod @ SY4278 @ SY4278 ) @ tc_bool ) ) @ SY4278 )
| ~ ( c_Relation_Orefl__on @ SV749 @ SY4280 @ SY4278 )
| ~ ( c_Relation_Orefl__on @ SV110 @ SY4279 @ SY4278 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2416]) ).
thf(3072,plain,
! [SV750: $i,SV111: $i] :
( ( ~ ( class_Lattices_Olattice @ SV111 )
| ! [SY4281: $i,SY4282: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV750 @ SY4281 @ SV111 ) @ SY4282 @ SV111 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV750 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4281 @ SY4282 @ SV111 ) @ SV111 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2417]) ).
thf(3073,plain,
! [SV751: $i,SV112: $i] :
( ( ~ ( class_Lattices_Olattice @ SV112 )
| ! [SY4283: $i,SY4284: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV751 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4283 @ SY4284 @ SV112 ) @ SV112 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY4283 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV751 @ SY4284 @ SV112 ) @ SV112 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2418]) ).
thf(3074,plain,
! [SV752: $i,SV113: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV113 )
| ! [SY4285: $i,SY4286: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV752 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4285 @ SY4286 @ SV113 ) @ SV113 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY4285 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV752 @ SY4286 @ SV113 ) @ SV113 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2419]) ).
thf(3075,plain,
! [SV753: $i,SV114: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV114 )
| ! [SY4287: $i,SY4288: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV753 @ SY4287 @ SV114 ) @ SY4288 @ SV114 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV753 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4287 @ SY4288 @ SV114 ) @ SV114 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2420]) ).
thf(3076,plain,
! [SV754: $i,SV115: $i] :
( ( ! [SY4289: $i,SY4290: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV115 @ SV754 @ ( tc_fun @ SY4289 @ tc_bool ) ) @ SY4290 @ ( tc_fun @ SY4289 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV115 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV754 @ SY4290 @ ( tc_fun @ SY4289 @ tc_bool ) ) @ ( tc_fun @ SY4289 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2421]) ).
thf(3077,plain,
! [SV755: $i,SV116: $i] :
( ( ! [SY4291: $i,SY4292: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV116 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV755 @ SY4291 @ ( tc_fun @ SY4292 @ tc_bool ) ) @ ( tc_fun @ SY4292 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV755 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV116 @ SY4291 @ ( tc_fun @ SY4292 @ tc_bool ) ) @ ( tc_fun @ SY4292 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2422]) ).
thf(3078,plain,
! [SV117: $i] :
( ( ( ~ ( class_Lattices_Obounded__lattice @ SV117 ) )
= $true )
| ( ( ! [SY2691: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2691 @ ( c_Orderings_Obot__class_Obot @ SV117 ) @ SV117 )
= SY2691 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2423]) ).
thf(3079,plain,
! [SV118: $i] :
( ( ( ~ ( class_Lattices_Obounded__lattice @ SV118 ) )
= $true )
| ( ( ! [SY2692: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ SV118 ) @ SY2692 @ SV118 )
= SY2692 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2424]) ).
thf(3080,plain,
! [SV756: $i,SV119: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV119 @ tc_bool ) ) @ SV756 @ ( tc_fun @ SV119 @ tc_bool ) )
= SV756 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2425]) ).
thf(3081,plain,
! [SV757: $i,SV120: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV120 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV757 @ tc_bool ) ) @ ( tc_fun @ SV757 @ tc_bool ) )
= SV120 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2426]) ).
thf(3082,plain,
! [SV758: $i,SV121: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV121 @ tc_bool ) ) @ SV758 @ ( tc_fun @ SV121 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV121 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2427]) ).
thf(3083,plain,
! [SV759: $i,SV122: $i] :
( ( ! [SY4293: $i,SY4294: $i,SY4295: $i,SY4296: $i] :
( ( c_Product__Type_OSigma @ ( c_Set_Oinsert @ SV122 @ SV759 @ SY4293 ) @ ( c_COMBK @ ( c_Set_Oinsert @ SY4294 @ SY4295 @ SY4296 ) @ ( tc_fun @ SY4296 @ tc_bool ) @ SY4293 ) @ SY4293 @ SY4296 )
= ( c_Set_Oinsert @ ( c_Pair @ SV122 @ SY4294 @ SY4293 @ SY4296 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Product__Type_OSigma @ SV759 @ ( c_COMBK @ ( c_Set_Oinsert @ SY4294 @ SY4295 @ SY4296 ) @ ( tc_fun @ SY4296 @ tc_bool ) @ SY4293 ) @ SY4293 @ SY4296 ) @ ( c_Product__Type_OSigma @ ( c_Set_Oinsert @ SV122 @ SV759 @ SY4293 ) @ ( c_COMBK @ SY4295 @ ( tc_fun @ SY4296 @ tc_bool ) @ SY4293 ) @ SY4293 @ SY4296 ) @ ( tc_fun @ ( tc_prod @ SY4293 @ SY4296 ) @ tc_bool ) ) @ ( tc_prod @ SY4293 @ SY4296 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2428]) ).
thf(3084,plain,
! [SV760: $i,SV123: $i] :
( ( ( SV123
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV760 @ tc_bool ) ) )
| ! [SY4297: $i] :
( ~ ( c_lessequals @ SV123 @ ( c_Relation_OImage @ SY4297 @ SV123 @ SV760 @ SV760 ) @ ( tc_fun @ SV760 @ tc_bool ) )
| ~ ( c_Wellfounded_Owf @ SY4297 @ SV760 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2429]) ).
thf(3085,plain,
! [SV761: $i,SV124: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV124 @ tc_bool ) ) @ SV761 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2430]) ).
thf(3086,plain,
! [SV762: $i,SV125: $i] :
( ( ! [SY4298: $i,SY4299: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV125 @ ( c_HOL_Ominus__class_Ominus @ SV762 @ SY4298 @ ( tc_fun @ SY4299 @ tc_bool ) ) @ ( tc_fun @ SY4299 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV125 @ SV762 @ ( tc_fun @ SY4299 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV125 @ SY4298 @ ( tc_fun @ SY4299 @ tc_bool ) ) @ ( tc_fun @ SY4299 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2431]) ).
thf(3087,plain,
! [SV763: $i,SV126: $i] :
( ( ! [SY4300: $i,SY4301: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_HOL_Ominus__class_Ominus @ SV126 @ SV763 @ ( tc_fun @ SY4300 @ tc_bool ) ) @ SY4301 @ ( tc_fun @ SY4300 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV126 @ SY4301 @ ( tc_fun @ SY4300 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV763 @ SY4301 @ ( tc_fun @ SY4300 @ tc_bool ) ) @ ( tc_fun @ SY4300 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2432]) ).
thf(3088,plain,
! [SV764: $i,SV127: $i] :
( ( ! [SY4302: $i,SY4303: $i] :
( ( ( c_Set_Oimage @ ( c_COMBK @ SV127 @ SV764 @ SY4302 ) @ SY4303 @ SY4302 @ SV764 )
= ( c_Set_Oinsert @ SV127 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV764 @ tc_bool ) ) @ SV764 ) )
| ( SY4303
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4302 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2433]) ).
thf(3089,plain,
! [SV765: $i,SV128: $i] :
( ( ! [SY4304: $i,SY4305: $i,SY4306: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV128 @ SV765 @ ( tc_fun @ SY4304 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SY4305 @ SY4306 @ ( tc_fun @ SY4304 @ tc_bool ) ) @ ( tc_fun @ SY4304 @ tc_bool ) )
| ~ ( c_lessequals @ SY4306 @ SV765 @ ( tc_fun @ SY4304 @ tc_bool ) )
| ~ ( c_lessequals @ SV128 @ SY4305 @ ( tc_fun @ SY4304 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2434]) ).
thf(3090,plain,
! [SV766: $i,SV129: $i] :
( ( ! [SY4307: $i] :
( ~ ( c_in @ SV129 @ SV766 @ SY4307 )
| ! [SY4308: $i] :
( ~ ( c_in @ SV129 @ SY4308 @ SY4307 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SY4308 @ SV766 @ ( tc_fun @ SY4307 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4307 @ tc_bool ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2435]) ).
thf(3091,plain,
! [SV767: $i,SV130: $i] :
( ( ! [SY4309: $i] :
( ( c_Relation_Otrans @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV130 @ SV767 @ ( tc_fun @ ( tc_prod @ SY4309 @ SY4309 ) @ tc_bool ) ) @ SY4309 )
| ~ ( c_Relation_Otrans @ SV767 @ SY4309 )
| ~ ( c_Relation_Otrans @ SV130 @ SY4309 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2436]) ).
thf(3092,plain,
! [SV768: $i,SV131: $i] :
( ( ~ ( class_Lattices_Olattice @ SV131 )
| ! [SY4310: $i,SY4311: $i] : ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV768 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4310 @ SY4311 @ SV131 ) @ SV131 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV768 @ SY4310 @ SV131 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV768 @ SY4311 @ SV131 ) @ SV131 ) @ SV131 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2437]) ).
thf(3093,plain,
! [SV769: $i,SV132: $i] :
( ( ! [SY4312: $i,SY4313: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV132 @ SV769 @ ( tc_fun @ SY4312 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4313 @ SV769 @ ( tc_fun @ SY4312 @ tc_bool ) ) @ ( tc_fun @ SY4312 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV132 @ SV769 @ ( tc_fun @ SY4312 @ tc_bool ) ) @ SY4313 @ ( tc_fun @ SY4312 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2438]) ).
thf(3094,plain,
! [SV133: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV133 ) )
= $true )
| ( ( ! [SY2728: $i,SY2729: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2728 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2728 @ SY2729 @ SV133 ) @ SV133 )
= SY2728 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2439]) ).
thf(3095,plain,
! [SV770: $i,SV134: $i] :
( ( ! [SY4314: $i] :
( ( ( c_Relation_Orel__comp @ SV134 @ SV770 @ SY4314 @ SY4314 @ SY4314 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SY4314 @ SY4314 ) @ tc_bool ) ) )
| ! [SY4315: $i] :
( ( ( c_Relation_Orel__comp @ SY4315 @ SV770 @ SY4314 @ SY4314 @ SY4314 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SY4314 @ SY4314 ) @ tc_bool ) ) )
| ( ( c_Relation_Orel__comp @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4315 @ SV134 @ ( tc_fun @ ( tc_prod @ SY4314 @ SY4314 ) @ tc_bool ) ) @ SV770 @ SY4314 @ SY4314 @ SY4314 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SY4314 @ SY4314 ) @ tc_bool ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2440]) ).
thf(3096,plain,
! [SV771: $i,SV135: $i] :
( ( ! [SY4316: $i] :
( ( ( c_Relation_Orel__comp @ SV135 @ SV771 @ SY4316 @ SY4316 @ SY4316 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SY4316 @ SY4316 ) @ tc_bool ) ) )
| ! [SY4317: $i] :
( ( ( c_Relation_Orel__comp @ SV135 @ SY4317 @ SY4316 @ SY4316 @ SY4316 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SY4316 @ SY4316 ) @ tc_bool ) ) )
| ( ( c_Relation_Orel__comp @ SV135 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4317 @ SV771 @ ( tc_fun @ ( tc_prod @ SY4316 @ SY4316 ) @ tc_bool ) ) @ SY4316 @ SY4316 @ SY4316 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SY4316 @ SY4316 ) @ tc_bool ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2441]) ).
thf(3097,plain,
! [SV772: $i,SV136: $i] :
( ( ( hBOOL @ ( hAPP @ SV136 @ SV772 ) )
| ! [SY2737: $i,SY2738: $i] :
( ~ ( hBOOL @ ( hAPP @ SV136 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1 @ SV136 @ SY2737 @ SY2738 ) ) )
| ~ ( c_Wellfounded_Owf @ SY2737 @ SY2738 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2442]) ).
thf(3098,plain,
! [SV773: $i,SV137: $i] :
( ( ( c_Wellfounded_Oacyclic @ SV137 @ SV773 )
| ~ ( c_Wellfounded_Oacyclic @ ( c_Relation_Oconverse @ SV137 @ SV773 @ SV773 ) @ SV773 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2443]) ).
thf(3099,plain,
! [SV774: $i,SV138: $i] :
( ( ( c_Wellfounded_Oacyclic @ ( c_Relation_Oconverse @ SV138 @ SV774 @ SV774 ) @ SV774 )
| ~ ( c_Wellfounded_Oacyclic @ SV138 @ SV774 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2444]) ).
thf(3100,plain,
! [SV775: $i,SV139: $i] :
( ( ( SV139 = SV775 )
| ! [SY4320: $i] :
( ~ ( c_lessequals @ SV775 @ SV139 @ ( tc_fun @ SY4320 @ tc_bool ) )
| ~ ( c_lessequals @ SV139 @ SV775 @ ( tc_fun @ SY4320 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2445]) ).
thf(3101,plain,
! [SV776: $i,SV140: $i] :
( ( ( SV140 = SV776 )
| ! [SY4321: $i] :
( ~ ( c_lessequals @ SV776 @ SV140 @ ( tc_fun @ SY4321 @ tc_bool ) )
| ~ ( c_lessequals @ SV140 @ SV776 @ ( tc_fun @ SY4321 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2446]) ).
thf(3102,plain,
! [SV141: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV141 ) )
= $true )
| ( ( ! [SY2745: $i,SY2746: $i] :
( ( SY2745 = SY2746 )
| ~ ( c_lessequals @ SY2746 @ SY2745 @ SV141 )
| ~ ( c_lessequals @ SY2745 @ SY2746 @ SV141 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2447]) ).
thf(3103,plain,
! [SV142: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV142 ) )
= $true )
| ( ( ! [SY2747: $i,SY2748: $i] :
( ( SY2747 = SY2748 )
| ~ ( c_lessequals @ SY2748 @ SY2747 @ SV142 )
| ~ ( c_lessequals @ SY2747 @ SY2748 @ SV142 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2448]) ).
thf(3104,plain,
! [SV777: $i,SV143: $i] :
( ( ! [SY4322: $i,SY4323: $i,SY4324: $i] :
( ( hAPP @ ( c_split @ SV143 @ SV777 @ SY4322 @ SY4323 ) @ SY4324 )
= ( hAPP @ ( hAPP @ SV143 @ ( hAPP @ ( c_fst @ SV777 @ SY4322 ) @ SY4324 ) ) @ ( hAPP @ ( c_snd @ SV777 @ SY4322 ) @ SY4324 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2449]) ).
thf(3105,plain,
! [SV144: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV144 ) )
= $true )
| ( ( ! [SY2753: $i,SY2754: $i] :
( ( SY2753 = SY2754 )
| ~ ( c_lessequals @ SY2753 @ SY2754 @ SV144 )
| ~ ( c_lessequals @ SY2754 @ SY2753 @ SV144 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2450]) ).
thf(3106,plain,
! [SV145: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV145 ) )
= $true )
| ( ( ! [SY2755: $i,SY2756: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY2755 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2755 @ SY2756 @ SV145 ) @ SV145 )
= SY2755 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2451]) ).
thf(3107,plain,
! [SV778: $i,SV146: $i] :
( ( ! [SY4325: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ SV146 @ SV778 @ ( tc_fun @ SY4325 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV146 @ SV778 @ ( tc_fun @ SY4325 @ tc_bool ) ) @ ( tc_fun @ SY4325 @ tc_bool ) )
= SV146 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2452]) ).
thf(3108,plain,
! [SV147: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV147 ) )
= $true )
| ( ( ! [SY2759: $i,SY2760: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2759 @ SY2760 @ SV147 )
= SY2759 )
| ~ ( c_lessequals @ SY2760 @ SY2759 @ SV147 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2453]) ).
thf(3109,plain,
! [SV148: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV148 ) )
= $true )
| ( ( ! [SY2761: $i,SY2762: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2761 @ SY2762 @ SV148 )
!= SY2762 )
| ( c_lessequals @ SY2761 @ SY2762 @ SV148 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2454]) ).
thf(3110,plain,
! [SV149: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV149 ) )
= $true )
| ( ( ! [SY2763: $i,SY2764: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2763 @ SY2764 @ SV149 )
= SY2764 )
| ~ ( c_lessequals @ SY2763 @ SY2764 @ SV149 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2455]) ).
thf(3111,plain,
! [SV779: $i,SV150: $i] :
( ( ! [SY4326: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV150 @ SV779 @ ( tc_fun @ SY4326 @ tc_bool ) )
= SV779 )
| ~ ( c_lessequals @ SV150 @ SV779 @ ( tc_fun @ SY4326 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2456]) ).
thf(3112,plain,
! [SV780: $i,SV151: $i] :
( ( ! [SY4327: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV151 @ SV780 @ ( tc_fun @ SY4327 @ tc_bool ) )
= SV151 )
| ~ ( c_lessequals @ SV780 @ SV151 @ ( tc_fun @ SY4327 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2457]) ).
thf(3113,plain,
! [SV781: $i,SV152: $i] :
( ( ! [SY4328: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV152 @ SV781 @ ( tc_fun @ SY4328 @ tc_bool ) )
!= SV781 )
| ( c_lessequals @ SV152 @ SV781 @ ( tc_fun @ SY4328 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2458]) ).
thf(3114,plain,
! [SV782: $i,SV153: $i] :
( ( ! [SY4329: $i,SY4330: $i,SY4331: $i] :
( ( c_Relation_Orefl__on @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV153 @ SV782 @ ( tc_fun @ SY4329 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4330 @ SY4331 @ ( tc_fun @ ( tc_prod @ SY4329 @ SY4329 ) @ tc_bool ) ) @ SY4329 )
| ~ ( c_Relation_Orefl__on @ SV782 @ SY4331 @ SY4329 )
| ~ ( c_Relation_Orefl__on @ SV153 @ SY4330 @ SY4329 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2459]) ).
thf(3115,plain,
! [SV783: $i,SV155: $i] :
( ( ( c_Relation_ORange @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV155 @ SV783 ) @ tc_bool ) ) @ SV155 @ SV783 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV783 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2461]) ).
thf(3116,plain,
! [SV784: $i,SV156: $i] :
( ( ! [SY4332: $i,SY4333: $i,SY4334: $i] :
( ( ( c_Set_Oinsert @ SV156 @ ( c_Set_Oinsert @ SV784 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4332 @ tc_bool ) ) @ SY4332 ) @ SY4332 )
!= ( c_Set_Oinsert @ SY4333 @ ( c_Set_Oinsert @ SY4334 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4332 @ tc_bool ) ) @ SY4332 ) @ SY4332 ) )
| ( SV156 = SY4334 )
| ( SV156 = SY4333 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2462]) ).
thf(3117,plain,
! [SV785: $i,SV157: $i] :
( ( ! [SY4335: $i,SY4336: $i] :
( ! [SY4337: $i] :
( ( c_Set_Oinsert @ SV157 @ ( c_Set_Oinsert @ SV785 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4335 @ tc_bool ) ) @ SY4335 ) @ SY4335 )
!= ( c_Set_Oinsert @ SY4336 @ ( c_Set_Oinsert @ SY4337 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4335 @ tc_bool ) ) @ SY4335 ) @ SY4335 ) )
| ( SV785 = SY4336 )
| ( SV157 = SY4336 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2463]) ).
thf(3118,plain,
! [SV786: $i,SV158: $i] :
( ( ! [SY4338: $i,SY4339: $i,SY4340: $i] :
( ( ( c_Set_Oinsert @ SV158 @ ( c_Set_Oinsert @ SV786 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4338 @ tc_bool ) ) @ SY4338 ) @ SY4338 )
!= ( c_Set_Oinsert @ SY4339 @ ( c_Set_Oinsert @ SY4340 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4338 @ tc_bool ) ) @ SY4338 ) @ SY4338 ) )
| ( SV158 = SY4340 )
| ( SV786 = SY4340 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2464]) ).
thf(3119,plain,
! [SV787: $i,SV159: $i] :
( ( ! [SY4341: $i,SY4342: $i,SY4343: $i] :
( ( ( c_Set_Oinsert @ SV159 @ ( c_Set_Oinsert @ SV787 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4341 @ tc_bool ) ) @ SY4341 ) @ SY4341 )
!= ( c_Set_Oinsert @ SY4342 @ ( c_Set_Oinsert @ SY4343 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4341 @ tc_bool ) ) @ SY4341 ) @ SY4341 ) )
| ( SV787 = SY4342 )
| ( SV787 = SY4343 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2465]) ).
thf(3120,plain,
! [SV788: $i,SV160: $i] :
( ( ! [SY4344: $i] :
( ( c_lessequals @ ( c_Transitive__Closure_Otrancl @ SV160 @ SV788 ) @ ( c_Product__Type_OSigma @ SY4344 @ ( c_COMBK @ SY4344 @ ( tc_fun @ SV788 @ tc_bool ) @ SV788 ) @ SV788 @ SV788 ) @ ( tc_fun @ ( tc_prod @ SV788 @ SV788 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV160 @ ( c_Product__Type_OSigma @ SY4344 @ ( c_COMBK @ SY4344 @ ( tc_fun @ SV788 @ tc_bool ) @ SV788 ) @ SV788 @ SV788 ) @ ( tc_fun @ ( tc_prod @ SV788 @ SV788 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2466]) ).
thf(3121,plain,
! [SV789: $i,SV161: $i] :
( ( ! [SY4345: $i] :
( ( c_lessequals @ ( c_Transitive__Closure_Ortrancl @ SV161 @ SV789 ) @ ( c_Transitive__Closure_Ortrancl @ SY4345 @ SV789 ) @ ( tc_fun @ ( tc_prod @ SV789 @ SV789 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV161 @ ( c_Transitive__Closure_Ortrancl @ SY4345 @ SV789 ) @ ( tc_fun @ ( tc_prod @ SV789 @ SV789 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2467]) ).
thf(3122,plain,
! [SV790: $i,SV162: $i] :
( ( ( SV162
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV790 @ tc_bool ) ) )
| ~ ( c_lessequals @ SV162 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV790 @ tc_bool ) ) @ ( tc_fun @ SV790 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2468]) ).
thf(3123,plain,
! [SV791: $i,SV164: $i] :
( ( ! [SY4346: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV164 @ tc_bool ) )
!= ( c_Set_Oinsert @ SV791 @ SY4346 @ SV164 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2470]) ).
thf(3124,plain,
! [SV792: $i,SV166: $i] :
( ( ! [SY4347: $i,SY4348: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ SV166 @ SV792 @ SY4347 ) @ SY4348 @ ( tc_fun @ SY4347 @ tc_bool ) )
= ( c_Set_Oinsert @ SV166 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV792 @ SY4348 @ ( tc_fun @ SY4347 @ tc_bool ) ) @ SY4347 ) )
| ~ ( c_in @ SV166 @ SY4348 @ SY4347 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2472]) ).
thf(3125,plain,
! [SV793: $i,SV167: $i] :
( ( ! [SY4349: $i,SY4350: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV167 @ ( c_Set_Oinsert @ SV793 @ SY4349 @ SY4350 ) @ ( tc_fun @ SY4350 @ tc_bool ) )
= ( c_Set_Oinsert @ SV793 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV167 @ SY4349 @ ( tc_fun @ SY4350 @ tc_bool ) ) @ SY4350 ) )
| ~ ( c_in @ SV793 @ SV167 @ SY4350 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2473]) ).
thf(3126,plain,
! [SV794: $i,SV168: $i] :
( ( ! [SY4351: $i,SY4352: $i,SY4353: $i] :
( ( c_Set_Oimage @ SV168 @ ( c_Set_Oinsert @ SV794 @ SY4351 @ SY4352 ) @ SY4352 @ SY4353 )
= ( c_Set_Oinsert @ ( hAPP @ SV168 @ SV794 ) @ ( c_Set_Oimage @ SV168 @ SY4351 @ SY4352 @ SY4353 ) @ SY4353 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2474]) ).
thf(3127,plain,
! [SV795: $i,SV169: $i] :
( ( c_Relation_Ototal__on @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV169 @ tc_bool ) ) @ SV795 @ SV169 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2475]) ).
thf(3128,plain,
! [SV796: $i,SV170: $i] :
( ( ! [SY4354: $i,SY4355: $i,SY4356: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV170 @ SV796 @ ( tc_fun @ SY4354 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4355 @ SY4356 @ ( tc_fun @ SY4354 @ tc_bool ) ) @ ( tc_fun @ SY4354 @ tc_bool ) )
| ~ ( c_lessequals @ SV796 @ SY4356 @ ( tc_fun @ SY4354 @ tc_bool ) )
| ~ ( c_lessequals @ SV170 @ SY4355 @ ( tc_fun @ SY4354 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2476]) ).
thf(3129,plain,
! [SV797: $i,SV171: $i] :
( ( ! [SY4357: $i,SY4358: $i] :
( ( c_Relation_Oconverse @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV171 @ SV797 @ ( tc_fun @ ( tc_prod @ SY4357 @ SY4358 ) @ tc_bool ) ) @ SY4357 @ SY4358 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Oconverse @ SV171 @ SY4357 @ SY4358 ) @ ( c_Relation_Oconverse @ SV797 @ SY4357 @ SY4358 ) @ ( tc_fun @ ( tc_prod @ SY4358 @ SY4357 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2477]) ).
thf(3130,plain,
! [SV172: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV172 ) )
= $true )
| ( ( ! [SY2817: $i,SY2818: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2817 @ SY2818 @ SV172 ) @ SY2817 @ SV172 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2478]) ).
thf(3131,plain,
! [SV173: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV173 ) )
= $true )
| ( ( ! [SY2819: $i,SY2820: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2819 @ SY2820 @ SV173 ) @ SY2820 @ SV173 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2479]) ).
thf(3132,plain,
! [SV798: $i,SV174: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV174 )
| ! [SY4359: $i,SY4360: $i] :
( ( c_lessequals @ SV798 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4359 @ SY4360 @ SV174 ) @ SV174 )
| ~ ( c_lessequals @ SV798 @ SY4360 @ SV174 )
| ~ ( c_lessequals @ SV798 @ SY4359 @ SV174 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2480]) ).
thf(3133,plain,
! [SV799: $i,SV175: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV175 )
| ! [SY4361: $i,SY4362: $i] :
( ( c_lessequals @ SV799 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4361 @ SY4362 @ SV175 ) @ SV175 )
| ~ ( c_lessequals @ SV799 @ SY4362 @ SV175 )
| ~ ( c_lessequals @ SV799 @ SY4361 @ SV175 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2481]) ).
thf(3134,plain,
! [SV800: $i,SV176: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV176 )
| ! [SY4363: $i,SY4364: $i] :
( ( c_lessequals @ SV800 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4363 @ SY4364 @ SV176 ) @ SV176 )
| ~ ( c_lessequals @ SV800 @ SY4364 @ SV176 )
| ~ ( c_lessequals @ SV800 @ SY4363 @ SV176 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2482]) ).
thf(3135,plain,
! [SV177: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV177 ) )
= $true )
| ( ( ! [SY2830: $i,SY2831: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2830 @ SY2831 @ SV177 ) @ SY2831 @ SV177 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2483]) ).
thf(3136,plain,
! [SV178: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV178 ) )
= $true )
| ( ( ! [SY2832: $i,SY2833: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2832 @ SY2833 @ SV178 ) @ SY2832 @ SV178 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2484]) ).
thf(3137,plain,
! [SV801: $i,SV179: $i] :
( ( ! [SY4365: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV179 @ SV801 @ ( tc_fun @ SY4365 @ tc_bool ) ) @ SV179 @ ( tc_fun @ SY4365 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2485]) ).
thf(3138,plain,
! [SV802: $i,SV180: $i] :
( ( ! [SY4366: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV180 @ SV802 @ ( tc_fun @ SY4366 @ tc_bool ) ) @ SV802 @ ( tc_fun @ SY4366 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2486]) ).
thf(3139,plain,
! [SV803: $i,SV181: $i] :
( ( ! [SY4367: $i,SY4368: $i] :
( ( c_lessequals @ SV181 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV803 @ SY4367 @ ( tc_fun @ SY4368 @ tc_bool ) ) @ ( tc_fun @ SY4368 @ tc_bool ) )
| ~ ( c_lessequals @ SV181 @ SY4367 @ ( tc_fun @ SY4368 @ tc_bool ) )
| ~ ( c_lessequals @ SV181 @ SV803 @ ( tc_fun @ SY4368 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2487]) ).
thf(3140,plain,
! [SV804: $i,SV182: $i] :
( ( ! [SY4369: $i,SY4370: $i] :
( ( c_lessequals @ SV182 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV804 @ SY4369 @ ( tc_fun @ SY4370 @ tc_bool ) ) @ ( tc_fun @ SY4370 @ tc_bool ) )
| ~ ( c_lessequals @ SV182 @ SY4369 @ ( tc_fun @ SY4370 @ tc_bool ) )
| ~ ( c_lessequals @ SV182 @ SV804 @ ( tc_fun @ SY4370 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2488]) ).
thf(3141,plain,
! [SV805: $i,SV183: $i] :
( ( ! [SY4371: $i,SY4372: $i,SY4373: $i] :
( ( c_Product__Type_OSigma @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV183 @ SV805 @ ( tc_fun @ SY4371 @ tc_bool ) ) @ ( c_COMBK @ SY4372 @ ( tc_fun @ SY4373 @ tc_bool ) @ SY4371 ) @ SY4371 @ SY4373 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Product__Type_OSigma @ SV183 @ ( c_COMBK @ SY4372 @ ( tc_fun @ SY4373 @ tc_bool ) @ SY4371 ) @ SY4371 @ SY4373 ) @ ( c_Product__Type_OSigma @ SV805 @ ( c_COMBK @ SY4372 @ ( tc_fun @ SY4373 @ tc_bool ) @ SY4371 ) @ SY4371 @ SY4373 ) @ ( tc_fun @ ( tc_prod @ SY4371 @ SY4373 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2489]) ).
thf(3142,plain,
! [SV806: $i,SV184: $i] :
( ( ~ ( class_Lattices_Olattice @ SV184 )
| ! [SY4374: $i,SY4375: $i] : ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV806 @ SY4374 @ SV184 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV806 @ SY4375 @ SV184 ) @ SV184 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV806 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4374 @ SY4375 @ SV184 ) @ SV184 ) @ SV184 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2490]) ).
thf(3143,plain,
! [SV807: $i,SV185: $i] :
( ( ! [SY4376: $i] :
( ( ( c_Transitive__Closure_Ortrancl @ SV185 @ SV807 )
= ( c_Transitive__Closure_Ortrancl @ SY4376 @ SV807 ) )
| ~ ( c_lessequals @ SV185 @ ( c_Transitive__Closure_Ortrancl @ SY4376 @ SV807 ) @ ( tc_fun @ ( tc_prod @ SV807 @ SV807 ) @ tc_bool ) )
| ~ ( c_lessequals @ SY4376 @ SV185 @ ( tc_fun @ ( tc_prod @ SV807 @ SV807 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2491]) ).
thf(3144,plain,
! [SV808: $i,SV186: $i] :
( ( ! [SY4377: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV186 @ SV808 @ ( tc_fun @ SY4377 @ tc_bool ) ) @ SV186 @ ( tc_fun @ SY4377 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2492]) ).
thf(3145,plain,
! [SV809: $i,SV187: $i] :
( ( ! [SY4378: $i] :
( ( c_Set_Oinsert @ SV187 @ ( c_HOL_Ominus__class_Ominus @ SV809 @ ( c_Set_Oinsert @ SV187 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4378 @ tc_bool ) ) @ SY4378 ) @ ( tc_fun @ SY4378 @ tc_bool ) ) @ SY4378 )
= ( c_Set_Oinsert @ SV187 @ SV809 @ SY4378 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2493]) ).
thf(3146,plain,
! [SV810: $i,SV188: $i] :
( ( ! [SY4379: $i] :
( ( ( c_Set_Oinsert @ SV188 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV810 @ tc_bool ) ) @ SV810 )
!= ( c_Set_Oinsert @ SY4379 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV810 @ tc_bool ) ) @ SV810 ) )
| ( SV188 = SY4379 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2494]) ).
thf(3147,plain,
! [SV811: $i,SV189: $i] :
( ( ! [SY4380: $i,SY4381: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV189 @ SV811 @ ( tc_fun @ SY4380 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV811 @ SY4381 @ ( tc_fun @ SY4380 @ tc_bool ) ) @ ( tc_fun @ SY4380 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4381 @ SV189 @ ( tc_fun @ SY4380 @ tc_bool ) ) @ ( tc_fun @ SY4380 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV189 @ SV811 @ ( tc_fun @ SY4380 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV811 @ SY4381 @ ( tc_fun @ SY4380 @ tc_bool ) ) @ ( tc_fun @ SY4380 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4381 @ SV189 @ ( tc_fun @ SY4380 @ tc_bool ) ) @ ( tc_fun @ SY4380 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2495]) ).
thf(3148,plain,
! [SV812: $i,SV191: $i] :
( ( ! [SY4382: $i] :
( ( c_Set_Oimage @ ( c_COMBK @ SV191 @ SV812 @ SY4382 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4382 @ tc_bool ) ) @ SY4382 @ SV812 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV812 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2497]) ).
thf(3149,plain,
! [SV813: $i,SV192: $i] :
( ( ! [SY4383: $i] :
( ( ( c_Set_Oinsert @ SV192 @ SV813 @ SY4383 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4383 @ tc_bool ) ) )
| ( c_in @ SV192 @ SV813 @ SY4383 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2498]) ).
thf(3150,plain,
! [SV814: $i,SV194: $i] :
( ( ! [SY4384: $i] :
( ( c_in @ SV194 @ SV814 @ SY4384 )
| ! [SY4385: $i] :
~ ( c_lessequals @ ( c_Set_Oinsert @ SV194 @ SY4385 @ SY4384 ) @ SV814 @ ( tc_fun @ SY4384 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2500]) ).
thf(3151,plain,
! [SV815: $i,SV195: $i] :
( ( ! [SY4386: $i,SY4387: $i,SY4388: $i] :
( ( c_Product__Type_OSigma @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV195 @ SV815 @ ( tc_fun @ SY4386 @ tc_bool ) ) @ SY4387 @ SY4386 @ SY4388 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Product__Type_OSigma @ SV195 @ SY4387 @ SY4386 @ SY4388 ) @ ( c_Product__Type_OSigma @ SV815 @ SY4387 @ SY4386 @ SY4388 ) @ ( tc_fun @ ( tc_prod @ SY4386 @ SY4388 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2501]) ).
thf(3152,plain,
! [SV816: $i,SV196: $i] :
( ( ! [SY4389: $i,SY4390: $i] :
( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV196 @ SV816 @ SY4389 ) @ SY4390 ) )
| ~ ( hBOOL @ ( hAPP @ SV816 @ SY4390 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2502]) ).
thf(3153,plain,
! [SV817: $i,SV197: $i] :
( ( ! [SY4391: $i,SY4392: $i] :
( ( c_lessequals @ SV197 @ ( c_Set_Oinsert @ SV817 @ SY4391 @ SY4392 ) @ ( tc_fun @ SY4392 @ tc_bool ) )
| ~ ( c_lessequals @ SV197 @ SY4391 @ ( tc_fun @ SY4392 @ tc_bool ) )
| ( c_in @ SV817 @ SV197 @ SY4392 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2503]) ).
thf(3154,plain,
! [SV818: $i,SV198: $i] :
( ( ! [SY4393: $i] :
( ( c_lessequals @ SV198 @ SV818 @ ( tc_fun @ SY4393 @ tc_bool ) )
| ! [SY4394: $i] :
( ( c_in @ SY4394 @ SV198 @ SY4393 )
| ~ ( c_lessequals @ SV198 @ ( c_Set_Oinsert @ SY4394 @ SV818 @ SY4393 ) @ ( tc_fun @ SY4393 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2504]) ).
thf(3155,plain,
! [SV819: $i,SV199: $i] :
( ( ! [SY4395: $i,SY4396: $i] :
( ( c_lessequals @ SV199 @ ( c_Set_Oinsert @ SV819 @ SY4395 @ SY4396 ) @ ( tc_fun @ SY4396 @ tc_bool ) )
| ~ ( c_lessequals @ SV199 @ SY4395 @ ( tc_fun @ SY4396 @ tc_bool ) )
| ( c_in @ SV819 @ SV199 @ SY4396 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2505]) ).
thf(3156,plain,
! [SV820: $i,SV200: $i] :
( ( ! [SY4397: $i] :
( ( c_lessequals @ SV200 @ SV820 @ ( tc_fun @ SY4397 @ tc_bool ) )
| ! [SY4398: $i] :
( ~ ( c_lessequals @ SV200 @ ( c_Set_Oinsert @ SY4398 @ SV820 @ SY4397 ) @ ( tc_fun @ SY4397 @ tc_bool ) )
| ( c_in @ SY4398 @ SV200 @ SY4397 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2506]) ).
thf(3157,plain,
! [SV821: $i,SV201: $i] :
( ( ! [SY4399: $i,SY4400: $i] :
( ( c_Relation_Oconverse @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV201 @ SV821 @ ( tc_fun @ ( tc_prod @ SY4399 @ SY4400 ) @ tc_bool ) ) @ SY4399 @ SY4400 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_Oconverse @ SV201 @ SY4399 @ SY4400 ) @ ( c_Relation_Oconverse @ SV821 @ SY4399 @ SY4400 ) @ ( tc_fun @ ( tc_prod @ SY4400 @ SY4399 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2507]) ).
thf(3158,plain,
! [SV822: $i,SV202: $i] :
( ( ! [SY4401: $i,SY4402: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV202 @ ( c_Set_Oinsert @ SV822 @ SY4401 @ SY4402 ) @ ( tc_fun @ SY4402 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV202 @ SY4401 @ ( tc_fun @ SY4402 @ tc_bool ) ) )
| ( c_in @ SV822 @ SV202 @ SY4402 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2508]) ).
thf(3159,plain,
! [SV823: $i,SV203: $i] :
( ( ! [SY4403: $i,SY4404: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ SV203 @ SV823 @ SY4403 ) @ SY4404 @ ( tc_fun @ SY4403 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV823 @ SY4404 @ ( tc_fun @ SY4403 @ tc_bool ) ) )
| ( c_in @ SV203 @ SY4404 @ SY4403 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2509]) ).
thf(3160,plain,
! [SV824: $i,SV204: $i] :
( ( ! [SY4405: $i] :
( ( c_Relation_Ototal__on @ SV204 @ SV824 @ SY4405 )
| ~ ( c_Order__Relation_Ostrict__linear__order__on @ SV204 @ SV824 @ SY4405 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2510]) ).
thf(3161,plain,
! [SV825: $i,SV205: $i] :
( ( ! [SY4406: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV205 @ SV825 @ ( tc_fun @ SY4406 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4406 @ tc_bool ) ) )
| ( SV825
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4406 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2511]) ).
thf(3162,plain,
! [SV826: $i,SV206: $i] :
( ( ! [SY4407: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV206 @ SV826 @ ( tc_fun @ SY4407 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4407 @ tc_bool ) ) )
| ( SV206
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4407 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2512]) ).
thf(3163,plain,
! [SV207: $i] :
( ( ( ~ ( class_Lattices_Obounded__lattice @ SV207 ) )
= $true )
| ( ( ! [SY2903: $i] :
( ! [SY2904: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2903 @ SY2904 @ SV207 )
!= ( c_Orderings_Obot__class_Obot @ SV207 ) )
| ( SY2903
= ( c_Orderings_Obot__class_Obot @ SV207 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2513]) ).
thf(3164,plain,
! [SV208: $i] :
( ( ( ~ ( class_Lattices_Obounded__lattice @ SV208 ) )
= $true )
| ( ( ! [SY2905: $i,SY2906: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2905 @ SY2906 @ SV208 )
!= ( c_Orderings_Obot__class_Obot @ SV208 ) )
| ( SY2906
= ( c_Orderings_Obot__class_Obot @ SV208 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2514]) ).
thf(3165,plain,
! [SV827: $i,SV209: $i] :
( ( ! [SY4408: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ SV209 @ SV827 @ ( tc_fun @ SY4408 @ tc_bool ) ) @ SV827 @ ( tc_fun @ SY4408 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV209 @ SV827 @ ( tc_fun @ SY4408 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2515]) ).
thf(3166,plain,
! [SV828: $i,SV210: $i] :
( ( ! [SY4409: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV210 @ ( c_HOL_Ominus__class_Ominus @ SV828 @ SV210 @ ( tc_fun @ SY4409 @ tc_bool ) ) @ ( tc_fun @ SY4409 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV210 @ SV828 @ ( tc_fun @ SY4409 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2516]) ).
thf(3167,plain,
! [SV829: $i,SV211: $i] :
( ( ! [SY4410: $i,SY4411: $i,SY4412: $i,SY4413: $i] :
( ( c_Relation_Orel__comp @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV211 @ SV829 @ ( tc_fun @ ( tc_prod @ SY4410 @ SY4411 ) @ tc_bool ) ) @ SY4412 @ SY4410 @ SY4411 @ SY4413 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ SV211 @ SY4412 @ SY4410 @ SY4411 @ SY4413 ) @ ( c_Relation_Orel__comp @ SV829 @ SY4412 @ SY4410 @ SY4411 @ SY4413 ) @ ( tc_fun @ ( tc_prod @ SY4410 @ SY4413 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2517]) ).
thf(3168,plain,
! [SV830: $i,SV212: $i] :
( ( ! [SY4414: $i,SY4415: $i,SY4416: $i,SY4417: $i] :
( ( c_Relation_Orel__comp @ SV212 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV830 @ SY4414 @ ( tc_fun @ ( tc_prod @ SY4415 @ SY4416 ) @ tc_bool ) ) @ SY4417 @ SY4415 @ SY4416 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ SV212 @ SV830 @ SY4417 @ SY4415 @ SY4416 ) @ ( c_Relation_Orel__comp @ SV212 @ SY4414 @ SY4417 @ SY4415 @ SY4416 ) @ ( tc_fun @ ( tc_prod @ SY4417 @ SY4416 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2518]) ).
thf(3169,plain,
! [SV831: $i,SV213: $i] :
( ( ! [SY4418: $i] :
( ( c_lessequals @ SV213 @ SV831 @ ( tc_fun @ SY4418 @ tc_bool ) )
| ! [SY4419: $i] :
~ ( c_lessequals @ SV213 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4419 @ SV831 @ ( tc_fun @ SY4418 @ tc_bool ) ) @ ( tc_fun @ SY4418 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2519]) ).
thf(3170,plain,
! [SV832: $i,SV214: $i] :
( ( ! [SY4420: $i] :
( ( c_lessequals @ SV214 @ SV832 @ ( tc_fun @ SY4420 @ tc_bool ) )
| ! [SY4421: $i] :
~ ( c_lessequals @ SV214 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV832 @ SY4421 @ ( tc_fun @ SY4420 @ tc_bool ) ) @ ( tc_fun @ SY4420 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2520]) ).
thf(3171,plain,
! [SV833: $i,SV215: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV215 )
| ! [SY4422: $i] :
( ( c_lessequals @ SV833 @ SY4422 @ SV215 )
| ! [SY4423: $i] :
~ ( c_lessequals @ SV833 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4422 @ SY4423 @ SV215 ) @ SV215 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2521]) ).
thf(3172,plain,
! [SV834: $i,SV216: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV216 )
| ! [SY4424: $i] :
( ( c_lessequals @ SV834 @ SY4424 @ SV216 )
| ! [SY4425: $i] :
~ ( c_lessequals @ SV834 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4425 @ SY4424 @ SV216 ) @ SV216 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2522]) ).
thf(3173,plain,
! [SV835: $i,SV217: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV217 )
| ! [SY4426: $i,SY4427: $i] :
( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV835 @ SY4426 @ SV217 ) @ SY4427 @ SV217 )
| ~ ( c_lessequals @ SV835 @ SY4427 @ SV217 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2523]) ).
thf(3174,plain,
! [SV836: $i,SV218: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV218 )
| ! [SY4428: $i,SY4429: $i] :
( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV836 @ SY4428 @ SV218 ) @ SY4429 @ SV218 )
| ~ ( c_lessequals @ SY4428 @ SY4429 @ SV218 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2524]) ).
thf(3175,plain,
! [SV837: $i,SV219: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV219 )
| ! [SY4430: $i] :
( ( c_lessequals @ SV837 @ SY4430 @ SV219 )
| ! [SY4431: $i] :
~ ( c_lessequals @ SV837 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4430 @ SY4431 @ SV219 ) @ SV219 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2525]) ).
thf(3176,plain,
! [SV838: $i,SV220: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV220 )
| ! [SY4432: $i] :
( ( c_lessequals @ SV838 @ SY4432 @ SV220 )
| ! [SY4433: $i] :
~ ( c_lessequals @ SV838 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4433 @ SY4432 @ SV220 ) @ SV220 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2526]) ).
thf(3177,plain,
! [SV839: $i,SV221: $i] :
( ( ! [SY4434: $i,SY4435: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV221 @ SV839 @ ( tc_fun @ SY4434 @ tc_bool ) ) @ SY4435 @ ( tc_fun @ SY4434 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ SV221 @ SY4435 @ ( tc_fun @ SY4434 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV839 @ SY4435 @ ( tc_fun @ SY4434 @ tc_bool ) ) @ ( tc_fun @ SY4434 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2527]) ).
thf(3178,plain,
! [SV840: $i,SV222: $i] :
( ( ! [SY4436: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV222 @ SV840 @ ( tc_fun @ SY4436 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV840 @ SV222 @ ( tc_fun @ SY4436 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2528]) ).
thf(3179,plain,
! [SV223: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV223 ) )
= $true )
| ( ( ! [SY2950: $i,SY2951: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2950 @ SY2951 @ SV223 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY2951 @ SY2950 @ SV223 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2529]) ).
thf(3180,plain,
! [SV224: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV224 ) )
= $true )
| ( ( ! [SY2952: $i,SY2953: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2952 @ SY2953 @ SV224 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY2953 @ SY2952 @ SV224 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2530]) ).
thf(3181,plain,
! [SV841: $i,SV225: $i] :
( ( ! [SY4437: $i,SY4438: $i] :
( ( c_Relation_ODomain @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV225 @ SV841 @ ( tc_fun @ ( tc_prod @ SY4437 @ SY4438 ) @ tc_bool ) ) @ SY4437 @ SY4438 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_ODomain @ SV225 @ SY4437 @ SY4438 ) @ ( c_Relation_ODomain @ SV841 @ SY4437 @ SY4438 ) @ ( tc_fun @ SY4437 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2531]) ).
thf(3182,plain,
! [SV842: $i,SV226: $i] :
( ( ! [SY4439: $i] :
( ( c_Set_Oinsert @ SV226 @ SV842 @ SY4439 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ SV226 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4439 @ tc_bool ) ) @ SY4439 ) @ SV842 @ ( tc_fun @ SY4439 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2532]) ).
thf(3183,plain,
! [SV843: $i,SV227: $i] :
( ( ! [SY4440: $i] :
( ( c_Product__Type_OSigma @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV227 @ tc_bool ) ) @ SV843 @ SV227 @ SY4440 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV227 @ SY4440 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2533]) ).
thf(3184,plain,
! [SV844: $i,SV228: $i] :
( ( ! [SY4441: $i] :
( ( c_lessequals @ ( c_Wellfounded_Oacc @ SV228 @ SV844 ) @ ( c_Wellfounded_Oacc @ SY4441 @ SV844 ) @ ( tc_fun @ SV844 @ tc_bool ) )
| ~ ( c_lessequals @ SY4441 @ SV228 @ ( tc_fun @ ( tc_prod @ SV844 @ SV844 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2534]) ).
thf(3185,plain,
! [SV845: $i,SV229: $i] :
( ( ! [SY4442: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV229 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV229 @ SV845 @ ( tc_fun @ SY4442 @ tc_bool ) ) @ ( tc_fun @ SY4442 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV229 @ SV845 @ ( tc_fun @ SY4442 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2535]) ).
thf(3186,plain,
! [SV230: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV230 ) )
= $true )
| ( ( ! [SY2965: $i,SY2966: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2965 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2965 @ SY2966 @ SV230 ) @ SV230 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY2965 @ SY2966 @ SV230 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2536]) ).
thf(3187,plain,
! [SV231: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV231 ) )
= $true )
| ( ( ! [SY2967: $i,SY2968: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2967 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2967 @ SY2968 @ SV231 ) @ SV231 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY2967 @ SY2968 @ SV231 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2537]) ).
thf(3188,plain,
! [SV846: $i,SV232: $i] :
( ( ! [SY4443: $i] :
( ( ( c_Relation_ODomain @ SV232 @ SV846 @ SY4443 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV846 @ tc_bool ) ) )
| ( SV232
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV846 @ SY4443 ) @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2538]) ).
thf(3189,plain,
! [SV847: $i,SV233: $i] :
( ( ! [SY4444: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV233 @ tc_bool ) )
= ( c_Set_Oimage @ SV847 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4444 @ tc_bool ) ) @ SY4444 @ SV233 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2539]) ).
thf(3190,plain,
! [SV848: $i,SV234: $i] :
( ( ! [SY4445: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV234 @ ( c_HOL_Ominus__class_Ominus @ SV848 @ SV234 @ ( tc_fun @ SY4445 @ tc_bool ) ) @ ( tc_fun @ SY4445 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4445 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2540]) ).
thf(3191,plain,
! [SV849: $i,SV235: $i] :
( ( ! [SY4446: $i,SY4447: $i] : ( c_lessequals @ ( c_Relation_ORange @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV235 @ SV849 @ ( tc_fun @ ( tc_prod @ SY4446 @ SY4447 ) @ tc_bool ) ) @ SY4446 @ SY4447 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_ORange @ SV235 @ SY4446 @ SY4447 ) @ ( c_Relation_ORange @ SV849 @ SY4446 @ SY4447 ) @ ( tc_fun @ SY4447 @ tc_bool ) ) @ ( tc_fun @ SY4447 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2541]) ).
thf(3192,plain,
! [SV850: $i,SV236: $i] :
( ( ( hBOOL @ ( hAPP @ SV236 @ SV850 ) )
| ! [SY2979: $i,SY2980: $i] :
( ~ ( hBOOL @ ( hAPP @ SV236 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1 @ SV236 @ SY2979 @ SY2980 ) ) )
| ~ ( c_Wellfounded_Owf @ SY2979 @ SY2980 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2542]) ).
thf(3193,plain,
! [SV851: $i,SV237: $i] :
( ( ! [SY4450: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Ortrancl @ SV237 @ SV851 ) @ ( c_Transitive__Closure_Ortrancl @ SY4450 @ SV851 ) @ ( tc_fun @ ( tc_prod @ SV851 @ SV851 ) @ tc_bool ) ) @ SV851 )
= ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV237 @ SY4450 @ ( tc_fun @ ( tc_prod @ SV851 @ SV851 ) @ tc_bool ) ) @ SV851 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2543]) ).
thf(3194,plain,
! [SV852: $i,SV238: $i] :
( ( ! [SY4451: $i,SY4452: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ SV238 @ SV852 @ SY4451 ) @ SY4452 @ ( tc_fun @ SY4451 @ tc_bool ) )
= ( c_Set_Oinsert @ SV238 @ ( c_HOL_Ominus__class_Ominus @ SV852 @ SY4452 @ ( tc_fun @ SY4451 @ tc_bool ) ) @ SY4451 ) )
| ( c_in @ SV238 @ SY4452 @ SY4451 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2544]) ).
thf(3195,plain,
! [SV853: $i,SV239: $i] :
( ( ! [SY4453: $i,SY4454: $i] :
( ( c_lessequals @ SV239 @ ( c_Set_Oinsert @ SV853 @ SY4453 @ SY4454 ) @ ( tc_fun @ SY4454 @ tc_bool ) )
| ~ ( c_lessequals @ SV239 @ SY4453 @ ( tc_fun @ SY4454 @ tc_bool ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV239 @ ( c_Set_Oinsert @ SV853 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4454 @ tc_bool ) ) @ SY4454 ) @ ( tc_fun @ SY4454 @ tc_bool ) ) @ SY4453 @ ( tc_fun @ SY4454 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2545]) ).
thf(3196,plain,
! [SV854: $i,SV240: $i] :
( ( ( hBOOL @ ( hAPP @ SV240 @ SV854 ) )
| ! [SY4455: $i,SY4456: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4455 @ SV240 @ ( tc_fun @ SY4456 @ tc_bool ) ) @ SV854 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2546]) ).
thf(3197,plain,
! [SV855: $i,SV241: $i] :
( ( ( hBOOL @ ( hAPP @ SV241 @ SV855 ) )
| ! [SY4457: $i,SY4458: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV241 @ SY4457 @ ( tc_fun @ SY4458 @ tc_bool ) ) @ SV855 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2547]) ).
thf(3198,plain,
! [SV856: $i,SV242: $i] :
( ( ! [SY4459: $i,SY4460: $i,SY4461: $i] :
( ( c_Relation_ORange @ ( c_Set_Oinsert @ ( c_Pair @ SV242 @ SV856 @ SY4459 @ SY4460 ) @ SY4461 @ ( tc_prod @ SY4459 @ SY4460 ) ) @ SY4459 @ SY4460 )
= ( c_Set_Oinsert @ SV856 @ ( c_Relation_ORange @ SY4461 @ SY4459 @ SY4460 ) @ SY4460 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2548]) ).
thf(3199,plain,
! [SV857: $i,SV243: $i] :
( ( ! [SY4462: $i] :
( ( c_Relation_Osym @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV243 @ SV857 @ ( tc_fun @ ( tc_prod @ SY4462 @ SY4462 ) @ tc_bool ) ) @ SY4462 )
| ~ ( c_Relation_Osym @ SV857 @ SY4462 )
| ~ ( c_Relation_Osym @ SV243 @ SY4462 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2549]) ).
thf(3200,plain,
! [SV858: $i,SV244: $i] :
( ( ! [SY4463: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ SV244 @ SV858 @ SY4463 ) @ ( c_Set_Oinsert @ SV244 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4463 @ tc_bool ) ) @ SY4463 ) @ ( tc_fun @ SY4463 @ tc_bool ) )
= SV858 )
| ( c_in @ SV244 @ SV858 @ SY4463 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2550]) ).
thf(3201,plain,
! [SV859: $i,SV245: $i] :
( ( ! [SY4464: $i,SY4465: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV245 @ SV859 @ ( tc_fun @ SY4464 @ tc_bool ) ) @ SY4465 @ ( tc_fun @ SY4464 @ tc_bool ) )
| ~ ( c_lessequals @ SV245 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV859 @ SY4465 @ ( tc_fun @ SY4464 @ tc_bool ) ) @ ( tc_fun @ SY4464 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2551]) ).
thf(3202,plain,
! [SV860: $i,SV246: $i] :
( ( ! [SY4466: $i,SY4467: $i] :
( ( c_lessequals @ SV246 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV860 @ SY4466 @ ( tc_fun @ SY4467 @ tc_bool ) ) @ ( tc_fun @ SY4467 @ tc_bool ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV246 @ SV860 @ ( tc_fun @ SY4467 @ tc_bool ) ) @ SY4466 @ ( tc_fun @ SY4467 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2552]) ).
thf(3203,plain,
! [SV861: $i,SV247: $i] :
( ( ! [SY4468: $i,SY4469: $i,SY4470: $i,SY4471: $i] :
( ( ( hAPP @ SV247 @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ SV247 @ SV861 @ SY4468 @ SY4469 @ SY4470 @ SY4471 ) )
!= ( hAPP @ SV861 @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ SV247 @ SV861 @ SY4468 @ SY4469 @ SY4470 @ SY4471 ) ) )
| ( ( c_Recdef_Ocut @ SV247 @ SY4468 @ SY4469 @ SY4470 @ SY4471 )
= ( c_Recdef_Ocut @ SV861 @ SY4468 @ SY4469 @ SY4470 @ SY4471 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2553]) ).
thf(3204,plain,
! [SV862: $i,SV248: $i] :
( ( ( c_Wellfounded_Oacyclic @ SV248 @ SV862 )
| ! [SY4472: $i,SY4473: $i] :
~ ( c_Wellfounded_Oacyclic @ ( c_Set_Oinsert @ ( c_Pair @ SY4472 @ SY4473 @ SV862 @ SV862 ) @ SV248 @ ( tc_prod @ SV862 @ SV862 ) ) @ SV862 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2554]) ).
thf(3205,plain,
! [SV863: $i,SV249: $i] :
( ( ! [SY4474: $i] :
( ~ ( class_HOL_Oord @ SV249 )
| ! [SY4475: $i] :
( ( c_lessequals @ ( hAPP @ SV863 @ SY4474 ) @ ( hAPP @ SY4475 @ SY4474 ) @ SV249 )
| ! [SY4476: $i] :
~ ( c_lessequals @ SV863 @ SY4475 @ ( tc_fun @ SY4476 @ SV249 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2555]) ).
thf(3206,plain,
! [SV864: $i,SV250: $i] :
( ( ! [SY4477: $i,SY4478: $i] :
( ( c_in @ SV250 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV864 @ SY4477 @ ( tc_fun @ SY4478 @ tc_bool ) ) @ SY4478 )
| ~ ( c_in @ SV250 @ SY4477 @ SY4478 )
| ~ ( c_in @ SV250 @ SV864 @ SY4478 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2556]) ).
thf(3207,plain,
! [SV865: $i,SV251: $i] :
( ( ! [SY4479: $i,SY4480: $i] :
( ( c_in @ SV251 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV865 @ SY4479 @ ( tc_fun @ SY4480 @ tc_bool ) ) @ SY4480 )
| ~ ( c_in @ SV251 @ SY4479 @ SY4480 )
| ~ ( c_in @ SV251 @ SV865 @ SY4480 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2557]) ).
thf(3208,plain,
! [SV866: $i,SV252: $i] :
( ( ! [SY4481: $i,SY4482: $i] :
( ( c_in @ SV252 @ ( c_Set_Oinsert @ SV866 @ SY4481 @ SY4482 ) @ SY4482 )
| ~ ( c_in @ SV252 @ SY4481 @ SY4482 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2558]) ).
thf(3209,plain,
! [SV867: $i,SV253: $i] :
( ( ! [SY4483: $i,SY4484: $i] :
( ( c_in @ SV253 @ ( c_Set_Oinsert @ SV867 @ SY4483 @ SY4484 ) @ SY4484 )
| ~ ( c_in @ SV253 @ SY4483 @ SY4484 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2559]) ).
thf(3210,plain,
! [SV868: $i,SV254: $i] :
( ( ! [SY4485: $i] :
( ( c_in @ SV254 @ SV868 @ SY4485 )
| ! [SY4486: $i] :
( ~ ( c_in @ SV254 @ SY4486 @ SY4485 )
| ~ ( c_lessequals @ SY4486 @ SV868 @ ( tc_fun @ SY4485 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2560]) ).
thf(3211,plain,
! [SV869: $i,SV255: $i] :
( ( ! [SY4487: $i] :
( ( c_in @ SV255 @ SV869 @ SY4487 )
| ! [SY4488: $i] :
( ~ ( c_lessequals @ SY4488 @ SV869 @ ( tc_fun @ SY4487 @ tc_bool ) )
| ~ ( c_in @ SV255 @ SY4488 @ SY4487 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2561]) ).
thf(3212,plain,
! [SV870: $i,SV256: $i] :
( ( ! [SY4489: $i] :
( ( c_in @ SV256 @ SV870 @ SY4489 )
| ! [SY4490: $i] :
( ~ ( c_in @ SV256 @ SY4490 @ SY4489 )
| ~ ( c_lessequals @ SY4490 @ SV870 @ ( tc_fun @ SY4489 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2562]) ).
thf(3213,plain,
! [SV871: $i,SV257: $i] :
( ( ! [SY4491: $i] :
( ( c_in @ SV257 @ SV871 @ SY4491 )
| ! [SY4492: $i] :
( ~ ( c_in @ SV257 @ SY4492 @ SY4491 )
| ~ ( c_lessequals @ SY4492 @ SV871 @ ( tc_fun @ SY4491 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2563]) ).
thf(3214,plain,
! [SV872: $i,SV258: $i] :
( ( ! [SY4493: $i,SY4494: $i] :
( ( c_in @ SV258 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV872 @ SY4493 @ ( tc_fun @ SY4494 @ tc_bool ) ) @ SY4494 )
| ~ ( c_in @ SV258 @ SV872 @ SY4494 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2564]) ).
thf(3215,plain,
! [SV873: $i,SV259: $i] :
( ( ! [SY4495: $i,SY4496: $i] :
( ( c_in @ SV259 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV873 @ SY4495 @ ( tc_fun @ SY4496 @ tc_bool ) ) @ SY4496 )
| ~ ( c_in @ SV259 @ SY4495 @ SY4496 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2565]) ).
thf(3216,plain,
! [SV874: $i,SV260: $i] :
( ( ~ ( c_in @ SV260 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV874 @ tc_bool ) ) @ SV874 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2566]) ).
thf(3217,plain,
! [SV875: $i,SV261: $i] :
( ( ( hBOOL @ ( hAPP @ SV261 @ SV875 ) )
| ! [SY4497: $i] :
~ ( c_in @ SV875 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4497 @ tc_bool ) ) @ SY4497 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2567]) ).
thf(3218,plain,
! [SV876: $i,SV262: $i] :
( ( ~ ( c_in @ SV262 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV876 @ tc_bool ) ) @ SV876 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2568]) ).
thf(3219,plain,
! [SV877: $i,SV263: $i] :
( ( ~ ( c_in @ SV263 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV877 @ tc_bool ) ) @ SV877 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2569]) ).
thf(3220,plain,
! [SV878: $i,SV264: $i] :
( ( ! [SY4498: $i] :
( ( c_in @ SV264 @ SV878 @ SY4498 )
| ! [SY4499: $i] :
( ( SV264 = SY4499 )
| ~ ( c_in @ SV264 @ ( c_Set_Oinsert @ SY4499 @ SV878 @ SY4498 ) @ SY4498 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2570]) ).
thf(3221,plain,
! [SV879: $i,SV265: $i] :
( ( ! [SY4500: $i] :
( ( c_in @ SV265 @ SV879 @ SY4500 )
| ! [SY4501: $i] :
( ( c_in @ SV265 @ SY4501 @ SY4500 )
| ~ ( c_in @ SV265 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4501 @ SV879 @ ( tc_fun @ SY4500 @ tc_bool ) ) @ SY4500 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2571]) ).
thf(3222,plain,
! [SV880: $i,SV266: $i] :
( ( ! [SY4502: $i] :
( ~ ( c_in @ SV266 @ SV880 @ SY4502 )
| ! [SY4503: $i] :
~ ( c_in @ SV266 @ ( c_HOL_Ominus__class_Ominus @ SY4503 @ SV880 @ ( tc_fun @ SY4502 @ tc_bool ) ) @ SY4502 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2572]) ).
thf(3223,plain,
! [SV881: $i,SV267: $i] :
( ( ! [SY4504: $i] :
( ( c_in @ SV267 @ SV881 @ SY4504 )
| ! [SY4505: $i] :
~ ( c_in @ SV267 @ ( c_HOL_Ominus__class_Ominus @ SV881 @ SY4505 @ ( tc_fun @ SY4504 @ tc_bool ) ) @ SY4504 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2573]) ).
thf(3224,plain,
! [SV882: $i,SV268: $i] :
( ( ! [SY4506: $i] : ( c_in @ SV268 @ ( c_Set_Oinsert @ SV268 @ SV882 @ SY4506 ) @ SY4506 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2574]) ).
thf(3225,plain,
! [SV883: $i,SV269: $i] :
( ( ! [SY4507: $i] : ( c_in @ SV269 @ ( c_Set_Oinsert @ SV269 @ SV883 @ SY4507 ) @ SY4507 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2575]) ).
thf(3226,plain,
! [SV884: $i,SV270: $i] :
( ( ! [SY4508: $i] : ( c_in @ SV270 @ ( c_Set_Oinsert @ SV270 @ SV884 @ SY4508 ) @ SY4508 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2576]) ).
thf(3227,plain,
! [SV885: $i,SV271: $i] :
( ( ! [SY4509: $i] :
( ( c_in @ SV271 @ SV885 @ SY4509 )
| ! [SY4510: $i] :
~ ( c_in @ SV271 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4510 @ SV885 @ ( tc_fun @ SY4509 @ tc_bool ) ) @ SY4509 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2577]) ).
thf(3228,plain,
! [SV886: $i,SV272: $i] :
( ( ! [SY4511: $i] :
( ( c_in @ SV272 @ SV886 @ SY4511 )
| ! [SY4512: $i] :
~ ( c_in @ SV272 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV886 @ SY4512 @ ( tc_fun @ SY4511 @ tc_bool ) ) @ SY4511 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2578]) ).
thf(3229,plain,
! [SV887: $i,SV273: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV273 @ SV887 ) )
| ! [SY4513: $i] :
~ ( c_in @ SV887 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4513 @ tc_bool ) ) @ SY4513 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2579]) ).
thf(3230,plain,
! [SV888: $i,SV274: $i] :
( ( ! [SY4514: $i,SY4515: $i] :
( ( c_in @ SV274 @ ( c_HOL_Ominus__class_Ominus @ SV888 @ SY4514 @ ( tc_fun @ SY4515 @ tc_bool ) ) @ SY4515 )
| ( c_in @ SV274 @ SY4514 @ SY4515 )
| ~ ( c_in @ SV274 @ SV888 @ SY4515 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2580]) ).
thf(3231,plain,
! [SV889: $i,SV275: $i] :
( ( ! [SY4516: $i,SY4517: $i] :
( ( c_in @ SV275 @ ( c_HOL_Ominus__class_Ominus @ SV889 @ SY4516 @ ( tc_fun @ SY4517 @ tc_bool ) ) @ SY4517 )
| ( c_in @ SV275 @ SY4516 @ SY4517 )
| ~ ( c_in @ SV275 @ SV889 @ SY4517 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2581]) ).
thf(3232,plain,
! [SV890: $i,SV276: $i] :
( ( ! [SY4518: $i,SY4519: $i] :
( ( ( c_Set_Oinsert @ SV276 @ SV890 @ SY4518 )
!= ( c_Set_Oinsert @ SV276 @ SY4519 @ SY4518 ) )
| ( c_in @ SV276 @ SY4519 @ SY4518 )
| ( SV890 = SY4519 )
| ( c_in @ SV276 @ SV890 @ SY4518 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2582]) ).
thf(3233,plain,
! [SV891: $i,SV277: $i] :
( ( ! [SY4520: $i] :
( ( ( c_Set_Oinsert @ SV277 @ SV891 @ SY4520 )
= SV891 )
| ~ ( c_in @ SV277 @ SV891 @ SY4520 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2583]) ).
thf(3234,plain,
! [SV892: $i,SV278: $i] :
( ( ! [SY4521: $i,SY4522: $i] :
( ( hAPP @ ( c_fst @ SV278 @ SV892 ) @ ( c_Pair @ SY4521 @ SY4522 @ SV278 @ SV892 ) )
= SY4521 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2584]) ).
thf(3235,plain,
! [SV893: $i,SV279: $i] :
( ( ! [SY4523: $i,SY4524: $i] :
( SV279
= ( hAPP @ ( c_fst @ SV893 @ SY4523 ) @ ( c_Pair @ SV279 @ SY4524 @ SV893 @ SY4523 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2585]) ).
thf(3236,plain,
! [SV894: $i,SV280: $i] :
( ( ! [SY4525: $i,SY4526: $i] :
( ( hAPP @ ( c_snd @ SV280 @ SV894 ) @ ( c_Pair @ SY4525 @ SY4526 @ SV280 @ SV894 ) )
= SY4526 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2586]) ).
thf(3237,plain,
! [SV895: $i,SV281: $i] :
( ( ! [SY4527: $i,SY4528: $i] :
( SV281
= ( hAPP @ ( c_snd @ SV895 @ SY4527 ) @ ( c_Pair @ SY4528 @ SV281 @ SV895 @ SY4527 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2587]) ).
thf(3238,plain,
! [SV896: $i,SV282: $i] :
( ( ! [SY4529: $i,SY4530: $i,SY4531: $i] :
( ( hBOOL @ ( hAPP @ SV282 @ ( hAPP @ ( c_fst @ SV896 @ SY4529 ) @ ( c_Pair @ SY4530 @ SY4531 @ SV896 @ SY4529 ) ) ) )
| ! [V_Q: $i] :
~ ( hBOOL @ ( hAPP @ V_Q @ SY4531 ) )
| ~ ( hBOOL @ ( hAPP @ SV282 @ SY4530 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2588]) ).
thf(3239,plain,
! [SV897: $i,SV283: $i] :
( ( ! [SY4533: $i,SY4534: $i,SY4535: $i] :
( ( hBOOL @ ( hAPP @ SV283 @ ( hAPP @ ( c_snd @ SV897 @ SY4533 ) @ ( c_Pair @ SY4534 @ SY4535 @ SV897 @ SY4533 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ SV283 @ SY4535 ) )
| ! [V_P: $i] :
~ ( hBOOL @ ( hAPP @ V_P @ SY4534 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2589]) ).
thf(3240,plain,
! [SV898: $i,SV284: $i] :
( ( ~ ( class_Lattices_Odistrib__lattice @ SV284 )
| ! [SY4537: $i,SY4538: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV898 @ SY4537 @ SV284 ) @ SY4538 @ SV284 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV898 @ SY4538 @ SV284 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4537 @ SY4538 @ SV284 ) @ SV284 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2590]) ).
thf(3241,plain,
! [SV899: $i,SV285: $i] :
( ( ~ ( class_Lattices_Odistrib__lattice @ SV285 )
| ! [SY4539: $i,SY4540: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV899 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4539 @ SY4540 @ SV285 ) @ SV285 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV899 @ SY4539 @ SV285 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV899 @ SY4540 @ SV285 ) @ SV285 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2591]) ).
thf(3242,plain,
! [SV900: $i,SV286: $i] :
( ( ! [SY4541: $i,SY4542: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV286 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV900 @ SY4541 @ ( tc_fun @ SY4542 @ tc_bool ) ) @ ( tc_fun @ SY4542 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV286 @ SV900 @ ( tc_fun @ SY4542 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV286 @ SY4541 @ ( tc_fun @ SY4542 @ tc_bool ) ) @ ( tc_fun @ SY4542 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2592]) ).
thf(3243,plain,
! [SV901: $i,SV287: $i] :
( ( ! [SY4543: $i,SY4544: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV287 @ SV901 @ ( tc_fun @ SY4543 @ tc_bool ) ) @ SY4544 @ ( tc_fun @ SY4543 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV287 @ SY4544 @ ( tc_fun @ SY4543 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV901 @ SY4544 @ ( tc_fun @ SY4543 @ tc_bool ) ) @ ( tc_fun @ SY4543 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2593]) ).
thf(3244,plain,
! [SV902: $i,SV288: $i] :
( ( ( c_Relation_Otrans @ SV288 @ SV902 )
| ! [SY4545: $i] :
~ ( c_Order__Relation_Ostrict__linear__order__on @ SY4545 @ SV288 @ SV902 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2594]) ).
thf(3245,plain,
! [SV903: $i,SV289: $i] :
( ( ! [SY4546: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV289 @ SV903 @ SY4546 ) @ SV289 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2595]) ).
thf(3246,plain,
! [SV904: $i,SV290: $i] :
( ( ! [SY4547: $i,SY4548: $i] :
( ( c_lessequals @ ( c_Set_Oinsert @ SV290 @ SV904 @ SY4547 ) @ SY4548 @ ( tc_fun @ SY4547 @ tc_bool ) )
| ~ ( c_lessequals @ SV904 @ SY4548 @ ( tc_fun @ SY4547 @ tc_bool ) )
| ~ ( c_in @ SV290 @ SY4548 @ SY4547 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2596]) ).
thf(3247,plain,
! [SV905: $i,SV291: $i] :
( ( ! [SY4549: $i,SY4550: $i,SY4551: $i] :
( ( c_Product__Type_OSigma @ ( c_HOL_Ominus__class_Ominus @ SV291 @ SV905 @ ( tc_fun @ SY4549 @ tc_bool ) ) @ ( c_COMBK @ SY4550 @ ( tc_fun @ SY4551 @ tc_bool ) @ SY4549 ) @ SY4549 @ SY4551 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Product__Type_OSigma @ SV291 @ ( c_COMBK @ SY4550 @ ( tc_fun @ SY4551 @ tc_bool ) @ SY4549 ) @ SY4549 @ SY4551 ) @ ( c_Product__Type_OSigma @ SV905 @ ( c_COMBK @ SY4550 @ ( tc_fun @ SY4551 @ tc_bool ) @ SY4549 ) @ SY4549 @ SY4551 ) @ ( tc_fun @ ( tc_prod @ SY4549 @ SY4551 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2597]) ).
thf(3248,plain,
! [SV292: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV292 ) )
= $true )
| ( ( ! [SY3138: $i,SY3139: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY3138 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3138 @ SY3139 @ SV292 ) @ SV292 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY3138 @ SY3139 @ SV292 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2598]) ).
thf(3249,plain,
! [SV293: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV293 ) )
= $true )
| ( ( ! [SY3140: $i,SY3141: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY3140 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3140 @ SY3141 @ SV293 ) @ SV293 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY3140 @ SY3141 @ SV293 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2599]) ).
thf(3250,plain,
! [SV906: $i,SV294: $i] :
( ( ! [SY4552: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV294 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV294 @ SV906 @ ( tc_fun @ SY4552 @ tc_bool ) ) @ ( tc_fun @ SY4552 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV294 @ SV906 @ ( tc_fun @ SY4552 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2600]) ).
thf(3251,plain,
! [SV907: $i,SV295: $i] :
( ( ! [SY4553: $i,SY4554: $i] :
( ( c_Relation_ORange @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV295 @ SV907 @ ( tc_fun @ ( tc_prod @ SY4553 @ SY4554 ) @ tc_bool ) ) @ SY4553 @ SY4554 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_ORange @ SV295 @ SY4553 @ SY4554 ) @ ( c_Relation_ORange @ SV907 @ SY4553 @ SY4554 ) @ ( tc_fun @ SY4554 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2601]) ).
thf(3252,plain,
! [SV908: $i,SV296: $i] :
( ( ! [SY4555: $i] :
( ( c_Wellfounded_Owf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV296 @ SV908 @ ( tc_fun @ ( tc_prod @ SY4555 @ SY4555 ) @ tc_bool ) ) @ SY4555 )
| ~ ( c_Wellfounded_Owf @ SV296 @ SY4555 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2602]) ).
thf(3253,plain,
! [SV909: $i,SV297: $i] :
( ( ! [SY4556: $i] :
( ( c_Wellfounded_Owf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV297 @ SV909 @ ( tc_fun @ ( tc_prod @ SY4556 @ SY4556 ) @ tc_bool ) ) @ SY4556 )
| ~ ( c_Wellfounded_Owf @ SV909 @ SY4556 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2603]) ).
thf(3254,plain,
! [SV910: $i,SV298: $i] :
( ( ! [SY4557: $i] :
( ( ( c_Set_Oinsert @ SV298 @ ( c_HOL_Ominus__class_Ominus @ SV910 @ ( c_Set_Oinsert @ SV298 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4557 @ tc_bool ) ) @ SY4557 ) @ ( tc_fun @ SY4557 @ tc_bool ) ) @ SY4557 )
= SV910 )
| ~ ( c_in @ SV298 @ SV910 @ SY4557 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2604]) ).
thf(3255,plain,
! [SV299: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV299 ) )
= $true )
| ( ( ! [SY3153: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY3153 @ SY3153 @ SV299 )
= SY3153 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2605]) ).
thf(3256,plain,
! [SV911: $i,SV300: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV300 @ SV300 @ ( tc_fun @ SV911 @ tc_bool ) )
= SV300 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2606]) ).
thf(3257,plain,
! [SV912: $i,SV301: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV301 )
| ! [SY4558: $i] :
( ( c_lessequals @ SV912 @ SY4558 @ SV301 )
| ! [SY4559: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4559 @ SV912 @ SV301 ) @ SY4558 @ SV301 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2607]) ).
thf(3258,plain,
! [SV913: $i,SV302: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV302 )
| ! [SY4560: $i] :
( ( c_lessequals @ SV913 @ SY4560 @ SV302 )
| ! [SY4561: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV913 @ SY4561 @ SV302 ) @ SY4560 @ SV302 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2608]) ).
thf(3259,plain,
! [SV914: $i,SV303: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV303 )
| ! [SY4562: $i,SY4563: $i] :
( ( c_lessequals @ SV914 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4562 @ SY4563 @ SV303 ) @ SV303 )
| ~ ( c_lessequals @ SV914 @ SY4563 @ SV303 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2609]) ).
thf(3260,plain,
! [SV915: $i,SV304: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV304 )
| ! [SY4564: $i] :
( ! [SY4565: $i] : ( c_lessequals @ SV915 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4564 @ SY4565 @ SV304 ) @ SV304 )
| ~ ( c_lessequals @ SV915 @ SY4564 @ SV304 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2610]) ).
thf(3261,plain,
! [SV916: $i,SV305: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV305 )
| ! [SY4566: $i] :
( ( c_lessequals @ SV916 @ SY4566 @ SV305 )
| ! [SY4567: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4567 @ SV916 @ SV305 ) @ SY4566 @ SV305 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2611]) ).
thf(3262,plain,
! [SV917: $i,SV306: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV306 )
| ! [SY4568: $i] :
( ( c_lessequals @ SV917 @ SY4568 @ SV306 )
| ! [SY4569: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV917 @ SY4569 @ SV306 ) @ SY4568 @ SV306 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2612]) ).
thf(3263,plain,
! [SV918: $i,SV307: $i] :
( ( ! [SY4570: $i] :
( ( c_lessequals @ SV307 @ SV918 @ ( tc_fun @ SY4570 @ tc_bool ) )
| ! [SY4571: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV307 @ SY4571 @ ( tc_fun @ SY4570 @ tc_bool ) ) @ SV918 @ ( tc_fun @ SY4570 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2613]) ).
thf(3264,plain,
! [SV919: $i,SV308: $i] :
( ( ! [SY4572: $i] :
( ( c_lessequals @ SV308 @ SV919 @ ( tc_fun @ SY4572 @ tc_bool ) )
| ! [SY4573: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4573 @ SV308 @ ( tc_fun @ SY4572 @ tc_bool ) ) @ SV919 @ ( tc_fun @ SY4572 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2614]) ).
thf(3265,plain,
! [SV920: $i,SV309: $i] :
( ( ~ ( class_Orderings_Oorder @ SV309 )
| ! [SY4574: $i] :
( ( c_lessequals @ SV920 @ SY4574 @ SV309 )
| ! [SY4575: $i] :
( ~ ( c_lessequals @ SV920 @ SY4575 @ SV309 )
| ~ ( c_lessequals @ SY4575 @ SY4574 @ SV309 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2615]) ).
thf(3266,plain,
! [SV921: $i,SV310: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV310 )
| ! [SY4576: $i] :
( ( c_lessequals @ SV921 @ SY4576 @ SV310 )
| ! [SY4577: $i] :
( ~ ( c_lessequals @ SY4577 @ SY4576 @ SV310 )
| ~ ( c_lessequals @ SV921 @ SY4577 @ SV310 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2616]) ).
thf(3267,plain,
! [SV922: $i,SV311: $i] :
( ( c_lessequals @ SV311 @ SV311 @ ( tc_fun @ SV922 @ tc_bool ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2617]) ).
thf(3268,plain,
! [SV923: $i,SV312: $i] :
( ( c_lessequals @ SV312 @ SV312 @ ( tc_fun @ SV923 @ tc_bool ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2618]) ).
thf(3269,plain,
! [SV924: $i,SV313: $i] :
( ( ! [SY4578: $i] :
( ( c_lessequals @ SV313 @ SV924 @ ( tc_fun @ SY4578 @ tc_bool ) )
| ! [SY4579: $i] :
( ~ ( c_lessequals @ SY4579 @ SV924 @ ( tc_fun @ SY4578 @ tc_bool ) )
| ~ ( c_lessequals @ SV313 @ SY4579 @ ( tc_fun @ SY4578 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2619]) ).
thf(3270,plain,
! [SV925: $i,SV314: $i] :
( ( ( hBOOL @ ( hAPP @ SV314 @ SV925 ) )
| ! [SY4580: $i] :
( ~ ( hBOOL @ ( hAPP @ SY4580 @ SV925 ) )
| ! [SY3192: $i] :
~ ( c_lessequals @ SY4580 @ SV314 @ ( tc_fun @ SY3192 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2620]) ).
thf(3271,plain,
! [SV926: $i,SV315: $i] :
( ( ( c_Wellfounded_Owf @ SV315 @ SV926 )
| ! [SY4582: $i] :
( ~ ( c_lessequals @ SV315 @ SY4582 @ ( tc_fun @ ( tc_prod @ SV926 @ SV926 ) @ tc_bool ) )
| ~ ( c_Wellfounded_Owf @ SY4582 @ SV926 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2621]) ).
thf(3272,plain,
! [SV316: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV316 ) )
= $true )
| ( ( ! [SY3195: $i] : ( c_lessequals @ SY3195 @ SY3195 @ SV316 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2622]) ).
thf(3273,plain,
! [SV317: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV317 ) )
= $true )
| ( ( ! [SY3196: $i] : ( c_lessequals @ SY3196 @ SY3196 @ SV317 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2623]) ).
thf(3274,plain,
! [SV927: $i,SV318: $i] :
( ( ( c_Relation_Oantisym @ SV318 @ SV927 )
| ! [SY4583: $i] :
( ~ ( c_Relation_Oantisym @ SY4583 @ SV927 )
| ~ ( c_lessequals @ SV318 @ SY4583 @ ( tc_fun @ ( tc_prod @ SV927 @ SV927 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2624]) ).
thf(3275,plain,
! [SV928: $i,SV319: $i] :
( ( ( hBOOL @ ( hAPP @ SV319 @ SV928 ) )
| ! [SY4584: $i] :
( ! [SY3201: $i] :
~ ( c_lessequals @ SY4584 @ SV319 @ ( tc_fun @ SY3201 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ SY4584 @ SV928 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2625]) ).
thf(3276,plain,
! [SV929: $i,SV320: $i] :
( ( ( c_Wellfounded_Oacyclic @ SV320 @ SV929 )
| ! [SY4586: $i] :
( ~ ( c_lessequals @ SV320 @ SY4586 @ ( tc_fun @ ( tc_prod @ SV929 @ SV929 ) @ tc_bool ) )
| ~ ( c_Wellfounded_Oacyclic @ SY4586 @ SV929 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2626]) ).
thf(3277,plain,
! [SV930: $i,SV321: $i] :
( ( ! [SY4587: $i] :
( ( c_Relation_Osingle__valued @ SV321 @ SV930 @ SY4587 )
| ! [SY4588: $i] :
( ~ ( c_Relation_Osingle__valued @ SY4588 @ SV930 @ SY4587 )
| ~ ( c_lessequals @ SV321 @ SY4588 @ ( tc_fun @ ( tc_prod @ SV930 @ SY4587 ) @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2627]) ).
thf(3278,plain,
! [SV931: $i,SV322: $i] :
( ( ! [SY4589: $i] :
( ! [SY4590: $i] :
( ( c_Set_Oimage @ SV322 @ SV931 @ SY4589 @ SY4590 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4590 @ tc_bool ) ) )
| ( SV931
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4589 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2628]) ).
thf(3279,plain,
! [SV932: $i,SV323: $i] :
( ( ! [SY4591: $i,SY4592: $i,SY4593: $i] :
( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV323 @ SV932 @ ( tc_fun @ SY4591 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4592 @ SY4593 @ ( tc_fun @ SY4591 @ tc_bool ) ) @ ( tc_fun @ SY4591 @ tc_bool ) )
| ~ ( c_lessequals @ SV932 @ SY4593 @ ( tc_fun @ SY4591 @ tc_bool ) )
| ~ ( c_lessequals @ SV323 @ SY4592 @ ( tc_fun @ SY4591 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2629]) ).
thf(3280,plain,
! [SV933: $i,SV324: $i] :
( ( ! [SY4594: $i,SY4595: $i] :
( ( c_HOL_Ominus__class_Ominus @ SV324 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV933 @ SY4594 @ ( tc_fun @ SY4595 @ tc_bool ) ) @ ( tc_fun @ SY4595 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_HOL_Ominus__class_Ominus @ SV324 @ SV933 @ ( tc_fun @ SY4595 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV324 @ SY4594 @ ( tc_fun @ SY4595 @ tc_bool ) ) @ ( tc_fun @ SY4595 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2630]) ).
thf(3281,plain,
! [SV934: $i,SV325: $i] :
( ( ! [SY4596: $i,SY4597: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV325 @ SV934 @ ( tc_fun @ SY4596 @ tc_bool ) ) @ SY4597 @ ( tc_fun @ SY4596 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV325 @ ( c_HOL_Ominus__class_Ominus @ SV934 @ SY4597 @ ( tc_fun @ SY4596 @ tc_bool ) ) @ ( tc_fun @ SY4596 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2631]) ).
thf(3282,plain,
! [SV935: $i,SV326: $i] :
( ( c_in @ SV326 @ ( c_Set_Oinsert @ SV326 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV935 @ tc_bool ) ) @ SV935 ) @ SV935 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2632]) ).
thf(3283,plain,
! [SV936: $i,SV327: $i] :
( ( ! [SY4598: $i,SY4599: $i] :
( ( c_lessequals @ ( c_Relation_ODomain @ SV327 @ SV936 @ SY4598 ) @ ( c_Relation_ODomain @ SY4599 @ SV936 @ SY4598 ) @ ( tc_fun @ SV936 @ tc_bool ) )
| ~ ( c_lessequals @ SV327 @ SY4599 @ ( tc_fun @ ( tc_prod @ SV936 @ SY4598 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2633]) ).
thf(3284,plain,
! [SV937: $i,SV328: $i] :
( ( ! [SY4600: $i] :
( ( SV328
= ( c_Set_Oinsert @ SV937 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4600 @ tc_bool ) ) @ SY4600 ) )
| ( SV328
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4600 @ tc_bool ) ) )
| ~ ( c_lessequals @ SV328 @ ( c_Set_Oinsert @ SV937 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4600 @ tc_bool ) ) @ SY4600 ) @ ( tc_fun @ SY4600 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2634]) ).
thf(3285,plain,
! [SV938: $i,SV329: $i] :
( ( ! [SY4601: $i,SY4602: $i] :
( ( c_HOL_Ominus__class_Ominus @ SV329 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV938 @ SY4601 @ ( tc_fun @ SY4602 @ tc_bool ) ) @ ( tc_fun @ SY4602 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ SV329 @ SV938 @ ( tc_fun @ SY4602 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV329 @ SY4601 @ ( tc_fun @ SY4602 @ tc_bool ) ) @ ( tc_fun @ SY4602 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2635]) ).
thf(3286,plain,
! [SV939: $i,SV330: $i] :
( ( ! [SY4603: $i] :
( ( c_Product__Type_OSigma @ SV330 @ ( c_COMBK @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV939 @ tc_bool ) ) @ ( tc_fun @ SV939 @ tc_bool ) @ SY4603 ) @ SY4603 @ SV939 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SY4603 @ SV939 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2636]) ).
thf(3287,plain,
! [SV940: $i,SV331: $i] :
( ( ! [SY4604: $i,SY4605: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV331 @ SV940 @ ( tc_fun @ SY4604 @ tc_bool ) ) @ SY4605 ) )
| ~ ( hBOOL @ ( hAPP @ SV940 @ SY4605 ) )
| ~ ( hBOOL @ ( hAPP @ SV331 @ SY4605 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2637]) ).
thf(3288,plain,
! [SV941: $i,SV332: $i] :
( ( ! [SY4606: $i,SY4607: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV332 @ ( c_HOL_Ominus__class_Ominus @ SV941 @ SY4606 @ ( tc_fun @ SY4607 @ tc_bool ) ) @ ( tc_fun @ SY4607 @ tc_bool ) )
= SY4606 )
| ~ ( c_lessequals @ SV332 @ SV941 @ ( tc_fun @ SY4607 @ tc_bool ) )
| ~ ( c_lessequals @ SY4606 @ SV332 @ ( tc_fun @ SY4607 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2638]) ).
thf(3289,plain,
! [SV942: $i,SV333: $i] :
( ( ! [SY4608: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV333 )
| ! [SY4609: $i,SY4610: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV942 @ SY4608 @ SV333 )
!= ( c_HOL_Ominus__class_Ominus @ SY4609 @ SY4610 @ SV333 ) )
| ( c_lessequals @ SY4610 @ SY4609 @ SV333 )
| ~ ( c_lessequals @ SY4608 @ SV942 @ SV333 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2639]) ).
thf(3290,plain,
! [SV943: $i,SV334: $i] :
( ( ! [SY4611: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV334 )
| ! [SY4612: $i,SY4613: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV943 @ SY4611 @ SV334 )
!= ( c_HOL_Ominus__class_Ominus @ SY4612 @ SY4613 @ SV334 ) )
| ( c_lessequals @ SY4611 @ SV943 @ SV334 )
| ~ ( c_lessequals @ SY4613 @ SY4612 @ SV334 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2640]) ).
thf(3291,plain,
! [SV944: $i,SV335: $i] :
( ( ! [SY4614: $i,SY4615: $i,SY4616: $i] :
( ( c_lessequals @ ( c_Set_Oimage @ SV335 @ SV944 @ SY4614 @ SY4615 ) @ ( c_Set_Oimage @ SV335 @ SY4616 @ SY4614 @ SY4615 ) @ ( tc_fun @ SY4615 @ tc_bool ) )
| ~ ( c_lessequals @ SV944 @ SY4616 @ ( tc_fun @ SY4614 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2641]) ).
thf(3292,plain,
! [SV945: $i,SV336: $i] :
( ( ! [SY4617: $i] :
( ~ ( c_lessequals @ SV336 @ SV945 @ ( tc_fun @ SY4617 @ tc_bool ) )
| ! [SY4618: $i,SY4619: $i] : ( c_lessequals @ ( c_Set_Oimage @ SY4618 @ SV336 @ SY4617 @ SY4619 ) @ ( c_Set_Oimage @ SY4618 @ SV945 @ SY4617 @ SY4619 ) @ ( tc_fun @ SY4619 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2642]) ).
thf(3293,plain,
! [SV946: $i,SV337: $i] :
( ( ! [SY4620: $i,SY4621: $i] :
( ( c_lessequals @ ( c_Set_Oinsert @ SV337 @ SV946 @ SY4620 ) @ ( c_Set_Oinsert @ SV337 @ SY4621 @ SY4620 ) @ ( tc_fun @ SY4620 @ tc_bool ) )
| ~ ( c_lessequals @ SV946 @ SY4621 @ ( tc_fun @ SY4620 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2643]) ).
thf(3294,plain,
! [SV947: $i,SV339: $i] :
( ( ! [SY4622: $i,SY4623: $i,SY4624: $i] :
( ( c_Set_Oimage @ SV339 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV947 @ SY4622 @ ( tc_fun @ SY4623 @ tc_bool ) ) @ SY4623 @ SY4624 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ SV339 @ SV947 @ SY4623 @ SY4624 ) @ ( c_Set_Oimage @ SV339 @ SY4622 @ SY4623 @ SY4624 ) @ ( tc_fun @ SY4624 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2645]) ).
thf(3295,plain,
! [SV948: $i,SV341: $i] :
( ( ! [SY4625: $i,SY4626: $i,SY4627: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV341 @ ( hAPP @ ( c_snd @ SV948 @ SY4625 ) @ ( c_Pair @ SY4626 @ SY4627 @ SV948 @ SY4625 ) ) ) @ ( hAPP @ ( c_fst @ SV948 @ SY4625 ) @ ( c_Pair @ SY4626 @ SY4627 @ SV948 @ SY4625 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV341 @ SY4627 ) @ SY4626 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2647]) ).
thf(3296,plain,
! [SV949: $i,SV342: $i] :
( ( ! [SY4628: $i] :
( ( ( c_Relation_ORange @ SV342 @ SV949 @ SY4628 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4628 @ tc_bool ) ) )
| ( SV342
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV949 @ SY4628 ) @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2648]) ).
thf(3297,plain,
! [SV950: $i,SV343: $i] :
( ( ! [SY4629: $i,SY4630: $i,SY4631: $i,SY4632: $i] :
( ( c_lessequals @ ( c_Relation_OImage @ SV343 @ SV950 @ SY4629 @ SY4630 ) @ ( c_Relation_OImage @ SY4631 @ SY4632 @ SY4629 @ SY4630 ) @ ( tc_fun @ SY4630 @ tc_bool ) )
| ~ ( c_lessequals @ SV950 @ SY4632 @ ( tc_fun @ SY4629 @ tc_bool ) )
| ~ ( c_lessequals @ SV343 @ SY4631 @ ( tc_fun @ ( tc_prod @ SY4629 @ SY4630 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2649]) ).
thf(3298,plain,
! [SV951: $i,SV344: $i] :
( ( ! [SY4633: $i] :
( ( c_lessequals @ SV344 @ ( c_Product__Type_OSigma @ SV951 @ ( c_COMBK @ SV951 @ ( tc_fun @ SY4633 @ tc_bool ) @ SY4633 ) @ SY4633 @ SY4633 ) @ ( tc_fun @ ( tc_prod @ SY4633 @ SY4633 ) @ tc_bool ) )
| ~ ( c_Equiv__Relations_Oequiv @ SV951 @ SV344 @ SY4633 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2650]) ).
thf(3299,plain,
! [SV345: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV345 ) )
= $true )
| ( ( ! [SY3273: $i,SY3274: $i] :
( ( c_lessequals @ SY3273 @ SY3274 @ SV345 )
| ( c_lessequals @ SY3274 @ SY3273 @ SV345 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2651]) ).
thf(3300,plain,
! [SV952: $i,SV346: $i] :
( ( ( c_Relation_Oirrefl @ SV346 @ SV952 )
| ! [SY4634: $i] :
~ ( c_Order__Relation_Ostrict__linear__order__on @ SY4634 @ SV346 @ SV952 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2652]) ).
thf(3301,plain,
! [SV953: $i,SV347: $i] :
( ( ! [SY4635: $i,SY4636: $i] :
( ( c_Wellfounded_Oacyclic @ ( c_Set_Oinsert @ ( c_Pair @ SV347 @ SV953 @ SY4635 @ SY4635 ) @ SY4636 @ ( tc_prod @ SY4635 @ SY4635 ) ) @ SY4635 )
| ( c_in @ ( c_Pair @ SV953 @ SV347 @ SY4635 @ SY4635 ) @ ( c_Transitive__Closure_Ortrancl @ SY4636 @ SY4635 ) @ ( tc_prod @ SY4635 @ SY4635 ) )
| ~ ( c_Wellfounded_Oacyclic @ SY4636 @ SY4635 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2653]) ).
thf(3302,plain,
! [SV954: $i,SV348: $i] :
( ( ! [SY4637: $i,SY4638: $i] :
( ~ ( c_in @ ( c_Pair @ SV348 @ SV954 @ SY4637 @ SY4637 ) @ ( c_Transitive__Closure_Ortrancl @ SY4638 @ SY4637 ) @ ( tc_prod @ SY4637 @ SY4637 ) )
| ~ ( c_Wellfounded_Oacyclic @ ( c_Set_Oinsert @ ( c_Pair @ SV954 @ SV348 @ SY4637 @ SY4637 ) @ SY4638 @ ( tc_prod @ SY4637 @ SY4637 ) ) @ SY4637 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2654]) ).
thf(3303,plain,
! [SV955: $i,SV349: $i] :
( ( ! [SY4639: $i] :
( ( hBOOL @ ( hAPP @ SV349 @ SV955 ) )
| ! [SY4640: $i,SY4641: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1 @ SV349 @ SY4639 @ SY4640 @ SY4641 ) @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 @ SV349 @ SY4639 @ SY4640 @ SY4641 ) @ SY4641 @ SY4641 ) @ SY4640 @ ( tc_prod @ SY4641 @ SY4641 ) )
| ~ ( hBOOL @ ( hAPP @ SV349 @ SY4639 ) )
| ~ ( c_in @ ( c_Pair @ SV955 @ SY4639 @ SY4641 @ SY4641 ) @ ( c_Transitive__Closure_Ortrancl @ SY4640 @ SY4641 ) @ ( tc_prod @ SY4641 @ SY4641 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2655]) ).
thf(3304,plain,
! [SV956: $i,SV350: $i] :
( ( ! [SY4642: $i] :
( ( hBOOL @ ( hAPP @ SV350 @ SV956 ) )
| ! [SY4643: $i,SY4644: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 @ SV350 @ SY4642 @ SY4643 @ SY4644 ) @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2 @ SV350 @ SY4642 @ SY4643 @ SY4644 ) @ SY4644 @ SY4644 ) @ SY4643 @ ( tc_prod @ SY4644 @ SY4644 ) )
| ~ ( hBOOL @ ( hAPP @ SV350 @ SY4642 ) )
| ~ ( c_in @ ( c_Pair @ SY4642 @ SV956 @ SY4644 @ SY4644 ) @ ( c_Transitive__Closure_Ortrancl @ SY4643 @ SY4644 ) @ ( tc_prod @ SY4644 @ SY4644 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2656]) ).
thf(3305,plain,
! [SV957: $i,SV351: $i] :
( ( ! [SY4645: $i] :
( ( c_in @ SV351 @ ( c_Relation_OImage @ SV957 @ ( c_Set_Oinsert @ SV351 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4645 @ tc_bool ) ) @ SY4645 ) @ SY4645 @ SY4645 ) @ SY4645 )
| ! [SY4646: $i] :
( ~ ( c_in @ SV351 @ SY4646 @ SY4645 )
| ~ ( c_Equiv__Relations_Oequiv @ SY4646 @ SV957 @ SY4645 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2657]) ).
thf(3306,plain,
! [SV958: $i,SV352: $i] :
( ( ! [SY4647: $i] :
( ( c_lessequals @ ( c_Transitive__Closure_Ortrancl @ SV352 @ SV958 ) @ SY4647 @ ( tc_fun @ ( tc_prod @ SV958 @ SV958 ) @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Relation_Orel__comp @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Transitive__Closure_Ortrancl @ SV352 @ SV958 ) @ SY4647 @ ( tc_fun @ ( tc_prod @ SV958 @ SV958 ) @ tc_bool ) ) @ SV352 @ SV958 @ SV958 @ SV958 ) @ SY4647 @ ( tc_fun @ ( tc_prod @ SV958 @ SV958 ) @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Relation_OId @ SV958 ) @ SY4647 @ ( tc_fun @ ( tc_prod @ SV958 @ SV958 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2658]) ).
thf(3307,plain,
! [SV959: $i,SV353: $i] :
( ( ! [SY4648: $i,SY4649: $i] :
( ( c_in @ ( c_Pair @ SV353 @ SV959 @ SY4648 @ SY4648 ) @ SY4649 @ ( tc_prod @ SY4648 @ SY4648 ) )
| ! [SY4650: $i] :
~ ( c_in @ SY4650 @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_OImage @ SY4649 @ ( c_Set_Oinsert @ SV353 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4648 @ tc_bool ) ) @ SY4648 ) @ SY4648 @ SY4648 ) @ ( c_Relation_OImage @ SY4649 @ ( c_Set_Oinsert @ SV959 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4648 @ tc_bool ) ) @ SY4648 ) @ SY4648 @ SY4648 ) @ ( tc_fun @ SY4648 @ tc_bool ) ) @ SY4648 )
| ! [V_A: $i] :
~ ( c_Equiv__Relations_Oequiv @ V_A @ SY4649 @ SY4648 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2659]) ).
thf(3308,plain,
! [SV960: $i,SV354: $i] :
( ( ! [SY4652: $i,SY4653: $i] :
( ( c_in @ ( c_Pair @ SV354 @ SV960 @ SY4652 @ SY4652 ) @ SY4653 @ ( tc_prod @ SY4652 @ SY4652 ) )
| ! [SY4654: $i] :
( ~ ( c_in @ SV960 @ SY4654 @ SY4652 )
| ~ ( c_lessequals @ ( c_Relation_OImage @ SY4653 @ ( c_Set_Oinsert @ SV960 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4652 @ tc_bool ) ) @ SY4652 ) @ SY4652 @ SY4652 ) @ ( c_Relation_OImage @ SY4653 @ ( c_Set_Oinsert @ SV354 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4652 @ tc_bool ) ) @ SY4652 ) @ SY4652 @ SY4652 ) @ ( tc_fun @ SY4652 @ tc_bool ) )
| ~ ( c_Equiv__Relations_Oequiv @ SY4654 @ SY4653 @ SY4652 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2660]) ).
thf(3309,plain,
! [SV961: $i,SV355: $i] :
( ( ! [SY4655: $i,SY4656: $i] :
( ! [SY4657: $i] :
( ( c_Set_Oinsert @ ( hAPP @ SV355 @ SV961 ) @ ( c_Set_Oimage @ SV355 @ SY4655 @ SY4656 @ SY4657 ) @ SY4657 )
= ( c_Set_Oimage @ SV355 @ SY4655 @ SY4656 @ SY4657 ) )
| ~ ( c_in @ SV961 @ SY4655 @ SY4656 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2661]) ).
thf(3310,plain,
! [SV962: $i,SV356: $i] :
( ( ! [SY4658: $i,SY4659: $i] :
( ( c_in @ ( hAPP @ SV356 @ SV962 ) @ SY4658 @ SY4659 )
| ! [SY4660: $i,SY4661: $i] :
( ~ ( c_in @ SV962 @ SY4660 @ SY4661 )
| ~ ( c_lessequals @ ( c_Set_Oimage @ SV356 @ SY4660 @ SY4661 @ SY4659 ) @ SY4658 @ ( tc_fun @ SY4659 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2662]) ).
thf(3311,plain,
! [SV963: $i,SV357: $i] :
( ( ! [SY4662: $i,SY4663: $i,SY4664: $i] :
( ( c_in @ ( c_Pair @ SV357 @ SV963 @ SY4662 @ SY4663 ) @ SY4664 @ ( tc_prod @ SY4662 @ SY4663 ) )
| ~ ( c_in @ SV963 @ ( c_Relation_OImage @ SY4664 @ ( c_Set_Oinsert @ SV357 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4662 @ tc_bool ) ) @ SY4662 ) @ SY4662 @ SY4663 ) @ SY4663 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2663]) ).
thf(3312,plain,
! [SV964: $i,SV358: $i] :
( ( ! [SY4665: $i,SY4666: $i,SY4667: $i] :
( ( c_in @ SV358 @ ( c_Relation_OImage @ SV964 @ ( c_Set_Oinsert @ SY4665 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4666 @ tc_bool ) ) @ SY4666 ) @ SY4666 @ SY4667 ) @ SY4667 )
| ~ ( c_in @ ( c_Pair @ SY4665 @ SV358 @ SY4666 @ SY4667 ) @ SV964 @ ( tc_prod @ SY4666 @ SY4667 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2664]) ).
thf(3313,plain,
! [SV965: $i,SV359: $i] :
( ( ! [SY4668: $i,SY4669: $i,SY4670: $i] :
( ( ( c_Product__Type_OSigma @ SV359 @ ( c_COMBK @ SV965 @ ( tc_fun @ SY4668 @ tc_bool ) @ SY4669 ) @ SY4669 @ SY4668 )
!= ( c_Product__Type_OSigma @ SY4670 @ ( c_COMBK @ SV965 @ ( tc_fun @ SY4668 @ tc_bool ) @ SY4669 ) @ SY4669 @ SY4668 ) )
| ! [SY4671: $i] :
~ ( c_in @ SY4671 @ SV965 @ SY4668 )
| ( SV359 = SY4670 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2665]) ).
thf(3314,plain,
! [SV966: $i,SV360: $i] :
( ( ( c_Wellfounded_Owf @ SV360 @ SV966 )
| ! [SY4672: $i,SY4673: $i] :
~ ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ SY4672 @ SY4673 @ SV966 @ SV966 ) @ SV360 @ ( tc_prod @ SV966 @ SV966 ) ) @ SV966 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2666]) ).
thf(3315,plain,
! [SV967: $i,SV361: $i] :
( ( ! [SY4674: $i,SY4675: $i] :
( ( c_in @ SV361 @ ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV967 @ SY4674 @ ( tc_fun @ ( tc_prod @ SY4675 @ SY4675 ) @ tc_bool ) ) @ SY4675 ) @ ( tc_prod @ SY4675 @ SY4675 ) )
| ~ ( c_in @ SV361 @ ( c_Transitive__Closure_Ortrancl @ SV967 @ SY4675 ) @ ( tc_prod @ SY4675 @ SY4675 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2667]) ).
thf(3316,plain,
! [SV968: $i,SV362: $i] :
( ( ! [SY4676: $i,SY4677: $i] :
( ( c_in @ SV362 @ ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV968 @ SY4676 @ ( tc_fun @ ( tc_prod @ SY4677 @ SY4677 ) @ tc_bool ) ) @ SY4677 ) @ ( tc_prod @ SY4677 @ SY4677 ) )
| ~ ( c_in @ SV362 @ ( c_Transitive__Closure_Ortrancl @ SY4676 @ SY4677 ) @ ( tc_prod @ SY4677 @ SY4677 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2668]) ).
thf(3317,plain,
! [SV969: $i,SV363: $i] :
( ( ! [SY4678: $i] :
( ( c_in @ SV363 @ ( c_Transitive__Closure_Otrancl @ SV969 @ SY4678 ) @ ( tc_prod @ SY4678 @ SY4678 ) )
| ! [SY4679: $i] :
( ~ ( c_lessequals @ SY4679 @ SV969 @ ( tc_fun @ ( tc_prod @ SY4678 @ SY4678 ) @ tc_bool ) )
| ~ ( c_in @ SV363 @ ( c_Transitive__Closure_Otrancl @ SY4679 @ SY4678 ) @ ( tc_prod @ SY4678 @ SY4678 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2669]) ).
thf(3318,plain,
! [SV970: $i,SV364: $i] :
( ( ! [SY4680: $i,SY4681: $i] :
( ( ( c_Relation_OImage @ SV364 @ ( c_Set_Oinsert @ SV970 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4680 @ tc_bool ) ) @ SY4680 ) @ SY4680 @ SY4680 )
= ( c_Relation_OImage @ SV364 @ ( c_Set_Oinsert @ SY4681 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4680 @ tc_bool ) ) @ SY4680 ) @ SY4680 @ SY4680 ) )
| ~ ( c_in @ ( c_Pair @ SV970 @ SY4681 @ SY4680 @ SY4680 ) @ SV364 @ ( tc_prod @ SY4680 @ SY4680 ) )
| ! [SY3342: $i] :
~ ( c_Equiv__Relations_Oequiv @ SY3342 @ SV364 @ SY4680 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2670]) ).
thf(3319,plain,
! [SV971: $i,SV365: $i] :
( ( ! [SY4683: $i,SY4684: $i] :
( ( ( c_Relation_OImage @ SV365 @ ( c_Set_Oinsert @ SV971 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4683 @ tc_bool ) ) @ SY4683 ) @ SY4683 @ SY4683 )
= ( c_Relation_OImage @ SV365 @ ( c_Set_Oinsert @ SY4684 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4683 @ tc_bool ) ) @ SY4683 ) @ SY4683 @ SY4683 ) )
| ~ ( c_in @ ( c_Pair @ SV971 @ SY4684 @ SY4683 @ SY4683 ) @ SV365 @ ( tc_prod @ SY4683 @ SY4683 ) )
| ! [SY3346: $i] :
~ ( c_Equiv__Relations_Oequiv @ SY3346 @ SV365 @ SY4683 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2671]) ).
thf(3320,plain,
! [SV972: $i,SV366: $i] :
( ( ! [SY4686: $i] :
( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ SV366 @ SV366 @ SV972 @ SV972 @ SV972 ) @ ( c_Relation_Orel__comp @ SY4686 @ SV366 @ SV972 @ SV972 @ SV972 ) @ ( tc_fun @ ( tc_prod @ SV972 @ SV972 ) @ tc_bool ) ) @ SY4686 @ ( tc_fun @ ( tc_prod @ SV972 @ SV972 ) @ tc_bool ) ) @ SV972 )
| ~ ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV366 @ SY4686 @ ( tc_fun @ ( tc_prod @ SV972 @ SV972 ) @ tc_bool ) ) @ SV972 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2672]) ).
thf(3321,plain,
! [SV973: $i,SV367: $i] :
( ( ! [SY4687: $i] :
( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV367 @ SV973 @ ( tc_fun @ ( tc_prod @ SY4687 @ SY4687 ) @ tc_bool ) ) @ SY4687 )
| ~ ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ SV367 @ SV367 @ SY4687 @ SY4687 @ SY4687 ) @ ( c_Relation_Orel__comp @ SV973 @ SV367 @ SY4687 @ SY4687 @ SY4687 ) @ ( tc_fun @ ( tc_prod @ SY4687 @ SY4687 ) @ tc_bool ) ) @ SV973 @ ( tc_fun @ ( tc_prod @ SY4687 @ SY4687 ) @ tc_bool ) ) @ SY4687 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2673]) ).
thf(3322,plain,
! [SV974: $i,SV368: $i] :
( ( ( ( c_Relation_Orel__comp @ SV368 @ SV368 @ SV974 @ SV974 @ SV974 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV974 @ SV974 ) @ tc_bool ) ) )
| ( c_Wellfounded_Owf @ SV368 @ SV974 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2674]) ).
thf(3323,plain,
! [SV975: $i,SV369: $i] :
( ( ( c_Transitive__Closure_Otrancl @ SV369 @ SV975 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV369 @ ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Otrancl @ SV369 @ SV975 ) @ SV369 @ SV975 @ SV975 @ SV975 ) @ ( tc_fun @ ( tc_prod @ SV975 @ SV975 ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2675]) ).
thf(3324,plain,
! [SV976: $i,SV370: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Ortrancl @ SV370 @ SV976 ) @ ( c_Relation_OId @ SV976 ) @ ( tc_fun @ ( tc_prod @ SV976 @ SV976 ) @ tc_bool ) )
= ( c_Transitive__Closure_Ortrancl @ SV370 @ SV976 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2676]) ).
thf(3325,plain,
! [SV977: $i,SV371: $i] :
( ( ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV371 @ ( c_Relation_OId @ SV977 ) @ ( tc_fun @ ( tc_prod @ SV977 @ SV977 ) @ tc_bool ) ) @ SV977 )
= ( c_Transitive__Closure_Ortrancl @ SV371 @ SV977 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2677]) ).
thf(3326,plain,
! [SV978: $i,SV373: $i] :
( ( ( c_Transitive__Closure_Ortrancl @ ( c_HOL_Ominus__class_Ominus @ SV373 @ ( c_Relation_OId @ SV978 ) @ ( tc_fun @ ( tc_prod @ SV978 @ SV978 ) @ tc_bool ) ) @ SV978 )
= ( c_Transitive__Closure_Ortrancl @ SV373 @ SV978 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2679]) ).
thf(3327,plain,
! [SV979: $i,SV374: $i] :
( ( ( c_Relation_Oantisym @ ( c_Transitive__Closure_Ortrancl @ SV374 @ SV979 ) @ SV979 )
| ~ ( c_Wellfounded_Oacyclic @ SV374 @ SV979 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2680]) ).
thf(3328,plain,
! [SV980: $i,SV375: $i] :
( ( ( c_lessequals @ ( c_Relation_Orel__comp @ SV375 @ SV375 @ SV980 @ SV980 @ SV980 ) @ SV375 @ ( tc_fun @ ( tc_prod @ SV980 @ SV980 ) @ tc_bool ) )
| ~ ( c_Relation_Otrans @ SV375 @ SV980 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2681]) ).
thf(3329,plain,
! [SV981: $i,SV376: $i] :
( ( c_Relation_Osym @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV376 @ ( c_Relation_Oconverse @ SV376 @ SV981 @ SV981 ) @ ( tc_fun @ ( tc_prod @ SV981 @ SV981 ) @ tc_bool ) ) @ SV981 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2682]) ).
thf(3330,plain,
! [SV982: $i,SV377: $i] :
( ( c_Relation_Osym @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV377 @ ( c_Relation_Oconverse @ SV377 @ SV982 @ SV982 ) @ ( tc_fun @ ( tc_prod @ SV982 @ SV982 ) @ tc_bool ) ) @ SV982 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2683]) ).
thf(3331,plain,
! [SV983: $i,SV378: $i] :
( ( ( c_Relation_Otrans @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV378 @ ( c_Relation_OId @ SV983 ) @ ( tc_fun @ ( tc_prod @ SV983 @ SV983 ) @ tc_bool ) ) @ SV983 )
| ~ ( c_Relation_Otrans @ SV378 @ SV983 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2684]) ).
thf(3332,plain,
! [SV984: $i,SV379: $i] :
( ( ! [SY4688: $i] :
( ( c_Relation_OImage @ ( c_Relation_OId__on @ SV379 @ SV984 ) @ SY4688 @ SV984 @ SV984 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV379 @ SY4688 @ ( tc_fun @ SV984 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2685]) ).
thf(3333,plain,
! [SV985: $i,SV380: $i] :
( ( ( c_Relation_Oantisym @ SV380 @ SV985 )
| ~ ( c_Relation_Oantisym @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV380 @ ( c_Relation_OId @ SV985 ) @ ( tc_fun @ ( tc_prod @ SV985 @ SV985 ) @ tc_bool ) ) @ SV985 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2686]) ).
thf(3334,plain,
! [SV986: $i,SV381: $i] :
( ( ( c_Relation_Oantisym @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV381 @ ( c_Relation_OId @ SV986 ) @ ( tc_fun @ ( tc_prod @ SV986 @ SV986 ) @ tc_bool ) ) @ SV986 )
| ~ ( c_Relation_Oantisym @ SV381 @ SV986 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2687]) ).
thf(3335,plain,
! [SV987: $i,SV382: $i] :
( ( ! [SY4689: $i] :
( ( c_Relation_Ototal__on @ SV382 @ SV987 @ SY4689 )
| ~ ( c_Relation_Ototal__on @ SV382 @ ( c_HOL_Ominus__class_Ominus @ SV987 @ ( c_Relation_OId @ SY4689 ) @ ( tc_fun @ ( tc_prod @ SY4689 @ SY4689 ) @ tc_bool ) ) @ SY4689 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2688]) ).
thf(3336,plain,
! [SV988: $i,SV383: $i] :
( ( ! [SY4690: $i] :
( ( c_Relation_Ototal__on @ SV383 @ ( c_HOL_Ominus__class_Ominus @ SV988 @ ( c_Relation_OId @ SY4690 ) @ ( tc_fun @ ( tc_prod @ SY4690 @ SY4690 ) @ tc_bool ) ) @ SY4690 )
| ~ ( c_Relation_Ototal__on @ SV383 @ SV988 @ SY4690 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2689]) ).
thf(3337,plain,
! [SV989: $i,SV384: $i] :
( ( ( c_lessequals @ ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ SV384 @ SV989 @ SV989 ) @ SV384 @ SV989 @ SV989 @ SV989 ) @ SV384 @ ( tc_fun @ ( tc_prod @ SV989 @ SV989 ) @ tc_bool ) )
| ~ ( c_Relation_Otrans @ SV384 @ SV989 )
| ~ ( c_Relation_Osym @ SV384 @ SV989 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2690]) ).
thf(3338,plain,
! [SV990: $i,SV385: $i] :
( ( ! [SY4691: $i,SY4692: $i] :
( ( c_in @ ( c_Pair @ SV385 @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1 @ SV990 @ SV385 @ SY4691 @ SY4692 ) @ SY4692 @ SY4692 ) @ ( c_Transitive__Closure_Ortrancl @ SV990 @ SY4692 ) @ ( tc_prod @ SY4692 @ SY4692 ) )
| ~ ( c_in @ ( c_Pair @ SV385 @ SY4691 @ SY4692 @ SY4692 ) @ ( c_Transitive__Closure_Otrancl @ SV990 @ SY4692 ) @ ( tc_prod @ SY4692 @ SY4692 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2691]) ).
thf(3339,plain,
! [SV991: $i,SV386: $i] :
( ( ! [SY4693: $i,SY4694: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1 @ SV386 @ SV991 @ SY4693 @ SY4694 ) @ SY4693 @ SY4694 @ SY4694 ) @ ( c_Transitive__Closure_Ortrancl @ SV386 @ SY4694 ) @ ( tc_prod @ SY4694 @ SY4694 ) )
| ~ ( c_in @ ( c_Pair @ SV991 @ SY4693 @ SY4694 @ SY4694 ) @ ( c_Transitive__Closure_Otrancl @ SV386 @ SY4694 ) @ ( tc_prod @ SY4694 @ SY4694 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2692]) ).
thf(3340,plain,
! [SV992: $i,SV387: $i] :
( ( ! [SY4695: $i,SY4696: $i] :
( ~ ( c_in @ ( c_Pair @ SV387 @ SV992 @ SY4695 @ SY4695 ) @ ( c_Transitive__Closure_Ortrancl @ SY4696 @ SY4695 ) @ ( tc_prod @ SY4695 @ SY4695 ) )
| ~ ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ SV992 @ SV387 @ SY4695 @ SY4695 ) @ SY4696 @ ( tc_prod @ SY4695 @ SY4695 ) ) @ SY4695 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2693]) ).
thf(3341,plain,
! [SV993: $i,SV388: $i] :
( ( ! [SY4697: $i,SY4698: $i] :
( ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ SV388 @ SV993 @ SY4697 @ SY4697 ) @ SY4698 @ ( tc_prod @ SY4697 @ SY4697 ) ) @ SY4697 )
| ( c_in @ ( c_Pair @ SV993 @ SV388 @ SY4697 @ SY4697 ) @ ( c_Transitive__Closure_Ortrancl @ SY4698 @ SY4697 ) @ ( tc_prod @ SY4697 @ SY4697 ) )
| ~ ( c_Wellfounded_Owf @ SY4698 @ SY4697 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2694]) ).
thf(3342,plain,
! [SV994: $i,SV389: $i] :
( ( ! [SY4699: $i] :
( ( c_Order__Relation_Ostrict__linear__order__on @ SV389 @ SV994 @ SY4699 )
| ~ ( c_Relation_Ototal__on @ SV389 @ SV994 @ SY4699 )
| ~ ( c_Relation_Oirrefl @ SV994 @ SY4699 )
| ~ ( c_Relation_Otrans @ SV994 @ SY4699 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2695]) ).
thf(3343,plain,
! [SV995: $i,SV390: $i] :
( ( ( c_Nitpick_Orefl_H @ SV390 @ SV995 )
| ~ ( c_in @ ( c_Pair @ ( c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1 @ SV390 @ SV995 ) @ ( c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1 @ SV390 @ SV995 ) @ SV995 @ SV995 ) @ SV390 @ ( tc_prod @ SV995 @ SV995 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2696]) ).
thf(3344,plain,
! [SV996: $i,SV391: $i] :
( ( ( c_Relation_Otrans @ ( c_HOL_Ominus__class_Ominus @ SV391 @ ( c_Relation_OId @ SV996 ) @ ( tc_fun @ ( tc_prod @ SV996 @ SV996 ) @ tc_bool ) ) @ SV996 )
| ~ ( c_Relation_Oantisym @ SV391 @ SV996 )
| ~ ( c_Relation_Otrans @ SV391 @ SV996 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2697]) ).
thf(3345,plain,
! [SV997: $i,SV392: $i] :
( ( ! [SY4700: $i,SY4701: $i,SY4702: $i] :
( ( ( c_Relation_OImage @ SV392 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV997 @ SY4700 @ ( tc_fun @ SY4701 @ tc_bool ) ) @ SY4701 @ SY4702 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_OImage @ SV392 @ SV997 @ SY4701 @ SY4702 ) @ ( c_Relation_OImage @ SV392 @ SY4700 @ SY4701 @ SY4702 ) @ ( tc_fun @ SY4702 @ tc_bool ) ) )
| ~ ( c_Relation_Osingle__valued @ ( c_Relation_Oconverse @ SV392 @ SY4701 @ SY4702 ) @ SY4702 @ SY4701 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2698]) ).
thf(3346,plain,
! [SV998: $i,SV393: $i] :
( ( ( c_Relation_Oirrefl @ SV393 @ SV998 )
| ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1 @ SV393 @ SV998 ) @ ( c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1 @ SV393 @ SV998 ) @ SV998 @ SV998 ) @ SV393 @ ( tc_prod @ SV998 @ SV998 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2699]) ).
thf(3347,plain,
! [SV999: $i,SV394: $i] :
( ( ( c_lessequals @ SV394 @ ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ SV394 @ SV999 @ SV999 ) @ SV394 @ SV999 @ SV999 @ SV999 ) @ ( tc_fun @ ( tc_prod @ SV999 @ SV999 ) @ tc_bool ) )
| ! [SY4703: $i] :
~ ( c_Relation_Orefl__on @ SY4703 @ SV394 @ SV999 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2700]) ).
thf(3348,plain,
! [SV1000: $i,SV395: $i] :
( ( ( c_Transitive__Closure_Ortrancl @ SV395 @ SV1000 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_OId @ SV1000 ) @ ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Ortrancl @ SV395 @ SV1000 ) @ SV395 @ SV1000 @ SV1000 @ SV1000 ) @ ( tc_fun @ ( tc_prod @ SV1000 @ SV1000 ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2701]) ).
thf(3349,plain,
! [SV1001: $i,SV396: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Otrancl @ SV396 @ SV1001 ) @ ( c_Relation_OId @ SV1001 ) @ ( tc_fun @ ( tc_prod @ SV1001 @ SV1001 ) @ tc_bool ) )
= ( c_Transitive__Closure_Ortrancl @ SV396 @ SV1001 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2702]) ).
thf(3350,plain,
! [SV1002: $i,SV397: $i] :
( ( ( c_Transitive__Closure_Otrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV397 @ ( c_Relation_OId @ SV1002 ) @ ( tc_fun @ ( tc_prod @ SV1002 @ SV1002 ) @ tc_bool ) ) @ SV1002 )
= ( c_Transitive__Closure_Ortrancl @ SV397 @ SV1002 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2703]) ).
thf(3351,plain,
! [SV1003: $i,SV398: $i] :
( ( ( c_Transitive__Closure_Ortrancl @ SV398 @ SV1003 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Otrancl @ SV398 @ SV1003 ) @ ( c_Relation_OId @ SV1003 ) @ ( tc_fun @ ( tc_prod @ SV1003 @ SV1003 ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2704]) ).
thf(3352,plain,
! [SV1004: $i,SV399: $i] :
( ( ! [SY4704: $i,SY4705: $i,SY4706: $i,SY4707: $i] :
( ( ( c_Recdef_Ocut @ SV399 @ SV1004 @ SY4704 @ SY4705 @ SY4706 )
= ( c_Recdef_Ocut @ SY4707 @ SV1004 @ SY4704 @ SY4705 @ SY4706 ) )
| ( c_in @ ( c_Pair @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ SV399 @ SY4707 @ SV1004 @ SY4704 @ SY4705 @ SY4706 ) @ SY4704 @ SY4705 @ SY4705 ) @ SV1004 @ ( tc_prod @ SY4705 @ SY4705 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2705]) ).
thf(3353,plain,
! [SV1005: $i,SV400: $i] :
( ( ! [SY4708: $i] :
( ( SV400
= ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XId__onE__1__1 @ SV1005 @ SV400 @ SY4708 ) @ ( c_ATP__Linkup_Osko__Relation__XId__onE__1__1 @ SV1005 @ SV400 @ SY4708 ) @ SY4708 @ SY4708 ) )
| ~ ( c_in @ SV400 @ ( c_Relation_OId__on @ SV1005 @ SY4708 ) @ ( tc_prod @ SY4708 @ SY4708 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2706]) ).
thf(3354,plain,
! [SV1006: $i,SV401: $i] :
( ( ! [SY4709: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Relation__XId__onE__1__1 @ SV401 @ SV1006 @ SY4709 ) @ SV401 @ SY4709 )
| ~ ( c_in @ SV1006 @ ( c_Relation_OId__on @ SV401 @ SY4709 ) @ ( tc_prod @ SY4709 @ SY4709 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2707]) ).
thf(3355,plain,
! [SV1007: $i,SV402: $i] :
( ( ( c_Wellfounded_Owf @ SV402 @ SV1007 )
| ~ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1 @ SV402 @ SV1007 ) @ ( c_Wellfounded_Oacc @ SV402 @ SV1007 ) @ SV1007 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2708]) ).
thf(3356,plain,
! [SV1008: $i,SV403: $i] :
( ( ( c_Wellfounded_Owf @ SV403 @ SV1008 )
| ~ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1 @ SV403 @ SV1008 ) @ ( c_Wellfounded_Oacc @ SV403 @ SV1008 ) @ SV1008 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2709]) ).
thf(3357,plain,
! [SV1009: $i,SV404: $i] :
( ( ( SV404
= ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XIdE__1__1 @ SV404 @ SV1009 ) @ ( c_ATP__Linkup_Osko__Relation__XIdE__1__1 @ SV404 @ SV1009 ) @ SV1009 @ SV1009 ) )
| ~ ( c_in @ SV404 @ ( c_Relation_OId @ SV1009 ) @ ( tc_prod @ SV1009 @ SV1009 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2710]) ).
thf(3358,plain,
! [SV1010: $i,SV405: $i] :
( ( ! [SY4710: $i,SY4711: $i,SY4712: $i,SY4713: $i,SY4714: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 @ SV405 @ SV1010 @ SY4710 @ SY4711 @ SY4712 @ SY4713 @ SY4714 ) @ SV1010 @ SY4714 @ SY4713 ) @ SY4711 @ ( tc_prod @ SY4714 @ SY4713 ) )
| ~ ( c_in @ ( c_Pair @ SV405 @ SV1010 @ SY4712 @ SY4713 ) @ ( c_Relation_Orel__comp @ SY4710 @ SY4711 @ SY4712 @ SY4714 @ SY4713 ) @ ( tc_prod @ SY4712 @ SY4713 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2711]) ).
thf(3359,plain,
! [SV1011: $i,SV406: $i] :
( ( ! [SY4715: $i,SY4716: $i,SY4717: $i,SY4718: $i,SY4719: $i] :
( ( c_in @ ( c_Pair @ SV406 @ ( c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 @ SV406 @ SV1011 @ SY4715 @ SY4716 @ SY4717 @ SY4718 @ SY4719 ) @ SY4717 @ SY4719 ) @ SY4715 @ ( tc_prod @ SY4717 @ SY4719 ) )
| ~ ( c_in @ ( c_Pair @ SV406 @ SV1011 @ SY4717 @ SY4718 ) @ ( c_Relation_Orel__comp @ SY4715 @ SY4716 @ SY4717 @ SY4719 @ SY4718 ) @ ( tc_prod @ SY4717 @ SY4718 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2712]) ).
thf(3360,plain,
! [SV1012: $i,SV407: $i] :
( ( ! [SY4720: $i] :
( ~ ( c_in @ ( c_Pair @ SV407 @ SV407 @ SV1012 @ SV1012 ) @ SY4720 @ ( tc_prod @ SV1012 @ SV1012 ) )
| ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1 @ SY4720 @ SV1012 ) @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1 @ SY4720 @ SV1012 ) @ SV1012 @ SV1012 ) @ ( c_Transitive__Closure_Otrancl @ SY4720 @ SV1012 ) @ ( tc_prod @ SV1012 @ SV1012 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2713]) ).
thf(3361,plain,
! [SV1013: $i,SV408: $i] :
( ( ! [SY4721: $i,SY4722: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1 @ SV408 @ SV1013 @ SY4721 @ SY4722 ) @ SY4721 @ SY4722 @ SY4722 ) @ ( c_Transitive__Closure_Otrancl @ SV408 @ SY4722 ) @ ( tc_prod @ SY4722 @ SY4722 ) )
| ( c_in @ ( c_Pair @ SV1013 @ SY4721 @ SY4722 @ SY4722 ) @ SV408 @ ( tc_prod @ SY4722 @ SY4722 ) )
| ~ ( c_in @ ( c_Pair @ SV1013 @ SY4721 @ SY4722 @ SY4722 ) @ ( c_Transitive__Closure_Otrancl @ SV408 @ SY4722 ) @ ( tc_prod @ SY4722 @ SY4722 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2714]) ).
thf(3362,plain,
! [SV1014: $i,SV409: $i] :
( ( ! [SY4723: $i,SY4724: $i] :
( ( c_in @ ( c_Pair @ SV409 @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1 @ SV1014 @ SV409 @ SY4723 @ SY4724 ) @ SY4724 @ SY4724 ) @ SV1014 @ ( tc_prod @ SY4724 @ SY4724 ) )
| ~ ( c_in @ ( c_Pair @ SV409 @ SY4723 @ SY4724 @ SY4724 ) @ ( c_Transitive__Closure_Otrancl @ SV1014 @ SY4724 ) @ ( tc_prod @ SY4724 @ SY4724 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2715]) ).
thf(3363,plain,
! [SV1015: $i,SV410: $i] :
( ( ! [SY4725: $i] :
( ( c_in @ ( c_Pair @ SV410 @ ( v_sko__Transitive__Closure__Xtrancl__Xcases__1 @ SV410 @ SV1015 @ SY4725 ) @ t_a @ t_a ) @ ( c_Transitive__Closure_Otrancl @ SY4725 @ t_a ) @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ ( c_Pair @ SV410 @ SV1015 @ t_a @ t_a ) @ SY4725 @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ ( c_Pair @ SV410 @ SV1015 @ t_a @ t_a ) @ ( c_Transitive__Closure_Otrancl @ SY4725 @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2716]) ).
thf(3364,plain,
! [SV1016: $i,SV411: $i] :
( ( ! [SY4726: $i] :
( ~ ( c_in @ ( c_Pair @ SV411 @ SV411 @ SV1016 @ SV1016 ) @ ( c_Transitive__Closure_Otrancl @ SY4726 @ SV1016 ) @ ( tc_prod @ SV1016 @ SV1016 ) )
| ~ ( c_Wellfounded_Oacyclic @ SY4726 @ SV1016 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2717]) ).
thf(3365,plain,
! [SV1017: $i,SV412: $i] :
( ( ! [SY4727: $i,SY4728: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1 @ SV412 @ SV1017 @ SY4727 @ SY4728 ) @ SV1017 @ SY4728 @ SY4728 ) @ SY4727 @ ( tc_prod @ SY4728 @ SY4728 ) )
| ( c_in @ ( c_Pair @ SV412 @ SV1017 @ SY4728 @ SY4728 ) @ SY4727 @ ( tc_prod @ SY4728 @ SY4728 ) )
| ~ ( c_in @ ( c_Pair @ SV412 @ SV1017 @ SY4728 @ SY4728 ) @ ( c_Transitive__Closure_Otrancl @ SY4727 @ SY4728 ) @ ( tc_prod @ SY4728 @ SY4728 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2718]) ).
thf(3366,plain,
! [SV1018: $i,SV413: $i] :
( ( ! [SY4729: $i,SY4730: $i] :
( ( c_in @ ( c_Pair @ SV413 @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1 @ SV413 @ SV1018 @ SY4729 @ SY4730 ) @ SY4730 @ SY4730 ) @ ( c_Transitive__Closure_Otrancl @ SY4729 @ SY4730 ) @ ( tc_prod @ SY4730 @ SY4730 ) )
| ( c_in @ ( c_Pair @ SV413 @ SV1018 @ SY4730 @ SY4730 ) @ SY4729 @ ( tc_prod @ SY4730 @ SY4730 ) )
| ~ ( c_in @ ( c_Pair @ SV413 @ SV1018 @ SY4730 @ SY4730 ) @ ( c_Transitive__Closure_Otrancl @ SY4729 @ SY4730 ) @ ( tc_prod @ SY4730 @ SY4730 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2719]) ).
thf(3367,plain,
! [SV1019: $i,SV414: $i] :
( ( ! [SY4731: $i,SY4732: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1 @ SV414 @ SV1019 @ SY4731 @ SY4732 ) @ SY4731 @ SY4732 @ SY4732 ) @ SV414 @ ( tc_prod @ SY4732 @ SY4732 ) )
| ~ ( c_in @ ( c_Pair @ SV1019 @ SY4731 @ SY4732 @ SY4732 ) @ ( c_Transitive__Closure_Otrancl @ SV414 @ SY4732 ) @ ( tc_prod @ SY4732 @ SY4732 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2720]) ).
thf(3368,plain,
! [SV1020: $i,SV415: $i] :
( ( ! [SY4733: $i,SY4734: $i] :
( ( c_in @ ( c_Pair @ SV415 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1 @ SV1020 @ SV415 @ SY4733 @ SY4734 ) @ SY4734 @ SY4734 ) @ SV1020 @ ( tc_prod @ SY4734 @ SY4734 ) )
| ( c_in @ ( c_Pair @ SV415 @ SY4733 @ SY4734 @ SY4734 ) @ SV1020 @ ( tc_prod @ SY4734 @ SY4734 ) )
| ~ ( c_in @ ( c_Pair @ SV415 @ SY4733 @ SY4734 @ SY4734 ) @ ( c_Transitive__Closure_Otrancl @ SV1020 @ SY4734 ) @ ( tc_prod @ SY4734 @ SY4734 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2721]) ).
thf(3369,plain,
! [SV1021: $i,SV416: $i] :
( ( ! [SY4735: $i] :
( ( c_in @ ( c_Pair @ ( v_sko__Transitive__Closure__Xtrancl__Xcases__1 @ SV416 @ SV1021 @ SY4735 ) @ SV1021 @ t_a @ t_a ) @ SY4735 @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ ( c_Pair @ SV416 @ SV1021 @ t_a @ t_a ) @ SY4735 @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ ( c_Pair @ SV416 @ SV1021 @ t_a @ t_a ) @ ( c_Transitive__Closure_Otrancl @ SY4735 @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2722]) ).
thf(3370,plain,
! [SV1022: $i,SV417: $i] :
( ( ! [SY4736: $i] :
( ( hBOOL @ ( hAPP @ SV417 @ SV1022 ) )
| ( hBOOL @ ( hAPP @ SV417 @ SY4736 ) )
| ! [SY3449: $i,SY3450: $i] :
( ~ ( c_in @ ( c_Pair @ SY4736 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1 @ SV417 @ SY3449 @ SY3450 ) @ SY3450 @ SY3450 ) @ SY3449 @ ( tc_prod @ SY3450 @ SY3450 ) )
| ~ ( c_Wellfounded_Owf @ SY3449 @ SY3450 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2723]) ).
thf(3371,plain,
! [SV1023: $i,SV418: $i] :
( ( ! [SY4739: $i] :
( ( hBOOL @ ( hAPP @ SV418 @ SV1023 ) )
| ( hBOOL @ ( hAPP @ SV418 @ SY4739 ) )
| ! [SY3453: $i,SY3454: $i] :
( ~ ( c_in @ ( c_Pair @ SY4739 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1 @ SV418 @ SY3453 @ SY3454 ) @ SY3454 @ SY3454 ) @ SY3453 @ ( tc_prod @ SY3454 @ SY3454 ) )
| ~ ( c_Wellfounded_Owf @ SY3453 @ SY3454 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2724]) ).
thf(3372,plain,
! [SV1024: $i,SV419: $i] :
( ( ! [SY4742: $i] :
( ( hBOOL @ ( hAPP @ SV419 @ SV1024 ) )
| ( hBOOL @ ( hAPP @ SV419 @ SY4742 ) )
| ! [SY3457: $i,SY3458: $i] :
( ~ ( c_in @ ( c_Pair @ SY4742 @ ( c_List_Osko__Recdef__Xtfl__wf__induct__1__1 @ SV419 @ SY3457 @ SY3458 ) @ SY3458 @ SY3458 ) @ SY3457 @ ( tc_prod @ SY3458 @ SY3458 ) )
| ~ ( c_Wellfounded_Owf @ SY3457 @ SY3458 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2725]) ).
thf(3373,plain,
! [SV1025: $i,SV420: $i] :
( ( ! [SY4745: $i] :
( ( hBOOL @ ( hAPP @ SV420 @ SV1025 ) )
| ( hBOOL @ ( hAPP @ SV420 @ SY4745 ) )
| ! [SY3461: $i,SY3462: $i] :
( ~ ( c_in @ ( c_Pair @ SY4745 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1 @ SV420 @ SY3461 @ SY3462 ) @ SY3462 @ SY3462 ) @ SY3461 @ ( tc_prod @ SY3462 @ SY3462 ) )
| ~ ( c_Wellfounded_Owf @ SY3461 @ SY3462 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2726]) ).
thf(3374,plain,
! [SV1026: $i,SV421: $i] :
( ( ! [SY4748: $i,SY4749: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1 @ SV421 @ SV1026 @ SY4748 @ SY4749 ) @ SV1026 @ SY4749 @ SY4749 ) @ SY4748 @ ( tc_prod @ SY4749 @ SY4749 ) )
| ( SV421 = SV1026 )
| ~ ( c_in @ ( c_Pair @ SV421 @ SV1026 @ SY4749 @ SY4749 ) @ ( c_Transitive__Closure_Ortrancl @ SY4748 @ SY4749 ) @ ( tc_prod @ SY4749 @ SY4749 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2727]) ).
thf(3375,plain,
! [SV1027: $i,SV422: $i] :
( ( ! [SY4750: $i,SY4751: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1 @ SV422 @ SV1027 @ SY4750 @ SY4751 ) @ SY4750 @ SY4751 @ SY4751 ) @ ( c_Transitive__Closure_Ortrancl @ SV422 @ SY4751 ) @ ( tc_prod @ SY4751 @ SY4751 ) )
| ( SV1027 = SY4750 )
| ~ ( c_in @ ( c_Pair @ SV1027 @ SY4750 @ SY4751 @ SY4751 ) @ ( c_Transitive__Closure_Ortrancl @ SV422 @ SY4751 ) @ ( tc_prod @ SY4751 @ SY4751 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2728]) ).
thf(3376,plain,
! [SV1028: $i,SV423: $i] :
( ( ! [SY4752: $i,SY4753: $i] :
( ( c_in @ ( c_Pair @ SV423 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1 @ SV1028 @ SV423 @ SY4752 @ SY4753 ) @ SY4753 @ SY4753 ) @ SV1028 @ ( tc_prod @ SY4753 @ SY4753 ) )
| ( SV423 = SY4752 )
| ~ ( c_in @ ( c_Pair @ SV423 @ SY4752 @ SY4753 @ SY4753 ) @ ( c_Transitive__Closure_Ortrancl @ SV1028 @ SY4753 ) @ ( tc_prod @ SY4753 @ SY4753 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2729]) ).
thf(3377,plain,
! [SV1029: $i,SV424: $i] :
( ( ! [SY4754: $i] :
( ( hBOOL @ ( hAPP @ SV424 @ SV1029 ) )
| ! [SY4755: $i,SY4756: $i] :
( ( hBOOL @ ( hAPP @ SV424 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 @ SV424 @ SY4754 @ SY4755 @ SY4756 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV424 @ SY4754 ) )
| ~ ( c_in @ ( c_Pair @ SV1029 @ SY4754 @ SY4756 @ SY4756 ) @ ( c_Transitive__Closure_Ortrancl @ SY4755 @ SY4756 ) @ ( tc_prod @ SY4756 @ SY4756 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2730]) ).
thf(3378,plain,
! [SV1030: $i,SV425: $i] :
( ( ! [SY4757: $i] :
( ( hBOOL @ ( hAPP @ SV425 @ SV1030 ) )
| ! [SY4758: $i,SY4759: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 @ SV425 @ SY4757 @ SY4758 @ SY4759 ) @ SY4757 @ SY4759 @ SY4759 ) @ ( c_Transitive__Closure_Ortrancl @ SY4758 @ SY4759 ) @ ( tc_prod @ SY4759 @ SY4759 ) )
| ~ ( hBOOL @ ( hAPP @ SV425 @ SY4757 ) )
| ~ ( c_in @ ( c_Pair @ SV1030 @ SY4757 @ SY4759 @ SY4759 ) @ ( c_Transitive__Closure_Ortrancl @ SY4758 @ SY4759 ) @ ( tc_prod @ SY4759 @ SY4759 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2731]) ).
thf(3379,plain,
! [SV1031: $i,SV426: $i] :
( ( ! [SY4760: $i] :
( ( hBOOL @ ( hAPP @ SV426 @ SV1031 ) )
| ! [SY4761: $i,SY4762: $i] :
( ( c_in @ ( c_Pair @ SY4760 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 @ SV426 @ SY4760 @ SY4761 @ SY4762 ) @ SY4762 @ SY4762 ) @ ( c_Transitive__Closure_Ortrancl @ SY4761 @ SY4762 ) @ ( tc_prod @ SY4762 @ SY4762 ) )
| ~ ( hBOOL @ ( hAPP @ SV426 @ SY4760 ) )
| ~ ( c_in @ ( c_Pair @ SY4760 @ SV1031 @ SY4762 @ SY4762 ) @ ( c_Transitive__Closure_Ortrancl @ SY4761 @ SY4762 ) @ ( tc_prod @ SY4762 @ SY4762 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2732]) ).
thf(3380,plain,
! [SV1032: $i,SV427: $i] :
( ( ! [SY4763: $i] :
( ( hBOOL @ ( hAPP @ SV427 @ SV1032 ) )
| ! [SY4764: $i,SY4765: $i] :
( ~ ( hBOOL @ ( hAPP @ SV427 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2 @ SV427 @ SY4763 @ SY4764 @ SY4765 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV427 @ SY4763 ) )
| ~ ( c_in @ ( c_Pair @ SY4763 @ SV1032 @ SY4765 @ SY4765 ) @ ( c_Transitive__Closure_Ortrancl @ SY4764 @ SY4765 ) @ ( tc_prod @ SY4765 @ SY4765 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2733]) ).
thf(3381,plain,
! [SV1033: $i,SV428: $i] :
( ( ! [SY4766: $i] :
( ( c_in @ ( c_Pair @ SV428 @ ( v_sko__Transitive__Closure__Xrtrancl__Xcases__1 @ SV428 @ SV1033 @ SY4766 ) @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ SY4766 @ t_a ) @ ( tc_prod @ t_a @ t_a ) )
| ( SV1033 = SV428 )
| ~ ( c_in @ ( c_Pair @ SV428 @ SV1033 @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ SY4766 @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2734]) ).
thf(3382,plain,
! [SV1034: $i,SV429: $i] :
( ( ! [SY4767: $i] :
( ( hBOOL @ ( hAPP @ SV429 @ SV1034 ) )
| ! [SY4768: $i,SY4769: $i] :
( ( hBOOL @ ( hAPP @ SV429 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 @ SV429 @ SY4767 @ SY4768 @ SY4769 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV429 @ SY4767 ) )
| ~ ( c_in @ ( c_Pair @ SY4767 @ SV1034 @ SY4769 @ SY4769 ) @ ( c_Transitive__Closure_Ortrancl @ SY4768 @ SY4769 ) @ ( tc_prod @ SY4769 @ SY4769 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2735]) ).
thf(3383,plain,
! [SV1035: $i,SV430: $i] :
( ( ! [SY4770: $i] :
( ( c_in @ ( c_Pair @ ( v_sko__Transitive__Closure__Xrtrancl__Xcases__1 @ SV430 @ SV1035 @ SY4770 ) @ SV1035 @ t_a @ t_a ) @ SY4770 @ ( tc_prod @ t_a @ t_a ) )
| ( SV1035 = SV430 )
| ~ ( c_in @ ( c_Pair @ SV430 @ SV1035 @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ SY4770 @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2736]) ).
thf(3384,plain,
! [SV1036: $i,SV431: $i] :
( ( ! [SY4771: $i] :
( ( hBOOL @ ( hAPP @ SV431 @ SV1036 ) )
| ! [SY4772: $i,SY4773: $i] :
( ~ ( hBOOL @ ( hAPP @ SV431 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1 @ SV431 @ SY4771 @ SY4772 @ SY4773 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV431 @ SY4771 ) )
| ~ ( c_in @ ( c_Pair @ SV1036 @ SY4771 @ SY4773 @ SY4773 ) @ ( c_Transitive__Closure_Ortrancl @ SY4772 @ SY4773 ) @ ( tc_prod @ SY4773 @ SY4773 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2737]) ).
thf(3385,plain,
! [SV1037: $i,SV432: $i] :
( ( ! [SY4774: $i,SY4775: $i] :
( ( c_in @ ( c_Pair @ SV432 @ ( c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1 @ SV432 @ SV1037 @ SY4774 @ SY4775 ) @ SY4775 @ SY4775 ) @ ( c_Transitive__Closure_Ortrancl @ SY4774 @ SY4775 ) @ ( tc_prod @ SY4775 @ SY4775 ) )
| ( SV432 = SV1037 )
| ~ ( c_in @ ( c_Pair @ SV432 @ SV1037 @ SY4775 @ SY4775 ) @ ( c_Transitive__Closure_Ortrancl @ SY4774 @ SY4775 ) @ ( tc_prod @ SY4775 @ SY4775 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2738]) ).
thf(3386,plain,
! [SV1038: $i,SV433: $i] :
( ( ! [SY4776: $i,SY4777: $i,SY4778: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Product__Type__XSigmaE__1__1 @ SV433 @ SV1038 @ SY4776 @ SY4777 @ SY4778 ) @ SV433 @ SY4777 )
| ~ ( c_in @ SY4776 @ ( c_Product__Type_OSigma @ SV433 @ SV1038 @ SY4777 @ SY4778 ) @ ( tc_prod @ SY4777 @ SY4778 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2739]) ).
thf(3387,plain,
! [SV1039: $i,SV434: $i] :
( ( ( c_Wellfounded_OwfP @ ( c_FunDef_Oin__rel @ SV434 @ SV1039 @ SV1039 ) @ SV1039 )
| ~ ( c_Wellfounded_Owf @ SV434 @ SV1039 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2740]) ).
thf(3388,plain,
! [SV1040: $i,SV435: $i] :
( ( c_Relation_Oirrefl @ ( c_HOL_Ominus__class_Ominus @ SV435 @ ( c_Relation_OId @ SV1040 ) @ ( tc_fun @ ( tc_prod @ SV1040 @ SV1040 ) @ tc_bool ) ) @ SV1040 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2741]) ).
thf(3389,plain,
! [SV1041: $i,SV436: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_Oconverse @ SV436 @ SV1041 @ SV1041 ) @ ( c_Transitive__Closure_Ortrancl @ SV436 @ SV1041 ) @ ( tc_fun @ ( tc_prod @ SV1041 @ SV1041 ) @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV1041 @ SV1041 ) @ tc_bool ) ) )
| ! [SY4779: $i] :
~ ( c_in @ ( c_Pair @ SY4779 @ SY4779 @ SV1041 @ SV1041 ) @ ( c_Transitive__Closure_Otrancl @ SV436 @ SV1041 ) @ ( tc_prod @ SV1041 @ SV1041 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2742]) ).
thf(3390,plain,
! [SV1042: $i,SV437: $i] :
( ( ! [SY4780: $i,SY4781: $i] :
( ( ( c_Relation_OImage @ SV437 @ ( c_Set_Oinsert @ SV1042 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4780 @ tc_bool ) ) @ SY4780 ) @ SY4780 @ SY4780 )
!= ( c_Relation_OImage @ SV437 @ ( c_Set_Oinsert @ SY4781 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4780 @ tc_bool ) ) @ SY4780 ) @ SY4780 @ SY4780 ) )
| ( c_in @ ( c_Pair @ SV1042 @ SY4781 @ SY4780 @ SY4780 ) @ SV437 @ ( tc_prod @ SY4780 @ SY4780 ) )
| ! [SY3514: $i] :
( ~ ( c_in @ SY4781 @ SY3514 @ SY4780 )
| ~ ( c_Equiv__Relations_Oequiv @ SY3514 @ SV437 @ SY4780 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2743]) ).
thf(3391,plain,
! [SV1043: $i,SV438: $i] :
( ( ! [SY4783: $i,SY4784: $i] :
( ( ( c_Relation_OImage @ SV438 @ ( c_Set_Oinsert @ SV1043 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4783 @ tc_bool ) ) @ SY4783 ) @ SY4783 @ SY4783 )
!= ( c_Relation_OImage @ SV438 @ ( c_Set_Oinsert @ SY4784 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4783 @ tc_bool ) ) @ SY4783 ) @ SY4783 @ SY4783 ) )
| ! [SY4785: $i] :
( ~ ( c_Equiv__Relations_Oequiv @ SY4785 @ SV438 @ SY4783 )
| ( c_in @ ( c_Pair @ SV1043 @ SY4784 @ SY4783 @ SY4783 ) @ SV438 @ ( tc_prod @ SY4783 @ SY4783 ) )
| ~ ( c_in @ SY4784 @ SY4785 @ SY4783 )
| ~ ( c_in @ SV1043 @ SY4785 @ SY4783 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2744]) ).
thf(3392,plain,
! [SV1044: $i,SV439: $i] :
( ( ! [SY4786: $i,SY4787: $i] :
( ( ( c_Relation_OImage @ SV439 @ ( c_Set_Oinsert @ SV1044 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4786 @ tc_bool ) ) @ SY4786 ) @ SY4786 @ SY4786 )
= ( c_Relation_OImage @ SV439 @ ( c_Set_Oinsert @ SY4787 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4786 @ tc_bool ) ) @ SY4786 ) @ SY4786 @ SY4786 ) )
| ~ ( c_in @ ( c_Pair @ SV1044 @ SY4787 @ SY4786 @ SY4786 ) @ SV439 @ ( tc_prod @ SY4786 @ SY4786 ) )
| ! [SY4788: $i] :
( ~ ( c_in @ SY4787 @ SY4788 @ SY4786 )
| ~ ( c_in @ SV1044 @ SY4788 @ SY4786 )
| ~ ( c_Equiv__Relations_Oequiv @ SY4788 @ SV439 @ SY4786 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2745]) ).
thf(3393,plain,
! [SV1045: $i,SV440: $i] :
( ( ! [SY4789: $i,SY4790: $i] :
( ( ( c_Relation_OImage @ SV440 @ ( c_Set_Oinsert @ SV1045 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4789 @ tc_bool ) ) @ SY4789 ) @ SY4789 @ SY4789 )
!= ( c_Relation_OImage @ SV440 @ ( c_Set_Oinsert @ SY4790 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4789 @ tc_bool ) ) @ SY4789 ) @ SY4789 @ SY4789 ) )
| ! [SY4791: $i] :
( ~ ( c_in @ SY4790 @ SY4791 @ SY4789 )
| ~ ( c_in @ SV1045 @ SY4791 @ SY4789 )
| ~ ( c_Equiv__Relations_Oequiv @ SY4791 @ SV440 @ SY4789 )
| ( c_in @ ( c_Pair @ SV1045 @ SY4790 @ SY4789 @ SY4789 ) @ SV440 @ ( tc_prod @ SY4789 @ SY4789 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2746]) ).
thf(3394,plain,
! [SV1046: $i,SV441: $i] :
( ( ! [SY4792: $i] :
( ( c_Set_Oimage @ ( c_snd @ SV441 @ SV1046 ) @ SY4792 @ ( tc_prod @ SV441 @ SV1046 ) @ SV1046 )
= ( c_Relation_ORange @ SY4792 @ SV441 @ SV1046 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2747]) ).
thf(3395,plain,
! [SV1047: $i,SV442: $i] :
( ( ! [SY4793: $i] :
( ( c_in @ SV442 @ SV1047 @ SY4793 )
| ! [SY4794: $i] :
( ( SV442 = SY4794 )
| ! [SY4795: $i] :
( ~ ( c_lessequals @ SY4795 @ ( c_Product__Type_OSigma @ SV1047 @ ( c_COMBK @ SV1047 @ ( tc_fun @ SY4793 @ tc_bool ) @ SY4793 ) @ SY4793 @ SY4793 ) @ ( tc_fun @ ( tc_prod @ SY4793 @ SY4793 ) @ tc_bool ) )
| ~ ( c_in @ ( c_Pair @ SV442 @ SY4794 @ SY4793 @ SY4793 ) @ ( c_Transitive__Closure_Ortrancl @ SY4795 @ SY4793 ) @ ( tc_prod @ SY4793 @ SY4793 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2748]) ).
thf(3396,plain,
! [SV1048: $i,SV443: $i] :
( ( ! [SY4796: $i] :
( ( c_Set_Oimage @ ( c_fst @ SV443 @ SV1048 ) @ SY4796 @ ( tc_prod @ SV443 @ SV1048 ) @ SV443 )
= ( c_Relation_ODomain @ SY4796 @ SV443 @ SV1048 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2749]) ).
thf(3397,plain,
! [SV1049: $i,SV444: $i] :
( ( ! [SY4797: $i] :
( ( c_in @ SV444 @ ( c_Transitive__Closure_Ortrancl @ SV1049 @ SY4797 ) @ ( tc_prod @ SY4797 @ SY4797 ) )
| ~ ( c_in @ SV444 @ SV1049 @ ( tc_prod @ SY4797 @ SY4797 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2750]) ).
thf(3398,plain,
! [SV1050: $i,SV445: $i] :
( ( ! [SY4798: $i] :
( ( c_in @ SV445 @ ( c_Transitive__Closure_Otrancl @ SV1050 @ SY4798 ) @ ( tc_prod @ SY4798 @ SY4798 ) )
| ~ ( c_in @ SV445 @ SV1050 @ ( tc_prod @ SY4798 @ SY4798 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2751]) ).
thf(3399,plain,
! [SV1051: $i,SV446: $i] :
( ( ! [SY4799: $i,SY4800: $i] :
( ( c_in @ ( c_Pair @ SV446 @ SV1051 @ SY4799 @ SY4799 ) @ ( c_Transitive__Closure_Otrancl @ SY4800 @ SY4799 ) @ ( tc_prod @ SY4799 @ SY4799 ) )
| ! [SY4801: $i] :
( ~ ( c_in @ ( c_Pair @ SY4801 @ SV1051 @ SY4799 @ SY4799 ) @ ( c_Transitive__Closure_Ortrancl @ SY4800 @ SY4799 ) @ ( tc_prod @ SY4799 @ SY4799 ) )
| ~ ( c_in @ ( c_Pair @ SV446 @ SY4801 @ SY4799 @ SY4799 ) @ SY4800 @ ( tc_prod @ SY4799 @ SY4799 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2752]) ).
thf(3400,plain,
! [SV1052: $i,SV447: $i] :
( ( ! [SY4802: $i,SY4803: $i] :
( ( c_in @ ( c_Pair @ SV447 @ SV1052 @ SY4802 @ SY4802 ) @ ( c_Transitive__Closure_Otrancl @ SY4803 @ SY4802 ) @ ( tc_prod @ SY4802 @ SY4802 ) )
| ! [SY4804: $i] :
( ~ ( c_in @ ( c_Pair @ SY4804 @ SV1052 @ SY4802 @ SY4802 ) @ SY4803 @ ( tc_prod @ SY4802 @ SY4802 ) )
| ~ ( c_in @ ( c_Pair @ SV447 @ SY4804 @ SY4802 @ SY4802 ) @ ( c_Transitive__Closure_Ortrancl @ SY4803 @ SY4802 ) @ ( tc_prod @ SY4802 @ SY4802 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2753]) ).
thf(3401,plain,
! [SV1053: $i,SV448: $i] :
( ( ! [SY4805: $i,SY4806: $i] :
( ( c_in @ ( c_Pair @ SV448 @ SV1053 @ SY4805 @ SY4805 ) @ ( c_Transitive__Closure_Ortrancl @ SY4806 @ SY4805 ) @ ( tc_prod @ SY4805 @ SY4805 ) )
| ~ ( c_in @ ( c_Pair @ SV448 @ SV1053 @ SY4805 @ SY4805 ) @ ( c_Transitive__Closure_Otrancl @ SY4806 @ SY4805 ) @ ( tc_prod @ SY4805 @ SY4805 ) )
| ( SV448 = SV1053 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2754]) ).
thf(3402,plain,
! [SV1054: $i,SV449: $i] :
( ( ! [SY4807: $i,SY4808: $i] :
( ( c_in @ ( c_Pair @ SV449 @ SV1054 @ SY4807 @ SY4807 ) @ ( c_Transitive__Closure_Otrancl @ SY4808 @ SY4807 ) @ ( tc_prod @ SY4807 @ SY4807 ) )
| ( SV449 = SV1054 )
| ~ ( c_in @ ( c_Pair @ SV449 @ SV1054 @ SY4807 @ SY4807 ) @ ( c_Transitive__Closure_Ortrancl @ SY4808 @ SY4807 ) @ ( tc_prod @ SY4807 @ SY4807 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2755]) ).
thf(3403,plain,
! [SV1055: $i,SV450: $i] :
( ( ! [SY4809: $i,SY4810: $i] :
( ( c_in @ ( c_Pair @ SV450 @ SV1055 @ SY4809 @ SY4809 ) @ ( c_Transitive__Closure_Otrancl @ SY4810 @ SY4809 ) @ ( tc_prod @ SY4809 @ SY4809 ) )
| ( SV450 = SV1055 )
| ~ ( c_in @ ( c_Pair @ SV450 @ SV1055 @ SY4809 @ SY4809 ) @ ( c_Transitive__Closure_Ortrancl @ SY4810 @ SY4809 ) @ ( tc_prod @ SY4809 @ SY4809 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2756]) ).
thf(3404,plain,
! [SV1056: $i,SV451: $i] :
( ( ! [SY4811: $i,SY4812: $i] :
( ( c_in @ ( c_Pair @ SV451 @ SV1056 @ SY4811 @ SY4811 ) @ ( c_Transitive__Closure_Ortrancl @ ( c_Relation_Oconverse @ SY4812 @ SY4811 @ SY4811 ) @ SY4811 ) @ ( tc_prod @ SY4811 @ SY4811 ) )
| ~ ( c_in @ ( c_Pair @ SV1056 @ SV451 @ SY4811 @ SY4811 ) @ ( c_Transitive__Closure_Ortrancl @ SY4812 @ SY4811 ) @ ( tc_prod @ SY4811 @ SY4811 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2757]) ).
thf(3405,plain,
! [SV1057: $i,SV452: $i] :
( ( ! [SY4813: $i,SY4814: $i] :
( ( c_in @ ( c_Pair @ SV452 @ SV1057 @ SY4813 @ SY4813 ) @ ( c_Transitive__Closure_Ortrancl @ SY4814 @ SY4813 ) @ ( tc_prod @ SY4813 @ SY4813 ) )
| ~ ( c_in @ ( c_Pair @ SV1057 @ SV452 @ SY4813 @ SY4813 ) @ ( c_Transitive__Closure_Ortrancl @ ( c_Relation_Oconverse @ SY4814 @ SY4813 @ SY4813 ) @ SY4813 ) @ ( tc_prod @ SY4813 @ SY4813 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2758]) ).
thf(3406,plain,
! [SV1058: $i,SV453: $i] :
( ( ! [SY4815: $i,SY4816: $i] :
( ( c_in @ ( c_Pair @ SV453 @ SV1058 @ SY4815 @ SY4815 ) @ ( c_Transitive__Closure_Ortrancl @ SY4816 @ SY4815 ) @ ( tc_prod @ SY4815 @ SY4815 ) )
| ( c_in @ ( c_Pair @ SV1058 @ SV453 @ SY4815 @ SY4815 ) @ ( c_Transitive__Closure_Ortrancl @ SY4816 @ SY4815 ) @ ( tc_prod @ SY4815 @ SY4815 ) )
| ! [SY4817: $i] :
( ~ ( c_in @ ( c_Pair @ SY4817 @ SV453 @ SY4815 @ SY4815 ) @ ( c_Transitive__Closure_Ortrancl @ SY4816 @ SY4815 ) @ ( tc_prod @ SY4815 @ SY4815 ) )
| ~ ( c_in @ ( c_Pair @ SY4817 @ SV1058 @ SY4815 @ SY4815 ) @ ( c_Transitive__Closure_Ortrancl @ SY4816 @ SY4815 ) @ ( tc_prod @ SY4815 @ SY4815 ) )
| ~ ( c_Relation_Osingle__valued @ SY4816 @ SY4815 @ SY4815 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2759]) ).
thf(3407,plain,
! [SV1059: $i,SV454: $i] :
( ( ! [SY4818: $i,SY4819: $i] :
( ( c_in @ ( c_Pair @ SV454 @ SV1059 @ SY4818 @ SY4818 ) @ ( c_Transitive__Closure_Ortrancl @ SY4819 @ SY4818 ) @ ( tc_prod @ SY4818 @ SY4818 ) )
| ~ ( c_in @ ( c_Pair @ SV454 @ SV1059 @ SY4818 @ SY4818 ) @ ( c_Transitive__Closure_Otrancl @ SY4819 @ SY4818 ) @ ( tc_prod @ SY4818 @ SY4818 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2760]) ).
thf(3408,plain,
! [SV1060: $i,SV455: $i] :
( ( ! [SY4820: $i,SY4821: $i] :
( ( c_in @ ( c_Pair @ SV455 @ SV1060 @ SY4820 @ SY4820 ) @ ( c_Transitive__Closure_Otrancl @ SY4821 @ SY4820 ) @ ( tc_prod @ SY4820 @ SY4820 ) )
| ! [SY4822: $i] :
( ~ ( c_in @ ( c_Pair @ SY4822 @ SV1060 @ SY4820 @ SY4820 ) @ ( c_Transitive__Closure_Ortrancl @ SY4821 @ SY4820 ) @ ( tc_prod @ SY4820 @ SY4820 ) )
| ~ ( c_in @ ( c_Pair @ SV455 @ SY4822 @ SY4820 @ SY4820 ) @ ( c_Transitive__Closure_Otrancl @ SY4821 @ SY4820 ) @ ( tc_prod @ SY4820 @ SY4820 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2761]) ).
thf(3409,plain,
! [SV1061: $i,SV456: $i] :
( ( ! [SY4823: $i,SY4824: $i] :
( ( c_in @ ( c_Pair @ SV456 @ SV1061 @ SY4823 @ SY4823 ) @ ( c_Transitive__Closure_Otrancl @ SY4824 @ SY4823 ) @ ( tc_prod @ SY4823 @ SY4823 ) )
| ! [SY4825: $i] :
( ~ ( c_in @ ( c_Pair @ SY4825 @ SV1061 @ SY4823 @ SY4823 ) @ ( c_Transitive__Closure_Otrancl @ SY4824 @ SY4823 ) @ ( tc_prod @ SY4823 @ SY4823 ) )
| ~ ( c_in @ ( c_Pair @ SV456 @ SY4825 @ SY4823 @ SY4823 ) @ ( c_Transitive__Closure_Ortrancl @ SY4824 @ SY4823 ) @ ( tc_prod @ SY4823 @ SY4823 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2762]) ).
thf(3410,plain,
! [SV1062: $i,SV457: $i] :
( ( ! [SY4826: $i,SY4827: $i] :
( ( c_in @ ( c_Pair @ SV457 @ SV1062 @ SY4826 @ SY4826 ) @ ( c_Relation_Oconverse @ ( c_Transitive__Closure_Otrancl @ SY4827 @ SY4826 ) @ SY4826 @ SY4826 ) @ ( tc_prod @ SY4826 @ SY4826 ) )
| ~ ( c_in @ ( c_Pair @ SV457 @ SV1062 @ SY4826 @ SY4826 ) @ ( c_Transitive__Closure_Otrancl @ ( c_Relation_Oconverse @ SY4827 @ SY4826 @ SY4826 ) @ SY4826 ) @ ( tc_prod @ SY4826 @ SY4826 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2763]) ).
thf(3411,plain,
! [SV1063: $i,SV458: $i] :
( ( ! [SY4828: $i,SY4829: $i] :
( ( c_in @ ( c_Pair @ SV458 @ SV1063 @ SY4828 @ SY4828 ) @ ( c_Transitive__Closure_Otrancl @ ( c_Relation_Oconverse @ SY4829 @ SY4828 @ SY4828 ) @ SY4828 ) @ ( tc_prod @ SY4828 @ SY4828 ) )
| ~ ( c_in @ ( c_Pair @ SV458 @ SV1063 @ SY4828 @ SY4828 ) @ ( c_Relation_Oconverse @ ( c_Transitive__Closure_Otrancl @ SY4829 @ SY4828 ) @ SY4828 @ SY4828 ) @ ( tc_prod @ SY4828 @ SY4828 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2764]) ).
thf(3412,plain,
! [SV1064: $i,SV459: $i] :
( ( ! [SY4830: $i,SY4831: $i,SY4832: $i,SY4833: $i] :
( ( hAPP @ ( c_split @ SV459 @ SV1064 @ SY4830 @ SY4831 ) @ ( c_Pair @ SY4832 @ SY4833 @ SV1064 @ SY4830 ) )
= ( hAPP @ ( hAPP @ SV459 @ SY4832 ) @ SY4833 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2765]) ).
thf(3413,plain,
! [SV1065: $i,SV460: $i] :
( ( ! [SY4834: $i,SY4835: $i,SY4836: $i,SY4837: $i] :
( ( hAPP @ ( c_split @ SV460 @ SV1065 @ SY4834 @ SY4835 ) @ ( c_Pair @ SY4836 @ SY4837 @ SV1065 @ SY4834 ) )
= ( hAPP @ ( hAPP @ SV460 @ SY4836 ) @ SY4837 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2766]) ).
thf(3414,plain,
! [SV1066: $i,SV461: $i] :
( ( ! [SY4838: $i,SY4839: $i,SY4840: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ SV461 @ SV1066 ) @ SY4838 ) @ SY4839 ) )
| ! [SY4841: $i,SY4842: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_split @ SV461 @ SY4840 @ SY4841 @ ( tc_fun @ SY4842 @ tc_bool ) ) @ ( c_Pair @ SV1066 @ SY4838 @ SY4840 @ SY4841 ) ) @ SY4839 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2767]) ).
thf(3415,plain,
! [SV1067: $i,SV462: $i] :
( ( ! [SY4843: $i,SY4844: $i] :
( ! [SY4845: $i] : ( c_in @ ( hAPP @ SV462 @ SV1067 ) @ ( c_Set_Oimage @ SV462 @ SY4843 @ SY4844 @ SY4845 ) @ SY4845 )
| ~ ( c_in @ SV1067 @ SY4843 @ SY4844 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2768]) ).
thf(3416,plain,
! [SV1068: $i,SV463: $i] :
( ( ! [SY4846: $i,SY4847: $i] :
( ! [SY4848: $i] : ( c_in @ ( hAPP @ SV463 @ SV1068 ) @ ( c_Set_Oimage @ SV463 @ SY4846 @ SY4847 @ SY4848 ) @ SY4848 )
| ~ ( c_in @ SV1068 @ SY4846 @ SY4847 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2769]) ).
thf(3417,plain,
! [SV1069: $i,SV464: $i] :
( ( ! [SY4849: $i] :
( ~ ( c_in @ SV464 @ SV1069 @ SY4849 )
| ! [SY4850: $i,SY4851: $i] : ( c_in @ ( hAPP @ SY4850 @ SV464 ) @ ( c_Set_Oimage @ SY4850 @ SV1069 @ SY4849 @ SY4851 ) @ SY4851 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2770]) ).
thf(3418,plain,
! [SV1070: $i,SV465: $i] :
( ( ! [SY4852: $i] :
( ~ ( c_in @ SV465 @ SV1070 @ SY4852 )
| ! [SY4853: $i,SY4854: $i] : ( c_in @ ( hAPP @ SY4853 @ SV465 ) @ ( c_Set_Oimage @ SY4853 @ SV1070 @ SY4852 @ SY4854 ) @ SY4854 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2771]) ).
thf(3419,plain,
! [SV1071: $i,SV466: $i] :
( ( ! [SY4855: $i] :
( ( c_in @ SV466 @ ( c_Wellfounded_Oacc @ SV1071 @ SY4855 ) @ SY4855 )
| ~ ( c_Wellfounded_Owf @ SV1071 @ SY4855 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2772]) ).
thf(3420,plain,
! [SV1072: $i,SV467: $i] :
( ( c_Relation_Osingle__valued @ ( c_Relation_OId__on @ SV467 @ SV1072 ) @ SV1072 @ SV1072 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2773]) ).
thf(3421,plain,
! [SV1073: $i,SV468: $i] :
( ( ! [SY4856: $i,SY4857: $i,SY4858: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Relation__XImageE__1__1 @ SV468 @ SV1073 @ SY4856 @ SY4857 @ SY4858 ) @ SV468 @ SY4857 )
| ~ ( c_in @ SV1073 @ ( c_Relation_OImage @ SY4856 @ SV468 @ SY4857 @ SY4858 ) @ SY4858 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2774]) ).
thf(3422,plain,
! [SV1074: $i,SV469: $i] :
( ( ( c_Relation_Osym @ ( c_Transitive__Closure_Otrancl @ SV469 @ SV1074 ) @ SV1074 )
| ~ ( c_Relation_Osym @ SV469 @ SV1074 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2775]) ).
thf(3423,plain,
! [SV1075: $i,SV470: $i] :
( ( ( hBOOL @ ( hAPP @ SV470 @ SV1075 ) )
| ! [SY4859: $i,SY4860: $i] :
( ~ ( hBOOL @ ( hAPP @ SV470 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ SV470 @ SY4859 @ SY4860 ) ) )
| ~ ( c_in @ SV1075 @ ( c_Wellfounded_Oacc @ SY4859 @ SY4860 ) @ SY4860 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2776]) ).
thf(3424,plain,
! [SV1076: $i,SV471: $i] :
( ( ( ( c_Transitive__Closure_Otrancl @ SV471 @ SV1076 )
= SV471 )
| ~ ( c_Relation_Otrans @ SV471 @ SV1076 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2777]) ).
thf(3425,plain,
! [SV1077: $i,SV472: $i] :
( ( ( hBOOL @ ( hAPP @ SV472 @ SV1077 ) )
| ! [SY4861: $i] :
( ~ ( hBOOL @ ( hAPP @ SV472 @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ SV472 @ SY4861 ) ) )
| ~ ( c_in @ SV1077 @ ( c_Wellfounded_Oacc @ SY4861 @ t_a ) @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2778]) ).
thf(3426,plain,
! [SV1078: $i,SV473: $i] :
( ( ( hBOOL @ ( hAPP @ SV473 @ SV1078 ) )
| ! [SY4862: $i,SY4863: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ SV473 @ SY4862 @ SY4863 ) @ ( c_Wellfounded_Oacc @ SY4862 @ SY4863 ) @ SY4863 )
| ~ ( c_in @ SV1078 @ ( c_Wellfounded_Oacc @ SY4862 @ SY4863 ) @ SY4863 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2779]) ).
thf(3427,plain,
! [SV1079: $i,SV474: $i] :
( ( ( c_Relation_Osym @ SV474 @ SV1079 )
| ~ ( c_Relation_Osym @ ( c_Relation_Oconverse @ SV474 @ SV1079 @ SV1079 ) @ SV1079 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2780]) ).
thf(3428,plain,
! [SV1080: $i,SV475: $i] :
( ( ( c_Relation_Osym @ ( c_Relation_Oconverse @ SV475 @ SV1080 @ SV1080 ) @ SV1080 )
| ~ ( c_Relation_Osym @ SV475 @ SV1080 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2781]) ).
thf(3429,plain,
! [SV1081: $i,SV476: $i] :
( ( ( c_Relation_ODomain @ ( c_Transitive__Closure_Otrancl @ SV476 @ SV1081 ) @ SV1081 @ SV1081 )
= ( c_Relation_ODomain @ SV476 @ SV1081 @ SV1081 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2782]) ).
thf(3430,plain,
! [SV1082: $i,SV477: $i] :
( ( ! [SY4864: $i,SY4865: $i,SY4866: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Relation__XImage__iff__1__1 @ SV477 @ SV1082 @ SY4864 @ SY4865 @ SY4866 ) @ SV477 @ SY4865 )
| ~ ( c_in @ SV1082 @ ( c_Relation_OImage @ SY4864 @ SV477 @ SY4865 @ SY4866 ) @ SY4866 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2783]) ).
thf(3431,plain,
! [SV1083: $i,SV478: $i] :
( ( ! [SY4867: $i] :
( ~ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1 @ SV478 @ SV1083 @ SY4867 ) @ ( c_Wellfounded_Oacc @ SV478 @ SY4867 ) @ SY4867 )
| ( c_in @ SV1083 @ ( c_Wellfounded_Oacc @ SV478 @ SY4867 ) @ SY4867 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2784]) ).
thf(3432,plain,
! [SV1084: $i,SV480: $i] :
( ( c_Relation_Otrans @ ( c_Relation_OId__on @ SV480 @ SV1084 ) @ SV1084 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2786]) ).
thf(3433,plain,
! [SV1085: $i,SV481: $i] :
( ( ! [SY4868: $i] :
( ( c_Relation_Orel__comp @ ( c_Relation_OId @ SV481 ) @ SV1085 @ SV481 @ SV481 @ SY4868 )
= SV1085 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2787]) ).
thf(3434,plain,
! [SV1086: $i,SV482: $i] :
( ( ! [SY4869: $i] :
( ( c_Relation_Orel__comp @ SV482 @ ( c_Relation_OId @ SV1086 ) @ SY4869 @ SV1086 @ SV1086 )
= SV482 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2788]) ).
thf(3435,plain,
! [SV1087: $i,SV483: $i] :
( ( c_Relation_Oantisym @ ( c_Relation_OId__on @ SV483 @ SV1087 ) @ SV1087 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2789]) ).
thf(3436,plain,
! [SV1088: $i,SV484: $i] :
( ( ( c_Wellfounded_Owf @ ( c_Relation_Oconverse @ ( c_Transitive__Closure_Otrancl @ SV484 @ SV1088 ) @ SV1088 @ SV1088 ) @ SV1088 )
| ~ ( c_Wellfounded_Owf @ ( c_Relation_Oconverse @ SV484 @ SV1088 @ SV1088 ) @ SV1088 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2790]) ).
thf(3437,plain,
! [SV1089: $i,SV485: $i] :
( ( ( hBOOL @ ( hAPP @ SV485 @ SV1089 ) )
| ! [SY4870: $i,SY4871: $i] :
( ~ ( hBOOL @ ( hAPP @ SV485 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ SV485 @ SY4870 @ SY4871 ) ) )
| ~ ( c_in @ SV1089 @ ( c_Wellfounded_Oacc @ SY4870 @ SY4871 ) @ SY4871 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2791]) ).
thf(3438,plain,
! [SV1090: $i,SV486: $i] :
( ( ! [SY4872: $i] :
( ( c_Relation_Orefl__on @ SV486 @ SV1090 @ SY4872 )
| ~ ( c_Relation_Orefl__on @ SV486 @ ( c_Relation_Oconverse @ SV1090 @ SY4872 @ SY4872 ) @ SY4872 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2792]) ).
thf(3439,plain,
! [SV1091: $i,SV487: $i] :
( ( ! [SY4873: $i] :
( ( c_Relation_Orefl__on @ SV487 @ ( c_Relation_Oconverse @ SV1091 @ SY4873 @ SY4873 ) @ SY4873 )
| ~ ( c_Relation_Orefl__on @ SV487 @ SV1091 @ SY4873 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2793]) ).
thf(3440,plain,
! [SV1092: $i,SV488: $i] :
( ( ( c_Relation_Osym @ ( c_Transitive__Closure_Ortrancl @ SV488 @ SV1092 ) @ SV1092 )
| ~ ( c_Relation_Osym @ SV488 @ SV1092 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2794]) ).
thf(3441,plain,
! [SV1093: $i,SV489: $i] :
( ( ( c_Wellfounded_Owf @ ( c_Relation_Orel__comp @ SV489 @ SV489 @ SV1093 @ SV1093 @ SV1093 ) @ SV1093 )
| ~ ( c_Wellfounded_Owf @ SV489 @ SV1093 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2795]) ).
thf(3442,plain,
! [SV1094: $i,SV490: $i] :
( ( ( c_Wellfounded_Owf @ SV490 @ SV1094 )
| ~ ( c_Wellfounded_Owf @ ( c_Relation_Orel__comp @ SV490 @ SV490 @ SV1094 @ SV1094 @ SV1094 ) @ SV1094 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2796]) ).
thf(3443,plain,
! [SV1095: $i,SV491: $i] :
( ( ( c_Relation_OImage @ ( c_Relation_OId @ SV491 ) @ SV1095 @ SV491 @ SV491 )
= SV1095 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2797]) ).
thf(3444,plain,
! [SV1096: $i,SV493: $i] :
( ( ( c_Relation_ODomain @ ( c_Relation_OId__on @ SV493 @ SV1096 ) @ SV1096 @ SV1096 )
= SV493 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2799]) ).
thf(3445,plain,
! [SV1097: $i,SV494: $i] :
( ( ( ( c_Relation_Oconverse @ SV494 @ SV1097 @ SV1097 )
= SV494 )
| ~ ( c_Relation_Osym @ SV494 @ SV1097 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2800]) ).
thf(3446,plain,
! [SV1098: $i,SV495: $i] :
( ( ( ( c_Relation_Oconverse @ SV495 @ SV1098 @ SV1098 )
!= SV495 )
| ( c_Relation_Osym @ SV495 @ SV1098 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2801]) ).
thf(3447,plain,
! [SV1099: $i,SV496: $i] :
( ( ( c_Relation_ORange @ ( c_Transitive__Closure_Otrancl @ SV496 @ SV1099 ) @ SV1099 @ SV1099 )
= ( c_Relation_ORange @ SV496 @ SV1099 @ SV1099 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2802]) ).
thf(3448,plain,
! [SV1100: $i,SV497: $i] :
( ( c_Relation_Otrans @ ( c_Transitive__Closure_Otrancl @ SV497 @ SV1100 ) @ SV1100 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2803]) ).
thf(3449,plain,
! [SV1101: $i,SV498: $i] :
( ( ! [SY4874: $i,SY4875: $i,SY4876: $i] :
( ( c_Relation_Oconverse @ ( c_Relation_Orel__comp @ SV498 @ SV1101 @ SY4874 @ SY4875 @ SY4876 ) @ SY4874 @ SY4876 )
= ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ SV1101 @ SY4875 @ SY4876 ) @ ( c_Relation_Oconverse @ SV498 @ SY4874 @ SY4875 ) @ SY4876 @ SY4875 @ SY4874 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2804]) ).
thf(3450,plain,
! [SV1102: $i,SV499: $i] :
( ( c_Relation_Osym @ ( c_Relation_OId__on @ SV499 @ SV1102 ) @ SV1102 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2805]) ).
thf(3451,plain,
! [SV1103: $i,SV500: $i] :
( ( c_Relation_Orefl__on @ SV500 @ ( c_Relation_OId__on @ SV500 @ SV1103 ) @ SV1103 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2806]) ).
thf(3452,plain,
! [SV1104: $i,SV501: $i] :
( ( ! [SY4877: $i] :
( ! [SY4878: $i] : ( c_Wellfounded_Owf @ ( c_Relation_Oinv__image @ SV501 @ SV1104 @ SY4877 @ SY4878 ) @ SY4878 )
| ~ ( c_Wellfounded_Owf @ SV501 @ SY4877 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2807]) ).
thf(3453,plain,
! [SV1105: $i,SV502: $i] :
( ( ( c_Relation_Orel__comp @ SV502 @ ( c_Transitive__Closure_Ortrancl @ SV502 @ SV1105 ) @ SV1105 @ SV1105 @ SV1105 )
= ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Ortrancl @ SV502 @ SV1105 ) @ SV502 @ SV1105 @ SV1105 @ SV1105 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2808]) ).
thf(3454,plain,
! [SV1106: $i,SV503: $i] :
( ( ! [SY4879: $i] :
( ! [SY4880: $i] : ( c_Relation_Osym @ ( c_Relation_Oinv__image @ SV503 @ SV1106 @ SY4879 @ SY4880 ) @ SY4880 )
| ~ ( c_Relation_Osym @ SV503 @ SY4879 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2809]) ).
thf(3455,plain,
! [SV1107: $i,SV504: $i] :
( ( ( c_Transitive__Closure_Otrancl @ ( c_Transitive__Closure_Ortrancl @ SV504 @ SV1107 ) @ SV1107 )
= ( c_Transitive__Closure_Ortrancl @ SV504 @ SV1107 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2810]) ).
thf(3456,plain,
! [SV1108: $i,SV505: $i] :
( ( c_Relation_Otrans @ ( c_Transitive__Closure_Ortrancl @ SV505 @ SV1108 ) @ SV1108 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2811]) ).
thf(3457,plain,
! [SV1109: $i,SV506: $i] :
( ( ( c_Relation_Otrans @ SV506 @ SV1109 )
| ~ ( c_Relation_Otrans @ ( c_Relation_Oconverse @ SV506 @ SV1109 @ SV1109 ) @ SV1109 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2812]) ).
thf(3458,plain,
! [SV1110: $i,SV507: $i] :
( ( ( c_Relation_Otrans @ ( c_Relation_Oconverse @ SV507 @ SV1110 @ SV1110 ) @ SV1110 )
| ~ ( c_Relation_Otrans @ SV507 @ SV1110 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2813]) ).
thf(3459,plain,
! [SV1111: $i,SV509: $i] :
( ( ( c_Wellfounded_Owf @ ( c_Transitive__Closure_Otrancl @ SV509 @ SV1111 ) @ SV1111 )
| ~ ( c_Wellfounded_Owf @ SV509 @ SV1111 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2815]) ).
thf(3460,plain,
! [SV1112: $i,SV510: $i] :
( ( ! [SY4881: $i,SY4882: $i,SY4883: $i,SY4884: $i,SY4885: $i] :
( ( c_Relation_Orel__comp @ ( c_Relation_Orel__comp @ SV510 @ SV1112 @ SY4881 @ SY4882 @ SY4883 ) @ SY4884 @ SY4881 @ SY4883 @ SY4885 )
= ( c_Relation_Orel__comp @ SV510 @ ( c_Relation_Orel__comp @ SV1112 @ SY4884 @ SY4882 @ SY4883 @ SY4885 ) @ SY4881 @ SY4882 @ SY4885 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2816]) ).
thf(3461,plain,
! [SV1113: $i,SV511: $i] :
( ( ! [SY4886: $i,SY4887: $i] :
( ( c_Relation_Oconverse @ ( c_Relation_Oinv__image @ SV511 @ SV1113 @ SY4886 @ SY4887 ) @ SY4887 @ SY4887 )
= ( c_Relation_Oinv__image @ ( c_Relation_Oconverse @ SV511 @ SY4886 @ SY4886 ) @ SV1113 @ SY4886 @ SY4887 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2817]) ).
thf(3462,plain,
! [SV1114: $i,SV512: $i] :
( ( ( c_Transitive__Closure_Otrancl @ ( c_Relation_Oconverse @ SV512 @ SV1114 @ SV1114 ) @ SV1114 )
= ( c_Relation_Oconverse @ ( c_Transitive__Closure_Otrancl @ SV512 @ SV1114 ) @ SV1114 @ SV1114 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2818]) ).
thf(3463,plain,
! [SV1115: $i,SV513: $i] :
( ( ! [SY4888: $i] :
( ! [SY4889: $i] : ( c_Relation_Otrans @ ( c_Relation_Oinv__image @ SV513 @ SV1115 @ SY4888 @ SY4889 ) @ SY4889 )
| ~ ( c_Relation_Otrans @ SV513 @ SY4888 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2819]) ).
thf(3464,plain,
! [SV1116: $i,SV514: $i] :
( ( ( c_Relation_Oconverse @ ( c_Relation_OId__on @ SV514 @ SV1116 ) @ SV1116 @ SV1116 )
= ( c_Relation_OId__on @ SV514 @ SV1116 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2820]) ).
thf(3465,plain,
! [SV1117: $i,SV515: $i] :
( ( ( ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ SV515 @ SV1117 @ SV1117 ) @ SV515 @ SV1117 @ SV1117 @ SV1117 )
!= SV515 )
| ( c_Equiv__Relations_Oequiv @ ( c_Relation_ODomain @ SV515 @ SV1117 @ SV1117 ) @ SV515 @ SV1117 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2821]) ).
thf(3466,plain,
! [SV1118: $i,SV517: $i] :
( ( ! [SY4890: $i] :
( ( c_Relation_ORange @ ( c_Relation_Oconverse @ SV517 @ SV1118 @ SY4890 ) @ SY4890 @ SV1118 )
= ( c_Relation_ODomain @ SV517 @ SV1118 @ SY4890 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2823]) ).
thf(3467,plain,
! [SV1119: $i,SV518: $i] :
( ( ! [SY4891: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 @ SV518 @ SV1119 @ SY4891 ) @ SV518 @ SY4891 )
| ! [SY3701: $i] :
~ ( c_in @ SY3701 @ SV518 @ SY4891 )
| ~ ( c_Wellfounded_Owf @ SV1119 @ SY4891 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2824]) ).
thf(3468,plain,
! [SV1120: $i,SV519: $i] :
( ( ( c_Relation_ORange @ ( c_Relation_OId__on @ SV519 @ SV1120 ) @ SV1120 @ SV1120 )
= SV519 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2825]) ).
thf(3469,plain,
! [SV1121: $i,SV520: $i] :
( ( ! [SY4893: $i,SY4894: $i,SY4895: $i] :
( ( c_Relation_Osingle__valued @ ( c_Relation_Orel__comp @ SV520 @ SV1121 @ SY4893 @ SY4894 @ SY4895 ) @ SY4893 @ SY4895 )
| ~ ( c_Relation_Osingle__valued @ SV1121 @ SY4894 @ SY4895 )
| ~ ( c_Relation_Osingle__valued @ SV520 @ SY4893 @ SY4894 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2826]) ).
thf(3470,plain,
! [SV1122: $i,SV521: $i] :
( ( ! [SY4896: $i] :
( ( c_Relation_Oconverse @ ( c_Relation_Oconverse @ SV521 @ SV1122 @ SY4896 ) @ SY4896 @ SV1122 )
= SV521 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2827]) ).
thf(3471,plain,
! [SV1123: $i,SV523: $i] :
( ( ( ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ SV523 @ SV1123 @ SV1123 ) @ SV523 @ SV1123 @ SV1123 @ SV1123 )
= SV523 )
| ! [SY4897: $i] :
~ ( c_Equiv__Relations_Oequiv @ SY4897 @ SV523 @ SV1123 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2829]) ).
thf(3472,plain,
! [SV1124: $i,SV524: $i] :
( ( ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Ortrancl @ SV524 @ SV1124 ) @ ( c_Transitive__Closure_Ortrancl @ SV524 @ SV1124 ) @ SV1124 @ SV1124 @ SV1124 )
= ( c_Transitive__Closure_Ortrancl @ SV524 @ SV1124 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2830]) ).
thf(3473,plain,
! [SV1125: $i,SV525: $i] :
( ( ( c_Relation_Oantisym @ SV525 @ SV1125 )
| ~ ( c_Relation_Oantisym @ ( c_Relation_Oconverse @ SV525 @ SV1125 @ SV1125 ) @ SV1125 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2831]) ).
thf(3474,plain,
! [SV1126: $i,SV526: $i] :
( ( ( c_Relation_Oantisym @ ( c_Relation_Oconverse @ SV526 @ SV1126 @ SV1126 ) @ SV1126 )
| ~ ( c_Relation_Oantisym @ SV526 @ SV1126 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2832]) ).
thf(3475,plain,
! [SV1127: $i,SV527: $i] :
( ( ( hBOOL @ ( hAPP @ SV527 @ SV1127 ) )
| ! [SY4898: $i] :
( ~ ( hBOOL @ ( hAPP @ SV527 @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ SV527 @ SY4898 ) ) )
| ~ ( c_in @ SV1127 @ ( c_Wellfounded_Oacc @ SY4898 @ t_a ) @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2833]) ).
thf(3476,plain,
! [SV1128: $i,SV528: $i] :
( ( ! [SY4899: $i] :
( ( c_Relation_Orefl__on @ SV528 @ SV1128 @ SY4899 )
| ~ ( c_Equiv__Relations_Oequiv @ SV528 @ SV1128 @ SY4899 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2834]) ).
thf(3477,plain,
! [SV1129: $i,SV529: $i] :
( ( ( c_Transitive__Closure_Ortrancl @ ( c_Relation_Oconverse @ SV529 @ SV1129 @ SV1129 ) @ SV1129 )
= ( c_Relation_Oconverse @ ( c_Transitive__Closure_Ortrancl @ SV529 @ SV1129 ) @ SV1129 @ SV1129 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2835]) ).
thf(3478,plain,
! [SV1130: $i,SV530: $i] :
( ( ! [SY4900: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 @ SV530 @ SV1130 @ SY4900 ) @ SV530 @ SY4900 )
| ! [SY3721: $i] :
~ ( c_in @ SY3721 @ SV530 @ SY4900 )
| ~ ( c_Wellfounded_Owf @ SV1130 @ SY4900 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2836]) ).
thf(3479,plain,
! [SV1131: $i,SV531: $i] :
( ( ( c_Relation_Osym @ SV531 @ SV1131 )
| ! [SY4902: $i] :
~ ( c_Equiv__Relations_Oequiv @ SY4902 @ SV531 @ SV1131 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2837]) ).
thf(3480,plain,
! [SV1132: $i,SV532: $i] :
( ( ! [SY4903: $i] :
( ( c_in @ SV532 @ ( c_Wellfounded_Oacc @ SV1132 @ SY4903 ) @ SY4903 )
| ~ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1 @ SV1132 @ SV532 @ SY4903 ) @ ( c_Wellfounded_Oacc @ SV1132 @ SY4903 ) @ SY4903 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2838]) ).
thf(3481,plain,
! [SV1133: $i,SV533: $i] :
( ( ! [SY4904: $i,SY4905: $i,SY4906: $i,SY4907: $i] :
( ( c_Equiv__Relations_Ocongruent @ SV533 @ ( hAPP @ SV1133 @ SY4904 ) @ SY4905 @ SY4906 )
| ! [SY4908: $i] :
( ~ ( c_in @ SY4904 @ SY4907 @ SY4908 )
| ! [SY4909: $i] :
( ~ ( c_Equiv__Relations_Ocongruent2 @ SY4909 @ SV533 @ SV1133 @ SY4908 @ SY4905 @ SY4906 )
| ~ ( c_Equiv__Relations_Oequiv @ SY4907 @ SY4909 @ SY4908 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2839]) ).
thf(3482,plain,
! [SV1134: $i,SV534: $i] :
( ( ! [SY4910: $i] :
( ( c_Relation_ODomain @ ( c_Relation_Oconverse @ SV534 @ SV1134 @ SY4910 ) @ SY4910 @ SV1134 )
= ( c_Relation_ORange @ SV534 @ SV1134 @ SY4910 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2840]) ).
thf(3483,plain,
! [SV1135: $i,SV535: $i] :
( ( ( c_Transitive__Closure_Otrancl @ SV535 @ SV1135 )
= ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Ortrancl @ SV535 @ SV1135 ) @ SV535 @ SV1135 @ SV1135 @ SV1135 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2841]) ).
thf(3484,plain,
! [SV1136: $i,SV536: $i] :
( ( ( c_Transitive__Closure_Otrancl @ SV536 @ SV1136 )
= ( c_Relation_Orel__comp @ SV536 @ ( c_Transitive__Closure_Ortrancl @ SV536 @ SV1136 ) @ SV1136 @ SV1136 @ SV1136 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2842]) ).
thf(3485,plain,
! [SV1137: $i,SV537: $i] :
( ( ! [SY4911: $i] :
( ( c_Relation_ORange @ SV537 @ SV1137 @ SY4911 )
= ( c_Relation_ODomain @ ( c_Relation_Oconverse @ SV537 @ SV1137 @ SY4911 ) @ SY4911 @ SV1137 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2843]) ).
thf(3486,plain,
! [SV1138: $i,SV538: $i] :
( ( ! [SY4912: $i] :
( ( c_Relation_Ototal__on @ SV538 @ SV1138 @ SY4912 )
| ~ ( c_Relation_Ototal__on @ SV538 @ ( c_Relation_Oconverse @ SV1138 @ SY4912 @ SY4912 ) @ SY4912 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2844]) ).
thf(3487,plain,
! [SV1139: $i,SV539: $i] :
( ( ! [SY4913: $i] :
( ( c_Relation_Ototal__on @ SV539 @ ( c_Relation_Oconverse @ SV1139 @ SY4913 @ SY4913 ) @ SY4913 )
| ~ ( c_Relation_Ototal__on @ SV539 @ SV1139 @ SY4913 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2845]) ).
thf(3488,plain,
! [SV1140: $i,SV540: $i] :
( ( ( c_Relation_Otrans @ SV540 @ SV1140 )
| ! [SY4914: $i] :
~ ( c_Equiv__Relations_Oequiv @ SY4914 @ SV540 @ SV1140 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2846]) ).
thf(3489,plain,
! [SV1141: $i,SV541: $i] :
( ( ( hBOOL @ ( hAPP @ SV541 @ SV1141 ) )
| ! [SY4915: $i,SY4916: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ SV541 @ SY4915 @ SY4916 ) @ ( c_Wellfounded_Oacc @ SY4915 @ SY4916 ) @ SY4916 )
| ~ ( c_in @ SV1141 @ ( c_Wellfounded_Oacc @ SY4915 @ SY4916 ) @ SY4916 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2847]) ).
thf(3490,plain,
! [SV1142: $i,SV542: $i] :
( ( ( c_Transitive__Closure_Ortrancl @ ( c_Transitive__Closure_Otrancl @ SV542 @ SV1142 ) @ SV1142 )
= ( c_Transitive__Closure_Ortrancl @ SV542 @ SV1142 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2848]) ).
thf(3491,plain,
! [SV1143: $i,SV543: $i] :
( ( ( c_Transitive__Closure_Ortrancl @ ( c_Transitive__Closure_Ortrancl @ SV543 @ SV1143 ) @ SV1143 )
= ( c_Transitive__Closure_Ortrancl @ SV543 @ SV1143 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2849]) ).
thf(3492,plain,
! [SV1144: $i,SV544: $i] :
( ( ! [SY4917: $i,SY4918: $i,SY4919: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XImageE__1__1 @ SV544 @ SV1144 @ SY4917 @ SY4918 @ SY4919 ) @ SV1144 @ SY4918 @ SY4919 ) @ SY4917 @ ( tc_prod @ SY4918 @ SY4919 ) )
| ~ ( c_in @ SV1144 @ ( c_Relation_OImage @ SY4917 @ SV544 @ SY4918 @ SY4919 ) @ SY4919 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2850]) ).
thf(3493,plain,
! [SV1145: $i,SV545: $i] :
( ( ! [SY4920: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1 @ SV545 @ SV1145 @ SY4920 ) @ SV1145 @ SY4920 @ SY4920 ) @ SV545 @ ( tc_prod @ SY4920 @ SY4920 ) )
| ( c_in @ SV1145 @ ( c_Wellfounded_Oacc @ SV545 @ SY4920 ) @ SY4920 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2851]) ).
thf(3494,plain,
! [SV1146: $i,SV546: $i] :
( ( ! [SY4921: $i] :
( ( hBOOL @ ( hAPP @ SV546 @ SV1146 ) )
| ( hBOOL @ ( hAPP @ SV546 @ SY4921 ) )
| ! [SY4922: $i,SY4923: $i] :
( ~ ( c_in @ ( c_Pair @ SY4921 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ SV546 @ SY4922 @ SY4923 ) @ SY4923 @ SY4923 ) @ SY4922 @ ( tc_prod @ SY4923 @ SY4923 ) )
| ~ ( c_in @ SV1146 @ ( c_Wellfounded_Oacc @ SY4922 @ SY4923 ) @ SY4923 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2852]) ).
thf(3495,plain,
! [SV1147: $i,SV547: $i] :
( ( ( hBOOL @ ( hAPP @ SV547 @ SV1147 ) )
| ! [SY4924: $i] :
( ( hBOOL @ ( hAPP @ SV547 @ SY4924 ) )
| ! [SY4925: $i] :
( ~ ( c_in @ ( c_Pair @ SY4924 @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ SV547 @ SY4925 ) @ t_a @ t_a ) @ SY4925 @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ SV1147 @ ( c_Wellfounded_Oacc @ SY4925 @ t_a ) @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2853]) ).
thf(3496,plain,
! [SV1148: $i,SV548: $i] :
( ( ! [SY4926: $i] :
( ~ ( c_in @ SV548 @ SV1148 @ SY4926 )
| ! [SY4927: $i] :
( ~ ( c_in @ ( c_Pair @ SV548 @ ( c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 @ SV1148 @ SY4927 @ SY4926 ) @ SY4926 @ SY4926 ) @ SY4927 @ ( tc_prod @ SY4926 @ SY4926 ) )
| ! [SY4928: $i] :
~ ( c_in @ SY4928 @ SV1148 @ SY4926 )
| ~ ( c_Wellfounded_Owf @ SY4927 @ SY4926 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2854]) ).
thf(3497,plain,
! [SV1149: $i,SV549: $i] :
( ( ! [SY4929: $i,SY4930: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XRangeE__1__1 @ SV549 @ SV1149 @ SY4929 @ SY4930 ) @ SV549 @ SY4930 @ SY4929 ) @ SV1149 @ ( tc_prod @ SY4930 @ SY4929 ) )
| ~ ( c_in @ SV549 @ ( c_Relation_ORange @ SV1149 @ SY4930 @ SY4929 ) @ SY4929 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2855]) ).
thf(3498,plain,
! [SV1150: $i,SV550: $i] :
( ( ! [SY4931: $i] :
( ( c_in @ SV550 @ ( c_Wellfounded_Oacc @ SV1150 @ SY4931 ) @ SY4931 )
| ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1 @ SV1150 @ SV550 @ SY4931 ) @ SV550 @ SY4931 @ SY4931 ) @ SV1150 @ ( tc_prod @ SY4931 @ SY4931 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2856]) ).
thf(3499,plain,
! [SV1151: $i,SV551: $i] :
( ( ! [SY4932: $i] :
( ( c_in @ SV551 @ ( c_Wellfounded_Oacc @ SV1151 @ SY4932 ) @ SY4932 )
| ! [SY4933: $i] :
( ~ ( c_in @ SY4933 @ ( c_Wellfounded_Oacc @ SV1151 @ SY4932 ) @ SY4932 )
| ~ ( c_in @ ( c_Pair @ SV551 @ SY4933 @ SY4932 @ SY4932 ) @ ( c_Transitive__Closure_Ortrancl @ SV1151 @ SY4932 ) @ ( tc_prod @ SY4932 @ SY4932 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2857]) ).
thf(3500,plain,
! [SV1152: $i,SV552: $i] :
( ( ! [SY4934: $i] :
( ( c_in @ SV552 @ ( c_Wellfounded_Oacc @ SV1152 @ SY4934 ) @ SY4934 )
| ! [SY4935: $i] :
( ~ ( c_in @ ( c_Pair @ SV552 @ SY4935 @ SY4934 @ SY4934 ) @ ( c_Transitive__Closure_Ortrancl @ SV1152 @ SY4934 ) @ ( tc_prod @ SY4934 @ SY4934 ) )
| ~ ( c_in @ SY4935 @ ( c_Wellfounded_Oacc @ SV1152 @ SY4934 ) @ SY4934 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2858]) ).
thf(3501,plain,
! [SV1153: $i,SV553: $i] :
( ( ( hBOOL @ ( hAPP @ SV553 @ SV1153 ) )
| ! [SY4936: $i,SY4937: $i] :
( ( c_in @ SY4936 @ ( c_Wellfounded_Oacc @ SY4937 @ t_a ) @ t_a )
| ~ ( c_in @ ( c_Pair @ SY4936 @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ SV553 @ SY4937 ) @ t_a @ t_a ) @ SY4937 @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ SV1153 @ ( c_Wellfounded_Oacc @ SY4937 @ t_a ) @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2859]) ).
thf(3502,plain,
! [SV1154: $i,SV554: $i] :
( ( ! [SY4938: $i] :
( ( c_in @ SV554 @ ( c_Relation_ODomain @ SV1154 @ SY4938 @ SY4938 ) @ SY4938 )
| ( c_in @ ( c_Pair @ SV554 @ SV554 @ SY4938 @ SY4938 ) @ ( c_Transitive__Closure_Ortrancl @ SV1154 @ SY4938 ) @ ( tc_prod @ SY4938 @ SY4938 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2860]) ).
thf(3503,plain,
! [SV1155: $i,SV555: $i] :
( ( ( hBOOL @ ( hAPP @ SV555 @ SV1155 ) )
| ! [SY4939: $i] :
( ( hBOOL @ ( hAPP @ SV555 @ SY4939 ) )
| ! [SY4940: $i] :
( ~ ( c_in @ ( c_Pair @ SY4939 @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ SV555 @ SY4940 ) @ t_a @ t_a ) @ SY4940 @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ SV1155 @ ( c_Wellfounded_Oacc @ SY4940 @ t_a ) @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2861]) ).
thf(3504,plain,
! [SV1156: $i,SV556: $i] :
( ( ! [SY4941: $i,SY4942: $i,SY4943: $i,SY4944: $i,SY4945: $i] :
( ( c_in @ ( hAPP @ ( hAPP @ SV556 @ SV1156 ) @ SY4941 ) @ ( c_Set_Oimage @ ( c_split @ SV556 @ SY4942 @ SY4943 @ SY4944 ) @ SY4945 @ ( tc_prod @ SY4942 @ SY4943 ) @ SY4944 ) @ SY4944 )
| ~ ( c_in @ ( c_Pair @ SV1156 @ SY4941 @ SY4942 @ SY4943 ) @ SY4945 @ ( tc_prod @ SY4942 @ SY4943 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2862]) ).
thf(3505,plain,
! [SV1157: $i,SV557: $i] :
( ( ! [SY4946: $i,SY4947: $i] :
( ( c_in @ ( c_Pair @ SV557 @ ( c_ATP__Linkup_Osko__Relation__XDomainE__1__1 @ SV557 @ SV1157 @ SY4946 @ SY4947 ) @ SY4946 @ SY4947 ) @ SV1157 @ ( tc_prod @ SY4946 @ SY4947 ) )
| ~ ( c_in @ SV557 @ ( c_Relation_ODomain @ SV1157 @ SY4946 @ SY4947 ) @ SY4946 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2863]) ).
thf(3506,plain,
! [SV1158: $i,SV558: $i] :
( ( ( hBOOL @ ( hAPP @ SV558 @ SV1158 ) )
| ! [SY4948: $i,SY4949: $i] :
( ( c_in @ SY4948 @ ( c_Wellfounded_Oacc @ SY4949 @ t_a ) @ t_a )
| ~ ( c_in @ ( c_Pair @ SY4948 @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ SV558 @ SY4949 ) @ t_a @ t_a ) @ SY4949 @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ SV1158 @ ( c_Wellfounded_Oacc @ SY4949 @ t_a ) @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2864]) ).
thf(3507,plain,
! [SV1159: $i,SV559: $i] :
( ( ! [SY4950: $i] :
( ( hBOOL @ ( hAPP @ SV559 @ SV1159 ) )
| ( hBOOL @ ( hAPP @ SV559 @ SY4950 ) )
| ! [SY4951: $i,SY4952: $i] :
( ~ ( c_in @ ( c_Pair @ SY4950 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ SV559 @ SY4951 @ SY4952 ) @ SY4952 @ SY4952 ) @ SY4951 @ ( tc_prod @ SY4952 @ SY4952 ) )
| ~ ( c_in @ SV1159 @ ( c_Wellfounded_Oacc @ SY4951 @ SY4952 ) @ SY4952 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2865]) ).
thf(3508,plain,
! [SV1160: $i,SV560: $i] :
( ( ! [SY4953: $i] :
( ~ ( c_in @ SV560 @ SV1160 @ SY4953 )
| ! [SY4954: $i] :
( ~ ( c_in @ ( c_Pair @ SV560 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 @ SV1160 @ SY4954 @ SY4953 ) @ SY4953 @ SY4953 ) @ SY4954 @ ( tc_prod @ SY4953 @ SY4953 ) )
| ! [SY4955: $i] :
~ ( c_in @ SY4955 @ SV1160 @ SY4953 )
| ~ ( c_Wellfounded_Owf @ SY4954 @ SY4953 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2866]) ).
thf(3509,plain,
! [SV1161: $i,SV561: $i] :
( ( ! [SY4956: $i,SY4957: $i] :
( ( c_in @ ( c_Pair @ SV561 @ ( c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1 @ SV561 @ SV1161 @ SY4956 @ SY4957 ) @ SY4956 @ SY4957 ) @ SV1161 @ ( tc_prod @ SY4956 @ SY4957 ) )
| ~ ( c_in @ SV561 @ ( c_Relation_ODomain @ SV1161 @ SY4956 @ SY4957 ) @ SY4956 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2867]) ).
thf(3510,plain,
! [SV1162: $i,SV562: $i] :
( ( ! [SY4958: $i,SY4959: $i,SY4960: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XImage__iff__1__1 @ SV562 @ SV1162 @ SY4958 @ SY4959 @ SY4960 ) @ SV1162 @ SY4959 @ SY4960 ) @ SY4958 @ ( tc_prod @ SY4959 @ SY4960 ) )
| ~ ( c_in @ SV1162 @ ( c_Relation_OImage @ SY4958 @ SV562 @ SY4959 @ SY4960 ) @ SY4960 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2868]) ).
thf(3511,plain,
! [SV1163: $i,SV563: $i] :
( ( ( SV563 = SV1163 )
| ! [SY4961: $i,SY4962: $i] :
( ~ ( c_in @ ( c_Pair @ SV563 @ SV1163 @ SY4961 @ SY4961 ) @ ( c_Transitive__Closure_Ortrancl @ SY4962 @ SY4961 ) @ ( tc_prod @ SY4961 @ SY4961 ) )
| ( c_in @ SV563 @ ( c_Relation_ODomain @ SY4962 @ SY4961 @ SY4961 ) @ SY4961 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2869]) ).
thf(3512,plain,
! [SV1164: $i,SV564: $i] :
( ( ! [SY4963: $i,SY4964: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XRange__iff__1__1 @ SV564 @ SV1164 @ SY4963 @ SY4964 ) @ SV564 @ SY4964 @ SY4963 ) @ SV1164 @ ( tc_prod @ SY4964 @ SY4963 ) )
| ~ ( c_in @ SV564 @ ( c_Relation_ORange @ SV1164 @ SY4964 @ SY4963 ) @ SY4963 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2870]) ).
thf(3513,plain,
! [SV1165: $i,SV565: $i] :
( ( ! [SY4965: $i,SY4966: $i,SY4967: $i,SY4968: $i,SY4969: $i] :
( ( c_in @ SV565 @ ( hAPP @ ( c_split @ SV1165 @ SY4965 @ SY4966 @ ( tc_fun @ SY4967 @ tc_bool ) ) @ ( c_Pair @ SY4968 @ SY4969 @ SY4965 @ SY4966 ) ) @ SY4967 )
| ~ ( c_in @ SV565 @ ( hAPP @ ( hAPP @ SV1165 @ SY4968 ) @ SY4969 ) @ SY4967 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2871]) ).
thf(3514,plain,
! [SV1166: $i,SV566: $i] :
( ( ! [SY4970: $i,SY4971: $i,SY4972: $i,SY4973: $i,SY4974: $i,SY4975: $i] :
( ( ( hAPP @ ( hAPP @ SV566 @ SV1166 ) @ SY4970 )
= ( hAPP @ ( hAPP @ SV566 @ SY4971 ) @ SY4972 ) )
| ~ ( c_in @ ( c_Pair @ SY4970 @ SY4972 @ SY4973 @ SY4973 ) @ SY4974 @ ( tc_prod @ SY4973 @ SY4973 ) )
| ! [SY4976: $i] :
( ~ ( c_in @ ( c_Pair @ SV1166 @ SY4971 @ SY4975 @ SY4975 ) @ SY4976 @ ( tc_prod @ SY4975 @ SY4975 ) )
| ! [SY3833: $i] :
~ ( c_Equiv__Relations_Ocongruent2 @ SY4976 @ SY4974 @ SV566 @ SY4975 @ SY4973 @ SY3833 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2872]) ).
thf(3515,plain,
! [SV1167: $i,SV567: $i] :
( ( ! [SY4978: $i,SY4979: $i] :
( ( SV567 = SV1167 )
| ! [SY4980: $i,SY4981: $i] :
( ~ ( c_in @ ( c_Pair @ SY4978 @ SV1167 @ SY4979 @ SY4980 ) @ SY4981 @ ( tc_prod @ SY4979 @ SY4980 ) )
| ~ ( c_in @ ( c_Pair @ SY4978 @ SV567 @ SY4979 @ SY4980 ) @ SY4981 @ ( tc_prod @ SY4979 @ SY4980 ) )
| ~ ( c_Relation_Osingle__valued @ SY4981 @ SY4979 @ SY4980 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2873]) ).
thf(3516,plain,
! [SV1168: $i,SV568: $i] :
( ( ! [SY4982: $i,SY4983: $i,SY4984: $i,SY4985: $i] :
( ( ( hAPP @ ( c_Recdef_Ocut @ SV568 @ SV1168 @ SY4982 @ SY4983 @ SY4984 ) @ SY4985 )
= ( hAPP @ SV568 @ SY4985 ) )
| ~ ( c_in @ ( c_Pair @ SY4985 @ SY4982 @ SY4983 @ SY4983 ) @ SV1168 @ ( tc_prod @ SY4983 @ SY4983 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2874]) ).
thf(3517,plain,
! [SV1169: $i,SV569: $i] :
( ( ! [SY4986: $i,SY4987: $i,SY4988: $i,SY4989: $i] :
( ( ( hAPP @ ( c_Recdef_Ocut @ SV569 @ SV1169 @ SY4986 @ SY4987 @ SY4988 ) @ SY4989 )
= ( hAPP @ SV569 @ SY4989 ) )
| ~ ( c_in @ ( c_Pair @ SY4989 @ SY4986 @ SY4987 @ SY4987 ) @ SV1169 @ ( tc_prod @ SY4987 @ SY4987 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2875]) ).
thf(3518,plain,
! [SV1170: $i,SV570: $i] :
( ( ! [SY4990: $i,SY4991: $i,SY4992: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_FunDef_Oin__rel @ SV570 @ SV1170 @ SY4990 ) @ SY4991 ) @ SY4992 ) )
| ~ ( c_in @ ( c_Pair @ SY4991 @ SY4992 @ SV1170 @ SY4990 ) @ SV570 @ ( tc_prod @ SV1170 @ SY4990 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2876]) ).
thf(3519,plain,
! [SV1171: $i,SV571: $i] :
( ( ! [SY4993: $i,SY4994: $i,SY4995: $i] :
( ( c_in @ ( c_Pair @ SV571 @ SV1171 @ SY4993 @ SY4994 ) @ SY4995 @ ( tc_prod @ SY4993 @ SY4994 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_FunDef_Oin__rel @ SY4995 @ SY4993 @ SY4994 ) @ SV571 ) @ SV1171 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2877]) ).
thf(3520,plain,
! [SV1172: $i,SV572: $i] :
( ( ! [SY4996: $i,SY4997: $i] :
( ( c_in @ ( c_Pair @ SV572 @ SV1172 @ SY4996 @ SY4996 ) @ SY4997 @ ( tc_prod @ SY4996 @ SY4996 ) )
| ! [SY4998: $i] :
( ~ ( c_in @ ( c_Pair @ SY4998 @ SV1172 @ SY4996 @ SY4996 ) @ SY4997 @ ( tc_prod @ SY4996 @ SY4996 ) )
| ~ ( c_in @ ( c_Pair @ SV572 @ SY4998 @ SY4996 @ SY4996 ) @ SY4997 @ ( tc_prod @ SY4996 @ SY4996 ) )
| ~ ( c_Relation_Otrans @ SY4997 @ SY4996 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2878]) ).
thf(3521,plain,
! [SV1173: $i,SV573: $i] :
( ( ! [SY4999: $i,SY5000: $i] :
( ( c_in @ ( c_Pair @ SV573 @ SV1173 @ SY4999 @ SY4999 ) @ SY5000 @ ( tc_prod @ SY4999 @ SY4999 ) )
| ! [SY5001: $i] :
( ~ ( c_in @ ( c_Pair @ SY5001 @ SV1173 @ SY4999 @ SY4999 ) @ SY5000 @ ( tc_prod @ SY4999 @ SY4999 ) )
| ~ ( c_in @ ( c_Pair @ SV573 @ SY5001 @ SY4999 @ SY4999 ) @ SY5000 @ ( tc_prod @ SY4999 @ SY4999 ) )
| ~ ( c_Relation_Otrans @ SY5000 @ SY4999 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2879]) ).
thf(3522,plain,
! [SV1174: $i,SV574: $i] :
( ( ! [SY5002: $i,SY5003: $i,SY5004: $i] :
( ( c_in @ ( c_Pair @ SV574 @ SV1174 @ SY5002 @ SY5003 ) @ ( c_Relation_Oconverse @ SY5004 @ SY5003 @ SY5002 ) @ ( tc_prod @ SY5002 @ SY5003 ) )
| ~ ( c_in @ ( c_Pair @ SV1174 @ SV574 @ SY5003 @ SY5002 ) @ SY5004 @ ( tc_prod @ SY5003 @ SY5002 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2880]) ).
thf(3523,plain,
! [SV1175: $i,SV575: $i] :
( ( ! [SY5005: $i,SY5006: $i,SY5007: $i] :
( ( c_in @ ( c_Pair @ SV575 @ SV1175 @ SY5005 @ SY5006 ) @ ( c_Relation_Oconverse @ SY5007 @ SY5006 @ SY5005 ) @ ( tc_prod @ SY5005 @ SY5006 ) )
| ~ ( c_in @ ( c_Pair @ SV1175 @ SV575 @ SY5006 @ SY5005 ) @ SY5007 @ ( tc_prod @ SY5006 @ SY5005 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2881]) ).
thf(3524,plain,
! [SV1176: $i,SV576: $i] :
( ( ! [SY5008: $i,SY5009: $i,SY5010: $i] :
( ( c_in @ ( c_Pair @ SV576 @ SV1176 @ SY5008 @ SY5009 ) @ SY5010 @ ( tc_prod @ SY5008 @ SY5009 ) )
| ~ ( c_in @ ( c_Pair @ SV1176 @ SV576 @ SY5009 @ SY5008 ) @ ( c_Relation_Oconverse @ SY5010 @ SY5008 @ SY5009 ) @ ( tc_prod @ SY5009 @ SY5008 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2882]) ).
thf(3525,plain,
! [SV1177: $i,SV577: $i] :
( ( ! [SY5011: $i] :
( ~ ( c_in @ ( c_Pair @ SV577 @ SV577 @ SV1177 @ SV1177 ) @ SY5011 @ ( tc_prod @ SV1177 @ SV1177 ) )
| ~ ( c_Relation_Oirrefl @ SY5011 @ SV1177 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2883]) ).
thf(3526,plain,
! [SV1178: $i,SV578: $i] :
( ( ! [SY5012: $i,SY5013: $i] :
( ( c_in @ ( c_Pair @ SV578 @ SV1178 @ SY5012 @ SY5012 ) @ ( c_Transitive__Closure_Otrancl @ SY5013 @ SY5012 ) @ ( tc_prod @ SY5012 @ SY5012 ) )
| ! [SY5014: $i] :
( ~ ( c_in @ ( c_Pair @ SY5014 @ SV1178 @ SY5012 @ SY5012 ) @ SY5013 @ ( tc_prod @ SY5012 @ SY5012 ) )
| ~ ( c_in @ ( c_Pair @ SV578 @ SY5014 @ SY5012 @ SY5012 ) @ ( c_Transitive__Closure_Otrancl @ SY5013 @ SY5012 ) @ ( tc_prod @ SY5012 @ SY5012 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2884]) ).
thf(3527,plain,
! [SV1179: $i,SV579: $i] :
( ( ! [SY5015: $i,SY5016: $i] :
( ( c_in @ ( c_Pair @ SV579 @ SV1179 @ SY5015 @ SY5015 ) @ ( c_Transitive__Closure_Otrancl @ SY5016 @ SY5015 ) @ ( tc_prod @ SY5015 @ SY5015 ) )
| ! [SY5017: $i] :
( ~ ( c_in @ ( c_Pair @ SY5017 @ SV1179 @ SY5015 @ SY5015 ) @ ( c_Transitive__Closure_Otrancl @ SY5016 @ SY5015 ) @ ( tc_prod @ SY5015 @ SY5015 ) )
| ~ ( c_in @ ( c_Pair @ SV579 @ SY5017 @ SY5015 @ SY5015 ) @ SY5016 @ ( tc_prod @ SY5015 @ SY5015 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2885]) ).
thf(3528,plain,
! [SV1180: $i,SV580: $i] :
( ( ! [SY5018: $i,SY5019: $i] :
( ( c_in @ ( c_Pair @ SV580 @ SV1180 @ SY5018 @ SY5018 ) @ ( c_Transitive__Closure_Ortrancl @ SY5019 @ SY5018 ) @ ( tc_prod @ SY5018 @ SY5018 ) )
| ! [SY5020: $i] :
( ~ ( c_in @ ( c_Pair @ SY5020 @ SV1180 @ SY5018 @ SY5018 ) @ SY5019 @ ( tc_prod @ SY5018 @ SY5018 ) )
| ~ ( c_in @ ( c_Pair @ SV580 @ SY5020 @ SY5018 @ SY5018 ) @ ( c_Transitive__Closure_Ortrancl @ SY5019 @ SY5018 ) @ ( tc_prod @ SY5018 @ SY5018 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2886]) ).
thf(3529,plain,
! [SV1181: $i,SV581: $i] :
( ( ! [SY5021: $i,SY5022: $i] :
( ( c_in @ ( c_Pair @ SV581 @ SV1181 @ SY5021 @ SY5021 ) @ ( c_Transitive__Closure_Ortrancl @ SY5022 @ SY5021 ) @ ( tc_prod @ SY5021 @ SY5021 ) )
| ! [SY5023: $i] :
( ~ ( c_in @ ( c_Pair @ SY5023 @ SV1181 @ SY5021 @ SY5021 ) @ ( c_Transitive__Closure_Ortrancl @ SY5022 @ SY5021 ) @ ( tc_prod @ SY5021 @ SY5021 ) )
| ~ ( c_in @ ( c_Pair @ SV581 @ SY5023 @ SY5021 @ SY5021 ) @ SY5022 @ ( tc_prod @ SY5021 @ SY5021 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2887]) ).
thf(3530,plain,
! [SV1182: $i,SV582: $i] :
( ( ! [SY5024: $i,SY5025: $i] :
( ( c_in @ ( c_Pair @ SV582 @ SV1182 @ SY5024 @ SY5024 ) @ ( c_Transitive__Closure_Otrancl @ SY5025 @ SY5024 ) @ ( tc_prod @ SY5024 @ SY5024 ) )
| ~ ( c_in @ ( c_Pair @ SV582 @ SV1182 @ SY5024 @ SY5024 ) @ SY5025 @ ( tc_prod @ SY5024 @ SY5024 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2888]) ).
thf(3531,plain,
! [SV1183: $i,SV583: $i] :
( ( ! [SY5026: $i,SY5027: $i] :
( ( c_in @ ( c_Pair @ SV583 @ SV1183 @ SY5026 @ SY5026 ) @ ( c_Transitive__Closure_Ortrancl @ SY5027 @ SY5026 ) @ ( tc_prod @ SY5026 @ SY5026 ) )
| ! [SY5028: $i] :
( ~ ( c_in @ ( c_Pair @ SY5028 @ SV1183 @ SY5026 @ SY5026 ) @ ( c_Transitive__Closure_Ortrancl @ SY5027 @ SY5026 ) @ ( tc_prod @ SY5026 @ SY5026 ) )
| ~ ( c_in @ ( c_Pair @ SV583 @ SY5028 @ SY5026 @ SY5026 ) @ ( c_Transitive__Closure_Ortrancl @ SY5027 @ SY5026 ) @ ( tc_prod @ SY5026 @ SY5026 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2889]) ).
thf(3532,plain,
! [SV1184: $i,SV584: $i] :
( ( ! [SY5029: $i] : ( c_in @ ( c_Pair @ SV584 @ SV584 @ SV1184 @ SV1184 ) @ ( c_Transitive__Closure_Ortrancl @ SY5029 @ SV1184 ) @ ( tc_prod @ SV1184 @ SV1184 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2890]) ).
thf(3533,plain,
! [SV1185: $i,SV585: $i] :
( ( ! [SY5030: $i] : ( c_in @ ( c_Pair @ SV585 @ SV585 @ SV1185 @ SV1185 ) @ ( c_Transitive__Closure_Ortrancl @ SY5030 @ SV1185 ) @ ( tc_prod @ SV1185 @ SV1185 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2891]) ).
thf(3534,plain,
! [SV1186: $i,SV586: $i] :
( ( ! [SY5031: $i,SY5032: $i] :
( ~ ( c_in @ ( c_Pair @ SV586 @ SV1186 @ SY5031 @ SY5031 ) @ SY5032 @ ( tc_prod @ SY5031 @ SY5031 ) )
| ~ ( c_in @ ( c_Pair @ SV1186 @ SV586 @ SY5031 @ SY5031 ) @ SY5032 @ ( tc_prod @ SY5031 @ SY5031 ) )
| ~ ( c_Wellfounded_Owf @ SY5032 @ SY5031 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2892]) ).
thf(3535,plain,
! [SV1187: $i,SV587: $i] :
( ( ( SV587 = SV1187 )
| ! [SY5033: $i,SY5034: $i] :
( ~ ( c_in @ ( c_Pair @ SV1187 @ SV587 @ SY5033 @ SY5033 ) @ SY5034 @ ( tc_prod @ SY5033 @ SY5033 ) )
| ~ ( c_in @ ( c_Pair @ SV587 @ SV1187 @ SY5033 @ SY5033 ) @ SY5034 @ ( tc_prod @ SY5033 @ SY5033 ) )
| ~ ( c_Relation_Oantisym @ SY5034 @ SY5033 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2893]) ).
thf(3536,plain,
! [SV1188: $i,SV588: $i] :
( ( ( SV588 = SV1188 )
| ! [SY5035: $i,SY5036: $i] :
( ~ ( c_in @ ( c_Pair @ SV1188 @ SV588 @ SY5035 @ SY5035 ) @ SY5036 @ ( tc_prod @ SY5035 @ SY5035 ) )
| ~ ( c_in @ ( c_Pair @ SV588 @ SV1188 @ SY5035 @ SY5035 ) @ SY5036 @ ( tc_prod @ SY5035 @ SY5035 ) )
| ~ ( c_Relation_Oantisym @ SY5036 @ SY5035 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2894]) ).
thf(3537,plain,
! [SV1189: $i,SV589: $i] :
( ( ! [SY5037: $i,SY5038: $i] :
( ( ( hAPP @ SV589 @ SV1189 )
= ( hAPP @ SV589 @ SY5037 ) )
| ! [SY5039: $i] :
( ~ ( c_in @ ( c_Pair @ SV1189 @ SY5037 @ SY5038 @ SY5038 ) @ SY5039 @ ( tc_prod @ SY5038 @ SY5038 ) )
| ! [SY3919: $i] :
~ ( c_Equiv__Relations_Ocongruent @ SY5039 @ SV589 @ SY5038 @ SY3919 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2895]) ).
thf(3538,plain,
! [SV1190: $i,SV590: $i] :
( ( ( SV590 = SV1190 )
| ! [SY5041: $i,SY5042: $i] :
~ ( c_in @ ( c_Pair @ SV590 @ SV1190 @ SY5041 @ SY5041 ) @ ( c_Relation_OId__on @ SY5042 @ SY5041 ) @ ( tc_prod @ SY5041 @ SY5041 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2896]) ).
thf(3539,plain,
! [SV1191: $i,SV591: $i] :
( ( ! [SY5043: $i,SY5044: $i,SY5045: $i,SY5046: $i] :
( ( ( c_Recdef_Ocut @ SV591 @ SV1191 @ SY5043 @ SY5044 @ SY5045 )
!= ( c_Recdef_Ocut @ SY5046 @ SV1191 @ SY5043 @ SY5044 @ SY5045 ) )
| ! [SY5047: $i] :
( ( ( hAPP @ SV591 @ SY5047 )
= ( hAPP @ SY5046 @ SY5047 ) )
| ~ ( c_in @ ( c_Pair @ SY5047 @ SY5043 @ SY5044 @ SY5044 ) @ SV1191 @ ( tc_prod @ SY5044 @ SY5044 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2897]) ).
thf(3540,plain,
! [SV1192: $i,SV592: $i] :
( ( ( SV592 = SV1192 )
| ! [SY5048: $i] :
~ ( c_in @ ( c_Pair @ SV592 @ SV1192 @ SY5048 @ SY5048 ) @ ( c_Relation_OId @ SY5048 ) @ ( tc_prod @ SY5048 @ SY5048 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2898]) ).
thf(3541,plain,
! [SV1193: $i,SV593: $i] :
( ( ! [SY5049: $i] :
( ( c_in @ ( c_Pair @ SV593 @ SV593 @ SV1193 @ SV1193 ) @ SY5049 @ ( tc_prod @ SV1193 @ SV1193 ) )
| ~ ( c_Nitpick_Orefl_H @ SY5049 @ SV1193 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2899]) ).
thf(3542,plain,
! [SV1194: $i,SV594: $i] :
( ( ! [SY5050: $i] :
( ~ ( c_in @ ( c_Pair @ SV594 @ SV594 @ SV1194 @ SV1194 ) @ SY5050 @ ( tc_prod @ SV1194 @ SV1194 ) )
| ~ ( c_Wellfounded_Owf @ SY5050 @ SV1194 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2900]) ).
thf(3543,plain,
! [SV1195: $i,SV595: $i] :
( ( ! [SY5051: $i,SY5052: $i,SY5053: $i,SY5054: $i] :
( ( c_in @ ( c_Pair @ SV595 @ SV1195 @ SY5051 @ SY5051 ) @ ( c_Relation_Oinv__image @ SY5052 @ SY5053 @ SY5054 @ SY5051 ) @ ( tc_prod @ SY5051 @ SY5051 ) )
| ~ ( c_in @ ( c_Pair @ ( hAPP @ SY5053 @ SV595 ) @ ( hAPP @ SY5053 @ SV1195 ) @ SY5054 @ SY5054 ) @ SY5052 @ ( tc_prod @ SY5054 @ SY5054 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2901]) ).
thf(3544,plain,
! [SV1196: $i,SV596: $i] :
( ( ! [SY5055: $i,SY5056: $i,SY5057: $i] :
( ( c_in @ ( c_Pair @ ( hAPP @ SV596 @ SV1196 ) @ ( hAPP @ SV596 @ SY5055 ) @ SY5056 @ SY5056 ) @ SY5057 @ ( tc_prod @ SY5056 @ SY5056 ) )
| ! [SY5058: $i] :
~ ( c_in @ ( c_Pair @ SV1196 @ SY5055 @ SY5058 @ SY5058 ) @ ( c_Relation_Oinv__image @ SY5057 @ SV596 @ SY5056 @ SY5058 ) @ ( tc_prod @ SY5058 @ SY5058 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2902]) ).
thf(3545,plain,
! [SV1197: $i,SV597: $i] :
( ( ! [SY5059: $i,SY5060: $i] :
( ( c_in @ ( c_Pair @ SV597 @ SV1197 @ SY5059 @ SY5059 ) @ SY5060 @ ( tc_prod @ SY5059 @ SY5059 ) )
| ~ ( c_in @ ( c_Pair @ SV1197 @ SV597 @ SY5059 @ SY5059 ) @ SY5060 @ ( tc_prod @ SY5059 @ SY5059 ) )
| ~ ( c_Relation_Osym @ SY5060 @ SY5059 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2903]) ).
thf(3546,plain,
! [SV1198: $i,SV598: $i] :
( ( ! [SY5061: $i,SY5062: $i] :
( ( c_in @ ( c_Pair @ SV598 @ SV1198 @ SY5061 @ SY5061 ) @ SY5062 @ ( tc_prod @ SY5061 @ SY5061 ) )
| ~ ( c_in @ ( c_Pair @ SV1198 @ SV598 @ SY5061 @ SY5061 ) @ SY5062 @ ( tc_prod @ SY5061 @ SY5061 ) )
| ~ ( c_Relation_Osym @ SY5062 @ SY5061 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2904]) ).
thf(3547,plain,
! [SV1199: $i,SV599: $i] :
( ( ! [SY5063: $i,SY5064: $i,SY5065: $i,SY5066: $i,SY5067: $i] :
( ( c_in @ ( c_Pair @ SV599 @ SV1199 @ SY5063 @ SY5064 ) @ ( c_Relation_Orel__comp @ SY5065 @ SY5066 @ SY5063 @ SY5067 @ SY5064 ) @ ( tc_prod @ SY5063 @ SY5064 ) )
| ! [SY5068: $i] :
( ~ ( c_in @ ( c_Pair @ SY5068 @ SV1199 @ SY5067 @ SY5064 ) @ SY5066 @ ( tc_prod @ SY5067 @ SY5064 ) )
| ~ ( c_in @ ( c_Pair @ SV599 @ SY5068 @ SY5063 @ SY5067 ) @ SY5065 @ ( tc_prod @ SY5063 @ SY5067 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2905]) ).
thf(3548,plain,
! [SV1200: $i,SV600: $i] :
( ( ! [SY5069: $i,SY5070: $i] :
( ( c_in @ ( c_Pair @ SV600 @ SV1200 @ SY5069 @ SY5069 ) @ ( c_Transitive__Closure_Otrancl @ SY5070 @ SY5069 ) @ ( tc_prod @ SY5069 @ SY5069 ) )
| ! [SY5071: $i] :
( ~ ( c_in @ ( c_Pair @ SY5071 @ SV1200 @ SY5069 @ SY5069 ) @ SY5070 @ ( tc_prod @ SY5069 @ SY5069 ) )
| ~ ( c_in @ ( c_Pair @ SV600 @ SY5071 @ SY5069 @ SY5069 ) @ SY5070 @ ( tc_prod @ SY5069 @ SY5069 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2906]) ).
thf(3549,plain,
! [SV1201: $i,SV601: $i] :
( ( ! [SY5072: $i,SY5073: $i] :
( ( c_in @ ( c_Pair @ SV601 @ SV1201 @ SY5072 @ SY5072 ) @ ( c_Transitive__Closure_Otrancl @ SY5073 @ SY5072 ) @ ( tc_prod @ SY5072 @ SY5072 ) )
| ! [SY5074: $i] :
( ~ ( c_in @ ( c_Pair @ SY5074 @ SV1201 @ SY5072 @ SY5072 ) @ ( c_Transitive__Closure_Otrancl @ SY5073 @ SY5072 ) @ ( tc_prod @ SY5072 @ SY5072 ) )
| ~ ( c_in @ ( c_Pair @ SV601 @ SY5074 @ SY5072 @ SY5072 ) @ ( c_Transitive__Closure_Otrancl @ SY5073 @ SY5072 ) @ ( tc_prod @ SY5072 @ SY5072 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2907]) ).
thf(3550,plain,
! [SV1202: $i,SV602: $i] :
( ( c_in @ ( c_Pair @ SV602 @ SV602 @ SV1202 @ SV1202 ) @ ( c_Relation_OId @ SV1202 ) @ ( tc_prod @ SV1202 @ SV1202 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2908]) ).
thf(3551,plain,
! [SV1203: $i,SV603: $i] :
( ( c_in @ ( c_Pair @ SV603 @ SV603 @ SV1203 @ SV1203 ) @ ( c_Relation_OId @ SV1203 ) @ ( tc_prod @ SV1203 @ SV1203 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2909]) ).
thf(3552,plain,
! [SV1204: $i,SV604: $i] :
( ( ! [SY5075: $i,SY5076: $i] :
( ( c_in @ ( c_Pair @ SV604 @ SV1204 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omktop @ SY5075 ) @ SY5076 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV604 @ SV1204 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY5075 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV604 = SV1204 )
| ( SV604 = SY5076 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2910]) ).
thf(3553,plain,
! [SV1205: $i,SV605: $i] :
( ( ! [SY5077: $i,SY5078: $i] :
( ( c_in @ ( c_Pair @ SV605 @ SV1205 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omktop @ SY5077 ) @ SY5078 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV605 @ SV1205 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY5077 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV1205 = SY5078 )
| ( SV605 = SY5078 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2911]) ).
thf(3554,plain,
! [SV1206: $i,SV606: $i] :
( ( ~ ( c_in @ ( c_Pair @ SV606 @ SV606 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omktop @ SV1206 ) @ SV606 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2912]) ).
thf(3555,plain,
! [SV1207: $i,SV607: $i] :
( ( ! [SY5079: $i] :
~ ( c_in @ ( c_Pair @ SV607 @ SV1207 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omktop @ SY5079 ) @ SV607 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2913]) ).
thf(3556,plain,
! [SV1208: $i,SV608: $i] :
( ( ! [SY5080: $i] :
( ( c_in @ ( c_Pair @ SV608 @ SV1208 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY5080 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ! [SY5081: $i] :
( ( SV1208 = SY5081 )
| ~ ( c_in @ ( c_Pair @ SV608 @ SV1208 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omktop @ SY5080 ) @ SY5081 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2914]) ).
thf(3557,plain,
! [SV1209: $i,SV609: $i] :
( ( ( SV609 = SV1209 )
| ( SV1209 = SV609 )
| ! [SY5082: $i] : ( c_in @ ( c_Pair @ SV609 @ SV1209 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omkbot @ SY5082 ) @ SV609 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2915]) ).
thf(3558,plain,
! [SV1210: $i,SV610: $i] :
( ( ~ ( c_in @ ( c_Pair @ SV610 @ SV610 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omkbot @ SV1210 ) @ SV610 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2916]) ).
thf(3559,plain,
! [SV1211: $i,SV611: $i] :
( ( ! [SY5083: $i] :
~ ( c_in @ ( c_Pair @ SV611 @ SV1211 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omkbot @ SY5083 ) @ SV1211 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2917]) ).
thf(3560,plain,
! [SV1212: $i,SV612: $i] :
( ( ! [SY5084: $i,SY5085: $i] :
( ( c_in @ ( c_Pair @ SV612 @ SV1212 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omkbot @ SY5084 ) @ SY5085 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV612 @ SV1212 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY5084 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV612 = SV1212 )
| ( SV1212 = SY5085 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2918]) ).
thf(3561,plain,
! [SV1213: $i,SV613: $i] :
( ( ! [SY5086: $i,SY5087: $i] :
( ( c_in @ ( c_Pair @ SV613 @ SV1213 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omkbot @ SY5086 ) @ SY5087 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV613 @ SV1213 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY5086 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV613 = SY5087 )
| ( SV1213 = SY5087 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2919]) ).
thf(3562,plain,
! [SV1214: $i,SV614: $i] :
( ( ( SV614 = SV1214 )
| ( SV614 = SV1214 )
| ! [SY5088: $i] : ( c_in @ ( c_Pair @ SV614 @ SV1214 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omktop @ SY5088 ) @ SV1214 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2920]) ).
thf(3563,plain,
! [SV1215: $i,SV615: $i] :
( ( ! [SY5089: $i] :
( ( c_in @ ( c_Pair @ SV615 @ SV1215 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SY5089 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ! [SY5090: $i] :
( ( SV615 = SY5090 )
| ~ ( c_in @ ( c_Pair @ SV615 @ SV1215 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omkbot @ SY5089 ) @ SY5090 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2921]) ).
thf(3564,plain,
! [SV1216: $i,SV616: $i] :
( ( ( SV616 = SV1216 )
| ( c_in @ ( c_Pair @ SV616 @ SV1216 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1 @ SV616 @ SV1216 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2922]) ).
thf(3565,plain,
! [SV1217: $i,SV617: $i] :
( ( ! [SY5091: $i,SY5092: $i,SY5093: $i,SY5094: $i] :
( ( c_in @ ( c_Pair @ SV617 @ SV1217 @ SY5091 @ SY5092 ) @ ( c_Product__Type_OSigma @ SY5093 @ SY5094 @ SY5091 @ SY5092 ) @ ( tc_prod @ SY5091 @ SY5092 ) )
| ~ ( c_in @ SV1217 @ ( hAPP @ SY5094 @ SV617 ) @ SY5092 )
| ~ ( c_in @ SV617 @ SY5093 @ SY5091 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2923]) ).
thf(3566,plain,
! [SV1218: $i,SV618: $i] :
( ( ! [SY5095: $i,SY5096: $i,SY5097: $i,SY5098: $i] :
( ( c_in @ ( c_Pair @ SV618 @ SV1218 @ SY5095 @ SY5096 ) @ ( c_Product__Type_OSigma @ SY5097 @ SY5098 @ SY5095 @ SY5096 ) @ ( tc_prod @ SY5095 @ SY5096 ) )
| ~ ( c_in @ SV1218 @ ( hAPP @ SY5098 @ SV618 ) @ SY5096 )
| ~ ( c_in @ SV618 @ SY5097 @ SY5095 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2924]) ).
thf(3567,plain,
! [SV1219: $i,SV619: $i] :
( ( ! [SY5099: $i] :
( ( c_in @ SV619 @ ( c_Wellfounded_Oacc @ SV1219 @ SY5099 ) @ SY5099 )
| ! [SY5100: $i] :
( ~ ( c_in @ ( c_Pair @ SV619 @ SY5100 @ SY5099 @ SY5099 ) @ SV1219 @ ( tc_prod @ SY5099 @ SY5099 ) )
| ~ ( c_in @ SY5100 @ ( c_Wellfounded_Oacc @ SV1219 @ SY5099 ) @ SY5099 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2925]) ).
thf(3568,plain,
! [SV1220: $i,SV620: $i] :
( ( ! [SY5101: $i] :
( ( c_in @ SV620 @ ( c_Wellfounded_Oacc @ SV1220 @ SY5101 ) @ SY5101 )
| ! [SY5102: $i] :
( ~ ( c_in @ ( c_Pair @ SV620 @ SY5102 @ SY5101 @ SY5101 ) @ SV1220 @ ( tc_prod @ SY5101 @ SY5101 ) )
| ~ ( c_in @ SY5102 @ ( c_Wellfounded_Oacc @ SV1220 @ SY5101 ) @ SY5101 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2926]) ).
thf(3569,plain,
! [SV1221: $i,SV621: $i] :
( ( ! [SY5103: $i,SY5104: $i,SY5105: $i] :
( ( c_in @ SV621 @ ( c_Relation_OImage @ SV1221 @ SY5103 @ SY5104 @ SY5105 ) @ SY5105 )
| ! [SY5106: $i] :
( ~ ( c_in @ ( c_Pair @ SY5106 @ SV621 @ SY5104 @ SY5105 ) @ SV1221 @ ( tc_prod @ SY5104 @ SY5105 ) )
| ~ ( c_in @ SY5106 @ SY5103 @ SY5104 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2927]) ).
thf(3570,plain,
! [SV1222: $i,SV622: $i] :
( ( ! [SY5107: $i,SY5108: $i,SY5109: $i] :
( ( c_in @ SV622 @ ( c_Relation_OImage @ SV1222 @ SY5107 @ SY5108 @ SY5109 ) @ SY5109 )
| ! [SY5110: $i] :
( ~ ( c_in @ ( c_Pair @ SY5110 @ SV622 @ SY5108 @ SY5109 ) @ SV1222 @ ( tc_prod @ SY5108 @ SY5109 ) )
| ~ ( c_in @ SY5110 @ SY5107 @ SY5108 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2928]) ).
thf(3571,plain,
! [SV1223: $i,SV623: $i] :
( ( ! [SY5111: $i] :
( ( c_in @ SV623 @ SV1223 @ SY5111 )
| ! [SY5112: $i] :
~ ( c_in @ ( c_Pair @ SV623 @ SY5112 @ SY5111 @ SY5111 ) @ ( c_Relation_OId__on @ SV1223 @ SY5111 ) @ ( tc_prod @ SY5111 @ SY5111 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2929]) ).
thf(3572,plain,
! [SV1224: $i,SV624: $i] :
( ( ! [SY5113: $i] :
( ( c_in @ ( c_Pair @ SV624 @ SV624 @ SV1224 @ SV1224 ) @ ( c_Relation_OId__on @ SY5113 @ SV1224 ) @ ( tc_prod @ SV1224 @ SV1224 ) )
| ~ ( c_in @ SV624 @ SY5113 @ SV1224 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2930]) ).
thf(3573,plain,
! [SV1225: $i,SV625: $i] :
( ( ! [SY5114: $i] :
( ( c_in @ SV625 @ SV1225 @ SY5114 )
| ! [SY5115: $i,SY5116: $i] :
( ~ ( c_in @ ( c_Pair @ SY5115 @ SV625 @ SY5114 @ SY5114 ) @ SY5116 @ ( tc_prod @ SY5114 @ SY5114 ) )
| ~ ( c_Equiv__Relations_Oequiv @ SV1225 @ SY5116 @ SY5114 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2931]) ).
thf(3574,plain,
! [SV1226: $i,SV626: $i] :
( ( ! [SY5117: $i] :
( ( c_in @ SV626 @ SV1226 @ SY5117 )
| ! [SY5118: $i,SY5119: $i] :
( ~ ( c_in @ ( c_Pair @ SV626 @ SY5118 @ SY5117 @ SY5117 ) @ SY5119 @ ( tc_prod @ SY5117 @ SY5117 ) )
| ~ ( c_Equiv__Relations_Oequiv @ SV1226 @ SY5119 @ SY5117 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2932]) ).
thf(3575,plain,
! [SV1227: $i,SV627: $i] :
( ( ! [SY5120: $i,SY5121: $i] :
( ( c_in @ SV627 @ ( c_Relation_ORange @ SV1227 @ SY5120 @ SY5121 ) @ SY5121 )
| ! [SY5122: $i] :
~ ( c_in @ ( c_Pair @ SY5122 @ SV627 @ SY5120 @ SY5121 ) @ SV1227 @ ( tc_prod @ SY5120 @ SY5121 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2933]) ).
thf(3576,plain,
! [SV1228: $i,SV628: $i] :
( ( ! [SY5123: $i,SY5124: $i] :
( ( c_in @ SV628 @ ( c_Relation_ORange @ SV1228 @ SY5123 @ SY5124 ) @ SY5124 )
| ! [SY5125: $i] :
~ ( c_in @ ( c_Pair @ SY5125 @ SV628 @ SY5123 @ SY5124 ) @ SV1228 @ ( tc_prod @ SY5123 @ SY5124 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2934]) ).
thf(3577,plain,
! [SV1229: $i,SV629: $i] :
( ( ! [SY5126: $i,SY5127: $i] :
( ( c_in @ SV629 @ ( c_Relation_ODomain @ SV1229 @ SY5126 @ SY5127 ) @ SY5126 )
| ! [SY5128: $i] :
~ ( c_in @ ( c_Pair @ SV629 @ SY5128 @ SY5126 @ SY5127 ) @ SV1229 @ ( tc_prod @ SY5126 @ SY5127 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2935]) ).
thf(3578,plain,
! [SV1230: $i,SV630: $i] :
( ( ! [SY5129: $i,SY5130: $i] :
( ( c_in @ SV630 @ ( c_Relation_ODomain @ SV1230 @ SY5129 @ SY5130 ) @ SY5129 )
| ! [SY5131: $i] :
~ ( c_in @ ( c_Pair @ SV630 @ SY5131 @ SY5129 @ SY5130 ) @ SV1230 @ ( tc_prod @ SY5129 @ SY5130 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2936]) ).
thf(3579,plain,
! [SV1231: $i,SV631: $i] :
( ( ! [SY5132: $i,SY5133: $i] :
( ( c_in @ SV631 @ ( hAPP @ SV1231 @ SY5132 ) @ SY5133 )
| ! [SY5134: $i,SY5135: $i] :
~ ( c_in @ ( c_Pair @ SY5132 @ SV631 @ SY5134 @ SY5133 ) @ ( c_Product__Type_OSigma @ SY5135 @ SV1231 @ SY5134 @ SY5133 ) @ ( tc_prod @ SY5134 @ SY5133 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2937]) ).
thf(3580,plain,
! [SV1232: $i,SV632: $i] :
( ( ! [SY5136: $i,SY5137: $i] :
( ( c_in @ SV632 @ SV1232 @ SY5136 )
| ! [SY5138: $i,SY5139: $i] :
~ ( c_in @ ( c_Pair @ SV632 @ SY5137 @ SY5136 @ SY5138 ) @ ( c_Product__Type_OSigma @ SV1232 @ SY5139 @ SY5136 @ SY5138 ) @ ( tc_prod @ SY5136 @ SY5138 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2938]) ).
thf(3581,plain,
! [SV1233: $i,SV633: $i] :
( ( ! [SY5140: $i,SY5141: $i] :
( ( c_in @ ( c_Pair @ SV633 @ SV1233 @ SY5140 @ SY5140 ) @ SY5141 @ ( tc_prod @ SY5140 @ SY5140 ) )
| ( c_in @ ( c_Pair @ SV1233 @ SV633 @ SY5140 @ SY5140 ) @ SY5141 @ ( tc_prod @ SY5140 @ SY5140 ) )
| ( SV1233 = SV633 )
| ! [SY5142: $i] :
( ~ ( c_in @ SV633 @ SY5142 @ SY5140 )
| ~ ( c_in @ SV1233 @ SY5142 @ SY5140 )
| ~ ( c_Relation_Ototal__on @ SY5142 @ SY5141 @ SY5140 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2939]) ).
thf(3582,plain,
! [SV1234: $i,SV634: $i] :
( ( ! [SY5143: $i] :
( ( c_in @ ( c_Pair @ SV634 @ SV634 @ SV1234 @ SV1234 ) @ SY5143 @ ( tc_prod @ SV1234 @ SV1234 ) )
| ! [SY5144: $i] :
( ~ ( c_in @ SV634 @ SY5144 @ SV1234 )
| ~ ( c_Relation_Orefl__on @ SY5144 @ SY5143 @ SV1234 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2940]) ).
thf(3583,plain,
! [SV1235: $i,SV635: $i] :
( ( ! [SY5145: $i] :
( ( c_in @ SV635 @ SV1235 @ SY5145 )
| ! [SY5146: $i,SY5147: $i] :
( ~ ( c_in @ ( c_Pair @ SY5146 @ SV635 @ SY5145 @ SY5145 ) @ SY5147 @ ( tc_prod @ SY5145 @ SY5145 ) )
| ~ ( c_Relation_Orefl__on @ SV1235 @ SY5147 @ SY5145 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2941]) ).
thf(3584,plain,
! [SV1236: $i,SV636: $i] :
( ( ! [SY5148: $i] :
( ( c_in @ SV636 @ SV1236 @ SY5148 )
| ! [SY5149: $i,SY5150: $i] :
( ~ ( c_in @ ( c_Pair @ SV636 @ SY5149 @ SY5148 @ SY5148 ) @ SY5150 @ ( tc_prod @ SY5148 @ SY5148 ) )
| ~ ( c_Relation_Orefl__on @ SV1236 @ SY5150 @ SY5148 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2942]) ).
thf(3585,plain,
! [SV1237: $i,SV637: $i] :
( ( ! [SY5151: $i] :
( ( c_in @ ( c_Pair @ SV637 @ SV637 @ SV1237 @ SV1237 ) @ SY5151 @ ( tc_prod @ SV1237 @ SV1237 ) )
| ! [SY5152: $i] :
( ~ ( c_in @ SV637 @ SY5152 @ SV1237 )
| ~ ( c_Relation_Orefl__on @ SY5152 @ SY5151 @ SV1237 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2943]) ).
thf(3586,plain,
! [SV1238: $i,SV638: $i] :
( ( ! [SY5153: $i,SY5154: $i,SY5155: $i,SY5156: $i] :
( ( ( c_Pair @ SV638 @ SV1238 @ SY5153 @ SY5154 )
!= ( c_Pair @ SY5155 @ SY5156 @ SY5153 @ SY5154 ) )
| ( SV1238 = SY5156 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2944]) ).
thf(3587,plain,
! [SV1239: $i,SV639: $i] :
( ( ! [SY5157: $i,SY5158: $i,SY5159: $i] :
( ! [SY5160: $i] :
( ( c_Pair @ SV639 @ SV1239 @ SY5157 @ SY5158 )
!= ( c_Pair @ SY5159 @ SY5160 @ SY5157 @ SY5158 ) )
| ( SV639 = SY5159 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2945]) ).
thf(3588,plain,
! [SV1240: $i,SV640: $i] :
( ( ! [SY5161: $i] : ( c_in @ SV640 @ SV1240 @ SY5161 )
| ~ ( hBOOL @ ( hAPP @ SV1240 @ SV640 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2946]) ).
thf(3589,plain,
! [SV1241: $i,SV641: $i] :
( ( ( hBOOL @ ( hAPP @ SV641 @ SV1241 ) )
| ! [SY5162: $i] :
~ ( c_in @ SV1241 @ SV641 @ SY5162 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2947]) ).
thf(3590,plain,
( ( ( c_in @ ( c_Pair @ v_c____ @ v_d____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_HOL_OIf @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ v_h____ @ tc_nat @ ( tc_fun @ tc_nat @ tc_bool ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ v_n____ @ tc_Arrow__Order__Mirabelle_Oindi @ tc_nat @ tc_bool ) @ tc_bool @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ ( c_COMBC @ ( c_COMBB @ c_Arrow__Order__Mirabelle_Omktop @ v_P____ @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ v_e____ @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_HOL_OIf @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ ( c_COMBC @ ( c_COMBB @ ( c_fequal @ tc_nat ) @ v_h____ @ tc_nat @ ( tc_fun @ tc_nat @ tc_bool ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ v_n____ @ tc_Arrow__Order__Mirabelle_Oindi @ tc_nat @ tc_bool ) @ tc_bool @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ ( c_COMBC @ ( c_COMBC @ ( c_COMBB @ c_Arrow__Order__Mirabelle_Oabove @ v_P____ @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ v_c____ @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ v_e____ @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ ( c_COMBC @ ( c_COMBB @ c_Arrow__Order__Mirabelle_Omkbot @ v_P____ @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ v_e____ @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ v_c____ @ v_d____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ v_P____ ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2948]) ).
thf(3591,plain,
( ( ( c_in @ ( c_Pair @ v_c____ @ v_d____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ v_P____ ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ v_c____ @ v_d____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_HOL_OIf @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ ( c_COMBC @ ( c_COMBB @ ( c_HOL_Oord__class_Oless @ tc_nat ) @ v_h____ @ tc_nat @ ( tc_fun @ tc_nat @ tc_bool ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ v_n____ @ tc_Arrow__Order__Mirabelle_Oindi @ tc_nat @ tc_bool ) @ tc_bool @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ ( c_COMBC @ ( c_COMBB @ c_Arrow__Order__Mirabelle_Omktop @ v_P____ @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ v_e____ @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_HOL_OIf @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ ( c_COMBC @ ( c_COMBB @ ( c_fequal @ tc_nat ) @ v_h____ @ tc_nat @ ( tc_fun @ tc_nat @ tc_bool ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ v_n____ @ tc_Arrow__Order__Mirabelle_Oindi @ tc_nat @ tc_bool ) @ tc_bool @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ ( c_COMBC @ ( c_COMBC @ ( c_COMBB @ c_Arrow__Order__Mirabelle_Oabove @ v_P____ @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ v_c____ @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ v_e____ @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ ( c_COMBC @ ( c_COMBB @ c_Arrow__Order__Mirabelle_Omkbot @ v_P____ @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ v_e____ @ tc_Arrow__Order__Mirabelle_Oindi @ tc_Arrow__Order__Mirabelle_Oalt @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2949]) ).
thf(3592,plain,
! [SV1242: $i,SV642: $i] :
( ( ( class_Lattices_Oupper__semilattice @ ( tc_fun @ SV642 @ SV1242 ) )
| ~ ( class_Lattices_Olattice @ SV1242 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2950]) ).
thf(3593,plain,
! [SV1243: $i,SV643: $i] :
( ( ( class_Lattices_Olower__semilattice @ ( tc_fun @ SV643 @ SV1243 ) )
| ~ ( class_Lattices_Olattice @ SV1243 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2951]) ).
thf(3594,plain,
! [SV1244: $i,SV644: $i] :
( ( ( class_Lattices_Odistrib__lattice @ ( tc_fun @ SV644 @ SV1244 ) )
| ~ ( class_Lattices_Odistrib__lattice @ SV1244 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2952]) ).
thf(3595,plain,
! [SV1245: $i,SV645: $i] :
( ( ( class_Lattices_Obounded__lattice @ ( tc_fun @ SV645 @ SV1245 ) )
| ~ ( class_Lattices_Obounded__lattice @ SV1245 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2953]) ).
thf(3596,plain,
! [SV1246: $i,SV646: $i] :
( ( ( class_Orderings_Opreorder @ ( tc_fun @ SV646 @ SV1246 ) )
| ~ ( class_Orderings_Opreorder @ SV1246 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2954]) ).
thf(3597,plain,
! [SV1247: $i,SV647: $i] :
( ( ( class_Lattices_Olattice @ ( tc_fun @ SV647 @ SV1247 ) )
| ~ ( class_Lattices_Olattice @ SV1247 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2955]) ).
thf(3598,plain,
! [SV1248: $i,SV648: $i] :
( ( ( class_Orderings_Oorder @ ( tc_fun @ SV648 @ SV1248 ) )
| ~ ( class_Orderings_Oorder @ SV1248 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2956]) ).
thf(3599,plain,
! [SV1249: $i,SV649: $i] :
( ( ( class_Orderings_Obot @ ( tc_fun @ SV649 @ SV1249 ) )
| ~ ( class_Orderings_Obot @ SV1249 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2957]) ).
thf(3600,plain,
! [SV1250: $i,SV650: $i] :
( ( ( class_HOL_Oord @ ( tc_fun @ SV650 @ SV1250 ) )
| ~ ( class_HOL_Oord @ SV1250 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2958]) ).
thf(3601,plain,
! [SV1251: $i,SV651: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ SV651 ) @ SV1251 ) @ SV1251 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2959]) ).
thf(3602,plain,
! [SV1252: $i,SV652: $i] :
( ( ( SV652 = SV1252 )
| ! [SY5163: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ SY5163 ) @ SV652 ) @ SV1252 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2960]) ).
thf(3603,plain,
! [SV1253: $i,SV653: $i,SV1: $i] :
( ( ! [SY5164: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ SV1 @ SV653 @ SV1253 ) @ ( c_Set_Oinsert @ SV1 @ SY5164 @ SV1253 ) @ ( tc_fun @ SV1253 @ tc_bool ) )
= ( c_Set_Oinsert @ SV1 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV653 @ SY5164 @ ( tc_fun @ SV1253 @ tc_bool ) ) @ SV1253 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2962]) ).
thf(3604,plain,
! [SV1254: $i,SV654: $i,SV2: $i] :
( ( ( c_Set_Oinsert @ SV2 @ SV654 @ SV1254 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1254 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2963]) ).
thf(3605,plain,
! [SV1255: $i,SV655: $i,SV3: $i] :
( ( ! [SY5165: $i] :
( ( c_HOL_Ominus__class_Ominus @ SV3 @ ( c_Set_Oinsert @ SV655 @ SV1255 @ SY5165 ) @ ( tc_fun @ SY5165 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV3 @ ( c_Set_Oinsert @ SV655 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5165 @ tc_bool ) ) @ SY5165 ) @ ( tc_fun @ SY5165 @ tc_bool ) ) @ SV1255 @ ( tc_fun @ SY5165 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2964]) ).
thf(3606,plain,
! [SV1256: $i,SV656: $i,SV4: $i] :
( ( ! [SY5166: $i] :
( ( c_HOL_Ominus__class_Ominus @ SV4 @ ( c_Set_Oinsert @ SV656 @ SV1256 @ SY5166 ) @ ( tc_fun @ SY5166 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV4 @ SV1256 @ ( tc_fun @ SY5166 @ tc_bool ) ) @ ( c_Set_Oinsert @ SV656 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5166 @ tc_bool ) ) @ SY5166 ) @ ( tc_fun @ SY5166 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2965]) ).
thf(3607,plain,
! [SV5: $i] :
( ( ( class_Orderings_Obot @ SV5 )
= $false )
| ( ( ! [SY2390: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ SV5 ) @ SY2390 @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2966]) ).
thf(3608,plain,
! [SV1257: $i,SV659: $i,SV8: $i] :
( ( ! [SY5167: $i] :
( ( c_Relation_Orel__comp @ SV8 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV659 @ SV1257 ) @ tc_bool ) ) @ SY5167 @ SV659 @ SV1257 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SY5167 @ SV1257 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2969]) ).
thf(3609,plain,
! [SV1258: $i,SV660: $i,SV9: $i] :
( ( ! [SY5168: $i] :
( ( c_Relation_Orel__comp @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV9 @ SV660 ) @ tc_bool ) ) @ SV1258 @ SV9 @ SV660 @ SY5168 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV9 @ SY5168 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2970]) ).
thf(3610,plain,
! [SV1259: $i,SV661: $i,SV10: $i] :
( ( ! [SY5169: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV10 @ ( c_Set_Oinsert @ SV661 @ SV1259 @ SY5169 ) @ ( tc_fun @ SY5169 @ tc_bool ) )
= ( c_Set_Oinsert @ SV661 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV10 @ SV1259 @ ( tc_fun @ SY5169 @ tc_bool ) ) @ SY5169 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2971]) ).
thf(3611,plain,
! [SV1260: $i,SV662: $i,SV11: $i] :
( ( ! [SY5170: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ SV11 @ SV662 @ SV1260 ) @ SY5170 @ ( tc_fun @ SV1260 @ tc_bool ) )
= ( c_Set_Oinsert @ SV11 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV662 @ SY5170 @ ( tc_fun @ SV1260 @ tc_bool ) ) @ SV1260 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2972]) ).
thf(3612,plain,
! [SV1261: $i,SV663: $i,SV12: $i] :
( ( ! [SY5171: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV12 @ tc_bool ) )
!= ( c_Set_Oimage @ SV663 @ SV1261 @ SY5171 @ SV12 ) )
| ( SV1261
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5171 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2973]) ).
thf(3613,plain,
! [SV1262: $i,SV664: $i,SV13: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Ortrancl @ SV13 @ SV664 ) @ ( c_Transitive__Closure_Ortrancl @ SV1262 @ SV664 ) @ ( tc_fun @ ( tc_prod @ SV664 @ SV664 ) @ tc_bool ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV13 @ SV1262 @ ( tc_fun @ ( tc_prod @ SV664 @ SV664 ) @ tc_bool ) ) @ SV664 ) @ ( tc_fun @ ( tc_prod @ SV664 @ SV664 ) @ tc_bool ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2974]) ).
thf(3614,plain,
! [SV1263: $i,SV665: $i,SV14: $i] :
( ( ! [SY5172: $i] :
( ( ( hAPP @ ( c_snd @ SV14 @ SV665 ) @ SV1263 )
!= ( hAPP @ ( c_snd @ SV14 @ SV665 ) @ SY5172 ) )
| ( ( hAPP @ ( c_fst @ SV14 @ SV665 ) @ SV1263 )
!= ( hAPP @ ( c_fst @ SV14 @ SV665 ) @ SY5172 ) )
| ( SV1263 = SY5172 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2975]) ).
thf(3615,plain,
! [SV1264: $i,SV666: $i,SV15: $i] :
( ( ! [SY5173: $i] :
( ( ( hAPP @ ( c_snd @ SV15 @ SV666 ) @ SV1264 )
!= ( hAPP @ ( c_snd @ SV15 @ SV666 ) @ SY5173 ) )
| ( ( hAPP @ ( c_fst @ SV15 @ SV666 ) @ SV1264 )
!= ( hAPP @ ( c_fst @ SV15 @ SV666 ) @ SY5173 ) )
| ( SV1264 = SY5173 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2976]) ).
thf(3616,plain,
! [SV667: $i,SV16: $i] :
( ( ( hBOOL @ ( hAPP @ SV16 @ SV667 ) )
= $true )
| ( ( ! [SY2417: $i,SY2418: $i] :
( ~ ( hBOOL @ ( hAPP @ SV16 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1 @ SV16 @ SY2417 @ SY2418 ) ) )
| ~ ( c_Wellfounded_Owf @ SY2417 @ SY2418 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2977]) ).
thf(3617,plain,
! [SV1265: $i,SV668: $i,SV17: $i] :
( ( ! [SY5174: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ ( c_Relation_ORange @ SV17 @ SV668 @ SV1265 ) @ ( c_Relation_ORange @ SY5174 @ SV668 @ SV1265 ) @ ( tc_fun @ SV1265 @ tc_bool ) ) @ ( c_Relation_ORange @ ( c_HOL_Ominus__class_Ominus @ SV17 @ SY5174 @ ( tc_fun @ ( tc_prod @ SV668 @ SV1265 ) @ tc_bool ) ) @ SV668 @ SV1265 ) @ ( tc_fun @ SV1265 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2978]) ).
thf(3618,plain,
! [SV1266: $i,SV669: $i,SV18: $i] :
( ( ! [SY5175: $i] :
( ( c_lessequals @ SV18 @ ( c_Set_Oinsert @ SV669 @ SV1266 @ SY5175 ) @ ( tc_fun @ SY5175 @ tc_bool ) )
| ~ ( c_lessequals @ SV18 @ SV1266 @ ( tc_fun @ SY5175 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2979]) ).
thf(3619,plain,
! [SV1267: $i,SV670: $i,SV19: $i] :
( ( ( c_lessequals @ SV19 @ SV670 @ ( tc_fun @ SV1267 @ tc_bool ) )
| ! [SY5176: $i] :
~ ( c_lessequals @ ( c_Set_Oinsert @ SY5176 @ SV19 @ SV1267 ) @ SV670 @ ( tc_fun @ SV1267 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2980]) ).
thf(3620,plain,
! [SV1268: $i,SV671: $i,SV20: $i] :
( ( ! [SY5177: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ SV20 @ SV671 @ SV1268 ) @ SY5177 @ ( tc_fun @ SV1268 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ SV671 @ SY5177 @ ( tc_fun @ SV1268 @ tc_bool ) ) )
| ~ ( c_in @ SV20 @ SY5177 @ SV1268 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2981]) ).
thf(3621,plain,
! [SV1269: $i,SV672: $i,SV21: $i] :
( ( ! [SY5178: $i,SY5179: $i] :
( ( c_lessequals @ ( c_Product__Type_OSigma @ SV21 @ ( c_COMBK @ SV672 @ ( tc_fun @ SV1269 @ tc_bool ) @ SY5178 ) @ SY5178 @ SV1269 ) @ ( c_Product__Type_OSigma @ SY5179 @ ( c_COMBK @ SV672 @ ( tc_fun @ SV1269 @ tc_bool ) @ SY5178 ) @ SY5178 @ SV1269 ) @ ( tc_fun @ ( tc_prod @ SY5178 @ SV1269 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV21 @ SY5179 @ ( tc_fun @ SY5178 @ tc_bool ) )
| ! [SY5180: $i] :
~ ( c_in @ SY5180 @ SV672 @ SV1269 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2982]) ).
thf(3622,plain,
! [SV1270: $i,SV673: $i,SV22: $i] :
( ( ! [SY5181: $i] :
( ( c_lessequals @ SV22 @ SV673 @ ( tc_fun @ SV1270 @ tc_bool ) )
| ! [SY5182: $i] :
( ~ ( c_lessequals @ ( c_Product__Type_OSigma @ SV22 @ ( c_COMBK @ SY5181 @ ( tc_fun @ SY5182 @ tc_bool ) @ SV1270 ) @ SV1270 @ SY5182 ) @ ( c_Product__Type_OSigma @ SV673 @ ( c_COMBK @ SY5181 @ ( tc_fun @ SY5182 @ tc_bool ) @ SV1270 ) @ SV1270 @ SY5182 ) @ ( tc_fun @ ( tc_prod @ SV1270 @ SY5182 ) @ tc_bool ) )
| ! [V_x: $i] :
~ ( c_in @ V_x @ SY5181 @ SY5182 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2983]) ).
thf(3623,plain,
! [SV1271: $i,SV674: $i,SV23: $i] :
( ( ! [SY5184: $i] :
( ( c_lessequals @ SV23 @ ( c_Set_Oinsert @ SV674 @ SV1271 @ SY5184 ) @ ( tc_fun @ SY5184 @ tc_bool ) )
| ~ ( c_in @ SV674 @ SV23 @ SY5184 )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV23 @ ( c_Set_Oinsert @ SV674 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5184 @ tc_bool ) ) @ SY5184 ) @ ( tc_fun @ SY5184 @ tc_bool ) ) @ SV1271 @ ( tc_fun @ SY5184 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2984]) ).
thf(3624,plain,
! [SV1272: $i,SV675: $i,SV24: $i] :
( ( ! [SY5185: $i] :
( ( c_lessequals @ SV24 @ ( c_Set_Oinsert @ SV675 @ SV1272 @ SY5185 ) @ ( tc_fun @ SY5185 @ tc_bool ) )
| ~ ( c_in @ SV675 @ SV24 @ SY5185 )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV24 @ ( c_Set_Oinsert @ SV675 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5185 @ tc_bool ) ) @ SY5185 ) @ ( tc_fun @ SY5185 @ tc_bool ) ) @ SV1272 @ ( tc_fun @ SY5185 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2985]) ).
thf(3625,plain,
! [SV1273: $i,SV676: $i,SV25: $i] :
( ( ! [SY5186: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV25 @ ( c_Set_Oinsert @ SV676 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1273 @ tc_bool ) ) @ SV1273 ) @ ( tc_fun @ SV1273 @ tc_bool ) ) @ SY5186 @ ( tc_fun @ SV1273 @ tc_bool ) )
| ~ ( c_in @ SV676 @ SV25 @ SV1273 )
| ~ ( c_lessequals @ SV25 @ ( c_Set_Oinsert @ SV676 @ SY5186 @ SV1273 ) @ ( tc_fun @ SV1273 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2986]) ).
thf(3626,plain,
! [SV1274: $i,SV677: $i,SV26: $i] :
( ( ! [SY5187: $i] :
( ( ( c_Set_Oimage @ ( c_COMBK @ SV26 @ SV677 @ SV1274 ) @ SY5187 @ SV1274 @ SV677 )
= ( c_Set_Oinsert @ SV26 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV677 @ tc_bool ) ) @ SV677 ) )
| ! [SY5188: $i] :
~ ( c_in @ SY5188 @ SY5187 @ SV1274 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2987]) ).
thf(3627,plain,
! [SV1275: $i,SV678: $i,SV27: $i] :
( ( ( c_lessequals @ ( c_Transitive__Closure_Otrancl @ SV27 @ SV678 ) @ SV1275 @ ( tc_fun @ ( tc_prod @ SV678 @ SV678 ) @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Relation_Orel__comp @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Transitive__Closure_Otrancl @ SV27 @ SV678 ) @ SV1275 @ ( tc_fun @ ( tc_prod @ SV678 @ SV678 ) @ tc_bool ) ) @ SV27 @ SV678 @ SV678 @ SV678 ) @ SV1275 @ ( tc_fun @ ( tc_prod @ SV678 @ SV678 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV27 @ SV1275 @ ( tc_fun @ ( tc_prod @ SV678 @ SV678 ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2988]) ).
thf(3628,plain,
! [SV1276: $i,SV679: $i,SV28: $i] :
( ( ! [SY5189: $i,SY5190: $i] :
( ( c_Product__Type_OSigma @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV28 @ SV679 @ ( tc_fun @ SV1276 @ tc_bool ) ) @ SY5189 @ SV1276 @ SY5190 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Product__Type_OSigma @ SV28 @ SY5189 @ SV1276 @ SY5190 ) @ ( c_Product__Type_OSigma @ SV679 @ SY5189 @ SV1276 @ SY5190 ) @ ( tc_fun @ ( tc_prod @ SV1276 @ SY5190 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2989]) ).
thf(3629,plain,
! [SV680: $i,SV29: $i] :
( ( ( SV29 = SV680 )
= $true )
| ( ( ! [SY4159: $i] :
~ ( c_in @ SV29 @ ( c_Set_Oinsert @ SV680 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4159 @ tc_bool ) ) @ SY4159 ) @ SY4159 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2990]) ).
thf(3630,plain,
! [SV1277: $i,SV681: $i,SV30: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV30 @ SV681 @ ( tc_fun @ SV1277 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1277 @ tc_bool ) ) )
| ( ( c_HOL_Ominus__class_Ominus @ SV30 @ SV681 @ ( tc_fun @ SV1277 @ tc_bool ) )
= SV30 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2991]) ).
thf(3631,plain,
! [SV1278: $i,SV682: $i,SV31: $i] :
( ( ! [SY5191: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ ( c_Relation_ODomain @ SV31 @ SV682 @ SV1278 ) @ ( c_Relation_ODomain @ SY5191 @ SV682 @ SV1278 ) @ ( tc_fun @ SV682 @ tc_bool ) ) @ ( c_Relation_ODomain @ ( c_HOL_Ominus__class_Ominus @ SV31 @ SY5191 @ ( tc_fun @ ( tc_prod @ SV682 @ SV1278 ) @ tc_bool ) ) @ SV682 @ SV1278 ) @ ( tc_fun @ SV682 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2992]) ).
thf(3632,plain,
! [SV1279: $i,SV683: $i,SV32: $i] :
( ( ! [SY5192: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV32 @ SV683 @ ( tc_fun @ SV1279 @ tc_bool ) ) @ SY5192 @ ( tc_fun @ SV1279 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV32 @ SY5192 @ ( tc_fun @ SV1279 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV683 @ SY5192 @ ( tc_fun @ SV1279 @ tc_bool ) ) @ ( tc_fun @ SV1279 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2993]) ).
thf(3633,plain,
! [SV1280: $i,SV684: $i,SV33: $i] :
( ( ! [SY5193: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV33 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV684 @ SV1280 @ ( tc_fun @ SY5193 @ tc_bool ) ) @ ( tc_fun @ SY5193 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV33 @ SV684 @ ( tc_fun @ SY5193 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV33 @ SV1280 @ ( tc_fun @ SY5193 @ tc_bool ) ) @ ( tc_fun @ SY5193 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2994]) ).
thf(3634,plain,
! [SV685: $i,SV34: $i] :
( ( ( ~ ( class_Lattices_Odistrib__lattice @ SV34 ) )
= $true )
| ( ( ! [SY4167: $i,SY4168: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV685 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4167 @ SY4168 @ SV34 ) @ SV34 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV685 @ SY4167 @ SV34 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV685 @ SY4168 @ SV34 ) @ SV34 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2995]) ).
thf(3635,plain,
! [SV686: $i,SV35: $i] :
( ( ( ~ ( class_Lattices_Odistrib__lattice @ SV35 ) )
= $true )
| ( ( ! [SY4169: $i,SY4170: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV686 @ SY4169 @ SV35 ) @ SY4170 @ SV35 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV686 @ SY4170 @ SV35 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4169 @ SY4170 @ SV35 ) @ SV35 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2996]) ).
thf(3636,plain,
! [SV1281: $i,SV688: $i,SV37: $i] :
( ( ( c_lessequals @ SV37 @ ( c_Product__Type_OSigma @ SV688 @ ( c_COMBK @ SV688 @ ( tc_fun @ SV1281 @ tc_bool ) @ SV1281 ) @ SV1281 @ SV1281 ) @ ( tc_fun @ ( tc_prod @ SV1281 @ SV1281 ) @ tc_bool ) )
| ~ ( c_Relation_Orefl__on @ SV688 @ SV37 @ SV1281 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2998]) ).
thf(3637,plain,
! [SV39: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV39 )
= $false )
| ( ( ! [SY2483: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2483 @ SY2483 @ SV39 )
= SY2483 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3000]) ).
thf(3638,plain,
! [SV1282: $i,SV690: $i,SV40: $i] :
( ( ! [SY5194: $i,SY5195: $i,SY5196: $i,SY5197: $i] :
( ( c_lessequals @ ( c_Relation_Orel__comp @ SV40 @ SV690 @ SV1282 @ SY5194 @ SY5195 ) @ ( c_Relation_Orel__comp @ SY5196 @ SY5197 @ SV1282 @ SY5194 @ SY5195 ) @ ( tc_fun @ ( tc_prod @ SV1282 @ SY5195 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV690 @ SY5197 @ ( tc_fun @ ( tc_prod @ SY5194 @ SY5195 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV40 @ SY5196 @ ( tc_fun @ ( tc_prod @ SV1282 @ SY5194 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3001]) ).
thf(3639,plain,
! [SV1283: $i,SV691: $i,SV41: $i] :
( ( ! [SY5198: $i,SY5199: $i] :
( ( c_Relation_OImage @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV41 @ SV691 @ ( tc_fun @ ( tc_prod @ SV1283 @ SY5198 ) @ tc_bool ) ) @ SY5199 @ SV1283 @ SY5198 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_OImage @ SV41 @ SY5199 @ SV1283 @ SY5198 ) @ ( c_Relation_OImage @ SV691 @ SY5199 @ SV1283 @ SY5198 ) @ ( tc_fun @ SY5198 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3002]) ).
thf(3640,plain,
! [SV1284: $i,SV692: $i,SV42: $i] :
( ( ! [SY5200: $i,SY5201: $i] :
( ( c_Relation_OImage @ SV42 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV692 @ SV1284 @ ( tc_fun @ SY5200 @ tc_bool ) ) @ SY5200 @ SY5201 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_OImage @ SV42 @ SV692 @ SY5200 @ SY5201 ) @ ( c_Relation_OImage @ SV42 @ SV1284 @ SY5200 @ SY5201 ) @ ( tc_fun @ SY5201 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3003]) ).
thf(3641,plain,
! [SV693: $i,SV43: $i] :
( ( ( hBOOL @ ( hAPP @ SV43 @ SV693 ) )
= $true )
| ( ( ! [SY2499: $i,SY2500: $i] :
( ~ ( hBOOL @ ( hAPP @ SV43 @ ( c_List_Osko__Recdef__Xtfl__wf__induct__1__1 @ SV43 @ SY2499 @ SY2500 ) ) )
| ~ ( c_Wellfounded_Owf @ SY2499 @ SY2500 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3004]) ).
thf(3642,plain,
! [SV1285: $i,SV695: $i,SV45: $i] :
( ( ! [SY5202: $i] :
( ( c_Set_Oinsert @ SV45 @ ( c_Set_Oinsert @ SV695 @ SV1285 @ SY5202 ) @ SY5202 )
= ( c_Set_Oinsert @ SV695 @ ( c_Set_Oinsert @ SV45 @ SV1285 @ SY5202 ) @ SY5202 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3006]) ).
thf(3643,plain,
! [SV1286: $i,SV696: $i,SV46: $i] :
( ( SV46
= ( c_Pair @ ( hAPP @ ( c_fst @ SV696 @ SV1286 ) @ SV46 ) @ ( hAPP @ ( c_snd @ SV696 @ SV1286 ) @ SV46 ) @ SV696 @ SV1286 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3007]) ).
thf(3644,plain,
! [SV1287: $i,SV697: $i,SV47: $i] :
( ( ( c_Pair @ ( hAPP @ ( c_fst @ SV47 @ SV697 ) @ SV1287 ) @ ( hAPP @ ( c_snd @ SV47 @ SV697 ) @ SV1287 ) @ SV47 @ SV697 )
= SV1287 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3008]) ).
thf(3645,plain,
! [SV1288: $i,SV698: $i,SV48: $i] :
( ( ! [SY5203: $i] :
( ( hAPP @ ( c_COMBK @ SV48 @ SV698 @ SV1288 ) @ SY5203 )
= SV48 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3009]) ).
thf(3646,plain,
! [SV1289: $i,SV699: $i,SV49: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV49 @ SV699 @ ( tc_fun @ SV1289 @ tc_bool ) ) @ SV699 @ ( tc_fun @ SV1289 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ SV49 @ SV699 @ ( tc_fun @ SV1289 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3010]) ).
thf(3647,plain,
! [SV1290: $i,SV700: $i,SV50: $i] :
( ( ( c_Set_Oinsert @ SV50 @ ( c_Set_Oinsert @ SV700 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1290 @ tc_bool ) ) @ SV1290 ) @ SV1290 )
= ( c_Set_Oinsert @ SV700 @ ( c_Set_Oinsert @ SV50 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1290 @ tc_bool ) ) @ SV1290 ) @ SV1290 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3011]) ).
thf(3648,plain,
! [SV1291: $i,SV701: $i,SV51: $i] :
( ( ! [SY5204: $i,SY5205: $i] :
( ( c_lessequals @ ( c_Relation_OImage @ SV51 @ SV701 @ SV1291 @ SY5204 ) @ SY5205 @ ( tc_fun @ SY5204 @ tc_bool ) )
| ! [SY5206: $i] :
~ ( c_lessequals @ SV51 @ ( c_Product__Type_OSigma @ SY5206 @ ( c_COMBK @ SY5205 @ ( tc_fun @ SY5204 @ tc_bool ) @ SV1291 ) @ SV1291 @ SY5204 ) @ ( tc_fun @ ( tc_prod @ SV1291 @ SY5204 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3012]) ).
thf(3649,plain,
! [SV702: $i,SV52: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV52 ) )
= $true )
| ( ( ! [SY4197: $i] :
( ! [SY4198: $i] :
( ( c_HOL_Ominus__class_Ominus @ SV702 @ SY4197 @ SV52 )
!= ( c_HOL_Ominus__class_Ominus @ SY4198 @ SY4198 @ SV52 ) )
| ( SV702 = SY4197 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3013]) ).
thf(3650,plain,
! [SV703: $i,SV53: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV53 ) )
= $true )
| ( ( ! [SY4199: $i,SY4200: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV703 @ SV703 @ SV53 )
!= ( c_HOL_Ominus__class_Ominus @ SY4199 @ SY4200 @ SV53 ) )
| ( SY4199 = SY4200 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3014]) ).
thf(3651,plain,
! [SV1292: $i,SV704: $i,SV54: $i] :
( ( ( c_Set_Oimage @ SV54 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV704 @ tc_bool ) ) @ SV704 @ SV1292 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1292 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3015]) ).
thf(3652,plain,
! [SV1293: $i,SV705: $i,SV55: $i] :
( ( ! [SY5207: $i,SY5208: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oimage @ SV55 @ SV705 @ SV1293 @ SY5207 ) @ ( c_Set_Oimage @ SV55 @ SY5208 @ SV1293 @ SY5207 ) @ ( tc_fun @ SY5207 @ tc_bool ) ) @ ( c_Set_Oimage @ SV55 @ ( c_HOL_Ominus__class_Ominus @ SV705 @ SY5208 @ ( tc_fun @ SV1293 @ tc_bool ) ) @ SV1293 @ SY5207 ) @ ( tc_fun @ SY5207 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3016]) ).
thf(3653,plain,
! [SV1294: $i,SV706: $i,SV56: $i] :
( ( ! [SY5209: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV56 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV706 @ SV1294 @ ( tc_fun @ SY5209 @ tc_bool ) ) @ ( tc_fun @ SY5209 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV706 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV56 @ SV1294 @ ( tc_fun @ SY5209 @ tc_bool ) ) @ ( tc_fun @ SY5209 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3017]) ).
thf(3654,plain,
! [SV1295: $i,SV707: $i,SV57: $i] :
( ( ! [SY5210: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV57 @ SV707 @ ( tc_fun @ SV1295 @ tc_bool ) ) @ SY5210 @ ( tc_fun @ SV1295 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV57 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV707 @ SY5210 @ ( tc_fun @ SV1295 @ tc_bool ) ) @ ( tc_fun @ SV1295 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3018]) ).
thf(3655,plain,
! [SV708: $i,SV58: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV58 ) )
= $true )
| ( ( ! [SY4209: $i,SY4210: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV708 @ SY4209 @ SV58 ) @ SY4210 @ SV58 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV708 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4209 @ SY4210 @ SV58 ) @ SV58 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3019]) ).
thf(3656,plain,
! [SV709: $i,SV59: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV59 ) )
= $true )
| ( ( ! [SY4211: $i,SY4212: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV709 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4211 @ SY4212 @ SV59 ) @ SV59 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY4211 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV709 @ SY4212 @ SV59 ) @ SV59 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3020]) ).
thf(3657,plain,
! [SV710: $i,SV60: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV60 ) )
= $true )
| ( ( ! [SY4213: $i,SY4214: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV710 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4213 @ SY4214 @ SV60 ) @ SV60 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY4213 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV710 @ SY4214 @ SV60 ) @ SV60 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3021]) ).
thf(3658,plain,
! [SV711: $i,SV61: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV61 ) )
= $true )
| ( ( ! [SY4215: $i,SY4216: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV711 @ SY4215 @ SV61 ) @ SY4216 @ SV61 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV711 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4215 @ SY4216 @ SV61 ) @ SV61 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3022]) ).
thf(3659,plain,
! [SV1296: $i,SV712: $i,SV62: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV62 @ SV712 @ ( tc_fun @ SV1296 @ tc_bool ) )
= SV62 )
| ~ ( c_lessequals @ SV62 @ SV712 @ ( tc_fun @ SV1296 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3023]) ).
thf(3660,plain,
! [SV1297: $i,SV713: $i,SV63: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV63 @ SV713 @ ( tc_fun @ SV1297 @ tc_bool ) )
= SV713 )
| ~ ( c_lessequals @ SV713 @ SV63 @ ( tc_fun @ SV1297 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3024]) ).
thf(3661,plain,
! [SV64: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV64 )
= $false )
| ( ( ! [SY2555: $i,SY2556: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SY2555 @ SY2556 @ SV64 )
= SY2555 )
| ~ ( c_lessequals @ SY2555 @ SY2556 @ SV64 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3025]) ).
thf(3662,plain,
! [SV65: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV65 )
= $false )
| ( ( ! [SY2557: $i,SY2558: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SY2557 @ SY2558 @ SV65 )
!= SY2557 )
| ( c_lessequals @ SY2557 @ SY2558 @ SV65 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3026]) ).
thf(3663,plain,
! [SV66: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV66 )
= $false )
| ( ( ! [SY2559: $i,SY2560: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SY2559 @ SY2560 @ SV66 )
= SY2560 )
| ~ ( c_lessequals @ SY2560 @ SY2559 @ SV66 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3027]) ).
thf(3664,plain,
! [SV1298: $i,SV714: $i,SV67: $i] :
( ( ! [SY5211: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV67 @ SV714 @ ( tc_fun @ SV1298 @ tc_bool ) ) @ SY5211 @ ( tc_fun @ SV1298 @ tc_bool ) )
| ~ ( c_lessequals @ SV714 @ SY5211 @ ( tc_fun @ SV1298 @ tc_bool ) )
| ~ ( c_lessequals @ SV67 @ SY5211 @ ( tc_fun @ SV1298 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3028]) ).
thf(3665,plain,
! [SV1299: $i,SV715: $i,SV68: $i] :
( ( c_lessequals @ SV68 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV715 @ SV68 @ ( tc_fun @ SV1299 @ tc_bool ) ) @ ( tc_fun @ SV1299 @ tc_bool ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3029]) ).
thf(3666,plain,
! [SV1300: $i,SV716: $i,SV69: $i] :
( ( c_lessequals @ SV69 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV69 @ SV716 @ ( tc_fun @ SV1300 @ tc_bool ) ) @ ( tc_fun @ SV1300 @ tc_bool ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3030]) ).
thf(3667,plain,
! [SV1301: $i,SV717: $i,SV70: $i] :
( ( ! [SY5212: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV70 @ SV717 @ ( tc_fun @ SV1301 @ tc_bool ) ) @ SY5212 @ ( tc_fun @ SV1301 @ tc_bool ) )
| ~ ( c_lessequals @ SV717 @ SY5212 @ ( tc_fun @ SV1301 @ tc_bool ) )
| ~ ( c_lessequals @ SV70 @ SY5212 @ ( tc_fun @ SV1301 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3031]) ).
thf(3668,plain,
! [SV718: $i,SV71: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV71 ) )
= $true )
| ( ( ! [SY4225: $i,SY4226: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV718 @ SY4225 @ SV71 ) @ SY4226 @ SV71 )
| ~ ( c_lessequals @ SY4225 @ SY4226 @ SV71 )
| ~ ( c_lessequals @ SV718 @ SY4226 @ SV71 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3032]) ).
thf(3669,plain,
! [SV72: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV72 )
= $false )
| ( ( ! [SY2574: $i,SY2575: $i] : ( c_lessequals @ SY2574 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2574 @ SY2575 @ SV72 ) @ SV72 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3033]) ).
thf(3670,plain,
! [SV73: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV73 )
= $false )
| ( ( ! [SY2576: $i,SY2577: $i] : ( c_lessequals @ SY2576 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2577 @ SY2576 @ SV73 ) @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3034]) ).
thf(3671,plain,
! [SV719: $i,SV74: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV74 ) )
= $true )
| ( ( ! [SY4227: $i,SY4228: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV719 @ SY4227 @ SV74 ) @ SY4228 @ SV74 )
| ~ ( c_lessequals @ SY4227 @ SY4228 @ SV74 )
| ~ ( c_lessequals @ SV719 @ SY4228 @ SV74 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3035]) ).
thf(3672,plain,
! [SV720: $i,SV75: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV75 ) )
= $true )
| ( ( ! [SY4229: $i,SY4230: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV720 @ SY4229 @ SV75 ) @ SY4230 @ SV75 )
| ~ ( c_lessequals @ SY4229 @ SY4230 @ SV75 )
| ~ ( c_lessequals @ SV720 @ SY4230 @ SV75 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3036]) ).
thf(3673,plain,
! [SV76: $i] :
( ( ( class_Lattices_Olattice @ SV76 )
= $false )
| ( ( ! [SY2584: $i,SY2585: $i] : ( c_lessequals @ SY2584 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2585 @ SY2584 @ SV76 ) @ SV76 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3037]) ).
thf(3674,plain,
! [SV77: $i] :
( ( ( class_Lattices_Olattice @ SV77 )
= $false )
| ( ( ! [SY2586: $i,SY2587: $i] : ( c_lessequals @ SY2586 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2586 @ SY2587 @ SV77 ) @ SV77 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3038]) ).
thf(3675,plain,
! [SV1302: $i,SV721: $i,SV78: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV78 @ SV721 @ ( tc_fun @ SV1302 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV721 @ SV78 @ ( tc_fun @ SV1302 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3039]) ).
thf(3676,plain,
! [SV79: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV79 )
= $false )
| ( ( ! [SY2590: $i,SY2591: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY2590 @ SY2591 @ SV79 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY2591 @ SY2590 @ SV79 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3040]) ).
thf(3677,plain,
! [SV80: $i] :
( ( ( class_Lattices_Olattice @ SV80 )
= $false )
| ( ( ! [SY2592: $i,SY2593: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY2592 @ SY2593 @ SV80 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY2593 @ SY2592 @ SV80 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3041]) ).
thf(3678,plain,
! [SV722: $i,SV81: $i] :
( ( ( c_Wellfounded_Oacyclic @ SV81 @ SV722 )
= $true )
| ( ( ~ ( c_Wellfounded_Owf @ SV81 @ SV722 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3042]) ).
thf(3679,plain,
! [SV1303: $i,SV723: $i,SV82: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV82 @ ( c_HOL_Ominus__class_Ominus @ SV723 @ SV82 @ ( tc_fun @ SV1303 @ tc_bool ) ) @ ( tc_fun @ SV1303 @ tc_bool ) )
= SV723 )
| ~ ( c_lessequals @ SV82 @ SV723 @ ( tc_fun @ SV1303 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3043]) ).
thf(3680,plain,
! [SV1304: $i,SV724: $i,SV83: $i] :
( ( ! [SY5213: $i] :
( ( c_lessequals @ ( c_Relation_OImage @ SV83 @ ( c_Set_Oinsert @ SV724 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1304 @ tc_bool ) ) @ SV1304 ) @ SV1304 @ SV1304 ) @ ( c_Relation_OImage @ SV83 @ ( c_Set_Oinsert @ SY5213 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1304 @ tc_bool ) ) @ SV1304 ) @ SV1304 @ SV1304 ) @ ( tc_fun @ SV1304 @ tc_bool ) )
| ~ ( c_in @ ( c_Pair @ SV724 @ SY5213 @ SV1304 @ SV1304 ) @ SV83 @ ( tc_prod @ SV1304 @ SV1304 ) )
| ! [SY5214: $i] :
~ ( c_Equiv__Relations_Oequiv @ SY5214 @ SV83 @ SV1304 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3044]) ).
thf(3681,plain,
! [SV1305: $i,SV725: $i,SV84: $i] :
( ( ( c_Relation_OImage @ SV84 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV725 @ tc_bool ) ) @ SV725 @ SV1305 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1305 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3045]) ).
thf(3682,plain,
! [SV1306: $i,SV726: $i,SV85: $i] :
( ( ( c_Set_Oinsert @ SV85 @ ( c_Set_Oinsert @ SV85 @ SV726 @ SV1306 ) @ SV1306 )
= ( c_Set_Oinsert @ SV85 @ SV726 @ SV1306 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3046]) ).
thf(3683,plain,
! [SV727: $i,SV86: $i] :
( ( ( hBOOL @ ( hAPP @ SV86 @ SV727 ) )
= $true )
| ( ( ! [SY4238: $i] :
( ( SY4238 = SV727 )
| ! [SY4239: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SY4238 @ SV86 @ SY4239 ) @ SV727 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3047]) ).
thf(3684,plain,
! [SV1307: $i,SV728: $i,SV87: $i] :
( ( ! [SY5215: $i,SY5216: $i] :
( ( c_Relation_ODomain @ ( c_Set_Oinsert @ ( c_Pair @ SV87 @ SV728 @ SV1307 @ SY5215 ) @ SY5216 @ ( tc_prod @ SV1307 @ SY5215 ) ) @ SV1307 @ SY5215 )
= ( c_Set_Oinsert @ SV87 @ ( c_Relation_ODomain @ SY5216 @ SV1307 @ SY5215 ) @ SV1307 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3048]) ).
thf(3685,plain,
! [SV1308: $i,SV729: $i,SV88: $i] :
( ( ( c_Relation_Osym @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV88 @ SV729 @ ( tc_fun @ ( tc_prod @ SV1308 @ SV1308 ) @ tc_bool ) ) @ SV1308 )
| ~ ( c_Relation_Osym @ SV729 @ SV1308 )
| ~ ( c_Relation_Osym @ SV88 @ SV1308 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3049]) ).
thf(3686,plain,
! [SV1309: $i,SV730: $i,SV89: $i] :
( ( ( c_lessequals @ ( c_Transitive__Closure_Ortrancl @ SV89 @ SV730 ) @ ( c_Transitive__Closure_Ortrancl @ SV1309 @ SV730 ) @ ( tc_fun @ ( tc_prod @ SV730 @ SV730 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV89 @ SV1309 @ ( tc_fun @ ( tc_prod @ SV730 @ SV730 ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3050]) ).
thf(3687,plain,
! [SV1310: $i,SV731: $i,SV90: $i] :
( ( ! [SY5217: $i] : ( c_lessequals @ ( c_Relation_ODomain @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV90 @ SV731 @ ( tc_fun @ ( tc_prod @ SV1310 @ SY5217 ) @ tc_bool ) ) @ SV1310 @ SY5217 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_ODomain @ SV90 @ SV1310 @ SY5217 ) @ ( c_Relation_ODomain @ SV731 @ SV1310 @ SY5217 ) @ ( tc_fun @ SV1310 @ tc_bool ) ) @ ( tc_fun @ SV1310 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3051]) ).
thf(3688,plain,
! [SV91: $i] :
( ( ( class_Lattices_Obounded__lattice @ SV91 )
= $false )
| ( ( ! [SY2619: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY2619 @ ( c_Orderings_Obot__class_Obot @ SV91 ) @ SV91 )
= ( c_Orderings_Obot__class_Obot @ SV91 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3052]) ).
thf(3689,plain,
! [SV92: $i] :
( ( ( class_Lattices_Obounded__lattice @ SV92 )
= $false )
| ( ( ! [SY2620: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Orderings_Obot__class_Obot @ SV92 ) @ SY2620 @ SV92 )
= ( c_Orderings_Obot__class_Obot @ SV92 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3053]) ).
thf(3690,plain,
! [SV1311: $i,SV734: $i,SV95: $i] :
( ( c_lessequals @ SV95 @ ( c_Set_Oinsert @ SV734 @ SV95 @ SV1311 ) @ ( tc_fun @ SV1311 @ tc_bool ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3056]) ).
thf(3691,plain,
! [SV1312: $i,SV735: $i,SV96: $i] :
( ( ! [SY5218: $i,SY5219: $i] : ( c_lessequals @ ( c_Set_Oimage @ SV96 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV735 @ SV1312 @ ( tc_fun @ SY5218 @ tc_bool ) ) @ SY5218 @ SY5219 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oimage @ SV96 @ SV735 @ SY5218 @ SY5219 ) @ ( c_Set_Oimage @ SV96 @ SV1312 @ SY5218 @ SY5219 ) @ ( tc_fun @ SY5219 @ tc_bool ) ) @ ( tc_fun @ SY5219 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3057]) ).
thf(3692,plain,
! [SV1313: $i,SV736: $i,SV97: $i] :
( ( ! [SY5220: $i,SY5221: $i] : ( c_lessequals @ ( c_Relation_OImage @ SV97 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV736 @ SV1313 @ ( tc_fun @ SY5220 @ tc_bool ) ) @ SY5220 @ SY5221 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_OImage @ SV97 @ SV736 @ SY5220 @ SY5221 ) @ ( c_Relation_OImage @ SV97 @ SV1313 @ SY5220 @ SY5221 ) @ ( tc_fun @ SY5221 @ tc_bool ) ) @ ( tc_fun @ SY5221 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3058]) ).
thf(3693,plain,
! [SV1314: $i,SV737: $i,SV98: $i] :
( ( ! [SY5222: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV98 @ SV737 @ ( tc_fun @ SV1314 @ tc_bool ) ) @ SY5222 @ ( tc_fun @ SV1314 @ tc_bool ) )
!= ( c_Lattices_Olower__semilattice__class_Oinf @ SV98 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV737 @ SY5222 @ ( tc_fun @ SV1314 @ tc_bool ) ) @ ( tc_fun @ SV1314 @ tc_bool ) ) )
| ( c_lessequals @ SY5222 @ SV98 @ ( tc_fun @ SV1314 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3059]) ).
thf(3694,plain,
! [SV1315: $i,SV738: $i,SV99: $i] :
( ( ! [SY5223: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV99 @ SV738 @ ( tc_fun @ SV1315 @ tc_bool ) ) @ SY5223 @ ( tc_fun @ SV1315 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV99 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV738 @ SY5223 @ ( tc_fun @ SV1315 @ tc_bool ) ) @ ( tc_fun @ SV1315 @ tc_bool ) ) )
| ~ ( c_lessequals @ SY5223 @ SV99 @ ( tc_fun @ SV1315 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3060]) ).
thf(3695,plain,
! [SV1316: $i,SV739: $i,SV100: $i] :
( ( ! [SY5224: $i,SY5225: $i] :
( ( c_Product__Type_OSigma @ ( c_HOL_Ominus__class_Ominus @ SV100 @ SV739 @ ( tc_fun @ SV1316 @ tc_bool ) ) @ SY5224 @ SV1316 @ SY5225 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Product__Type_OSigma @ SV100 @ SY5224 @ SV1316 @ SY5225 ) @ ( c_Product__Type_OSigma @ SV739 @ SY5224 @ SV1316 @ SY5225 ) @ ( tc_fun @ ( tc_prod @ SV1316 @ SY5225 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3061]) ).
thf(3696,plain,
! [SV1317: $i,SV742: $i,SV103: $i] :
( ( ! [SY5226: $i,SY5227: $i,SY5228: $i,SY5229: $i] :
( ( c_lessequals @ ( c_Relation_Orel__comp @ SV103 @ SV742 @ SV1317 @ SY5226 @ SY5227 ) @ ( c_Product__Type_OSigma @ SY5228 @ ( c_COMBK @ SY5229 @ ( tc_fun @ SY5227 @ tc_bool ) @ SV1317 ) @ SV1317 @ SY5227 ) @ ( tc_fun @ ( tc_prod @ SV1317 @ SY5227 ) @ tc_bool ) )
| ! [SY5230: $i] :
( ~ ( c_lessequals @ SV742 @ ( c_Product__Type_OSigma @ SY5230 @ ( c_COMBK @ SY5229 @ ( tc_fun @ SY5227 @ tc_bool ) @ SY5226 ) @ SY5226 @ SY5227 ) @ ( tc_fun @ ( tc_prod @ SY5226 @ SY5227 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV103 @ ( c_Product__Type_OSigma @ SY5228 @ ( c_COMBK @ SY5230 @ ( tc_fun @ SY5226 @ tc_bool ) @ SV1317 ) @ SV1317 @ SY5226 ) @ ( tc_fun @ ( tc_prod @ SV1317 @ SY5226 ) @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3064]) ).
thf(3697,plain,
! [SV1318: $i,SV743: $i,SV104: $i] :
( ( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV104 @ SV743 @ ( tc_fun @ ( tc_prod @ SV1318 @ SV1318 ) @ tc_bool ) ) @ SV1318 )
| ~ ( c_lessequals @ ( c_Relation_Orel__comp @ SV104 @ SV743 @ SV1318 @ SV1318 @ SV1318 ) @ SV104 @ ( tc_fun @ ( tc_prod @ SV1318 @ SV1318 ) @ tc_bool ) )
| ~ ( c_Wellfounded_Owf @ SV743 @ SV1318 )
| ~ ( c_Wellfounded_Owf @ SV104 @ SV1318 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3065]) ).
thf(3698,plain,
! [SV744: $i,SV105: $i] :
( ( ( hBOOL @ ( hAPP @ SV105 @ SV744 ) )
= $true )
| ( ( ! [SY4268: $i] :
( ( hBOOL @ ( hAPP @ SY4268 @ SV744 ) )
| ! [SY4269: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4268 @ SV105 @ ( tc_fun @ SY4269 @ tc_bool ) ) @ SV744 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3066]) ).
thf(3699,plain,
! [SV1319: $i,SV745: $i,SV106: $i] :
( ( ! [SY5231: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV106 @ SV745 @ ( tc_fun @ SV1319 @ tc_bool ) ) @ SY5231 ) )
| ~ ( hBOOL @ ( hAPP @ SV745 @ SY5231 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3067]) ).
thf(3700,plain,
! [SV1320: $i,SV746: $i,SV107: $i] :
( ( ! [SY5232: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV107 @ SV746 @ ( tc_fun @ SV1320 @ tc_bool ) ) @ SY5232 ) )
| ~ ( hBOOL @ ( hAPP @ SV107 @ SY5232 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3068]) ).
thf(3701,plain,
! [SV1321: $i,SV747: $i,SV108: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_ODomain @ SV108 @ SV747 @ SV747 ) @ ( c_Relation_ORange @ SV1321 @ SV747 @ SV747 ) @ ( tc_fun @ SV747 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV747 @ tc_bool ) ) )
| ~ ( c_Wellfounded_Owf @ SV1321 @ SV747 )
| ~ ( c_Wellfounded_Owf @ SV108 @ SV747 )
| ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV108 @ SV1321 @ ( tc_fun @ ( tc_prod @ SV747 @ SV747 ) @ tc_bool ) ) @ SV747 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3069]) ).
thf(3702,plain,
! [SV1322: $i,SV748: $i,SV109: $i] :
( ( ! [SY5233: $i,SY5234: $i] :
( ( c_Product__Type_OSigma @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV109 @ SV748 @ ( tc_fun @ SV1322 @ tc_bool ) ) @ ( c_COMBK @ SY5233 @ ( tc_fun @ SY5234 @ tc_bool ) @ SV1322 ) @ SV1322 @ SY5234 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Product__Type_OSigma @ SV109 @ ( c_COMBK @ SY5233 @ ( tc_fun @ SY5234 @ tc_bool ) @ SV1322 ) @ SV1322 @ SY5234 ) @ ( c_Product__Type_OSigma @ SV748 @ ( c_COMBK @ SY5233 @ ( tc_fun @ SY5234 @ tc_bool ) @ SV1322 ) @ SV1322 @ SY5234 ) @ ( tc_fun @ ( tc_prod @ SV1322 @ SY5234 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3070]) ).
thf(3703,plain,
! [SV1323: $i,SV749: $i,SV110: $i] :
( ( ! [SY5235: $i,SY5236: $i] :
( ( c_Relation_Orefl__on @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV110 @ SV749 @ ( tc_fun @ SV1323 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY5235 @ SY5236 @ ( tc_fun @ ( tc_prod @ SV1323 @ SV1323 ) @ tc_bool ) ) @ SV1323 )
| ~ ( c_Relation_Orefl__on @ SV749 @ SY5236 @ SV1323 )
| ~ ( c_Relation_Orefl__on @ SV110 @ SY5235 @ SV1323 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3071]) ).
thf(3704,plain,
! [SV750: $i,SV111: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV111 ) )
= $true )
| ( ( ! [SY4281: $i,SY4282: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV750 @ SY4281 @ SV111 ) @ SY4282 @ SV111 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV750 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4281 @ SY4282 @ SV111 ) @ SV111 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3072]) ).
thf(3705,plain,
! [SV751: $i,SV112: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV112 ) )
= $true )
| ( ( ! [SY4283: $i,SY4284: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV751 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4283 @ SY4284 @ SV112 ) @ SV112 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY4283 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV751 @ SY4284 @ SV112 ) @ SV112 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3073]) ).
thf(3706,plain,
! [SV752: $i,SV113: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV113 ) )
= $true )
| ( ( ! [SY4285: $i,SY4286: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV752 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4285 @ SY4286 @ SV113 ) @ SV113 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY4285 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV752 @ SY4286 @ SV113 ) @ SV113 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3074]) ).
thf(3707,plain,
! [SV753: $i,SV114: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV114 ) )
= $true )
| ( ( ! [SY4287: $i,SY4288: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV753 @ SY4287 @ SV114 ) @ SY4288 @ SV114 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV753 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4287 @ SY4288 @ SV114 ) @ SV114 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3075]) ).
thf(3708,plain,
! [SV1324: $i,SV754: $i,SV115: $i] :
( ( ! [SY5237: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV115 @ SV754 @ ( tc_fun @ SV1324 @ tc_bool ) ) @ SY5237 @ ( tc_fun @ SV1324 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV115 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV754 @ SY5237 @ ( tc_fun @ SV1324 @ tc_bool ) ) @ ( tc_fun @ SV1324 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3076]) ).
thf(3709,plain,
! [SV1325: $i,SV755: $i,SV116: $i] :
( ( ! [SY5238: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV116 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV755 @ SV1325 @ ( tc_fun @ SY5238 @ tc_bool ) ) @ ( tc_fun @ SY5238 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV755 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV116 @ SV1325 @ ( tc_fun @ SY5238 @ tc_bool ) ) @ ( tc_fun @ SY5238 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3077]) ).
thf(3710,plain,
! [SV117: $i] :
( ( ( class_Lattices_Obounded__lattice @ SV117 )
= $false )
| ( ( ! [SY2691: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2691 @ ( c_Orderings_Obot__class_Obot @ SV117 ) @ SV117 )
= SY2691 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3078]) ).
thf(3711,plain,
! [SV118: $i] :
( ( ( class_Lattices_Obounded__lattice @ SV118 )
= $false )
| ( ( ! [SY2692: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ SV118 ) @ SY2692 @ SV118 )
= SY2692 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3079]) ).
thf(3712,plain,
! [SV1326: $i,SV759: $i,SV122: $i] :
( ( ! [SY5239: $i,SY5240: $i,SY5241: $i] :
( ( c_Product__Type_OSigma @ ( c_Set_Oinsert @ SV122 @ SV759 @ SV1326 ) @ ( c_COMBK @ ( c_Set_Oinsert @ SY5239 @ SY5240 @ SY5241 ) @ ( tc_fun @ SY5241 @ tc_bool ) @ SV1326 ) @ SV1326 @ SY5241 )
= ( c_Set_Oinsert @ ( c_Pair @ SV122 @ SY5239 @ SV1326 @ SY5241 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Product__Type_OSigma @ SV759 @ ( c_COMBK @ ( c_Set_Oinsert @ SY5239 @ SY5240 @ SY5241 ) @ ( tc_fun @ SY5241 @ tc_bool ) @ SV1326 ) @ SV1326 @ SY5241 ) @ ( c_Product__Type_OSigma @ ( c_Set_Oinsert @ SV122 @ SV759 @ SV1326 ) @ ( c_COMBK @ SY5240 @ ( tc_fun @ SY5241 @ tc_bool ) @ SV1326 ) @ SV1326 @ SY5241 ) @ ( tc_fun @ ( tc_prod @ SV1326 @ SY5241 ) @ tc_bool ) ) @ ( tc_prod @ SV1326 @ SY5241 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3083]) ).
thf(3713,plain,
! [SV760: $i,SV123: $i] :
( ( ( SV123
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV760 @ tc_bool ) ) )
= $true )
| ( ( ! [SY4297: $i] :
( ~ ( c_lessequals @ SV123 @ ( c_Relation_OImage @ SY4297 @ SV123 @ SV760 @ SV760 ) @ ( tc_fun @ SV760 @ tc_bool ) )
| ~ ( c_Wellfounded_Owf @ SY4297 @ SV760 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3084]) ).
thf(3714,plain,
! [SV761: $i,SV124: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV124 @ tc_bool ) ) @ SV761 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3085]) ).
thf(3715,plain,
! [SV1327: $i,SV762: $i,SV125: $i] :
( ( ! [SY5242: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV125 @ ( c_HOL_Ominus__class_Ominus @ SV762 @ SV1327 @ ( tc_fun @ SY5242 @ tc_bool ) ) @ ( tc_fun @ SY5242 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV125 @ SV762 @ ( tc_fun @ SY5242 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV125 @ SV1327 @ ( tc_fun @ SY5242 @ tc_bool ) ) @ ( tc_fun @ SY5242 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3086]) ).
thf(3716,plain,
! [SV1328: $i,SV763: $i,SV126: $i] :
( ( ! [SY5243: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_HOL_Ominus__class_Ominus @ SV126 @ SV763 @ ( tc_fun @ SV1328 @ tc_bool ) ) @ SY5243 @ ( tc_fun @ SV1328 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV126 @ SY5243 @ ( tc_fun @ SV1328 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV763 @ SY5243 @ ( tc_fun @ SV1328 @ tc_bool ) ) @ ( tc_fun @ SV1328 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3087]) ).
thf(3717,plain,
! [SV1329: $i,SV764: $i,SV127: $i] :
( ( ! [SY5244: $i] :
( ( ( c_Set_Oimage @ ( c_COMBK @ SV127 @ SV764 @ SV1329 ) @ SY5244 @ SV1329 @ SV764 )
= ( c_Set_Oinsert @ SV127 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV764 @ tc_bool ) ) @ SV764 ) )
| ( SY5244
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1329 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3088]) ).
thf(3718,plain,
! [SV1330: $i,SV765: $i,SV128: $i] :
( ( ! [SY5245: $i,SY5246: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV128 @ SV765 @ ( tc_fun @ SV1330 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SY5245 @ SY5246 @ ( tc_fun @ SV1330 @ tc_bool ) ) @ ( tc_fun @ SV1330 @ tc_bool ) )
| ~ ( c_lessequals @ SY5246 @ SV765 @ ( tc_fun @ SV1330 @ tc_bool ) )
| ~ ( c_lessequals @ SV128 @ SY5245 @ ( tc_fun @ SV1330 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3089]) ).
thf(3719,plain,
! [SV1331: $i,SV766: $i,SV129: $i] :
( ( ~ ( c_in @ SV129 @ SV766 @ SV1331 )
| ! [SY5247: $i] :
( ~ ( c_in @ SV129 @ SY5247 @ SV1331 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SY5247 @ SV766 @ ( tc_fun @ SV1331 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1331 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3090]) ).
thf(3720,plain,
! [SV1332: $i,SV767: $i,SV130: $i] :
( ( ( c_Relation_Otrans @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV130 @ SV767 @ ( tc_fun @ ( tc_prod @ SV1332 @ SV1332 ) @ tc_bool ) ) @ SV1332 )
| ~ ( c_Relation_Otrans @ SV767 @ SV1332 )
| ~ ( c_Relation_Otrans @ SV130 @ SV1332 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3091]) ).
thf(3721,plain,
! [SV768: $i,SV131: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV131 ) )
= $true )
| ( ( ! [SY4310: $i,SY4311: $i] : ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV768 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4310 @ SY4311 @ SV131 ) @ SV131 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV768 @ SY4310 @ SV131 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV768 @ SY4311 @ SV131 ) @ SV131 ) @ SV131 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3092]) ).
thf(3722,plain,
! [SV1333: $i,SV769: $i,SV132: $i] :
( ( ! [SY5248: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV132 @ SV769 @ ( tc_fun @ SV1333 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY5248 @ SV769 @ ( tc_fun @ SV1333 @ tc_bool ) ) @ ( tc_fun @ SV1333 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV132 @ SV769 @ ( tc_fun @ SV1333 @ tc_bool ) ) @ SY5248 @ ( tc_fun @ SV1333 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3093]) ).
thf(3723,plain,
! [SV133: $i] :
( ( ( class_Lattices_Olattice @ SV133 )
= $false )
| ( ( ! [SY2728: $i,SY2729: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2728 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2728 @ SY2729 @ SV133 ) @ SV133 )
= SY2728 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3094]) ).
thf(3724,plain,
! [SV1334: $i,SV770: $i,SV134: $i] :
( ( ( ( c_Relation_Orel__comp @ SV134 @ SV770 @ SV1334 @ SV1334 @ SV1334 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV1334 @ SV1334 ) @ tc_bool ) ) )
| ! [SY5249: $i] :
( ( ( c_Relation_Orel__comp @ SY5249 @ SV770 @ SV1334 @ SV1334 @ SV1334 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV1334 @ SV1334 ) @ tc_bool ) ) )
| ( ( c_Relation_Orel__comp @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY5249 @ SV134 @ ( tc_fun @ ( tc_prod @ SV1334 @ SV1334 ) @ tc_bool ) ) @ SV770 @ SV1334 @ SV1334 @ SV1334 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV1334 @ SV1334 ) @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3095]) ).
thf(3725,plain,
! [SV1335: $i,SV771: $i,SV135: $i] :
( ( ( ( c_Relation_Orel__comp @ SV135 @ SV771 @ SV1335 @ SV1335 @ SV1335 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV1335 @ SV1335 ) @ tc_bool ) ) )
| ! [SY5250: $i] :
( ( ( c_Relation_Orel__comp @ SV135 @ SY5250 @ SV1335 @ SV1335 @ SV1335 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV1335 @ SV1335 ) @ tc_bool ) ) )
| ( ( c_Relation_Orel__comp @ SV135 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY5250 @ SV771 @ ( tc_fun @ ( tc_prod @ SV1335 @ SV1335 ) @ tc_bool ) ) @ SV1335 @ SV1335 @ SV1335 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV1335 @ SV1335 ) @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3096]) ).
thf(3726,plain,
! [SV772: $i,SV136: $i] :
( ( ( hBOOL @ ( hAPP @ SV136 @ SV772 ) )
= $true )
| ( ( ! [SY2737: $i,SY2738: $i] :
( ~ ( hBOOL @ ( hAPP @ SV136 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1 @ SV136 @ SY2737 @ SY2738 ) ) )
| ~ ( c_Wellfounded_Owf @ SY2737 @ SY2738 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3097]) ).
thf(3727,plain,
! [SV773: $i,SV137: $i] :
( ( ( c_Wellfounded_Oacyclic @ SV137 @ SV773 )
= $true )
| ( ( ~ ( c_Wellfounded_Oacyclic @ ( c_Relation_Oconverse @ SV137 @ SV773 @ SV773 ) @ SV773 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3098]) ).
thf(3728,plain,
! [SV774: $i,SV138: $i] :
( ( ( c_Wellfounded_Oacyclic @ ( c_Relation_Oconverse @ SV138 @ SV774 @ SV774 ) @ SV774 )
= $true )
| ( ( ~ ( c_Wellfounded_Oacyclic @ SV138 @ SV774 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3099]) ).
thf(3729,plain,
! [SV775: $i,SV139: $i] :
( ( ( SV139 = SV775 )
= $true )
| ( ( ! [SY4320: $i] :
( ~ ( c_lessequals @ SV775 @ SV139 @ ( tc_fun @ SY4320 @ tc_bool ) )
| ~ ( c_lessequals @ SV139 @ SV775 @ ( tc_fun @ SY4320 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3100]) ).
thf(3730,plain,
! [SV776: $i,SV140: $i] :
( ( ( SV140 = SV776 )
= $true )
| ( ( ! [SY4321: $i] :
( ~ ( c_lessequals @ SV776 @ SV140 @ ( tc_fun @ SY4321 @ tc_bool ) )
| ~ ( c_lessequals @ SV140 @ SV776 @ ( tc_fun @ SY4321 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3101]) ).
thf(3731,plain,
! [SV141: $i] :
( ( ( class_Orderings_Oorder @ SV141 )
= $false )
| ( ( ! [SY2745: $i,SY2746: $i] :
( ( SY2745 = SY2746 )
| ~ ( c_lessequals @ SY2746 @ SY2745 @ SV141 )
| ~ ( c_lessequals @ SY2745 @ SY2746 @ SV141 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3102]) ).
thf(3732,plain,
! [SV142: $i] :
( ( ( class_Orderings_Oorder @ SV142 )
= $false )
| ( ( ! [SY2747: $i,SY2748: $i] :
( ( SY2747 = SY2748 )
| ~ ( c_lessequals @ SY2748 @ SY2747 @ SV142 )
| ~ ( c_lessequals @ SY2747 @ SY2748 @ SV142 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3103]) ).
thf(3733,plain,
! [SV1336: $i,SV777: $i,SV143: $i] :
( ( ! [SY5251: $i,SY5252: $i] :
( ( hAPP @ ( c_split @ SV143 @ SV777 @ SV1336 @ SY5251 ) @ SY5252 )
= ( hAPP @ ( hAPP @ SV143 @ ( hAPP @ ( c_fst @ SV777 @ SV1336 ) @ SY5252 ) ) @ ( hAPP @ ( c_snd @ SV777 @ SV1336 ) @ SY5252 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3104]) ).
thf(3734,plain,
! [SV144: $i] :
( ( ( class_Orderings_Oorder @ SV144 )
= $false )
| ( ( ! [SY2753: $i,SY2754: $i] :
( ( SY2753 = SY2754 )
| ~ ( c_lessequals @ SY2753 @ SY2754 @ SV144 )
| ~ ( c_lessequals @ SY2754 @ SY2753 @ SV144 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3105]) ).
thf(3735,plain,
! [SV145: $i] :
( ( ( class_Lattices_Olattice @ SV145 )
= $false )
| ( ( ! [SY2755: $i,SY2756: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY2755 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2755 @ SY2756 @ SV145 ) @ SV145 )
= SY2755 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3106]) ).
thf(3736,plain,
! [SV1337: $i,SV778: $i,SV146: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ SV146 @ SV778 @ ( tc_fun @ SV1337 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV146 @ SV778 @ ( tc_fun @ SV1337 @ tc_bool ) ) @ ( tc_fun @ SV1337 @ tc_bool ) )
= SV146 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3107]) ).
thf(3737,plain,
! [SV147: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV147 )
= $false )
| ( ( ! [SY2759: $i,SY2760: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2759 @ SY2760 @ SV147 )
= SY2759 )
| ~ ( c_lessequals @ SY2760 @ SY2759 @ SV147 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3108]) ).
thf(3738,plain,
! [SV148: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV148 )
= $false )
| ( ( ! [SY2761: $i,SY2762: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2761 @ SY2762 @ SV148 )
!= SY2762 )
| ( c_lessequals @ SY2761 @ SY2762 @ SV148 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3109]) ).
thf(3739,plain,
! [SV149: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV149 )
= $false )
| ( ( ! [SY2763: $i,SY2764: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2763 @ SY2764 @ SV149 )
= SY2764 )
| ~ ( c_lessequals @ SY2763 @ SY2764 @ SV149 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3110]) ).
thf(3740,plain,
! [SV1338: $i,SV779: $i,SV150: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV150 @ SV779 @ ( tc_fun @ SV1338 @ tc_bool ) )
= SV779 )
| ~ ( c_lessequals @ SV150 @ SV779 @ ( tc_fun @ SV1338 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3111]) ).
thf(3741,plain,
! [SV1339: $i,SV780: $i,SV151: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV151 @ SV780 @ ( tc_fun @ SV1339 @ tc_bool ) )
= SV151 )
| ~ ( c_lessequals @ SV780 @ SV151 @ ( tc_fun @ SV1339 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3112]) ).
thf(3742,plain,
! [SV1340: $i,SV781: $i,SV152: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV152 @ SV781 @ ( tc_fun @ SV1340 @ tc_bool ) )
!= SV781 )
| ( c_lessequals @ SV152 @ SV781 @ ( tc_fun @ SV1340 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3113]) ).
thf(3743,plain,
! [SV1341: $i,SV782: $i,SV153: $i] :
( ( ! [SY5253: $i,SY5254: $i] :
( ( c_Relation_Orefl__on @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV153 @ SV782 @ ( tc_fun @ SV1341 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY5253 @ SY5254 @ ( tc_fun @ ( tc_prod @ SV1341 @ SV1341 ) @ tc_bool ) ) @ SV1341 )
| ~ ( c_Relation_Orefl__on @ SV782 @ SY5254 @ SV1341 )
| ~ ( c_Relation_Orefl__on @ SV153 @ SY5253 @ SV1341 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3114]) ).
thf(3744,plain,
! [SV1342: $i,SV784: $i,SV156: $i] :
( ( ! [SY5255: $i,SY5256: $i] :
( ( ( c_Set_Oinsert @ SV156 @ ( c_Set_Oinsert @ SV784 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1342 @ tc_bool ) ) @ SV1342 ) @ SV1342 )
!= ( c_Set_Oinsert @ SY5255 @ ( c_Set_Oinsert @ SY5256 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1342 @ tc_bool ) ) @ SV1342 ) @ SV1342 ) )
| ( SV156 = SY5256 )
| ( SV156 = SY5255 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3116]) ).
thf(3745,plain,
! [SV1343: $i,SV785: $i,SV157: $i] :
( ( ! [SY5257: $i] :
( ! [SY5258: $i] :
( ( c_Set_Oinsert @ SV157 @ ( c_Set_Oinsert @ SV785 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1343 @ tc_bool ) ) @ SV1343 ) @ SV1343 )
!= ( c_Set_Oinsert @ SY5257 @ ( c_Set_Oinsert @ SY5258 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1343 @ tc_bool ) ) @ SV1343 ) @ SV1343 ) )
| ( SV785 = SY5257 )
| ( SV157 = SY5257 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3117]) ).
thf(3746,plain,
! [SV1344: $i,SV786: $i,SV158: $i] :
( ( ! [SY5259: $i,SY5260: $i] :
( ( ( c_Set_Oinsert @ SV158 @ ( c_Set_Oinsert @ SV786 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1344 @ tc_bool ) ) @ SV1344 ) @ SV1344 )
!= ( c_Set_Oinsert @ SY5259 @ ( c_Set_Oinsert @ SY5260 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1344 @ tc_bool ) ) @ SV1344 ) @ SV1344 ) )
| ( SV158 = SY5260 )
| ( SV786 = SY5260 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3118]) ).
thf(3747,plain,
! [SV1345: $i,SV787: $i,SV159: $i] :
( ( ! [SY5261: $i,SY5262: $i] :
( ( ( c_Set_Oinsert @ SV159 @ ( c_Set_Oinsert @ SV787 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1345 @ tc_bool ) ) @ SV1345 ) @ SV1345 )
!= ( c_Set_Oinsert @ SY5261 @ ( c_Set_Oinsert @ SY5262 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1345 @ tc_bool ) ) @ SV1345 ) @ SV1345 ) )
| ( SV787 = SY5261 )
| ( SV787 = SY5262 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3119]) ).
thf(3748,plain,
! [SV1346: $i,SV788: $i,SV160: $i] :
( ( ( c_lessequals @ ( c_Transitive__Closure_Otrancl @ SV160 @ SV788 ) @ ( c_Product__Type_OSigma @ SV1346 @ ( c_COMBK @ SV1346 @ ( tc_fun @ SV788 @ tc_bool ) @ SV788 ) @ SV788 @ SV788 ) @ ( tc_fun @ ( tc_prod @ SV788 @ SV788 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV160 @ ( c_Product__Type_OSigma @ SV1346 @ ( c_COMBK @ SV1346 @ ( tc_fun @ SV788 @ tc_bool ) @ SV788 ) @ SV788 @ SV788 ) @ ( tc_fun @ ( tc_prod @ SV788 @ SV788 ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3120]) ).
thf(3749,plain,
! [SV1347: $i,SV789: $i,SV161: $i] :
( ( ( c_lessequals @ ( c_Transitive__Closure_Ortrancl @ SV161 @ SV789 ) @ ( c_Transitive__Closure_Ortrancl @ SV1347 @ SV789 ) @ ( tc_fun @ ( tc_prod @ SV789 @ SV789 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV161 @ ( c_Transitive__Closure_Ortrancl @ SV1347 @ SV789 ) @ ( tc_fun @ ( tc_prod @ SV789 @ SV789 ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3121]) ).
thf(3750,plain,
! [SV790: $i,SV162: $i] :
( ( ( SV162
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV790 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV162 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV790 @ tc_bool ) ) @ ( tc_fun @ SV790 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3122]) ).
thf(3751,plain,
! [SV1348: $i,SV791: $i,SV164: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV164 @ tc_bool ) )
!= ( c_Set_Oinsert @ SV791 @ SV1348 @ SV164 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3123]) ).
thf(3752,plain,
! [SV1349: $i,SV792: $i,SV166: $i] :
( ( ! [SY5263: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ SV166 @ SV792 @ SV1349 ) @ SY5263 @ ( tc_fun @ SV1349 @ tc_bool ) )
= ( c_Set_Oinsert @ SV166 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV792 @ SY5263 @ ( tc_fun @ SV1349 @ tc_bool ) ) @ SV1349 ) )
| ~ ( c_in @ SV166 @ SY5263 @ SV1349 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3124]) ).
thf(3753,plain,
! [SV1350: $i,SV793: $i,SV167: $i] :
( ( ! [SY5264: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV167 @ ( c_Set_Oinsert @ SV793 @ SV1350 @ SY5264 ) @ ( tc_fun @ SY5264 @ tc_bool ) )
= ( c_Set_Oinsert @ SV793 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV167 @ SV1350 @ ( tc_fun @ SY5264 @ tc_bool ) ) @ SY5264 ) )
| ~ ( c_in @ SV793 @ SV167 @ SY5264 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3125]) ).
thf(3754,plain,
! [SV1351: $i,SV794: $i,SV168: $i] :
( ( ! [SY5265: $i,SY5266: $i] :
( ( c_Set_Oimage @ SV168 @ ( c_Set_Oinsert @ SV794 @ SV1351 @ SY5265 ) @ SY5265 @ SY5266 )
= ( c_Set_Oinsert @ ( hAPP @ SV168 @ SV794 ) @ ( c_Set_Oimage @ SV168 @ SV1351 @ SY5265 @ SY5266 ) @ SY5266 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3126]) ).
thf(3755,plain,
! [SV1352: $i,SV796: $i,SV170: $i] :
( ( ! [SY5267: $i,SY5268: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV170 @ SV796 @ ( tc_fun @ SV1352 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY5267 @ SY5268 @ ( tc_fun @ SV1352 @ tc_bool ) ) @ ( tc_fun @ SV1352 @ tc_bool ) )
| ~ ( c_lessequals @ SV796 @ SY5268 @ ( tc_fun @ SV1352 @ tc_bool ) )
| ~ ( c_lessequals @ SV170 @ SY5267 @ ( tc_fun @ SV1352 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3128]) ).
thf(3756,plain,
! [SV1353: $i,SV797: $i,SV171: $i] :
( ( ! [SY5269: $i] :
( ( c_Relation_Oconverse @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV171 @ SV797 @ ( tc_fun @ ( tc_prod @ SV1353 @ SY5269 ) @ tc_bool ) ) @ SV1353 @ SY5269 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Oconverse @ SV171 @ SV1353 @ SY5269 ) @ ( c_Relation_Oconverse @ SV797 @ SV1353 @ SY5269 ) @ ( tc_fun @ ( tc_prod @ SY5269 @ SV1353 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3129]) ).
thf(3757,plain,
! [SV172: $i] :
( ( ( class_Lattices_Olattice @ SV172 )
= $false )
| ( ( ! [SY2817: $i,SY2818: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2817 @ SY2818 @ SV172 ) @ SY2817 @ SV172 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3130]) ).
thf(3758,plain,
! [SV173: $i] :
( ( ( class_Lattices_Olattice @ SV173 )
= $false )
| ( ( ! [SY2819: $i,SY2820: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2819 @ SY2820 @ SV173 ) @ SY2820 @ SV173 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3131]) ).
thf(3759,plain,
! [SV798: $i,SV174: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV174 ) )
= $true )
| ( ( ! [SY4359: $i,SY4360: $i] :
( ( c_lessequals @ SV798 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4359 @ SY4360 @ SV174 ) @ SV174 )
| ~ ( c_lessequals @ SV798 @ SY4360 @ SV174 )
| ~ ( c_lessequals @ SV798 @ SY4359 @ SV174 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3132]) ).
thf(3760,plain,
! [SV799: $i,SV175: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV175 ) )
= $true )
| ( ( ! [SY4361: $i,SY4362: $i] :
( ( c_lessequals @ SV799 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4361 @ SY4362 @ SV175 ) @ SV175 )
| ~ ( c_lessequals @ SV799 @ SY4362 @ SV175 )
| ~ ( c_lessequals @ SV799 @ SY4361 @ SV175 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3133]) ).
thf(3761,plain,
! [SV800: $i,SV176: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV176 ) )
= $true )
| ( ( ! [SY4363: $i,SY4364: $i] :
( ( c_lessequals @ SV800 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4363 @ SY4364 @ SV176 ) @ SV176 )
| ~ ( c_lessequals @ SV800 @ SY4364 @ SV176 )
| ~ ( c_lessequals @ SV800 @ SY4363 @ SV176 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3134]) ).
thf(3762,plain,
! [SV177: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV177 )
= $false )
| ( ( ! [SY2830: $i,SY2831: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2830 @ SY2831 @ SV177 ) @ SY2831 @ SV177 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3135]) ).
thf(3763,plain,
! [SV178: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV178 )
= $false )
| ( ( ! [SY2832: $i,SY2833: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2832 @ SY2833 @ SV178 ) @ SY2832 @ SV178 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3136]) ).
thf(3764,plain,
! [SV1354: $i,SV801: $i,SV179: $i] :
( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV179 @ SV801 @ ( tc_fun @ SV1354 @ tc_bool ) ) @ SV179 @ ( tc_fun @ SV1354 @ tc_bool ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3137]) ).
thf(3765,plain,
! [SV1355: $i,SV802: $i,SV180: $i] :
( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV180 @ SV802 @ ( tc_fun @ SV1355 @ tc_bool ) ) @ SV802 @ ( tc_fun @ SV1355 @ tc_bool ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3138]) ).
thf(3766,plain,
! [SV1356: $i,SV803: $i,SV181: $i] :
( ( ! [SY5270: $i] :
( ( c_lessequals @ SV181 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV803 @ SV1356 @ ( tc_fun @ SY5270 @ tc_bool ) ) @ ( tc_fun @ SY5270 @ tc_bool ) )
| ~ ( c_lessequals @ SV181 @ SV1356 @ ( tc_fun @ SY5270 @ tc_bool ) )
| ~ ( c_lessequals @ SV181 @ SV803 @ ( tc_fun @ SY5270 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3139]) ).
thf(3767,plain,
! [SV1357: $i,SV804: $i,SV182: $i] :
( ( ! [SY5271: $i] :
( ( c_lessequals @ SV182 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV804 @ SV1357 @ ( tc_fun @ SY5271 @ tc_bool ) ) @ ( tc_fun @ SY5271 @ tc_bool ) )
| ~ ( c_lessequals @ SV182 @ SV1357 @ ( tc_fun @ SY5271 @ tc_bool ) )
| ~ ( c_lessequals @ SV182 @ SV804 @ ( tc_fun @ SY5271 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3140]) ).
thf(3768,plain,
! [SV1358: $i,SV805: $i,SV183: $i] :
( ( ! [SY5272: $i,SY5273: $i] :
( ( c_Product__Type_OSigma @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV183 @ SV805 @ ( tc_fun @ SV1358 @ tc_bool ) ) @ ( c_COMBK @ SY5272 @ ( tc_fun @ SY5273 @ tc_bool ) @ SV1358 ) @ SV1358 @ SY5273 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Product__Type_OSigma @ SV183 @ ( c_COMBK @ SY5272 @ ( tc_fun @ SY5273 @ tc_bool ) @ SV1358 ) @ SV1358 @ SY5273 ) @ ( c_Product__Type_OSigma @ SV805 @ ( c_COMBK @ SY5272 @ ( tc_fun @ SY5273 @ tc_bool ) @ SV1358 ) @ SV1358 @ SY5273 ) @ ( tc_fun @ ( tc_prod @ SV1358 @ SY5273 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3141]) ).
thf(3769,plain,
! [SV806: $i,SV184: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV184 ) )
= $true )
| ( ( ! [SY4374: $i,SY4375: $i] : ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV806 @ SY4374 @ SV184 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV806 @ SY4375 @ SV184 ) @ SV184 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV806 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4374 @ SY4375 @ SV184 ) @ SV184 ) @ SV184 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3142]) ).
thf(3770,plain,
! [SV1359: $i,SV807: $i,SV185: $i] :
( ( ( ( c_Transitive__Closure_Ortrancl @ SV185 @ SV807 )
= ( c_Transitive__Closure_Ortrancl @ SV1359 @ SV807 ) )
| ~ ( c_lessequals @ SV185 @ ( c_Transitive__Closure_Ortrancl @ SV1359 @ SV807 ) @ ( tc_fun @ ( tc_prod @ SV807 @ SV807 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV1359 @ SV185 @ ( tc_fun @ ( tc_prod @ SV807 @ SV807 ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3143]) ).
thf(3771,plain,
! [SV1360: $i,SV808: $i,SV186: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV186 @ SV808 @ ( tc_fun @ SV1360 @ tc_bool ) ) @ SV186 @ ( tc_fun @ SV1360 @ tc_bool ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3144]) ).
thf(3772,plain,
! [SV1361: $i,SV809: $i,SV187: $i] :
( ( ( c_Set_Oinsert @ SV187 @ ( c_HOL_Ominus__class_Ominus @ SV809 @ ( c_Set_Oinsert @ SV187 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1361 @ tc_bool ) ) @ SV1361 ) @ ( tc_fun @ SV1361 @ tc_bool ) ) @ SV1361 )
= ( c_Set_Oinsert @ SV187 @ SV809 @ SV1361 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3145]) ).
thf(3773,plain,
! [SV1362: $i,SV810: $i,SV188: $i] :
( ( ( ( c_Set_Oinsert @ SV188 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV810 @ tc_bool ) ) @ SV810 )
!= ( c_Set_Oinsert @ SV1362 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV810 @ tc_bool ) ) @ SV810 ) )
| ( SV188 = SV1362 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3146]) ).
thf(3774,plain,
! [SV1363: $i,SV811: $i,SV189: $i] :
( ( ! [SY5274: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV189 @ SV811 @ ( tc_fun @ SV1363 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV811 @ SY5274 @ ( tc_fun @ SV1363 @ tc_bool ) ) @ ( tc_fun @ SV1363 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY5274 @ SV189 @ ( tc_fun @ SV1363 @ tc_bool ) ) @ ( tc_fun @ SV1363 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV189 @ SV811 @ ( tc_fun @ SV1363 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV811 @ SY5274 @ ( tc_fun @ SV1363 @ tc_bool ) ) @ ( tc_fun @ SV1363 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY5274 @ SV189 @ ( tc_fun @ SV1363 @ tc_bool ) ) @ ( tc_fun @ SV1363 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3147]) ).
thf(3775,plain,
! [SV1364: $i,SV812: $i,SV191: $i] :
( ( ( c_Set_Oimage @ ( c_COMBK @ SV191 @ SV812 @ SV1364 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1364 @ tc_bool ) ) @ SV1364 @ SV812 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV812 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3148]) ).
thf(3776,plain,
! [SV1365: $i,SV813: $i,SV192: $i] :
( ( ( ( c_Set_Oinsert @ SV192 @ SV813 @ SV1365 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1365 @ tc_bool ) ) )
| ( c_in @ SV192 @ SV813 @ SV1365 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3149]) ).
thf(3777,plain,
! [SV1366: $i,SV814: $i,SV194: $i] :
( ( ( c_in @ SV194 @ SV814 @ SV1366 )
| ! [SY5275: $i] :
~ ( c_lessequals @ ( c_Set_Oinsert @ SV194 @ SY5275 @ SV1366 ) @ SV814 @ ( tc_fun @ SV1366 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3150]) ).
thf(3778,plain,
! [SV1367: $i,SV815: $i,SV195: $i] :
( ( ! [SY5276: $i,SY5277: $i] :
( ( c_Product__Type_OSigma @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV195 @ SV815 @ ( tc_fun @ SV1367 @ tc_bool ) ) @ SY5276 @ SV1367 @ SY5277 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Product__Type_OSigma @ SV195 @ SY5276 @ SV1367 @ SY5277 ) @ ( c_Product__Type_OSigma @ SV815 @ SY5276 @ SV1367 @ SY5277 ) @ ( tc_fun @ ( tc_prod @ SV1367 @ SY5277 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3151]) ).
thf(3779,plain,
! [SV1368: $i,SV816: $i,SV196: $i] :
( ( ! [SY5278: $i] :
( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV196 @ SV816 @ SV1368 ) @ SY5278 ) )
| ~ ( hBOOL @ ( hAPP @ SV816 @ SY5278 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3152]) ).
thf(3780,plain,
! [SV1369: $i,SV817: $i,SV197: $i] :
( ( ! [SY5279: $i] :
( ( c_lessequals @ SV197 @ ( c_Set_Oinsert @ SV817 @ SV1369 @ SY5279 ) @ ( tc_fun @ SY5279 @ tc_bool ) )
| ~ ( c_lessequals @ SV197 @ SV1369 @ ( tc_fun @ SY5279 @ tc_bool ) )
| ( c_in @ SV817 @ SV197 @ SY5279 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3153]) ).
thf(3781,plain,
! [SV1370: $i,SV818: $i,SV198: $i] :
( ( ( c_lessequals @ SV198 @ SV818 @ ( tc_fun @ SV1370 @ tc_bool ) )
| ! [SY5280: $i] :
( ( c_in @ SY5280 @ SV198 @ SV1370 )
| ~ ( c_lessequals @ SV198 @ ( c_Set_Oinsert @ SY5280 @ SV818 @ SV1370 ) @ ( tc_fun @ SV1370 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3154]) ).
thf(3782,plain,
! [SV1371: $i,SV819: $i,SV199: $i] :
( ( ! [SY5281: $i] :
( ( c_lessequals @ SV199 @ ( c_Set_Oinsert @ SV819 @ SV1371 @ SY5281 ) @ ( tc_fun @ SY5281 @ tc_bool ) )
| ~ ( c_lessequals @ SV199 @ SV1371 @ ( tc_fun @ SY5281 @ tc_bool ) )
| ( c_in @ SV819 @ SV199 @ SY5281 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3155]) ).
thf(3783,plain,
! [SV1372: $i,SV820: $i,SV200: $i] :
( ( ( c_lessequals @ SV200 @ SV820 @ ( tc_fun @ SV1372 @ tc_bool ) )
| ! [SY5282: $i] :
( ~ ( c_lessequals @ SV200 @ ( c_Set_Oinsert @ SY5282 @ SV820 @ SV1372 ) @ ( tc_fun @ SV1372 @ tc_bool ) )
| ( c_in @ SY5282 @ SV200 @ SV1372 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3156]) ).
thf(3784,plain,
! [SV1373: $i,SV821: $i,SV201: $i] :
( ( ! [SY5283: $i] :
( ( c_Relation_Oconverse @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV201 @ SV821 @ ( tc_fun @ ( tc_prod @ SV1373 @ SY5283 ) @ tc_bool ) ) @ SV1373 @ SY5283 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_Oconverse @ SV201 @ SV1373 @ SY5283 ) @ ( c_Relation_Oconverse @ SV821 @ SV1373 @ SY5283 ) @ ( tc_fun @ ( tc_prod @ SY5283 @ SV1373 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3157]) ).
thf(3785,plain,
! [SV1374: $i,SV822: $i,SV202: $i] :
( ( ! [SY5284: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV202 @ ( c_Set_Oinsert @ SV822 @ SV1374 @ SY5284 ) @ ( tc_fun @ SY5284 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV202 @ SV1374 @ ( tc_fun @ SY5284 @ tc_bool ) ) )
| ( c_in @ SV822 @ SV202 @ SY5284 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3158]) ).
thf(3786,plain,
! [SV1375: $i,SV823: $i,SV203: $i] :
( ( ! [SY5285: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ SV203 @ SV823 @ SV1375 ) @ SY5285 @ ( tc_fun @ SV1375 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV823 @ SY5285 @ ( tc_fun @ SV1375 @ tc_bool ) ) )
| ( c_in @ SV203 @ SY5285 @ SV1375 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3159]) ).
thf(3787,plain,
! [SV1376: $i,SV824: $i,SV204: $i] :
( ( ( c_Relation_Ototal__on @ SV204 @ SV824 @ SV1376 )
| ~ ( c_Order__Relation_Ostrict__linear__order__on @ SV204 @ SV824 @ SV1376 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3160]) ).
thf(3788,plain,
! [SV1377: $i,SV825: $i,SV205: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV205 @ SV825 @ ( tc_fun @ SV1377 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1377 @ tc_bool ) ) )
| ( SV825
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1377 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3161]) ).
thf(3789,plain,
! [SV1378: $i,SV826: $i,SV206: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV206 @ SV826 @ ( tc_fun @ SV1378 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1378 @ tc_bool ) ) )
| ( SV206
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1378 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3162]) ).
thf(3790,plain,
! [SV207: $i] :
( ( ( class_Lattices_Obounded__lattice @ SV207 )
= $false )
| ( ( ! [SY2903: $i] :
( ! [SY2904: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2903 @ SY2904 @ SV207 )
!= ( c_Orderings_Obot__class_Obot @ SV207 ) )
| ( SY2903
= ( c_Orderings_Obot__class_Obot @ SV207 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3163]) ).
thf(3791,plain,
! [SV208: $i] :
( ( ( class_Lattices_Obounded__lattice @ SV208 )
= $false )
| ( ( ! [SY2905: $i,SY2906: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2905 @ SY2906 @ SV208 )
!= ( c_Orderings_Obot__class_Obot @ SV208 ) )
| ( SY2906
= ( c_Orderings_Obot__class_Obot @ SV208 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3164]) ).
thf(3792,plain,
! [SV1379: $i,SV827: $i,SV209: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ SV209 @ SV827 @ ( tc_fun @ SV1379 @ tc_bool ) ) @ SV827 @ ( tc_fun @ SV1379 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV209 @ SV827 @ ( tc_fun @ SV1379 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3165]) ).
thf(3793,plain,
! [SV1380: $i,SV828: $i,SV210: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV210 @ ( c_HOL_Ominus__class_Ominus @ SV828 @ SV210 @ ( tc_fun @ SV1380 @ tc_bool ) ) @ ( tc_fun @ SV1380 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV210 @ SV828 @ ( tc_fun @ SV1380 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3166]) ).
thf(3794,plain,
! [SV1381: $i,SV829: $i,SV211: $i] :
( ( ! [SY5286: $i,SY5287: $i,SY5288: $i] :
( ( c_Relation_Orel__comp @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV211 @ SV829 @ ( tc_fun @ ( tc_prod @ SV1381 @ SY5286 ) @ tc_bool ) ) @ SY5287 @ SV1381 @ SY5286 @ SY5288 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ SV211 @ SY5287 @ SV1381 @ SY5286 @ SY5288 ) @ ( c_Relation_Orel__comp @ SV829 @ SY5287 @ SV1381 @ SY5286 @ SY5288 ) @ ( tc_fun @ ( tc_prod @ SV1381 @ SY5288 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3167]) ).
thf(3795,plain,
! [SV1382: $i,SV830: $i,SV212: $i] :
( ( ! [SY5289: $i,SY5290: $i,SY5291: $i] :
( ( c_Relation_Orel__comp @ SV212 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV830 @ SV1382 @ ( tc_fun @ ( tc_prod @ SY5289 @ SY5290 ) @ tc_bool ) ) @ SY5291 @ SY5289 @ SY5290 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ SV212 @ SV830 @ SY5291 @ SY5289 @ SY5290 ) @ ( c_Relation_Orel__comp @ SV212 @ SV1382 @ SY5291 @ SY5289 @ SY5290 ) @ ( tc_fun @ ( tc_prod @ SY5291 @ SY5290 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3168]) ).
thf(3796,plain,
! [SV1383: $i,SV831: $i,SV213: $i] :
( ( ( c_lessequals @ SV213 @ SV831 @ ( tc_fun @ SV1383 @ tc_bool ) )
| ! [SY5292: $i] :
~ ( c_lessequals @ SV213 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY5292 @ SV831 @ ( tc_fun @ SV1383 @ tc_bool ) ) @ ( tc_fun @ SV1383 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3169]) ).
thf(3797,plain,
! [SV1384: $i,SV832: $i,SV214: $i] :
( ( ( c_lessequals @ SV214 @ SV832 @ ( tc_fun @ SV1384 @ tc_bool ) )
| ! [SY5293: $i] :
~ ( c_lessequals @ SV214 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV832 @ SY5293 @ ( tc_fun @ SV1384 @ tc_bool ) ) @ ( tc_fun @ SV1384 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3170]) ).
thf(3798,plain,
! [SV833: $i,SV215: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV215 ) )
= $true )
| ( ( ! [SY4422: $i] :
( ( c_lessequals @ SV833 @ SY4422 @ SV215 )
| ! [SY4423: $i] :
~ ( c_lessequals @ SV833 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4422 @ SY4423 @ SV215 ) @ SV215 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3171]) ).
thf(3799,plain,
! [SV834: $i,SV216: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV216 ) )
= $true )
| ( ( ! [SY4424: $i] :
( ( c_lessequals @ SV834 @ SY4424 @ SV216 )
| ! [SY4425: $i] :
~ ( c_lessequals @ SV834 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4425 @ SY4424 @ SV216 ) @ SV216 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3172]) ).
thf(3800,plain,
! [SV835: $i,SV217: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV217 ) )
= $true )
| ( ( ! [SY4426: $i,SY4427: $i] :
( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV835 @ SY4426 @ SV217 ) @ SY4427 @ SV217 )
| ~ ( c_lessequals @ SV835 @ SY4427 @ SV217 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3173]) ).
thf(3801,plain,
! [SV836: $i,SV218: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV218 ) )
= $true )
| ( ( ! [SY4428: $i,SY4429: $i] :
( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV836 @ SY4428 @ SV218 ) @ SY4429 @ SV218 )
| ~ ( c_lessequals @ SY4428 @ SY4429 @ SV218 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3174]) ).
thf(3802,plain,
! [SV837: $i,SV219: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV219 ) )
= $true )
| ( ( ! [SY4430: $i] :
( ( c_lessequals @ SV837 @ SY4430 @ SV219 )
| ! [SY4431: $i] :
~ ( c_lessequals @ SV837 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4430 @ SY4431 @ SV219 ) @ SV219 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3175]) ).
thf(3803,plain,
! [SV838: $i,SV220: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV220 ) )
= $true )
| ( ( ! [SY4432: $i] :
( ( c_lessequals @ SV838 @ SY4432 @ SV220 )
| ! [SY4433: $i] :
~ ( c_lessequals @ SV838 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4433 @ SY4432 @ SV220 ) @ SV220 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3176]) ).
thf(3804,plain,
! [SV1385: $i,SV839: $i,SV221: $i] :
( ( ! [SY5294: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV221 @ SV839 @ ( tc_fun @ SV1385 @ tc_bool ) ) @ SY5294 @ ( tc_fun @ SV1385 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ SV221 @ SY5294 @ ( tc_fun @ SV1385 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV839 @ SY5294 @ ( tc_fun @ SV1385 @ tc_bool ) ) @ ( tc_fun @ SV1385 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3177]) ).
thf(3805,plain,
! [SV1386: $i,SV840: $i,SV222: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV222 @ SV840 @ ( tc_fun @ SV1386 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV840 @ SV222 @ ( tc_fun @ SV1386 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3178]) ).
thf(3806,plain,
! [SV223: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV223 )
= $false )
| ( ( ! [SY2950: $i,SY2951: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2950 @ SY2951 @ SV223 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY2951 @ SY2950 @ SV223 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3179]) ).
thf(3807,plain,
! [SV224: $i] :
( ( ( class_Lattices_Olattice @ SV224 )
= $false )
| ( ( ! [SY2952: $i,SY2953: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2952 @ SY2953 @ SV224 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY2953 @ SY2952 @ SV224 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3180]) ).
thf(3808,plain,
! [SV1387: $i,SV841: $i,SV225: $i] :
( ( ! [SY5295: $i] :
( ( c_Relation_ODomain @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV225 @ SV841 @ ( tc_fun @ ( tc_prod @ SV1387 @ SY5295 ) @ tc_bool ) ) @ SV1387 @ SY5295 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_ODomain @ SV225 @ SV1387 @ SY5295 ) @ ( c_Relation_ODomain @ SV841 @ SV1387 @ SY5295 ) @ ( tc_fun @ SV1387 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3181]) ).
thf(3809,plain,
! [SV1388: $i,SV842: $i,SV226: $i] :
( ( ( c_Set_Oinsert @ SV226 @ SV842 @ SV1388 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ SV226 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1388 @ tc_bool ) ) @ SV1388 ) @ SV842 @ ( tc_fun @ SV1388 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3182]) ).
thf(3810,plain,
! [SV1389: $i,SV843: $i,SV227: $i] :
( ( ( c_Product__Type_OSigma @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV227 @ tc_bool ) ) @ SV843 @ SV227 @ SV1389 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV227 @ SV1389 ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3183]) ).
thf(3811,plain,
! [SV1390: $i,SV844: $i,SV228: $i] :
( ( ( c_lessequals @ ( c_Wellfounded_Oacc @ SV228 @ SV844 ) @ ( c_Wellfounded_Oacc @ SV1390 @ SV844 ) @ ( tc_fun @ SV844 @ tc_bool ) )
| ~ ( c_lessequals @ SV1390 @ SV228 @ ( tc_fun @ ( tc_prod @ SV844 @ SV844 ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3184]) ).
thf(3812,plain,
! [SV1391: $i,SV845: $i,SV229: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV229 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV229 @ SV845 @ ( tc_fun @ SV1391 @ tc_bool ) ) @ ( tc_fun @ SV1391 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV229 @ SV845 @ ( tc_fun @ SV1391 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3185]) ).
thf(3813,plain,
! [SV230: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV230 )
= $false )
| ( ( ! [SY2965: $i,SY2966: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2965 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2965 @ SY2966 @ SV230 ) @ SV230 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY2965 @ SY2966 @ SV230 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3186]) ).
thf(3814,plain,
! [SV231: $i] :
( ( ( class_Lattices_Olattice @ SV231 )
= $false )
| ( ( ! [SY2967: $i,SY2968: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2967 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2967 @ SY2968 @ SV231 ) @ SV231 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY2967 @ SY2968 @ SV231 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3187]) ).
thf(3815,plain,
! [SV1392: $i,SV846: $i,SV232: $i] :
( ( ( ( c_Relation_ODomain @ SV232 @ SV846 @ SV1392 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV846 @ tc_bool ) ) )
| ( SV232
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV846 @ SV1392 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3188]) ).
thf(3816,plain,
! [SV1393: $i,SV847: $i,SV233: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV233 @ tc_bool ) )
= ( c_Set_Oimage @ SV847 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1393 @ tc_bool ) ) @ SV1393 @ SV233 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3189]) ).
thf(3817,plain,
! [SV1394: $i,SV848: $i,SV234: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV234 @ ( c_HOL_Ominus__class_Ominus @ SV848 @ SV234 @ ( tc_fun @ SV1394 @ tc_bool ) ) @ ( tc_fun @ SV1394 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1394 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3190]) ).
thf(3818,plain,
! [SV1395: $i,SV849: $i,SV235: $i] :
( ( ! [SY5296: $i] : ( c_lessequals @ ( c_Relation_ORange @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV235 @ SV849 @ ( tc_fun @ ( tc_prod @ SV1395 @ SY5296 ) @ tc_bool ) ) @ SV1395 @ SY5296 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_ORange @ SV235 @ SV1395 @ SY5296 ) @ ( c_Relation_ORange @ SV849 @ SV1395 @ SY5296 ) @ ( tc_fun @ SY5296 @ tc_bool ) ) @ ( tc_fun @ SY5296 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3191]) ).
thf(3819,plain,
! [SV850: $i,SV236: $i] :
( ( ( hBOOL @ ( hAPP @ SV236 @ SV850 ) )
= $true )
| ( ( ! [SY2979: $i,SY2980: $i] :
( ~ ( hBOOL @ ( hAPP @ SV236 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1 @ SV236 @ SY2979 @ SY2980 ) ) )
| ~ ( c_Wellfounded_Owf @ SY2979 @ SY2980 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3192]) ).
thf(3820,plain,
! [SV1396: $i,SV851: $i,SV237: $i] :
( ( ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Ortrancl @ SV237 @ SV851 ) @ ( c_Transitive__Closure_Ortrancl @ SV1396 @ SV851 ) @ ( tc_fun @ ( tc_prod @ SV851 @ SV851 ) @ tc_bool ) ) @ SV851 )
= ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV237 @ SV1396 @ ( tc_fun @ ( tc_prod @ SV851 @ SV851 ) @ tc_bool ) ) @ SV851 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3193]) ).
thf(3821,plain,
! [SV1397: $i,SV852: $i,SV238: $i] :
( ( ! [SY5297: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ SV238 @ SV852 @ SV1397 ) @ SY5297 @ ( tc_fun @ SV1397 @ tc_bool ) )
= ( c_Set_Oinsert @ SV238 @ ( c_HOL_Ominus__class_Ominus @ SV852 @ SY5297 @ ( tc_fun @ SV1397 @ tc_bool ) ) @ SV1397 ) )
| ( c_in @ SV238 @ SY5297 @ SV1397 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3194]) ).
thf(3822,plain,
! [SV1398: $i,SV853: $i,SV239: $i] :
( ( ! [SY5298: $i] :
( ( c_lessequals @ SV239 @ ( c_Set_Oinsert @ SV853 @ SV1398 @ SY5298 ) @ ( tc_fun @ SY5298 @ tc_bool ) )
| ~ ( c_lessequals @ SV239 @ SV1398 @ ( tc_fun @ SY5298 @ tc_bool ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV239 @ ( c_Set_Oinsert @ SV853 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5298 @ tc_bool ) ) @ SY5298 ) @ ( tc_fun @ SY5298 @ tc_bool ) ) @ SV1398 @ ( tc_fun @ SY5298 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3195]) ).
thf(3823,plain,
! [SV854: $i,SV240: $i] :
( ( ( hBOOL @ ( hAPP @ SV240 @ SV854 ) )
= $true )
| ( ( ! [SY4455: $i,SY4456: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4455 @ SV240 @ ( tc_fun @ SY4456 @ tc_bool ) ) @ SV854 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3196]) ).
thf(3824,plain,
! [SV855: $i,SV241: $i] :
( ( ( hBOOL @ ( hAPP @ SV241 @ SV855 ) )
= $true )
| ( ( ! [SY4457: $i,SY4458: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV241 @ SY4457 @ ( tc_fun @ SY4458 @ tc_bool ) ) @ SV855 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3197]) ).
thf(3825,plain,
! [SV1399: $i,SV856: $i,SV242: $i] :
( ( ! [SY5299: $i,SY5300: $i] :
( ( c_Relation_ORange @ ( c_Set_Oinsert @ ( c_Pair @ SV242 @ SV856 @ SV1399 @ SY5299 ) @ SY5300 @ ( tc_prod @ SV1399 @ SY5299 ) ) @ SV1399 @ SY5299 )
= ( c_Set_Oinsert @ SV856 @ ( c_Relation_ORange @ SY5300 @ SV1399 @ SY5299 ) @ SY5299 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3198]) ).
thf(3826,plain,
! [SV1400: $i,SV857: $i,SV243: $i] :
( ( ( c_Relation_Osym @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV243 @ SV857 @ ( tc_fun @ ( tc_prod @ SV1400 @ SV1400 ) @ tc_bool ) ) @ SV1400 )
| ~ ( c_Relation_Osym @ SV857 @ SV1400 )
| ~ ( c_Relation_Osym @ SV243 @ SV1400 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3199]) ).
thf(3827,plain,
! [SV1401: $i,SV858: $i,SV244: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ SV244 @ SV858 @ SV1401 ) @ ( c_Set_Oinsert @ SV244 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1401 @ tc_bool ) ) @ SV1401 ) @ ( tc_fun @ SV1401 @ tc_bool ) )
= SV858 )
| ( c_in @ SV244 @ SV858 @ SV1401 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3200]) ).
thf(3828,plain,
! [SV1402: $i,SV859: $i,SV245: $i] :
( ( ! [SY5301: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV245 @ SV859 @ ( tc_fun @ SV1402 @ tc_bool ) ) @ SY5301 @ ( tc_fun @ SV1402 @ tc_bool ) )
| ~ ( c_lessequals @ SV245 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV859 @ SY5301 @ ( tc_fun @ SV1402 @ tc_bool ) ) @ ( tc_fun @ SV1402 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3201]) ).
thf(3829,plain,
! [SV1403: $i,SV860: $i,SV246: $i] :
( ( ! [SY5302: $i] :
( ( c_lessequals @ SV246 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV860 @ SV1403 @ ( tc_fun @ SY5302 @ tc_bool ) ) @ ( tc_fun @ SY5302 @ tc_bool ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV246 @ SV860 @ ( tc_fun @ SY5302 @ tc_bool ) ) @ SV1403 @ ( tc_fun @ SY5302 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3202]) ).
thf(3830,plain,
! [SV1404: $i,SV861: $i,SV247: $i] :
( ( ! [SY5303: $i,SY5304: $i,SY5305: $i] :
( ( ( hAPP @ SV247 @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ SV247 @ SV861 @ SV1404 @ SY5303 @ SY5304 @ SY5305 ) )
!= ( hAPP @ SV861 @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ SV247 @ SV861 @ SV1404 @ SY5303 @ SY5304 @ SY5305 ) ) )
| ( ( c_Recdef_Ocut @ SV247 @ SV1404 @ SY5303 @ SY5304 @ SY5305 )
= ( c_Recdef_Ocut @ SV861 @ SV1404 @ SY5303 @ SY5304 @ SY5305 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3203]) ).
thf(3831,plain,
! [SV862: $i,SV248: $i] :
( ( ( c_Wellfounded_Oacyclic @ SV248 @ SV862 )
= $true )
| ( ( ! [SY4472: $i,SY4473: $i] :
~ ( c_Wellfounded_Oacyclic @ ( c_Set_Oinsert @ ( c_Pair @ SY4472 @ SY4473 @ SV862 @ SV862 ) @ SV248 @ ( tc_prod @ SV862 @ SV862 ) ) @ SV862 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3204]) ).
thf(3832,plain,
! [SV1405: $i,SV863: $i,SV249: $i] :
( ( ~ ( class_HOL_Oord @ SV249 )
| ! [SY5306: $i] :
( ( c_lessequals @ ( hAPP @ SV863 @ SV1405 ) @ ( hAPP @ SY5306 @ SV1405 ) @ SV249 )
| ! [SY4476: $i] :
~ ( c_lessequals @ SV863 @ SY5306 @ ( tc_fun @ SY4476 @ SV249 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3205]) ).
thf(3833,plain,
! [SV1406: $i,SV864: $i,SV250: $i] :
( ( ! [SY5308: $i] :
( ( c_in @ SV250 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV864 @ SV1406 @ ( tc_fun @ SY5308 @ tc_bool ) ) @ SY5308 )
| ~ ( c_in @ SV250 @ SV1406 @ SY5308 )
| ~ ( c_in @ SV250 @ SV864 @ SY5308 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3206]) ).
thf(3834,plain,
! [SV1407: $i,SV865: $i,SV251: $i] :
( ( ! [SY5309: $i] :
( ( c_in @ SV251 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV865 @ SV1407 @ ( tc_fun @ SY5309 @ tc_bool ) ) @ SY5309 )
| ~ ( c_in @ SV251 @ SV1407 @ SY5309 )
| ~ ( c_in @ SV251 @ SV865 @ SY5309 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3207]) ).
thf(3835,plain,
! [SV1408: $i,SV866: $i,SV252: $i] :
( ( ! [SY5310: $i] :
( ( c_in @ SV252 @ ( c_Set_Oinsert @ SV866 @ SV1408 @ SY5310 ) @ SY5310 )
| ~ ( c_in @ SV252 @ SV1408 @ SY5310 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3208]) ).
thf(3836,plain,
! [SV1409: $i,SV867: $i,SV253: $i] :
( ( ! [SY5311: $i] :
( ( c_in @ SV253 @ ( c_Set_Oinsert @ SV867 @ SV1409 @ SY5311 ) @ SY5311 )
| ~ ( c_in @ SV253 @ SV1409 @ SY5311 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3209]) ).
thf(3837,plain,
! [SV1410: $i,SV868: $i,SV254: $i] :
( ( ( c_in @ SV254 @ SV868 @ SV1410 )
| ! [SY5312: $i] :
( ~ ( c_in @ SV254 @ SY5312 @ SV1410 )
| ~ ( c_lessequals @ SY5312 @ SV868 @ ( tc_fun @ SV1410 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3210]) ).
thf(3838,plain,
! [SV1411: $i,SV869: $i,SV255: $i] :
( ( ( c_in @ SV255 @ SV869 @ SV1411 )
| ! [SY5313: $i] :
( ~ ( c_lessequals @ SY5313 @ SV869 @ ( tc_fun @ SV1411 @ tc_bool ) )
| ~ ( c_in @ SV255 @ SY5313 @ SV1411 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3211]) ).
thf(3839,plain,
! [SV1412: $i,SV870: $i,SV256: $i] :
( ( ( c_in @ SV256 @ SV870 @ SV1412 )
| ! [SY5314: $i] :
( ~ ( c_in @ SV256 @ SY5314 @ SV1412 )
| ~ ( c_lessequals @ SY5314 @ SV870 @ ( tc_fun @ SV1412 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3212]) ).
thf(3840,plain,
! [SV1413: $i,SV871: $i,SV257: $i] :
( ( ( c_in @ SV257 @ SV871 @ SV1413 )
| ! [SY5315: $i] :
( ~ ( c_in @ SV257 @ SY5315 @ SV1413 )
| ~ ( c_lessequals @ SY5315 @ SV871 @ ( tc_fun @ SV1413 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3213]) ).
thf(3841,plain,
! [SV1414: $i,SV872: $i,SV258: $i] :
( ( ! [SY5316: $i] :
( ( c_in @ SV258 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV872 @ SV1414 @ ( tc_fun @ SY5316 @ tc_bool ) ) @ SY5316 )
| ~ ( c_in @ SV258 @ SV872 @ SY5316 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3214]) ).
thf(3842,plain,
! [SV1415: $i,SV873: $i,SV259: $i] :
( ( ! [SY5317: $i] :
( ( c_in @ SV259 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV873 @ SV1415 @ ( tc_fun @ SY5317 @ tc_bool ) ) @ SY5317 )
| ~ ( c_in @ SV259 @ SV1415 @ SY5317 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3215]) ).
thf(3843,plain,
! [SV874: $i,SV260: $i] :
( ( c_in @ SV260 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV874 @ tc_bool ) ) @ SV874 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3216]) ).
thf(3844,plain,
! [SV875: $i,SV261: $i] :
( ( ( hBOOL @ ( hAPP @ SV261 @ SV875 ) )
= $true )
| ( ( ! [SY4497: $i] :
~ ( c_in @ SV875 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4497 @ tc_bool ) ) @ SY4497 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3217]) ).
thf(3845,plain,
! [SV876: $i,SV262: $i] :
( ( c_in @ SV262 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV876 @ tc_bool ) ) @ SV876 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3218]) ).
thf(3846,plain,
! [SV877: $i,SV263: $i] :
( ( c_in @ SV263 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV877 @ tc_bool ) ) @ SV877 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3219]) ).
thf(3847,plain,
! [SV1416: $i,SV878: $i,SV264: $i] :
( ( ( c_in @ SV264 @ SV878 @ SV1416 )
| ! [SY5318: $i] :
( ( SV264 = SY5318 )
| ~ ( c_in @ SV264 @ ( c_Set_Oinsert @ SY5318 @ SV878 @ SV1416 ) @ SV1416 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3220]) ).
thf(3848,plain,
! [SV1417: $i,SV879: $i,SV265: $i] :
( ( ( c_in @ SV265 @ SV879 @ SV1417 )
| ! [SY5319: $i] :
( ( c_in @ SV265 @ SY5319 @ SV1417 )
| ~ ( c_in @ SV265 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY5319 @ SV879 @ ( tc_fun @ SV1417 @ tc_bool ) ) @ SV1417 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3221]) ).
thf(3849,plain,
! [SV1418: $i,SV880: $i,SV266: $i] :
( ( ~ ( c_in @ SV266 @ SV880 @ SV1418 )
| ! [SY5320: $i] :
~ ( c_in @ SV266 @ ( c_HOL_Ominus__class_Ominus @ SY5320 @ SV880 @ ( tc_fun @ SV1418 @ tc_bool ) ) @ SV1418 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3222]) ).
thf(3850,plain,
! [SV1419: $i,SV881: $i,SV267: $i] :
( ( ( c_in @ SV267 @ SV881 @ SV1419 )
| ! [SY5321: $i] :
~ ( c_in @ SV267 @ ( c_HOL_Ominus__class_Ominus @ SV881 @ SY5321 @ ( tc_fun @ SV1419 @ tc_bool ) ) @ SV1419 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3223]) ).
thf(3851,plain,
! [SV1420: $i,SV882: $i,SV268: $i] :
( ( c_in @ SV268 @ ( c_Set_Oinsert @ SV268 @ SV882 @ SV1420 ) @ SV1420 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3224]) ).
thf(3852,plain,
! [SV1421: $i,SV883: $i,SV269: $i] :
( ( c_in @ SV269 @ ( c_Set_Oinsert @ SV269 @ SV883 @ SV1421 ) @ SV1421 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3225]) ).
thf(3853,plain,
! [SV1422: $i,SV884: $i,SV270: $i] :
( ( c_in @ SV270 @ ( c_Set_Oinsert @ SV270 @ SV884 @ SV1422 ) @ SV1422 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3226]) ).
thf(3854,plain,
! [SV1423: $i,SV885: $i,SV271: $i] :
( ( ( c_in @ SV271 @ SV885 @ SV1423 )
| ! [SY5322: $i] :
~ ( c_in @ SV271 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY5322 @ SV885 @ ( tc_fun @ SV1423 @ tc_bool ) ) @ SV1423 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3227]) ).
thf(3855,plain,
! [SV1424: $i,SV886: $i,SV272: $i] :
( ( ( c_in @ SV272 @ SV886 @ SV1424 )
| ! [SY5323: $i] :
~ ( c_in @ SV272 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV886 @ SY5323 @ ( tc_fun @ SV1424 @ tc_bool ) ) @ SV1424 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3228]) ).
thf(3856,plain,
! [SV887: $i,SV273: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV273 @ SV887 ) ) )
= $true )
| ( ( ! [SY4513: $i] :
~ ( c_in @ SV887 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4513 @ tc_bool ) ) @ SY4513 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3229]) ).
thf(3857,plain,
! [SV1425: $i,SV888: $i,SV274: $i] :
( ( ! [SY5324: $i] :
( ( c_in @ SV274 @ ( c_HOL_Ominus__class_Ominus @ SV888 @ SV1425 @ ( tc_fun @ SY5324 @ tc_bool ) ) @ SY5324 )
| ( c_in @ SV274 @ SV1425 @ SY5324 )
| ~ ( c_in @ SV274 @ SV888 @ SY5324 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3230]) ).
thf(3858,plain,
! [SV1426: $i,SV889: $i,SV275: $i] :
( ( ! [SY5325: $i] :
( ( c_in @ SV275 @ ( c_HOL_Ominus__class_Ominus @ SV889 @ SV1426 @ ( tc_fun @ SY5325 @ tc_bool ) ) @ SY5325 )
| ( c_in @ SV275 @ SV1426 @ SY5325 )
| ~ ( c_in @ SV275 @ SV889 @ SY5325 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3231]) ).
thf(3859,plain,
! [SV1427: $i,SV890: $i,SV276: $i] :
( ( ! [SY5326: $i] :
( ( ( c_Set_Oinsert @ SV276 @ SV890 @ SV1427 )
!= ( c_Set_Oinsert @ SV276 @ SY5326 @ SV1427 ) )
| ( c_in @ SV276 @ SY5326 @ SV1427 )
| ( SV890 = SY5326 )
| ( c_in @ SV276 @ SV890 @ SV1427 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3232]) ).
thf(3860,plain,
! [SV1428: $i,SV891: $i,SV277: $i] :
( ( ( ( c_Set_Oinsert @ SV277 @ SV891 @ SV1428 )
= SV891 )
| ~ ( c_in @ SV277 @ SV891 @ SV1428 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3233]) ).
thf(3861,plain,
! [SV1429: $i,SV892: $i,SV278: $i] :
( ( ! [SY5327: $i] :
( ( hAPP @ ( c_fst @ SV278 @ SV892 ) @ ( c_Pair @ SV1429 @ SY5327 @ SV278 @ SV892 ) )
= SV1429 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3234]) ).
thf(3862,plain,
! [SV1430: $i,SV893: $i,SV279: $i] :
( ( ! [SY5328: $i] :
( SV279
= ( hAPP @ ( c_fst @ SV893 @ SV1430 ) @ ( c_Pair @ SV279 @ SY5328 @ SV893 @ SV1430 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3235]) ).
thf(3863,plain,
! [SV1431: $i,SV894: $i,SV280: $i] :
( ( ! [SY5329: $i] :
( ( hAPP @ ( c_snd @ SV280 @ SV894 ) @ ( c_Pair @ SV1431 @ SY5329 @ SV280 @ SV894 ) )
= SY5329 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3236]) ).
thf(3864,plain,
! [SV1432: $i,SV895: $i,SV281: $i] :
( ( ! [SY5330: $i] :
( SV281
= ( hAPP @ ( c_snd @ SV895 @ SV1432 ) @ ( c_Pair @ SY5330 @ SV281 @ SV895 @ SV1432 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3237]) ).
thf(3865,plain,
! [SV1433: $i,SV896: $i,SV282: $i] :
( ( ! [SY5331: $i,SY5332: $i] :
( ( hBOOL @ ( hAPP @ SV282 @ ( hAPP @ ( c_fst @ SV896 @ SV1433 ) @ ( c_Pair @ SY5331 @ SY5332 @ SV896 @ SV1433 ) ) ) )
| ! [V_Q: $i] :
~ ( hBOOL @ ( hAPP @ V_Q @ SY5332 ) )
| ~ ( hBOOL @ ( hAPP @ SV282 @ SY5331 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3238]) ).
thf(3866,plain,
! [SV1434: $i,SV897: $i,SV283: $i] :
( ( ! [SY5334: $i,SY5335: $i] :
( ( hBOOL @ ( hAPP @ SV283 @ ( hAPP @ ( c_snd @ SV897 @ SV1434 ) @ ( c_Pair @ SY5334 @ SY5335 @ SV897 @ SV1434 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ SV283 @ SY5335 ) )
| ! [V_P: $i] :
~ ( hBOOL @ ( hAPP @ V_P @ SY5334 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3239]) ).
thf(3867,plain,
! [SV898: $i,SV284: $i] :
( ( ( ~ ( class_Lattices_Odistrib__lattice @ SV284 ) )
= $true )
| ( ( ! [SY4537: $i,SY4538: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV898 @ SY4537 @ SV284 ) @ SY4538 @ SV284 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV898 @ SY4538 @ SV284 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4537 @ SY4538 @ SV284 ) @ SV284 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3240]) ).
thf(3868,plain,
! [SV899: $i,SV285: $i] :
( ( ( ~ ( class_Lattices_Odistrib__lattice @ SV285 ) )
= $true )
| ( ( ! [SY4539: $i,SY4540: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV899 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4539 @ SY4540 @ SV285 ) @ SV285 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV899 @ SY4539 @ SV285 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV899 @ SY4540 @ SV285 ) @ SV285 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3241]) ).
thf(3869,plain,
! [SV1435: $i,SV900: $i,SV286: $i] :
( ( ! [SY5337: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV286 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV900 @ SV1435 @ ( tc_fun @ SY5337 @ tc_bool ) ) @ ( tc_fun @ SY5337 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV286 @ SV900 @ ( tc_fun @ SY5337 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV286 @ SV1435 @ ( tc_fun @ SY5337 @ tc_bool ) ) @ ( tc_fun @ SY5337 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3242]) ).
thf(3870,plain,
! [SV1436: $i,SV901: $i,SV287: $i] :
( ( ! [SY5338: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV287 @ SV901 @ ( tc_fun @ SV1436 @ tc_bool ) ) @ SY5338 @ ( tc_fun @ SV1436 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV287 @ SY5338 @ ( tc_fun @ SV1436 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV901 @ SY5338 @ ( tc_fun @ SV1436 @ tc_bool ) ) @ ( tc_fun @ SV1436 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3243]) ).
thf(3871,plain,
! [SV902: $i,SV288: $i] :
( ( ( c_Relation_Otrans @ SV288 @ SV902 )
= $true )
| ( ( ! [SY4545: $i] :
~ ( c_Order__Relation_Ostrict__linear__order__on @ SY4545 @ SV288 @ SV902 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3244]) ).
thf(3872,plain,
! [SV1437: $i,SV903: $i,SV289: $i] :
( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV289 @ SV903 @ SV1437 ) @ SV289 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3245]) ).
thf(3873,plain,
! [SV1438: $i,SV904: $i,SV290: $i] :
( ( ! [SY5339: $i] :
( ( c_lessequals @ ( c_Set_Oinsert @ SV290 @ SV904 @ SV1438 ) @ SY5339 @ ( tc_fun @ SV1438 @ tc_bool ) )
| ~ ( c_lessequals @ SV904 @ SY5339 @ ( tc_fun @ SV1438 @ tc_bool ) )
| ~ ( c_in @ SV290 @ SY5339 @ SV1438 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3246]) ).
thf(3874,plain,
! [SV1439: $i,SV905: $i,SV291: $i] :
( ( ! [SY5340: $i,SY5341: $i] :
( ( c_Product__Type_OSigma @ ( c_HOL_Ominus__class_Ominus @ SV291 @ SV905 @ ( tc_fun @ SV1439 @ tc_bool ) ) @ ( c_COMBK @ SY5340 @ ( tc_fun @ SY5341 @ tc_bool ) @ SV1439 ) @ SV1439 @ SY5341 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Product__Type_OSigma @ SV291 @ ( c_COMBK @ SY5340 @ ( tc_fun @ SY5341 @ tc_bool ) @ SV1439 ) @ SV1439 @ SY5341 ) @ ( c_Product__Type_OSigma @ SV905 @ ( c_COMBK @ SY5340 @ ( tc_fun @ SY5341 @ tc_bool ) @ SV1439 ) @ SV1439 @ SY5341 ) @ ( tc_fun @ ( tc_prod @ SV1439 @ SY5341 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3247]) ).
thf(3875,plain,
! [SV292: $i] :
( ( ( class_Lattices_Olattice @ SV292 )
= $false )
| ( ( ! [SY3138: $i,SY3139: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY3138 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3138 @ SY3139 @ SV292 ) @ SV292 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY3138 @ SY3139 @ SV292 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3248]) ).
thf(3876,plain,
! [SV293: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV293 )
= $false )
| ( ( ! [SY3140: $i,SY3141: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY3140 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3140 @ SY3141 @ SV293 ) @ SV293 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY3140 @ SY3141 @ SV293 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3249]) ).
thf(3877,plain,
! [SV1440: $i,SV906: $i,SV294: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV294 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV294 @ SV906 @ ( tc_fun @ SV1440 @ tc_bool ) ) @ ( tc_fun @ SV1440 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV294 @ SV906 @ ( tc_fun @ SV1440 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3250]) ).
thf(3878,plain,
! [SV1441: $i,SV907: $i,SV295: $i] :
( ( ! [SY5342: $i] :
( ( c_Relation_ORange @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV295 @ SV907 @ ( tc_fun @ ( tc_prod @ SV1441 @ SY5342 ) @ tc_bool ) ) @ SV1441 @ SY5342 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_ORange @ SV295 @ SV1441 @ SY5342 ) @ ( c_Relation_ORange @ SV907 @ SV1441 @ SY5342 ) @ ( tc_fun @ SY5342 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3251]) ).
thf(3879,plain,
! [SV1442: $i,SV908: $i,SV296: $i] :
( ( ( c_Wellfounded_Owf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV296 @ SV908 @ ( tc_fun @ ( tc_prod @ SV1442 @ SV1442 ) @ tc_bool ) ) @ SV1442 )
| ~ ( c_Wellfounded_Owf @ SV296 @ SV1442 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3252]) ).
thf(3880,plain,
! [SV1443: $i,SV909: $i,SV297: $i] :
( ( ( c_Wellfounded_Owf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV297 @ SV909 @ ( tc_fun @ ( tc_prod @ SV1443 @ SV1443 ) @ tc_bool ) ) @ SV1443 )
| ~ ( c_Wellfounded_Owf @ SV909 @ SV1443 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3253]) ).
thf(3881,plain,
! [SV1444: $i,SV910: $i,SV298: $i] :
( ( ( ( c_Set_Oinsert @ SV298 @ ( c_HOL_Ominus__class_Ominus @ SV910 @ ( c_Set_Oinsert @ SV298 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1444 @ tc_bool ) ) @ SV1444 ) @ ( tc_fun @ SV1444 @ tc_bool ) ) @ SV1444 )
= SV910 )
| ~ ( c_in @ SV298 @ SV910 @ SV1444 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3254]) ).
thf(3882,plain,
! [SV299: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV299 )
= $false )
| ( ( ! [SY3153: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY3153 @ SY3153 @ SV299 )
= SY3153 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3255]) ).
thf(3883,plain,
! [SV912: $i,SV301: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV301 ) )
= $true )
| ( ( ! [SY4558: $i] :
( ( c_lessequals @ SV912 @ SY4558 @ SV301 )
| ! [SY4559: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4559 @ SV912 @ SV301 ) @ SY4558 @ SV301 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3257]) ).
thf(3884,plain,
! [SV913: $i,SV302: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV302 ) )
= $true )
| ( ( ! [SY4560: $i] :
( ( c_lessequals @ SV913 @ SY4560 @ SV302 )
| ! [SY4561: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV913 @ SY4561 @ SV302 ) @ SY4560 @ SV302 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3258]) ).
thf(3885,plain,
! [SV914: $i,SV303: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV303 ) )
= $true )
| ( ( ! [SY4562: $i,SY4563: $i] :
( ( c_lessequals @ SV914 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4562 @ SY4563 @ SV303 ) @ SV303 )
| ~ ( c_lessequals @ SV914 @ SY4563 @ SV303 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3259]) ).
thf(3886,plain,
! [SV915: $i,SV304: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV304 ) )
= $true )
| ( ( ! [SY4564: $i] :
( ! [SY4565: $i] : ( c_lessequals @ SV915 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4564 @ SY4565 @ SV304 ) @ SV304 )
| ~ ( c_lessequals @ SV915 @ SY4564 @ SV304 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3260]) ).
thf(3887,plain,
! [SV916: $i,SV305: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV305 ) )
= $true )
| ( ( ! [SY4566: $i] :
( ( c_lessequals @ SV916 @ SY4566 @ SV305 )
| ! [SY4567: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4567 @ SV916 @ SV305 ) @ SY4566 @ SV305 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3261]) ).
thf(3888,plain,
! [SV917: $i,SV306: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV306 ) )
= $true )
| ( ( ! [SY4568: $i] :
( ( c_lessequals @ SV917 @ SY4568 @ SV306 )
| ! [SY4569: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV917 @ SY4569 @ SV306 ) @ SY4568 @ SV306 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3262]) ).
thf(3889,plain,
! [SV1445: $i,SV918: $i,SV307: $i] :
( ( ( c_lessequals @ SV307 @ SV918 @ ( tc_fun @ SV1445 @ tc_bool ) )
| ! [SY5343: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV307 @ SY5343 @ ( tc_fun @ SV1445 @ tc_bool ) ) @ SV918 @ ( tc_fun @ SV1445 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3263]) ).
thf(3890,plain,
! [SV1446: $i,SV919: $i,SV308: $i] :
( ( ( c_lessequals @ SV308 @ SV919 @ ( tc_fun @ SV1446 @ tc_bool ) )
| ! [SY5344: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY5344 @ SV308 @ ( tc_fun @ SV1446 @ tc_bool ) ) @ SV919 @ ( tc_fun @ SV1446 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3264]) ).
thf(3891,plain,
! [SV920: $i,SV309: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV309 ) )
= $true )
| ( ( ! [SY4574: $i] :
( ( c_lessequals @ SV920 @ SY4574 @ SV309 )
| ! [SY4575: $i] :
( ~ ( c_lessequals @ SV920 @ SY4575 @ SV309 )
| ~ ( c_lessequals @ SY4575 @ SY4574 @ SV309 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3265]) ).
thf(3892,plain,
! [SV921: $i,SV310: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV310 ) )
= $true )
| ( ( ! [SY4576: $i] :
( ( c_lessequals @ SV921 @ SY4576 @ SV310 )
| ! [SY4577: $i] :
( ~ ( c_lessequals @ SY4577 @ SY4576 @ SV310 )
| ~ ( c_lessequals @ SV921 @ SY4577 @ SV310 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3266]) ).
thf(3893,plain,
! [SV1447: $i,SV924: $i,SV313: $i] :
( ( ( c_lessequals @ SV313 @ SV924 @ ( tc_fun @ SV1447 @ tc_bool ) )
| ! [SY5345: $i] :
( ~ ( c_lessequals @ SY5345 @ SV924 @ ( tc_fun @ SV1447 @ tc_bool ) )
| ~ ( c_lessequals @ SV313 @ SY5345 @ ( tc_fun @ SV1447 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3269]) ).
thf(3894,plain,
! [SV925: $i,SV314: $i] :
( ( ( hBOOL @ ( hAPP @ SV314 @ SV925 ) )
= $true )
| ( ( ! [SY4580: $i] :
( ~ ( hBOOL @ ( hAPP @ SY4580 @ SV925 ) )
| ! [SY3192: $i] :
~ ( c_lessequals @ SY4580 @ SV314 @ ( tc_fun @ SY3192 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3270]) ).
thf(3895,plain,
! [SV926: $i,SV315: $i] :
( ( ( c_Wellfounded_Owf @ SV315 @ SV926 )
= $true )
| ( ( ! [SY4582: $i] :
( ~ ( c_lessequals @ SV315 @ SY4582 @ ( tc_fun @ ( tc_prod @ SV926 @ SV926 ) @ tc_bool ) )
| ~ ( c_Wellfounded_Owf @ SY4582 @ SV926 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3271]) ).
thf(3896,plain,
! [SV316: $i] :
( ( ( class_Orderings_Oorder @ SV316 )
= $false )
| ( ( ! [SY3195: $i] : ( c_lessequals @ SY3195 @ SY3195 @ SV316 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3272]) ).
thf(3897,plain,
! [SV317: $i] :
( ( ( class_Orderings_Opreorder @ SV317 )
= $false )
| ( ( ! [SY3196: $i] : ( c_lessequals @ SY3196 @ SY3196 @ SV317 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3273]) ).
thf(3898,plain,
! [SV927: $i,SV318: $i] :
( ( ( c_Relation_Oantisym @ SV318 @ SV927 )
= $true )
| ( ( ! [SY4583: $i] :
( ~ ( c_Relation_Oantisym @ SY4583 @ SV927 )
| ~ ( c_lessequals @ SV318 @ SY4583 @ ( tc_fun @ ( tc_prod @ SV927 @ SV927 ) @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3274]) ).
thf(3899,plain,
! [SV928: $i,SV319: $i] :
( ( ( hBOOL @ ( hAPP @ SV319 @ SV928 ) )
= $true )
| ( ( ! [SY4584: $i] :
( ! [SY3201: $i] :
~ ( c_lessequals @ SY4584 @ SV319 @ ( tc_fun @ SY3201 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ SY4584 @ SV928 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3275]) ).
thf(3900,plain,
! [SV929: $i,SV320: $i] :
( ( ( c_Wellfounded_Oacyclic @ SV320 @ SV929 )
= $true )
| ( ( ! [SY4586: $i] :
( ~ ( c_lessequals @ SV320 @ SY4586 @ ( tc_fun @ ( tc_prod @ SV929 @ SV929 ) @ tc_bool ) )
| ~ ( c_Wellfounded_Oacyclic @ SY4586 @ SV929 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3276]) ).
thf(3901,plain,
! [SV1448: $i,SV930: $i,SV321: $i] :
( ( ( c_Relation_Osingle__valued @ SV321 @ SV930 @ SV1448 )
| ! [SY5346: $i] :
( ~ ( c_Relation_Osingle__valued @ SY5346 @ SV930 @ SV1448 )
| ~ ( c_lessequals @ SV321 @ SY5346 @ ( tc_fun @ ( tc_prod @ SV930 @ SV1448 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3277]) ).
thf(3902,plain,
! [SV1449: $i,SV931: $i,SV322: $i] :
( ( ! [SY5347: $i] :
( ( c_Set_Oimage @ SV322 @ SV931 @ SV1449 @ SY5347 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5347 @ tc_bool ) ) )
| ( SV931
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1449 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3278]) ).
thf(3903,plain,
! [SV1450: $i,SV932: $i,SV323: $i] :
( ( ! [SY5348: $i,SY5349: $i] :
( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV323 @ SV932 @ ( tc_fun @ SV1450 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY5348 @ SY5349 @ ( tc_fun @ SV1450 @ tc_bool ) ) @ ( tc_fun @ SV1450 @ tc_bool ) )
| ~ ( c_lessequals @ SV932 @ SY5349 @ ( tc_fun @ SV1450 @ tc_bool ) )
| ~ ( c_lessequals @ SV323 @ SY5348 @ ( tc_fun @ SV1450 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3279]) ).
thf(3904,plain,
! [SV1451: $i,SV933: $i,SV324: $i] :
( ( ! [SY5350: $i] :
( ( c_HOL_Ominus__class_Ominus @ SV324 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV933 @ SV1451 @ ( tc_fun @ SY5350 @ tc_bool ) ) @ ( tc_fun @ SY5350 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_HOL_Ominus__class_Ominus @ SV324 @ SV933 @ ( tc_fun @ SY5350 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV324 @ SV1451 @ ( tc_fun @ SY5350 @ tc_bool ) ) @ ( tc_fun @ SY5350 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3280]) ).
thf(3905,plain,
! [SV1452: $i,SV934: $i,SV325: $i] :
( ( ! [SY5351: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV325 @ SV934 @ ( tc_fun @ SV1452 @ tc_bool ) ) @ SY5351 @ ( tc_fun @ SV1452 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV325 @ ( c_HOL_Ominus__class_Ominus @ SV934 @ SY5351 @ ( tc_fun @ SV1452 @ tc_bool ) ) @ ( tc_fun @ SV1452 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3281]) ).
thf(3906,plain,
! [SV1453: $i,SV936: $i,SV327: $i] :
( ( ! [SY5352: $i] :
( ( c_lessequals @ ( c_Relation_ODomain @ SV327 @ SV936 @ SV1453 ) @ ( c_Relation_ODomain @ SY5352 @ SV936 @ SV1453 ) @ ( tc_fun @ SV936 @ tc_bool ) )
| ~ ( c_lessequals @ SV327 @ SY5352 @ ( tc_fun @ ( tc_prod @ SV936 @ SV1453 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3283]) ).
thf(3907,plain,
! [SV1454: $i,SV937: $i,SV328: $i] :
( ( ( SV328
= ( c_Set_Oinsert @ SV937 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1454 @ tc_bool ) ) @ SV1454 ) )
| ( SV328
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1454 @ tc_bool ) ) )
| ~ ( c_lessequals @ SV328 @ ( c_Set_Oinsert @ SV937 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1454 @ tc_bool ) ) @ SV1454 ) @ ( tc_fun @ SV1454 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3284]) ).
thf(3908,plain,
! [SV1455: $i,SV938: $i,SV329: $i] :
( ( ! [SY5353: $i] :
( ( c_HOL_Ominus__class_Ominus @ SV329 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV938 @ SV1455 @ ( tc_fun @ SY5353 @ tc_bool ) ) @ ( tc_fun @ SY5353 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ SV329 @ SV938 @ ( tc_fun @ SY5353 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV329 @ SV1455 @ ( tc_fun @ SY5353 @ tc_bool ) ) @ ( tc_fun @ SY5353 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3285]) ).
thf(3909,plain,
! [SV1456: $i,SV939: $i,SV330: $i] :
( ( ( c_Product__Type_OSigma @ SV330 @ ( c_COMBK @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV939 @ tc_bool ) ) @ ( tc_fun @ SV939 @ tc_bool ) @ SV1456 ) @ SV1456 @ SV939 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV1456 @ SV939 ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3286]) ).
thf(3910,plain,
! [SV1457: $i,SV940: $i,SV331: $i] :
( ( ! [SY5354: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV331 @ SV940 @ ( tc_fun @ SV1457 @ tc_bool ) ) @ SY5354 ) )
| ~ ( hBOOL @ ( hAPP @ SV940 @ SY5354 ) )
| ~ ( hBOOL @ ( hAPP @ SV331 @ SY5354 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3287]) ).
thf(3911,plain,
! [SV1458: $i,SV941: $i,SV332: $i] :
( ( ! [SY5355: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV332 @ ( c_HOL_Ominus__class_Ominus @ SV941 @ SV1458 @ ( tc_fun @ SY5355 @ tc_bool ) ) @ ( tc_fun @ SY5355 @ tc_bool ) )
= SV1458 )
| ~ ( c_lessequals @ SV332 @ SV941 @ ( tc_fun @ SY5355 @ tc_bool ) )
| ~ ( c_lessequals @ SV1458 @ SV332 @ ( tc_fun @ SY5355 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3288]) ).
thf(3912,plain,
! [SV1459: $i,SV942: $i,SV333: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV333 )
| ! [SY5356: $i,SY5357: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV942 @ SV1459 @ SV333 )
!= ( c_HOL_Ominus__class_Ominus @ SY5356 @ SY5357 @ SV333 ) )
| ( c_lessequals @ SY5357 @ SY5356 @ SV333 )
| ~ ( c_lessequals @ SV1459 @ SV942 @ SV333 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3289]) ).
thf(3913,plain,
! [SV1460: $i,SV943: $i,SV334: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV334 )
| ! [SY5358: $i,SY5359: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV943 @ SV1460 @ SV334 )
!= ( c_HOL_Ominus__class_Ominus @ SY5358 @ SY5359 @ SV334 ) )
| ( c_lessequals @ SV1460 @ SV943 @ SV334 )
| ~ ( c_lessequals @ SY5359 @ SY5358 @ SV334 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3290]) ).
thf(3914,plain,
! [SV1461: $i,SV944: $i,SV335: $i] :
( ( ! [SY5360: $i,SY5361: $i] :
( ( c_lessequals @ ( c_Set_Oimage @ SV335 @ SV944 @ SV1461 @ SY5360 ) @ ( c_Set_Oimage @ SV335 @ SY5361 @ SV1461 @ SY5360 ) @ ( tc_fun @ SY5360 @ tc_bool ) )
| ~ ( c_lessequals @ SV944 @ SY5361 @ ( tc_fun @ SV1461 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3291]) ).
thf(3915,plain,
! [SV1462: $i,SV945: $i,SV336: $i] :
( ( ~ ( c_lessequals @ SV336 @ SV945 @ ( tc_fun @ SV1462 @ tc_bool ) )
| ! [SY5362: $i,SY5363: $i] : ( c_lessequals @ ( c_Set_Oimage @ SY5362 @ SV336 @ SV1462 @ SY5363 ) @ ( c_Set_Oimage @ SY5362 @ SV945 @ SV1462 @ SY5363 ) @ ( tc_fun @ SY5363 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3292]) ).
thf(3916,plain,
! [SV1463: $i,SV946: $i,SV337: $i] :
( ( ! [SY5364: $i] :
( ( c_lessequals @ ( c_Set_Oinsert @ SV337 @ SV946 @ SV1463 ) @ ( c_Set_Oinsert @ SV337 @ SY5364 @ SV1463 ) @ ( tc_fun @ SV1463 @ tc_bool ) )
| ~ ( c_lessequals @ SV946 @ SY5364 @ ( tc_fun @ SV1463 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3293]) ).
thf(3917,plain,
! [SV1464: $i,SV947: $i,SV339: $i] :
( ( ! [SY5365: $i,SY5366: $i] :
( ( c_Set_Oimage @ SV339 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV947 @ SV1464 @ ( tc_fun @ SY5365 @ tc_bool ) ) @ SY5365 @ SY5366 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ SV339 @ SV947 @ SY5365 @ SY5366 ) @ ( c_Set_Oimage @ SV339 @ SV1464 @ SY5365 @ SY5366 ) @ ( tc_fun @ SY5366 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3294]) ).
thf(3918,plain,
! [SV1465: $i,SV948: $i,SV341: $i] :
( ( ! [SY5367: $i,SY5368: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV341 @ ( hAPP @ ( c_snd @ SV948 @ SV1465 ) @ ( c_Pair @ SY5367 @ SY5368 @ SV948 @ SV1465 ) ) ) @ ( hAPP @ ( c_fst @ SV948 @ SV1465 ) @ ( c_Pair @ SY5367 @ SY5368 @ SV948 @ SV1465 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV341 @ SY5368 ) @ SY5367 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3295]) ).
thf(3919,plain,
! [SV1466: $i,SV949: $i,SV342: $i] :
( ( ( ( c_Relation_ORange @ SV342 @ SV949 @ SV1466 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1466 @ tc_bool ) ) )
| ( SV342
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV949 @ SV1466 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3296]) ).
thf(3920,plain,
! [SV1467: $i,SV950: $i,SV343: $i] :
( ( ! [SY5369: $i,SY5370: $i,SY5371: $i] :
( ( c_lessequals @ ( c_Relation_OImage @ SV343 @ SV950 @ SV1467 @ SY5369 ) @ ( c_Relation_OImage @ SY5370 @ SY5371 @ SV1467 @ SY5369 ) @ ( tc_fun @ SY5369 @ tc_bool ) )
| ~ ( c_lessequals @ SV950 @ SY5371 @ ( tc_fun @ SV1467 @ tc_bool ) )
| ~ ( c_lessequals @ SV343 @ SY5370 @ ( tc_fun @ ( tc_prod @ SV1467 @ SY5369 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3297]) ).
thf(3921,plain,
! [SV1468: $i,SV951: $i,SV344: $i] :
( ( ( c_lessequals @ SV344 @ ( c_Product__Type_OSigma @ SV951 @ ( c_COMBK @ SV951 @ ( tc_fun @ SV1468 @ tc_bool ) @ SV1468 ) @ SV1468 @ SV1468 ) @ ( tc_fun @ ( tc_prod @ SV1468 @ SV1468 ) @ tc_bool ) )
| ~ ( c_Equiv__Relations_Oequiv @ SV951 @ SV344 @ SV1468 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3298]) ).
thf(3922,plain,
! [SV345: $i] :
( ( ( class_Orderings_Olinorder @ SV345 )
= $false )
| ( ( ! [SY3273: $i,SY3274: $i] :
( ( c_lessequals @ SY3273 @ SY3274 @ SV345 )
| ( c_lessequals @ SY3274 @ SY3273 @ SV345 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3299]) ).
thf(3923,plain,
! [SV952: $i,SV346: $i] :
( ( ( c_Relation_Oirrefl @ SV346 @ SV952 )
= $true )
| ( ( ! [SY4634: $i] :
~ ( c_Order__Relation_Ostrict__linear__order__on @ SY4634 @ SV346 @ SV952 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3300]) ).
thf(3924,plain,
! [SV1469: $i,SV953: $i,SV347: $i] :
( ( ! [SY5372: $i] :
( ( c_Wellfounded_Oacyclic @ ( c_Set_Oinsert @ ( c_Pair @ SV347 @ SV953 @ SV1469 @ SV1469 ) @ SY5372 @ ( tc_prod @ SV1469 @ SV1469 ) ) @ SV1469 )
| ( c_in @ ( c_Pair @ SV953 @ SV347 @ SV1469 @ SV1469 ) @ ( c_Transitive__Closure_Ortrancl @ SY5372 @ SV1469 ) @ ( tc_prod @ SV1469 @ SV1469 ) )
| ~ ( c_Wellfounded_Oacyclic @ SY5372 @ SV1469 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3301]) ).
thf(3925,plain,
! [SV1470: $i,SV954: $i,SV348: $i] :
( ( ! [SY5373: $i] :
( ~ ( c_in @ ( c_Pair @ SV348 @ SV954 @ SV1470 @ SV1470 ) @ ( c_Transitive__Closure_Ortrancl @ SY5373 @ SV1470 ) @ ( tc_prod @ SV1470 @ SV1470 ) )
| ~ ( c_Wellfounded_Oacyclic @ ( c_Set_Oinsert @ ( c_Pair @ SV954 @ SV348 @ SV1470 @ SV1470 ) @ SY5373 @ ( tc_prod @ SV1470 @ SV1470 ) ) @ SV1470 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3302]) ).
thf(3926,plain,
! [SV1471: $i,SV955: $i,SV349: $i] :
( ( ( hBOOL @ ( hAPP @ SV349 @ SV955 ) )
| ! [SY5374: $i,SY5375: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1 @ SV349 @ SV1471 @ SY5374 @ SY5375 ) @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 @ SV349 @ SV1471 @ SY5374 @ SY5375 ) @ SY5375 @ SY5375 ) @ SY5374 @ ( tc_prod @ SY5375 @ SY5375 ) )
| ~ ( hBOOL @ ( hAPP @ SV349 @ SV1471 ) )
| ~ ( c_in @ ( c_Pair @ SV955 @ SV1471 @ SY5375 @ SY5375 ) @ ( c_Transitive__Closure_Ortrancl @ SY5374 @ SY5375 ) @ ( tc_prod @ SY5375 @ SY5375 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3303]) ).
thf(3927,plain,
! [SV1472: $i,SV956: $i,SV350: $i] :
( ( ( hBOOL @ ( hAPP @ SV350 @ SV956 ) )
| ! [SY5376: $i,SY5377: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 @ SV350 @ SV1472 @ SY5376 @ SY5377 ) @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2 @ SV350 @ SV1472 @ SY5376 @ SY5377 ) @ SY5377 @ SY5377 ) @ SY5376 @ ( tc_prod @ SY5377 @ SY5377 ) )
| ~ ( hBOOL @ ( hAPP @ SV350 @ SV1472 ) )
| ~ ( c_in @ ( c_Pair @ SV1472 @ SV956 @ SY5377 @ SY5377 ) @ ( c_Transitive__Closure_Ortrancl @ SY5376 @ SY5377 ) @ ( tc_prod @ SY5377 @ SY5377 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3304]) ).
thf(3928,plain,
! [SV1473: $i,SV957: $i,SV351: $i] :
( ( ( c_in @ SV351 @ ( c_Relation_OImage @ SV957 @ ( c_Set_Oinsert @ SV351 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1473 @ tc_bool ) ) @ SV1473 ) @ SV1473 @ SV1473 ) @ SV1473 )
| ! [SY5378: $i] :
( ~ ( c_in @ SV351 @ SY5378 @ SV1473 )
| ~ ( c_Equiv__Relations_Oequiv @ SY5378 @ SV957 @ SV1473 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3305]) ).
thf(3929,plain,
! [SV1474: $i,SV958: $i,SV352: $i] :
( ( ( c_lessequals @ ( c_Transitive__Closure_Ortrancl @ SV352 @ SV958 ) @ SV1474 @ ( tc_fun @ ( tc_prod @ SV958 @ SV958 ) @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Relation_Orel__comp @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Transitive__Closure_Ortrancl @ SV352 @ SV958 ) @ SV1474 @ ( tc_fun @ ( tc_prod @ SV958 @ SV958 ) @ tc_bool ) ) @ SV352 @ SV958 @ SV958 @ SV958 ) @ SV1474 @ ( tc_fun @ ( tc_prod @ SV958 @ SV958 ) @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Relation_OId @ SV958 ) @ SV1474 @ ( tc_fun @ ( tc_prod @ SV958 @ SV958 ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3306]) ).
thf(3930,plain,
! [SV1475: $i,SV959: $i,SV353: $i] :
( ( ! [SY5379: $i] :
( ( c_in @ ( c_Pair @ SV353 @ SV959 @ SV1475 @ SV1475 ) @ SY5379 @ ( tc_prod @ SV1475 @ SV1475 ) )
| ! [SY5380: $i] :
~ ( c_in @ SY5380 @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_OImage @ SY5379 @ ( c_Set_Oinsert @ SV353 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1475 @ tc_bool ) ) @ SV1475 ) @ SV1475 @ SV1475 ) @ ( c_Relation_OImage @ SY5379 @ ( c_Set_Oinsert @ SV959 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1475 @ tc_bool ) ) @ SV1475 ) @ SV1475 @ SV1475 ) @ ( tc_fun @ SV1475 @ tc_bool ) ) @ SV1475 )
| ! [SY5381: $i] :
~ ( c_Equiv__Relations_Oequiv @ SY5381 @ SY5379 @ SV1475 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3307]) ).
thf(3931,plain,
! [SV1476: $i,SV960: $i,SV354: $i] :
( ( ! [SY5382: $i] :
( ( c_in @ ( c_Pair @ SV354 @ SV960 @ SV1476 @ SV1476 ) @ SY5382 @ ( tc_prod @ SV1476 @ SV1476 ) )
| ! [SY5383: $i] :
( ~ ( c_in @ SV960 @ SY5383 @ SV1476 )
| ~ ( c_lessequals @ ( c_Relation_OImage @ SY5382 @ ( c_Set_Oinsert @ SV960 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1476 @ tc_bool ) ) @ SV1476 ) @ SV1476 @ SV1476 ) @ ( c_Relation_OImage @ SY5382 @ ( c_Set_Oinsert @ SV354 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1476 @ tc_bool ) ) @ SV1476 ) @ SV1476 @ SV1476 ) @ ( tc_fun @ SV1476 @ tc_bool ) )
| ~ ( c_Equiv__Relations_Oequiv @ SY5383 @ SY5382 @ SV1476 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3308]) ).
thf(3932,plain,
! [SV1477: $i,SV961: $i,SV355: $i] :
( ( ! [SY5384: $i] :
( ! [SY5385: $i] :
( ( c_Set_Oinsert @ ( hAPP @ SV355 @ SV961 ) @ ( c_Set_Oimage @ SV355 @ SV1477 @ SY5384 @ SY5385 ) @ SY5385 )
= ( c_Set_Oimage @ SV355 @ SV1477 @ SY5384 @ SY5385 ) )
| ~ ( c_in @ SV961 @ SV1477 @ SY5384 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3309]) ).
thf(3933,plain,
! [SV1478: $i,SV962: $i,SV356: $i] :
( ( ! [SY5386: $i] :
( ( c_in @ ( hAPP @ SV356 @ SV962 ) @ SV1478 @ SY5386 )
| ! [SY5387: $i,SY5388: $i] :
( ~ ( c_in @ SV962 @ SY5387 @ SY5388 )
| ~ ( c_lessequals @ ( c_Set_Oimage @ SV356 @ SY5387 @ SY5388 @ SY5386 ) @ SV1478 @ ( tc_fun @ SY5386 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3310]) ).
thf(3934,plain,
! [SV1479: $i,SV963: $i,SV357: $i] :
( ( ! [SY5389: $i,SY5390: $i] :
( ( c_in @ ( c_Pair @ SV357 @ SV963 @ SV1479 @ SY5389 ) @ SY5390 @ ( tc_prod @ SV1479 @ SY5389 ) )
| ~ ( c_in @ SV963 @ ( c_Relation_OImage @ SY5390 @ ( c_Set_Oinsert @ SV357 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1479 @ tc_bool ) ) @ SV1479 ) @ SV1479 @ SY5389 ) @ SY5389 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3311]) ).
thf(3935,plain,
! [SV1480: $i,SV964: $i,SV358: $i] :
( ( ! [SY5391: $i,SY5392: $i] :
( ( c_in @ SV358 @ ( c_Relation_OImage @ SV964 @ ( c_Set_Oinsert @ SV1480 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5391 @ tc_bool ) ) @ SY5391 ) @ SY5391 @ SY5392 ) @ SY5392 )
| ~ ( c_in @ ( c_Pair @ SV1480 @ SV358 @ SY5391 @ SY5392 ) @ SV964 @ ( tc_prod @ SY5391 @ SY5392 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3312]) ).
thf(3936,plain,
! [SV1481: $i,SV965: $i,SV359: $i] :
( ( ! [SY5393: $i,SY5394: $i] :
( ( ( c_Product__Type_OSigma @ SV359 @ ( c_COMBK @ SV965 @ ( tc_fun @ SV1481 @ tc_bool ) @ SY5393 ) @ SY5393 @ SV1481 )
!= ( c_Product__Type_OSigma @ SY5394 @ ( c_COMBK @ SV965 @ ( tc_fun @ SV1481 @ tc_bool ) @ SY5393 ) @ SY5393 @ SV1481 ) )
| ! [SY5395: $i] :
~ ( c_in @ SY5395 @ SV965 @ SV1481 )
| ( SV359 = SY5394 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3313]) ).
thf(3937,plain,
! [SV966: $i,SV360: $i] :
( ( ( c_Wellfounded_Owf @ SV360 @ SV966 )
= $true )
| ( ( ! [SY4672: $i,SY4673: $i] :
~ ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ SY4672 @ SY4673 @ SV966 @ SV966 ) @ SV360 @ ( tc_prod @ SV966 @ SV966 ) ) @ SV966 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3314]) ).
thf(3938,plain,
! [SV1482: $i,SV967: $i,SV361: $i] :
( ( ! [SY5396: $i] :
( ( c_in @ SV361 @ ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV967 @ SV1482 @ ( tc_fun @ ( tc_prod @ SY5396 @ SY5396 ) @ tc_bool ) ) @ SY5396 ) @ ( tc_prod @ SY5396 @ SY5396 ) )
| ~ ( c_in @ SV361 @ ( c_Transitive__Closure_Ortrancl @ SV967 @ SY5396 ) @ ( tc_prod @ SY5396 @ SY5396 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3315]) ).
thf(3939,plain,
! [SV1483: $i,SV968: $i,SV362: $i] :
( ( ! [SY5397: $i] :
( ( c_in @ SV362 @ ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV968 @ SV1483 @ ( tc_fun @ ( tc_prod @ SY5397 @ SY5397 ) @ tc_bool ) ) @ SY5397 ) @ ( tc_prod @ SY5397 @ SY5397 ) )
| ~ ( c_in @ SV362 @ ( c_Transitive__Closure_Ortrancl @ SV1483 @ SY5397 ) @ ( tc_prod @ SY5397 @ SY5397 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3316]) ).
thf(3940,plain,
! [SV1484: $i,SV969: $i,SV363: $i] :
( ( ( c_in @ SV363 @ ( c_Transitive__Closure_Otrancl @ SV969 @ SV1484 ) @ ( tc_prod @ SV1484 @ SV1484 ) )
| ! [SY5398: $i] :
( ~ ( c_lessequals @ SY5398 @ SV969 @ ( tc_fun @ ( tc_prod @ SV1484 @ SV1484 ) @ tc_bool ) )
| ~ ( c_in @ SV363 @ ( c_Transitive__Closure_Otrancl @ SY5398 @ SV1484 ) @ ( tc_prod @ SV1484 @ SV1484 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3317]) ).
thf(3941,plain,
! [SV1485: $i,SV970: $i,SV364: $i] :
( ( ! [SY5399: $i] :
( ( ( c_Relation_OImage @ SV364 @ ( c_Set_Oinsert @ SV970 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1485 @ tc_bool ) ) @ SV1485 ) @ SV1485 @ SV1485 )
= ( c_Relation_OImage @ SV364 @ ( c_Set_Oinsert @ SY5399 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1485 @ tc_bool ) ) @ SV1485 ) @ SV1485 @ SV1485 ) )
| ~ ( c_in @ ( c_Pair @ SV970 @ SY5399 @ SV1485 @ SV1485 ) @ SV364 @ ( tc_prod @ SV1485 @ SV1485 ) )
| ! [SY5400: $i] :
~ ( c_Equiv__Relations_Oequiv @ SY5400 @ SV364 @ SV1485 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3318]) ).
thf(3942,plain,
! [SV1486: $i,SV971: $i,SV365: $i] :
( ( ! [SY5401: $i] :
( ( ( c_Relation_OImage @ SV365 @ ( c_Set_Oinsert @ SV971 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1486 @ tc_bool ) ) @ SV1486 ) @ SV1486 @ SV1486 )
= ( c_Relation_OImage @ SV365 @ ( c_Set_Oinsert @ SY5401 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1486 @ tc_bool ) ) @ SV1486 ) @ SV1486 @ SV1486 ) )
| ~ ( c_in @ ( c_Pair @ SV971 @ SY5401 @ SV1486 @ SV1486 ) @ SV365 @ ( tc_prod @ SV1486 @ SV1486 ) )
| ! [SY5402: $i] :
~ ( c_Equiv__Relations_Oequiv @ SY5402 @ SV365 @ SV1486 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3319]) ).
thf(3943,plain,
! [SV1487: $i,SV972: $i,SV366: $i] :
( ( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ SV366 @ SV366 @ SV972 @ SV972 @ SV972 ) @ ( c_Relation_Orel__comp @ SV1487 @ SV366 @ SV972 @ SV972 @ SV972 ) @ ( tc_fun @ ( tc_prod @ SV972 @ SV972 ) @ tc_bool ) ) @ SV1487 @ ( tc_fun @ ( tc_prod @ SV972 @ SV972 ) @ tc_bool ) ) @ SV972 )
| ~ ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV366 @ SV1487 @ ( tc_fun @ ( tc_prod @ SV972 @ SV972 ) @ tc_bool ) ) @ SV972 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3320]) ).
thf(3944,plain,
! [SV1488: $i,SV973: $i,SV367: $i] :
( ( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV367 @ SV973 @ ( tc_fun @ ( tc_prod @ SV1488 @ SV1488 ) @ tc_bool ) ) @ SV1488 )
| ~ ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ SV367 @ SV367 @ SV1488 @ SV1488 @ SV1488 ) @ ( c_Relation_Orel__comp @ SV973 @ SV367 @ SV1488 @ SV1488 @ SV1488 ) @ ( tc_fun @ ( tc_prod @ SV1488 @ SV1488 ) @ tc_bool ) ) @ SV973 @ ( tc_fun @ ( tc_prod @ SV1488 @ SV1488 ) @ tc_bool ) ) @ SV1488 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3321]) ).
thf(3945,plain,
! [SV974: $i,SV368: $i] :
( ( ( ( c_Relation_Orel__comp @ SV368 @ SV368 @ SV974 @ SV974 @ SV974 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV974 @ SV974 ) @ tc_bool ) ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV368 @ SV974 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3322]) ).
thf(3946,plain,
! [SV979: $i,SV374: $i] :
( ( ( c_Relation_Oantisym @ ( c_Transitive__Closure_Ortrancl @ SV374 @ SV979 ) @ SV979 )
= $true )
| ( ( ~ ( c_Wellfounded_Oacyclic @ SV374 @ SV979 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3327]) ).
thf(3947,plain,
! [SV980: $i,SV375: $i] :
( ( ( c_lessequals @ ( c_Relation_Orel__comp @ SV375 @ SV375 @ SV980 @ SV980 @ SV980 ) @ SV375 @ ( tc_fun @ ( tc_prod @ SV980 @ SV980 ) @ tc_bool ) )
= $true )
| ( ( ~ ( c_Relation_Otrans @ SV375 @ SV980 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3328]) ).
thf(3948,plain,
! [SV983: $i,SV378: $i] :
( ( ( c_Relation_Otrans @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV378 @ ( c_Relation_OId @ SV983 ) @ ( tc_fun @ ( tc_prod @ SV983 @ SV983 ) @ tc_bool ) ) @ SV983 )
= $true )
| ( ( ~ ( c_Relation_Otrans @ SV378 @ SV983 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3331]) ).
thf(3949,plain,
! [SV1489: $i,SV984: $i,SV379: $i] :
( ( ( c_Relation_OImage @ ( c_Relation_OId__on @ SV379 @ SV984 ) @ SV1489 @ SV984 @ SV984 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV379 @ SV1489 @ ( tc_fun @ SV984 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3332]) ).
thf(3950,plain,
! [SV985: $i,SV380: $i] :
( ( ( c_Relation_Oantisym @ SV380 @ SV985 )
= $true )
| ( ( ~ ( c_Relation_Oantisym @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV380 @ ( c_Relation_OId @ SV985 ) @ ( tc_fun @ ( tc_prod @ SV985 @ SV985 ) @ tc_bool ) ) @ SV985 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3333]) ).
thf(3951,plain,
! [SV986: $i,SV381: $i] :
( ( ( c_Relation_Oantisym @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV381 @ ( c_Relation_OId @ SV986 ) @ ( tc_fun @ ( tc_prod @ SV986 @ SV986 ) @ tc_bool ) ) @ SV986 )
= $true )
| ( ( ~ ( c_Relation_Oantisym @ SV381 @ SV986 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3334]) ).
thf(3952,plain,
! [SV1490: $i,SV987: $i,SV382: $i] :
( ( ( c_Relation_Ototal__on @ SV382 @ SV987 @ SV1490 )
| ~ ( c_Relation_Ototal__on @ SV382 @ ( c_HOL_Ominus__class_Ominus @ SV987 @ ( c_Relation_OId @ SV1490 ) @ ( tc_fun @ ( tc_prod @ SV1490 @ SV1490 ) @ tc_bool ) ) @ SV1490 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3335]) ).
thf(3953,plain,
! [SV1491: $i,SV988: $i,SV383: $i] :
( ( ( c_Relation_Ototal__on @ SV383 @ ( c_HOL_Ominus__class_Ominus @ SV988 @ ( c_Relation_OId @ SV1491 ) @ ( tc_fun @ ( tc_prod @ SV1491 @ SV1491 ) @ tc_bool ) ) @ SV1491 )
| ~ ( c_Relation_Ototal__on @ SV383 @ SV988 @ SV1491 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3336]) ).
thf(3954,plain,
! [SV989: $i,SV384: $i] :
( ( ( c_lessequals @ ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ SV384 @ SV989 @ SV989 ) @ SV384 @ SV989 @ SV989 @ SV989 ) @ SV384 @ ( tc_fun @ ( tc_prod @ SV989 @ SV989 ) @ tc_bool ) )
= $true )
| ( ( ~ ( c_Relation_Otrans @ SV384 @ SV989 )
| ~ ( c_Relation_Osym @ SV384 @ SV989 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3337]) ).
thf(3955,plain,
! [SV1492: $i,SV990: $i,SV385: $i] :
( ( ! [SY5403: $i] :
( ( c_in @ ( c_Pair @ SV385 @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1 @ SV990 @ SV385 @ SV1492 @ SY5403 ) @ SY5403 @ SY5403 ) @ ( c_Transitive__Closure_Ortrancl @ SV990 @ SY5403 ) @ ( tc_prod @ SY5403 @ SY5403 ) )
| ~ ( c_in @ ( c_Pair @ SV385 @ SV1492 @ SY5403 @ SY5403 ) @ ( c_Transitive__Closure_Otrancl @ SV990 @ SY5403 ) @ ( tc_prod @ SY5403 @ SY5403 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3338]) ).
thf(3956,plain,
! [SV1493: $i,SV991: $i,SV386: $i] :
( ( ! [SY5404: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1 @ SV386 @ SV991 @ SV1493 @ SY5404 ) @ SV1493 @ SY5404 @ SY5404 ) @ ( c_Transitive__Closure_Ortrancl @ SV386 @ SY5404 ) @ ( tc_prod @ SY5404 @ SY5404 ) )
| ~ ( c_in @ ( c_Pair @ SV991 @ SV1493 @ SY5404 @ SY5404 ) @ ( c_Transitive__Closure_Otrancl @ SV386 @ SY5404 ) @ ( tc_prod @ SY5404 @ SY5404 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3339]) ).
thf(3957,plain,
! [SV1494: $i,SV992: $i,SV387: $i] :
( ( ! [SY5405: $i] :
( ~ ( c_in @ ( c_Pair @ SV387 @ SV992 @ SV1494 @ SV1494 ) @ ( c_Transitive__Closure_Ortrancl @ SY5405 @ SV1494 ) @ ( tc_prod @ SV1494 @ SV1494 ) )
| ~ ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ SV992 @ SV387 @ SV1494 @ SV1494 ) @ SY5405 @ ( tc_prod @ SV1494 @ SV1494 ) ) @ SV1494 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3340]) ).
thf(3958,plain,
! [SV1495: $i,SV993: $i,SV388: $i] :
( ( ! [SY5406: $i] :
( ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ SV388 @ SV993 @ SV1495 @ SV1495 ) @ SY5406 @ ( tc_prod @ SV1495 @ SV1495 ) ) @ SV1495 )
| ( c_in @ ( c_Pair @ SV993 @ SV388 @ SV1495 @ SV1495 ) @ ( c_Transitive__Closure_Ortrancl @ SY5406 @ SV1495 ) @ ( tc_prod @ SV1495 @ SV1495 ) )
| ~ ( c_Wellfounded_Owf @ SY5406 @ SV1495 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3341]) ).
thf(3959,plain,
! [SV1496: $i,SV994: $i,SV389: $i] :
( ( ( c_Order__Relation_Ostrict__linear__order__on @ SV389 @ SV994 @ SV1496 )
| ~ ( c_Relation_Ototal__on @ SV389 @ SV994 @ SV1496 )
| ~ ( c_Relation_Oirrefl @ SV994 @ SV1496 )
| ~ ( c_Relation_Otrans @ SV994 @ SV1496 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3342]) ).
thf(3960,plain,
! [SV995: $i,SV390: $i] :
( ( ( c_Nitpick_Orefl_H @ SV390 @ SV995 )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ ( c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1 @ SV390 @ SV995 ) @ ( c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1 @ SV390 @ SV995 ) @ SV995 @ SV995 ) @ SV390 @ ( tc_prod @ SV995 @ SV995 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3343]) ).
thf(3961,plain,
! [SV996: $i,SV391: $i] :
( ( ( c_Relation_Otrans @ ( c_HOL_Ominus__class_Ominus @ SV391 @ ( c_Relation_OId @ SV996 ) @ ( tc_fun @ ( tc_prod @ SV996 @ SV996 ) @ tc_bool ) ) @ SV996 )
= $true )
| ( ( ~ ( c_Relation_Oantisym @ SV391 @ SV996 )
| ~ ( c_Relation_Otrans @ SV391 @ SV996 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3344]) ).
thf(3962,plain,
! [SV1497: $i,SV997: $i,SV392: $i] :
( ( ! [SY5407: $i,SY5408: $i] :
( ( ( c_Relation_OImage @ SV392 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV997 @ SV1497 @ ( tc_fun @ SY5407 @ tc_bool ) ) @ SY5407 @ SY5408 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_OImage @ SV392 @ SV997 @ SY5407 @ SY5408 ) @ ( c_Relation_OImage @ SV392 @ SV1497 @ SY5407 @ SY5408 ) @ ( tc_fun @ SY5408 @ tc_bool ) ) )
| ~ ( c_Relation_Osingle__valued @ ( c_Relation_Oconverse @ SV392 @ SY5407 @ SY5408 ) @ SY5408 @ SY5407 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3345]) ).
thf(3963,plain,
! [SV998: $i,SV393: $i] :
( ( ( c_Relation_Oirrefl @ SV393 @ SV998 )
= $true )
| ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1 @ SV393 @ SV998 ) @ ( c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1 @ SV393 @ SV998 ) @ SV998 @ SV998 ) @ SV393 @ ( tc_prod @ SV998 @ SV998 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3346]) ).
thf(3964,plain,
! [SV999: $i,SV394: $i] :
( ( ( c_lessequals @ SV394 @ ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ SV394 @ SV999 @ SV999 ) @ SV394 @ SV999 @ SV999 @ SV999 ) @ ( tc_fun @ ( tc_prod @ SV999 @ SV999 ) @ tc_bool ) )
= $true )
| ( ( ! [SY4703: $i] :
~ ( c_Relation_Orefl__on @ SY4703 @ SV394 @ SV999 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3347]) ).
thf(3965,plain,
! [SV1498: $i,SV1004: $i,SV399: $i] :
( ( ! [SY5409: $i,SY5410: $i,SY5411: $i] :
( ( ( c_Recdef_Ocut @ SV399 @ SV1004 @ SV1498 @ SY5409 @ SY5410 )
= ( c_Recdef_Ocut @ SY5411 @ SV1004 @ SV1498 @ SY5409 @ SY5410 ) )
| ( c_in @ ( c_Pair @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ SV399 @ SY5411 @ SV1004 @ SV1498 @ SY5409 @ SY5410 ) @ SV1498 @ SY5409 @ SY5409 ) @ SV1004 @ ( tc_prod @ SY5409 @ SY5409 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3352]) ).
thf(3966,plain,
! [SV1499: $i,SV1005: $i,SV400: $i] :
( ( ( SV400
= ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XId__onE__1__1 @ SV1005 @ SV400 @ SV1499 ) @ ( c_ATP__Linkup_Osko__Relation__XId__onE__1__1 @ SV1005 @ SV400 @ SV1499 ) @ SV1499 @ SV1499 ) )
| ~ ( c_in @ SV400 @ ( c_Relation_OId__on @ SV1005 @ SV1499 ) @ ( tc_prod @ SV1499 @ SV1499 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3353]) ).
thf(3967,plain,
! [SV1500: $i,SV1006: $i,SV401: $i] :
( ( ( c_in @ ( c_ATP__Linkup_Osko__Relation__XId__onE__1__1 @ SV401 @ SV1006 @ SV1500 ) @ SV401 @ SV1500 )
| ~ ( c_in @ SV1006 @ ( c_Relation_OId__on @ SV401 @ SV1500 ) @ ( tc_prod @ SV1500 @ SV1500 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3354]) ).
thf(3968,plain,
! [SV1007: $i,SV402: $i] :
( ( ( c_Wellfounded_Owf @ SV402 @ SV1007 )
= $true )
| ( ( ~ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1 @ SV402 @ SV1007 ) @ ( c_Wellfounded_Oacc @ SV402 @ SV1007 ) @ SV1007 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3355]) ).
thf(3969,plain,
! [SV1008: $i,SV403: $i] :
( ( ( c_Wellfounded_Owf @ SV403 @ SV1008 )
= $true )
| ( ( ~ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1 @ SV403 @ SV1008 ) @ ( c_Wellfounded_Oacc @ SV403 @ SV1008 ) @ SV1008 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3356]) ).
thf(3970,plain,
! [SV1009: $i,SV404: $i] :
( ( ( SV404
= ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XIdE__1__1 @ SV404 @ SV1009 ) @ ( c_ATP__Linkup_Osko__Relation__XIdE__1__1 @ SV404 @ SV1009 ) @ SV1009 @ SV1009 ) )
= $true )
| ( ( ~ ( c_in @ SV404 @ ( c_Relation_OId @ SV1009 ) @ ( tc_prod @ SV1009 @ SV1009 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3357]) ).
thf(3971,plain,
! [SV1501: $i,SV1010: $i,SV405: $i] :
( ( ! [SY5412: $i,SY5413: $i,SY5414: $i,SY5415: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 @ SV405 @ SV1010 @ SV1501 @ SY5412 @ SY5413 @ SY5414 @ SY5415 ) @ SV1010 @ SY5415 @ SY5414 ) @ SY5412 @ ( tc_prod @ SY5415 @ SY5414 ) )
| ~ ( c_in @ ( c_Pair @ SV405 @ SV1010 @ SY5413 @ SY5414 ) @ ( c_Relation_Orel__comp @ SV1501 @ SY5412 @ SY5413 @ SY5415 @ SY5414 ) @ ( tc_prod @ SY5413 @ SY5414 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3358]) ).
thf(3972,plain,
! [SV1502: $i,SV1011: $i,SV406: $i] :
( ( ! [SY5416: $i,SY5417: $i,SY5418: $i,SY5419: $i] :
( ( c_in @ ( c_Pair @ SV406 @ ( c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 @ SV406 @ SV1011 @ SV1502 @ SY5416 @ SY5417 @ SY5418 @ SY5419 ) @ SY5417 @ SY5419 ) @ SV1502 @ ( tc_prod @ SY5417 @ SY5419 ) )
| ~ ( c_in @ ( c_Pair @ SV406 @ SV1011 @ SY5417 @ SY5418 ) @ ( c_Relation_Orel__comp @ SV1502 @ SY5416 @ SY5417 @ SY5419 @ SY5418 ) @ ( tc_prod @ SY5417 @ SY5418 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3359]) ).
thf(3973,plain,
! [SV1503: $i,SV1012: $i,SV407: $i] :
( ( ~ ( c_in @ ( c_Pair @ SV407 @ SV407 @ SV1012 @ SV1012 ) @ SV1503 @ ( tc_prod @ SV1012 @ SV1012 ) )
| ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1 @ SV1503 @ SV1012 ) @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1 @ SV1503 @ SV1012 ) @ SV1012 @ SV1012 ) @ ( c_Transitive__Closure_Otrancl @ SV1503 @ SV1012 ) @ ( tc_prod @ SV1012 @ SV1012 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3360]) ).
thf(3974,plain,
! [SV1504: $i,SV1013: $i,SV408: $i] :
( ( ! [SY5420: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1 @ SV408 @ SV1013 @ SV1504 @ SY5420 ) @ SV1504 @ SY5420 @ SY5420 ) @ ( c_Transitive__Closure_Otrancl @ SV408 @ SY5420 ) @ ( tc_prod @ SY5420 @ SY5420 ) )
| ( c_in @ ( c_Pair @ SV1013 @ SV1504 @ SY5420 @ SY5420 ) @ SV408 @ ( tc_prod @ SY5420 @ SY5420 ) )
| ~ ( c_in @ ( c_Pair @ SV1013 @ SV1504 @ SY5420 @ SY5420 ) @ ( c_Transitive__Closure_Otrancl @ SV408 @ SY5420 ) @ ( tc_prod @ SY5420 @ SY5420 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3361]) ).
thf(3975,plain,
! [SV1505: $i,SV1014: $i,SV409: $i] :
( ( ! [SY5421: $i] :
( ( c_in @ ( c_Pair @ SV409 @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1 @ SV1014 @ SV409 @ SV1505 @ SY5421 ) @ SY5421 @ SY5421 ) @ SV1014 @ ( tc_prod @ SY5421 @ SY5421 ) )
| ~ ( c_in @ ( c_Pair @ SV409 @ SV1505 @ SY5421 @ SY5421 ) @ ( c_Transitive__Closure_Otrancl @ SV1014 @ SY5421 ) @ ( tc_prod @ SY5421 @ SY5421 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3362]) ).
thf(3976,plain,
! [SV1506: $i,SV1015: $i,SV410: $i] :
( ( ( c_in @ ( c_Pair @ SV410 @ ( v_sko__Transitive__Closure__Xtrancl__Xcases__1 @ SV410 @ SV1015 @ SV1506 ) @ t_a @ t_a ) @ ( c_Transitive__Closure_Otrancl @ SV1506 @ t_a ) @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ ( c_Pair @ SV410 @ SV1015 @ t_a @ t_a ) @ SV1506 @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ ( c_Pair @ SV410 @ SV1015 @ t_a @ t_a ) @ ( c_Transitive__Closure_Otrancl @ SV1506 @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3363]) ).
thf(3977,plain,
! [SV1507: $i,SV1016: $i,SV411: $i] :
( ( ~ ( c_in @ ( c_Pair @ SV411 @ SV411 @ SV1016 @ SV1016 ) @ ( c_Transitive__Closure_Otrancl @ SV1507 @ SV1016 ) @ ( tc_prod @ SV1016 @ SV1016 ) )
| ~ ( c_Wellfounded_Oacyclic @ SV1507 @ SV1016 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3364]) ).
thf(3978,plain,
! [SV1508: $i,SV1017: $i,SV412: $i] :
( ( ! [SY5422: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1 @ SV412 @ SV1017 @ SV1508 @ SY5422 ) @ SV1017 @ SY5422 @ SY5422 ) @ SV1508 @ ( tc_prod @ SY5422 @ SY5422 ) )
| ( c_in @ ( c_Pair @ SV412 @ SV1017 @ SY5422 @ SY5422 ) @ SV1508 @ ( tc_prod @ SY5422 @ SY5422 ) )
| ~ ( c_in @ ( c_Pair @ SV412 @ SV1017 @ SY5422 @ SY5422 ) @ ( c_Transitive__Closure_Otrancl @ SV1508 @ SY5422 ) @ ( tc_prod @ SY5422 @ SY5422 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3365]) ).
thf(3979,plain,
! [SV1509: $i,SV1018: $i,SV413: $i] :
( ( ! [SY5423: $i] :
( ( c_in @ ( c_Pair @ SV413 @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1 @ SV413 @ SV1018 @ SV1509 @ SY5423 ) @ SY5423 @ SY5423 ) @ ( c_Transitive__Closure_Otrancl @ SV1509 @ SY5423 ) @ ( tc_prod @ SY5423 @ SY5423 ) )
| ( c_in @ ( c_Pair @ SV413 @ SV1018 @ SY5423 @ SY5423 ) @ SV1509 @ ( tc_prod @ SY5423 @ SY5423 ) )
| ~ ( c_in @ ( c_Pair @ SV413 @ SV1018 @ SY5423 @ SY5423 ) @ ( c_Transitive__Closure_Otrancl @ SV1509 @ SY5423 ) @ ( tc_prod @ SY5423 @ SY5423 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3366]) ).
thf(3980,plain,
! [SV1510: $i,SV1019: $i,SV414: $i] :
( ( ! [SY5424: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1 @ SV414 @ SV1019 @ SV1510 @ SY5424 ) @ SV1510 @ SY5424 @ SY5424 ) @ SV414 @ ( tc_prod @ SY5424 @ SY5424 ) )
| ~ ( c_in @ ( c_Pair @ SV1019 @ SV1510 @ SY5424 @ SY5424 ) @ ( c_Transitive__Closure_Otrancl @ SV414 @ SY5424 ) @ ( tc_prod @ SY5424 @ SY5424 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3367]) ).
thf(3981,plain,
! [SV1511: $i,SV1020: $i,SV415: $i] :
( ( ! [SY5425: $i] :
( ( c_in @ ( c_Pair @ SV415 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1 @ SV1020 @ SV415 @ SV1511 @ SY5425 ) @ SY5425 @ SY5425 ) @ SV1020 @ ( tc_prod @ SY5425 @ SY5425 ) )
| ( c_in @ ( c_Pair @ SV415 @ SV1511 @ SY5425 @ SY5425 ) @ SV1020 @ ( tc_prod @ SY5425 @ SY5425 ) )
| ~ ( c_in @ ( c_Pair @ SV415 @ SV1511 @ SY5425 @ SY5425 ) @ ( c_Transitive__Closure_Otrancl @ SV1020 @ SY5425 ) @ ( tc_prod @ SY5425 @ SY5425 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3368]) ).
thf(3982,plain,
! [SV1512: $i,SV1021: $i,SV416: $i] :
( ( ( c_in @ ( c_Pair @ ( v_sko__Transitive__Closure__Xtrancl__Xcases__1 @ SV416 @ SV1021 @ SV1512 ) @ SV1021 @ t_a @ t_a ) @ SV1512 @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ ( c_Pair @ SV416 @ SV1021 @ t_a @ t_a ) @ SV1512 @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ ( c_Pair @ SV416 @ SV1021 @ t_a @ t_a ) @ ( c_Transitive__Closure_Otrancl @ SV1512 @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3369]) ).
thf(3983,plain,
! [SV1513: $i,SV1022: $i,SV417: $i] :
( ( ( hBOOL @ ( hAPP @ SV417 @ SV1022 ) )
| ( hBOOL @ ( hAPP @ SV417 @ SV1513 ) )
| ! [SY5426: $i,SY5427: $i] :
( ~ ( c_in @ ( c_Pair @ SV1513 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1 @ SV417 @ SY5426 @ SY5427 ) @ SY5427 @ SY5427 ) @ SY5426 @ ( tc_prod @ SY5427 @ SY5427 ) )
| ~ ( c_Wellfounded_Owf @ SY5426 @ SY5427 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3370]) ).
thf(3984,plain,
! [SV1514: $i,SV1023: $i,SV418: $i] :
( ( ( hBOOL @ ( hAPP @ SV418 @ SV1023 ) )
| ( hBOOL @ ( hAPP @ SV418 @ SV1514 ) )
| ! [SY5428: $i,SY5429: $i] :
( ~ ( c_in @ ( c_Pair @ SV1514 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1 @ SV418 @ SY5428 @ SY5429 ) @ SY5429 @ SY5429 ) @ SY5428 @ ( tc_prod @ SY5429 @ SY5429 ) )
| ~ ( c_Wellfounded_Owf @ SY5428 @ SY5429 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3371]) ).
thf(3985,plain,
! [SV1515: $i,SV1024: $i,SV419: $i] :
( ( ( hBOOL @ ( hAPP @ SV419 @ SV1024 ) )
| ( hBOOL @ ( hAPP @ SV419 @ SV1515 ) )
| ! [SY5430: $i,SY5431: $i] :
( ~ ( c_in @ ( c_Pair @ SV1515 @ ( c_List_Osko__Recdef__Xtfl__wf__induct__1__1 @ SV419 @ SY5430 @ SY5431 ) @ SY5431 @ SY5431 ) @ SY5430 @ ( tc_prod @ SY5431 @ SY5431 ) )
| ~ ( c_Wellfounded_Owf @ SY5430 @ SY5431 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3372]) ).
thf(3986,plain,
! [SV1516: $i,SV1025: $i,SV420: $i] :
( ( ( hBOOL @ ( hAPP @ SV420 @ SV1025 ) )
| ( hBOOL @ ( hAPP @ SV420 @ SV1516 ) )
| ! [SY5432: $i,SY5433: $i] :
( ~ ( c_in @ ( c_Pair @ SV1516 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1 @ SV420 @ SY5432 @ SY5433 ) @ SY5433 @ SY5433 ) @ SY5432 @ ( tc_prod @ SY5433 @ SY5433 ) )
| ~ ( c_Wellfounded_Owf @ SY5432 @ SY5433 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3373]) ).
thf(3987,plain,
! [SV1517: $i,SV1026: $i,SV421: $i] :
( ( ! [SY5434: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1 @ SV421 @ SV1026 @ SV1517 @ SY5434 ) @ SV1026 @ SY5434 @ SY5434 ) @ SV1517 @ ( tc_prod @ SY5434 @ SY5434 ) )
| ( SV421 = SV1026 )
| ~ ( c_in @ ( c_Pair @ SV421 @ SV1026 @ SY5434 @ SY5434 ) @ ( c_Transitive__Closure_Ortrancl @ SV1517 @ SY5434 ) @ ( tc_prod @ SY5434 @ SY5434 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3374]) ).
thf(3988,plain,
! [SV1518: $i,SV1027: $i,SV422: $i] :
( ( ! [SY5435: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1 @ SV422 @ SV1027 @ SV1518 @ SY5435 ) @ SV1518 @ SY5435 @ SY5435 ) @ ( c_Transitive__Closure_Ortrancl @ SV422 @ SY5435 ) @ ( tc_prod @ SY5435 @ SY5435 ) )
| ( SV1027 = SV1518 )
| ~ ( c_in @ ( c_Pair @ SV1027 @ SV1518 @ SY5435 @ SY5435 ) @ ( c_Transitive__Closure_Ortrancl @ SV422 @ SY5435 ) @ ( tc_prod @ SY5435 @ SY5435 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3375]) ).
thf(3989,plain,
! [SV1519: $i,SV1028: $i,SV423: $i] :
( ( ! [SY5436: $i] :
( ( c_in @ ( c_Pair @ SV423 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1 @ SV1028 @ SV423 @ SV1519 @ SY5436 ) @ SY5436 @ SY5436 ) @ SV1028 @ ( tc_prod @ SY5436 @ SY5436 ) )
| ( SV423 = SV1519 )
| ~ ( c_in @ ( c_Pair @ SV423 @ SV1519 @ SY5436 @ SY5436 ) @ ( c_Transitive__Closure_Ortrancl @ SV1028 @ SY5436 ) @ ( tc_prod @ SY5436 @ SY5436 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3376]) ).
thf(3990,plain,
! [SV1520: $i,SV1029: $i,SV424: $i] :
( ( ( hBOOL @ ( hAPP @ SV424 @ SV1029 ) )
| ! [SY5437: $i,SY5438: $i] :
( ( hBOOL @ ( hAPP @ SV424 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 @ SV424 @ SV1520 @ SY5437 @ SY5438 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV424 @ SV1520 ) )
| ~ ( c_in @ ( c_Pair @ SV1029 @ SV1520 @ SY5438 @ SY5438 ) @ ( c_Transitive__Closure_Ortrancl @ SY5437 @ SY5438 ) @ ( tc_prod @ SY5438 @ SY5438 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3377]) ).
thf(3991,plain,
! [SV1521: $i,SV1030: $i,SV425: $i] :
( ( ( hBOOL @ ( hAPP @ SV425 @ SV1030 ) )
| ! [SY5439: $i,SY5440: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 @ SV425 @ SV1521 @ SY5439 @ SY5440 ) @ SV1521 @ SY5440 @ SY5440 ) @ ( c_Transitive__Closure_Ortrancl @ SY5439 @ SY5440 ) @ ( tc_prod @ SY5440 @ SY5440 ) )
| ~ ( hBOOL @ ( hAPP @ SV425 @ SV1521 ) )
| ~ ( c_in @ ( c_Pair @ SV1030 @ SV1521 @ SY5440 @ SY5440 ) @ ( c_Transitive__Closure_Ortrancl @ SY5439 @ SY5440 ) @ ( tc_prod @ SY5440 @ SY5440 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3378]) ).
thf(3992,plain,
! [SV1522: $i,SV1031: $i,SV426: $i] :
( ( ( hBOOL @ ( hAPP @ SV426 @ SV1031 ) )
| ! [SY5441: $i,SY5442: $i] :
( ( c_in @ ( c_Pair @ SV1522 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 @ SV426 @ SV1522 @ SY5441 @ SY5442 ) @ SY5442 @ SY5442 ) @ ( c_Transitive__Closure_Ortrancl @ SY5441 @ SY5442 ) @ ( tc_prod @ SY5442 @ SY5442 ) )
| ~ ( hBOOL @ ( hAPP @ SV426 @ SV1522 ) )
| ~ ( c_in @ ( c_Pair @ SV1522 @ SV1031 @ SY5442 @ SY5442 ) @ ( c_Transitive__Closure_Ortrancl @ SY5441 @ SY5442 ) @ ( tc_prod @ SY5442 @ SY5442 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3379]) ).
thf(3993,plain,
! [SV1523: $i,SV1032: $i,SV427: $i] :
( ( ( hBOOL @ ( hAPP @ SV427 @ SV1032 ) )
| ! [SY5443: $i,SY5444: $i] :
( ~ ( hBOOL @ ( hAPP @ SV427 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2 @ SV427 @ SV1523 @ SY5443 @ SY5444 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV427 @ SV1523 ) )
| ~ ( c_in @ ( c_Pair @ SV1523 @ SV1032 @ SY5444 @ SY5444 ) @ ( c_Transitive__Closure_Ortrancl @ SY5443 @ SY5444 ) @ ( tc_prod @ SY5444 @ SY5444 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3380]) ).
thf(3994,plain,
! [SV1524: $i,SV1033: $i,SV428: $i] :
( ( ( c_in @ ( c_Pair @ SV428 @ ( v_sko__Transitive__Closure__Xrtrancl__Xcases__1 @ SV428 @ SV1033 @ SV1524 ) @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ SV1524 @ t_a ) @ ( tc_prod @ t_a @ t_a ) )
| ( SV1033 = SV428 )
| ~ ( c_in @ ( c_Pair @ SV428 @ SV1033 @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ SV1524 @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3381]) ).
thf(3995,plain,
! [SV1525: $i,SV1034: $i,SV429: $i] :
( ( ( hBOOL @ ( hAPP @ SV429 @ SV1034 ) )
| ! [SY5445: $i,SY5446: $i] :
( ( hBOOL @ ( hAPP @ SV429 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 @ SV429 @ SV1525 @ SY5445 @ SY5446 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV429 @ SV1525 ) )
| ~ ( c_in @ ( c_Pair @ SV1525 @ SV1034 @ SY5446 @ SY5446 ) @ ( c_Transitive__Closure_Ortrancl @ SY5445 @ SY5446 ) @ ( tc_prod @ SY5446 @ SY5446 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3382]) ).
thf(3996,plain,
! [SV1526: $i,SV1035: $i,SV430: $i] :
( ( ( c_in @ ( c_Pair @ ( v_sko__Transitive__Closure__Xrtrancl__Xcases__1 @ SV430 @ SV1035 @ SV1526 ) @ SV1035 @ t_a @ t_a ) @ SV1526 @ ( tc_prod @ t_a @ t_a ) )
| ( SV1035 = SV430 )
| ~ ( c_in @ ( c_Pair @ SV430 @ SV1035 @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ SV1526 @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3383]) ).
thf(3997,plain,
! [SV1527: $i,SV1036: $i,SV431: $i] :
( ( ( hBOOL @ ( hAPP @ SV431 @ SV1036 ) )
| ! [SY5447: $i,SY5448: $i] :
( ~ ( hBOOL @ ( hAPP @ SV431 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1 @ SV431 @ SV1527 @ SY5447 @ SY5448 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV431 @ SV1527 ) )
| ~ ( c_in @ ( c_Pair @ SV1036 @ SV1527 @ SY5448 @ SY5448 ) @ ( c_Transitive__Closure_Ortrancl @ SY5447 @ SY5448 ) @ ( tc_prod @ SY5448 @ SY5448 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3384]) ).
thf(3998,plain,
! [SV1528: $i,SV1037: $i,SV432: $i] :
( ( ! [SY5449: $i] :
( ( c_in @ ( c_Pair @ SV432 @ ( c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1 @ SV432 @ SV1037 @ SV1528 @ SY5449 ) @ SY5449 @ SY5449 ) @ ( c_Transitive__Closure_Ortrancl @ SV1528 @ SY5449 ) @ ( tc_prod @ SY5449 @ SY5449 ) )
| ( SV432 = SV1037 )
| ~ ( c_in @ ( c_Pair @ SV432 @ SV1037 @ SY5449 @ SY5449 ) @ ( c_Transitive__Closure_Ortrancl @ SV1528 @ SY5449 ) @ ( tc_prod @ SY5449 @ SY5449 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3385]) ).
thf(3999,plain,
! [SV1529: $i,SV1038: $i,SV433: $i] :
( ( ! [SY5450: $i,SY5451: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Product__Type__XSigmaE__1__1 @ SV433 @ SV1038 @ SV1529 @ SY5450 @ SY5451 ) @ SV433 @ SY5450 )
| ~ ( c_in @ SV1529 @ ( c_Product__Type_OSigma @ SV433 @ SV1038 @ SY5450 @ SY5451 ) @ ( tc_prod @ SY5450 @ SY5451 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3386]) ).
thf(4000,plain,
! [SV1039: $i,SV434: $i] :
( ( ( c_Wellfounded_OwfP @ ( c_FunDef_Oin__rel @ SV434 @ SV1039 @ SV1039 ) @ SV1039 )
= $true )
| ( ( ~ ( c_Wellfounded_Owf @ SV434 @ SV1039 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3387]) ).
thf(4001,plain,
! [SV1041: $i,SV436: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_Oconverse @ SV436 @ SV1041 @ SV1041 ) @ ( c_Transitive__Closure_Ortrancl @ SV436 @ SV1041 ) @ ( tc_fun @ ( tc_prod @ SV1041 @ SV1041 ) @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV1041 @ SV1041 ) @ tc_bool ) ) )
= $true )
| ( ( ! [SY4779: $i] :
~ ( c_in @ ( c_Pair @ SY4779 @ SY4779 @ SV1041 @ SV1041 ) @ ( c_Transitive__Closure_Otrancl @ SV436 @ SV1041 ) @ ( tc_prod @ SV1041 @ SV1041 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3389]) ).
thf(4002,plain,
! [SV1530: $i,SV1042: $i,SV437: $i] :
( ( ! [SY5452: $i] :
( ( ( c_Relation_OImage @ SV437 @ ( c_Set_Oinsert @ SV1042 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1530 @ tc_bool ) ) @ SV1530 ) @ SV1530 @ SV1530 )
!= ( c_Relation_OImage @ SV437 @ ( c_Set_Oinsert @ SY5452 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1530 @ tc_bool ) ) @ SV1530 ) @ SV1530 @ SV1530 ) )
| ( c_in @ ( c_Pair @ SV1042 @ SY5452 @ SV1530 @ SV1530 ) @ SV437 @ ( tc_prod @ SV1530 @ SV1530 ) )
| ! [SY5453: $i] :
( ~ ( c_in @ SY5452 @ SY5453 @ SV1530 )
| ~ ( c_Equiv__Relations_Oequiv @ SY5453 @ SV437 @ SV1530 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3390]) ).
thf(4003,plain,
! [SV1531: $i,SV1043: $i,SV438: $i] :
( ( ! [SY5454: $i] :
( ( ( c_Relation_OImage @ SV438 @ ( c_Set_Oinsert @ SV1043 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1531 @ tc_bool ) ) @ SV1531 ) @ SV1531 @ SV1531 )
!= ( c_Relation_OImage @ SV438 @ ( c_Set_Oinsert @ SY5454 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1531 @ tc_bool ) ) @ SV1531 ) @ SV1531 @ SV1531 ) )
| ! [SY5455: $i] :
( ~ ( c_Equiv__Relations_Oequiv @ SY5455 @ SV438 @ SV1531 )
| ( c_in @ ( c_Pair @ SV1043 @ SY5454 @ SV1531 @ SV1531 ) @ SV438 @ ( tc_prod @ SV1531 @ SV1531 ) )
| ~ ( c_in @ SY5454 @ SY5455 @ SV1531 )
| ~ ( c_in @ SV1043 @ SY5455 @ SV1531 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3391]) ).
thf(4004,plain,
! [SV1532: $i,SV1044: $i,SV439: $i] :
( ( ! [SY5456: $i] :
( ( ( c_Relation_OImage @ SV439 @ ( c_Set_Oinsert @ SV1044 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1532 @ tc_bool ) ) @ SV1532 ) @ SV1532 @ SV1532 )
= ( c_Relation_OImage @ SV439 @ ( c_Set_Oinsert @ SY5456 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1532 @ tc_bool ) ) @ SV1532 ) @ SV1532 @ SV1532 ) )
| ~ ( c_in @ ( c_Pair @ SV1044 @ SY5456 @ SV1532 @ SV1532 ) @ SV439 @ ( tc_prod @ SV1532 @ SV1532 ) )
| ! [SY5457: $i] :
( ~ ( c_in @ SY5456 @ SY5457 @ SV1532 )
| ~ ( c_in @ SV1044 @ SY5457 @ SV1532 )
| ~ ( c_Equiv__Relations_Oequiv @ SY5457 @ SV439 @ SV1532 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3392]) ).
thf(4005,plain,
! [SV1533: $i,SV1045: $i,SV440: $i] :
( ( ! [SY5458: $i] :
( ( ( c_Relation_OImage @ SV440 @ ( c_Set_Oinsert @ SV1045 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1533 @ tc_bool ) ) @ SV1533 ) @ SV1533 @ SV1533 )
!= ( c_Relation_OImage @ SV440 @ ( c_Set_Oinsert @ SY5458 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1533 @ tc_bool ) ) @ SV1533 ) @ SV1533 @ SV1533 ) )
| ! [SY5459: $i] :
( ~ ( c_in @ SY5458 @ SY5459 @ SV1533 )
| ~ ( c_in @ SV1045 @ SY5459 @ SV1533 )
| ~ ( c_Equiv__Relations_Oequiv @ SY5459 @ SV440 @ SV1533 )
| ( c_in @ ( c_Pair @ SV1045 @ SY5458 @ SV1533 @ SV1533 ) @ SV440 @ ( tc_prod @ SV1533 @ SV1533 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3393]) ).
thf(4006,plain,
! [SV1534: $i,SV1046: $i,SV441: $i] :
( ( ( c_Set_Oimage @ ( c_snd @ SV441 @ SV1046 ) @ SV1534 @ ( tc_prod @ SV441 @ SV1046 ) @ SV1046 )
= ( c_Relation_ORange @ SV1534 @ SV441 @ SV1046 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3394]) ).
thf(4007,plain,
! [SV1535: $i,SV1047: $i,SV442: $i] :
( ( ( c_in @ SV442 @ SV1047 @ SV1535 )
| ! [SY5460: $i] :
( ( SV442 = SY5460 )
| ! [SY5461: $i] :
( ~ ( c_lessequals @ SY5461 @ ( c_Product__Type_OSigma @ SV1047 @ ( c_COMBK @ SV1047 @ ( tc_fun @ SV1535 @ tc_bool ) @ SV1535 ) @ SV1535 @ SV1535 ) @ ( tc_fun @ ( tc_prod @ SV1535 @ SV1535 ) @ tc_bool ) )
| ~ ( c_in @ ( c_Pair @ SV442 @ SY5460 @ SV1535 @ SV1535 ) @ ( c_Transitive__Closure_Ortrancl @ SY5461 @ SV1535 ) @ ( tc_prod @ SV1535 @ SV1535 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3395]) ).
thf(4008,plain,
! [SV1536: $i,SV1048: $i,SV443: $i] :
( ( ( c_Set_Oimage @ ( c_fst @ SV443 @ SV1048 ) @ SV1536 @ ( tc_prod @ SV443 @ SV1048 ) @ SV443 )
= ( c_Relation_ODomain @ SV1536 @ SV443 @ SV1048 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3396]) ).
thf(4009,plain,
! [SV1537: $i,SV1049: $i,SV444: $i] :
( ( ( c_in @ SV444 @ ( c_Transitive__Closure_Ortrancl @ SV1049 @ SV1537 ) @ ( tc_prod @ SV1537 @ SV1537 ) )
| ~ ( c_in @ SV444 @ SV1049 @ ( tc_prod @ SV1537 @ SV1537 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3397]) ).
thf(4010,plain,
! [SV1538: $i,SV1050: $i,SV445: $i] :
( ( ( c_in @ SV445 @ ( c_Transitive__Closure_Otrancl @ SV1050 @ SV1538 ) @ ( tc_prod @ SV1538 @ SV1538 ) )
| ~ ( c_in @ SV445 @ SV1050 @ ( tc_prod @ SV1538 @ SV1538 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3398]) ).
thf(4011,plain,
! [SV1539: $i,SV1051: $i,SV446: $i] :
( ( ! [SY5462: $i] :
( ( c_in @ ( c_Pair @ SV446 @ SV1051 @ SV1539 @ SV1539 ) @ ( c_Transitive__Closure_Otrancl @ SY5462 @ SV1539 ) @ ( tc_prod @ SV1539 @ SV1539 ) )
| ! [SY5463: $i] :
( ~ ( c_in @ ( c_Pair @ SY5463 @ SV1051 @ SV1539 @ SV1539 ) @ ( c_Transitive__Closure_Ortrancl @ SY5462 @ SV1539 ) @ ( tc_prod @ SV1539 @ SV1539 ) )
| ~ ( c_in @ ( c_Pair @ SV446 @ SY5463 @ SV1539 @ SV1539 ) @ SY5462 @ ( tc_prod @ SV1539 @ SV1539 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3399]) ).
thf(4012,plain,
! [SV1540: $i,SV1052: $i,SV447: $i] :
( ( ! [SY5464: $i] :
( ( c_in @ ( c_Pair @ SV447 @ SV1052 @ SV1540 @ SV1540 ) @ ( c_Transitive__Closure_Otrancl @ SY5464 @ SV1540 ) @ ( tc_prod @ SV1540 @ SV1540 ) )
| ! [SY5465: $i] :
( ~ ( c_in @ ( c_Pair @ SY5465 @ SV1052 @ SV1540 @ SV1540 ) @ SY5464 @ ( tc_prod @ SV1540 @ SV1540 ) )
| ~ ( c_in @ ( c_Pair @ SV447 @ SY5465 @ SV1540 @ SV1540 ) @ ( c_Transitive__Closure_Ortrancl @ SY5464 @ SV1540 ) @ ( tc_prod @ SV1540 @ SV1540 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3400]) ).
thf(4013,plain,
! [SV1541: $i,SV1053: $i,SV448: $i] :
( ( ! [SY5466: $i] :
( ( c_in @ ( c_Pair @ SV448 @ SV1053 @ SV1541 @ SV1541 ) @ ( c_Transitive__Closure_Ortrancl @ SY5466 @ SV1541 ) @ ( tc_prod @ SV1541 @ SV1541 ) )
| ~ ( c_in @ ( c_Pair @ SV448 @ SV1053 @ SV1541 @ SV1541 ) @ ( c_Transitive__Closure_Otrancl @ SY5466 @ SV1541 ) @ ( tc_prod @ SV1541 @ SV1541 ) )
| ( SV448 = SV1053 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3401]) ).
thf(4014,plain,
! [SV1542: $i,SV1054: $i,SV449: $i] :
( ( ! [SY5467: $i] :
( ( c_in @ ( c_Pair @ SV449 @ SV1054 @ SV1542 @ SV1542 ) @ ( c_Transitive__Closure_Otrancl @ SY5467 @ SV1542 ) @ ( tc_prod @ SV1542 @ SV1542 ) )
| ( SV449 = SV1054 )
| ~ ( c_in @ ( c_Pair @ SV449 @ SV1054 @ SV1542 @ SV1542 ) @ ( c_Transitive__Closure_Ortrancl @ SY5467 @ SV1542 ) @ ( tc_prod @ SV1542 @ SV1542 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3402]) ).
thf(4015,plain,
! [SV1543: $i,SV1055: $i,SV450: $i] :
( ( ! [SY5468: $i] :
( ( c_in @ ( c_Pair @ SV450 @ SV1055 @ SV1543 @ SV1543 ) @ ( c_Transitive__Closure_Otrancl @ SY5468 @ SV1543 ) @ ( tc_prod @ SV1543 @ SV1543 ) )
| ( SV450 = SV1055 )
| ~ ( c_in @ ( c_Pair @ SV450 @ SV1055 @ SV1543 @ SV1543 ) @ ( c_Transitive__Closure_Ortrancl @ SY5468 @ SV1543 ) @ ( tc_prod @ SV1543 @ SV1543 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3403]) ).
thf(4016,plain,
! [SV1544: $i,SV1056: $i,SV451: $i] :
( ( ! [SY5469: $i] :
( ( c_in @ ( c_Pair @ SV451 @ SV1056 @ SV1544 @ SV1544 ) @ ( c_Transitive__Closure_Ortrancl @ ( c_Relation_Oconverse @ SY5469 @ SV1544 @ SV1544 ) @ SV1544 ) @ ( tc_prod @ SV1544 @ SV1544 ) )
| ~ ( c_in @ ( c_Pair @ SV1056 @ SV451 @ SV1544 @ SV1544 ) @ ( c_Transitive__Closure_Ortrancl @ SY5469 @ SV1544 ) @ ( tc_prod @ SV1544 @ SV1544 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3404]) ).
thf(4017,plain,
! [SV1545: $i,SV1057: $i,SV452: $i] :
( ( ! [SY5470: $i] :
( ( c_in @ ( c_Pair @ SV452 @ SV1057 @ SV1545 @ SV1545 ) @ ( c_Transitive__Closure_Ortrancl @ SY5470 @ SV1545 ) @ ( tc_prod @ SV1545 @ SV1545 ) )
| ~ ( c_in @ ( c_Pair @ SV1057 @ SV452 @ SV1545 @ SV1545 ) @ ( c_Transitive__Closure_Ortrancl @ ( c_Relation_Oconverse @ SY5470 @ SV1545 @ SV1545 ) @ SV1545 ) @ ( tc_prod @ SV1545 @ SV1545 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3405]) ).
thf(4018,plain,
! [SV1546: $i,SV1058: $i,SV453: $i] :
( ( ! [SY5471: $i] :
( ( c_in @ ( c_Pair @ SV453 @ SV1058 @ SV1546 @ SV1546 ) @ ( c_Transitive__Closure_Ortrancl @ SY5471 @ SV1546 ) @ ( tc_prod @ SV1546 @ SV1546 ) )
| ( c_in @ ( c_Pair @ SV1058 @ SV453 @ SV1546 @ SV1546 ) @ ( c_Transitive__Closure_Ortrancl @ SY5471 @ SV1546 ) @ ( tc_prod @ SV1546 @ SV1546 ) )
| ! [SY5472: $i] :
( ~ ( c_in @ ( c_Pair @ SY5472 @ SV453 @ SV1546 @ SV1546 ) @ ( c_Transitive__Closure_Ortrancl @ SY5471 @ SV1546 ) @ ( tc_prod @ SV1546 @ SV1546 ) )
| ~ ( c_in @ ( c_Pair @ SY5472 @ SV1058 @ SV1546 @ SV1546 ) @ ( c_Transitive__Closure_Ortrancl @ SY5471 @ SV1546 ) @ ( tc_prod @ SV1546 @ SV1546 ) )
| ~ ( c_Relation_Osingle__valued @ SY5471 @ SV1546 @ SV1546 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3406]) ).
thf(4019,plain,
! [SV1547: $i,SV1059: $i,SV454: $i] :
( ( ! [SY5473: $i] :
( ( c_in @ ( c_Pair @ SV454 @ SV1059 @ SV1547 @ SV1547 ) @ ( c_Transitive__Closure_Ortrancl @ SY5473 @ SV1547 ) @ ( tc_prod @ SV1547 @ SV1547 ) )
| ~ ( c_in @ ( c_Pair @ SV454 @ SV1059 @ SV1547 @ SV1547 ) @ ( c_Transitive__Closure_Otrancl @ SY5473 @ SV1547 ) @ ( tc_prod @ SV1547 @ SV1547 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3407]) ).
thf(4020,plain,
! [SV1548: $i,SV1060: $i,SV455: $i] :
( ( ! [SY5474: $i] :
( ( c_in @ ( c_Pair @ SV455 @ SV1060 @ SV1548 @ SV1548 ) @ ( c_Transitive__Closure_Otrancl @ SY5474 @ SV1548 ) @ ( tc_prod @ SV1548 @ SV1548 ) )
| ! [SY5475: $i] :
( ~ ( c_in @ ( c_Pair @ SY5475 @ SV1060 @ SV1548 @ SV1548 ) @ ( c_Transitive__Closure_Ortrancl @ SY5474 @ SV1548 ) @ ( tc_prod @ SV1548 @ SV1548 ) )
| ~ ( c_in @ ( c_Pair @ SV455 @ SY5475 @ SV1548 @ SV1548 ) @ ( c_Transitive__Closure_Otrancl @ SY5474 @ SV1548 ) @ ( tc_prod @ SV1548 @ SV1548 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3408]) ).
thf(4021,plain,
! [SV1549: $i,SV1061: $i,SV456: $i] :
( ( ! [SY5476: $i] :
( ( c_in @ ( c_Pair @ SV456 @ SV1061 @ SV1549 @ SV1549 ) @ ( c_Transitive__Closure_Otrancl @ SY5476 @ SV1549 ) @ ( tc_prod @ SV1549 @ SV1549 ) )
| ! [SY5477: $i] :
( ~ ( c_in @ ( c_Pair @ SY5477 @ SV1061 @ SV1549 @ SV1549 ) @ ( c_Transitive__Closure_Otrancl @ SY5476 @ SV1549 ) @ ( tc_prod @ SV1549 @ SV1549 ) )
| ~ ( c_in @ ( c_Pair @ SV456 @ SY5477 @ SV1549 @ SV1549 ) @ ( c_Transitive__Closure_Ortrancl @ SY5476 @ SV1549 ) @ ( tc_prod @ SV1549 @ SV1549 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3409]) ).
thf(4022,plain,
! [SV1550: $i,SV1062: $i,SV457: $i] :
( ( ! [SY5478: $i] :
( ( c_in @ ( c_Pair @ SV457 @ SV1062 @ SV1550 @ SV1550 ) @ ( c_Relation_Oconverse @ ( c_Transitive__Closure_Otrancl @ SY5478 @ SV1550 ) @ SV1550 @ SV1550 ) @ ( tc_prod @ SV1550 @ SV1550 ) )
| ~ ( c_in @ ( c_Pair @ SV457 @ SV1062 @ SV1550 @ SV1550 ) @ ( c_Transitive__Closure_Otrancl @ ( c_Relation_Oconverse @ SY5478 @ SV1550 @ SV1550 ) @ SV1550 ) @ ( tc_prod @ SV1550 @ SV1550 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3410]) ).
thf(4023,plain,
! [SV1551: $i,SV1063: $i,SV458: $i] :
( ( ! [SY5479: $i] :
( ( c_in @ ( c_Pair @ SV458 @ SV1063 @ SV1551 @ SV1551 ) @ ( c_Transitive__Closure_Otrancl @ ( c_Relation_Oconverse @ SY5479 @ SV1551 @ SV1551 ) @ SV1551 ) @ ( tc_prod @ SV1551 @ SV1551 ) )
| ~ ( c_in @ ( c_Pair @ SV458 @ SV1063 @ SV1551 @ SV1551 ) @ ( c_Relation_Oconverse @ ( c_Transitive__Closure_Otrancl @ SY5479 @ SV1551 ) @ SV1551 @ SV1551 ) @ ( tc_prod @ SV1551 @ SV1551 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3411]) ).
thf(4024,plain,
! [SV1552: $i,SV1064: $i,SV459: $i] :
( ( ! [SY5480: $i,SY5481: $i,SY5482: $i] :
( ( hAPP @ ( c_split @ SV459 @ SV1064 @ SV1552 @ SY5480 ) @ ( c_Pair @ SY5481 @ SY5482 @ SV1064 @ SV1552 ) )
= ( hAPP @ ( hAPP @ SV459 @ SY5481 ) @ SY5482 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3412]) ).
thf(4025,plain,
! [SV1553: $i,SV1065: $i,SV460: $i] :
( ( ! [SY5483: $i,SY5484: $i,SY5485: $i] :
( ( hAPP @ ( c_split @ SV460 @ SV1065 @ SV1553 @ SY5483 ) @ ( c_Pair @ SY5484 @ SY5485 @ SV1065 @ SV1553 ) )
= ( hAPP @ ( hAPP @ SV460 @ SY5484 ) @ SY5485 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3413]) ).
thf(4026,plain,
! [SV1554: $i,SV1066: $i,SV461: $i] :
( ( ! [SY5486: $i,SY5487: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ SV461 @ SV1066 ) @ SV1554 ) @ SY5486 ) )
| ! [SY5488: $i,SY5489: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_split @ SV461 @ SY5487 @ SY5488 @ ( tc_fun @ SY5489 @ tc_bool ) ) @ ( c_Pair @ SV1066 @ SV1554 @ SY5487 @ SY5488 ) ) @ SY5486 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3414]) ).
thf(4027,plain,
! [SV1555: $i,SV1067: $i,SV462: $i] :
( ( ! [SY5490: $i] :
( ! [SY5491: $i] : ( c_in @ ( hAPP @ SV462 @ SV1067 ) @ ( c_Set_Oimage @ SV462 @ SV1555 @ SY5490 @ SY5491 ) @ SY5491 )
| ~ ( c_in @ SV1067 @ SV1555 @ SY5490 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3415]) ).
thf(4028,plain,
! [SV1556: $i,SV1068: $i,SV463: $i] :
( ( ! [SY5492: $i] :
( ! [SY5493: $i] : ( c_in @ ( hAPP @ SV463 @ SV1068 ) @ ( c_Set_Oimage @ SV463 @ SV1556 @ SY5492 @ SY5493 ) @ SY5493 )
| ~ ( c_in @ SV1068 @ SV1556 @ SY5492 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3416]) ).
thf(4029,plain,
! [SV1557: $i,SV1069: $i,SV464: $i] :
( ( ~ ( c_in @ SV464 @ SV1069 @ SV1557 )
| ! [SY5494: $i,SY5495: $i] : ( c_in @ ( hAPP @ SY5494 @ SV464 ) @ ( c_Set_Oimage @ SY5494 @ SV1069 @ SV1557 @ SY5495 ) @ SY5495 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3417]) ).
thf(4030,plain,
! [SV1558: $i,SV1070: $i,SV465: $i] :
( ( ~ ( c_in @ SV465 @ SV1070 @ SV1558 )
| ! [SY5496: $i,SY5497: $i] : ( c_in @ ( hAPP @ SY5496 @ SV465 ) @ ( c_Set_Oimage @ SY5496 @ SV1070 @ SV1558 @ SY5497 ) @ SY5497 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3418]) ).
thf(4031,plain,
! [SV1559: $i,SV1071: $i,SV466: $i] :
( ( ( c_in @ SV466 @ ( c_Wellfounded_Oacc @ SV1071 @ SV1559 ) @ SV1559 )
| ~ ( c_Wellfounded_Owf @ SV1071 @ SV1559 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3419]) ).
thf(4032,plain,
! [SV1560: $i,SV1073: $i,SV468: $i] :
( ( ! [SY5498: $i,SY5499: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Relation__XImageE__1__1 @ SV468 @ SV1073 @ SV1560 @ SY5498 @ SY5499 ) @ SV468 @ SY5498 )
| ~ ( c_in @ SV1073 @ ( c_Relation_OImage @ SV1560 @ SV468 @ SY5498 @ SY5499 ) @ SY5499 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3421]) ).
thf(4033,plain,
! [SV1074: $i,SV469: $i] :
( ( ( c_Relation_Osym @ ( c_Transitive__Closure_Otrancl @ SV469 @ SV1074 ) @ SV1074 )
= $true )
| ( ( ~ ( c_Relation_Osym @ SV469 @ SV1074 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3422]) ).
thf(4034,plain,
! [SV1075: $i,SV470: $i] :
( ( ( hBOOL @ ( hAPP @ SV470 @ SV1075 ) )
= $true )
| ( ( ! [SY4859: $i,SY4860: $i] :
( ~ ( hBOOL @ ( hAPP @ SV470 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ SV470 @ SY4859 @ SY4860 ) ) )
| ~ ( c_in @ SV1075 @ ( c_Wellfounded_Oacc @ SY4859 @ SY4860 ) @ SY4860 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3423]) ).
thf(4035,plain,
! [SV1076: $i,SV471: $i] :
( ( ( ( c_Transitive__Closure_Otrancl @ SV471 @ SV1076 )
= SV471 )
= $true )
| ( ( ~ ( c_Relation_Otrans @ SV471 @ SV1076 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3424]) ).
thf(4036,plain,
! [SV1077: $i,SV472: $i] :
( ( ( hBOOL @ ( hAPP @ SV472 @ SV1077 ) )
= $true )
| ( ( ! [SY4861: $i] :
( ~ ( hBOOL @ ( hAPP @ SV472 @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ SV472 @ SY4861 ) ) )
| ~ ( c_in @ SV1077 @ ( c_Wellfounded_Oacc @ SY4861 @ t_a ) @ t_a ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3425]) ).
thf(4037,plain,
! [SV1078: $i,SV473: $i] :
( ( ( hBOOL @ ( hAPP @ SV473 @ SV1078 ) )
= $true )
| ( ( ! [SY4862: $i,SY4863: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ SV473 @ SY4862 @ SY4863 ) @ ( c_Wellfounded_Oacc @ SY4862 @ SY4863 ) @ SY4863 )
| ~ ( c_in @ SV1078 @ ( c_Wellfounded_Oacc @ SY4862 @ SY4863 ) @ SY4863 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3426]) ).
thf(4038,plain,
! [SV1079: $i,SV474: $i] :
( ( ( c_Relation_Osym @ SV474 @ SV1079 )
= $true )
| ( ( ~ ( c_Relation_Osym @ ( c_Relation_Oconverse @ SV474 @ SV1079 @ SV1079 ) @ SV1079 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3427]) ).
thf(4039,plain,
! [SV1080: $i,SV475: $i] :
( ( ( c_Relation_Osym @ ( c_Relation_Oconverse @ SV475 @ SV1080 @ SV1080 ) @ SV1080 )
= $true )
| ( ( ~ ( c_Relation_Osym @ SV475 @ SV1080 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3428]) ).
thf(4040,plain,
! [SV1561: $i,SV1082: $i,SV477: $i] :
( ( ! [SY5500: $i,SY5501: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Relation__XImage__iff__1__1 @ SV477 @ SV1082 @ SV1561 @ SY5500 @ SY5501 ) @ SV477 @ SY5500 )
| ~ ( c_in @ SV1082 @ ( c_Relation_OImage @ SV1561 @ SV477 @ SY5500 @ SY5501 ) @ SY5501 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3430]) ).
thf(4041,plain,
! [SV1562: $i,SV1083: $i,SV478: $i] :
( ( ~ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1 @ SV478 @ SV1083 @ SV1562 ) @ ( c_Wellfounded_Oacc @ SV478 @ SV1562 ) @ SV1562 )
| ( c_in @ SV1083 @ ( c_Wellfounded_Oacc @ SV478 @ SV1562 ) @ SV1562 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3431]) ).
thf(4042,plain,
! [SV1563: $i,SV1085: $i,SV481: $i] :
( ( ( c_Relation_Orel__comp @ ( c_Relation_OId @ SV481 ) @ SV1085 @ SV481 @ SV481 @ SV1563 )
= SV1085 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3433]) ).
thf(4043,plain,
! [SV1564: $i,SV1086: $i,SV482: $i] :
( ( ( c_Relation_Orel__comp @ SV482 @ ( c_Relation_OId @ SV1086 ) @ SV1564 @ SV1086 @ SV1086 )
= SV482 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3434]) ).
thf(4044,plain,
! [SV1088: $i,SV484: $i] :
( ( ( c_Wellfounded_Owf @ ( c_Relation_Oconverse @ ( c_Transitive__Closure_Otrancl @ SV484 @ SV1088 ) @ SV1088 @ SV1088 ) @ SV1088 )
= $true )
| ( ( ~ ( c_Wellfounded_Owf @ ( c_Relation_Oconverse @ SV484 @ SV1088 @ SV1088 ) @ SV1088 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3436]) ).
thf(4045,plain,
! [SV1089: $i,SV485: $i] :
( ( ( hBOOL @ ( hAPP @ SV485 @ SV1089 ) )
= $true )
| ( ( ! [SY4870: $i,SY4871: $i] :
( ~ ( hBOOL @ ( hAPP @ SV485 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ SV485 @ SY4870 @ SY4871 ) ) )
| ~ ( c_in @ SV1089 @ ( c_Wellfounded_Oacc @ SY4870 @ SY4871 ) @ SY4871 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3437]) ).
thf(4046,plain,
! [SV1565: $i,SV1090: $i,SV486: $i] :
( ( ( c_Relation_Orefl__on @ SV486 @ SV1090 @ SV1565 )
| ~ ( c_Relation_Orefl__on @ SV486 @ ( c_Relation_Oconverse @ SV1090 @ SV1565 @ SV1565 ) @ SV1565 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3438]) ).
thf(4047,plain,
! [SV1566: $i,SV1091: $i,SV487: $i] :
( ( ( c_Relation_Orefl__on @ SV487 @ ( c_Relation_Oconverse @ SV1091 @ SV1566 @ SV1566 ) @ SV1566 )
| ~ ( c_Relation_Orefl__on @ SV487 @ SV1091 @ SV1566 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3439]) ).
thf(4048,plain,
! [SV1092: $i,SV488: $i] :
( ( ( c_Relation_Osym @ ( c_Transitive__Closure_Ortrancl @ SV488 @ SV1092 ) @ SV1092 )
= $true )
| ( ( ~ ( c_Relation_Osym @ SV488 @ SV1092 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3440]) ).
thf(4049,plain,
! [SV1093: $i,SV489: $i] :
( ( ( c_Wellfounded_Owf @ ( c_Relation_Orel__comp @ SV489 @ SV489 @ SV1093 @ SV1093 @ SV1093 ) @ SV1093 )
= $true )
| ( ( ~ ( c_Wellfounded_Owf @ SV489 @ SV1093 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3441]) ).
thf(4050,plain,
! [SV1094: $i,SV490: $i] :
( ( ( c_Wellfounded_Owf @ SV490 @ SV1094 )
= $true )
| ( ( ~ ( c_Wellfounded_Owf @ ( c_Relation_Orel__comp @ SV490 @ SV490 @ SV1094 @ SV1094 @ SV1094 ) @ SV1094 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3442]) ).
thf(4051,plain,
! [SV1097: $i,SV494: $i] :
( ( ( ( c_Relation_Oconverse @ SV494 @ SV1097 @ SV1097 )
= SV494 )
= $true )
| ( ( ~ ( c_Relation_Osym @ SV494 @ SV1097 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3445]) ).
thf(4052,plain,
! [SV1098: $i,SV495: $i] :
( ( ( ( c_Relation_Oconverse @ SV495 @ SV1098 @ SV1098 )
!= SV495 )
= $true )
| ( ( c_Relation_Osym @ SV495 @ SV1098 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3446]) ).
thf(4053,plain,
! [SV1567: $i,SV1101: $i,SV498: $i] :
( ( ! [SY5502: $i,SY5503: $i] :
( ( c_Relation_Oconverse @ ( c_Relation_Orel__comp @ SV498 @ SV1101 @ SV1567 @ SY5502 @ SY5503 ) @ SV1567 @ SY5503 )
= ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ SV1101 @ SY5502 @ SY5503 ) @ ( c_Relation_Oconverse @ SV498 @ SV1567 @ SY5502 ) @ SY5503 @ SY5502 @ SV1567 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3449]) ).
thf(4054,plain,
! [SV1568: $i,SV1104: $i,SV501: $i] :
( ( ! [SY5504: $i] : ( c_Wellfounded_Owf @ ( c_Relation_Oinv__image @ SV501 @ SV1104 @ SV1568 @ SY5504 ) @ SY5504 )
| ~ ( c_Wellfounded_Owf @ SV501 @ SV1568 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3452]) ).
thf(4055,plain,
! [SV1569: $i,SV1106: $i,SV503: $i] :
( ( ! [SY5505: $i] : ( c_Relation_Osym @ ( c_Relation_Oinv__image @ SV503 @ SV1106 @ SV1569 @ SY5505 ) @ SY5505 )
| ~ ( c_Relation_Osym @ SV503 @ SV1569 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3454]) ).
thf(4056,plain,
! [SV1109: $i,SV506: $i] :
( ( ( c_Relation_Otrans @ SV506 @ SV1109 )
= $true )
| ( ( ~ ( c_Relation_Otrans @ ( c_Relation_Oconverse @ SV506 @ SV1109 @ SV1109 ) @ SV1109 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3457]) ).
thf(4057,plain,
! [SV1110: $i,SV507: $i] :
( ( ( c_Relation_Otrans @ ( c_Relation_Oconverse @ SV507 @ SV1110 @ SV1110 ) @ SV1110 )
= $true )
| ( ( ~ ( c_Relation_Otrans @ SV507 @ SV1110 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3458]) ).
thf(4058,plain,
! [SV1111: $i,SV509: $i] :
( ( ( c_Wellfounded_Owf @ ( c_Transitive__Closure_Otrancl @ SV509 @ SV1111 ) @ SV1111 )
= $true )
| ( ( ~ ( c_Wellfounded_Owf @ SV509 @ SV1111 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3459]) ).
thf(4059,plain,
! [SV1570: $i,SV1112: $i,SV510: $i] :
( ( ! [SY5506: $i,SY5507: $i,SY5508: $i,SY5509: $i] :
( ( c_Relation_Orel__comp @ ( c_Relation_Orel__comp @ SV510 @ SV1112 @ SV1570 @ SY5506 @ SY5507 ) @ SY5508 @ SV1570 @ SY5507 @ SY5509 )
= ( c_Relation_Orel__comp @ SV510 @ ( c_Relation_Orel__comp @ SV1112 @ SY5508 @ SY5506 @ SY5507 @ SY5509 ) @ SV1570 @ SY5506 @ SY5509 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3460]) ).
thf(4060,plain,
! [SV1571: $i,SV1113: $i,SV511: $i] :
( ( ! [SY5510: $i] :
( ( c_Relation_Oconverse @ ( c_Relation_Oinv__image @ SV511 @ SV1113 @ SV1571 @ SY5510 ) @ SY5510 @ SY5510 )
= ( c_Relation_Oinv__image @ ( c_Relation_Oconverse @ SV511 @ SV1571 @ SV1571 ) @ SV1113 @ SV1571 @ SY5510 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3461]) ).
thf(4061,plain,
! [SV1572: $i,SV1115: $i,SV513: $i] :
( ( ! [SY5511: $i] : ( c_Relation_Otrans @ ( c_Relation_Oinv__image @ SV513 @ SV1115 @ SV1572 @ SY5511 ) @ SY5511 )
| ~ ( c_Relation_Otrans @ SV513 @ SV1572 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3463]) ).
thf(4062,plain,
! [SV1117: $i,SV515: $i] :
( ( ( ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ SV515 @ SV1117 @ SV1117 ) @ SV515 @ SV1117 @ SV1117 @ SV1117 )
!= SV515 )
= $true )
| ( ( c_Equiv__Relations_Oequiv @ ( c_Relation_ODomain @ SV515 @ SV1117 @ SV1117 ) @ SV515 @ SV1117 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3465]) ).
thf(4063,plain,
! [SV1573: $i,SV1118: $i,SV517: $i] :
( ( ( c_Relation_ORange @ ( c_Relation_Oconverse @ SV517 @ SV1118 @ SV1573 ) @ SV1573 @ SV1118 )
= ( c_Relation_ODomain @ SV517 @ SV1118 @ SV1573 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3466]) ).
thf(4064,plain,
! [SV1574: $i,SV1119: $i,SV518: $i] :
( ( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 @ SV518 @ SV1119 @ SV1574 ) @ SV518 @ SV1574 )
| ! [SY5512: $i] :
~ ( c_in @ SY5512 @ SV518 @ SV1574 )
| ~ ( c_Wellfounded_Owf @ SV1119 @ SV1574 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3467]) ).
thf(4065,plain,
! [SV1575: $i,SV1121: $i,SV520: $i] :
( ( ! [SY5513: $i,SY5514: $i] :
( ( c_Relation_Osingle__valued @ ( c_Relation_Orel__comp @ SV520 @ SV1121 @ SV1575 @ SY5513 @ SY5514 ) @ SV1575 @ SY5514 )
| ~ ( c_Relation_Osingle__valued @ SV1121 @ SY5513 @ SY5514 )
| ~ ( c_Relation_Osingle__valued @ SV520 @ SV1575 @ SY5513 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3469]) ).
thf(4066,plain,
! [SV1576: $i,SV1122: $i,SV521: $i] :
( ( ( c_Relation_Oconverse @ ( c_Relation_Oconverse @ SV521 @ SV1122 @ SV1576 ) @ SV1576 @ SV1122 )
= SV521 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3470]) ).
thf(4067,plain,
! [SV1123: $i,SV523: $i] :
( ( ( ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ SV523 @ SV1123 @ SV1123 ) @ SV523 @ SV1123 @ SV1123 @ SV1123 )
= SV523 )
= $true )
| ( ( ! [SY4897: $i] :
~ ( c_Equiv__Relations_Oequiv @ SY4897 @ SV523 @ SV1123 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3471]) ).
thf(4068,plain,
! [SV1125: $i,SV525: $i] :
( ( ( c_Relation_Oantisym @ SV525 @ SV1125 )
= $true )
| ( ( ~ ( c_Relation_Oantisym @ ( c_Relation_Oconverse @ SV525 @ SV1125 @ SV1125 ) @ SV1125 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3473]) ).
thf(4069,plain,
! [SV1126: $i,SV526: $i] :
( ( ( c_Relation_Oantisym @ ( c_Relation_Oconverse @ SV526 @ SV1126 @ SV1126 ) @ SV1126 )
= $true )
| ( ( ~ ( c_Relation_Oantisym @ SV526 @ SV1126 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3474]) ).
thf(4070,plain,
! [SV1127: $i,SV527: $i] :
( ( ( hBOOL @ ( hAPP @ SV527 @ SV1127 ) )
= $true )
| ( ( ! [SY4898: $i] :
( ~ ( hBOOL @ ( hAPP @ SV527 @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ SV527 @ SY4898 ) ) )
| ~ ( c_in @ SV1127 @ ( c_Wellfounded_Oacc @ SY4898 @ t_a ) @ t_a ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3475]) ).
thf(4071,plain,
! [SV1577: $i,SV1128: $i,SV528: $i] :
( ( ( c_Relation_Orefl__on @ SV528 @ SV1128 @ SV1577 )
| ~ ( c_Equiv__Relations_Oequiv @ SV528 @ SV1128 @ SV1577 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3476]) ).
thf(4072,plain,
! [SV1578: $i,SV1130: $i,SV530: $i] :
( ( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 @ SV530 @ SV1130 @ SV1578 ) @ SV530 @ SV1578 )
| ! [SY5515: $i] :
~ ( c_in @ SY5515 @ SV530 @ SV1578 )
| ~ ( c_Wellfounded_Owf @ SV1130 @ SV1578 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3478]) ).
thf(4073,plain,
! [SV1131: $i,SV531: $i] :
( ( ( c_Relation_Osym @ SV531 @ SV1131 )
= $true )
| ( ( ! [SY4902: $i] :
~ ( c_Equiv__Relations_Oequiv @ SY4902 @ SV531 @ SV1131 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3479]) ).
thf(4074,plain,
! [SV1579: $i,SV1132: $i,SV532: $i] :
( ( ( c_in @ SV532 @ ( c_Wellfounded_Oacc @ SV1132 @ SV1579 ) @ SV1579 )
| ~ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1 @ SV1132 @ SV532 @ SV1579 ) @ ( c_Wellfounded_Oacc @ SV1132 @ SV1579 ) @ SV1579 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3480]) ).
thf(4075,plain,
! [SV1580: $i,SV1133: $i,SV533: $i] :
( ( ! [SY5516: $i,SY5517: $i,SY5518: $i] :
( ( c_Equiv__Relations_Ocongruent @ SV533 @ ( hAPP @ SV1133 @ SV1580 ) @ SY5516 @ SY5517 )
| ! [SY5519: $i] :
( ~ ( c_in @ SV1580 @ SY5518 @ SY5519 )
| ! [SY4909: $i] :
( ~ ( c_Equiv__Relations_Ocongruent2 @ SY4909 @ SV533 @ SV1133 @ SY5519 @ SY5516 @ SY5517 )
| ~ ( c_Equiv__Relations_Oequiv @ SY5518 @ SY4909 @ SY5519 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3481]) ).
thf(4076,plain,
! [SV1581: $i,SV1134: $i,SV534: $i] :
( ( ( c_Relation_ODomain @ ( c_Relation_Oconverse @ SV534 @ SV1134 @ SV1581 ) @ SV1581 @ SV1134 )
= ( c_Relation_ORange @ SV534 @ SV1134 @ SV1581 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3482]) ).
thf(4077,plain,
! [SV1582: $i,SV1137: $i,SV537: $i] :
( ( ( c_Relation_ORange @ SV537 @ SV1137 @ SV1582 )
= ( c_Relation_ODomain @ ( c_Relation_Oconverse @ SV537 @ SV1137 @ SV1582 ) @ SV1582 @ SV1137 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3485]) ).
thf(4078,plain,
! [SV1583: $i,SV1138: $i,SV538: $i] :
( ( ( c_Relation_Ototal__on @ SV538 @ SV1138 @ SV1583 )
| ~ ( c_Relation_Ototal__on @ SV538 @ ( c_Relation_Oconverse @ SV1138 @ SV1583 @ SV1583 ) @ SV1583 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3486]) ).
thf(4079,plain,
! [SV1584: $i,SV1139: $i,SV539: $i] :
( ( ( c_Relation_Ototal__on @ SV539 @ ( c_Relation_Oconverse @ SV1139 @ SV1584 @ SV1584 ) @ SV1584 )
| ~ ( c_Relation_Ototal__on @ SV539 @ SV1139 @ SV1584 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3487]) ).
thf(4080,plain,
! [SV1140: $i,SV540: $i] :
( ( ( c_Relation_Otrans @ SV540 @ SV1140 )
= $true )
| ( ( ! [SY4914: $i] :
~ ( c_Equiv__Relations_Oequiv @ SY4914 @ SV540 @ SV1140 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3488]) ).
thf(4081,plain,
! [SV1141: $i,SV541: $i] :
( ( ( hBOOL @ ( hAPP @ SV541 @ SV1141 ) )
= $true )
| ( ( ! [SY4915: $i,SY4916: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ SV541 @ SY4915 @ SY4916 ) @ ( c_Wellfounded_Oacc @ SY4915 @ SY4916 ) @ SY4916 )
| ~ ( c_in @ SV1141 @ ( c_Wellfounded_Oacc @ SY4915 @ SY4916 ) @ SY4916 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3489]) ).
thf(4082,plain,
! [SV1585: $i,SV1144: $i,SV544: $i] :
( ( ! [SY5521: $i,SY5522: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XImageE__1__1 @ SV544 @ SV1144 @ SV1585 @ SY5521 @ SY5522 ) @ SV1144 @ SY5521 @ SY5522 ) @ SV1585 @ ( tc_prod @ SY5521 @ SY5522 ) )
| ~ ( c_in @ SV1144 @ ( c_Relation_OImage @ SV1585 @ SV544 @ SY5521 @ SY5522 ) @ SY5522 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3492]) ).
thf(4083,plain,
! [SV1586: $i,SV1145: $i,SV545: $i] :
( ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1 @ SV545 @ SV1145 @ SV1586 ) @ SV1145 @ SV1586 @ SV1586 ) @ SV545 @ ( tc_prod @ SV1586 @ SV1586 ) )
| ( c_in @ SV1145 @ ( c_Wellfounded_Oacc @ SV545 @ SV1586 ) @ SV1586 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3493]) ).
thf(4084,plain,
! [SV1587: $i,SV1146: $i,SV546: $i] :
( ( ( hBOOL @ ( hAPP @ SV546 @ SV1146 ) )
| ( hBOOL @ ( hAPP @ SV546 @ SV1587 ) )
| ! [SY5523: $i,SY5524: $i] :
( ~ ( c_in @ ( c_Pair @ SV1587 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ SV546 @ SY5523 @ SY5524 ) @ SY5524 @ SY5524 ) @ SY5523 @ ( tc_prod @ SY5524 @ SY5524 ) )
| ~ ( c_in @ SV1146 @ ( c_Wellfounded_Oacc @ SY5523 @ SY5524 ) @ SY5524 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3494]) ).
thf(4085,plain,
! [SV1147: $i,SV547: $i] :
( ( ( hBOOL @ ( hAPP @ SV547 @ SV1147 ) )
= $true )
| ( ( ! [SY4924: $i] :
( ( hBOOL @ ( hAPP @ SV547 @ SY4924 ) )
| ! [SY4925: $i] :
( ~ ( c_in @ ( c_Pair @ SY4924 @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ SV547 @ SY4925 ) @ t_a @ t_a ) @ SY4925 @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ SV1147 @ ( c_Wellfounded_Oacc @ SY4925 @ t_a ) @ t_a ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3495]) ).
thf(4086,plain,
! [SV1588: $i,SV1148: $i,SV548: $i] :
( ( ~ ( c_in @ SV548 @ SV1148 @ SV1588 )
| ! [SY5525: $i] :
( ~ ( c_in @ ( c_Pair @ SV548 @ ( c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 @ SV1148 @ SY5525 @ SV1588 ) @ SV1588 @ SV1588 ) @ SY5525 @ ( tc_prod @ SV1588 @ SV1588 ) )
| ! [SY5526: $i] :
~ ( c_in @ SY5526 @ SV1148 @ SV1588 )
| ~ ( c_Wellfounded_Owf @ SY5525 @ SV1588 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3496]) ).
thf(4087,plain,
! [SV1589: $i,SV1149: $i,SV549: $i] :
( ( ! [SY5527: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XRangeE__1__1 @ SV549 @ SV1149 @ SV1589 @ SY5527 ) @ SV549 @ SY5527 @ SV1589 ) @ SV1149 @ ( tc_prod @ SY5527 @ SV1589 ) )
| ~ ( c_in @ SV549 @ ( c_Relation_ORange @ SV1149 @ SY5527 @ SV1589 ) @ SV1589 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3497]) ).
thf(4088,plain,
! [SV1590: $i,SV1150: $i,SV550: $i] :
( ( ( c_in @ SV550 @ ( c_Wellfounded_Oacc @ SV1150 @ SV1590 ) @ SV1590 )
| ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1 @ SV1150 @ SV550 @ SV1590 ) @ SV550 @ SV1590 @ SV1590 ) @ SV1150 @ ( tc_prod @ SV1590 @ SV1590 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3498]) ).
thf(4089,plain,
! [SV1591: $i,SV1151: $i,SV551: $i] :
( ( ( c_in @ SV551 @ ( c_Wellfounded_Oacc @ SV1151 @ SV1591 ) @ SV1591 )
| ! [SY5528: $i] :
( ~ ( c_in @ SY5528 @ ( c_Wellfounded_Oacc @ SV1151 @ SV1591 ) @ SV1591 )
| ~ ( c_in @ ( c_Pair @ SV551 @ SY5528 @ SV1591 @ SV1591 ) @ ( c_Transitive__Closure_Ortrancl @ SV1151 @ SV1591 ) @ ( tc_prod @ SV1591 @ SV1591 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3499]) ).
thf(4090,plain,
! [SV1592: $i,SV1152: $i,SV552: $i] :
( ( ( c_in @ SV552 @ ( c_Wellfounded_Oacc @ SV1152 @ SV1592 ) @ SV1592 )
| ! [SY5529: $i] :
( ~ ( c_in @ ( c_Pair @ SV552 @ SY5529 @ SV1592 @ SV1592 ) @ ( c_Transitive__Closure_Ortrancl @ SV1152 @ SV1592 ) @ ( tc_prod @ SV1592 @ SV1592 ) )
| ~ ( c_in @ SY5529 @ ( c_Wellfounded_Oacc @ SV1152 @ SV1592 ) @ SV1592 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3500]) ).
thf(4091,plain,
! [SV1153: $i,SV553: $i] :
( ( ( hBOOL @ ( hAPP @ SV553 @ SV1153 ) )
= $true )
| ( ( ! [SY4936: $i,SY4937: $i] :
( ( c_in @ SY4936 @ ( c_Wellfounded_Oacc @ SY4937 @ t_a ) @ t_a )
| ~ ( c_in @ ( c_Pair @ SY4936 @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ SV553 @ SY4937 ) @ t_a @ t_a ) @ SY4937 @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ SV1153 @ ( c_Wellfounded_Oacc @ SY4937 @ t_a ) @ t_a ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3501]) ).
thf(4092,plain,
! [SV1593: $i,SV1154: $i,SV554: $i] :
( ( ( c_in @ SV554 @ ( c_Relation_ODomain @ SV1154 @ SV1593 @ SV1593 ) @ SV1593 )
| ( c_in @ ( c_Pair @ SV554 @ SV554 @ SV1593 @ SV1593 ) @ ( c_Transitive__Closure_Ortrancl @ SV1154 @ SV1593 ) @ ( tc_prod @ SV1593 @ SV1593 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3502]) ).
thf(4093,plain,
! [SV1155: $i,SV555: $i] :
( ( ( hBOOL @ ( hAPP @ SV555 @ SV1155 ) )
= $true )
| ( ( ! [SY4939: $i] :
( ( hBOOL @ ( hAPP @ SV555 @ SY4939 ) )
| ! [SY4940: $i] :
( ~ ( c_in @ ( c_Pair @ SY4939 @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ SV555 @ SY4940 ) @ t_a @ t_a ) @ SY4940 @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ SV1155 @ ( c_Wellfounded_Oacc @ SY4940 @ t_a ) @ t_a ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3503]) ).
thf(4094,plain,
! [SV1594: $i,SV1156: $i,SV556: $i] :
( ( ! [SY5530: $i,SY5531: $i,SY5532: $i,SY5533: $i] :
( ( c_in @ ( hAPP @ ( hAPP @ SV556 @ SV1156 ) @ SV1594 ) @ ( c_Set_Oimage @ ( c_split @ SV556 @ SY5530 @ SY5531 @ SY5532 ) @ SY5533 @ ( tc_prod @ SY5530 @ SY5531 ) @ SY5532 ) @ SY5532 )
| ~ ( c_in @ ( c_Pair @ SV1156 @ SV1594 @ SY5530 @ SY5531 ) @ SY5533 @ ( tc_prod @ SY5530 @ SY5531 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3504]) ).
thf(4095,plain,
! [SV1595: $i,SV1157: $i,SV557: $i] :
( ( ! [SY5534: $i] :
( ( c_in @ ( c_Pair @ SV557 @ ( c_ATP__Linkup_Osko__Relation__XDomainE__1__1 @ SV557 @ SV1157 @ SV1595 @ SY5534 ) @ SV1595 @ SY5534 ) @ SV1157 @ ( tc_prod @ SV1595 @ SY5534 ) )
| ~ ( c_in @ SV557 @ ( c_Relation_ODomain @ SV1157 @ SV1595 @ SY5534 ) @ SV1595 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3505]) ).
thf(4096,plain,
! [SV1158: $i,SV558: $i] :
( ( ( hBOOL @ ( hAPP @ SV558 @ SV1158 ) )
= $true )
| ( ( ! [SY4948: $i,SY4949: $i] :
( ( c_in @ SY4948 @ ( c_Wellfounded_Oacc @ SY4949 @ t_a ) @ t_a )
| ~ ( c_in @ ( c_Pair @ SY4948 @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ SV558 @ SY4949 ) @ t_a @ t_a ) @ SY4949 @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ SV1158 @ ( c_Wellfounded_Oacc @ SY4949 @ t_a ) @ t_a ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3506]) ).
thf(4097,plain,
! [SV1596: $i,SV1159: $i,SV559: $i] :
( ( ( hBOOL @ ( hAPP @ SV559 @ SV1159 ) )
| ( hBOOL @ ( hAPP @ SV559 @ SV1596 ) )
| ! [SY5535: $i,SY5536: $i] :
( ~ ( c_in @ ( c_Pair @ SV1596 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ SV559 @ SY5535 @ SY5536 ) @ SY5536 @ SY5536 ) @ SY5535 @ ( tc_prod @ SY5536 @ SY5536 ) )
| ~ ( c_in @ SV1159 @ ( c_Wellfounded_Oacc @ SY5535 @ SY5536 ) @ SY5536 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3507]) ).
thf(4098,plain,
! [SV1597: $i,SV1160: $i,SV560: $i] :
( ( ~ ( c_in @ SV560 @ SV1160 @ SV1597 )
| ! [SY5537: $i] :
( ~ ( c_in @ ( c_Pair @ SV560 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 @ SV1160 @ SY5537 @ SV1597 ) @ SV1597 @ SV1597 ) @ SY5537 @ ( tc_prod @ SV1597 @ SV1597 ) )
| ! [SY5538: $i] :
~ ( c_in @ SY5538 @ SV1160 @ SV1597 )
| ~ ( c_Wellfounded_Owf @ SY5537 @ SV1597 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3508]) ).
thf(4099,plain,
! [SV1598: $i,SV1161: $i,SV561: $i] :
( ( ! [SY5539: $i] :
( ( c_in @ ( c_Pair @ SV561 @ ( c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1 @ SV561 @ SV1161 @ SV1598 @ SY5539 ) @ SV1598 @ SY5539 ) @ SV1161 @ ( tc_prod @ SV1598 @ SY5539 ) )
| ~ ( c_in @ SV561 @ ( c_Relation_ODomain @ SV1161 @ SV1598 @ SY5539 ) @ SV1598 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3509]) ).
thf(4100,plain,
! [SV1599: $i,SV1162: $i,SV562: $i] :
( ( ! [SY5540: $i,SY5541: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XImage__iff__1__1 @ SV562 @ SV1162 @ SV1599 @ SY5540 @ SY5541 ) @ SV1162 @ SY5540 @ SY5541 ) @ SV1599 @ ( tc_prod @ SY5540 @ SY5541 ) )
| ~ ( c_in @ SV1162 @ ( c_Relation_OImage @ SV1599 @ SV562 @ SY5540 @ SY5541 ) @ SY5541 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3510]) ).
thf(4101,plain,
! [SV1163: $i,SV563: $i] :
( ( ( SV563 = SV1163 )
= $true )
| ( ( ! [SY4961: $i,SY4962: $i] :
( ~ ( c_in @ ( c_Pair @ SV563 @ SV1163 @ SY4961 @ SY4961 ) @ ( c_Transitive__Closure_Ortrancl @ SY4962 @ SY4961 ) @ ( tc_prod @ SY4961 @ SY4961 ) )
| ( c_in @ SV563 @ ( c_Relation_ODomain @ SY4962 @ SY4961 @ SY4961 ) @ SY4961 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3511]) ).
thf(4102,plain,
! [SV1600: $i,SV1164: $i,SV564: $i] :
( ( ! [SY5542: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XRange__iff__1__1 @ SV564 @ SV1164 @ SV1600 @ SY5542 ) @ SV564 @ SY5542 @ SV1600 ) @ SV1164 @ ( tc_prod @ SY5542 @ SV1600 ) )
| ~ ( c_in @ SV564 @ ( c_Relation_ORange @ SV1164 @ SY5542 @ SV1600 ) @ SV1600 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3512]) ).
thf(4103,plain,
! [SV1601: $i,SV1165: $i,SV565: $i] :
( ( ! [SY5543: $i,SY5544: $i,SY5545: $i,SY5546: $i] :
( ( c_in @ SV565 @ ( hAPP @ ( c_split @ SV1165 @ SV1601 @ SY5543 @ ( tc_fun @ SY5544 @ tc_bool ) ) @ ( c_Pair @ SY5545 @ SY5546 @ SV1601 @ SY5543 ) ) @ SY5544 )
| ~ ( c_in @ SV565 @ ( hAPP @ ( hAPP @ SV1165 @ SY5545 ) @ SY5546 ) @ SY5544 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3513]) ).
thf(4104,plain,
! [SV1602: $i,SV1166: $i,SV566: $i] :
( ( ! [SY5547: $i,SY5548: $i,SY5549: $i,SY5550: $i,SY5551: $i] :
( ( ( hAPP @ ( hAPP @ SV566 @ SV1166 ) @ SV1602 )
= ( hAPP @ ( hAPP @ SV566 @ SY5547 ) @ SY5548 ) )
| ~ ( c_in @ ( c_Pair @ SV1602 @ SY5548 @ SY5549 @ SY5549 ) @ SY5550 @ ( tc_prod @ SY5549 @ SY5549 ) )
| ! [SY4976: $i] :
( ~ ( c_in @ ( c_Pair @ SV1166 @ SY5547 @ SY5551 @ SY5551 ) @ SY4976 @ ( tc_prod @ SY5551 @ SY5551 ) )
| ! [SY3833: $i] :
~ ( c_Equiv__Relations_Ocongruent2 @ SY4976 @ SY5550 @ SV566 @ SY5551 @ SY5549 @ SY3833 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3514]) ).
thf(4105,plain,
! [SV1603: $i,SV1167: $i,SV567: $i] :
( ( ! [SY5554: $i] :
( ( SV567 = SV1167 )
| ! [SY5555: $i,SY5556: $i] :
( ~ ( c_in @ ( c_Pair @ SV1603 @ SV1167 @ SY5554 @ SY5555 ) @ SY5556 @ ( tc_prod @ SY5554 @ SY5555 ) )
| ~ ( c_in @ ( c_Pair @ SV1603 @ SV567 @ SY5554 @ SY5555 ) @ SY5556 @ ( tc_prod @ SY5554 @ SY5555 ) )
| ~ ( c_Relation_Osingle__valued @ SY5556 @ SY5554 @ SY5555 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3515]) ).
thf(4106,plain,
! [SV1604: $i,SV1168: $i,SV568: $i] :
( ( ! [SY5557: $i,SY5558: $i,SY5559: $i] :
( ( ( hAPP @ ( c_Recdef_Ocut @ SV568 @ SV1168 @ SV1604 @ SY5557 @ SY5558 ) @ SY5559 )
= ( hAPP @ SV568 @ SY5559 ) )
| ~ ( c_in @ ( c_Pair @ SY5559 @ SV1604 @ SY5557 @ SY5557 ) @ SV1168 @ ( tc_prod @ SY5557 @ SY5557 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3516]) ).
thf(4107,plain,
! [SV1605: $i,SV1169: $i,SV569: $i] :
( ( ! [SY5560: $i,SY5561: $i,SY5562: $i] :
( ( ( hAPP @ ( c_Recdef_Ocut @ SV569 @ SV1169 @ SV1605 @ SY5560 @ SY5561 ) @ SY5562 )
= ( hAPP @ SV569 @ SY5562 ) )
| ~ ( c_in @ ( c_Pair @ SY5562 @ SV1605 @ SY5560 @ SY5560 ) @ SV1169 @ ( tc_prod @ SY5560 @ SY5560 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3517]) ).
thf(4108,plain,
! [SV1606: $i,SV1170: $i,SV570: $i] :
( ( ! [SY5563: $i,SY5564: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_FunDef_Oin__rel @ SV570 @ SV1170 @ SV1606 ) @ SY5563 ) @ SY5564 ) )
| ~ ( c_in @ ( c_Pair @ SY5563 @ SY5564 @ SV1170 @ SV1606 ) @ SV570 @ ( tc_prod @ SV1170 @ SV1606 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3518]) ).
thf(4109,plain,
! [SV1607: $i,SV1171: $i,SV571: $i] :
( ( ! [SY5565: $i,SY5566: $i] :
( ( c_in @ ( c_Pair @ SV571 @ SV1171 @ SV1607 @ SY5565 ) @ SY5566 @ ( tc_prod @ SV1607 @ SY5565 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_FunDef_Oin__rel @ SY5566 @ SV1607 @ SY5565 ) @ SV571 ) @ SV1171 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3519]) ).
thf(4110,plain,
! [SV1608: $i,SV1172: $i,SV572: $i] :
( ( ! [SY5567: $i] :
( ( c_in @ ( c_Pair @ SV572 @ SV1172 @ SV1608 @ SV1608 ) @ SY5567 @ ( tc_prod @ SV1608 @ SV1608 ) )
| ! [SY5568: $i] :
( ~ ( c_in @ ( c_Pair @ SY5568 @ SV1172 @ SV1608 @ SV1608 ) @ SY5567 @ ( tc_prod @ SV1608 @ SV1608 ) )
| ~ ( c_in @ ( c_Pair @ SV572 @ SY5568 @ SV1608 @ SV1608 ) @ SY5567 @ ( tc_prod @ SV1608 @ SV1608 ) )
| ~ ( c_Relation_Otrans @ SY5567 @ SV1608 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3520]) ).
thf(4111,plain,
! [SV1609: $i,SV1173: $i,SV573: $i] :
( ( ! [SY5569: $i] :
( ( c_in @ ( c_Pair @ SV573 @ SV1173 @ SV1609 @ SV1609 ) @ SY5569 @ ( tc_prod @ SV1609 @ SV1609 ) )
| ! [SY5570: $i] :
( ~ ( c_in @ ( c_Pair @ SY5570 @ SV1173 @ SV1609 @ SV1609 ) @ SY5569 @ ( tc_prod @ SV1609 @ SV1609 ) )
| ~ ( c_in @ ( c_Pair @ SV573 @ SY5570 @ SV1609 @ SV1609 ) @ SY5569 @ ( tc_prod @ SV1609 @ SV1609 ) )
| ~ ( c_Relation_Otrans @ SY5569 @ SV1609 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3521]) ).
thf(4112,plain,
! [SV1610: $i,SV1174: $i,SV574: $i] :
( ( ! [SY5571: $i,SY5572: $i] :
( ( c_in @ ( c_Pair @ SV574 @ SV1174 @ SV1610 @ SY5571 ) @ ( c_Relation_Oconverse @ SY5572 @ SY5571 @ SV1610 ) @ ( tc_prod @ SV1610 @ SY5571 ) )
| ~ ( c_in @ ( c_Pair @ SV1174 @ SV574 @ SY5571 @ SV1610 ) @ SY5572 @ ( tc_prod @ SY5571 @ SV1610 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3522]) ).
thf(4113,plain,
! [SV1611: $i,SV1175: $i,SV575: $i] :
( ( ! [SY5573: $i,SY5574: $i] :
( ( c_in @ ( c_Pair @ SV575 @ SV1175 @ SV1611 @ SY5573 ) @ ( c_Relation_Oconverse @ SY5574 @ SY5573 @ SV1611 ) @ ( tc_prod @ SV1611 @ SY5573 ) )
| ~ ( c_in @ ( c_Pair @ SV1175 @ SV575 @ SY5573 @ SV1611 ) @ SY5574 @ ( tc_prod @ SY5573 @ SV1611 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3523]) ).
thf(4114,plain,
! [SV1612: $i,SV1176: $i,SV576: $i] :
( ( ! [SY5575: $i,SY5576: $i] :
( ( c_in @ ( c_Pair @ SV576 @ SV1176 @ SV1612 @ SY5575 ) @ SY5576 @ ( tc_prod @ SV1612 @ SY5575 ) )
| ~ ( c_in @ ( c_Pair @ SV1176 @ SV576 @ SY5575 @ SV1612 ) @ ( c_Relation_Oconverse @ SY5576 @ SV1612 @ SY5575 ) @ ( tc_prod @ SY5575 @ SV1612 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3524]) ).
thf(4115,plain,
! [SV1613: $i,SV1177: $i,SV577: $i] :
( ( ~ ( c_in @ ( c_Pair @ SV577 @ SV577 @ SV1177 @ SV1177 ) @ SV1613 @ ( tc_prod @ SV1177 @ SV1177 ) )
| ~ ( c_Relation_Oirrefl @ SV1613 @ SV1177 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3525]) ).
thf(4116,plain,
! [SV1614: $i,SV1178: $i,SV578: $i] :
( ( ! [SY5577: $i] :
( ( c_in @ ( c_Pair @ SV578 @ SV1178 @ SV1614 @ SV1614 ) @ ( c_Transitive__Closure_Otrancl @ SY5577 @ SV1614 ) @ ( tc_prod @ SV1614 @ SV1614 ) )
| ! [SY5578: $i] :
( ~ ( c_in @ ( c_Pair @ SY5578 @ SV1178 @ SV1614 @ SV1614 ) @ SY5577 @ ( tc_prod @ SV1614 @ SV1614 ) )
| ~ ( c_in @ ( c_Pair @ SV578 @ SY5578 @ SV1614 @ SV1614 ) @ ( c_Transitive__Closure_Otrancl @ SY5577 @ SV1614 ) @ ( tc_prod @ SV1614 @ SV1614 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3526]) ).
thf(4117,plain,
! [SV1615: $i,SV1179: $i,SV579: $i] :
( ( ! [SY5579: $i] :
( ( c_in @ ( c_Pair @ SV579 @ SV1179 @ SV1615 @ SV1615 ) @ ( c_Transitive__Closure_Otrancl @ SY5579 @ SV1615 ) @ ( tc_prod @ SV1615 @ SV1615 ) )
| ! [SY5580: $i] :
( ~ ( c_in @ ( c_Pair @ SY5580 @ SV1179 @ SV1615 @ SV1615 ) @ ( c_Transitive__Closure_Otrancl @ SY5579 @ SV1615 ) @ ( tc_prod @ SV1615 @ SV1615 ) )
| ~ ( c_in @ ( c_Pair @ SV579 @ SY5580 @ SV1615 @ SV1615 ) @ SY5579 @ ( tc_prod @ SV1615 @ SV1615 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3527]) ).
thf(4118,plain,
! [SV1616: $i,SV1180: $i,SV580: $i] :
( ( ! [SY5581: $i] :
( ( c_in @ ( c_Pair @ SV580 @ SV1180 @ SV1616 @ SV1616 ) @ ( c_Transitive__Closure_Ortrancl @ SY5581 @ SV1616 ) @ ( tc_prod @ SV1616 @ SV1616 ) )
| ! [SY5582: $i] :
( ~ ( c_in @ ( c_Pair @ SY5582 @ SV1180 @ SV1616 @ SV1616 ) @ SY5581 @ ( tc_prod @ SV1616 @ SV1616 ) )
| ~ ( c_in @ ( c_Pair @ SV580 @ SY5582 @ SV1616 @ SV1616 ) @ ( c_Transitive__Closure_Ortrancl @ SY5581 @ SV1616 ) @ ( tc_prod @ SV1616 @ SV1616 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3528]) ).
thf(4119,plain,
! [SV1617: $i,SV1181: $i,SV581: $i] :
( ( ! [SY5583: $i] :
( ( c_in @ ( c_Pair @ SV581 @ SV1181 @ SV1617 @ SV1617 ) @ ( c_Transitive__Closure_Ortrancl @ SY5583 @ SV1617 ) @ ( tc_prod @ SV1617 @ SV1617 ) )
| ! [SY5584: $i] :
( ~ ( c_in @ ( c_Pair @ SY5584 @ SV1181 @ SV1617 @ SV1617 ) @ ( c_Transitive__Closure_Ortrancl @ SY5583 @ SV1617 ) @ ( tc_prod @ SV1617 @ SV1617 ) )
| ~ ( c_in @ ( c_Pair @ SV581 @ SY5584 @ SV1617 @ SV1617 ) @ SY5583 @ ( tc_prod @ SV1617 @ SV1617 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3529]) ).
thf(4120,plain,
! [SV1618: $i,SV1182: $i,SV582: $i] :
( ( ! [SY5585: $i] :
( ( c_in @ ( c_Pair @ SV582 @ SV1182 @ SV1618 @ SV1618 ) @ ( c_Transitive__Closure_Otrancl @ SY5585 @ SV1618 ) @ ( tc_prod @ SV1618 @ SV1618 ) )
| ~ ( c_in @ ( c_Pair @ SV582 @ SV1182 @ SV1618 @ SV1618 ) @ SY5585 @ ( tc_prod @ SV1618 @ SV1618 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3530]) ).
thf(4121,plain,
! [SV1619: $i,SV1183: $i,SV583: $i] :
( ( ! [SY5586: $i] :
( ( c_in @ ( c_Pair @ SV583 @ SV1183 @ SV1619 @ SV1619 ) @ ( c_Transitive__Closure_Ortrancl @ SY5586 @ SV1619 ) @ ( tc_prod @ SV1619 @ SV1619 ) )
| ! [SY5587: $i] :
( ~ ( c_in @ ( c_Pair @ SY5587 @ SV1183 @ SV1619 @ SV1619 ) @ ( c_Transitive__Closure_Ortrancl @ SY5586 @ SV1619 ) @ ( tc_prod @ SV1619 @ SV1619 ) )
| ~ ( c_in @ ( c_Pair @ SV583 @ SY5587 @ SV1619 @ SV1619 ) @ ( c_Transitive__Closure_Ortrancl @ SY5586 @ SV1619 ) @ ( tc_prod @ SV1619 @ SV1619 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3531]) ).
thf(4122,plain,
! [SV1620: $i,SV1184: $i,SV584: $i] :
( ( c_in @ ( c_Pair @ SV584 @ SV584 @ SV1184 @ SV1184 ) @ ( c_Transitive__Closure_Ortrancl @ SV1620 @ SV1184 ) @ ( tc_prod @ SV1184 @ SV1184 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3532]) ).
thf(4123,plain,
! [SV1621: $i,SV1185: $i,SV585: $i] :
( ( c_in @ ( c_Pair @ SV585 @ SV585 @ SV1185 @ SV1185 ) @ ( c_Transitive__Closure_Ortrancl @ SV1621 @ SV1185 ) @ ( tc_prod @ SV1185 @ SV1185 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3533]) ).
thf(4124,plain,
! [SV1622: $i,SV1186: $i,SV586: $i] :
( ( ! [SY5588: $i] :
( ~ ( c_in @ ( c_Pair @ SV586 @ SV1186 @ SV1622 @ SV1622 ) @ SY5588 @ ( tc_prod @ SV1622 @ SV1622 ) )
| ~ ( c_in @ ( c_Pair @ SV1186 @ SV586 @ SV1622 @ SV1622 ) @ SY5588 @ ( tc_prod @ SV1622 @ SV1622 ) )
| ~ ( c_Wellfounded_Owf @ SY5588 @ SV1622 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3534]) ).
thf(4125,plain,
! [SV1187: $i,SV587: $i] :
( ( ( SV587 = SV1187 )
= $true )
| ( ( ! [SY5033: $i,SY5034: $i] :
( ~ ( c_in @ ( c_Pair @ SV1187 @ SV587 @ SY5033 @ SY5033 ) @ SY5034 @ ( tc_prod @ SY5033 @ SY5033 ) )
| ~ ( c_in @ ( c_Pair @ SV587 @ SV1187 @ SY5033 @ SY5033 ) @ SY5034 @ ( tc_prod @ SY5033 @ SY5033 ) )
| ~ ( c_Relation_Oantisym @ SY5034 @ SY5033 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3535]) ).
thf(4126,plain,
! [SV1188: $i,SV588: $i] :
( ( ( SV588 = SV1188 )
= $true )
| ( ( ! [SY5035: $i,SY5036: $i] :
( ~ ( c_in @ ( c_Pair @ SV1188 @ SV588 @ SY5035 @ SY5035 ) @ SY5036 @ ( tc_prod @ SY5035 @ SY5035 ) )
| ~ ( c_in @ ( c_Pair @ SV588 @ SV1188 @ SY5035 @ SY5035 ) @ SY5036 @ ( tc_prod @ SY5035 @ SY5035 ) )
| ~ ( c_Relation_Oantisym @ SY5036 @ SY5035 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3536]) ).
thf(4127,plain,
! [SV1623: $i,SV1189: $i,SV589: $i] :
( ( ! [SY5589: $i] :
( ( ( hAPP @ SV589 @ SV1189 )
= ( hAPP @ SV589 @ SV1623 ) )
| ! [SY5590: $i] :
( ~ ( c_in @ ( c_Pair @ SV1189 @ SV1623 @ SY5589 @ SY5589 ) @ SY5590 @ ( tc_prod @ SY5589 @ SY5589 ) )
| ! [SY3919: $i] :
~ ( c_Equiv__Relations_Ocongruent @ SY5590 @ SV589 @ SY5589 @ SY3919 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3537]) ).
thf(4128,plain,
! [SV1190: $i,SV590: $i] :
( ( ( SV590 = SV1190 )
= $true )
| ( ( ! [SY5041: $i,SY5042: $i] :
~ ( c_in @ ( c_Pair @ SV590 @ SV1190 @ SY5041 @ SY5041 ) @ ( c_Relation_OId__on @ SY5042 @ SY5041 ) @ ( tc_prod @ SY5041 @ SY5041 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3538]) ).
thf(4129,plain,
! [SV1624: $i,SV1191: $i,SV591: $i] :
( ( ! [SY5592: $i,SY5593: $i,SY5594: $i] :
( ( ( c_Recdef_Ocut @ SV591 @ SV1191 @ SV1624 @ SY5592 @ SY5593 )
!= ( c_Recdef_Ocut @ SY5594 @ SV1191 @ SV1624 @ SY5592 @ SY5593 ) )
| ! [SY5595: $i] :
( ( ( hAPP @ SV591 @ SY5595 )
= ( hAPP @ SY5594 @ SY5595 ) )
| ~ ( c_in @ ( c_Pair @ SY5595 @ SV1624 @ SY5592 @ SY5592 ) @ SV1191 @ ( tc_prod @ SY5592 @ SY5592 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3539]) ).
thf(4130,plain,
! [SV1192: $i,SV592: $i] :
( ( ( SV592 = SV1192 )
= $true )
| ( ( ! [SY5048: $i] :
~ ( c_in @ ( c_Pair @ SV592 @ SV1192 @ SY5048 @ SY5048 ) @ ( c_Relation_OId @ SY5048 ) @ ( tc_prod @ SY5048 @ SY5048 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3540]) ).
thf(4131,plain,
! [SV1625: $i,SV1193: $i,SV593: $i] :
( ( ( c_in @ ( c_Pair @ SV593 @ SV593 @ SV1193 @ SV1193 ) @ SV1625 @ ( tc_prod @ SV1193 @ SV1193 ) )
| ~ ( c_Nitpick_Orefl_H @ SV1625 @ SV1193 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3541]) ).
thf(4132,plain,
! [SV1626: $i,SV1194: $i,SV594: $i] :
( ( ~ ( c_in @ ( c_Pair @ SV594 @ SV594 @ SV1194 @ SV1194 ) @ SV1626 @ ( tc_prod @ SV1194 @ SV1194 ) )
| ~ ( c_Wellfounded_Owf @ SV1626 @ SV1194 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3542]) ).
thf(4133,plain,
! [SV1627: $i,SV1195: $i,SV595: $i] :
( ( ! [SY5596: $i,SY5597: $i,SY5598: $i] :
( ( c_in @ ( c_Pair @ SV595 @ SV1195 @ SV1627 @ SV1627 ) @ ( c_Relation_Oinv__image @ SY5596 @ SY5597 @ SY5598 @ SV1627 ) @ ( tc_prod @ SV1627 @ SV1627 ) )
| ~ ( c_in @ ( c_Pair @ ( hAPP @ SY5597 @ SV595 ) @ ( hAPP @ SY5597 @ SV1195 ) @ SY5598 @ SY5598 ) @ SY5596 @ ( tc_prod @ SY5598 @ SY5598 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3543]) ).
thf(4134,plain,
! [SV1628: $i,SV1196: $i,SV596: $i] :
( ( ! [SY5599: $i,SY5600: $i] :
( ( c_in @ ( c_Pair @ ( hAPP @ SV596 @ SV1196 ) @ ( hAPP @ SV596 @ SV1628 ) @ SY5599 @ SY5599 ) @ SY5600 @ ( tc_prod @ SY5599 @ SY5599 ) )
| ! [SY5601: $i] :
~ ( c_in @ ( c_Pair @ SV1196 @ SV1628 @ SY5601 @ SY5601 ) @ ( c_Relation_Oinv__image @ SY5600 @ SV596 @ SY5599 @ SY5601 ) @ ( tc_prod @ SY5601 @ SY5601 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3544]) ).
thf(4135,plain,
! [SV1629: $i,SV1197: $i,SV597: $i] :
( ( ! [SY5602: $i] :
( ( c_in @ ( c_Pair @ SV597 @ SV1197 @ SV1629 @ SV1629 ) @ SY5602 @ ( tc_prod @ SV1629 @ SV1629 ) )
| ~ ( c_in @ ( c_Pair @ SV1197 @ SV597 @ SV1629 @ SV1629 ) @ SY5602 @ ( tc_prod @ SV1629 @ SV1629 ) )
| ~ ( c_Relation_Osym @ SY5602 @ SV1629 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3545]) ).
thf(4136,plain,
! [SV1630: $i,SV1198: $i,SV598: $i] :
( ( ! [SY5603: $i] :
( ( c_in @ ( c_Pair @ SV598 @ SV1198 @ SV1630 @ SV1630 ) @ SY5603 @ ( tc_prod @ SV1630 @ SV1630 ) )
| ~ ( c_in @ ( c_Pair @ SV1198 @ SV598 @ SV1630 @ SV1630 ) @ SY5603 @ ( tc_prod @ SV1630 @ SV1630 ) )
| ~ ( c_Relation_Osym @ SY5603 @ SV1630 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3546]) ).
thf(4137,plain,
! [SV1631: $i,SV1199: $i,SV599: $i] :
( ( ! [SY5604: $i,SY5605: $i,SY5606: $i,SY5607: $i] :
( ( c_in @ ( c_Pair @ SV599 @ SV1199 @ SV1631 @ SY5604 ) @ ( c_Relation_Orel__comp @ SY5605 @ SY5606 @ SV1631 @ SY5607 @ SY5604 ) @ ( tc_prod @ SV1631 @ SY5604 ) )
| ! [SY5608: $i] :
( ~ ( c_in @ ( c_Pair @ SY5608 @ SV1199 @ SY5607 @ SY5604 ) @ SY5606 @ ( tc_prod @ SY5607 @ SY5604 ) )
| ~ ( c_in @ ( c_Pair @ SV599 @ SY5608 @ SV1631 @ SY5607 ) @ SY5605 @ ( tc_prod @ SV1631 @ SY5607 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3547]) ).
thf(4138,plain,
! [SV1632: $i,SV1200: $i,SV600: $i] :
( ( ! [SY5609: $i] :
( ( c_in @ ( c_Pair @ SV600 @ SV1200 @ SV1632 @ SV1632 ) @ ( c_Transitive__Closure_Otrancl @ SY5609 @ SV1632 ) @ ( tc_prod @ SV1632 @ SV1632 ) )
| ! [SY5610: $i] :
( ~ ( c_in @ ( c_Pair @ SY5610 @ SV1200 @ SV1632 @ SV1632 ) @ SY5609 @ ( tc_prod @ SV1632 @ SV1632 ) )
| ~ ( c_in @ ( c_Pair @ SV600 @ SY5610 @ SV1632 @ SV1632 ) @ SY5609 @ ( tc_prod @ SV1632 @ SV1632 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3548]) ).
thf(4139,plain,
! [SV1633: $i,SV1201: $i,SV601: $i] :
( ( ! [SY5611: $i] :
( ( c_in @ ( c_Pair @ SV601 @ SV1201 @ SV1633 @ SV1633 ) @ ( c_Transitive__Closure_Otrancl @ SY5611 @ SV1633 ) @ ( tc_prod @ SV1633 @ SV1633 ) )
| ! [SY5612: $i] :
( ~ ( c_in @ ( c_Pair @ SY5612 @ SV1201 @ SV1633 @ SV1633 ) @ ( c_Transitive__Closure_Otrancl @ SY5611 @ SV1633 ) @ ( tc_prod @ SV1633 @ SV1633 ) )
| ~ ( c_in @ ( c_Pair @ SV601 @ SY5612 @ SV1633 @ SV1633 ) @ ( c_Transitive__Closure_Otrancl @ SY5611 @ SV1633 ) @ ( tc_prod @ SV1633 @ SV1633 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3549]) ).
thf(4140,plain,
! [SV1634: $i,SV1204: $i,SV604: $i] :
( ( ! [SY5613: $i] :
( ( c_in @ ( c_Pair @ SV604 @ SV1204 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omktop @ SV1634 ) @ SY5613 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV604 @ SV1204 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1634 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV604 = SV1204 )
| ( SV604 = SY5613 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3552]) ).
thf(4141,plain,
! [SV1635: $i,SV1205: $i,SV605: $i] :
( ( ! [SY5614: $i] :
( ( c_in @ ( c_Pair @ SV605 @ SV1205 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omktop @ SV1635 ) @ SY5614 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV605 @ SV1205 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1635 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV1205 = SY5614 )
| ( SV605 = SY5614 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3553]) ).
thf(4142,plain,
! [SV1206: $i,SV606: $i] :
( ( c_in @ ( c_Pair @ SV606 @ SV606 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omktop @ SV1206 ) @ SV606 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3554]) ).
thf(4143,plain,
! [SV1636: $i,SV1207: $i,SV607: $i] :
( ( ~ ( c_in @ ( c_Pair @ SV607 @ SV1207 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omktop @ SV1636 ) @ SV607 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3555]) ).
thf(4144,plain,
! [SV1637: $i,SV1208: $i,SV608: $i] :
( ( ( c_in @ ( c_Pair @ SV608 @ SV1208 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1637 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ! [SY5615: $i] :
( ( SV1208 = SY5615 )
| ~ ( c_in @ ( c_Pair @ SV608 @ SV1208 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omktop @ SV1637 ) @ SY5615 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3556]) ).
thf(4145,plain,
! [SV1209: $i,SV609: $i] :
( ( ( SV609 = SV1209 )
= $true )
| ( ( ( SV1209 = SV609 )
| ! [SY5082: $i] : ( c_in @ ( c_Pair @ SV609 @ SV1209 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omkbot @ SY5082 ) @ SV609 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3557]) ).
thf(4146,plain,
! [SV1210: $i,SV610: $i] :
( ( c_in @ ( c_Pair @ SV610 @ SV610 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omkbot @ SV1210 ) @ SV610 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3558]) ).
thf(4147,plain,
! [SV1638: $i,SV1211: $i,SV611: $i] :
( ( ~ ( c_in @ ( c_Pair @ SV611 @ SV1211 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omkbot @ SV1638 ) @ SV1211 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3559]) ).
thf(4148,plain,
! [SV1639: $i,SV1212: $i,SV612: $i] :
( ( ! [SY5616: $i] :
( ( c_in @ ( c_Pair @ SV612 @ SV1212 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omkbot @ SV1639 ) @ SY5616 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV612 @ SV1212 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1639 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV612 = SV1212 )
| ( SV1212 = SY5616 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3560]) ).
thf(4149,plain,
! [SV1640: $i,SV1213: $i,SV613: $i] :
( ( ! [SY5617: $i] :
( ( c_in @ ( c_Pair @ SV613 @ SV1213 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omkbot @ SV1640 ) @ SY5617 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV613 @ SV1213 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1640 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV613 = SY5617 )
| ( SV1213 = SY5617 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3561]) ).
thf(4150,plain,
! [SV1214: $i,SV614: $i] :
( ( ( SV614 = SV1214 )
= $true )
| ( ( ( SV614 = SV1214 )
| ! [SY5088: $i] : ( c_in @ ( c_Pair @ SV614 @ SV1214 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omktop @ SY5088 ) @ SV1214 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3562]) ).
thf(4151,plain,
! [SV1641: $i,SV1215: $i,SV615: $i] :
( ( ( c_in @ ( c_Pair @ SV615 @ SV1215 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1641 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ! [SY5618: $i] :
( ( SV615 = SY5618 )
| ~ ( c_in @ ( c_Pair @ SV615 @ SV1215 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omkbot @ SV1641 ) @ SY5618 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3563]) ).
thf(4152,plain,
! [SV1216: $i,SV616: $i] :
( ( ( SV616 = SV1216 )
= $true )
| ( ( c_in @ ( c_Pair @ SV616 @ SV1216 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1 @ SV616 @ SV1216 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3564]) ).
thf(4153,plain,
! [SV1642: $i,SV1217: $i,SV617: $i] :
( ( ! [SY5619: $i,SY5620: $i,SY5621: $i] :
( ( c_in @ ( c_Pair @ SV617 @ SV1217 @ SV1642 @ SY5619 ) @ ( c_Product__Type_OSigma @ SY5620 @ SY5621 @ SV1642 @ SY5619 ) @ ( tc_prod @ SV1642 @ SY5619 ) )
| ~ ( c_in @ SV1217 @ ( hAPP @ SY5621 @ SV617 ) @ SY5619 )
| ~ ( c_in @ SV617 @ SY5620 @ SV1642 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3565]) ).
thf(4154,plain,
! [SV1643: $i,SV1218: $i,SV618: $i] :
( ( ! [SY5622: $i,SY5623: $i,SY5624: $i] :
( ( c_in @ ( c_Pair @ SV618 @ SV1218 @ SV1643 @ SY5622 ) @ ( c_Product__Type_OSigma @ SY5623 @ SY5624 @ SV1643 @ SY5622 ) @ ( tc_prod @ SV1643 @ SY5622 ) )
| ~ ( c_in @ SV1218 @ ( hAPP @ SY5624 @ SV618 ) @ SY5622 )
| ~ ( c_in @ SV618 @ SY5623 @ SV1643 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3566]) ).
thf(4155,plain,
! [SV1644: $i,SV1219: $i,SV619: $i] :
( ( ( c_in @ SV619 @ ( c_Wellfounded_Oacc @ SV1219 @ SV1644 ) @ SV1644 )
| ! [SY5625: $i] :
( ~ ( c_in @ ( c_Pair @ SV619 @ SY5625 @ SV1644 @ SV1644 ) @ SV1219 @ ( tc_prod @ SV1644 @ SV1644 ) )
| ~ ( c_in @ SY5625 @ ( c_Wellfounded_Oacc @ SV1219 @ SV1644 ) @ SV1644 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3567]) ).
thf(4156,plain,
! [SV1645: $i,SV1220: $i,SV620: $i] :
( ( ( c_in @ SV620 @ ( c_Wellfounded_Oacc @ SV1220 @ SV1645 ) @ SV1645 )
| ! [SY5626: $i] :
( ~ ( c_in @ ( c_Pair @ SV620 @ SY5626 @ SV1645 @ SV1645 ) @ SV1220 @ ( tc_prod @ SV1645 @ SV1645 ) )
| ~ ( c_in @ SY5626 @ ( c_Wellfounded_Oacc @ SV1220 @ SV1645 ) @ SV1645 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3568]) ).
thf(4157,plain,
! [SV1646: $i,SV1221: $i,SV621: $i] :
( ( ! [SY5627: $i,SY5628: $i] :
( ( c_in @ SV621 @ ( c_Relation_OImage @ SV1221 @ SV1646 @ SY5627 @ SY5628 ) @ SY5628 )
| ! [SY5629: $i] :
( ~ ( c_in @ ( c_Pair @ SY5629 @ SV621 @ SY5627 @ SY5628 ) @ SV1221 @ ( tc_prod @ SY5627 @ SY5628 ) )
| ~ ( c_in @ SY5629 @ SV1646 @ SY5627 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3569]) ).
thf(4158,plain,
! [SV1647: $i,SV1222: $i,SV622: $i] :
( ( ! [SY5630: $i,SY5631: $i] :
( ( c_in @ SV622 @ ( c_Relation_OImage @ SV1222 @ SV1647 @ SY5630 @ SY5631 ) @ SY5631 )
| ! [SY5632: $i] :
( ~ ( c_in @ ( c_Pair @ SY5632 @ SV622 @ SY5630 @ SY5631 ) @ SV1222 @ ( tc_prod @ SY5630 @ SY5631 ) )
| ~ ( c_in @ SY5632 @ SV1647 @ SY5630 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3570]) ).
thf(4159,plain,
! [SV1648: $i,SV1223: $i,SV623: $i] :
( ( ( c_in @ SV623 @ SV1223 @ SV1648 )
| ! [SY5633: $i] :
~ ( c_in @ ( c_Pair @ SV623 @ SY5633 @ SV1648 @ SV1648 ) @ ( c_Relation_OId__on @ SV1223 @ SV1648 ) @ ( tc_prod @ SV1648 @ SV1648 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3571]) ).
thf(4160,plain,
! [SV1649: $i,SV1224: $i,SV624: $i] :
( ( ( c_in @ ( c_Pair @ SV624 @ SV624 @ SV1224 @ SV1224 ) @ ( c_Relation_OId__on @ SV1649 @ SV1224 ) @ ( tc_prod @ SV1224 @ SV1224 ) )
| ~ ( c_in @ SV624 @ SV1649 @ SV1224 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3572]) ).
thf(4161,plain,
! [SV1650: $i,SV1225: $i,SV625: $i] :
( ( ( c_in @ SV625 @ SV1225 @ SV1650 )
| ! [SY5634: $i,SY5635: $i] :
( ~ ( c_in @ ( c_Pair @ SY5634 @ SV625 @ SV1650 @ SV1650 ) @ SY5635 @ ( tc_prod @ SV1650 @ SV1650 ) )
| ~ ( c_Equiv__Relations_Oequiv @ SV1225 @ SY5635 @ SV1650 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3573]) ).
thf(4162,plain,
! [SV1651: $i,SV1226: $i,SV626: $i] :
( ( ( c_in @ SV626 @ SV1226 @ SV1651 )
| ! [SY5636: $i,SY5637: $i] :
( ~ ( c_in @ ( c_Pair @ SV626 @ SY5636 @ SV1651 @ SV1651 ) @ SY5637 @ ( tc_prod @ SV1651 @ SV1651 ) )
| ~ ( c_Equiv__Relations_Oequiv @ SV1226 @ SY5637 @ SV1651 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3574]) ).
thf(4163,plain,
! [SV1652: $i,SV1227: $i,SV627: $i] :
( ( ! [SY5638: $i] :
( ( c_in @ SV627 @ ( c_Relation_ORange @ SV1227 @ SV1652 @ SY5638 ) @ SY5638 )
| ! [SY5639: $i] :
~ ( c_in @ ( c_Pair @ SY5639 @ SV627 @ SV1652 @ SY5638 ) @ SV1227 @ ( tc_prod @ SV1652 @ SY5638 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3575]) ).
thf(4164,plain,
! [SV1653: $i,SV1228: $i,SV628: $i] :
( ( ! [SY5640: $i] :
( ( c_in @ SV628 @ ( c_Relation_ORange @ SV1228 @ SV1653 @ SY5640 ) @ SY5640 )
| ! [SY5641: $i] :
~ ( c_in @ ( c_Pair @ SY5641 @ SV628 @ SV1653 @ SY5640 ) @ SV1228 @ ( tc_prod @ SV1653 @ SY5640 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3576]) ).
thf(4165,plain,
! [SV1654: $i,SV1229: $i,SV629: $i] :
( ( ! [SY5642: $i] :
( ( c_in @ SV629 @ ( c_Relation_ODomain @ SV1229 @ SV1654 @ SY5642 ) @ SV1654 )
| ! [SY5643: $i] :
~ ( c_in @ ( c_Pair @ SV629 @ SY5643 @ SV1654 @ SY5642 ) @ SV1229 @ ( tc_prod @ SV1654 @ SY5642 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3577]) ).
thf(4166,plain,
! [SV1655: $i,SV1230: $i,SV630: $i] :
( ( ! [SY5644: $i] :
( ( c_in @ SV630 @ ( c_Relation_ODomain @ SV1230 @ SV1655 @ SY5644 ) @ SV1655 )
| ! [SY5645: $i] :
~ ( c_in @ ( c_Pair @ SV630 @ SY5645 @ SV1655 @ SY5644 ) @ SV1230 @ ( tc_prod @ SV1655 @ SY5644 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3578]) ).
thf(4167,plain,
! [SV1656: $i,SV1231: $i,SV631: $i] :
( ( ! [SY5646: $i] :
( ( c_in @ SV631 @ ( hAPP @ SV1231 @ SV1656 ) @ SY5646 )
| ! [SY5647: $i,SY5648: $i] :
~ ( c_in @ ( c_Pair @ SV1656 @ SV631 @ SY5647 @ SY5646 ) @ ( c_Product__Type_OSigma @ SY5648 @ SV1231 @ SY5647 @ SY5646 ) @ ( tc_prod @ SY5647 @ SY5646 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3579]) ).
thf(4168,plain,
! [SV1657: $i,SV1232: $i,SV632: $i] :
( ( ! [SY5649: $i] :
( ( c_in @ SV632 @ SV1232 @ SV1657 )
| ! [SY5650: $i,SY5651: $i] :
~ ( c_in @ ( c_Pair @ SV632 @ SY5649 @ SV1657 @ SY5650 ) @ ( c_Product__Type_OSigma @ SV1232 @ SY5651 @ SV1657 @ SY5650 ) @ ( tc_prod @ SV1657 @ SY5650 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3580]) ).
thf(4169,plain,
! [SV1658: $i,SV1233: $i,SV633: $i] :
( ( ! [SY5652: $i] :
( ( c_in @ ( c_Pair @ SV633 @ SV1233 @ SV1658 @ SV1658 ) @ SY5652 @ ( tc_prod @ SV1658 @ SV1658 ) )
| ( c_in @ ( c_Pair @ SV1233 @ SV633 @ SV1658 @ SV1658 ) @ SY5652 @ ( tc_prod @ SV1658 @ SV1658 ) )
| ( SV1233 = SV633 )
| ! [SY5653: $i] :
( ~ ( c_in @ SV633 @ SY5653 @ SV1658 )
| ~ ( c_in @ SV1233 @ SY5653 @ SV1658 )
| ~ ( c_Relation_Ototal__on @ SY5653 @ SY5652 @ SV1658 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3581]) ).
thf(4170,plain,
! [SV1659: $i,SV1234: $i,SV634: $i] :
( ( ( c_in @ ( c_Pair @ SV634 @ SV634 @ SV1234 @ SV1234 ) @ SV1659 @ ( tc_prod @ SV1234 @ SV1234 ) )
| ! [SY5654: $i] :
( ~ ( c_in @ SV634 @ SY5654 @ SV1234 )
| ~ ( c_Relation_Orefl__on @ SY5654 @ SV1659 @ SV1234 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3582]) ).
thf(4171,plain,
! [SV1660: $i,SV1235: $i,SV635: $i] :
( ( ( c_in @ SV635 @ SV1235 @ SV1660 )
| ! [SY5655: $i,SY5656: $i] :
( ~ ( c_in @ ( c_Pair @ SY5655 @ SV635 @ SV1660 @ SV1660 ) @ SY5656 @ ( tc_prod @ SV1660 @ SV1660 ) )
| ~ ( c_Relation_Orefl__on @ SV1235 @ SY5656 @ SV1660 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3583]) ).
thf(4172,plain,
! [SV1661: $i,SV1236: $i,SV636: $i] :
( ( ( c_in @ SV636 @ SV1236 @ SV1661 )
| ! [SY5657: $i,SY5658: $i] :
( ~ ( c_in @ ( c_Pair @ SV636 @ SY5657 @ SV1661 @ SV1661 ) @ SY5658 @ ( tc_prod @ SV1661 @ SV1661 ) )
| ~ ( c_Relation_Orefl__on @ SV1236 @ SY5658 @ SV1661 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3584]) ).
thf(4173,plain,
! [SV1662: $i,SV1237: $i,SV637: $i] :
( ( ( c_in @ ( c_Pair @ SV637 @ SV637 @ SV1237 @ SV1237 ) @ SV1662 @ ( tc_prod @ SV1237 @ SV1237 ) )
| ! [SY5659: $i] :
( ~ ( c_in @ SV637 @ SY5659 @ SV1237 )
| ~ ( c_Relation_Orefl__on @ SY5659 @ SV1662 @ SV1237 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3585]) ).
thf(4174,plain,
! [SV1663: $i,SV1238: $i,SV638: $i] :
( ( ! [SY5660: $i,SY5661: $i,SY5662: $i] :
( ( ( c_Pair @ SV638 @ SV1238 @ SV1663 @ SY5660 )
!= ( c_Pair @ SY5661 @ SY5662 @ SV1663 @ SY5660 ) )
| ( SV1238 = SY5662 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3586]) ).
thf(4175,plain,
! [SV1664: $i,SV1239: $i,SV639: $i] :
( ( ! [SY5663: $i,SY5664: $i] :
( ! [SY5665: $i] :
( ( c_Pair @ SV639 @ SV1239 @ SV1664 @ SY5663 )
!= ( c_Pair @ SY5664 @ SY5665 @ SV1664 @ SY5663 ) )
| ( SV639 = SY5664 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3587]) ).
thf(4176,plain,
! [SV1240: $i,SV640: $i] :
( ( ( ! [SY5161: $i] : ( c_in @ SV640 @ SV1240 @ SY5161 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV1240 @ SV640 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3588]) ).
thf(4177,plain,
! [SV1241: $i,SV641: $i] :
( ( ( hBOOL @ ( hAPP @ SV641 @ SV1241 ) )
= $true )
| ( ( ! [SY5162: $i] :
~ ( c_in @ SV1241 @ SV641 @ SY5162 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3589]) ).
thf(4178,plain,
! [SV1242: $i,SV642: $i] :
( ( ( class_Lattices_Oupper__semilattice @ ( tc_fun @ SV642 @ SV1242 ) )
= $true )
| ( ( ~ ( class_Lattices_Olattice @ SV1242 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3592]) ).
thf(4179,plain,
! [SV1243: $i,SV643: $i] :
( ( ( class_Lattices_Olower__semilattice @ ( tc_fun @ SV643 @ SV1243 ) )
= $true )
| ( ( ~ ( class_Lattices_Olattice @ SV1243 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3593]) ).
thf(4180,plain,
! [SV1244: $i,SV644: $i] :
( ( ( class_Lattices_Odistrib__lattice @ ( tc_fun @ SV644 @ SV1244 ) )
= $true )
| ( ( ~ ( class_Lattices_Odistrib__lattice @ SV1244 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3594]) ).
thf(4181,plain,
! [SV1245: $i,SV645: $i] :
( ( ( class_Lattices_Obounded__lattice @ ( tc_fun @ SV645 @ SV1245 ) )
= $true )
| ( ( ~ ( class_Lattices_Obounded__lattice @ SV1245 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3595]) ).
thf(4182,plain,
! [SV1246: $i,SV646: $i] :
( ( ( class_Orderings_Opreorder @ ( tc_fun @ SV646 @ SV1246 ) )
= $true )
| ( ( ~ ( class_Orderings_Opreorder @ SV1246 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3596]) ).
thf(4183,plain,
! [SV1247: $i,SV647: $i] :
( ( ( class_Lattices_Olattice @ ( tc_fun @ SV647 @ SV1247 ) )
= $true )
| ( ( ~ ( class_Lattices_Olattice @ SV1247 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3597]) ).
thf(4184,plain,
! [SV1248: $i,SV648: $i] :
( ( ( class_Orderings_Oorder @ ( tc_fun @ SV648 @ SV1248 ) )
= $true )
| ( ( ~ ( class_Orderings_Oorder @ SV1248 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3598]) ).
thf(4185,plain,
! [SV1249: $i,SV649: $i] :
( ( ( class_Orderings_Obot @ ( tc_fun @ SV649 @ SV1249 ) )
= $true )
| ( ( ~ ( class_Orderings_Obot @ SV1249 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3599]) ).
thf(4186,plain,
! [SV1250: $i,SV650: $i] :
( ( ( class_HOL_Oord @ ( tc_fun @ SV650 @ SV1250 ) )
= $true )
| ( ( ~ ( class_HOL_Oord @ SV1250 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3600]) ).
thf(4187,plain,
! [SV1252: $i,SV652: $i] :
( ( ( SV652 = SV1252 )
= $true )
| ( ( ! [SY5163: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ SY5163 ) @ SV652 ) @ SV1252 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3602]) ).
thf(4188,plain,
! [SV1665: $i,SV1253: $i,SV653: $i,SV1: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ SV1 @ SV653 @ SV1253 ) @ ( c_Set_Oinsert @ SV1 @ SV1665 @ SV1253 ) @ ( tc_fun @ SV1253 @ tc_bool ) )
= ( c_Set_Oinsert @ SV1 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV653 @ SV1665 @ ( tc_fun @ SV1253 @ tc_bool ) ) @ SV1253 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3603]) ).
thf(4189,plain,
! [SV1254: $i,SV654: $i,SV2: $i] :
( ( ( c_Set_Oinsert @ SV2 @ SV654 @ SV1254 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1254 @ tc_bool ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3604]) ).
thf(4190,plain,
! [SV1666: $i,SV1255: $i,SV655: $i,SV3: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV3 @ ( c_Set_Oinsert @ SV655 @ SV1255 @ SV1666 ) @ ( tc_fun @ SV1666 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV3 @ ( c_Set_Oinsert @ SV655 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1666 @ tc_bool ) ) @ SV1666 ) @ ( tc_fun @ SV1666 @ tc_bool ) ) @ SV1255 @ ( tc_fun @ SV1666 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3605]) ).
thf(4191,plain,
! [SV1667: $i,SV1256: $i,SV656: $i,SV4: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV4 @ ( c_Set_Oinsert @ SV656 @ SV1256 @ SV1667 ) @ ( tc_fun @ SV1667 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV4 @ SV1256 @ ( tc_fun @ SV1667 @ tc_bool ) ) @ ( c_Set_Oinsert @ SV656 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1667 @ tc_bool ) ) @ SV1667 ) @ ( tc_fun @ SV1667 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3606]) ).
thf(4192,plain,
! [SV1668: $i,SV5: $i] :
( ( ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ SV5 ) @ SV1668 @ SV5 )
= $true )
| ( ( class_Orderings_Obot @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3607]) ).
thf(4193,plain,
! [SV1669: $i,SV1257: $i,SV659: $i,SV8: $i] :
( ( ( c_Relation_Orel__comp @ SV8 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV659 @ SV1257 ) @ tc_bool ) ) @ SV1669 @ SV659 @ SV1257 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV1669 @ SV1257 ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3608]) ).
thf(4194,plain,
! [SV1670: $i,SV1258: $i,SV660: $i,SV9: $i] :
( ( ( c_Relation_Orel__comp @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV9 @ SV660 ) @ tc_bool ) ) @ SV1258 @ SV9 @ SV660 @ SV1670 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV9 @ SV1670 ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3609]) ).
thf(4195,plain,
! [SV1671: $i,SV1259: $i,SV661: $i,SV10: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV10 @ ( c_Set_Oinsert @ SV661 @ SV1259 @ SV1671 ) @ ( tc_fun @ SV1671 @ tc_bool ) )
= ( c_Set_Oinsert @ SV661 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV10 @ SV1259 @ ( tc_fun @ SV1671 @ tc_bool ) ) @ SV1671 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3610]) ).
thf(4196,plain,
! [SV1672: $i,SV1260: $i,SV662: $i,SV11: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ SV11 @ SV662 @ SV1260 ) @ SV1672 @ ( tc_fun @ SV1260 @ tc_bool ) )
= ( c_Set_Oinsert @ SV11 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV662 @ SV1672 @ ( tc_fun @ SV1260 @ tc_bool ) ) @ SV1260 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3611]) ).
thf(4197,plain,
! [SV1673: $i,SV1261: $i,SV663: $i,SV12: $i] :
( ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV12 @ tc_bool ) )
!= ( c_Set_Oimage @ SV663 @ SV1261 @ SV1673 @ SV12 ) )
| ( SV1261
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1673 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3612]) ).
thf(4198,plain,
! [SV1674: $i,SV1263: $i,SV665: $i,SV14: $i] :
( ( ( ( hAPP @ ( c_snd @ SV14 @ SV665 ) @ SV1263 )
!= ( hAPP @ ( c_snd @ SV14 @ SV665 ) @ SV1674 ) )
| ( ( hAPP @ ( c_fst @ SV14 @ SV665 ) @ SV1263 )
!= ( hAPP @ ( c_fst @ SV14 @ SV665 ) @ SV1674 ) )
| ( SV1263 = SV1674 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3614]) ).
thf(4199,plain,
! [SV1675: $i,SV1264: $i,SV666: $i,SV15: $i] :
( ( ( ( hAPP @ ( c_snd @ SV15 @ SV666 ) @ SV1264 )
!= ( hAPP @ ( c_snd @ SV15 @ SV666 ) @ SV1675 ) )
| ( ( hAPP @ ( c_fst @ SV15 @ SV666 ) @ SV1264 )
!= ( hAPP @ ( c_fst @ SV15 @ SV666 ) @ SV1675 ) )
| ( SV1264 = SV1675 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3615]) ).
thf(4200,plain,
! [SV667: $i,SV1676: $i,SV16: $i] :
( ( ( ! [SY5666: $i] :
( ~ ( hBOOL @ ( hAPP @ SV16 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1 @ SV16 @ SV1676 @ SY5666 ) ) )
| ~ ( c_Wellfounded_Owf @ SV1676 @ SY5666 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV16 @ SV667 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3616]) ).
thf(4201,plain,
! [SV1677: $i,SV1265: $i,SV668: $i,SV17: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ ( c_Relation_ORange @ SV17 @ SV668 @ SV1265 ) @ ( c_Relation_ORange @ SV1677 @ SV668 @ SV1265 ) @ ( tc_fun @ SV1265 @ tc_bool ) ) @ ( c_Relation_ORange @ ( c_HOL_Ominus__class_Ominus @ SV17 @ SV1677 @ ( tc_fun @ ( tc_prod @ SV668 @ SV1265 ) @ tc_bool ) ) @ SV668 @ SV1265 ) @ ( tc_fun @ SV1265 @ tc_bool ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3617]) ).
thf(4202,plain,
! [SV1678: $i,SV1266: $i,SV669: $i,SV18: $i] :
( ( ( c_lessequals @ SV18 @ ( c_Set_Oinsert @ SV669 @ SV1266 @ SV1678 ) @ ( tc_fun @ SV1678 @ tc_bool ) )
| ~ ( c_lessequals @ SV18 @ SV1266 @ ( tc_fun @ SV1678 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3618]) ).
thf(4203,plain,
! [SV1267: $i,SV670: $i,SV19: $i] :
( ( ( c_lessequals @ SV19 @ SV670 @ ( tc_fun @ SV1267 @ tc_bool ) )
= $true )
| ( ( ! [SY5176: $i] :
~ ( c_lessequals @ ( c_Set_Oinsert @ SY5176 @ SV19 @ SV1267 ) @ SV670 @ ( tc_fun @ SV1267 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3619]) ).
thf(4204,plain,
! [SV1679: $i,SV1268: $i,SV671: $i,SV20: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ SV20 @ SV671 @ SV1268 ) @ SV1679 @ ( tc_fun @ SV1268 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ SV671 @ SV1679 @ ( tc_fun @ SV1268 @ tc_bool ) ) )
| ~ ( c_in @ SV20 @ SV1679 @ SV1268 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3620]) ).
thf(4205,plain,
! [SV1680: $i,SV1269: $i,SV672: $i,SV21: $i] :
( ( ! [SY5667: $i] :
( ( c_lessequals @ ( c_Product__Type_OSigma @ SV21 @ ( c_COMBK @ SV672 @ ( tc_fun @ SV1269 @ tc_bool ) @ SV1680 ) @ SV1680 @ SV1269 ) @ ( c_Product__Type_OSigma @ SY5667 @ ( c_COMBK @ SV672 @ ( tc_fun @ SV1269 @ tc_bool ) @ SV1680 ) @ SV1680 @ SV1269 ) @ ( tc_fun @ ( tc_prod @ SV1680 @ SV1269 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV21 @ SY5667 @ ( tc_fun @ SV1680 @ tc_bool ) )
| ! [SY5180: $i] :
~ ( c_in @ SY5180 @ SV672 @ SV1269 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3621]) ).
thf(4206,plain,
! [SV1681: $i,SV1270: $i,SV673: $i,SV22: $i] :
( ( ( c_lessequals @ SV22 @ SV673 @ ( tc_fun @ SV1270 @ tc_bool ) )
| ! [SY5669: $i] :
( ~ ( c_lessequals @ ( c_Product__Type_OSigma @ SV22 @ ( c_COMBK @ SV1681 @ ( tc_fun @ SY5669 @ tc_bool ) @ SV1270 ) @ SV1270 @ SY5669 ) @ ( c_Product__Type_OSigma @ SV673 @ ( c_COMBK @ SV1681 @ ( tc_fun @ SY5669 @ tc_bool ) @ SV1270 ) @ SV1270 @ SY5669 ) @ ( tc_fun @ ( tc_prod @ SV1270 @ SY5669 ) @ tc_bool ) )
| ! [SY5670: $i] :
~ ( c_in @ SY5670 @ SV1681 @ SY5669 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3622]) ).
thf(4207,plain,
! [SV1682: $i,SV1271: $i,SV674: $i,SV23: $i] :
( ( ( c_lessequals @ SV23 @ ( c_Set_Oinsert @ SV674 @ SV1271 @ SV1682 ) @ ( tc_fun @ SV1682 @ tc_bool ) )
| ~ ( c_in @ SV674 @ SV23 @ SV1682 )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV23 @ ( c_Set_Oinsert @ SV674 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1682 @ tc_bool ) ) @ SV1682 ) @ ( tc_fun @ SV1682 @ tc_bool ) ) @ SV1271 @ ( tc_fun @ SV1682 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3623]) ).
thf(4208,plain,
! [SV1683: $i,SV1272: $i,SV675: $i,SV24: $i] :
( ( ( c_lessequals @ SV24 @ ( c_Set_Oinsert @ SV675 @ SV1272 @ SV1683 ) @ ( tc_fun @ SV1683 @ tc_bool ) )
| ~ ( c_in @ SV675 @ SV24 @ SV1683 )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV24 @ ( c_Set_Oinsert @ SV675 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1683 @ tc_bool ) ) @ SV1683 ) @ ( tc_fun @ SV1683 @ tc_bool ) ) @ SV1272 @ ( tc_fun @ SV1683 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3624]) ).
thf(4209,plain,
! [SV1684: $i,SV1273: $i,SV676: $i,SV25: $i] :
( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV25 @ ( c_Set_Oinsert @ SV676 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1273 @ tc_bool ) ) @ SV1273 ) @ ( tc_fun @ SV1273 @ tc_bool ) ) @ SV1684 @ ( tc_fun @ SV1273 @ tc_bool ) )
| ~ ( c_in @ SV676 @ SV25 @ SV1273 )
| ~ ( c_lessequals @ SV25 @ ( c_Set_Oinsert @ SV676 @ SV1684 @ SV1273 ) @ ( tc_fun @ SV1273 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3625]) ).
thf(4210,plain,
! [SV1685: $i,SV1274: $i,SV677: $i,SV26: $i] :
( ( ( ( c_Set_Oimage @ ( c_COMBK @ SV26 @ SV677 @ SV1274 ) @ SV1685 @ SV1274 @ SV677 )
= ( c_Set_Oinsert @ SV26 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV677 @ tc_bool ) ) @ SV677 ) )
| ! [SY5671: $i] :
~ ( c_in @ SY5671 @ SV1685 @ SV1274 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3626]) ).
thf(4211,plain,
! [SV1275: $i,SV678: $i,SV27: $i] :
( ( ( c_lessequals @ ( c_Transitive__Closure_Otrancl @ SV27 @ SV678 ) @ SV1275 @ ( tc_fun @ ( tc_prod @ SV678 @ SV678 ) @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Relation_Orel__comp @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Transitive__Closure_Otrancl @ SV27 @ SV678 ) @ SV1275 @ ( tc_fun @ ( tc_prod @ SV678 @ SV678 ) @ tc_bool ) ) @ SV27 @ SV678 @ SV678 @ SV678 ) @ SV1275 @ ( tc_fun @ ( tc_prod @ SV678 @ SV678 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV27 @ SV1275 @ ( tc_fun @ ( tc_prod @ SV678 @ SV678 ) @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3627]) ).
thf(4212,plain,
! [SV1686: $i,SV1276: $i,SV679: $i,SV28: $i] :
( ( ! [SY5672: $i] :
( ( c_Product__Type_OSigma @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV28 @ SV679 @ ( tc_fun @ SV1276 @ tc_bool ) ) @ SV1686 @ SV1276 @ SY5672 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Product__Type_OSigma @ SV28 @ SV1686 @ SV1276 @ SY5672 ) @ ( c_Product__Type_OSigma @ SV679 @ SV1686 @ SV1276 @ SY5672 ) @ ( tc_fun @ ( tc_prod @ SV1276 @ SY5672 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3628]) ).
thf(4213,plain,
! [SV1687: $i,SV680: $i,SV29: $i] :
( ( ( ~ ( c_in @ SV29 @ ( c_Set_Oinsert @ SV680 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1687 @ tc_bool ) ) @ SV1687 ) @ SV1687 ) )
= $true )
| ( ( SV29 = SV680 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3629]) ).
thf(4214,plain,
! [SV1277: $i,SV681: $i,SV30: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV30 @ SV681 @ ( tc_fun @ SV1277 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1277 @ tc_bool ) ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV30 @ SV681 @ ( tc_fun @ SV1277 @ tc_bool ) )
= SV30 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3630]) ).
thf(4215,plain,
! [SV1688: $i,SV1278: $i,SV682: $i,SV31: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ ( c_Relation_ODomain @ SV31 @ SV682 @ SV1278 ) @ ( c_Relation_ODomain @ SV1688 @ SV682 @ SV1278 ) @ ( tc_fun @ SV682 @ tc_bool ) ) @ ( c_Relation_ODomain @ ( c_HOL_Ominus__class_Ominus @ SV31 @ SV1688 @ ( tc_fun @ ( tc_prod @ SV682 @ SV1278 ) @ tc_bool ) ) @ SV682 @ SV1278 ) @ ( tc_fun @ SV682 @ tc_bool ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3631]) ).
thf(4216,plain,
! [SV1689: $i,SV1279: $i,SV683: $i,SV32: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV32 @ SV683 @ ( tc_fun @ SV1279 @ tc_bool ) ) @ SV1689 @ ( tc_fun @ SV1279 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV32 @ SV1689 @ ( tc_fun @ SV1279 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV683 @ SV1689 @ ( tc_fun @ SV1279 @ tc_bool ) ) @ ( tc_fun @ SV1279 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3632]) ).
thf(4217,plain,
! [SV1690: $i,SV1280: $i,SV684: $i,SV33: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV33 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV684 @ SV1280 @ ( tc_fun @ SV1690 @ tc_bool ) ) @ ( tc_fun @ SV1690 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV33 @ SV684 @ ( tc_fun @ SV1690 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV33 @ SV1280 @ ( tc_fun @ SV1690 @ tc_bool ) ) @ ( tc_fun @ SV1690 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3633]) ).
thf(4218,plain,
! [SV685: $i,SV34: $i] :
( ( ( class_Lattices_Odistrib__lattice @ SV34 )
= $false )
| ( ( ! [SY4167: $i,SY4168: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV685 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4167 @ SY4168 @ SV34 ) @ SV34 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV685 @ SY4167 @ SV34 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV685 @ SY4168 @ SV34 ) @ SV34 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3634]) ).
thf(4219,plain,
! [SV686: $i,SV35: $i] :
( ( ( class_Lattices_Odistrib__lattice @ SV35 )
= $false )
| ( ( ! [SY4169: $i,SY4170: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV686 @ SY4169 @ SV35 ) @ SY4170 @ SV35 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV686 @ SY4170 @ SV35 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4169 @ SY4170 @ SV35 ) @ SV35 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3635]) ).
thf(4220,plain,
! [SV1281: $i,SV688: $i,SV37: $i] :
( ( ( c_lessequals @ SV37 @ ( c_Product__Type_OSigma @ SV688 @ ( c_COMBK @ SV688 @ ( tc_fun @ SV1281 @ tc_bool ) @ SV1281 ) @ SV1281 @ SV1281 ) @ ( tc_fun @ ( tc_prod @ SV1281 @ SV1281 ) @ tc_bool ) )
= $true )
| ( ( ~ ( c_Relation_Orefl__on @ SV688 @ SV37 @ SV1281 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3636]) ).
thf(4221,plain,
! [SV39: $i,SV1691: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1691 @ SV1691 @ SV39 )
= SV1691 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV39 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3637]) ).
thf(4222,plain,
! [SV1692: $i,SV1282: $i,SV690: $i,SV40: $i] :
( ( ! [SY5673: $i,SY5674: $i,SY5675: $i] :
( ( c_lessequals @ ( c_Relation_Orel__comp @ SV40 @ SV690 @ SV1282 @ SV1692 @ SY5673 ) @ ( c_Relation_Orel__comp @ SY5674 @ SY5675 @ SV1282 @ SV1692 @ SY5673 ) @ ( tc_fun @ ( tc_prod @ SV1282 @ SY5673 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV690 @ SY5675 @ ( tc_fun @ ( tc_prod @ SV1692 @ SY5673 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV40 @ SY5674 @ ( tc_fun @ ( tc_prod @ SV1282 @ SV1692 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3638]) ).
thf(4223,plain,
! [SV1693: $i,SV1283: $i,SV691: $i,SV41: $i] :
( ( ! [SY5676: $i] :
( ( c_Relation_OImage @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV41 @ SV691 @ ( tc_fun @ ( tc_prod @ SV1283 @ SV1693 ) @ tc_bool ) ) @ SY5676 @ SV1283 @ SV1693 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_OImage @ SV41 @ SY5676 @ SV1283 @ SV1693 ) @ ( c_Relation_OImage @ SV691 @ SY5676 @ SV1283 @ SV1693 ) @ ( tc_fun @ SV1693 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3639]) ).
thf(4224,plain,
! [SV1694: $i,SV1284: $i,SV692: $i,SV42: $i] :
( ( ! [SY5677: $i] :
( ( c_Relation_OImage @ SV42 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV692 @ SV1284 @ ( tc_fun @ SV1694 @ tc_bool ) ) @ SV1694 @ SY5677 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_OImage @ SV42 @ SV692 @ SV1694 @ SY5677 ) @ ( c_Relation_OImage @ SV42 @ SV1284 @ SV1694 @ SY5677 ) @ ( tc_fun @ SY5677 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3640]) ).
thf(4225,plain,
! [SV693: $i,SV1695: $i,SV43: $i] :
( ( ( ! [SY5678: $i] :
( ~ ( hBOOL @ ( hAPP @ SV43 @ ( c_List_Osko__Recdef__Xtfl__wf__induct__1__1 @ SV43 @ SV1695 @ SY5678 ) ) )
| ~ ( c_Wellfounded_Owf @ SV1695 @ SY5678 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV43 @ SV693 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3641]) ).
thf(4226,plain,
! [SV1696: $i,SV1285: $i,SV695: $i,SV45: $i] :
( ( ( c_Set_Oinsert @ SV45 @ ( c_Set_Oinsert @ SV695 @ SV1285 @ SV1696 ) @ SV1696 )
= ( c_Set_Oinsert @ SV695 @ ( c_Set_Oinsert @ SV45 @ SV1285 @ SV1696 ) @ SV1696 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3642]) ).
thf(4227,plain,
! [SV1697: $i,SV1288: $i,SV698: $i,SV48: $i] :
( ( ( hAPP @ ( c_COMBK @ SV48 @ SV698 @ SV1288 ) @ SV1697 )
= SV48 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3645]) ).
thf(4228,plain,
! [SV1698: $i,SV1291: $i,SV701: $i,SV51: $i] :
( ( ! [SY5679: $i] :
( ( c_lessequals @ ( c_Relation_OImage @ SV51 @ SV701 @ SV1291 @ SV1698 ) @ SY5679 @ ( tc_fun @ SV1698 @ tc_bool ) )
| ! [SY5680: $i] :
~ ( c_lessequals @ SV51 @ ( c_Product__Type_OSigma @ SY5680 @ ( c_COMBK @ SY5679 @ ( tc_fun @ SV1698 @ tc_bool ) @ SV1291 ) @ SV1291 @ SV1698 ) @ ( tc_fun @ ( tc_prod @ SV1291 @ SV1698 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3648]) ).
thf(4229,plain,
! [SV702: $i,SV52: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV52 )
= $false )
| ( ( ! [SY4197: $i] :
( ! [SY4198: $i] :
( ( c_HOL_Ominus__class_Ominus @ SV702 @ SY4197 @ SV52 )
!= ( c_HOL_Ominus__class_Ominus @ SY4198 @ SY4198 @ SV52 ) )
| ( SV702 = SY4197 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3649]) ).
thf(4230,plain,
! [SV703: $i,SV53: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV53 )
= $false )
| ( ( ! [SY4199: $i,SY4200: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV703 @ SV703 @ SV53 )
!= ( c_HOL_Ominus__class_Ominus @ SY4199 @ SY4200 @ SV53 ) )
| ( SY4199 = SY4200 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3650]) ).
thf(4231,plain,
! [SV1699: $i,SV1293: $i,SV705: $i,SV55: $i] :
( ( ! [SY5681: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oimage @ SV55 @ SV705 @ SV1293 @ SV1699 ) @ ( c_Set_Oimage @ SV55 @ SY5681 @ SV1293 @ SV1699 ) @ ( tc_fun @ SV1699 @ tc_bool ) ) @ ( c_Set_Oimage @ SV55 @ ( c_HOL_Ominus__class_Ominus @ SV705 @ SY5681 @ ( tc_fun @ SV1293 @ tc_bool ) ) @ SV1293 @ SV1699 ) @ ( tc_fun @ SV1699 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3652]) ).
thf(4232,plain,
! [SV1700: $i,SV1294: $i,SV706: $i,SV56: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV56 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV706 @ SV1294 @ ( tc_fun @ SV1700 @ tc_bool ) ) @ ( tc_fun @ SV1700 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV706 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV56 @ SV1294 @ ( tc_fun @ SV1700 @ tc_bool ) ) @ ( tc_fun @ SV1700 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3653]) ).
thf(4233,plain,
! [SV1701: $i,SV1295: $i,SV707: $i,SV57: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV57 @ SV707 @ ( tc_fun @ SV1295 @ tc_bool ) ) @ SV1701 @ ( tc_fun @ SV1295 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV57 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV707 @ SV1701 @ ( tc_fun @ SV1295 @ tc_bool ) ) @ ( tc_fun @ SV1295 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3654]) ).
thf(4234,plain,
! [SV708: $i,SV58: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV58 )
= $false )
| ( ( ! [SY4209: $i,SY4210: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV708 @ SY4209 @ SV58 ) @ SY4210 @ SV58 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV708 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4209 @ SY4210 @ SV58 ) @ SV58 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3655]) ).
thf(4235,plain,
! [SV709: $i,SV59: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV59 )
= $false )
| ( ( ! [SY4211: $i,SY4212: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV709 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4211 @ SY4212 @ SV59 ) @ SV59 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY4211 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV709 @ SY4212 @ SV59 ) @ SV59 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3656]) ).
thf(4236,plain,
! [SV710: $i,SV60: $i] :
( ( ( class_Lattices_Olattice @ SV60 )
= $false )
| ( ( ! [SY4213: $i,SY4214: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV710 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4213 @ SY4214 @ SV60 ) @ SV60 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY4213 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV710 @ SY4214 @ SV60 ) @ SV60 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3657]) ).
thf(4237,plain,
! [SV711: $i,SV61: $i] :
( ( ( class_Lattices_Olattice @ SV61 )
= $false )
| ( ( ! [SY4215: $i,SY4216: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV711 @ SY4215 @ SV61 ) @ SY4216 @ SV61 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV711 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4215 @ SY4216 @ SV61 ) @ SV61 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3658]) ).
thf(4238,plain,
! [SV1296: $i,SV712: $i,SV62: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV62 @ SV712 @ ( tc_fun @ SV1296 @ tc_bool ) )
= SV62 )
= $true )
| ( ( ~ ( c_lessequals @ SV62 @ SV712 @ ( tc_fun @ SV1296 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3659]) ).
thf(4239,plain,
! [SV1297: $i,SV713: $i,SV63: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV63 @ SV713 @ ( tc_fun @ SV1297 @ tc_bool ) )
= SV713 )
= $true )
| ( ( ~ ( c_lessequals @ SV713 @ SV63 @ ( tc_fun @ SV1297 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3660]) ).
thf(4240,plain,
! [SV64: $i,SV1702: $i] :
( ( ( ! [SY5682: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV1702 @ SY5682 @ SV64 )
= SV1702 )
| ~ ( c_lessequals @ SV1702 @ SY5682 @ SV64 ) ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV64 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3661]) ).
thf(4241,plain,
! [SV65: $i,SV1703: $i] :
( ( ( ! [SY5683: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV1703 @ SY5683 @ SV65 )
!= SV1703 )
| ( c_lessequals @ SV1703 @ SY5683 @ SV65 ) ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV65 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3662]) ).
thf(4242,plain,
! [SV66: $i,SV1704: $i] :
( ( ( ! [SY5684: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV1704 @ SY5684 @ SV66 )
= SY5684 )
| ~ ( c_lessequals @ SY5684 @ SV1704 @ SV66 ) ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV66 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3663]) ).
thf(4243,plain,
! [SV1705: $i,SV1298: $i,SV714: $i,SV67: $i] :
( ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV67 @ SV714 @ ( tc_fun @ SV1298 @ tc_bool ) ) @ SV1705 @ ( tc_fun @ SV1298 @ tc_bool ) )
| ~ ( c_lessequals @ SV714 @ SV1705 @ ( tc_fun @ SV1298 @ tc_bool ) )
| ~ ( c_lessequals @ SV67 @ SV1705 @ ( tc_fun @ SV1298 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3664]) ).
thf(4244,plain,
! [SV1706: $i,SV1301: $i,SV717: $i,SV70: $i] :
( ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV70 @ SV717 @ ( tc_fun @ SV1301 @ tc_bool ) ) @ SV1706 @ ( tc_fun @ SV1301 @ tc_bool ) )
| ~ ( c_lessequals @ SV717 @ SV1706 @ ( tc_fun @ SV1301 @ tc_bool ) )
| ~ ( c_lessequals @ SV70 @ SV1706 @ ( tc_fun @ SV1301 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3667]) ).
thf(4245,plain,
! [SV718: $i,SV71: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV71 )
= $false )
| ( ( ! [SY4225: $i,SY4226: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV718 @ SY4225 @ SV71 ) @ SY4226 @ SV71 )
| ~ ( c_lessequals @ SY4225 @ SY4226 @ SV71 )
| ~ ( c_lessequals @ SV718 @ SY4226 @ SV71 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3668]) ).
thf(4246,plain,
! [SV72: $i,SV1707: $i] :
( ( ( ! [SY5685: $i] : ( c_lessequals @ SV1707 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1707 @ SY5685 @ SV72 ) @ SV72 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV72 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3669]) ).
thf(4247,plain,
! [SV73: $i,SV1708: $i] :
( ( ( ! [SY5686: $i] : ( c_lessequals @ SV1708 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY5686 @ SV1708 @ SV73 ) @ SV73 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV73 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3670]) ).
thf(4248,plain,
! [SV719: $i,SV74: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV74 )
= $false )
| ( ( ! [SY4227: $i,SY4228: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV719 @ SY4227 @ SV74 ) @ SY4228 @ SV74 )
| ~ ( c_lessequals @ SY4227 @ SY4228 @ SV74 )
| ~ ( c_lessequals @ SV719 @ SY4228 @ SV74 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3671]) ).
thf(4249,plain,
! [SV720: $i,SV75: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV75 )
= $false )
| ( ( ! [SY4229: $i,SY4230: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV720 @ SY4229 @ SV75 ) @ SY4230 @ SV75 )
| ~ ( c_lessequals @ SY4229 @ SY4230 @ SV75 )
| ~ ( c_lessequals @ SV720 @ SY4230 @ SV75 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3672]) ).
thf(4250,plain,
! [SV76: $i,SV1709: $i] :
( ( ( ! [SY5687: $i] : ( c_lessequals @ SV1709 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY5687 @ SV1709 @ SV76 ) @ SV76 ) )
= $true )
| ( ( class_Lattices_Olattice @ SV76 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3673]) ).
thf(4251,plain,
! [SV77: $i,SV1710: $i] :
( ( ( ! [SY5688: $i] : ( c_lessequals @ SV1710 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1710 @ SY5688 @ SV77 ) @ SV77 ) )
= $true )
| ( ( class_Lattices_Olattice @ SV77 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3674]) ).
thf(4252,plain,
! [SV79: $i,SV1711: $i] :
( ( ( ! [SY5689: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV1711 @ SY5689 @ SV79 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY5689 @ SV1711 @ SV79 ) ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV79 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3676]) ).
thf(4253,plain,
! [SV80: $i,SV1712: $i] :
( ( ( ! [SY5690: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV1712 @ SY5690 @ SV80 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY5690 @ SV1712 @ SV80 ) ) )
= $true )
| ( ( class_Lattices_Olattice @ SV80 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3677]) ).
thf(4254,plain,
! [SV722: $i,SV81: $i] :
( ( ( c_Wellfounded_Owf @ SV81 @ SV722 )
= $false )
| ( ( c_Wellfounded_Oacyclic @ SV81 @ SV722 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3678]) ).
thf(4255,plain,
! [SV1303: $i,SV723: $i,SV82: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV82 @ ( c_HOL_Ominus__class_Ominus @ SV723 @ SV82 @ ( tc_fun @ SV1303 @ tc_bool ) ) @ ( tc_fun @ SV1303 @ tc_bool ) )
= SV723 )
= $true )
| ( ( ~ ( c_lessequals @ SV82 @ SV723 @ ( tc_fun @ SV1303 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3679]) ).
thf(4256,plain,
! [SV1713: $i,SV1304: $i,SV724: $i,SV83: $i] :
( ( ( c_lessequals @ ( c_Relation_OImage @ SV83 @ ( c_Set_Oinsert @ SV724 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1304 @ tc_bool ) ) @ SV1304 ) @ SV1304 @ SV1304 ) @ ( c_Relation_OImage @ SV83 @ ( c_Set_Oinsert @ SV1713 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1304 @ tc_bool ) ) @ SV1304 ) @ SV1304 @ SV1304 ) @ ( tc_fun @ SV1304 @ tc_bool ) )
| ~ ( c_in @ ( c_Pair @ SV724 @ SV1713 @ SV1304 @ SV1304 ) @ SV83 @ ( tc_prod @ SV1304 @ SV1304 ) )
| ! [SY5214: $i] :
~ ( c_Equiv__Relations_Oequiv @ SY5214 @ SV83 @ SV1304 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3680]) ).
thf(4257,plain,
! [SV86: $i,SV727: $i,SV1714: $i] :
( ( ( ( SV1714 = SV727 )
| ! [SY5692: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV1714 @ SV86 @ SY5692 ) @ SV727 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV86 @ SV727 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3683]) ).
thf(4258,plain,
! [SV1715: $i,SV1307: $i,SV728: $i,SV87: $i] :
( ( ! [SY5693: $i] :
( ( c_Relation_ODomain @ ( c_Set_Oinsert @ ( c_Pair @ SV87 @ SV728 @ SV1307 @ SV1715 ) @ SY5693 @ ( tc_prod @ SV1307 @ SV1715 ) ) @ SV1307 @ SV1715 )
= ( c_Set_Oinsert @ SV87 @ ( c_Relation_ODomain @ SY5693 @ SV1307 @ SV1715 ) @ SV1307 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3684]) ).
thf(4259,plain,
! [SV1308: $i,SV729: $i,SV88: $i] :
( ( ( c_Relation_Osym @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV88 @ SV729 @ ( tc_fun @ ( tc_prod @ SV1308 @ SV1308 ) @ tc_bool ) ) @ SV1308 )
= $true )
| ( ( ~ ( c_Relation_Osym @ SV729 @ SV1308 )
| ~ ( c_Relation_Osym @ SV88 @ SV1308 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3685]) ).
thf(4260,plain,
! [SV1309: $i,SV730: $i,SV89: $i] :
( ( ( c_lessequals @ ( c_Transitive__Closure_Ortrancl @ SV89 @ SV730 ) @ ( c_Transitive__Closure_Ortrancl @ SV1309 @ SV730 ) @ ( tc_fun @ ( tc_prod @ SV730 @ SV730 ) @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV89 @ SV1309 @ ( tc_fun @ ( tc_prod @ SV730 @ SV730 ) @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3686]) ).
thf(4261,plain,
! [SV1716: $i,SV1310: $i,SV731: $i,SV90: $i] :
( ( c_lessequals @ ( c_Relation_ODomain @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV90 @ SV731 @ ( tc_fun @ ( tc_prod @ SV1310 @ SV1716 ) @ tc_bool ) ) @ SV1310 @ SV1716 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_ODomain @ SV90 @ SV1310 @ SV1716 ) @ ( c_Relation_ODomain @ SV731 @ SV1310 @ SV1716 ) @ ( tc_fun @ SV1310 @ tc_bool ) ) @ ( tc_fun @ SV1310 @ tc_bool ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3687]) ).
thf(4262,plain,
! [SV91: $i,SV1717: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV1717 @ ( c_Orderings_Obot__class_Obot @ SV91 ) @ SV91 )
= ( c_Orderings_Obot__class_Obot @ SV91 ) )
= $true )
| ( ( class_Lattices_Obounded__lattice @ SV91 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3688]) ).
thf(4263,plain,
! [SV1718: $i,SV92: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Orderings_Obot__class_Obot @ SV92 ) @ SV1718 @ SV92 )
= ( c_Orderings_Obot__class_Obot @ SV92 ) )
= $true )
| ( ( class_Lattices_Obounded__lattice @ SV92 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3689]) ).
thf(4264,plain,
! [SV1719: $i,SV1312: $i,SV735: $i,SV96: $i] :
( ( ! [SY5694: $i] : ( c_lessequals @ ( c_Set_Oimage @ SV96 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV735 @ SV1312 @ ( tc_fun @ SV1719 @ tc_bool ) ) @ SV1719 @ SY5694 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oimage @ SV96 @ SV735 @ SV1719 @ SY5694 ) @ ( c_Set_Oimage @ SV96 @ SV1312 @ SV1719 @ SY5694 ) @ ( tc_fun @ SY5694 @ tc_bool ) ) @ ( tc_fun @ SY5694 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3691]) ).
thf(4265,plain,
! [SV1720: $i,SV1313: $i,SV736: $i,SV97: $i] :
( ( ! [SY5695: $i] : ( c_lessequals @ ( c_Relation_OImage @ SV97 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV736 @ SV1313 @ ( tc_fun @ SV1720 @ tc_bool ) ) @ SV1720 @ SY5695 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_OImage @ SV97 @ SV736 @ SV1720 @ SY5695 ) @ ( c_Relation_OImage @ SV97 @ SV1313 @ SV1720 @ SY5695 ) @ ( tc_fun @ SY5695 @ tc_bool ) ) @ ( tc_fun @ SY5695 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3692]) ).
thf(4266,plain,
! [SV1721: $i,SV1314: $i,SV737: $i,SV98: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV98 @ SV737 @ ( tc_fun @ SV1314 @ tc_bool ) ) @ SV1721 @ ( tc_fun @ SV1314 @ tc_bool ) )
!= ( c_Lattices_Olower__semilattice__class_Oinf @ SV98 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV737 @ SV1721 @ ( tc_fun @ SV1314 @ tc_bool ) ) @ ( tc_fun @ SV1314 @ tc_bool ) ) )
| ( c_lessequals @ SV1721 @ SV98 @ ( tc_fun @ SV1314 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3693]) ).
thf(4267,plain,
! [SV1722: $i,SV1315: $i,SV738: $i,SV99: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV99 @ SV738 @ ( tc_fun @ SV1315 @ tc_bool ) ) @ SV1722 @ ( tc_fun @ SV1315 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV99 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV738 @ SV1722 @ ( tc_fun @ SV1315 @ tc_bool ) ) @ ( tc_fun @ SV1315 @ tc_bool ) ) )
| ~ ( c_lessequals @ SV1722 @ SV99 @ ( tc_fun @ SV1315 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3694]) ).
thf(4268,plain,
! [SV1723: $i,SV1316: $i,SV739: $i,SV100: $i] :
( ( ! [SY5696: $i] :
( ( c_Product__Type_OSigma @ ( c_HOL_Ominus__class_Ominus @ SV100 @ SV739 @ ( tc_fun @ SV1316 @ tc_bool ) ) @ SV1723 @ SV1316 @ SY5696 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Product__Type_OSigma @ SV100 @ SV1723 @ SV1316 @ SY5696 ) @ ( c_Product__Type_OSigma @ SV739 @ SV1723 @ SV1316 @ SY5696 ) @ ( tc_fun @ ( tc_prod @ SV1316 @ SY5696 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3695]) ).
thf(4269,plain,
! [SV1724: $i,SV1317: $i,SV742: $i,SV103: $i] :
( ( ! [SY5697: $i,SY5698: $i,SY5699: $i] :
( ( c_lessequals @ ( c_Relation_Orel__comp @ SV103 @ SV742 @ SV1317 @ SV1724 @ SY5697 ) @ ( c_Product__Type_OSigma @ SY5698 @ ( c_COMBK @ SY5699 @ ( tc_fun @ SY5697 @ tc_bool ) @ SV1317 ) @ SV1317 @ SY5697 ) @ ( tc_fun @ ( tc_prod @ SV1317 @ SY5697 ) @ tc_bool ) )
| ! [SY5700: $i] :
( ~ ( c_lessequals @ SV742 @ ( c_Product__Type_OSigma @ SY5700 @ ( c_COMBK @ SY5699 @ ( tc_fun @ SY5697 @ tc_bool ) @ SV1724 ) @ SV1724 @ SY5697 ) @ ( tc_fun @ ( tc_prod @ SV1724 @ SY5697 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV103 @ ( c_Product__Type_OSigma @ SY5698 @ ( c_COMBK @ SY5700 @ ( tc_fun @ SV1724 @ tc_bool ) @ SV1317 ) @ SV1317 @ SV1724 ) @ ( tc_fun @ ( tc_prod @ SV1317 @ SV1724 ) @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3696]) ).
thf(4270,plain,
! [SV1318: $i,SV743: $i,SV104: $i] :
( ( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV104 @ SV743 @ ( tc_fun @ ( tc_prod @ SV1318 @ SV1318 ) @ tc_bool ) ) @ SV1318 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Relation_Orel__comp @ SV104 @ SV743 @ SV1318 @ SV1318 @ SV1318 ) @ SV104 @ ( tc_fun @ ( tc_prod @ SV1318 @ SV1318 ) @ tc_bool ) )
| ~ ( c_Wellfounded_Owf @ SV743 @ SV1318 )
| ~ ( c_Wellfounded_Owf @ SV104 @ SV1318 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3697]) ).
thf(4271,plain,
! [SV105: $i,SV744: $i,SV1725: $i] :
( ( ( ( hBOOL @ ( hAPP @ SV1725 @ SV744 ) )
| ! [SY5701: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1725 @ SV105 @ ( tc_fun @ SY5701 @ tc_bool ) ) @ SV744 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV105 @ SV744 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3698]) ).
thf(4272,plain,
! [SV1726: $i,SV1319: $i,SV745: $i,SV106: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV106 @ SV745 @ ( tc_fun @ SV1319 @ tc_bool ) ) @ SV1726 ) )
| ~ ( hBOOL @ ( hAPP @ SV745 @ SV1726 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3699]) ).
thf(4273,plain,
! [SV1727: $i,SV1320: $i,SV746: $i,SV107: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV107 @ SV746 @ ( tc_fun @ SV1320 @ tc_bool ) ) @ SV1727 ) )
| ~ ( hBOOL @ ( hAPP @ SV107 @ SV1727 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3700]) ).
thf(4274,plain,
! [SV1321: $i,SV747: $i,SV108: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_ODomain @ SV108 @ SV747 @ SV747 ) @ ( c_Relation_ORange @ SV1321 @ SV747 @ SV747 ) @ ( tc_fun @ SV747 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV747 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_Wellfounded_Owf @ SV1321 @ SV747 )
| ~ ( c_Wellfounded_Owf @ SV108 @ SV747 )
| ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV108 @ SV1321 @ ( tc_fun @ ( tc_prod @ SV747 @ SV747 ) @ tc_bool ) ) @ SV747 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3701]) ).
thf(4275,plain,
! [SV1728: $i,SV1322: $i,SV748: $i,SV109: $i] :
( ( ! [SY5702: $i] :
( ( c_Product__Type_OSigma @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV109 @ SV748 @ ( tc_fun @ SV1322 @ tc_bool ) ) @ ( c_COMBK @ SV1728 @ ( tc_fun @ SY5702 @ tc_bool ) @ SV1322 ) @ SV1322 @ SY5702 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Product__Type_OSigma @ SV109 @ ( c_COMBK @ SV1728 @ ( tc_fun @ SY5702 @ tc_bool ) @ SV1322 ) @ SV1322 @ SY5702 ) @ ( c_Product__Type_OSigma @ SV748 @ ( c_COMBK @ SV1728 @ ( tc_fun @ SY5702 @ tc_bool ) @ SV1322 ) @ SV1322 @ SY5702 ) @ ( tc_fun @ ( tc_prod @ SV1322 @ SY5702 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3702]) ).
thf(4276,plain,
! [SV1729: $i,SV1323: $i,SV749: $i,SV110: $i] :
( ( ! [SY5703: $i] :
( ( c_Relation_Orefl__on @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV110 @ SV749 @ ( tc_fun @ SV1323 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1729 @ SY5703 @ ( tc_fun @ ( tc_prod @ SV1323 @ SV1323 ) @ tc_bool ) ) @ SV1323 )
| ~ ( c_Relation_Orefl__on @ SV749 @ SY5703 @ SV1323 )
| ~ ( c_Relation_Orefl__on @ SV110 @ SV1729 @ SV1323 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3703]) ).
thf(4277,plain,
! [SV750: $i,SV111: $i] :
( ( ( class_Lattices_Olattice @ SV111 )
= $false )
| ( ( ! [SY4281: $i,SY4282: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV750 @ SY4281 @ SV111 ) @ SY4282 @ SV111 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV750 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4281 @ SY4282 @ SV111 ) @ SV111 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3704]) ).
thf(4278,plain,
! [SV751: $i,SV112: $i] :
( ( ( class_Lattices_Olattice @ SV112 )
= $false )
| ( ( ! [SY4283: $i,SY4284: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV751 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4283 @ SY4284 @ SV112 ) @ SV112 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY4283 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV751 @ SY4284 @ SV112 ) @ SV112 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3705]) ).
thf(4279,plain,
! [SV752: $i,SV113: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV113 )
= $false )
| ( ( ! [SY4285: $i,SY4286: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV752 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4285 @ SY4286 @ SV113 ) @ SV113 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY4285 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV752 @ SY4286 @ SV113 ) @ SV113 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3706]) ).
thf(4280,plain,
! [SV753: $i,SV114: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV114 )
= $false )
| ( ( ! [SY4287: $i,SY4288: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV753 @ SY4287 @ SV114 ) @ SY4288 @ SV114 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV753 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4287 @ SY4288 @ SV114 ) @ SV114 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3707]) ).
thf(4281,plain,
! [SV1730: $i,SV1324: $i,SV754: $i,SV115: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV115 @ SV754 @ ( tc_fun @ SV1324 @ tc_bool ) ) @ SV1730 @ ( tc_fun @ SV1324 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV115 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV754 @ SV1730 @ ( tc_fun @ SV1324 @ tc_bool ) ) @ ( tc_fun @ SV1324 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3708]) ).
thf(4282,plain,
! [SV1731: $i,SV1325: $i,SV755: $i,SV116: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV116 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV755 @ SV1325 @ ( tc_fun @ SV1731 @ tc_bool ) ) @ ( tc_fun @ SV1731 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV755 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV116 @ SV1325 @ ( tc_fun @ SV1731 @ tc_bool ) ) @ ( tc_fun @ SV1731 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3709]) ).
thf(4283,plain,
! [SV117: $i,SV1732: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1732 @ ( c_Orderings_Obot__class_Obot @ SV117 ) @ SV117 )
= SV1732 )
= $true )
| ( ( class_Lattices_Obounded__lattice @ SV117 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3710]) ).
thf(4284,plain,
! [SV1733: $i,SV118: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ SV118 ) @ SV1733 @ SV118 )
= SV1733 )
= $true )
| ( ( class_Lattices_Obounded__lattice @ SV118 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3711]) ).
thf(4285,plain,
! [SV1734: $i,SV1326: $i,SV759: $i,SV122: $i] :
( ( ! [SY5704: $i,SY5705: $i] :
( ( c_Product__Type_OSigma @ ( c_Set_Oinsert @ SV122 @ SV759 @ SV1326 ) @ ( c_COMBK @ ( c_Set_Oinsert @ SV1734 @ SY5704 @ SY5705 ) @ ( tc_fun @ SY5705 @ tc_bool ) @ SV1326 ) @ SV1326 @ SY5705 )
= ( c_Set_Oinsert @ ( c_Pair @ SV122 @ SV1734 @ SV1326 @ SY5705 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Product__Type_OSigma @ SV759 @ ( c_COMBK @ ( c_Set_Oinsert @ SV1734 @ SY5704 @ SY5705 ) @ ( tc_fun @ SY5705 @ tc_bool ) @ SV1326 ) @ SV1326 @ SY5705 ) @ ( c_Product__Type_OSigma @ ( c_Set_Oinsert @ SV122 @ SV759 @ SV1326 ) @ ( c_COMBK @ SY5704 @ ( tc_fun @ SY5705 @ tc_bool ) @ SV1326 ) @ SV1326 @ SY5705 ) @ ( tc_fun @ ( tc_prod @ SV1326 @ SY5705 ) @ tc_bool ) ) @ ( tc_prod @ SV1326 @ SY5705 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3712]) ).
thf(4286,plain,
! [SV760: $i,SV1735: $i,SV123: $i] :
( ( ( ~ ( c_lessequals @ SV123 @ ( c_Relation_OImage @ SV1735 @ SV123 @ SV760 @ SV760 ) @ ( tc_fun @ SV760 @ tc_bool ) )
| ~ ( c_Wellfounded_Owf @ SV1735 @ SV760 ) )
= $true )
| ( ( SV123
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV760 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3713]) ).
thf(4287,plain,
! [SV1736: $i,SV1327: $i,SV762: $i,SV125: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV125 @ ( c_HOL_Ominus__class_Ominus @ SV762 @ SV1327 @ ( tc_fun @ SV1736 @ tc_bool ) ) @ ( tc_fun @ SV1736 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV125 @ SV762 @ ( tc_fun @ SV1736 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV125 @ SV1327 @ ( tc_fun @ SV1736 @ tc_bool ) ) @ ( tc_fun @ SV1736 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3715]) ).
thf(4288,plain,
! [SV1737: $i,SV1328: $i,SV763: $i,SV126: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_HOL_Ominus__class_Ominus @ SV126 @ SV763 @ ( tc_fun @ SV1328 @ tc_bool ) ) @ SV1737 @ ( tc_fun @ SV1328 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV126 @ SV1737 @ ( tc_fun @ SV1328 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV763 @ SV1737 @ ( tc_fun @ SV1328 @ tc_bool ) ) @ ( tc_fun @ SV1328 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3716]) ).
thf(4289,plain,
! [SV1738: $i,SV1329: $i,SV764: $i,SV127: $i] :
( ( ( ( c_Set_Oimage @ ( c_COMBK @ SV127 @ SV764 @ SV1329 ) @ SV1738 @ SV1329 @ SV764 )
= ( c_Set_Oinsert @ SV127 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV764 @ tc_bool ) ) @ SV764 ) )
| ( SV1738
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1329 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3717]) ).
thf(4290,plain,
! [SV1739: $i,SV1330: $i,SV765: $i,SV128: $i] :
( ( ! [SY5706: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV128 @ SV765 @ ( tc_fun @ SV1330 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV1739 @ SY5706 @ ( tc_fun @ SV1330 @ tc_bool ) ) @ ( tc_fun @ SV1330 @ tc_bool ) )
| ~ ( c_lessequals @ SY5706 @ SV765 @ ( tc_fun @ SV1330 @ tc_bool ) )
| ~ ( c_lessequals @ SV128 @ SV1739 @ ( tc_fun @ SV1330 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3718]) ).
thf(4291,plain,
! [SV1331: $i,SV766: $i,SV129: $i] :
( ( ( ~ ( c_in @ SV129 @ SV766 @ SV1331 ) )
= $true )
| ( ( ! [SY5247: $i] :
( ~ ( c_in @ SV129 @ SY5247 @ SV1331 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SY5247 @ SV766 @ ( tc_fun @ SV1331 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1331 @ tc_bool ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3719]) ).
thf(4292,plain,
! [SV1332: $i,SV767: $i,SV130: $i] :
( ( ( c_Relation_Otrans @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV130 @ SV767 @ ( tc_fun @ ( tc_prod @ SV1332 @ SV1332 ) @ tc_bool ) ) @ SV1332 )
= $true )
| ( ( ~ ( c_Relation_Otrans @ SV767 @ SV1332 )
| ~ ( c_Relation_Otrans @ SV130 @ SV1332 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3720]) ).
thf(4293,plain,
! [SV768: $i,SV131: $i] :
( ( ( class_Lattices_Olattice @ SV131 )
= $false )
| ( ( ! [SY4310: $i,SY4311: $i] : ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV768 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4310 @ SY4311 @ SV131 ) @ SV131 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV768 @ SY4310 @ SV131 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV768 @ SY4311 @ SV131 ) @ SV131 ) @ SV131 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3721]) ).
thf(4294,plain,
! [SV1740: $i,SV1333: $i,SV769: $i,SV132: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV132 @ SV769 @ ( tc_fun @ SV1333 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1740 @ SV769 @ ( tc_fun @ SV1333 @ tc_bool ) ) @ ( tc_fun @ SV1333 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV132 @ SV769 @ ( tc_fun @ SV1333 @ tc_bool ) ) @ SV1740 @ ( tc_fun @ SV1333 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3722]) ).
thf(4295,plain,
! [SV133: $i,SV1741: $i] :
( ( ( ! [SY5707: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1741 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1741 @ SY5707 @ SV133 ) @ SV133 )
= SV1741 ) )
= $true )
| ( ( class_Lattices_Olattice @ SV133 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3723]) ).
thf(4296,plain,
! [SV1334: $i,SV770: $i,SV134: $i] :
( ( ( ( c_Relation_Orel__comp @ SV134 @ SV770 @ SV1334 @ SV1334 @ SV1334 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV1334 @ SV1334 ) @ tc_bool ) ) )
= $true )
| ( ( ! [SY5249: $i] :
( ( ( c_Relation_Orel__comp @ SY5249 @ SV770 @ SV1334 @ SV1334 @ SV1334 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV1334 @ SV1334 ) @ tc_bool ) ) )
| ( ( c_Relation_Orel__comp @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY5249 @ SV134 @ ( tc_fun @ ( tc_prod @ SV1334 @ SV1334 ) @ tc_bool ) ) @ SV770 @ SV1334 @ SV1334 @ SV1334 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV1334 @ SV1334 ) @ tc_bool ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3724]) ).
thf(4297,plain,
! [SV1335: $i,SV771: $i,SV135: $i] :
( ( ( ( c_Relation_Orel__comp @ SV135 @ SV771 @ SV1335 @ SV1335 @ SV1335 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV1335 @ SV1335 ) @ tc_bool ) ) )
= $true )
| ( ( ! [SY5250: $i] :
( ( ( c_Relation_Orel__comp @ SV135 @ SY5250 @ SV1335 @ SV1335 @ SV1335 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV1335 @ SV1335 ) @ tc_bool ) ) )
| ( ( c_Relation_Orel__comp @ SV135 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY5250 @ SV771 @ ( tc_fun @ ( tc_prod @ SV1335 @ SV1335 ) @ tc_bool ) ) @ SV1335 @ SV1335 @ SV1335 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV1335 @ SV1335 ) @ tc_bool ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3725]) ).
thf(4298,plain,
! [SV772: $i,SV1742: $i,SV136: $i] :
( ( ( ! [SY5708: $i] :
( ~ ( hBOOL @ ( hAPP @ SV136 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1 @ SV136 @ SV1742 @ SY5708 ) ) )
| ~ ( c_Wellfounded_Owf @ SV1742 @ SY5708 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV136 @ SV772 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3726]) ).
thf(4299,plain,
! [SV773: $i,SV137: $i] :
( ( ( c_Wellfounded_Oacyclic @ ( c_Relation_Oconverse @ SV137 @ SV773 @ SV773 ) @ SV773 )
= $false )
| ( ( c_Wellfounded_Oacyclic @ SV137 @ SV773 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3727]) ).
thf(4300,plain,
! [SV774: $i,SV138: $i] :
( ( ( c_Wellfounded_Oacyclic @ SV138 @ SV774 )
= $false )
| ( ( c_Wellfounded_Oacyclic @ ( c_Relation_Oconverse @ SV138 @ SV774 @ SV774 ) @ SV774 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3728]) ).
thf(4301,plain,
! [SV1743: $i,SV139: $i,SV775: $i] :
( ( ( ~ ( c_lessequals @ SV775 @ SV139 @ ( tc_fun @ SV1743 @ tc_bool ) )
| ~ ( c_lessequals @ SV139 @ SV775 @ ( tc_fun @ SV1743 @ tc_bool ) ) )
= $true )
| ( ( SV139 = SV775 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3729]) ).
thf(4302,plain,
! [SV1744: $i,SV140: $i,SV776: $i] :
( ( ( ~ ( c_lessequals @ SV776 @ SV140 @ ( tc_fun @ SV1744 @ tc_bool ) )
| ~ ( c_lessequals @ SV140 @ SV776 @ ( tc_fun @ SV1744 @ tc_bool ) ) )
= $true )
| ( ( SV140 = SV776 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3730]) ).
thf(4303,plain,
! [SV141: $i,SV1745: $i] :
( ( ( ! [SY5709: $i] :
( ( SV1745 = SY5709 )
| ~ ( c_lessequals @ SY5709 @ SV1745 @ SV141 )
| ~ ( c_lessequals @ SV1745 @ SY5709 @ SV141 ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV141 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3731]) ).
thf(4304,plain,
! [SV142: $i,SV1746: $i] :
( ( ( ! [SY5710: $i] :
( ( SV1746 = SY5710 )
| ~ ( c_lessequals @ SY5710 @ SV1746 @ SV142 )
| ~ ( c_lessequals @ SV1746 @ SY5710 @ SV142 ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV142 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3732]) ).
thf(4305,plain,
! [SV1747: $i,SV1336: $i,SV777: $i,SV143: $i] :
( ( ! [SY5711: $i] :
( ( hAPP @ ( c_split @ SV143 @ SV777 @ SV1336 @ SV1747 ) @ SY5711 )
= ( hAPP @ ( hAPP @ SV143 @ ( hAPP @ ( c_fst @ SV777 @ SV1336 ) @ SY5711 ) ) @ ( hAPP @ ( c_snd @ SV777 @ SV1336 ) @ SY5711 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3733]) ).
thf(4306,plain,
! [SV144: $i,SV1748: $i] :
( ( ( ! [SY5712: $i] :
( ( SV1748 = SY5712 )
| ~ ( c_lessequals @ SV1748 @ SY5712 @ SV144 )
| ~ ( c_lessequals @ SY5712 @ SV1748 @ SV144 ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV144 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3734]) ).
thf(4307,plain,
! [SV145: $i,SV1749: $i] :
( ( ( ! [SY5713: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV1749 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1749 @ SY5713 @ SV145 ) @ SV145 )
= SV1749 ) )
= $true )
| ( ( class_Lattices_Olattice @ SV145 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3735]) ).
thf(4308,plain,
! [SV147: $i,SV1750: $i] :
( ( ( ! [SY5714: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1750 @ SY5714 @ SV147 )
= SV1750 )
| ~ ( c_lessequals @ SY5714 @ SV1750 @ SV147 ) ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV147 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3737]) ).
thf(4309,plain,
! [SV148: $i,SV1751: $i] :
( ( ( ! [SY5715: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1751 @ SY5715 @ SV148 )
!= SY5715 )
| ( c_lessequals @ SV1751 @ SY5715 @ SV148 ) ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV148 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3738]) ).
thf(4310,plain,
! [SV149: $i,SV1752: $i] :
( ( ( ! [SY5716: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1752 @ SY5716 @ SV149 )
= SY5716 )
| ~ ( c_lessequals @ SV1752 @ SY5716 @ SV149 ) ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV149 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3739]) ).
thf(4311,plain,
! [SV1338: $i,SV779: $i,SV150: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV150 @ SV779 @ ( tc_fun @ SV1338 @ tc_bool ) )
= SV779 )
= $true )
| ( ( ~ ( c_lessequals @ SV150 @ SV779 @ ( tc_fun @ SV1338 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3740]) ).
thf(4312,plain,
! [SV1339: $i,SV780: $i,SV151: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV151 @ SV780 @ ( tc_fun @ SV1339 @ tc_bool ) )
= SV151 )
= $true )
| ( ( ~ ( c_lessequals @ SV780 @ SV151 @ ( tc_fun @ SV1339 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3741]) ).
thf(4313,plain,
! [SV1340: $i,SV781: $i,SV152: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV152 @ SV781 @ ( tc_fun @ SV1340 @ tc_bool ) )
!= SV781 )
= $true )
| ( ( c_lessequals @ SV152 @ SV781 @ ( tc_fun @ SV1340 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3742]) ).
thf(4314,plain,
! [SV1753: $i,SV1341: $i,SV782: $i,SV153: $i] :
( ( ! [SY5717: $i] :
( ( c_Relation_Orefl__on @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV153 @ SV782 @ ( tc_fun @ SV1341 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1753 @ SY5717 @ ( tc_fun @ ( tc_prod @ SV1341 @ SV1341 ) @ tc_bool ) ) @ SV1341 )
| ~ ( c_Relation_Orefl__on @ SV782 @ SY5717 @ SV1341 )
| ~ ( c_Relation_Orefl__on @ SV153 @ SV1753 @ SV1341 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3743]) ).
thf(4315,plain,
! [SV1754: $i,SV1342: $i,SV784: $i,SV156: $i] :
( ( ! [SY5718: $i] :
( ( ( c_Set_Oinsert @ SV156 @ ( c_Set_Oinsert @ SV784 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1342 @ tc_bool ) ) @ SV1342 ) @ SV1342 )
!= ( c_Set_Oinsert @ SV1754 @ ( c_Set_Oinsert @ SY5718 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1342 @ tc_bool ) ) @ SV1342 ) @ SV1342 ) )
| ( SV156 = SY5718 )
| ( SV156 = SV1754 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3744]) ).
thf(4316,plain,
! [SV1755: $i,SV1343: $i,SV785: $i,SV157: $i] :
( ( ! [SY5719: $i] :
( ( c_Set_Oinsert @ SV157 @ ( c_Set_Oinsert @ SV785 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1343 @ tc_bool ) ) @ SV1343 ) @ SV1343 )
!= ( c_Set_Oinsert @ SV1755 @ ( c_Set_Oinsert @ SY5719 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1343 @ tc_bool ) ) @ SV1343 ) @ SV1343 ) )
| ( SV785 = SV1755 )
| ( SV157 = SV1755 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3745]) ).
thf(4317,plain,
! [SV1756: $i,SV1344: $i,SV786: $i,SV158: $i] :
( ( ! [SY5720: $i] :
( ( ( c_Set_Oinsert @ SV158 @ ( c_Set_Oinsert @ SV786 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1344 @ tc_bool ) ) @ SV1344 ) @ SV1344 )
!= ( c_Set_Oinsert @ SV1756 @ ( c_Set_Oinsert @ SY5720 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1344 @ tc_bool ) ) @ SV1344 ) @ SV1344 ) )
| ( SV158 = SY5720 )
| ( SV786 = SY5720 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3746]) ).
thf(4318,plain,
! [SV1757: $i,SV1345: $i,SV787: $i,SV159: $i] :
( ( ! [SY5721: $i] :
( ( ( c_Set_Oinsert @ SV159 @ ( c_Set_Oinsert @ SV787 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1345 @ tc_bool ) ) @ SV1345 ) @ SV1345 )
!= ( c_Set_Oinsert @ SV1757 @ ( c_Set_Oinsert @ SY5721 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1345 @ tc_bool ) ) @ SV1345 ) @ SV1345 ) )
| ( SV787 = SV1757 )
| ( SV787 = SY5721 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3747]) ).
thf(4319,plain,
! [SV1346: $i,SV788: $i,SV160: $i] :
( ( ( c_lessequals @ ( c_Transitive__Closure_Otrancl @ SV160 @ SV788 ) @ ( c_Product__Type_OSigma @ SV1346 @ ( c_COMBK @ SV1346 @ ( tc_fun @ SV788 @ tc_bool ) @ SV788 ) @ SV788 @ SV788 ) @ ( tc_fun @ ( tc_prod @ SV788 @ SV788 ) @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV160 @ ( c_Product__Type_OSigma @ SV1346 @ ( c_COMBK @ SV1346 @ ( tc_fun @ SV788 @ tc_bool ) @ SV788 ) @ SV788 @ SV788 ) @ ( tc_fun @ ( tc_prod @ SV788 @ SV788 ) @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3748]) ).
thf(4320,plain,
! [SV1347: $i,SV789: $i,SV161: $i] :
( ( ( c_lessequals @ ( c_Transitive__Closure_Ortrancl @ SV161 @ SV789 ) @ ( c_Transitive__Closure_Ortrancl @ SV1347 @ SV789 ) @ ( tc_fun @ ( tc_prod @ SV789 @ SV789 ) @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV161 @ ( c_Transitive__Closure_Ortrancl @ SV1347 @ SV789 ) @ ( tc_fun @ ( tc_prod @ SV789 @ SV789 ) @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3749]) ).
thf(4321,plain,
! [SV790: $i,SV162: $i] :
( ( ( c_lessequals @ SV162 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV790 @ tc_bool ) ) @ ( tc_fun @ SV790 @ tc_bool ) )
= $false )
| ( ( SV162
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV790 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3750]) ).
thf(4322,plain,
! [SV1348: $i,SV791: $i,SV164: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV164 @ tc_bool ) )
= ( c_Set_Oinsert @ SV791 @ SV1348 @ SV164 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3751]) ).
thf(4323,plain,
! [SV1758: $i,SV1349: $i,SV792: $i,SV166: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ SV166 @ SV792 @ SV1349 ) @ SV1758 @ ( tc_fun @ SV1349 @ tc_bool ) )
= ( c_Set_Oinsert @ SV166 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV792 @ SV1758 @ ( tc_fun @ SV1349 @ tc_bool ) ) @ SV1349 ) )
| ~ ( c_in @ SV166 @ SV1758 @ SV1349 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3752]) ).
thf(4324,plain,
! [SV1759: $i,SV1350: $i,SV793: $i,SV167: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV167 @ ( c_Set_Oinsert @ SV793 @ SV1350 @ SV1759 ) @ ( tc_fun @ SV1759 @ tc_bool ) )
= ( c_Set_Oinsert @ SV793 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV167 @ SV1350 @ ( tc_fun @ SV1759 @ tc_bool ) ) @ SV1759 ) )
| ~ ( c_in @ SV793 @ SV167 @ SV1759 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3753]) ).
thf(4325,plain,
! [SV1760: $i,SV1351: $i,SV794: $i,SV168: $i] :
( ( ! [SY5722: $i] :
( ( c_Set_Oimage @ SV168 @ ( c_Set_Oinsert @ SV794 @ SV1351 @ SV1760 ) @ SV1760 @ SY5722 )
= ( c_Set_Oinsert @ ( hAPP @ SV168 @ SV794 ) @ ( c_Set_Oimage @ SV168 @ SV1351 @ SV1760 @ SY5722 ) @ SY5722 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3754]) ).
thf(4326,plain,
! [SV1761: $i,SV1352: $i,SV796: $i,SV170: $i] :
( ( ! [SY5723: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV170 @ SV796 @ ( tc_fun @ SV1352 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1761 @ SY5723 @ ( tc_fun @ SV1352 @ tc_bool ) ) @ ( tc_fun @ SV1352 @ tc_bool ) )
| ~ ( c_lessequals @ SV796 @ SY5723 @ ( tc_fun @ SV1352 @ tc_bool ) )
| ~ ( c_lessequals @ SV170 @ SV1761 @ ( tc_fun @ SV1352 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3755]) ).
thf(4327,plain,
! [SV1762: $i,SV1353: $i,SV797: $i,SV171: $i] :
( ( ( c_Relation_Oconverse @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV171 @ SV797 @ ( tc_fun @ ( tc_prod @ SV1353 @ SV1762 ) @ tc_bool ) ) @ SV1353 @ SV1762 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Oconverse @ SV171 @ SV1353 @ SV1762 ) @ ( c_Relation_Oconverse @ SV797 @ SV1353 @ SV1762 ) @ ( tc_fun @ ( tc_prod @ SV1762 @ SV1353 ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3756]) ).
thf(4328,plain,
! [SV172: $i,SV1763: $i] :
( ( ( ! [SY5724: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1763 @ SY5724 @ SV172 ) @ SV1763 @ SV172 ) )
= $true )
| ( ( class_Lattices_Olattice @ SV172 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3757]) ).
thf(4329,plain,
! [SV173: $i,SV1764: $i] :
( ( ( ! [SY5725: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1764 @ SY5725 @ SV173 ) @ SY5725 @ SV173 ) )
= $true )
| ( ( class_Lattices_Olattice @ SV173 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3758]) ).
thf(4330,plain,
! [SV798: $i,SV174: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV174 )
= $false )
| ( ( ! [SY4359: $i,SY4360: $i] :
( ( c_lessequals @ SV798 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4359 @ SY4360 @ SV174 ) @ SV174 )
| ~ ( c_lessequals @ SV798 @ SY4360 @ SV174 )
| ~ ( c_lessequals @ SV798 @ SY4359 @ SV174 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3759]) ).
thf(4331,plain,
! [SV799: $i,SV175: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV175 )
= $false )
| ( ( ! [SY4361: $i,SY4362: $i] :
( ( c_lessequals @ SV799 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4361 @ SY4362 @ SV175 ) @ SV175 )
| ~ ( c_lessequals @ SV799 @ SY4362 @ SV175 )
| ~ ( c_lessequals @ SV799 @ SY4361 @ SV175 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3760]) ).
thf(4332,plain,
! [SV800: $i,SV176: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV176 )
= $false )
| ( ( ! [SY4363: $i,SY4364: $i] :
( ( c_lessequals @ SV800 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4363 @ SY4364 @ SV176 ) @ SV176 )
| ~ ( c_lessequals @ SV800 @ SY4364 @ SV176 )
| ~ ( c_lessequals @ SV800 @ SY4363 @ SV176 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3761]) ).
thf(4333,plain,
! [SV177: $i,SV1765: $i] :
( ( ( ! [SY5726: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1765 @ SY5726 @ SV177 ) @ SY5726 @ SV177 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV177 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3762]) ).
thf(4334,plain,
! [SV178: $i,SV1766: $i] :
( ( ( ! [SY5727: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1766 @ SY5727 @ SV178 ) @ SV1766 @ SV178 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV178 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3763]) ).
thf(4335,plain,
! [SV1767: $i,SV1356: $i,SV803: $i,SV181: $i] :
( ( ( c_lessequals @ SV181 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV803 @ SV1356 @ ( tc_fun @ SV1767 @ tc_bool ) ) @ ( tc_fun @ SV1767 @ tc_bool ) )
| ~ ( c_lessequals @ SV181 @ SV1356 @ ( tc_fun @ SV1767 @ tc_bool ) )
| ~ ( c_lessequals @ SV181 @ SV803 @ ( tc_fun @ SV1767 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3766]) ).
thf(4336,plain,
! [SV1768: $i,SV1357: $i,SV804: $i,SV182: $i] :
( ( ( c_lessequals @ SV182 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV804 @ SV1357 @ ( tc_fun @ SV1768 @ tc_bool ) ) @ ( tc_fun @ SV1768 @ tc_bool ) )
| ~ ( c_lessequals @ SV182 @ SV1357 @ ( tc_fun @ SV1768 @ tc_bool ) )
| ~ ( c_lessequals @ SV182 @ SV804 @ ( tc_fun @ SV1768 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3767]) ).
thf(4337,plain,
! [SV1769: $i,SV1358: $i,SV805: $i,SV183: $i] :
( ( ! [SY5728: $i] :
( ( c_Product__Type_OSigma @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV183 @ SV805 @ ( tc_fun @ SV1358 @ tc_bool ) ) @ ( c_COMBK @ SV1769 @ ( tc_fun @ SY5728 @ tc_bool ) @ SV1358 ) @ SV1358 @ SY5728 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Product__Type_OSigma @ SV183 @ ( c_COMBK @ SV1769 @ ( tc_fun @ SY5728 @ tc_bool ) @ SV1358 ) @ SV1358 @ SY5728 ) @ ( c_Product__Type_OSigma @ SV805 @ ( c_COMBK @ SV1769 @ ( tc_fun @ SY5728 @ tc_bool ) @ SV1358 ) @ SV1358 @ SY5728 ) @ ( tc_fun @ ( tc_prod @ SV1358 @ SY5728 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3768]) ).
thf(4338,plain,
! [SV806: $i,SV184: $i] :
( ( ( class_Lattices_Olattice @ SV184 )
= $false )
| ( ( ! [SY4374: $i,SY4375: $i] : ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV806 @ SY4374 @ SV184 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV806 @ SY4375 @ SV184 ) @ SV184 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV806 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4374 @ SY4375 @ SV184 ) @ SV184 ) @ SV184 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3769]) ).
thf(4339,plain,
! [SV1359: $i,SV807: $i,SV185: $i] :
( ( ( ( c_Transitive__Closure_Ortrancl @ SV185 @ SV807 )
= ( c_Transitive__Closure_Ortrancl @ SV1359 @ SV807 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV185 @ ( c_Transitive__Closure_Ortrancl @ SV1359 @ SV807 ) @ ( tc_fun @ ( tc_prod @ SV807 @ SV807 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV1359 @ SV185 @ ( tc_fun @ ( tc_prod @ SV807 @ SV807 ) @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3770]) ).
thf(4340,plain,
! [SV1362: $i,SV810: $i,SV188: $i] :
( ( ( ( c_Set_Oinsert @ SV188 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV810 @ tc_bool ) ) @ SV810 )
!= ( c_Set_Oinsert @ SV1362 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV810 @ tc_bool ) ) @ SV810 ) )
= $true )
| ( ( SV188 = SV1362 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3773]) ).
thf(4341,plain,
! [SV1770: $i,SV1363: $i,SV811: $i,SV189: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV189 @ SV811 @ ( tc_fun @ SV1363 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV811 @ SV1770 @ ( tc_fun @ SV1363 @ tc_bool ) ) @ ( tc_fun @ SV1363 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1770 @ SV189 @ ( tc_fun @ SV1363 @ tc_bool ) ) @ ( tc_fun @ SV1363 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV189 @ SV811 @ ( tc_fun @ SV1363 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV811 @ SV1770 @ ( tc_fun @ SV1363 @ tc_bool ) ) @ ( tc_fun @ SV1363 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1770 @ SV189 @ ( tc_fun @ SV1363 @ tc_bool ) ) @ ( tc_fun @ SV1363 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3774]) ).
thf(4342,plain,
! [SV1365: $i,SV813: $i,SV192: $i] :
( ( ( ( c_Set_Oinsert @ SV192 @ SV813 @ SV1365 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1365 @ tc_bool ) ) )
= $true )
| ( ( c_in @ SV192 @ SV813 @ SV1365 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3776]) ).
thf(4343,plain,
! [SV1366: $i,SV814: $i,SV194: $i] :
( ( ( c_in @ SV194 @ SV814 @ SV1366 )
= $true )
| ( ( ! [SY5275: $i] :
~ ( c_lessequals @ ( c_Set_Oinsert @ SV194 @ SY5275 @ SV1366 ) @ SV814 @ ( tc_fun @ SV1366 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3777]) ).
thf(4344,plain,
! [SV1771: $i,SV1367: $i,SV815: $i,SV195: $i] :
( ( ! [SY5729: $i] :
( ( c_Product__Type_OSigma @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV195 @ SV815 @ ( tc_fun @ SV1367 @ tc_bool ) ) @ SV1771 @ SV1367 @ SY5729 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Product__Type_OSigma @ SV195 @ SV1771 @ SV1367 @ SY5729 ) @ ( c_Product__Type_OSigma @ SV815 @ SV1771 @ SV1367 @ SY5729 ) @ ( tc_fun @ ( tc_prod @ SV1367 @ SY5729 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3778]) ).
thf(4345,plain,
! [SV1772: $i,SV1368: $i,SV816: $i,SV196: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV196 @ SV816 @ SV1368 ) @ SV1772 ) )
| ~ ( hBOOL @ ( hAPP @ SV816 @ SV1772 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3779]) ).
thf(4346,plain,
! [SV1773: $i,SV1369: $i,SV817: $i,SV197: $i] :
( ( ( c_lessequals @ SV197 @ ( c_Set_Oinsert @ SV817 @ SV1369 @ SV1773 ) @ ( tc_fun @ SV1773 @ tc_bool ) )
| ~ ( c_lessequals @ SV197 @ SV1369 @ ( tc_fun @ SV1773 @ tc_bool ) )
| ( c_in @ SV817 @ SV197 @ SV1773 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3780]) ).
thf(4347,plain,
! [SV1370: $i,SV818: $i,SV198: $i] :
( ( ( c_lessequals @ SV198 @ SV818 @ ( tc_fun @ SV1370 @ tc_bool ) )
= $true )
| ( ( ! [SY5280: $i] :
( ( c_in @ SY5280 @ SV198 @ SV1370 )
| ~ ( c_lessequals @ SV198 @ ( c_Set_Oinsert @ SY5280 @ SV818 @ SV1370 ) @ ( tc_fun @ SV1370 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3781]) ).
thf(4348,plain,
! [SV1774: $i,SV1371: $i,SV819: $i,SV199: $i] :
( ( ( c_lessequals @ SV199 @ ( c_Set_Oinsert @ SV819 @ SV1371 @ SV1774 ) @ ( tc_fun @ SV1774 @ tc_bool ) )
| ~ ( c_lessequals @ SV199 @ SV1371 @ ( tc_fun @ SV1774 @ tc_bool ) )
| ( c_in @ SV819 @ SV199 @ SV1774 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3782]) ).
thf(4349,plain,
! [SV1372: $i,SV820: $i,SV200: $i] :
( ( ( c_lessequals @ SV200 @ SV820 @ ( tc_fun @ SV1372 @ tc_bool ) )
= $true )
| ( ( ! [SY5282: $i] :
( ~ ( c_lessequals @ SV200 @ ( c_Set_Oinsert @ SY5282 @ SV820 @ SV1372 ) @ ( tc_fun @ SV1372 @ tc_bool ) )
| ( c_in @ SY5282 @ SV200 @ SV1372 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3783]) ).
thf(4350,plain,
! [SV1775: $i,SV1373: $i,SV821: $i,SV201: $i] :
( ( ( c_Relation_Oconverse @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV201 @ SV821 @ ( tc_fun @ ( tc_prod @ SV1373 @ SV1775 ) @ tc_bool ) ) @ SV1373 @ SV1775 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_Oconverse @ SV201 @ SV1373 @ SV1775 ) @ ( c_Relation_Oconverse @ SV821 @ SV1373 @ SV1775 ) @ ( tc_fun @ ( tc_prod @ SV1775 @ SV1373 ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3784]) ).
thf(4351,plain,
! [SV1776: $i,SV1374: $i,SV822: $i,SV202: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV202 @ ( c_Set_Oinsert @ SV822 @ SV1374 @ SV1776 ) @ ( tc_fun @ SV1776 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV202 @ SV1374 @ ( tc_fun @ SV1776 @ tc_bool ) ) )
| ( c_in @ SV822 @ SV202 @ SV1776 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3785]) ).
thf(4352,plain,
! [SV1777: $i,SV1375: $i,SV823: $i,SV203: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ SV203 @ SV823 @ SV1375 ) @ SV1777 @ ( tc_fun @ SV1375 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV823 @ SV1777 @ ( tc_fun @ SV1375 @ tc_bool ) ) )
| ( c_in @ SV203 @ SV1777 @ SV1375 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3786]) ).
thf(4353,plain,
! [SV1376: $i,SV824: $i,SV204: $i] :
( ( ( c_Relation_Ototal__on @ SV204 @ SV824 @ SV1376 )
= $true )
| ( ( ~ ( c_Order__Relation_Ostrict__linear__order__on @ SV204 @ SV824 @ SV1376 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3787]) ).
thf(4354,plain,
! [SV1377: $i,SV825: $i,SV205: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV205 @ SV825 @ ( tc_fun @ SV1377 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1377 @ tc_bool ) ) )
= $true )
| ( ( SV825
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1377 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3788]) ).
thf(4355,plain,
! [SV1378: $i,SV826: $i,SV206: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV206 @ SV826 @ ( tc_fun @ SV1378 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1378 @ tc_bool ) ) )
= $true )
| ( ( SV206
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1378 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3789]) ).
thf(4356,plain,
! [SV207: $i,SV1778: $i] :
( ( ( ! [SY5730: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1778 @ SY5730 @ SV207 )
!= ( c_Orderings_Obot__class_Obot @ SV207 ) )
| ( SV1778
= ( c_Orderings_Obot__class_Obot @ SV207 ) ) )
= $true )
| ( ( class_Lattices_Obounded__lattice @ SV207 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3790]) ).
thf(4357,plain,
! [SV208: $i,SV1779: $i] :
( ( ( ! [SY5731: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1779 @ SY5731 @ SV208 )
!= ( c_Orderings_Obot__class_Obot @ SV208 ) )
| ( SY5731
= ( c_Orderings_Obot__class_Obot @ SV208 ) ) ) )
= $true )
| ( ( class_Lattices_Obounded__lattice @ SV208 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3791]) ).
thf(4358,plain,
! [SV1780: $i,SV1381: $i,SV829: $i,SV211: $i] :
( ( ! [SY5732: $i,SY5733: $i] :
( ( c_Relation_Orel__comp @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV211 @ SV829 @ ( tc_fun @ ( tc_prod @ SV1381 @ SV1780 ) @ tc_bool ) ) @ SY5732 @ SV1381 @ SV1780 @ SY5733 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ SV211 @ SY5732 @ SV1381 @ SV1780 @ SY5733 ) @ ( c_Relation_Orel__comp @ SV829 @ SY5732 @ SV1381 @ SV1780 @ SY5733 ) @ ( tc_fun @ ( tc_prod @ SV1381 @ SY5733 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3794]) ).
thf(4359,plain,
! [SV1781: $i,SV1382: $i,SV830: $i,SV212: $i] :
( ( ! [SY5734: $i,SY5735: $i] :
( ( c_Relation_Orel__comp @ SV212 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV830 @ SV1382 @ ( tc_fun @ ( tc_prod @ SV1781 @ SY5734 ) @ tc_bool ) ) @ SY5735 @ SV1781 @ SY5734 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ SV212 @ SV830 @ SY5735 @ SV1781 @ SY5734 ) @ ( c_Relation_Orel__comp @ SV212 @ SV1382 @ SY5735 @ SV1781 @ SY5734 ) @ ( tc_fun @ ( tc_prod @ SY5735 @ SY5734 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3795]) ).
thf(4360,plain,
! [SV1383: $i,SV831: $i,SV213: $i] :
( ( ( c_lessequals @ SV213 @ SV831 @ ( tc_fun @ SV1383 @ tc_bool ) )
= $true )
| ( ( ! [SY5292: $i] :
~ ( c_lessequals @ SV213 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY5292 @ SV831 @ ( tc_fun @ SV1383 @ tc_bool ) ) @ ( tc_fun @ SV1383 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3796]) ).
thf(4361,plain,
! [SV1384: $i,SV832: $i,SV214: $i] :
( ( ( c_lessequals @ SV214 @ SV832 @ ( tc_fun @ SV1384 @ tc_bool ) )
= $true )
| ( ( ! [SY5293: $i] :
~ ( c_lessequals @ SV214 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV832 @ SY5293 @ ( tc_fun @ SV1384 @ tc_bool ) ) @ ( tc_fun @ SV1384 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3797]) ).
thf(4362,plain,
! [SV833: $i,SV215: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV215 )
= $false )
| ( ( ! [SY4422: $i] :
( ( c_lessequals @ SV833 @ SY4422 @ SV215 )
| ! [SY4423: $i] :
~ ( c_lessequals @ SV833 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4422 @ SY4423 @ SV215 ) @ SV215 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3798]) ).
thf(4363,plain,
! [SV834: $i,SV216: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV216 )
= $false )
| ( ( ! [SY4424: $i] :
( ( c_lessequals @ SV834 @ SY4424 @ SV216 )
| ! [SY4425: $i] :
~ ( c_lessequals @ SV834 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4425 @ SY4424 @ SV216 ) @ SV216 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3799]) ).
thf(4364,plain,
! [SV835: $i,SV217: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV217 )
= $false )
| ( ( ! [SY4426: $i,SY4427: $i] :
( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV835 @ SY4426 @ SV217 ) @ SY4427 @ SV217 )
| ~ ( c_lessequals @ SV835 @ SY4427 @ SV217 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3800]) ).
thf(4365,plain,
! [SV836: $i,SV218: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV218 )
= $false )
| ( ( ! [SY4428: $i,SY4429: $i] :
( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV836 @ SY4428 @ SV218 ) @ SY4429 @ SV218 )
| ~ ( c_lessequals @ SY4428 @ SY4429 @ SV218 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3801]) ).
thf(4366,plain,
! [SV837: $i,SV219: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV219 )
= $false )
| ( ( ! [SY4430: $i] :
( ( c_lessequals @ SV837 @ SY4430 @ SV219 )
| ! [SY4431: $i] :
~ ( c_lessequals @ SV837 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4430 @ SY4431 @ SV219 ) @ SV219 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3802]) ).
thf(4367,plain,
! [SV838: $i,SV220: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV220 )
= $false )
| ( ( ! [SY4432: $i] :
( ( c_lessequals @ SV838 @ SY4432 @ SV220 )
| ! [SY4433: $i] :
~ ( c_lessequals @ SV838 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4433 @ SY4432 @ SV220 ) @ SV220 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3803]) ).
thf(4368,plain,
! [SV1782: $i,SV1385: $i,SV839: $i,SV221: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV221 @ SV839 @ ( tc_fun @ SV1385 @ tc_bool ) ) @ SV1782 @ ( tc_fun @ SV1385 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ SV221 @ SV1782 @ ( tc_fun @ SV1385 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV839 @ SV1782 @ ( tc_fun @ SV1385 @ tc_bool ) ) @ ( tc_fun @ SV1385 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3804]) ).
thf(4369,plain,
! [SV223: $i,SV1783: $i] :
( ( ( ! [SY5736: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1783 @ SY5736 @ SV223 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY5736 @ SV1783 @ SV223 ) ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV223 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3806]) ).
thf(4370,plain,
! [SV224: $i,SV1784: $i] :
( ( ( ! [SY5737: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1784 @ SY5737 @ SV224 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY5737 @ SV1784 @ SV224 ) ) )
= $true )
| ( ( class_Lattices_Olattice @ SV224 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3807]) ).
thf(4371,plain,
! [SV1785: $i,SV1387: $i,SV841: $i,SV225: $i] :
( ( ( c_Relation_ODomain @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV225 @ SV841 @ ( tc_fun @ ( tc_prod @ SV1387 @ SV1785 ) @ tc_bool ) ) @ SV1387 @ SV1785 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_ODomain @ SV225 @ SV1387 @ SV1785 ) @ ( c_Relation_ODomain @ SV841 @ SV1387 @ SV1785 ) @ ( tc_fun @ SV1387 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3808]) ).
thf(4372,plain,
! [SV1390: $i,SV844: $i,SV228: $i] :
( ( ( c_lessequals @ ( c_Wellfounded_Oacc @ SV228 @ SV844 ) @ ( c_Wellfounded_Oacc @ SV1390 @ SV844 ) @ ( tc_fun @ SV844 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1390 @ SV228 @ ( tc_fun @ ( tc_prod @ SV844 @ SV844 ) @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3811]) ).
thf(4373,plain,
! [SV230: $i,SV1786: $i] :
( ( ( ! [SY5738: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1786 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1786 @ SY5738 @ SV230 ) @ SV230 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV1786 @ SY5738 @ SV230 ) ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV230 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3813]) ).
thf(4374,plain,
! [SV231: $i,SV1787: $i] :
( ( ( ! [SY5739: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1787 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1787 @ SY5739 @ SV231 ) @ SV231 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV1787 @ SY5739 @ SV231 ) ) )
= $true )
| ( ( class_Lattices_Olattice @ SV231 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3814]) ).
thf(4375,plain,
! [SV1392: $i,SV846: $i,SV232: $i] :
( ( ( ( c_Relation_ODomain @ SV232 @ SV846 @ SV1392 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV846 @ tc_bool ) ) )
= $true )
| ( ( SV232
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV846 @ SV1392 ) @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3815]) ).
thf(4376,plain,
! [SV1788: $i,SV1395: $i,SV849: $i,SV235: $i] :
( ( c_lessequals @ ( c_Relation_ORange @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV235 @ SV849 @ ( tc_fun @ ( tc_prod @ SV1395 @ SV1788 ) @ tc_bool ) ) @ SV1395 @ SV1788 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_ORange @ SV235 @ SV1395 @ SV1788 ) @ ( c_Relation_ORange @ SV849 @ SV1395 @ SV1788 ) @ ( tc_fun @ SV1788 @ tc_bool ) ) @ ( tc_fun @ SV1788 @ tc_bool ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3818]) ).
thf(4377,plain,
! [SV850: $i,SV1789: $i,SV236: $i] :
( ( ( ! [SY5740: $i] :
( ~ ( hBOOL @ ( hAPP @ SV236 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1 @ SV236 @ SV1789 @ SY5740 ) ) )
| ~ ( c_Wellfounded_Owf @ SV1789 @ SY5740 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV236 @ SV850 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3819]) ).
thf(4378,plain,
! [SV1790: $i,SV1397: $i,SV852: $i,SV238: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ SV238 @ SV852 @ SV1397 ) @ SV1790 @ ( tc_fun @ SV1397 @ tc_bool ) )
= ( c_Set_Oinsert @ SV238 @ ( c_HOL_Ominus__class_Ominus @ SV852 @ SV1790 @ ( tc_fun @ SV1397 @ tc_bool ) ) @ SV1397 ) )
| ( c_in @ SV238 @ SV1790 @ SV1397 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3821]) ).
thf(4379,plain,
! [SV1791: $i,SV1398: $i,SV853: $i,SV239: $i] :
( ( ( c_lessequals @ SV239 @ ( c_Set_Oinsert @ SV853 @ SV1398 @ SV1791 ) @ ( tc_fun @ SV1791 @ tc_bool ) )
| ~ ( c_lessequals @ SV239 @ SV1398 @ ( tc_fun @ SV1791 @ tc_bool ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV239 @ ( c_Set_Oinsert @ SV853 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1791 @ tc_bool ) ) @ SV1791 ) @ ( tc_fun @ SV1791 @ tc_bool ) ) @ SV1398 @ ( tc_fun @ SV1791 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3822]) ).
thf(4380,plain,
! [SV854: $i,SV240: $i,SV1792: $i] :
( ( ( ! [SY5741: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1792 @ SV240 @ ( tc_fun @ SY5741 @ tc_bool ) ) @ SV854 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV240 @ SV854 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3823]) ).
thf(4381,plain,
! [SV855: $i,SV1793: $i,SV241: $i] :
( ( ( ! [SY5742: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV241 @ SV1793 @ ( tc_fun @ SY5742 @ tc_bool ) ) @ SV855 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV241 @ SV855 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3824]) ).
thf(4382,plain,
! [SV1794: $i,SV1399: $i,SV856: $i,SV242: $i] :
( ( ! [SY5743: $i] :
( ( c_Relation_ORange @ ( c_Set_Oinsert @ ( c_Pair @ SV242 @ SV856 @ SV1399 @ SV1794 ) @ SY5743 @ ( tc_prod @ SV1399 @ SV1794 ) ) @ SV1399 @ SV1794 )
= ( c_Set_Oinsert @ SV856 @ ( c_Relation_ORange @ SY5743 @ SV1399 @ SV1794 ) @ SV1794 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3825]) ).
thf(4383,plain,
! [SV1400: $i,SV857: $i,SV243: $i] :
( ( ( c_Relation_Osym @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV243 @ SV857 @ ( tc_fun @ ( tc_prod @ SV1400 @ SV1400 ) @ tc_bool ) ) @ SV1400 )
= $true )
| ( ( ~ ( c_Relation_Osym @ SV857 @ SV1400 )
| ~ ( c_Relation_Osym @ SV243 @ SV1400 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3826]) ).
thf(4384,plain,
! [SV1401: $i,SV858: $i,SV244: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ SV244 @ SV858 @ SV1401 ) @ ( c_Set_Oinsert @ SV244 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1401 @ tc_bool ) ) @ SV1401 ) @ ( tc_fun @ SV1401 @ tc_bool ) )
= SV858 )
= $true )
| ( ( c_in @ SV244 @ SV858 @ SV1401 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3827]) ).
thf(4385,plain,
! [SV1795: $i,SV1402: $i,SV859: $i,SV245: $i] :
( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV245 @ SV859 @ ( tc_fun @ SV1402 @ tc_bool ) ) @ SV1795 @ ( tc_fun @ SV1402 @ tc_bool ) )
| ~ ( c_lessequals @ SV245 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV859 @ SV1795 @ ( tc_fun @ SV1402 @ tc_bool ) ) @ ( tc_fun @ SV1402 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3828]) ).
thf(4386,plain,
! [SV1796: $i,SV1403: $i,SV860: $i,SV246: $i] :
( ( ( c_lessequals @ SV246 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV860 @ SV1403 @ ( tc_fun @ SV1796 @ tc_bool ) ) @ ( tc_fun @ SV1796 @ tc_bool ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV246 @ SV860 @ ( tc_fun @ SV1796 @ tc_bool ) ) @ SV1403 @ ( tc_fun @ SV1796 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3829]) ).
thf(4387,plain,
! [SV1797: $i,SV1404: $i,SV861: $i,SV247: $i] :
( ( ! [SY5744: $i,SY5745: $i] :
( ( ( hAPP @ SV247 @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ SV247 @ SV861 @ SV1404 @ SV1797 @ SY5744 @ SY5745 ) )
!= ( hAPP @ SV861 @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ SV247 @ SV861 @ SV1404 @ SV1797 @ SY5744 @ SY5745 ) ) )
| ( ( c_Recdef_Ocut @ SV247 @ SV1404 @ SV1797 @ SY5744 @ SY5745 )
= ( c_Recdef_Ocut @ SV861 @ SV1404 @ SV1797 @ SY5744 @ SY5745 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3830]) ).
thf(4388,plain,
! [SV248: $i,SV862: $i,SV1798: $i] :
( ( ( ! [SY5746: $i] :
~ ( c_Wellfounded_Oacyclic @ ( c_Set_Oinsert @ ( c_Pair @ SV1798 @ SY5746 @ SV862 @ SV862 ) @ SV248 @ ( tc_prod @ SV862 @ SV862 ) ) @ SV862 ) )
= $true )
| ( ( c_Wellfounded_Oacyclic @ SV248 @ SV862 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3831]) ).
thf(4389,plain,
! [SV1405: $i,SV863: $i,SV249: $i] :
( ( ( ~ ( class_HOL_Oord @ SV249 ) )
= $true )
| ( ( ! [SY5306: $i] :
( ( c_lessequals @ ( hAPP @ SV863 @ SV1405 ) @ ( hAPP @ SY5306 @ SV1405 ) @ SV249 )
| ! [SY4476: $i] :
~ ( c_lessequals @ SV863 @ SY5306 @ ( tc_fun @ SY4476 @ SV249 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3832]) ).
thf(4390,plain,
! [SV1799: $i,SV1406: $i,SV864: $i,SV250: $i] :
( ( ( c_in @ SV250 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV864 @ SV1406 @ ( tc_fun @ SV1799 @ tc_bool ) ) @ SV1799 )
| ~ ( c_in @ SV250 @ SV1406 @ SV1799 )
| ~ ( c_in @ SV250 @ SV864 @ SV1799 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3833]) ).
thf(4391,plain,
! [SV1800: $i,SV1407: $i,SV865: $i,SV251: $i] :
( ( ( c_in @ SV251 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV865 @ SV1407 @ ( tc_fun @ SV1800 @ tc_bool ) ) @ SV1800 )
| ~ ( c_in @ SV251 @ SV1407 @ SV1800 )
| ~ ( c_in @ SV251 @ SV865 @ SV1800 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3834]) ).
thf(4392,plain,
! [SV1801: $i,SV1408: $i,SV866: $i,SV252: $i] :
( ( ( c_in @ SV252 @ ( c_Set_Oinsert @ SV866 @ SV1408 @ SV1801 ) @ SV1801 )
| ~ ( c_in @ SV252 @ SV1408 @ SV1801 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3835]) ).
thf(4393,plain,
! [SV1802: $i,SV1409: $i,SV867: $i,SV253: $i] :
( ( ( c_in @ SV253 @ ( c_Set_Oinsert @ SV867 @ SV1409 @ SV1802 ) @ SV1802 )
| ~ ( c_in @ SV253 @ SV1409 @ SV1802 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3836]) ).
thf(4394,plain,
! [SV1410: $i,SV868: $i,SV254: $i] :
( ( ( c_in @ SV254 @ SV868 @ SV1410 )
= $true )
| ( ( ! [SY5312: $i] :
( ~ ( c_in @ SV254 @ SY5312 @ SV1410 )
| ~ ( c_lessequals @ SY5312 @ SV868 @ ( tc_fun @ SV1410 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3837]) ).
thf(4395,plain,
! [SV1411: $i,SV869: $i,SV255: $i] :
( ( ( c_in @ SV255 @ SV869 @ SV1411 )
= $true )
| ( ( ! [SY5313: $i] :
( ~ ( c_lessequals @ SY5313 @ SV869 @ ( tc_fun @ SV1411 @ tc_bool ) )
| ~ ( c_in @ SV255 @ SY5313 @ SV1411 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3838]) ).
thf(4396,plain,
! [SV1412: $i,SV870: $i,SV256: $i] :
( ( ( c_in @ SV256 @ SV870 @ SV1412 )
= $true )
| ( ( ! [SY5314: $i] :
( ~ ( c_in @ SV256 @ SY5314 @ SV1412 )
| ~ ( c_lessequals @ SY5314 @ SV870 @ ( tc_fun @ SV1412 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3839]) ).
thf(4397,plain,
! [SV1413: $i,SV871: $i,SV257: $i] :
( ( ( c_in @ SV257 @ SV871 @ SV1413 )
= $true )
| ( ( ! [SY5315: $i] :
( ~ ( c_in @ SV257 @ SY5315 @ SV1413 )
| ~ ( c_lessequals @ SY5315 @ SV871 @ ( tc_fun @ SV1413 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3840]) ).
thf(4398,plain,
! [SV1803: $i,SV1414: $i,SV872: $i,SV258: $i] :
( ( ( c_in @ SV258 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV872 @ SV1414 @ ( tc_fun @ SV1803 @ tc_bool ) ) @ SV1803 )
| ~ ( c_in @ SV258 @ SV872 @ SV1803 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3841]) ).
thf(4399,plain,
! [SV1804: $i,SV1415: $i,SV873: $i,SV259: $i] :
( ( ( c_in @ SV259 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV873 @ SV1415 @ ( tc_fun @ SV1804 @ tc_bool ) ) @ SV1804 )
| ~ ( c_in @ SV259 @ SV1415 @ SV1804 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3842]) ).
thf(4400,plain,
! [SV261: $i,SV1805: $i,SV875: $i] :
( ( ( ~ ( c_in @ SV875 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1805 @ tc_bool ) ) @ SV1805 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV261 @ SV875 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3844]) ).
thf(4401,plain,
! [SV1416: $i,SV878: $i,SV264: $i] :
( ( ( c_in @ SV264 @ SV878 @ SV1416 )
= $true )
| ( ( ! [SY5318: $i] :
( ( SV264 = SY5318 )
| ~ ( c_in @ SV264 @ ( c_Set_Oinsert @ SY5318 @ SV878 @ SV1416 ) @ SV1416 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3847]) ).
thf(4402,plain,
! [SV1417: $i,SV879: $i,SV265: $i] :
( ( ( c_in @ SV265 @ SV879 @ SV1417 )
= $true )
| ( ( ! [SY5319: $i] :
( ( c_in @ SV265 @ SY5319 @ SV1417 )
| ~ ( c_in @ SV265 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY5319 @ SV879 @ ( tc_fun @ SV1417 @ tc_bool ) ) @ SV1417 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3848]) ).
thf(4403,plain,
! [SV1418: $i,SV880: $i,SV266: $i] :
( ( ( ~ ( c_in @ SV266 @ SV880 @ SV1418 ) )
= $true )
| ( ( ! [SY5320: $i] :
~ ( c_in @ SV266 @ ( c_HOL_Ominus__class_Ominus @ SY5320 @ SV880 @ ( tc_fun @ SV1418 @ tc_bool ) ) @ SV1418 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3849]) ).
thf(4404,plain,
! [SV1419: $i,SV881: $i,SV267: $i] :
( ( ( c_in @ SV267 @ SV881 @ SV1419 )
= $true )
| ( ( ! [SY5321: $i] :
~ ( c_in @ SV267 @ ( c_HOL_Ominus__class_Ominus @ SV881 @ SY5321 @ ( tc_fun @ SV1419 @ tc_bool ) ) @ SV1419 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3850]) ).
thf(4405,plain,
! [SV1423: $i,SV885: $i,SV271: $i] :
( ( ( c_in @ SV271 @ SV885 @ SV1423 )
= $true )
| ( ( ! [SY5322: $i] :
~ ( c_in @ SV271 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY5322 @ SV885 @ ( tc_fun @ SV1423 @ tc_bool ) ) @ SV1423 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3854]) ).
thf(4406,plain,
! [SV1424: $i,SV886: $i,SV272: $i] :
( ( ( c_in @ SV272 @ SV886 @ SV1424 )
= $true )
| ( ( ! [SY5323: $i] :
~ ( c_in @ SV272 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV886 @ SY5323 @ ( tc_fun @ SV1424 @ tc_bool ) ) @ SV1424 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3855]) ).
thf(4407,plain,
! [SV887: $i,SV273: $i] :
( ( ( hBOOL @ ( hAPP @ SV273 @ SV887 ) )
= $false )
| ( ( ! [SY4513: $i] :
~ ( c_in @ SV887 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4513 @ tc_bool ) ) @ SY4513 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3856]) ).
thf(4408,plain,
! [SV1806: $i,SV1425: $i,SV888: $i,SV274: $i] :
( ( ( c_in @ SV274 @ ( c_HOL_Ominus__class_Ominus @ SV888 @ SV1425 @ ( tc_fun @ SV1806 @ tc_bool ) ) @ SV1806 )
| ( c_in @ SV274 @ SV1425 @ SV1806 )
| ~ ( c_in @ SV274 @ SV888 @ SV1806 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3857]) ).
thf(4409,plain,
! [SV1807: $i,SV1426: $i,SV889: $i,SV275: $i] :
( ( ( c_in @ SV275 @ ( c_HOL_Ominus__class_Ominus @ SV889 @ SV1426 @ ( tc_fun @ SV1807 @ tc_bool ) ) @ SV1807 )
| ( c_in @ SV275 @ SV1426 @ SV1807 )
| ~ ( c_in @ SV275 @ SV889 @ SV1807 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3858]) ).
thf(4410,plain,
! [SV1808: $i,SV1427: $i,SV890: $i,SV276: $i] :
( ( ( ( c_Set_Oinsert @ SV276 @ SV890 @ SV1427 )
!= ( c_Set_Oinsert @ SV276 @ SV1808 @ SV1427 ) )
| ( c_in @ SV276 @ SV1808 @ SV1427 )
| ( SV890 = SV1808 )
| ( c_in @ SV276 @ SV890 @ SV1427 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3859]) ).
thf(4411,plain,
! [SV1428: $i,SV891: $i,SV277: $i] :
( ( ( ( c_Set_Oinsert @ SV277 @ SV891 @ SV1428 )
= SV891 )
= $true )
| ( ( ~ ( c_in @ SV277 @ SV891 @ SV1428 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3860]) ).
thf(4412,plain,
! [SV1809: $i,SV1429: $i,SV892: $i,SV278: $i] :
( ( ( hAPP @ ( c_fst @ SV278 @ SV892 ) @ ( c_Pair @ SV1429 @ SV1809 @ SV278 @ SV892 ) )
= SV1429 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3861]) ).
thf(4413,plain,
! [SV1810: $i,SV1430: $i,SV893: $i,SV279: $i] :
( ( SV279
= ( hAPP @ ( c_fst @ SV893 @ SV1430 ) @ ( c_Pair @ SV279 @ SV1810 @ SV893 @ SV1430 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3862]) ).
thf(4414,plain,
! [SV1811: $i,SV1431: $i,SV894: $i,SV280: $i] :
( ( ( hAPP @ ( c_snd @ SV280 @ SV894 ) @ ( c_Pair @ SV1431 @ SV1811 @ SV280 @ SV894 ) )
= SV1811 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3863]) ).
thf(4415,plain,
! [SV1812: $i,SV1432: $i,SV895: $i,SV281: $i] :
( ( SV281
= ( hAPP @ ( c_snd @ SV895 @ SV1432 ) @ ( c_Pair @ SV1812 @ SV281 @ SV895 @ SV1432 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3864]) ).
thf(4416,plain,
! [SV1813: $i,SV1433: $i,SV896: $i,SV282: $i] :
( ( ! [SY5747: $i] :
( ( hBOOL @ ( hAPP @ SV282 @ ( hAPP @ ( c_fst @ SV896 @ SV1433 ) @ ( c_Pair @ SV1813 @ SY5747 @ SV896 @ SV1433 ) ) ) )
| ! [V_Q: $i] :
~ ( hBOOL @ ( hAPP @ V_Q @ SY5747 ) )
| ~ ( hBOOL @ ( hAPP @ SV282 @ SV1813 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3865]) ).
thf(4417,plain,
! [SV1814: $i,SV1434: $i,SV897: $i,SV283: $i] :
( ( ! [SY5749: $i] :
( ( hBOOL @ ( hAPP @ SV283 @ ( hAPP @ ( c_snd @ SV897 @ SV1434 ) @ ( c_Pair @ SV1814 @ SY5749 @ SV897 @ SV1434 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ SV283 @ SY5749 ) )
| ! [SY5750: $i] :
~ ( hBOOL @ ( hAPP @ SY5750 @ SV1814 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3866]) ).
thf(4418,plain,
! [SV898: $i,SV284: $i] :
( ( ( class_Lattices_Odistrib__lattice @ SV284 )
= $false )
| ( ( ! [SY4537: $i,SY4538: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV898 @ SY4537 @ SV284 ) @ SY4538 @ SV284 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV898 @ SY4538 @ SV284 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4537 @ SY4538 @ SV284 ) @ SV284 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3867]) ).
thf(4419,plain,
! [SV899: $i,SV285: $i] :
( ( ( class_Lattices_Odistrib__lattice @ SV285 )
= $false )
| ( ( ! [SY4539: $i,SY4540: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV899 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4539 @ SY4540 @ SV285 ) @ SV285 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV899 @ SY4539 @ SV285 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV899 @ SY4540 @ SV285 ) @ SV285 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3868]) ).
thf(4420,plain,
! [SV1815: $i,SV1435: $i,SV900: $i,SV286: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV286 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV900 @ SV1435 @ ( tc_fun @ SV1815 @ tc_bool ) ) @ ( tc_fun @ SV1815 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV286 @ SV900 @ ( tc_fun @ SV1815 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV286 @ SV1435 @ ( tc_fun @ SV1815 @ tc_bool ) ) @ ( tc_fun @ SV1815 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3869]) ).
thf(4421,plain,
! [SV1816: $i,SV1436: $i,SV901: $i,SV287: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV287 @ SV901 @ ( tc_fun @ SV1436 @ tc_bool ) ) @ SV1816 @ ( tc_fun @ SV1436 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV287 @ SV1816 @ ( tc_fun @ SV1436 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV901 @ SV1816 @ ( tc_fun @ SV1436 @ tc_bool ) ) @ ( tc_fun @ SV1436 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3870]) ).
thf(4422,plain,
! [SV902: $i,SV288: $i,SV1817: $i] :
( ( ( ~ ( c_Order__Relation_Ostrict__linear__order__on @ SV1817 @ SV288 @ SV902 ) )
= $true )
| ( ( c_Relation_Otrans @ SV288 @ SV902 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3871]) ).
thf(4423,plain,
! [SV1818: $i,SV1438: $i,SV904: $i,SV290: $i] :
( ( ( c_lessequals @ ( c_Set_Oinsert @ SV290 @ SV904 @ SV1438 ) @ SV1818 @ ( tc_fun @ SV1438 @ tc_bool ) )
| ~ ( c_lessequals @ SV904 @ SV1818 @ ( tc_fun @ SV1438 @ tc_bool ) )
| ~ ( c_in @ SV290 @ SV1818 @ SV1438 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3873]) ).
thf(4424,plain,
! [SV1819: $i,SV1439: $i,SV905: $i,SV291: $i] :
( ( ! [SY5751: $i] :
( ( c_Product__Type_OSigma @ ( c_HOL_Ominus__class_Ominus @ SV291 @ SV905 @ ( tc_fun @ SV1439 @ tc_bool ) ) @ ( c_COMBK @ SV1819 @ ( tc_fun @ SY5751 @ tc_bool ) @ SV1439 ) @ SV1439 @ SY5751 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Product__Type_OSigma @ SV291 @ ( c_COMBK @ SV1819 @ ( tc_fun @ SY5751 @ tc_bool ) @ SV1439 ) @ SV1439 @ SY5751 ) @ ( c_Product__Type_OSigma @ SV905 @ ( c_COMBK @ SV1819 @ ( tc_fun @ SY5751 @ tc_bool ) @ SV1439 ) @ SV1439 @ SY5751 ) @ ( tc_fun @ ( tc_prod @ SV1439 @ SY5751 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3874]) ).
thf(4425,plain,
! [SV292: $i,SV1820: $i] :
( ( ( ! [SY5752: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV1820 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1820 @ SY5752 @ SV292 ) @ SV292 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV1820 @ SY5752 @ SV292 ) ) )
= $true )
| ( ( class_Lattices_Olattice @ SV292 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3875]) ).
thf(4426,plain,
! [SV293: $i,SV1821: $i] :
( ( ( ! [SY5753: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV1821 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1821 @ SY5753 @ SV293 ) @ SV293 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV1821 @ SY5753 @ SV293 ) ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV293 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3876]) ).
thf(4427,plain,
! [SV1822: $i,SV1441: $i,SV907: $i,SV295: $i] :
( ( ( c_Relation_ORange @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV295 @ SV907 @ ( tc_fun @ ( tc_prod @ SV1441 @ SV1822 ) @ tc_bool ) ) @ SV1441 @ SV1822 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_ORange @ SV295 @ SV1441 @ SV1822 ) @ ( c_Relation_ORange @ SV907 @ SV1441 @ SV1822 ) @ ( tc_fun @ SV1822 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3878]) ).
thf(4428,plain,
! [SV1442: $i,SV908: $i,SV296: $i] :
( ( ( c_Wellfounded_Owf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV296 @ SV908 @ ( tc_fun @ ( tc_prod @ SV1442 @ SV1442 ) @ tc_bool ) ) @ SV1442 )
= $true )
| ( ( ~ ( c_Wellfounded_Owf @ SV296 @ SV1442 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3879]) ).
thf(4429,plain,
! [SV1443: $i,SV909: $i,SV297: $i] :
( ( ( c_Wellfounded_Owf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV297 @ SV909 @ ( tc_fun @ ( tc_prod @ SV1443 @ SV1443 ) @ tc_bool ) ) @ SV1443 )
= $true )
| ( ( ~ ( c_Wellfounded_Owf @ SV909 @ SV1443 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3880]) ).
thf(4430,plain,
! [SV1444: $i,SV910: $i,SV298: $i] :
( ( ( ( c_Set_Oinsert @ SV298 @ ( c_HOL_Ominus__class_Ominus @ SV910 @ ( c_Set_Oinsert @ SV298 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1444 @ tc_bool ) ) @ SV1444 ) @ ( tc_fun @ SV1444 @ tc_bool ) ) @ SV1444 )
= SV910 )
= $true )
| ( ( ~ ( c_in @ SV298 @ SV910 @ SV1444 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3881]) ).
thf(4431,plain,
! [SV299: $i,SV1823: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV1823 @ SV1823 @ SV299 )
= SV1823 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV299 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3882]) ).
thf(4432,plain,
! [SV912: $i,SV301: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV301 )
= $false )
| ( ( ! [SY4558: $i] :
( ( c_lessequals @ SV912 @ SY4558 @ SV301 )
| ! [SY4559: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4559 @ SV912 @ SV301 ) @ SY4558 @ SV301 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3883]) ).
thf(4433,plain,
! [SV913: $i,SV302: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV302 )
= $false )
| ( ( ! [SY4560: $i] :
( ( c_lessequals @ SV913 @ SY4560 @ SV302 )
| ! [SY4561: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV913 @ SY4561 @ SV302 ) @ SY4560 @ SV302 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3884]) ).
thf(4434,plain,
! [SV914: $i,SV303: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV303 )
= $false )
| ( ( ! [SY4562: $i,SY4563: $i] :
( ( c_lessequals @ SV914 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4562 @ SY4563 @ SV303 ) @ SV303 )
| ~ ( c_lessequals @ SV914 @ SY4563 @ SV303 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3885]) ).
thf(4435,plain,
! [SV915: $i,SV304: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV304 )
= $false )
| ( ( ! [SY4564: $i] :
( ! [SY4565: $i] : ( c_lessequals @ SV915 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4564 @ SY4565 @ SV304 ) @ SV304 )
| ~ ( c_lessequals @ SV915 @ SY4564 @ SV304 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3886]) ).
thf(4436,plain,
! [SV916: $i,SV305: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV305 )
= $false )
| ( ( ! [SY4566: $i] :
( ( c_lessequals @ SV916 @ SY4566 @ SV305 )
| ! [SY4567: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4567 @ SV916 @ SV305 ) @ SY4566 @ SV305 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3887]) ).
thf(4437,plain,
! [SV917: $i,SV306: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV306 )
= $false )
| ( ( ! [SY4568: $i] :
( ( c_lessequals @ SV917 @ SY4568 @ SV306 )
| ! [SY4569: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV917 @ SY4569 @ SV306 ) @ SY4568 @ SV306 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3888]) ).
thf(4438,plain,
! [SV1445: $i,SV918: $i,SV307: $i] :
( ( ( c_lessequals @ SV307 @ SV918 @ ( tc_fun @ SV1445 @ tc_bool ) )
= $true )
| ( ( ! [SY5343: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV307 @ SY5343 @ ( tc_fun @ SV1445 @ tc_bool ) ) @ SV918 @ ( tc_fun @ SV1445 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3889]) ).
thf(4439,plain,
! [SV1446: $i,SV919: $i,SV308: $i] :
( ( ( c_lessequals @ SV308 @ SV919 @ ( tc_fun @ SV1446 @ tc_bool ) )
= $true )
| ( ( ! [SY5344: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY5344 @ SV308 @ ( tc_fun @ SV1446 @ tc_bool ) ) @ SV919 @ ( tc_fun @ SV1446 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3890]) ).
thf(4440,plain,
! [SV920: $i,SV309: $i] :
( ( ( class_Orderings_Oorder @ SV309 )
= $false )
| ( ( ! [SY4574: $i] :
( ( c_lessequals @ SV920 @ SY4574 @ SV309 )
| ! [SY4575: $i] :
( ~ ( c_lessequals @ SV920 @ SY4575 @ SV309 )
| ~ ( c_lessequals @ SY4575 @ SY4574 @ SV309 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3891]) ).
thf(4441,plain,
! [SV921: $i,SV310: $i] :
( ( ( class_Orderings_Opreorder @ SV310 )
= $false )
| ( ( ! [SY4576: $i] :
( ( c_lessequals @ SV921 @ SY4576 @ SV310 )
| ! [SY4577: $i] :
( ~ ( c_lessequals @ SY4577 @ SY4576 @ SV310 )
| ~ ( c_lessequals @ SV921 @ SY4577 @ SV310 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3892]) ).
thf(4442,plain,
! [SV1447: $i,SV924: $i,SV313: $i] :
( ( ( c_lessequals @ SV313 @ SV924 @ ( tc_fun @ SV1447 @ tc_bool ) )
= $true )
| ( ( ! [SY5345: $i] :
( ~ ( c_lessequals @ SY5345 @ SV924 @ ( tc_fun @ SV1447 @ tc_bool ) )
| ~ ( c_lessequals @ SV313 @ SY5345 @ ( tc_fun @ SV1447 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3893]) ).
thf(4443,plain,
! [SV314: $i,SV925: $i,SV1824: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV1824 @ SV925 ) )
| ! [SY5754: $i] :
~ ( c_lessequals @ SV1824 @ SV314 @ ( tc_fun @ SY5754 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV314 @ SV925 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3894]) ).
thf(4444,plain,
! [SV926: $i,SV1825: $i,SV315: $i] :
( ( ( ~ ( c_lessequals @ SV315 @ SV1825 @ ( tc_fun @ ( tc_prod @ SV926 @ SV926 ) @ tc_bool ) )
| ~ ( c_Wellfounded_Owf @ SV1825 @ SV926 ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV315 @ SV926 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3895]) ).
thf(4445,plain,
! [SV316: $i,SV1826: $i] :
( ( ( c_lessequals @ SV1826 @ SV1826 @ SV316 )
= $true )
| ( ( class_Orderings_Oorder @ SV316 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3896]) ).
thf(4446,plain,
! [SV317: $i,SV1827: $i] :
( ( ( c_lessequals @ SV1827 @ SV1827 @ SV317 )
= $true )
| ( ( class_Orderings_Opreorder @ SV317 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3897]) ).
thf(4447,plain,
! [SV318: $i,SV927: $i,SV1828: $i] :
( ( ( ~ ( c_Relation_Oantisym @ SV1828 @ SV927 )
| ~ ( c_lessequals @ SV318 @ SV1828 @ ( tc_fun @ ( tc_prod @ SV927 @ SV927 ) @ tc_bool ) ) )
= $true )
| ( ( c_Relation_Oantisym @ SV318 @ SV927 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3898]) ).
thf(4448,plain,
! [SV928: $i,SV319: $i,SV1829: $i] :
( ( ( ! [SY5755: $i] :
~ ( c_lessequals @ SV1829 @ SV319 @ ( tc_fun @ SY5755 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ SV1829 @ SV928 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV319 @ SV928 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3899]) ).
thf(4449,plain,
! [SV929: $i,SV1830: $i,SV320: $i] :
( ( ( ~ ( c_lessequals @ SV320 @ SV1830 @ ( tc_fun @ ( tc_prod @ SV929 @ SV929 ) @ tc_bool ) )
| ~ ( c_Wellfounded_Oacyclic @ SV1830 @ SV929 ) )
= $true )
| ( ( c_Wellfounded_Oacyclic @ SV320 @ SV929 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3900]) ).
thf(4450,plain,
! [SV1448: $i,SV930: $i,SV321: $i] :
( ( ( c_Relation_Osingle__valued @ SV321 @ SV930 @ SV1448 )
= $true )
| ( ( ! [SY5346: $i] :
( ~ ( c_Relation_Osingle__valued @ SY5346 @ SV930 @ SV1448 )
| ~ ( c_lessequals @ SV321 @ SY5346 @ ( tc_fun @ ( tc_prod @ SV930 @ SV1448 ) @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3901]) ).
thf(4451,plain,
! [SV1449: $i,SV931: $i,SV322: $i] :
( ( ( ! [SY5347: $i] :
( ( c_Set_Oimage @ SV322 @ SV931 @ SV1449 @ SY5347 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5347 @ tc_bool ) ) ) )
= $true )
| ( ( SV931
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1449 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3902]) ).
thf(4452,plain,
! [SV1831: $i,SV1450: $i,SV932: $i,SV323: $i] :
( ( ! [SY5756: $i] :
( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV323 @ SV932 @ ( tc_fun @ SV1450 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1831 @ SY5756 @ ( tc_fun @ SV1450 @ tc_bool ) ) @ ( tc_fun @ SV1450 @ tc_bool ) )
| ~ ( c_lessequals @ SV932 @ SY5756 @ ( tc_fun @ SV1450 @ tc_bool ) )
| ~ ( c_lessequals @ SV323 @ SV1831 @ ( tc_fun @ SV1450 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3903]) ).
thf(4453,plain,
! [SV1832: $i,SV1451: $i,SV933: $i,SV324: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV324 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV933 @ SV1451 @ ( tc_fun @ SV1832 @ tc_bool ) ) @ ( tc_fun @ SV1832 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_HOL_Ominus__class_Ominus @ SV324 @ SV933 @ ( tc_fun @ SV1832 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV324 @ SV1451 @ ( tc_fun @ SV1832 @ tc_bool ) ) @ ( tc_fun @ SV1832 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3904]) ).
thf(4454,plain,
! [SV1833: $i,SV1452: $i,SV934: $i,SV325: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV325 @ SV934 @ ( tc_fun @ SV1452 @ tc_bool ) ) @ SV1833 @ ( tc_fun @ SV1452 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV325 @ ( c_HOL_Ominus__class_Ominus @ SV934 @ SV1833 @ ( tc_fun @ SV1452 @ tc_bool ) ) @ ( tc_fun @ SV1452 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3905]) ).
thf(4455,plain,
! [SV1834: $i,SV1453: $i,SV936: $i,SV327: $i] :
( ( ( c_lessequals @ ( c_Relation_ODomain @ SV327 @ SV936 @ SV1453 ) @ ( c_Relation_ODomain @ SV1834 @ SV936 @ SV1453 ) @ ( tc_fun @ SV936 @ tc_bool ) )
| ~ ( c_lessequals @ SV327 @ SV1834 @ ( tc_fun @ ( tc_prod @ SV936 @ SV1453 ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3906]) ).
thf(4456,plain,
! [SV1454: $i,SV937: $i,SV328: $i] :
( ( ( SV328
= ( c_Set_Oinsert @ SV937 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1454 @ tc_bool ) ) @ SV1454 ) )
= $true )
| ( ( ( SV328
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1454 @ tc_bool ) ) )
| ~ ( c_lessequals @ SV328 @ ( c_Set_Oinsert @ SV937 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1454 @ tc_bool ) ) @ SV1454 ) @ ( tc_fun @ SV1454 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3907]) ).
thf(4457,plain,
! [SV1835: $i,SV1455: $i,SV938: $i,SV329: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV329 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV938 @ SV1455 @ ( tc_fun @ SV1835 @ tc_bool ) ) @ ( tc_fun @ SV1835 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ SV329 @ SV938 @ ( tc_fun @ SV1835 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV329 @ SV1455 @ ( tc_fun @ SV1835 @ tc_bool ) ) @ ( tc_fun @ SV1835 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3908]) ).
thf(4458,plain,
! [SV1836: $i,SV1457: $i,SV940: $i,SV331: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV331 @ SV940 @ ( tc_fun @ SV1457 @ tc_bool ) ) @ SV1836 ) )
| ~ ( hBOOL @ ( hAPP @ SV940 @ SV1836 ) )
| ~ ( hBOOL @ ( hAPP @ SV331 @ SV1836 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3910]) ).
thf(4459,plain,
! [SV1837: $i,SV1458: $i,SV941: $i,SV332: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV332 @ ( c_HOL_Ominus__class_Ominus @ SV941 @ SV1458 @ ( tc_fun @ SV1837 @ tc_bool ) ) @ ( tc_fun @ SV1837 @ tc_bool ) )
= SV1458 )
| ~ ( c_lessequals @ SV332 @ SV941 @ ( tc_fun @ SV1837 @ tc_bool ) )
| ~ ( c_lessequals @ SV1458 @ SV332 @ ( tc_fun @ SV1837 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3911]) ).
thf(4460,plain,
! [SV1459: $i,SV942: $i,SV333: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV333 ) )
= $true )
| ( ( ! [SY5356: $i,SY5357: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV942 @ SV1459 @ SV333 )
!= ( c_HOL_Ominus__class_Ominus @ SY5356 @ SY5357 @ SV333 ) )
| ( c_lessequals @ SY5357 @ SY5356 @ SV333 )
| ~ ( c_lessequals @ SV1459 @ SV942 @ SV333 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3912]) ).
thf(4461,plain,
! [SV1460: $i,SV943: $i,SV334: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV334 ) )
= $true )
| ( ( ! [SY5358: $i,SY5359: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV943 @ SV1460 @ SV334 )
!= ( c_HOL_Ominus__class_Ominus @ SY5358 @ SY5359 @ SV334 ) )
| ( c_lessequals @ SV1460 @ SV943 @ SV334 )
| ~ ( c_lessequals @ SY5359 @ SY5358 @ SV334 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3913]) ).
thf(4462,plain,
! [SV1838: $i,SV1461: $i,SV944: $i,SV335: $i] :
( ( ! [SY5757: $i] :
( ( c_lessequals @ ( c_Set_Oimage @ SV335 @ SV944 @ SV1461 @ SV1838 ) @ ( c_Set_Oimage @ SV335 @ SY5757 @ SV1461 @ SV1838 ) @ ( tc_fun @ SV1838 @ tc_bool ) )
| ~ ( c_lessequals @ SV944 @ SY5757 @ ( tc_fun @ SV1461 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3914]) ).
thf(4463,plain,
! [SV1462: $i,SV945: $i,SV336: $i] :
( ( ( ~ ( c_lessequals @ SV336 @ SV945 @ ( tc_fun @ SV1462 @ tc_bool ) ) )
= $true )
| ( ( ! [SY5362: $i,SY5363: $i] : ( c_lessequals @ ( c_Set_Oimage @ SY5362 @ SV336 @ SV1462 @ SY5363 ) @ ( c_Set_Oimage @ SY5362 @ SV945 @ SV1462 @ SY5363 ) @ ( tc_fun @ SY5363 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3915]) ).
thf(4464,plain,
! [SV1839: $i,SV1463: $i,SV946: $i,SV337: $i] :
( ( ( c_lessequals @ ( c_Set_Oinsert @ SV337 @ SV946 @ SV1463 ) @ ( c_Set_Oinsert @ SV337 @ SV1839 @ SV1463 ) @ ( tc_fun @ SV1463 @ tc_bool ) )
| ~ ( c_lessequals @ SV946 @ SV1839 @ ( tc_fun @ SV1463 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3916]) ).
thf(4465,plain,
! [SV1840: $i,SV1464: $i,SV947: $i,SV339: $i] :
( ( ! [SY5758: $i] :
( ( c_Set_Oimage @ SV339 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV947 @ SV1464 @ ( tc_fun @ SV1840 @ tc_bool ) ) @ SV1840 @ SY5758 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ SV339 @ SV947 @ SV1840 @ SY5758 ) @ ( c_Set_Oimage @ SV339 @ SV1464 @ SV1840 @ SY5758 ) @ ( tc_fun @ SY5758 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3917]) ).
thf(4466,plain,
! [SV1841: $i,SV1465: $i,SV948: $i,SV341: $i] :
( ( ! [SY5759: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV341 @ ( hAPP @ ( c_snd @ SV948 @ SV1465 ) @ ( c_Pair @ SV1841 @ SY5759 @ SV948 @ SV1465 ) ) ) @ ( hAPP @ ( c_fst @ SV948 @ SV1465 ) @ ( c_Pair @ SV1841 @ SY5759 @ SV948 @ SV1465 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV341 @ SY5759 ) @ SV1841 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3918]) ).
thf(4467,plain,
! [SV1466: $i,SV949: $i,SV342: $i] :
( ( ( ( c_Relation_ORange @ SV342 @ SV949 @ SV1466 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1466 @ tc_bool ) ) )
= $true )
| ( ( SV342
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV949 @ SV1466 ) @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3919]) ).
thf(4468,plain,
! [SV1842: $i,SV1467: $i,SV950: $i,SV343: $i] :
( ( ! [SY5760: $i,SY5761: $i] :
( ( c_lessequals @ ( c_Relation_OImage @ SV343 @ SV950 @ SV1467 @ SV1842 ) @ ( c_Relation_OImage @ SY5760 @ SY5761 @ SV1467 @ SV1842 ) @ ( tc_fun @ SV1842 @ tc_bool ) )
| ~ ( c_lessequals @ SV950 @ SY5761 @ ( tc_fun @ SV1467 @ tc_bool ) )
| ~ ( c_lessequals @ SV343 @ SY5760 @ ( tc_fun @ ( tc_prod @ SV1467 @ SV1842 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3920]) ).
thf(4469,plain,
! [SV1468: $i,SV951: $i,SV344: $i] :
( ( ( c_lessequals @ SV344 @ ( c_Product__Type_OSigma @ SV951 @ ( c_COMBK @ SV951 @ ( tc_fun @ SV1468 @ tc_bool ) @ SV1468 ) @ SV1468 @ SV1468 ) @ ( tc_fun @ ( tc_prod @ SV1468 @ SV1468 ) @ tc_bool ) )
= $true )
| ( ( ~ ( c_Equiv__Relations_Oequiv @ SV951 @ SV344 @ SV1468 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3921]) ).
thf(4470,plain,
! [SV345: $i,SV1843: $i] :
( ( ( ! [SY5762: $i] :
( ( c_lessequals @ SV1843 @ SY5762 @ SV345 )
| ( c_lessequals @ SY5762 @ SV1843 @ SV345 ) ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV345 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3922]) ).
thf(4471,plain,
! [SV952: $i,SV346: $i,SV1844: $i] :
( ( ( ~ ( c_Order__Relation_Ostrict__linear__order__on @ SV1844 @ SV346 @ SV952 ) )
= $true )
| ( ( c_Relation_Oirrefl @ SV346 @ SV952 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3923]) ).
thf(4472,plain,
! [SV1845: $i,SV1469: $i,SV953: $i,SV347: $i] :
( ( ( c_Wellfounded_Oacyclic @ ( c_Set_Oinsert @ ( c_Pair @ SV347 @ SV953 @ SV1469 @ SV1469 ) @ SV1845 @ ( tc_prod @ SV1469 @ SV1469 ) ) @ SV1469 )
| ( c_in @ ( c_Pair @ SV953 @ SV347 @ SV1469 @ SV1469 ) @ ( c_Transitive__Closure_Ortrancl @ SV1845 @ SV1469 ) @ ( tc_prod @ SV1469 @ SV1469 ) )
| ~ ( c_Wellfounded_Oacyclic @ SV1845 @ SV1469 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3924]) ).
thf(4473,plain,
! [SV1846: $i,SV1470: $i,SV954: $i,SV348: $i] :
( ( ~ ( c_in @ ( c_Pair @ SV348 @ SV954 @ SV1470 @ SV1470 ) @ ( c_Transitive__Closure_Ortrancl @ SV1846 @ SV1470 ) @ ( tc_prod @ SV1470 @ SV1470 ) )
| ~ ( c_Wellfounded_Oacyclic @ ( c_Set_Oinsert @ ( c_Pair @ SV954 @ SV348 @ SV1470 @ SV1470 ) @ SV1846 @ ( tc_prod @ SV1470 @ SV1470 ) ) @ SV1470 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3925]) ).
thf(4474,plain,
! [SV1471: $i,SV955: $i,SV349: $i] :
( ( ( hBOOL @ ( hAPP @ SV349 @ SV955 ) )
= $true )
| ( ( ! [SY5374: $i,SY5375: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1 @ SV349 @ SV1471 @ SY5374 @ SY5375 ) @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 @ SV349 @ SV1471 @ SY5374 @ SY5375 ) @ SY5375 @ SY5375 ) @ SY5374 @ ( tc_prod @ SY5375 @ SY5375 ) )
| ~ ( hBOOL @ ( hAPP @ SV349 @ SV1471 ) )
| ~ ( c_in @ ( c_Pair @ SV955 @ SV1471 @ SY5375 @ SY5375 ) @ ( c_Transitive__Closure_Ortrancl @ SY5374 @ SY5375 ) @ ( tc_prod @ SY5375 @ SY5375 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3926]) ).
thf(4475,plain,
! [SV1472: $i,SV956: $i,SV350: $i] :
( ( ( hBOOL @ ( hAPP @ SV350 @ SV956 ) )
= $true )
| ( ( ! [SY5376: $i,SY5377: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 @ SV350 @ SV1472 @ SY5376 @ SY5377 ) @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2 @ SV350 @ SV1472 @ SY5376 @ SY5377 ) @ SY5377 @ SY5377 ) @ SY5376 @ ( tc_prod @ SY5377 @ SY5377 ) )
| ~ ( hBOOL @ ( hAPP @ SV350 @ SV1472 ) )
| ~ ( c_in @ ( c_Pair @ SV1472 @ SV956 @ SY5377 @ SY5377 ) @ ( c_Transitive__Closure_Ortrancl @ SY5376 @ SY5377 ) @ ( tc_prod @ SY5377 @ SY5377 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3927]) ).
thf(4476,plain,
! [SV1473: $i,SV957: $i,SV351: $i] :
( ( ( c_in @ SV351 @ ( c_Relation_OImage @ SV957 @ ( c_Set_Oinsert @ SV351 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1473 @ tc_bool ) ) @ SV1473 ) @ SV1473 @ SV1473 ) @ SV1473 )
= $true )
| ( ( ! [SY5378: $i] :
( ~ ( c_in @ SV351 @ SY5378 @ SV1473 )
| ~ ( c_Equiv__Relations_Oequiv @ SY5378 @ SV957 @ SV1473 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3928]) ).
thf(4477,plain,
! [SV1474: $i,SV958: $i,SV352: $i] :
( ( ( c_lessequals @ ( c_Transitive__Closure_Ortrancl @ SV352 @ SV958 ) @ SV1474 @ ( tc_fun @ ( tc_prod @ SV958 @ SV958 ) @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Relation_Orel__comp @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Transitive__Closure_Ortrancl @ SV352 @ SV958 ) @ SV1474 @ ( tc_fun @ ( tc_prod @ SV958 @ SV958 ) @ tc_bool ) ) @ SV352 @ SV958 @ SV958 @ SV958 ) @ SV1474 @ ( tc_fun @ ( tc_prod @ SV958 @ SV958 ) @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Relation_OId @ SV958 ) @ SV1474 @ ( tc_fun @ ( tc_prod @ SV958 @ SV958 ) @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3929]) ).
thf(4478,plain,
! [SV1847: $i,SV1475: $i,SV959: $i,SV353: $i] :
( ( ( c_in @ ( c_Pair @ SV353 @ SV959 @ SV1475 @ SV1475 ) @ SV1847 @ ( tc_prod @ SV1475 @ SV1475 ) )
| ! [SY5763: $i] :
~ ( c_in @ SY5763 @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_OImage @ SV1847 @ ( c_Set_Oinsert @ SV353 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1475 @ tc_bool ) ) @ SV1475 ) @ SV1475 @ SV1475 ) @ ( c_Relation_OImage @ SV1847 @ ( c_Set_Oinsert @ SV959 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1475 @ tc_bool ) ) @ SV1475 ) @ SV1475 @ SV1475 ) @ ( tc_fun @ SV1475 @ tc_bool ) ) @ SV1475 )
| ! [SY5764: $i] :
~ ( c_Equiv__Relations_Oequiv @ SY5764 @ SV1847 @ SV1475 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3930]) ).
thf(4479,plain,
! [SV1848: $i,SV1476: $i,SV960: $i,SV354: $i] :
( ( ( c_in @ ( c_Pair @ SV354 @ SV960 @ SV1476 @ SV1476 ) @ SV1848 @ ( tc_prod @ SV1476 @ SV1476 ) )
| ! [SY5765: $i] :
( ~ ( c_in @ SV960 @ SY5765 @ SV1476 )
| ~ ( c_lessequals @ ( c_Relation_OImage @ SV1848 @ ( c_Set_Oinsert @ SV960 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1476 @ tc_bool ) ) @ SV1476 ) @ SV1476 @ SV1476 ) @ ( c_Relation_OImage @ SV1848 @ ( c_Set_Oinsert @ SV354 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1476 @ tc_bool ) ) @ SV1476 ) @ SV1476 @ SV1476 ) @ ( tc_fun @ SV1476 @ tc_bool ) )
| ~ ( c_Equiv__Relations_Oequiv @ SY5765 @ SV1848 @ SV1476 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3931]) ).
thf(4480,plain,
! [SV1849: $i,SV1477: $i,SV961: $i,SV355: $i] :
( ( ! [SY5766: $i] :
( ( c_Set_Oinsert @ ( hAPP @ SV355 @ SV961 ) @ ( c_Set_Oimage @ SV355 @ SV1477 @ SV1849 @ SY5766 ) @ SY5766 )
= ( c_Set_Oimage @ SV355 @ SV1477 @ SV1849 @ SY5766 ) )
| ~ ( c_in @ SV961 @ SV1477 @ SV1849 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3932]) ).
thf(4481,plain,
! [SV1850: $i,SV1478: $i,SV962: $i,SV356: $i] :
( ( ( c_in @ ( hAPP @ SV356 @ SV962 ) @ SV1478 @ SV1850 )
| ! [SY5767: $i,SY5768: $i] :
( ~ ( c_in @ SV962 @ SY5767 @ SY5768 )
| ~ ( c_lessequals @ ( c_Set_Oimage @ SV356 @ SY5767 @ SY5768 @ SV1850 ) @ SV1478 @ ( tc_fun @ SV1850 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3933]) ).
thf(4482,plain,
! [SV1851: $i,SV1479: $i,SV963: $i,SV357: $i] :
( ( ! [SY5769: $i] :
( ( c_in @ ( c_Pair @ SV357 @ SV963 @ SV1479 @ SV1851 ) @ SY5769 @ ( tc_prod @ SV1479 @ SV1851 ) )
| ~ ( c_in @ SV963 @ ( c_Relation_OImage @ SY5769 @ ( c_Set_Oinsert @ SV357 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1479 @ tc_bool ) ) @ SV1479 ) @ SV1479 @ SV1851 ) @ SV1851 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3934]) ).
thf(4483,plain,
! [SV1852: $i,SV1480: $i,SV964: $i,SV358: $i] :
( ( ! [SY5770: $i] :
( ( c_in @ SV358 @ ( c_Relation_OImage @ SV964 @ ( c_Set_Oinsert @ SV1480 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1852 @ tc_bool ) ) @ SV1852 ) @ SV1852 @ SY5770 ) @ SY5770 )
| ~ ( c_in @ ( c_Pair @ SV1480 @ SV358 @ SV1852 @ SY5770 ) @ SV964 @ ( tc_prod @ SV1852 @ SY5770 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3935]) ).
thf(4484,plain,
! [SV1853: $i,SV1481: $i,SV965: $i,SV359: $i] :
( ( ! [SY5771: $i] :
( ( ( c_Product__Type_OSigma @ SV359 @ ( c_COMBK @ SV965 @ ( tc_fun @ SV1481 @ tc_bool ) @ SV1853 ) @ SV1853 @ SV1481 )
!= ( c_Product__Type_OSigma @ SY5771 @ ( c_COMBK @ SV965 @ ( tc_fun @ SV1481 @ tc_bool ) @ SV1853 ) @ SV1853 @ SV1481 ) )
| ! [SY5395: $i] :
~ ( c_in @ SY5395 @ SV965 @ SV1481 )
| ( SV359 = SY5771 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3936]) ).
thf(4485,plain,
! [SV360: $i,SV966: $i,SV1854: $i] :
( ( ( ! [SY5773: $i] :
~ ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ SV1854 @ SY5773 @ SV966 @ SV966 ) @ SV360 @ ( tc_prod @ SV966 @ SV966 ) ) @ SV966 ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV360 @ SV966 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3937]) ).
thf(4486,plain,
! [SV1855: $i,SV1482: $i,SV967: $i,SV361: $i] :
( ( ( c_in @ SV361 @ ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV967 @ SV1482 @ ( tc_fun @ ( tc_prod @ SV1855 @ SV1855 ) @ tc_bool ) ) @ SV1855 ) @ ( tc_prod @ SV1855 @ SV1855 ) )
| ~ ( c_in @ SV361 @ ( c_Transitive__Closure_Ortrancl @ SV967 @ SV1855 ) @ ( tc_prod @ SV1855 @ SV1855 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3938]) ).
thf(4487,plain,
! [SV1856: $i,SV1483: $i,SV968: $i,SV362: $i] :
( ( ( c_in @ SV362 @ ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV968 @ SV1483 @ ( tc_fun @ ( tc_prod @ SV1856 @ SV1856 ) @ tc_bool ) ) @ SV1856 ) @ ( tc_prod @ SV1856 @ SV1856 ) )
| ~ ( c_in @ SV362 @ ( c_Transitive__Closure_Ortrancl @ SV1483 @ SV1856 ) @ ( tc_prod @ SV1856 @ SV1856 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3939]) ).
thf(4488,plain,
! [SV1484: $i,SV969: $i,SV363: $i] :
( ( ( c_in @ SV363 @ ( c_Transitive__Closure_Otrancl @ SV969 @ SV1484 ) @ ( tc_prod @ SV1484 @ SV1484 ) )
= $true )
| ( ( ! [SY5398: $i] :
( ~ ( c_lessequals @ SY5398 @ SV969 @ ( tc_fun @ ( tc_prod @ SV1484 @ SV1484 ) @ tc_bool ) )
| ~ ( c_in @ SV363 @ ( c_Transitive__Closure_Otrancl @ SY5398 @ SV1484 ) @ ( tc_prod @ SV1484 @ SV1484 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3940]) ).
thf(4489,plain,
! [SV1857: $i,SV1485: $i,SV970: $i,SV364: $i] :
( ( ( ( c_Relation_OImage @ SV364 @ ( c_Set_Oinsert @ SV970 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1485 @ tc_bool ) ) @ SV1485 ) @ SV1485 @ SV1485 )
= ( c_Relation_OImage @ SV364 @ ( c_Set_Oinsert @ SV1857 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1485 @ tc_bool ) ) @ SV1485 ) @ SV1485 @ SV1485 ) )
| ~ ( c_in @ ( c_Pair @ SV970 @ SV1857 @ SV1485 @ SV1485 ) @ SV364 @ ( tc_prod @ SV1485 @ SV1485 ) )
| ! [SY5400: $i] :
~ ( c_Equiv__Relations_Oequiv @ SY5400 @ SV364 @ SV1485 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3941]) ).
thf(4490,plain,
! [SV1858: $i,SV1486: $i,SV971: $i,SV365: $i] :
( ( ( ( c_Relation_OImage @ SV365 @ ( c_Set_Oinsert @ SV971 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1486 @ tc_bool ) ) @ SV1486 ) @ SV1486 @ SV1486 )
= ( c_Relation_OImage @ SV365 @ ( c_Set_Oinsert @ SV1858 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1486 @ tc_bool ) ) @ SV1486 ) @ SV1486 @ SV1486 ) )
| ~ ( c_in @ ( c_Pair @ SV971 @ SV1858 @ SV1486 @ SV1486 ) @ SV365 @ ( tc_prod @ SV1486 @ SV1486 ) )
| ! [SY5402: $i] :
~ ( c_Equiv__Relations_Oequiv @ SY5402 @ SV365 @ SV1486 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3942]) ).
thf(4491,plain,
! [SV1487: $i,SV972: $i,SV366: $i] :
( ( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ SV366 @ SV366 @ SV972 @ SV972 @ SV972 ) @ ( c_Relation_Orel__comp @ SV1487 @ SV366 @ SV972 @ SV972 @ SV972 ) @ ( tc_fun @ ( tc_prod @ SV972 @ SV972 ) @ tc_bool ) ) @ SV1487 @ ( tc_fun @ ( tc_prod @ SV972 @ SV972 ) @ tc_bool ) ) @ SV972 )
= $true )
| ( ( ~ ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV366 @ SV1487 @ ( tc_fun @ ( tc_prod @ SV972 @ SV972 ) @ tc_bool ) ) @ SV972 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3943]) ).
thf(4492,plain,
! [SV1488: $i,SV973: $i,SV367: $i] :
( ( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV367 @ SV973 @ ( tc_fun @ ( tc_prod @ SV1488 @ SV1488 ) @ tc_bool ) ) @ SV1488 )
= $true )
| ( ( ~ ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ SV367 @ SV367 @ SV1488 @ SV1488 @ SV1488 ) @ ( c_Relation_Orel__comp @ SV973 @ SV367 @ SV1488 @ SV1488 @ SV1488 ) @ ( tc_fun @ ( tc_prod @ SV1488 @ SV1488 ) @ tc_bool ) ) @ SV973 @ ( tc_fun @ ( tc_prod @ SV1488 @ SV1488 ) @ tc_bool ) ) @ SV1488 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3944]) ).
thf(4493,plain,
! [SV974: $i,SV368: $i] :
( ( ( ( c_Relation_Orel__comp @ SV368 @ SV368 @ SV974 @ SV974 @ SV974 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV974 @ SV974 ) @ tc_bool ) ) )
= $false )
| ( ( c_Wellfounded_Owf @ SV368 @ SV974 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3945]) ).
thf(4494,plain,
! [SV979: $i,SV374: $i] :
( ( ( c_Wellfounded_Oacyclic @ SV374 @ SV979 )
= $false )
| ( ( c_Relation_Oantisym @ ( c_Transitive__Closure_Ortrancl @ SV374 @ SV979 ) @ SV979 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3946]) ).
thf(4495,plain,
! [SV980: $i,SV375: $i] :
( ( ( c_Relation_Otrans @ SV375 @ SV980 )
= $false )
| ( ( c_lessequals @ ( c_Relation_Orel__comp @ SV375 @ SV375 @ SV980 @ SV980 @ SV980 ) @ SV375 @ ( tc_fun @ ( tc_prod @ SV980 @ SV980 ) @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3947]) ).
thf(4496,plain,
! [SV983: $i,SV378: $i] :
( ( ( c_Relation_Otrans @ SV378 @ SV983 )
= $false )
| ( ( c_Relation_Otrans @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV378 @ ( c_Relation_OId @ SV983 ) @ ( tc_fun @ ( tc_prod @ SV983 @ SV983 ) @ tc_bool ) ) @ SV983 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3948]) ).
thf(4497,plain,
! [SV985: $i,SV380: $i] :
( ( ( c_Relation_Oantisym @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV380 @ ( c_Relation_OId @ SV985 ) @ ( tc_fun @ ( tc_prod @ SV985 @ SV985 ) @ tc_bool ) ) @ SV985 )
= $false )
| ( ( c_Relation_Oantisym @ SV380 @ SV985 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3950]) ).
thf(4498,plain,
! [SV986: $i,SV381: $i] :
( ( ( c_Relation_Oantisym @ SV381 @ SV986 )
= $false )
| ( ( c_Relation_Oantisym @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV381 @ ( c_Relation_OId @ SV986 ) @ ( tc_fun @ ( tc_prod @ SV986 @ SV986 ) @ tc_bool ) ) @ SV986 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3951]) ).
thf(4499,plain,
! [SV1490: $i,SV987: $i,SV382: $i] :
( ( ( c_Relation_Ototal__on @ SV382 @ SV987 @ SV1490 )
= $true )
| ( ( ~ ( c_Relation_Ototal__on @ SV382 @ ( c_HOL_Ominus__class_Ominus @ SV987 @ ( c_Relation_OId @ SV1490 ) @ ( tc_fun @ ( tc_prod @ SV1490 @ SV1490 ) @ tc_bool ) ) @ SV1490 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3952]) ).
thf(4500,plain,
! [SV1491: $i,SV988: $i,SV383: $i] :
( ( ( c_Relation_Ototal__on @ SV383 @ ( c_HOL_Ominus__class_Ominus @ SV988 @ ( c_Relation_OId @ SV1491 ) @ ( tc_fun @ ( tc_prod @ SV1491 @ SV1491 ) @ tc_bool ) ) @ SV1491 )
= $true )
| ( ( ~ ( c_Relation_Ototal__on @ SV383 @ SV988 @ SV1491 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3953]) ).
thf(4501,plain,
! [SV989: $i,SV384: $i] :
( ( ( ~ ( c_Relation_Otrans @ SV384 @ SV989 ) )
= $true )
| ( ( ~ ( c_Relation_Osym @ SV384 @ SV989 ) )
= $true )
| ( ( c_lessequals @ ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ SV384 @ SV989 @ SV989 ) @ SV384 @ SV989 @ SV989 @ SV989 ) @ SV384 @ ( tc_fun @ ( tc_prod @ SV989 @ SV989 ) @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3954]) ).
thf(4502,plain,
! [SV1859: $i,SV1492: $i,SV990: $i,SV385: $i] :
( ( ( c_in @ ( c_Pair @ SV385 @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1 @ SV990 @ SV385 @ SV1492 @ SV1859 ) @ SV1859 @ SV1859 ) @ ( c_Transitive__Closure_Ortrancl @ SV990 @ SV1859 ) @ ( tc_prod @ SV1859 @ SV1859 ) )
| ~ ( c_in @ ( c_Pair @ SV385 @ SV1492 @ SV1859 @ SV1859 ) @ ( c_Transitive__Closure_Otrancl @ SV990 @ SV1859 ) @ ( tc_prod @ SV1859 @ SV1859 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3955]) ).
thf(4503,plain,
! [SV1860: $i,SV1493: $i,SV991: $i,SV386: $i] :
( ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1 @ SV386 @ SV991 @ SV1493 @ SV1860 ) @ SV1493 @ SV1860 @ SV1860 ) @ ( c_Transitive__Closure_Ortrancl @ SV386 @ SV1860 ) @ ( tc_prod @ SV1860 @ SV1860 ) )
| ~ ( c_in @ ( c_Pair @ SV991 @ SV1493 @ SV1860 @ SV1860 ) @ ( c_Transitive__Closure_Otrancl @ SV386 @ SV1860 ) @ ( tc_prod @ SV1860 @ SV1860 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3956]) ).
thf(4504,plain,
! [SV1861: $i,SV1494: $i,SV992: $i,SV387: $i] :
( ( ~ ( c_in @ ( c_Pair @ SV387 @ SV992 @ SV1494 @ SV1494 ) @ ( c_Transitive__Closure_Ortrancl @ SV1861 @ SV1494 ) @ ( tc_prod @ SV1494 @ SV1494 ) )
| ~ ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ SV992 @ SV387 @ SV1494 @ SV1494 ) @ SV1861 @ ( tc_prod @ SV1494 @ SV1494 ) ) @ SV1494 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3957]) ).
thf(4505,plain,
! [SV1862: $i,SV1495: $i,SV993: $i,SV388: $i] :
( ( ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ SV388 @ SV993 @ SV1495 @ SV1495 ) @ SV1862 @ ( tc_prod @ SV1495 @ SV1495 ) ) @ SV1495 )
| ( c_in @ ( c_Pair @ SV993 @ SV388 @ SV1495 @ SV1495 ) @ ( c_Transitive__Closure_Ortrancl @ SV1862 @ SV1495 ) @ ( tc_prod @ SV1495 @ SV1495 ) )
| ~ ( c_Wellfounded_Owf @ SV1862 @ SV1495 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3958]) ).
thf(4506,plain,
! [SV1496: $i,SV994: $i,SV389: $i] :
( ( ( c_Order__Relation_Ostrict__linear__order__on @ SV389 @ SV994 @ SV1496 )
= $true )
| ( ( ~ ( c_Relation_Ototal__on @ SV389 @ SV994 @ SV1496 )
| ~ ( c_Relation_Oirrefl @ SV994 @ SV1496 )
| ~ ( c_Relation_Otrans @ SV994 @ SV1496 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3959]) ).
thf(4507,plain,
! [SV995: $i,SV390: $i] :
( ( ( c_in @ ( c_Pair @ ( c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1 @ SV390 @ SV995 ) @ ( c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1 @ SV390 @ SV995 ) @ SV995 @ SV995 ) @ SV390 @ ( tc_prod @ SV995 @ SV995 ) )
= $false )
| ( ( c_Nitpick_Orefl_H @ SV390 @ SV995 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3960]) ).
thf(4508,plain,
! [SV996: $i,SV391: $i] :
( ( ( ~ ( c_Relation_Oantisym @ SV391 @ SV996 ) )
= $true )
| ( ( ~ ( c_Relation_Otrans @ SV391 @ SV996 ) )
= $true )
| ( ( c_Relation_Otrans @ ( c_HOL_Ominus__class_Ominus @ SV391 @ ( c_Relation_OId @ SV996 ) @ ( tc_fun @ ( tc_prod @ SV996 @ SV996 ) @ tc_bool ) ) @ SV996 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3961]) ).
thf(4509,plain,
! [SV1863: $i,SV1497: $i,SV997: $i,SV392: $i] :
( ( ! [SY5776: $i] :
( ( ( c_Relation_OImage @ SV392 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV997 @ SV1497 @ ( tc_fun @ SV1863 @ tc_bool ) ) @ SV1863 @ SY5776 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_OImage @ SV392 @ SV997 @ SV1863 @ SY5776 ) @ ( c_Relation_OImage @ SV392 @ SV1497 @ SV1863 @ SY5776 ) @ ( tc_fun @ SY5776 @ tc_bool ) ) )
| ~ ( c_Relation_Osingle__valued @ ( c_Relation_Oconverse @ SV392 @ SV1863 @ SY5776 ) @ SY5776 @ SV1863 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3962]) ).
thf(4510,plain,
! [SV999: $i,SV394: $i,SV1864: $i] :
( ( ( ~ ( c_Relation_Orefl__on @ SV1864 @ SV394 @ SV999 ) )
= $true )
| ( ( c_lessequals @ SV394 @ ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ SV394 @ SV999 @ SV999 ) @ SV394 @ SV999 @ SV999 @ SV999 ) @ ( tc_fun @ ( tc_prod @ SV999 @ SV999 ) @ tc_bool ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3964]) ).
thf(4511,plain,
! [SV1865: $i,SV1498: $i,SV1004: $i,SV399: $i] :
( ( ! [SY5777: $i,SY5778: $i] :
( ( ( c_Recdef_Ocut @ SV399 @ SV1004 @ SV1498 @ SV1865 @ SY5777 )
= ( c_Recdef_Ocut @ SY5778 @ SV1004 @ SV1498 @ SV1865 @ SY5777 ) )
| ( c_in @ ( c_Pair @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ SV399 @ SY5778 @ SV1004 @ SV1498 @ SV1865 @ SY5777 ) @ SV1498 @ SV1865 @ SV1865 ) @ SV1004 @ ( tc_prod @ SV1865 @ SV1865 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3965]) ).
thf(4512,plain,
! [SV1499: $i,SV1005: $i,SV400: $i] :
( ( ( SV400
= ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XId__onE__1__1 @ SV1005 @ SV400 @ SV1499 ) @ ( c_ATP__Linkup_Osko__Relation__XId__onE__1__1 @ SV1005 @ SV400 @ SV1499 ) @ SV1499 @ SV1499 ) )
= $true )
| ( ( ~ ( c_in @ SV400 @ ( c_Relation_OId__on @ SV1005 @ SV1499 ) @ ( tc_prod @ SV1499 @ SV1499 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3966]) ).
thf(4513,plain,
! [SV1500: $i,SV1006: $i,SV401: $i] :
( ( ( c_in @ ( c_ATP__Linkup_Osko__Relation__XId__onE__1__1 @ SV401 @ SV1006 @ SV1500 ) @ SV401 @ SV1500 )
= $true )
| ( ( ~ ( c_in @ SV1006 @ ( c_Relation_OId__on @ SV401 @ SV1500 ) @ ( tc_prod @ SV1500 @ SV1500 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3967]) ).
thf(4514,plain,
! [SV1007: $i,SV402: $i] :
( ( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1 @ SV402 @ SV1007 ) @ ( c_Wellfounded_Oacc @ SV402 @ SV1007 ) @ SV1007 )
= $false )
| ( ( c_Wellfounded_Owf @ SV402 @ SV1007 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3968]) ).
thf(4515,plain,
! [SV1008: $i,SV403: $i] :
( ( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1 @ SV403 @ SV1008 ) @ ( c_Wellfounded_Oacc @ SV403 @ SV1008 ) @ SV1008 )
= $false )
| ( ( c_Wellfounded_Owf @ SV403 @ SV1008 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3969]) ).
thf(4516,plain,
! [SV1009: $i,SV404: $i] :
( ( ( c_in @ SV404 @ ( c_Relation_OId @ SV1009 ) @ ( tc_prod @ SV1009 @ SV1009 ) )
= $false )
| ( ( SV404
= ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XIdE__1__1 @ SV404 @ SV1009 ) @ ( c_ATP__Linkup_Osko__Relation__XIdE__1__1 @ SV404 @ SV1009 ) @ SV1009 @ SV1009 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3970]) ).
thf(4517,plain,
! [SV1866: $i,SV1501: $i,SV1010: $i,SV405: $i] :
( ( ! [SY5779: $i,SY5780: $i,SY5781: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 @ SV405 @ SV1010 @ SV1501 @ SV1866 @ SY5779 @ SY5780 @ SY5781 ) @ SV1010 @ SY5781 @ SY5780 ) @ SV1866 @ ( tc_prod @ SY5781 @ SY5780 ) )
| ~ ( c_in @ ( c_Pair @ SV405 @ SV1010 @ SY5779 @ SY5780 ) @ ( c_Relation_Orel__comp @ SV1501 @ SV1866 @ SY5779 @ SY5781 @ SY5780 ) @ ( tc_prod @ SY5779 @ SY5780 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3971]) ).
thf(4518,plain,
! [SV1867: $i,SV1502: $i,SV1011: $i,SV406: $i] :
( ( ! [SY5782: $i,SY5783: $i,SY5784: $i] :
( ( c_in @ ( c_Pair @ SV406 @ ( c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 @ SV406 @ SV1011 @ SV1502 @ SV1867 @ SY5782 @ SY5783 @ SY5784 ) @ SY5782 @ SY5784 ) @ SV1502 @ ( tc_prod @ SY5782 @ SY5784 ) )
| ~ ( c_in @ ( c_Pair @ SV406 @ SV1011 @ SY5782 @ SY5783 ) @ ( c_Relation_Orel__comp @ SV1502 @ SV1867 @ SY5782 @ SY5784 @ SY5783 ) @ ( tc_prod @ SY5782 @ SY5783 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3972]) ).
thf(4519,plain,
! [SV1503: $i,SV1012: $i,SV407: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV407 @ SV407 @ SV1012 @ SV1012 ) @ SV1503 @ ( tc_prod @ SV1012 @ SV1012 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1 @ SV1503 @ SV1012 ) @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1 @ SV1503 @ SV1012 ) @ SV1012 @ SV1012 ) @ ( c_Transitive__Closure_Otrancl @ SV1503 @ SV1012 ) @ ( tc_prod @ SV1012 @ SV1012 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3973]) ).
thf(4520,plain,
! [SV1868: $i,SV1504: $i,SV1013: $i,SV408: $i] :
( ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1 @ SV408 @ SV1013 @ SV1504 @ SV1868 ) @ SV1504 @ SV1868 @ SV1868 ) @ ( c_Transitive__Closure_Otrancl @ SV408 @ SV1868 ) @ ( tc_prod @ SV1868 @ SV1868 ) )
| ( c_in @ ( c_Pair @ SV1013 @ SV1504 @ SV1868 @ SV1868 ) @ SV408 @ ( tc_prod @ SV1868 @ SV1868 ) )
| ~ ( c_in @ ( c_Pair @ SV1013 @ SV1504 @ SV1868 @ SV1868 ) @ ( c_Transitive__Closure_Otrancl @ SV408 @ SV1868 ) @ ( tc_prod @ SV1868 @ SV1868 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3974]) ).
thf(4521,plain,
! [SV1869: $i,SV1505: $i,SV1014: $i,SV409: $i] :
( ( ( c_in @ ( c_Pair @ SV409 @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1 @ SV1014 @ SV409 @ SV1505 @ SV1869 ) @ SV1869 @ SV1869 ) @ SV1014 @ ( tc_prod @ SV1869 @ SV1869 ) )
| ~ ( c_in @ ( c_Pair @ SV409 @ SV1505 @ SV1869 @ SV1869 ) @ ( c_Transitive__Closure_Otrancl @ SV1014 @ SV1869 ) @ ( tc_prod @ SV1869 @ SV1869 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3975]) ).
thf(4522,plain,
! [SV1506: $i,SV1015: $i,SV410: $i] :
( ( ( c_in @ ( c_Pair @ SV410 @ ( v_sko__Transitive__Closure__Xtrancl__Xcases__1 @ SV410 @ SV1015 @ SV1506 ) @ t_a @ t_a ) @ ( c_Transitive__Closure_Otrancl @ SV1506 @ t_a ) @ ( tc_prod @ t_a @ t_a ) )
= $true )
| ( ( ( c_in @ ( c_Pair @ SV410 @ SV1015 @ t_a @ t_a ) @ SV1506 @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ ( c_Pair @ SV410 @ SV1015 @ t_a @ t_a ) @ ( c_Transitive__Closure_Otrancl @ SV1506 @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3976]) ).
thf(4523,plain,
! [SV1507: $i,SV1016: $i,SV411: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV411 @ SV411 @ SV1016 @ SV1016 ) @ ( c_Transitive__Closure_Otrancl @ SV1507 @ SV1016 ) @ ( tc_prod @ SV1016 @ SV1016 ) ) )
= $true )
| ( ( ~ ( c_Wellfounded_Oacyclic @ SV1507 @ SV1016 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3977]) ).
thf(4524,plain,
! [SV1870: $i,SV1508: $i,SV1017: $i,SV412: $i] :
( ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1 @ SV412 @ SV1017 @ SV1508 @ SV1870 ) @ SV1017 @ SV1870 @ SV1870 ) @ SV1508 @ ( tc_prod @ SV1870 @ SV1870 ) )
| ( c_in @ ( c_Pair @ SV412 @ SV1017 @ SV1870 @ SV1870 ) @ SV1508 @ ( tc_prod @ SV1870 @ SV1870 ) )
| ~ ( c_in @ ( c_Pair @ SV412 @ SV1017 @ SV1870 @ SV1870 ) @ ( c_Transitive__Closure_Otrancl @ SV1508 @ SV1870 ) @ ( tc_prod @ SV1870 @ SV1870 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3978]) ).
thf(4525,plain,
! [SV1871: $i,SV1509: $i,SV1018: $i,SV413: $i] :
( ( ( c_in @ ( c_Pair @ SV413 @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1 @ SV413 @ SV1018 @ SV1509 @ SV1871 ) @ SV1871 @ SV1871 ) @ ( c_Transitive__Closure_Otrancl @ SV1509 @ SV1871 ) @ ( tc_prod @ SV1871 @ SV1871 ) )
| ( c_in @ ( c_Pair @ SV413 @ SV1018 @ SV1871 @ SV1871 ) @ SV1509 @ ( tc_prod @ SV1871 @ SV1871 ) )
| ~ ( c_in @ ( c_Pair @ SV413 @ SV1018 @ SV1871 @ SV1871 ) @ ( c_Transitive__Closure_Otrancl @ SV1509 @ SV1871 ) @ ( tc_prod @ SV1871 @ SV1871 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3979]) ).
thf(4526,plain,
! [SV1872: $i,SV1510: $i,SV1019: $i,SV414: $i] :
( ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1 @ SV414 @ SV1019 @ SV1510 @ SV1872 ) @ SV1510 @ SV1872 @ SV1872 ) @ SV414 @ ( tc_prod @ SV1872 @ SV1872 ) )
| ~ ( c_in @ ( c_Pair @ SV1019 @ SV1510 @ SV1872 @ SV1872 ) @ ( c_Transitive__Closure_Otrancl @ SV414 @ SV1872 ) @ ( tc_prod @ SV1872 @ SV1872 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3980]) ).
thf(4527,plain,
! [SV1873: $i,SV1511: $i,SV1020: $i,SV415: $i] :
( ( ( c_in @ ( c_Pair @ SV415 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1 @ SV1020 @ SV415 @ SV1511 @ SV1873 ) @ SV1873 @ SV1873 ) @ SV1020 @ ( tc_prod @ SV1873 @ SV1873 ) )
| ( c_in @ ( c_Pair @ SV415 @ SV1511 @ SV1873 @ SV1873 ) @ SV1020 @ ( tc_prod @ SV1873 @ SV1873 ) )
| ~ ( c_in @ ( c_Pair @ SV415 @ SV1511 @ SV1873 @ SV1873 ) @ ( c_Transitive__Closure_Otrancl @ SV1020 @ SV1873 ) @ ( tc_prod @ SV1873 @ SV1873 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3981]) ).
thf(4528,plain,
! [SV1512: $i,SV1021: $i,SV416: $i] :
( ( ( c_in @ ( c_Pair @ ( v_sko__Transitive__Closure__Xtrancl__Xcases__1 @ SV416 @ SV1021 @ SV1512 ) @ SV1021 @ t_a @ t_a ) @ SV1512 @ ( tc_prod @ t_a @ t_a ) )
= $true )
| ( ( ( c_in @ ( c_Pair @ SV416 @ SV1021 @ t_a @ t_a ) @ SV1512 @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ ( c_Pair @ SV416 @ SV1021 @ t_a @ t_a ) @ ( c_Transitive__Closure_Otrancl @ SV1512 @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3982]) ).
thf(4529,plain,
! [SV1513: $i,SV1022: $i,SV417: $i] :
( ( ( hBOOL @ ( hAPP @ SV417 @ SV1022 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ SV417 @ SV1513 ) )
| ! [SY5426: $i,SY5427: $i] :
( ~ ( c_in @ ( c_Pair @ SV1513 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1 @ SV417 @ SY5426 @ SY5427 ) @ SY5427 @ SY5427 ) @ SY5426 @ ( tc_prod @ SY5427 @ SY5427 ) )
| ~ ( c_Wellfounded_Owf @ SY5426 @ SY5427 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3983]) ).
thf(4530,plain,
! [SV1514: $i,SV1023: $i,SV418: $i] :
( ( ( hBOOL @ ( hAPP @ SV418 @ SV1023 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ SV418 @ SV1514 ) )
| ! [SY5428: $i,SY5429: $i] :
( ~ ( c_in @ ( c_Pair @ SV1514 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1 @ SV418 @ SY5428 @ SY5429 ) @ SY5429 @ SY5429 ) @ SY5428 @ ( tc_prod @ SY5429 @ SY5429 ) )
| ~ ( c_Wellfounded_Owf @ SY5428 @ SY5429 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3984]) ).
thf(4531,plain,
! [SV1515: $i,SV1024: $i,SV419: $i] :
( ( ( hBOOL @ ( hAPP @ SV419 @ SV1024 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ SV419 @ SV1515 ) )
| ! [SY5430: $i,SY5431: $i] :
( ~ ( c_in @ ( c_Pair @ SV1515 @ ( c_List_Osko__Recdef__Xtfl__wf__induct__1__1 @ SV419 @ SY5430 @ SY5431 ) @ SY5431 @ SY5431 ) @ SY5430 @ ( tc_prod @ SY5431 @ SY5431 ) )
| ~ ( c_Wellfounded_Owf @ SY5430 @ SY5431 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3985]) ).
thf(4532,plain,
! [SV1516: $i,SV1025: $i,SV420: $i] :
( ( ( hBOOL @ ( hAPP @ SV420 @ SV1025 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ SV420 @ SV1516 ) )
| ! [SY5432: $i,SY5433: $i] :
( ~ ( c_in @ ( c_Pair @ SV1516 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1 @ SV420 @ SY5432 @ SY5433 ) @ SY5433 @ SY5433 ) @ SY5432 @ ( tc_prod @ SY5433 @ SY5433 ) )
| ~ ( c_Wellfounded_Owf @ SY5432 @ SY5433 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3986]) ).
thf(4533,plain,
! [SV1874: $i,SV1517: $i,SV1026: $i,SV421: $i] :
( ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1 @ SV421 @ SV1026 @ SV1517 @ SV1874 ) @ SV1026 @ SV1874 @ SV1874 ) @ SV1517 @ ( tc_prod @ SV1874 @ SV1874 ) )
| ( SV421 = SV1026 )
| ~ ( c_in @ ( c_Pair @ SV421 @ SV1026 @ SV1874 @ SV1874 ) @ ( c_Transitive__Closure_Ortrancl @ SV1517 @ SV1874 ) @ ( tc_prod @ SV1874 @ SV1874 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3987]) ).
thf(4534,plain,
! [SV1875: $i,SV1518: $i,SV1027: $i,SV422: $i] :
( ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1 @ SV422 @ SV1027 @ SV1518 @ SV1875 ) @ SV1518 @ SV1875 @ SV1875 ) @ ( c_Transitive__Closure_Ortrancl @ SV422 @ SV1875 ) @ ( tc_prod @ SV1875 @ SV1875 ) )
| ( SV1027 = SV1518 )
| ~ ( c_in @ ( c_Pair @ SV1027 @ SV1518 @ SV1875 @ SV1875 ) @ ( c_Transitive__Closure_Ortrancl @ SV422 @ SV1875 ) @ ( tc_prod @ SV1875 @ SV1875 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3988]) ).
thf(4535,plain,
! [SV1876: $i,SV1519: $i,SV1028: $i,SV423: $i] :
( ( ( c_in @ ( c_Pair @ SV423 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1 @ SV1028 @ SV423 @ SV1519 @ SV1876 ) @ SV1876 @ SV1876 ) @ SV1028 @ ( tc_prod @ SV1876 @ SV1876 ) )
| ( SV423 = SV1519 )
| ~ ( c_in @ ( c_Pair @ SV423 @ SV1519 @ SV1876 @ SV1876 ) @ ( c_Transitive__Closure_Ortrancl @ SV1028 @ SV1876 ) @ ( tc_prod @ SV1876 @ SV1876 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3989]) ).
thf(4536,plain,
! [SV1520: $i,SV1029: $i,SV424: $i] :
( ( ( hBOOL @ ( hAPP @ SV424 @ SV1029 ) )
= $true )
| ( ( ! [SY5437: $i,SY5438: $i] :
( ( hBOOL @ ( hAPP @ SV424 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 @ SV424 @ SV1520 @ SY5437 @ SY5438 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV424 @ SV1520 ) )
| ~ ( c_in @ ( c_Pair @ SV1029 @ SV1520 @ SY5438 @ SY5438 ) @ ( c_Transitive__Closure_Ortrancl @ SY5437 @ SY5438 ) @ ( tc_prod @ SY5438 @ SY5438 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3990]) ).
thf(4537,plain,
! [SV1521: $i,SV1030: $i,SV425: $i] :
( ( ( hBOOL @ ( hAPP @ SV425 @ SV1030 ) )
= $true )
| ( ( ! [SY5439: $i,SY5440: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 @ SV425 @ SV1521 @ SY5439 @ SY5440 ) @ SV1521 @ SY5440 @ SY5440 ) @ ( c_Transitive__Closure_Ortrancl @ SY5439 @ SY5440 ) @ ( tc_prod @ SY5440 @ SY5440 ) )
| ~ ( hBOOL @ ( hAPP @ SV425 @ SV1521 ) )
| ~ ( c_in @ ( c_Pair @ SV1030 @ SV1521 @ SY5440 @ SY5440 ) @ ( c_Transitive__Closure_Ortrancl @ SY5439 @ SY5440 ) @ ( tc_prod @ SY5440 @ SY5440 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3991]) ).
thf(4538,plain,
! [SV1522: $i,SV1031: $i,SV426: $i] :
( ( ( hBOOL @ ( hAPP @ SV426 @ SV1031 ) )
= $true )
| ( ( ! [SY5441: $i,SY5442: $i] :
( ( c_in @ ( c_Pair @ SV1522 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 @ SV426 @ SV1522 @ SY5441 @ SY5442 ) @ SY5442 @ SY5442 ) @ ( c_Transitive__Closure_Ortrancl @ SY5441 @ SY5442 ) @ ( tc_prod @ SY5442 @ SY5442 ) )
| ~ ( hBOOL @ ( hAPP @ SV426 @ SV1522 ) )
| ~ ( c_in @ ( c_Pair @ SV1522 @ SV1031 @ SY5442 @ SY5442 ) @ ( c_Transitive__Closure_Ortrancl @ SY5441 @ SY5442 ) @ ( tc_prod @ SY5442 @ SY5442 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3992]) ).
thf(4539,plain,
! [SV1523: $i,SV1032: $i,SV427: $i] :
( ( ( hBOOL @ ( hAPP @ SV427 @ SV1032 ) )
= $true )
| ( ( ! [SY5443: $i,SY5444: $i] :
( ~ ( hBOOL @ ( hAPP @ SV427 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2 @ SV427 @ SV1523 @ SY5443 @ SY5444 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV427 @ SV1523 ) )
| ~ ( c_in @ ( c_Pair @ SV1523 @ SV1032 @ SY5444 @ SY5444 ) @ ( c_Transitive__Closure_Ortrancl @ SY5443 @ SY5444 ) @ ( tc_prod @ SY5444 @ SY5444 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3993]) ).
thf(4540,plain,
! [SV1524: $i,SV1033: $i,SV428: $i] :
( ( ( c_in @ ( c_Pair @ SV428 @ ( v_sko__Transitive__Closure__Xrtrancl__Xcases__1 @ SV428 @ SV1033 @ SV1524 ) @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ SV1524 @ t_a ) @ ( tc_prod @ t_a @ t_a ) )
= $true )
| ( ( ( SV1033 = SV428 )
| ~ ( c_in @ ( c_Pair @ SV428 @ SV1033 @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ SV1524 @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3994]) ).
thf(4541,plain,
! [SV1525: $i,SV1034: $i,SV429: $i] :
( ( ( hBOOL @ ( hAPP @ SV429 @ SV1034 ) )
= $true )
| ( ( ! [SY5445: $i,SY5446: $i] :
( ( hBOOL @ ( hAPP @ SV429 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 @ SV429 @ SV1525 @ SY5445 @ SY5446 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV429 @ SV1525 ) )
| ~ ( c_in @ ( c_Pair @ SV1525 @ SV1034 @ SY5446 @ SY5446 ) @ ( c_Transitive__Closure_Ortrancl @ SY5445 @ SY5446 ) @ ( tc_prod @ SY5446 @ SY5446 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3995]) ).
thf(4542,plain,
! [SV1526: $i,SV1035: $i,SV430: $i] :
( ( ( c_in @ ( c_Pair @ ( v_sko__Transitive__Closure__Xrtrancl__Xcases__1 @ SV430 @ SV1035 @ SV1526 ) @ SV1035 @ t_a @ t_a ) @ SV1526 @ ( tc_prod @ t_a @ t_a ) )
= $true )
| ( ( ( SV1035 = SV430 )
| ~ ( c_in @ ( c_Pair @ SV430 @ SV1035 @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ SV1526 @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3996]) ).
thf(4543,plain,
! [SV1527: $i,SV1036: $i,SV431: $i] :
( ( ( hBOOL @ ( hAPP @ SV431 @ SV1036 ) )
= $true )
| ( ( ! [SY5447: $i,SY5448: $i] :
( ~ ( hBOOL @ ( hAPP @ SV431 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1 @ SV431 @ SV1527 @ SY5447 @ SY5448 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV431 @ SV1527 ) )
| ~ ( c_in @ ( c_Pair @ SV1036 @ SV1527 @ SY5448 @ SY5448 ) @ ( c_Transitive__Closure_Ortrancl @ SY5447 @ SY5448 ) @ ( tc_prod @ SY5448 @ SY5448 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3997]) ).
thf(4544,plain,
! [SV1877: $i,SV1528: $i,SV1037: $i,SV432: $i] :
( ( ( c_in @ ( c_Pair @ SV432 @ ( c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1 @ SV432 @ SV1037 @ SV1528 @ SV1877 ) @ SV1877 @ SV1877 ) @ ( c_Transitive__Closure_Ortrancl @ SV1528 @ SV1877 ) @ ( tc_prod @ SV1877 @ SV1877 ) )
| ( SV432 = SV1037 )
| ~ ( c_in @ ( c_Pair @ SV432 @ SV1037 @ SV1877 @ SV1877 ) @ ( c_Transitive__Closure_Ortrancl @ SV1528 @ SV1877 ) @ ( tc_prod @ SV1877 @ SV1877 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3998]) ).
thf(4545,plain,
! [SV1878: $i,SV1529: $i,SV1038: $i,SV433: $i] :
( ( ! [SY5785: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Product__Type__XSigmaE__1__1 @ SV433 @ SV1038 @ SV1529 @ SV1878 @ SY5785 ) @ SV433 @ SV1878 )
| ~ ( c_in @ SV1529 @ ( c_Product__Type_OSigma @ SV433 @ SV1038 @ SV1878 @ SY5785 ) @ ( tc_prod @ SV1878 @ SY5785 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3999]) ).
thf(4546,plain,
! [SV1039: $i,SV434: $i] :
( ( ( c_Wellfounded_Owf @ SV434 @ SV1039 )
= $false )
| ( ( c_Wellfounded_OwfP @ ( c_FunDef_Oin__rel @ SV434 @ SV1039 @ SV1039 ) @ SV1039 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4000]) ).
thf(4547,plain,
! [SV1041: $i,SV436: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_Oconverse @ SV436 @ SV1041 @ SV1041 ) @ ( c_Transitive__Closure_Ortrancl @ SV436 @ SV1041 ) @ ( tc_fun @ ( tc_prod @ SV1041 @ SV1041 ) @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV1041 @ SV1041 ) @ tc_bool ) ) )
= $false )
| ( ( ! [SY4779: $i] :
~ ( c_in @ ( c_Pair @ SY4779 @ SY4779 @ SV1041 @ SV1041 ) @ ( c_Transitive__Closure_Otrancl @ SV436 @ SV1041 ) @ ( tc_prod @ SV1041 @ SV1041 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4001]) ).
thf(4548,plain,
! [SV1879: $i,SV1530: $i,SV1042: $i,SV437: $i] :
( ( ( ( c_Relation_OImage @ SV437 @ ( c_Set_Oinsert @ SV1042 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1530 @ tc_bool ) ) @ SV1530 ) @ SV1530 @ SV1530 )
!= ( c_Relation_OImage @ SV437 @ ( c_Set_Oinsert @ SV1879 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1530 @ tc_bool ) ) @ SV1530 ) @ SV1530 @ SV1530 ) )
| ( c_in @ ( c_Pair @ SV1042 @ SV1879 @ SV1530 @ SV1530 ) @ SV437 @ ( tc_prod @ SV1530 @ SV1530 ) )
| ! [SY5786: $i] :
( ~ ( c_in @ SV1879 @ SY5786 @ SV1530 )
| ~ ( c_Equiv__Relations_Oequiv @ SY5786 @ SV437 @ SV1530 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4002]) ).
thf(4549,plain,
! [SV1880: $i,SV1531: $i,SV1043: $i,SV438: $i] :
( ( ( ( c_Relation_OImage @ SV438 @ ( c_Set_Oinsert @ SV1043 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1531 @ tc_bool ) ) @ SV1531 ) @ SV1531 @ SV1531 )
!= ( c_Relation_OImage @ SV438 @ ( c_Set_Oinsert @ SV1880 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1531 @ tc_bool ) ) @ SV1531 ) @ SV1531 @ SV1531 ) )
| ! [SY5787: $i] :
( ~ ( c_Equiv__Relations_Oequiv @ SY5787 @ SV438 @ SV1531 )
| ( c_in @ ( c_Pair @ SV1043 @ SV1880 @ SV1531 @ SV1531 ) @ SV438 @ ( tc_prod @ SV1531 @ SV1531 ) )
| ~ ( c_in @ SV1880 @ SY5787 @ SV1531 )
| ~ ( c_in @ SV1043 @ SY5787 @ SV1531 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4003]) ).
thf(4550,plain,
! [SV1881: $i,SV1532: $i,SV1044: $i,SV439: $i] :
( ( ( ( c_Relation_OImage @ SV439 @ ( c_Set_Oinsert @ SV1044 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1532 @ tc_bool ) ) @ SV1532 ) @ SV1532 @ SV1532 )
= ( c_Relation_OImage @ SV439 @ ( c_Set_Oinsert @ SV1881 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1532 @ tc_bool ) ) @ SV1532 ) @ SV1532 @ SV1532 ) )
| ~ ( c_in @ ( c_Pair @ SV1044 @ SV1881 @ SV1532 @ SV1532 ) @ SV439 @ ( tc_prod @ SV1532 @ SV1532 ) )
| ! [SY5788: $i] :
( ~ ( c_in @ SV1881 @ SY5788 @ SV1532 )
| ~ ( c_in @ SV1044 @ SY5788 @ SV1532 )
| ~ ( c_Equiv__Relations_Oequiv @ SY5788 @ SV439 @ SV1532 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4004]) ).
thf(4551,plain,
! [SV1882: $i,SV1533: $i,SV1045: $i,SV440: $i] :
( ( ( ( c_Relation_OImage @ SV440 @ ( c_Set_Oinsert @ SV1045 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1533 @ tc_bool ) ) @ SV1533 ) @ SV1533 @ SV1533 )
!= ( c_Relation_OImage @ SV440 @ ( c_Set_Oinsert @ SV1882 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1533 @ tc_bool ) ) @ SV1533 ) @ SV1533 @ SV1533 ) )
| ! [SY5789: $i] :
( ~ ( c_in @ SV1882 @ SY5789 @ SV1533 )
| ~ ( c_in @ SV1045 @ SY5789 @ SV1533 )
| ~ ( c_Equiv__Relations_Oequiv @ SY5789 @ SV440 @ SV1533 )
| ( c_in @ ( c_Pair @ SV1045 @ SV1882 @ SV1533 @ SV1533 ) @ SV440 @ ( tc_prod @ SV1533 @ SV1533 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4005]) ).
thf(4552,plain,
! [SV1535: $i,SV1047: $i,SV442: $i] :
( ( ( c_in @ SV442 @ SV1047 @ SV1535 )
= $true )
| ( ( ! [SY5460: $i] :
( ( SV442 = SY5460 )
| ! [SY5461: $i] :
( ~ ( c_lessequals @ SY5461 @ ( c_Product__Type_OSigma @ SV1047 @ ( c_COMBK @ SV1047 @ ( tc_fun @ SV1535 @ tc_bool ) @ SV1535 ) @ SV1535 @ SV1535 ) @ ( tc_fun @ ( tc_prod @ SV1535 @ SV1535 ) @ tc_bool ) )
| ~ ( c_in @ ( c_Pair @ SV442 @ SY5460 @ SV1535 @ SV1535 ) @ ( c_Transitive__Closure_Ortrancl @ SY5461 @ SV1535 ) @ ( tc_prod @ SV1535 @ SV1535 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4007]) ).
thf(4553,plain,
! [SV1537: $i,SV1049: $i,SV444: $i] :
( ( ( c_in @ SV444 @ ( c_Transitive__Closure_Ortrancl @ SV1049 @ SV1537 ) @ ( tc_prod @ SV1537 @ SV1537 ) )
= $true )
| ( ( ~ ( c_in @ SV444 @ SV1049 @ ( tc_prod @ SV1537 @ SV1537 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4009]) ).
thf(4554,plain,
! [SV1538: $i,SV1050: $i,SV445: $i] :
( ( ( c_in @ SV445 @ ( c_Transitive__Closure_Otrancl @ SV1050 @ SV1538 ) @ ( tc_prod @ SV1538 @ SV1538 ) )
= $true )
| ( ( ~ ( c_in @ SV445 @ SV1050 @ ( tc_prod @ SV1538 @ SV1538 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4010]) ).
thf(4555,plain,
! [SV1883: $i,SV1539: $i,SV1051: $i,SV446: $i] :
( ( ( c_in @ ( c_Pair @ SV446 @ SV1051 @ SV1539 @ SV1539 ) @ ( c_Transitive__Closure_Otrancl @ SV1883 @ SV1539 ) @ ( tc_prod @ SV1539 @ SV1539 ) )
| ! [SY5790: $i] :
( ~ ( c_in @ ( c_Pair @ SY5790 @ SV1051 @ SV1539 @ SV1539 ) @ ( c_Transitive__Closure_Ortrancl @ SV1883 @ SV1539 ) @ ( tc_prod @ SV1539 @ SV1539 ) )
| ~ ( c_in @ ( c_Pair @ SV446 @ SY5790 @ SV1539 @ SV1539 ) @ SV1883 @ ( tc_prod @ SV1539 @ SV1539 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4011]) ).
thf(4556,plain,
! [SV1884: $i,SV1540: $i,SV1052: $i,SV447: $i] :
( ( ( c_in @ ( c_Pair @ SV447 @ SV1052 @ SV1540 @ SV1540 ) @ ( c_Transitive__Closure_Otrancl @ SV1884 @ SV1540 ) @ ( tc_prod @ SV1540 @ SV1540 ) )
| ! [SY5791: $i] :
( ~ ( c_in @ ( c_Pair @ SY5791 @ SV1052 @ SV1540 @ SV1540 ) @ SV1884 @ ( tc_prod @ SV1540 @ SV1540 ) )
| ~ ( c_in @ ( c_Pair @ SV447 @ SY5791 @ SV1540 @ SV1540 ) @ ( c_Transitive__Closure_Ortrancl @ SV1884 @ SV1540 ) @ ( tc_prod @ SV1540 @ SV1540 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4012]) ).
thf(4557,plain,
! [SV1885: $i,SV1541: $i,SV1053: $i,SV448: $i] :
( ( ( c_in @ ( c_Pair @ SV448 @ SV1053 @ SV1541 @ SV1541 ) @ ( c_Transitive__Closure_Ortrancl @ SV1885 @ SV1541 ) @ ( tc_prod @ SV1541 @ SV1541 ) )
| ~ ( c_in @ ( c_Pair @ SV448 @ SV1053 @ SV1541 @ SV1541 ) @ ( c_Transitive__Closure_Otrancl @ SV1885 @ SV1541 ) @ ( tc_prod @ SV1541 @ SV1541 ) )
| ( SV448 = SV1053 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4013]) ).
thf(4558,plain,
! [SV1886: $i,SV1542: $i,SV1054: $i,SV449: $i] :
( ( ( c_in @ ( c_Pair @ SV449 @ SV1054 @ SV1542 @ SV1542 ) @ ( c_Transitive__Closure_Otrancl @ SV1886 @ SV1542 ) @ ( tc_prod @ SV1542 @ SV1542 ) )
| ( SV449 = SV1054 )
| ~ ( c_in @ ( c_Pair @ SV449 @ SV1054 @ SV1542 @ SV1542 ) @ ( c_Transitive__Closure_Ortrancl @ SV1886 @ SV1542 ) @ ( tc_prod @ SV1542 @ SV1542 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4014]) ).
thf(4559,plain,
! [SV1887: $i,SV1543: $i,SV1055: $i,SV450: $i] :
( ( ( c_in @ ( c_Pair @ SV450 @ SV1055 @ SV1543 @ SV1543 ) @ ( c_Transitive__Closure_Otrancl @ SV1887 @ SV1543 ) @ ( tc_prod @ SV1543 @ SV1543 ) )
| ( SV450 = SV1055 )
| ~ ( c_in @ ( c_Pair @ SV450 @ SV1055 @ SV1543 @ SV1543 ) @ ( c_Transitive__Closure_Ortrancl @ SV1887 @ SV1543 ) @ ( tc_prod @ SV1543 @ SV1543 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4015]) ).
thf(4560,plain,
! [SV1888: $i,SV1544: $i,SV1056: $i,SV451: $i] :
( ( ( c_in @ ( c_Pair @ SV451 @ SV1056 @ SV1544 @ SV1544 ) @ ( c_Transitive__Closure_Ortrancl @ ( c_Relation_Oconverse @ SV1888 @ SV1544 @ SV1544 ) @ SV1544 ) @ ( tc_prod @ SV1544 @ SV1544 ) )
| ~ ( c_in @ ( c_Pair @ SV1056 @ SV451 @ SV1544 @ SV1544 ) @ ( c_Transitive__Closure_Ortrancl @ SV1888 @ SV1544 ) @ ( tc_prod @ SV1544 @ SV1544 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4016]) ).
thf(4561,plain,
! [SV1889: $i,SV1545: $i,SV1057: $i,SV452: $i] :
( ( ( c_in @ ( c_Pair @ SV452 @ SV1057 @ SV1545 @ SV1545 ) @ ( c_Transitive__Closure_Ortrancl @ SV1889 @ SV1545 ) @ ( tc_prod @ SV1545 @ SV1545 ) )
| ~ ( c_in @ ( c_Pair @ SV1057 @ SV452 @ SV1545 @ SV1545 ) @ ( c_Transitive__Closure_Ortrancl @ ( c_Relation_Oconverse @ SV1889 @ SV1545 @ SV1545 ) @ SV1545 ) @ ( tc_prod @ SV1545 @ SV1545 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4017]) ).
thf(4562,plain,
! [SV1890: $i,SV1546: $i,SV1058: $i,SV453: $i] :
( ( ( c_in @ ( c_Pair @ SV453 @ SV1058 @ SV1546 @ SV1546 ) @ ( c_Transitive__Closure_Ortrancl @ SV1890 @ SV1546 ) @ ( tc_prod @ SV1546 @ SV1546 ) )
| ( c_in @ ( c_Pair @ SV1058 @ SV453 @ SV1546 @ SV1546 ) @ ( c_Transitive__Closure_Ortrancl @ SV1890 @ SV1546 ) @ ( tc_prod @ SV1546 @ SV1546 ) )
| ! [SY5792: $i] :
( ~ ( c_in @ ( c_Pair @ SY5792 @ SV453 @ SV1546 @ SV1546 ) @ ( c_Transitive__Closure_Ortrancl @ SV1890 @ SV1546 ) @ ( tc_prod @ SV1546 @ SV1546 ) )
| ~ ( c_in @ ( c_Pair @ SY5792 @ SV1058 @ SV1546 @ SV1546 ) @ ( c_Transitive__Closure_Ortrancl @ SV1890 @ SV1546 ) @ ( tc_prod @ SV1546 @ SV1546 ) )
| ~ ( c_Relation_Osingle__valued @ SV1890 @ SV1546 @ SV1546 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4018]) ).
thf(4563,plain,
! [SV1891: $i,SV1547: $i,SV1059: $i,SV454: $i] :
( ( ( c_in @ ( c_Pair @ SV454 @ SV1059 @ SV1547 @ SV1547 ) @ ( c_Transitive__Closure_Ortrancl @ SV1891 @ SV1547 ) @ ( tc_prod @ SV1547 @ SV1547 ) )
| ~ ( c_in @ ( c_Pair @ SV454 @ SV1059 @ SV1547 @ SV1547 ) @ ( c_Transitive__Closure_Otrancl @ SV1891 @ SV1547 ) @ ( tc_prod @ SV1547 @ SV1547 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4019]) ).
thf(4564,plain,
! [SV1892: $i,SV1548: $i,SV1060: $i,SV455: $i] :
( ( ( c_in @ ( c_Pair @ SV455 @ SV1060 @ SV1548 @ SV1548 ) @ ( c_Transitive__Closure_Otrancl @ SV1892 @ SV1548 ) @ ( tc_prod @ SV1548 @ SV1548 ) )
| ! [SY5793: $i] :
( ~ ( c_in @ ( c_Pair @ SY5793 @ SV1060 @ SV1548 @ SV1548 ) @ ( c_Transitive__Closure_Ortrancl @ SV1892 @ SV1548 ) @ ( tc_prod @ SV1548 @ SV1548 ) )
| ~ ( c_in @ ( c_Pair @ SV455 @ SY5793 @ SV1548 @ SV1548 ) @ ( c_Transitive__Closure_Otrancl @ SV1892 @ SV1548 ) @ ( tc_prod @ SV1548 @ SV1548 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4020]) ).
thf(4565,plain,
! [SV1893: $i,SV1549: $i,SV1061: $i,SV456: $i] :
( ( ( c_in @ ( c_Pair @ SV456 @ SV1061 @ SV1549 @ SV1549 ) @ ( c_Transitive__Closure_Otrancl @ SV1893 @ SV1549 ) @ ( tc_prod @ SV1549 @ SV1549 ) )
| ! [SY5794: $i] :
( ~ ( c_in @ ( c_Pair @ SY5794 @ SV1061 @ SV1549 @ SV1549 ) @ ( c_Transitive__Closure_Otrancl @ SV1893 @ SV1549 ) @ ( tc_prod @ SV1549 @ SV1549 ) )
| ~ ( c_in @ ( c_Pair @ SV456 @ SY5794 @ SV1549 @ SV1549 ) @ ( c_Transitive__Closure_Ortrancl @ SV1893 @ SV1549 ) @ ( tc_prod @ SV1549 @ SV1549 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4021]) ).
thf(4566,plain,
! [SV1894: $i,SV1550: $i,SV1062: $i,SV457: $i] :
( ( ( c_in @ ( c_Pair @ SV457 @ SV1062 @ SV1550 @ SV1550 ) @ ( c_Relation_Oconverse @ ( c_Transitive__Closure_Otrancl @ SV1894 @ SV1550 ) @ SV1550 @ SV1550 ) @ ( tc_prod @ SV1550 @ SV1550 ) )
| ~ ( c_in @ ( c_Pair @ SV457 @ SV1062 @ SV1550 @ SV1550 ) @ ( c_Transitive__Closure_Otrancl @ ( c_Relation_Oconverse @ SV1894 @ SV1550 @ SV1550 ) @ SV1550 ) @ ( tc_prod @ SV1550 @ SV1550 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4022]) ).
thf(4567,plain,
! [SV1895: $i,SV1551: $i,SV1063: $i,SV458: $i] :
( ( ( c_in @ ( c_Pair @ SV458 @ SV1063 @ SV1551 @ SV1551 ) @ ( c_Transitive__Closure_Otrancl @ ( c_Relation_Oconverse @ SV1895 @ SV1551 @ SV1551 ) @ SV1551 ) @ ( tc_prod @ SV1551 @ SV1551 ) )
| ~ ( c_in @ ( c_Pair @ SV458 @ SV1063 @ SV1551 @ SV1551 ) @ ( c_Relation_Oconverse @ ( c_Transitive__Closure_Otrancl @ SV1895 @ SV1551 ) @ SV1551 @ SV1551 ) @ ( tc_prod @ SV1551 @ SV1551 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4023]) ).
thf(4568,plain,
! [SV1896: $i,SV1552: $i,SV1064: $i,SV459: $i] :
( ( ! [SY5795: $i,SY5796: $i] :
( ( hAPP @ ( c_split @ SV459 @ SV1064 @ SV1552 @ SV1896 ) @ ( c_Pair @ SY5795 @ SY5796 @ SV1064 @ SV1552 ) )
= ( hAPP @ ( hAPP @ SV459 @ SY5795 ) @ SY5796 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4024]) ).
thf(4569,plain,
! [SV1897: $i,SV1553: $i,SV1065: $i,SV460: $i] :
( ( ! [SY5797: $i,SY5798: $i] :
( ( hAPP @ ( c_split @ SV460 @ SV1065 @ SV1553 @ SV1897 ) @ ( c_Pair @ SY5797 @ SY5798 @ SV1065 @ SV1553 ) )
= ( hAPP @ ( hAPP @ SV460 @ SY5797 ) @ SY5798 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4025]) ).
thf(4570,plain,
! [SV1898: $i,SV1554: $i,SV1066: $i,SV461: $i] :
( ( ! [SY5799: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ SV461 @ SV1066 ) @ SV1554 ) @ SV1898 ) )
| ! [SY5800: $i,SY5801: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_split @ SV461 @ SY5799 @ SY5800 @ ( tc_fun @ SY5801 @ tc_bool ) ) @ ( c_Pair @ SV1066 @ SV1554 @ SY5799 @ SY5800 ) ) @ SV1898 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4026]) ).
thf(4571,plain,
! [SV1899: $i,SV1555: $i,SV1067: $i,SV462: $i] :
( ( ! [SY5802: $i] : ( c_in @ ( hAPP @ SV462 @ SV1067 ) @ ( c_Set_Oimage @ SV462 @ SV1555 @ SV1899 @ SY5802 ) @ SY5802 )
| ~ ( c_in @ SV1067 @ SV1555 @ SV1899 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4027]) ).
thf(4572,plain,
! [SV1900: $i,SV1556: $i,SV1068: $i,SV463: $i] :
( ( ! [SY5803: $i] : ( c_in @ ( hAPP @ SV463 @ SV1068 ) @ ( c_Set_Oimage @ SV463 @ SV1556 @ SV1900 @ SY5803 ) @ SY5803 )
| ~ ( c_in @ SV1068 @ SV1556 @ SV1900 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4028]) ).
thf(4573,plain,
! [SV1557: $i,SV1069: $i,SV464: $i] :
( ( ( ~ ( c_in @ SV464 @ SV1069 @ SV1557 ) )
= $true )
| ( ( ! [SY5494: $i,SY5495: $i] : ( c_in @ ( hAPP @ SY5494 @ SV464 ) @ ( c_Set_Oimage @ SY5494 @ SV1069 @ SV1557 @ SY5495 ) @ SY5495 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4029]) ).
thf(4574,plain,
! [SV1558: $i,SV1070: $i,SV465: $i] :
( ( ( ~ ( c_in @ SV465 @ SV1070 @ SV1558 ) )
= $true )
| ( ( ! [SY5496: $i,SY5497: $i] : ( c_in @ ( hAPP @ SY5496 @ SV465 ) @ ( c_Set_Oimage @ SY5496 @ SV1070 @ SV1558 @ SY5497 ) @ SY5497 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4030]) ).
thf(4575,plain,
! [SV1559: $i,SV1071: $i,SV466: $i] :
( ( ( c_in @ SV466 @ ( c_Wellfounded_Oacc @ SV1071 @ SV1559 ) @ SV1559 )
= $true )
| ( ( ~ ( c_Wellfounded_Owf @ SV1071 @ SV1559 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4031]) ).
thf(4576,plain,
! [SV1901: $i,SV1560: $i,SV1073: $i,SV468: $i] :
( ( ! [SY5804: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Relation__XImageE__1__1 @ SV468 @ SV1073 @ SV1560 @ SV1901 @ SY5804 ) @ SV468 @ SV1901 )
| ~ ( c_in @ SV1073 @ ( c_Relation_OImage @ SV1560 @ SV468 @ SV1901 @ SY5804 ) @ SY5804 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4032]) ).
thf(4577,plain,
! [SV1074: $i,SV469: $i] :
( ( ( c_Relation_Osym @ SV469 @ SV1074 )
= $false )
| ( ( c_Relation_Osym @ ( c_Transitive__Closure_Otrancl @ SV469 @ SV1074 ) @ SV1074 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4033]) ).
thf(4578,plain,
! [SV1075: $i,SV1902: $i,SV470: $i] :
( ( ( ! [SY5805: $i] :
( ~ ( hBOOL @ ( hAPP @ SV470 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ SV470 @ SV1902 @ SY5805 ) ) )
| ~ ( c_in @ SV1075 @ ( c_Wellfounded_Oacc @ SV1902 @ SY5805 ) @ SY5805 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV470 @ SV1075 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4034]) ).
thf(4579,plain,
! [SV1076: $i,SV471: $i] :
( ( ( c_Relation_Otrans @ SV471 @ SV1076 )
= $false )
| ( ( ( c_Transitive__Closure_Otrancl @ SV471 @ SV1076 )
= SV471 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4035]) ).
thf(4580,plain,
! [SV1077: $i,SV1903: $i,SV472: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV472 @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ SV472 @ SV1903 ) ) )
| ~ ( c_in @ SV1077 @ ( c_Wellfounded_Oacc @ SV1903 @ t_a ) @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV472 @ SV1077 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4036]) ).
thf(4581,plain,
! [SV1078: $i,SV1904: $i,SV473: $i] :
( ( ( ! [SY5806: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ SV473 @ SV1904 @ SY5806 ) @ ( c_Wellfounded_Oacc @ SV1904 @ SY5806 ) @ SY5806 )
| ~ ( c_in @ SV1078 @ ( c_Wellfounded_Oacc @ SV1904 @ SY5806 ) @ SY5806 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV473 @ SV1078 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4037]) ).
thf(4582,plain,
! [SV1079: $i,SV474: $i] :
( ( ( c_Relation_Osym @ ( c_Relation_Oconverse @ SV474 @ SV1079 @ SV1079 ) @ SV1079 )
= $false )
| ( ( c_Relation_Osym @ SV474 @ SV1079 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4038]) ).
thf(4583,plain,
! [SV1080: $i,SV475: $i] :
( ( ( c_Relation_Osym @ SV475 @ SV1080 )
= $false )
| ( ( c_Relation_Osym @ ( c_Relation_Oconverse @ SV475 @ SV1080 @ SV1080 ) @ SV1080 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4039]) ).
thf(4584,plain,
! [SV1905: $i,SV1561: $i,SV1082: $i,SV477: $i] :
( ( ! [SY5807: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Relation__XImage__iff__1__1 @ SV477 @ SV1082 @ SV1561 @ SV1905 @ SY5807 ) @ SV477 @ SV1905 )
| ~ ( c_in @ SV1082 @ ( c_Relation_OImage @ SV1561 @ SV477 @ SV1905 @ SY5807 ) @ SY5807 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4040]) ).
thf(4585,plain,
! [SV1562: $i,SV1083: $i,SV478: $i] :
( ( ( ~ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1 @ SV478 @ SV1083 @ SV1562 ) @ ( c_Wellfounded_Oacc @ SV478 @ SV1562 ) @ SV1562 ) )
= $true )
| ( ( c_in @ SV1083 @ ( c_Wellfounded_Oacc @ SV478 @ SV1562 ) @ SV1562 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4041]) ).
thf(4586,plain,
! [SV1088: $i,SV484: $i] :
( ( ( c_Wellfounded_Owf @ ( c_Relation_Oconverse @ SV484 @ SV1088 @ SV1088 ) @ SV1088 )
= $false )
| ( ( c_Wellfounded_Owf @ ( c_Relation_Oconverse @ ( c_Transitive__Closure_Otrancl @ SV484 @ SV1088 ) @ SV1088 @ SV1088 ) @ SV1088 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4044]) ).
thf(4587,plain,
! [SV1089: $i,SV1906: $i,SV485: $i] :
( ( ( ! [SY5808: $i] :
( ~ ( hBOOL @ ( hAPP @ SV485 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ SV485 @ SV1906 @ SY5808 ) ) )
| ~ ( c_in @ SV1089 @ ( c_Wellfounded_Oacc @ SV1906 @ SY5808 ) @ SY5808 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV485 @ SV1089 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4045]) ).
thf(4588,plain,
! [SV1565: $i,SV1090: $i,SV486: $i] :
( ( ( c_Relation_Orefl__on @ SV486 @ SV1090 @ SV1565 )
= $true )
| ( ( ~ ( c_Relation_Orefl__on @ SV486 @ ( c_Relation_Oconverse @ SV1090 @ SV1565 @ SV1565 ) @ SV1565 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4046]) ).
thf(4589,plain,
! [SV1566: $i,SV1091: $i,SV487: $i] :
( ( ( c_Relation_Orefl__on @ SV487 @ ( c_Relation_Oconverse @ SV1091 @ SV1566 @ SV1566 ) @ SV1566 )
= $true )
| ( ( ~ ( c_Relation_Orefl__on @ SV487 @ SV1091 @ SV1566 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4047]) ).
thf(4590,plain,
! [SV1092: $i,SV488: $i] :
( ( ( c_Relation_Osym @ SV488 @ SV1092 )
= $false )
| ( ( c_Relation_Osym @ ( c_Transitive__Closure_Ortrancl @ SV488 @ SV1092 ) @ SV1092 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4048]) ).
thf(4591,plain,
! [SV1093: $i,SV489: $i] :
( ( ( c_Wellfounded_Owf @ SV489 @ SV1093 )
= $false )
| ( ( c_Wellfounded_Owf @ ( c_Relation_Orel__comp @ SV489 @ SV489 @ SV1093 @ SV1093 @ SV1093 ) @ SV1093 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4049]) ).
thf(4592,plain,
! [SV1094: $i,SV490: $i] :
( ( ( c_Wellfounded_Owf @ ( c_Relation_Orel__comp @ SV490 @ SV490 @ SV1094 @ SV1094 @ SV1094 ) @ SV1094 )
= $false )
| ( ( c_Wellfounded_Owf @ SV490 @ SV1094 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4050]) ).
thf(4593,plain,
! [SV1097: $i,SV494: $i] :
( ( ( c_Relation_Osym @ SV494 @ SV1097 )
= $false )
| ( ( ( c_Relation_Oconverse @ SV494 @ SV1097 @ SV1097 )
= SV494 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4051]) ).
thf(4594,plain,
! [SV1098: $i,SV495: $i] :
( ( ( ( c_Relation_Oconverse @ SV495 @ SV1098 @ SV1098 )
= SV495 )
= $false )
| ( ( c_Relation_Osym @ SV495 @ SV1098 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4052]) ).
thf(4595,plain,
! [SV1907: $i,SV1567: $i,SV1101: $i,SV498: $i] :
( ( ! [SY5809: $i] :
( ( c_Relation_Oconverse @ ( c_Relation_Orel__comp @ SV498 @ SV1101 @ SV1567 @ SV1907 @ SY5809 ) @ SV1567 @ SY5809 )
= ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ SV1101 @ SV1907 @ SY5809 ) @ ( c_Relation_Oconverse @ SV498 @ SV1567 @ SV1907 ) @ SY5809 @ SV1907 @ SV1567 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4053]) ).
thf(4596,plain,
! [SV1568: $i,SV1104: $i,SV501: $i] :
( ( ( ! [SY5504: $i] : ( c_Wellfounded_Owf @ ( c_Relation_Oinv__image @ SV501 @ SV1104 @ SV1568 @ SY5504 ) @ SY5504 ) )
= $true )
| ( ( ~ ( c_Wellfounded_Owf @ SV501 @ SV1568 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4054]) ).
thf(4597,plain,
! [SV1569: $i,SV1106: $i,SV503: $i] :
( ( ( ! [SY5505: $i] : ( c_Relation_Osym @ ( c_Relation_Oinv__image @ SV503 @ SV1106 @ SV1569 @ SY5505 ) @ SY5505 ) )
= $true )
| ( ( ~ ( c_Relation_Osym @ SV503 @ SV1569 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4055]) ).
thf(4598,plain,
! [SV1109: $i,SV506: $i] :
( ( ( c_Relation_Otrans @ ( c_Relation_Oconverse @ SV506 @ SV1109 @ SV1109 ) @ SV1109 )
= $false )
| ( ( c_Relation_Otrans @ SV506 @ SV1109 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4056]) ).
thf(4599,plain,
! [SV1110: $i,SV507: $i] :
( ( ( c_Relation_Otrans @ SV507 @ SV1110 )
= $false )
| ( ( c_Relation_Otrans @ ( c_Relation_Oconverse @ SV507 @ SV1110 @ SV1110 ) @ SV1110 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4057]) ).
thf(4600,plain,
! [SV1111: $i,SV509: $i] :
( ( ( c_Wellfounded_Owf @ SV509 @ SV1111 )
= $false )
| ( ( c_Wellfounded_Owf @ ( c_Transitive__Closure_Otrancl @ SV509 @ SV1111 ) @ SV1111 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4058]) ).
thf(4601,plain,
! [SV1908: $i,SV1570: $i,SV1112: $i,SV510: $i] :
( ( ! [SY5810: $i,SY5811: $i,SY5812: $i] :
( ( c_Relation_Orel__comp @ ( c_Relation_Orel__comp @ SV510 @ SV1112 @ SV1570 @ SV1908 @ SY5810 ) @ SY5811 @ SV1570 @ SY5810 @ SY5812 )
= ( c_Relation_Orel__comp @ SV510 @ ( c_Relation_Orel__comp @ SV1112 @ SY5811 @ SV1908 @ SY5810 @ SY5812 ) @ SV1570 @ SV1908 @ SY5812 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4059]) ).
thf(4602,plain,
! [SV1909: $i,SV1571: $i,SV1113: $i,SV511: $i] :
( ( ( c_Relation_Oconverse @ ( c_Relation_Oinv__image @ SV511 @ SV1113 @ SV1571 @ SV1909 ) @ SV1909 @ SV1909 )
= ( c_Relation_Oinv__image @ ( c_Relation_Oconverse @ SV511 @ SV1571 @ SV1571 ) @ SV1113 @ SV1571 @ SV1909 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4060]) ).
thf(4603,plain,
! [SV1572: $i,SV1115: $i,SV513: $i] :
( ( ( ! [SY5511: $i] : ( c_Relation_Otrans @ ( c_Relation_Oinv__image @ SV513 @ SV1115 @ SV1572 @ SY5511 ) @ SY5511 ) )
= $true )
| ( ( ~ ( c_Relation_Otrans @ SV513 @ SV1572 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4061]) ).
thf(4604,plain,
! [SV1117: $i,SV515: $i] :
( ( ( ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ SV515 @ SV1117 @ SV1117 ) @ SV515 @ SV1117 @ SV1117 @ SV1117 )
= SV515 )
= $false )
| ( ( c_Equiv__Relations_Oequiv @ ( c_Relation_ODomain @ SV515 @ SV1117 @ SV1117 ) @ SV515 @ SV1117 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4062]) ).
thf(4605,plain,
! [SV1574: $i,SV1119: $i,SV518: $i] :
( ( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 @ SV518 @ SV1119 @ SV1574 ) @ SV518 @ SV1574 )
= $true )
| ( ( ! [SY5512: $i] :
~ ( c_in @ SY5512 @ SV518 @ SV1574 )
| ~ ( c_Wellfounded_Owf @ SV1119 @ SV1574 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4064]) ).
thf(4606,plain,
! [SV1910: $i,SV1575: $i,SV1121: $i,SV520: $i] :
( ( ! [SY5813: $i] :
( ( c_Relation_Osingle__valued @ ( c_Relation_Orel__comp @ SV520 @ SV1121 @ SV1575 @ SV1910 @ SY5813 ) @ SV1575 @ SY5813 )
| ~ ( c_Relation_Osingle__valued @ SV1121 @ SV1910 @ SY5813 )
| ~ ( c_Relation_Osingle__valued @ SV520 @ SV1575 @ SV1910 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4065]) ).
thf(4607,plain,
! [SV1123: $i,SV523: $i,SV1911: $i] :
( ( ( ~ ( c_Equiv__Relations_Oequiv @ SV1911 @ SV523 @ SV1123 ) )
= $true )
| ( ( ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ SV523 @ SV1123 @ SV1123 ) @ SV523 @ SV1123 @ SV1123 @ SV1123 )
= SV523 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4067]) ).
thf(4608,plain,
! [SV1125: $i,SV525: $i] :
( ( ( c_Relation_Oantisym @ ( c_Relation_Oconverse @ SV525 @ SV1125 @ SV1125 ) @ SV1125 )
= $false )
| ( ( c_Relation_Oantisym @ SV525 @ SV1125 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4068]) ).
thf(4609,plain,
! [SV1126: $i,SV526: $i] :
( ( ( c_Relation_Oantisym @ SV526 @ SV1126 )
= $false )
| ( ( c_Relation_Oantisym @ ( c_Relation_Oconverse @ SV526 @ SV1126 @ SV1126 ) @ SV1126 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4069]) ).
thf(4610,plain,
! [SV1127: $i,SV1912: $i,SV527: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV527 @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ SV527 @ SV1912 ) ) )
| ~ ( c_in @ SV1127 @ ( c_Wellfounded_Oacc @ SV1912 @ t_a ) @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV527 @ SV1127 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4070]) ).
thf(4611,plain,
! [SV1577: $i,SV1128: $i,SV528: $i] :
( ( ( c_Relation_Orefl__on @ SV528 @ SV1128 @ SV1577 )
= $true )
| ( ( ~ ( c_Equiv__Relations_Oequiv @ SV528 @ SV1128 @ SV1577 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4071]) ).
thf(4612,plain,
! [SV1578: $i,SV1130: $i,SV530: $i] :
( ( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 @ SV530 @ SV1130 @ SV1578 ) @ SV530 @ SV1578 )
= $true )
| ( ( ! [SY5515: $i] :
~ ( c_in @ SY5515 @ SV530 @ SV1578 )
| ~ ( c_Wellfounded_Owf @ SV1130 @ SV1578 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4072]) ).
thf(4613,plain,
! [SV1131: $i,SV531: $i,SV1913: $i] :
( ( ( ~ ( c_Equiv__Relations_Oequiv @ SV1913 @ SV531 @ SV1131 ) )
= $true )
| ( ( c_Relation_Osym @ SV531 @ SV1131 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4073]) ).
thf(4614,plain,
! [SV1579: $i,SV1132: $i,SV532: $i] :
( ( ( c_in @ SV532 @ ( c_Wellfounded_Oacc @ SV1132 @ SV1579 ) @ SV1579 )
= $true )
| ( ( ~ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1 @ SV1132 @ SV532 @ SV1579 ) @ ( c_Wellfounded_Oacc @ SV1132 @ SV1579 ) @ SV1579 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4074]) ).
thf(4615,plain,
! [SV1914: $i,SV1580: $i,SV1133: $i,SV533: $i] :
( ( ! [SY5814: $i,SY5815: $i] :
( ( c_Equiv__Relations_Ocongruent @ SV533 @ ( hAPP @ SV1133 @ SV1580 ) @ SV1914 @ SY5814 )
| ! [SY5816: $i] :
( ~ ( c_in @ SV1580 @ SY5815 @ SY5816 )
| ! [SY5817: $i] :
( ~ ( c_Equiv__Relations_Ocongruent2 @ SY5817 @ SV533 @ SV1133 @ SY5816 @ SV1914 @ SY5814 )
| ~ ( c_Equiv__Relations_Oequiv @ SY5815 @ SY5817 @ SY5816 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4075]) ).
thf(4616,plain,
! [SV1583: $i,SV1138: $i,SV538: $i] :
( ( ( c_Relation_Ototal__on @ SV538 @ SV1138 @ SV1583 )
= $true )
| ( ( ~ ( c_Relation_Ototal__on @ SV538 @ ( c_Relation_Oconverse @ SV1138 @ SV1583 @ SV1583 ) @ SV1583 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4078]) ).
thf(4617,plain,
! [SV1584: $i,SV1139: $i,SV539: $i] :
( ( ( c_Relation_Ototal__on @ SV539 @ ( c_Relation_Oconverse @ SV1139 @ SV1584 @ SV1584 ) @ SV1584 )
= $true )
| ( ( ~ ( c_Relation_Ototal__on @ SV539 @ SV1139 @ SV1584 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4079]) ).
thf(4618,plain,
! [SV1140: $i,SV540: $i,SV1915: $i] :
( ( ( ~ ( c_Equiv__Relations_Oequiv @ SV1915 @ SV540 @ SV1140 ) )
= $true )
| ( ( c_Relation_Otrans @ SV540 @ SV1140 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4080]) ).
thf(4619,plain,
! [SV1141: $i,SV1916: $i,SV541: $i] :
( ( ( ! [SY5818: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ SV541 @ SV1916 @ SY5818 ) @ ( c_Wellfounded_Oacc @ SV1916 @ SY5818 ) @ SY5818 )
| ~ ( c_in @ SV1141 @ ( c_Wellfounded_Oacc @ SV1916 @ SY5818 ) @ SY5818 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV541 @ SV1141 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4081]) ).
thf(4620,plain,
! [SV1917: $i,SV1585: $i,SV1144: $i,SV544: $i] :
( ( ! [SY5819: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XImageE__1__1 @ SV544 @ SV1144 @ SV1585 @ SV1917 @ SY5819 ) @ SV1144 @ SV1917 @ SY5819 ) @ SV1585 @ ( tc_prod @ SV1917 @ SY5819 ) )
| ~ ( c_in @ SV1144 @ ( c_Relation_OImage @ SV1585 @ SV544 @ SV1917 @ SY5819 ) @ SY5819 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4082]) ).
thf(4621,plain,
! [SV1586: $i,SV1145: $i,SV545: $i] :
( ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1 @ SV545 @ SV1145 @ SV1586 ) @ SV1145 @ SV1586 @ SV1586 ) @ SV545 @ ( tc_prod @ SV1586 @ SV1586 ) )
= $true )
| ( ( c_in @ SV1145 @ ( c_Wellfounded_Oacc @ SV545 @ SV1586 ) @ SV1586 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4083]) ).
thf(4622,plain,
! [SV1587: $i,SV1146: $i,SV546: $i] :
( ( ( hBOOL @ ( hAPP @ SV546 @ SV1146 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ SV546 @ SV1587 ) )
| ! [SY5523: $i,SY5524: $i] :
( ~ ( c_in @ ( c_Pair @ SV1587 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ SV546 @ SY5523 @ SY5524 ) @ SY5524 @ SY5524 ) @ SY5523 @ ( tc_prod @ SY5524 @ SY5524 ) )
| ~ ( c_in @ SV1146 @ ( c_Wellfounded_Oacc @ SY5523 @ SY5524 ) @ SY5524 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4084]) ).
thf(4623,plain,
! [SV1147: $i,SV1918: $i,SV547: $i] :
( ( ( ( hBOOL @ ( hAPP @ SV547 @ SV1918 ) )
| ! [SY5820: $i] :
( ~ ( c_in @ ( c_Pair @ SV1918 @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ SV547 @ SY5820 ) @ t_a @ t_a ) @ SY5820 @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ SV1147 @ ( c_Wellfounded_Oacc @ SY5820 @ t_a ) @ t_a ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV547 @ SV1147 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4085]) ).
thf(4624,plain,
! [SV1588: $i,SV1148: $i,SV548: $i] :
( ( ( ~ ( c_in @ SV548 @ SV1148 @ SV1588 ) )
= $true )
| ( ( ! [SY5525: $i] :
( ~ ( c_in @ ( c_Pair @ SV548 @ ( c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 @ SV1148 @ SY5525 @ SV1588 ) @ SV1588 @ SV1588 ) @ SY5525 @ ( tc_prod @ SV1588 @ SV1588 ) )
| ! [SY5526: $i] :
~ ( c_in @ SY5526 @ SV1148 @ SV1588 )
| ~ ( c_Wellfounded_Owf @ SY5525 @ SV1588 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4086]) ).
thf(4625,plain,
! [SV1919: $i,SV1589: $i,SV1149: $i,SV549: $i] :
( ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XRangeE__1__1 @ SV549 @ SV1149 @ SV1589 @ SV1919 ) @ SV549 @ SV1919 @ SV1589 ) @ SV1149 @ ( tc_prod @ SV1919 @ SV1589 ) )
| ~ ( c_in @ SV549 @ ( c_Relation_ORange @ SV1149 @ SV1919 @ SV1589 ) @ SV1589 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4087]) ).
thf(4626,plain,
! [SV1590: $i,SV1150: $i,SV550: $i] :
( ( ( c_in @ SV550 @ ( c_Wellfounded_Oacc @ SV1150 @ SV1590 ) @ SV1590 )
= $true )
| ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1 @ SV1150 @ SV550 @ SV1590 ) @ SV550 @ SV1590 @ SV1590 ) @ SV1150 @ ( tc_prod @ SV1590 @ SV1590 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4088]) ).
thf(4627,plain,
! [SV1591: $i,SV1151: $i,SV551: $i] :
( ( ( c_in @ SV551 @ ( c_Wellfounded_Oacc @ SV1151 @ SV1591 ) @ SV1591 )
= $true )
| ( ( ! [SY5528: $i] :
( ~ ( c_in @ SY5528 @ ( c_Wellfounded_Oacc @ SV1151 @ SV1591 ) @ SV1591 )
| ~ ( c_in @ ( c_Pair @ SV551 @ SY5528 @ SV1591 @ SV1591 ) @ ( c_Transitive__Closure_Ortrancl @ SV1151 @ SV1591 ) @ ( tc_prod @ SV1591 @ SV1591 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4089]) ).
thf(4628,plain,
! [SV1592: $i,SV1152: $i,SV552: $i] :
( ( ( c_in @ SV552 @ ( c_Wellfounded_Oacc @ SV1152 @ SV1592 ) @ SV1592 )
= $true )
| ( ( ! [SY5529: $i] :
( ~ ( c_in @ ( c_Pair @ SV552 @ SY5529 @ SV1592 @ SV1592 ) @ ( c_Transitive__Closure_Ortrancl @ SV1152 @ SV1592 ) @ ( tc_prod @ SV1592 @ SV1592 ) )
| ~ ( c_in @ SY5529 @ ( c_Wellfounded_Oacc @ SV1152 @ SV1592 ) @ SV1592 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4090]) ).
thf(4629,plain,
! [SV1153: $i,SV553: $i,SV1920: $i] :
( ( ( ! [SY5821: $i] :
( ( c_in @ SV1920 @ ( c_Wellfounded_Oacc @ SY5821 @ t_a ) @ t_a )
| ~ ( c_in @ ( c_Pair @ SV1920 @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ SV553 @ SY5821 ) @ t_a @ t_a ) @ SY5821 @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ SV1153 @ ( c_Wellfounded_Oacc @ SY5821 @ t_a ) @ t_a ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV553 @ SV1153 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4091]) ).
thf(4630,plain,
! [SV1593: $i,SV1154: $i,SV554: $i] :
( ( ( c_in @ SV554 @ ( c_Relation_ODomain @ SV1154 @ SV1593 @ SV1593 ) @ SV1593 )
= $true )
| ( ( c_in @ ( c_Pair @ SV554 @ SV554 @ SV1593 @ SV1593 ) @ ( c_Transitive__Closure_Ortrancl @ SV1154 @ SV1593 ) @ ( tc_prod @ SV1593 @ SV1593 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4092]) ).
thf(4631,plain,
! [SV1155: $i,SV1921: $i,SV555: $i] :
( ( ( ( hBOOL @ ( hAPP @ SV555 @ SV1921 ) )
| ! [SY5822: $i] :
( ~ ( c_in @ ( c_Pair @ SV1921 @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ SV555 @ SY5822 ) @ t_a @ t_a ) @ SY5822 @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ SV1155 @ ( c_Wellfounded_Oacc @ SY5822 @ t_a ) @ t_a ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV555 @ SV1155 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4093]) ).
thf(4632,plain,
! [SV1922: $i,SV1594: $i,SV1156: $i,SV556: $i] :
( ( ! [SY5823: $i,SY5824: $i,SY5825: $i] :
( ( c_in @ ( hAPP @ ( hAPP @ SV556 @ SV1156 ) @ SV1594 ) @ ( c_Set_Oimage @ ( c_split @ SV556 @ SV1922 @ SY5823 @ SY5824 ) @ SY5825 @ ( tc_prod @ SV1922 @ SY5823 ) @ SY5824 ) @ SY5824 )
| ~ ( c_in @ ( c_Pair @ SV1156 @ SV1594 @ SV1922 @ SY5823 ) @ SY5825 @ ( tc_prod @ SV1922 @ SY5823 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4094]) ).
thf(4633,plain,
! [SV1923: $i,SV1595: $i,SV1157: $i,SV557: $i] :
( ( ( c_in @ ( c_Pair @ SV557 @ ( c_ATP__Linkup_Osko__Relation__XDomainE__1__1 @ SV557 @ SV1157 @ SV1595 @ SV1923 ) @ SV1595 @ SV1923 ) @ SV1157 @ ( tc_prod @ SV1595 @ SV1923 ) )
| ~ ( c_in @ SV557 @ ( c_Relation_ODomain @ SV1157 @ SV1595 @ SV1923 ) @ SV1595 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4095]) ).
thf(4634,plain,
! [SV1158: $i,SV558: $i,SV1924: $i] :
( ( ( ! [SY5826: $i] :
( ( c_in @ SV1924 @ ( c_Wellfounded_Oacc @ SY5826 @ t_a ) @ t_a )
| ~ ( c_in @ ( c_Pair @ SV1924 @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ SV558 @ SY5826 ) @ t_a @ t_a ) @ SY5826 @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ SV1158 @ ( c_Wellfounded_Oacc @ SY5826 @ t_a ) @ t_a ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV558 @ SV1158 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4096]) ).
thf(4635,plain,
! [SV1596: $i,SV1159: $i,SV559: $i] :
( ( ( hBOOL @ ( hAPP @ SV559 @ SV1159 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ SV559 @ SV1596 ) )
| ! [SY5535: $i,SY5536: $i] :
( ~ ( c_in @ ( c_Pair @ SV1596 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ SV559 @ SY5535 @ SY5536 ) @ SY5536 @ SY5536 ) @ SY5535 @ ( tc_prod @ SY5536 @ SY5536 ) )
| ~ ( c_in @ SV1159 @ ( c_Wellfounded_Oacc @ SY5535 @ SY5536 ) @ SY5536 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4097]) ).
thf(4636,plain,
! [SV1597: $i,SV1160: $i,SV560: $i] :
( ( ( ~ ( c_in @ SV560 @ SV1160 @ SV1597 ) )
= $true )
| ( ( ! [SY5537: $i] :
( ~ ( c_in @ ( c_Pair @ SV560 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 @ SV1160 @ SY5537 @ SV1597 ) @ SV1597 @ SV1597 ) @ SY5537 @ ( tc_prod @ SV1597 @ SV1597 ) )
| ! [SY5538: $i] :
~ ( c_in @ SY5538 @ SV1160 @ SV1597 )
| ~ ( c_Wellfounded_Owf @ SY5537 @ SV1597 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4098]) ).
thf(4637,plain,
! [SV1925: $i,SV1598: $i,SV1161: $i,SV561: $i] :
( ( ( c_in @ ( c_Pair @ SV561 @ ( c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1 @ SV561 @ SV1161 @ SV1598 @ SV1925 ) @ SV1598 @ SV1925 ) @ SV1161 @ ( tc_prod @ SV1598 @ SV1925 ) )
| ~ ( c_in @ SV561 @ ( c_Relation_ODomain @ SV1161 @ SV1598 @ SV1925 ) @ SV1598 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4099]) ).
thf(4638,plain,
! [SV1926: $i,SV1599: $i,SV1162: $i,SV562: $i] :
( ( ! [SY5827: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XImage__iff__1__1 @ SV562 @ SV1162 @ SV1599 @ SV1926 @ SY5827 ) @ SV1162 @ SV1926 @ SY5827 ) @ SV1599 @ ( tc_prod @ SV1926 @ SY5827 ) )
| ~ ( c_in @ SV1162 @ ( c_Relation_OImage @ SV1599 @ SV562 @ SV1926 @ SY5827 ) @ SY5827 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4100]) ).
thf(4639,plain,
! [SV1927: $i,SV1163: $i,SV563: $i] :
( ( ( ! [SY5828: $i] :
( ~ ( c_in @ ( c_Pair @ SV563 @ SV1163 @ SV1927 @ SV1927 ) @ ( c_Transitive__Closure_Ortrancl @ SY5828 @ SV1927 ) @ ( tc_prod @ SV1927 @ SV1927 ) )
| ( c_in @ SV563 @ ( c_Relation_ODomain @ SY5828 @ SV1927 @ SV1927 ) @ SV1927 ) ) )
= $true )
| ( ( SV563 = SV1163 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4101]) ).
thf(4640,plain,
! [SV1928: $i,SV1600: $i,SV1164: $i,SV564: $i] :
( ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XRange__iff__1__1 @ SV564 @ SV1164 @ SV1600 @ SV1928 ) @ SV564 @ SV1928 @ SV1600 ) @ SV1164 @ ( tc_prod @ SV1928 @ SV1600 ) )
| ~ ( c_in @ SV564 @ ( c_Relation_ORange @ SV1164 @ SV1928 @ SV1600 ) @ SV1600 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4102]) ).
thf(4641,plain,
! [SV1929: $i,SV1601: $i,SV1165: $i,SV565: $i] :
( ( ! [SY5829: $i,SY5830: $i,SY5831: $i] :
( ( c_in @ SV565 @ ( hAPP @ ( c_split @ SV1165 @ SV1601 @ SV1929 @ ( tc_fun @ SY5829 @ tc_bool ) ) @ ( c_Pair @ SY5830 @ SY5831 @ SV1601 @ SV1929 ) ) @ SY5829 )
| ~ ( c_in @ SV565 @ ( hAPP @ ( hAPP @ SV1165 @ SY5830 ) @ SY5831 ) @ SY5829 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4103]) ).
thf(4642,plain,
! [SV1930: $i,SV1602: $i,SV1166: $i,SV566: $i] :
( ( ! [SY5832: $i,SY5833: $i,SY5834: $i,SY5835: $i] :
( ( ( hAPP @ ( hAPP @ SV566 @ SV1166 ) @ SV1602 )
= ( hAPP @ ( hAPP @ SV566 @ SV1930 ) @ SY5832 ) )
| ~ ( c_in @ ( c_Pair @ SV1602 @ SY5832 @ SY5833 @ SY5833 ) @ SY5834 @ ( tc_prod @ SY5833 @ SY5833 ) )
| ! [SY5836: $i] :
( ~ ( c_in @ ( c_Pair @ SV1166 @ SV1930 @ SY5835 @ SY5835 ) @ SY5836 @ ( tc_prod @ SY5835 @ SY5835 ) )
| ! [SY3833: $i] :
~ ( c_Equiv__Relations_Ocongruent2 @ SY5836 @ SY5834 @ SV566 @ SY5835 @ SY5833 @ SY3833 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4104]) ).
thf(4643,plain,
! [SV1931: $i,SV1603: $i,SV1167: $i,SV567: $i] :
( ( ( SV567 = SV1167 )
| ! [SY5838: $i,SY5839: $i] :
( ~ ( c_in @ ( c_Pair @ SV1603 @ SV1167 @ SV1931 @ SY5838 ) @ SY5839 @ ( tc_prod @ SV1931 @ SY5838 ) )
| ~ ( c_in @ ( c_Pair @ SV1603 @ SV567 @ SV1931 @ SY5838 ) @ SY5839 @ ( tc_prod @ SV1931 @ SY5838 ) )
| ~ ( c_Relation_Osingle__valued @ SY5839 @ SV1931 @ SY5838 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4105]) ).
thf(4644,plain,
! [SV1932: $i,SV1604: $i,SV1168: $i,SV568: $i] :
( ( ! [SY5840: $i,SY5841: $i] :
( ( ( hAPP @ ( c_Recdef_Ocut @ SV568 @ SV1168 @ SV1604 @ SV1932 @ SY5840 ) @ SY5841 )
= ( hAPP @ SV568 @ SY5841 ) )
| ~ ( c_in @ ( c_Pair @ SY5841 @ SV1604 @ SV1932 @ SV1932 ) @ SV1168 @ ( tc_prod @ SV1932 @ SV1932 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4106]) ).
thf(4645,plain,
! [SV1933: $i,SV1605: $i,SV1169: $i,SV569: $i] :
( ( ! [SY5842: $i,SY5843: $i] :
( ( ( hAPP @ ( c_Recdef_Ocut @ SV569 @ SV1169 @ SV1605 @ SV1933 @ SY5842 ) @ SY5843 )
= ( hAPP @ SV569 @ SY5843 ) )
| ~ ( c_in @ ( c_Pair @ SY5843 @ SV1605 @ SV1933 @ SV1933 ) @ SV1169 @ ( tc_prod @ SV1933 @ SV1933 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4107]) ).
thf(4646,plain,
! [SV1934: $i,SV1606: $i,SV1170: $i,SV570: $i] :
( ( ! [SY5844: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_FunDef_Oin__rel @ SV570 @ SV1170 @ SV1606 ) @ SV1934 ) @ SY5844 ) )
| ~ ( c_in @ ( c_Pair @ SV1934 @ SY5844 @ SV1170 @ SV1606 ) @ SV570 @ ( tc_prod @ SV1170 @ SV1606 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4108]) ).
thf(4647,plain,
! [SV1935: $i,SV1607: $i,SV1171: $i,SV571: $i] :
( ( ! [SY5845: $i] :
( ( c_in @ ( c_Pair @ SV571 @ SV1171 @ SV1607 @ SV1935 ) @ SY5845 @ ( tc_prod @ SV1607 @ SV1935 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_FunDef_Oin__rel @ SY5845 @ SV1607 @ SV1935 ) @ SV571 ) @ SV1171 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4109]) ).
thf(4648,plain,
! [SV1936: $i,SV1608: $i,SV1172: $i,SV572: $i] :
( ( ( c_in @ ( c_Pair @ SV572 @ SV1172 @ SV1608 @ SV1608 ) @ SV1936 @ ( tc_prod @ SV1608 @ SV1608 ) )
| ! [SY5846: $i] :
( ~ ( c_in @ ( c_Pair @ SY5846 @ SV1172 @ SV1608 @ SV1608 ) @ SV1936 @ ( tc_prod @ SV1608 @ SV1608 ) )
| ~ ( c_in @ ( c_Pair @ SV572 @ SY5846 @ SV1608 @ SV1608 ) @ SV1936 @ ( tc_prod @ SV1608 @ SV1608 ) )
| ~ ( c_Relation_Otrans @ SV1936 @ SV1608 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4110]) ).
thf(4649,plain,
! [SV1937: $i,SV1609: $i,SV1173: $i,SV573: $i] :
( ( ( c_in @ ( c_Pair @ SV573 @ SV1173 @ SV1609 @ SV1609 ) @ SV1937 @ ( tc_prod @ SV1609 @ SV1609 ) )
| ! [SY5847: $i] :
( ~ ( c_in @ ( c_Pair @ SY5847 @ SV1173 @ SV1609 @ SV1609 ) @ SV1937 @ ( tc_prod @ SV1609 @ SV1609 ) )
| ~ ( c_in @ ( c_Pair @ SV573 @ SY5847 @ SV1609 @ SV1609 ) @ SV1937 @ ( tc_prod @ SV1609 @ SV1609 ) )
| ~ ( c_Relation_Otrans @ SV1937 @ SV1609 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4111]) ).
thf(4650,plain,
! [SV1938: $i,SV1610: $i,SV1174: $i,SV574: $i] :
( ( ! [SY5848: $i] :
( ( c_in @ ( c_Pair @ SV574 @ SV1174 @ SV1610 @ SV1938 ) @ ( c_Relation_Oconverse @ SY5848 @ SV1938 @ SV1610 ) @ ( tc_prod @ SV1610 @ SV1938 ) )
| ~ ( c_in @ ( c_Pair @ SV1174 @ SV574 @ SV1938 @ SV1610 ) @ SY5848 @ ( tc_prod @ SV1938 @ SV1610 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4112]) ).
thf(4651,plain,
! [SV1939: $i,SV1611: $i,SV1175: $i,SV575: $i] :
( ( ! [SY5849: $i] :
( ( c_in @ ( c_Pair @ SV575 @ SV1175 @ SV1611 @ SV1939 ) @ ( c_Relation_Oconverse @ SY5849 @ SV1939 @ SV1611 ) @ ( tc_prod @ SV1611 @ SV1939 ) )
| ~ ( c_in @ ( c_Pair @ SV1175 @ SV575 @ SV1939 @ SV1611 ) @ SY5849 @ ( tc_prod @ SV1939 @ SV1611 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4113]) ).
thf(4652,plain,
! [SV1940: $i,SV1612: $i,SV1176: $i,SV576: $i] :
( ( ! [SY5850: $i] :
( ( c_in @ ( c_Pair @ SV576 @ SV1176 @ SV1612 @ SV1940 ) @ SY5850 @ ( tc_prod @ SV1612 @ SV1940 ) )
| ~ ( c_in @ ( c_Pair @ SV1176 @ SV576 @ SV1940 @ SV1612 ) @ ( c_Relation_Oconverse @ SY5850 @ SV1612 @ SV1940 ) @ ( tc_prod @ SV1940 @ SV1612 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4114]) ).
thf(4653,plain,
! [SV1613: $i,SV1177: $i,SV577: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV577 @ SV577 @ SV1177 @ SV1177 ) @ SV1613 @ ( tc_prod @ SV1177 @ SV1177 ) ) )
= $true )
| ( ( ~ ( c_Relation_Oirrefl @ SV1613 @ SV1177 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4115]) ).
thf(4654,plain,
! [SV1941: $i,SV1614: $i,SV1178: $i,SV578: $i] :
( ( ( c_in @ ( c_Pair @ SV578 @ SV1178 @ SV1614 @ SV1614 ) @ ( c_Transitive__Closure_Otrancl @ SV1941 @ SV1614 ) @ ( tc_prod @ SV1614 @ SV1614 ) )
| ! [SY5851: $i] :
( ~ ( c_in @ ( c_Pair @ SY5851 @ SV1178 @ SV1614 @ SV1614 ) @ SV1941 @ ( tc_prod @ SV1614 @ SV1614 ) )
| ~ ( c_in @ ( c_Pair @ SV578 @ SY5851 @ SV1614 @ SV1614 ) @ ( c_Transitive__Closure_Otrancl @ SV1941 @ SV1614 ) @ ( tc_prod @ SV1614 @ SV1614 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4116]) ).
thf(4655,plain,
! [SV1942: $i,SV1615: $i,SV1179: $i,SV579: $i] :
( ( ( c_in @ ( c_Pair @ SV579 @ SV1179 @ SV1615 @ SV1615 ) @ ( c_Transitive__Closure_Otrancl @ SV1942 @ SV1615 ) @ ( tc_prod @ SV1615 @ SV1615 ) )
| ! [SY5852: $i] :
( ~ ( c_in @ ( c_Pair @ SY5852 @ SV1179 @ SV1615 @ SV1615 ) @ ( c_Transitive__Closure_Otrancl @ SV1942 @ SV1615 ) @ ( tc_prod @ SV1615 @ SV1615 ) )
| ~ ( c_in @ ( c_Pair @ SV579 @ SY5852 @ SV1615 @ SV1615 ) @ SV1942 @ ( tc_prod @ SV1615 @ SV1615 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4117]) ).
thf(4656,plain,
! [SV1943: $i,SV1616: $i,SV1180: $i,SV580: $i] :
( ( ( c_in @ ( c_Pair @ SV580 @ SV1180 @ SV1616 @ SV1616 ) @ ( c_Transitive__Closure_Ortrancl @ SV1943 @ SV1616 ) @ ( tc_prod @ SV1616 @ SV1616 ) )
| ! [SY5853: $i] :
( ~ ( c_in @ ( c_Pair @ SY5853 @ SV1180 @ SV1616 @ SV1616 ) @ SV1943 @ ( tc_prod @ SV1616 @ SV1616 ) )
| ~ ( c_in @ ( c_Pair @ SV580 @ SY5853 @ SV1616 @ SV1616 ) @ ( c_Transitive__Closure_Ortrancl @ SV1943 @ SV1616 ) @ ( tc_prod @ SV1616 @ SV1616 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4118]) ).
thf(4657,plain,
! [SV1944: $i,SV1617: $i,SV1181: $i,SV581: $i] :
( ( ( c_in @ ( c_Pair @ SV581 @ SV1181 @ SV1617 @ SV1617 ) @ ( c_Transitive__Closure_Ortrancl @ SV1944 @ SV1617 ) @ ( tc_prod @ SV1617 @ SV1617 ) )
| ! [SY5854: $i] :
( ~ ( c_in @ ( c_Pair @ SY5854 @ SV1181 @ SV1617 @ SV1617 ) @ ( c_Transitive__Closure_Ortrancl @ SV1944 @ SV1617 ) @ ( tc_prod @ SV1617 @ SV1617 ) )
| ~ ( c_in @ ( c_Pair @ SV581 @ SY5854 @ SV1617 @ SV1617 ) @ SV1944 @ ( tc_prod @ SV1617 @ SV1617 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4119]) ).
thf(4658,plain,
! [SV1945: $i,SV1618: $i,SV1182: $i,SV582: $i] :
( ( ( c_in @ ( c_Pair @ SV582 @ SV1182 @ SV1618 @ SV1618 ) @ ( c_Transitive__Closure_Otrancl @ SV1945 @ SV1618 ) @ ( tc_prod @ SV1618 @ SV1618 ) )
| ~ ( c_in @ ( c_Pair @ SV582 @ SV1182 @ SV1618 @ SV1618 ) @ SV1945 @ ( tc_prod @ SV1618 @ SV1618 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4120]) ).
thf(4659,plain,
! [SV1946: $i,SV1619: $i,SV1183: $i,SV583: $i] :
( ( ( c_in @ ( c_Pair @ SV583 @ SV1183 @ SV1619 @ SV1619 ) @ ( c_Transitive__Closure_Ortrancl @ SV1946 @ SV1619 ) @ ( tc_prod @ SV1619 @ SV1619 ) )
| ! [SY5855: $i] :
( ~ ( c_in @ ( c_Pair @ SY5855 @ SV1183 @ SV1619 @ SV1619 ) @ ( c_Transitive__Closure_Ortrancl @ SV1946 @ SV1619 ) @ ( tc_prod @ SV1619 @ SV1619 ) )
| ~ ( c_in @ ( c_Pair @ SV583 @ SY5855 @ SV1619 @ SV1619 ) @ ( c_Transitive__Closure_Ortrancl @ SV1946 @ SV1619 ) @ ( tc_prod @ SV1619 @ SV1619 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4121]) ).
thf(4660,plain,
! [SV1947: $i,SV1622: $i,SV1186: $i,SV586: $i] :
( ( ~ ( c_in @ ( c_Pair @ SV586 @ SV1186 @ SV1622 @ SV1622 ) @ SV1947 @ ( tc_prod @ SV1622 @ SV1622 ) )
| ~ ( c_in @ ( c_Pair @ SV1186 @ SV586 @ SV1622 @ SV1622 ) @ SV1947 @ ( tc_prod @ SV1622 @ SV1622 ) )
| ~ ( c_Wellfounded_Owf @ SV1947 @ SV1622 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4124]) ).
thf(4661,plain,
! [SV1948: $i,SV587: $i,SV1187: $i] :
( ( ( ! [SY5856: $i] :
( ~ ( c_in @ ( c_Pair @ SV1187 @ SV587 @ SV1948 @ SV1948 ) @ SY5856 @ ( tc_prod @ SV1948 @ SV1948 ) )
| ~ ( c_in @ ( c_Pair @ SV587 @ SV1187 @ SV1948 @ SV1948 ) @ SY5856 @ ( tc_prod @ SV1948 @ SV1948 ) )
| ~ ( c_Relation_Oantisym @ SY5856 @ SV1948 ) ) )
= $true )
| ( ( SV587 = SV1187 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4125]) ).
thf(4662,plain,
! [SV1949: $i,SV588: $i,SV1188: $i] :
( ( ( ! [SY5857: $i] :
( ~ ( c_in @ ( c_Pair @ SV1188 @ SV588 @ SV1949 @ SV1949 ) @ SY5857 @ ( tc_prod @ SV1949 @ SV1949 ) )
| ~ ( c_in @ ( c_Pair @ SV588 @ SV1188 @ SV1949 @ SV1949 ) @ SY5857 @ ( tc_prod @ SV1949 @ SV1949 ) )
| ~ ( c_Relation_Oantisym @ SY5857 @ SV1949 ) ) )
= $true )
| ( ( SV588 = SV1188 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4126]) ).
thf(4663,plain,
! [SV1950: $i,SV1623: $i,SV1189: $i,SV589: $i] :
( ( ( ( hAPP @ SV589 @ SV1189 )
= ( hAPP @ SV589 @ SV1623 ) )
| ! [SY5858: $i] :
( ~ ( c_in @ ( c_Pair @ SV1189 @ SV1623 @ SV1950 @ SV1950 ) @ SY5858 @ ( tc_prod @ SV1950 @ SV1950 ) )
| ! [SY5859: $i] :
~ ( c_Equiv__Relations_Ocongruent @ SY5858 @ SV589 @ SV1950 @ SY5859 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4127]) ).
thf(4664,plain,
! [SV1951: $i,SV1190: $i,SV590: $i] :
( ( ( ! [SY5860: $i] :
~ ( c_in @ ( c_Pair @ SV590 @ SV1190 @ SV1951 @ SV1951 ) @ ( c_Relation_OId__on @ SY5860 @ SV1951 ) @ ( tc_prod @ SV1951 @ SV1951 ) ) )
= $true )
| ( ( SV590 = SV1190 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4128]) ).
thf(4665,plain,
! [SV1952: $i,SV1624: $i,SV1191: $i,SV591: $i] :
( ( ! [SY5861: $i,SY5862: $i] :
( ( ( c_Recdef_Ocut @ SV591 @ SV1191 @ SV1624 @ SV1952 @ SY5861 )
!= ( c_Recdef_Ocut @ SY5862 @ SV1191 @ SV1624 @ SV1952 @ SY5861 ) )
| ! [SY5863: $i] :
( ( ( hAPP @ SV591 @ SY5863 )
= ( hAPP @ SY5862 @ SY5863 ) )
| ~ ( c_in @ ( c_Pair @ SY5863 @ SV1624 @ SV1952 @ SV1952 ) @ SV1191 @ ( tc_prod @ SV1952 @ SV1952 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4129]) ).
thf(4666,plain,
! [SV1953: $i,SV1192: $i,SV592: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV592 @ SV1192 @ SV1953 @ SV1953 ) @ ( c_Relation_OId @ SV1953 ) @ ( tc_prod @ SV1953 @ SV1953 ) ) )
= $true )
| ( ( SV592 = SV1192 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4130]) ).
thf(4667,plain,
! [SV1625: $i,SV1193: $i,SV593: $i] :
( ( ( c_in @ ( c_Pair @ SV593 @ SV593 @ SV1193 @ SV1193 ) @ SV1625 @ ( tc_prod @ SV1193 @ SV1193 ) )
= $true )
| ( ( ~ ( c_Nitpick_Orefl_H @ SV1625 @ SV1193 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4131]) ).
thf(4668,plain,
! [SV1626: $i,SV1194: $i,SV594: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV594 @ SV594 @ SV1194 @ SV1194 ) @ SV1626 @ ( tc_prod @ SV1194 @ SV1194 ) ) )
= $true )
| ( ( ~ ( c_Wellfounded_Owf @ SV1626 @ SV1194 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4132]) ).
thf(4669,plain,
! [SV1954: $i,SV1627: $i,SV1195: $i,SV595: $i] :
( ( ! [SY5864: $i,SY5865: $i] :
( ( c_in @ ( c_Pair @ SV595 @ SV1195 @ SV1627 @ SV1627 ) @ ( c_Relation_Oinv__image @ SV1954 @ SY5864 @ SY5865 @ SV1627 ) @ ( tc_prod @ SV1627 @ SV1627 ) )
| ~ ( c_in @ ( c_Pair @ ( hAPP @ SY5864 @ SV595 ) @ ( hAPP @ SY5864 @ SV1195 ) @ SY5865 @ SY5865 ) @ SV1954 @ ( tc_prod @ SY5865 @ SY5865 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4133]) ).
thf(4670,plain,
! [SV1955: $i,SV1628: $i,SV1196: $i,SV596: $i] :
( ( ! [SY5866: $i] :
( ( c_in @ ( c_Pair @ ( hAPP @ SV596 @ SV1196 ) @ ( hAPP @ SV596 @ SV1628 ) @ SV1955 @ SV1955 ) @ SY5866 @ ( tc_prod @ SV1955 @ SV1955 ) )
| ! [SY5867: $i] :
~ ( c_in @ ( c_Pair @ SV1196 @ SV1628 @ SY5867 @ SY5867 ) @ ( c_Relation_Oinv__image @ SY5866 @ SV596 @ SV1955 @ SY5867 ) @ ( tc_prod @ SY5867 @ SY5867 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4134]) ).
thf(4671,plain,
! [SV1956: $i,SV1629: $i,SV1197: $i,SV597: $i] :
( ( ( c_in @ ( c_Pair @ SV597 @ SV1197 @ SV1629 @ SV1629 ) @ SV1956 @ ( tc_prod @ SV1629 @ SV1629 ) )
| ~ ( c_in @ ( c_Pair @ SV1197 @ SV597 @ SV1629 @ SV1629 ) @ SV1956 @ ( tc_prod @ SV1629 @ SV1629 ) )
| ~ ( c_Relation_Osym @ SV1956 @ SV1629 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4135]) ).
thf(4672,plain,
! [SV1957: $i,SV1630: $i,SV1198: $i,SV598: $i] :
( ( ( c_in @ ( c_Pair @ SV598 @ SV1198 @ SV1630 @ SV1630 ) @ SV1957 @ ( tc_prod @ SV1630 @ SV1630 ) )
| ~ ( c_in @ ( c_Pair @ SV1198 @ SV598 @ SV1630 @ SV1630 ) @ SV1957 @ ( tc_prod @ SV1630 @ SV1630 ) )
| ~ ( c_Relation_Osym @ SV1957 @ SV1630 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4136]) ).
thf(4673,plain,
! [SV1958: $i,SV1631: $i,SV1199: $i,SV599: $i] :
( ( ! [SY5868: $i,SY5869: $i,SY5870: $i] :
( ( c_in @ ( c_Pair @ SV599 @ SV1199 @ SV1631 @ SV1958 ) @ ( c_Relation_Orel__comp @ SY5868 @ SY5869 @ SV1631 @ SY5870 @ SV1958 ) @ ( tc_prod @ SV1631 @ SV1958 ) )
| ! [SY5871: $i] :
( ~ ( c_in @ ( c_Pair @ SY5871 @ SV1199 @ SY5870 @ SV1958 ) @ SY5869 @ ( tc_prod @ SY5870 @ SV1958 ) )
| ~ ( c_in @ ( c_Pair @ SV599 @ SY5871 @ SV1631 @ SY5870 ) @ SY5868 @ ( tc_prod @ SV1631 @ SY5870 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4137]) ).
thf(4674,plain,
! [SV1959: $i,SV1632: $i,SV1200: $i,SV600: $i] :
( ( ( c_in @ ( c_Pair @ SV600 @ SV1200 @ SV1632 @ SV1632 ) @ ( c_Transitive__Closure_Otrancl @ SV1959 @ SV1632 ) @ ( tc_prod @ SV1632 @ SV1632 ) )
| ! [SY5872: $i] :
( ~ ( c_in @ ( c_Pair @ SY5872 @ SV1200 @ SV1632 @ SV1632 ) @ SV1959 @ ( tc_prod @ SV1632 @ SV1632 ) )
| ~ ( c_in @ ( c_Pair @ SV600 @ SY5872 @ SV1632 @ SV1632 ) @ SV1959 @ ( tc_prod @ SV1632 @ SV1632 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4138]) ).
thf(4675,plain,
! [SV1960: $i,SV1633: $i,SV1201: $i,SV601: $i] :
( ( ( c_in @ ( c_Pair @ SV601 @ SV1201 @ SV1633 @ SV1633 ) @ ( c_Transitive__Closure_Otrancl @ SV1960 @ SV1633 ) @ ( tc_prod @ SV1633 @ SV1633 ) )
| ! [SY5873: $i] :
( ~ ( c_in @ ( c_Pair @ SY5873 @ SV1201 @ SV1633 @ SV1633 ) @ ( c_Transitive__Closure_Otrancl @ SV1960 @ SV1633 ) @ ( tc_prod @ SV1633 @ SV1633 ) )
| ~ ( c_in @ ( c_Pair @ SV601 @ SY5873 @ SV1633 @ SV1633 ) @ ( c_Transitive__Closure_Otrancl @ SV1960 @ SV1633 ) @ ( tc_prod @ SV1633 @ SV1633 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4139]) ).
thf(4676,plain,
! [SV1961: $i,SV1634: $i,SV1204: $i,SV604: $i] :
( ( ( c_in @ ( c_Pair @ SV604 @ SV1204 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omktop @ SV1634 ) @ SV1961 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV604 @ SV1204 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1634 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV604 = SV1204 )
| ( SV604 = SV1961 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4140]) ).
thf(4677,plain,
! [SV1962: $i,SV1635: $i,SV1205: $i,SV605: $i] :
( ( ( c_in @ ( c_Pair @ SV605 @ SV1205 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omktop @ SV1635 ) @ SV1962 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV605 @ SV1205 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1635 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV1205 = SV1962 )
| ( SV605 = SV1962 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4141]) ).
thf(4678,plain,
! [SV1636: $i,SV1207: $i,SV607: $i] :
( ( c_in @ ( c_Pair @ SV607 @ SV1207 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omktop @ SV1636 ) @ SV607 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4143]) ).
thf(4679,plain,
! [SV1637: $i,SV1208: $i,SV608: $i] :
( ( ( c_in @ ( c_Pair @ SV608 @ SV1208 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1637 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( ! [SY5615: $i] :
( ( SV1208 = SY5615 )
| ~ ( c_in @ ( c_Pair @ SV608 @ SV1208 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omktop @ SV1637 ) @ SY5615 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4144]) ).
thf(4680,plain,
! [SV609: $i,SV1209: $i] :
( ( ( SV1209 = SV609 )
= $true )
| ( ( ! [SY5082: $i] : ( c_in @ ( c_Pair @ SV609 @ SV1209 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omkbot @ SY5082 ) @ SV609 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( SV609 = SV1209 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4145]) ).
thf(4681,plain,
! [SV1638: $i,SV1211: $i,SV611: $i] :
( ( c_in @ ( c_Pair @ SV611 @ SV1211 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omkbot @ SV1638 ) @ SV1211 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4147]) ).
thf(4682,plain,
! [SV1963: $i,SV1639: $i,SV1212: $i,SV612: $i] :
( ( ( c_in @ ( c_Pair @ SV612 @ SV1212 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omkbot @ SV1639 ) @ SV1963 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV612 @ SV1212 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1639 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV612 = SV1212 )
| ( SV1212 = SV1963 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4148]) ).
thf(4683,plain,
! [SV1964: $i,SV1640: $i,SV1213: $i,SV613: $i] :
( ( ( c_in @ ( c_Pair @ SV613 @ SV1213 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omkbot @ SV1640 ) @ SV1964 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ SV613 @ SV1213 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1640 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV613 = SV1964 )
| ( SV1213 = SV1964 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4149]) ).
thf(4684,plain,
! [SV1214: $i,SV614: $i] :
( ( ( SV614 = SV1214 )
= $true )
| ( ( ! [SY5088: $i] : ( c_in @ ( c_Pair @ SV614 @ SV1214 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omktop @ SY5088 ) @ SV1214 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( SV614 = SV1214 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4150]) ).
thf(4685,plain,
! [SV1641: $i,SV1215: $i,SV615: $i] :
( ( ( c_in @ ( c_Pair @ SV615 @ SV1215 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1641 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( ! [SY5618: $i] :
( ( SV615 = SY5618 )
| ~ ( c_in @ ( c_Pair @ SV615 @ SV1215 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omkbot @ SV1641 ) @ SY5618 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4151]) ).
thf(4686,plain,
! [SV1965: $i,SV1642: $i,SV1217: $i,SV617: $i] :
( ( ! [SY5874: $i,SY5875: $i] :
( ( c_in @ ( c_Pair @ SV617 @ SV1217 @ SV1642 @ SV1965 ) @ ( c_Product__Type_OSigma @ SY5874 @ SY5875 @ SV1642 @ SV1965 ) @ ( tc_prod @ SV1642 @ SV1965 ) )
| ~ ( c_in @ SV1217 @ ( hAPP @ SY5875 @ SV617 ) @ SV1965 )
| ~ ( c_in @ SV617 @ SY5874 @ SV1642 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4153]) ).
thf(4687,plain,
! [SV1966: $i,SV1643: $i,SV1218: $i,SV618: $i] :
( ( ! [SY5876: $i,SY5877: $i] :
( ( c_in @ ( c_Pair @ SV618 @ SV1218 @ SV1643 @ SV1966 ) @ ( c_Product__Type_OSigma @ SY5876 @ SY5877 @ SV1643 @ SV1966 ) @ ( tc_prod @ SV1643 @ SV1966 ) )
| ~ ( c_in @ SV1218 @ ( hAPP @ SY5877 @ SV618 ) @ SV1966 )
| ~ ( c_in @ SV618 @ SY5876 @ SV1643 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4154]) ).
thf(4688,plain,
! [SV1644: $i,SV1219: $i,SV619: $i] :
( ( ( c_in @ SV619 @ ( c_Wellfounded_Oacc @ SV1219 @ SV1644 ) @ SV1644 )
= $true )
| ( ( ! [SY5625: $i] :
( ~ ( c_in @ ( c_Pair @ SV619 @ SY5625 @ SV1644 @ SV1644 ) @ SV1219 @ ( tc_prod @ SV1644 @ SV1644 ) )
| ~ ( c_in @ SY5625 @ ( c_Wellfounded_Oacc @ SV1219 @ SV1644 ) @ SV1644 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4155]) ).
thf(4689,plain,
! [SV1645: $i,SV1220: $i,SV620: $i] :
( ( ( c_in @ SV620 @ ( c_Wellfounded_Oacc @ SV1220 @ SV1645 ) @ SV1645 )
= $true )
| ( ( ! [SY5626: $i] :
( ~ ( c_in @ ( c_Pair @ SV620 @ SY5626 @ SV1645 @ SV1645 ) @ SV1220 @ ( tc_prod @ SV1645 @ SV1645 ) )
| ~ ( c_in @ SY5626 @ ( c_Wellfounded_Oacc @ SV1220 @ SV1645 ) @ SV1645 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4156]) ).
thf(4690,plain,
! [SV1967: $i,SV1646: $i,SV1221: $i,SV621: $i] :
( ( ! [SY5878: $i] :
( ( c_in @ SV621 @ ( c_Relation_OImage @ SV1221 @ SV1646 @ SV1967 @ SY5878 ) @ SY5878 )
| ! [SY5879: $i] :
( ~ ( c_in @ ( c_Pair @ SY5879 @ SV621 @ SV1967 @ SY5878 ) @ SV1221 @ ( tc_prod @ SV1967 @ SY5878 ) )
| ~ ( c_in @ SY5879 @ SV1646 @ SV1967 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4157]) ).
thf(4691,plain,
! [SV1968: $i,SV1647: $i,SV1222: $i,SV622: $i] :
( ( ! [SY5880: $i] :
( ( c_in @ SV622 @ ( c_Relation_OImage @ SV1222 @ SV1647 @ SV1968 @ SY5880 ) @ SY5880 )
| ! [SY5881: $i] :
( ~ ( c_in @ ( c_Pair @ SY5881 @ SV622 @ SV1968 @ SY5880 ) @ SV1222 @ ( tc_prod @ SV1968 @ SY5880 ) )
| ~ ( c_in @ SY5881 @ SV1647 @ SV1968 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4158]) ).
thf(4692,plain,
! [SV1648: $i,SV1223: $i,SV623: $i] :
( ( ( c_in @ SV623 @ SV1223 @ SV1648 )
= $true )
| ( ( ! [SY5633: $i] :
~ ( c_in @ ( c_Pair @ SV623 @ SY5633 @ SV1648 @ SV1648 ) @ ( c_Relation_OId__on @ SV1223 @ SV1648 ) @ ( tc_prod @ SV1648 @ SV1648 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4159]) ).
thf(4693,plain,
! [SV1649: $i,SV1224: $i,SV624: $i] :
( ( ( c_in @ ( c_Pair @ SV624 @ SV624 @ SV1224 @ SV1224 ) @ ( c_Relation_OId__on @ SV1649 @ SV1224 ) @ ( tc_prod @ SV1224 @ SV1224 ) )
= $true )
| ( ( ~ ( c_in @ SV624 @ SV1649 @ SV1224 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4160]) ).
thf(4694,plain,
! [SV1650: $i,SV1225: $i,SV625: $i] :
( ( ( c_in @ SV625 @ SV1225 @ SV1650 )
= $true )
| ( ( ! [SY5634: $i,SY5635: $i] :
( ~ ( c_in @ ( c_Pair @ SY5634 @ SV625 @ SV1650 @ SV1650 ) @ SY5635 @ ( tc_prod @ SV1650 @ SV1650 ) )
| ~ ( c_Equiv__Relations_Oequiv @ SV1225 @ SY5635 @ SV1650 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4161]) ).
thf(4695,plain,
! [SV1651: $i,SV1226: $i,SV626: $i] :
( ( ( c_in @ SV626 @ SV1226 @ SV1651 )
= $true )
| ( ( ! [SY5636: $i,SY5637: $i] :
( ~ ( c_in @ ( c_Pair @ SV626 @ SY5636 @ SV1651 @ SV1651 ) @ SY5637 @ ( tc_prod @ SV1651 @ SV1651 ) )
| ~ ( c_Equiv__Relations_Oequiv @ SV1226 @ SY5637 @ SV1651 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4162]) ).
thf(4696,plain,
! [SV1969: $i,SV1652: $i,SV1227: $i,SV627: $i] :
( ( ( c_in @ SV627 @ ( c_Relation_ORange @ SV1227 @ SV1652 @ SV1969 ) @ SV1969 )
| ! [SY5882: $i] :
~ ( c_in @ ( c_Pair @ SY5882 @ SV627 @ SV1652 @ SV1969 ) @ SV1227 @ ( tc_prod @ SV1652 @ SV1969 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4163]) ).
thf(4697,plain,
! [SV1970: $i,SV1653: $i,SV1228: $i,SV628: $i] :
( ( ( c_in @ SV628 @ ( c_Relation_ORange @ SV1228 @ SV1653 @ SV1970 ) @ SV1970 )
| ! [SY5883: $i] :
~ ( c_in @ ( c_Pair @ SY5883 @ SV628 @ SV1653 @ SV1970 ) @ SV1228 @ ( tc_prod @ SV1653 @ SV1970 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4164]) ).
thf(4698,plain,
! [SV1971: $i,SV1654: $i,SV1229: $i,SV629: $i] :
( ( ( c_in @ SV629 @ ( c_Relation_ODomain @ SV1229 @ SV1654 @ SV1971 ) @ SV1654 )
| ! [SY5884: $i] :
~ ( c_in @ ( c_Pair @ SV629 @ SY5884 @ SV1654 @ SV1971 ) @ SV1229 @ ( tc_prod @ SV1654 @ SV1971 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4165]) ).
thf(4699,plain,
! [SV1972: $i,SV1655: $i,SV1230: $i,SV630: $i] :
( ( ( c_in @ SV630 @ ( c_Relation_ODomain @ SV1230 @ SV1655 @ SV1972 ) @ SV1655 )
| ! [SY5885: $i] :
~ ( c_in @ ( c_Pair @ SV630 @ SY5885 @ SV1655 @ SV1972 ) @ SV1230 @ ( tc_prod @ SV1655 @ SV1972 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4166]) ).
thf(4700,plain,
! [SV1973: $i,SV1656: $i,SV1231: $i,SV631: $i] :
( ( ( c_in @ SV631 @ ( hAPP @ SV1231 @ SV1656 ) @ SV1973 )
| ! [SY5886: $i,SY5887: $i] :
~ ( c_in @ ( c_Pair @ SV1656 @ SV631 @ SY5886 @ SV1973 ) @ ( c_Product__Type_OSigma @ SY5887 @ SV1231 @ SY5886 @ SV1973 ) @ ( tc_prod @ SY5886 @ SV1973 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4167]) ).
thf(4701,plain,
! [SV1974: $i,SV1657: $i,SV1232: $i,SV632: $i] :
( ( ( c_in @ SV632 @ SV1232 @ SV1657 )
| ! [SY5888: $i,SY5889: $i] :
~ ( c_in @ ( c_Pair @ SV632 @ SV1974 @ SV1657 @ SY5888 ) @ ( c_Product__Type_OSigma @ SV1232 @ SY5889 @ SV1657 @ SY5888 ) @ ( tc_prod @ SV1657 @ SY5888 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4168]) ).
thf(4702,plain,
! [SV1975: $i,SV1658: $i,SV1233: $i,SV633: $i] :
( ( ( c_in @ ( c_Pair @ SV633 @ SV1233 @ SV1658 @ SV1658 ) @ SV1975 @ ( tc_prod @ SV1658 @ SV1658 ) )
| ( c_in @ ( c_Pair @ SV1233 @ SV633 @ SV1658 @ SV1658 ) @ SV1975 @ ( tc_prod @ SV1658 @ SV1658 ) )
| ( SV1233 = SV633 )
| ! [SY5890: $i] :
( ~ ( c_in @ SV633 @ SY5890 @ SV1658 )
| ~ ( c_in @ SV1233 @ SY5890 @ SV1658 )
| ~ ( c_Relation_Ototal__on @ SY5890 @ SV1975 @ SV1658 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4169]) ).
thf(4703,plain,
! [SV1659: $i,SV1234: $i,SV634: $i] :
( ( ( c_in @ ( c_Pair @ SV634 @ SV634 @ SV1234 @ SV1234 ) @ SV1659 @ ( tc_prod @ SV1234 @ SV1234 ) )
= $true )
| ( ( ! [SY5654: $i] :
( ~ ( c_in @ SV634 @ SY5654 @ SV1234 )
| ~ ( c_Relation_Orefl__on @ SY5654 @ SV1659 @ SV1234 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4170]) ).
thf(4704,plain,
! [SV1660: $i,SV1235: $i,SV635: $i] :
( ( ( c_in @ SV635 @ SV1235 @ SV1660 )
= $true )
| ( ( ! [SY5655: $i,SY5656: $i] :
( ~ ( c_in @ ( c_Pair @ SY5655 @ SV635 @ SV1660 @ SV1660 ) @ SY5656 @ ( tc_prod @ SV1660 @ SV1660 ) )
| ~ ( c_Relation_Orefl__on @ SV1235 @ SY5656 @ SV1660 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4171]) ).
thf(4705,plain,
! [SV1661: $i,SV1236: $i,SV636: $i] :
( ( ( c_in @ SV636 @ SV1236 @ SV1661 )
= $true )
| ( ( ! [SY5657: $i,SY5658: $i] :
( ~ ( c_in @ ( c_Pair @ SV636 @ SY5657 @ SV1661 @ SV1661 ) @ SY5658 @ ( tc_prod @ SV1661 @ SV1661 ) )
| ~ ( c_Relation_Orefl__on @ SV1236 @ SY5658 @ SV1661 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4172]) ).
thf(4706,plain,
! [SV1662: $i,SV1237: $i,SV637: $i] :
( ( ( c_in @ ( c_Pair @ SV637 @ SV637 @ SV1237 @ SV1237 ) @ SV1662 @ ( tc_prod @ SV1237 @ SV1237 ) )
= $true )
| ( ( ! [SY5659: $i] :
( ~ ( c_in @ SV637 @ SY5659 @ SV1237 )
| ~ ( c_Relation_Orefl__on @ SY5659 @ SV1662 @ SV1237 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4173]) ).
thf(4707,plain,
! [SV1976: $i,SV1663: $i,SV1238: $i,SV638: $i] :
( ( ! [SY5891: $i,SY5892: $i] :
( ( ( c_Pair @ SV638 @ SV1238 @ SV1663 @ SV1976 )
!= ( c_Pair @ SY5891 @ SY5892 @ SV1663 @ SV1976 ) )
| ( SV1238 = SY5892 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4174]) ).
thf(4708,plain,
! [SV1977: $i,SV1664: $i,SV1239: $i,SV639: $i] :
( ( ! [SY5893: $i] :
( ! [SY5894: $i] :
( ( c_Pair @ SV639 @ SV1239 @ SV1664 @ SV1977 )
!= ( c_Pair @ SY5893 @ SY5894 @ SV1664 @ SV1977 ) )
| ( SV639 = SY5893 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4175]) ).
thf(4709,plain,
! [SV1978: $i,SV1240: $i,SV640: $i] :
( ( ( c_in @ SV640 @ SV1240 @ SV1978 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV1240 @ SV640 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4176]) ).
thf(4710,plain,
! [SV1979: $i,SV641: $i,SV1241: $i] :
( ( ( ~ ( c_in @ SV1241 @ SV641 @ SV1979 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV641 @ SV1241 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4177]) ).
thf(4711,plain,
! [SV642: $i,SV1242: $i] :
( ( ( class_Lattices_Olattice @ SV1242 )
= $false )
| ( ( class_Lattices_Oupper__semilattice @ ( tc_fun @ SV642 @ SV1242 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4178]) ).
thf(4712,plain,
! [SV643: $i,SV1243: $i] :
( ( ( class_Lattices_Olattice @ SV1243 )
= $false )
| ( ( class_Lattices_Olower__semilattice @ ( tc_fun @ SV643 @ SV1243 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4179]) ).
thf(4713,plain,
! [SV644: $i,SV1244: $i] :
( ( ( class_Lattices_Odistrib__lattice @ SV1244 )
= $false )
| ( ( class_Lattices_Odistrib__lattice @ ( tc_fun @ SV644 @ SV1244 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4180]) ).
thf(4714,plain,
! [SV645: $i,SV1245: $i] :
( ( ( class_Lattices_Obounded__lattice @ SV1245 )
= $false )
| ( ( class_Lattices_Obounded__lattice @ ( tc_fun @ SV645 @ SV1245 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4181]) ).
thf(4715,plain,
! [SV646: $i,SV1246: $i] :
( ( ( class_Orderings_Opreorder @ SV1246 )
= $false )
| ( ( class_Orderings_Opreorder @ ( tc_fun @ SV646 @ SV1246 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4182]) ).
thf(4716,plain,
! [SV647: $i,SV1247: $i] :
( ( ( class_Lattices_Olattice @ SV1247 )
= $false )
| ( ( class_Lattices_Olattice @ ( tc_fun @ SV647 @ SV1247 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4183]) ).
thf(4717,plain,
! [SV648: $i,SV1248: $i] :
( ( ( class_Orderings_Oorder @ SV1248 )
= $false )
| ( ( class_Orderings_Oorder @ ( tc_fun @ SV648 @ SV1248 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4184]) ).
thf(4718,plain,
! [SV649: $i,SV1249: $i] :
( ( ( class_Orderings_Obot @ SV1249 )
= $false )
| ( ( class_Orderings_Obot @ ( tc_fun @ SV649 @ SV1249 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4185]) ).
thf(4719,plain,
! [SV650: $i,SV1250: $i] :
( ( ( class_HOL_Oord @ SV1250 )
= $false )
| ( ( class_HOL_Oord @ ( tc_fun @ SV650 @ SV1250 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4186]) ).
thf(4720,plain,
! [SV1252: $i,SV652: $i,SV1980: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ SV1980 ) @ SV652 ) @ SV1252 ) ) )
= $true )
| ( ( SV652 = SV1252 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4187]) ).
thf(4721,plain,
! [SV1673: $i,SV1261: $i,SV663: $i,SV12: $i] :
( ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV12 @ tc_bool ) )
!= ( c_Set_Oimage @ SV663 @ SV1261 @ SV1673 @ SV12 ) )
= $true )
| ( ( SV1261
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1673 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4197]) ).
thf(4722,plain,
! [SV1674: $i,SV1263: $i,SV665: $i,SV14: $i] :
( ( ( ( hAPP @ ( c_snd @ SV14 @ SV665 ) @ SV1263 )
!= ( hAPP @ ( c_snd @ SV14 @ SV665 ) @ SV1674 ) )
= $true )
| ( ( ( ( hAPP @ ( c_fst @ SV14 @ SV665 ) @ SV1263 )
!= ( hAPP @ ( c_fst @ SV14 @ SV665 ) @ SV1674 ) )
| ( SV1263 = SV1674 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4198]) ).
thf(4723,plain,
! [SV1675: $i,SV1264: $i,SV666: $i,SV15: $i] :
( ( ( ( hAPP @ ( c_snd @ SV15 @ SV666 ) @ SV1264 )
!= ( hAPP @ ( c_snd @ SV15 @ SV666 ) @ SV1675 ) )
= $true )
| ( ( ( ( hAPP @ ( c_fst @ SV15 @ SV666 ) @ SV1264 )
!= ( hAPP @ ( c_fst @ SV15 @ SV666 ) @ SV1675 ) )
| ( SV1264 = SV1675 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4199]) ).
thf(4724,plain,
! [SV667: $i,SV1981: $i,SV1676: $i,SV16: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV16 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1 @ SV16 @ SV1676 @ SV1981 ) ) )
| ~ ( c_Wellfounded_Owf @ SV1676 @ SV1981 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV16 @ SV667 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4200]) ).
thf(4725,plain,
! [SV1678: $i,SV1266: $i,SV669: $i,SV18: $i] :
( ( ( c_lessequals @ SV18 @ ( c_Set_Oinsert @ SV669 @ SV1266 @ SV1678 ) @ ( tc_fun @ SV1678 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV18 @ SV1266 @ ( tc_fun @ SV1678 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4202]) ).
thf(4726,plain,
! [SV670: $i,SV1267: $i,SV19: $i,SV1982: $i] :
( ( ( ~ ( c_lessequals @ ( c_Set_Oinsert @ SV1982 @ SV19 @ SV1267 ) @ SV670 @ ( tc_fun @ SV1267 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV19 @ SV670 @ ( tc_fun @ SV1267 @ tc_bool ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4203]) ).
thf(4727,plain,
! [SV1679: $i,SV1268: $i,SV671: $i,SV20: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ SV20 @ SV671 @ SV1268 ) @ SV1679 @ ( tc_fun @ SV1268 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ SV671 @ SV1679 @ ( tc_fun @ SV1268 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_in @ SV20 @ SV1679 @ SV1268 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4204]) ).
thf(4728,plain,
! [SV1983: $i,SV1680: $i,SV1269: $i,SV672: $i,SV21: $i] :
( ( ( c_lessequals @ ( c_Product__Type_OSigma @ SV21 @ ( c_COMBK @ SV672 @ ( tc_fun @ SV1269 @ tc_bool ) @ SV1680 ) @ SV1680 @ SV1269 ) @ ( c_Product__Type_OSigma @ SV1983 @ ( c_COMBK @ SV672 @ ( tc_fun @ SV1269 @ tc_bool ) @ SV1680 ) @ SV1680 @ SV1269 ) @ ( tc_fun @ ( tc_prod @ SV1680 @ SV1269 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV21 @ SV1983 @ ( tc_fun @ SV1680 @ tc_bool ) )
| ! [SY5180: $i] :
~ ( c_in @ SY5180 @ SV672 @ SV1269 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4205]) ).
thf(4729,plain,
! [SV1681: $i,SV1270: $i,SV673: $i,SV22: $i] :
( ( ( c_lessequals @ SV22 @ SV673 @ ( tc_fun @ SV1270 @ tc_bool ) )
= $true )
| ( ( ! [SY5669: $i] :
( ~ ( c_lessequals @ ( c_Product__Type_OSigma @ SV22 @ ( c_COMBK @ SV1681 @ ( tc_fun @ SY5669 @ tc_bool ) @ SV1270 ) @ SV1270 @ SY5669 ) @ ( c_Product__Type_OSigma @ SV673 @ ( c_COMBK @ SV1681 @ ( tc_fun @ SY5669 @ tc_bool ) @ SV1270 ) @ SV1270 @ SY5669 ) @ ( tc_fun @ ( tc_prod @ SV1270 @ SY5669 ) @ tc_bool ) )
| ! [SY5670: $i] :
~ ( c_in @ SY5670 @ SV1681 @ SY5669 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4206]) ).
thf(4730,plain,
! [SV1682: $i,SV1271: $i,SV674: $i,SV23: $i] :
( ( ( c_lessequals @ SV23 @ ( c_Set_Oinsert @ SV674 @ SV1271 @ SV1682 ) @ ( tc_fun @ SV1682 @ tc_bool ) )
= $true )
| ( ( ~ ( c_in @ SV674 @ SV23 @ SV1682 )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV23 @ ( c_Set_Oinsert @ SV674 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1682 @ tc_bool ) ) @ SV1682 ) @ ( tc_fun @ SV1682 @ tc_bool ) ) @ SV1271 @ ( tc_fun @ SV1682 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4207]) ).
thf(4731,plain,
! [SV1683: $i,SV1272: $i,SV675: $i,SV24: $i] :
( ( ( c_lessequals @ SV24 @ ( c_Set_Oinsert @ SV675 @ SV1272 @ SV1683 ) @ ( tc_fun @ SV1683 @ tc_bool ) )
= $true )
| ( ( ~ ( c_in @ SV675 @ SV24 @ SV1683 )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV24 @ ( c_Set_Oinsert @ SV675 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1683 @ tc_bool ) ) @ SV1683 ) @ ( tc_fun @ SV1683 @ tc_bool ) ) @ SV1272 @ ( tc_fun @ SV1683 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4208]) ).
thf(4732,plain,
! [SV1684: $i,SV1273: $i,SV676: $i,SV25: $i] :
( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV25 @ ( c_Set_Oinsert @ SV676 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1273 @ tc_bool ) ) @ SV1273 ) @ ( tc_fun @ SV1273 @ tc_bool ) ) @ SV1684 @ ( tc_fun @ SV1273 @ tc_bool ) )
= $true )
| ( ( ~ ( c_in @ SV676 @ SV25 @ SV1273 )
| ~ ( c_lessequals @ SV25 @ ( c_Set_Oinsert @ SV676 @ SV1684 @ SV1273 ) @ ( tc_fun @ SV1273 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4209]) ).
thf(4733,plain,
! [SV1685: $i,SV1274: $i,SV677: $i,SV26: $i] :
( ( ( ( c_Set_Oimage @ ( c_COMBK @ SV26 @ SV677 @ SV1274 ) @ SV1685 @ SV1274 @ SV677 )
= ( c_Set_Oinsert @ SV26 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV677 @ tc_bool ) ) @ SV677 ) )
= $true )
| ( ( ! [SY5671: $i] :
~ ( c_in @ SY5671 @ SV1685 @ SV1274 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4210]) ).
thf(4734,plain,
! [SV1275: $i,SV678: $i,SV27: $i] :
( ( ( ~ ( c_lessequals @ ( c_Relation_Orel__comp @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Transitive__Closure_Otrancl @ SV27 @ SV678 ) @ SV1275 @ ( tc_fun @ ( tc_prod @ SV678 @ SV678 ) @ tc_bool ) ) @ SV27 @ SV678 @ SV678 @ SV678 ) @ SV1275 @ ( tc_fun @ ( tc_prod @ SV678 @ SV678 ) @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV27 @ SV1275 @ ( tc_fun @ ( tc_prod @ SV678 @ SV678 ) @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( c_Transitive__Closure_Otrancl @ SV27 @ SV678 ) @ SV1275 @ ( tc_fun @ ( tc_prod @ SV678 @ SV678 ) @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4211]) ).
thf(4735,plain,
! [SV1984: $i,SV1686: $i,SV1276: $i,SV679: $i,SV28: $i] :
( ( ( c_Product__Type_OSigma @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV28 @ SV679 @ ( tc_fun @ SV1276 @ tc_bool ) ) @ SV1686 @ SV1276 @ SV1984 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Product__Type_OSigma @ SV28 @ SV1686 @ SV1276 @ SV1984 ) @ ( c_Product__Type_OSigma @ SV679 @ SV1686 @ SV1276 @ SV1984 ) @ ( tc_fun @ ( tc_prod @ SV1276 @ SV1984 ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4212]) ).
thf(4736,plain,
! [SV1687: $i,SV680: $i,SV29: $i] :
( ( ( c_in @ SV29 @ ( c_Set_Oinsert @ SV680 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1687 @ tc_bool ) ) @ SV1687 ) @ SV1687 )
= $false )
| ( ( SV29 = SV680 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4213]) ).
thf(4737,plain,
! [SV1277: $i,SV681: $i,SV30: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV30 @ SV681 @ ( tc_fun @ SV1277 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1277 @ tc_bool ) ) )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV30 @ SV681 @ ( tc_fun @ SV1277 @ tc_bool ) )
= SV30 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4214]) ).
thf(4738,plain,
! [SV34: $i,SV1985: $i,SV685: $i] :
( ( ( ! [SY5896: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV685 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1985 @ SY5896 @ SV34 ) @ SV34 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV685 @ SV1985 @ SV34 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV685 @ SY5896 @ SV34 ) @ SV34 ) ) )
= $true )
| ( ( class_Lattices_Odistrib__lattice @ SV34 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4218]) ).
thf(4739,plain,
! [SV35: $i,SV1986: $i,SV686: $i] :
( ( ( ! [SY5897: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV686 @ SV1986 @ SV35 ) @ SY5897 @ SV35 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV686 @ SY5897 @ SV35 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1986 @ SY5897 @ SV35 ) @ SV35 ) ) )
= $true )
| ( ( class_Lattices_Odistrib__lattice @ SV35 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4219]) ).
thf(4740,plain,
! [SV1281: $i,SV37: $i,SV688: $i] :
( ( ( c_Relation_Orefl__on @ SV688 @ SV37 @ SV1281 )
= $false )
| ( ( c_lessequals @ SV37 @ ( c_Product__Type_OSigma @ SV688 @ ( c_COMBK @ SV688 @ ( tc_fun @ SV1281 @ tc_bool ) @ SV1281 ) @ SV1281 @ SV1281 ) @ ( tc_fun @ ( tc_prod @ SV1281 @ SV1281 ) @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4220]) ).
thf(4741,plain,
! [SV1987: $i,SV1692: $i,SV1282: $i,SV690: $i,SV40: $i] :
( ( ! [SY5898: $i,SY5899: $i] :
( ( c_lessequals @ ( c_Relation_Orel__comp @ SV40 @ SV690 @ SV1282 @ SV1692 @ SV1987 ) @ ( c_Relation_Orel__comp @ SY5898 @ SY5899 @ SV1282 @ SV1692 @ SV1987 ) @ ( tc_fun @ ( tc_prod @ SV1282 @ SV1987 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV690 @ SY5899 @ ( tc_fun @ ( tc_prod @ SV1692 @ SV1987 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV40 @ SY5898 @ ( tc_fun @ ( tc_prod @ SV1282 @ SV1692 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4222]) ).
thf(4742,plain,
! [SV1988: $i,SV1693: $i,SV1283: $i,SV691: $i,SV41: $i] :
( ( ( c_Relation_OImage @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV41 @ SV691 @ ( tc_fun @ ( tc_prod @ SV1283 @ SV1693 ) @ tc_bool ) ) @ SV1988 @ SV1283 @ SV1693 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_OImage @ SV41 @ SV1988 @ SV1283 @ SV1693 ) @ ( c_Relation_OImage @ SV691 @ SV1988 @ SV1283 @ SV1693 ) @ ( tc_fun @ SV1693 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4223]) ).
thf(4743,plain,
! [SV1989: $i,SV1694: $i,SV1284: $i,SV692: $i,SV42: $i] :
( ( ( c_Relation_OImage @ SV42 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV692 @ SV1284 @ ( tc_fun @ SV1694 @ tc_bool ) ) @ SV1694 @ SV1989 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_OImage @ SV42 @ SV692 @ SV1694 @ SV1989 ) @ ( c_Relation_OImage @ SV42 @ SV1284 @ SV1694 @ SV1989 ) @ ( tc_fun @ SV1989 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4224]) ).
thf(4744,plain,
! [SV693: $i,SV1990: $i,SV1695: $i,SV43: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV43 @ ( c_List_Osko__Recdef__Xtfl__wf__induct__1__1 @ SV43 @ SV1695 @ SV1990 ) ) )
| ~ ( c_Wellfounded_Owf @ SV1695 @ SV1990 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV43 @ SV693 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4225]) ).
thf(4745,plain,
! [SV1991: $i,SV1698: $i,SV1291: $i,SV701: $i,SV51: $i] :
( ( ( c_lessequals @ ( c_Relation_OImage @ SV51 @ SV701 @ SV1291 @ SV1698 ) @ SV1991 @ ( tc_fun @ SV1698 @ tc_bool ) )
| ! [SY5900: $i] :
~ ( c_lessequals @ SV51 @ ( c_Product__Type_OSigma @ SY5900 @ ( c_COMBK @ SV1991 @ ( tc_fun @ SV1698 @ tc_bool ) @ SV1291 ) @ SV1291 @ SV1698 ) @ ( tc_fun @ ( tc_prod @ SV1291 @ SV1698 ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4228]) ).
thf(4746,plain,
! [SV52: $i,SV1992: $i,SV702: $i] :
( ( ( ! [SY5901: $i] :
( ( c_HOL_Ominus__class_Ominus @ SV702 @ SV1992 @ SV52 )
!= ( c_HOL_Ominus__class_Ominus @ SY5901 @ SY5901 @ SV52 ) )
| ( SV702 = SV1992 ) )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV52 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4229]) ).
thf(4747,plain,
! [SV1993: $i,SV53: $i,SV703: $i] :
( ( ( ! [SY5902: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV703 @ SV703 @ SV53 )
!= ( c_HOL_Ominus__class_Ominus @ SV1993 @ SY5902 @ SV53 ) )
| ( SV1993 = SY5902 ) ) )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV53 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4230]) ).
thf(4748,plain,
! [SV1994: $i,SV1699: $i,SV1293: $i,SV705: $i,SV55: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oimage @ SV55 @ SV705 @ SV1293 @ SV1699 ) @ ( c_Set_Oimage @ SV55 @ SV1994 @ SV1293 @ SV1699 ) @ ( tc_fun @ SV1699 @ tc_bool ) ) @ ( c_Set_Oimage @ SV55 @ ( c_HOL_Ominus__class_Ominus @ SV705 @ SV1994 @ ( tc_fun @ SV1293 @ tc_bool ) ) @ SV1293 @ SV1699 ) @ ( tc_fun @ SV1699 @ tc_bool ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4231]) ).
thf(4749,plain,
! [SV58: $i,SV1995: $i,SV708: $i] :
( ( ( ! [SY5903: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV708 @ SV1995 @ SV58 ) @ SY5903 @ SV58 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV708 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1995 @ SY5903 @ SV58 ) @ SV58 ) ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV58 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4234]) ).
thf(4750,plain,
! [SV59: $i,SV1996: $i,SV709: $i] :
( ( ( ! [SY5904: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV709 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1996 @ SY5904 @ SV59 ) @ SV59 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV1996 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV709 @ SY5904 @ SV59 ) @ SV59 ) ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV59 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4235]) ).
thf(4751,plain,
! [SV60: $i,SV1997: $i,SV710: $i] :
( ( ( ! [SY5905: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV710 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1997 @ SY5905 @ SV60 ) @ SV60 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV1997 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV710 @ SY5905 @ SV60 ) @ SV60 ) ) )
= $true )
| ( ( class_Lattices_Olattice @ SV60 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4236]) ).
thf(4752,plain,
! [SV61: $i,SV1998: $i,SV711: $i] :
( ( ( ! [SY5906: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV711 @ SV1998 @ SV61 ) @ SY5906 @ SV61 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV711 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1998 @ SY5906 @ SV61 ) @ SV61 ) ) )
= $true )
| ( ( class_Lattices_Olattice @ SV61 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4237]) ).
thf(4753,plain,
! [SV1296: $i,SV712: $i,SV62: $i] :
( ( ( c_lessequals @ SV62 @ SV712 @ ( tc_fun @ SV1296 @ tc_bool ) )
= $false )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV62 @ SV712 @ ( tc_fun @ SV1296 @ tc_bool ) )
= SV62 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4238]) ).
thf(4754,plain,
! [SV1297: $i,SV63: $i,SV713: $i] :
( ( ( c_lessequals @ SV713 @ SV63 @ ( tc_fun @ SV1297 @ tc_bool ) )
= $false )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV63 @ SV713 @ ( tc_fun @ SV1297 @ tc_bool ) )
= SV713 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4239]) ).
thf(4755,plain,
! [SV64: $i,SV1999: $i,SV1702: $i] :
( ( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV1702 @ SV1999 @ SV64 )
= SV1702 )
| ~ ( c_lessequals @ SV1702 @ SV1999 @ SV64 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV64 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4240]) ).
thf(4756,plain,
! [SV65: $i,SV2000: $i,SV1703: $i] :
( ( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV1703 @ SV2000 @ SV65 )
!= SV1703 )
| ( c_lessequals @ SV1703 @ SV2000 @ SV65 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV65 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4241]) ).
thf(4757,plain,
! [SV66: $i,SV2001: $i,SV1704: $i] :
( ( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV1704 @ SV2001 @ SV66 )
= SV2001 )
| ~ ( c_lessequals @ SV2001 @ SV1704 @ SV66 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV66 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4242]) ).
thf(4758,plain,
! [SV1705: $i,SV1298: $i,SV714: $i,SV67: $i] :
( ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV67 @ SV714 @ ( tc_fun @ SV1298 @ tc_bool ) ) @ SV1705 @ ( tc_fun @ SV1298 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV714 @ SV1705 @ ( tc_fun @ SV1298 @ tc_bool ) )
| ~ ( c_lessequals @ SV67 @ SV1705 @ ( tc_fun @ SV1298 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4243]) ).
thf(4759,plain,
! [SV1706: $i,SV1301: $i,SV717: $i,SV70: $i] :
( ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV70 @ SV717 @ ( tc_fun @ SV1301 @ tc_bool ) ) @ SV1706 @ ( tc_fun @ SV1301 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV717 @ SV1706 @ ( tc_fun @ SV1301 @ tc_bool ) )
| ~ ( c_lessequals @ SV70 @ SV1706 @ ( tc_fun @ SV1301 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4244]) ).
thf(4760,plain,
! [SV71: $i,SV2002: $i,SV718: $i] :
( ( ( ! [SY5907: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV718 @ SV2002 @ SV71 ) @ SY5907 @ SV71 )
| ~ ( c_lessequals @ SV2002 @ SY5907 @ SV71 )
| ~ ( c_lessequals @ SV718 @ SY5907 @ SV71 ) ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV71 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4245]) ).
thf(4761,plain,
! [SV72: $i,SV2003: $i,SV1707: $i] :
( ( ( c_lessequals @ SV1707 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1707 @ SV2003 @ SV72 ) @ SV72 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV72 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4246]) ).
thf(4762,plain,
! [SV73: $i,SV2004: $i,SV1708: $i] :
( ( ( c_lessequals @ SV1708 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV2004 @ SV1708 @ SV73 ) @ SV73 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV73 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4247]) ).
thf(4763,plain,
! [SV74: $i,SV2005: $i,SV719: $i] :
( ( ( ! [SY5908: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV719 @ SV2005 @ SV74 ) @ SY5908 @ SV74 )
| ~ ( c_lessequals @ SV2005 @ SY5908 @ SV74 )
| ~ ( c_lessequals @ SV719 @ SY5908 @ SV74 ) ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV74 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4248]) ).
thf(4764,plain,
! [SV75: $i,SV2006: $i,SV720: $i] :
( ( ( ! [SY5909: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV720 @ SV2006 @ SV75 ) @ SY5909 @ SV75 )
| ~ ( c_lessequals @ SV2006 @ SY5909 @ SV75 )
| ~ ( c_lessequals @ SV720 @ SY5909 @ SV75 ) ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV75 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4249]) ).
thf(4765,plain,
! [SV76: $i,SV2007: $i,SV1709: $i] :
( ( ( c_lessequals @ SV1709 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV2007 @ SV1709 @ SV76 ) @ SV76 )
= $true )
| ( ( class_Lattices_Olattice @ SV76 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4250]) ).
thf(4766,plain,
! [SV77: $i,SV2008: $i,SV1710: $i] :
( ( ( c_lessequals @ SV1710 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1710 @ SV2008 @ SV77 ) @ SV77 )
= $true )
| ( ( class_Lattices_Olattice @ SV77 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4251]) ).
thf(4767,plain,
! [SV79: $i,SV2009: $i,SV1711: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV1711 @ SV2009 @ SV79 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV2009 @ SV1711 @ SV79 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV79 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4252]) ).
thf(4768,plain,
! [SV80: $i,SV2010: $i,SV1712: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV1712 @ SV2010 @ SV80 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV2010 @ SV1712 @ SV80 ) )
= $true )
| ( ( class_Lattices_Olattice @ SV80 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4253]) ).
thf(4769,plain,
! [SV1303: $i,SV723: $i,SV82: $i] :
( ( ( c_lessequals @ SV82 @ SV723 @ ( tc_fun @ SV1303 @ tc_bool ) )
= $false )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV82 @ ( c_HOL_Ominus__class_Ominus @ SV723 @ SV82 @ ( tc_fun @ SV1303 @ tc_bool ) ) @ ( tc_fun @ SV1303 @ tc_bool ) )
= SV723 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4255]) ).
thf(4770,plain,
! [SV1713: $i,SV1304: $i,SV724: $i,SV83: $i] :
( ( ( c_lessequals @ ( c_Relation_OImage @ SV83 @ ( c_Set_Oinsert @ SV724 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1304 @ tc_bool ) ) @ SV1304 ) @ SV1304 @ SV1304 ) @ ( c_Relation_OImage @ SV83 @ ( c_Set_Oinsert @ SV1713 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1304 @ tc_bool ) ) @ SV1304 ) @ SV1304 @ SV1304 ) @ ( tc_fun @ SV1304 @ tc_bool ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV724 @ SV1713 @ SV1304 @ SV1304 ) @ SV83 @ ( tc_prod @ SV1304 @ SV1304 ) )
| ! [SY5214: $i] :
~ ( c_Equiv__Relations_Oequiv @ SY5214 @ SV83 @ SV1304 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4256]) ).
thf(4771,plain,
! [SV86: $i,SV727: $i,SV1714: $i] :
( ( ( SV1714 = SV727 )
= $true )
| ( ( ! [SY5692: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV1714 @ SV86 @ SY5692 ) @ SV727 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV86 @ SV727 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4257]) ).
thf(4772,plain,
! [SV2011: $i,SV1715: $i,SV1307: $i,SV728: $i,SV87: $i] :
( ( ( c_Relation_ODomain @ ( c_Set_Oinsert @ ( c_Pair @ SV87 @ SV728 @ SV1307 @ SV1715 ) @ SV2011 @ ( tc_prod @ SV1307 @ SV1715 ) ) @ SV1307 @ SV1715 )
= ( c_Set_Oinsert @ SV87 @ ( c_Relation_ODomain @ SV2011 @ SV1307 @ SV1715 ) @ SV1307 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4258]) ).
thf(4773,plain,
! [SV88: $i,SV1308: $i,SV729: $i] :
( ( ( ~ ( c_Relation_Osym @ SV729 @ SV1308 ) )
= $true )
| ( ( ~ ( c_Relation_Osym @ SV88 @ SV1308 ) )
= $true )
| ( ( c_Relation_Osym @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV88 @ SV729 @ ( tc_fun @ ( tc_prod @ SV1308 @ SV1308 ) @ tc_bool ) ) @ SV1308 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4259]) ).
thf(4774,plain,
! [SV730: $i,SV1309: $i,SV89: $i] :
( ( ( c_lessequals @ SV89 @ SV1309 @ ( tc_fun @ ( tc_prod @ SV730 @ SV730 ) @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( c_Transitive__Closure_Ortrancl @ SV89 @ SV730 ) @ ( c_Transitive__Closure_Ortrancl @ SV1309 @ SV730 ) @ ( tc_fun @ ( tc_prod @ SV730 @ SV730 ) @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4260]) ).
thf(4775,plain,
! [SV2012: $i,SV1719: $i,SV1312: $i,SV735: $i,SV96: $i] :
( ( c_lessequals @ ( c_Set_Oimage @ SV96 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV735 @ SV1312 @ ( tc_fun @ SV1719 @ tc_bool ) ) @ SV1719 @ SV2012 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oimage @ SV96 @ SV735 @ SV1719 @ SV2012 ) @ ( c_Set_Oimage @ SV96 @ SV1312 @ SV1719 @ SV2012 ) @ ( tc_fun @ SV2012 @ tc_bool ) ) @ ( tc_fun @ SV2012 @ tc_bool ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4264]) ).
thf(4776,plain,
! [SV2013: $i,SV1720: $i,SV1313: $i,SV736: $i,SV97: $i] :
( ( c_lessequals @ ( c_Relation_OImage @ SV97 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV736 @ SV1313 @ ( tc_fun @ SV1720 @ tc_bool ) ) @ SV1720 @ SV2013 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_OImage @ SV97 @ SV736 @ SV1720 @ SV2013 ) @ ( c_Relation_OImage @ SV97 @ SV1313 @ SV1720 @ SV2013 ) @ ( tc_fun @ SV2013 @ tc_bool ) ) @ ( tc_fun @ SV2013 @ tc_bool ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4265]) ).
thf(4777,plain,
! [SV1721: $i,SV1314: $i,SV737: $i,SV98: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV98 @ SV737 @ ( tc_fun @ SV1314 @ tc_bool ) ) @ SV1721 @ ( tc_fun @ SV1314 @ tc_bool ) )
!= ( c_Lattices_Olower__semilattice__class_Oinf @ SV98 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV737 @ SV1721 @ ( tc_fun @ SV1314 @ tc_bool ) ) @ ( tc_fun @ SV1314 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV1721 @ SV98 @ ( tc_fun @ SV1314 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4266]) ).
thf(4778,plain,
! [SV1722: $i,SV1315: $i,SV738: $i,SV99: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV99 @ SV738 @ ( tc_fun @ SV1315 @ tc_bool ) ) @ SV1722 @ ( tc_fun @ SV1315 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV99 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV738 @ SV1722 @ ( tc_fun @ SV1315 @ tc_bool ) ) @ ( tc_fun @ SV1315 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1722 @ SV99 @ ( tc_fun @ SV1315 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4267]) ).
thf(4779,plain,
! [SV2014: $i,SV1723: $i,SV1316: $i,SV739: $i,SV100: $i] :
( ( ( c_Product__Type_OSigma @ ( c_HOL_Ominus__class_Ominus @ SV100 @ SV739 @ ( tc_fun @ SV1316 @ tc_bool ) ) @ SV1723 @ SV1316 @ SV2014 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Product__Type_OSigma @ SV100 @ SV1723 @ SV1316 @ SV2014 ) @ ( c_Product__Type_OSigma @ SV739 @ SV1723 @ SV1316 @ SV2014 ) @ ( tc_fun @ ( tc_prod @ SV1316 @ SV2014 ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4268]) ).
thf(4780,plain,
! [SV2015: $i,SV1724: $i,SV1317: $i,SV742: $i,SV103: $i] :
( ( ! [SY5910: $i,SY5911: $i] :
( ( c_lessequals @ ( c_Relation_Orel__comp @ SV103 @ SV742 @ SV1317 @ SV1724 @ SV2015 ) @ ( c_Product__Type_OSigma @ SY5910 @ ( c_COMBK @ SY5911 @ ( tc_fun @ SV2015 @ tc_bool ) @ SV1317 ) @ SV1317 @ SV2015 ) @ ( tc_fun @ ( tc_prod @ SV1317 @ SV2015 ) @ tc_bool ) )
| ! [SY5912: $i] :
( ~ ( c_lessequals @ SV742 @ ( c_Product__Type_OSigma @ SY5912 @ ( c_COMBK @ SY5911 @ ( tc_fun @ SV2015 @ tc_bool ) @ SV1724 ) @ SV1724 @ SV2015 ) @ ( tc_fun @ ( tc_prod @ SV1724 @ SV2015 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV103 @ ( c_Product__Type_OSigma @ SY5910 @ ( c_COMBK @ SY5912 @ ( tc_fun @ SV1724 @ tc_bool ) @ SV1317 ) @ SV1317 @ SV1724 ) @ ( tc_fun @ ( tc_prod @ SV1317 @ SV1724 ) @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4269]) ).
thf(4781,plain,
! [SV1318: $i,SV743: $i,SV104: $i] :
( ( ( ~ ( c_lessequals @ ( c_Relation_Orel__comp @ SV104 @ SV743 @ SV1318 @ SV1318 @ SV1318 ) @ SV104 @ ( tc_fun @ ( tc_prod @ SV1318 @ SV1318 ) @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_Wellfounded_Owf @ SV743 @ SV1318 )
| ~ ( c_Wellfounded_Owf @ SV104 @ SV1318 ) )
= $true )
| ( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV104 @ SV743 @ ( tc_fun @ ( tc_prod @ SV1318 @ SV1318 ) @ tc_bool ) ) @ SV1318 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4270]) ).
thf(4782,plain,
! [SV105: $i,SV744: $i,SV1725: $i] :
( ( ( hBOOL @ ( hAPP @ SV1725 @ SV744 ) )
= $true )
| ( ( ! [SY5701: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1725 @ SV105 @ ( tc_fun @ SY5701 @ tc_bool ) ) @ SV744 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV105 @ SV744 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4271]) ).
thf(4783,plain,
! [SV1726: $i,SV1319: $i,SV745: $i,SV106: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV106 @ SV745 @ ( tc_fun @ SV1319 @ tc_bool ) ) @ SV1726 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV745 @ SV1726 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4272]) ).
thf(4784,plain,
! [SV1727: $i,SV1320: $i,SV746: $i,SV107: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV107 @ SV746 @ ( tc_fun @ SV1320 @ tc_bool ) ) @ SV1727 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV107 @ SV1727 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4273]) ).
thf(4785,plain,
! [SV1321: $i,SV747: $i,SV108: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_ODomain @ SV108 @ SV747 @ SV747 ) @ ( c_Relation_ORange @ SV1321 @ SV747 @ SV747 ) @ ( tc_fun @ SV747 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV747 @ tc_bool ) ) )
= $false )
| ( ( ~ ( c_Wellfounded_Owf @ SV1321 @ SV747 )
| ~ ( c_Wellfounded_Owf @ SV108 @ SV747 )
| ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV108 @ SV1321 @ ( tc_fun @ ( tc_prod @ SV747 @ SV747 ) @ tc_bool ) ) @ SV747 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4274]) ).
thf(4786,plain,
! [SV2016: $i,SV1728: $i,SV1322: $i,SV748: $i,SV109: $i] :
( ( ( c_Product__Type_OSigma @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV109 @ SV748 @ ( tc_fun @ SV1322 @ tc_bool ) ) @ ( c_COMBK @ SV1728 @ ( tc_fun @ SV2016 @ tc_bool ) @ SV1322 ) @ SV1322 @ SV2016 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Product__Type_OSigma @ SV109 @ ( c_COMBK @ SV1728 @ ( tc_fun @ SV2016 @ tc_bool ) @ SV1322 ) @ SV1322 @ SV2016 ) @ ( c_Product__Type_OSigma @ SV748 @ ( c_COMBK @ SV1728 @ ( tc_fun @ SV2016 @ tc_bool ) @ SV1322 ) @ SV1322 @ SV2016 ) @ ( tc_fun @ ( tc_prod @ SV1322 @ SV2016 ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4275]) ).
thf(4787,plain,
! [SV2017: $i,SV1729: $i,SV1323: $i,SV749: $i,SV110: $i] :
( ( ( c_Relation_Orefl__on @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV110 @ SV749 @ ( tc_fun @ SV1323 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1729 @ SV2017 @ ( tc_fun @ ( tc_prod @ SV1323 @ SV1323 ) @ tc_bool ) ) @ SV1323 )
| ~ ( c_Relation_Orefl__on @ SV749 @ SV2017 @ SV1323 )
| ~ ( c_Relation_Orefl__on @ SV110 @ SV1729 @ SV1323 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4276]) ).
thf(4788,plain,
! [SV111: $i,SV2018: $i,SV750: $i] :
( ( ( ! [SY5913: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV750 @ SV2018 @ SV111 ) @ SY5913 @ SV111 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV750 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2018 @ SY5913 @ SV111 ) @ SV111 ) ) )
= $true )
| ( ( class_Lattices_Olattice @ SV111 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4277]) ).
thf(4789,plain,
! [SV112: $i,SV2019: $i,SV751: $i] :
( ( ( ! [SY5914: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV751 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2019 @ SY5914 @ SV112 ) @ SV112 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV2019 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV751 @ SY5914 @ SV112 ) @ SV112 ) ) )
= $true )
| ( ( class_Lattices_Olattice @ SV112 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4278]) ).
thf(4790,plain,
! [SV113: $i,SV2020: $i,SV752: $i] :
( ( ( ! [SY5915: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV752 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2020 @ SY5915 @ SV113 ) @ SV113 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV2020 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV752 @ SY5915 @ SV113 ) @ SV113 ) ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV113 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4279]) ).
thf(4791,plain,
! [SV114: $i,SV2021: $i,SV753: $i] :
( ( ( ! [SY5916: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV753 @ SV2021 @ SV114 ) @ SY5916 @ SV114 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV753 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2021 @ SY5916 @ SV114 ) @ SV114 ) ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV114 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4280]) ).
thf(4792,plain,
! [SV2022: $i,SV1734: $i,SV1326: $i,SV759: $i,SV122: $i] :
( ( ! [SY5917: $i] :
( ( c_Product__Type_OSigma @ ( c_Set_Oinsert @ SV122 @ SV759 @ SV1326 ) @ ( c_COMBK @ ( c_Set_Oinsert @ SV1734 @ SV2022 @ SY5917 ) @ ( tc_fun @ SY5917 @ tc_bool ) @ SV1326 ) @ SV1326 @ SY5917 )
= ( c_Set_Oinsert @ ( c_Pair @ SV122 @ SV1734 @ SV1326 @ SY5917 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Product__Type_OSigma @ SV759 @ ( c_COMBK @ ( c_Set_Oinsert @ SV1734 @ SV2022 @ SY5917 ) @ ( tc_fun @ SY5917 @ tc_bool ) @ SV1326 ) @ SV1326 @ SY5917 ) @ ( c_Product__Type_OSigma @ ( c_Set_Oinsert @ SV122 @ SV759 @ SV1326 ) @ ( c_COMBK @ SV2022 @ ( tc_fun @ SY5917 @ tc_bool ) @ SV1326 ) @ SV1326 @ SY5917 ) @ ( tc_fun @ ( tc_prod @ SV1326 @ SY5917 ) @ tc_bool ) ) @ ( tc_prod @ SV1326 @ SY5917 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4285]) ).
thf(4793,plain,
! [SV760: $i,SV1735: $i,SV123: $i] :
( ( ( ~ ( c_lessequals @ SV123 @ ( c_Relation_OImage @ SV1735 @ SV123 @ SV760 @ SV760 ) @ ( tc_fun @ SV760 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_Wellfounded_Owf @ SV1735 @ SV760 ) )
= $true )
| ( ( SV123
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV760 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4286]) ).
thf(4794,plain,
! [SV1738: $i,SV1329: $i,SV764: $i,SV127: $i] :
( ( ( ( c_Set_Oimage @ ( c_COMBK @ SV127 @ SV764 @ SV1329 ) @ SV1738 @ SV1329 @ SV764 )
= ( c_Set_Oinsert @ SV127 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV764 @ tc_bool ) ) @ SV764 ) )
= $true )
| ( ( SV1738
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1329 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4289]) ).
thf(4795,plain,
! [SV2023: $i,SV1739: $i,SV1330: $i,SV765: $i,SV128: $i] :
( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV128 @ SV765 @ ( tc_fun @ SV1330 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV1739 @ SV2023 @ ( tc_fun @ SV1330 @ tc_bool ) ) @ ( tc_fun @ SV1330 @ tc_bool ) )
| ~ ( c_lessequals @ SV2023 @ SV765 @ ( tc_fun @ SV1330 @ tc_bool ) )
| ~ ( c_lessequals @ SV128 @ SV1739 @ ( tc_fun @ SV1330 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4290]) ).
thf(4796,plain,
! [SV1331: $i,SV766: $i,SV129: $i] :
( ( ( c_in @ SV129 @ SV766 @ SV1331 )
= $false )
| ( ( ! [SY5247: $i] :
( ~ ( c_in @ SV129 @ SY5247 @ SV1331 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SY5247 @ SV766 @ ( tc_fun @ SV1331 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1331 @ tc_bool ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4291]) ).
thf(4797,plain,
! [SV130: $i,SV1332: $i,SV767: $i] :
( ( ( ~ ( c_Relation_Otrans @ SV767 @ SV1332 ) )
= $true )
| ( ( ~ ( c_Relation_Otrans @ SV130 @ SV1332 ) )
= $true )
| ( ( c_Relation_Otrans @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV130 @ SV767 @ ( tc_fun @ ( tc_prod @ SV1332 @ SV1332 ) @ tc_bool ) ) @ SV1332 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4292]) ).
thf(4798,plain,
! [SV131: $i,SV2024: $i,SV768: $i] :
( ( ( ! [SY5918: $i] : ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV768 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2024 @ SY5918 @ SV131 ) @ SV131 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV768 @ SV2024 @ SV131 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV768 @ SY5918 @ SV131 ) @ SV131 ) @ SV131 ) )
= $true )
| ( ( class_Lattices_Olattice @ SV131 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4293]) ).
thf(4799,plain,
! [SV133: $i,SV2025: $i,SV1741: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1741 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1741 @ SV2025 @ SV133 ) @ SV133 )
= SV1741 )
= $true )
| ( ( class_Lattices_Olattice @ SV133 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4295]) ).
thf(4800,plain,
! [SV1334: $i,SV770: $i,SV134: $i] :
( ( ( ( c_Relation_Orel__comp @ SV134 @ SV770 @ SV1334 @ SV1334 @ SV1334 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV1334 @ SV1334 ) @ tc_bool ) ) )
= $false )
| ( ( ! [SY5249: $i] :
( ( ( c_Relation_Orel__comp @ SY5249 @ SV770 @ SV1334 @ SV1334 @ SV1334 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV1334 @ SV1334 ) @ tc_bool ) ) )
| ( ( c_Relation_Orel__comp @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY5249 @ SV134 @ ( tc_fun @ ( tc_prod @ SV1334 @ SV1334 ) @ tc_bool ) ) @ SV770 @ SV1334 @ SV1334 @ SV1334 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV1334 @ SV1334 ) @ tc_bool ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4296]) ).
thf(4801,plain,
! [SV1335: $i,SV771: $i,SV135: $i] :
( ( ( ( c_Relation_Orel__comp @ SV135 @ SV771 @ SV1335 @ SV1335 @ SV1335 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV1335 @ SV1335 ) @ tc_bool ) ) )
= $false )
| ( ( ! [SY5250: $i] :
( ( ( c_Relation_Orel__comp @ SV135 @ SY5250 @ SV1335 @ SV1335 @ SV1335 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV1335 @ SV1335 ) @ tc_bool ) ) )
| ( ( c_Relation_Orel__comp @ SV135 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY5250 @ SV771 @ ( tc_fun @ ( tc_prod @ SV1335 @ SV1335 ) @ tc_bool ) ) @ SV1335 @ SV1335 @ SV1335 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV1335 @ SV1335 ) @ tc_bool ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4297]) ).
thf(4802,plain,
! [SV772: $i,SV2026: $i,SV1742: $i,SV136: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV136 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1 @ SV136 @ SV1742 @ SV2026 ) ) )
| ~ ( c_Wellfounded_Owf @ SV1742 @ SV2026 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV136 @ SV772 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4298]) ).
thf(4803,plain,
! [SV1743: $i,SV139: $i,SV775: $i] :
( ( ( ~ ( c_lessequals @ SV775 @ SV139 @ ( tc_fun @ SV1743 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV139 @ SV775 @ ( tc_fun @ SV1743 @ tc_bool ) ) )
= $true )
| ( ( SV139 = SV775 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4301]) ).
thf(4804,plain,
! [SV1744: $i,SV140: $i,SV776: $i] :
( ( ( ~ ( c_lessequals @ SV776 @ SV140 @ ( tc_fun @ SV1744 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV140 @ SV776 @ ( tc_fun @ SV1744 @ tc_bool ) ) )
= $true )
| ( ( SV140 = SV776 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4302]) ).
thf(4805,plain,
! [SV141: $i,SV2027: $i,SV1745: $i] :
( ( ( ( SV1745 = SV2027 )
| ~ ( c_lessequals @ SV2027 @ SV1745 @ SV141 )
| ~ ( c_lessequals @ SV1745 @ SV2027 @ SV141 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV141 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4303]) ).
thf(4806,plain,
! [SV142: $i,SV2028: $i,SV1746: $i] :
( ( ( ( SV1746 = SV2028 )
| ~ ( c_lessequals @ SV2028 @ SV1746 @ SV142 )
| ~ ( c_lessequals @ SV1746 @ SV2028 @ SV142 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV142 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4304]) ).
thf(4807,plain,
! [SV2029: $i,SV1747: $i,SV1336: $i,SV777: $i,SV143: $i] :
( ( ( hAPP @ ( c_split @ SV143 @ SV777 @ SV1336 @ SV1747 ) @ SV2029 )
= ( hAPP @ ( hAPP @ SV143 @ ( hAPP @ ( c_fst @ SV777 @ SV1336 ) @ SV2029 ) ) @ ( hAPP @ ( c_snd @ SV777 @ SV1336 ) @ SV2029 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4305]) ).
thf(4808,plain,
! [SV144: $i,SV2030: $i,SV1748: $i] :
( ( ( ( SV1748 = SV2030 )
| ~ ( c_lessequals @ SV1748 @ SV2030 @ SV144 )
| ~ ( c_lessequals @ SV2030 @ SV1748 @ SV144 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV144 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4306]) ).
thf(4809,plain,
! [SV145: $i,SV2031: $i,SV1749: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV1749 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1749 @ SV2031 @ SV145 ) @ SV145 )
= SV1749 )
= $true )
| ( ( class_Lattices_Olattice @ SV145 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4307]) ).
thf(4810,plain,
! [SV147: $i,SV2032: $i,SV1750: $i] :
( ( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1750 @ SV2032 @ SV147 )
= SV1750 )
| ~ ( c_lessequals @ SV2032 @ SV1750 @ SV147 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV147 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4308]) ).
thf(4811,plain,
! [SV148: $i,SV2033: $i,SV1751: $i] :
( ( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1751 @ SV2033 @ SV148 )
!= SV2033 )
| ( c_lessequals @ SV1751 @ SV2033 @ SV148 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV148 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4309]) ).
thf(4812,plain,
! [SV149: $i,SV2034: $i,SV1752: $i] :
( ( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1752 @ SV2034 @ SV149 )
= SV2034 )
| ~ ( c_lessequals @ SV1752 @ SV2034 @ SV149 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV149 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4310]) ).
thf(4813,plain,
! [SV1338: $i,SV779: $i,SV150: $i] :
( ( ( c_lessequals @ SV150 @ SV779 @ ( tc_fun @ SV1338 @ tc_bool ) )
= $false )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV150 @ SV779 @ ( tc_fun @ SV1338 @ tc_bool ) )
= SV779 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4311]) ).
thf(4814,plain,
! [SV1339: $i,SV151: $i,SV780: $i] :
( ( ( c_lessequals @ SV780 @ SV151 @ ( tc_fun @ SV1339 @ tc_bool ) )
= $false )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV151 @ SV780 @ ( tc_fun @ SV1339 @ tc_bool ) )
= SV151 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4312]) ).
thf(4815,plain,
! [SV1340: $i,SV781: $i,SV152: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV152 @ SV781 @ ( tc_fun @ SV1340 @ tc_bool ) )
= SV781 )
= $false )
| ( ( c_lessequals @ SV152 @ SV781 @ ( tc_fun @ SV1340 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4313]) ).
thf(4816,plain,
! [SV2035: $i,SV1753: $i,SV1341: $i,SV782: $i,SV153: $i] :
( ( ( c_Relation_Orefl__on @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV153 @ SV782 @ ( tc_fun @ SV1341 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1753 @ SV2035 @ ( tc_fun @ ( tc_prod @ SV1341 @ SV1341 ) @ tc_bool ) ) @ SV1341 )
| ~ ( c_Relation_Orefl__on @ SV782 @ SV2035 @ SV1341 )
| ~ ( c_Relation_Orefl__on @ SV153 @ SV1753 @ SV1341 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4314]) ).
thf(4817,plain,
! [SV2036: $i,SV1754: $i,SV1342: $i,SV784: $i,SV156: $i] :
( ( ( ( c_Set_Oinsert @ SV156 @ ( c_Set_Oinsert @ SV784 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1342 @ tc_bool ) ) @ SV1342 ) @ SV1342 )
!= ( c_Set_Oinsert @ SV1754 @ ( c_Set_Oinsert @ SV2036 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1342 @ tc_bool ) ) @ SV1342 ) @ SV1342 ) )
| ( SV156 = SV2036 )
| ( SV156 = SV1754 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4315]) ).
thf(4818,plain,
! [SV1755: $i,SV1343: $i,SV785: $i,SV157: $i] :
( ( ( ! [SY5719: $i] :
( ( c_Set_Oinsert @ SV157 @ ( c_Set_Oinsert @ SV785 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1343 @ tc_bool ) ) @ SV1343 ) @ SV1343 )
!= ( c_Set_Oinsert @ SV1755 @ ( c_Set_Oinsert @ SY5719 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1343 @ tc_bool ) ) @ SV1343 ) @ SV1343 ) ) )
= $true )
| ( ( ( SV785 = SV1755 )
| ( SV157 = SV1755 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4316]) ).
thf(4819,plain,
! [SV2037: $i,SV1756: $i,SV1344: $i,SV786: $i,SV158: $i] :
( ( ( ( c_Set_Oinsert @ SV158 @ ( c_Set_Oinsert @ SV786 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1344 @ tc_bool ) ) @ SV1344 ) @ SV1344 )
!= ( c_Set_Oinsert @ SV1756 @ ( c_Set_Oinsert @ SV2037 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1344 @ tc_bool ) ) @ SV1344 ) @ SV1344 ) )
| ( SV158 = SV2037 )
| ( SV786 = SV2037 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4317]) ).
thf(4820,plain,
! [SV2038: $i,SV1757: $i,SV1345: $i,SV787: $i,SV159: $i] :
( ( ( ( c_Set_Oinsert @ SV159 @ ( c_Set_Oinsert @ SV787 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1345 @ tc_bool ) ) @ SV1345 ) @ SV1345 )
!= ( c_Set_Oinsert @ SV1757 @ ( c_Set_Oinsert @ SV2038 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1345 @ tc_bool ) ) @ SV1345 ) @ SV1345 ) )
| ( SV787 = SV1757 )
| ( SV787 = SV2038 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4318]) ).
thf(4821,plain,
! [SV788: $i,SV1346: $i,SV160: $i] :
( ( ( c_lessequals @ SV160 @ ( c_Product__Type_OSigma @ SV1346 @ ( c_COMBK @ SV1346 @ ( tc_fun @ SV788 @ tc_bool ) @ SV788 ) @ SV788 @ SV788 ) @ ( tc_fun @ ( tc_prod @ SV788 @ SV788 ) @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( c_Transitive__Closure_Otrancl @ SV160 @ SV788 ) @ ( c_Product__Type_OSigma @ SV1346 @ ( c_COMBK @ SV1346 @ ( tc_fun @ SV788 @ tc_bool ) @ SV788 ) @ SV788 @ SV788 ) @ ( tc_fun @ ( tc_prod @ SV788 @ SV788 ) @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4319]) ).
thf(4822,plain,
! [SV789: $i,SV1347: $i,SV161: $i] :
( ( ( c_lessequals @ SV161 @ ( c_Transitive__Closure_Ortrancl @ SV1347 @ SV789 ) @ ( tc_fun @ ( tc_prod @ SV789 @ SV789 ) @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( c_Transitive__Closure_Ortrancl @ SV161 @ SV789 ) @ ( c_Transitive__Closure_Ortrancl @ SV1347 @ SV789 ) @ ( tc_fun @ ( tc_prod @ SV789 @ SV789 ) @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4320]) ).
thf(4823,plain,
! [SV1758: $i,SV1349: $i,SV792: $i,SV166: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ SV166 @ SV792 @ SV1349 ) @ SV1758 @ ( tc_fun @ SV1349 @ tc_bool ) )
= ( c_Set_Oinsert @ SV166 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV792 @ SV1758 @ ( tc_fun @ SV1349 @ tc_bool ) ) @ SV1349 ) )
= $true )
| ( ( ~ ( c_in @ SV166 @ SV1758 @ SV1349 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4323]) ).
thf(4824,plain,
! [SV1759: $i,SV1350: $i,SV793: $i,SV167: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV167 @ ( c_Set_Oinsert @ SV793 @ SV1350 @ SV1759 ) @ ( tc_fun @ SV1759 @ tc_bool ) )
= ( c_Set_Oinsert @ SV793 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV167 @ SV1350 @ ( tc_fun @ SV1759 @ tc_bool ) ) @ SV1759 ) )
= $true )
| ( ( ~ ( c_in @ SV793 @ SV167 @ SV1759 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4324]) ).
thf(4825,plain,
! [SV2039: $i,SV1760: $i,SV1351: $i,SV794: $i,SV168: $i] :
( ( ( c_Set_Oimage @ SV168 @ ( c_Set_Oinsert @ SV794 @ SV1351 @ SV1760 ) @ SV1760 @ SV2039 )
= ( c_Set_Oinsert @ ( hAPP @ SV168 @ SV794 ) @ ( c_Set_Oimage @ SV168 @ SV1351 @ SV1760 @ SV2039 ) @ SV2039 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4325]) ).
thf(4826,plain,
! [SV2040: $i,SV1761: $i,SV1352: $i,SV796: $i,SV170: $i] :
( ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV170 @ SV796 @ ( tc_fun @ SV1352 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1761 @ SV2040 @ ( tc_fun @ SV1352 @ tc_bool ) ) @ ( tc_fun @ SV1352 @ tc_bool ) )
| ~ ( c_lessequals @ SV796 @ SV2040 @ ( tc_fun @ SV1352 @ tc_bool ) )
| ~ ( c_lessequals @ SV170 @ SV1761 @ ( tc_fun @ SV1352 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4326]) ).
thf(4827,plain,
! [SV172: $i,SV2041: $i,SV1763: $i] :
( ( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1763 @ SV2041 @ SV172 ) @ SV1763 @ SV172 )
= $true )
| ( ( class_Lattices_Olattice @ SV172 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4328]) ).
thf(4828,plain,
! [SV173: $i,SV2042: $i,SV1764: $i] :
( ( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1764 @ SV2042 @ SV173 ) @ SV2042 @ SV173 )
= $true )
| ( ( class_Lattices_Olattice @ SV173 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4329]) ).
thf(4829,plain,
! [SV174: $i,SV2043: $i,SV798: $i] :
( ( ( ! [SY5919: $i] :
( ( c_lessequals @ SV798 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2043 @ SY5919 @ SV174 ) @ SV174 )
| ~ ( c_lessequals @ SV798 @ SY5919 @ SV174 )
| ~ ( c_lessequals @ SV798 @ SV2043 @ SV174 ) ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV174 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4330]) ).
thf(4830,plain,
! [SV175: $i,SV2044: $i,SV799: $i] :
( ( ( ! [SY5920: $i] :
( ( c_lessequals @ SV799 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2044 @ SY5920 @ SV175 ) @ SV175 )
| ~ ( c_lessequals @ SV799 @ SY5920 @ SV175 )
| ~ ( c_lessequals @ SV799 @ SV2044 @ SV175 ) ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV175 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4331]) ).
thf(4831,plain,
! [SV176: $i,SV2045: $i,SV800: $i] :
( ( ( ! [SY5921: $i] :
( ( c_lessequals @ SV800 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2045 @ SY5921 @ SV176 ) @ SV176 )
| ~ ( c_lessequals @ SV800 @ SY5921 @ SV176 )
| ~ ( c_lessequals @ SV800 @ SV2045 @ SV176 ) ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV176 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4332]) ).
thf(4832,plain,
! [SV177: $i,SV2046: $i,SV1765: $i] :
( ( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1765 @ SV2046 @ SV177 ) @ SV2046 @ SV177 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV177 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4333]) ).
thf(4833,plain,
! [SV178: $i,SV2047: $i,SV1766: $i] :
( ( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1766 @ SV2047 @ SV178 ) @ SV1766 @ SV178 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV178 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4334]) ).
thf(4834,plain,
! [SV1767: $i,SV1356: $i,SV803: $i,SV181: $i] :
( ( ( c_lessequals @ SV181 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV803 @ SV1356 @ ( tc_fun @ SV1767 @ tc_bool ) ) @ ( tc_fun @ SV1767 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV181 @ SV1356 @ ( tc_fun @ SV1767 @ tc_bool ) )
| ~ ( c_lessequals @ SV181 @ SV803 @ ( tc_fun @ SV1767 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4335]) ).
thf(4835,plain,
! [SV1768: $i,SV1357: $i,SV804: $i,SV182: $i] :
( ( ( c_lessequals @ SV182 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV804 @ SV1357 @ ( tc_fun @ SV1768 @ tc_bool ) ) @ ( tc_fun @ SV1768 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV182 @ SV1357 @ ( tc_fun @ SV1768 @ tc_bool ) )
| ~ ( c_lessequals @ SV182 @ SV804 @ ( tc_fun @ SV1768 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4336]) ).
thf(4836,plain,
! [SV2048: $i,SV1769: $i,SV1358: $i,SV805: $i,SV183: $i] :
( ( ( c_Product__Type_OSigma @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV183 @ SV805 @ ( tc_fun @ SV1358 @ tc_bool ) ) @ ( c_COMBK @ SV1769 @ ( tc_fun @ SV2048 @ tc_bool ) @ SV1358 ) @ SV1358 @ SV2048 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Product__Type_OSigma @ SV183 @ ( c_COMBK @ SV1769 @ ( tc_fun @ SV2048 @ tc_bool ) @ SV1358 ) @ SV1358 @ SV2048 ) @ ( c_Product__Type_OSigma @ SV805 @ ( c_COMBK @ SV1769 @ ( tc_fun @ SV2048 @ tc_bool ) @ SV1358 ) @ SV1358 @ SV2048 ) @ ( tc_fun @ ( tc_prod @ SV1358 @ SV2048 ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4337]) ).
thf(4837,plain,
! [SV184: $i,SV2049: $i,SV806: $i] :
( ( ( ! [SY5922: $i] : ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV806 @ SV2049 @ SV184 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV806 @ SY5922 @ SV184 ) @ SV184 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV806 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV2049 @ SY5922 @ SV184 ) @ SV184 ) @ SV184 ) )
= $true )
| ( ( class_Lattices_Olattice @ SV184 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4338]) ).
thf(4838,plain,
! [SV807: $i,SV1359: $i,SV185: $i] :
( ( ( ~ ( c_lessequals @ SV185 @ ( c_Transitive__Closure_Ortrancl @ SV1359 @ SV807 ) @ ( tc_fun @ ( tc_prod @ SV807 @ SV807 ) @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1359 @ SV185 @ ( tc_fun @ ( tc_prod @ SV807 @ SV807 ) @ tc_bool ) ) )
= $true )
| ( ( ( c_Transitive__Closure_Ortrancl @ SV185 @ SV807 )
= ( c_Transitive__Closure_Ortrancl @ SV1359 @ SV807 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4339]) ).
thf(4839,plain,
! [SV1362: $i,SV810: $i,SV188: $i] :
( ( ( ( c_Set_Oinsert @ SV188 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV810 @ tc_bool ) ) @ SV810 )
= ( c_Set_Oinsert @ SV1362 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV810 @ tc_bool ) ) @ SV810 ) )
= $false )
| ( ( SV188 = SV1362 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4340]) ).
thf(4840,plain,
! [SV1365: $i,SV813: $i,SV192: $i] :
( ( ( ( c_Set_Oinsert @ SV192 @ SV813 @ SV1365 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1365 @ tc_bool ) ) )
= $false )
| ( ( c_in @ SV192 @ SV813 @ SV1365 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4342]) ).
thf(4841,plain,
! [SV814: $i,SV1366: $i,SV2050: $i,SV194: $i] :
( ( ( ~ ( c_lessequals @ ( c_Set_Oinsert @ SV194 @ SV2050 @ SV1366 ) @ SV814 @ ( tc_fun @ SV1366 @ tc_bool ) ) )
= $true )
| ( ( c_in @ SV194 @ SV814 @ SV1366 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4343]) ).
thf(4842,plain,
! [SV2051: $i,SV1771: $i,SV1367: $i,SV815: $i,SV195: $i] :
( ( ( c_Product__Type_OSigma @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV195 @ SV815 @ ( tc_fun @ SV1367 @ tc_bool ) ) @ SV1771 @ SV1367 @ SV2051 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Product__Type_OSigma @ SV195 @ SV1771 @ SV1367 @ SV2051 ) @ ( c_Product__Type_OSigma @ SV815 @ SV1771 @ SV1367 @ SV2051 ) @ ( tc_fun @ ( tc_prod @ SV1367 @ SV2051 ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4344]) ).
thf(4843,plain,
! [SV1772: $i,SV1368: $i,SV816: $i,SV196: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV196 @ SV816 @ SV1368 ) @ SV1772 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV816 @ SV1772 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4345]) ).
thf(4844,plain,
! [SV1773: $i,SV1369: $i,SV817: $i,SV197: $i] :
( ( ( c_lessequals @ SV197 @ ( c_Set_Oinsert @ SV817 @ SV1369 @ SV1773 ) @ ( tc_fun @ SV1773 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV197 @ SV1369 @ ( tc_fun @ SV1773 @ tc_bool ) )
| ( c_in @ SV817 @ SV197 @ SV1773 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4346]) ).
thf(4845,plain,
! [SV818: $i,SV1370: $i,SV198: $i,SV2052: $i] :
( ( ( ( c_in @ SV2052 @ SV198 @ SV1370 )
| ~ ( c_lessequals @ SV198 @ ( c_Set_Oinsert @ SV2052 @ SV818 @ SV1370 ) @ ( tc_fun @ SV1370 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV198 @ SV818 @ ( tc_fun @ SV1370 @ tc_bool ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4347]) ).
thf(4846,plain,
! [SV1774: $i,SV1371: $i,SV819: $i,SV199: $i] :
( ( ( c_lessequals @ SV199 @ ( c_Set_Oinsert @ SV819 @ SV1371 @ SV1774 ) @ ( tc_fun @ SV1774 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV199 @ SV1371 @ ( tc_fun @ SV1774 @ tc_bool ) )
| ( c_in @ SV819 @ SV199 @ SV1774 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4348]) ).
thf(4847,plain,
! [SV1372: $i,SV820: $i,SV2053: $i,SV200: $i] :
( ( ( ~ ( c_lessequals @ SV200 @ ( c_Set_Oinsert @ SV2053 @ SV820 @ SV1372 ) @ ( tc_fun @ SV1372 @ tc_bool ) )
| ( c_in @ SV2053 @ SV200 @ SV1372 ) )
= $true )
| ( ( c_lessequals @ SV200 @ SV820 @ ( tc_fun @ SV1372 @ tc_bool ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4349]) ).
thf(4848,plain,
! [SV1776: $i,SV1374: $i,SV822: $i,SV202: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV202 @ ( c_Set_Oinsert @ SV822 @ SV1374 @ SV1776 ) @ ( tc_fun @ SV1776 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV202 @ SV1374 @ ( tc_fun @ SV1776 @ tc_bool ) ) )
= $true )
| ( ( c_in @ SV822 @ SV202 @ SV1776 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4351]) ).
thf(4849,plain,
! [SV1777: $i,SV1375: $i,SV823: $i,SV203: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ SV203 @ SV823 @ SV1375 ) @ SV1777 @ ( tc_fun @ SV1375 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV823 @ SV1777 @ ( tc_fun @ SV1375 @ tc_bool ) ) )
= $true )
| ( ( c_in @ SV203 @ SV1777 @ SV1375 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4352]) ).
thf(4850,plain,
! [SV1376: $i,SV824: $i,SV204: $i] :
( ( ( c_Order__Relation_Ostrict__linear__order__on @ SV204 @ SV824 @ SV1376 )
= $false )
| ( ( c_Relation_Ototal__on @ SV204 @ SV824 @ SV1376 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4353]) ).
thf(4851,plain,
! [SV1377: $i,SV825: $i,SV205: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV205 @ SV825 @ ( tc_fun @ SV1377 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1377 @ tc_bool ) ) )
= $false )
| ( ( SV825
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1377 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4354]) ).
thf(4852,plain,
! [SV1378: $i,SV826: $i,SV206: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV206 @ SV826 @ ( tc_fun @ SV1378 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1378 @ tc_bool ) ) )
= $false )
| ( ( SV206
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1378 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4355]) ).
thf(4853,plain,
! [SV207: $i,SV1778: $i] :
( ( ( ! [SY5730: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1778 @ SY5730 @ SV207 )
!= ( c_Orderings_Obot__class_Obot @ SV207 ) ) )
= $true )
| ( ( SV1778
= ( c_Orderings_Obot__class_Obot @ SV207 ) )
= $true )
| ( ( class_Lattices_Obounded__lattice @ SV207 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4356]) ).
thf(4854,plain,
! [SV208: $i,SV2054: $i,SV1779: $i] :
( ( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1779 @ SV2054 @ SV208 )
!= ( c_Orderings_Obot__class_Obot @ SV208 ) )
| ( SV2054
= ( c_Orderings_Obot__class_Obot @ SV208 ) ) )
= $true )
| ( ( class_Lattices_Obounded__lattice @ SV208 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4357]) ).
thf(4855,plain,
! [SV2055: $i,SV1780: $i,SV1381: $i,SV829: $i,SV211: $i] :
( ( ! [SY5923: $i] :
( ( c_Relation_Orel__comp @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV211 @ SV829 @ ( tc_fun @ ( tc_prod @ SV1381 @ SV1780 ) @ tc_bool ) ) @ SV2055 @ SV1381 @ SV1780 @ SY5923 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ SV211 @ SV2055 @ SV1381 @ SV1780 @ SY5923 ) @ ( c_Relation_Orel__comp @ SV829 @ SV2055 @ SV1381 @ SV1780 @ SY5923 ) @ ( tc_fun @ ( tc_prod @ SV1381 @ SY5923 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4358]) ).
thf(4856,plain,
! [SV2056: $i,SV1781: $i,SV1382: $i,SV830: $i,SV212: $i] :
( ( ! [SY5924: $i] :
( ( c_Relation_Orel__comp @ SV212 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV830 @ SV1382 @ ( tc_fun @ ( tc_prod @ SV1781 @ SV2056 ) @ tc_bool ) ) @ SY5924 @ SV1781 @ SV2056 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ SV212 @ SV830 @ SY5924 @ SV1781 @ SV2056 ) @ ( c_Relation_Orel__comp @ SV212 @ SV1382 @ SY5924 @ SV1781 @ SV2056 ) @ ( tc_fun @ ( tc_prod @ SY5924 @ SV2056 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4359]) ).
thf(4857,plain,
! [SV1383: $i,SV831: $i,SV2057: $i,SV213: $i] :
( ( ( ~ ( c_lessequals @ SV213 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2057 @ SV831 @ ( tc_fun @ SV1383 @ tc_bool ) ) @ ( tc_fun @ SV1383 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV213 @ SV831 @ ( tc_fun @ SV1383 @ tc_bool ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4360]) ).
thf(4858,plain,
! [SV1384: $i,SV2058: $i,SV832: $i,SV214: $i] :
( ( ( ~ ( c_lessequals @ SV214 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV832 @ SV2058 @ ( tc_fun @ SV1384 @ tc_bool ) ) @ ( tc_fun @ SV1384 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV214 @ SV832 @ ( tc_fun @ SV1384 @ tc_bool ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4361]) ).
thf(4859,plain,
! [SV215: $i,SV2059: $i,SV833: $i] :
( ( ( ( c_lessequals @ SV833 @ SV2059 @ SV215 )
| ! [SY5925: $i] :
~ ( c_lessequals @ SV833 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2059 @ SY5925 @ SV215 ) @ SV215 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV215 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4362]) ).
thf(4860,plain,
! [SV216: $i,SV2060: $i,SV834: $i] :
( ( ( ( c_lessequals @ SV834 @ SV2060 @ SV216 )
| ! [SY5926: $i] :
~ ( c_lessequals @ SV834 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY5926 @ SV2060 @ SV216 ) @ SV216 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV216 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4363]) ).
thf(4861,plain,
! [SV217: $i,SV2061: $i,SV835: $i] :
( ( ( ! [SY5927: $i] :
( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV835 @ SV2061 @ SV217 ) @ SY5927 @ SV217 )
| ~ ( c_lessequals @ SV835 @ SY5927 @ SV217 ) ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV217 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4364]) ).
thf(4862,plain,
! [SV218: $i,SV2062: $i,SV836: $i] :
( ( ( ! [SY5928: $i] :
( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV836 @ SV2062 @ SV218 ) @ SY5928 @ SV218 )
| ~ ( c_lessequals @ SV2062 @ SY5928 @ SV218 ) ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV218 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4365]) ).
thf(4863,plain,
! [SV219: $i,SV2063: $i,SV837: $i] :
( ( ( ( c_lessequals @ SV837 @ SV2063 @ SV219 )
| ! [SY5929: $i] :
~ ( c_lessequals @ SV837 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2063 @ SY5929 @ SV219 ) @ SV219 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV219 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4366]) ).
thf(4864,plain,
! [SV220: $i,SV2064: $i,SV838: $i] :
( ( ( ( c_lessequals @ SV838 @ SV2064 @ SV220 )
| ! [SY5930: $i] :
~ ( c_lessequals @ SV838 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY5930 @ SV2064 @ SV220 ) @ SV220 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV220 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4367]) ).
thf(4865,plain,
! [SV223: $i,SV2065: $i,SV1783: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1783 @ SV2065 @ SV223 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV2065 @ SV1783 @ SV223 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV223 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4369]) ).
thf(4866,plain,
! [SV224: $i,SV2066: $i,SV1784: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1784 @ SV2066 @ SV224 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV2066 @ SV1784 @ SV224 ) )
= $true )
| ( ( class_Lattices_Olattice @ SV224 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4370]) ).
thf(4867,plain,
! [SV844: $i,SV228: $i,SV1390: $i] :
( ( ( c_lessequals @ SV1390 @ SV228 @ ( tc_fun @ ( tc_prod @ SV844 @ SV844 ) @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( c_Wellfounded_Oacc @ SV228 @ SV844 ) @ ( c_Wellfounded_Oacc @ SV1390 @ SV844 ) @ ( tc_fun @ SV844 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4372]) ).
thf(4868,plain,
! [SV230: $i,SV2067: $i,SV1786: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1786 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1786 @ SV2067 @ SV230 ) @ SV230 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV1786 @ SV2067 @ SV230 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV230 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4373]) ).
thf(4869,plain,
! [SV231: $i,SV2068: $i,SV1787: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1787 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1787 @ SV2068 @ SV231 ) @ SV231 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV1787 @ SV2068 @ SV231 ) )
= $true )
| ( ( class_Lattices_Olattice @ SV231 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4374]) ).
thf(4870,plain,
! [SV1392: $i,SV846: $i,SV232: $i] :
( ( ( ( c_Relation_ODomain @ SV232 @ SV846 @ SV1392 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV846 @ tc_bool ) ) )
= $false )
| ( ( SV232
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV846 @ SV1392 ) @ tc_bool ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4375]) ).
thf(4871,plain,
! [SV850: $i,SV2069: $i,SV1789: $i,SV236: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV236 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1 @ SV236 @ SV1789 @ SV2069 ) ) )
| ~ ( c_Wellfounded_Owf @ SV1789 @ SV2069 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV236 @ SV850 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4377]) ).
thf(4872,plain,
! [SV1790: $i,SV1397: $i,SV852: $i,SV238: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ SV238 @ SV852 @ SV1397 ) @ SV1790 @ ( tc_fun @ SV1397 @ tc_bool ) )
= ( c_Set_Oinsert @ SV238 @ ( c_HOL_Ominus__class_Ominus @ SV852 @ SV1790 @ ( tc_fun @ SV1397 @ tc_bool ) ) @ SV1397 ) )
= $true )
| ( ( c_in @ SV238 @ SV1790 @ SV1397 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4378]) ).
thf(4873,plain,
! [SV1791: $i,SV1398: $i,SV853: $i,SV239: $i] :
( ( ( c_lessequals @ SV239 @ ( c_Set_Oinsert @ SV853 @ SV1398 @ SV1791 ) @ ( tc_fun @ SV1791 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV239 @ SV1398 @ ( tc_fun @ SV1791 @ tc_bool ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV239 @ ( c_Set_Oinsert @ SV853 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1791 @ tc_bool ) ) @ SV1791 ) @ ( tc_fun @ SV1791 @ tc_bool ) ) @ SV1398 @ ( tc_fun @ SV1791 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4379]) ).
thf(4874,plain,
! [SV854: $i,SV2070: $i,SV240: $i,SV1792: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1792 @ SV240 @ ( tc_fun @ SV2070 @ tc_bool ) ) @ SV854 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV240 @ SV854 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4380]) ).
thf(4875,plain,
! [SV855: $i,SV2071: $i,SV1793: $i,SV241: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV241 @ SV1793 @ ( tc_fun @ SV2071 @ tc_bool ) ) @ SV855 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV241 @ SV855 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4381]) ).
thf(4876,plain,
! [SV2072: $i,SV1794: $i,SV1399: $i,SV856: $i,SV242: $i] :
( ( ( c_Relation_ORange @ ( c_Set_Oinsert @ ( c_Pair @ SV242 @ SV856 @ SV1399 @ SV1794 ) @ SV2072 @ ( tc_prod @ SV1399 @ SV1794 ) ) @ SV1399 @ SV1794 )
= ( c_Set_Oinsert @ SV856 @ ( c_Relation_ORange @ SV2072 @ SV1399 @ SV1794 ) @ SV1794 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4382]) ).
thf(4877,plain,
! [SV243: $i,SV1400: $i,SV857: $i] :
( ( ( ~ ( c_Relation_Osym @ SV857 @ SV1400 ) )
= $true )
| ( ( ~ ( c_Relation_Osym @ SV243 @ SV1400 ) )
= $true )
| ( ( c_Relation_Osym @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV243 @ SV857 @ ( tc_fun @ ( tc_prod @ SV1400 @ SV1400 ) @ tc_bool ) ) @ SV1400 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4383]) ).
thf(4878,plain,
! [SV1795: $i,SV1402: $i,SV859: $i,SV245: $i] :
( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV245 @ SV859 @ ( tc_fun @ SV1402 @ tc_bool ) ) @ SV1795 @ ( tc_fun @ SV1402 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV245 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV859 @ SV1795 @ ( tc_fun @ SV1402 @ tc_bool ) ) @ ( tc_fun @ SV1402 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4385]) ).
thf(4879,plain,
! [SV1796: $i,SV1403: $i,SV860: $i,SV246: $i] :
( ( ( c_lessequals @ SV246 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV860 @ SV1403 @ ( tc_fun @ SV1796 @ tc_bool ) ) @ ( tc_fun @ SV1796 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV246 @ SV860 @ ( tc_fun @ SV1796 @ tc_bool ) ) @ SV1403 @ ( tc_fun @ SV1796 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4386]) ).
thf(4880,plain,
! [SV2073: $i,SV1797: $i,SV1404: $i,SV861: $i,SV247: $i] :
( ( ! [SY5931: $i] :
( ( ( hAPP @ SV247 @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ SV247 @ SV861 @ SV1404 @ SV1797 @ SV2073 @ SY5931 ) )
!= ( hAPP @ SV861 @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ SV247 @ SV861 @ SV1404 @ SV1797 @ SV2073 @ SY5931 ) ) )
| ( ( c_Recdef_Ocut @ SV247 @ SV1404 @ SV1797 @ SV2073 @ SY5931 )
= ( c_Recdef_Ocut @ SV861 @ SV1404 @ SV1797 @ SV2073 @ SY5931 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4387]) ).
thf(4881,plain,
! [SV248: $i,SV862: $i,SV2074: $i,SV1798: $i] :
( ( ( ~ ( c_Wellfounded_Oacyclic @ ( c_Set_Oinsert @ ( c_Pair @ SV1798 @ SV2074 @ SV862 @ SV862 ) @ SV248 @ ( tc_prod @ SV862 @ SV862 ) ) @ SV862 ) )
= $true )
| ( ( c_Wellfounded_Oacyclic @ SV248 @ SV862 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4388]) ).
thf(4882,plain,
! [SV1405: $i,SV863: $i,SV249: $i] :
( ( ( class_HOL_Oord @ SV249 )
= $false )
| ( ( ! [SY5306: $i] :
( ( c_lessequals @ ( hAPP @ SV863 @ SV1405 ) @ ( hAPP @ SY5306 @ SV1405 ) @ SV249 )
| ! [SY4476: $i] :
~ ( c_lessequals @ SV863 @ SY5306 @ ( tc_fun @ SY4476 @ SV249 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4389]) ).
thf(4883,plain,
! [SV1799: $i,SV1406: $i,SV864: $i,SV250: $i] :
( ( ( c_in @ SV250 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV864 @ SV1406 @ ( tc_fun @ SV1799 @ tc_bool ) ) @ SV1799 )
= $true )
| ( ( ~ ( c_in @ SV250 @ SV1406 @ SV1799 )
| ~ ( c_in @ SV250 @ SV864 @ SV1799 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4390]) ).
thf(4884,plain,
! [SV1800: $i,SV1407: $i,SV865: $i,SV251: $i] :
( ( ( c_in @ SV251 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV865 @ SV1407 @ ( tc_fun @ SV1800 @ tc_bool ) ) @ SV1800 )
= $true )
| ( ( ~ ( c_in @ SV251 @ SV1407 @ SV1800 )
| ~ ( c_in @ SV251 @ SV865 @ SV1800 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4391]) ).
thf(4885,plain,
! [SV1801: $i,SV1408: $i,SV866: $i,SV252: $i] :
( ( ( c_in @ SV252 @ ( c_Set_Oinsert @ SV866 @ SV1408 @ SV1801 ) @ SV1801 )
= $true )
| ( ( ~ ( c_in @ SV252 @ SV1408 @ SV1801 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4392]) ).
thf(4886,plain,
! [SV1802: $i,SV1409: $i,SV867: $i,SV253: $i] :
( ( ( c_in @ SV253 @ ( c_Set_Oinsert @ SV867 @ SV1409 @ SV1802 ) @ SV1802 )
= $true )
| ( ( ~ ( c_in @ SV253 @ SV1409 @ SV1802 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4393]) ).
thf(4887,plain,
! [SV868: $i,SV1410: $i,SV2075: $i,SV254: $i] :
( ( ( ~ ( c_in @ SV254 @ SV2075 @ SV1410 )
| ~ ( c_lessequals @ SV2075 @ SV868 @ ( tc_fun @ SV1410 @ tc_bool ) ) )
= $true )
| ( ( c_in @ SV254 @ SV868 @ SV1410 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4394]) ).
thf(4888,plain,
! [SV255: $i,SV1411: $i,SV869: $i,SV2076: $i] :
( ( ( ~ ( c_lessequals @ SV2076 @ SV869 @ ( tc_fun @ SV1411 @ tc_bool ) )
| ~ ( c_in @ SV255 @ SV2076 @ SV1411 ) )
= $true )
| ( ( c_in @ SV255 @ SV869 @ SV1411 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4395]) ).
thf(4889,plain,
! [SV870: $i,SV1412: $i,SV2077: $i,SV256: $i] :
( ( ( ~ ( c_in @ SV256 @ SV2077 @ SV1412 )
| ~ ( c_lessequals @ SV2077 @ SV870 @ ( tc_fun @ SV1412 @ tc_bool ) ) )
= $true )
| ( ( c_in @ SV256 @ SV870 @ SV1412 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4396]) ).
thf(4890,plain,
! [SV871: $i,SV1413: $i,SV2078: $i,SV257: $i] :
( ( ( ~ ( c_in @ SV257 @ SV2078 @ SV1413 )
| ~ ( c_lessequals @ SV2078 @ SV871 @ ( tc_fun @ SV1413 @ tc_bool ) ) )
= $true )
| ( ( c_in @ SV257 @ SV871 @ SV1413 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4397]) ).
thf(4891,plain,
! [SV1803: $i,SV1414: $i,SV872: $i,SV258: $i] :
( ( ( c_in @ SV258 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV872 @ SV1414 @ ( tc_fun @ SV1803 @ tc_bool ) ) @ SV1803 )
= $true )
| ( ( ~ ( c_in @ SV258 @ SV872 @ SV1803 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4398]) ).
thf(4892,plain,
! [SV1804: $i,SV1415: $i,SV873: $i,SV259: $i] :
( ( ( c_in @ SV259 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV873 @ SV1415 @ ( tc_fun @ SV1804 @ tc_bool ) ) @ SV1804 )
= $true )
| ( ( ~ ( c_in @ SV259 @ SV1415 @ SV1804 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4399]) ).
thf(4893,plain,
! [SV261: $i,SV1805: $i,SV875: $i] :
( ( ( c_in @ SV875 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1805 @ tc_bool ) ) @ SV1805 )
= $false )
| ( ( hBOOL @ ( hAPP @ SV261 @ SV875 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4400]) ).
thf(4894,plain,
! [SV1416: $i,SV878: $i,SV2079: $i,SV264: $i] :
( ( ( ( SV264 = SV2079 )
| ~ ( c_in @ SV264 @ ( c_Set_Oinsert @ SV2079 @ SV878 @ SV1416 ) @ SV1416 ) )
= $true )
| ( ( c_in @ SV264 @ SV878 @ SV1416 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4401]) ).
thf(4895,plain,
! [SV879: $i,SV1417: $i,SV2080: $i,SV265: $i] :
( ( ( ( c_in @ SV265 @ SV2080 @ SV1417 )
| ~ ( c_in @ SV265 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV2080 @ SV879 @ ( tc_fun @ SV1417 @ tc_bool ) ) @ SV1417 ) )
= $true )
| ( ( c_in @ SV265 @ SV879 @ SV1417 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4402]) ).
thf(4896,plain,
! [SV1418: $i,SV880: $i,SV266: $i] :
( ( ( c_in @ SV266 @ SV880 @ SV1418 )
= $false )
| ( ( ! [SY5320: $i] :
~ ( c_in @ SV266 @ ( c_HOL_Ominus__class_Ominus @ SY5320 @ SV880 @ ( tc_fun @ SV1418 @ tc_bool ) ) @ SV1418 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4403]) ).
thf(4897,plain,
! [SV1419: $i,SV2081: $i,SV881: $i,SV267: $i] :
( ( ( ~ ( c_in @ SV267 @ ( c_HOL_Ominus__class_Ominus @ SV881 @ SV2081 @ ( tc_fun @ SV1419 @ tc_bool ) ) @ SV1419 ) )
= $true )
| ( ( c_in @ SV267 @ SV881 @ SV1419 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4404]) ).
thf(4898,plain,
! [SV1423: $i,SV885: $i,SV2082: $i,SV271: $i] :
( ( ( ~ ( c_in @ SV271 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2082 @ SV885 @ ( tc_fun @ SV1423 @ tc_bool ) ) @ SV1423 ) )
= $true )
| ( ( c_in @ SV271 @ SV885 @ SV1423 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4405]) ).
thf(4899,plain,
! [SV1424: $i,SV2083: $i,SV886: $i,SV272: $i] :
( ( ( ~ ( c_in @ SV272 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV886 @ SV2083 @ ( tc_fun @ SV1424 @ tc_bool ) ) @ SV1424 ) )
= $true )
| ( ( c_in @ SV272 @ SV886 @ SV1424 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4406]) ).
thf(4900,plain,
! [SV273: $i,SV2084: $i,SV887: $i] :
( ( ( ~ ( c_in @ SV887 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV2084 @ tc_bool ) ) @ SV2084 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV273 @ SV887 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4407]) ).
thf(4901,plain,
! [SV1806: $i,SV1425: $i,SV888: $i,SV274: $i] :
( ( ( c_in @ SV274 @ ( c_HOL_Ominus__class_Ominus @ SV888 @ SV1425 @ ( tc_fun @ SV1806 @ tc_bool ) ) @ SV1806 )
= $true )
| ( ( ( c_in @ SV274 @ SV1425 @ SV1806 )
| ~ ( c_in @ SV274 @ SV888 @ SV1806 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4408]) ).
thf(4902,plain,
! [SV1807: $i,SV1426: $i,SV889: $i,SV275: $i] :
( ( ( c_in @ SV275 @ ( c_HOL_Ominus__class_Ominus @ SV889 @ SV1426 @ ( tc_fun @ SV1807 @ tc_bool ) ) @ SV1807 )
= $true )
| ( ( ( c_in @ SV275 @ SV1426 @ SV1807 )
| ~ ( c_in @ SV275 @ SV889 @ SV1807 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4409]) ).
thf(4903,plain,
! [SV1808: $i,SV1427: $i,SV890: $i,SV276: $i] :
( ( ( ( c_Set_Oinsert @ SV276 @ SV890 @ SV1427 )
!= ( c_Set_Oinsert @ SV276 @ SV1808 @ SV1427 ) )
= $true )
| ( ( ( c_in @ SV276 @ SV1808 @ SV1427 )
| ( SV890 = SV1808 )
| ( c_in @ SV276 @ SV890 @ SV1427 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4410]) ).
thf(4904,plain,
! [SV1428: $i,SV891: $i,SV277: $i] :
( ( ( c_in @ SV277 @ SV891 @ SV1428 )
= $false )
| ( ( ( c_Set_Oinsert @ SV277 @ SV891 @ SV1428 )
= SV891 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4411]) ).
thf(4905,plain,
! [SV2085: $i,SV1813: $i,SV1433: $i,SV896: $i,SV282: $i] :
( ( ( hBOOL @ ( hAPP @ SV282 @ ( hAPP @ ( c_fst @ SV896 @ SV1433 ) @ ( c_Pair @ SV1813 @ SV2085 @ SV896 @ SV1433 ) ) ) )
| ! [SY5932: $i] :
~ ( hBOOL @ ( hAPP @ SY5932 @ SV2085 ) )
| ~ ( hBOOL @ ( hAPP @ SV282 @ SV1813 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4416]) ).
thf(4906,plain,
! [SV2086: $i,SV1814: $i,SV1434: $i,SV897: $i,SV283: $i] :
( ( ( hBOOL @ ( hAPP @ SV283 @ ( hAPP @ ( c_snd @ SV897 @ SV1434 ) @ ( c_Pair @ SV1814 @ SV2086 @ SV897 @ SV1434 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ SV283 @ SV2086 ) )
| ! [SY5750: $i] :
~ ( hBOOL @ ( hAPP @ SY5750 @ SV1814 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4417]) ).
thf(4907,plain,
! [SV284: $i,SV2087: $i,SV898: $i] :
( ( ( ! [SY5934: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV898 @ SV2087 @ SV284 ) @ SY5934 @ SV284 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV898 @ SY5934 @ SV284 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV2087 @ SY5934 @ SV284 ) @ SV284 ) ) )
= $true )
| ( ( class_Lattices_Odistrib__lattice @ SV284 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4418]) ).
thf(4908,plain,
! [SV285: $i,SV2088: $i,SV899: $i] :
( ( ( ! [SY5935: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV899 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2088 @ SY5935 @ SV285 ) @ SV285 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV899 @ SV2088 @ SV285 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV899 @ SY5935 @ SV285 ) @ SV285 ) ) )
= $true )
| ( ( class_Lattices_Odistrib__lattice @ SV285 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4419]) ).
thf(4909,plain,
! [SV902: $i,SV288: $i,SV1817: $i] :
( ( ( c_Order__Relation_Ostrict__linear__order__on @ SV1817 @ SV288 @ SV902 )
= $false )
| ( ( c_Relation_Otrans @ SV288 @ SV902 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4422]) ).
thf(4910,plain,
! [SV1818: $i,SV1438: $i,SV904: $i,SV290: $i] :
( ( ( c_lessequals @ ( c_Set_Oinsert @ SV290 @ SV904 @ SV1438 ) @ SV1818 @ ( tc_fun @ SV1438 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV904 @ SV1818 @ ( tc_fun @ SV1438 @ tc_bool ) )
| ~ ( c_in @ SV290 @ SV1818 @ SV1438 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4423]) ).
thf(4911,plain,
! [SV2089: $i,SV1819: $i,SV1439: $i,SV905: $i,SV291: $i] :
( ( ( c_Product__Type_OSigma @ ( c_HOL_Ominus__class_Ominus @ SV291 @ SV905 @ ( tc_fun @ SV1439 @ tc_bool ) ) @ ( c_COMBK @ SV1819 @ ( tc_fun @ SV2089 @ tc_bool ) @ SV1439 ) @ SV1439 @ SV2089 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Product__Type_OSigma @ SV291 @ ( c_COMBK @ SV1819 @ ( tc_fun @ SV2089 @ tc_bool ) @ SV1439 ) @ SV1439 @ SV2089 ) @ ( c_Product__Type_OSigma @ SV905 @ ( c_COMBK @ SV1819 @ ( tc_fun @ SV2089 @ tc_bool ) @ SV1439 ) @ SV1439 @ SV2089 ) @ ( tc_fun @ ( tc_prod @ SV1439 @ SV2089 ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4424]) ).
thf(4912,plain,
! [SV292: $i,SV2090: $i,SV1820: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV1820 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1820 @ SV2090 @ SV292 ) @ SV292 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV1820 @ SV2090 @ SV292 ) )
= $true )
| ( ( class_Lattices_Olattice @ SV292 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4425]) ).
thf(4913,plain,
! [SV293: $i,SV2091: $i,SV1821: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV1821 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1821 @ SV2091 @ SV293 ) @ SV293 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV1821 @ SV2091 @ SV293 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV293 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4426]) ).
thf(4914,plain,
! [SV908: $i,SV1442: $i,SV296: $i] :
( ( ( c_Wellfounded_Owf @ SV296 @ SV1442 )
= $false )
| ( ( c_Wellfounded_Owf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV296 @ SV908 @ ( tc_fun @ ( tc_prod @ SV1442 @ SV1442 ) @ tc_bool ) ) @ SV1442 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4428]) ).
thf(4915,plain,
! [SV297: $i,SV1443: $i,SV909: $i] :
( ( ( c_Wellfounded_Owf @ SV909 @ SV1443 )
= $false )
| ( ( c_Wellfounded_Owf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV297 @ SV909 @ ( tc_fun @ ( tc_prod @ SV1443 @ SV1443 ) @ tc_bool ) ) @ SV1443 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4429]) ).
thf(4916,plain,
! [SV1444: $i,SV910: $i,SV298: $i] :
( ( ( c_in @ SV298 @ SV910 @ SV1444 )
= $false )
| ( ( ( c_Set_Oinsert @ SV298 @ ( c_HOL_Ominus__class_Ominus @ SV910 @ ( c_Set_Oinsert @ SV298 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1444 @ tc_bool ) ) @ SV1444 ) @ ( tc_fun @ SV1444 @ tc_bool ) ) @ SV1444 )
= SV910 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4430]) ).
thf(4917,plain,
! [SV301: $i,SV2092: $i,SV912: $i] :
( ( ( ( c_lessequals @ SV912 @ SV2092 @ SV301 )
| ! [SY5936: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY5936 @ SV912 @ SV301 ) @ SV2092 @ SV301 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV301 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4432]) ).
thf(4918,plain,
! [SV302: $i,SV2093: $i,SV913: $i] :
( ( ( ( c_lessequals @ SV913 @ SV2093 @ SV302 )
| ! [SY5937: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV913 @ SY5937 @ SV302 ) @ SV2093 @ SV302 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV302 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4433]) ).
thf(4919,plain,
! [SV303: $i,SV2094: $i,SV914: $i] :
( ( ( ! [SY5938: $i] :
( ( c_lessequals @ SV914 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV2094 @ SY5938 @ SV303 ) @ SV303 )
| ~ ( c_lessequals @ SV914 @ SY5938 @ SV303 ) ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV303 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4434]) ).
thf(4920,plain,
! [SV304: $i,SV2095: $i,SV915: $i] :
( ( ( ! [SY5939: $i] : ( c_lessequals @ SV915 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV2095 @ SY5939 @ SV304 ) @ SV304 )
| ~ ( c_lessequals @ SV915 @ SV2095 @ SV304 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV304 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4435]) ).
thf(4921,plain,
! [SV305: $i,SV2096: $i,SV916: $i] :
( ( ( ( c_lessequals @ SV916 @ SV2096 @ SV305 )
| ! [SY5940: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY5940 @ SV916 @ SV305 ) @ SV2096 @ SV305 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV305 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4436]) ).
thf(4922,plain,
! [SV306: $i,SV2097: $i,SV917: $i] :
( ( ( ( c_lessequals @ SV917 @ SV2097 @ SV306 )
| ! [SY5941: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV917 @ SY5941 @ SV306 ) @ SV2097 @ SV306 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV306 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4437]) ).
thf(4923,plain,
! [SV918: $i,SV1445: $i,SV2098: $i,SV307: $i] :
( ( ( ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV307 @ SV2098 @ ( tc_fun @ SV1445 @ tc_bool ) ) @ SV918 @ ( tc_fun @ SV1445 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV307 @ SV918 @ ( tc_fun @ SV1445 @ tc_bool ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4438]) ).
thf(4924,plain,
! [SV919: $i,SV1446: $i,SV308: $i,SV2099: $i] :
( ( ( ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV2099 @ SV308 @ ( tc_fun @ SV1446 @ tc_bool ) ) @ SV919 @ ( tc_fun @ SV1446 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV308 @ SV919 @ ( tc_fun @ SV1446 @ tc_bool ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4439]) ).
thf(4925,plain,
! [SV309: $i,SV2100: $i,SV920: $i] :
( ( ( ( c_lessequals @ SV920 @ SV2100 @ SV309 )
| ! [SY5942: $i] :
( ~ ( c_lessequals @ SV920 @ SY5942 @ SV309 )
| ~ ( c_lessequals @ SY5942 @ SV2100 @ SV309 ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV309 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4440]) ).
thf(4926,plain,
! [SV310: $i,SV2101: $i,SV921: $i] :
( ( ( ( c_lessequals @ SV921 @ SV2101 @ SV310 )
| ! [SY5943: $i] :
( ~ ( c_lessequals @ SY5943 @ SV2101 @ SV310 )
| ~ ( c_lessequals @ SV921 @ SY5943 @ SV310 ) ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV310 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4441]) ).
thf(4927,plain,
! [SV313: $i,SV1447: $i,SV924: $i,SV2102: $i] :
( ( ( ~ ( c_lessequals @ SV2102 @ SV924 @ ( tc_fun @ SV1447 @ tc_bool ) )
| ~ ( c_lessequals @ SV313 @ SV2102 @ ( tc_fun @ SV1447 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV313 @ SV924 @ ( tc_fun @ SV1447 @ tc_bool ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4442]) ).
thf(4928,plain,
! [SV314: $i,SV925: $i,SV1824: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV1824 @ SV925 ) ) )
= $true )
| ( ( ! [SY5754: $i] :
~ ( c_lessequals @ SV1824 @ SV314 @ ( tc_fun @ SY5754 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV314 @ SV925 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4443]) ).
thf(4929,plain,
! [SV926: $i,SV1825: $i,SV315: $i] :
( ( ( ~ ( c_lessequals @ SV315 @ SV1825 @ ( tc_fun @ ( tc_prod @ SV926 @ SV926 ) @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_Wellfounded_Owf @ SV1825 @ SV926 ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV315 @ SV926 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4444]) ).
thf(4930,plain,
! [SV318: $i,SV927: $i,SV1828: $i] :
( ( ( ~ ( c_Relation_Oantisym @ SV1828 @ SV927 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV318 @ SV1828 @ ( tc_fun @ ( tc_prod @ SV927 @ SV927 ) @ tc_bool ) ) )
= $true )
| ( ( c_Relation_Oantisym @ SV318 @ SV927 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4447]) ).
thf(4931,plain,
! [SV928: $i,SV319: $i,SV1829: $i] :
( ( ( ! [SY5755: $i] :
~ ( c_lessequals @ SV1829 @ SV319 @ ( tc_fun @ SY5755 @ tc_bool ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV1829 @ SV928 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV319 @ SV928 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4448]) ).
thf(4932,plain,
! [SV929: $i,SV1830: $i,SV320: $i] :
( ( ( ~ ( c_lessequals @ SV320 @ SV1830 @ ( tc_fun @ ( tc_prod @ SV929 @ SV929 ) @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_Wellfounded_Oacyclic @ SV1830 @ SV929 ) )
= $true )
| ( ( c_Wellfounded_Oacyclic @ SV320 @ SV929 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4449]) ).
thf(4933,plain,
! [SV321: $i,SV1448: $i,SV930: $i,SV2103: $i] :
( ( ( ~ ( c_Relation_Osingle__valued @ SV2103 @ SV930 @ SV1448 )
| ~ ( c_lessequals @ SV321 @ SV2103 @ ( tc_fun @ ( tc_prod @ SV930 @ SV1448 ) @ tc_bool ) ) )
= $true )
| ( ( c_Relation_Osingle__valued @ SV321 @ SV930 @ SV1448 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4450]) ).
thf(4934,plain,
! [SV2104: $i,SV1449: $i,SV931: $i,SV322: $i] :
( ( ( ( c_Set_Oimage @ SV322 @ SV931 @ SV1449 @ SV2104 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV2104 @ tc_bool ) ) )
= $true )
| ( ( SV931
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1449 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4451]) ).
thf(4935,plain,
! [SV2105: $i,SV1831: $i,SV1450: $i,SV932: $i,SV323: $i] :
( ( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV323 @ SV932 @ ( tc_fun @ SV1450 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1831 @ SV2105 @ ( tc_fun @ SV1450 @ tc_bool ) ) @ ( tc_fun @ SV1450 @ tc_bool ) )
| ~ ( c_lessequals @ SV932 @ SV2105 @ ( tc_fun @ SV1450 @ tc_bool ) )
| ~ ( c_lessequals @ SV323 @ SV1831 @ ( tc_fun @ SV1450 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4452]) ).
thf(4936,plain,
! [SV1834: $i,SV1453: $i,SV936: $i,SV327: $i] :
( ( ( c_lessequals @ ( c_Relation_ODomain @ SV327 @ SV936 @ SV1453 ) @ ( c_Relation_ODomain @ SV1834 @ SV936 @ SV1453 ) @ ( tc_fun @ SV936 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV327 @ SV1834 @ ( tc_fun @ ( tc_prod @ SV936 @ SV1453 ) @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4455]) ).
thf(4937,plain,
! [SV937: $i,SV1454: $i,SV328: $i] :
( ( ( SV328
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1454 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV328 @ ( c_Set_Oinsert @ SV937 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1454 @ tc_bool ) ) @ SV1454 ) @ ( tc_fun @ SV1454 @ tc_bool ) ) )
= $true )
| ( ( SV328
= ( c_Set_Oinsert @ SV937 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1454 @ tc_bool ) ) @ SV1454 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4456]) ).
thf(4938,plain,
! [SV1836: $i,SV1457: $i,SV940: $i,SV331: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV331 @ SV940 @ ( tc_fun @ SV1457 @ tc_bool ) ) @ SV1836 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV940 @ SV1836 ) )
| ~ ( hBOOL @ ( hAPP @ SV331 @ SV1836 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4458]) ).
thf(4939,plain,
! [SV1837: $i,SV1458: $i,SV941: $i,SV332: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV332 @ ( c_HOL_Ominus__class_Ominus @ SV941 @ SV1458 @ ( tc_fun @ SV1837 @ tc_bool ) ) @ ( tc_fun @ SV1837 @ tc_bool ) )
= SV1458 )
= $true )
| ( ( ~ ( c_lessequals @ SV332 @ SV941 @ ( tc_fun @ SV1837 @ tc_bool ) )
| ~ ( c_lessequals @ SV1458 @ SV332 @ ( tc_fun @ SV1837 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4459]) ).
thf(4940,plain,
! [SV1459: $i,SV942: $i,SV333: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV333 )
= $false )
| ( ( ! [SY5356: $i,SY5357: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV942 @ SV1459 @ SV333 )
!= ( c_HOL_Ominus__class_Ominus @ SY5356 @ SY5357 @ SV333 ) )
| ( c_lessequals @ SY5357 @ SY5356 @ SV333 )
| ~ ( c_lessequals @ SV1459 @ SV942 @ SV333 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4460]) ).
thf(4941,plain,
! [SV1460: $i,SV943: $i,SV334: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV334 )
= $false )
| ( ( ! [SY5358: $i,SY5359: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV943 @ SV1460 @ SV334 )
!= ( c_HOL_Ominus__class_Ominus @ SY5358 @ SY5359 @ SV334 ) )
| ( c_lessequals @ SV1460 @ SV943 @ SV334 )
| ~ ( c_lessequals @ SY5359 @ SY5358 @ SV334 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4461]) ).
thf(4942,plain,
! [SV2106: $i,SV1838: $i,SV1461: $i,SV944: $i,SV335: $i] :
( ( ( c_lessequals @ ( c_Set_Oimage @ SV335 @ SV944 @ SV1461 @ SV1838 ) @ ( c_Set_Oimage @ SV335 @ SV2106 @ SV1461 @ SV1838 ) @ ( tc_fun @ SV1838 @ tc_bool ) )
| ~ ( c_lessequals @ SV944 @ SV2106 @ ( tc_fun @ SV1461 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4462]) ).
thf(4943,plain,
! [SV1462: $i,SV945: $i,SV336: $i] :
( ( ( c_lessequals @ SV336 @ SV945 @ ( tc_fun @ SV1462 @ tc_bool ) )
= $false )
| ( ( ! [SY5362: $i,SY5363: $i] : ( c_lessequals @ ( c_Set_Oimage @ SY5362 @ SV336 @ SV1462 @ SY5363 ) @ ( c_Set_Oimage @ SY5362 @ SV945 @ SV1462 @ SY5363 ) @ ( tc_fun @ SY5363 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4463]) ).
thf(4944,plain,
! [SV1839: $i,SV1463: $i,SV946: $i,SV337: $i] :
( ( ( c_lessequals @ ( c_Set_Oinsert @ SV337 @ SV946 @ SV1463 ) @ ( c_Set_Oinsert @ SV337 @ SV1839 @ SV1463 ) @ ( tc_fun @ SV1463 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV946 @ SV1839 @ ( tc_fun @ SV1463 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4464]) ).
thf(4945,plain,
! [SV2107: $i,SV1840: $i,SV1464: $i,SV947: $i,SV339: $i] :
( ( ( c_Set_Oimage @ SV339 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV947 @ SV1464 @ ( tc_fun @ SV1840 @ tc_bool ) ) @ SV1840 @ SV2107 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ SV339 @ SV947 @ SV1840 @ SV2107 ) @ ( c_Set_Oimage @ SV339 @ SV1464 @ SV1840 @ SV2107 ) @ ( tc_fun @ SV2107 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4465]) ).
thf(4946,plain,
! [SV2108: $i,SV1841: $i,SV1465: $i,SV948: $i,SV341: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV341 @ ( hAPP @ ( c_snd @ SV948 @ SV1465 ) @ ( c_Pair @ SV1841 @ SV2108 @ SV948 @ SV1465 ) ) ) @ ( hAPP @ ( c_fst @ SV948 @ SV1465 ) @ ( c_Pair @ SV1841 @ SV2108 @ SV948 @ SV1465 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV341 @ SV2108 ) @ SV1841 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4466]) ).
thf(4947,plain,
! [SV1466: $i,SV949: $i,SV342: $i] :
( ( ( ( c_Relation_ORange @ SV342 @ SV949 @ SV1466 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1466 @ tc_bool ) ) )
= $false )
| ( ( SV342
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV949 @ SV1466 ) @ tc_bool ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4467]) ).
thf(4948,plain,
! [SV2109: $i,SV1842: $i,SV1467: $i,SV950: $i,SV343: $i] :
( ( ! [SY5944: $i] :
( ( c_lessequals @ ( c_Relation_OImage @ SV343 @ SV950 @ SV1467 @ SV1842 ) @ ( c_Relation_OImage @ SV2109 @ SY5944 @ SV1467 @ SV1842 ) @ ( tc_fun @ SV1842 @ tc_bool ) )
| ~ ( c_lessequals @ SV950 @ SY5944 @ ( tc_fun @ SV1467 @ tc_bool ) )
| ~ ( c_lessequals @ SV343 @ SV2109 @ ( tc_fun @ ( tc_prod @ SV1467 @ SV1842 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4468]) ).
thf(4949,plain,
! [SV1468: $i,SV344: $i,SV951: $i] :
( ( ( c_Equiv__Relations_Oequiv @ SV951 @ SV344 @ SV1468 )
= $false )
| ( ( c_lessequals @ SV344 @ ( c_Product__Type_OSigma @ SV951 @ ( c_COMBK @ SV951 @ ( tc_fun @ SV1468 @ tc_bool ) @ SV1468 ) @ SV1468 @ SV1468 ) @ ( tc_fun @ ( tc_prod @ SV1468 @ SV1468 ) @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4469]) ).
thf(4950,plain,
! [SV345: $i,SV2110: $i,SV1843: $i] :
( ( ( ( c_lessequals @ SV1843 @ SV2110 @ SV345 )
| ( c_lessequals @ SV2110 @ SV1843 @ SV345 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV345 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4470]) ).
thf(4951,plain,
! [SV952: $i,SV346: $i,SV1844: $i] :
( ( ( c_Order__Relation_Ostrict__linear__order__on @ SV1844 @ SV346 @ SV952 )
= $false )
| ( ( c_Relation_Oirrefl @ SV346 @ SV952 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4471]) ).
thf(4952,plain,
! [SV1845: $i,SV1469: $i,SV953: $i,SV347: $i] :
( ( ( c_Wellfounded_Oacyclic @ ( c_Set_Oinsert @ ( c_Pair @ SV347 @ SV953 @ SV1469 @ SV1469 ) @ SV1845 @ ( tc_prod @ SV1469 @ SV1469 ) ) @ SV1469 )
= $true )
| ( ( ( c_in @ ( c_Pair @ SV953 @ SV347 @ SV1469 @ SV1469 ) @ ( c_Transitive__Closure_Ortrancl @ SV1845 @ SV1469 ) @ ( tc_prod @ SV1469 @ SV1469 ) )
| ~ ( c_Wellfounded_Oacyclic @ SV1845 @ SV1469 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4472]) ).
thf(4953,plain,
! [SV1846: $i,SV1470: $i,SV954: $i,SV348: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV348 @ SV954 @ SV1470 @ SV1470 ) @ ( c_Transitive__Closure_Ortrancl @ SV1846 @ SV1470 ) @ ( tc_prod @ SV1470 @ SV1470 ) ) )
= $true )
| ( ( ~ ( c_Wellfounded_Oacyclic @ ( c_Set_Oinsert @ ( c_Pair @ SV954 @ SV348 @ SV1470 @ SV1470 ) @ SV1846 @ ( tc_prod @ SV1470 @ SV1470 ) ) @ SV1470 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4473]) ).
thf(4954,plain,
! [SV955: $i,SV2111: $i,SV1471: $i,SV349: $i] :
( ( ( ! [SY5945: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1 @ SV349 @ SV1471 @ SV2111 @ SY5945 ) @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 @ SV349 @ SV1471 @ SV2111 @ SY5945 ) @ SY5945 @ SY5945 ) @ SV2111 @ ( tc_prod @ SY5945 @ SY5945 ) )
| ~ ( hBOOL @ ( hAPP @ SV349 @ SV1471 ) )
| ~ ( c_in @ ( c_Pair @ SV955 @ SV1471 @ SY5945 @ SY5945 ) @ ( c_Transitive__Closure_Ortrancl @ SV2111 @ SY5945 ) @ ( tc_prod @ SY5945 @ SY5945 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV349 @ SV955 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4474]) ).
thf(4955,plain,
! [SV956: $i,SV2112: $i,SV1472: $i,SV350: $i] :
( ( ( ! [SY5946: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 @ SV350 @ SV1472 @ SV2112 @ SY5946 ) @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2 @ SV350 @ SV1472 @ SV2112 @ SY5946 ) @ SY5946 @ SY5946 ) @ SV2112 @ ( tc_prod @ SY5946 @ SY5946 ) )
| ~ ( hBOOL @ ( hAPP @ SV350 @ SV1472 ) )
| ~ ( c_in @ ( c_Pair @ SV1472 @ SV956 @ SY5946 @ SY5946 ) @ ( c_Transitive__Closure_Ortrancl @ SV2112 @ SY5946 ) @ ( tc_prod @ SY5946 @ SY5946 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV350 @ SV956 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4475]) ).
thf(4956,plain,
! [SV957: $i,SV1473: $i,SV2113: $i,SV351: $i] :
( ( ( ~ ( c_in @ SV351 @ SV2113 @ SV1473 )
| ~ ( c_Equiv__Relations_Oequiv @ SV2113 @ SV957 @ SV1473 ) )
= $true )
| ( ( c_in @ SV351 @ ( c_Relation_OImage @ SV957 @ ( c_Set_Oinsert @ SV351 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1473 @ tc_bool ) ) @ SV1473 ) @ SV1473 @ SV1473 ) @ SV1473 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4476]) ).
thf(4957,plain,
! [SV1474: $i,SV958: $i,SV352: $i] :
( ( ( ~ ( c_lessequals @ ( c_Relation_Orel__comp @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Transitive__Closure_Ortrancl @ SV352 @ SV958 ) @ SV1474 @ ( tc_fun @ ( tc_prod @ SV958 @ SV958 ) @ tc_bool ) ) @ SV352 @ SV958 @ SV958 @ SV958 ) @ SV1474 @ ( tc_fun @ ( tc_prod @ SV958 @ SV958 ) @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Relation_OId @ SV958 ) @ SV1474 @ ( tc_fun @ ( tc_prod @ SV958 @ SV958 ) @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( c_Transitive__Closure_Ortrancl @ SV352 @ SV958 ) @ SV1474 @ ( tc_fun @ ( tc_prod @ SV958 @ SV958 ) @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4477]) ).
thf(4958,plain,
! [SV1847: $i,SV1475: $i,SV959: $i,SV353: $i] :
( ( ( c_in @ ( c_Pair @ SV353 @ SV959 @ SV1475 @ SV1475 ) @ SV1847 @ ( tc_prod @ SV1475 @ SV1475 ) )
= $true )
| ( ( ! [SY5763: $i] :
~ ( c_in @ SY5763 @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_OImage @ SV1847 @ ( c_Set_Oinsert @ SV353 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1475 @ tc_bool ) ) @ SV1475 ) @ SV1475 @ SV1475 ) @ ( c_Relation_OImage @ SV1847 @ ( c_Set_Oinsert @ SV959 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1475 @ tc_bool ) ) @ SV1475 ) @ SV1475 @ SV1475 ) @ ( tc_fun @ SV1475 @ tc_bool ) ) @ SV1475 )
| ! [SY5764: $i] :
~ ( c_Equiv__Relations_Oequiv @ SY5764 @ SV1847 @ SV1475 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4478]) ).
thf(4959,plain,
! [SV1848: $i,SV1476: $i,SV960: $i,SV354: $i] :
( ( ( c_in @ ( c_Pair @ SV354 @ SV960 @ SV1476 @ SV1476 ) @ SV1848 @ ( tc_prod @ SV1476 @ SV1476 ) )
= $true )
| ( ( ! [SY5765: $i] :
( ~ ( c_in @ SV960 @ SY5765 @ SV1476 )
| ~ ( c_lessequals @ ( c_Relation_OImage @ SV1848 @ ( c_Set_Oinsert @ SV960 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1476 @ tc_bool ) ) @ SV1476 ) @ SV1476 @ SV1476 ) @ ( c_Relation_OImage @ SV1848 @ ( c_Set_Oinsert @ SV354 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1476 @ tc_bool ) ) @ SV1476 ) @ SV1476 @ SV1476 ) @ ( tc_fun @ SV1476 @ tc_bool ) )
| ~ ( c_Equiv__Relations_Oequiv @ SY5765 @ SV1848 @ SV1476 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4479]) ).
thf(4960,plain,
! [SV1849: $i,SV1477: $i,SV961: $i,SV355: $i] :
( ( ( ! [SY5766: $i] :
( ( c_Set_Oinsert @ ( hAPP @ SV355 @ SV961 ) @ ( c_Set_Oimage @ SV355 @ SV1477 @ SV1849 @ SY5766 ) @ SY5766 )
= ( c_Set_Oimage @ SV355 @ SV1477 @ SV1849 @ SY5766 ) ) )
= $true )
| ( ( ~ ( c_in @ SV961 @ SV1477 @ SV1849 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4480]) ).
thf(4961,plain,
! [SV1850: $i,SV1478: $i,SV962: $i,SV356: $i] :
( ( ( c_in @ ( hAPP @ SV356 @ SV962 ) @ SV1478 @ SV1850 )
= $true )
| ( ( ! [SY5767: $i,SY5768: $i] :
( ~ ( c_in @ SV962 @ SY5767 @ SY5768 )
| ~ ( c_lessequals @ ( c_Set_Oimage @ SV356 @ SY5767 @ SY5768 @ SV1850 ) @ SV1478 @ ( tc_fun @ SV1850 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4481]) ).
thf(4962,plain,
! [SV2114: $i,SV1851: $i,SV1479: $i,SV963: $i,SV357: $i] :
( ( ( c_in @ ( c_Pair @ SV357 @ SV963 @ SV1479 @ SV1851 ) @ SV2114 @ ( tc_prod @ SV1479 @ SV1851 ) )
| ~ ( c_in @ SV963 @ ( c_Relation_OImage @ SV2114 @ ( c_Set_Oinsert @ SV357 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1479 @ tc_bool ) ) @ SV1479 ) @ SV1479 @ SV1851 ) @ SV1851 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4482]) ).
thf(4963,plain,
! [SV2115: $i,SV1852: $i,SV1480: $i,SV964: $i,SV358: $i] :
( ( ( c_in @ SV358 @ ( c_Relation_OImage @ SV964 @ ( c_Set_Oinsert @ SV1480 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1852 @ tc_bool ) ) @ SV1852 ) @ SV1852 @ SV2115 ) @ SV2115 )
| ~ ( c_in @ ( c_Pair @ SV1480 @ SV358 @ SV1852 @ SV2115 ) @ SV964 @ ( tc_prod @ SV1852 @ SV2115 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4483]) ).
thf(4964,plain,
! [SV2116: $i,SV1853: $i,SV1481: $i,SV965: $i,SV359: $i] :
( ( ( ( c_Product__Type_OSigma @ SV359 @ ( c_COMBK @ SV965 @ ( tc_fun @ SV1481 @ tc_bool ) @ SV1853 ) @ SV1853 @ SV1481 )
!= ( c_Product__Type_OSigma @ SV2116 @ ( c_COMBK @ SV965 @ ( tc_fun @ SV1481 @ tc_bool ) @ SV1853 ) @ SV1853 @ SV1481 ) )
| ! [SY5395: $i] :
~ ( c_in @ SY5395 @ SV965 @ SV1481 )
| ( SV359 = SV2116 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4484]) ).
thf(4965,plain,
! [SV360: $i,SV966: $i,SV2117: $i,SV1854: $i] :
( ( ( ~ ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ SV1854 @ SV2117 @ SV966 @ SV966 ) @ SV360 @ ( tc_prod @ SV966 @ SV966 ) ) @ SV966 ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV360 @ SV966 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4485]) ).
thf(4966,plain,
! [SV1855: $i,SV1482: $i,SV967: $i,SV361: $i] :
( ( ( c_in @ SV361 @ ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV967 @ SV1482 @ ( tc_fun @ ( tc_prod @ SV1855 @ SV1855 ) @ tc_bool ) ) @ SV1855 ) @ ( tc_prod @ SV1855 @ SV1855 ) )
= $true )
| ( ( ~ ( c_in @ SV361 @ ( c_Transitive__Closure_Ortrancl @ SV967 @ SV1855 ) @ ( tc_prod @ SV1855 @ SV1855 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4486]) ).
thf(4967,plain,
! [SV1856: $i,SV1483: $i,SV968: $i,SV362: $i] :
( ( ( c_in @ SV362 @ ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV968 @ SV1483 @ ( tc_fun @ ( tc_prod @ SV1856 @ SV1856 ) @ tc_bool ) ) @ SV1856 ) @ ( tc_prod @ SV1856 @ SV1856 ) )
= $true )
| ( ( ~ ( c_in @ SV362 @ ( c_Transitive__Closure_Ortrancl @ SV1483 @ SV1856 ) @ ( tc_prod @ SV1856 @ SV1856 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4487]) ).
thf(4968,plain,
! [SV363: $i,SV1484: $i,SV969: $i,SV2118: $i] :
( ( ( ~ ( c_lessequals @ SV2118 @ SV969 @ ( tc_fun @ ( tc_prod @ SV1484 @ SV1484 ) @ tc_bool ) )
| ~ ( c_in @ SV363 @ ( c_Transitive__Closure_Otrancl @ SV2118 @ SV1484 ) @ ( tc_prod @ SV1484 @ SV1484 ) ) )
= $true )
| ( ( c_in @ SV363 @ ( c_Transitive__Closure_Otrancl @ SV969 @ SV1484 ) @ ( tc_prod @ SV1484 @ SV1484 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4488]) ).
thf(4969,plain,
! [SV1857: $i,SV1485: $i,SV970: $i,SV364: $i] :
( ( ( ( c_Relation_OImage @ SV364 @ ( c_Set_Oinsert @ SV970 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1485 @ tc_bool ) ) @ SV1485 ) @ SV1485 @ SV1485 )
= ( c_Relation_OImage @ SV364 @ ( c_Set_Oinsert @ SV1857 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1485 @ tc_bool ) ) @ SV1485 ) @ SV1485 @ SV1485 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV970 @ SV1857 @ SV1485 @ SV1485 ) @ SV364 @ ( tc_prod @ SV1485 @ SV1485 ) )
| ! [SY5400: $i] :
~ ( c_Equiv__Relations_Oequiv @ SY5400 @ SV364 @ SV1485 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4489]) ).
thf(4970,plain,
! [SV1858: $i,SV1486: $i,SV971: $i,SV365: $i] :
( ( ( ( c_Relation_OImage @ SV365 @ ( c_Set_Oinsert @ SV971 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1486 @ tc_bool ) ) @ SV1486 ) @ SV1486 @ SV1486 )
= ( c_Relation_OImage @ SV365 @ ( c_Set_Oinsert @ SV1858 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1486 @ tc_bool ) ) @ SV1486 ) @ SV1486 @ SV1486 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV971 @ SV1858 @ SV1486 @ SV1486 ) @ SV365 @ ( tc_prod @ SV1486 @ SV1486 ) )
| ! [SY5402: $i] :
~ ( c_Equiv__Relations_Oequiv @ SY5402 @ SV365 @ SV1486 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4490]) ).
thf(4971,plain,
! [SV972: $i,SV1487: $i,SV366: $i] :
( ( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV366 @ SV1487 @ ( tc_fun @ ( tc_prod @ SV972 @ SV972 ) @ tc_bool ) ) @ SV972 )
= $false )
| ( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ SV366 @ SV366 @ SV972 @ SV972 @ SV972 ) @ ( c_Relation_Orel__comp @ SV1487 @ SV366 @ SV972 @ SV972 @ SV972 ) @ ( tc_fun @ ( tc_prod @ SV972 @ SV972 ) @ tc_bool ) ) @ SV1487 @ ( tc_fun @ ( tc_prod @ SV972 @ SV972 ) @ tc_bool ) ) @ SV972 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4491]) ).
thf(4972,plain,
! [SV973: $i,SV1488: $i,SV367: $i] :
( ( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ SV367 @ SV367 @ SV1488 @ SV1488 @ SV1488 ) @ ( c_Relation_Orel__comp @ SV973 @ SV367 @ SV1488 @ SV1488 @ SV1488 ) @ ( tc_fun @ ( tc_prod @ SV1488 @ SV1488 ) @ tc_bool ) ) @ SV973 @ ( tc_fun @ ( tc_prod @ SV1488 @ SV1488 ) @ tc_bool ) ) @ SV1488 )
= $false )
| ( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV367 @ SV973 @ ( tc_fun @ ( tc_prod @ SV1488 @ SV1488 ) @ tc_bool ) ) @ SV1488 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4492]) ).
thf(4973,plain,
! [SV1490: $i,SV987: $i,SV382: $i] :
( ( ( c_Relation_Ototal__on @ SV382 @ ( c_HOL_Ominus__class_Ominus @ SV987 @ ( c_Relation_OId @ SV1490 ) @ ( tc_fun @ ( tc_prod @ SV1490 @ SV1490 ) @ tc_bool ) ) @ SV1490 )
= $false )
| ( ( c_Relation_Ototal__on @ SV382 @ SV987 @ SV1490 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4499]) ).
thf(4974,plain,
! [SV1491: $i,SV988: $i,SV383: $i] :
( ( ( c_Relation_Ototal__on @ SV383 @ SV988 @ SV1491 )
= $false )
| ( ( c_Relation_Ototal__on @ SV383 @ ( c_HOL_Ominus__class_Ominus @ SV988 @ ( c_Relation_OId @ SV1491 ) @ ( tc_fun @ ( tc_prod @ SV1491 @ SV1491 ) @ tc_bool ) ) @ SV1491 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4500]) ).
thf(4975,plain,
! [SV989: $i,SV384: $i] :
( ( ( c_Relation_Otrans @ SV384 @ SV989 )
= $false )
| ( ( ~ ( c_Relation_Osym @ SV384 @ SV989 ) )
= $true )
| ( ( c_lessequals @ ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ SV384 @ SV989 @ SV989 ) @ SV384 @ SV989 @ SV989 @ SV989 ) @ SV384 @ ( tc_fun @ ( tc_prod @ SV989 @ SV989 ) @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4501]) ).
thf(4976,plain,
! [SV1859: $i,SV1492: $i,SV990: $i,SV385: $i] :
( ( ( c_in @ ( c_Pair @ SV385 @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1 @ SV990 @ SV385 @ SV1492 @ SV1859 ) @ SV1859 @ SV1859 ) @ ( c_Transitive__Closure_Ortrancl @ SV990 @ SV1859 ) @ ( tc_prod @ SV1859 @ SV1859 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV385 @ SV1492 @ SV1859 @ SV1859 ) @ ( c_Transitive__Closure_Otrancl @ SV990 @ SV1859 ) @ ( tc_prod @ SV1859 @ SV1859 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4502]) ).
thf(4977,plain,
! [SV1860: $i,SV1493: $i,SV991: $i,SV386: $i] :
( ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1 @ SV386 @ SV991 @ SV1493 @ SV1860 ) @ SV1493 @ SV1860 @ SV1860 ) @ ( c_Transitive__Closure_Ortrancl @ SV386 @ SV1860 ) @ ( tc_prod @ SV1860 @ SV1860 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV991 @ SV1493 @ SV1860 @ SV1860 ) @ ( c_Transitive__Closure_Otrancl @ SV386 @ SV1860 ) @ ( tc_prod @ SV1860 @ SV1860 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4503]) ).
thf(4978,plain,
! [SV1861: $i,SV1494: $i,SV992: $i,SV387: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV387 @ SV992 @ SV1494 @ SV1494 ) @ ( c_Transitive__Closure_Ortrancl @ SV1861 @ SV1494 ) @ ( tc_prod @ SV1494 @ SV1494 ) ) )
= $true )
| ( ( ~ ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ SV992 @ SV387 @ SV1494 @ SV1494 ) @ SV1861 @ ( tc_prod @ SV1494 @ SV1494 ) ) @ SV1494 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4504]) ).
thf(4979,plain,
! [SV1862: $i,SV1495: $i,SV993: $i,SV388: $i] :
( ( ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ SV388 @ SV993 @ SV1495 @ SV1495 ) @ SV1862 @ ( tc_prod @ SV1495 @ SV1495 ) ) @ SV1495 )
= $true )
| ( ( ( c_in @ ( c_Pair @ SV993 @ SV388 @ SV1495 @ SV1495 ) @ ( c_Transitive__Closure_Ortrancl @ SV1862 @ SV1495 ) @ ( tc_prod @ SV1495 @ SV1495 ) )
| ~ ( c_Wellfounded_Owf @ SV1862 @ SV1495 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4505]) ).
thf(4980,plain,
! [SV1496: $i,SV994: $i,SV389: $i] :
( ( ( ~ ( c_Relation_Ototal__on @ SV389 @ SV994 @ SV1496 ) )
= $true )
| ( ( ~ ( c_Relation_Oirrefl @ SV994 @ SV1496 )
| ~ ( c_Relation_Otrans @ SV994 @ SV1496 ) )
= $true )
| ( ( c_Order__Relation_Ostrict__linear__order__on @ SV389 @ SV994 @ SV1496 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4506]) ).
thf(4981,plain,
! [SV996: $i,SV391: $i] :
( ( ( c_Relation_Oantisym @ SV391 @ SV996 )
= $false )
| ( ( ~ ( c_Relation_Otrans @ SV391 @ SV996 ) )
= $true )
| ( ( c_Relation_Otrans @ ( c_HOL_Ominus__class_Ominus @ SV391 @ ( c_Relation_OId @ SV996 ) @ ( tc_fun @ ( tc_prod @ SV996 @ SV996 ) @ tc_bool ) ) @ SV996 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4508]) ).
thf(4982,plain,
! [SV2119: $i,SV1863: $i,SV1497: $i,SV997: $i,SV392: $i] :
( ( ( ( c_Relation_OImage @ SV392 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV997 @ SV1497 @ ( tc_fun @ SV1863 @ tc_bool ) ) @ SV1863 @ SV2119 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_OImage @ SV392 @ SV997 @ SV1863 @ SV2119 ) @ ( c_Relation_OImage @ SV392 @ SV1497 @ SV1863 @ SV2119 ) @ ( tc_fun @ SV2119 @ tc_bool ) ) )
| ~ ( c_Relation_Osingle__valued @ ( c_Relation_Oconverse @ SV392 @ SV1863 @ SV2119 ) @ SV2119 @ SV1863 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4509]) ).
thf(4983,plain,
! [SV999: $i,SV394: $i,SV1864: $i] :
( ( ( c_Relation_Orefl__on @ SV1864 @ SV394 @ SV999 )
= $false )
| ( ( c_lessequals @ SV394 @ ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ SV394 @ SV999 @ SV999 ) @ SV394 @ SV999 @ SV999 @ SV999 ) @ ( tc_fun @ ( tc_prod @ SV999 @ SV999 ) @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4510]) ).
thf(4984,plain,
! [SV2120: $i,SV1865: $i,SV1498: $i,SV1004: $i,SV399: $i] :
( ( ! [SY5948: $i] :
( ( ( c_Recdef_Ocut @ SV399 @ SV1004 @ SV1498 @ SV1865 @ SV2120 )
= ( c_Recdef_Ocut @ SY5948 @ SV1004 @ SV1498 @ SV1865 @ SV2120 ) )
| ( c_in @ ( c_Pair @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ SV399 @ SY5948 @ SV1004 @ SV1498 @ SV1865 @ SV2120 ) @ SV1498 @ SV1865 @ SV1865 ) @ SV1004 @ ( tc_prod @ SV1865 @ SV1865 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4511]) ).
thf(4985,plain,
! [SV1499: $i,SV1005: $i,SV400: $i] :
( ( ( c_in @ SV400 @ ( c_Relation_OId__on @ SV1005 @ SV1499 ) @ ( tc_prod @ SV1499 @ SV1499 ) )
= $false )
| ( ( SV400
= ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XId__onE__1__1 @ SV1005 @ SV400 @ SV1499 ) @ ( c_ATP__Linkup_Osko__Relation__XId__onE__1__1 @ SV1005 @ SV400 @ SV1499 ) @ SV1499 @ SV1499 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4512]) ).
thf(4986,plain,
! [SV1500: $i,SV401: $i,SV1006: $i] :
( ( ( c_in @ SV1006 @ ( c_Relation_OId__on @ SV401 @ SV1500 ) @ ( tc_prod @ SV1500 @ SV1500 ) )
= $false )
| ( ( c_in @ ( c_ATP__Linkup_Osko__Relation__XId__onE__1__1 @ SV401 @ SV1006 @ SV1500 ) @ SV401 @ SV1500 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4513]) ).
thf(4987,plain,
! [SV2121: $i,SV1866: $i,SV1501: $i,SV1010: $i,SV405: $i] :
( ( ! [SY5949: $i,SY5950: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 @ SV405 @ SV1010 @ SV1501 @ SV1866 @ SV2121 @ SY5949 @ SY5950 ) @ SV1010 @ SY5950 @ SY5949 ) @ SV1866 @ ( tc_prod @ SY5950 @ SY5949 ) )
| ~ ( c_in @ ( c_Pair @ SV405 @ SV1010 @ SV2121 @ SY5949 ) @ ( c_Relation_Orel__comp @ SV1501 @ SV1866 @ SV2121 @ SY5950 @ SY5949 ) @ ( tc_prod @ SV2121 @ SY5949 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4517]) ).
thf(4988,plain,
! [SV2122: $i,SV1867: $i,SV1502: $i,SV1011: $i,SV406: $i] :
( ( ! [SY5951: $i,SY5952: $i] :
( ( c_in @ ( c_Pair @ SV406 @ ( c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 @ SV406 @ SV1011 @ SV1502 @ SV1867 @ SV2122 @ SY5951 @ SY5952 ) @ SV2122 @ SY5952 ) @ SV1502 @ ( tc_prod @ SV2122 @ SY5952 ) )
| ~ ( c_in @ ( c_Pair @ SV406 @ SV1011 @ SV2122 @ SY5951 ) @ ( c_Relation_Orel__comp @ SV1502 @ SV1867 @ SV2122 @ SY5952 @ SY5951 ) @ ( tc_prod @ SV2122 @ SY5951 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4518]) ).
thf(4989,plain,
! [SV1503: $i,SV1012: $i,SV407: $i] :
( ( ( c_in @ ( c_Pair @ SV407 @ SV407 @ SV1012 @ SV1012 ) @ SV1503 @ ( tc_prod @ SV1012 @ SV1012 ) )
= $false )
| ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1 @ SV1503 @ SV1012 ) @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1 @ SV1503 @ SV1012 ) @ SV1012 @ SV1012 ) @ ( c_Transitive__Closure_Otrancl @ SV1503 @ SV1012 ) @ ( tc_prod @ SV1012 @ SV1012 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4519]) ).
thf(4990,plain,
! [SV1868: $i,SV1504: $i,SV1013: $i,SV408: $i] :
( ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1 @ SV408 @ SV1013 @ SV1504 @ SV1868 ) @ SV1504 @ SV1868 @ SV1868 ) @ ( c_Transitive__Closure_Otrancl @ SV408 @ SV1868 ) @ ( tc_prod @ SV1868 @ SV1868 ) )
= $true )
| ( ( ( c_in @ ( c_Pair @ SV1013 @ SV1504 @ SV1868 @ SV1868 ) @ SV408 @ ( tc_prod @ SV1868 @ SV1868 ) )
| ~ ( c_in @ ( c_Pair @ SV1013 @ SV1504 @ SV1868 @ SV1868 ) @ ( c_Transitive__Closure_Otrancl @ SV408 @ SV1868 ) @ ( tc_prod @ SV1868 @ SV1868 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4520]) ).
thf(4991,plain,
! [SV1869: $i,SV1505: $i,SV1014: $i,SV409: $i] :
( ( ( c_in @ ( c_Pair @ SV409 @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1 @ SV1014 @ SV409 @ SV1505 @ SV1869 ) @ SV1869 @ SV1869 ) @ SV1014 @ ( tc_prod @ SV1869 @ SV1869 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV409 @ SV1505 @ SV1869 @ SV1869 ) @ ( c_Transitive__Closure_Otrancl @ SV1014 @ SV1869 ) @ ( tc_prod @ SV1869 @ SV1869 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4521]) ).
thf(4992,plain,
! [SV1506: $i,SV1015: $i,SV410: $i] :
( ( ( c_in @ ( c_Pair @ SV410 @ SV1015 @ t_a @ t_a ) @ SV1506 @ ( tc_prod @ t_a @ t_a ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV410 @ SV1015 @ t_a @ t_a ) @ ( c_Transitive__Closure_Otrancl @ SV1506 @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV410 @ ( v_sko__Transitive__Closure__Xtrancl__Xcases__1 @ SV410 @ SV1015 @ SV1506 ) @ t_a @ t_a ) @ ( c_Transitive__Closure_Otrancl @ SV1506 @ t_a ) @ ( tc_prod @ t_a @ t_a ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4522]) ).
thf(4993,plain,
! [SV1507: $i,SV1016: $i,SV411: $i] :
( ( ( c_in @ ( c_Pair @ SV411 @ SV411 @ SV1016 @ SV1016 ) @ ( c_Transitive__Closure_Otrancl @ SV1507 @ SV1016 ) @ ( tc_prod @ SV1016 @ SV1016 ) )
= $false )
| ( ( ~ ( c_Wellfounded_Oacyclic @ SV1507 @ SV1016 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4523]) ).
thf(4994,plain,
! [SV1870: $i,SV1508: $i,SV1017: $i,SV412: $i] :
( ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1 @ SV412 @ SV1017 @ SV1508 @ SV1870 ) @ SV1017 @ SV1870 @ SV1870 ) @ SV1508 @ ( tc_prod @ SV1870 @ SV1870 ) )
= $true )
| ( ( ( c_in @ ( c_Pair @ SV412 @ SV1017 @ SV1870 @ SV1870 ) @ SV1508 @ ( tc_prod @ SV1870 @ SV1870 ) )
| ~ ( c_in @ ( c_Pair @ SV412 @ SV1017 @ SV1870 @ SV1870 ) @ ( c_Transitive__Closure_Otrancl @ SV1508 @ SV1870 ) @ ( tc_prod @ SV1870 @ SV1870 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4524]) ).
thf(4995,plain,
! [SV1871: $i,SV1509: $i,SV1018: $i,SV413: $i] :
( ( ( c_in @ ( c_Pair @ SV413 @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1 @ SV413 @ SV1018 @ SV1509 @ SV1871 ) @ SV1871 @ SV1871 ) @ ( c_Transitive__Closure_Otrancl @ SV1509 @ SV1871 ) @ ( tc_prod @ SV1871 @ SV1871 ) )
= $true )
| ( ( ( c_in @ ( c_Pair @ SV413 @ SV1018 @ SV1871 @ SV1871 ) @ SV1509 @ ( tc_prod @ SV1871 @ SV1871 ) )
| ~ ( c_in @ ( c_Pair @ SV413 @ SV1018 @ SV1871 @ SV1871 ) @ ( c_Transitive__Closure_Otrancl @ SV1509 @ SV1871 ) @ ( tc_prod @ SV1871 @ SV1871 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4525]) ).
thf(4996,plain,
! [SV1872: $i,SV1510: $i,SV1019: $i,SV414: $i] :
( ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1 @ SV414 @ SV1019 @ SV1510 @ SV1872 ) @ SV1510 @ SV1872 @ SV1872 ) @ SV414 @ ( tc_prod @ SV1872 @ SV1872 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV1019 @ SV1510 @ SV1872 @ SV1872 ) @ ( c_Transitive__Closure_Otrancl @ SV414 @ SV1872 ) @ ( tc_prod @ SV1872 @ SV1872 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4526]) ).
thf(4997,plain,
! [SV1873: $i,SV1511: $i,SV1020: $i,SV415: $i] :
( ( ( c_in @ ( c_Pair @ SV415 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1 @ SV1020 @ SV415 @ SV1511 @ SV1873 ) @ SV1873 @ SV1873 ) @ SV1020 @ ( tc_prod @ SV1873 @ SV1873 ) )
= $true )
| ( ( ( c_in @ ( c_Pair @ SV415 @ SV1511 @ SV1873 @ SV1873 ) @ SV1020 @ ( tc_prod @ SV1873 @ SV1873 ) )
| ~ ( c_in @ ( c_Pair @ SV415 @ SV1511 @ SV1873 @ SV1873 ) @ ( c_Transitive__Closure_Otrancl @ SV1020 @ SV1873 ) @ ( tc_prod @ SV1873 @ SV1873 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4527]) ).
thf(4998,plain,
! [SV1512: $i,SV1021: $i,SV416: $i] :
( ( ( c_in @ ( c_Pair @ SV416 @ SV1021 @ t_a @ t_a ) @ SV1512 @ ( tc_prod @ t_a @ t_a ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV416 @ SV1021 @ t_a @ t_a ) @ ( c_Transitive__Closure_Otrancl @ SV1512 @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ ( v_sko__Transitive__Closure__Xtrancl__Xcases__1 @ SV416 @ SV1021 @ SV1512 ) @ SV1021 @ t_a @ t_a ) @ SV1512 @ ( tc_prod @ t_a @ t_a ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4528]) ).
thf(4999,plain,
! [SV1022: $i,SV1513: $i,SV417: $i] :
( ( ( hBOOL @ ( hAPP @ SV417 @ SV1513 ) )
= $true )
| ( ( ! [SY5426: $i,SY5427: $i] :
( ~ ( c_in @ ( c_Pair @ SV1513 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1 @ SV417 @ SY5426 @ SY5427 ) @ SY5427 @ SY5427 ) @ SY5426 @ ( tc_prod @ SY5427 @ SY5427 ) )
| ~ ( c_Wellfounded_Owf @ SY5426 @ SY5427 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV417 @ SV1022 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4529]) ).
thf(5000,plain,
! [SV1023: $i,SV1514: $i,SV418: $i] :
( ( ( hBOOL @ ( hAPP @ SV418 @ SV1514 ) )
= $true )
| ( ( ! [SY5428: $i,SY5429: $i] :
( ~ ( c_in @ ( c_Pair @ SV1514 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1 @ SV418 @ SY5428 @ SY5429 ) @ SY5429 @ SY5429 ) @ SY5428 @ ( tc_prod @ SY5429 @ SY5429 ) )
| ~ ( c_Wellfounded_Owf @ SY5428 @ SY5429 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV418 @ SV1023 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4530]) ).
thf(5001,plain,
! [SV1024: $i,SV1515: $i,SV419: $i] :
( ( ( hBOOL @ ( hAPP @ SV419 @ SV1515 ) )
= $true )
| ( ( ! [SY5430: $i,SY5431: $i] :
( ~ ( c_in @ ( c_Pair @ SV1515 @ ( c_List_Osko__Recdef__Xtfl__wf__induct__1__1 @ SV419 @ SY5430 @ SY5431 ) @ SY5431 @ SY5431 ) @ SY5430 @ ( tc_prod @ SY5431 @ SY5431 ) )
| ~ ( c_Wellfounded_Owf @ SY5430 @ SY5431 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV419 @ SV1024 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4531]) ).
thf(5002,plain,
! [SV1025: $i,SV1516: $i,SV420: $i] :
( ( ( hBOOL @ ( hAPP @ SV420 @ SV1516 ) )
= $true )
| ( ( ! [SY5432: $i,SY5433: $i] :
( ~ ( c_in @ ( c_Pair @ SV1516 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1 @ SV420 @ SY5432 @ SY5433 ) @ SY5433 @ SY5433 ) @ SY5432 @ ( tc_prod @ SY5433 @ SY5433 ) )
| ~ ( c_Wellfounded_Owf @ SY5432 @ SY5433 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV420 @ SV1025 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4532]) ).
thf(5003,plain,
! [SV1874: $i,SV1517: $i,SV1026: $i,SV421: $i] :
( ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1 @ SV421 @ SV1026 @ SV1517 @ SV1874 ) @ SV1026 @ SV1874 @ SV1874 ) @ SV1517 @ ( tc_prod @ SV1874 @ SV1874 ) )
= $true )
| ( ( ( SV421 = SV1026 )
| ~ ( c_in @ ( c_Pair @ SV421 @ SV1026 @ SV1874 @ SV1874 ) @ ( c_Transitive__Closure_Ortrancl @ SV1517 @ SV1874 ) @ ( tc_prod @ SV1874 @ SV1874 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4533]) ).
thf(5004,plain,
! [SV1875: $i,SV1518: $i,SV1027: $i,SV422: $i] :
( ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1 @ SV422 @ SV1027 @ SV1518 @ SV1875 ) @ SV1518 @ SV1875 @ SV1875 ) @ ( c_Transitive__Closure_Ortrancl @ SV422 @ SV1875 ) @ ( tc_prod @ SV1875 @ SV1875 ) )
= $true )
| ( ( ( SV1027 = SV1518 )
| ~ ( c_in @ ( c_Pair @ SV1027 @ SV1518 @ SV1875 @ SV1875 ) @ ( c_Transitive__Closure_Ortrancl @ SV422 @ SV1875 ) @ ( tc_prod @ SV1875 @ SV1875 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4534]) ).
thf(5005,plain,
! [SV1876: $i,SV1519: $i,SV1028: $i,SV423: $i] :
( ( ( c_in @ ( c_Pair @ SV423 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1 @ SV1028 @ SV423 @ SV1519 @ SV1876 ) @ SV1876 @ SV1876 ) @ SV1028 @ ( tc_prod @ SV1876 @ SV1876 ) )
= $true )
| ( ( ( SV423 = SV1519 )
| ~ ( c_in @ ( c_Pair @ SV423 @ SV1519 @ SV1876 @ SV1876 ) @ ( c_Transitive__Closure_Ortrancl @ SV1028 @ SV1876 ) @ ( tc_prod @ SV1876 @ SV1876 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4535]) ).
thf(5006,plain,
! [SV1029: $i,SV2123: $i,SV1520: $i,SV424: $i] :
( ( ( ! [SY5953: $i] :
( ( hBOOL @ ( hAPP @ SV424 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 @ SV424 @ SV1520 @ SV2123 @ SY5953 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV424 @ SV1520 ) )
| ~ ( c_in @ ( c_Pair @ SV1029 @ SV1520 @ SY5953 @ SY5953 ) @ ( c_Transitive__Closure_Ortrancl @ SV2123 @ SY5953 ) @ ( tc_prod @ SY5953 @ SY5953 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV424 @ SV1029 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4536]) ).
thf(5007,plain,
! [SV1030: $i,SV2124: $i,SV1521: $i,SV425: $i] :
( ( ( ! [SY5954: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 @ SV425 @ SV1521 @ SV2124 @ SY5954 ) @ SV1521 @ SY5954 @ SY5954 ) @ ( c_Transitive__Closure_Ortrancl @ SV2124 @ SY5954 ) @ ( tc_prod @ SY5954 @ SY5954 ) )
| ~ ( hBOOL @ ( hAPP @ SV425 @ SV1521 ) )
| ~ ( c_in @ ( c_Pair @ SV1030 @ SV1521 @ SY5954 @ SY5954 ) @ ( c_Transitive__Closure_Ortrancl @ SV2124 @ SY5954 ) @ ( tc_prod @ SY5954 @ SY5954 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV425 @ SV1030 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4537]) ).
thf(5008,plain,
! [SV1031: $i,SV2125: $i,SV426: $i,SV1522: $i] :
( ( ( ! [SY5955: $i] :
( ( c_in @ ( c_Pair @ SV1522 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 @ SV426 @ SV1522 @ SV2125 @ SY5955 ) @ SY5955 @ SY5955 ) @ ( c_Transitive__Closure_Ortrancl @ SV2125 @ SY5955 ) @ ( tc_prod @ SY5955 @ SY5955 ) )
| ~ ( hBOOL @ ( hAPP @ SV426 @ SV1522 ) )
| ~ ( c_in @ ( c_Pair @ SV1522 @ SV1031 @ SY5955 @ SY5955 ) @ ( c_Transitive__Closure_Ortrancl @ SV2125 @ SY5955 ) @ ( tc_prod @ SY5955 @ SY5955 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV426 @ SV1031 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4538]) ).
thf(5009,plain,
! [SV1032: $i,SV2126: $i,SV1523: $i,SV427: $i] :
( ( ( ! [SY5956: $i] :
( ~ ( hBOOL @ ( hAPP @ SV427 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2 @ SV427 @ SV1523 @ SV2126 @ SY5956 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV427 @ SV1523 ) )
| ~ ( c_in @ ( c_Pair @ SV1523 @ SV1032 @ SY5956 @ SY5956 ) @ ( c_Transitive__Closure_Ortrancl @ SV2126 @ SY5956 ) @ ( tc_prod @ SY5956 @ SY5956 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV427 @ SV1032 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4539]) ).
thf(5010,plain,
! [SV1524: $i,SV428: $i,SV1033: $i] :
( ( ( SV1033 = SV428 )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV428 @ SV1033 @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ SV1524 @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV428 @ ( v_sko__Transitive__Closure__Xrtrancl__Xcases__1 @ SV428 @ SV1033 @ SV1524 ) @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ SV1524 @ t_a ) @ ( tc_prod @ t_a @ t_a ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4540]) ).
thf(5011,plain,
! [SV1034: $i,SV2127: $i,SV1525: $i,SV429: $i] :
( ( ( ! [SY5957: $i] :
( ( hBOOL @ ( hAPP @ SV429 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 @ SV429 @ SV1525 @ SV2127 @ SY5957 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV429 @ SV1525 ) )
| ~ ( c_in @ ( c_Pair @ SV1525 @ SV1034 @ SY5957 @ SY5957 ) @ ( c_Transitive__Closure_Ortrancl @ SV2127 @ SY5957 ) @ ( tc_prod @ SY5957 @ SY5957 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV429 @ SV1034 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4541]) ).
thf(5012,plain,
! [SV1526: $i,SV430: $i,SV1035: $i] :
( ( ( SV1035 = SV430 )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV430 @ SV1035 @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ SV1526 @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ ( v_sko__Transitive__Closure__Xrtrancl__Xcases__1 @ SV430 @ SV1035 @ SV1526 ) @ SV1035 @ t_a @ t_a ) @ SV1526 @ ( tc_prod @ t_a @ t_a ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4542]) ).
thf(5013,plain,
! [SV1036: $i,SV2128: $i,SV1527: $i,SV431: $i] :
( ( ( ! [SY5958: $i] :
( ~ ( hBOOL @ ( hAPP @ SV431 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1 @ SV431 @ SV1527 @ SV2128 @ SY5958 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV431 @ SV1527 ) )
| ~ ( c_in @ ( c_Pair @ SV1036 @ SV1527 @ SY5958 @ SY5958 ) @ ( c_Transitive__Closure_Ortrancl @ SV2128 @ SY5958 ) @ ( tc_prod @ SY5958 @ SY5958 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV431 @ SV1036 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4543]) ).
thf(5014,plain,
! [SV1877: $i,SV1528: $i,SV1037: $i,SV432: $i] :
( ( ( c_in @ ( c_Pair @ SV432 @ ( c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1 @ SV432 @ SV1037 @ SV1528 @ SV1877 ) @ SV1877 @ SV1877 ) @ ( c_Transitive__Closure_Ortrancl @ SV1528 @ SV1877 ) @ ( tc_prod @ SV1877 @ SV1877 ) )
= $true )
| ( ( ( SV432 = SV1037 )
| ~ ( c_in @ ( c_Pair @ SV432 @ SV1037 @ SV1877 @ SV1877 ) @ ( c_Transitive__Closure_Ortrancl @ SV1528 @ SV1877 ) @ ( tc_prod @ SV1877 @ SV1877 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4544]) ).
thf(5015,plain,
! [SV2129: $i,SV1878: $i,SV1529: $i,SV1038: $i,SV433: $i] :
( ( ( c_in @ ( c_ATP__Linkup_Osko__Product__Type__XSigmaE__1__1 @ SV433 @ SV1038 @ SV1529 @ SV1878 @ SV2129 ) @ SV433 @ SV1878 )
| ~ ( c_in @ SV1529 @ ( c_Product__Type_OSigma @ SV433 @ SV1038 @ SV1878 @ SV2129 ) @ ( tc_prod @ SV1878 @ SV2129 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4545]) ).
thf(5016,plain,
! [SV436: $i,SV1041: $i,SV2130: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV2130 @ SV2130 @ SV1041 @ SV1041 ) @ ( c_Transitive__Closure_Otrancl @ SV436 @ SV1041 ) @ ( tc_prod @ SV1041 @ SV1041 ) ) )
= $true )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_Oconverse @ SV436 @ SV1041 @ SV1041 ) @ ( c_Transitive__Closure_Ortrancl @ SV436 @ SV1041 ) @ ( tc_fun @ ( tc_prod @ SV1041 @ SV1041 ) @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV1041 @ SV1041 ) @ tc_bool ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4547]) ).
thf(5017,plain,
! [SV1879: $i,SV1530: $i,SV1042: $i,SV437: $i] :
( ( ( ( c_Relation_OImage @ SV437 @ ( c_Set_Oinsert @ SV1042 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1530 @ tc_bool ) ) @ SV1530 ) @ SV1530 @ SV1530 )
!= ( c_Relation_OImage @ SV437 @ ( c_Set_Oinsert @ SV1879 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1530 @ tc_bool ) ) @ SV1530 ) @ SV1530 @ SV1530 ) )
= $true )
| ( ( ( c_in @ ( c_Pair @ SV1042 @ SV1879 @ SV1530 @ SV1530 ) @ SV437 @ ( tc_prod @ SV1530 @ SV1530 ) )
| ! [SY5786: $i] :
( ~ ( c_in @ SV1879 @ SY5786 @ SV1530 )
| ~ ( c_Equiv__Relations_Oequiv @ SY5786 @ SV437 @ SV1530 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4548]) ).
thf(5018,plain,
! [SV1880: $i,SV1531: $i,SV1043: $i,SV438: $i] :
( ( ( ( c_Relation_OImage @ SV438 @ ( c_Set_Oinsert @ SV1043 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1531 @ tc_bool ) ) @ SV1531 ) @ SV1531 @ SV1531 )
!= ( c_Relation_OImage @ SV438 @ ( c_Set_Oinsert @ SV1880 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1531 @ tc_bool ) ) @ SV1531 ) @ SV1531 @ SV1531 ) )
= $true )
| ( ( ! [SY5787: $i] :
( ~ ( c_Equiv__Relations_Oequiv @ SY5787 @ SV438 @ SV1531 )
| ( c_in @ ( c_Pair @ SV1043 @ SV1880 @ SV1531 @ SV1531 ) @ SV438 @ ( tc_prod @ SV1531 @ SV1531 ) )
| ~ ( c_in @ SV1880 @ SY5787 @ SV1531 )
| ~ ( c_in @ SV1043 @ SY5787 @ SV1531 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4549]) ).
thf(5019,plain,
! [SV1881: $i,SV1532: $i,SV1044: $i,SV439: $i] :
( ( ( ( c_Relation_OImage @ SV439 @ ( c_Set_Oinsert @ SV1044 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1532 @ tc_bool ) ) @ SV1532 ) @ SV1532 @ SV1532 )
= ( c_Relation_OImage @ SV439 @ ( c_Set_Oinsert @ SV1881 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1532 @ tc_bool ) ) @ SV1532 ) @ SV1532 @ SV1532 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV1044 @ SV1881 @ SV1532 @ SV1532 ) @ SV439 @ ( tc_prod @ SV1532 @ SV1532 ) )
| ! [SY5788: $i] :
( ~ ( c_in @ SV1881 @ SY5788 @ SV1532 )
| ~ ( c_in @ SV1044 @ SY5788 @ SV1532 )
| ~ ( c_Equiv__Relations_Oequiv @ SY5788 @ SV439 @ SV1532 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4550]) ).
thf(5020,plain,
! [SV1882: $i,SV1533: $i,SV1045: $i,SV440: $i] :
( ( ( ( c_Relation_OImage @ SV440 @ ( c_Set_Oinsert @ SV1045 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1533 @ tc_bool ) ) @ SV1533 ) @ SV1533 @ SV1533 )
!= ( c_Relation_OImage @ SV440 @ ( c_Set_Oinsert @ SV1882 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1533 @ tc_bool ) ) @ SV1533 ) @ SV1533 @ SV1533 ) )
= $true )
| ( ( ! [SY5789: $i] :
( ~ ( c_in @ SV1882 @ SY5789 @ SV1533 )
| ~ ( c_in @ SV1045 @ SY5789 @ SV1533 )
| ~ ( c_Equiv__Relations_Oequiv @ SY5789 @ SV440 @ SV1533 )
| ( c_in @ ( c_Pair @ SV1045 @ SV1882 @ SV1533 @ SV1533 ) @ SV440 @ ( tc_prod @ SV1533 @ SV1533 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4551]) ).
thf(5021,plain,
! [SV1535: $i,SV1047: $i,SV2131: $i,SV442: $i] :
( ( ( ( SV442 = SV2131 )
| ! [SY5959: $i] :
( ~ ( c_lessequals @ SY5959 @ ( c_Product__Type_OSigma @ SV1047 @ ( c_COMBK @ SV1047 @ ( tc_fun @ SV1535 @ tc_bool ) @ SV1535 ) @ SV1535 @ SV1535 ) @ ( tc_fun @ ( tc_prod @ SV1535 @ SV1535 ) @ tc_bool ) )
| ~ ( c_in @ ( c_Pair @ SV442 @ SV2131 @ SV1535 @ SV1535 ) @ ( c_Transitive__Closure_Ortrancl @ SY5959 @ SV1535 ) @ ( tc_prod @ SV1535 @ SV1535 ) ) ) )
= $true )
| ( ( c_in @ SV442 @ SV1047 @ SV1535 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4552]) ).
thf(5022,plain,
! [SV1537: $i,SV1049: $i,SV444: $i] :
( ( ( c_in @ SV444 @ SV1049 @ ( tc_prod @ SV1537 @ SV1537 ) )
= $false )
| ( ( c_in @ SV444 @ ( c_Transitive__Closure_Ortrancl @ SV1049 @ SV1537 ) @ ( tc_prod @ SV1537 @ SV1537 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4553]) ).
thf(5023,plain,
! [SV1538: $i,SV1050: $i,SV445: $i] :
( ( ( c_in @ SV445 @ SV1050 @ ( tc_prod @ SV1538 @ SV1538 ) )
= $false )
| ( ( c_in @ SV445 @ ( c_Transitive__Closure_Otrancl @ SV1050 @ SV1538 ) @ ( tc_prod @ SV1538 @ SV1538 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4554]) ).
thf(5024,plain,
! [SV1883: $i,SV1539: $i,SV1051: $i,SV446: $i] :
( ( ( c_in @ ( c_Pair @ SV446 @ SV1051 @ SV1539 @ SV1539 ) @ ( c_Transitive__Closure_Otrancl @ SV1883 @ SV1539 ) @ ( tc_prod @ SV1539 @ SV1539 ) )
= $true )
| ( ( ! [SY5790: $i] :
( ~ ( c_in @ ( c_Pair @ SY5790 @ SV1051 @ SV1539 @ SV1539 ) @ ( c_Transitive__Closure_Ortrancl @ SV1883 @ SV1539 ) @ ( tc_prod @ SV1539 @ SV1539 ) )
| ~ ( c_in @ ( c_Pair @ SV446 @ SY5790 @ SV1539 @ SV1539 ) @ SV1883 @ ( tc_prod @ SV1539 @ SV1539 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4555]) ).
thf(5025,plain,
! [SV1884: $i,SV1540: $i,SV1052: $i,SV447: $i] :
( ( ( c_in @ ( c_Pair @ SV447 @ SV1052 @ SV1540 @ SV1540 ) @ ( c_Transitive__Closure_Otrancl @ SV1884 @ SV1540 ) @ ( tc_prod @ SV1540 @ SV1540 ) )
= $true )
| ( ( ! [SY5791: $i] :
( ~ ( c_in @ ( c_Pair @ SY5791 @ SV1052 @ SV1540 @ SV1540 ) @ SV1884 @ ( tc_prod @ SV1540 @ SV1540 ) )
| ~ ( c_in @ ( c_Pair @ SV447 @ SY5791 @ SV1540 @ SV1540 ) @ ( c_Transitive__Closure_Ortrancl @ SV1884 @ SV1540 ) @ ( tc_prod @ SV1540 @ SV1540 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4556]) ).
thf(5026,plain,
! [SV1885: $i,SV1541: $i,SV1053: $i,SV448: $i] :
( ( ( c_in @ ( c_Pair @ SV448 @ SV1053 @ SV1541 @ SV1541 ) @ ( c_Transitive__Closure_Ortrancl @ SV1885 @ SV1541 ) @ ( tc_prod @ SV1541 @ SV1541 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV448 @ SV1053 @ SV1541 @ SV1541 ) @ ( c_Transitive__Closure_Otrancl @ SV1885 @ SV1541 ) @ ( tc_prod @ SV1541 @ SV1541 ) )
| ( SV448 = SV1053 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4557]) ).
thf(5027,plain,
! [SV1886: $i,SV1542: $i,SV1054: $i,SV449: $i] :
( ( ( c_in @ ( c_Pair @ SV449 @ SV1054 @ SV1542 @ SV1542 ) @ ( c_Transitive__Closure_Otrancl @ SV1886 @ SV1542 ) @ ( tc_prod @ SV1542 @ SV1542 ) )
= $true )
| ( ( ( SV449 = SV1054 )
| ~ ( c_in @ ( c_Pair @ SV449 @ SV1054 @ SV1542 @ SV1542 ) @ ( c_Transitive__Closure_Ortrancl @ SV1886 @ SV1542 ) @ ( tc_prod @ SV1542 @ SV1542 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4558]) ).
thf(5028,plain,
! [SV1887: $i,SV1543: $i,SV1055: $i,SV450: $i] :
( ( ( c_in @ ( c_Pair @ SV450 @ SV1055 @ SV1543 @ SV1543 ) @ ( c_Transitive__Closure_Otrancl @ SV1887 @ SV1543 ) @ ( tc_prod @ SV1543 @ SV1543 ) )
= $true )
| ( ( ( SV450 = SV1055 )
| ~ ( c_in @ ( c_Pair @ SV450 @ SV1055 @ SV1543 @ SV1543 ) @ ( c_Transitive__Closure_Ortrancl @ SV1887 @ SV1543 ) @ ( tc_prod @ SV1543 @ SV1543 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4559]) ).
thf(5029,plain,
! [SV1888: $i,SV1544: $i,SV1056: $i,SV451: $i] :
( ( ( c_in @ ( c_Pair @ SV451 @ SV1056 @ SV1544 @ SV1544 ) @ ( c_Transitive__Closure_Ortrancl @ ( c_Relation_Oconverse @ SV1888 @ SV1544 @ SV1544 ) @ SV1544 ) @ ( tc_prod @ SV1544 @ SV1544 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV1056 @ SV451 @ SV1544 @ SV1544 ) @ ( c_Transitive__Closure_Ortrancl @ SV1888 @ SV1544 ) @ ( tc_prod @ SV1544 @ SV1544 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4560]) ).
thf(5030,plain,
! [SV1889: $i,SV1545: $i,SV1057: $i,SV452: $i] :
( ( ( c_in @ ( c_Pair @ SV452 @ SV1057 @ SV1545 @ SV1545 ) @ ( c_Transitive__Closure_Ortrancl @ SV1889 @ SV1545 ) @ ( tc_prod @ SV1545 @ SV1545 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV1057 @ SV452 @ SV1545 @ SV1545 ) @ ( c_Transitive__Closure_Ortrancl @ ( c_Relation_Oconverse @ SV1889 @ SV1545 @ SV1545 ) @ SV1545 ) @ ( tc_prod @ SV1545 @ SV1545 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4561]) ).
thf(5031,plain,
! [SV1890: $i,SV1546: $i,SV1058: $i,SV453: $i] :
( ( ( c_in @ ( c_Pair @ SV453 @ SV1058 @ SV1546 @ SV1546 ) @ ( c_Transitive__Closure_Ortrancl @ SV1890 @ SV1546 ) @ ( tc_prod @ SV1546 @ SV1546 ) )
= $true )
| ( ( ( c_in @ ( c_Pair @ SV1058 @ SV453 @ SV1546 @ SV1546 ) @ ( c_Transitive__Closure_Ortrancl @ SV1890 @ SV1546 ) @ ( tc_prod @ SV1546 @ SV1546 ) )
| ! [SY5792: $i] :
( ~ ( c_in @ ( c_Pair @ SY5792 @ SV453 @ SV1546 @ SV1546 ) @ ( c_Transitive__Closure_Ortrancl @ SV1890 @ SV1546 ) @ ( tc_prod @ SV1546 @ SV1546 ) )
| ~ ( c_in @ ( c_Pair @ SY5792 @ SV1058 @ SV1546 @ SV1546 ) @ ( c_Transitive__Closure_Ortrancl @ SV1890 @ SV1546 ) @ ( tc_prod @ SV1546 @ SV1546 ) )
| ~ ( c_Relation_Osingle__valued @ SV1890 @ SV1546 @ SV1546 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4562]) ).
thf(5032,plain,
! [SV1891: $i,SV1547: $i,SV1059: $i,SV454: $i] :
( ( ( c_in @ ( c_Pair @ SV454 @ SV1059 @ SV1547 @ SV1547 ) @ ( c_Transitive__Closure_Ortrancl @ SV1891 @ SV1547 ) @ ( tc_prod @ SV1547 @ SV1547 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV454 @ SV1059 @ SV1547 @ SV1547 ) @ ( c_Transitive__Closure_Otrancl @ SV1891 @ SV1547 ) @ ( tc_prod @ SV1547 @ SV1547 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4563]) ).
thf(5033,plain,
! [SV1892: $i,SV1548: $i,SV1060: $i,SV455: $i] :
( ( ( c_in @ ( c_Pair @ SV455 @ SV1060 @ SV1548 @ SV1548 ) @ ( c_Transitive__Closure_Otrancl @ SV1892 @ SV1548 ) @ ( tc_prod @ SV1548 @ SV1548 ) )
= $true )
| ( ( ! [SY5793: $i] :
( ~ ( c_in @ ( c_Pair @ SY5793 @ SV1060 @ SV1548 @ SV1548 ) @ ( c_Transitive__Closure_Ortrancl @ SV1892 @ SV1548 ) @ ( tc_prod @ SV1548 @ SV1548 ) )
| ~ ( c_in @ ( c_Pair @ SV455 @ SY5793 @ SV1548 @ SV1548 ) @ ( c_Transitive__Closure_Otrancl @ SV1892 @ SV1548 ) @ ( tc_prod @ SV1548 @ SV1548 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4564]) ).
thf(5034,plain,
! [SV1893: $i,SV1549: $i,SV1061: $i,SV456: $i] :
( ( ( c_in @ ( c_Pair @ SV456 @ SV1061 @ SV1549 @ SV1549 ) @ ( c_Transitive__Closure_Otrancl @ SV1893 @ SV1549 ) @ ( tc_prod @ SV1549 @ SV1549 ) )
= $true )
| ( ( ! [SY5794: $i] :
( ~ ( c_in @ ( c_Pair @ SY5794 @ SV1061 @ SV1549 @ SV1549 ) @ ( c_Transitive__Closure_Otrancl @ SV1893 @ SV1549 ) @ ( tc_prod @ SV1549 @ SV1549 ) )
| ~ ( c_in @ ( c_Pair @ SV456 @ SY5794 @ SV1549 @ SV1549 ) @ ( c_Transitive__Closure_Ortrancl @ SV1893 @ SV1549 ) @ ( tc_prod @ SV1549 @ SV1549 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4565]) ).
thf(5035,plain,
! [SV1894: $i,SV1550: $i,SV1062: $i,SV457: $i] :
( ( ( c_in @ ( c_Pair @ SV457 @ SV1062 @ SV1550 @ SV1550 ) @ ( c_Relation_Oconverse @ ( c_Transitive__Closure_Otrancl @ SV1894 @ SV1550 ) @ SV1550 @ SV1550 ) @ ( tc_prod @ SV1550 @ SV1550 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV457 @ SV1062 @ SV1550 @ SV1550 ) @ ( c_Transitive__Closure_Otrancl @ ( c_Relation_Oconverse @ SV1894 @ SV1550 @ SV1550 ) @ SV1550 ) @ ( tc_prod @ SV1550 @ SV1550 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4566]) ).
thf(5036,plain,
! [SV1895: $i,SV1551: $i,SV1063: $i,SV458: $i] :
( ( ( c_in @ ( c_Pair @ SV458 @ SV1063 @ SV1551 @ SV1551 ) @ ( c_Transitive__Closure_Otrancl @ ( c_Relation_Oconverse @ SV1895 @ SV1551 @ SV1551 ) @ SV1551 ) @ ( tc_prod @ SV1551 @ SV1551 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV458 @ SV1063 @ SV1551 @ SV1551 ) @ ( c_Relation_Oconverse @ ( c_Transitive__Closure_Otrancl @ SV1895 @ SV1551 ) @ SV1551 @ SV1551 ) @ ( tc_prod @ SV1551 @ SV1551 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4567]) ).
thf(5037,plain,
! [SV2132: $i,SV1896: $i,SV1552: $i,SV1064: $i,SV459: $i] :
( ( ! [SY5960: $i] :
( ( hAPP @ ( c_split @ SV459 @ SV1064 @ SV1552 @ SV1896 ) @ ( c_Pair @ SV2132 @ SY5960 @ SV1064 @ SV1552 ) )
= ( hAPP @ ( hAPP @ SV459 @ SV2132 ) @ SY5960 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4568]) ).
thf(5038,plain,
! [SV2133: $i,SV1897: $i,SV1553: $i,SV1065: $i,SV460: $i] :
( ( ! [SY5961: $i] :
( ( hAPP @ ( c_split @ SV460 @ SV1065 @ SV1553 @ SV1897 ) @ ( c_Pair @ SV2133 @ SY5961 @ SV1065 @ SV1553 ) )
= ( hAPP @ ( hAPP @ SV460 @ SV2133 ) @ SY5961 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4569]) ).
thf(5039,plain,
! [SV2134: $i,SV1898: $i,SV1554: $i,SV1066: $i,SV461: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ SV461 @ SV1066 ) @ SV1554 ) @ SV1898 ) )
| ! [SY5962: $i,SY5963: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_split @ SV461 @ SV2134 @ SY5962 @ ( tc_fun @ SY5963 @ tc_bool ) ) @ ( c_Pair @ SV1066 @ SV1554 @ SV2134 @ SY5962 ) ) @ SV1898 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4570]) ).
thf(5040,plain,
! [SV1899: $i,SV1555: $i,SV1067: $i,SV462: $i] :
( ( ( ! [SY5802: $i] : ( c_in @ ( hAPP @ SV462 @ SV1067 ) @ ( c_Set_Oimage @ SV462 @ SV1555 @ SV1899 @ SY5802 ) @ SY5802 ) )
= $true )
| ( ( ~ ( c_in @ SV1067 @ SV1555 @ SV1899 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4571]) ).
thf(5041,plain,
! [SV1900: $i,SV1556: $i,SV1068: $i,SV463: $i] :
( ( ( ! [SY5803: $i] : ( c_in @ ( hAPP @ SV463 @ SV1068 ) @ ( c_Set_Oimage @ SV463 @ SV1556 @ SV1900 @ SY5803 ) @ SY5803 ) )
= $true )
| ( ( ~ ( c_in @ SV1068 @ SV1556 @ SV1900 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4572]) ).
thf(5042,plain,
! [SV1557: $i,SV1069: $i,SV464: $i] :
( ( ( c_in @ SV464 @ SV1069 @ SV1557 )
= $false )
| ( ( ! [SY5494: $i,SY5495: $i] : ( c_in @ ( hAPP @ SY5494 @ SV464 ) @ ( c_Set_Oimage @ SY5494 @ SV1069 @ SV1557 @ SY5495 ) @ SY5495 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4573]) ).
thf(5043,plain,
! [SV1558: $i,SV1070: $i,SV465: $i] :
( ( ( c_in @ SV465 @ SV1070 @ SV1558 )
= $false )
| ( ( ! [SY5496: $i,SY5497: $i] : ( c_in @ ( hAPP @ SY5496 @ SV465 ) @ ( c_Set_Oimage @ SY5496 @ SV1070 @ SV1558 @ SY5497 ) @ SY5497 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4574]) ).
thf(5044,plain,
! [SV466: $i,SV1559: $i,SV1071: $i] :
( ( ( c_Wellfounded_Owf @ SV1071 @ SV1559 )
= $false )
| ( ( c_in @ SV466 @ ( c_Wellfounded_Oacc @ SV1071 @ SV1559 ) @ SV1559 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4575]) ).
thf(5045,plain,
! [SV2135: $i,SV1901: $i,SV1560: $i,SV1073: $i,SV468: $i] :
( ( ( c_in @ ( c_ATP__Linkup_Osko__Relation__XImageE__1__1 @ SV468 @ SV1073 @ SV1560 @ SV1901 @ SV2135 ) @ SV468 @ SV1901 )
| ~ ( c_in @ SV1073 @ ( c_Relation_OImage @ SV1560 @ SV468 @ SV1901 @ SV2135 ) @ SV2135 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4576]) ).
thf(5046,plain,
! [SV1075: $i,SV2136: $i,SV1902: $i,SV470: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV470 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ SV470 @ SV1902 @ SV2136 ) ) )
| ~ ( c_in @ SV1075 @ ( c_Wellfounded_Oacc @ SV1902 @ SV2136 ) @ SV2136 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV470 @ SV1075 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4578]) ).
thf(5047,plain,
! [SV1077: $i,SV1903: $i,SV472: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV472 @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ SV472 @ SV1903 ) ) ) )
= $true )
| ( ( ~ ( c_in @ SV1077 @ ( c_Wellfounded_Oacc @ SV1903 @ t_a ) @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV472 @ SV1077 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4580]) ).
thf(5048,plain,
! [SV1078: $i,SV2137: $i,SV1904: $i,SV473: $i] :
( ( ( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ SV473 @ SV1904 @ SV2137 ) @ ( c_Wellfounded_Oacc @ SV1904 @ SV2137 ) @ SV2137 )
| ~ ( c_in @ SV1078 @ ( c_Wellfounded_Oacc @ SV1904 @ SV2137 ) @ SV2137 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV473 @ SV1078 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4581]) ).
thf(5049,plain,
! [SV2138: $i,SV1905: $i,SV1561: $i,SV1082: $i,SV477: $i] :
( ( ( c_in @ ( c_ATP__Linkup_Osko__Relation__XImage__iff__1__1 @ SV477 @ SV1082 @ SV1561 @ SV1905 @ SV2138 ) @ SV477 @ SV1905 )
| ~ ( c_in @ SV1082 @ ( c_Relation_OImage @ SV1561 @ SV477 @ SV1905 @ SV2138 ) @ SV2138 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4584]) ).
thf(5050,plain,
! [SV1562: $i,SV1083: $i,SV478: $i] :
( ( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1 @ SV478 @ SV1083 @ SV1562 ) @ ( c_Wellfounded_Oacc @ SV478 @ SV1562 ) @ SV1562 )
= $false )
| ( ( c_in @ SV1083 @ ( c_Wellfounded_Oacc @ SV478 @ SV1562 ) @ SV1562 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4585]) ).
thf(5051,plain,
! [SV1089: $i,SV2139: $i,SV1906: $i,SV485: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV485 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ SV485 @ SV1906 @ SV2139 ) ) )
| ~ ( c_in @ SV1089 @ ( c_Wellfounded_Oacc @ SV1906 @ SV2139 ) @ SV2139 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV485 @ SV1089 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4587]) ).
thf(5052,plain,
! [SV1565: $i,SV1090: $i,SV486: $i] :
( ( ( c_Relation_Orefl__on @ SV486 @ ( c_Relation_Oconverse @ SV1090 @ SV1565 @ SV1565 ) @ SV1565 )
= $false )
| ( ( c_Relation_Orefl__on @ SV486 @ SV1090 @ SV1565 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4588]) ).
thf(5053,plain,
! [SV1566: $i,SV1091: $i,SV487: $i] :
( ( ( c_Relation_Orefl__on @ SV487 @ SV1091 @ SV1566 )
= $false )
| ( ( c_Relation_Orefl__on @ SV487 @ ( c_Relation_Oconverse @ SV1091 @ SV1566 @ SV1566 ) @ SV1566 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4589]) ).
thf(5054,plain,
! [SV2140: $i,SV1907: $i,SV1567: $i,SV1101: $i,SV498: $i] :
( ( ( c_Relation_Oconverse @ ( c_Relation_Orel__comp @ SV498 @ SV1101 @ SV1567 @ SV1907 @ SV2140 ) @ SV1567 @ SV2140 )
= ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ SV1101 @ SV1907 @ SV2140 ) @ ( c_Relation_Oconverse @ SV498 @ SV1567 @ SV1907 ) @ SV2140 @ SV1907 @ SV1567 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4595]) ).
thf(5055,plain,
! [SV2141: $i,SV1568: $i,SV1104: $i,SV501: $i] :
( ( ( c_Wellfounded_Owf @ ( c_Relation_Oinv__image @ SV501 @ SV1104 @ SV1568 @ SV2141 ) @ SV2141 )
= $true )
| ( ( ~ ( c_Wellfounded_Owf @ SV501 @ SV1568 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4596]) ).
thf(5056,plain,
! [SV2142: $i,SV1569: $i,SV1106: $i,SV503: $i] :
( ( ( c_Relation_Osym @ ( c_Relation_Oinv__image @ SV503 @ SV1106 @ SV1569 @ SV2142 ) @ SV2142 )
= $true )
| ( ( ~ ( c_Relation_Osym @ SV503 @ SV1569 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4597]) ).
thf(5057,plain,
! [SV2143: $i,SV1908: $i,SV1570: $i,SV1112: $i,SV510: $i] :
( ( ! [SY5964: $i,SY5965: $i] :
( ( c_Relation_Orel__comp @ ( c_Relation_Orel__comp @ SV510 @ SV1112 @ SV1570 @ SV1908 @ SV2143 ) @ SY5964 @ SV1570 @ SV2143 @ SY5965 )
= ( c_Relation_Orel__comp @ SV510 @ ( c_Relation_Orel__comp @ SV1112 @ SY5964 @ SV1908 @ SV2143 @ SY5965 ) @ SV1570 @ SV1908 @ SY5965 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4601]) ).
thf(5058,plain,
! [SV2144: $i,SV1572: $i,SV1115: $i,SV513: $i] :
( ( ( c_Relation_Otrans @ ( c_Relation_Oinv__image @ SV513 @ SV1115 @ SV1572 @ SV2144 ) @ SV2144 )
= $true )
| ( ( ~ ( c_Relation_Otrans @ SV513 @ SV1572 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4603]) ).
thf(5059,plain,
! [SV1119: $i,SV1574: $i,SV518: $i] :
( ( ( ! [SY5512: $i] :
~ ( c_in @ SY5512 @ SV518 @ SV1574 ) )
= $true )
| ( ( ~ ( c_Wellfounded_Owf @ SV1119 @ SV1574 ) )
= $true )
| ( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 @ SV518 @ SV1119 @ SV1574 ) @ SV518 @ SV1574 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4605]) ).
thf(5060,plain,
! [SV2145: $i,SV1910: $i,SV1575: $i,SV1121: $i,SV520: $i] :
( ( ( c_Relation_Osingle__valued @ ( c_Relation_Orel__comp @ SV520 @ SV1121 @ SV1575 @ SV1910 @ SV2145 ) @ SV1575 @ SV2145 )
| ~ ( c_Relation_Osingle__valued @ SV1121 @ SV1910 @ SV2145 )
| ~ ( c_Relation_Osingle__valued @ SV520 @ SV1575 @ SV1910 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4606]) ).
thf(5061,plain,
! [SV1123: $i,SV523: $i,SV1911: $i] :
( ( ( c_Equiv__Relations_Oequiv @ SV1911 @ SV523 @ SV1123 )
= $false )
| ( ( ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ SV523 @ SV1123 @ SV1123 ) @ SV523 @ SV1123 @ SV1123 @ SV1123 )
= SV523 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4607]) ).
thf(5062,plain,
! [SV1127: $i,SV1912: $i,SV527: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV527 @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ SV527 @ SV1912 ) ) ) )
= $true )
| ( ( ~ ( c_in @ SV1127 @ ( c_Wellfounded_Oacc @ SV1912 @ t_a ) @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV527 @ SV1127 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4610]) ).
thf(5063,plain,
! [SV1577: $i,SV1128: $i,SV528: $i] :
( ( ( c_Equiv__Relations_Oequiv @ SV528 @ SV1128 @ SV1577 )
= $false )
| ( ( c_Relation_Orefl__on @ SV528 @ SV1128 @ SV1577 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4611]) ).
thf(5064,plain,
! [SV1130: $i,SV1578: $i,SV530: $i] :
( ( ( ! [SY5515: $i] :
~ ( c_in @ SY5515 @ SV530 @ SV1578 ) )
= $true )
| ( ( ~ ( c_Wellfounded_Owf @ SV1130 @ SV1578 ) )
= $true )
| ( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 @ SV530 @ SV1130 @ SV1578 ) @ SV530 @ SV1578 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4612]) ).
thf(5065,plain,
! [SV1131: $i,SV531: $i,SV1913: $i] :
( ( ( c_Equiv__Relations_Oequiv @ SV1913 @ SV531 @ SV1131 )
= $false )
| ( ( c_Relation_Osym @ SV531 @ SV1131 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4613]) ).
thf(5066,plain,
! [SV1579: $i,SV532: $i,SV1132: $i] :
( ( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1 @ SV1132 @ SV532 @ SV1579 ) @ ( c_Wellfounded_Oacc @ SV1132 @ SV1579 ) @ SV1579 )
= $false )
| ( ( c_in @ SV532 @ ( c_Wellfounded_Oacc @ SV1132 @ SV1579 ) @ SV1579 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4614]) ).
thf(5067,plain,
! [SV2146: $i,SV1914: $i,SV1580: $i,SV1133: $i,SV533: $i] :
( ( ! [SY5966: $i] :
( ( c_Equiv__Relations_Ocongruent @ SV533 @ ( hAPP @ SV1133 @ SV1580 ) @ SV1914 @ SV2146 )
| ! [SY5967: $i] :
( ~ ( c_in @ SV1580 @ SY5966 @ SY5967 )
| ! [SY5968: $i] :
( ~ ( c_Equiv__Relations_Ocongruent2 @ SY5968 @ SV533 @ SV1133 @ SY5967 @ SV1914 @ SV2146 )
| ~ ( c_Equiv__Relations_Oequiv @ SY5966 @ SY5968 @ SY5967 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4615]) ).
thf(5068,plain,
! [SV1583: $i,SV1138: $i,SV538: $i] :
( ( ( c_Relation_Ototal__on @ SV538 @ ( c_Relation_Oconverse @ SV1138 @ SV1583 @ SV1583 ) @ SV1583 )
= $false )
| ( ( c_Relation_Ototal__on @ SV538 @ SV1138 @ SV1583 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4616]) ).
thf(5069,plain,
! [SV1584: $i,SV1139: $i,SV539: $i] :
( ( ( c_Relation_Ototal__on @ SV539 @ SV1139 @ SV1584 )
= $false )
| ( ( c_Relation_Ototal__on @ SV539 @ ( c_Relation_Oconverse @ SV1139 @ SV1584 @ SV1584 ) @ SV1584 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4617]) ).
thf(5070,plain,
! [SV1140: $i,SV540: $i,SV1915: $i] :
( ( ( c_Equiv__Relations_Oequiv @ SV1915 @ SV540 @ SV1140 )
= $false )
| ( ( c_Relation_Otrans @ SV540 @ SV1140 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4618]) ).
thf(5071,plain,
! [SV1141: $i,SV2147: $i,SV1916: $i,SV541: $i] :
( ( ( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ SV541 @ SV1916 @ SV2147 ) @ ( c_Wellfounded_Oacc @ SV1916 @ SV2147 ) @ SV2147 )
| ~ ( c_in @ SV1141 @ ( c_Wellfounded_Oacc @ SV1916 @ SV2147 ) @ SV2147 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV541 @ SV1141 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4619]) ).
thf(5072,plain,
! [SV2148: $i,SV1917: $i,SV1585: $i,SV1144: $i,SV544: $i] :
( ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XImageE__1__1 @ SV544 @ SV1144 @ SV1585 @ SV1917 @ SV2148 ) @ SV1144 @ SV1917 @ SV2148 ) @ SV1585 @ ( tc_prod @ SV1917 @ SV2148 ) )
| ~ ( c_in @ SV1144 @ ( c_Relation_OImage @ SV1585 @ SV544 @ SV1917 @ SV2148 ) @ SV2148 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4620]) ).
thf(5073,plain,
! [SV1146: $i,SV1587: $i,SV546: $i] :
( ( ( hBOOL @ ( hAPP @ SV546 @ SV1587 ) )
= $true )
| ( ( ! [SY5523: $i,SY5524: $i] :
( ~ ( c_in @ ( c_Pair @ SV1587 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ SV546 @ SY5523 @ SY5524 ) @ SY5524 @ SY5524 ) @ SY5523 @ ( tc_prod @ SY5524 @ SY5524 ) )
| ~ ( c_in @ SV1146 @ ( c_Wellfounded_Oacc @ SY5523 @ SY5524 ) @ SY5524 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV546 @ SV1146 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4622]) ).
thf(5074,plain,
! [SV1147: $i,SV1918: $i,SV547: $i] :
( ( ( hBOOL @ ( hAPP @ SV547 @ SV1918 ) )
= $true )
| ( ( ! [SY5820: $i] :
( ~ ( c_in @ ( c_Pair @ SV1918 @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ SV547 @ SY5820 ) @ t_a @ t_a ) @ SY5820 @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ SV1147 @ ( c_Wellfounded_Oacc @ SY5820 @ t_a ) @ t_a ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV547 @ SV1147 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4623]) ).
thf(5075,plain,
! [SV1588: $i,SV1148: $i,SV548: $i] :
( ( ( c_in @ SV548 @ SV1148 @ SV1588 )
= $false )
| ( ( ! [SY5525: $i] :
( ~ ( c_in @ ( c_Pair @ SV548 @ ( c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 @ SV1148 @ SY5525 @ SV1588 ) @ SV1588 @ SV1588 ) @ SY5525 @ ( tc_prod @ SV1588 @ SV1588 ) )
| ! [SY5526: $i] :
~ ( c_in @ SY5526 @ SV1148 @ SV1588 )
| ~ ( c_Wellfounded_Owf @ SY5525 @ SV1588 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4624]) ).
thf(5076,plain,
! [SV1919: $i,SV1589: $i,SV1149: $i,SV549: $i] :
( ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XRangeE__1__1 @ SV549 @ SV1149 @ SV1589 @ SV1919 ) @ SV549 @ SV1919 @ SV1589 ) @ SV1149 @ ( tc_prod @ SV1919 @ SV1589 ) )
= $true )
| ( ( ~ ( c_in @ SV549 @ ( c_Relation_ORange @ SV1149 @ SV1919 @ SV1589 ) @ SV1589 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4625]) ).
thf(5077,plain,
! [SV551: $i,SV1591: $i,SV1151: $i,SV2149: $i] :
( ( ( ~ ( c_in @ SV2149 @ ( c_Wellfounded_Oacc @ SV1151 @ SV1591 ) @ SV1591 )
| ~ ( c_in @ ( c_Pair @ SV551 @ SV2149 @ SV1591 @ SV1591 ) @ ( c_Transitive__Closure_Ortrancl @ SV1151 @ SV1591 ) @ ( tc_prod @ SV1591 @ SV1591 ) ) )
= $true )
| ( ( c_in @ SV551 @ ( c_Wellfounded_Oacc @ SV1151 @ SV1591 ) @ SV1591 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4627]) ).
thf(5078,plain,
! [SV1152: $i,SV1592: $i,SV2150: $i,SV552: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV552 @ SV2150 @ SV1592 @ SV1592 ) @ ( c_Transitive__Closure_Ortrancl @ SV1152 @ SV1592 ) @ ( tc_prod @ SV1592 @ SV1592 ) )
| ~ ( c_in @ SV2150 @ ( c_Wellfounded_Oacc @ SV1152 @ SV1592 ) @ SV1592 ) )
= $true )
| ( ( c_in @ SV552 @ ( c_Wellfounded_Oacc @ SV1152 @ SV1592 ) @ SV1592 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4628]) ).
thf(5079,plain,
! [SV1153: $i,SV553: $i,SV2151: $i,SV1920: $i] :
( ( ( ( c_in @ SV1920 @ ( c_Wellfounded_Oacc @ SV2151 @ t_a ) @ t_a )
| ~ ( c_in @ ( c_Pair @ SV1920 @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ SV553 @ SV2151 ) @ t_a @ t_a ) @ SV2151 @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ SV1153 @ ( c_Wellfounded_Oacc @ SV2151 @ t_a ) @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV553 @ SV1153 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4629]) ).
thf(5080,plain,
! [SV1155: $i,SV1921: $i,SV555: $i] :
( ( ( hBOOL @ ( hAPP @ SV555 @ SV1921 ) )
= $true )
| ( ( ! [SY5822: $i] :
( ~ ( c_in @ ( c_Pair @ SV1921 @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ SV555 @ SY5822 ) @ t_a @ t_a ) @ SY5822 @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ SV1155 @ ( c_Wellfounded_Oacc @ SY5822 @ t_a ) @ t_a ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV555 @ SV1155 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4631]) ).
thf(5081,plain,
! [SV2152: $i,SV1922: $i,SV1594: $i,SV1156: $i,SV556: $i] :
( ( ! [SY5969: $i,SY5970: $i] :
( ( c_in @ ( hAPP @ ( hAPP @ SV556 @ SV1156 ) @ SV1594 ) @ ( c_Set_Oimage @ ( c_split @ SV556 @ SV1922 @ SV2152 @ SY5969 ) @ SY5970 @ ( tc_prod @ SV1922 @ SV2152 ) @ SY5969 ) @ SY5969 )
| ~ ( c_in @ ( c_Pair @ SV1156 @ SV1594 @ SV1922 @ SV2152 ) @ SY5970 @ ( tc_prod @ SV1922 @ SV2152 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4632]) ).
thf(5082,plain,
! [SV1923: $i,SV1595: $i,SV1157: $i,SV557: $i] :
( ( ( c_in @ ( c_Pair @ SV557 @ ( c_ATP__Linkup_Osko__Relation__XDomainE__1__1 @ SV557 @ SV1157 @ SV1595 @ SV1923 ) @ SV1595 @ SV1923 ) @ SV1157 @ ( tc_prod @ SV1595 @ SV1923 ) )
= $true )
| ( ( ~ ( c_in @ SV557 @ ( c_Relation_ODomain @ SV1157 @ SV1595 @ SV1923 ) @ SV1595 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4633]) ).
thf(5083,plain,
! [SV1158: $i,SV558: $i,SV2153: $i,SV1924: $i] :
( ( ( ( c_in @ SV1924 @ ( c_Wellfounded_Oacc @ SV2153 @ t_a ) @ t_a )
| ~ ( c_in @ ( c_Pair @ SV1924 @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ SV558 @ SV2153 ) @ t_a @ t_a ) @ SV2153 @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ SV1158 @ ( c_Wellfounded_Oacc @ SV2153 @ t_a ) @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV558 @ SV1158 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4634]) ).
thf(5084,plain,
! [SV1159: $i,SV1596: $i,SV559: $i] :
( ( ( hBOOL @ ( hAPP @ SV559 @ SV1596 ) )
= $true )
| ( ( ! [SY5535: $i,SY5536: $i] :
( ~ ( c_in @ ( c_Pair @ SV1596 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ SV559 @ SY5535 @ SY5536 ) @ SY5536 @ SY5536 ) @ SY5535 @ ( tc_prod @ SY5536 @ SY5536 ) )
| ~ ( c_in @ SV1159 @ ( c_Wellfounded_Oacc @ SY5535 @ SY5536 ) @ SY5536 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV559 @ SV1159 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4635]) ).
thf(5085,plain,
! [SV1597: $i,SV1160: $i,SV560: $i] :
( ( ( c_in @ SV560 @ SV1160 @ SV1597 )
= $false )
| ( ( ! [SY5537: $i] :
( ~ ( c_in @ ( c_Pair @ SV560 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 @ SV1160 @ SY5537 @ SV1597 ) @ SV1597 @ SV1597 ) @ SY5537 @ ( tc_prod @ SV1597 @ SV1597 ) )
| ! [SY5538: $i] :
~ ( c_in @ SY5538 @ SV1160 @ SV1597 )
| ~ ( c_Wellfounded_Owf @ SY5537 @ SV1597 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4636]) ).
thf(5086,plain,
! [SV1925: $i,SV1598: $i,SV1161: $i,SV561: $i] :
( ( ( c_in @ ( c_Pair @ SV561 @ ( c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1 @ SV561 @ SV1161 @ SV1598 @ SV1925 ) @ SV1598 @ SV1925 ) @ SV1161 @ ( tc_prod @ SV1598 @ SV1925 ) )
= $true )
| ( ( ~ ( c_in @ SV561 @ ( c_Relation_ODomain @ SV1161 @ SV1598 @ SV1925 ) @ SV1598 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4637]) ).
thf(5087,plain,
! [SV2154: $i,SV1926: $i,SV1599: $i,SV1162: $i,SV562: $i] :
( ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XImage__iff__1__1 @ SV562 @ SV1162 @ SV1599 @ SV1926 @ SV2154 ) @ SV1162 @ SV1926 @ SV2154 ) @ SV1599 @ ( tc_prod @ SV1926 @ SV2154 ) )
| ~ ( c_in @ SV1162 @ ( c_Relation_OImage @ SV1599 @ SV562 @ SV1926 @ SV2154 ) @ SV2154 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4638]) ).
thf(5088,plain,
! [SV2155: $i,SV1927: $i,SV1163: $i,SV563: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV563 @ SV1163 @ SV1927 @ SV1927 ) @ ( c_Transitive__Closure_Ortrancl @ SV2155 @ SV1927 ) @ ( tc_prod @ SV1927 @ SV1927 ) )
| ( c_in @ SV563 @ ( c_Relation_ODomain @ SV2155 @ SV1927 @ SV1927 ) @ SV1927 ) )
= $true )
| ( ( SV563 = SV1163 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4639]) ).
thf(5089,plain,
! [SV1928: $i,SV1600: $i,SV1164: $i,SV564: $i] :
( ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XRange__iff__1__1 @ SV564 @ SV1164 @ SV1600 @ SV1928 ) @ SV564 @ SV1928 @ SV1600 ) @ SV1164 @ ( tc_prod @ SV1928 @ SV1600 ) )
= $true )
| ( ( ~ ( c_in @ SV564 @ ( c_Relation_ORange @ SV1164 @ SV1928 @ SV1600 ) @ SV1600 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4640]) ).
thf(5090,plain,
! [SV2156: $i,SV1929: $i,SV1601: $i,SV1165: $i,SV565: $i] :
( ( ! [SY5971: $i,SY5972: $i] :
( ( c_in @ SV565 @ ( hAPP @ ( c_split @ SV1165 @ SV1601 @ SV1929 @ ( tc_fun @ SV2156 @ tc_bool ) ) @ ( c_Pair @ SY5971 @ SY5972 @ SV1601 @ SV1929 ) ) @ SV2156 )
| ~ ( c_in @ SV565 @ ( hAPP @ ( hAPP @ SV1165 @ SY5971 ) @ SY5972 ) @ SV2156 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4641]) ).
thf(5091,plain,
! [SV2157: $i,SV1930: $i,SV1602: $i,SV1166: $i,SV566: $i] :
( ( ! [SY5973: $i,SY5974: $i,SY5975: $i] :
( ( ( hAPP @ ( hAPP @ SV566 @ SV1166 ) @ SV1602 )
= ( hAPP @ ( hAPP @ SV566 @ SV1930 ) @ SV2157 ) )
| ~ ( c_in @ ( c_Pair @ SV1602 @ SV2157 @ SY5973 @ SY5973 ) @ SY5974 @ ( tc_prod @ SY5973 @ SY5973 ) )
| ! [SY5836: $i] :
( ~ ( c_in @ ( c_Pair @ SV1166 @ SV1930 @ SY5975 @ SY5975 ) @ SY5836 @ ( tc_prod @ SY5975 @ SY5975 ) )
| ! [SY3833: $i] :
~ ( c_Equiv__Relations_Ocongruent2 @ SY5836 @ SY5974 @ SV566 @ SY5975 @ SY5973 @ SY3833 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4642]) ).
thf(5092,plain,
! [SV1931: $i,SV1603: $i,SV1167: $i,SV567: $i] :
( ( ( SV567 = SV1167 )
= $true )
| ( ( ! [SY5838: $i,SY5839: $i] :
( ~ ( c_in @ ( c_Pair @ SV1603 @ SV1167 @ SV1931 @ SY5838 ) @ SY5839 @ ( tc_prod @ SV1931 @ SY5838 ) )
| ~ ( c_in @ ( c_Pair @ SV1603 @ SV567 @ SV1931 @ SY5838 ) @ SY5839 @ ( tc_prod @ SV1931 @ SY5838 ) )
| ~ ( c_Relation_Osingle__valued @ SY5839 @ SV1931 @ SY5838 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4643]) ).
thf(5093,plain,
! [SV2158: $i,SV1932: $i,SV1604: $i,SV1168: $i,SV568: $i] :
( ( ! [SY5978: $i] :
( ( ( hAPP @ ( c_Recdef_Ocut @ SV568 @ SV1168 @ SV1604 @ SV1932 @ SV2158 ) @ SY5978 )
= ( hAPP @ SV568 @ SY5978 ) )
| ~ ( c_in @ ( c_Pair @ SY5978 @ SV1604 @ SV1932 @ SV1932 ) @ SV1168 @ ( tc_prod @ SV1932 @ SV1932 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4644]) ).
thf(5094,plain,
! [SV2159: $i,SV1933: $i,SV1605: $i,SV1169: $i,SV569: $i] :
( ( ! [SY5979: $i] :
( ( ( hAPP @ ( c_Recdef_Ocut @ SV569 @ SV1169 @ SV1605 @ SV1933 @ SV2159 ) @ SY5979 )
= ( hAPP @ SV569 @ SY5979 ) )
| ~ ( c_in @ ( c_Pair @ SY5979 @ SV1605 @ SV1933 @ SV1933 ) @ SV1169 @ ( tc_prod @ SV1933 @ SV1933 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4645]) ).
thf(5095,plain,
! [SV2160: $i,SV1934: $i,SV1606: $i,SV1170: $i,SV570: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_FunDef_Oin__rel @ SV570 @ SV1170 @ SV1606 ) @ SV1934 ) @ SV2160 ) )
| ~ ( c_in @ ( c_Pair @ SV1934 @ SV2160 @ SV1170 @ SV1606 ) @ SV570 @ ( tc_prod @ SV1170 @ SV1606 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4646]) ).
thf(5096,plain,
! [SV2161: $i,SV1935: $i,SV1607: $i,SV1171: $i,SV571: $i] :
( ( ( c_in @ ( c_Pair @ SV571 @ SV1171 @ SV1607 @ SV1935 ) @ SV2161 @ ( tc_prod @ SV1607 @ SV1935 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_FunDef_Oin__rel @ SV2161 @ SV1607 @ SV1935 ) @ SV571 ) @ SV1171 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4647]) ).
thf(5097,plain,
! [SV1936: $i,SV1608: $i,SV1172: $i,SV572: $i] :
( ( ( c_in @ ( c_Pair @ SV572 @ SV1172 @ SV1608 @ SV1608 ) @ SV1936 @ ( tc_prod @ SV1608 @ SV1608 ) )
= $true )
| ( ( ! [SY5846: $i] :
( ~ ( c_in @ ( c_Pair @ SY5846 @ SV1172 @ SV1608 @ SV1608 ) @ SV1936 @ ( tc_prod @ SV1608 @ SV1608 ) )
| ~ ( c_in @ ( c_Pair @ SV572 @ SY5846 @ SV1608 @ SV1608 ) @ SV1936 @ ( tc_prod @ SV1608 @ SV1608 ) )
| ~ ( c_Relation_Otrans @ SV1936 @ SV1608 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4648]) ).
thf(5098,plain,
! [SV1937: $i,SV1609: $i,SV1173: $i,SV573: $i] :
( ( ( c_in @ ( c_Pair @ SV573 @ SV1173 @ SV1609 @ SV1609 ) @ SV1937 @ ( tc_prod @ SV1609 @ SV1609 ) )
= $true )
| ( ( ! [SY5847: $i] :
( ~ ( c_in @ ( c_Pair @ SY5847 @ SV1173 @ SV1609 @ SV1609 ) @ SV1937 @ ( tc_prod @ SV1609 @ SV1609 ) )
| ~ ( c_in @ ( c_Pair @ SV573 @ SY5847 @ SV1609 @ SV1609 ) @ SV1937 @ ( tc_prod @ SV1609 @ SV1609 ) )
| ~ ( c_Relation_Otrans @ SV1937 @ SV1609 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4649]) ).
thf(5099,plain,
! [SV2162: $i,SV1938: $i,SV1610: $i,SV1174: $i,SV574: $i] :
( ( ( c_in @ ( c_Pair @ SV574 @ SV1174 @ SV1610 @ SV1938 ) @ ( c_Relation_Oconverse @ SV2162 @ SV1938 @ SV1610 ) @ ( tc_prod @ SV1610 @ SV1938 ) )
| ~ ( c_in @ ( c_Pair @ SV1174 @ SV574 @ SV1938 @ SV1610 ) @ SV2162 @ ( tc_prod @ SV1938 @ SV1610 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4650]) ).
thf(5100,plain,
! [SV2163: $i,SV1939: $i,SV1611: $i,SV1175: $i,SV575: $i] :
( ( ( c_in @ ( c_Pair @ SV575 @ SV1175 @ SV1611 @ SV1939 ) @ ( c_Relation_Oconverse @ SV2163 @ SV1939 @ SV1611 ) @ ( tc_prod @ SV1611 @ SV1939 ) )
| ~ ( c_in @ ( c_Pair @ SV1175 @ SV575 @ SV1939 @ SV1611 ) @ SV2163 @ ( tc_prod @ SV1939 @ SV1611 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4651]) ).
thf(5101,plain,
! [SV2164: $i,SV1940: $i,SV1612: $i,SV1176: $i,SV576: $i] :
( ( ( c_in @ ( c_Pair @ SV576 @ SV1176 @ SV1612 @ SV1940 ) @ SV2164 @ ( tc_prod @ SV1612 @ SV1940 ) )
| ~ ( c_in @ ( c_Pair @ SV1176 @ SV576 @ SV1940 @ SV1612 ) @ ( c_Relation_Oconverse @ SV2164 @ SV1612 @ SV1940 ) @ ( tc_prod @ SV1940 @ SV1612 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4652]) ).
thf(5102,plain,
! [SV1613: $i,SV1177: $i,SV577: $i] :
( ( ( c_in @ ( c_Pair @ SV577 @ SV577 @ SV1177 @ SV1177 ) @ SV1613 @ ( tc_prod @ SV1177 @ SV1177 ) )
= $false )
| ( ( ~ ( c_Relation_Oirrefl @ SV1613 @ SV1177 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4653]) ).
thf(5103,plain,
! [SV1941: $i,SV1614: $i,SV1178: $i,SV578: $i] :
( ( ( c_in @ ( c_Pair @ SV578 @ SV1178 @ SV1614 @ SV1614 ) @ ( c_Transitive__Closure_Otrancl @ SV1941 @ SV1614 ) @ ( tc_prod @ SV1614 @ SV1614 ) )
= $true )
| ( ( ! [SY5851: $i] :
( ~ ( c_in @ ( c_Pair @ SY5851 @ SV1178 @ SV1614 @ SV1614 ) @ SV1941 @ ( tc_prod @ SV1614 @ SV1614 ) )
| ~ ( c_in @ ( c_Pair @ SV578 @ SY5851 @ SV1614 @ SV1614 ) @ ( c_Transitive__Closure_Otrancl @ SV1941 @ SV1614 ) @ ( tc_prod @ SV1614 @ SV1614 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4654]) ).
thf(5104,plain,
! [SV1942: $i,SV1615: $i,SV1179: $i,SV579: $i] :
( ( ( c_in @ ( c_Pair @ SV579 @ SV1179 @ SV1615 @ SV1615 ) @ ( c_Transitive__Closure_Otrancl @ SV1942 @ SV1615 ) @ ( tc_prod @ SV1615 @ SV1615 ) )
= $true )
| ( ( ! [SY5852: $i] :
( ~ ( c_in @ ( c_Pair @ SY5852 @ SV1179 @ SV1615 @ SV1615 ) @ ( c_Transitive__Closure_Otrancl @ SV1942 @ SV1615 ) @ ( tc_prod @ SV1615 @ SV1615 ) )
| ~ ( c_in @ ( c_Pair @ SV579 @ SY5852 @ SV1615 @ SV1615 ) @ SV1942 @ ( tc_prod @ SV1615 @ SV1615 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4655]) ).
thf(5105,plain,
! [SV1943: $i,SV1616: $i,SV1180: $i,SV580: $i] :
( ( ( c_in @ ( c_Pair @ SV580 @ SV1180 @ SV1616 @ SV1616 ) @ ( c_Transitive__Closure_Ortrancl @ SV1943 @ SV1616 ) @ ( tc_prod @ SV1616 @ SV1616 ) )
= $true )
| ( ( ! [SY5853: $i] :
( ~ ( c_in @ ( c_Pair @ SY5853 @ SV1180 @ SV1616 @ SV1616 ) @ SV1943 @ ( tc_prod @ SV1616 @ SV1616 ) )
| ~ ( c_in @ ( c_Pair @ SV580 @ SY5853 @ SV1616 @ SV1616 ) @ ( c_Transitive__Closure_Ortrancl @ SV1943 @ SV1616 ) @ ( tc_prod @ SV1616 @ SV1616 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4656]) ).
thf(5106,plain,
! [SV1944: $i,SV1617: $i,SV1181: $i,SV581: $i] :
( ( ( c_in @ ( c_Pair @ SV581 @ SV1181 @ SV1617 @ SV1617 ) @ ( c_Transitive__Closure_Ortrancl @ SV1944 @ SV1617 ) @ ( tc_prod @ SV1617 @ SV1617 ) )
= $true )
| ( ( ! [SY5854: $i] :
( ~ ( c_in @ ( c_Pair @ SY5854 @ SV1181 @ SV1617 @ SV1617 ) @ ( c_Transitive__Closure_Ortrancl @ SV1944 @ SV1617 ) @ ( tc_prod @ SV1617 @ SV1617 ) )
| ~ ( c_in @ ( c_Pair @ SV581 @ SY5854 @ SV1617 @ SV1617 ) @ SV1944 @ ( tc_prod @ SV1617 @ SV1617 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4657]) ).
thf(5107,plain,
! [SV1945: $i,SV1618: $i,SV1182: $i,SV582: $i] :
( ( ( c_in @ ( c_Pair @ SV582 @ SV1182 @ SV1618 @ SV1618 ) @ ( c_Transitive__Closure_Otrancl @ SV1945 @ SV1618 ) @ ( tc_prod @ SV1618 @ SV1618 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV582 @ SV1182 @ SV1618 @ SV1618 ) @ SV1945 @ ( tc_prod @ SV1618 @ SV1618 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4658]) ).
thf(5108,plain,
! [SV1946: $i,SV1619: $i,SV1183: $i,SV583: $i] :
( ( ( c_in @ ( c_Pair @ SV583 @ SV1183 @ SV1619 @ SV1619 ) @ ( c_Transitive__Closure_Ortrancl @ SV1946 @ SV1619 ) @ ( tc_prod @ SV1619 @ SV1619 ) )
= $true )
| ( ( ! [SY5855: $i] :
( ~ ( c_in @ ( c_Pair @ SY5855 @ SV1183 @ SV1619 @ SV1619 ) @ ( c_Transitive__Closure_Ortrancl @ SV1946 @ SV1619 ) @ ( tc_prod @ SV1619 @ SV1619 ) )
| ~ ( c_in @ ( c_Pair @ SV583 @ SY5855 @ SV1619 @ SV1619 ) @ ( c_Transitive__Closure_Ortrancl @ SV1946 @ SV1619 ) @ ( tc_prod @ SV1619 @ SV1619 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4659]) ).
thf(5109,plain,
! [SV1947: $i,SV1622: $i,SV1186: $i,SV586: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV586 @ SV1186 @ SV1622 @ SV1622 ) @ SV1947 @ ( tc_prod @ SV1622 @ SV1622 ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV1186 @ SV586 @ SV1622 @ SV1622 ) @ SV1947 @ ( tc_prod @ SV1622 @ SV1622 ) )
| ~ ( c_Wellfounded_Owf @ SV1947 @ SV1622 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4660]) ).
thf(5110,plain,
! [SV2165: $i,SV1948: $i,SV587: $i,SV1187: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1187 @ SV587 @ SV1948 @ SV1948 ) @ SV2165 @ ( tc_prod @ SV1948 @ SV1948 ) )
| ~ ( c_in @ ( c_Pair @ SV587 @ SV1187 @ SV1948 @ SV1948 ) @ SV2165 @ ( tc_prod @ SV1948 @ SV1948 ) )
| ~ ( c_Relation_Oantisym @ SV2165 @ SV1948 ) )
= $true )
| ( ( SV587 = SV1187 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4661]) ).
thf(5111,plain,
! [SV2166: $i,SV1949: $i,SV588: $i,SV1188: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1188 @ SV588 @ SV1949 @ SV1949 ) @ SV2166 @ ( tc_prod @ SV1949 @ SV1949 ) )
| ~ ( c_in @ ( c_Pair @ SV588 @ SV1188 @ SV1949 @ SV1949 ) @ SV2166 @ ( tc_prod @ SV1949 @ SV1949 ) )
| ~ ( c_Relation_Oantisym @ SV2166 @ SV1949 ) )
= $true )
| ( ( SV588 = SV1188 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4662]) ).
thf(5112,plain,
! [SV1950: $i,SV1623: $i,SV1189: $i,SV589: $i] :
( ( ( ( hAPP @ SV589 @ SV1189 )
= ( hAPP @ SV589 @ SV1623 ) )
= $true )
| ( ( ! [SY5858: $i] :
( ~ ( c_in @ ( c_Pair @ SV1189 @ SV1623 @ SV1950 @ SV1950 ) @ SY5858 @ ( tc_prod @ SV1950 @ SV1950 ) )
| ! [SY5859: $i] :
~ ( c_Equiv__Relations_Ocongruent @ SY5858 @ SV589 @ SV1950 @ SY5859 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4663]) ).
thf(5113,plain,
! [SV2167: $i,SV1951: $i,SV1190: $i,SV590: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV590 @ SV1190 @ SV1951 @ SV1951 ) @ ( c_Relation_OId__on @ SV2167 @ SV1951 ) @ ( tc_prod @ SV1951 @ SV1951 ) ) )
= $true )
| ( ( SV590 = SV1190 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4664]) ).
thf(5114,plain,
! [SV2168: $i,SV1952: $i,SV1624: $i,SV1191: $i,SV591: $i] :
( ( ! [SY5980: $i] :
( ( ( c_Recdef_Ocut @ SV591 @ SV1191 @ SV1624 @ SV1952 @ SV2168 )
!= ( c_Recdef_Ocut @ SY5980 @ SV1191 @ SV1624 @ SV1952 @ SV2168 ) )
| ! [SY5863: $i] :
( ( ( hAPP @ SV591 @ SY5863 )
= ( hAPP @ SY5980 @ SY5863 ) )
| ~ ( c_in @ ( c_Pair @ SY5863 @ SV1624 @ SV1952 @ SV1952 ) @ SV1191 @ ( tc_prod @ SV1952 @ SV1952 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4665]) ).
thf(5115,plain,
! [SV1953: $i,SV1192: $i,SV592: $i] :
( ( ( c_in @ ( c_Pair @ SV592 @ SV1192 @ SV1953 @ SV1953 ) @ ( c_Relation_OId @ SV1953 ) @ ( tc_prod @ SV1953 @ SV1953 ) )
= $false )
| ( ( SV592 = SV1192 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4666]) ).
thf(5116,plain,
! [SV593: $i,SV1193: $i,SV1625: $i] :
( ( ( c_Nitpick_Orefl_H @ SV1625 @ SV1193 )
= $false )
| ( ( c_in @ ( c_Pair @ SV593 @ SV593 @ SV1193 @ SV1193 ) @ SV1625 @ ( tc_prod @ SV1193 @ SV1193 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4667]) ).
thf(5117,plain,
! [SV1626: $i,SV1194: $i,SV594: $i] :
( ( ( c_in @ ( c_Pair @ SV594 @ SV594 @ SV1194 @ SV1194 ) @ SV1626 @ ( tc_prod @ SV1194 @ SV1194 ) )
= $false )
| ( ( ~ ( c_Wellfounded_Owf @ SV1626 @ SV1194 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4668]) ).
thf(5118,plain,
! [SV2169: $i,SV1954: $i,SV1627: $i,SV1195: $i,SV595: $i] :
( ( ! [SY5982: $i] :
( ( c_in @ ( c_Pair @ SV595 @ SV1195 @ SV1627 @ SV1627 ) @ ( c_Relation_Oinv__image @ SV1954 @ SV2169 @ SY5982 @ SV1627 ) @ ( tc_prod @ SV1627 @ SV1627 ) )
| ~ ( c_in @ ( c_Pair @ ( hAPP @ SV2169 @ SV595 ) @ ( hAPP @ SV2169 @ SV1195 ) @ SY5982 @ SY5982 ) @ SV1954 @ ( tc_prod @ SY5982 @ SY5982 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4669]) ).
thf(5119,plain,
! [SV2170: $i,SV1955: $i,SV1628: $i,SV1196: $i,SV596: $i] :
( ( ( c_in @ ( c_Pair @ ( hAPP @ SV596 @ SV1196 ) @ ( hAPP @ SV596 @ SV1628 ) @ SV1955 @ SV1955 ) @ SV2170 @ ( tc_prod @ SV1955 @ SV1955 ) )
| ! [SY5983: $i] :
~ ( c_in @ ( c_Pair @ SV1196 @ SV1628 @ SY5983 @ SY5983 ) @ ( c_Relation_Oinv__image @ SV2170 @ SV596 @ SV1955 @ SY5983 ) @ ( tc_prod @ SY5983 @ SY5983 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4670]) ).
thf(5120,plain,
! [SV1956: $i,SV1629: $i,SV1197: $i,SV597: $i] :
( ( ( c_in @ ( c_Pair @ SV597 @ SV1197 @ SV1629 @ SV1629 ) @ SV1956 @ ( tc_prod @ SV1629 @ SV1629 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV1197 @ SV597 @ SV1629 @ SV1629 ) @ SV1956 @ ( tc_prod @ SV1629 @ SV1629 ) )
| ~ ( c_Relation_Osym @ SV1956 @ SV1629 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4671]) ).
thf(5121,plain,
! [SV1957: $i,SV1630: $i,SV1198: $i,SV598: $i] :
( ( ( c_in @ ( c_Pair @ SV598 @ SV1198 @ SV1630 @ SV1630 ) @ SV1957 @ ( tc_prod @ SV1630 @ SV1630 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV1198 @ SV598 @ SV1630 @ SV1630 ) @ SV1957 @ ( tc_prod @ SV1630 @ SV1630 ) )
| ~ ( c_Relation_Osym @ SV1957 @ SV1630 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4672]) ).
thf(5122,plain,
! [SV2171: $i,SV1958: $i,SV1631: $i,SV1199: $i,SV599: $i] :
( ( ! [SY5984: $i,SY5985: $i] :
( ( c_in @ ( c_Pair @ SV599 @ SV1199 @ SV1631 @ SV1958 ) @ ( c_Relation_Orel__comp @ SV2171 @ SY5984 @ SV1631 @ SY5985 @ SV1958 ) @ ( tc_prod @ SV1631 @ SV1958 ) )
| ! [SY5986: $i] :
( ~ ( c_in @ ( c_Pair @ SY5986 @ SV1199 @ SY5985 @ SV1958 ) @ SY5984 @ ( tc_prod @ SY5985 @ SV1958 ) )
| ~ ( c_in @ ( c_Pair @ SV599 @ SY5986 @ SV1631 @ SY5985 ) @ SV2171 @ ( tc_prod @ SV1631 @ SY5985 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4673]) ).
thf(5123,plain,
! [SV1959: $i,SV1632: $i,SV1200: $i,SV600: $i] :
( ( ( c_in @ ( c_Pair @ SV600 @ SV1200 @ SV1632 @ SV1632 ) @ ( c_Transitive__Closure_Otrancl @ SV1959 @ SV1632 ) @ ( tc_prod @ SV1632 @ SV1632 ) )
= $true )
| ( ( ! [SY5872: $i] :
( ~ ( c_in @ ( c_Pair @ SY5872 @ SV1200 @ SV1632 @ SV1632 ) @ SV1959 @ ( tc_prod @ SV1632 @ SV1632 ) )
| ~ ( c_in @ ( c_Pair @ SV600 @ SY5872 @ SV1632 @ SV1632 ) @ SV1959 @ ( tc_prod @ SV1632 @ SV1632 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4674]) ).
thf(5124,plain,
! [SV1960: $i,SV1633: $i,SV1201: $i,SV601: $i] :
( ( ( c_in @ ( c_Pair @ SV601 @ SV1201 @ SV1633 @ SV1633 ) @ ( c_Transitive__Closure_Otrancl @ SV1960 @ SV1633 ) @ ( tc_prod @ SV1633 @ SV1633 ) )
= $true )
| ( ( ! [SY5873: $i] :
( ~ ( c_in @ ( c_Pair @ SY5873 @ SV1201 @ SV1633 @ SV1633 ) @ ( c_Transitive__Closure_Otrancl @ SV1960 @ SV1633 ) @ ( tc_prod @ SV1633 @ SV1633 ) )
| ~ ( c_in @ ( c_Pair @ SV601 @ SY5873 @ SV1633 @ SV1633 ) @ ( c_Transitive__Closure_Otrancl @ SV1960 @ SV1633 ) @ ( tc_prod @ SV1633 @ SV1633 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4675]) ).
thf(5125,plain,
! [SV1961: $i,SV1634: $i,SV1204: $i,SV604: $i] :
( ( ( c_in @ ( c_Pair @ SV604 @ SV1204 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omktop @ SV1634 ) @ SV1961 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV604 @ SV1204 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1634 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV604 = SV1204 )
| ( SV604 = SV1961 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4676]) ).
thf(5126,plain,
! [SV1962: $i,SV1635: $i,SV1205: $i,SV605: $i] :
( ( ( c_in @ ( c_Pair @ SV605 @ SV1205 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omktop @ SV1635 ) @ SV1962 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV605 @ SV1205 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1635 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV1205 = SV1962 )
| ( SV605 = SV1962 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4677]) ).
thf(5127,plain,
! [SV1637: $i,SV608: $i,SV2172: $i,SV1208: $i] :
( ( ( ( SV1208 = SV2172 )
| ~ ( c_in @ ( c_Pair @ SV608 @ SV1208 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omktop @ SV1637 ) @ SV2172 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV608 @ SV1208 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1637 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4679]) ).
thf(5128,plain,
! [SV2173: $i,SV1209: $i,SV609: $i] :
( ( ( c_in @ ( c_Pair @ SV609 @ SV1209 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omkbot @ SV2173 ) @ SV609 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( SV1209 = SV609 )
= $true )
| ( ( SV609 = SV1209 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4680]) ).
thf(5129,plain,
! [SV1963: $i,SV1639: $i,SV1212: $i,SV612: $i] :
( ( ( c_in @ ( c_Pair @ SV612 @ SV1212 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omkbot @ SV1639 ) @ SV1963 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV612 @ SV1212 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1639 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV612 = SV1212 )
| ( SV1212 = SV1963 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4682]) ).
thf(5130,plain,
! [SV1964: $i,SV1640: $i,SV1213: $i,SV613: $i] :
( ( ( c_in @ ( c_Pair @ SV613 @ SV1213 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omkbot @ SV1640 ) @ SV1964 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV613 @ SV1213 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1640 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( SV613 = SV1964 )
| ( SV1213 = SV1964 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4683]) ).
thf(5131,plain,
! [SV2174: $i,SV1214: $i,SV614: $i] :
( ( ( c_in @ ( c_Pair @ SV614 @ SV1214 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omktop @ SV2174 ) @ SV1214 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true )
| ( ( SV614 = SV1214 )
= $true )
| ( ( SV614 = SV1214 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4684]) ).
thf(5132,plain,
! [SV1641: $i,SV1215: $i,SV2175: $i,SV615: $i] :
( ( ( ( SV615 = SV2175 )
| ~ ( c_in @ ( c_Pair @ SV615 @ SV1215 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omkbot @ SV1641 ) @ SV2175 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV615 @ SV1215 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1641 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4685]) ).
thf(5133,plain,
! [SV2176: $i,SV1965: $i,SV1642: $i,SV1217: $i,SV617: $i] :
( ( ! [SY5987: $i] :
( ( c_in @ ( c_Pair @ SV617 @ SV1217 @ SV1642 @ SV1965 ) @ ( c_Product__Type_OSigma @ SV2176 @ SY5987 @ SV1642 @ SV1965 ) @ ( tc_prod @ SV1642 @ SV1965 ) )
| ~ ( c_in @ SV1217 @ ( hAPP @ SY5987 @ SV617 ) @ SV1965 )
| ~ ( c_in @ SV617 @ SV2176 @ SV1642 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4686]) ).
thf(5134,plain,
! [SV2177: $i,SV1966: $i,SV1643: $i,SV1218: $i,SV618: $i] :
( ( ! [SY5988: $i] :
( ( c_in @ ( c_Pair @ SV618 @ SV1218 @ SV1643 @ SV1966 ) @ ( c_Product__Type_OSigma @ SV2177 @ SY5988 @ SV1643 @ SV1966 ) @ ( tc_prod @ SV1643 @ SV1966 ) )
| ~ ( c_in @ SV1218 @ ( hAPP @ SY5988 @ SV618 ) @ SV1966 )
| ~ ( c_in @ SV618 @ SV2177 @ SV1643 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4687]) ).
thf(5135,plain,
! [SV1219: $i,SV1644: $i,SV2178: $i,SV619: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV619 @ SV2178 @ SV1644 @ SV1644 ) @ SV1219 @ ( tc_prod @ SV1644 @ SV1644 ) )
| ~ ( c_in @ SV2178 @ ( c_Wellfounded_Oacc @ SV1219 @ SV1644 ) @ SV1644 ) )
= $true )
| ( ( c_in @ SV619 @ ( c_Wellfounded_Oacc @ SV1219 @ SV1644 ) @ SV1644 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4688]) ).
thf(5136,plain,
! [SV1220: $i,SV1645: $i,SV2179: $i,SV620: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV620 @ SV2179 @ SV1645 @ SV1645 ) @ SV1220 @ ( tc_prod @ SV1645 @ SV1645 ) )
| ~ ( c_in @ SV2179 @ ( c_Wellfounded_Oacc @ SV1220 @ SV1645 ) @ SV1645 ) )
= $true )
| ( ( c_in @ SV620 @ ( c_Wellfounded_Oacc @ SV1220 @ SV1645 ) @ SV1645 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4689]) ).
thf(5137,plain,
! [SV2180: $i,SV1967: $i,SV1646: $i,SV1221: $i,SV621: $i] :
( ( ( c_in @ SV621 @ ( c_Relation_OImage @ SV1221 @ SV1646 @ SV1967 @ SV2180 ) @ SV2180 )
| ! [SY5989: $i] :
( ~ ( c_in @ ( c_Pair @ SY5989 @ SV621 @ SV1967 @ SV2180 ) @ SV1221 @ ( tc_prod @ SV1967 @ SV2180 ) )
| ~ ( c_in @ SY5989 @ SV1646 @ SV1967 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4690]) ).
thf(5138,plain,
! [SV2181: $i,SV1968: $i,SV1647: $i,SV1222: $i,SV622: $i] :
( ( ( c_in @ SV622 @ ( c_Relation_OImage @ SV1222 @ SV1647 @ SV1968 @ SV2181 ) @ SV2181 )
| ! [SY5990: $i] :
( ~ ( c_in @ ( c_Pair @ SY5990 @ SV622 @ SV1968 @ SV2181 ) @ SV1222 @ ( tc_prod @ SV1968 @ SV2181 ) )
| ~ ( c_in @ SY5990 @ SV1647 @ SV1968 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4691]) ).
thf(5139,plain,
! [SV1223: $i,SV1648: $i,SV2182: $i,SV623: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV623 @ SV2182 @ SV1648 @ SV1648 ) @ ( c_Relation_OId__on @ SV1223 @ SV1648 ) @ ( tc_prod @ SV1648 @ SV1648 ) ) )
= $true )
| ( ( c_in @ SV623 @ SV1223 @ SV1648 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4692]) ).
thf(5140,plain,
! [SV1224: $i,SV1649: $i,SV624: $i] :
( ( ( c_in @ SV624 @ SV1649 @ SV1224 )
= $false )
| ( ( c_in @ ( c_Pair @ SV624 @ SV624 @ SV1224 @ SV1224 ) @ ( c_Relation_OId__on @ SV1649 @ SV1224 ) @ ( tc_prod @ SV1224 @ SV1224 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4693]) ).
thf(5141,plain,
! [SV1225: $i,SV1650: $i,SV625: $i,SV2183: $i] :
( ( ( ! [SY5991: $i] :
( ~ ( c_in @ ( c_Pair @ SV2183 @ SV625 @ SV1650 @ SV1650 ) @ SY5991 @ ( tc_prod @ SV1650 @ SV1650 ) )
| ~ ( c_Equiv__Relations_Oequiv @ SV1225 @ SY5991 @ SV1650 ) ) )
= $true )
| ( ( c_in @ SV625 @ SV1225 @ SV1650 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4694]) ).
thf(5142,plain,
! [SV1226: $i,SV1651: $i,SV2184: $i,SV626: $i] :
( ( ( ! [SY5992: $i] :
( ~ ( c_in @ ( c_Pair @ SV626 @ SV2184 @ SV1651 @ SV1651 ) @ SY5992 @ ( tc_prod @ SV1651 @ SV1651 ) )
| ~ ( c_Equiv__Relations_Oequiv @ SV1226 @ SY5992 @ SV1651 ) ) )
= $true )
| ( ( c_in @ SV626 @ SV1226 @ SV1651 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4695]) ).
thf(5143,plain,
! [SV1969: $i,SV1652: $i,SV1227: $i,SV627: $i] :
( ( ( c_in @ SV627 @ ( c_Relation_ORange @ SV1227 @ SV1652 @ SV1969 ) @ SV1969 )
= $true )
| ( ( ! [SY5882: $i] :
~ ( c_in @ ( c_Pair @ SY5882 @ SV627 @ SV1652 @ SV1969 ) @ SV1227 @ ( tc_prod @ SV1652 @ SV1969 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4696]) ).
thf(5144,plain,
! [SV1970: $i,SV1653: $i,SV1228: $i,SV628: $i] :
( ( ( c_in @ SV628 @ ( c_Relation_ORange @ SV1228 @ SV1653 @ SV1970 ) @ SV1970 )
= $true )
| ( ( ! [SY5883: $i] :
~ ( c_in @ ( c_Pair @ SY5883 @ SV628 @ SV1653 @ SV1970 ) @ SV1228 @ ( tc_prod @ SV1653 @ SV1970 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4697]) ).
thf(5145,plain,
! [SV1971: $i,SV1654: $i,SV1229: $i,SV629: $i] :
( ( ( c_in @ SV629 @ ( c_Relation_ODomain @ SV1229 @ SV1654 @ SV1971 ) @ SV1654 )
= $true )
| ( ( ! [SY5884: $i] :
~ ( c_in @ ( c_Pair @ SV629 @ SY5884 @ SV1654 @ SV1971 ) @ SV1229 @ ( tc_prod @ SV1654 @ SV1971 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4698]) ).
thf(5146,plain,
! [SV1972: $i,SV1655: $i,SV1230: $i,SV630: $i] :
( ( ( c_in @ SV630 @ ( c_Relation_ODomain @ SV1230 @ SV1655 @ SV1972 ) @ SV1655 )
= $true )
| ( ( ! [SY5885: $i] :
~ ( c_in @ ( c_Pair @ SV630 @ SY5885 @ SV1655 @ SV1972 ) @ SV1230 @ ( tc_prod @ SV1655 @ SV1972 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4699]) ).
thf(5147,plain,
! [SV1973: $i,SV1656: $i,SV1231: $i,SV631: $i] :
( ( ( c_in @ SV631 @ ( hAPP @ SV1231 @ SV1656 ) @ SV1973 )
= $true )
| ( ( ! [SY5886: $i,SY5887: $i] :
~ ( c_in @ ( c_Pair @ SV1656 @ SV631 @ SY5886 @ SV1973 ) @ ( c_Product__Type_OSigma @ SY5887 @ SV1231 @ SY5886 @ SV1973 ) @ ( tc_prod @ SY5886 @ SV1973 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4700]) ).
thf(5148,plain,
! [SV1974: $i,SV1657: $i,SV1232: $i,SV632: $i] :
( ( ( c_in @ SV632 @ SV1232 @ SV1657 )
= $true )
| ( ( ! [SY5888: $i,SY5889: $i] :
~ ( c_in @ ( c_Pair @ SV632 @ SV1974 @ SV1657 @ SY5888 ) @ ( c_Product__Type_OSigma @ SV1232 @ SY5889 @ SV1657 @ SY5888 ) @ ( tc_prod @ SV1657 @ SY5888 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4701]) ).
thf(5149,plain,
! [SV1975: $i,SV1658: $i,SV1233: $i,SV633: $i] :
( ( ( c_in @ ( c_Pair @ SV633 @ SV1233 @ SV1658 @ SV1658 ) @ SV1975 @ ( tc_prod @ SV1658 @ SV1658 ) )
= $true )
| ( ( ( c_in @ ( c_Pair @ SV1233 @ SV633 @ SV1658 @ SV1658 ) @ SV1975 @ ( tc_prod @ SV1658 @ SV1658 ) )
| ( SV1233 = SV633 )
| ! [SY5890: $i] :
( ~ ( c_in @ SV633 @ SY5890 @ SV1658 )
| ~ ( c_in @ SV1233 @ SY5890 @ SV1658 )
| ~ ( c_Relation_Ototal__on @ SY5890 @ SV1975 @ SV1658 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4702]) ).
thf(5150,plain,
! [SV1659: $i,SV1234: $i,SV2185: $i,SV634: $i] :
( ( ( ~ ( c_in @ SV634 @ SV2185 @ SV1234 )
| ~ ( c_Relation_Orefl__on @ SV2185 @ SV1659 @ SV1234 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV634 @ SV634 @ SV1234 @ SV1234 ) @ SV1659 @ ( tc_prod @ SV1234 @ SV1234 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4703]) ).
thf(5151,plain,
! [SV1235: $i,SV1660: $i,SV635: $i,SV2186: $i] :
( ( ( ! [SY5993: $i] :
( ~ ( c_in @ ( c_Pair @ SV2186 @ SV635 @ SV1660 @ SV1660 ) @ SY5993 @ ( tc_prod @ SV1660 @ SV1660 ) )
| ~ ( c_Relation_Orefl__on @ SV1235 @ SY5993 @ SV1660 ) ) )
= $true )
| ( ( c_in @ SV635 @ SV1235 @ SV1660 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4704]) ).
thf(5152,plain,
! [SV1236: $i,SV1661: $i,SV2187: $i,SV636: $i] :
( ( ( ! [SY5994: $i] :
( ~ ( c_in @ ( c_Pair @ SV636 @ SV2187 @ SV1661 @ SV1661 ) @ SY5994 @ ( tc_prod @ SV1661 @ SV1661 ) )
| ~ ( c_Relation_Orefl__on @ SV1236 @ SY5994 @ SV1661 ) ) )
= $true )
| ( ( c_in @ SV636 @ SV1236 @ SV1661 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4705]) ).
thf(5153,plain,
! [SV1662: $i,SV1237: $i,SV2188: $i,SV637: $i] :
( ( ( ~ ( c_in @ SV637 @ SV2188 @ SV1237 )
| ~ ( c_Relation_Orefl__on @ SV2188 @ SV1662 @ SV1237 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV637 @ SV637 @ SV1237 @ SV1237 ) @ SV1662 @ ( tc_prod @ SV1237 @ SV1237 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4706]) ).
thf(5154,plain,
! [SV2189: $i,SV1976: $i,SV1663: $i,SV1238: $i,SV638: $i] :
( ( ! [SY5995: $i] :
( ( ( c_Pair @ SV638 @ SV1238 @ SV1663 @ SV1976 )
!= ( c_Pair @ SV2189 @ SY5995 @ SV1663 @ SV1976 ) )
| ( SV1238 = SY5995 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4707]) ).
thf(5155,plain,
! [SV2190: $i,SV1977: $i,SV1664: $i,SV1239: $i,SV639: $i] :
( ( ! [SY5996: $i] :
( ( c_Pair @ SV639 @ SV1239 @ SV1664 @ SV1977 )
!= ( c_Pair @ SV2190 @ SY5996 @ SV1664 @ SV1977 ) )
| ( SV639 = SV2190 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4708]) ).
thf(5156,plain,
! [SV1978: $i,SV640: $i,SV1240: $i] :
( ( ( hBOOL @ ( hAPP @ SV1240 @ SV640 ) )
= $false )
| ( ( c_in @ SV640 @ SV1240 @ SV1978 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4709]) ).
thf(5157,plain,
! [SV1979: $i,SV641: $i,SV1241: $i] :
( ( ( c_in @ SV1241 @ SV641 @ SV1979 )
= $false )
| ( ( hBOOL @ ( hAPP @ SV641 @ SV1241 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4710]) ).
thf(5158,plain,
! [SV1252: $i,SV652: $i,SV1980: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ SV1980 ) @ SV652 ) @ SV1252 ) )
= $false )
| ( ( SV652 = SV1252 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4720]) ).
thf(5159,plain,
! [SV1673: $i,SV1261: $i,SV663: $i,SV12: $i] :
( ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV12 @ tc_bool ) )
= ( c_Set_Oimage @ SV663 @ SV1261 @ SV1673 @ SV12 ) )
= $false )
| ( ( SV1261
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1673 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4721]) ).
thf(5160,plain,
! [SV1674: $i,SV1263: $i,SV665: $i,SV14: $i] :
( ( ( ( hAPP @ ( c_snd @ SV14 @ SV665 ) @ SV1263 )
= ( hAPP @ ( c_snd @ SV14 @ SV665 ) @ SV1674 ) )
= $false )
| ( ( ( ( hAPP @ ( c_fst @ SV14 @ SV665 ) @ SV1263 )
!= ( hAPP @ ( c_fst @ SV14 @ SV665 ) @ SV1674 ) )
| ( SV1263 = SV1674 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4722]) ).
thf(5161,plain,
! [SV1675: $i,SV1264: $i,SV666: $i,SV15: $i] :
( ( ( ( hAPP @ ( c_snd @ SV15 @ SV666 ) @ SV1264 )
= ( hAPP @ ( c_snd @ SV15 @ SV666 ) @ SV1675 ) )
= $false )
| ( ( ( ( hAPP @ ( c_fst @ SV15 @ SV666 ) @ SV1264 )
!= ( hAPP @ ( c_fst @ SV15 @ SV666 ) @ SV1675 ) )
| ( SV1264 = SV1675 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4723]) ).
thf(5162,plain,
! [SV667: $i,SV1981: $i,SV1676: $i,SV16: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV16 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1 @ SV16 @ SV1676 @ SV1981 ) ) ) )
= $true )
| ( ( ~ ( c_Wellfounded_Owf @ SV1676 @ SV1981 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV16 @ SV667 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4724]) ).
thf(5163,plain,
! [SV669: $i,SV1678: $i,SV1266: $i,SV18: $i] :
( ( ( c_lessequals @ SV18 @ SV1266 @ ( tc_fun @ SV1678 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV18 @ ( c_Set_Oinsert @ SV669 @ SV1266 @ SV1678 ) @ ( tc_fun @ SV1678 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4725]) ).
thf(5164,plain,
! [SV670: $i,SV1267: $i,SV19: $i,SV1982: $i] :
( ( ( c_lessequals @ ( c_Set_Oinsert @ SV1982 @ SV19 @ SV1267 ) @ SV670 @ ( tc_fun @ SV1267 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV19 @ SV670 @ ( tc_fun @ SV1267 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4726]) ).
thf(5165,plain,
! [SV671: $i,SV1268: $i,SV1679: $i,SV20: $i] :
( ( ( c_in @ SV20 @ SV1679 @ SV1268 )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ SV20 @ SV671 @ SV1268 ) @ SV1679 @ ( tc_fun @ SV1268 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ SV671 @ SV1679 @ ( tc_fun @ SV1268 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4727]) ).
thf(5166,plain,
! [SV1983: $i,SV1680: $i,SV1269: $i,SV672: $i,SV21: $i] :
( ( ( c_lessequals @ ( c_Product__Type_OSigma @ SV21 @ ( c_COMBK @ SV672 @ ( tc_fun @ SV1269 @ tc_bool ) @ SV1680 ) @ SV1680 @ SV1269 ) @ ( c_Product__Type_OSigma @ SV1983 @ ( c_COMBK @ SV672 @ ( tc_fun @ SV1269 @ tc_bool ) @ SV1680 ) @ SV1680 @ SV1269 ) @ ( tc_fun @ ( tc_prod @ SV1680 @ SV1269 ) @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV21 @ SV1983 @ ( tc_fun @ SV1680 @ tc_bool ) )
| ! [SY5180: $i] :
~ ( c_in @ SY5180 @ SV672 @ SV1269 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4728]) ).
thf(5167,plain,
! [SV673: $i,SV1270: $i,SV2191: $i,SV1681: $i,SV22: $i] :
( ( ( ~ ( c_lessequals @ ( c_Product__Type_OSigma @ SV22 @ ( c_COMBK @ SV1681 @ ( tc_fun @ SV2191 @ tc_bool ) @ SV1270 ) @ SV1270 @ SV2191 ) @ ( c_Product__Type_OSigma @ SV673 @ ( c_COMBK @ SV1681 @ ( tc_fun @ SV2191 @ tc_bool ) @ SV1270 ) @ SV1270 @ SV2191 ) @ ( tc_fun @ ( tc_prod @ SV1270 @ SV2191 ) @ tc_bool ) )
| ! [SY5997: $i] :
~ ( c_in @ SY5997 @ SV1681 @ SV2191 ) )
= $true )
| ( ( c_lessequals @ SV22 @ SV673 @ ( tc_fun @ SV1270 @ tc_bool ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4729]) ).
thf(5168,plain,
! [SV1271: $i,SV1682: $i,SV23: $i,SV674: $i] :
( ( ( ~ ( c_in @ SV674 @ SV23 @ SV1682 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV23 @ ( c_Set_Oinsert @ SV674 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1682 @ tc_bool ) ) @ SV1682 ) @ ( tc_fun @ SV1682 @ tc_bool ) ) @ SV1271 @ ( tc_fun @ SV1682 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV23 @ ( c_Set_Oinsert @ SV674 @ SV1271 @ SV1682 ) @ ( tc_fun @ SV1682 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4730]) ).
thf(5169,plain,
! [SV1272: $i,SV1683: $i,SV24: $i,SV675: $i] :
( ( ( ~ ( c_in @ SV675 @ SV24 @ SV1683 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV24 @ ( c_Set_Oinsert @ SV675 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1683 @ tc_bool ) ) @ SV1683 ) @ ( tc_fun @ SV1683 @ tc_bool ) ) @ SV1272 @ ( tc_fun @ SV1683 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV24 @ ( c_Set_Oinsert @ SV675 @ SV1272 @ SV1683 ) @ ( tc_fun @ SV1683 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4731]) ).
thf(5170,plain,
! [SV1684: $i,SV1273: $i,SV25: $i,SV676: $i] :
( ( ( ~ ( c_in @ SV676 @ SV25 @ SV1273 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV25 @ ( c_Set_Oinsert @ SV676 @ SV1684 @ SV1273 ) @ ( tc_fun @ SV1273 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV25 @ ( c_Set_Oinsert @ SV676 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1273 @ tc_bool ) ) @ SV1273 ) @ ( tc_fun @ SV1273 @ tc_bool ) ) @ SV1684 @ ( tc_fun @ SV1273 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4732]) ).
thf(5171,plain,
! [SV677: $i,SV26: $i,SV1274: $i,SV1685: $i,SV2192: $i] :
( ( ( ~ ( c_in @ SV2192 @ SV1685 @ SV1274 ) )
= $true )
| ( ( ( c_Set_Oimage @ ( c_COMBK @ SV26 @ SV677 @ SV1274 ) @ SV1685 @ SV1274 @ SV677 )
= ( c_Set_Oinsert @ SV26 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV677 @ tc_bool ) ) @ SV677 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4733]) ).
thf(5172,plain,
! [SV1275: $i,SV678: $i,SV27: $i] :
( ( ( c_lessequals @ ( c_Relation_Orel__comp @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Transitive__Closure_Otrancl @ SV27 @ SV678 ) @ SV1275 @ ( tc_fun @ ( tc_prod @ SV678 @ SV678 ) @ tc_bool ) ) @ SV27 @ SV678 @ SV678 @ SV678 ) @ SV1275 @ ( tc_fun @ ( tc_prod @ SV678 @ SV678 ) @ tc_bool ) )
= $false )
| ( ( ~ ( c_lessequals @ SV27 @ SV1275 @ ( tc_fun @ ( tc_prod @ SV678 @ SV678 ) @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( c_Transitive__Closure_Otrancl @ SV27 @ SV678 ) @ SV1275 @ ( tc_fun @ ( tc_prod @ SV678 @ SV678 ) @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4734]) ).
thf(5173,plain,
! [SV34: $i,SV2193: $i,SV1985: $i,SV685: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV685 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1985 @ SV2193 @ SV34 ) @ SV34 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV685 @ SV1985 @ SV34 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV685 @ SV2193 @ SV34 ) @ SV34 ) )
= $true )
| ( ( class_Lattices_Odistrib__lattice @ SV34 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4738]) ).
thf(5174,plain,
! [SV2194: $i,SV35: $i,SV1986: $i,SV686: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV686 @ SV1986 @ SV35 ) @ SV2194 @ SV35 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV686 @ SV2194 @ SV35 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1986 @ SV2194 @ SV35 ) @ SV35 ) )
= $true )
| ( ( class_Lattices_Odistrib__lattice @ SV35 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4739]) ).
thf(5175,plain,
! [SV2195: $i,SV1987: $i,SV1692: $i,SV1282: $i,SV690: $i,SV40: $i] :
( ( ! [SY5998: $i] :
( ( c_lessequals @ ( c_Relation_Orel__comp @ SV40 @ SV690 @ SV1282 @ SV1692 @ SV1987 ) @ ( c_Relation_Orel__comp @ SV2195 @ SY5998 @ SV1282 @ SV1692 @ SV1987 ) @ ( tc_fun @ ( tc_prod @ SV1282 @ SV1987 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV690 @ SY5998 @ ( tc_fun @ ( tc_prod @ SV1692 @ SV1987 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV40 @ SV2195 @ ( tc_fun @ ( tc_prod @ SV1282 @ SV1692 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4741]) ).
thf(5176,plain,
! [SV693: $i,SV1990: $i,SV1695: $i,SV43: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV43 @ ( c_List_Osko__Recdef__Xtfl__wf__induct__1__1 @ SV43 @ SV1695 @ SV1990 ) ) ) )
= $true )
| ( ( ~ ( c_Wellfounded_Owf @ SV1695 @ SV1990 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV43 @ SV693 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4744]) ).
thf(5177,plain,
! [SV1991: $i,SV1698: $i,SV1291: $i,SV701: $i,SV51: $i] :
( ( ( c_lessequals @ ( c_Relation_OImage @ SV51 @ SV701 @ SV1291 @ SV1698 ) @ SV1991 @ ( tc_fun @ SV1698 @ tc_bool ) )
= $true )
| ( ( ! [SY5900: $i] :
~ ( c_lessequals @ SV51 @ ( c_Product__Type_OSigma @ SY5900 @ ( c_COMBK @ SV1991 @ ( tc_fun @ SV1698 @ tc_bool ) @ SV1291 ) @ SV1291 @ SV1698 ) @ ( tc_fun @ ( tc_prod @ SV1291 @ SV1698 ) @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4745]) ).
thf(5178,plain,
! [SV52: $i,SV1992: $i,SV702: $i] :
( ( ( ! [SY5901: $i] :
( ( c_HOL_Ominus__class_Ominus @ SV702 @ SV1992 @ SV52 )
!= ( c_HOL_Ominus__class_Ominus @ SY5901 @ SY5901 @ SV52 ) ) )
= $true )
| ( ( SV702 = SV1992 )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV52 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4746]) ).
thf(5179,plain,
! [SV2196: $i,SV1993: $i,SV53: $i,SV703: $i] :
( ( ( ( ( c_HOL_Ominus__class_Ominus @ SV703 @ SV703 @ SV53 )
!= ( c_HOL_Ominus__class_Ominus @ SV1993 @ SV2196 @ SV53 ) )
| ( SV1993 = SV2196 ) )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV53 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4747]) ).
thf(5180,plain,
! [SV2197: $i,SV58: $i,SV1995: $i,SV708: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV708 @ SV1995 @ SV58 ) @ SV2197 @ SV58 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV708 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1995 @ SV2197 @ SV58 ) @ SV58 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV58 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4749]) ).
thf(5181,plain,
! [SV59: $i,SV2198: $i,SV1996: $i,SV709: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV709 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1996 @ SV2198 @ SV59 ) @ SV59 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV1996 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV709 @ SV2198 @ SV59 ) @ SV59 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV59 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4750]) ).
thf(5182,plain,
! [SV60: $i,SV2199: $i,SV1997: $i,SV710: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV710 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1997 @ SV2199 @ SV60 ) @ SV60 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV1997 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV710 @ SV2199 @ SV60 ) @ SV60 ) )
= $true )
| ( ( class_Lattices_Olattice @ SV60 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4751]) ).
thf(5183,plain,
! [SV2200: $i,SV61: $i,SV1998: $i,SV711: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV711 @ SV1998 @ SV61 ) @ SV2200 @ SV61 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV711 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1998 @ SV2200 @ SV61 ) @ SV61 ) )
= $true )
| ( ( class_Lattices_Olattice @ SV61 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4752]) ).
thf(5184,plain,
! [SV64: $i,SV1999: $i,SV1702: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV1702 @ SV1999 @ SV64 )
= SV1702 )
= $true )
| ( ( ~ ( c_lessequals @ SV1702 @ SV1999 @ SV64 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV64 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4755]) ).
thf(5185,plain,
! [SV65: $i,SV2000: $i,SV1703: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV1703 @ SV2000 @ SV65 )
!= SV1703 )
= $true )
| ( ( c_lessequals @ SV1703 @ SV2000 @ SV65 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV65 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4756]) ).
thf(5186,plain,
! [SV66: $i,SV2001: $i,SV1704: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV1704 @ SV2001 @ SV66 )
= SV2001 )
= $true )
| ( ( ~ ( c_lessequals @ SV2001 @ SV1704 @ SV66 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV66 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4757]) ).
thf(5187,plain,
! [SV67: $i,SV1298: $i,SV1705: $i,SV714: $i] :
( ( ( ~ ( c_lessequals @ SV714 @ SV1705 @ ( tc_fun @ SV1298 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV67 @ SV1705 @ ( tc_fun @ SV1298 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV67 @ SV714 @ ( tc_fun @ SV1298 @ tc_bool ) ) @ SV1705 @ ( tc_fun @ SV1298 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4758]) ).
thf(5188,plain,
! [SV70: $i,SV1301: $i,SV1706: $i,SV717: $i] :
( ( ( ~ ( c_lessequals @ SV717 @ SV1706 @ ( tc_fun @ SV1301 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV70 @ SV1706 @ ( tc_fun @ SV1301 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV70 @ SV717 @ ( tc_fun @ SV1301 @ tc_bool ) ) @ SV1706 @ ( tc_fun @ SV1301 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4759]) ).
thf(5189,plain,
! [SV2201: $i,SV71: $i,SV2002: $i,SV718: $i] :
( ( ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV718 @ SV2002 @ SV71 ) @ SV2201 @ SV71 )
| ~ ( c_lessequals @ SV2002 @ SV2201 @ SV71 )
| ~ ( c_lessequals @ SV718 @ SV2201 @ SV71 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV71 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4760]) ).
thf(5190,plain,
! [SV2202: $i,SV74: $i,SV2005: $i,SV719: $i] :
( ( ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV719 @ SV2005 @ SV74 ) @ SV2202 @ SV74 )
| ~ ( c_lessequals @ SV2005 @ SV2202 @ SV74 )
| ~ ( c_lessequals @ SV719 @ SV2202 @ SV74 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV74 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4763]) ).
thf(5191,plain,
! [SV2203: $i,SV75: $i,SV2006: $i,SV720: $i] :
( ( ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV720 @ SV2006 @ SV75 ) @ SV2203 @ SV75 )
| ~ ( c_lessequals @ SV2006 @ SV2203 @ SV75 )
| ~ ( c_lessequals @ SV720 @ SV2203 @ SV75 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV75 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4764]) ).
thf(5192,plain,
! [SV83: $i,SV1304: $i,SV1713: $i,SV724: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV724 @ SV1713 @ SV1304 @ SV1304 ) @ SV83 @ ( tc_prod @ SV1304 @ SV1304 ) ) )
= $true )
| ( ( ! [SY5214: $i] :
~ ( c_Equiv__Relations_Oequiv @ SY5214 @ SV83 @ SV1304 ) )
= $true )
| ( ( c_lessequals @ ( c_Relation_OImage @ SV83 @ ( c_Set_Oinsert @ SV724 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1304 @ tc_bool ) ) @ SV1304 ) @ SV1304 @ SV1304 ) @ ( c_Relation_OImage @ SV83 @ ( c_Set_Oinsert @ SV1713 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1304 @ tc_bool ) ) @ SV1304 ) @ SV1304 @ SV1304 ) @ ( tc_fun @ SV1304 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4770]) ).
thf(5193,plain,
! [SV727: $i,SV2204: $i,SV86: $i,SV1714: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV1714 @ SV86 @ SV2204 ) @ SV727 ) ) )
= $true )
| ( ( SV1714 = SV727 )
= $true )
| ( ( hBOOL @ ( hAPP @ SV86 @ SV727 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4771]) ).
thf(5194,plain,
! [SV88: $i,SV1308: $i,SV729: $i] :
( ( ( c_Relation_Osym @ SV729 @ SV1308 )
= $false )
| ( ( ~ ( c_Relation_Osym @ SV88 @ SV1308 ) )
= $true )
| ( ( c_Relation_Osym @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV88 @ SV729 @ ( tc_fun @ ( tc_prod @ SV1308 @ SV1308 ) @ tc_bool ) ) @ SV1308 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4773]) ).
thf(5195,plain,
! [SV1721: $i,SV1314: $i,SV737: $i,SV98: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV98 @ SV737 @ ( tc_fun @ SV1314 @ tc_bool ) ) @ SV1721 @ ( tc_fun @ SV1314 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV98 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV737 @ SV1721 @ ( tc_fun @ SV1314 @ tc_bool ) ) @ ( tc_fun @ SV1314 @ tc_bool ) ) )
= $false )
| ( ( c_lessequals @ SV1721 @ SV98 @ ( tc_fun @ SV1314 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4777]) ).
thf(5196,plain,
! [SV738: $i,SV1315: $i,SV99: $i,SV1722: $i] :
( ( ( c_lessequals @ SV1722 @ SV99 @ ( tc_fun @ SV1315 @ tc_bool ) )
= $false )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV99 @ SV738 @ ( tc_fun @ SV1315 @ tc_bool ) ) @ SV1722 @ ( tc_fun @ SV1315 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV99 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV738 @ SV1722 @ ( tc_fun @ SV1315 @ tc_bool ) ) @ ( tc_fun @ SV1315 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4778]) ).
thf(5197,plain,
! [SV2205: $i,SV2015: $i,SV1724: $i,SV1317: $i,SV742: $i,SV103: $i] :
( ( ! [SY5999: $i] :
( ( c_lessequals @ ( c_Relation_Orel__comp @ SV103 @ SV742 @ SV1317 @ SV1724 @ SV2015 ) @ ( c_Product__Type_OSigma @ SV2205 @ ( c_COMBK @ SY5999 @ ( tc_fun @ SV2015 @ tc_bool ) @ SV1317 ) @ SV1317 @ SV2015 ) @ ( tc_fun @ ( tc_prod @ SV1317 @ SV2015 ) @ tc_bool ) )
| ! [SY6000: $i] :
( ~ ( c_lessequals @ SV742 @ ( c_Product__Type_OSigma @ SY6000 @ ( c_COMBK @ SY5999 @ ( tc_fun @ SV2015 @ tc_bool ) @ SV1724 ) @ SV1724 @ SV2015 ) @ ( tc_fun @ ( tc_prod @ SV1724 @ SV2015 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV103 @ ( c_Product__Type_OSigma @ SV2205 @ ( c_COMBK @ SY6000 @ ( tc_fun @ SV1724 @ tc_bool ) @ SV1317 ) @ SV1317 @ SV1724 ) @ ( tc_fun @ ( tc_prod @ SV1317 @ SV1724 ) @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4780]) ).
thf(5198,plain,
! [SV1318: $i,SV743: $i,SV104: $i] :
( ( ( c_lessequals @ ( c_Relation_Orel__comp @ SV104 @ SV743 @ SV1318 @ SV1318 @ SV1318 ) @ SV104 @ ( tc_fun @ ( tc_prod @ SV1318 @ SV1318 ) @ tc_bool ) )
= $false )
| ( ( ~ ( c_Wellfounded_Owf @ SV743 @ SV1318 )
| ~ ( c_Wellfounded_Owf @ SV104 @ SV1318 ) )
= $true )
| ( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV104 @ SV743 @ ( tc_fun @ ( tc_prod @ SV1318 @ SV1318 ) @ tc_bool ) ) @ SV1318 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4781]) ).
thf(5199,plain,
! [SV744: $i,SV2206: $i,SV105: $i,SV1725: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1725 @ SV105 @ ( tc_fun @ SV2206 @ tc_bool ) ) @ SV744 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV1725 @ SV744 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV105 @ SV744 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4782]) ).
thf(5200,plain,
! [SV1319: $i,SV106: $i,SV1726: $i,SV745: $i] :
( ( ( hBOOL @ ( hAPP @ SV745 @ SV1726 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV106 @ SV745 @ ( tc_fun @ SV1319 @ tc_bool ) ) @ SV1726 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4783]) ).
thf(5201,plain,
! [SV1320: $i,SV746: $i,SV1727: $i,SV107: $i] :
( ( ( hBOOL @ ( hAPP @ SV107 @ SV1727 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV107 @ SV746 @ ( tc_fun @ SV1320 @ tc_bool ) ) @ SV1727 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4784]) ).
thf(5202,plain,
! [SV108: $i,SV747: $i,SV1321: $i] :
( ( ( ~ ( c_Wellfounded_Owf @ SV1321 @ SV747 ) )
= $true )
| ( ( ~ ( c_Wellfounded_Owf @ SV108 @ SV747 )
| ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV108 @ SV1321 @ ( tc_fun @ ( tc_prod @ SV747 @ SV747 ) @ tc_bool ) ) @ SV747 ) )
= $true )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_ODomain @ SV108 @ SV747 @ SV747 ) @ ( c_Relation_ORange @ SV1321 @ SV747 @ SV747 ) @ ( tc_fun @ SV747 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV747 @ tc_bool ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4785]) ).
thf(5203,plain,
! [SV2017: $i,SV1729: $i,SV1323: $i,SV749: $i,SV110: $i] :
( ( ( c_Relation_Orefl__on @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV110 @ SV749 @ ( tc_fun @ SV1323 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1729 @ SV2017 @ ( tc_fun @ ( tc_prod @ SV1323 @ SV1323 ) @ tc_bool ) ) @ SV1323 )
= $true )
| ( ( ~ ( c_Relation_Orefl__on @ SV749 @ SV2017 @ SV1323 )
| ~ ( c_Relation_Orefl__on @ SV110 @ SV1729 @ SV1323 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4787]) ).
thf(5204,plain,
! [SV2207: $i,SV111: $i,SV2018: $i,SV750: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV750 @ SV2018 @ SV111 ) @ SV2207 @ SV111 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV750 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2018 @ SV2207 @ SV111 ) @ SV111 ) )
= $true )
| ( ( class_Lattices_Olattice @ SV111 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4788]) ).
thf(5205,plain,
! [SV112: $i,SV2208: $i,SV2019: $i,SV751: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV751 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2019 @ SV2208 @ SV112 ) @ SV112 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV2019 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV751 @ SV2208 @ SV112 ) @ SV112 ) )
= $true )
| ( ( class_Lattices_Olattice @ SV112 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4789]) ).
thf(5206,plain,
! [SV113: $i,SV2209: $i,SV2020: $i,SV752: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV752 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2020 @ SV2209 @ SV113 ) @ SV113 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV2020 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV752 @ SV2209 @ SV113 ) @ SV113 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV113 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4790]) ).
thf(5207,plain,
! [SV2210: $i,SV114: $i,SV2021: $i,SV753: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV753 @ SV2021 @ SV114 ) @ SV2210 @ SV114 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV753 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2021 @ SV2210 @ SV114 ) @ SV114 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV114 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4791]) ).
thf(5208,plain,
! [SV2211: $i,SV2022: $i,SV1734: $i,SV1326: $i,SV759: $i,SV122: $i] :
( ( ( c_Product__Type_OSigma @ ( c_Set_Oinsert @ SV122 @ SV759 @ SV1326 ) @ ( c_COMBK @ ( c_Set_Oinsert @ SV1734 @ SV2022 @ SV2211 ) @ ( tc_fun @ SV2211 @ tc_bool ) @ SV1326 ) @ SV1326 @ SV2211 )
= ( c_Set_Oinsert @ ( c_Pair @ SV122 @ SV1734 @ SV1326 @ SV2211 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Product__Type_OSigma @ SV759 @ ( c_COMBK @ ( c_Set_Oinsert @ SV1734 @ SV2022 @ SV2211 ) @ ( tc_fun @ SV2211 @ tc_bool ) @ SV1326 ) @ SV1326 @ SV2211 ) @ ( c_Product__Type_OSigma @ ( c_Set_Oinsert @ SV122 @ SV759 @ SV1326 ) @ ( c_COMBK @ SV2022 @ ( tc_fun @ SV2211 @ tc_bool ) @ SV1326 ) @ SV1326 @ SV2211 ) @ ( tc_fun @ ( tc_prod @ SV1326 @ SV2211 ) @ tc_bool ) ) @ ( tc_prod @ SV1326 @ SV2211 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4792]) ).
thf(5209,plain,
! [SV760: $i,SV1735: $i,SV123: $i] :
( ( ( c_lessequals @ SV123 @ ( c_Relation_OImage @ SV1735 @ SV123 @ SV760 @ SV760 ) @ ( tc_fun @ SV760 @ tc_bool ) )
= $false )
| ( ( ~ ( c_Wellfounded_Owf @ SV1735 @ SV760 ) )
= $true )
| ( ( SV123
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV760 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4793]) ).
thf(5210,plain,
! [SV2023: $i,SV1739: $i,SV1330: $i,SV765: $i,SV128: $i] :
( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV128 @ SV765 @ ( tc_fun @ SV1330 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV1739 @ SV2023 @ ( tc_fun @ SV1330 @ tc_bool ) ) @ ( tc_fun @ SV1330 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV2023 @ SV765 @ ( tc_fun @ SV1330 @ tc_bool ) )
| ~ ( c_lessequals @ SV128 @ SV1739 @ ( tc_fun @ SV1330 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4795]) ).
thf(5211,plain,
! [SV766: $i,SV1331: $i,SV2212: $i,SV129: $i] :
( ( ( ~ ( c_in @ SV129 @ SV2212 @ SV1331 )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV2212 @ SV766 @ ( tc_fun @ SV1331 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1331 @ tc_bool ) ) ) )
= $true )
| ( ( c_in @ SV129 @ SV766 @ SV1331 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4796]) ).
thf(5212,plain,
! [SV130: $i,SV1332: $i,SV767: $i] :
( ( ( c_Relation_Otrans @ SV767 @ SV1332 )
= $false )
| ( ( ~ ( c_Relation_Otrans @ SV130 @ SV1332 ) )
= $true )
| ( ( c_Relation_Otrans @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV130 @ SV767 @ ( tc_fun @ ( tc_prod @ SV1332 @ SV1332 ) @ tc_bool ) ) @ SV1332 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4797]) ).
thf(5213,plain,
! [SV131: $i,SV2213: $i,SV2024: $i,SV768: $i] :
( ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV768 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2024 @ SV2213 @ SV131 ) @ SV131 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV768 @ SV2024 @ SV131 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV768 @ SV2213 @ SV131 ) @ SV131 ) @ SV131 )
= $true )
| ( ( class_Lattices_Olattice @ SV131 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4798]) ).
thf(5214,plain,
! [SV134: $i,SV1334: $i,SV770: $i,SV2214: $i] :
( ( ( ( ( c_Relation_Orel__comp @ SV2214 @ SV770 @ SV1334 @ SV1334 @ SV1334 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV1334 @ SV1334 ) @ tc_bool ) ) )
| ( ( c_Relation_Orel__comp @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV2214 @ SV134 @ ( tc_fun @ ( tc_prod @ SV1334 @ SV1334 ) @ tc_bool ) ) @ SV770 @ SV1334 @ SV1334 @ SV1334 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV1334 @ SV1334 ) @ tc_bool ) ) ) )
= $true )
| ( ( ( c_Relation_Orel__comp @ SV134 @ SV770 @ SV1334 @ SV1334 @ SV1334 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV1334 @ SV1334 ) @ tc_bool ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4800]) ).
thf(5215,plain,
! [SV771: $i,SV1335: $i,SV2215: $i,SV135: $i] :
( ( ( ( ( c_Relation_Orel__comp @ SV135 @ SV2215 @ SV1335 @ SV1335 @ SV1335 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV1335 @ SV1335 ) @ tc_bool ) ) )
| ( ( c_Relation_Orel__comp @ SV135 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV2215 @ SV771 @ ( tc_fun @ ( tc_prod @ SV1335 @ SV1335 ) @ tc_bool ) ) @ SV1335 @ SV1335 @ SV1335 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV1335 @ SV1335 ) @ tc_bool ) ) ) )
= $true )
| ( ( ( c_Relation_Orel__comp @ SV135 @ SV771 @ SV1335 @ SV1335 @ SV1335 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV1335 @ SV1335 ) @ tc_bool ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4801]) ).
thf(5216,plain,
! [SV772: $i,SV2026: $i,SV1742: $i,SV136: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV136 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1 @ SV136 @ SV1742 @ SV2026 ) ) ) )
= $true )
| ( ( ~ ( c_Wellfounded_Owf @ SV1742 @ SV2026 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV136 @ SV772 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4802]) ).
thf(5217,plain,
! [SV1743: $i,SV139: $i,SV775: $i] :
( ( ( c_lessequals @ SV775 @ SV139 @ ( tc_fun @ SV1743 @ tc_bool ) )
= $false )
| ( ( ~ ( c_lessequals @ SV139 @ SV775 @ ( tc_fun @ SV1743 @ tc_bool ) ) )
= $true )
| ( ( SV139 = SV775 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4803]) ).
thf(5218,plain,
! [SV1744: $i,SV140: $i,SV776: $i] :
( ( ( c_lessequals @ SV776 @ SV140 @ ( tc_fun @ SV1744 @ tc_bool ) )
= $false )
| ( ( ~ ( c_lessequals @ SV140 @ SV776 @ ( tc_fun @ SV1744 @ tc_bool ) ) )
= $true )
| ( ( SV140 = SV776 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4804]) ).
thf(5219,plain,
! [SV141: $i,SV2027: $i,SV1745: $i] :
( ( ( SV1745 = SV2027 )
= $true )
| ( ( ~ ( c_lessequals @ SV2027 @ SV1745 @ SV141 )
| ~ ( c_lessequals @ SV1745 @ SV2027 @ SV141 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV141 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4805]) ).
thf(5220,plain,
! [SV142: $i,SV2028: $i,SV1746: $i] :
( ( ( SV1746 = SV2028 )
= $true )
| ( ( ~ ( c_lessequals @ SV2028 @ SV1746 @ SV142 )
| ~ ( c_lessequals @ SV1746 @ SV2028 @ SV142 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV142 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4806]) ).
thf(5221,plain,
! [SV144: $i,SV2030: $i,SV1748: $i] :
( ( ( SV1748 = SV2030 )
= $true )
| ( ( ~ ( c_lessequals @ SV1748 @ SV2030 @ SV144 )
| ~ ( c_lessequals @ SV2030 @ SV1748 @ SV144 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV144 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4808]) ).
thf(5222,plain,
! [SV147: $i,SV2032: $i,SV1750: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1750 @ SV2032 @ SV147 )
= SV1750 )
= $true )
| ( ( ~ ( c_lessequals @ SV2032 @ SV1750 @ SV147 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV147 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4810]) ).
thf(5223,plain,
! [SV148: $i,SV2033: $i,SV1751: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1751 @ SV2033 @ SV148 )
!= SV2033 )
= $true )
| ( ( c_lessequals @ SV1751 @ SV2033 @ SV148 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV148 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4811]) ).
thf(5224,plain,
! [SV149: $i,SV2034: $i,SV1752: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1752 @ SV2034 @ SV149 )
= SV2034 )
= $true )
| ( ( ~ ( c_lessequals @ SV1752 @ SV2034 @ SV149 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV149 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4812]) ).
thf(5225,plain,
! [SV2035: $i,SV1753: $i,SV1341: $i,SV782: $i,SV153: $i] :
( ( ( c_Relation_Orefl__on @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV153 @ SV782 @ ( tc_fun @ SV1341 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1753 @ SV2035 @ ( tc_fun @ ( tc_prod @ SV1341 @ SV1341 ) @ tc_bool ) ) @ SV1341 )
= $true )
| ( ( ~ ( c_Relation_Orefl__on @ SV782 @ SV2035 @ SV1341 )
| ~ ( c_Relation_Orefl__on @ SV153 @ SV1753 @ SV1341 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4816]) ).
thf(5226,plain,
! [SV2036: $i,SV1754: $i,SV1342: $i,SV784: $i,SV156: $i] :
( ( ( ( c_Set_Oinsert @ SV156 @ ( c_Set_Oinsert @ SV784 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1342 @ tc_bool ) ) @ SV1342 ) @ SV1342 )
!= ( c_Set_Oinsert @ SV1754 @ ( c_Set_Oinsert @ SV2036 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1342 @ tc_bool ) ) @ SV1342 ) @ SV1342 ) )
= $true )
| ( ( ( SV156 = SV2036 )
| ( SV156 = SV1754 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4817]) ).
thf(5227,plain,
! [SV2216: $i,SV1755: $i,SV1343: $i,SV785: $i,SV157: $i] :
( ( ( ( c_Set_Oinsert @ SV157 @ ( c_Set_Oinsert @ SV785 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1343 @ tc_bool ) ) @ SV1343 ) @ SV1343 )
!= ( c_Set_Oinsert @ SV1755 @ ( c_Set_Oinsert @ SV2216 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1343 @ tc_bool ) ) @ SV1343 ) @ SV1343 ) )
= $true )
| ( ( ( SV785 = SV1755 )
| ( SV157 = SV1755 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4818]) ).
thf(5228,plain,
! [SV2037: $i,SV1756: $i,SV1344: $i,SV786: $i,SV158: $i] :
( ( ( ( c_Set_Oinsert @ SV158 @ ( c_Set_Oinsert @ SV786 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1344 @ tc_bool ) ) @ SV1344 ) @ SV1344 )
!= ( c_Set_Oinsert @ SV1756 @ ( c_Set_Oinsert @ SV2037 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1344 @ tc_bool ) ) @ SV1344 ) @ SV1344 ) )
= $true )
| ( ( ( SV158 = SV2037 )
| ( SV786 = SV2037 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4819]) ).
thf(5229,plain,
! [SV2038: $i,SV1757: $i,SV1345: $i,SV787: $i,SV159: $i] :
( ( ( ( c_Set_Oinsert @ SV159 @ ( c_Set_Oinsert @ SV787 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1345 @ tc_bool ) ) @ SV1345 ) @ SV1345 )
!= ( c_Set_Oinsert @ SV1757 @ ( c_Set_Oinsert @ SV2038 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1345 @ tc_bool ) ) @ SV1345 ) @ SV1345 ) )
= $true )
| ( ( ( SV787 = SV1757 )
| ( SV787 = SV2038 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4820]) ).
thf(5230,plain,
! [SV792: $i,SV1349: $i,SV1758: $i,SV166: $i] :
( ( ( c_in @ SV166 @ SV1758 @ SV1349 )
= $false )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ SV166 @ SV792 @ SV1349 ) @ SV1758 @ ( tc_fun @ SV1349 @ tc_bool ) )
= ( c_Set_Oinsert @ SV166 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV792 @ SV1758 @ ( tc_fun @ SV1349 @ tc_bool ) ) @ SV1349 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4823]) ).
thf(5231,plain,
! [SV1350: $i,SV1759: $i,SV167: $i,SV793: $i] :
( ( ( c_in @ SV793 @ SV167 @ SV1759 )
= $false )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV167 @ ( c_Set_Oinsert @ SV793 @ SV1350 @ SV1759 ) @ ( tc_fun @ SV1759 @ tc_bool ) )
= ( c_Set_Oinsert @ SV793 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV167 @ SV1350 @ ( tc_fun @ SV1759 @ tc_bool ) ) @ SV1759 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4824]) ).
thf(5232,plain,
! [SV2040: $i,SV1761: $i,SV1352: $i,SV796: $i,SV170: $i] :
( ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV170 @ SV796 @ ( tc_fun @ SV1352 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1761 @ SV2040 @ ( tc_fun @ SV1352 @ tc_bool ) ) @ ( tc_fun @ SV1352 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV796 @ SV2040 @ ( tc_fun @ SV1352 @ tc_bool ) )
| ~ ( c_lessequals @ SV170 @ SV1761 @ ( tc_fun @ SV1352 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4826]) ).
thf(5233,plain,
! [SV174: $i,SV2217: $i,SV2043: $i,SV798: $i] :
( ( ( ( c_lessequals @ SV798 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2043 @ SV2217 @ SV174 ) @ SV174 )
| ~ ( c_lessequals @ SV798 @ SV2217 @ SV174 )
| ~ ( c_lessequals @ SV798 @ SV2043 @ SV174 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV174 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4829]) ).
thf(5234,plain,
! [SV175: $i,SV2218: $i,SV2044: $i,SV799: $i] :
( ( ( ( c_lessequals @ SV799 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2044 @ SV2218 @ SV175 ) @ SV175 )
| ~ ( c_lessequals @ SV799 @ SV2218 @ SV175 )
| ~ ( c_lessequals @ SV799 @ SV2044 @ SV175 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV175 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4830]) ).
thf(5235,plain,
! [SV176: $i,SV2219: $i,SV2045: $i,SV800: $i] :
( ( ( ( c_lessequals @ SV800 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2045 @ SV2219 @ SV176 ) @ SV176 )
| ~ ( c_lessequals @ SV800 @ SV2219 @ SV176 )
| ~ ( c_lessequals @ SV800 @ SV2045 @ SV176 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV176 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4831]) ).
thf(5236,plain,
! [SV803: $i,SV1767: $i,SV1356: $i,SV181: $i] :
( ( ( ~ ( c_lessequals @ SV181 @ SV1356 @ ( tc_fun @ SV1767 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV181 @ SV803 @ ( tc_fun @ SV1767 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV181 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV803 @ SV1356 @ ( tc_fun @ SV1767 @ tc_bool ) ) @ ( tc_fun @ SV1767 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4834]) ).
thf(5237,plain,
! [SV804: $i,SV1768: $i,SV1357: $i,SV182: $i] :
( ( ( ~ ( c_lessequals @ SV182 @ SV1357 @ ( tc_fun @ SV1768 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV182 @ SV804 @ ( tc_fun @ SV1768 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV182 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV804 @ SV1357 @ ( tc_fun @ SV1768 @ tc_bool ) ) @ ( tc_fun @ SV1768 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4835]) ).
thf(5238,plain,
! [SV2220: $i,SV184: $i,SV2049: $i,SV806: $i] :
( ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV806 @ SV2049 @ SV184 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV806 @ SV2220 @ SV184 ) @ SV184 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV806 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV2049 @ SV2220 @ SV184 ) @ SV184 ) @ SV184 )
= $true )
| ( ( class_Lattices_Olattice @ SV184 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4837]) ).
thf(5239,plain,
! [SV807: $i,SV1359: $i,SV185: $i] :
( ( ( c_lessequals @ SV185 @ ( c_Transitive__Closure_Ortrancl @ SV1359 @ SV807 ) @ ( tc_fun @ ( tc_prod @ SV807 @ SV807 ) @ tc_bool ) )
= $false )
| ( ( ~ ( c_lessequals @ SV1359 @ SV185 @ ( tc_fun @ ( tc_prod @ SV807 @ SV807 ) @ tc_bool ) ) )
= $true )
| ( ( ( c_Transitive__Closure_Ortrancl @ SV185 @ SV807 )
= ( c_Transitive__Closure_Ortrancl @ SV1359 @ SV807 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4838]) ).
thf(5240,plain,
! [SV814: $i,SV1366: $i,SV2050: $i,SV194: $i] :
( ( ( c_lessequals @ ( c_Set_Oinsert @ SV194 @ SV2050 @ SV1366 ) @ SV814 @ ( tc_fun @ SV1366 @ tc_bool ) )
= $false )
| ( ( c_in @ SV194 @ SV814 @ SV1366 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4841]) ).
thf(5241,plain,
! [SV1368: $i,SV196: $i,SV1772: $i,SV816: $i] :
( ( ( hBOOL @ ( hAPP @ SV816 @ SV1772 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV196 @ SV816 @ SV1368 ) @ SV1772 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4843]) ).
thf(5242,plain,
! [SV817: $i,SV1773: $i,SV1369: $i,SV197: $i] :
( ( ( ~ ( c_lessequals @ SV197 @ SV1369 @ ( tc_fun @ SV1773 @ tc_bool ) ) )
= $true )
| ( ( c_in @ SV817 @ SV197 @ SV1773 )
= $true )
| ( ( c_lessequals @ SV197 @ ( c_Set_Oinsert @ SV817 @ SV1369 @ SV1773 ) @ ( tc_fun @ SV1773 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4844]) ).
thf(5243,plain,
! [SV818: $i,SV1370: $i,SV198: $i,SV2052: $i] :
( ( ( c_in @ SV2052 @ SV198 @ SV1370 )
= $true )
| ( ( ~ ( c_lessequals @ SV198 @ ( c_Set_Oinsert @ SV2052 @ SV818 @ SV1370 ) @ ( tc_fun @ SV1370 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV198 @ SV818 @ ( tc_fun @ SV1370 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4845]) ).
thf(5244,plain,
! [SV819: $i,SV1774: $i,SV1371: $i,SV199: $i] :
( ( ( ~ ( c_lessequals @ SV199 @ SV1371 @ ( tc_fun @ SV1774 @ tc_bool ) ) )
= $true )
| ( ( c_in @ SV819 @ SV199 @ SV1774 )
= $true )
| ( ( c_lessequals @ SV199 @ ( c_Set_Oinsert @ SV819 @ SV1371 @ SV1774 ) @ ( tc_fun @ SV1774 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4846]) ).
thf(5245,plain,
! [SV1372: $i,SV820: $i,SV2053: $i,SV200: $i] :
( ( ( ~ ( c_lessequals @ SV200 @ ( c_Set_Oinsert @ SV2053 @ SV820 @ SV1372 ) @ ( tc_fun @ SV1372 @ tc_bool ) ) )
= $true )
| ( ( c_in @ SV2053 @ SV200 @ SV1372 )
= $true )
| ( ( c_lessequals @ SV200 @ SV820 @ ( tc_fun @ SV1372 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4847]) ).
thf(5246,plain,
! [SV207: $i,SV2221: $i,SV1778: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1778 @ SV2221 @ SV207 )
!= ( c_Orderings_Obot__class_Obot @ SV207 ) )
= $true )
| ( ( SV1778
= ( c_Orderings_Obot__class_Obot @ SV207 ) )
= $true )
| ( ( class_Lattices_Obounded__lattice @ SV207 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4853]) ).
thf(5247,plain,
! [SV208: $i,SV2054: $i,SV1779: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1779 @ SV2054 @ SV208 )
!= ( c_Orderings_Obot__class_Obot @ SV208 ) )
= $true )
| ( ( SV2054
= ( c_Orderings_Obot__class_Obot @ SV208 ) )
= $true )
| ( ( class_Lattices_Obounded__lattice @ SV208 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4854]) ).
thf(5248,plain,
! [SV2222: $i,SV2055: $i,SV1780: $i,SV1381: $i,SV829: $i,SV211: $i] :
( ( ( c_Relation_Orel__comp @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV211 @ SV829 @ ( tc_fun @ ( tc_prod @ SV1381 @ SV1780 ) @ tc_bool ) ) @ SV2055 @ SV1381 @ SV1780 @ SV2222 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ SV211 @ SV2055 @ SV1381 @ SV1780 @ SV2222 ) @ ( c_Relation_Orel__comp @ SV829 @ SV2055 @ SV1381 @ SV1780 @ SV2222 ) @ ( tc_fun @ ( tc_prod @ SV1381 @ SV2222 ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4855]) ).
thf(5249,plain,
! [SV2223: $i,SV2056: $i,SV1781: $i,SV1382: $i,SV830: $i,SV212: $i] :
( ( ( c_Relation_Orel__comp @ SV212 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV830 @ SV1382 @ ( tc_fun @ ( tc_prod @ SV1781 @ SV2056 ) @ tc_bool ) ) @ SV2223 @ SV1781 @ SV2056 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ SV212 @ SV830 @ SV2223 @ SV1781 @ SV2056 ) @ ( c_Relation_Orel__comp @ SV212 @ SV1382 @ SV2223 @ SV1781 @ SV2056 ) @ ( tc_fun @ ( tc_prod @ SV2223 @ SV2056 ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4856]) ).
thf(5250,plain,
! [SV1383: $i,SV831: $i,SV2057: $i,SV213: $i] :
( ( ( c_lessequals @ SV213 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2057 @ SV831 @ ( tc_fun @ SV1383 @ tc_bool ) ) @ ( tc_fun @ SV1383 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV213 @ SV831 @ ( tc_fun @ SV1383 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4857]) ).
thf(5251,plain,
! [SV1384: $i,SV2058: $i,SV832: $i,SV214: $i] :
( ( ( c_lessequals @ SV214 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV832 @ SV2058 @ ( tc_fun @ SV1384 @ tc_bool ) ) @ ( tc_fun @ SV1384 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV214 @ SV832 @ ( tc_fun @ SV1384 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4858]) ).
thf(5252,plain,
! [SV215: $i,SV2059: $i,SV833: $i] :
( ( ( c_lessequals @ SV833 @ SV2059 @ SV215 )
= $true )
| ( ( ! [SY5925: $i] :
~ ( c_lessequals @ SV833 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2059 @ SY5925 @ SV215 ) @ SV215 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV215 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4859]) ).
thf(5253,plain,
! [SV216: $i,SV2060: $i,SV834: $i] :
( ( ( c_lessequals @ SV834 @ SV2060 @ SV216 )
= $true )
| ( ( ! [SY5926: $i] :
~ ( c_lessequals @ SV834 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY5926 @ SV2060 @ SV216 ) @ SV216 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV216 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4860]) ).
thf(5254,plain,
! [SV2224: $i,SV217: $i,SV2061: $i,SV835: $i] :
( ( ( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV835 @ SV2061 @ SV217 ) @ SV2224 @ SV217 )
| ~ ( c_lessequals @ SV835 @ SV2224 @ SV217 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV217 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4861]) ).
thf(5255,plain,
! [SV2225: $i,SV218: $i,SV2062: $i,SV836: $i] :
( ( ( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV836 @ SV2062 @ SV218 ) @ SV2225 @ SV218 )
| ~ ( c_lessequals @ SV2062 @ SV2225 @ SV218 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV218 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4862]) ).
thf(5256,plain,
! [SV219: $i,SV2063: $i,SV837: $i] :
( ( ( c_lessequals @ SV837 @ SV2063 @ SV219 )
= $true )
| ( ( ! [SY5929: $i] :
~ ( c_lessequals @ SV837 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2063 @ SY5929 @ SV219 ) @ SV219 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV219 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4863]) ).
thf(5257,plain,
! [SV220: $i,SV2064: $i,SV838: $i] :
( ( ( c_lessequals @ SV838 @ SV2064 @ SV220 )
= $true )
| ( ( ! [SY5930: $i] :
~ ( c_lessequals @ SV838 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY5930 @ SV2064 @ SV220 ) @ SV220 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV220 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4864]) ).
thf(5258,plain,
! [SV850: $i,SV2069: $i,SV1789: $i,SV236: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV236 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1 @ SV236 @ SV1789 @ SV2069 ) ) ) )
= $true )
| ( ( ~ ( c_Wellfounded_Owf @ SV1789 @ SV2069 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV236 @ SV850 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4871]) ).
thf(5259,plain,
! [SV853: $i,SV1791: $i,SV1398: $i,SV239: $i] :
( ( ( ~ ( c_lessequals @ SV239 @ SV1398 @ ( tc_fun @ SV1791 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV239 @ ( c_Set_Oinsert @ SV853 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1791 @ tc_bool ) ) @ SV1791 ) @ ( tc_fun @ SV1791 @ tc_bool ) ) @ SV1398 @ ( tc_fun @ SV1791 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV239 @ ( c_Set_Oinsert @ SV853 @ SV1398 @ SV1791 ) @ ( tc_fun @ SV1791 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4873]) ).
thf(5260,plain,
! [SV854: $i,SV2070: $i,SV240: $i,SV1792: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1792 @ SV240 @ ( tc_fun @ SV2070 @ tc_bool ) ) @ SV854 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV240 @ SV854 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4874]) ).
thf(5261,plain,
! [SV855: $i,SV2071: $i,SV1793: $i,SV241: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV241 @ SV1793 @ ( tc_fun @ SV2071 @ tc_bool ) ) @ SV855 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV241 @ SV855 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4875]) ).
thf(5262,plain,
! [SV243: $i,SV1400: $i,SV857: $i] :
( ( ( c_Relation_Osym @ SV857 @ SV1400 )
= $false )
| ( ( ~ ( c_Relation_Osym @ SV243 @ SV1400 ) )
= $true )
| ( ( c_Relation_Osym @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV243 @ SV857 @ ( tc_fun @ ( tc_prod @ SV1400 @ SV1400 ) @ tc_bool ) ) @ SV1400 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4877]) ).
thf(5263,plain,
! [SV1402: $i,SV1795: $i,SV859: $i,SV245: $i] :
( ( ( c_lessequals @ SV245 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV859 @ SV1795 @ ( tc_fun @ SV1402 @ tc_bool ) ) @ ( tc_fun @ SV1402 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV245 @ SV859 @ ( tc_fun @ SV1402 @ tc_bool ) ) @ SV1795 @ ( tc_fun @ SV1402 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4878]) ).
thf(5264,plain,
! [SV1403: $i,SV1796: $i,SV860: $i,SV246: $i] :
( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV246 @ SV860 @ ( tc_fun @ SV1796 @ tc_bool ) ) @ SV1403 @ ( tc_fun @ SV1796 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV246 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV860 @ SV1403 @ ( tc_fun @ SV1796 @ tc_bool ) ) @ ( tc_fun @ SV1796 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4879]) ).
thf(5265,plain,
! [SV2226: $i,SV2073: $i,SV1797: $i,SV1404: $i,SV861: $i,SV247: $i] :
( ( ( ( hAPP @ SV247 @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ SV247 @ SV861 @ SV1404 @ SV1797 @ SV2073 @ SV2226 ) )
!= ( hAPP @ SV861 @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ SV247 @ SV861 @ SV1404 @ SV1797 @ SV2073 @ SV2226 ) ) )
| ( ( c_Recdef_Ocut @ SV247 @ SV1404 @ SV1797 @ SV2073 @ SV2226 )
= ( c_Recdef_Ocut @ SV861 @ SV1404 @ SV1797 @ SV2073 @ SV2226 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4880]) ).
thf(5266,plain,
! [SV248: $i,SV862: $i,SV2074: $i,SV1798: $i] :
( ( ( c_Wellfounded_Oacyclic @ ( c_Set_Oinsert @ ( c_Pair @ SV1798 @ SV2074 @ SV862 @ SV862 ) @ SV248 @ ( tc_prod @ SV862 @ SV862 ) ) @ SV862 )
= $false )
| ( ( c_Wellfounded_Oacyclic @ SV248 @ SV862 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4881]) ).
thf(5267,plain,
! [SV249: $i,SV2227: $i,SV1405: $i,SV863: $i] :
( ( ( ( c_lessequals @ ( hAPP @ SV863 @ SV1405 ) @ ( hAPP @ SV2227 @ SV1405 ) @ SV249 )
| ! [SY6001: $i] :
~ ( c_lessequals @ SV863 @ SV2227 @ ( tc_fun @ SY6001 @ SV249 ) ) )
= $true )
| ( ( class_HOL_Oord @ SV249 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4882]) ).
thf(5268,plain,
! [SV864: $i,SV1799: $i,SV1406: $i,SV250: $i] :
( ( ( ~ ( c_in @ SV250 @ SV1406 @ SV1799 ) )
= $true )
| ( ( ~ ( c_in @ SV250 @ SV864 @ SV1799 ) )
= $true )
| ( ( c_in @ SV250 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV864 @ SV1406 @ ( tc_fun @ SV1799 @ tc_bool ) ) @ SV1799 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4883]) ).
thf(5269,plain,
! [SV865: $i,SV1800: $i,SV1407: $i,SV251: $i] :
( ( ( ~ ( c_in @ SV251 @ SV1407 @ SV1800 ) )
= $true )
| ( ( ~ ( c_in @ SV251 @ SV865 @ SV1800 ) )
= $true )
| ( ( c_in @ SV251 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV865 @ SV1407 @ ( tc_fun @ SV1800 @ tc_bool ) ) @ SV1800 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4884]) ).
thf(5270,plain,
! [SV866: $i,SV1801: $i,SV1408: $i,SV252: $i] :
( ( ( c_in @ SV252 @ SV1408 @ SV1801 )
= $false )
| ( ( c_in @ SV252 @ ( c_Set_Oinsert @ SV866 @ SV1408 @ SV1801 ) @ SV1801 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4885]) ).
thf(5271,plain,
! [SV867: $i,SV1802: $i,SV1409: $i,SV253: $i] :
( ( ( c_in @ SV253 @ SV1409 @ SV1802 )
= $false )
| ( ( c_in @ SV253 @ ( c_Set_Oinsert @ SV867 @ SV1409 @ SV1802 ) @ SV1802 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4886]) ).
thf(5272,plain,
! [SV868: $i,SV1410: $i,SV2075: $i,SV254: $i] :
( ( ( ~ ( c_in @ SV254 @ SV2075 @ SV1410 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV2075 @ SV868 @ ( tc_fun @ SV1410 @ tc_bool ) ) )
= $true )
| ( ( c_in @ SV254 @ SV868 @ SV1410 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4887]) ).
thf(5273,plain,
! [SV255: $i,SV1411: $i,SV869: $i,SV2076: $i] :
( ( ( ~ ( c_lessequals @ SV2076 @ SV869 @ ( tc_fun @ SV1411 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_in @ SV255 @ SV2076 @ SV1411 ) )
= $true )
| ( ( c_in @ SV255 @ SV869 @ SV1411 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4888]) ).
thf(5274,plain,
! [SV870: $i,SV1412: $i,SV2077: $i,SV256: $i] :
( ( ( ~ ( c_in @ SV256 @ SV2077 @ SV1412 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV2077 @ SV870 @ ( tc_fun @ SV1412 @ tc_bool ) ) )
= $true )
| ( ( c_in @ SV256 @ SV870 @ SV1412 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4889]) ).
thf(5275,plain,
! [SV871: $i,SV1413: $i,SV2078: $i,SV257: $i] :
( ( ( ~ ( c_in @ SV257 @ SV2078 @ SV1413 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV2078 @ SV871 @ ( tc_fun @ SV1413 @ tc_bool ) ) )
= $true )
| ( ( c_in @ SV257 @ SV871 @ SV1413 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4890]) ).
thf(5276,plain,
! [SV1414: $i,SV1803: $i,SV872: $i,SV258: $i] :
( ( ( c_in @ SV258 @ SV872 @ SV1803 )
= $false )
| ( ( c_in @ SV258 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV872 @ SV1414 @ ( tc_fun @ SV1803 @ tc_bool ) ) @ SV1803 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4891]) ).
thf(5277,plain,
! [SV873: $i,SV1804: $i,SV1415: $i,SV259: $i] :
( ( ( c_in @ SV259 @ SV1415 @ SV1804 )
= $false )
| ( ( c_in @ SV259 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV873 @ SV1415 @ ( tc_fun @ SV1804 @ tc_bool ) ) @ SV1804 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4892]) ).
thf(5278,plain,
! [SV1416: $i,SV878: $i,SV2079: $i,SV264: $i] :
( ( ( SV264 = SV2079 )
= $true )
| ( ( ~ ( c_in @ SV264 @ ( c_Set_Oinsert @ SV2079 @ SV878 @ SV1416 ) @ SV1416 ) )
= $true )
| ( ( c_in @ SV264 @ SV878 @ SV1416 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4894]) ).
thf(5279,plain,
! [SV879: $i,SV1417: $i,SV2080: $i,SV265: $i] :
( ( ( c_in @ SV265 @ SV2080 @ SV1417 )
= $true )
| ( ( ~ ( c_in @ SV265 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV2080 @ SV879 @ ( tc_fun @ SV1417 @ tc_bool ) ) @ SV1417 ) )
= $true )
| ( ( c_in @ SV265 @ SV879 @ SV1417 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4895]) ).
thf(5280,plain,
! [SV1418: $i,SV880: $i,SV2228: $i,SV266: $i] :
( ( ( ~ ( c_in @ SV266 @ ( c_HOL_Ominus__class_Ominus @ SV2228 @ SV880 @ ( tc_fun @ SV1418 @ tc_bool ) ) @ SV1418 ) )
= $true )
| ( ( c_in @ SV266 @ SV880 @ SV1418 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4896]) ).
thf(5281,plain,
! [SV1419: $i,SV2081: $i,SV881: $i,SV267: $i] :
( ( ( c_in @ SV267 @ ( c_HOL_Ominus__class_Ominus @ SV881 @ SV2081 @ ( tc_fun @ SV1419 @ tc_bool ) ) @ SV1419 )
= $false )
| ( ( c_in @ SV267 @ SV881 @ SV1419 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4897]) ).
thf(5282,plain,
! [SV1423: $i,SV885: $i,SV2082: $i,SV271: $i] :
( ( ( c_in @ SV271 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2082 @ SV885 @ ( tc_fun @ SV1423 @ tc_bool ) ) @ SV1423 )
= $false )
| ( ( c_in @ SV271 @ SV885 @ SV1423 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4898]) ).
thf(5283,plain,
! [SV1424: $i,SV2083: $i,SV886: $i,SV272: $i] :
( ( ( c_in @ SV272 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV886 @ SV2083 @ ( tc_fun @ SV1424 @ tc_bool ) ) @ SV1424 )
= $false )
| ( ( c_in @ SV272 @ SV886 @ SV1424 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4899]) ).
thf(5284,plain,
! [SV273: $i,SV2084: $i,SV887: $i] :
( ( ( c_in @ SV887 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV2084 @ tc_bool ) ) @ SV2084 )
= $false )
| ( ( hBOOL @ ( hAPP @ SV273 @ SV887 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4900]) ).
thf(5285,plain,
! [SV888: $i,SV1806: $i,SV1425: $i,SV274: $i] :
( ( ( c_in @ SV274 @ SV1425 @ SV1806 )
= $true )
| ( ( ~ ( c_in @ SV274 @ SV888 @ SV1806 ) )
= $true )
| ( ( c_in @ SV274 @ ( c_HOL_Ominus__class_Ominus @ SV888 @ SV1425 @ ( tc_fun @ SV1806 @ tc_bool ) ) @ SV1806 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4901]) ).
thf(5286,plain,
! [SV889: $i,SV1807: $i,SV1426: $i,SV275: $i] :
( ( ( c_in @ SV275 @ SV1426 @ SV1807 )
= $true )
| ( ( ~ ( c_in @ SV275 @ SV889 @ SV1807 ) )
= $true )
| ( ( c_in @ SV275 @ ( c_HOL_Ominus__class_Ominus @ SV889 @ SV1426 @ ( tc_fun @ SV1807 @ tc_bool ) ) @ SV1807 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4902]) ).
thf(5287,plain,
! [SV1808: $i,SV1427: $i,SV890: $i,SV276: $i] :
( ( ( ( c_Set_Oinsert @ SV276 @ SV890 @ SV1427 )
= ( c_Set_Oinsert @ SV276 @ SV1808 @ SV1427 ) )
= $false )
| ( ( ( c_in @ SV276 @ SV1808 @ SV1427 )
| ( SV890 = SV1808 )
| ( c_in @ SV276 @ SV890 @ SV1427 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4903]) ).
thf(5288,plain,
! [SV2085: $i,SV1813: $i,SV1433: $i,SV896: $i,SV282: $i] :
( ( ( hBOOL @ ( hAPP @ SV282 @ ( hAPP @ ( c_fst @ SV896 @ SV1433 ) @ ( c_Pair @ SV1813 @ SV2085 @ SV896 @ SV1433 ) ) ) )
= $true )
| ( ( ! [SY5932: $i] :
~ ( hBOOL @ ( hAPP @ SY5932 @ SV2085 ) )
| ~ ( hBOOL @ ( hAPP @ SV282 @ SV1813 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4905]) ).
thf(5289,plain,
! [SV2086: $i,SV1814: $i,SV1434: $i,SV897: $i,SV283: $i] :
( ( ( hBOOL @ ( hAPP @ SV283 @ ( hAPP @ ( c_snd @ SV897 @ SV1434 ) @ ( c_Pair @ SV1814 @ SV2086 @ SV897 @ SV1434 ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV283 @ SV2086 ) )
| ! [SY5750: $i] :
~ ( hBOOL @ ( hAPP @ SY5750 @ SV1814 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4906]) ).
thf(5290,plain,
! [SV2229: $i,SV284: $i,SV2087: $i,SV898: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV898 @ SV2087 @ SV284 ) @ SV2229 @ SV284 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV898 @ SV2229 @ SV284 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV2087 @ SV2229 @ SV284 ) @ SV284 ) )
= $true )
| ( ( class_Lattices_Odistrib__lattice @ SV284 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4907]) ).
thf(5291,plain,
! [SV285: $i,SV2230: $i,SV2088: $i,SV899: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV899 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2088 @ SV2230 @ SV285 ) @ SV285 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV899 @ SV2088 @ SV285 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV899 @ SV2230 @ SV285 ) @ SV285 ) )
= $true )
| ( ( class_Lattices_Odistrib__lattice @ SV285 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4908]) ).
thf(5292,plain,
! [SV290: $i,SV1438: $i,SV1818: $i,SV904: $i] :
( ( ( ~ ( c_lessequals @ SV904 @ SV1818 @ ( tc_fun @ SV1438 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_in @ SV290 @ SV1818 @ SV1438 ) )
= $true )
| ( ( c_lessequals @ ( c_Set_Oinsert @ SV290 @ SV904 @ SV1438 ) @ SV1818 @ ( tc_fun @ SV1438 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4910]) ).
thf(5293,plain,
! [SV301: $i,SV2092: $i,SV912: $i] :
( ( ( c_lessequals @ SV912 @ SV2092 @ SV301 )
= $true )
| ( ( ! [SY5936: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY5936 @ SV912 @ SV301 ) @ SV2092 @ SV301 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV301 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4917]) ).
thf(5294,plain,
! [SV302: $i,SV2093: $i,SV913: $i] :
( ( ( c_lessequals @ SV913 @ SV2093 @ SV302 )
= $true )
| ( ( ! [SY5937: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV913 @ SY5937 @ SV302 ) @ SV2093 @ SV302 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV302 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4918]) ).
thf(5295,plain,
! [SV303: $i,SV2231: $i,SV2094: $i,SV914: $i] :
( ( ( ( c_lessequals @ SV914 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV2094 @ SV2231 @ SV303 ) @ SV303 )
| ~ ( c_lessequals @ SV914 @ SV2231 @ SV303 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV303 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4919]) ).
thf(5296,plain,
! [SV304: $i,SV2095: $i,SV915: $i] :
( ( ( ! [SY5939: $i] : ( c_lessequals @ SV915 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV2095 @ SY5939 @ SV304 ) @ SV304 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV915 @ SV2095 @ SV304 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV304 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4920]) ).
thf(5297,plain,
! [SV305: $i,SV2096: $i,SV916: $i] :
( ( ( c_lessequals @ SV916 @ SV2096 @ SV305 )
= $true )
| ( ( ! [SY5940: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY5940 @ SV916 @ SV305 ) @ SV2096 @ SV305 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV305 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4921]) ).
thf(5298,plain,
! [SV306: $i,SV2097: $i,SV917: $i] :
( ( ( c_lessequals @ SV917 @ SV2097 @ SV306 )
= $true )
| ( ( ! [SY5941: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV917 @ SY5941 @ SV306 ) @ SV2097 @ SV306 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV306 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4922]) ).
thf(5299,plain,
! [SV918: $i,SV1445: $i,SV2098: $i,SV307: $i] :
( ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV307 @ SV2098 @ ( tc_fun @ SV1445 @ tc_bool ) ) @ SV918 @ ( tc_fun @ SV1445 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV307 @ SV918 @ ( tc_fun @ SV1445 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4923]) ).
thf(5300,plain,
! [SV919: $i,SV1446: $i,SV308: $i,SV2099: $i] :
( ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV2099 @ SV308 @ ( tc_fun @ SV1446 @ tc_bool ) ) @ SV919 @ ( tc_fun @ SV1446 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV308 @ SV919 @ ( tc_fun @ SV1446 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4924]) ).
thf(5301,plain,
! [SV309: $i,SV2100: $i,SV920: $i] :
( ( ( c_lessequals @ SV920 @ SV2100 @ SV309 )
= $true )
| ( ( ! [SY5942: $i] :
( ~ ( c_lessequals @ SV920 @ SY5942 @ SV309 )
| ~ ( c_lessequals @ SY5942 @ SV2100 @ SV309 ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV309 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4925]) ).
thf(5302,plain,
! [SV310: $i,SV2101: $i,SV921: $i] :
( ( ( c_lessequals @ SV921 @ SV2101 @ SV310 )
= $true )
| ( ( ! [SY5943: $i] :
( ~ ( c_lessequals @ SY5943 @ SV2101 @ SV310 )
| ~ ( c_lessequals @ SV921 @ SY5943 @ SV310 ) ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV310 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4926]) ).
thf(5303,plain,
! [SV313: $i,SV1447: $i,SV924: $i,SV2102: $i] :
( ( ( ~ ( c_lessequals @ SV2102 @ SV924 @ ( tc_fun @ SV1447 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV313 @ SV2102 @ ( tc_fun @ SV1447 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV313 @ SV924 @ ( tc_fun @ SV1447 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4927]) ).
thf(5304,plain,
! [SV314: $i,SV925: $i,SV1824: $i] :
( ( ( hBOOL @ ( hAPP @ SV1824 @ SV925 ) )
= $false )
| ( ( ! [SY5754: $i] :
~ ( c_lessequals @ SV1824 @ SV314 @ ( tc_fun @ SY5754 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV314 @ SV925 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4928]) ).
thf(5305,plain,
! [SV926: $i,SV1825: $i,SV315: $i] :
( ( ( c_lessequals @ SV315 @ SV1825 @ ( tc_fun @ ( tc_prod @ SV926 @ SV926 ) @ tc_bool ) )
= $false )
| ( ( ~ ( c_Wellfounded_Owf @ SV1825 @ SV926 ) )
= $true )
| ( ( c_Wellfounded_Owf @ SV315 @ SV926 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4929]) ).
thf(5306,plain,
! [SV318: $i,SV927: $i,SV1828: $i] :
( ( ( c_Relation_Oantisym @ SV1828 @ SV927 )
= $false )
| ( ( ~ ( c_lessequals @ SV318 @ SV1828 @ ( tc_fun @ ( tc_prod @ SV927 @ SV927 ) @ tc_bool ) ) )
= $true )
| ( ( c_Relation_Oantisym @ SV318 @ SV927 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4930]) ).
thf(5307,plain,
! [SV928: $i,SV2232: $i,SV319: $i,SV1829: $i] :
( ( ( ~ ( c_lessequals @ SV1829 @ SV319 @ ( tc_fun @ SV2232 @ tc_bool ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV1829 @ SV928 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV319 @ SV928 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4931]) ).
thf(5308,plain,
! [SV929: $i,SV1830: $i,SV320: $i] :
( ( ( c_lessequals @ SV320 @ SV1830 @ ( tc_fun @ ( tc_prod @ SV929 @ SV929 ) @ tc_bool ) )
= $false )
| ( ( ~ ( c_Wellfounded_Oacyclic @ SV1830 @ SV929 ) )
= $true )
| ( ( c_Wellfounded_Oacyclic @ SV320 @ SV929 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4932]) ).
thf(5309,plain,
! [SV321: $i,SV1448: $i,SV930: $i,SV2103: $i] :
( ( ( ~ ( c_Relation_Osingle__valued @ SV2103 @ SV930 @ SV1448 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV321 @ SV2103 @ ( tc_fun @ ( tc_prod @ SV930 @ SV1448 ) @ tc_bool ) ) )
= $true )
| ( ( c_Relation_Osingle__valued @ SV321 @ SV930 @ SV1448 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4933]) ).
thf(5310,plain,
! [SV2104: $i,SV1449: $i,SV931: $i,SV322: $i] :
( ( ( ( c_Set_Oimage @ SV322 @ SV931 @ SV1449 @ SV2104 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV2104 @ tc_bool ) ) )
= $false )
| ( ( SV931
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1449 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4934]) ).
thf(5311,plain,
! [SV2105: $i,SV1831: $i,SV1450: $i,SV932: $i,SV323: $i] :
( ( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV323 @ SV932 @ ( tc_fun @ SV1450 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1831 @ SV2105 @ ( tc_fun @ SV1450 @ tc_bool ) ) @ ( tc_fun @ SV1450 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV932 @ SV2105 @ ( tc_fun @ SV1450 @ tc_bool ) )
| ~ ( c_lessequals @ SV323 @ SV1831 @ ( tc_fun @ SV1450 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4935]) ).
thf(5312,plain,
! [SV1453: $i,SV936: $i,SV1834: $i,SV327: $i] :
( ( ( c_lessequals @ SV327 @ SV1834 @ ( tc_fun @ ( tc_prod @ SV936 @ SV1453 ) @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( c_Relation_ODomain @ SV327 @ SV936 @ SV1453 ) @ ( c_Relation_ODomain @ SV1834 @ SV936 @ SV1453 ) @ ( tc_fun @ SV936 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4936]) ).
thf(5313,plain,
! [SV1454: $i,SV937: $i,SV328: $i] :
( ( ( c_lessequals @ SV328 @ ( c_Set_Oinsert @ SV937 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1454 @ tc_bool ) ) @ SV1454 ) @ ( tc_fun @ SV1454 @ tc_bool ) )
= $false )
| ( ( SV328
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1454 @ tc_bool ) ) )
= $true )
| ( ( SV328
= ( c_Set_Oinsert @ SV937 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1454 @ tc_bool ) ) @ SV1454 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4937]) ).
thf(5314,plain,
! [SV1457: $i,SV331: $i,SV1836: $i,SV940: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV940 @ SV1836 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV331 @ SV1836 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV331 @ SV940 @ ( tc_fun @ SV1457 @ tc_bool ) ) @ SV1836 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4938]) ).
thf(5315,plain,
! [SV1458: $i,SV1837: $i,SV941: $i,SV332: $i] :
( ( ( ~ ( c_lessequals @ SV332 @ SV941 @ ( tc_fun @ SV1837 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1458 @ SV332 @ ( tc_fun @ SV1837 @ tc_bool ) ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV332 @ ( c_HOL_Ominus__class_Ominus @ SV941 @ SV1458 @ ( tc_fun @ SV1837 @ tc_bool ) ) @ ( tc_fun @ SV1837 @ tc_bool ) )
= SV1458 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4939]) ).
thf(5316,plain,
! [SV2233: $i,SV333: $i,SV1459: $i,SV942: $i] :
( ( ( ! [SY6002: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV942 @ SV1459 @ SV333 )
!= ( c_HOL_Ominus__class_Ominus @ SV2233 @ SY6002 @ SV333 ) )
| ( c_lessequals @ SY6002 @ SV2233 @ SV333 )
| ~ ( c_lessequals @ SV1459 @ SV942 @ SV333 ) ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV333 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4940]) ).
thf(5317,plain,
! [SV2234: $i,SV334: $i,SV1460: $i,SV943: $i] :
( ( ( ! [SY6003: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV943 @ SV1460 @ SV334 )
!= ( c_HOL_Ominus__class_Ominus @ SV2234 @ SY6003 @ SV334 ) )
| ( c_lessequals @ SV1460 @ SV943 @ SV334 )
| ~ ( c_lessequals @ SY6003 @ SV2234 @ SV334 ) ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV334 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4941]) ).
thf(5318,plain,
! [SV2106: $i,SV1838: $i,SV1461: $i,SV944: $i,SV335: $i] :
( ( ( c_lessequals @ ( c_Set_Oimage @ SV335 @ SV944 @ SV1461 @ SV1838 ) @ ( c_Set_Oimage @ SV335 @ SV2106 @ SV1461 @ SV1838 ) @ ( tc_fun @ SV1838 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV944 @ SV2106 @ ( tc_fun @ SV1461 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4942]) ).
thf(5319,plain,
! [SV945: $i,SV1462: $i,SV336: $i,SV2235: $i] :
( ( ( ! [SY6004: $i] : ( c_lessequals @ ( c_Set_Oimage @ SV2235 @ SV336 @ SV1462 @ SY6004 ) @ ( c_Set_Oimage @ SV2235 @ SV945 @ SV1462 @ SY6004 ) @ ( tc_fun @ SY6004 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV336 @ SV945 @ ( tc_fun @ SV1462 @ tc_bool ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4943]) ).
thf(5320,plain,
! [SV337: $i,SV1463: $i,SV1839: $i,SV946: $i] :
( ( ( c_lessequals @ SV946 @ SV1839 @ ( tc_fun @ SV1463 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( c_Set_Oinsert @ SV337 @ SV946 @ SV1463 ) @ ( c_Set_Oinsert @ SV337 @ SV1839 @ SV1463 ) @ ( tc_fun @ SV1463 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4944]) ).
thf(5321,plain,
! [SV2108: $i,SV1841: $i,SV1465: $i,SV948: $i,SV341: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV341 @ ( hAPP @ ( c_snd @ SV948 @ SV1465 ) @ ( c_Pair @ SV1841 @ SV2108 @ SV948 @ SV1465 ) ) ) @ ( hAPP @ ( c_fst @ SV948 @ SV1465 ) @ ( c_Pair @ SV1841 @ SV2108 @ SV948 @ SV1465 ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV341 @ SV2108 ) @ SV1841 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4946]) ).
thf(5322,plain,
! [SV2236: $i,SV2109: $i,SV1842: $i,SV1467: $i,SV950: $i,SV343: $i] :
( ( ( c_lessequals @ ( c_Relation_OImage @ SV343 @ SV950 @ SV1467 @ SV1842 ) @ ( c_Relation_OImage @ SV2109 @ SV2236 @ SV1467 @ SV1842 ) @ ( tc_fun @ SV1842 @ tc_bool ) )
| ~ ( c_lessequals @ SV950 @ SV2236 @ ( tc_fun @ SV1467 @ tc_bool ) )
| ~ ( c_lessequals @ SV343 @ SV2109 @ ( tc_fun @ ( tc_prod @ SV1467 @ SV1842 ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4948]) ).
thf(5323,plain,
! [SV345: $i,SV2110: $i,SV1843: $i] :
( ( ( c_lessequals @ SV1843 @ SV2110 @ SV345 )
= $true )
| ( ( c_lessequals @ SV2110 @ SV1843 @ SV345 )
= $true )
| ( ( class_Orderings_Olinorder @ SV345 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4950]) ).
thf(5324,plain,
! [SV1845: $i,SV1469: $i,SV347: $i,SV953: $i] :
( ( ( c_in @ ( c_Pair @ SV953 @ SV347 @ SV1469 @ SV1469 ) @ ( c_Transitive__Closure_Ortrancl @ SV1845 @ SV1469 ) @ ( tc_prod @ SV1469 @ SV1469 ) )
= $true )
| ( ( ~ ( c_Wellfounded_Oacyclic @ SV1845 @ SV1469 ) )
= $true )
| ( ( c_Wellfounded_Oacyclic @ ( c_Set_Oinsert @ ( c_Pair @ SV347 @ SV953 @ SV1469 @ SV1469 ) @ SV1845 @ ( tc_prod @ SV1469 @ SV1469 ) ) @ SV1469 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4952]) ).
thf(5325,plain,
! [SV1846: $i,SV1470: $i,SV954: $i,SV348: $i] :
( ( ( c_in @ ( c_Pair @ SV348 @ SV954 @ SV1470 @ SV1470 ) @ ( c_Transitive__Closure_Ortrancl @ SV1846 @ SV1470 ) @ ( tc_prod @ SV1470 @ SV1470 ) )
= $false )
| ( ( ~ ( c_Wellfounded_Oacyclic @ ( c_Set_Oinsert @ ( c_Pair @ SV954 @ SV348 @ SV1470 @ SV1470 ) @ SV1846 @ ( tc_prod @ SV1470 @ SV1470 ) ) @ SV1470 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4953]) ).
thf(5326,plain,
! [SV955: $i,SV2237: $i,SV2111: $i,SV1471: $i,SV349: $i] :
( ( ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1 @ SV349 @ SV1471 @ SV2111 @ SV2237 ) @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 @ SV349 @ SV1471 @ SV2111 @ SV2237 ) @ SV2237 @ SV2237 ) @ SV2111 @ ( tc_prod @ SV2237 @ SV2237 ) )
| ~ ( hBOOL @ ( hAPP @ SV349 @ SV1471 ) )
| ~ ( c_in @ ( c_Pair @ SV955 @ SV1471 @ SV2237 @ SV2237 ) @ ( c_Transitive__Closure_Ortrancl @ SV2111 @ SV2237 ) @ ( tc_prod @ SV2237 @ SV2237 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV349 @ SV955 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4954]) ).
thf(5327,plain,
! [SV956: $i,SV2238: $i,SV2112: $i,SV1472: $i,SV350: $i] :
( ( ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 @ SV350 @ SV1472 @ SV2112 @ SV2238 ) @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2 @ SV350 @ SV1472 @ SV2112 @ SV2238 ) @ SV2238 @ SV2238 ) @ SV2112 @ ( tc_prod @ SV2238 @ SV2238 ) )
| ~ ( hBOOL @ ( hAPP @ SV350 @ SV1472 ) )
| ~ ( c_in @ ( c_Pair @ SV1472 @ SV956 @ SV2238 @ SV2238 ) @ ( c_Transitive__Closure_Ortrancl @ SV2112 @ SV2238 ) @ ( tc_prod @ SV2238 @ SV2238 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV350 @ SV956 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4955]) ).
thf(5328,plain,
! [SV957: $i,SV1473: $i,SV2113: $i,SV351: $i] :
( ( ( ~ ( c_in @ SV351 @ SV2113 @ SV1473 ) )
= $true )
| ( ( ~ ( c_Equiv__Relations_Oequiv @ SV2113 @ SV957 @ SV1473 ) )
= $true )
| ( ( c_in @ SV351 @ ( c_Relation_OImage @ SV957 @ ( c_Set_Oinsert @ SV351 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1473 @ tc_bool ) ) @ SV1473 ) @ SV1473 @ SV1473 ) @ SV1473 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4956]) ).
thf(5329,plain,
! [SV1474: $i,SV958: $i,SV352: $i] :
( ( ( c_lessequals @ ( c_Relation_Orel__comp @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Transitive__Closure_Ortrancl @ SV352 @ SV958 ) @ SV1474 @ ( tc_fun @ ( tc_prod @ SV958 @ SV958 ) @ tc_bool ) ) @ SV352 @ SV958 @ SV958 @ SV958 ) @ SV1474 @ ( tc_fun @ ( tc_prod @ SV958 @ SV958 ) @ tc_bool ) )
= $false )
| ( ( ~ ( c_lessequals @ ( c_Relation_OId @ SV958 ) @ SV1474 @ ( tc_fun @ ( tc_prod @ SV958 @ SV958 ) @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( c_Transitive__Closure_Ortrancl @ SV352 @ SV958 ) @ SV1474 @ ( tc_fun @ ( tc_prod @ SV958 @ SV958 ) @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4957]) ).
thf(5330,plain,
! [SV959: $i,SV1475: $i,SV353: $i,SV1847: $i] :
( ( ( ! [SY5763: $i] :
~ ( c_in @ SY5763 @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_OImage @ SV1847 @ ( c_Set_Oinsert @ SV353 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1475 @ tc_bool ) ) @ SV1475 ) @ SV1475 @ SV1475 ) @ ( c_Relation_OImage @ SV1847 @ ( c_Set_Oinsert @ SV959 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1475 @ tc_bool ) ) @ SV1475 ) @ SV1475 @ SV1475 ) @ ( tc_fun @ SV1475 @ tc_bool ) ) @ SV1475 ) )
= $true )
| ( ( ! [SY5764: $i] :
~ ( c_Equiv__Relations_Oequiv @ SY5764 @ SV1847 @ SV1475 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV353 @ SV959 @ SV1475 @ SV1475 ) @ SV1847 @ ( tc_prod @ SV1475 @ SV1475 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4958]) ).
thf(5331,plain,
! [SV354: $i,SV1848: $i,SV1476: $i,SV2239: $i,SV960: $i] :
( ( ( ~ ( c_in @ SV960 @ SV2239 @ SV1476 )
| ~ ( c_lessequals @ ( c_Relation_OImage @ SV1848 @ ( c_Set_Oinsert @ SV960 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1476 @ tc_bool ) ) @ SV1476 ) @ SV1476 @ SV1476 ) @ ( c_Relation_OImage @ SV1848 @ ( c_Set_Oinsert @ SV354 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1476 @ tc_bool ) ) @ SV1476 ) @ SV1476 @ SV1476 ) @ ( tc_fun @ SV1476 @ tc_bool ) )
| ~ ( c_Equiv__Relations_Oequiv @ SV2239 @ SV1848 @ SV1476 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV354 @ SV960 @ SV1476 @ SV1476 ) @ SV1848 @ ( tc_prod @ SV1476 @ SV1476 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4959]) ).
thf(5332,plain,
! [SV2240: $i,SV1849: $i,SV1477: $i,SV961: $i,SV355: $i] :
( ( ( ( c_Set_Oinsert @ ( hAPP @ SV355 @ SV961 ) @ ( c_Set_Oimage @ SV355 @ SV1477 @ SV1849 @ SV2240 ) @ SV2240 )
= ( c_Set_Oimage @ SV355 @ SV1477 @ SV1849 @ SV2240 ) )
= $true )
| ( ( ~ ( c_in @ SV961 @ SV1477 @ SV1849 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4960]) ).
thf(5333,plain,
! [SV1478: $i,SV1850: $i,SV356: $i,SV2241: $i,SV962: $i] :
( ( ( ! [SY6005: $i] :
( ~ ( c_in @ SV962 @ SV2241 @ SY6005 )
| ~ ( c_lessequals @ ( c_Set_Oimage @ SV356 @ SV2241 @ SY6005 @ SV1850 ) @ SV1478 @ ( tc_fun @ SV1850 @ tc_bool ) ) ) )
= $true )
| ( ( c_in @ ( hAPP @ SV356 @ SV962 ) @ SV1478 @ SV1850 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4961]) ).
thf(5334,plain,
! [SV2114: $i,SV1851: $i,SV1479: $i,SV963: $i,SV357: $i] :
( ( ( c_in @ ( c_Pair @ SV357 @ SV963 @ SV1479 @ SV1851 ) @ SV2114 @ ( tc_prod @ SV1479 @ SV1851 ) )
= $true )
| ( ( ~ ( c_in @ SV963 @ ( c_Relation_OImage @ SV2114 @ ( c_Set_Oinsert @ SV357 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1479 @ tc_bool ) ) @ SV1479 ) @ SV1479 @ SV1851 ) @ SV1851 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4962]) ).
thf(5335,plain,
! [SV2115: $i,SV1852: $i,SV1480: $i,SV964: $i,SV358: $i] :
( ( ( c_in @ SV358 @ ( c_Relation_OImage @ SV964 @ ( c_Set_Oinsert @ SV1480 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1852 @ tc_bool ) ) @ SV1852 ) @ SV1852 @ SV2115 ) @ SV2115 )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV1480 @ SV358 @ SV1852 @ SV2115 ) @ SV964 @ ( tc_prod @ SV1852 @ SV2115 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4963]) ).
thf(5336,plain,
! [SV2116: $i,SV1853: $i,SV1481: $i,SV965: $i,SV359: $i] :
( ( ( ( c_Product__Type_OSigma @ SV359 @ ( c_COMBK @ SV965 @ ( tc_fun @ SV1481 @ tc_bool ) @ SV1853 ) @ SV1853 @ SV1481 )
!= ( c_Product__Type_OSigma @ SV2116 @ ( c_COMBK @ SV965 @ ( tc_fun @ SV1481 @ tc_bool ) @ SV1853 ) @ SV1853 @ SV1481 ) )
= $true )
| ( ( ! [SY5395: $i] :
~ ( c_in @ SY5395 @ SV965 @ SV1481 )
| ( SV359 = SV2116 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4964]) ).
thf(5337,plain,
! [SV360: $i,SV966: $i,SV2117: $i,SV1854: $i] :
( ( ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ SV1854 @ SV2117 @ SV966 @ SV966 ) @ SV360 @ ( tc_prod @ SV966 @ SV966 ) ) @ SV966 )
= $false )
| ( ( c_Wellfounded_Owf @ SV360 @ SV966 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4965]) ).
thf(5338,plain,
! [SV1482: $i,SV1855: $i,SV967: $i,SV361: $i] :
( ( ( c_in @ SV361 @ ( c_Transitive__Closure_Ortrancl @ SV967 @ SV1855 ) @ ( tc_prod @ SV1855 @ SV1855 ) )
= $false )
| ( ( c_in @ SV361 @ ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV967 @ SV1482 @ ( tc_fun @ ( tc_prod @ SV1855 @ SV1855 ) @ tc_bool ) ) @ SV1855 ) @ ( tc_prod @ SV1855 @ SV1855 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4966]) ).
thf(5339,plain,
! [SV968: $i,SV1856: $i,SV1483: $i,SV362: $i] :
( ( ( c_in @ SV362 @ ( c_Transitive__Closure_Ortrancl @ SV1483 @ SV1856 ) @ ( tc_prod @ SV1856 @ SV1856 ) )
= $false )
| ( ( c_in @ SV362 @ ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV968 @ SV1483 @ ( tc_fun @ ( tc_prod @ SV1856 @ SV1856 ) @ tc_bool ) ) @ SV1856 ) @ ( tc_prod @ SV1856 @ SV1856 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4967]) ).
thf(5340,plain,
! [SV363: $i,SV1484: $i,SV969: $i,SV2118: $i] :
( ( ( ~ ( c_lessequals @ SV2118 @ SV969 @ ( tc_fun @ ( tc_prod @ SV1484 @ SV1484 ) @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_in @ SV363 @ ( c_Transitive__Closure_Otrancl @ SV2118 @ SV1484 ) @ ( tc_prod @ SV1484 @ SV1484 ) ) )
= $true )
| ( ( c_in @ SV363 @ ( c_Transitive__Closure_Otrancl @ SV969 @ SV1484 ) @ ( tc_prod @ SV1484 @ SV1484 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4968]) ).
thf(5341,plain,
! [SV364: $i,SV1485: $i,SV1857: $i,SV970: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV970 @ SV1857 @ SV1485 @ SV1485 ) @ SV364 @ ( tc_prod @ SV1485 @ SV1485 ) ) )
= $true )
| ( ( ! [SY5400: $i] :
~ ( c_Equiv__Relations_Oequiv @ SY5400 @ SV364 @ SV1485 ) )
= $true )
| ( ( ( c_Relation_OImage @ SV364 @ ( c_Set_Oinsert @ SV970 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1485 @ tc_bool ) ) @ SV1485 ) @ SV1485 @ SV1485 )
= ( c_Relation_OImage @ SV364 @ ( c_Set_Oinsert @ SV1857 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1485 @ tc_bool ) ) @ SV1485 ) @ SV1485 @ SV1485 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4969]) ).
thf(5342,plain,
! [SV365: $i,SV1486: $i,SV1858: $i,SV971: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV971 @ SV1858 @ SV1486 @ SV1486 ) @ SV365 @ ( tc_prod @ SV1486 @ SV1486 ) ) )
= $true )
| ( ( ! [SY5402: $i] :
~ ( c_Equiv__Relations_Oequiv @ SY5402 @ SV365 @ SV1486 ) )
= $true )
| ( ( ( c_Relation_OImage @ SV365 @ ( c_Set_Oinsert @ SV971 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1486 @ tc_bool ) ) @ SV1486 ) @ SV1486 @ SV1486 )
= ( c_Relation_OImage @ SV365 @ ( c_Set_Oinsert @ SV1858 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1486 @ tc_bool ) ) @ SV1486 ) @ SV1486 @ SV1486 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4970]) ).
thf(5343,plain,
! [SV989: $i,SV384: $i] :
( ( ( c_Relation_Osym @ SV384 @ SV989 )
= $false )
| ( ( c_Relation_Otrans @ SV384 @ SV989 )
= $false )
| ( ( c_lessequals @ ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ SV384 @ SV989 @ SV989 ) @ SV384 @ SV989 @ SV989 @ SV989 ) @ SV384 @ ( tc_fun @ ( tc_prod @ SV989 @ SV989 ) @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4975]) ).
thf(5344,plain,
! [SV990: $i,SV1859: $i,SV1492: $i,SV385: $i] :
( ( ( c_in @ ( c_Pair @ SV385 @ SV1492 @ SV1859 @ SV1859 ) @ ( c_Transitive__Closure_Otrancl @ SV990 @ SV1859 ) @ ( tc_prod @ SV1859 @ SV1859 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV385 @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1 @ SV990 @ SV385 @ SV1492 @ SV1859 ) @ SV1859 @ SV1859 ) @ ( c_Transitive__Closure_Ortrancl @ SV990 @ SV1859 ) @ ( tc_prod @ SV1859 @ SV1859 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4976]) ).
thf(5345,plain,
! [SV386: $i,SV1860: $i,SV1493: $i,SV991: $i] :
( ( ( c_in @ ( c_Pair @ SV991 @ SV1493 @ SV1860 @ SV1860 ) @ ( c_Transitive__Closure_Otrancl @ SV386 @ SV1860 ) @ ( tc_prod @ SV1860 @ SV1860 ) )
= $false )
| ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1 @ SV386 @ SV991 @ SV1493 @ SV1860 ) @ SV1493 @ SV1860 @ SV1860 ) @ ( c_Transitive__Closure_Ortrancl @ SV386 @ SV1860 ) @ ( tc_prod @ SV1860 @ SV1860 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4977]) ).
thf(5346,plain,
! [SV1861: $i,SV1494: $i,SV992: $i,SV387: $i] :
( ( ( c_in @ ( c_Pair @ SV387 @ SV992 @ SV1494 @ SV1494 ) @ ( c_Transitive__Closure_Ortrancl @ SV1861 @ SV1494 ) @ ( tc_prod @ SV1494 @ SV1494 ) )
= $false )
| ( ( ~ ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ SV992 @ SV387 @ SV1494 @ SV1494 ) @ SV1861 @ ( tc_prod @ SV1494 @ SV1494 ) ) @ SV1494 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4978]) ).
thf(5347,plain,
! [SV1862: $i,SV1495: $i,SV388: $i,SV993: $i] :
( ( ( c_in @ ( c_Pair @ SV993 @ SV388 @ SV1495 @ SV1495 ) @ ( c_Transitive__Closure_Ortrancl @ SV1862 @ SV1495 ) @ ( tc_prod @ SV1495 @ SV1495 ) )
= $true )
| ( ( ~ ( c_Wellfounded_Owf @ SV1862 @ SV1495 ) )
= $true )
| ( ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ SV388 @ SV993 @ SV1495 @ SV1495 ) @ SV1862 @ ( tc_prod @ SV1495 @ SV1495 ) ) @ SV1495 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4979]) ).
thf(5348,plain,
! [SV1496: $i,SV994: $i,SV389: $i] :
( ( ( c_Relation_Ototal__on @ SV389 @ SV994 @ SV1496 )
= $false )
| ( ( ~ ( c_Relation_Oirrefl @ SV994 @ SV1496 )
| ~ ( c_Relation_Otrans @ SV994 @ SV1496 ) )
= $true )
| ( ( c_Order__Relation_Ostrict__linear__order__on @ SV389 @ SV994 @ SV1496 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4980]) ).
thf(5349,plain,
! [SV996: $i,SV391: $i] :
( ( ( c_Relation_Otrans @ SV391 @ SV996 )
= $false )
| ( ( c_Relation_Oantisym @ SV391 @ SV996 )
= $false )
| ( ( c_Relation_Otrans @ ( c_HOL_Ominus__class_Ominus @ SV391 @ ( c_Relation_OId @ SV996 ) @ ( tc_fun @ ( tc_prod @ SV996 @ SV996 ) @ tc_bool ) ) @ SV996 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4981]) ).
thf(5350,plain,
! [SV2119: $i,SV1863: $i,SV1497: $i,SV997: $i,SV392: $i] :
( ( ( ( c_Relation_OImage @ SV392 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV997 @ SV1497 @ ( tc_fun @ SV1863 @ tc_bool ) ) @ SV1863 @ SV2119 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_OImage @ SV392 @ SV997 @ SV1863 @ SV2119 ) @ ( c_Relation_OImage @ SV392 @ SV1497 @ SV1863 @ SV2119 ) @ ( tc_fun @ SV2119 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_Relation_Osingle__valued @ ( c_Relation_Oconverse @ SV392 @ SV1863 @ SV2119 ) @ SV2119 @ SV1863 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4982]) ).
thf(5351,plain,
! [SV2242: $i,SV2120: $i,SV1865: $i,SV1498: $i,SV1004: $i,SV399: $i] :
( ( ( ( c_Recdef_Ocut @ SV399 @ SV1004 @ SV1498 @ SV1865 @ SV2120 )
= ( c_Recdef_Ocut @ SV2242 @ SV1004 @ SV1498 @ SV1865 @ SV2120 ) )
| ( c_in @ ( c_Pair @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ SV399 @ SV2242 @ SV1004 @ SV1498 @ SV1865 @ SV2120 ) @ SV1498 @ SV1865 @ SV1865 ) @ SV1004 @ ( tc_prod @ SV1865 @ SV1865 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4984]) ).
thf(5352,plain,
! [SV2243: $i,SV2121: $i,SV1866: $i,SV1501: $i,SV1010: $i,SV405: $i] :
( ( ! [SY6006: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 @ SV405 @ SV1010 @ SV1501 @ SV1866 @ SV2121 @ SV2243 @ SY6006 ) @ SV1010 @ SY6006 @ SV2243 ) @ SV1866 @ ( tc_prod @ SY6006 @ SV2243 ) )
| ~ ( c_in @ ( c_Pair @ SV405 @ SV1010 @ SV2121 @ SV2243 ) @ ( c_Relation_Orel__comp @ SV1501 @ SV1866 @ SV2121 @ SY6006 @ SV2243 ) @ ( tc_prod @ SV2121 @ SV2243 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4987]) ).
thf(5353,plain,
! [SV2244: $i,SV2122: $i,SV1867: $i,SV1502: $i,SV1011: $i,SV406: $i] :
( ( ! [SY6007: $i] :
( ( c_in @ ( c_Pair @ SV406 @ ( c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 @ SV406 @ SV1011 @ SV1502 @ SV1867 @ SV2122 @ SV2244 @ SY6007 ) @ SV2122 @ SY6007 ) @ SV1502 @ ( tc_prod @ SV2122 @ SY6007 ) )
| ~ ( c_in @ ( c_Pair @ SV406 @ SV1011 @ SV2122 @ SV2244 ) @ ( c_Relation_Orel__comp @ SV1502 @ SV1867 @ SV2122 @ SY6007 @ SV2244 ) @ ( tc_prod @ SV2122 @ SV2244 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4988]) ).
thf(5354,plain,
! [SV408: $i,SV1868: $i,SV1504: $i,SV1013: $i] :
( ( ( c_in @ ( c_Pair @ SV1013 @ SV1504 @ SV1868 @ SV1868 ) @ SV408 @ ( tc_prod @ SV1868 @ SV1868 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV1013 @ SV1504 @ SV1868 @ SV1868 ) @ ( c_Transitive__Closure_Otrancl @ SV408 @ SV1868 ) @ ( tc_prod @ SV1868 @ SV1868 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1 @ SV408 @ SV1013 @ SV1504 @ SV1868 ) @ SV1504 @ SV1868 @ SV1868 ) @ ( c_Transitive__Closure_Otrancl @ SV408 @ SV1868 ) @ ( tc_prod @ SV1868 @ SV1868 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4990]) ).
thf(5355,plain,
! [SV1014: $i,SV1869: $i,SV1505: $i,SV409: $i] :
( ( ( c_in @ ( c_Pair @ SV409 @ SV1505 @ SV1869 @ SV1869 ) @ ( c_Transitive__Closure_Otrancl @ SV1014 @ SV1869 ) @ ( tc_prod @ SV1869 @ SV1869 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV409 @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1 @ SV1014 @ SV409 @ SV1505 @ SV1869 ) @ SV1869 @ SV1869 ) @ SV1014 @ ( tc_prod @ SV1869 @ SV1869 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4991]) ).
thf(5356,plain,
! [SV1506: $i,SV1015: $i,SV410: $i] :
( ( ( c_in @ ( c_Pair @ SV410 @ SV1015 @ t_a @ t_a ) @ ( c_Transitive__Closure_Otrancl @ SV1506 @ t_a ) @ ( tc_prod @ t_a @ t_a ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV410 @ SV1015 @ t_a @ t_a ) @ SV1506 @ ( tc_prod @ t_a @ t_a ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV410 @ ( v_sko__Transitive__Closure__Xtrancl__Xcases__1 @ SV410 @ SV1015 @ SV1506 ) @ t_a @ t_a ) @ ( c_Transitive__Closure_Otrancl @ SV1506 @ t_a ) @ ( tc_prod @ t_a @ t_a ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4992]) ).
thf(5357,plain,
! [SV411: $i,SV1016: $i,SV1507: $i] :
( ( ( c_Wellfounded_Oacyclic @ SV1507 @ SV1016 )
= $false )
| ( ( c_in @ ( c_Pair @ SV411 @ SV411 @ SV1016 @ SV1016 ) @ ( c_Transitive__Closure_Otrancl @ SV1507 @ SV1016 ) @ ( tc_prod @ SV1016 @ SV1016 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4993]) ).
thf(5358,plain,
! [SV1508: $i,SV1870: $i,SV1017: $i,SV412: $i] :
( ( ( c_in @ ( c_Pair @ SV412 @ SV1017 @ SV1870 @ SV1870 ) @ SV1508 @ ( tc_prod @ SV1870 @ SV1870 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV412 @ SV1017 @ SV1870 @ SV1870 ) @ ( c_Transitive__Closure_Otrancl @ SV1508 @ SV1870 ) @ ( tc_prod @ SV1870 @ SV1870 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1 @ SV412 @ SV1017 @ SV1508 @ SV1870 ) @ SV1017 @ SV1870 @ SV1870 ) @ SV1508 @ ( tc_prod @ SV1870 @ SV1870 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4994]) ).
thf(5359,plain,
! [SV1509: $i,SV1871: $i,SV1018: $i,SV413: $i] :
( ( ( c_in @ ( c_Pair @ SV413 @ SV1018 @ SV1871 @ SV1871 ) @ SV1509 @ ( tc_prod @ SV1871 @ SV1871 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV413 @ SV1018 @ SV1871 @ SV1871 ) @ ( c_Transitive__Closure_Otrancl @ SV1509 @ SV1871 ) @ ( tc_prod @ SV1871 @ SV1871 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV413 @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1 @ SV413 @ SV1018 @ SV1509 @ SV1871 ) @ SV1871 @ SV1871 ) @ ( c_Transitive__Closure_Otrancl @ SV1509 @ SV1871 ) @ ( tc_prod @ SV1871 @ SV1871 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4995]) ).
thf(5360,plain,
! [SV414: $i,SV1872: $i,SV1510: $i,SV1019: $i] :
( ( ( c_in @ ( c_Pair @ SV1019 @ SV1510 @ SV1872 @ SV1872 ) @ ( c_Transitive__Closure_Otrancl @ SV414 @ SV1872 ) @ ( tc_prod @ SV1872 @ SV1872 ) )
= $false )
| ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1 @ SV414 @ SV1019 @ SV1510 @ SV1872 ) @ SV1510 @ SV1872 @ SV1872 ) @ SV414 @ ( tc_prod @ SV1872 @ SV1872 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4996]) ).
thf(5361,plain,
! [SV1020: $i,SV1873: $i,SV1511: $i,SV415: $i] :
( ( ( c_in @ ( c_Pair @ SV415 @ SV1511 @ SV1873 @ SV1873 ) @ SV1020 @ ( tc_prod @ SV1873 @ SV1873 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV415 @ SV1511 @ SV1873 @ SV1873 ) @ ( c_Transitive__Closure_Otrancl @ SV1020 @ SV1873 ) @ ( tc_prod @ SV1873 @ SV1873 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV415 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1 @ SV1020 @ SV415 @ SV1511 @ SV1873 ) @ SV1873 @ SV1873 ) @ SV1020 @ ( tc_prod @ SV1873 @ SV1873 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4997]) ).
thf(5362,plain,
! [SV1512: $i,SV1021: $i,SV416: $i] :
( ( ( c_in @ ( c_Pair @ SV416 @ SV1021 @ t_a @ t_a ) @ ( c_Transitive__Closure_Otrancl @ SV1512 @ t_a ) @ ( tc_prod @ t_a @ t_a ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV416 @ SV1021 @ t_a @ t_a ) @ SV1512 @ ( tc_prod @ t_a @ t_a ) )
= $true )
| ( ( c_in @ ( c_Pair @ ( v_sko__Transitive__Closure__Xtrancl__Xcases__1 @ SV416 @ SV1021 @ SV1512 ) @ SV1021 @ t_a @ t_a ) @ SV1512 @ ( tc_prod @ t_a @ t_a ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4998]) ).
thf(5363,plain,
! [SV1022: $i,SV2245: $i,SV417: $i,SV1513: $i] :
( ( ( ! [SY6008: $i] :
( ~ ( c_in @ ( c_Pair @ SV1513 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1 @ SV417 @ SV2245 @ SY6008 ) @ SY6008 @ SY6008 ) @ SV2245 @ ( tc_prod @ SY6008 @ SY6008 ) )
| ~ ( c_Wellfounded_Owf @ SV2245 @ SY6008 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV417 @ SV1513 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV417 @ SV1022 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4999]) ).
thf(5364,plain,
! [SV1023: $i,SV2246: $i,SV418: $i,SV1514: $i] :
( ( ( ! [SY6009: $i] :
( ~ ( c_in @ ( c_Pair @ SV1514 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1 @ SV418 @ SV2246 @ SY6009 ) @ SY6009 @ SY6009 ) @ SV2246 @ ( tc_prod @ SY6009 @ SY6009 ) )
| ~ ( c_Wellfounded_Owf @ SV2246 @ SY6009 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV418 @ SV1514 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV418 @ SV1023 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5000]) ).
thf(5365,plain,
! [SV1024: $i,SV2247: $i,SV419: $i,SV1515: $i] :
( ( ( ! [SY6010: $i] :
( ~ ( c_in @ ( c_Pair @ SV1515 @ ( c_List_Osko__Recdef__Xtfl__wf__induct__1__1 @ SV419 @ SV2247 @ SY6010 ) @ SY6010 @ SY6010 ) @ SV2247 @ ( tc_prod @ SY6010 @ SY6010 ) )
| ~ ( c_Wellfounded_Owf @ SV2247 @ SY6010 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV419 @ SV1515 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV419 @ SV1024 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5001]) ).
thf(5366,plain,
! [SV1025: $i,SV2248: $i,SV420: $i,SV1516: $i] :
( ( ( ! [SY6011: $i] :
( ~ ( c_in @ ( c_Pair @ SV1516 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1 @ SV420 @ SV2248 @ SY6011 ) @ SY6011 @ SY6011 ) @ SV2248 @ ( tc_prod @ SY6011 @ SY6011 ) )
| ~ ( c_Wellfounded_Owf @ SV2248 @ SY6011 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV420 @ SV1516 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV420 @ SV1025 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5002]) ).
thf(5367,plain,
! [SV1517: $i,SV1874: $i,SV1026: $i,SV421: $i] :
( ( ( SV421 = SV1026 )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV421 @ SV1026 @ SV1874 @ SV1874 ) @ ( c_Transitive__Closure_Ortrancl @ SV1517 @ SV1874 ) @ ( tc_prod @ SV1874 @ SV1874 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1 @ SV421 @ SV1026 @ SV1517 @ SV1874 ) @ SV1026 @ SV1874 @ SV1874 ) @ SV1517 @ ( tc_prod @ SV1874 @ SV1874 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5003]) ).
thf(5368,plain,
! [SV422: $i,SV1875: $i,SV1518: $i,SV1027: $i] :
( ( ( SV1027 = SV1518 )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV1027 @ SV1518 @ SV1875 @ SV1875 ) @ ( c_Transitive__Closure_Ortrancl @ SV422 @ SV1875 ) @ ( tc_prod @ SV1875 @ SV1875 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1 @ SV422 @ SV1027 @ SV1518 @ SV1875 ) @ SV1518 @ SV1875 @ SV1875 ) @ ( c_Transitive__Closure_Ortrancl @ SV422 @ SV1875 ) @ ( tc_prod @ SV1875 @ SV1875 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5004]) ).
thf(5369,plain,
! [SV1028: $i,SV1876: $i,SV1519: $i,SV423: $i] :
( ( ( SV423 = SV1519 )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV423 @ SV1519 @ SV1876 @ SV1876 ) @ ( c_Transitive__Closure_Ortrancl @ SV1028 @ SV1876 ) @ ( tc_prod @ SV1876 @ SV1876 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV423 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1 @ SV1028 @ SV423 @ SV1519 @ SV1876 ) @ SV1876 @ SV1876 ) @ SV1028 @ ( tc_prod @ SV1876 @ SV1876 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5005]) ).
thf(5370,plain,
! [SV1029: $i,SV2249: $i,SV2123: $i,SV1520: $i,SV424: $i] :
( ( ( ( hBOOL @ ( hAPP @ SV424 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 @ SV424 @ SV1520 @ SV2123 @ SV2249 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV424 @ SV1520 ) )
| ~ ( c_in @ ( c_Pair @ SV1029 @ SV1520 @ SV2249 @ SV2249 ) @ ( c_Transitive__Closure_Ortrancl @ SV2123 @ SV2249 ) @ ( tc_prod @ SV2249 @ SV2249 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV424 @ SV1029 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5006]) ).
thf(5371,plain,
! [SV1030: $i,SV2250: $i,SV2124: $i,SV1521: $i,SV425: $i] :
( ( ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 @ SV425 @ SV1521 @ SV2124 @ SV2250 ) @ SV1521 @ SV2250 @ SV2250 ) @ ( c_Transitive__Closure_Ortrancl @ SV2124 @ SV2250 ) @ ( tc_prod @ SV2250 @ SV2250 ) )
| ~ ( hBOOL @ ( hAPP @ SV425 @ SV1521 ) )
| ~ ( c_in @ ( c_Pair @ SV1030 @ SV1521 @ SV2250 @ SV2250 ) @ ( c_Transitive__Closure_Ortrancl @ SV2124 @ SV2250 ) @ ( tc_prod @ SV2250 @ SV2250 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV425 @ SV1030 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5007]) ).
thf(5372,plain,
! [SV1031: $i,SV2251: $i,SV2125: $i,SV426: $i,SV1522: $i] :
( ( ( ( c_in @ ( c_Pair @ SV1522 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 @ SV426 @ SV1522 @ SV2125 @ SV2251 ) @ SV2251 @ SV2251 ) @ ( c_Transitive__Closure_Ortrancl @ SV2125 @ SV2251 ) @ ( tc_prod @ SV2251 @ SV2251 ) )
| ~ ( hBOOL @ ( hAPP @ SV426 @ SV1522 ) )
| ~ ( c_in @ ( c_Pair @ SV1522 @ SV1031 @ SV2251 @ SV2251 ) @ ( c_Transitive__Closure_Ortrancl @ SV2125 @ SV2251 ) @ ( tc_prod @ SV2251 @ SV2251 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV426 @ SV1031 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5008]) ).
thf(5373,plain,
! [SV1032: $i,SV2252: $i,SV2126: $i,SV1523: $i,SV427: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV427 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2 @ SV427 @ SV1523 @ SV2126 @ SV2252 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV427 @ SV1523 ) )
| ~ ( c_in @ ( c_Pair @ SV1523 @ SV1032 @ SV2252 @ SV2252 ) @ ( c_Transitive__Closure_Ortrancl @ SV2126 @ SV2252 ) @ ( tc_prod @ SV2252 @ SV2252 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV427 @ SV1032 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5009]) ).
thf(5374,plain,
! [SV1524: $i,SV1033: $i,SV428: $i] :
( ( ( c_in @ ( c_Pair @ SV428 @ SV1033 @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ SV1524 @ t_a ) @ ( tc_prod @ t_a @ t_a ) )
= $false )
| ( ( SV1033 = SV428 )
= $true )
| ( ( c_in @ ( c_Pair @ SV428 @ ( v_sko__Transitive__Closure__Xrtrancl__Xcases__1 @ SV428 @ SV1033 @ SV1524 ) @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ SV1524 @ t_a ) @ ( tc_prod @ t_a @ t_a ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5010]) ).
thf(5375,plain,
! [SV1034: $i,SV2253: $i,SV2127: $i,SV1525: $i,SV429: $i] :
( ( ( ( hBOOL @ ( hAPP @ SV429 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 @ SV429 @ SV1525 @ SV2127 @ SV2253 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV429 @ SV1525 ) )
| ~ ( c_in @ ( c_Pair @ SV1525 @ SV1034 @ SV2253 @ SV2253 ) @ ( c_Transitive__Closure_Ortrancl @ SV2127 @ SV2253 ) @ ( tc_prod @ SV2253 @ SV2253 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV429 @ SV1034 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5011]) ).
thf(5376,plain,
! [SV1526: $i,SV1035: $i,SV430: $i] :
( ( ( c_in @ ( c_Pair @ SV430 @ SV1035 @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ SV1526 @ t_a ) @ ( tc_prod @ t_a @ t_a ) )
= $false )
| ( ( SV1035 = SV430 )
= $true )
| ( ( c_in @ ( c_Pair @ ( v_sko__Transitive__Closure__Xrtrancl__Xcases__1 @ SV430 @ SV1035 @ SV1526 ) @ SV1035 @ t_a @ t_a ) @ SV1526 @ ( tc_prod @ t_a @ t_a ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5012]) ).
thf(5377,plain,
! [SV1036: $i,SV2254: $i,SV2128: $i,SV1527: $i,SV431: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV431 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1 @ SV431 @ SV1527 @ SV2128 @ SV2254 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV431 @ SV1527 ) )
| ~ ( c_in @ ( c_Pair @ SV1036 @ SV1527 @ SV2254 @ SV2254 ) @ ( c_Transitive__Closure_Ortrancl @ SV2128 @ SV2254 ) @ ( tc_prod @ SV2254 @ SV2254 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV431 @ SV1036 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5013]) ).
thf(5378,plain,
! [SV1528: $i,SV1877: $i,SV1037: $i,SV432: $i] :
( ( ( SV432 = SV1037 )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV432 @ SV1037 @ SV1877 @ SV1877 ) @ ( c_Transitive__Closure_Ortrancl @ SV1528 @ SV1877 ) @ ( tc_prod @ SV1877 @ SV1877 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV432 @ ( c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1 @ SV432 @ SV1037 @ SV1528 @ SV1877 ) @ SV1877 @ SV1877 ) @ ( c_Transitive__Closure_Ortrancl @ SV1528 @ SV1877 ) @ ( tc_prod @ SV1877 @ SV1877 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5014]) ).
thf(5379,plain,
! [SV2129: $i,SV1878: $i,SV1529: $i,SV1038: $i,SV433: $i] :
( ( ( c_in @ ( c_ATP__Linkup_Osko__Product__Type__XSigmaE__1__1 @ SV433 @ SV1038 @ SV1529 @ SV1878 @ SV2129 ) @ SV433 @ SV1878 )
= $true )
| ( ( ~ ( c_in @ SV1529 @ ( c_Product__Type_OSigma @ SV433 @ SV1038 @ SV1878 @ SV2129 ) @ ( tc_prod @ SV1878 @ SV2129 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5015]) ).
thf(5380,plain,
! [SV436: $i,SV1041: $i,SV2130: $i] :
( ( ( c_in @ ( c_Pair @ SV2130 @ SV2130 @ SV1041 @ SV1041 ) @ ( c_Transitive__Closure_Otrancl @ SV436 @ SV1041 ) @ ( tc_prod @ SV1041 @ SV1041 ) )
= $false )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_Oconverse @ SV436 @ SV1041 @ SV1041 ) @ ( c_Transitive__Closure_Ortrancl @ SV436 @ SV1041 ) @ ( tc_fun @ ( tc_prod @ SV1041 @ SV1041 ) @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV1041 @ SV1041 ) @ tc_bool ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5016]) ).
thf(5381,plain,
! [SV1879: $i,SV1530: $i,SV1042: $i,SV437: $i] :
( ( ( ( c_Relation_OImage @ SV437 @ ( c_Set_Oinsert @ SV1042 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1530 @ tc_bool ) ) @ SV1530 ) @ SV1530 @ SV1530 )
= ( c_Relation_OImage @ SV437 @ ( c_Set_Oinsert @ SV1879 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1530 @ tc_bool ) ) @ SV1530 ) @ SV1530 @ SV1530 ) )
= $false )
| ( ( ( c_in @ ( c_Pair @ SV1042 @ SV1879 @ SV1530 @ SV1530 ) @ SV437 @ ( tc_prod @ SV1530 @ SV1530 ) )
| ! [SY5786: $i] :
( ~ ( c_in @ SV1879 @ SY5786 @ SV1530 )
| ~ ( c_Equiv__Relations_Oequiv @ SY5786 @ SV437 @ SV1530 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5017]) ).
thf(5382,plain,
! [SV1880: $i,SV1531: $i,SV1043: $i,SV438: $i] :
( ( ( ( c_Relation_OImage @ SV438 @ ( c_Set_Oinsert @ SV1043 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1531 @ tc_bool ) ) @ SV1531 ) @ SV1531 @ SV1531 )
= ( c_Relation_OImage @ SV438 @ ( c_Set_Oinsert @ SV1880 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1531 @ tc_bool ) ) @ SV1531 ) @ SV1531 @ SV1531 ) )
= $false )
| ( ( ! [SY5787: $i] :
( ~ ( c_Equiv__Relations_Oequiv @ SY5787 @ SV438 @ SV1531 )
| ( c_in @ ( c_Pair @ SV1043 @ SV1880 @ SV1531 @ SV1531 ) @ SV438 @ ( tc_prod @ SV1531 @ SV1531 ) )
| ~ ( c_in @ SV1880 @ SY5787 @ SV1531 )
| ~ ( c_in @ SV1043 @ SY5787 @ SV1531 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5018]) ).
thf(5383,plain,
! [SV439: $i,SV1532: $i,SV1881: $i,SV1044: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1044 @ SV1881 @ SV1532 @ SV1532 ) @ SV439 @ ( tc_prod @ SV1532 @ SV1532 ) ) )
= $true )
| ( ( ! [SY5788: $i] :
( ~ ( c_in @ SV1881 @ SY5788 @ SV1532 )
| ~ ( c_in @ SV1044 @ SY5788 @ SV1532 )
| ~ ( c_Equiv__Relations_Oequiv @ SY5788 @ SV439 @ SV1532 ) ) )
= $true )
| ( ( ( c_Relation_OImage @ SV439 @ ( c_Set_Oinsert @ SV1044 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1532 @ tc_bool ) ) @ SV1532 ) @ SV1532 @ SV1532 )
= ( c_Relation_OImage @ SV439 @ ( c_Set_Oinsert @ SV1881 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1532 @ tc_bool ) ) @ SV1532 ) @ SV1532 @ SV1532 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5019]) ).
thf(5384,plain,
! [SV1882: $i,SV1533: $i,SV1045: $i,SV440: $i] :
( ( ( ( c_Relation_OImage @ SV440 @ ( c_Set_Oinsert @ SV1045 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1533 @ tc_bool ) ) @ SV1533 ) @ SV1533 @ SV1533 )
= ( c_Relation_OImage @ SV440 @ ( c_Set_Oinsert @ SV1882 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1533 @ tc_bool ) ) @ SV1533 ) @ SV1533 @ SV1533 ) )
= $false )
| ( ( ! [SY5789: $i] :
( ~ ( c_in @ SV1882 @ SY5789 @ SV1533 )
| ~ ( c_in @ SV1045 @ SY5789 @ SV1533 )
| ~ ( c_Equiv__Relations_Oequiv @ SY5789 @ SV440 @ SV1533 )
| ( c_in @ ( c_Pair @ SV1045 @ SV1882 @ SV1533 @ SV1533 ) @ SV440 @ ( tc_prod @ SV1533 @ SV1533 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5020]) ).
thf(5385,plain,
! [SV1535: $i,SV1047: $i,SV2131: $i,SV442: $i] :
( ( ( SV442 = SV2131 )
= $true )
| ( ( ! [SY5959: $i] :
( ~ ( c_lessequals @ SY5959 @ ( c_Product__Type_OSigma @ SV1047 @ ( c_COMBK @ SV1047 @ ( tc_fun @ SV1535 @ tc_bool ) @ SV1535 ) @ SV1535 @ SV1535 ) @ ( tc_fun @ ( tc_prod @ SV1535 @ SV1535 ) @ tc_bool ) )
| ~ ( c_in @ ( c_Pair @ SV442 @ SV2131 @ SV1535 @ SV1535 ) @ ( c_Transitive__Closure_Ortrancl @ SY5959 @ SV1535 ) @ ( tc_prod @ SV1535 @ SV1535 ) ) ) )
= $true )
| ( ( c_in @ SV442 @ SV1047 @ SV1535 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5021]) ).
thf(5386,plain,
! [SV446: $i,SV1883: $i,SV1539: $i,SV1051: $i,SV2255: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV2255 @ SV1051 @ SV1539 @ SV1539 ) @ ( c_Transitive__Closure_Ortrancl @ SV1883 @ SV1539 ) @ ( tc_prod @ SV1539 @ SV1539 ) )
| ~ ( c_in @ ( c_Pair @ SV446 @ SV2255 @ SV1539 @ SV1539 ) @ SV1883 @ ( tc_prod @ SV1539 @ SV1539 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV446 @ SV1051 @ SV1539 @ SV1539 ) @ ( c_Transitive__Closure_Otrancl @ SV1883 @ SV1539 ) @ ( tc_prod @ SV1539 @ SV1539 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5024]) ).
thf(5387,plain,
! [SV447: $i,SV1884: $i,SV1540: $i,SV1052: $i,SV2256: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV2256 @ SV1052 @ SV1540 @ SV1540 ) @ SV1884 @ ( tc_prod @ SV1540 @ SV1540 ) )
| ~ ( c_in @ ( c_Pair @ SV447 @ SV2256 @ SV1540 @ SV1540 ) @ ( c_Transitive__Closure_Ortrancl @ SV1884 @ SV1540 ) @ ( tc_prod @ SV1540 @ SV1540 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV447 @ SV1052 @ SV1540 @ SV1540 ) @ ( c_Transitive__Closure_Otrancl @ SV1884 @ SV1540 ) @ ( tc_prod @ SV1540 @ SV1540 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5025]) ).
thf(5388,plain,
! [SV1885: $i,SV1541: $i,SV1053: $i,SV448: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV448 @ SV1053 @ SV1541 @ SV1541 ) @ ( c_Transitive__Closure_Otrancl @ SV1885 @ SV1541 ) @ ( tc_prod @ SV1541 @ SV1541 ) ) )
= $true )
| ( ( SV448 = SV1053 )
= $true )
| ( ( c_in @ ( c_Pair @ SV448 @ SV1053 @ SV1541 @ SV1541 ) @ ( c_Transitive__Closure_Ortrancl @ SV1885 @ SV1541 ) @ ( tc_prod @ SV1541 @ SV1541 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5026]) ).
thf(5389,plain,
! [SV1886: $i,SV1542: $i,SV1054: $i,SV449: $i] :
( ( ( SV449 = SV1054 )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV449 @ SV1054 @ SV1542 @ SV1542 ) @ ( c_Transitive__Closure_Ortrancl @ SV1886 @ SV1542 ) @ ( tc_prod @ SV1542 @ SV1542 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV449 @ SV1054 @ SV1542 @ SV1542 ) @ ( c_Transitive__Closure_Otrancl @ SV1886 @ SV1542 ) @ ( tc_prod @ SV1542 @ SV1542 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5027]) ).
thf(5390,plain,
! [SV1887: $i,SV1543: $i,SV1055: $i,SV450: $i] :
( ( ( SV450 = SV1055 )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV450 @ SV1055 @ SV1543 @ SV1543 ) @ ( c_Transitive__Closure_Ortrancl @ SV1887 @ SV1543 ) @ ( tc_prod @ SV1543 @ SV1543 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV450 @ SV1055 @ SV1543 @ SV1543 ) @ ( c_Transitive__Closure_Otrancl @ SV1887 @ SV1543 ) @ ( tc_prod @ SV1543 @ SV1543 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5028]) ).
thf(5391,plain,
! [SV1888: $i,SV1544: $i,SV451: $i,SV1056: $i] :
( ( ( c_in @ ( c_Pair @ SV1056 @ SV451 @ SV1544 @ SV1544 ) @ ( c_Transitive__Closure_Ortrancl @ SV1888 @ SV1544 ) @ ( tc_prod @ SV1544 @ SV1544 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV451 @ SV1056 @ SV1544 @ SV1544 ) @ ( c_Transitive__Closure_Ortrancl @ ( c_Relation_Oconverse @ SV1888 @ SV1544 @ SV1544 ) @ SV1544 ) @ ( tc_prod @ SV1544 @ SV1544 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5029]) ).
thf(5392,plain,
! [SV1889: $i,SV1545: $i,SV452: $i,SV1057: $i] :
( ( ( c_in @ ( c_Pair @ SV1057 @ SV452 @ SV1545 @ SV1545 ) @ ( c_Transitive__Closure_Ortrancl @ ( c_Relation_Oconverse @ SV1889 @ SV1545 @ SV1545 ) @ SV1545 ) @ ( tc_prod @ SV1545 @ SV1545 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV452 @ SV1057 @ SV1545 @ SV1545 ) @ ( c_Transitive__Closure_Ortrancl @ SV1889 @ SV1545 ) @ ( tc_prod @ SV1545 @ SV1545 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5030]) ).
thf(5393,plain,
! [SV1890: $i,SV1546: $i,SV453: $i,SV1058: $i] :
( ( ( c_in @ ( c_Pair @ SV1058 @ SV453 @ SV1546 @ SV1546 ) @ ( c_Transitive__Closure_Ortrancl @ SV1890 @ SV1546 ) @ ( tc_prod @ SV1546 @ SV1546 ) )
= $true )
| ( ( ! [SY5792: $i] :
( ~ ( c_in @ ( c_Pair @ SY5792 @ SV453 @ SV1546 @ SV1546 ) @ ( c_Transitive__Closure_Ortrancl @ SV1890 @ SV1546 ) @ ( tc_prod @ SV1546 @ SV1546 ) )
| ~ ( c_in @ ( c_Pair @ SY5792 @ SV1058 @ SV1546 @ SV1546 ) @ ( c_Transitive__Closure_Ortrancl @ SV1890 @ SV1546 ) @ ( tc_prod @ SV1546 @ SV1546 ) )
| ~ ( c_Relation_Osingle__valued @ SV1890 @ SV1546 @ SV1546 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV453 @ SV1058 @ SV1546 @ SV1546 ) @ ( c_Transitive__Closure_Ortrancl @ SV1890 @ SV1546 ) @ ( tc_prod @ SV1546 @ SV1546 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5031]) ).
thf(5394,plain,
! [SV1891: $i,SV1547: $i,SV1059: $i,SV454: $i] :
( ( ( c_in @ ( c_Pair @ SV454 @ SV1059 @ SV1547 @ SV1547 ) @ ( c_Transitive__Closure_Otrancl @ SV1891 @ SV1547 ) @ ( tc_prod @ SV1547 @ SV1547 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV454 @ SV1059 @ SV1547 @ SV1547 ) @ ( c_Transitive__Closure_Ortrancl @ SV1891 @ SV1547 ) @ ( tc_prod @ SV1547 @ SV1547 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5032]) ).
thf(5395,plain,
! [SV455: $i,SV1892: $i,SV1548: $i,SV1060: $i,SV2257: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV2257 @ SV1060 @ SV1548 @ SV1548 ) @ ( c_Transitive__Closure_Ortrancl @ SV1892 @ SV1548 ) @ ( tc_prod @ SV1548 @ SV1548 ) )
| ~ ( c_in @ ( c_Pair @ SV455 @ SV2257 @ SV1548 @ SV1548 ) @ ( c_Transitive__Closure_Otrancl @ SV1892 @ SV1548 ) @ ( tc_prod @ SV1548 @ SV1548 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV455 @ SV1060 @ SV1548 @ SV1548 ) @ ( c_Transitive__Closure_Otrancl @ SV1892 @ SV1548 ) @ ( tc_prod @ SV1548 @ SV1548 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5033]) ).
thf(5396,plain,
! [SV456: $i,SV1893: $i,SV1549: $i,SV1061: $i,SV2258: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV2258 @ SV1061 @ SV1549 @ SV1549 ) @ ( c_Transitive__Closure_Otrancl @ SV1893 @ SV1549 ) @ ( tc_prod @ SV1549 @ SV1549 ) )
| ~ ( c_in @ ( c_Pair @ SV456 @ SV2258 @ SV1549 @ SV1549 ) @ ( c_Transitive__Closure_Ortrancl @ SV1893 @ SV1549 ) @ ( tc_prod @ SV1549 @ SV1549 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV456 @ SV1061 @ SV1549 @ SV1549 ) @ ( c_Transitive__Closure_Otrancl @ SV1893 @ SV1549 ) @ ( tc_prod @ SV1549 @ SV1549 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5034]) ).
thf(5397,plain,
! [SV1894: $i,SV1550: $i,SV1062: $i,SV457: $i] :
( ( ( c_in @ ( c_Pair @ SV457 @ SV1062 @ SV1550 @ SV1550 ) @ ( c_Transitive__Closure_Otrancl @ ( c_Relation_Oconverse @ SV1894 @ SV1550 @ SV1550 ) @ SV1550 ) @ ( tc_prod @ SV1550 @ SV1550 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV457 @ SV1062 @ SV1550 @ SV1550 ) @ ( c_Relation_Oconverse @ ( c_Transitive__Closure_Otrancl @ SV1894 @ SV1550 ) @ SV1550 @ SV1550 ) @ ( tc_prod @ SV1550 @ SV1550 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5035]) ).
thf(5398,plain,
! [SV1895: $i,SV1551: $i,SV1063: $i,SV458: $i] :
( ( ( c_in @ ( c_Pair @ SV458 @ SV1063 @ SV1551 @ SV1551 ) @ ( c_Relation_Oconverse @ ( c_Transitive__Closure_Otrancl @ SV1895 @ SV1551 ) @ SV1551 @ SV1551 ) @ ( tc_prod @ SV1551 @ SV1551 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV458 @ SV1063 @ SV1551 @ SV1551 ) @ ( c_Transitive__Closure_Otrancl @ ( c_Relation_Oconverse @ SV1895 @ SV1551 @ SV1551 ) @ SV1551 ) @ ( tc_prod @ SV1551 @ SV1551 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5036]) ).
thf(5399,plain,
! [SV2259: $i,SV2132: $i,SV1896: $i,SV1552: $i,SV1064: $i,SV459: $i] :
( ( ( hAPP @ ( c_split @ SV459 @ SV1064 @ SV1552 @ SV1896 ) @ ( c_Pair @ SV2132 @ SV2259 @ SV1064 @ SV1552 ) )
= ( hAPP @ ( hAPP @ SV459 @ SV2132 ) @ SV2259 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5037]) ).
thf(5400,plain,
! [SV2260: $i,SV2133: $i,SV1897: $i,SV1553: $i,SV1065: $i,SV460: $i] :
( ( ( hAPP @ ( c_split @ SV460 @ SV1065 @ SV1553 @ SV1897 ) @ ( c_Pair @ SV2133 @ SV2260 @ SV1065 @ SV1553 ) )
= ( hAPP @ ( hAPP @ SV460 @ SV2133 ) @ SV2260 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5038]) ).
thf(5401,plain,
! [SV2134: $i,SV1898: $i,SV1554: $i,SV1066: $i,SV461: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ SV461 @ SV1066 ) @ SV1554 ) @ SV1898 ) )
= $true )
| ( ( ! [SY5962: $i,SY5963: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_split @ SV461 @ SV2134 @ SY5962 @ ( tc_fun @ SY5963 @ tc_bool ) ) @ ( c_Pair @ SV1066 @ SV1554 @ SV2134 @ SY5962 ) ) @ SV1898 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5039]) ).
thf(5402,plain,
! [SV2261: $i,SV1899: $i,SV1555: $i,SV1067: $i,SV462: $i] :
( ( ( c_in @ ( hAPP @ SV462 @ SV1067 ) @ ( c_Set_Oimage @ SV462 @ SV1555 @ SV1899 @ SV2261 ) @ SV2261 )
= $true )
| ( ( ~ ( c_in @ SV1067 @ SV1555 @ SV1899 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5040]) ).
thf(5403,plain,
! [SV2262: $i,SV1900: $i,SV1556: $i,SV1068: $i,SV463: $i] :
( ( ( c_in @ ( hAPP @ SV463 @ SV1068 ) @ ( c_Set_Oimage @ SV463 @ SV1556 @ SV1900 @ SV2262 ) @ SV2262 )
= $true )
| ( ( ~ ( c_in @ SV1068 @ SV1556 @ SV1900 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5041]) ).
thf(5404,plain,
! [SV1557: $i,SV1069: $i,SV464: $i,SV2263: $i] :
( ( ( ! [SY6012: $i] : ( c_in @ ( hAPP @ SV2263 @ SV464 ) @ ( c_Set_Oimage @ SV2263 @ SV1069 @ SV1557 @ SY6012 ) @ SY6012 ) )
= $true )
| ( ( c_in @ SV464 @ SV1069 @ SV1557 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5042]) ).
thf(5405,plain,
! [SV1558: $i,SV1070: $i,SV465: $i,SV2264: $i] :
( ( ( ! [SY6013: $i] : ( c_in @ ( hAPP @ SV2264 @ SV465 ) @ ( c_Set_Oimage @ SV2264 @ SV1070 @ SV1558 @ SY6013 ) @ SY6013 ) )
= $true )
| ( ( c_in @ SV465 @ SV1070 @ SV1558 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5043]) ).
thf(5406,plain,
! [SV2135: $i,SV1901: $i,SV1560: $i,SV1073: $i,SV468: $i] :
( ( ( c_in @ ( c_ATP__Linkup_Osko__Relation__XImageE__1__1 @ SV468 @ SV1073 @ SV1560 @ SV1901 @ SV2135 ) @ SV468 @ SV1901 )
= $true )
| ( ( ~ ( c_in @ SV1073 @ ( c_Relation_OImage @ SV1560 @ SV468 @ SV1901 @ SV2135 ) @ SV2135 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5045]) ).
thf(5407,plain,
! [SV1075: $i,SV2136: $i,SV1902: $i,SV470: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV470 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ SV470 @ SV1902 @ SV2136 ) ) ) )
= $true )
| ( ( ~ ( c_in @ SV1075 @ ( c_Wellfounded_Oacc @ SV1902 @ SV2136 ) @ SV2136 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV470 @ SV1075 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5046]) ).
thf(5408,plain,
! [SV1077: $i,SV1903: $i,SV472: $i] :
( ( ( hBOOL @ ( hAPP @ SV472 @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ SV472 @ SV1903 ) ) )
= $false )
| ( ( ~ ( c_in @ SV1077 @ ( c_Wellfounded_Oacc @ SV1903 @ t_a ) @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV472 @ SV1077 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5047]) ).
thf(5409,plain,
! [SV1078: $i,SV2137: $i,SV1904: $i,SV473: $i] :
( ( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ SV473 @ SV1904 @ SV2137 ) @ ( c_Wellfounded_Oacc @ SV1904 @ SV2137 ) @ SV2137 )
= $true )
| ( ( ~ ( c_in @ SV1078 @ ( c_Wellfounded_Oacc @ SV1904 @ SV2137 ) @ SV2137 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV473 @ SV1078 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5048]) ).
thf(5410,plain,
! [SV2138: $i,SV1905: $i,SV1561: $i,SV1082: $i,SV477: $i] :
( ( ( c_in @ ( c_ATP__Linkup_Osko__Relation__XImage__iff__1__1 @ SV477 @ SV1082 @ SV1561 @ SV1905 @ SV2138 ) @ SV477 @ SV1905 )
= $true )
| ( ( ~ ( c_in @ SV1082 @ ( c_Relation_OImage @ SV1561 @ SV477 @ SV1905 @ SV2138 ) @ SV2138 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5049]) ).
thf(5411,plain,
! [SV1089: $i,SV2139: $i,SV1906: $i,SV485: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV485 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ SV485 @ SV1906 @ SV2139 ) ) ) )
= $true )
| ( ( ~ ( c_in @ SV1089 @ ( c_Wellfounded_Oacc @ SV1906 @ SV2139 ) @ SV2139 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV485 @ SV1089 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5051]) ).
thf(5412,plain,
! [SV2141: $i,SV1104: $i,SV1568: $i,SV501: $i] :
( ( ( c_Wellfounded_Owf @ SV501 @ SV1568 )
= $false )
| ( ( c_Wellfounded_Owf @ ( c_Relation_Oinv__image @ SV501 @ SV1104 @ SV1568 @ SV2141 ) @ SV2141 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5055]) ).
thf(5413,plain,
! [SV2142: $i,SV1106: $i,SV1569: $i,SV503: $i] :
( ( ( c_Relation_Osym @ SV503 @ SV1569 )
= $false )
| ( ( c_Relation_Osym @ ( c_Relation_Oinv__image @ SV503 @ SV1106 @ SV1569 @ SV2142 ) @ SV2142 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5056]) ).
thf(5414,plain,
! [SV2265: $i,SV2143: $i,SV1908: $i,SV1570: $i,SV1112: $i,SV510: $i] :
( ( ! [SY6014: $i] :
( ( c_Relation_Orel__comp @ ( c_Relation_Orel__comp @ SV510 @ SV1112 @ SV1570 @ SV1908 @ SV2143 ) @ SV2265 @ SV1570 @ SV2143 @ SY6014 )
= ( c_Relation_Orel__comp @ SV510 @ ( c_Relation_Orel__comp @ SV1112 @ SV2265 @ SV1908 @ SV2143 @ SY6014 ) @ SV1570 @ SV1908 @ SY6014 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5057]) ).
thf(5415,plain,
! [SV2144: $i,SV1115: $i,SV1572: $i,SV513: $i] :
( ( ( c_Relation_Otrans @ SV513 @ SV1572 )
= $false )
| ( ( c_Relation_Otrans @ ( c_Relation_Oinv__image @ SV513 @ SV1115 @ SV1572 @ SV2144 ) @ SV2144 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5058]) ).
thf(5416,plain,
! [SV1119: $i,SV1574: $i,SV518: $i,SV2266: $i] :
( ( ( ~ ( c_in @ SV2266 @ SV518 @ SV1574 ) )
= $true )
| ( ( ~ ( c_Wellfounded_Owf @ SV1119 @ SV1574 ) )
= $true )
| ( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 @ SV518 @ SV1119 @ SV1574 ) @ SV518 @ SV1574 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5059]) ).
thf(5417,plain,
! [SV2145: $i,SV1910: $i,SV1575: $i,SV1121: $i,SV520: $i] :
( ( ( c_Relation_Osingle__valued @ ( c_Relation_Orel__comp @ SV520 @ SV1121 @ SV1575 @ SV1910 @ SV2145 ) @ SV1575 @ SV2145 )
= $true )
| ( ( ~ ( c_Relation_Osingle__valued @ SV1121 @ SV1910 @ SV2145 )
| ~ ( c_Relation_Osingle__valued @ SV520 @ SV1575 @ SV1910 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5060]) ).
thf(5418,plain,
! [SV1127: $i,SV1912: $i,SV527: $i] :
( ( ( hBOOL @ ( hAPP @ SV527 @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ SV527 @ SV1912 ) ) )
= $false )
| ( ( ~ ( c_in @ SV1127 @ ( c_Wellfounded_Oacc @ SV1912 @ t_a ) @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV527 @ SV1127 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5062]) ).
thf(5419,plain,
! [SV1130: $i,SV1578: $i,SV530: $i,SV2267: $i] :
( ( ( ~ ( c_in @ SV2267 @ SV530 @ SV1578 ) )
= $true )
| ( ( ~ ( c_Wellfounded_Owf @ SV1130 @ SV1578 ) )
= $true )
| ( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 @ SV530 @ SV1130 @ SV1578 ) @ SV530 @ SV1578 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5064]) ).
thf(5420,plain,
! [SV2268: $i,SV2146: $i,SV1914: $i,SV1580: $i,SV1133: $i,SV533: $i] :
( ( ( c_Equiv__Relations_Ocongruent @ SV533 @ ( hAPP @ SV1133 @ SV1580 ) @ SV1914 @ SV2146 )
| ! [SY6015: $i] :
( ~ ( c_in @ SV1580 @ SV2268 @ SY6015 )
| ! [SY6016: $i] :
( ~ ( c_Equiv__Relations_Ocongruent2 @ SY6016 @ SV533 @ SV1133 @ SY6015 @ SV1914 @ SV2146 )
| ~ ( c_Equiv__Relations_Oequiv @ SV2268 @ SY6016 @ SY6015 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5067]) ).
thf(5421,plain,
! [SV1141: $i,SV2147: $i,SV1916: $i,SV541: $i] :
( ( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ SV541 @ SV1916 @ SV2147 ) @ ( c_Wellfounded_Oacc @ SV1916 @ SV2147 ) @ SV2147 )
= $true )
| ( ( ~ ( c_in @ SV1141 @ ( c_Wellfounded_Oacc @ SV1916 @ SV2147 ) @ SV2147 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV541 @ SV1141 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5071]) ).
thf(5422,plain,
! [SV2148: $i,SV1917: $i,SV1585: $i,SV1144: $i,SV544: $i] :
( ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XImageE__1__1 @ SV544 @ SV1144 @ SV1585 @ SV1917 @ SV2148 ) @ SV1144 @ SV1917 @ SV2148 ) @ SV1585 @ ( tc_prod @ SV1917 @ SV2148 ) )
= $true )
| ( ( ~ ( c_in @ SV1144 @ ( c_Relation_OImage @ SV1585 @ SV544 @ SV1917 @ SV2148 ) @ SV2148 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5072]) ).
thf(5423,plain,
! [SV1146: $i,SV2269: $i,SV546: $i,SV1587: $i] :
( ( ( ! [SY6017: $i] :
( ~ ( c_in @ ( c_Pair @ SV1587 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ SV546 @ SV2269 @ SY6017 ) @ SY6017 @ SY6017 ) @ SV2269 @ ( tc_prod @ SY6017 @ SY6017 ) )
| ~ ( c_in @ SV1146 @ ( c_Wellfounded_Oacc @ SV2269 @ SY6017 ) @ SY6017 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV546 @ SV1587 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV546 @ SV1146 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5073]) ).
thf(5424,plain,
! [SV1147: $i,SV2270: $i,SV547: $i,SV1918: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1918 @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ SV547 @ SV2270 ) @ t_a @ t_a ) @ SV2270 @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ SV1147 @ ( c_Wellfounded_Oacc @ SV2270 @ t_a ) @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV547 @ SV1918 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV547 @ SV1147 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5074]) ).
thf(5425,plain,
! [SV1588: $i,SV2271: $i,SV1148: $i,SV548: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV548 @ ( c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 @ SV1148 @ SV2271 @ SV1588 ) @ SV1588 @ SV1588 ) @ SV2271 @ ( tc_prod @ SV1588 @ SV1588 ) )
| ! [SY5526: $i] :
~ ( c_in @ SY5526 @ SV1148 @ SV1588 )
| ~ ( c_Wellfounded_Owf @ SV2271 @ SV1588 ) )
= $true )
| ( ( c_in @ SV548 @ SV1148 @ SV1588 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5075]) ).
thf(5426,plain,
! [SV1589: $i,SV1919: $i,SV1149: $i,SV549: $i] :
( ( ( c_in @ SV549 @ ( c_Relation_ORange @ SV1149 @ SV1919 @ SV1589 ) @ SV1589 )
= $false )
| ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XRangeE__1__1 @ SV549 @ SV1149 @ SV1589 @ SV1919 ) @ SV549 @ SV1919 @ SV1589 ) @ SV1149 @ ( tc_prod @ SV1919 @ SV1589 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5076]) ).
thf(5427,plain,
! [SV551: $i,SV1591: $i,SV1151: $i,SV2149: $i] :
( ( ( ~ ( c_in @ SV2149 @ ( c_Wellfounded_Oacc @ SV1151 @ SV1591 ) @ SV1591 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV551 @ SV2149 @ SV1591 @ SV1591 ) @ ( c_Transitive__Closure_Ortrancl @ SV1151 @ SV1591 ) @ ( tc_prod @ SV1591 @ SV1591 ) ) )
= $true )
| ( ( c_in @ SV551 @ ( c_Wellfounded_Oacc @ SV1151 @ SV1591 ) @ SV1591 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5077]) ).
thf(5428,plain,
! [SV1152: $i,SV1592: $i,SV2150: $i,SV552: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV552 @ SV2150 @ SV1592 @ SV1592 ) @ ( c_Transitive__Closure_Ortrancl @ SV1152 @ SV1592 ) @ ( tc_prod @ SV1592 @ SV1592 ) ) )
= $true )
| ( ( ~ ( c_in @ SV2150 @ ( c_Wellfounded_Oacc @ SV1152 @ SV1592 ) @ SV1592 ) )
= $true )
| ( ( c_in @ SV552 @ ( c_Wellfounded_Oacc @ SV1152 @ SV1592 ) @ SV1592 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5078]) ).
thf(5429,plain,
! [SV1153: $i,SV553: $i,SV2151: $i,SV1920: $i] :
( ( ( c_in @ SV1920 @ ( c_Wellfounded_Oacc @ SV2151 @ t_a ) @ t_a )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV1920 @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ SV553 @ SV2151 ) @ t_a @ t_a ) @ SV2151 @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ SV1153 @ ( c_Wellfounded_Oacc @ SV2151 @ t_a ) @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV553 @ SV1153 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5079]) ).
thf(5430,plain,
! [SV1155: $i,SV2272: $i,SV555: $i,SV1921: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1921 @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ SV555 @ SV2272 ) @ t_a @ t_a ) @ SV2272 @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ SV1155 @ ( c_Wellfounded_Oacc @ SV2272 @ t_a ) @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV555 @ SV1921 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV555 @ SV1155 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5080]) ).
thf(5431,plain,
! [SV2273: $i,SV2152: $i,SV1922: $i,SV1594: $i,SV1156: $i,SV556: $i] :
( ( ! [SY6019: $i] :
( ( c_in @ ( hAPP @ ( hAPP @ SV556 @ SV1156 ) @ SV1594 ) @ ( c_Set_Oimage @ ( c_split @ SV556 @ SV1922 @ SV2152 @ SV2273 ) @ SY6019 @ ( tc_prod @ SV1922 @ SV2152 ) @ SV2273 ) @ SV2273 )
| ~ ( c_in @ ( c_Pair @ SV1156 @ SV1594 @ SV1922 @ SV2152 ) @ SY6019 @ ( tc_prod @ SV1922 @ SV2152 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5081]) ).
thf(5432,plain,
! [SV1923: $i,SV1595: $i,SV1157: $i,SV557: $i] :
( ( ( c_in @ SV557 @ ( c_Relation_ODomain @ SV1157 @ SV1595 @ SV1923 ) @ SV1595 )
= $false )
| ( ( c_in @ ( c_Pair @ SV557 @ ( c_ATP__Linkup_Osko__Relation__XDomainE__1__1 @ SV557 @ SV1157 @ SV1595 @ SV1923 ) @ SV1595 @ SV1923 ) @ SV1157 @ ( tc_prod @ SV1595 @ SV1923 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5082]) ).
thf(5433,plain,
! [SV1158: $i,SV558: $i,SV2153: $i,SV1924: $i] :
( ( ( c_in @ SV1924 @ ( c_Wellfounded_Oacc @ SV2153 @ t_a ) @ t_a )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV1924 @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ SV558 @ SV2153 ) @ t_a @ t_a ) @ SV2153 @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ SV1158 @ ( c_Wellfounded_Oacc @ SV2153 @ t_a ) @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV558 @ SV1158 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5083]) ).
thf(5434,plain,
! [SV1159: $i,SV2274: $i,SV559: $i,SV1596: $i] :
( ( ( ! [SY6020: $i] :
( ~ ( c_in @ ( c_Pair @ SV1596 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ SV559 @ SV2274 @ SY6020 ) @ SY6020 @ SY6020 ) @ SV2274 @ ( tc_prod @ SY6020 @ SY6020 ) )
| ~ ( c_in @ SV1159 @ ( c_Wellfounded_Oacc @ SV2274 @ SY6020 ) @ SY6020 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV559 @ SV1596 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV559 @ SV1159 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5084]) ).
thf(5435,plain,
! [SV1597: $i,SV2275: $i,SV1160: $i,SV560: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV560 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 @ SV1160 @ SV2275 @ SV1597 ) @ SV1597 @ SV1597 ) @ SV2275 @ ( tc_prod @ SV1597 @ SV1597 ) )
| ! [SY5538: $i] :
~ ( c_in @ SY5538 @ SV1160 @ SV1597 )
| ~ ( c_Wellfounded_Owf @ SV2275 @ SV1597 ) )
= $true )
| ( ( c_in @ SV560 @ SV1160 @ SV1597 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5085]) ).
thf(5436,plain,
! [SV1925: $i,SV1598: $i,SV1161: $i,SV561: $i] :
( ( ( c_in @ SV561 @ ( c_Relation_ODomain @ SV1161 @ SV1598 @ SV1925 ) @ SV1598 )
= $false )
| ( ( c_in @ ( c_Pair @ SV561 @ ( c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1 @ SV561 @ SV1161 @ SV1598 @ SV1925 ) @ SV1598 @ SV1925 ) @ SV1161 @ ( tc_prod @ SV1598 @ SV1925 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5086]) ).
thf(5437,plain,
! [SV2154: $i,SV1926: $i,SV1599: $i,SV1162: $i,SV562: $i] :
( ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XImage__iff__1__1 @ SV562 @ SV1162 @ SV1599 @ SV1926 @ SV2154 ) @ SV1162 @ SV1926 @ SV2154 ) @ SV1599 @ ( tc_prod @ SV1926 @ SV2154 ) )
= $true )
| ( ( ~ ( c_in @ SV1162 @ ( c_Relation_OImage @ SV1599 @ SV562 @ SV1926 @ SV2154 ) @ SV2154 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5087]) ).
thf(5438,plain,
! [SV2155: $i,SV1927: $i,SV1163: $i,SV563: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV563 @ SV1163 @ SV1927 @ SV1927 ) @ ( c_Transitive__Closure_Ortrancl @ SV2155 @ SV1927 ) @ ( tc_prod @ SV1927 @ SV1927 ) ) )
= $true )
| ( ( c_in @ SV563 @ ( c_Relation_ODomain @ SV2155 @ SV1927 @ SV1927 ) @ SV1927 )
= $true )
| ( ( SV563 = SV1163 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5088]) ).
thf(5439,plain,
! [SV1600: $i,SV1928: $i,SV1164: $i,SV564: $i] :
( ( ( c_in @ SV564 @ ( c_Relation_ORange @ SV1164 @ SV1928 @ SV1600 ) @ SV1600 )
= $false )
| ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XRange__iff__1__1 @ SV564 @ SV1164 @ SV1600 @ SV1928 ) @ SV564 @ SV1928 @ SV1600 ) @ SV1164 @ ( tc_prod @ SV1928 @ SV1600 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5089]) ).
thf(5440,plain,
! [SV2276: $i,SV2156: $i,SV1929: $i,SV1601: $i,SV1165: $i,SV565: $i] :
( ( ! [SY6022: $i] :
( ( c_in @ SV565 @ ( hAPP @ ( c_split @ SV1165 @ SV1601 @ SV1929 @ ( tc_fun @ SV2156 @ tc_bool ) ) @ ( c_Pair @ SV2276 @ SY6022 @ SV1601 @ SV1929 ) ) @ SV2156 )
| ~ ( c_in @ SV565 @ ( hAPP @ ( hAPP @ SV1165 @ SV2276 ) @ SY6022 ) @ SV2156 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5090]) ).
thf(5441,plain,
! [SV2277: $i,SV2157: $i,SV1930: $i,SV1602: $i,SV1166: $i,SV566: $i] :
( ( ! [SY6023: $i,SY6024: $i] :
( ( ( hAPP @ ( hAPP @ SV566 @ SV1166 ) @ SV1602 )
= ( hAPP @ ( hAPP @ SV566 @ SV1930 ) @ SV2157 ) )
| ~ ( c_in @ ( c_Pair @ SV1602 @ SV2157 @ SV2277 @ SV2277 ) @ SY6023 @ ( tc_prod @ SV2277 @ SV2277 ) )
| ! [SY6025: $i] :
( ~ ( c_in @ ( c_Pair @ SV1166 @ SV1930 @ SY6024 @ SY6024 ) @ SY6025 @ ( tc_prod @ SY6024 @ SY6024 ) )
| ! [SY6026: $i] :
~ ( c_Equiv__Relations_Ocongruent2 @ SY6025 @ SY6023 @ SV566 @ SY6024 @ SV2277 @ SY6026 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5091]) ).
thf(5442,plain,
! [SV567: $i,SV2278: $i,SV1931: $i,SV1167: $i,SV1603: $i] :
( ( ( ! [SY6027: $i] :
( ~ ( c_in @ ( c_Pair @ SV1603 @ SV1167 @ SV1931 @ SV2278 ) @ SY6027 @ ( tc_prod @ SV1931 @ SV2278 ) )
| ~ ( c_in @ ( c_Pair @ SV1603 @ SV567 @ SV1931 @ SV2278 ) @ SY6027 @ ( tc_prod @ SV1931 @ SV2278 ) )
| ~ ( c_Relation_Osingle__valued @ SY6027 @ SV1931 @ SV2278 ) ) )
= $true )
| ( ( SV567 = SV1167 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5092]) ).
thf(5443,plain,
! [SV2279: $i,SV2158: $i,SV1932: $i,SV1604: $i,SV1168: $i,SV568: $i] :
( ( ( ( hAPP @ ( c_Recdef_Ocut @ SV568 @ SV1168 @ SV1604 @ SV1932 @ SV2158 ) @ SV2279 )
= ( hAPP @ SV568 @ SV2279 ) )
| ~ ( c_in @ ( c_Pair @ SV2279 @ SV1604 @ SV1932 @ SV1932 ) @ SV1168 @ ( tc_prod @ SV1932 @ SV1932 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5093]) ).
thf(5444,plain,
! [SV2280: $i,SV2159: $i,SV1933: $i,SV1605: $i,SV1169: $i,SV569: $i] :
( ( ( ( hAPP @ ( c_Recdef_Ocut @ SV569 @ SV1169 @ SV1605 @ SV1933 @ SV2159 ) @ SV2280 )
= ( hAPP @ SV569 @ SV2280 ) )
| ~ ( c_in @ ( c_Pair @ SV2280 @ SV1605 @ SV1933 @ SV1933 ) @ SV1169 @ ( tc_prod @ SV1933 @ SV1933 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5094]) ).
thf(5445,plain,
! [SV2160: $i,SV1934: $i,SV1606: $i,SV1170: $i,SV570: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_FunDef_Oin__rel @ SV570 @ SV1170 @ SV1606 ) @ SV1934 ) @ SV2160 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV1934 @ SV2160 @ SV1170 @ SV1606 ) @ SV570 @ ( tc_prod @ SV1170 @ SV1606 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5095]) ).
thf(5446,plain,
! [SV2161: $i,SV1935: $i,SV1607: $i,SV1171: $i,SV571: $i] :
( ( ( c_in @ ( c_Pair @ SV571 @ SV1171 @ SV1607 @ SV1935 ) @ SV2161 @ ( tc_prod @ SV1607 @ SV1935 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_FunDef_Oin__rel @ SV2161 @ SV1607 @ SV1935 ) @ SV571 ) @ SV1171 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5096]) ).
thf(5447,plain,
! [SV572: $i,SV1936: $i,SV1608: $i,SV1172: $i,SV2281: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV2281 @ SV1172 @ SV1608 @ SV1608 ) @ SV1936 @ ( tc_prod @ SV1608 @ SV1608 ) )
| ~ ( c_in @ ( c_Pair @ SV572 @ SV2281 @ SV1608 @ SV1608 ) @ SV1936 @ ( tc_prod @ SV1608 @ SV1608 ) )
| ~ ( c_Relation_Otrans @ SV1936 @ SV1608 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV572 @ SV1172 @ SV1608 @ SV1608 ) @ SV1936 @ ( tc_prod @ SV1608 @ SV1608 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5097]) ).
thf(5448,plain,
! [SV573: $i,SV1937: $i,SV1609: $i,SV1173: $i,SV2282: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV2282 @ SV1173 @ SV1609 @ SV1609 ) @ SV1937 @ ( tc_prod @ SV1609 @ SV1609 ) )
| ~ ( c_in @ ( c_Pair @ SV573 @ SV2282 @ SV1609 @ SV1609 ) @ SV1937 @ ( tc_prod @ SV1609 @ SV1609 ) )
| ~ ( c_Relation_Otrans @ SV1937 @ SV1609 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV573 @ SV1173 @ SV1609 @ SV1609 ) @ SV1937 @ ( tc_prod @ SV1609 @ SV1609 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5098]) ).
thf(5449,plain,
! [SV2162: $i,SV1938: $i,SV1610: $i,SV1174: $i,SV574: $i] :
( ( ( c_in @ ( c_Pair @ SV574 @ SV1174 @ SV1610 @ SV1938 ) @ ( c_Relation_Oconverse @ SV2162 @ SV1938 @ SV1610 ) @ ( tc_prod @ SV1610 @ SV1938 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV1174 @ SV574 @ SV1938 @ SV1610 ) @ SV2162 @ ( tc_prod @ SV1938 @ SV1610 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5099]) ).
thf(5450,plain,
! [SV2163: $i,SV1939: $i,SV1611: $i,SV1175: $i,SV575: $i] :
( ( ( c_in @ ( c_Pair @ SV575 @ SV1175 @ SV1611 @ SV1939 ) @ ( c_Relation_Oconverse @ SV2163 @ SV1939 @ SV1611 ) @ ( tc_prod @ SV1611 @ SV1939 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV1175 @ SV575 @ SV1939 @ SV1611 ) @ SV2163 @ ( tc_prod @ SV1939 @ SV1611 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5100]) ).
thf(5451,plain,
! [SV2164: $i,SV1940: $i,SV1612: $i,SV1176: $i,SV576: $i] :
( ( ( c_in @ ( c_Pair @ SV576 @ SV1176 @ SV1612 @ SV1940 ) @ SV2164 @ ( tc_prod @ SV1612 @ SV1940 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV1176 @ SV576 @ SV1940 @ SV1612 ) @ ( c_Relation_Oconverse @ SV2164 @ SV1612 @ SV1940 ) @ ( tc_prod @ SV1940 @ SV1612 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5101]) ).
thf(5452,plain,
! [SV577: $i,SV1177: $i,SV1613: $i] :
( ( ( c_Relation_Oirrefl @ SV1613 @ SV1177 )
= $false )
| ( ( c_in @ ( c_Pair @ SV577 @ SV577 @ SV1177 @ SV1177 ) @ SV1613 @ ( tc_prod @ SV1177 @ SV1177 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5102]) ).
thf(5453,plain,
! [SV578: $i,SV1941: $i,SV1614: $i,SV1178: $i,SV2283: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV2283 @ SV1178 @ SV1614 @ SV1614 ) @ SV1941 @ ( tc_prod @ SV1614 @ SV1614 ) )
| ~ ( c_in @ ( c_Pair @ SV578 @ SV2283 @ SV1614 @ SV1614 ) @ ( c_Transitive__Closure_Otrancl @ SV1941 @ SV1614 ) @ ( tc_prod @ SV1614 @ SV1614 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV578 @ SV1178 @ SV1614 @ SV1614 ) @ ( c_Transitive__Closure_Otrancl @ SV1941 @ SV1614 ) @ ( tc_prod @ SV1614 @ SV1614 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5103]) ).
thf(5454,plain,
! [SV579: $i,SV1942: $i,SV1615: $i,SV1179: $i,SV2284: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV2284 @ SV1179 @ SV1615 @ SV1615 ) @ ( c_Transitive__Closure_Otrancl @ SV1942 @ SV1615 ) @ ( tc_prod @ SV1615 @ SV1615 ) )
| ~ ( c_in @ ( c_Pair @ SV579 @ SV2284 @ SV1615 @ SV1615 ) @ SV1942 @ ( tc_prod @ SV1615 @ SV1615 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV579 @ SV1179 @ SV1615 @ SV1615 ) @ ( c_Transitive__Closure_Otrancl @ SV1942 @ SV1615 ) @ ( tc_prod @ SV1615 @ SV1615 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5104]) ).
thf(5455,plain,
! [SV580: $i,SV1943: $i,SV1616: $i,SV1180: $i,SV2285: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV2285 @ SV1180 @ SV1616 @ SV1616 ) @ SV1943 @ ( tc_prod @ SV1616 @ SV1616 ) )
| ~ ( c_in @ ( c_Pair @ SV580 @ SV2285 @ SV1616 @ SV1616 ) @ ( c_Transitive__Closure_Ortrancl @ SV1943 @ SV1616 ) @ ( tc_prod @ SV1616 @ SV1616 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV580 @ SV1180 @ SV1616 @ SV1616 ) @ ( c_Transitive__Closure_Ortrancl @ SV1943 @ SV1616 ) @ ( tc_prod @ SV1616 @ SV1616 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5105]) ).
thf(5456,plain,
! [SV581: $i,SV1944: $i,SV1617: $i,SV1181: $i,SV2286: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV2286 @ SV1181 @ SV1617 @ SV1617 ) @ ( c_Transitive__Closure_Ortrancl @ SV1944 @ SV1617 ) @ ( tc_prod @ SV1617 @ SV1617 ) )
| ~ ( c_in @ ( c_Pair @ SV581 @ SV2286 @ SV1617 @ SV1617 ) @ SV1944 @ ( tc_prod @ SV1617 @ SV1617 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV581 @ SV1181 @ SV1617 @ SV1617 ) @ ( c_Transitive__Closure_Ortrancl @ SV1944 @ SV1617 ) @ ( tc_prod @ SV1617 @ SV1617 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5106]) ).
thf(5457,plain,
! [SV1945: $i,SV1618: $i,SV1182: $i,SV582: $i] :
( ( ( c_in @ ( c_Pair @ SV582 @ SV1182 @ SV1618 @ SV1618 ) @ SV1945 @ ( tc_prod @ SV1618 @ SV1618 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV582 @ SV1182 @ SV1618 @ SV1618 ) @ ( c_Transitive__Closure_Otrancl @ SV1945 @ SV1618 ) @ ( tc_prod @ SV1618 @ SV1618 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5107]) ).
thf(5458,plain,
! [SV583: $i,SV1946: $i,SV1619: $i,SV1183: $i,SV2287: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV2287 @ SV1183 @ SV1619 @ SV1619 ) @ ( c_Transitive__Closure_Ortrancl @ SV1946 @ SV1619 ) @ ( tc_prod @ SV1619 @ SV1619 ) )
| ~ ( c_in @ ( c_Pair @ SV583 @ SV2287 @ SV1619 @ SV1619 ) @ ( c_Transitive__Closure_Ortrancl @ SV1946 @ SV1619 ) @ ( tc_prod @ SV1619 @ SV1619 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV583 @ SV1183 @ SV1619 @ SV1619 ) @ ( c_Transitive__Closure_Ortrancl @ SV1946 @ SV1619 ) @ ( tc_prod @ SV1619 @ SV1619 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5108]) ).
thf(5459,plain,
! [SV1947: $i,SV1622: $i,SV1186: $i,SV586: $i] :
( ( ( c_in @ ( c_Pair @ SV586 @ SV1186 @ SV1622 @ SV1622 ) @ SV1947 @ ( tc_prod @ SV1622 @ SV1622 ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV1186 @ SV586 @ SV1622 @ SV1622 ) @ SV1947 @ ( tc_prod @ SV1622 @ SV1622 ) )
| ~ ( c_Wellfounded_Owf @ SV1947 @ SV1622 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5109]) ).
thf(5460,plain,
! [SV2165: $i,SV1948: $i,SV587: $i,SV1187: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1187 @ SV587 @ SV1948 @ SV1948 ) @ SV2165 @ ( tc_prod @ SV1948 @ SV1948 ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV587 @ SV1187 @ SV1948 @ SV1948 ) @ SV2165 @ ( tc_prod @ SV1948 @ SV1948 ) )
| ~ ( c_Relation_Oantisym @ SV2165 @ SV1948 ) )
= $true )
| ( ( SV587 = SV1187 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5110]) ).
thf(5461,plain,
! [SV2166: $i,SV1949: $i,SV588: $i,SV1188: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1188 @ SV588 @ SV1949 @ SV1949 ) @ SV2166 @ ( tc_prod @ SV1949 @ SV1949 ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV588 @ SV1188 @ SV1949 @ SV1949 ) @ SV2166 @ ( tc_prod @ SV1949 @ SV1949 ) )
| ~ ( c_Relation_Oantisym @ SV2166 @ SV1949 ) )
= $true )
| ( ( SV588 = SV1188 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5111]) ).
thf(5462,plain,
! [SV589: $i,SV2288: $i,SV1950: $i,SV1623: $i,SV1189: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1189 @ SV1623 @ SV1950 @ SV1950 ) @ SV2288 @ ( tc_prod @ SV1950 @ SV1950 ) )
| ! [SY6028: $i] :
~ ( c_Equiv__Relations_Ocongruent @ SV2288 @ SV589 @ SV1950 @ SY6028 ) )
= $true )
| ( ( ( hAPP @ SV589 @ SV1189 )
= ( hAPP @ SV589 @ SV1623 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5112]) ).
thf(5463,plain,
! [SV2167: $i,SV1951: $i,SV1190: $i,SV590: $i] :
( ( ( c_in @ ( c_Pair @ SV590 @ SV1190 @ SV1951 @ SV1951 ) @ ( c_Relation_OId__on @ SV2167 @ SV1951 ) @ ( tc_prod @ SV1951 @ SV1951 ) )
= $false )
| ( ( SV590 = SV1190 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5113]) ).
thf(5464,plain,
! [SV2289: $i,SV2168: $i,SV1952: $i,SV1624: $i,SV1191: $i,SV591: $i] :
( ( ( ( c_Recdef_Ocut @ SV591 @ SV1191 @ SV1624 @ SV1952 @ SV2168 )
!= ( c_Recdef_Ocut @ SV2289 @ SV1191 @ SV1624 @ SV1952 @ SV2168 ) )
| ! [SY6029: $i] :
( ( ( hAPP @ SV591 @ SY6029 )
= ( hAPP @ SV2289 @ SY6029 ) )
| ~ ( c_in @ ( c_Pair @ SY6029 @ SV1624 @ SV1952 @ SV1952 ) @ SV1191 @ ( tc_prod @ SV1952 @ SV1952 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5114]) ).
thf(5465,plain,
! [SV594: $i,SV1194: $i,SV1626: $i] :
( ( ( c_Wellfounded_Owf @ SV1626 @ SV1194 )
= $false )
| ( ( c_in @ ( c_Pair @ SV594 @ SV594 @ SV1194 @ SV1194 ) @ SV1626 @ ( tc_prod @ SV1194 @ SV1194 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5117]) ).
thf(5466,plain,
! [SV2290: $i,SV2169: $i,SV1954: $i,SV1627: $i,SV1195: $i,SV595: $i] :
( ( ( c_in @ ( c_Pair @ SV595 @ SV1195 @ SV1627 @ SV1627 ) @ ( c_Relation_Oinv__image @ SV1954 @ SV2169 @ SV2290 @ SV1627 ) @ ( tc_prod @ SV1627 @ SV1627 ) )
| ~ ( c_in @ ( c_Pair @ ( hAPP @ SV2169 @ SV595 ) @ ( hAPP @ SV2169 @ SV1195 ) @ SV2290 @ SV2290 ) @ SV1954 @ ( tc_prod @ SV2290 @ SV2290 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5118]) ).
thf(5467,plain,
! [SV2170: $i,SV1955: $i,SV1628: $i,SV1196: $i,SV596: $i] :
( ( ( c_in @ ( c_Pair @ ( hAPP @ SV596 @ SV1196 ) @ ( hAPP @ SV596 @ SV1628 ) @ SV1955 @ SV1955 ) @ SV2170 @ ( tc_prod @ SV1955 @ SV1955 ) )
= $true )
| ( ( ! [SY5983: $i] :
~ ( c_in @ ( c_Pair @ SV1196 @ SV1628 @ SY5983 @ SY5983 ) @ ( c_Relation_Oinv__image @ SV2170 @ SV596 @ SV1955 @ SY5983 ) @ ( tc_prod @ SY5983 @ SY5983 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5119]) ).
thf(5468,plain,
! [SV1956: $i,SV1629: $i,SV597: $i,SV1197: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1197 @ SV597 @ SV1629 @ SV1629 ) @ SV1956 @ ( tc_prod @ SV1629 @ SV1629 ) ) )
= $true )
| ( ( ~ ( c_Relation_Osym @ SV1956 @ SV1629 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV597 @ SV1197 @ SV1629 @ SV1629 ) @ SV1956 @ ( tc_prod @ SV1629 @ SV1629 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5120]) ).
thf(5469,plain,
! [SV1957: $i,SV1630: $i,SV598: $i,SV1198: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1198 @ SV598 @ SV1630 @ SV1630 ) @ SV1957 @ ( tc_prod @ SV1630 @ SV1630 ) ) )
= $true )
| ( ( ~ ( c_Relation_Osym @ SV1957 @ SV1630 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV598 @ SV1198 @ SV1630 @ SV1630 ) @ SV1957 @ ( tc_prod @ SV1630 @ SV1630 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5121]) ).
thf(5470,plain,
! [SV2291: $i,SV2171: $i,SV1958: $i,SV1631: $i,SV1199: $i,SV599: $i] :
( ( ! [SY6030: $i] :
( ( c_in @ ( c_Pair @ SV599 @ SV1199 @ SV1631 @ SV1958 ) @ ( c_Relation_Orel__comp @ SV2171 @ SV2291 @ SV1631 @ SY6030 @ SV1958 ) @ ( tc_prod @ SV1631 @ SV1958 ) )
| ! [SY6031: $i] :
( ~ ( c_in @ ( c_Pair @ SY6031 @ SV1199 @ SY6030 @ SV1958 ) @ SV2291 @ ( tc_prod @ SY6030 @ SV1958 ) )
| ~ ( c_in @ ( c_Pair @ SV599 @ SY6031 @ SV1631 @ SY6030 ) @ SV2171 @ ( tc_prod @ SV1631 @ SY6030 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5122]) ).
thf(5471,plain,
! [SV600: $i,SV1959: $i,SV1632: $i,SV1200: $i,SV2292: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV2292 @ SV1200 @ SV1632 @ SV1632 ) @ SV1959 @ ( tc_prod @ SV1632 @ SV1632 ) )
| ~ ( c_in @ ( c_Pair @ SV600 @ SV2292 @ SV1632 @ SV1632 ) @ SV1959 @ ( tc_prod @ SV1632 @ SV1632 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV600 @ SV1200 @ SV1632 @ SV1632 ) @ ( c_Transitive__Closure_Otrancl @ SV1959 @ SV1632 ) @ ( tc_prod @ SV1632 @ SV1632 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5123]) ).
thf(5472,plain,
! [SV601: $i,SV1960: $i,SV1633: $i,SV1201: $i,SV2293: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV2293 @ SV1201 @ SV1633 @ SV1633 ) @ ( c_Transitive__Closure_Otrancl @ SV1960 @ SV1633 ) @ ( tc_prod @ SV1633 @ SV1633 ) )
| ~ ( c_in @ ( c_Pair @ SV601 @ SV2293 @ SV1633 @ SV1633 ) @ ( c_Transitive__Closure_Otrancl @ SV1960 @ SV1633 ) @ ( tc_prod @ SV1633 @ SV1633 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV601 @ SV1201 @ SV1633 @ SV1633 ) @ ( c_Transitive__Closure_Otrancl @ SV1960 @ SV1633 ) @ ( tc_prod @ SV1633 @ SV1633 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5124]) ).
thf(5473,plain,
! [SV1961: $i,SV1634: $i,SV1204: $i,SV604: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV604 @ SV1204 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1634 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( ( SV604 = SV1204 )
| ( SV604 = SV1961 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV604 @ SV1204 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omktop @ SV1634 ) @ SV1961 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5125]) ).
thf(5474,plain,
! [SV1962: $i,SV1635: $i,SV1205: $i,SV605: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV605 @ SV1205 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1635 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( ( SV1205 = SV1962 )
| ( SV605 = SV1962 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV605 @ SV1205 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omktop @ SV1635 ) @ SV1962 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5126]) ).
thf(5475,plain,
! [SV1637: $i,SV608: $i,SV2172: $i,SV1208: $i] :
( ( ( SV1208 = SV2172 )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV608 @ SV1208 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omktop @ SV1637 ) @ SV2172 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV608 @ SV1208 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1637 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5127]) ).
thf(5476,plain,
! [SV1963: $i,SV1639: $i,SV1212: $i,SV612: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV612 @ SV1212 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1639 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( ( SV612 = SV1212 )
| ( SV1212 = SV1963 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV612 @ SV1212 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omkbot @ SV1639 ) @ SV1963 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5129]) ).
thf(5477,plain,
! [SV1964: $i,SV1640: $i,SV1213: $i,SV613: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV613 @ SV1213 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1640 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( ( SV613 = SV1964 )
| ( SV1213 = SV1964 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV613 @ SV1213 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omkbot @ SV1640 ) @ SV1964 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5130]) ).
thf(5478,plain,
! [SV1641: $i,SV1215: $i,SV2175: $i,SV615: $i] :
( ( ( SV615 = SV2175 )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV615 @ SV1215 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omkbot @ SV1641 ) @ SV2175 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV615 @ SV1215 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1641 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5132]) ).
thf(5479,plain,
! [SV2294: $i,SV2176: $i,SV1965: $i,SV1642: $i,SV1217: $i,SV617: $i] :
( ( ( c_in @ ( c_Pair @ SV617 @ SV1217 @ SV1642 @ SV1965 ) @ ( c_Product__Type_OSigma @ SV2176 @ SV2294 @ SV1642 @ SV1965 ) @ ( tc_prod @ SV1642 @ SV1965 ) )
| ~ ( c_in @ SV1217 @ ( hAPP @ SV2294 @ SV617 ) @ SV1965 )
| ~ ( c_in @ SV617 @ SV2176 @ SV1642 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5133]) ).
thf(5480,plain,
! [SV2295: $i,SV2177: $i,SV1966: $i,SV1643: $i,SV1218: $i,SV618: $i] :
( ( ( c_in @ ( c_Pair @ SV618 @ SV1218 @ SV1643 @ SV1966 ) @ ( c_Product__Type_OSigma @ SV2177 @ SV2295 @ SV1643 @ SV1966 ) @ ( tc_prod @ SV1643 @ SV1966 ) )
| ~ ( c_in @ SV1218 @ ( hAPP @ SV2295 @ SV618 ) @ SV1966 )
| ~ ( c_in @ SV618 @ SV2177 @ SV1643 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5134]) ).
thf(5481,plain,
! [SV1219: $i,SV1644: $i,SV2178: $i,SV619: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV619 @ SV2178 @ SV1644 @ SV1644 ) @ SV1219 @ ( tc_prod @ SV1644 @ SV1644 ) ) )
= $true )
| ( ( ~ ( c_in @ SV2178 @ ( c_Wellfounded_Oacc @ SV1219 @ SV1644 ) @ SV1644 ) )
= $true )
| ( ( c_in @ SV619 @ ( c_Wellfounded_Oacc @ SV1219 @ SV1644 ) @ SV1644 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5135]) ).
thf(5482,plain,
! [SV1220: $i,SV1645: $i,SV2179: $i,SV620: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV620 @ SV2179 @ SV1645 @ SV1645 ) @ SV1220 @ ( tc_prod @ SV1645 @ SV1645 ) ) )
= $true )
| ( ( ~ ( c_in @ SV2179 @ ( c_Wellfounded_Oacc @ SV1220 @ SV1645 ) @ SV1645 ) )
= $true )
| ( ( c_in @ SV620 @ ( c_Wellfounded_Oacc @ SV1220 @ SV1645 ) @ SV1645 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5136]) ).
thf(5483,plain,
! [SV2180: $i,SV1967: $i,SV1646: $i,SV1221: $i,SV621: $i] :
( ( ( c_in @ SV621 @ ( c_Relation_OImage @ SV1221 @ SV1646 @ SV1967 @ SV2180 ) @ SV2180 )
= $true )
| ( ( ! [SY5989: $i] :
( ~ ( c_in @ ( c_Pair @ SY5989 @ SV621 @ SV1967 @ SV2180 ) @ SV1221 @ ( tc_prod @ SV1967 @ SV2180 ) )
| ~ ( c_in @ SY5989 @ SV1646 @ SV1967 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5137]) ).
thf(5484,plain,
! [SV2181: $i,SV1968: $i,SV1647: $i,SV1222: $i,SV622: $i] :
( ( ( c_in @ SV622 @ ( c_Relation_OImage @ SV1222 @ SV1647 @ SV1968 @ SV2181 ) @ SV2181 )
= $true )
| ( ( ! [SY5990: $i] :
( ~ ( c_in @ ( c_Pair @ SY5990 @ SV622 @ SV1968 @ SV2181 ) @ SV1222 @ ( tc_prod @ SV1968 @ SV2181 ) )
| ~ ( c_in @ SY5990 @ SV1647 @ SV1968 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5138]) ).
thf(5485,plain,
! [SV1223: $i,SV1648: $i,SV2182: $i,SV623: $i] :
( ( ( c_in @ ( c_Pair @ SV623 @ SV2182 @ SV1648 @ SV1648 ) @ ( c_Relation_OId__on @ SV1223 @ SV1648 ) @ ( tc_prod @ SV1648 @ SV1648 ) )
= $false )
| ( ( c_in @ SV623 @ SV1223 @ SV1648 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5139]) ).
thf(5486,plain,
! [SV1225: $i,SV2296: $i,SV1650: $i,SV625: $i,SV2183: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV2183 @ SV625 @ SV1650 @ SV1650 ) @ SV2296 @ ( tc_prod @ SV1650 @ SV1650 ) )
| ~ ( c_Equiv__Relations_Oequiv @ SV1225 @ SV2296 @ SV1650 ) )
= $true )
| ( ( c_in @ SV625 @ SV1225 @ SV1650 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5141]) ).
thf(5487,plain,
! [SV1226: $i,SV2297: $i,SV1651: $i,SV2184: $i,SV626: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV626 @ SV2184 @ SV1651 @ SV1651 ) @ SV2297 @ ( tc_prod @ SV1651 @ SV1651 ) )
| ~ ( c_Equiv__Relations_Oequiv @ SV1226 @ SV2297 @ SV1651 ) )
= $true )
| ( ( c_in @ SV626 @ SV1226 @ SV1651 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5142]) ).
thf(5488,plain,
! [SV1227: $i,SV1969: $i,SV1652: $i,SV627: $i,SV2298: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV2298 @ SV627 @ SV1652 @ SV1969 ) @ SV1227 @ ( tc_prod @ SV1652 @ SV1969 ) ) )
= $true )
| ( ( c_in @ SV627 @ ( c_Relation_ORange @ SV1227 @ SV1652 @ SV1969 ) @ SV1969 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5143]) ).
thf(5489,plain,
! [SV1228: $i,SV1970: $i,SV1653: $i,SV628: $i,SV2299: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV2299 @ SV628 @ SV1653 @ SV1970 ) @ SV1228 @ ( tc_prod @ SV1653 @ SV1970 ) ) )
= $true )
| ( ( c_in @ SV628 @ ( c_Relation_ORange @ SV1228 @ SV1653 @ SV1970 ) @ SV1970 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5144]) ).
thf(5490,plain,
! [SV1229: $i,SV1971: $i,SV1654: $i,SV2300: $i,SV629: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV629 @ SV2300 @ SV1654 @ SV1971 ) @ SV1229 @ ( tc_prod @ SV1654 @ SV1971 ) ) )
= $true )
| ( ( c_in @ SV629 @ ( c_Relation_ODomain @ SV1229 @ SV1654 @ SV1971 ) @ SV1654 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5145]) ).
thf(5491,plain,
! [SV1230: $i,SV1972: $i,SV1655: $i,SV2301: $i,SV630: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV630 @ SV2301 @ SV1655 @ SV1972 ) @ SV1230 @ ( tc_prod @ SV1655 @ SV1972 ) ) )
= $true )
| ( ( c_in @ SV630 @ ( c_Relation_ODomain @ SV1230 @ SV1655 @ SV1972 ) @ SV1655 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5146]) ).
thf(5492,plain,
! [SV1231: $i,SV1973: $i,SV2302: $i,SV631: $i,SV1656: $i] :
( ( ( ! [SY6032: $i] :
~ ( c_in @ ( c_Pair @ SV1656 @ SV631 @ SV2302 @ SV1973 ) @ ( c_Product__Type_OSigma @ SY6032 @ SV1231 @ SV2302 @ SV1973 ) @ ( tc_prod @ SV2302 @ SV1973 ) ) )
= $true )
| ( ( c_in @ SV631 @ ( hAPP @ SV1231 @ SV1656 ) @ SV1973 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5147]) ).
thf(5493,plain,
! [SV1232: $i,SV2303: $i,SV1657: $i,SV1974: $i,SV632: $i] :
( ( ( ! [SY6033: $i] :
~ ( c_in @ ( c_Pair @ SV632 @ SV1974 @ SV1657 @ SV2303 ) @ ( c_Product__Type_OSigma @ SV1232 @ SY6033 @ SV1657 @ SV2303 ) @ ( tc_prod @ SV1657 @ SV2303 ) ) )
= $true )
| ( ( c_in @ SV632 @ SV1232 @ SV1657 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5148]) ).
thf(5494,plain,
! [SV1975: $i,SV1658: $i,SV633: $i,SV1233: $i] :
( ( ( c_in @ ( c_Pair @ SV1233 @ SV633 @ SV1658 @ SV1658 ) @ SV1975 @ ( tc_prod @ SV1658 @ SV1658 ) )
= $true )
| ( ( ( SV1233 = SV633 )
| ! [SY5890: $i] :
( ~ ( c_in @ SV633 @ SY5890 @ SV1658 )
| ~ ( c_in @ SV1233 @ SY5890 @ SV1658 )
| ~ ( c_Relation_Ototal__on @ SY5890 @ SV1975 @ SV1658 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV633 @ SV1233 @ SV1658 @ SV1658 ) @ SV1975 @ ( tc_prod @ SV1658 @ SV1658 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5149]) ).
thf(5495,plain,
! [SV1659: $i,SV1234: $i,SV2185: $i,SV634: $i] :
( ( ( ~ ( c_in @ SV634 @ SV2185 @ SV1234 ) )
= $true )
| ( ( ~ ( c_Relation_Orefl__on @ SV2185 @ SV1659 @ SV1234 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV634 @ SV634 @ SV1234 @ SV1234 ) @ SV1659 @ ( tc_prod @ SV1234 @ SV1234 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5150]) ).
thf(5496,plain,
! [SV1235: $i,SV2304: $i,SV1660: $i,SV635: $i,SV2186: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV2186 @ SV635 @ SV1660 @ SV1660 ) @ SV2304 @ ( tc_prod @ SV1660 @ SV1660 ) )
| ~ ( c_Relation_Orefl__on @ SV1235 @ SV2304 @ SV1660 ) )
= $true )
| ( ( c_in @ SV635 @ SV1235 @ SV1660 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5151]) ).
thf(5497,plain,
! [SV1236: $i,SV2305: $i,SV1661: $i,SV2187: $i,SV636: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV636 @ SV2187 @ SV1661 @ SV1661 ) @ SV2305 @ ( tc_prod @ SV1661 @ SV1661 ) )
| ~ ( c_Relation_Orefl__on @ SV1236 @ SV2305 @ SV1661 ) )
= $true )
| ( ( c_in @ SV636 @ SV1236 @ SV1661 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5152]) ).
thf(5498,plain,
! [SV1662: $i,SV1237: $i,SV2188: $i,SV637: $i] :
( ( ( ~ ( c_in @ SV637 @ SV2188 @ SV1237 ) )
= $true )
| ( ( ~ ( c_Relation_Orefl__on @ SV2188 @ SV1662 @ SV1237 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV637 @ SV637 @ SV1237 @ SV1237 ) @ SV1662 @ ( tc_prod @ SV1237 @ SV1237 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5153]) ).
thf(5499,plain,
! [SV2306: $i,SV2189: $i,SV1976: $i,SV1663: $i,SV1238: $i,SV638: $i] :
( ( ( ( c_Pair @ SV638 @ SV1238 @ SV1663 @ SV1976 )
!= ( c_Pair @ SV2189 @ SV2306 @ SV1663 @ SV1976 ) )
| ( SV1238 = SV2306 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5154]) ).
thf(5500,plain,
! [SV2190: $i,SV1977: $i,SV1664: $i,SV1239: $i,SV639: $i] :
( ( ( ! [SY5996: $i] :
( ( c_Pair @ SV639 @ SV1239 @ SV1664 @ SV1977 )
!= ( c_Pair @ SV2190 @ SY5996 @ SV1664 @ SV1977 ) ) )
= $true )
| ( ( SV639 = SV2190 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5155]) ).
thf(5501,plain,
! [SV1674: $i,SV1263: $i,SV665: $i,SV14: $i] :
( ( ( ( hAPP @ ( c_fst @ SV14 @ SV665 ) @ SV1263 )
!= ( hAPP @ ( c_fst @ SV14 @ SV665 ) @ SV1674 ) )
= $true )
| ( ( SV1263 = SV1674 )
= $true )
| ( ( ( hAPP @ ( c_snd @ SV14 @ SV665 ) @ SV1263 )
= ( hAPP @ ( c_snd @ SV14 @ SV665 ) @ SV1674 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5160]) ).
thf(5502,plain,
! [SV1675: $i,SV1264: $i,SV666: $i,SV15: $i] :
( ( ( ( hAPP @ ( c_fst @ SV15 @ SV666 ) @ SV1264 )
!= ( hAPP @ ( c_fst @ SV15 @ SV666 ) @ SV1675 ) )
= $true )
| ( ( SV1264 = SV1675 )
= $true )
| ( ( ( hAPP @ ( c_snd @ SV15 @ SV666 ) @ SV1264 )
= ( hAPP @ ( c_snd @ SV15 @ SV666 ) @ SV1675 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5161]) ).
thf(5503,plain,
! [SV667: $i,SV1981: $i,SV1676: $i,SV16: $i] :
( ( ( hBOOL @ ( hAPP @ SV16 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1 @ SV16 @ SV1676 @ SV1981 ) ) )
= $false )
| ( ( ~ ( c_Wellfounded_Owf @ SV1676 @ SV1981 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV16 @ SV667 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5162]) ).
thf(5504,plain,
! [SV1269: $i,SV672: $i,SV1680: $i,SV1983: $i,SV21: $i] :
( ( ( ~ ( c_lessequals @ SV21 @ SV1983 @ ( tc_fun @ SV1680 @ tc_bool ) ) )
= $true )
| ( ( ! [SY5180: $i] :
~ ( c_in @ SY5180 @ SV672 @ SV1269 ) )
= $true )
| ( ( c_lessequals @ ( c_Product__Type_OSigma @ SV21 @ ( c_COMBK @ SV672 @ ( tc_fun @ SV1269 @ tc_bool ) @ SV1680 ) @ SV1680 @ SV1269 ) @ ( c_Product__Type_OSigma @ SV1983 @ ( c_COMBK @ SV672 @ ( tc_fun @ SV1269 @ tc_bool ) @ SV1680 ) @ SV1680 @ SV1269 ) @ ( tc_fun @ ( tc_prod @ SV1680 @ SV1269 ) @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5166]) ).
thf(5505,plain,
! [SV673: $i,SV1270: $i,SV2191: $i,SV1681: $i,SV22: $i] :
( ( ( ~ ( c_lessequals @ ( c_Product__Type_OSigma @ SV22 @ ( c_COMBK @ SV1681 @ ( tc_fun @ SV2191 @ tc_bool ) @ SV1270 ) @ SV1270 @ SV2191 ) @ ( c_Product__Type_OSigma @ SV673 @ ( c_COMBK @ SV1681 @ ( tc_fun @ SV2191 @ tc_bool ) @ SV1270 ) @ SV1270 @ SV2191 ) @ ( tc_fun @ ( tc_prod @ SV1270 @ SV2191 ) @ tc_bool ) ) )
= $true )
| ( ( ! [SY5997: $i] :
~ ( c_in @ SY5997 @ SV1681 @ SV2191 ) )
= $true )
| ( ( c_lessequals @ SV22 @ SV673 @ ( tc_fun @ SV1270 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5167]) ).
thf(5506,plain,
! [SV1271: $i,SV1682: $i,SV23: $i,SV674: $i] :
( ( ( c_in @ SV674 @ SV23 @ SV1682 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV23 @ ( c_Set_Oinsert @ SV674 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1682 @ tc_bool ) ) @ SV1682 ) @ ( tc_fun @ SV1682 @ tc_bool ) ) @ SV1271 @ ( tc_fun @ SV1682 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV23 @ ( c_Set_Oinsert @ SV674 @ SV1271 @ SV1682 ) @ ( tc_fun @ SV1682 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5168]) ).
thf(5507,plain,
! [SV1272: $i,SV1683: $i,SV24: $i,SV675: $i] :
( ( ( c_in @ SV675 @ SV24 @ SV1683 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV24 @ ( c_Set_Oinsert @ SV675 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1683 @ tc_bool ) ) @ SV1683 ) @ ( tc_fun @ SV1683 @ tc_bool ) ) @ SV1272 @ ( tc_fun @ SV1683 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV24 @ ( c_Set_Oinsert @ SV675 @ SV1272 @ SV1683 ) @ ( tc_fun @ SV1683 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5169]) ).
thf(5508,plain,
! [SV1684: $i,SV1273: $i,SV25: $i,SV676: $i] :
( ( ( c_in @ SV676 @ SV25 @ SV1273 )
= $false )
| ( ( ~ ( c_lessequals @ SV25 @ ( c_Set_Oinsert @ SV676 @ SV1684 @ SV1273 ) @ ( tc_fun @ SV1273 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV25 @ ( c_Set_Oinsert @ SV676 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1273 @ tc_bool ) ) @ SV1273 ) @ ( tc_fun @ SV1273 @ tc_bool ) ) @ SV1684 @ ( tc_fun @ SV1273 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5170]) ).
thf(5509,plain,
! [SV677: $i,SV26: $i,SV1274: $i,SV1685: $i,SV2192: $i] :
( ( ( c_in @ SV2192 @ SV1685 @ SV1274 )
= $false )
| ( ( ( c_Set_Oimage @ ( c_COMBK @ SV26 @ SV677 @ SV1274 ) @ SV1685 @ SV1274 @ SV677 )
= ( c_Set_Oinsert @ SV26 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV677 @ tc_bool ) ) @ SV677 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5171]) ).
thf(5510,plain,
! [SV678: $i,SV1275: $i,SV27: $i] :
( ( ( c_lessequals @ SV27 @ SV1275 @ ( tc_fun @ ( tc_prod @ SV678 @ SV678 ) @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( c_Relation_Orel__comp @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Transitive__Closure_Otrancl @ SV27 @ SV678 ) @ SV1275 @ ( tc_fun @ ( tc_prod @ SV678 @ SV678 ) @ tc_bool ) ) @ SV27 @ SV678 @ SV678 @ SV678 ) @ SV1275 @ ( tc_fun @ ( tc_prod @ SV678 @ SV678 ) @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( c_Transitive__Closure_Otrancl @ SV27 @ SV678 ) @ SV1275 @ ( tc_fun @ ( tc_prod @ SV678 @ SV678 ) @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5172]) ).
thf(5511,plain,
! [SV2307: $i,SV2195: $i,SV1987: $i,SV1692: $i,SV1282: $i,SV690: $i,SV40: $i] :
( ( ( c_lessequals @ ( c_Relation_Orel__comp @ SV40 @ SV690 @ SV1282 @ SV1692 @ SV1987 ) @ ( c_Relation_Orel__comp @ SV2195 @ SV2307 @ SV1282 @ SV1692 @ SV1987 ) @ ( tc_fun @ ( tc_prod @ SV1282 @ SV1987 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV690 @ SV2307 @ ( tc_fun @ ( tc_prod @ SV1692 @ SV1987 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV40 @ SV2195 @ ( tc_fun @ ( tc_prod @ SV1282 @ SV1692 ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5175]) ).
thf(5512,plain,
! [SV693: $i,SV1990: $i,SV1695: $i,SV43: $i] :
( ( ( hBOOL @ ( hAPP @ SV43 @ ( c_List_Osko__Recdef__Xtfl__wf__induct__1__1 @ SV43 @ SV1695 @ SV1990 ) ) )
= $false )
| ( ( ~ ( c_Wellfounded_Owf @ SV1695 @ SV1990 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV43 @ SV693 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5176]) ).
thf(5513,plain,
! [SV701: $i,SV1291: $i,SV1698: $i,SV1991: $i,SV2308: $i,SV51: $i] :
( ( ( ~ ( c_lessequals @ SV51 @ ( c_Product__Type_OSigma @ SV2308 @ ( c_COMBK @ SV1991 @ ( tc_fun @ SV1698 @ tc_bool ) @ SV1291 ) @ SV1291 @ SV1698 ) @ ( tc_fun @ ( tc_prod @ SV1291 @ SV1698 ) @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( c_Relation_OImage @ SV51 @ SV701 @ SV1291 @ SV1698 ) @ SV1991 @ ( tc_fun @ SV1698 @ tc_bool ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5177]) ).
thf(5514,plain,
! [SV2309: $i,SV52: $i,SV1992: $i,SV702: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV702 @ SV1992 @ SV52 )
!= ( c_HOL_Ominus__class_Ominus @ SV2309 @ SV2309 @ SV52 ) )
= $true )
| ( ( SV702 = SV1992 )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV52 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5178]) ).
thf(5515,plain,
! [SV2196: $i,SV1993: $i,SV53: $i,SV703: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV703 @ SV703 @ SV53 )
!= ( c_HOL_Ominus__class_Ominus @ SV1993 @ SV2196 @ SV53 ) )
= $true )
| ( ( SV1993 = SV2196 )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV53 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5179]) ).
thf(5516,plain,
! [SV64: $i,SV1999: $i,SV1702: $i] :
( ( ( c_lessequals @ SV1702 @ SV1999 @ SV64 )
= $false )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV1702 @ SV1999 @ SV64 )
= SV1702 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV64 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5184]) ).
thf(5517,plain,
! [SV65: $i,SV2000: $i,SV1703: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV1703 @ SV2000 @ SV65 )
= SV1703 )
= $false )
| ( ( c_lessequals @ SV1703 @ SV2000 @ SV65 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV65 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5185]) ).
thf(5518,plain,
! [SV66: $i,SV1704: $i,SV2001: $i] :
( ( ( c_lessequals @ SV2001 @ SV1704 @ SV66 )
= $false )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV1704 @ SV2001 @ SV66 )
= SV2001 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV66 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5186]) ).
thf(5519,plain,
! [SV67: $i,SV1298: $i,SV1705: $i,SV714: $i] :
( ( ( c_lessequals @ SV714 @ SV1705 @ ( tc_fun @ SV1298 @ tc_bool ) )
= $false )
| ( ( ~ ( c_lessequals @ SV67 @ SV1705 @ ( tc_fun @ SV1298 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV67 @ SV714 @ ( tc_fun @ SV1298 @ tc_bool ) ) @ SV1705 @ ( tc_fun @ SV1298 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5187]) ).
thf(5520,plain,
! [SV70: $i,SV1301: $i,SV1706: $i,SV717: $i] :
( ( ( c_lessequals @ SV717 @ SV1706 @ ( tc_fun @ SV1301 @ tc_bool ) )
= $false )
| ( ( ~ ( c_lessequals @ SV70 @ SV1706 @ ( tc_fun @ SV1301 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV70 @ SV717 @ ( tc_fun @ SV1301 @ tc_bool ) ) @ SV1706 @ ( tc_fun @ SV1301 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5188]) ).
thf(5521,plain,
! [SV2201: $i,SV71: $i,SV2002: $i,SV718: $i] :
( ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV718 @ SV2002 @ SV71 ) @ SV2201 @ SV71 )
= $true )
| ( ( ~ ( c_lessequals @ SV2002 @ SV2201 @ SV71 )
| ~ ( c_lessequals @ SV718 @ SV2201 @ SV71 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV71 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5189]) ).
thf(5522,plain,
! [SV2202: $i,SV74: $i,SV2005: $i,SV719: $i] :
( ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV719 @ SV2005 @ SV74 ) @ SV2202 @ SV74 )
= $true )
| ( ( ~ ( c_lessequals @ SV2005 @ SV2202 @ SV74 )
| ~ ( c_lessequals @ SV719 @ SV2202 @ SV74 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV74 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5190]) ).
thf(5523,plain,
! [SV2203: $i,SV75: $i,SV2006: $i,SV720: $i] :
( ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV720 @ SV2006 @ SV75 ) @ SV2203 @ SV75 )
= $true )
| ( ( ~ ( c_lessequals @ SV2006 @ SV2203 @ SV75 )
| ~ ( c_lessequals @ SV720 @ SV2203 @ SV75 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV75 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5191]) ).
thf(5524,plain,
! [SV83: $i,SV1304: $i,SV1713: $i,SV724: $i] :
( ( ( c_in @ ( c_Pair @ SV724 @ SV1713 @ SV1304 @ SV1304 ) @ SV83 @ ( tc_prod @ SV1304 @ SV1304 ) )
= $false )
| ( ( ! [SY5214: $i] :
~ ( c_Equiv__Relations_Oequiv @ SY5214 @ SV83 @ SV1304 ) )
= $true )
| ( ( c_lessequals @ ( c_Relation_OImage @ SV83 @ ( c_Set_Oinsert @ SV724 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1304 @ tc_bool ) ) @ SV1304 ) @ SV1304 @ SV1304 ) @ ( c_Relation_OImage @ SV83 @ ( c_Set_Oinsert @ SV1713 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1304 @ tc_bool ) ) @ SV1304 ) @ SV1304 @ SV1304 ) @ ( tc_fun @ SV1304 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5192]) ).
thf(5525,plain,
! [SV727: $i,SV2204: $i,SV86: $i,SV1714: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV1714 @ SV86 @ SV2204 ) @ SV727 ) )
= $false )
| ( ( SV1714 = SV727 )
= $true )
| ( ( hBOOL @ ( hAPP @ SV86 @ SV727 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5193]) ).
thf(5526,plain,
! [SV729: $i,SV1308: $i,SV88: $i] :
( ( ( c_Relation_Osym @ SV88 @ SV1308 )
= $false )
| ( ( c_Relation_Osym @ SV729 @ SV1308 )
= $false )
| ( ( c_Relation_Osym @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV88 @ SV729 @ ( tc_fun @ ( tc_prod @ SV1308 @ SV1308 ) @ tc_bool ) ) @ SV1308 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5194]) ).
thf(5527,plain,
! [SV2310: $i,SV2205: $i,SV2015: $i,SV1724: $i,SV1317: $i,SV742: $i,SV103: $i] :
( ( ( c_lessequals @ ( c_Relation_Orel__comp @ SV103 @ SV742 @ SV1317 @ SV1724 @ SV2015 ) @ ( c_Product__Type_OSigma @ SV2205 @ ( c_COMBK @ SV2310 @ ( tc_fun @ SV2015 @ tc_bool ) @ SV1317 ) @ SV1317 @ SV2015 ) @ ( tc_fun @ ( tc_prod @ SV1317 @ SV2015 ) @ tc_bool ) )
| ! [SY6034: $i] :
( ~ ( c_lessequals @ SV742 @ ( c_Product__Type_OSigma @ SY6034 @ ( c_COMBK @ SV2310 @ ( tc_fun @ SV2015 @ tc_bool ) @ SV1724 ) @ SV1724 @ SV2015 ) @ ( tc_fun @ ( tc_prod @ SV1724 @ SV2015 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV103 @ ( c_Product__Type_OSigma @ SV2205 @ ( c_COMBK @ SY6034 @ ( tc_fun @ SV1724 @ tc_bool ) @ SV1317 ) @ SV1317 @ SV1724 ) @ ( tc_fun @ ( tc_prod @ SV1317 @ SV1724 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5197]) ).
thf(5528,plain,
! [SV104: $i,SV1318: $i,SV743: $i] :
( ( ( ~ ( c_Wellfounded_Owf @ SV743 @ SV1318 ) )
= $true )
| ( ( ~ ( c_Wellfounded_Owf @ SV104 @ SV1318 ) )
= $true )
| ( ( c_lessequals @ ( c_Relation_Orel__comp @ SV104 @ SV743 @ SV1318 @ SV1318 @ SV1318 ) @ SV104 @ ( tc_fun @ ( tc_prod @ SV1318 @ SV1318 ) @ tc_bool ) )
= $false )
| ( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV104 @ SV743 @ ( tc_fun @ ( tc_prod @ SV1318 @ SV1318 ) @ tc_bool ) ) @ SV1318 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5198]) ).
thf(5529,plain,
! [SV744: $i,SV2206: $i,SV105: $i,SV1725: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1725 @ SV105 @ ( tc_fun @ SV2206 @ tc_bool ) ) @ SV744 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV1725 @ SV744 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV105 @ SV744 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5199]) ).
thf(5530,plain,
! [SV108: $i,SV747: $i,SV1321: $i] :
( ( ( c_Wellfounded_Owf @ SV1321 @ SV747 )
= $false )
| ( ( ~ ( c_Wellfounded_Owf @ SV108 @ SV747 )
| ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV108 @ SV1321 @ ( tc_fun @ ( tc_prod @ SV747 @ SV747 ) @ tc_bool ) ) @ SV747 ) )
= $true )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_ODomain @ SV108 @ SV747 @ SV747 ) @ ( c_Relation_ORange @ SV1321 @ SV747 @ SV747 ) @ ( tc_fun @ SV747 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV747 @ tc_bool ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5202]) ).
thf(5531,plain,
! [SV1729: $i,SV110: $i,SV1323: $i,SV2017: $i,SV749: $i] :
( ( ( ~ ( c_Relation_Orefl__on @ SV749 @ SV2017 @ SV1323 ) )
= $true )
| ( ( ~ ( c_Relation_Orefl__on @ SV110 @ SV1729 @ SV1323 ) )
= $true )
| ( ( c_Relation_Orefl__on @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV110 @ SV749 @ ( tc_fun @ SV1323 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1729 @ SV2017 @ ( tc_fun @ ( tc_prod @ SV1323 @ SV1323 ) @ tc_bool ) ) @ SV1323 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5203]) ).
thf(5532,plain,
! [SV123: $i,SV760: $i,SV1735: $i] :
( ( ( c_Wellfounded_Owf @ SV1735 @ SV760 )
= $false )
| ( ( c_lessequals @ SV123 @ ( c_Relation_OImage @ SV1735 @ SV123 @ SV760 @ SV760 ) @ ( tc_fun @ SV760 @ tc_bool ) )
= $false )
| ( ( SV123
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV760 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5209]) ).
thf(5533,plain,
! [SV1739: $i,SV128: $i,SV1330: $i,SV765: $i,SV2023: $i] :
( ( ( ~ ( c_lessequals @ SV2023 @ SV765 @ ( tc_fun @ SV1330 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV128 @ SV1739 @ ( tc_fun @ SV1330 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV128 @ SV765 @ ( tc_fun @ SV1330 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV1739 @ SV2023 @ ( tc_fun @ SV1330 @ tc_bool ) ) @ ( tc_fun @ SV1330 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5210]) ).
thf(5534,plain,
! [SV766: $i,SV1331: $i,SV2212: $i,SV129: $i] :
( ( ( ~ ( c_in @ SV129 @ SV2212 @ SV1331 ) )
= $true )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV2212 @ SV766 @ ( tc_fun @ SV1331 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1331 @ tc_bool ) ) )
= $true )
| ( ( c_in @ SV129 @ SV766 @ SV1331 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5211]) ).
thf(5535,plain,
! [SV767: $i,SV1332: $i,SV130: $i] :
( ( ( c_Relation_Otrans @ SV130 @ SV1332 )
= $false )
| ( ( c_Relation_Otrans @ SV767 @ SV1332 )
= $false )
| ( ( c_Relation_Otrans @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV130 @ SV767 @ ( tc_fun @ ( tc_prod @ SV1332 @ SV1332 ) @ tc_bool ) ) @ SV1332 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5212]) ).
thf(5536,plain,
! [SV134: $i,SV1334: $i,SV770: $i,SV2214: $i] :
( ( ( ( c_Relation_Orel__comp @ SV2214 @ SV770 @ SV1334 @ SV1334 @ SV1334 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV1334 @ SV1334 ) @ tc_bool ) ) )
= $true )
| ( ( ( c_Relation_Orel__comp @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV2214 @ SV134 @ ( tc_fun @ ( tc_prod @ SV1334 @ SV1334 ) @ tc_bool ) ) @ SV770 @ SV1334 @ SV1334 @ SV1334 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV1334 @ SV1334 ) @ tc_bool ) ) )
= $true )
| ( ( ( c_Relation_Orel__comp @ SV134 @ SV770 @ SV1334 @ SV1334 @ SV1334 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV1334 @ SV1334 ) @ tc_bool ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5214]) ).
thf(5537,plain,
! [SV771: $i,SV1335: $i,SV2215: $i,SV135: $i] :
( ( ( ( c_Relation_Orel__comp @ SV135 @ SV2215 @ SV1335 @ SV1335 @ SV1335 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV1335 @ SV1335 ) @ tc_bool ) ) )
= $true )
| ( ( ( c_Relation_Orel__comp @ SV135 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV2215 @ SV771 @ ( tc_fun @ ( tc_prod @ SV1335 @ SV1335 ) @ tc_bool ) ) @ SV1335 @ SV1335 @ SV1335 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV1335 @ SV1335 ) @ tc_bool ) ) )
= $true )
| ( ( ( c_Relation_Orel__comp @ SV135 @ SV771 @ SV1335 @ SV1335 @ SV1335 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV1335 @ SV1335 ) @ tc_bool ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5215]) ).
thf(5538,plain,
! [SV772: $i,SV2026: $i,SV1742: $i,SV136: $i] :
( ( ( hBOOL @ ( hAPP @ SV136 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1 @ SV136 @ SV1742 @ SV2026 ) ) )
= $false )
| ( ( ~ ( c_Wellfounded_Owf @ SV1742 @ SV2026 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV136 @ SV772 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5216]) ).
thf(5539,plain,
! [SV1743: $i,SV775: $i,SV139: $i] :
( ( ( c_lessequals @ SV139 @ SV775 @ ( tc_fun @ SV1743 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV775 @ SV139 @ ( tc_fun @ SV1743 @ tc_bool ) )
= $false )
| ( ( SV139 = SV775 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5217]) ).
thf(5540,plain,
! [SV1744: $i,SV776: $i,SV140: $i] :
( ( ( c_lessequals @ SV140 @ SV776 @ ( tc_fun @ SV1744 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV776 @ SV140 @ ( tc_fun @ SV1744 @ tc_bool ) )
= $false )
| ( ( SV140 = SV776 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5218]) ).
thf(5541,plain,
! [SV141: $i,SV1745: $i,SV2027: $i] :
( ( ( ~ ( c_lessequals @ SV2027 @ SV1745 @ SV141 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1745 @ SV2027 @ SV141 ) )
= $true )
| ( ( SV1745 = SV2027 )
= $true )
| ( ( class_Orderings_Oorder @ SV141 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5219]) ).
thf(5542,plain,
! [SV142: $i,SV1746: $i,SV2028: $i] :
( ( ( ~ ( c_lessequals @ SV2028 @ SV1746 @ SV142 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1746 @ SV2028 @ SV142 ) )
= $true )
| ( ( SV1746 = SV2028 )
= $true )
| ( ( class_Orderings_Oorder @ SV142 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5220]) ).
thf(5543,plain,
! [SV144: $i,SV2030: $i,SV1748: $i] :
( ( ( ~ ( c_lessequals @ SV1748 @ SV2030 @ SV144 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV2030 @ SV1748 @ SV144 ) )
= $true )
| ( ( SV1748 = SV2030 )
= $true )
| ( ( class_Orderings_Oorder @ SV144 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5221]) ).
thf(5544,plain,
! [SV147: $i,SV1750: $i,SV2032: $i] :
( ( ( c_lessequals @ SV2032 @ SV1750 @ SV147 )
= $false )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1750 @ SV2032 @ SV147 )
= SV1750 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV147 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5222]) ).
thf(5545,plain,
! [SV148: $i,SV2033: $i,SV1751: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1751 @ SV2033 @ SV148 )
= SV2033 )
= $false )
| ( ( c_lessequals @ SV1751 @ SV2033 @ SV148 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV148 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5223]) ).
thf(5546,plain,
! [SV149: $i,SV2034: $i,SV1752: $i] :
( ( ( c_lessequals @ SV1752 @ SV2034 @ SV149 )
= $false )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1752 @ SV2034 @ SV149 )
= SV2034 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV149 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5224]) ).
thf(5547,plain,
! [SV1753: $i,SV153: $i,SV1341: $i,SV2035: $i,SV782: $i] :
( ( ( ~ ( c_Relation_Orefl__on @ SV782 @ SV2035 @ SV1341 ) )
= $true )
| ( ( ~ ( c_Relation_Orefl__on @ SV153 @ SV1753 @ SV1341 ) )
= $true )
| ( ( c_Relation_Orefl__on @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV153 @ SV782 @ ( tc_fun @ SV1341 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1753 @ SV2035 @ ( tc_fun @ ( tc_prod @ SV1341 @ SV1341 ) @ tc_bool ) ) @ SV1341 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5225]) ).
thf(5548,plain,
! [SV2036: $i,SV1754: $i,SV1342: $i,SV784: $i,SV156: $i] :
( ( ( ( c_Set_Oinsert @ SV156 @ ( c_Set_Oinsert @ SV784 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1342 @ tc_bool ) ) @ SV1342 ) @ SV1342 )
= ( c_Set_Oinsert @ SV1754 @ ( c_Set_Oinsert @ SV2036 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1342 @ tc_bool ) ) @ SV1342 ) @ SV1342 ) )
= $false )
| ( ( ( SV156 = SV2036 )
| ( SV156 = SV1754 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5226]) ).
thf(5549,plain,
! [SV2216: $i,SV1755: $i,SV1343: $i,SV785: $i,SV157: $i] :
( ( ( ( c_Set_Oinsert @ SV157 @ ( c_Set_Oinsert @ SV785 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1343 @ tc_bool ) ) @ SV1343 ) @ SV1343 )
= ( c_Set_Oinsert @ SV1755 @ ( c_Set_Oinsert @ SV2216 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1343 @ tc_bool ) ) @ SV1343 ) @ SV1343 ) )
= $false )
| ( ( ( SV785 = SV1755 )
| ( SV157 = SV1755 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5227]) ).
thf(5550,plain,
! [SV2037: $i,SV1756: $i,SV1344: $i,SV786: $i,SV158: $i] :
( ( ( ( c_Set_Oinsert @ SV158 @ ( c_Set_Oinsert @ SV786 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1344 @ tc_bool ) ) @ SV1344 ) @ SV1344 )
= ( c_Set_Oinsert @ SV1756 @ ( c_Set_Oinsert @ SV2037 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1344 @ tc_bool ) ) @ SV1344 ) @ SV1344 ) )
= $false )
| ( ( ( SV158 = SV2037 )
| ( SV786 = SV2037 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5228]) ).
thf(5551,plain,
! [SV2038: $i,SV1757: $i,SV1345: $i,SV787: $i,SV159: $i] :
( ( ( ( c_Set_Oinsert @ SV159 @ ( c_Set_Oinsert @ SV787 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1345 @ tc_bool ) ) @ SV1345 ) @ SV1345 )
= ( c_Set_Oinsert @ SV1757 @ ( c_Set_Oinsert @ SV2038 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1345 @ tc_bool ) ) @ SV1345 ) @ SV1345 ) )
= $false )
| ( ( ( SV787 = SV1757 )
| ( SV787 = SV2038 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5229]) ).
thf(5552,plain,
! [SV1761: $i,SV170: $i,SV1352: $i,SV2040: $i,SV796: $i] :
( ( ( ~ ( c_lessequals @ SV796 @ SV2040 @ ( tc_fun @ SV1352 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV170 @ SV1761 @ ( tc_fun @ SV1352 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV170 @ SV796 @ ( tc_fun @ SV1352 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1761 @ SV2040 @ ( tc_fun @ SV1352 @ tc_bool ) ) @ ( tc_fun @ SV1352 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5232]) ).
thf(5553,plain,
! [SV174: $i,SV2217: $i,SV2043: $i,SV798: $i] :
( ( ( c_lessequals @ SV798 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2043 @ SV2217 @ SV174 ) @ SV174 )
= $true )
| ( ( ~ ( c_lessequals @ SV798 @ SV2217 @ SV174 )
| ~ ( c_lessequals @ SV798 @ SV2043 @ SV174 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV174 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5233]) ).
thf(5554,plain,
! [SV175: $i,SV2218: $i,SV2044: $i,SV799: $i] :
( ( ( c_lessequals @ SV799 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2044 @ SV2218 @ SV175 ) @ SV175 )
= $true )
| ( ( ~ ( c_lessequals @ SV799 @ SV2218 @ SV175 )
| ~ ( c_lessequals @ SV799 @ SV2044 @ SV175 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV175 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5234]) ).
thf(5555,plain,
! [SV176: $i,SV2219: $i,SV2045: $i,SV800: $i] :
( ( ( c_lessequals @ SV800 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2045 @ SV2219 @ SV176 ) @ SV176 )
= $true )
| ( ( ~ ( c_lessequals @ SV800 @ SV2219 @ SV176 )
| ~ ( c_lessequals @ SV800 @ SV2045 @ SV176 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV176 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5235]) ).
thf(5556,plain,
! [SV803: $i,SV1767: $i,SV1356: $i,SV181: $i] :
( ( ( c_lessequals @ SV181 @ SV1356 @ ( tc_fun @ SV1767 @ tc_bool ) )
= $false )
| ( ( ~ ( c_lessequals @ SV181 @ SV803 @ ( tc_fun @ SV1767 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV181 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV803 @ SV1356 @ ( tc_fun @ SV1767 @ tc_bool ) ) @ ( tc_fun @ SV1767 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5236]) ).
thf(5557,plain,
! [SV804: $i,SV1768: $i,SV1357: $i,SV182: $i] :
( ( ( c_lessequals @ SV182 @ SV1357 @ ( tc_fun @ SV1768 @ tc_bool ) )
= $false )
| ( ( ~ ( c_lessequals @ SV182 @ SV804 @ ( tc_fun @ SV1768 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV182 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV804 @ SV1357 @ ( tc_fun @ SV1768 @ tc_bool ) ) @ ( tc_fun @ SV1768 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5237]) ).
thf(5558,plain,
! [SV807: $i,SV185: $i,SV1359: $i] :
( ( ( c_lessequals @ SV1359 @ SV185 @ ( tc_fun @ ( tc_prod @ SV807 @ SV807 ) @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV185 @ ( c_Transitive__Closure_Ortrancl @ SV1359 @ SV807 ) @ ( tc_fun @ ( tc_prod @ SV807 @ SV807 ) @ tc_bool ) )
= $false )
| ( ( ( c_Transitive__Closure_Ortrancl @ SV185 @ SV807 )
= ( c_Transitive__Closure_Ortrancl @ SV1359 @ SV807 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5239]) ).
thf(5559,plain,
! [SV817: $i,SV1773: $i,SV1369: $i,SV197: $i] :
( ( ( c_lessequals @ SV197 @ SV1369 @ ( tc_fun @ SV1773 @ tc_bool ) )
= $false )
| ( ( c_in @ SV817 @ SV197 @ SV1773 )
= $true )
| ( ( c_lessequals @ SV197 @ ( c_Set_Oinsert @ SV817 @ SV1369 @ SV1773 ) @ ( tc_fun @ SV1773 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5242]) ).
thf(5560,plain,
! [SV1370: $i,SV818: $i,SV2052: $i,SV198: $i] :
( ( ( c_lessequals @ SV198 @ ( c_Set_Oinsert @ SV2052 @ SV818 @ SV1370 ) @ ( tc_fun @ SV1370 @ tc_bool ) )
= $false )
| ( ( c_in @ SV2052 @ SV198 @ SV1370 )
= $true )
| ( ( c_lessequals @ SV198 @ SV818 @ ( tc_fun @ SV1370 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5243]) ).
thf(5561,plain,
! [SV819: $i,SV1774: $i,SV1371: $i,SV199: $i] :
( ( ( c_lessequals @ SV199 @ SV1371 @ ( tc_fun @ SV1774 @ tc_bool ) )
= $false )
| ( ( c_in @ SV819 @ SV199 @ SV1774 )
= $true )
| ( ( c_lessequals @ SV199 @ ( c_Set_Oinsert @ SV819 @ SV1371 @ SV1774 ) @ ( tc_fun @ SV1774 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5244]) ).
thf(5562,plain,
! [SV1372: $i,SV820: $i,SV2053: $i,SV200: $i] :
( ( ( c_lessequals @ SV200 @ ( c_Set_Oinsert @ SV2053 @ SV820 @ SV1372 ) @ ( tc_fun @ SV1372 @ tc_bool ) )
= $false )
| ( ( c_in @ SV2053 @ SV200 @ SV1372 )
= $true )
| ( ( c_lessequals @ SV200 @ SV820 @ ( tc_fun @ SV1372 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5245]) ).
thf(5563,plain,
! [SV207: $i,SV2221: $i,SV1778: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1778 @ SV2221 @ SV207 )
= ( c_Orderings_Obot__class_Obot @ SV207 ) )
= $false )
| ( ( SV1778
= ( c_Orderings_Obot__class_Obot @ SV207 ) )
= $true )
| ( ( class_Lattices_Obounded__lattice @ SV207 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5246]) ).
thf(5564,plain,
! [SV208: $i,SV2054: $i,SV1779: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1779 @ SV2054 @ SV208 )
= ( c_Orderings_Obot__class_Obot @ SV208 ) )
= $false )
| ( ( SV2054
= ( c_Orderings_Obot__class_Obot @ SV208 ) )
= $true )
| ( ( class_Lattices_Obounded__lattice @ SV208 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5247]) ).
thf(5565,plain,
! [SV215: $i,SV2311: $i,SV2059: $i,SV833: $i] :
( ( ( ~ ( c_lessequals @ SV833 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2059 @ SV2311 @ SV215 ) @ SV215 ) )
= $true )
| ( ( c_lessequals @ SV833 @ SV2059 @ SV215 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV215 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5252]) ).
thf(5566,plain,
! [SV216: $i,SV2060: $i,SV2312: $i,SV834: $i] :
( ( ( ~ ( c_lessequals @ SV834 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2312 @ SV2060 @ SV216 ) @ SV216 ) )
= $true )
| ( ( c_lessequals @ SV834 @ SV2060 @ SV216 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV216 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5253]) ).
thf(5567,plain,
! [SV2224: $i,SV217: $i,SV2061: $i,SV835: $i] :
( ( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV835 @ SV2061 @ SV217 ) @ SV2224 @ SV217 )
= $true )
| ( ( ~ ( c_lessequals @ SV835 @ SV2224 @ SV217 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV217 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5254]) ).
thf(5568,plain,
! [SV2225: $i,SV218: $i,SV2062: $i,SV836: $i] :
( ( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV836 @ SV2062 @ SV218 ) @ SV2225 @ SV218 )
= $true )
| ( ( ~ ( c_lessequals @ SV2062 @ SV2225 @ SV218 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV218 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5255]) ).
thf(5569,plain,
! [SV219: $i,SV2313: $i,SV2063: $i,SV837: $i] :
( ( ( ~ ( c_lessequals @ SV837 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2063 @ SV2313 @ SV219 ) @ SV219 ) )
= $true )
| ( ( c_lessequals @ SV837 @ SV2063 @ SV219 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV219 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5256]) ).
thf(5570,plain,
! [SV220: $i,SV2064: $i,SV2314: $i,SV838: $i] :
( ( ( ~ ( c_lessequals @ SV838 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2314 @ SV2064 @ SV220 ) @ SV220 ) )
= $true )
| ( ( c_lessequals @ SV838 @ SV2064 @ SV220 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV220 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5257]) ).
thf(5571,plain,
! [SV850: $i,SV2069: $i,SV1789: $i,SV236: $i] :
( ( ( hBOOL @ ( hAPP @ SV236 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1 @ SV236 @ SV1789 @ SV2069 ) ) )
= $false )
| ( ( ~ ( c_Wellfounded_Owf @ SV1789 @ SV2069 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV236 @ SV850 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5258]) ).
thf(5572,plain,
! [SV853: $i,SV1791: $i,SV1398: $i,SV239: $i] :
( ( ( c_lessequals @ SV239 @ SV1398 @ ( tc_fun @ SV1791 @ tc_bool ) )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV239 @ ( c_Set_Oinsert @ SV853 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1791 @ tc_bool ) ) @ SV1791 ) @ ( tc_fun @ SV1791 @ tc_bool ) ) @ SV1398 @ ( tc_fun @ SV1791 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV239 @ ( c_Set_Oinsert @ SV853 @ SV1398 @ SV1791 ) @ ( tc_fun @ SV1791 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5259]) ).
thf(5573,plain,
! [SV857: $i,SV1400: $i,SV243: $i] :
( ( ( c_Relation_Osym @ SV243 @ SV1400 )
= $false )
| ( ( c_Relation_Osym @ SV857 @ SV1400 )
= $false )
| ( ( c_Relation_Osym @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV243 @ SV857 @ ( tc_fun @ ( tc_prod @ SV1400 @ SV1400 ) @ tc_bool ) ) @ SV1400 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5262]) ).
thf(5574,plain,
! [SV2226: $i,SV2073: $i,SV1797: $i,SV1404: $i,SV861: $i,SV247: $i] :
( ( ( ( hAPP @ SV247 @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ SV247 @ SV861 @ SV1404 @ SV1797 @ SV2073 @ SV2226 ) )
!= ( hAPP @ SV861 @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ SV247 @ SV861 @ SV1404 @ SV1797 @ SV2073 @ SV2226 ) ) )
= $true )
| ( ( ( c_Recdef_Ocut @ SV247 @ SV1404 @ SV1797 @ SV2073 @ SV2226 )
= ( c_Recdef_Ocut @ SV861 @ SV1404 @ SV1797 @ SV2073 @ SV2226 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5265]) ).
thf(5575,plain,
! [SV249: $i,SV2227: $i,SV1405: $i,SV863: $i] :
( ( ( c_lessequals @ ( hAPP @ SV863 @ SV1405 ) @ ( hAPP @ SV2227 @ SV1405 ) @ SV249 )
= $true )
| ( ( ! [SY6001: $i] :
~ ( c_lessequals @ SV863 @ SV2227 @ ( tc_fun @ SY6001 @ SV249 ) ) )
= $true )
| ( ( class_HOL_Oord @ SV249 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5267]) ).
thf(5576,plain,
! [SV864: $i,SV1799: $i,SV1406: $i,SV250: $i] :
( ( ( c_in @ SV250 @ SV1406 @ SV1799 )
= $false )
| ( ( ~ ( c_in @ SV250 @ SV864 @ SV1799 ) )
= $true )
| ( ( c_in @ SV250 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV864 @ SV1406 @ ( tc_fun @ SV1799 @ tc_bool ) ) @ SV1799 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5268]) ).
thf(5577,plain,
! [SV865: $i,SV1800: $i,SV1407: $i,SV251: $i] :
( ( ( c_in @ SV251 @ SV1407 @ SV1800 )
= $false )
| ( ( ~ ( c_in @ SV251 @ SV865 @ SV1800 ) )
= $true )
| ( ( c_in @ SV251 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV865 @ SV1407 @ ( tc_fun @ SV1800 @ tc_bool ) ) @ SV1800 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5269]) ).
thf(5578,plain,
! [SV868: $i,SV1410: $i,SV2075: $i,SV254: $i] :
( ( ( c_in @ SV254 @ SV2075 @ SV1410 )
= $false )
| ( ( ~ ( c_lessequals @ SV2075 @ SV868 @ ( tc_fun @ SV1410 @ tc_bool ) ) )
= $true )
| ( ( c_in @ SV254 @ SV868 @ SV1410 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5272]) ).
thf(5579,plain,
! [SV255: $i,SV1411: $i,SV869: $i,SV2076: $i] :
( ( ( c_lessequals @ SV2076 @ SV869 @ ( tc_fun @ SV1411 @ tc_bool ) )
= $false )
| ( ( ~ ( c_in @ SV255 @ SV2076 @ SV1411 ) )
= $true )
| ( ( c_in @ SV255 @ SV869 @ SV1411 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5273]) ).
thf(5580,plain,
! [SV870: $i,SV1412: $i,SV2077: $i,SV256: $i] :
( ( ( c_in @ SV256 @ SV2077 @ SV1412 )
= $false )
| ( ( ~ ( c_lessequals @ SV2077 @ SV870 @ ( tc_fun @ SV1412 @ tc_bool ) ) )
= $true )
| ( ( c_in @ SV256 @ SV870 @ SV1412 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5274]) ).
thf(5581,plain,
! [SV871: $i,SV1413: $i,SV2078: $i,SV257: $i] :
( ( ( c_in @ SV257 @ SV2078 @ SV1413 )
= $false )
| ( ( ~ ( c_lessequals @ SV2078 @ SV871 @ ( tc_fun @ SV1413 @ tc_bool ) ) )
= $true )
| ( ( c_in @ SV257 @ SV871 @ SV1413 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5275]) ).
thf(5582,plain,
! [SV1416: $i,SV878: $i,SV2079: $i,SV264: $i] :
( ( ( c_in @ SV264 @ ( c_Set_Oinsert @ SV2079 @ SV878 @ SV1416 ) @ SV1416 )
= $false )
| ( ( SV264 = SV2079 )
= $true )
| ( ( c_in @ SV264 @ SV878 @ SV1416 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5278]) ).
thf(5583,plain,
! [SV1417: $i,SV879: $i,SV2080: $i,SV265: $i] :
( ( ( c_in @ SV265 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV2080 @ SV879 @ ( tc_fun @ SV1417 @ tc_bool ) ) @ SV1417 )
= $false )
| ( ( c_in @ SV265 @ SV2080 @ SV1417 )
= $true )
| ( ( c_in @ SV265 @ SV879 @ SV1417 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5279]) ).
thf(5584,plain,
! [SV1418: $i,SV880: $i,SV2228: $i,SV266: $i] :
( ( ( c_in @ SV266 @ ( c_HOL_Ominus__class_Ominus @ SV2228 @ SV880 @ ( tc_fun @ SV1418 @ tc_bool ) ) @ SV1418 )
= $false )
| ( ( c_in @ SV266 @ SV880 @ SV1418 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5280]) ).
thf(5585,plain,
! [SV1425: $i,SV1806: $i,SV888: $i,SV274: $i] :
( ( ( c_in @ SV274 @ SV888 @ SV1806 )
= $false )
| ( ( c_in @ SV274 @ SV1425 @ SV1806 )
= $true )
| ( ( c_in @ SV274 @ ( c_HOL_Ominus__class_Ominus @ SV888 @ SV1425 @ ( tc_fun @ SV1806 @ tc_bool ) ) @ SV1806 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5285]) ).
thf(5586,plain,
! [SV1426: $i,SV1807: $i,SV889: $i,SV275: $i] :
( ( ( c_in @ SV275 @ SV889 @ SV1807 )
= $false )
| ( ( c_in @ SV275 @ SV1426 @ SV1807 )
= $true )
| ( ( c_in @ SV275 @ ( c_HOL_Ominus__class_Ominus @ SV889 @ SV1426 @ ( tc_fun @ SV1807 @ tc_bool ) ) @ SV1807 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5286]) ).
thf(5587,plain,
! [SV890: $i,SV1427: $i,SV1808: $i,SV276: $i] :
( ( ( c_in @ SV276 @ SV1808 @ SV1427 )
= $true )
| ( ( ( SV890 = SV1808 )
| ( c_in @ SV276 @ SV890 @ SV1427 ) )
= $true )
| ( ( ( c_Set_Oinsert @ SV276 @ SV890 @ SV1427 )
= ( c_Set_Oinsert @ SV276 @ SV1808 @ SV1427 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5287]) ).
thf(5588,plain,
! [SV1433: $i,SV896: $i,SV1813: $i,SV282: $i,SV2085: $i] :
( ( ( ! [SY5932: $i] :
~ ( hBOOL @ ( hAPP @ SY5932 @ SV2085 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV282 @ SV1813 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV282 @ ( hAPP @ ( c_fst @ SV896 @ SV1433 ) @ ( c_Pair @ SV1813 @ SV2085 @ SV896 @ SV1433 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5288]) ).
thf(5589,plain,
! [SV1434: $i,SV897: $i,SV1814: $i,SV2086: $i,SV283: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV283 @ SV2086 ) ) )
= $true )
| ( ( ! [SY5750: $i] :
~ ( hBOOL @ ( hAPP @ SY5750 @ SV1814 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV283 @ ( hAPP @ ( c_snd @ SV897 @ SV1434 ) @ ( c_Pair @ SV1814 @ SV2086 @ SV897 @ SV1434 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5289]) ).
thf(5590,plain,
! [SV290: $i,SV1438: $i,SV1818: $i,SV904: $i] :
( ( ( c_lessequals @ SV904 @ SV1818 @ ( tc_fun @ SV1438 @ tc_bool ) )
= $false )
| ( ( ~ ( c_in @ SV290 @ SV1818 @ SV1438 ) )
= $true )
| ( ( c_lessequals @ ( c_Set_Oinsert @ SV290 @ SV904 @ SV1438 ) @ SV1818 @ ( tc_fun @ SV1438 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5292]) ).
thf(5591,plain,
! [SV2092: $i,SV301: $i,SV912: $i,SV2315: $i] :
( ( ( ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV2315 @ SV912 @ SV301 ) @ SV2092 @ SV301 ) )
= $true )
| ( ( c_lessequals @ SV912 @ SV2092 @ SV301 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV301 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5293]) ).
thf(5592,plain,
! [SV2093: $i,SV302: $i,SV2316: $i,SV913: $i] :
( ( ( ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV913 @ SV2316 @ SV302 ) @ SV2093 @ SV302 ) )
= $true )
| ( ( c_lessequals @ SV913 @ SV2093 @ SV302 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV302 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5294]) ).
thf(5593,plain,
! [SV303: $i,SV2231: $i,SV2094: $i,SV914: $i] :
( ( ( c_lessequals @ SV914 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV2094 @ SV2231 @ SV303 ) @ SV303 )
= $true )
| ( ( ~ ( c_lessequals @ SV914 @ SV2231 @ SV303 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV303 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5295]) ).
thf(5594,plain,
! [SV304: $i,SV2317: $i,SV2095: $i,SV915: $i] :
( ( ( c_lessequals @ SV915 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV2095 @ SV2317 @ SV304 ) @ SV304 )
= $true )
| ( ( ~ ( c_lessequals @ SV915 @ SV2095 @ SV304 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV304 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5296]) ).
thf(5595,plain,
! [SV2096: $i,SV305: $i,SV916: $i,SV2318: $i] :
( ( ( ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV2318 @ SV916 @ SV305 ) @ SV2096 @ SV305 ) )
= $true )
| ( ( c_lessequals @ SV916 @ SV2096 @ SV305 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV305 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5297]) ).
thf(5596,plain,
! [SV2097: $i,SV306: $i,SV2319: $i,SV917: $i] :
( ( ( ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV917 @ SV2319 @ SV306 ) @ SV2097 @ SV306 ) )
= $true )
| ( ( c_lessequals @ SV917 @ SV2097 @ SV306 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV306 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5298]) ).
thf(5597,plain,
! [SV2100: $i,SV309: $i,SV2320: $i,SV920: $i] :
( ( ( ~ ( c_lessequals @ SV920 @ SV2320 @ SV309 )
| ~ ( c_lessequals @ SV2320 @ SV2100 @ SV309 ) )
= $true )
| ( ( c_lessequals @ SV920 @ SV2100 @ SV309 )
= $true )
| ( ( class_Orderings_Oorder @ SV309 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5301]) ).
thf(5598,plain,
! [SV921: $i,SV310: $i,SV2101: $i,SV2321: $i] :
( ( ( ~ ( c_lessequals @ SV2321 @ SV2101 @ SV310 )
| ~ ( c_lessequals @ SV921 @ SV2321 @ SV310 ) )
= $true )
| ( ( c_lessequals @ SV921 @ SV2101 @ SV310 )
= $true )
| ( ( class_Orderings_Opreorder @ SV310 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5302]) ).
thf(5599,plain,
! [SV313: $i,SV1447: $i,SV924: $i,SV2102: $i] :
( ( ( c_lessequals @ SV2102 @ SV924 @ ( tc_fun @ SV1447 @ tc_bool ) )
= $false )
| ( ( ~ ( c_lessequals @ SV313 @ SV2102 @ ( tc_fun @ SV1447 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV313 @ SV924 @ ( tc_fun @ SV1447 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5303]) ).
thf(5600,plain,
! [SV925: $i,SV2322: $i,SV314: $i,SV1824: $i] :
( ( ( ~ ( c_lessequals @ SV1824 @ SV314 @ ( tc_fun @ SV2322 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV1824 @ SV925 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV314 @ SV925 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5304]) ).
thf(5601,plain,
! [SV315: $i,SV926: $i,SV1825: $i] :
( ( ( c_Wellfounded_Owf @ SV1825 @ SV926 )
= $false )
| ( ( c_lessequals @ SV315 @ SV1825 @ ( tc_fun @ ( tc_prod @ SV926 @ SV926 ) @ tc_bool ) )
= $false )
| ( ( c_Wellfounded_Owf @ SV315 @ SV926 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5305]) ).
thf(5602,plain,
! [SV927: $i,SV1828: $i,SV318: $i] :
( ( ( c_lessequals @ SV318 @ SV1828 @ ( tc_fun @ ( tc_prod @ SV927 @ SV927 ) @ tc_bool ) )
= $false )
| ( ( c_Relation_Oantisym @ SV1828 @ SV927 )
= $false )
| ( ( c_Relation_Oantisym @ SV318 @ SV927 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5306]) ).
thf(5603,plain,
! [SV928: $i,SV2232: $i,SV319: $i,SV1829: $i] :
( ( ( c_lessequals @ SV1829 @ SV319 @ ( tc_fun @ SV2232 @ tc_bool ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV1829 @ SV928 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV319 @ SV928 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5307]) ).
thf(5604,plain,
! [SV320: $i,SV929: $i,SV1830: $i] :
( ( ( c_Wellfounded_Oacyclic @ SV1830 @ SV929 )
= $false )
| ( ( c_lessequals @ SV320 @ SV1830 @ ( tc_fun @ ( tc_prod @ SV929 @ SV929 ) @ tc_bool ) )
= $false )
| ( ( c_Wellfounded_Oacyclic @ SV320 @ SV929 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5308]) ).
thf(5605,plain,
! [SV321: $i,SV1448: $i,SV930: $i,SV2103: $i] :
( ( ( c_Relation_Osingle__valued @ SV2103 @ SV930 @ SV1448 )
= $false )
| ( ( ~ ( c_lessequals @ SV321 @ SV2103 @ ( tc_fun @ ( tc_prod @ SV930 @ SV1448 ) @ tc_bool ) ) )
= $true )
| ( ( c_Relation_Osingle__valued @ SV321 @ SV930 @ SV1448 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5309]) ).
thf(5606,plain,
! [SV1831: $i,SV323: $i,SV1450: $i,SV2105: $i,SV932: $i] :
( ( ( ~ ( c_lessequals @ SV932 @ SV2105 @ ( tc_fun @ SV1450 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV323 @ SV1831 @ ( tc_fun @ SV1450 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV323 @ SV932 @ ( tc_fun @ SV1450 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1831 @ SV2105 @ ( tc_fun @ SV1450 @ tc_bool ) ) @ ( tc_fun @ SV1450 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5311]) ).
thf(5607,plain,
! [SV1457: $i,SV331: $i,SV1836: $i,SV940: $i] :
( ( ( hBOOL @ ( hAPP @ SV940 @ SV1836 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV331 @ SV1836 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV331 @ SV940 @ ( tc_fun @ SV1457 @ tc_bool ) ) @ SV1836 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5314]) ).
thf(5608,plain,
! [SV1458: $i,SV1837: $i,SV941: $i,SV332: $i] :
( ( ( c_lessequals @ SV332 @ SV941 @ ( tc_fun @ SV1837 @ tc_bool ) )
= $false )
| ( ( ~ ( c_lessequals @ SV1458 @ SV332 @ ( tc_fun @ SV1837 @ tc_bool ) ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV332 @ ( c_HOL_Ominus__class_Ominus @ SV941 @ SV1458 @ ( tc_fun @ SV1837 @ tc_bool ) ) @ ( tc_fun @ SV1837 @ tc_bool ) )
= SV1458 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5315]) ).
thf(5609,plain,
! [SV2323: $i,SV2233: $i,SV333: $i,SV1459: $i,SV942: $i] :
( ( ( ( ( c_HOL_Ominus__class_Ominus @ SV942 @ SV1459 @ SV333 )
!= ( c_HOL_Ominus__class_Ominus @ SV2233 @ SV2323 @ SV333 ) )
| ( c_lessequals @ SV2323 @ SV2233 @ SV333 )
| ~ ( c_lessequals @ SV1459 @ SV942 @ SV333 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV333 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5316]) ).
thf(5610,plain,
! [SV2324: $i,SV2234: $i,SV334: $i,SV1460: $i,SV943: $i] :
( ( ( ( ( c_HOL_Ominus__class_Ominus @ SV943 @ SV1460 @ SV334 )
!= ( c_HOL_Ominus__class_Ominus @ SV2234 @ SV2324 @ SV334 ) )
| ( c_lessequals @ SV1460 @ SV943 @ SV334 )
| ~ ( c_lessequals @ SV2324 @ SV2234 @ SV334 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV334 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5317]) ).
thf(5611,plain,
! [SV1838: $i,SV335: $i,SV1461: $i,SV2106: $i,SV944: $i] :
( ( ( c_lessequals @ SV944 @ SV2106 @ ( tc_fun @ SV1461 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( c_Set_Oimage @ SV335 @ SV944 @ SV1461 @ SV1838 ) @ ( c_Set_Oimage @ SV335 @ SV2106 @ SV1461 @ SV1838 ) @ ( tc_fun @ SV1838 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5318]) ).
thf(5612,plain,
! [SV945: $i,SV2325: $i,SV1462: $i,SV336: $i,SV2235: $i] :
( ( ( c_lessequals @ ( c_Set_Oimage @ SV2235 @ SV336 @ SV1462 @ SV2325 ) @ ( c_Set_Oimage @ SV2235 @ SV945 @ SV1462 @ SV2325 ) @ ( tc_fun @ SV2325 @ tc_bool ) )
= $true )
| ( ( c_lessequals @ SV336 @ SV945 @ ( tc_fun @ SV1462 @ tc_bool ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5319]) ).
thf(5613,plain,
! [SV1465: $i,SV948: $i,SV1841: $i,SV2108: $i,SV341: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV341 @ SV2108 ) @ SV1841 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV341 @ ( hAPP @ ( c_snd @ SV948 @ SV1465 ) @ ( c_Pair @ SV1841 @ SV2108 @ SV948 @ SV1465 ) ) ) @ ( hAPP @ ( c_fst @ SV948 @ SV1465 ) @ ( c_Pair @ SV1841 @ SV2108 @ SV948 @ SV1465 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5321]) ).
thf(5614,plain,
! [SV2236: $i,SV2109: $i,SV1842: $i,SV1467: $i,SV950: $i,SV343: $i] :
( ( ( c_lessequals @ ( c_Relation_OImage @ SV343 @ SV950 @ SV1467 @ SV1842 ) @ ( c_Relation_OImage @ SV2109 @ SV2236 @ SV1467 @ SV1842 ) @ ( tc_fun @ SV1842 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV950 @ SV2236 @ ( tc_fun @ SV1467 @ tc_bool ) )
| ~ ( c_lessequals @ SV343 @ SV2109 @ ( tc_fun @ ( tc_prod @ SV1467 @ SV1842 ) @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5322]) ).
thf(5615,plain,
! [SV347: $i,SV953: $i,SV1469: $i,SV1845: $i] :
( ( ( c_Wellfounded_Oacyclic @ SV1845 @ SV1469 )
= $false )
| ( ( c_in @ ( c_Pair @ SV953 @ SV347 @ SV1469 @ SV1469 ) @ ( c_Transitive__Closure_Ortrancl @ SV1845 @ SV1469 ) @ ( tc_prod @ SV1469 @ SV1469 ) )
= $true )
| ( ( c_Wellfounded_Oacyclic @ ( c_Set_Oinsert @ ( c_Pair @ SV347 @ SV953 @ SV1469 @ SV1469 ) @ SV1845 @ ( tc_prod @ SV1469 @ SV1469 ) ) @ SV1469 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5324]) ).
thf(5616,plain,
! [SV1846: $i,SV1470: $i,SV348: $i,SV954: $i] :
( ( ( c_Wellfounded_Oacyclic @ ( c_Set_Oinsert @ ( c_Pair @ SV954 @ SV348 @ SV1470 @ SV1470 ) @ SV1846 @ ( tc_prod @ SV1470 @ SV1470 ) ) @ SV1470 )
= $false )
| ( ( c_in @ ( c_Pair @ SV348 @ SV954 @ SV1470 @ SV1470 ) @ ( c_Transitive__Closure_Ortrancl @ SV1846 @ SV1470 ) @ ( tc_prod @ SV1470 @ SV1470 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5325]) ).
thf(5617,plain,
! [SV955: $i,SV2237: $i,SV2111: $i,SV1471: $i,SV349: $i] :
( ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1 @ SV349 @ SV1471 @ SV2111 @ SV2237 ) @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 @ SV349 @ SV1471 @ SV2111 @ SV2237 ) @ SV2237 @ SV2237 ) @ SV2111 @ ( tc_prod @ SV2237 @ SV2237 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV349 @ SV1471 ) )
| ~ ( c_in @ ( c_Pair @ SV955 @ SV1471 @ SV2237 @ SV2237 ) @ ( c_Transitive__Closure_Ortrancl @ SV2111 @ SV2237 ) @ ( tc_prod @ SV2237 @ SV2237 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV349 @ SV955 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5326]) ).
thf(5618,plain,
! [SV956: $i,SV2238: $i,SV2112: $i,SV1472: $i,SV350: $i] :
( ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 @ SV350 @ SV1472 @ SV2112 @ SV2238 ) @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2 @ SV350 @ SV1472 @ SV2112 @ SV2238 ) @ SV2238 @ SV2238 ) @ SV2112 @ ( tc_prod @ SV2238 @ SV2238 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV350 @ SV1472 ) )
| ~ ( c_in @ ( c_Pair @ SV1472 @ SV956 @ SV2238 @ SV2238 ) @ ( c_Transitive__Closure_Ortrancl @ SV2112 @ SV2238 ) @ ( tc_prod @ SV2238 @ SV2238 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV350 @ SV956 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5327]) ).
thf(5619,plain,
! [SV957: $i,SV1473: $i,SV2113: $i,SV351: $i] :
( ( ( c_in @ SV351 @ SV2113 @ SV1473 )
= $false )
| ( ( ~ ( c_Equiv__Relations_Oequiv @ SV2113 @ SV957 @ SV1473 ) )
= $true )
| ( ( c_in @ SV351 @ ( c_Relation_OImage @ SV957 @ ( c_Set_Oinsert @ SV351 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1473 @ tc_bool ) ) @ SV1473 ) @ SV1473 @ SV1473 ) @ SV1473 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5328]) ).
thf(5620,plain,
! [SV352: $i,SV1474: $i,SV958: $i] :
( ( ( c_lessequals @ ( c_Relation_OId @ SV958 ) @ SV1474 @ ( tc_fun @ ( tc_prod @ SV958 @ SV958 ) @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( c_Relation_Orel__comp @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Transitive__Closure_Ortrancl @ SV352 @ SV958 ) @ SV1474 @ ( tc_fun @ ( tc_prod @ SV958 @ SV958 ) @ tc_bool ) ) @ SV352 @ SV958 @ SV958 @ SV958 ) @ SV1474 @ ( tc_fun @ ( tc_prod @ SV958 @ SV958 ) @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( c_Transitive__Closure_Ortrancl @ SV352 @ SV958 ) @ SV1474 @ ( tc_fun @ ( tc_prod @ SV958 @ SV958 ) @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5329]) ).
thf(5621,plain,
! [SV959: $i,SV1475: $i,SV353: $i,SV1847: $i,SV2326: $i] :
( ( ( ~ ( c_in @ SV2326 @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_OImage @ SV1847 @ ( c_Set_Oinsert @ SV353 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1475 @ tc_bool ) ) @ SV1475 ) @ SV1475 @ SV1475 ) @ ( c_Relation_OImage @ SV1847 @ ( c_Set_Oinsert @ SV959 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1475 @ tc_bool ) ) @ SV1475 ) @ SV1475 @ SV1475 ) @ ( tc_fun @ SV1475 @ tc_bool ) ) @ SV1475 ) )
= $true )
| ( ( ! [SY5764: $i] :
~ ( c_Equiv__Relations_Oequiv @ SY5764 @ SV1847 @ SV1475 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV353 @ SV959 @ SV1475 @ SV1475 ) @ SV1847 @ ( tc_prod @ SV1475 @ SV1475 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5330]) ).
thf(5622,plain,
! [SV354: $i,SV1848: $i,SV1476: $i,SV2239: $i,SV960: $i] :
( ( ( ~ ( c_in @ SV960 @ SV2239 @ SV1476 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Relation_OImage @ SV1848 @ ( c_Set_Oinsert @ SV960 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1476 @ tc_bool ) ) @ SV1476 ) @ SV1476 @ SV1476 ) @ ( c_Relation_OImage @ SV1848 @ ( c_Set_Oinsert @ SV354 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1476 @ tc_bool ) ) @ SV1476 ) @ SV1476 @ SV1476 ) @ ( tc_fun @ SV1476 @ tc_bool ) )
| ~ ( c_Equiv__Relations_Oequiv @ SV2239 @ SV1848 @ SV1476 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV354 @ SV960 @ SV1476 @ SV1476 ) @ SV1848 @ ( tc_prod @ SV1476 @ SV1476 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5331]) ).
thf(5623,plain,
! [SV2240: $i,SV355: $i,SV1849: $i,SV1477: $i,SV961: $i] :
( ( ( c_in @ SV961 @ SV1477 @ SV1849 )
= $false )
| ( ( ( c_Set_Oinsert @ ( hAPP @ SV355 @ SV961 ) @ ( c_Set_Oimage @ SV355 @ SV1477 @ SV1849 @ SV2240 ) @ SV2240 )
= ( c_Set_Oimage @ SV355 @ SV1477 @ SV1849 @ SV2240 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5332]) ).
thf(5624,plain,
! [SV1478: $i,SV1850: $i,SV356: $i,SV2327: $i,SV2241: $i,SV962: $i] :
( ( ( ~ ( c_in @ SV962 @ SV2241 @ SV2327 )
| ~ ( c_lessequals @ ( c_Set_Oimage @ SV356 @ SV2241 @ SV2327 @ SV1850 ) @ SV1478 @ ( tc_fun @ SV1850 @ tc_bool ) ) )
= $true )
| ( ( c_in @ ( hAPP @ SV356 @ SV962 ) @ SV1478 @ SV1850 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5333]) ).
thf(5625,plain,
! [SV1851: $i,SV1479: $i,SV357: $i,SV2114: $i,SV963: $i] :
( ( ( c_in @ SV963 @ ( c_Relation_OImage @ SV2114 @ ( c_Set_Oinsert @ SV357 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1479 @ tc_bool ) ) @ SV1479 ) @ SV1479 @ SV1851 ) @ SV1851 )
= $false )
| ( ( c_in @ ( c_Pair @ SV357 @ SV963 @ SV1479 @ SV1851 ) @ SV2114 @ ( tc_prod @ SV1479 @ SV1851 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5334]) ).
thf(5626,plain,
! [SV964: $i,SV2115: $i,SV1852: $i,SV358: $i,SV1480: $i] :
( ( ( c_in @ ( c_Pair @ SV1480 @ SV358 @ SV1852 @ SV2115 ) @ SV964 @ ( tc_prod @ SV1852 @ SV2115 ) )
= $false )
| ( ( c_in @ SV358 @ ( c_Relation_OImage @ SV964 @ ( c_Set_Oinsert @ SV1480 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1852 @ tc_bool ) ) @ SV1852 ) @ SV1852 @ SV2115 ) @ SV2115 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5335]) ).
thf(5627,plain,
! [SV2116: $i,SV1853: $i,SV1481: $i,SV965: $i,SV359: $i] :
( ( ( ( c_Product__Type_OSigma @ SV359 @ ( c_COMBK @ SV965 @ ( tc_fun @ SV1481 @ tc_bool ) @ SV1853 ) @ SV1853 @ SV1481 )
= ( c_Product__Type_OSigma @ SV2116 @ ( c_COMBK @ SV965 @ ( tc_fun @ SV1481 @ tc_bool ) @ SV1853 ) @ SV1853 @ SV1481 ) )
= $false )
| ( ( ! [SY5395: $i] :
~ ( c_in @ SY5395 @ SV965 @ SV1481 )
| ( SV359 = SV2116 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5336]) ).
thf(5628,plain,
! [SV363: $i,SV1484: $i,SV969: $i,SV2118: $i] :
( ( ( c_lessequals @ SV2118 @ SV969 @ ( tc_fun @ ( tc_prod @ SV1484 @ SV1484 ) @ tc_bool ) )
= $false )
| ( ( ~ ( c_in @ SV363 @ ( c_Transitive__Closure_Otrancl @ SV2118 @ SV1484 ) @ ( tc_prod @ SV1484 @ SV1484 ) ) )
= $true )
| ( ( c_in @ SV363 @ ( c_Transitive__Closure_Otrancl @ SV969 @ SV1484 ) @ ( tc_prod @ SV1484 @ SV1484 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5340]) ).
thf(5629,plain,
! [SV364: $i,SV1485: $i,SV1857: $i,SV970: $i] :
( ( ( c_in @ ( c_Pair @ SV970 @ SV1857 @ SV1485 @ SV1485 ) @ SV364 @ ( tc_prod @ SV1485 @ SV1485 ) )
= $false )
| ( ( ! [SY5400: $i] :
~ ( c_Equiv__Relations_Oequiv @ SY5400 @ SV364 @ SV1485 ) )
= $true )
| ( ( ( c_Relation_OImage @ SV364 @ ( c_Set_Oinsert @ SV970 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1485 @ tc_bool ) ) @ SV1485 ) @ SV1485 @ SV1485 )
= ( c_Relation_OImage @ SV364 @ ( c_Set_Oinsert @ SV1857 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1485 @ tc_bool ) ) @ SV1485 ) @ SV1485 @ SV1485 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5341]) ).
thf(5630,plain,
! [SV365: $i,SV1486: $i,SV1858: $i,SV971: $i] :
( ( ( c_in @ ( c_Pair @ SV971 @ SV1858 @ SV1486 @ SV1486 ) @ SV365 @ ( tc_prod @ SV1486 @ SV1486 ) )
= $false )
| ( ( ! [SY5402: $i] :
~ ( c_Equiv__Relations_Oequiv @ SY5402 @ SV365 @ SV1486 ) )
= $true )
| ( ( ( c_Relation_OImage @ SV365 @ ( c_Set_Oinsert @ SV971 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1486 @ tc_bool ) ) @ SV1486 ) @ SV1486 @ SV1486 )
= ( c_Relation_OImage @ SV365 @ ( c_Set_Oinsert @ SV1858 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1486 @ tc_bool ) ) @ SV1486 ) @ SV1486 @ SV1486 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5342]) ).
thf(5631,plain,
! [SV1861: $i,SV1494: $i,SV387: $i,SV992: $i] :
( ( ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ SV992 @ SV387 @ SV1494 @ SV1494 ) @ SV1861 @ ( tc_prod @ SV1494 @ SV1494 ) ) @ SV1494 )
= $false )
| ( ( c_in @ ( c_Pair @ SV387 @ SV992 @ SV1494 @ SV1494 ) @ ( c_Transitive__Closure_Ortrancl @ SV1861 @ SV1494 ) @ ( tc_prod @ SV1494 @ SV1494 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5346]) ).
thf(5632,plain,
! [SV388: $i,SV993: $i,SV1495: $i,SV1862: $i] :
( ( ( c_Wellfounded_Owf @ SV1862 @ SV1495 )
= $false )
| ( ( c_in @ ( c_Pair @ SV993 @ SV388 @ SV1495 @ SV1495 ) @ ( c_Transitive__Closure_Ortrancl @ SV1862 @ SV1495 ) @ ( tc_prod @ SV1495 @ SV1495 ) )
= $true )
| ( ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ SV388 @ SV993 @ SV1495 @ SV1495 ) @ SV1862 @ ( tc_prod @ SV1495 @ SV1495 ) ) @ SV1495 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5347]) ).
thf(5633,plain,
! [SV389: $i,SV1496: $i,SV994: $i] :
( ( ( ~ ( c_Relation_Oirrefl @ SV994 @ SV1496 ) )
= $true )
| ( ( ~ ( c_Relation_Otrans @ SV994 @ SV1496 ) )
= $true )
| ( ( c_Relation_Ototal__on @ SV389 @ SV994 @ SV1496 )
= $false )
| ( ( c_Order__Relation_Ostrict__linear__order__on @ SV389 @ SV994 @ SV1496 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5348]) ).
thf(5634,plain,
! [SV1497: $i,SV997: $i,SV2119: $i,SV1863: $i,SV392: $i] :
( ( ( c_Relation_Osingle__valued @ ( c_Relation_Oconverse @ SV392 @ SV1863 @ SV2119 ) @ SV2119 @ SV1863 )
= $false )
| ( ( ( c_Relation_OImage @ SV392 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV997 @ SV1497 @ ( tc_fun @ SV1863 @ tc_bool ) ) @ SV1863 @ SV2119 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_OImage @ SV392 @ SV997 @ SV1863 @ SV2119 ) @ ( c_Relation_OImage @ SV392 @ SV1497 @ SV1863 @ SV2119 ) @ ( tc_fun @ SV2119 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5350]) ).
thf(5635,plain,
! [SV2242: $i,SV2120: $i,SV1865: $i,SV1498: $i,SV1004: $i,SV399: $i] :
( ( ( ( c_Recdef_Ocut @ SV399 @ SV1004 @ SV1498 @ SV1865 @ SV2120 )
= ( c_Recdef_Ocut @ SV2242 @ SV1004 @ SV1498 @ SV1865 @ SV2120 ) )
= $true )
| ( ( c_in @ ( c_Pair @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ SV399 @ SV2242 @ SV1004 @ SV1498 @ SV1865 @ SV2120 ) @ SV1498 @ SV1865 @ SV1865 ) @ SV1004 @ ( tc_prod @ SV1865 @ SV1865 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5351]) ).
thf(5636,plain,
! [SV2328: $i,SV2243: $i,SV2121: $i,SV1866: $i,SV1501: $i,SV1010: $i,SV405: $i] :
( ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 @ SV405 @ SV1010 @ SV1501 @ SV1866 @ SV2121 @ SV2243 @ SV2328 ) @ SV1010 @ SV2328 @ SV2243 ) @ SV1866 @ ( tc_prod @ SV2328 @ SV2243 ) )
| ~ ( c_in @ ( c_Pair @ SV405 @ SV1010 @ SV2121 @ SV2243 ) @ ( c_Relation_Orel__comp @ SV1501 @ SV1866 @ SV2121 @ SV2328 @ SV2243 ) @ ( tc_prod @ SV2121 @ SV2243 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5352]) ).
thf(5637,plain,
! [SV2329: $i,SV2244: $i,SV2122: $i,SV1867: $i,SV1502: $i,SV1011: $i,SV406: $i] :
( ( ( c_in @ ( c_Pair @ SV406 @ ( c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 @ SV406 @ SV1011 @ SV1502 @ SV1867 @ SV2122 @ SV2244 @ SV2329 ) @ SV2122 @ SV2329 ) @ SV1502 @ ( tc_prod @ SV2122 @ SV2329 ) )
| ~ ( c_in @ ( c_Pair @ SV406 @ SV1011 @ SV2122 @ SV2244 ) @ ( c_Relation_Orel__comp @ SV1502 @ SV1867 @ SV2122 @ SV2329 @ SV2244 ) @ ( tc_prod @ SV2122 @ SV2244 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5353]) ).
thf(5638,plain,
! [SV408: $i,SV1868: $i,SV1504: $i,SV1013: $i] :
( ( ( c_in @ ( c_Pair @ SV1013 @ SV1504 @ SV1868 @ SV1868 ) @ ( c_Transitive__Closure_Otrancl @ SV408 @ SV1868 ) @ ( tc_prod @ SV1868 @ SV1868 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1013 @ SV1504 @ SV1868 @ SV1868 ) @ SV408 @ ( tc_prod @ SV1868 @ SV1868 ) )
= $true )
| ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1 @ SV408 @ SV1013 @ SV1504 @ SV1868 ) @ SV1504 @ SV1868 @ SV1868 ) @ ( c_Transitive__Closure_Otrancl @ SV408 @ SV1868 ) @ ( tc_prod @ SV1868 @ SV1868 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5354]) ).
thf(5639,plain,
! [SV1508: $i,SV1870: $i,SV1017: $i,SV412: $i] :
( ( ( c_in @ ( c_Pair @ SV412 @ SV1017 @ SV1870 @ SV1870 ) @ ( c_Transitive__Closure_Otrancl @ SV1508 @ SV1870 ) @ ( tc_prod @ SV1870 @ SV1870 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV412 @ SV1017 @ SV1870 @ SV1870 ) @ SV1508 @ ( tc_prod @ SV1870 @ SV1870 ) )
= $true )
| ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1 @ SV412 @ SV1017 @ SV1508 @ SV1870 ) @ SV1017 @ SV1870 @ SV1870 ) @ SV1508 @ ( tc_prod @ SV1870 @ SV1870 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5358]) ).
thf(5640,plain,
! [SV1509: $i,SV1871: $i,SV1018: $i,SV413: $i] :
( ( ( c_in @ ( c_Pair @ SV413 @ SV1018 @ SV1871 @ SV1871 ) @ ( c_Transitive__Closure_Otrancl @ SV1509 @ SV1871 ) @ ( tc_prod @ SV1871 @ SV1871 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV413 @ SV1018 @ SV1871 @ SV1871 ) @ SV1509 @ ( tc_prod @ SV1871 @ SV1871 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV413 @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1 @ SV413 @ SV1018 @ SV1509 @ SV1871 ) @ SV1871 @ SV1871 ) @ ( c_Transitive__Closure_Otrancl @ SV1509 @ SV1871 ) @ ( tc_prod @ SV1871 @ SV1871 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5359]) ).
thf(5641,plain,
! [SV1020: $i,SV1873: $i,SV1511: $i,SV415: $i] :
( ( ( c_in @ ( c_Pair @ SV415 @ SV1511 @ SV1873 @ SV1873 ) @ ( c_Transitive__Closure_Otrancl @ SV1020 @ SV1873 ) @ ( tc_prod @ SV1873 @ SV1873 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV415 @ SV1511 @ SV1873 @ SV1873 ) @ SV1020 @ ( tc_prod @ SV1873 @ SV1873 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV415 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1 @ SV1020 @ SV415 @ SV1511 @ SV1873 ) @ SV1873 @ SV1873 ) @ SV1020 @ ( tc_prod @ SV1873 @ SV1873 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5361]) ).
thf(5642,plain,
! [SV1022: $i,SV2330: $i,SV2245: $i,SV417: $i,SV1513: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1513 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1 @ SV417 @ SV2245 @ SV2330 ) @ SV2330 @ SV2330 ) @ SV2245 @ ( tc_prod @ SV2330 @ SV2330 ) )
| ~ ( c_Wellfounded_Owf @ SV2245 @ SV2330 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV417 @ SV1513 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV417 @ SV1022 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5363]) ).
thf(5643,plain,
! [SV1023: $i,SV2331: $i,SV2246: $i,SV418: $i,SV1514: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1514 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1 @ SV418 @ SV2246 @ SV2331 ) @ SV2331 @ SV2331 ) @ SV2246 @ ( tc_prod @ SV2331 @ SV2331 ) )
| ~ ( c_Wellfounded_Owf @ SV2246 @ SV2331 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV418 @ SV1514 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV418 @ SV1023 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5364]) ).
thf(5644,plain,
! [SV1024: $i,SV2332: $i,SV2247: $i,SV419: $i,SV1515: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1515 @ ( c_List_Osko__Recdef__Xtfl__wf__induct__1__1 @ SV419 @ SV2247 @ SV2332 ) @ SV2332 @ SV2332 ) @ SV2247 @ ( tc_prod @ SV2332 @ SV2332 ) )
| ~ ( c_Wellfounded_Owf @ SV2247 @ SV2332 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV419 @ SV1515 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV419 @ SV1024 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5365]) ).
thf(5645,plain,
! [SV1025: $i,SV2333: $i,SV2248: $i,SV420: $i,SV1516: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1516 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1 @ SV420 @ SV2248 @ SV2333 ) @ SV2333 @ SV2333 ) @ SV2248 @ ( tc_prod @ SV2333 @ SV2333 ) )
| ~ ( c_Wellfounded_Owf @ SV2248 @ SV2333 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV420 @ SV1516 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV420 @ SV1025 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5366]) ).
thf(5646,plain,
! [SV1517: $i,SV1874: $i,SV1026: $i,SV421: $i] :
( ( ( c_in @ ( c_Pair @ SV421 @ SV1026 @ SV1874 @ SV1874 ) @ ( c_Transitive__Closure_Ortrancl @ SV1517 @ SV1874 ) @ ( tc_prod @ SV1874 @ SV1874 ) )
= $false )
| ( ( SV421 = SV1026 )
= $true )
| ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1 @ SV421 @ SV1026 @ SV1517 @ SV1874 ) @ SV1026 @ SV1874 @ SV1874 ) @ SV1517 @ ( tc_prod @ SV1874 @ SV1874 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5367]) ).
thf(5647,plain,
! [SV422: $i,SV1875: $i,SV1518: $i,SV1027: $i] :
( ( ( c_in @ ( c_Pair @ SV1027 @ SV1518 @ SV1875 @ SV1875 ) @ ( c_Transitive__Closure_Ortrancl @ SV422 @ SV1875 ) @ ( tc_prod @ SV1875 @ SV1875 ) )
= $false )
| ( ( SV1027 = SV1518 )
= $true )
| ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1 @ SV422 @ SV1027 @ SV1518 @ SV1875 ) @ SV1518 @ SV1875 @ SV1875 ) @ ( c_Transitive__Closure_Ortrancl @ SV422 @ SV1875 ) @ ( tc_prod @ SV1875 @ SV1875 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5368]) ).
thf(5648,plain,
! [SV1028: $i,SV1876: $i,SV1519: $i,SV423: $i] :
( ( ( c_in @ ( c_Pair @ SV423 @ SV1519 @ SV1876 @ SV1876 ) @ ( c_Transitive__Closure_Ortrancl @ SV1028 @ SV1876 ) @ ( tc_prod @ SV1876 @ SV1876 ) )
= $false )
| ( ( SV423 = SV1519 )
= $true )
| ( ( c_in @ ( c_Pair @ SV423 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1 @ SV1028 @ SV423 @ SV1519 @ SV1876 ) @ SV1876 @ SV1876 ) @ SV1028 @ ( tc_prod @ SV1876 @ SV1876 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5369]) ).
thf(5649,plain,
! [SV1029: $i,SV2249: $i,SV2123: $i,SV1520: $i,SV424: $i] :
( ( ( hBOOL @ ( hAPP @ SV424 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 @ SV424 @ SV1520 @ SV2123 @ SV2249 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV424 @ SV1520 ) )
| ~ ( c_in @ ( c_Pair @ SV1029 @ SV1520 @ SV2249 @ SV2249 ) @ ( c_Transitive__Closure_Ortrancl @ SV2123 @ SV2249 ) @ ( tc_prod @ SV2249 @ SV2249 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV424 @ SV1029 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5370]) ).
thf(5650,plain,
! [SV1030: $i,SV2250: $i,SV2124: $i,SV1521: $i,SV425: $i] :
( ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 @ SV425 @ SV1521 @ SV2124 @ SV2250 ) @ SV1521 @ SV2250 @ SV2250 ) @ ( c_Transitive__Closure_Ortrancl @ SV2124 @ SV2250 ) @ ( tc_prod @ SV2250 @ SV2250 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV425 @ SV1521 ) )
| ~ ( c_in @ ( c_Pair @ SV1030 @ SV1521 @ SV2250 @ SV2250 ) @ ( c_Transitive__Closure_Ortrancl @ SV2124 @ SV2250 ) @ ( tc_prod @ SV2250 @ SV2250 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV425 @ SV1030 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5371]) ).
thf(5651,plain,
! [SV1031: $i,SV2251: $i,SV2125: $i,SV426: $i,SV1522: $i] :
( ( ( c_in @ ( c_Pair @ SV1522 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 @ SV426 @ SV1522 @ SV2125 @ SV2251 ) @ SV2251 @ SV2251 ) @ ( c_Transitive__Closure_Ortrancl @ SV2125 @ SV2251 ) @ ( tc_prod @ SV2251 @ SV2251 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV426 @ SV1522 ) )
| ~ ( c_in @ ( c_Pair @ SV1522 @ SV1031 @ SV2251 @ SV2251 ) @ ( c_Transitive__Closure_Ortrancl @ SV2125 @ SV2251 ) @ ( tc_prod @ SV2251 @ SV2251 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV426 @ SV1031 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5372]) ).
thf(5652,plain,
! [SV1032: $i,SV2252: $i,SV2126: $i,SV1523: $i,SV427: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV427 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2 @ SV427 @ SV1523 @ SV2126 @ SV2252 ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV427 @ SV1523 ) )
| ~ ( c_in @ ( c_Pair @ SV1523 @ SV1032 @ SV2252 @ SV2252 ) @ ( c_Transitive__Closure_Ortrancl @ SV2126 @ SV2252 ) @ ( tc_prod @ SV2252 @ SV2252 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV427 @ SV1032 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5373]) ).
thf(5653,plain,
! [SV1034: $i,SV2253: $i,SV2127: $i,SV1525: $i,SV429: $i] :
( ( ( hBOOL @ ( hAPP @ SV429 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 @ SV429 @ SV1525 @ SV2127 @ SV2253 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV429 @ SV1525 ) )
| ~ ( c_in @ ( c_Pair @ SV1525 @ SV1034 @ SV2253 @ SV2253 ) @ ( c_Transitive__Closure_Ortrancl @ SV2127 @ SV2253 ) @ ( tc_prod @ SV2253 @ SV2253 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV429 @ SV1034 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5375]) ).
thf(5654,plain,
! [SV1036: $i,SV2254: $i,SV2128: $i,SV1527: $i,SV431: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV431 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1 @ SV431 @ SV1527 @ SV2128 @ SV2254 ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV431 @ SV1527 ) )
| ~ ( c_in @ ( c_Pair @ SV1036 @ SV1527 @ SV2254 @ SV2254 ) @ ( c_Transitive__Closure_Ortrancl @ SV2128 @ SV2254 ) @ ( tc_prod @ SV2254 @ SV2254 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV431 @ SV1036 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5377]) ).
thf(5655,plain,
! [SV1528: $i,SV1877: $i,SV1037: $i,SV432: $i] :
( ( ( c_in @ ( c_Pair @ SV432 @ SV1037 @ SV1877 @ SV1877 ) @ ( c_Transitive__Closure_Ortrancl @ SV1528 @ SV1877 ) @ ( tc_prod @ SV1877 @ SV1877 ) )
= $false )
| ( ( SV432 = SV1037 )
= $true )
| ( ( c_in @ ( c_Pair @ SV432 @ ( c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1 @ SV432 @ SV1037 @ SV1528 @ SV1877 ) @ SV1877 @ SV1877 ) @ ( c_Transitive__Closure_Ortrancl @ SV1528 @ SV1877 ) @ ( tc_prod @ SV1877 @ SV1877 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5378]) ).
thf(5656,plain,
! [SV2129: $i,SV1878: $i,SV1038: $i,SV433: $i,SV1529: $i] :
( ( ( c_in @ SV1529 @ ( c_Product__Type_OSigma @ SV433 @ SV1038 @ SV1878 @ SV2129 ) @ ( tc_prod @ SV1878 @ SV2129 ) )
= $false )
| ( ( c_in @ ( c_ATP__Linkup_Osko__Product__Type__XSigmaE__1__1 @ SV433 @ SV1038 @ SV1529 @ SV1878 @ SV2129 ) @ SV433 @ SV1878 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5379]) ).
thf(5657,plain,
! [SV437: $i,SV1530: $i,SV1879: $i,SV1042: $i] :
( ( ( c_in @ ( c_Pair @ SV1042 @ SV1879 @ SV1530 @ SV1530 ) @ SV437 @ ( tc_prod @ SV1530 @ SV1530 ) )
= $true )
| ( ( ! [SY5786: $i] :
( ~ ( c_in @ SV1879 @ SY5786 @ SV1530 )
| ~ ( c_Equiv__Relations_Oequiv @ SY5786 @ SV437 @ SV1530 ) ) )
= $true )
| ( ( ( c_Relation_OImage @ SV437 @ ( c_Set_Oinsert @ SV1042 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1530 @ tc_bool ) ) @ SV1530 ) @ SV1530 @ SV1530 )
= ( c_Relation_OImage @ SV437 @ ( c_Set_Oinsert @ SV1879 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1530 @ tc_bool ) ) @ SV1530 ) @ SV1530 @ SV1530 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5381]) ).
thf(5658,plain,
! [SV1880: $i,SV1043: $i,SV1531: $i,SV438: $i,SV2334: $i] :
( ( ( ~ ( c_Equiv__Relations_Oequiv @ SV2334 @ SV438 @ SV1531 )
| ( c_in @ ( c_Pair @ SV1043 @ SV1880 @ SV1531 @ SV1531 ) @ SV438 @ ( tc_prod @ SV1531 @ SV1531 ) )
| ~ ( c_in @ SV1880 @ SV2334 @ SV1531 )
| ~ ( c_in @ SV1043 @ SV2334 @ SV1531 ) )
= $true )
| ( ( ( c_Relation_OImage @ SV438 @ ( c_Set_Oinsert @ SV1043 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1531 @ tc_bool ) ) @ SV1531 ) @ SV1531 @ SV1531 )
= ( c_Relation_OImage @ SV438 @ ( c_Set_Oinsert @ SV1880 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1531 @ tc_bool ) ) @ SV1531 ) @ SV1531 @ SV1531 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5382]) ).
thf(5659,plain,
! [SV439: $i,SV1532: $i,SV1881: $i,SV1044: $i] :
( ( ( c_in @ ( c_Pair @ SV1044 @ SV1881 @ SV1532 @ SV1532 ) @ SV439 @ ( tc_prod @ SV1532 @ SV1532 ) )
= $false )
| ( ( ! [SY5788: $i] :
( ~ ( c_in @ SV1881 @ SY5788 @ SV1532 )
| ~ ( c_in @ SV1044 @ SY5788 @ SV1532 )
| ~ ( c_Equiv__Relations_Oequiv @ SY5788 @ SV439 @ SV1532 ) ) )
= $true )
| ( ( ( c_Relation_OImage @ SV439 @ ( c_Set_Oinsert @ SV1044 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1532 @ tc_bool ) ) @ SV1532 ) @ SV1532 @ SV1532 )
= ( c_Relation_OImage @ SV439 @ ( c_Set_Oinsert @ SV1881 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1532 @ tc_bool ) ) @ SV1532 ) @ SV1532 @ SV1532 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5383]) ).
thf(5660,plain,
! [SV440: $i,SV1045: $i,SV1533: $i,SV2335: $i,SV1882: $i] :
( ( ( ~ ( c_in @ SV1882 @ SV2335 @ SV1533 )
| ~ ( c_in @ SV1045 @ SV2335 @ SV1533 )
| ~ ( c_Equiv__Relations_Oequiv @ SV2335 @ SV440 @ SV1533 )
| ( c_in @ ( c_Pair @ SV1045 @ SV1882 @ SV1533 @ SV1533 ) @ SV440 @ ( tc_prod @ SV1533 @ SV1533 ) ) )
= $true )
| ( ( ( c_Relation_OImage @ SV440 @ ( c_Set_Oinsert @ SV1045 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1533 @ tc_bool ) ) @ SV1533 ) @ SV1533 @ SV1533 )
= ( c_Relation_OImage @ SV440 @ ( c_Set_Oinsert @ SV1882 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1533 @ tc_bool ) ) @ SV1533 ) @ SV1533 @ SV1533 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5384]) ).
thf(5661,plain,
! [SV2131: $i,SV442: $i,SV1535: $i,SV1047: $i,SV2336: $i] :
( ( ( ~ ( c_lessequals @ SV2336 @ ( c_Product__Type_OSigma @ SV1047 @ ( c_COMBK @ SV1047 @ ( tc_fun @ SV1535 @ tc_bool ) @ SV1535 ) @ SV1535 @ SV1535 ) @ ( tc_fun @ ( tc_prod @ SV1535 @ SV1535 ) @ tc_bool ) )
| ~ ( c_in @ ( c_Pair @ SV442 @ SV2131 @ SV1535 @ SV1535 ) @ ( c_Transitive__Closure_Ortrancl @ SV2336 @ SV1535 ) @ ( tc_prod @ SV1535 @ SV1535 ) ) )
= $true )
| ( ( SV442 = SV2131 )
= $true )
| ( ( c_in @ SV442 @ SV1047 @ SV1535 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5385]) ).
thf(5662,plain,
! [SV446: $i,SV1883: $i,SV1539: $i,SV1051: $i,SV2255: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV2255 @ SV1051 @ SV1539 @ SV1539 ) @ ( c_Transitive__Closure_Ortrancl @ SV1883 @ SV1539 ) @ ( tc_prod @ SV1539 @ SV1539 ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV446 @ SV2255 @ SV1539 @ SV1539 ) @ SV1883 @ ( tc_prod @ SV1539 @ SV1539 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV446 @ SV1051 @ SV1539 @ SV1539 ) @ ( c_Transitive__Closure_Otrancl @ SV1883 @ SV1539 ) @ ( tc_prod @ SV1539 @ SV1539 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5386]) ).
thf(5663,plain,
! [SV447: $i,SV1884: $i,SV1540: $i,SV1052: $i,SV2256: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV2256 @ SV1052 @ SV1540 @ SV1540 ) @ SV1884 @ ( tc_prod @ SV1540 @ SV1540 ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV447 @ SV2256 @ SV1540 @ SV1540 ) @ ( c_Transitive__Closure_Ortrancl @ SV1884 @ SV1540 ) @ ( tc_prod @ SV1540 @ SV1540 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV447 @ SV1052 @ SV1540 @ SV1540 ) @ ( c_Transitive__Closure_Otrancl @ SV1884 @ SV1540 ) @ ( tc_prod @ SV1540 @ SV1540 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5387]) ).
thf(5664,plain,
! [SV1885: $i,SV1541: $i,SV1053: $i,SV448: $i] :
( ( ( c_in @ ( c_Pair @ SV448 @ SV1053 @ SV1541 @ SV1541 ) @ ( c_Transitive__Closure_Otrancl @ SV1885 @ SV1541 ) @ ( tc_prod @ SV1541 @ SV1541 ) )
= $false )
| ( ( SV448 = SV1053 )
= $true )
| ( ( c_in @ ( c_Pair @ SV448 @ SV1053 @ SV1541 @ SV1541 ) @ ( c_Transitive__Closure_Ortrancl @ SV1885 @ SV1541 ) @ ( tc_prod @ SV1541 @ SV1541 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5388]) ).
thf(5665,plain,
! [SV1886: $i,SV1542: $i,SV1054: $i,SV449: $i] :
( ( ( c_in @ ( c_Pair @ SV449 @ SV1054 @ SV1542 @ SV1542 ) @ ( c_Transitive__Closure_Ortrancl @ SV1886 @ SV1542 ) @ ( tc_prod @ SV1542 @ SV1542 ) )
= $false )
| ( ( SV449 = SV1054 )
= $true )
| ( ( c_in @ ( c_Pair @ SV449 @ SV1054 @ SV1542 @ SV1542 ) @ ( c_Transitive__Closure_Otrancl @ SV1886 @ SV1542 ) @ ( tc_prod @ SV1542 @ SV1542 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5389]) ).
thf(5666,plain,
! [SV1887: $i,SV1543: $i,SV1055: $i,SV450: $i] :
( ( ( c_in @ ( c_Pair @ SV450 @ SV1055 @ SV1543 @ SV1543 ) @ ( c_Transitive__Closure_Ortrancl @ SV1887 @ SV1543 ) @ ( tc_prod @ SV1543 @ SV1543 ) )
= $false )
| ( ( SV450 = SV1055 )
= $true )
| ( ( c_in @ ( c_Pair @ SV450 @ SV1055 @ SV1543 @ SV1543 ) @ ( c_Transitive__Closure_Otrancl @ SV1887 @ SV1543 ) @ ( tc_prod @ SV1543 @ SV1543 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5390]) ).
thf(5667,plain,
! [SV1058: $i,SV1890: $i,SV1546: $i,SV453: $i,SV2337: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV2337 @ SV453 @ SV1546 @ SV1546 ) @ ( c_Transitive__Closure_Ortrancl @ SV1890 @ SV1546 ) @ ( tc_prod @ SV1546 @ SV1546 ) )
| ~ ( c_in @ ( c_Pair @ SV2337 @ SV1058 @ SV1546 @ SV1546 ) @ ( c_Transitive__Closure_Ortrancl @ SV1890 @ SV1546 ) @ ( tc_prod @ SV1546 @ SV1546 ) )
| ~ ( c_Relation_Osingle__valued @ SV1890 @ SV1546 @ SV1546 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1058 @ SV453 @ SV1546 @ SV1546 ) @ ( c_Transitive__Closure_Ortrancl @ SV1890 @ SV1546 ) @ ( tc_prod @ SV1546 @ SV1546 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV453 @ SV1058 @ SV1546 @ SV1546 ) @ ( c_Transitive__Closure_Ortrancl @ SV1890 @ SV1546 ) @ ( tc_prod @ SV1546 @ SV1546 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5393]) ).
thf(5668,plain,
! [SV455: $i,SV1892: $i,SV1548: $i,SV1060: $i,SV2257: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV2257 @ SV1060 @ SV1548 @ SV1548 ) @ ( c_Transitive__Closure_Ortrancl @ SV1892 @ SV1548 ) @ ( tc_prod @ SV1548 @ SV1548 ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV455 @ SV2257 @ SV1548 @ SV1548 ) @ ( c_Transitive__Closure_Otrancl @ SV1892 @ SV1548 ) @ ( tc_prod @ SV1548 @ SV1548 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV455 @ SV1060 @ SV1548 @ SV1548 ) @ ( c_Transitive__Closure_Otrancl @ SV1892 @ SV1548 ) @ ( tc_prod @ SV1548 @ SV1548 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5395]) ).
thf(5669,plain,
! [SV456: $i,SV1893: $i,SV1549: $i,SV1061: $i,SV2258: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV2258 @ SV1061 @ SV1549 @ SV1549 ) @ ( c_Transitive__Closure_Otrancl @ SV1893 @ SV1549 ) @ ( tc_prod @ SV1549 @ SV1549 ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV456 @ SV2258 @ SV1549 @ SV1549 ) @ ( c_Transitive__Closure_Ortrancl @ SV1893 @ SV1549 ) @ ( tc_prod @ SV1549 @ SV1549 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV456 @ SV1061 @ SV1549 @ SV1549 ) @ ( c_Transitive__Closure_Otrancl @ SV1893 @ SV1549 ) @ ( tc_prod @ SV1549 @ SV1549 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5396]) ).
thf(5670,plain,
! [SV1898: $i,SV1554: $i,SV1066: $i,SV2338: $i,SV2134: $i,SV461: $i] :
( ( ( ! [SY6035: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_split @ SV461 @ SV2134 @ SV2338 @ ( tc_fun @ SY6035 @ tc_bool ) ) @ ( c_Pair @ SV1066 @ SV1554 @ SV2134 @ SV2338 ) ) @ SV1898 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ SV461 @ SV1066 ) @ SV1554 ) @ SV1898 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5401]) ).
thf(5671,plain,
! [SV2261: $i,SV462: $i,SV1899: $i,SV1555: $i,SV1067: $i] :
( ( ( c_in @ SV1067 @ SV1555 @ SV1899 )
= $false )
| ( ( c_in @ ( hAPP @ SV462 @ SV1067 ) @ ( c_Set_Oimage @ SV462 @ SV1555 @ SV1899 @ SV2261 ) @ SV2261 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5402]) ).
thf(5672,plain,
! [SV2262: $i,SV463: $i,SV1900: $i,SV1556: $i,SV1068: $i] :
( ( ( c_in @ SV1068 @ SV1556 @ SV1900 )
= $false )
| ( ( c_in @ ( hAPP @ SV463 @ SV1068 ) @ ( c_Set_Oimage @ SV463 @ SV1556 @ SV1900 @ SV2262 ) @ SV2262 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5403]) ).
thf(5673,plain,
! [SV2339: $i,SV1557: $i,SV1069: $i,SV464: $i,SV2263: $i] :
( ( ( c_in @ ( hAPP @ SV2263 @ SV464 ) @ ( c_Set_Oimage @ SV2263 @ SV1069 @ SV1557 @ SV2339 ) @ SV2339 )
= $true )
| ( ( c_in @ SV464 @ SV1069 @ SV1557 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5404]) ).
thf(5674,plain,
! [SV2340: $i,SV1558: $i,SV1070: $i,SV465: $i,SV2264: $i] :
( ( ( c_in @ ( hAPP @ SV2264 @ SV465 ) @ ( c_Set_Oimage @ SV2264 @ SV1070 @ SV1558 @ SV2340 ) @ SV2340 )
= $true )
| ( ( c_in @ SV465 @ SV1070 @ SV1558 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5405]) ).
thf(5675,plain,
! [SV2135: $i,SV1901: $i,SV468: $i,SV1560: $i,SV1073: $i] :
( ( ( c_in @ SV1073 @ ( c_Relation_OImage @ SV1560 @ SV468 @ SV1901 @ SV2135 ) @ SV2135 )
= $false )
| ( ( c_in @ ( c_ATP__Linkup_Osko__Relation__XImageE__1__1 @ SV468 @ SV1073 @ SV1560 @ SV1901 @ SV2135 ) @ SV468 @ SV1901 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5406]) ).
thf(5676,plain,
! [SV1075: $i,SV2136: $i,SV1902: $i,SV470: $i] :
( ( ( hBOOL @ ( hAPP @ SV470 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ SV470 @ SV1902 @ SV2136 ) ) )
= $false )
| ( ( ~ ( c_in @ SV1075 @ ( c_Wellfounded_Oacc @ SV1902 @ SV2136 ) @ SV2136 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV470 @ SV1075 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5407]) ).
thf(5677,plain,
! [SV472: $i,SV1903: $i,SV1077: $i] :
( ( ( c_in @ SV1077 @ ( c_Wellfounded_Oacc @ SV1903 @ t_a ) @ t_a )
= $false )
| ( ( hBOOL @ ( hAPP @ SV472 @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ SV472 @ SV1903 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV472 @ SV1077 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5408]) ).
thf(5678,plain,
! [SV473: $i,SV2137: $i,SV1904: $i,SV1078: $i] :
( ( ( c_in @ SV1078 @ ( c_Wellfounded_Oacc @ SV1904 @ SV2137 ) @ SV2137 )
= $false )
| ( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ SV473 @ SV1904 @ SV2137 ) @ ( c_Wellfounded_Oacc @ SV1904 @ SV2137 ) @ SV2137 )
= $true )
| ( ( hBOOL @ ( hAPP @ SV473 @ SV1078 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5409]) ).
thf(5679,plain,
! [SV2138: $i,SV1905: $i,SV477: $i,SV1561: $i,SV1082: $i] :
( ( ( c_in @ SV1082 @ ( c_Relation_OImage @ SV1561 @ SV477 @ SV1905 @ SV2138 ) @ SV2138 )
= $false )
| ( ( c_in @ ( c_ATP__Linkup_Osko__Relation__XImage__iff__1__1 @ SV477 @ SV1082 @ SV1561 @ SV1905 @ SV2138 ) @ SV477 @ SV1905 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5410]) ).
thf(5680,plain,
! [SV1089: $i,SV2139: $i,SV1906: $i,SV485: $i] :
( ( ( hBOOL @ ( hAPP @ SV485 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ SV485 @ SV1906 @ SV2139 ) ) )
= $false )
| ( ( ~ ( c_in @ SV1089 @ ( c_Wellfounded_Oacc @ SV1906 @ SV2139 ) @ SV2139 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV485 @ SV1089 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5411]) ).
thf(5681,plain,
! [SV2341: $i,SV2265: $i,SV2143: $i,SV1908: $i,SV1570: $i,SV1112: $i,SV510: $i] :
( ( ( c_Relation_Orel__comp @ ( c_Relation_Orel__comp @ SV510 @ SV1112 @ SV1570 @ SV1908 @ SV2143 ) @ SV2265 @ SV1570 @ SV2143 @ SV2341 )
= ( c_Relation_Orel__comp @ SV510 @ ( c_Relation_Orel__comp @ SV1112 @ SV2265 @ SV1908 @ SV2143 @ SV2341 ) @ SV1570 @ SV1908 @ SV2341 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5414]) ).
thf(5682,plain,
! [SV1119: $i,SV1574: $i,SV518: $i,SV2266: $i] :
( ( ( c_in @ SV2266 @ SV518 @ SV1574 )
= $false )
| ( ( ~ ( c_Wellfounded_Owf @ SV1119 @ SV1574 ) )
= $true )
| ( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 @ SV518 @ SV1119 @ SV1574 ) @ SV518 @ SV1574 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5416]) ).
thf(5683,plain,
! [SV1575: $i,SV520: $i,SV2145: $i,SV1910: $i,SV1121: $i] :
( ( ( ~ ( c_Relation_Osingle__valued @ SV1121 @ SV1910 @ SV2145 ) )
= $true )
| ( ( ~ ( c_Relation_Osingle__valued @ SV520 @ SV1575 @ SV1910 ) )
= $true )
| ( ( c_Relation_Osingle__valued @ ( c_Relation_Orel__comp @ SV520 @ SV1121 @ SV1575 @ SV1910 @ SV2145 ) @ SV1575 @ SV2145 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5417]) ).
thf(5684,plain,
! [SV527: $i,SV1912: $i,SV1127: $i] :
( ( ( c_in @ SV1127 @ ( c_Wellfounded_Oacc @ SV1912 @ t_a ) @ t_a )
= $false )
| ( ( hBOOL @ ( hAPP @ SV527 @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ SV527 @ SV1912 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV527 @ SV1127 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5418]) ).
thf(5685,plain,
! [SV1130: $i,SV1578: $i,SV530: $i,SV2267: $i] :
( ( ( c_in @ SV2267 @ SV530 @ SV1578 )
= $false )
| ( ( ~ ( c_Wellfounded_Owf @ SV1130 @ SV1578 ) )
= $true )
| ( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 @ SV530 @ SV1130 @ SV1578 ) @ SV530 @ SV1578 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5419]) ).
thf(5686,plain,
! [SV2268: $i,SV2146: $i,SV1914: $i,SV1580: $i,SV1133: $i,SV533: $i] :
( ( ( c_Equiv__Relations_Ocongruent @ SV533 @ ( hAPP @ SV1133 @ SV1580 ) @ SV1914 @ SV2146 )
= $true )
| ( ( ! [SY6015: $i] :
( ~ ( c_in @ SV1580 @ SV2268 @ SY6015 )
| ! [SY6016: $i] :
( ~ ( c_Equiv__Relations_Ocongruent2 @ SY6016 @ SV533 @ SV1133 @ SY6015 @ SV1914 @ SV2146 )
| ~ ( c_Equiv__Relations_Oequiv @ SV2268 @ SY6016 @ SY6015 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5420]) ).
thf(5687,plain,
! [SV541: $i,SV2147: $i,SV1916: $i,SV1141: $i] :
( ( ( c_in @ SV1141 @ ( c_Wellfounded_Oacc @ SV1916 @ SV2147 ) @ SV2147 )
= $false )
| ( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ SV541 @ SV1916 @ SV2147 ) @ ( c_Wellfounded_Oacc @ SV1916 @ SV2147 ) @ SV2147 )
= $true )
| ( ( hBOOL @ ( hAPP @ SV541 @ SV1141 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5421]) ).
thf(5688,plain,
! [SV2148: $i,SV1917: $i,SV544: $i,SV1585: $i,SV1144: $i] :
( ( ( c_in @ SV1144 @ ( c_Relation_OImage @ SV1585 @ SV544 @ SV1917 @ SV2148 ) @ SV2148 )
= $false )
| ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XImageE__1__1 @ SV544 @ SV1144 @ SV1585 @ SV1917 @ SV2148 ) @ SV1144 @ SV1917 @ SV2148 ) @ SV1585 @ ( tc_prod @ SV1917 @ SV2148 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5422]) ).
thf(5689,plain,
! [SV1146: $i,SV2342: $i,SV2269: $i,SV546: $i,SV1587: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1587 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ SV546 @ SV2269 @ SV2342 ) @ SV2342 @ SV2342 ) @ SV2269 @ ( tc_prod @ SV2342 @ SV2342 ) )
| ~ ( c_in @ SV1146 @ ( c_Wellfounded_Oacc @ SV2269 @ SV2342 ) @ SV2342 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV546 @ SV1587 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV546 @ SV1146 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5423]) ).
thf(5690,plain,
! [SV1147: $i,SV2270: $i,SV547: $i,SV1918: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1918 @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ SV547 @ SV2270 ) @ t_a @ t_a ) @ SV2270 @ ( tc_prod @ t_a @ t_a ) ) )
= $true )
| ( ( ~ ( c_in @ SV1147 @ ( c_Wellfounded_Oacc @ SV2270 @ t_a ) @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV547 @ SV1918 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV547 @ SV1147 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5424]) ).
thf(5691,plain,
! [SV1588: $i,SV2271: $i,SV1148: $i,SV548: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV548 @ ( c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 @ SV1148 @ SV2271 @ SV1588 ) @ SV1588 @ SV1588 ) @ SV2271 @ ( tc_prod @ SV1588 @ SV1588 ) ) )
= $true )
| ( ( ! [SY5526: $i] :
~ ( c_in @ SY5526 @ SV1148 @ SV1588 )
| ~ ( c_Wellfounded_Owf @ SV2271 @ SV1588 ) )
= $true )
| ( ( c_in @ SV548 @ SV1148 @ SV1588 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5425]) ).
thf(5692,plain,
! [SV551: $i,SV1591: $i,SV1151: $i,SV2149: $i] :
( ( ( c_in @ SV2149 @ ( c_Wellfounded_Oacc @ SV1151 @ SV1591 ) @ SV1591 )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV551 @ SV2149 @ SV1591 @ SV1591 ) @ ( c_Transitive__Closure_Ortrancl @ SV1151 @ SV1591 ) @ ( tc_prod @ SV1591 @ SV1591 ) ) )
= $true )
| ( ( c_in @ SV551 @ ( c_Wellfounded_Oacc @ SV1151 @ SV1591 ) @ SV1591 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5427]) ).
thf(5693,plain,
! [SV1152: $i,SV1592: $i,SV2150: $i,SV552: $i] :
( ( ( c_in @ ( c_Pair @ SV552 @ SV2150 @ SV1592 @ SV1592 ) @ ( c_Transitive__Closure_Ortrancl @ SV1152 @ SV1592 ) @ ( tc_prod @ SV1592 @ SV1592 ) )
= $false )
| ( ( ~ ( c_in @ SV2150 @ ( c_Wellfounded_Oacc @ SV1152 @ SV1592 ) @ SV1592 ) )
= $true )
| ( ( c_in @ SV552 @ ( c_Wellfounded_Oacc @ SV1152 @ SV1592 ) @ SV1592 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5428]) ).
thf(5694,plain,
! [SV1153: $i,SV2151: $i,SV553: $i,SV1920: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1920 @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ SV553 @ SV2151 ) @ t_a @ t_a ) @ SV2151 @ ( tc_prod @ t_a @ t_a ) ) )
= $true )
| ( ( ~ ( c_in @ SV1153 @ ( c_Wellfounded_Oacc @ SV2151 @ t_a ) @ t_a ) )
= $true )
| ( ( c_in @ SV1920 @ ( c_Wellfounded_Oacc @ SV2151 @ t_a ) @ t_a )
= $true )
| ( ( hBOOL @ ( hAPP @ SV553 @ SV1153 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5429]) ).
thf(5695,plain,
! [SV1155: $i,SV2272: $i,SV555: $i,SV1921: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1921 @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ SV555 @ SV2272 ) @ t_a @ t_a ) @ SV2272 @ ( tc_prod @ t_a @ t_a ) ) )
= $true )
| ( ( ~ ( c_in @ SV1155 @ ( c_Wellfounded_Oacc @ SV2272 @ t_a ) @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV555 @ SV1921 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV555 @ SV1155 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5430]) ).
thf(5696,plain,
! [SV2343: $i,SV2273: $i,SV2152: $i,SV1922: $i,SV1594: $i,SV1156: $i,SV556: $i] :
( ( ( c_in @ ( hAPP @ ( hAPP @ SV556 @ SV1156 ) @ SV1594 ) @ ( c_Set_Oimage @ ( c_split @ SV556 @ SV1922 @ SV2152 @ SV2273 ) @ SV2343 @ ( tc_prod @ SV1922 @ SV2152 ) @ SV2273 ) @ SV2273 )
| ~ ( c_in @ ( c_Pair @ SV1156 @ SV1594 @ SV1922 @ SV2152 ) @ SV2343 @ ( tc_prod @ SV1922 @ SV2152 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5431]) ).
thf(5697,plain,
! [SV1158: $i,SV2153: $i,SV558: $i,SV1924: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1924 @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ SV558 @ SV2153 ) @ t_a @ t_a ) @ SV2153 @ ( tc_prod @ t_a @ t_a ) ) )
= $true )
| ( ( ~ ( c_in @ SV1158 @ ( c_Wellfounded_Oacc @ SV2153 @ t_a ) @ t_a ) )
= $true )
| ( ( c_in @ SV1924 @ ( c_Wellfounded_Oacc @ SV2153 @ t_a ) @ t_a )
= $true )
| ( ( hBOOL @ ( hAPP @ SV558 @ SV1158 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5433]) ).
thf(5698,plain,
! [SV1159: $i,SV2344: $i,SV2274: $i,SV559: $i,SV1596: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1596 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ SV559 @ SV2274 @ SV2344 ) @ SV2344 @ SV2344 ) @ SV2274 @ ( tc_prod @ SV2344 @ SV2344 ) )
| ~ ( c_in @ SV1159 @ ( c_Wellfounded_Oacc @ SV2274 @ SV2344 ) @ SV2344 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV559 @ SV1596 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV559 @ SV1159 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5434]) ).
thf(5699,plain,
! [SV1597: $i,SV2275: $i,SV1160: $i,SV560: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV560 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 @ SV1160 @ SV2275 @ SV1597 ) @ SV1597 @ SV1597 ) @ SV2275 @ ( tc_prod @ SV1597 @ SV1597 ) ) )
= $true )
| ( ( ! [SY5538: $i] :
~ ( c_in @ SY5538 @ SV1160 @ SV1597 )
| ~ ( c_Wellfounded_Owf @ SV2275 @ SV1597 ) )
= $true )
| ( ( c_in @ SV560 @ SV1160 @ SV1597 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5435]) ).
thf(5700,plain,
! [SV2154: $i,SV1926: $i,SV562: $i,SV1599: $i,SV1162: $i] :
( ( ( c_in @ SV1162 @ ( c_Relation_OImage @ SV1599 @ SV562 @ SV1926 @ SV2154 ) @ SV2154 )
= $false )
| ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XImage__iff__1__1 @ SV562 @ SV1162 @ SV1599 @ SV1926 @ SV2154 ) @ SV1162 @ SV1926 @ SV2154 ) @ SV1599 @ ( tc_prod @ SV1926 @ SV2154 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5437]) ).
thf(5701,plain,
! [SV2155: $i,SV1927: $i,SV1163: $i,SV563: $i] :
( ( ( c_in @ ( c_Pair @ SV563 @ SV1163 @ SV1927 @ SV1927 ) @ ( c_Transitive__Closure_Ortrancl @ SV2155 @ SV1927 ) @ ( tc_prod @ SV1927 @ SV1927 ) )
= $false )
| ( ( c_in @ SV563 @ ( c_Relation_ODomain @ SV2155 @ SV1927 @ SV1927 ) @ SV1927 )
= $true )
| ( ( SV563 = SV1163 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5438]) ).
thf(5702,plain,
! [SV2345: $i,SV2276: $i,SV2156: $i,SV1929: $i,SV1601: $i,SV1165: $i,SV565: $i] :
( ( ( c_in @ SV565 @ ( hAPP @ ( c_split @ SV1165 @ SV1601 @ SV1929 @ ( tc_fun @ SV2156 @ tc_bool ) ) @ ( c_Pair @ SV2276 @ SV2345 @ SV1601 @ SV1929 ) ) @ SV2156 )
| ~ ( c_in @ SV565 @ ( hAPP @ ( hAPP @ SV1165 @ SV2276 ) @ SV2345 ) @ SV2156 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5440]) ).
thf(5703,plain,
! [SV2346: $i,SV2277: $i,SV2157: $i,SV1930: $i,SV1602: $i,SV1166: $i,SV566: $i] :
( ( ! [SY6036: $i] :
( ( ( hAPP @ ( hAPP @ SV566 @ SV1166 ) @ SV1602 )
= ( hAPP @ ( hAPP @ SV566 @ SV1930 ) @ SV2157 ) )
| ~ ( c_in @ ( c_Pair @ SV1602 @ SV2157 @ SV2277 @ SV2277 ) @ SV2346 @ ( tc_prod @ SV2277 @ SV2277 ) )
| ! [SY6037: $i] :
( ~ ( c_in @ ( c_Pair @ SV1166 @ SV1930 @ SY6036 @ SY6036 ) @ SY6037 @ ( tc_prod @ SY6036 @ SY6036 ) )
| ! [SY6038: $i] :
~ ( c_Equiv__Relations_Ocongruent2 @ SY6037 @ SV2346 @ SV566 @ SY6036 @ SV2277 @ SY6038 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5441]) ).
thf(5704,plain,
! [SV567: $i,SV2347: $i,SV2278: $i,SV1931: $i,SV1167: $i,SV1603: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1603 @ SV1167 @ SV1931 @ SV2278 ) @ SV2347 @ ( tc_prod @ SV1931 @ SV2278 ) )
| ~ ( c_in @ ( c_Pair @ SV1603 @ SV567 @ SV1931 @ SV2278 ) @ SV2347 @ ( tc_prod @ SV1931 @ SV2278 ) )
| ~ ( c_Relation_Osingle__valued @ SV2347 @ SV1931 @ SV2278 ) )
= $true )
| ( ( SV567 = SV1167 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5442]) ).
thf(5705,plain,
! [SV2279: $i,SV2158: $i,SV1932: $i,SV1604: $i,SV1168: $i,SV568: $i] :
( ( ( ( hAPP @ ( c_Recdef_Ocut @ SV568 @ SV1168 @ SV1604 @ SV1932 @ SV2158 ) @ SV2279 )
= ( hAPP @ SV568 @ SV2279 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV2279 @ SV1604 @ SV1932 @ SV1932 ) @ SV1168 @ ( tc_prod @ SV1932 @ SV1932 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5443]) ).
thf(5706,plain,
! [SV2280: $i,SV2159: $i,SV1933: $i,SV1605: $i,SV1169: $i,SV569: $i] :
( ( ( ( hAPP @ ( c_Recdef_Ocut @ SV569 @ SV1169 @ SV1605 @ SV1933 @ SV2159 ) @ SV2280 )
= ( hAPP @ SV569 @ SV2280 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV2280 @ SV1605 @ SV1933 @ SV1933 ) @ SV1169 @ ( tc_prod @ SV1933 @ SV1933 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5444]) ).
thf(5707,plain,
! [SV570: $i,SV1606: $i,SV1170: $i,SV2160: $i,SV1934: $i] :
( ( ( c_in @ ( c_Pair @ SV1934 @ SV2160 @ SV1170 @ SV1606 ) @ SV570 @ ( tc_prod @ SV1170 @ SV1606 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_FunDef_Oin__rel @ SV570 @ SV1170 @ SV1606 ) @ SV1934 ) @ SV2160 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5445]) ).
thf(5708,plain,
! [SV1171: $i,SV571: $i,SV1935: $i,SV1607: $i,SV2161: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_FunDef_Oin__rel @ SV2161 @ SV1607 @ SV1935 ) @ SV571 ) @ SV1171 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV571 @ SV1171 @ SV1607 @ SV1935 ) @ SV2161 @ ( tc_prod @ SV1607 @ SV1935 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5446]) ).
thf(5709,plain,
! [SV572: $i,SV1936: $i,SV1608: $i,SV1172: $i,SV2281: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV2281 @ SV1172 @ SV1608 @ SV1608 ) @ SV1936 @ ( tc_prod @ SV1608 @ SV1608 ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV572 @ SV2281 @ SV1608 @ SV1608 ) @ SV1936 @ ( tc_prod @ SV1608 @ SV1608 ) )
| ~ ( c_Relation_Otrans @ SV1936 @ SV1608 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV572 @ SV1172 @ SV1608 @ SV1608 ) @ SV1936 @ ( tc_prod @ SV1608 @ SV1608 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5447]) ).
thf(5710,plain,
! [SV573: $i,SV1937: $i,SV1609: $i,SV1173: $i,SV2282: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV2282 @ SV1173 @ SV1609 @ SV1609 ) @ SV1937 @ ( tc_prod @ SV1609 @ SV1609 ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV573 @ SV2282 @ SV1609 @ SV1609 ) @ SV1937 @ ( tc_prod @ SV1609 @ SV1609 ) )
| ~ ( c_Relation_Otrans @ SV1937 @ SV1609 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV573 @ SV1173 @ SV1609 @ SV1609 ) @ SV1937 @ ( tc_prod @ SV1609 @ SV1609 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5448]) ).
thf(5711,plain,
! [SV2162: $i,SV1610: $i,SV1938: $i,SV574: $i,SV1174: $i] :
( ( ( c_in @ ( c_Pair @ SV1174 @ SV574 @ SV1938 @ SV1610 ) @ SV2162 @ ( tc_prod @ SV1938 @ SV1610 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV574 @ SV1174 @ SV1610 @ SV1938 ) @ ( c_Relation_Oconverse @ SV2162 @ SV1938 @ SV1610 ) @ ( tc_prod @ SV1610 @ SV1938 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5449]) ).
thf(5712,plain,
! [SV2163: $i,SV1611: $i,SV1939: $i,SV575: $i,SV1175: $i] :
( ( ( c_in @ ( c_Pair @ SV1175 @ SV575 @ SV1939 @ SV1611 ) @ SV2163 @ ( tc_prod @ SV1939 @ SV1611 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV575 @ SV1175 @ SV1611 @ SV1939 ) @ ( c_Relation_Oconverse @ SV2163 @ SV1939 @ SV1611 ) @ ( tc_prod @ SV1611 @ SV1939 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5450]) ).
thf(5713,plain,
! [SV2164: $i,SV1612: $i,SV1940: $i,SV576: $i,SV1176: $i] :
( ( ( c_in @ ( c_Pair @ SV1176 @ SV576 @ SV1940 @ SV1612 ) @ ( c_Relation_Oconverse @ SV2164 @ SV1612 @ SV1940 ) @ ( tc_prod @ SV1940 @ SV1612 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV576 @ SV1176 @ SV1612 @ SV1940 ) @ SV2164 @ ( tc_prod @ SV1612 @ SV1940 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5451]) ).
thf(5714,plain,
! [SV578: $i,SV1941: $i,SV1614: $i,SV1178: $i,SV2283: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV2283 @ SV1178 @ SV1614 @ SV1614 ) @ SV1941 @ ( tc_prod @ SV1614 @ SV1614 ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV578 @ SV2283 @ SV1614 @ SV1614 ) @ ( c_Transitive__Closure_Otrancl @ SV1941 @ SV1614 ) @ ( tc_prod @ SV1614 @ SV1614 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV578 @ SV1178 @ SV1614 @ SV1614 ) @ ( c_Transitive__Closure_Otrancl @ SV1941 @ SV1614 ) @ ( tc_prod @ SV1614 @ SV1614 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5453]) ).
thf(5715,plain,
! [SV579: $i,SV1942: $i,SV1615: $i,SV1179: $i,SV2284: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV2284 @ SV1179 @ SV1615 @ SV1615 ) @ ( c_Transitive__Closure_Otrancl @ SV1942 @ SV1615 ) @ ( tc_prod @ SV1615 @ SV1615 ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV579 @ SV2284 @ SV1615 @ SV1615 ) @ SV1942 @ ( tc_prod @ SV1615 @ SV1615 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV579 @ SV1179 @ SV1615 @ SV1615 ) @ ( c_Transitive__Closure_Otrancl @ SV1942 @ SV1615 ) @ ( tc_prod @ SV1615 @ SV1615 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5454]) ).
thf(5716,plain,
! [SV580: $i,SV1943: $i,SV1616: $i,SV1180: $i,SV2285: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV2285 @ SV1180 @ SV1616 @ SV1616 ) @ SV1943 @ ( tc_prod @ SV1616 @ SV1616 ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV580 @ SV2285 @ SV1616 @ SV1616 ) @ ( c_Transitive__Closure_Ortrancl @ SV1943 @ SV1616 ) @ ( tc_prod @ SV1616 @ SV1616 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV580 @ SV1180 @ SV1616 @ SV1616 ) @ ( c_Transitive__Closure_Ortrancl @ SV1943 @ SV1616 ) @ ( tc_prod @ SV1616 @ SV1616 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5455]) ).
thf(5717,plain,
! [SV581: $i,SV1944: $i,SV1617: $i,SV1181: $i,SV2286: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV2286 @ SV1181 @ SV1617 @ SV1617 ) @ ( c_Transitive__Closure_Ortrancl @ SV1944 @ SV1617 ) @ ( tc_prod @ SV1617 @ SV1617 ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV581 @ SV2286 @ SV1617 @ SV1617 ) @ SV1944 @ ( tc_prod @ SV1617 @ SV1617 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV581 @ SV1181 @ SV1617 @ SV1617 ) @ ( c_Transitive__Closure_Ortrancl @ SV1944 @ SV1617 ) @ ( tc_prod @ SV1617 @ SV1617 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5456]) ).
thf(5718,plain,
! [SV583: $i,SV1946: $i,SV1619: $i,SV1183: $i,SV2287: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV2287 @ SV1183 @ SV1619 @ SV1619 ) @ ( c_Transitive__Closure_Ortrancl @ SV1946 @ SV1619 ) @ ( tc_prod @ SV1619 @ SV1619 ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV583 @ SV2287 @ SV1619 @ SV1619 ) @ ( c_Transitive__Closure_Ortrancl @ SV1946 @ SV1619 ) @ ( tc_prod @ SV1619 @ SV1619 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV583 @ SV1183 @ SV1619 @ SV1619 ) @ ( c_Transitive__Closure_Ortrancl @ SV1946 @ SV1619 ) @ ( tc_prod @ SV1619 @ SV1619 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5458]) ).
thf(5719,plain,
! [SV1947: $i,SV1622: $i,SV586: $i,SV1186: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1186 @ SV586 @ SV1622 @ SV1622 ) @ SV1947 @ ( tc_prod @ SV1622 @ SV1622 ) ) )
= $true )
| ( ( ~ ( c_Wellfounded_Owf @ SV1947 @ SV1622 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV586 @ SV1186 @ SV1622 @ SV1622 ) @ SV1947 @ ( tc_prod @ SV1622 @ SV1622 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5459]) ).
thf(5720,plain,
! [SV2165: $i,SV1948: $i,SV587: $i,SV1187: $i] :
( ( ( c_in @ ( c_Pair @ SV1187 @ SV587 @ SV1948 @ SV1948 ) @ SV2165 @ ( tc_prod @ SV1948 @ SV1948 ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV587 @ SV1187 @ SV1948 @ SV1948 ) @ SV2165 @ ( tc_prod @ SV1948 @ SV1948 ) )
| ~ ( c_Relation_Oantisym @ SV2165 @ SV1948 ) )
= $true )
| ( ( SV587 = SV1187 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5460]) ).
thf(5721,plain,
! [SV2166: $i,SV1949: $i,SV588: $i,SV1188: $i] :
( ( ( c_in @ ( c_Pair @ SV1188 @ SV588 @ SV1949 @ SV1949 ) @ SV2166 @ ( tc_prod @ SV1949 @ SV1949 ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV588 @ SV1188 @ SV1949 @ SV1949 ) @ SV2166 @ ( tc_prod @ SV1949 @ SV1949 ) )
| ~ ( c_Relation_Oantisym @ SV2166 @ SV1949 ) )
= $true )
| ( ( SV588 = SV1188 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5461]) ).
thf(5722,plain,
! [SV589: $i,SV2288: $i,SV1950: $i,SV1623: $i,SV1189: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1189 @ SV1623 @ SV1950 @ SV1950 ) @ SV2288 @ ( tc_prod @ SV1950 @ SV1950 ) ) )
= $true )
| ( ( ! [SY6028: $i] :
~ ( c_Equiv__Relations_Ocongruent @ SV2288 @ SV589 @ SV1950 @ SY6028 ) )
= $true )
| ( ( ( hAPP @ SV589 @ SV1189 )
= ( hAPP @ SV589 @ SV1623 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5462]) ).
thf(5723,plain,
! [SV2289: $i,SV2168: $i,SV1952: $i,SV1624: $i,SV1191: $i,SV591: $i] :
( ( ( ( c_Recdef_Ocut @ SV591 @ SV1191 @ SV1624 @ SV1952 @ SV2168 )
!= ( c_Recdef_Ocut @ SV2289 @ SV1191 @ SV1624 @ SV1952 @ SV2168 ) )
= $true )
| ( ( ! [SY6029: $i] :
( ( ( hAPP @ SV591 @ SY6029 )
= ( hAPP @ SV2289 @ SY6029 ) )
| ~ ( c_in @ ( c_Pair @ SY6029 @ SV1624 @ SV1952 @ SV1952 ) @ SV1191 @ ( tc_prod @ SV1952 @ SV1952 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5464]) ).
thf(5724,plain,
! [SV2290: $i,SV2169: $i,SV1954: $i,SV1627: $i,SV1195: $i,SV595: $i] :
( ( ( c_in @ ( c_Pair @ SV595 @ SV1195 @ SV1627 @ SV1627 ) @ ( c_Relation_Oinv__image @ SV1954 @ SV2169 @ SV2290 @ SV1627 ) @ ( tc_prod @ SV1627 @ SV1627 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ ( hAPP @ SV2169 @ SV595 ) @ ( hAPP @ SV2169 @ SV1195 ) @ SV2290 @ SV2290 ) @ SV1954 @ ( tc_prod @ SV2290 @ SV2290 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5466]) ).
thf(5725,plain,
! [SV1955: $i,SV596: $i,SV2170: $i,SV2348: $i,SV1628: $i,SV1196: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1196 @ SV1628 @ SV2348 @ SV2348 ) @ ( c_Relation_Oinv__image @ SV2170 @ SV596 @ SV1955 @ SV2348 ) @ ( tc_prod @ SV2348 @ SV2348 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ ( hAPP @ SV596 @ SV1196 ) @ ( hAPP @ SV596 @ SV1628 ) @ SV1955 @ SV1955 ) @ SV2170 @ ( tc_prod @ SV1955 @ SV1955 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5467]) ).
thf(5726,plain,
! [SV1956: $i,SV1629: $i,SV597: $i,SV1197: $i] :
( ( ( c_in @ ( c_Pair @ SV1197 @ SV597 @ SV1629 @ SV1629 ) @ SV1956 @ ( tc_prod @ SV1629 @ SV1629 ) )
= $false )
| ( ( ~ ( c_Relation_Osym @ SV1956 @ SV1629 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV597 @ SV1197 @ SV1629 @ SV1629 ) @ SV1956 @ ( tc_prod @ SV1629 @ SV1629 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5468]) ).
thf(5727,plain,
! [SV1957: $i,SV1630: $i,SV598: $i,SV1198: $i] :
( ( ( c_in @ ( c_Pair @ SV1198 @ SV598 @ SV1630 @ SV1630 ) @ SV1957 @ ( tc_prod @ SV1630 @ SV1630 ) )
= $false )
| ( ( ~ ( c_Relation_Osym @ SV1957 @ SV1630 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV598 @ SV1198 @ SV1630 @ SV1630 ) @ SV1957 @ ( tc_prod @ SV1630 @ SV1630 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5469]) ).
thf(5728,plain,
! [SV2349: $i,SV2291: $i,SV2171: $i,SV1958: $i,SV1631: $i,SV1199: $i,SV599: $i] :
( ( ( c_in @ ( c_Pair @ SV599 @ SV1199 @ SV1631 @ SV1958 ) @ ( c_Relation_Orel__comp @ SV2171 @ SV2291 @ SV1631 @ SV2349 @ SV1958 ) @ ( tc_prod @ SV1631 @ SV1958 ) )
| ! [SY6039: $i] :
( ~ ( c_in @ ( c_Pair @ SY6039 @ SV1199 @ SV2349 @ SV1958 ) @ SV2291 @ ( tc_prod @ SV2349 @ SV1958 ) )
| ~ ( c_in @ ( c_Pair @ SV599 @ SY6039 @ SV1631 @ SV2349 ) @ SV2171 @ ( tc_prod @ SV1631 @ SV2349 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5470]) ).
thf(5729,plain,
! [SV600: $i,SV1959: $i,SV1632: $i,SV1200: $i,SV2292: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV2292 @ SV1200 @ SV1632 @ SV1632 ) @ SV1959 @ ( tc_prod @ SV1632 @ SV1632 ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV600 @ SV2292 @ SV1632 @ SV1632 ) @ SV1959 @ ( tc_prod @ SV1632 @ SV1632 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV600 @ SV1200 @ SV1632 @ SV1632 ) @ ( c_Transitive__Closure_Otrancl @ SV1959 @ SV1632 ) @ ( tc_prod @ SV1632 @ SV1632 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5471]) ).
thf(5730,plain,
! [SV601: $i,SV1960: $i,SV1633: $i,SV1201: $i,SV2293: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV2293 @ SV1201 @ SV1633 @ SV1633 ) @ ( c_Transitive__Closure_Otrancl @ SV1960 @ SV1633 ) @ ( tc_prod @ SV1633 @ SV1633 ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV601 @ SV2293 @ SV1633 @ SV1633 ) @ ( c_Transitive__Closure_Otrancl @ SV1960 @ SV1633 ) @ ( tc_prod @ SV1633 @ SV1633 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV601 @ SV1201 @ SV1633 @ SV1633 ) @ ( c_Transitive__Closure_Otrancl @ SV1960 @ SV1633 ) @ ( tc_prod @ SV1633 @ SV1633 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5472]) ).
thf(5731,plain,
! [SV1961: $i,SV1634: $i,SV1204: $i,SV604: $i] :
( ( ( c_in @ ( c_Pair @ SV604 @ SV1204 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1634 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( ( SV604 = SV1204 )
| ( SV604 = SV1961 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV604 @ SV1204 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omktop @ SV1634 ) @ SV1961 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5473]) ).
thf(5732,plain,
! [SV1962: $i,SV1635: $i,SV1205: $i,SV605: $i] :
( ( ( c_in @ ( c_Pair @ SV605 @ SV1205 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1635 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( ( SV1205 = SV1962 )
| ( SV605 = SV1962 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV605 @ SV1205 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omktop @ SV1635 ) @ SV1962 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5474]) ).
thf(5733,plain,
! [SV2172: $i,SV1637: $i,SV1208: $i,SV608: $i] :
( ( ( c_in @ ( c_Pair @ SV608 @ SV1208 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omktop @ SV1637 ) @ SV2172 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( SV1208 = SV2172 )
= $true )
| ( ( c_in @ ( c_Pair @ SV608 @ SV1208 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1637 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5475]) ).
thf(5734,plain,
! [SV1963: $i,SV1639: $i,SV1212: $i,SV612: $i] :
( ( ( c_in @ ( c_Pair @ SV612 @ SV1212 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1639 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( ( SV612 = SV1212 )
| ( SV1212 = SV1963 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV612 @ SV1212 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omkbot @ SV1639 ) @ SV1963 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5476]) ).
thf(5735,plain,
! [SV1964: $i,SV1640: $i,SV1213: $i,SV613: $i] :
( ( ( c_in @ ( c_Pair @ SV613 @ SV1213 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1640 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( ( SV613 = SV1964 )
| ( SV1213 = SV1964 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV613 @ SV1213 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omkbot @ SV1640 ) @ SV1964 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5477]) ).
thf(5736,plain,
! [SV2175: $i,SV1641: $i,SV1215: $i,SV615: $i] :
( ( ( c_in @ ( c_Pair @ SV615 @ SV1215 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omkbot @ SV1641 ) @ SV2175 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( SV615 = SV2175 )
= $true )
| ( ( c_in @ ( c_Pair @ SV615 @ SV1215 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1641 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5478]) ).
thf(5737,plain,
! [SV2294: $i,SV2176: $i,SV1965: $i,SV1642: $i,SV1217: $i,SV617: $i] :
( ( ( c_in @ ( c_Pair @ SV617 @ SV1217 @ SV1642 @ SV1965 ) @ ( c_Product__Type_OSigma @ SV2176 @ SV2294 @ SV1642 @ SV1965 ) @ ( tc_prod @ SV1642 @ SV1965 ) )
= $true )
| ( ( ~ ( c_in @ SV1217 @ ( hAPP @ SV2294 @ SV617 ) @ SV1965 )
| ~ ( c_in @ SV617 @ SV2176 @ SV1642 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5479]) ).
thf(5738,plain,
! [SV2295: $i,SV2177: $i,SV1966: $i,SV1643: $i,SV1218: $i,SV618: $i] :
( ( ( c_in @ ( c_Pair @ SV618 @ SV1218 @ SV1643 @ SV1966 ) @ ( c_Product__Type_OSigma @ SV2177 @ SV2295 @ SV1643 @ SV1966 ) @ ( tc_prod @ SV1643 @ SV1966 ) )
= $true )
| ( ( ~ ( c_in @ SV1218 @ ( hAPP @ SV2295 @ SV618 ) @ SV1966 )
| ~ ( c_in @ SV618 @ SV2177 @ SV1643 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5480]) ).
thf(5739,plain,
! [SV1219: $i,SV1644: $i,SV2178: $i,SV619: $i] :
( ( ( c_in @ ( c_Pair @ SV619 @ SV2178 @ SV1644 @ SV1644 ) @ SV1219 @ ( tc_prod @ SV1644 @ SV1644 ) )
= $false )
| ( ( ~ ( c_in @ SV2178 @ ( c_Wellfounded_Oacc @ SV1219 @ SV1644 ) @ SV1644 ) )
= $true )
| ( ( c_in @ SV619 @ ( c_Wellfounded_Oacc @ SV1219 @ SV1644 ) @ SV1644 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5481]) ).
thf(5740,plain,
! [SV1220: $i,SV1645: $i,SV2179: $i,SV620: $i] :
( ( ( c_in @ ( c_Pair @ SV620 @ SV2179 @ SV1645 @ SV1645 ) @ SV1220 @ ( tc_prod @ SV1645 @ SV1645 ) )
= $false )
| ( ( ~ ( c_in @ SV2179 @ ( c_Wellfounded_Oacc @ SV1220 @ SV1645 ) @ SV1645 ) )
= $true )
| ( ( c_in @ SV620 @ ( c_Wellfounded_Oacc @ SV1220 @ SV1645 ) @ SV1645 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5482]) ).
thf(5741,plain,
! [SV1646: $i,SV1221: $i,SV2180: $i,SV1967: $i,SV621: $i,SV2350: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV2350 @ SV621 @ SV1967 @ SV2180 ) @ SV1221 @ ( tc_prod @ SV1967 @ SV2180 ) )
| ~ ( c_in @ SV2350 @ SV1646 @ SV1967 ) )
= $true )
| ( ( c_in @ SV621 @ ( c_Relation_OImage @ SV1221 @ SV1646 @ SV1967 @ SV2180 ) @ SV2180 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5483]) ).
thf(5742,plain,
! [SV1647: $i,SV1222: $i,SV2181: $i,SV1968: $i,SV622: $i,SV2351: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV2351 @ SV622 @ SV1968 @ SV2181 ) @ SV1222 @ ( tc_prod @ SV1968 @ SV2181 ) )
| ~ ( c_in @ SV2351 @ SV1647 @ SV1968 ) )
= $true )
| ( ( c_in @ SV622 @ ( c_Relation_OImage @ SV1222 @ SV1647 @ SV1968 @ SV2181 ) @ SV2181 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5484]) ).
thf(5743,plain,
! [SV1225: $i,SV2296: $i,SV1650: $i,SV625: $i,SV2183: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV2183 @ SV625 @ SV1650 @ SV1650 ) @ SV2296 @ ( tc_prod @ SV1650 @ SV1650 ) ) )
= $true )
| ( ( ~ ( c_Equiv__Relations_Oequiv @ SV1225 @ SV2296 @ SV1650 ) )
= $true )
| ( ( c_in @ SV625 @ SV1225 @ SV1650 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5486]) ).
thf(5744,plain,
! [SV1226: $i,SV2297: $i,SV1651: $i,SV2184: $i,SV626: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV626 @ SV2184 @ SV1651 @ SV1651 ) @ SV2297 @ ( tc_prod @ SV1651 @ SV1651 ) ) )
= $true )
| ( ( ~ ( c_Equiv__Relations_Oequiv @ SV1226 @ SV2297 @ SV1651 ) )
= $true )
| ( ( c_in @ SV626 @ SV1226 @ SV1651 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5487]) ).
thf(5745,plain,
! [SV1227: $i,SV1969: $i,SV1652: $i,SV627: $i,SV2298: $i] :
( ( ( c_in @ ( c_Pair @ SV2298 @ SV627 @ SV1652 @ SV1969 ) @ SV1227 @ ( tc_prod @ SV1652 @ SV1969 ) )
= $false )
| ( ( c_in @ SV627 @ ( c_Relation_ORange @ SV1227 @ SV1652 @ SV1969 ) @ SV1969 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5488]) ).
thf(5746,plain,
! [SV1228: $i,SV1970: $i,SV1653: $i,SV628: $i,SV2299: $i] :
( ( ( c_in @ ( c_Pair @ SV2299 @ SV628 @ SV1653 @ SV1970 ) @ SV1228 @ ( tc_prod @ SV1653 @ SV1970 ) )
= $false )
| ( ( c_in @ SV628 @ ( c_Relation_ORange @ SV1228 @ SV1653 @ SV1970 ) @ SV1970 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5489]) ).
thf(5747,plain,
! [SV1229: $i,SV1971: $i,SV1654: $i,SV2300: $i,SV629: $i] :
( ( ( c_in @ ( c_Pair @ SV629 @ SV2300 @ SV1654 @ SV1971 ) @ SV1229 @ ( tc_prod @ SV1654 @ SV1971 ) )
= $false )
| ( ( c_in @ SV629 @ ( c_Relation_ODomain @ SV1229 @ SV1654 @ SV1971 ) @ SV1654 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5490]) ).
thf(5748,plain,
! [SV1230: $i,SV1972: $i,SV1655: $i,SV2301: $i,SV630: $i] :
( ( ( c_in @ ( c_Pair @ SV630 @ SV2301 @ SV1655 @ SV1972 ) @ SV1230 @ ( tc_prod @ SV1655 @ SV1972 ) )
= $false )
| ( ( c_in @ SV630 @ ( c_Relation_ODomain @ SV1230 @ SV1655 @ SV1972 ) @ SV1655 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5491]) ).
thf(5749,plain,
! [SV1231: $i,SV2352: $i,SV1973: $i,SV2302: $i,SV631: $i,SV1656: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1656 @ SV631 @ SV2302 @ SV1973 ) @ ( c_Product__Type_OSigma @ SV2352 @ SV1231 @ SV2302 @ SV1973 ) @ ( tc_prod @ SV2302 @ SV1973 ) ) )
= $true )
| ( ( c_in @ SV631 @ ( hAPP @ SV1231 @ SV1656 ) @ SV1973 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5492]) ).
thf(5750,plain,
! [SV2353: $i,SV1232: $i,SV2303: $i,SV1657: $i,SV1974: $i,SV632: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV632 @ SV1974 @ SV1657 @ SV2303 ) @ ( c_Product__Type_OSigma @ SV1232 @ SV2353 @ SV1657 @ SV2303 ) @ ( tc_prod @ SV1657 @ SV2303 ) ) )
= $true )
| ( ( c_in @ SV632 @ SV1232 @ SV1657 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5493]) ).
thf(5751,plain,
! [SV1975: $i,SV1658: $i,SV633: $i,SV1233: $i] :
( ( ( SV1233 = SV633 )
= $true )
| ( ( ! [SY5890: $i] :
( ~ ( c_in @ SV633 @ SY5890 @ SV1658 )
| ~ ( c_in @ SV1233 @ SY5890 @ SV1658 )
| ~ ( c_Relation_Ototal__on @ SY5890 @ SV1975 @ SV1658 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1233 @ SV633 @ SV1658 @ SV1658 ) @ SV1975 @ ( tc_prod @ SV1658 @ SV1658 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV633 @ SV1233 @ SV1658 @ SV1658 ) @ SV1975 @ ( tc_prod @ SV1658 @ SV1658 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5494]) ).
thf(5752,plain,
! [SV1659: $i,SV1234: $i,SV2185: $i,SV634: $i] :
( ( ( c_in @ SV634 @ SV2185 @ SV1234 )
= $false )
| ( ( ~ ( c_Relation_Orefl__on @ SV2185 @ SV1659 @ SV1234 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV634 @ SV634 @ SV1234 @ SV1234 ) @ SV1659 @ ( tc_prod @ SV1234 @ SV1234 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5495]) ).
thf(5753,plain,
! [SV1235: $i,SV2304: $i,SV1660: $i,SV635: $i,SV2186: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV2186 @ SV635 @ SV1660 @ SV1660 ) @ SV2304 @ ( tc_prod @ SV1660 @ SV1660 ) ) )
= $true )
| ( ( ~ ( c_Relation_Orefl__on @ SV1235 @ SV2304 @ SV1660 ) )
= $true )
| ( ( c_in @ SV635 @ SV1235 @ SV1660 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5496]) ).
thf(5754,plain,
! [SV1236: $i,SV2305: $i,SV1661: $i,SV2187: $i,SV636: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV636 @ SV2187 @ SV1661 @ SV1661 ) @ SV2305 @ ( tc_prod @ SV1661 @ SV1661 ) ) )
= $true )
| ( ( ~ ( c_Relation_Orefl__on @ SV1236 @ SV2305 @ SV1661 ) )
= $true )
| ( ( c_in @ SV636 @ SV1236 @ SV1661 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5497]) ).
thf(5755,plain,
! [SV1662: $i,SV1237: $i,SV2188: $i,SV637: $i] :
( ( ( c_in @ SV637 @ SV2188 @ SV1237 )
= $false )
| ( ( ~ ( c_Relation_Orefl__on @ SV2188 @ SV1662 @ SV1237 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV637 @ SV637 @ SV1237 @ SV1237 ) @ SV1662 @ ( tc_prod @ SV1237 @ SV1237 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5498]) ).
thf(5756,plain,
! [SV2306: $i,SV2189: $i,SV1976: $i,SV1663: $i,SV1238: $i,SV638: $i] :
( ( ( ( c_Pair @ SV638 @ SV1238 @ SV1663 @ SV1976 )
!= ( c_Pair @ SV2189 @ SV2306 @ SV1663 @ SV1976 ) )
= $true )
| ( ( SV1238 = SV2306 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5499]) ).
thf(5757,plain,
! [SV2354: $i,SV2190: $i,SV1977: $i,SV1664: $i,SV1239: $i,SV639: $i] :
( ( ( ( c_Pair @ SV639 @ SV1239 @ SV1664 @ SV1977 )
!= ( c_Pair @ SV2190 @ SV2354 @ SV1664 @ SV1977 ) )
= $true )
| ( ( SV639 = SV2190 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5500]) ).
thf(5758,plain,
! [SV1674: $i,SV1263: $i,SV665: $i,SV14: $i] :
( ( ( ( hAPP @ ( c_fst @ SV14 @ SV665 ) @ SV1263 )
= ( hAPP @ ( c_fst @ SV14 @ SV665 ) @ SV1674 ) )
= $false )
| ( ( SV1263 = SV1674 )
= $true )
| ( ( ( hAPP @ ( c_snd @ SV14 @ SV665 ) @ SV1263 )
= ( hAPP @ ( c_snd @ SV14 @ SV665 ) @ SV1674 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5501]) ).
thf(5759,plain,
! [SV1675: $i,SV1264: $i,SV666: $i,SV15: $i] :
( ( ( ( hAPP @ ( c_fst @ SV15 @ SV666 ) @ SV1264 )
= ( hAPP @ ( c_fst @ SV15 @ SV666 ) @ SV1675 ) )
= $false )
| ( ( SV1264 = SV1675 )
= $true )
| ( ( ( hAPP @ ( c_snd @ SV15 @ SV666 ) @ SV1264 )
= ( hAPP @ ( c_snd @ SV15 @ SV666 ) @ SV1675 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5502]) ).
thf(5760,plain,
! [SV667: $i,SV16: $i,SV1981: $i,SV1676: $i] :
( ( ( c_Wellfounded_Owf @ SV1676 @ SV1981 )
= $false )
| ( ( hBOOL @ ( hAPP @ SV16 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1 @ SV16 @ SV1676 @ SV1981 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV16 @ SV667 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5503]) ).
thf(5761,plain,
! [SV1269: $i,SV672: $i,SV1680: $i,SV1983: $i,SV21: $i] :
( ( ( c_lessequals @ SV21 @ SV1983 @ ( tc_fun @ SV1680 @ tc_bool ) )
= $false )
| ( ( ! [SY5180: $i] :
~ ( c_in @ SY5180 @ SV672 @ SV1269 ) )
= $true )
| ( ( c_lessequals @ ( c_Product__Type_OSigma @ SV21 @ ( c_COMBK @ SV672 @ ( tc_fun @ SV1269 @ tc_bool ) @ SV1680 ) @ SV1680 @ SV1269 ) @ ( c_Product__Type_OSigma @ SV1983 @ ( c_COMBK @ SV672 @ ( tc_fun @ SV1269 @ tc_bool ) @ SV1680 ) @ SV1680 @ SV1269 ) @ ( tc_fun @ ( tc_prod @ SV1680 @ SV1269 ) @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5504]) ).
thf(5762,plain,
! [SV673: $i,SV1270: $i,SV2191: $i,SV1681: $i,SV22: $i] :
( ( ( c_lessequals @ ( c_Product__Type_OSigma @ SV22 @ ( c_COMBK @ SV1681 @ ( tc_fun @ SV2191 @ tc_bool ) @ SV1270 ) @ SV1270 @ SV2191 ) @ ( c_Product__Type_OSigma @ SV673 @ ( c_COMBK @ SV1681 @ ( tc_fun @ SV2191 @ tc_bool ) @ SV1270 ) @ SV1270 @ SV2191 ) @ ( tc_fun @ ( tc_prod @ SV1270 @ SV2191 ) @ tc_bool ) )
= $false )
| ( ( ! [SY5997: $i] :
~ ( c_in @ SY5997 @ SV1681 @ SV2191 ) )
= $true )
| ( ( c_lessequals @ SV22 @ SV673 @ ( tc_fun @ SV1270 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5505]) ).
thf(5763,plain,
! [SV1271: $i,SV1682: $i,SV674: $i,SV23: $i] :
( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV23 @ ( c_Set_Oinsert @ SV674 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1682 @ tc_bool ) ) @ SV1682 ) @ ( tc_fun @ SV1682 @ tc_bool ) ) @ SV1271 @ ( tc_fun @ SV1682 @ tc_bool ) )
= $false )
| ( ( c_in @ SV674 @ SV23 @ SV1682 )
= $false )
| ( ( c_lessequals @ SV23 @ ( c_Set_Oinsert @ SV674 @ SV1271 @ SV1682 ) @ ( tc_fun @ SV1682 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5506]) ).
thf(5764,plain,
! [SV1272: $i,SV1683: $i,SV675: $i,SV24: $i] :
( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV24 @ ( c_Set_Oinsert @ SV675 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1683 @ tc_bool ) ) @ SV1683 ) @ ( tc_fun @ SV1683 @ tc_bool ) ) @ SV1272 @ ( tc_fun @ SV1683 @ tc_bool ) )
= $false )
| ( ( c_in @ SV675 @ SV24 @ SV1683 )
= $false )
| ( ( c_lessequals @ SV24 @ ( c_Set_Oinsert @ SV675 @ SV1272 @ SV1683 ) @ ( tc_fun @ SV1683 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5507]) ).
thf(5765,plain,
! [SV1273: $i,SV1684: $i,SV676: $i,SV25: $i] :
( ( ( c_lessequals @ SV25 @ ( c_Set_Oinsert @ SV676 @ SV1684 @ SV1273 ) @ ( tc_fun @ SV1273 @ tc_bool ) )
= $false )
| ( ( c_in @ SV676 @ SV25 @ SV1273 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV25 @ ( c_Set_Oinsert @ SV676 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1273 @ tc_bool ) ) @ SV1273 ) @ ( tc_fun @ SV1273 @ tc_bool ) ) @ SV1684 @ ( tc_fun @ SV1273 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5508]) ).
thf(5766,plain,
! [SV2307: $i,SV2195: $i,SV1987: $i,SV1692: $i,SV1282: $i,SV690: $i,SV40: $i] :
( ( ( c_lessequals @ ( c_Relation_Orel__comp @ SV40 @ SV690 @ SV1282 @ SV1692 @ SV1987 ) @ ( c_Relation_Orel__comp @ SV2195 @ SV2307 @ SV1282 @ SV1692 @ SV1987 ) @ ( tc_fun @ ( tc_prod @ SV1282 @ SV1987 ) @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV690 @ SV2307 @ ( tc_fun @ ( tc_prod @ SV1692 @ SV1987 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV40 @ SV2195 @ ( tc_fun @ ( tc_prod @ SV1282 @ SV1692 ) @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5511]) ).
thf(5767,plain,
! [SV693: $i,SV43: $i,SV1990: $i,SV1695: $i] :
( ( ( c_Wellfounded_Owf @ SV1695 @ SV1990 )
= $false )
| ( ( hBOOL @ ( hAPP @ SV43 @ ( c_List_Osko__Recdef__Xtfl__wf__induct__1__1 @ SV43 @ SV1695 @ SV1990 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV43 @ SV693 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5512]) ).
thf(5768,plain,
! [SV701: $i,SV1291: $i,SV1698: $i,SV1991: $i,SV2308: $i,SV51: $i] :
( ( ( c_lessequals @ SV51 @ ( c_Product__Type_OSigma @ SV2308 @ ( c_COMBK @ SV1991 @ ( tc_fun @ SV1698 @ tc_bool ) @ SV1291 ) @ SV1291 @ SV1698 ) @ ( tc_fun @ ( tc_prod @ SV1291 @ SV1698 ) @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( c_Relation_OImage @ SV51 @ SV701 @ SV1291 @ SV1698 ) @ SV1991 @ ( tc_fun @ SV1698 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5513]) ).
thf(5769,plain,
! [SV2309: $i,SV52: $i,SV1992: $i,SV702: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV702 @ SV1992 @ SV52 )
= ( c_HOL_Ominus__class_Ominus @ SV2309 @ SV2309 @ SV52 ) )
= $false )
| ( ( SV702 = SV1992 )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV52 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5514]) ).
thf(5770,plain,
! [SV2196: $i,SV1993: $i,SV53: $i,SV703: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV703 @ SV703 @ SV53 )
= ( c_HOL_Ominus__class_Ominus @ SV1993 @ SV2196 @ SV53 ) )
= $false )
| ( ( SV1993 = SV2196 )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV53 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5515]) ).
thf(5771,plain,
! [SV714: $i,SV1298: $i,SV1705: $i,SV67: $i] :
( ( ( c_lessequals @ SV67 @ SV1705 @ ( tc_fun @ SV1298 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV714 @ SV1705 @ ( tc_fun @ SV1298 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV67 @ SV714 @ ( tc_fun @ SV1298 @ tc_bool ) ) @ SV1705 @ ( tc_fun @ SV1298 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5519]) ).
thf(5772,plain,
! [SV717: $i,SV1301: $i,SV1706: $i,SV70: $i] :
( ( ( c_lessequals @ SV70 @ SV1706 @ ( tc_fun @ SV1301 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV717 @ SV1706 @ ( tc_fun @ SV1301 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV70 @ SV717 @ ( tc_fun @ SV1301 @ tc_bool ) ) @ SV1706 @ ( tc_fun @ SV1301 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5520]) ).
thf(5773,plain,
! [SV718: $i,SV71: $i,SV2201: $i,SV2002: $i] :
( ( ( ~ ( c_lessequals @ SV2002 @ SV2201 @ SV71 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV718 @ SV2201 @ SV71 ) )
= $true )
| ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV718 @ SV2002 @ SV71 ) @ SV2201 @ SV71 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV71 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5521]) ).
thf(5774,plain,
! [SV719: $i,SV74: $i,SV2202: $i,SV2005: $i] :
( ( ( ~ ( c_lessequals @ SV2005 @ SV2202 @ SV74 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV719 @ SV2202 @ SV74 ) )
= $true )
| ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV719 @ SV2005 @ SV74 ) @ SV2202 @ SV74 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV74 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5522]) ).
thf(5775,plain,
! [SV720: $i,SV75: $i,SV2203: $i,SV2006: $i] :
( ( ( ~ ( c_lessequals @ SV2006 @ SV2203 @ SV75 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV720 @ SV2203 @ SV75 ) )
= $true )
| ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV720 @ SV2006 @ SV75 ) @ SV2203 @ SV75 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV75 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5523]) ).
thf(5776,plain,
! [SV1713: $i,SV724: $i,SV1304: $i,SV83: $i,SV2355: $i] :
( ( ( ~ ( c_Equiv__Relations_Oequiv @ SV2355 @ SV83 @ SV1304 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV724 @ SV1713 @ SV1304 @ SV1304 ) @ SV83 @ ( tc_prod @ SV1304 @ SV1304 ) )
= $false )
| ( ( c_lessequals @ ( c_Relation_OImage @ SV83 @ ( c_Set_Oinsert @ SV724 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1304 @ tc_bool ) ) @ SV1304 ) @ SV1304 @ SV1304 ) @ ( c_Relation_OImage @ SV83 @ ( c_Set_Oinsert @ SV1713 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1304 @ tc_bool ) ) @ SV1304 ) @ SV1304 @ SV1304 ) @ ( tc_fun @ SV1304 @ tc_bool ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5524]) ).
thf(5777,plain,
! [SV2310: $i,SV2205: $i,SV2015: $i,SV1724: $i,SV1317: $i,SV742: $i,SV103: $i] :
( ( ( c_lessequals @ ( c_Relation_Orel__comp @ SV103 @ SV742 @ SV1317 @ SV1724 @ SV2015 ) @ ( c_Product__Type_OSigma @ SV2205 @ ( c_COMBK @ SV2310 @ ( tc_fun @ SV2015 @ tc_bool ) @ SV1317 ) @ SV1317 @ SV2015 ) @ ( tc_fun @ ( tc_prod @ SV1317 @ SV2015 ) @ tc_bool ) )
= $true )
| ( ( ! [SY6034: $i] :
( ~ ( c_lessequals @ SV742 @ ( c_Product__Type_OSigma @ SY6034 @ ( c_COMBK @ SV2310 @ ( tc_fun @ SV2015 @ tc_bool ) @ SV1724 ) @ SV1724 @ SV2015 ) @ ( tc_fun @ ( tc_prod @ SV1724 @ SV2015 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV103 @ ( c_Product__Type_OSigma @ SV2205 @ ( c_COMBK @ SY6034 @ ( tc_fun @ SV1724 @ tc_bool ) @ SV1317 ) @ SV1317 @ SV1724 ) @ ( tc_fun @ ( tc_prod @ SV1317 @ SV1724 ) @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5527]) ).
thf(5778,plain,
! [SV104: $i,SV1318: $i,SV743: $i] :
( ( ( c_Wellfounded_Owf @ SV743 @ SV1318 )
= $false )
| ( ( ~ ( c_Wellfounded_Owf @ SV104 @ SV1318 ) )
= $true )
| ( ( c_lessequals @ ( c_Relation_Orel__comp @ SV104 @ SV743 @ SV1318 @ SV1318 @ SV1318 ) @ SV104 @ ( tc_fun @ ( tc_prod @ SV1318 @ SV1318 ) @ tc_bool ) )
= $false )
| ( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV104 @ SV743 @ ( tc_fun @ ( tc_prod @ SV1318 @ SV1318 ) @ tc_bool ) ) @ SV1318 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5528]) ).
thf(5779,plain,
! [SV1321: $i,SV747: $i,SV108: $i] :
( ( ( ~ ( c_Wellfounded_Owf @ SV108 @ SV747 ) )
= $true )
| ( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV108 @ SV1321 @ ( tc_fun @ ( tc_prod @ SV747 @ SV747 ) @ tc_bool ) ) @ SV747 )
= $true )
| ( ( c_Wellfounded_Owf @ SV1321 @ SV747 )
= $false )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_ODomain @ SV108 @ SV747 @ SV747 ) @ ( c_Relation_ORange @ SV1321 @ SV747 @ SV747 ) @ ( tc_fun @ SV747 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV747 @ tc_bool ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5530]) ).
thf(5780,plain,
! [SV1729: $i,SV110: $i,SV1323: $i,SV2017: $i,SV749: $i] :
( ( ( c_Relation_Orefl__on @ SV749 @ SV2017 @ SV1323 )
= $false )
| ( ( ~ ( c_Relation_Orefl__on @ SV110 @ SV1729 @ SV1323 ) )
= $true )
| ( ( c_Relation_Orefl__on @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV110 @ SV749 @ ( tc_fun @ SV1323 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1729 @ SV2017 @ ( tc_fun @ ( tc_prod @ SV1323 @ SV1323 ) @ tc_bool ) ) @ SV1323 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5531]) ).
thf(5781,plain,
! [SV1739: $i,SV128: $i,SV1330: $i,SV765: $i,SV2023: $i] :
( ( ( c_lessequals @ SV2023 @ SV765 @ ( tc_fun @ SV1330 @ tc_bool ) )
= $false )
| ( ( ~ ( c_lessequals @ SV128 @ SV1739 @ ( tc_fun @ SV1330 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV128 @ SV765 @ ( tc_fun @ SV1330 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV1739 @ SV2023 @ ( tc_fun @ SV1330 @ tc_bool ) ) @ ( tc_fun @ SV1330 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5533]) ).
thf(5782,plain,
! [SV766: $i,SV1331: $i,SV2212: $i,SV129: $i] :
( ( ( c_in @ SV129 @ SV2212 @ SV1331 )
= $false )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV2212 @ SV766 @ ( tc_fun @ SV1331 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1331 @ tc_bool ) ) )
= $true )
| ( ( c_in @ SV129 @ SV766 @ SV1331 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5534]) ).
thf(5783,plain,
! [SV134: $i,SV1334: $i,SV770: $i,SV2214: $i] :
( ( ( ( c_Relation_Orel__comp @ SV2214 @ SV770 @ SV1334 @ SV1334 @ SV1334 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV1334 @ SV1334 ) @ tc_bool ) ) )
= $false )
| ( ( ( c_Relation_Orel__comp @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV2214 @ SV134 @ ( tc_fun @ ( tc_prod @ SV1334 @ SV1334 ) @ tc_bool ) ) @ SV770 @ SV1334 @ SV1334 @ SV1334 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV1334 @ SV1334 ) @ tc_bool ) ) )
= $true )
| ( ( ( c_Relation_Orel__comp @ SV134 @ SV770 @ SV1334 @ SV1334 @ SV1334 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV1334 @ SV1334 ) @ tc_bool ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5536]) ).
thf(5784,plain,
! [SV771: $i,SV1335: $i,SV2215: $i,SV135: $i] :
( ( ( ( c_Relation_Orel__comp @ SV135 @ SV2215 @ SV1335 @ SV1335 @ SV1335 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV1335 @ SV1335 ) @ tc_bool ) ) )
= $false )
| ( ( ( c_Relation_Orel__comp @ SV135 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV2215 @ SV771 @ ( tc_fun @ ( tc_prod @ SV1335 @ SV1335 ) @ tc_bool ) ) @ SV1335 @ SV1335 @ SV1335 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV1335 @ SV1335 ) @ tc_bool ) ) )
= $true )
| ( ( ( c_Relation_Orel__comp @ SV135 @ SV771 @ SV1335 @ SV1335 @ SV1335 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ SV1335 @ SV1335 ) @ tc_bool ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5537]) ).
thf(5785,plain,
! [SV772: $i,SV136: $i,SV2026: $i,SV1742: $i] :
( ( ( c_Wellfounded_Owf @ SV1742 @ SV2026 )
= $false )
| ( ( hBOOL @ ( hAPP @ SV136 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1 @ SV136 @ SV1742 @ SV2026 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV136 @ SV772 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5538]) ).
thf(5786,plain,
! [SV141: $i,SV1745: $i,SV2027: $i] :
( ( ( c_lessequals @ SV2027 @ SV1745 @ SV141 )
= $false )
| ( ( ~ ( c_lessequals @ SV1745 @ SV2027 @ SV141 ) )
= $true )
| ( ( SV1745 = SV2027 )
= $true )
| ( ( class_Orderings_Oorder @ SV141 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5541]) ).
thf(5787,plain,
! [SV142: $i,SV1746: $i,SV2028: $i] :
( ( ( c_lessequals @ SV2028 @ SV1746 @ SV142 )
= $false )
| ( ( ~ ( c_lessequals @ SV1746 @ SV2028 @ SV142 ) )
= $true )
| ( ( SV1746 = SV2028 )
= $true )
| ( ( class_Orderings_Oorder @ SV142 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5542]) ).
thf(5788,plain,
! [SV144: $i,SV2030: $i,SV1748: $i] :
( ( ( c_lessequals @ SV1748 @ SV2030 @ SV144 )
= $false )
| ( ( ~ ( c_lessequals @ SV2030 @ SV1748 @ SV144 ) )
= $true )
| ( ( SV1748 = SV2030 )
= $true )
| ( ( class_Orderings_Oorder @ SV144 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5543]) ).
thf(5789,plain,
! [SV1753: $i,SV153: $i,SV1341: $i,SV2035: $i,SV782: $i] :
( ( ( c_Relation_Orefl__on @ SV782 @ SV2035 @ SV1341 )
= $false )
| ( ( ~ ( c_Relation_Orefl__on @ SV153 @ SV1753 @ SV1341 ) )
= $true )
| ( ( c_Relation_Orefl__on @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV153 @ SV782 @ ( tc_fun @ SV1341 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1753 @ SV2035 @ ( tc_fun @ ( tc_prod @ SV1341 @ SV1341 ) @ tc_bool ) ) @ SV1341 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5547]) ).
thf(5790,plain,
! [SV1342: $i,SV784: $i,SV1754: $i,SV2036: $i,SV156: $i] :
( ( ( SV156 = SV2036 )
= $true )
| ( ( SV156 = SV1754 )
= $true )
| ( ( ( c_Set_Oinsert @ SV156 @ ( c_Set_Oinsert @ SV784 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1342 @ tc_bool ) ) @ SV1342 ) @ SV1342 )
= ( c_Set_Oinsert @ SV1754 @ ( c_Set_Oinsert @ SV2036 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1342 @ tc_bool ) ) @ SV1342 ) @ SV1342 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5548]) ).
thf(5791,plain,
! [SV2216: $i,SV1343: $i,SV157: $i,SV1755: $i,SV785: $i] :
( ( ( SV785 = SV1755 )
= $true )
| ( ( SV157 = SV1755 )
= $true )
| ( ( ( c_Set_Oinsert @ SV157 @ ( c_Set_Oinsert @ SV785 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1343 @ tc_bool ) ) @ SV1343 ) @ SV1343 )
= ( c_Set_Oinsert @ SV1755 @ ( c_Set_Oinsert @ SV2216 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1343 @ tc_bool ) ) @ SV1343 ) @ SV1343 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5549]) ).
thf(5792,plain,
! [SV1756: $i,SV1344: $i,SV786: $i,SV2037: $i,SV158: $i] :
( ( ( SV158 = SV2037 )
= $true )
| ( ( SV786 = SV2037 )
= $true )
| ( ( ( c_Set_Oinsert @ SV158 @ ( c_Set_Oinsert @ SV786 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1344 @ tc_bool ) ) @ SV1344 ) @ SV1344 )
= ( c_Set_Oinsert @ SV1756 @ ( c_Set_Oinsert @ SV2037 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1344 @ tc_bool ) ) @ SV1344 ) @ SV1344 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5550]) ).
thf(5793,plain,
! [SV1345: $i,SV159: $i,SV2038: $i,SV1757: $i,SV787: $i] :
( ( ( SV787 = SV1757 )
= $true )
| ( ( SV787 = SV2038 )
= $true )
| ( ( ( c_Set_Oinsert @ SV159 @ ( c_Set_Oinsert @ SV787 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1345 @ tc_bool ) ) @ SV1345 ) @ SV1345 )
= ( c_Set_Oinsert @ SV1757 @ ( c_Set_Oinsert @ SV2038 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1345 @ tc_bool ) ) @ SV1345 ) @ SV1345 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5551]) ).
thf(5794,plain,
! [SV1761: $i,SV170: $i,SV1352: $i,SV2040: $i,SV796: $i] :
( ( ( c_lessequals @ SV796 @ SV2040 @ ( tc_fun @ SV1352 @ tc_bool ) )
= $false )
| ( ( ~ ( c_lessequals @ SV170 @ SV1761 @ ( tc_fun @ SV1352 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV170 @ SV796 @ ( tc_fun @ SV1352 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1761 @ SV2040 @ ( tc_fun @ SV1352 @ tc_bool ) ) @ ( tc_fun @ SV1352 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5552]) ).
thf(5795,plain,
! [SV2043: $i,SV174: $i,SV2217: $i,SV798: $i] :
( ( ( ~ ( c_lessequals @ SV798 @ SV2217 @ SV174 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV798 @ SV2043 @ SV174 ) )
= $true )
| ( ( c_lessequals @ SV798 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2043 @ SV2217 @ SV174 ) @ SV174 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV174 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5553]) ).
thf(5796,plain,
! [SV2044: $i,SV175: $i,SV2218: $i,SV799: $i] :
( ( ( ~ ( c_lessequals @ SV799 @ SV2218 @ SV175 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV799 @ SV2044 @ SV175 ) )
= $true )
| ( ( c_lessequals @ SV799 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2044 @ SV2218 @ SV175 ) @ SV175 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV175 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5554]) ).
thf(5797,plain,
! [SV2045: $i,SV176: $i,SV2219: $i,SV800: $i] :
( ( ( ~ ( c_lessequals @ SV800 @ SV2219 @ SV176 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV800 @ SV2045 @ SV176 ) )
= $true )
| ( ( c_lessequals @ SV800 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2045 @ SV2219 @ SV176 ) @ SV176 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV176 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5555]) ).
thf(5798,plain,
! [SV1356: $i,SV1767: $i,SV803: $i,SV181: $i] :
( ( ( c_lessequals @ SV181 @ SV803 @ ( tc_fun @ SV1767 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV181 @ SV1356 @ ( tc_fun @ SV1767 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV181 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV803 @ SV1356 @ ( tc_fun @ SV1767 @ tc_bool ) ) @ ( tc_fun @ SV1767 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5556]) ).
thf(5799,plain,
! [SV1357: $i,SV1768: $i,SV804: $i,SV182: $i] :
( ( ( c_lessequals @ SV182 @ SV804 @ ( tc_fun @ SV1768 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV182 @ SV1357 @ ( tc_fun @ SV1768 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV182 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV804 @ SV1357 @ ( tc_fun @ SV1768 @ tc_bool ) ) @ ( tc_fun @ SV1768 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5557]) ).
thf(5800,plain,
! [SV215: $i,SV2311: $i,SV2059: $i,SV833: $i] :
( ( ( c_lessequals @ SV833 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2059 @ SV2311 @ SV215 ) @ SV215 )
= $false )
| ( ( c_lessequals @ SV833 @ SV2059 @ SV215 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV215 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5565]) ).
thf(5801,plain,
! [SV216: $i,SV2060: $i,SV2312: $i,SV834: $i] :
( ( ( c_lessequals @ SV834 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2312 @ SV2060 @ SV216 ) @ SV216 )
= $false )
| ( ( c_lessequals @ SV834 @ SV2060 @ SV216 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV216 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5566]) ).
thf(5802,plain,
! [SV2061: $i,SV217: $i,SV2224: $i,SV835: $i] :
( ( ( c_lessequals @ SV835 @ SV2224 @ SV217 )
= $false )
| ( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV835 @ SV2061 @ SV217 ) @ SV2224 @ SV217 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV217 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5567]) ).
thf(5803,plain,
! [SV836: $i,SV218: $i,SV2225: $i,SV2062: $i] :
( ( ( c_lessequals @ SV2062 @ SV2225 @ SV218 )
= $false )
| ( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV836 @ SV2062 @ SV218 ) @ SV2225 @ SV218 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV218 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5568]) ).
thf(5804,plain,
! [SV219: $i,SV2313: $i,SV2063: $i,SV837: $i] :
( ( ( c_lessequals @ SV837 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2063 @ SV2313 @ SV219 ) @ SV219 )
= $false )
| ( ( c_lessequals @ SV837 @ SV2063 @ SV219 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV219 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5569]) ).
thf(5805,plain,
! [SV220: $i,SV2064: $i,SV2314: $i,SV838: $i] :
( ( ( c_lessequals @ SV838 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2314 @ SV2064 @ SV220 ) @ SV220 )
= $false )
| ( ( c_lessequals @ SV838 @ SV2064 @ SV220 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV220 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5570]) ).
thf(5806,plain,
! [SV850: $i,SV236: $i,SV2069: $i,SV1789: $i] :
( ( ( c_Wellfounded_Owf @ SV1789 @ SV2069 )
= $false )
| ( ( hBOOL @ ( hAPP @ SV236 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1 @ SV236 @ SV1789 @ SV2069 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV236 @ SV850 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5571]) ).
thf(5807,plain,
! [SV1398: $i,SV1791: $i,SV853: $i,SV239: $i] :
( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV239 @ ( c_Set_Oinsert @ SV853 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1791 @ tc_bool ) ) @ SV1791 ) @ ( tc_fun @ SV1791 @ tc_bool ) ) @ SV1398 @ ( tc_fun @ SV1791 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV239 @ SV1398 @ ( tc_fun @ SV1791 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV239 @ ( c_Set_Oinsert @ SV853 @ SV1398 @ SV1791 ) @ ( tc_fun @ SV1791 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5572]) ).
thf(5808,plain,
! [SV2226: $i,SV2073: $i,SV1797: $i,SV1404: $i,SV861: $i,SV247: $i] :
( ( ( ( hAPP @ SV247 @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ SV247 @ SV861 @ SV1404 @ SV1797 @ SV2073 @ SV2226 ) )
= ( hAPP @ SV861 @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ SV247 @ SV861 @ SV1404 @ SV1797 @ SV2073 @ SV2226 ) ) )
= $false )
| ( ( ( c_Recdef_Ocut @ SV247 @ SV1404 @ SV1797 @ SV2073 @ SV2226 )
= ( c_Recdef_Ocut @ SV861 @ SV1404 @ SV1797 @ SV2073 @ SV2226 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5574]) ).
thf(5809,plain,
! [SV1405: $i,SV249: $i,SV2356: $i,SV2227: $i,SV863: $i] :
( ( ( ~ ( c_lessequals @ SV863 @ SV2227 @ ( tc_fun @ SV2356 @ SV249 ) ) )
= $true )
| ( ( c_lessequals @ ( hAPP @ SV863 @ SV1405 ) @ ( hAPP @ SV2227 @ SV1405 ) @ SV249 )
= $true )
| ( ( class_HOL_Oord @ SV249 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5575]) ).
thf(5810,plain,
! [SV1406: $i,SV1799: $i,SV864: $i,SV250: $i] :
( ( ( c_in @ SV250 @ SV864 @ SV1799 )
= $false )
| ( ( c_in @ SV250 @ SV1406 @ SV1799 )
= $false )
| ( ( c_in @ SV250 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV864 @ SV1406 @ ( tc_fun @ SV1799 @ tc_bool ) ) @ SV1799 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5576]) ).
thf(5811,plain,
! [SV1407: $i,SV1800: $i,SV865: $i,SV251: $i] :
( ( ( c_in @ SV251 @ SV865 @ SV1800 )
= $false )
| ( ( c_in @ SV251 @ SV1407 @ SV1800 )
= $false )
| ( ( c_in @ SV251 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV865 @ SV1407 @ ( tc_fun @ SV1800 @ tc_bool ) ) @ SV1800 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5577]) ).
thf(5812,plain,
! [SV254: $i,SV1410: $i,SV868: $i,SV2075: $i] :
( ( ( c_lessequals @ SV2075 @ SV868 @ ( tc_fun @ SV1410 @ tc_bool ) )
= $false )
| ( ( c_in @ SV254 @ SV2075 @ SV1410 )
= $false )
| ( ( c_in @ SV254 @ SV868 @ SV1410 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5578]) ).
thf(5813,plain,
! [SV869: $i,SV1411: $i,SV2076: $i,SV255: $i] :
( ( ( c_in @ SV255 @ SV2076 @ SV1411 )
= $false )
| ( ( c_lessequals @ SV2076 @ SV869 @ ( tc_fun @ SV1411 @ tc_bool ) )
= $false )
| ( ( c_in @ SV255 @ SV869 @ SV1411 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5579]) ).
thf(5814,plain,
! [SV256: $i,SV1412: $i,SV870: $i,SV2077: $i] :
( ( ( c_lessequals @ SV2077 @ SV870 @ ( tc_fun @ SV1412 @ tc_bool ) )
= $false )
| ( ( c_in @ SV256 @ SV2077 @ SV1412 )
= $false )
| ( ( c_in @ SV256 @ SV870 @ SV1412 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5580]) ).
thf(5815,plain,
! [SV257: $i,SV1413: $i,SV871: $i,SV2078: $i] :
( ( ( c_lessequals @ SV2078 @ SV871 @ ( tc_fun @ SV1413 @ tc_bool ) )
= $false )
| ( ( c_in @ SV257 @ SV2078 @ SV1413 )
= $false )
| ( ( c_in @ SV257 @ SV871 @ SV1413 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5581]) ).
thf(5816,plain,
! [SV1427: $i,SV276: $i,SV1808: $i,SV890: $i] :
( ( ( SV890 = SV1808 )
= $true )
| ( ( c_in @ SV276 @ SV890 @ SV1427 )
= $true )
| ( ( c_in @ SV276 @ SV1808 @ SV1427 )
= $true )
| ( ( ( c_Set_Oinsert @ SV276 @ SV890 @ SV1427 )
= ( c_Set_Oinsert @ SV276 @ SV1808 @ SV1427 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5587]) ).
thf(5817,plain,
! [SV1433: $i,SV896: $i,SV1813: $i,SV282: $i,SV2085: $i,SV2357: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV2357 @ SV2085 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV282 @ SV1813 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV282 @ ( hAPP @ ( c_fst @ SV896 @ SV1433 ) @ ( c_Pair @ SV1813 @ SV2085 @ SV896 @ SV1433 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5588]) ).
thf(5818,plain,
! [SV1434: $i,SV897: $i,SV1814: $i,SV2086: $i,SV283: $i] :
( ( ( hBOOL @ ( hAPP @ SV283 @ SV2086 ) )
= $false )
| ( ( ! [SY5750: $i] :
~ ( hBOOL @ ( hAPP @ SY5750 @ SV1814 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV283 @ ( hAPP @ ( c_snd @ SV897 @ SV1434 ) @ ( c_Pair @ SV1814 @ SV2086 @ SV897 @ SV1434 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5589]) ).
thf(5819,plain,
! [SV904: $i,SV1438: $i,SV1818: $i,SV290: $i] :
( ( ( c_in @ SV290 @ SV1818 @ SV1438 )
= $false )
| ( ( c_lessequals @ SV904 @ SV1818 @ ( tc_fun @ SV1438 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( c_Set_Oinsert @ SV290 @ SV904 @ SV1438 ) @ SV1818 @ ( tc_fun @ SV1438 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5590]) ).
thf(5820,plain,
! [SV2092: $i,SV301: $i,SV912: $i,SV2315: $i] :
( ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV2315 @ SV912 @ SV301 ) @ SV2092 @ SV301 )
= $false )
| ( ( c_lessequals @ SV912 @ SV2092 @ SV301 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV301 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5591]) ).
thf(5821,plain,
! [SV2093: $i,SV302: $i,SV2316: $i,SV913: $i] :
( ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV913 @ SV2316 @ SV302 ) @ SV2093 @ SV302 )
= $false )
| ( ( c_lessequals @ SV913 @ SV2093 @ SV302 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV302 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5592]) ).
thf(5822,plain,
! [SV2094: $i,SV303: $i,SV2231: $i,SV914: $i] :
( ( ( c_lessequals @ SV914 @ SV2231 @ SV303 )
= $false )
| ( ( c_lessequals @ SV914 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV2094 @ SV2231 @ SV303 ) @ SV303 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV303 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5593]) ).
thf(5823,plain,
! [SV2317: $i,SV304: $i,SV2095: $i,SV915: $i] :
( ( ( c_lessequals @ SV915 @ SV2095 @ SV304 )
= $false )
| ( ( c_lessequals @ SV915 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV2095 @ SV2317 @ SV304 ) @ SV304 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV304 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5594]) ).
thf(5824,plain,
! [SV2096: $i,SV305: $i,SV916: $i,SV2318: $i] :
( ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV2318 @ SV916 @ SV305 ) @ SV2096 @ SV305 )
= $false )
| ( ( c_lessequals @ SV916 @ SV2096 @ SV305 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV305 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5595]) ).
thf(5825,plain,
! [SV2097: $i,SV306: $i,SV2319: $i,SV917: $i] :
( ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV917 @ SV2319 @ SV306 ) @ SV2097 @ SV306 )
= $false )
| ( ( c_lessequals @ SV917 @ SV2097 @ SV306 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV306 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5596]) ).
thf(5826,plain,
! [SV2100: $i,SV309: $i,SV2320: $i,SV920: $i] :
( ( ( ~ ( c_lessequals @ SV920 @ SV2320 @ SV309 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV2320 @ SV2100 @ SV309 ) )
= $true )
| ( ( c_lessequals @ SV920 @ SV2100 @ SV309 )
= $true )
| ( ( class_Orderings_Oorder @ SV309 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5597]) ).
thf(5827,plain,
! [SV921: $i,SV310: $i,SV2101: $i,SV2321: $i] :
( ( ( ~ ( c_lessequals @ SV2321 @ SV2101 @ SV310 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV921 @ SV2321 @ SV310 ) )
= $true )
| ( ( c_lessequals @ SV921 @ SV2101 @ SV310 )
= $true )
| ( ( class_Orderings_Opreorder @ SV310 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5598]) ).
thf(5828,plain,
! [SV924: $i,SV1447: $i,SV2102: $i,SV313: $i] :
( ( ( c_lessequals @ SV313 @ SV2102 @ ( tc_fun @ SV1447 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV2102 @ SV924 @ ( tc_fun @ SV1447 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV313 @ SV924 @ ( tc_fun @ SV1447 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5599]) ).
thf(5829,plain,
! [SV925: $i,SV2322: $i,SV314: $i,SV1824: $i] :
( ( ( c_lessequals @ SV1824 @ SV314 @ ( tc_fun @ SV2322 @ tc_bool ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV1824 @ SV925 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV314 @ SV925 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5600]) ).
thf(5830,plain,
! [SV2232: $i,SV319: $i,SV928: $i,SV1829: $i] :
( ( ( hBOOL @ ( hAPP @ SV1829 @ SV928 ) )
= $false )
| ( ( c_lessequals @ SV1829 @ SV319 @ ( tc_fun @ SV2232 @ tc_bool ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV319 @ SV928 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5603]) ).
thf(5831,plain,
! [SV1448: $i,SV930: $i,SV2103: $i,SV321: $i] :
( ( ( c_lessequals @ SV321 @ SV2103 @ ( tc_fun @ ( tc_prod @ SV930 @ SV1448 ) @ tc_bool ) )
= $false )
| ( ( c_Relation_Osingle__valued @ SV2103 @ SV930 @ SV1448 )
= $false )
| ( ( c_Relation_Osingle__valued @ SV321 @ SV930 @ SV1448 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5605]) ).
thf(5832,plain,
! [SV1831: $i,SV323: $i,SV1450: $i,SV2105: $i,SV932: $i] :
( ( ( c_lessequals @ SV932 @ SV2105 @ ( tc_fun @ SV1450 @ tc_bool ) )
= $false )
| ( ( ~ ( c_lessequals @ SV323 @ SV1831 @ ( tc_fun @ SV1450 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV323 @ SV932 @ ( tc_fun @ SV1450 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1831 @ SV2105 @ ( tc_fun @ SV1450 @ tc_bool ) ) @ ( tc_fun @ SV1450 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5606]) ).
thf(5833,plain,
! [SV1457: $i,SV940: $i,SV1836: $i,SV331: $i] :
( ( ( hBOOL @ ( hAPP @ SV331 @ SV1836 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV940 @ SV1836 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV331 @ SV940 @ ( tc_fun @ SV1457 @ tc_bool ) ) @ SV1836 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5607]) ).
thf(5834,plain,
! [SV941: $i,SV1837: $i,SV332: $i,SV1458: $i] :
( ( ( c_lessequals @ SV1458 @ SV332 @ ( tc_fun @ SV1837 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV332 @ SV941 @ ( tc_fun @ SV1837 @ tc_bool ) )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV332 @ ( c_HOL_Ominus__class_Ominus @ SV941 @ SV1458 @ ( tc_fun @ SV1837 @ tc_bool ) ) @ ( tc_fun @ SV1837 @ tc_bool ) )
= SV1458 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5608]) ).
thf(5835,plain,
! [SV2323: $i,SV2233: $i,SV333: $i,SV1459: $i,SV942: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV942 @ SV1459 @ SV333 )
!= ( c_HOL_Ominus__class_Ominus @ SV2233 @ SV2323 @ SV333 ) )
= $true )
| ( ( ( c_lessequals @ SV2323 @ SV2233 @ SV333 )
| ~ ( c_lessequals @ SV1459 @ SV942 @ SV333 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV333 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5609]) ).
thf(5836,plain,
! [SV2324: $i,SV2234: $i,SV334: $i,SV1460: $i,SV943: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV943 @ SV1460 @ SV334 )
!= ( c_HOL_Ominus__class_Ominus @ SV2234 @ SV2324 @ SV334 ) )
= $true )
| ( ( ( c_lessequals @ SV1460 @ SV943 @ SV334 )
| ~ ( c_lessequals @ SV2324 @ SV2234 @ SV334 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV334 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5610]) ).
thf(5837,plain,
! [SV1842: $i,SV2109: $i,SV343: $i,SV1467: $i,SV2236: $i,SV950: $i] :
( ( ( ~ ( c_lessequals @ SV950 @ SV2236 @ ( tc_fun @ SV1467 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV343 @ SV2109 @ ( tc_fun @ ( tc_prod @ SV1467 @ SV1842 ) @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( c_Relation_OImage @ SV343 @ SV950 @ SV1467 @ SV1842 ) @ ( c_Relation_OImage @ SV2109 @ SV2236 @ SV1467 @ SV1842 ) @ ( tc_fun @ SV1842 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5614]) ).
thf(5838,plain,
! [SV2111: $i,SV2237: $i,SV955: $i,SV1471: $i,SV349: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV349 @ SV1471 ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV955 @ SV1471 @ SV2237 @ SV2237 ) @ ( c_Transitive__Closure_Ortrancl @ SV2111 @ SV2237 ) @ ( tc_prod @ SV2237 @ SV2237 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1 @ SV349 @ SV1471 @ SV2111 @ SV2237 ) @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 @ SV349 @ SV1471 @ SV2111 @ SV2237 ) @ SV2237 @ SV2237 ) @ SV2111 @ ( tc_prod @ SV2237 @ SV2237 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV349 @ SV955 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5617]) ).
thf(5839,plain,
! [SV2112: $i,SV2238: $i,SV956: $i,SV1472: $i,SV350: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV350 @ SV1472 ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV1472 @ SV956 @ SV2238 @ SV2238 ) @ ( c_Transitive__Closure_Ortrancl @ SV2112 @ SV2238 ) @ ( tc_prod @ SV2238 @ SV2238 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 @ SV350 @ SV1472 @ SV2112 @ SV2238 ) @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2 @ SV350 @ SV1472 @ SV2112 @ SV2238 ) @ SV2238 @ SV2238 ) @ SV2112 @ ( tc_prod @ SV2238 @ SV2238 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV350 @ SV956 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5618]) ).
thf(5840,plain,
! [SV351: $i,SV1473: $i,SV957: $i,SV2113: $i] :
( ( ( c_Equiv__Relations_Oequiv @ SV2113 @ SV957 @ SV1473 )
= $false )
| ( ( c_in @ SV351 @ SV2113 @ SV1473 )
= $false )
| ( ( c_in @ SV351 @ ( c_Relation_OImage @ SV957 @ ( c_Set_Oinsert @ SV351 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1473 @ tc_bool ) ) @ SV1473 ) @ SV1473 @ SV1473 ) @ SV1473 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5619]) ).
thf(5841,plain,
! [SV959: $i,SV1475: $i,SV353: $i,SV1847: $i,SV2326: $i] :
( ( ( c_in @ SV2326 @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_OImage @ SV1847 @ ( c_Set_Oinsert @ SV353 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1475 @ tc_bool ) ) @ SV1475 ) @ SV1475 @ SV1475 ) @ ( c_Relation_OImage @ SV1847 @ ( c_Set_Oinsert @ SV959 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1475 @ tc_bool ) ) @ SV1475 ) @ SV1475 @ SV1475 ) @ ( tc_fun @ SV1475 @ tc_bool ) ) @ SV1475 )
= $false )
| ( ( ! [SY5764: $i] :
~ ( c_Equiv__Relations_Oequiv @ SY5764 @ SV1847 @ SV1475 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV353 @ SV959 @ SV1475 @ SV1475 ) @ SV1847 @ ( tc_prod @ SV1475 @ SV1475 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5621]) ).
thf(5842,plain,
! [SV354: $i,SV1848: $i,SV1476: $i,SV2239: $i,SV960: $i] :
( ( ( c_in @ SV960 @ SV2239 @ SV1476 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_Relation_OImage @ SV1848 @ ( c_Set_Oinsert @ SV960 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1476 @ tc_bool ) ) @ SV1476 ) @ SV1476 @ SV1476 ) @ ( c_Relation_OImage @ SV1848 @ ( c_Set_Oinsert @ SV354 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1476 @ tc_bool ) ) @ SV1476 ) @ SV1476 @ SV1476 ) @ ( tc_fun @ SV1476 @ tc_bool ) )
| ~ ( c_Equiv__Relations_Oequiv @ SV2239 @ SV1848 @ SV1476 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV354 @ SV960 @ SV1476 @ SV1476 ) @ SV1848 @ ( tc_prod @ SV1476 @ SV1476 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5622]) ).
thf(5843,plain,
! [SV1478: $i,SV1850: $i,SV356: $i,SV2327: $i,SV2241: $i,SV962: $i] :
( ( ( ~ ( c_in @ SV962 @ SV2241 @ SV2327 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Set_Oimage @ SV356 @ SV2241 @ SV2327 @ SV1850 ) @ SV1478 @ ( tc_fun @ SV1850 @ tc_bool ) ) )
= $true )
| ( ( c_in @ ( hAPP @ SV356 @ SV962 ) @ SV1478 @ SV1850 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5624]) ).
thf(5844,plain,
! [SV1853: $i,SV2116: $i,SV359: $i,SV1481: $i,SV965: $i] :
( ( ( ! [SY5395: $i] :
~ ( c_in @ SY5395 @ SV965 @ SV1481 ) )
= $true )
| ( ( SV359 = SV2116 )
= $true )
| ( ( ( c_Product__Type_OSigma @ SV359 @ ( c_COMBK @ SV965 @ ( tc_fun @ SV1481 @ tc_bool ) @ SV1853 ) @ SV1853 @ SV1481 )
= ( c_Product__Type_OSigma @ SV2116 @ ( c_COMBK @ SV965 @ ( tc_fun @ SV1481 @ tc_bool ) @ SV1853 ) @ SV1853 @ SV1481 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5627]) ).
thf(5845,plain,
! [SV969: $i,SV1484: $i,SV2118: $i,SV363: $i] :
( ( ( c_in @ SV363 @ ( c_Transitive__Closure_Otrancl @ SV2118 @ SV1484 ) @ ( tc_prod @ SV1484 @ SV1484 ) )
= $false )
| ( ( c_lessequals @ SV2118 @ SV969 @ ( tc_fun @ ( tc_prod @ SV1484 @ SV1484 ) @ tc_bool ) )
= $false )
| ( ( c_in @ SV363 @ ( c_Transitive__Closure_Otrancl @ SV969 @ SV1484 ) @ ( tc_prod @ SV1484 @ SV1484 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5628]) ).
thf(5846,plain,
! [SV1857: $i,SV970: $i,SV1485: $i,SV364: $i,SV2358: $i] :
( ( ( ~ ( c_Equiv__Relations_Oequiv @ SV2358 @ SV364 @ SV1485 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV970 @ SV1857 @ SV1485 @ SV1485 ) @ SV364 @ ( tc_prod @ SV1485 @ SV1485 ) )
= $false )
| ( ( ( c_Relation_OImage @ SV364 @ ( c_Set_Oinsert @ SV970 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1485 @ tc_bool ) ) @ SV1485 ) @ SV1485 @ SV1485 )
= ( c_Relation_OImage @ SV364 @ ( c_Set_Oinsert @ SV1857 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1485 @ tc_bool ) ) @ SV1485 ) @ SV1485 @ SV1485 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5629]) ).
thf(5847,plain,
! [SV1858: $i,SV971: $i,SV1486: $i,SV365: $i,SV2359: $i] :
( ( ( ~ ( c_Equiv__Relations_Oequiv @ SV2359 @ SV365 @ SV1486 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV971 @ SV1858 @ SV1486 @ SV1486 ) @ SV365 @ ( tc_prod @ SV1486 @ SV1486 ) )
= $false )
| ( ( ( c_Relation_OImage @ SV365 @ ( c_Set_Oinsert @ SV971 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1486 @ tc_bool ) ) @ SV1486 ) @ SV1486 @ SV1486 )
= ( c_Relation_OImage @ SV365 @ ( c_Set_Oinsert @ SV1858 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1486 @ tc_bool ) ) @ SV1486 ) @ SV1486 @ SV1486 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5630]) ).
thf(5848,plain,
! [SV389: $i,SV1496: $i,SV994: $i] :
( ( ( c_Relation_Oirrefl @ SV994 @ SV1496 )
= $false )
| ( ( ~ ( c_Relation_Otrans @ SV994 @ SV1496 ) )
= $true )
| ( ( c_Relation_Ototal__on @ SV389 @ SV994 @ SV1496 )
= $false )
| ( ( c_Order__Relation_Ostrict__linear__order__on @ SV389 @ SV994 @ SV1496 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5633]) ).
thf(5849,plain,
! [SV2328: $i,SV2243: $i,SV2121: $i,SV1866: $i,SV1501: $i,SV1010: $i,SV405: $i] :
( ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 @ SV405 @ SV1010 @ SV1501 @ SV1866 @ SV2121 @ SV2243 @ SV2328 ) @ SV1010 @ SV2328 @ SV2243 ) @ SV1866 @ ( tc_prod @ SV2328 @ SV2243 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV405 @ SV1010 @ SV2121 @ SV2243 ) @ ( c_Relation_Orel__comp @ SV1501 @ SV1866 @ SV2121 @ SV2328 @ SV2243 ) @ ( tc_prod @ SV2121 @ SV2243 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5636]) ).
thf(5850,plain,
! [SV2329: $i,SV2244: $i,SV2122: $i,SV1867: $i,SV1502: $i,SV1011: $i,SV406: $i] :
( ( ( c_in @ ( c_Pair @ SV406 @ ( c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 @ SV406 @ SV1011 @ SV1502 @ SV1867 @ SV2122 @ SV2244 @ SV2329 ) @ SV2122 @ SV2329 ) @ SV1502 @ ( tc_prod @ SV2122 @ SV2329 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV406 @ SV1011 @ SV2122 @ SV2244 ) @ ( c_Relation_Orel__comp @ SV1502 @ SV1867 @ SV2122 @ SV2329 @ SV2244 ) @ ( tc_prod @ SV2122 @ SV2244 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5637]) ).
thf(5851,plain,
! [SV1022: $i,SV2330: $i,SV2245: $i,SV417: $i,SV1513: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1513 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1 @ SV417 @ SV2245 @ SV2330 ) @ SV2330 @ SV2330 ) @ SV2245 @ ( tc_prod @ SV2330 @ SV2330 ) ) )
= $true )
| ( ( ~ ( c_Wellfounded_Owf @ SV2245 @ SV2330 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV417 @ SV1513 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV417 @ SV1022 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5642]) ).
thf(5852,plain,
! [SV1023: $i,SV2331: $i,SV2246: $i,SV418: $i,SV1514: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1514 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1 @ SV418 @ SV2246 @ SV2331 ) @ SV2331 @ SV2331 ) @ SV2246 @ ( tc_prod @ SV2331 @ SV2331 ) ) )
= $true )
| ( ( ~ ( c_Wellfounded_Owf @ SV2246 @ SV2331 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV418 @ SV1514 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV418 @ SV1023 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5643]) ).
thf(5853,plain,
! [SV1024: $i,SV2332: $i,SV2247: $i,SV419: $i,SV1515: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1515 @ ( c_List_Osko__Recdef__Xtfl__wf__induct__1__1 @ SV419 @ SV2247 @ SV2332 ) @ SV2332 @ SV2332 ) @ SV2247 @ ( tc_prod @ SV2332 @ SV2332 ) ) )
= $true )
| ( ( ~ ( c_Wellfounded_Owf @ SV2247 @ SV2332 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV419 @ SV1515 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV419 @ SV1024 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5644]) ).
thf(5854,plain,
! [SV1025: $i,SV2333: $i,SV2248: $i,SV420: $i,SV1516: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1516 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1 @ SV420 @ SV2248 @ SV2333 ) @ SV2333 @ SV2333 ) @ SV2248 @ ( tc_prod @ SV2333 @ SV2333 ) ) )
= $true )
| ( ( ~ ( c_Wellfounded_Owf @ SV2248 @ SV2333 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV420 @ SV1516 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV420 @ SV1025 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5645]) ).
thf(5855,plain,
! [SV2123: $i,SV2249: $i,SV1029: $i,SV1520: $i,SV424: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV424 @ SV1520 ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV1029 @ SV1520 @ SV2249 @ SV2249 ) @ ( c_Transitive__Closure_Ortrancl @ SV2123 @ SV2249 ) @ ( tc_prod @ SV2249 @ SV2249 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV424 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 @ SV424 @ SV1520 @ SV2123 @ SV2249 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV424 @ SV1029 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5649]) ).
thf(5856,plain,
! [SV2124: $i,SV2250: $i,SV1030: $i,SV1521: $i,SV425: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV425 @ SV1521 ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV1030 @ SV1521 @ SV2250 @ SV2250 ) @ ( c_Transitive__Closure_Ortrancl @ SV2124 @ SV2250 ) @ ( tc_prod @ SV2250 @ SV2250 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 @ SV425 @ SV1521 @ SV2124 @ SV2250 ) @ SV1521 @ SV2250 @ SV2250 ) @ ( c_Transitive__Closure_Ortrancl @ SV2124 @ SV2250 ) @ ( tc_prod @ SV2250 @ SV2250 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV425 @ SV1030 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5650]) ).
thf(5857,plain,
! [SV2125: $i,SV2251: $i,SV1031: $i,SV1522: $i,SV426: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV426 @ SV1522 ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV1522 @ SV1031 @ SV2251 @ SV2251 ) @ ( c_Transitive__Closure_Ortrancl @ SV2125 @ SV2251 ) @ ( tc_prod @ SV2251 @ SV2251 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1522 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 @ SV426 @ SV1522 @ SV2125 @ SV2251 ) @ SV2251 @ SV2251 ) @ ( c_Transitive__Closure_Ortrancl @ SV2125 @ SV2251 ) @ ( tc_prod @ SV2251 @ SV2251 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV426 @ SV1031 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5651]) ).
thf(5858,plain,
! [SV1032: $i,SV2252: $i,SV2126: $i,SV1523: $i,SV427: $i] :
( ( ( hBOOL @ ( hAPP @ SV427 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2 @ SV427 @ SV1523 @ SV2126 @ SV2252 ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV427 @ SV1523 ) )
| ~ ( c_in @ ( c_Pair @ SV1523 @ SV1032 @ SV2252 @ SV2252 ) @ ( c_Transitive__Closure_Ortrancl @ SV2126 @ SV2252 ) @ ( tc_prod @ SV2252 @ SV2252 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV427 @ SV1032 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5652]) ).
thf(5859,plain,
! [SV2127: $i,SV2253: $i,SV1034: $i,SV1525: $i,SV429: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV429 @ SV1525 ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV1525 @ SV1034 @ SV2253 @ SV2253 ) @ ( c_Transitive__Closure_Ortrancl @ SV2127 @ SV2253 ) @ ( tc_prod @ SV2253 @ SV2253 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV429 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 @ SV429 @ SV1525 @ SV2127 @ SV2253 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV429 @ SV1034 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5653]) ).
thf(5860,plain,
! [SV1036: $i,SV2254: $i,SV2128: $i,SV1527: $i,SV431: $i] :
( ( ( hBOOL @ ( hAPP @ SV431 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1 @ SV431 @ SV1527 @ SV2128 @ SV2254 ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV431 @ SV1527 ) )
| ~ ( c_in @ ( c_Pair @ SV1036 @ SV1527 @ SV2254 @ SV2254 ) @ ( c_Transitive__Closure_Ortrancl @ SV2128 @ SV2254 ) @ ( tc_prod @ SV2254 @ SV2254 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV431 @ SV1036 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5654]) ).
thf(5861,plain,
! [SV1042: $i,SV437: $i,SV1530: $i,SV2360: $i,SV1879: $i] :
( ( ( ~ ( c_in @ SV1879 @ SV2360 @ SV1530 )
| ~ ( c_Equiv__Relations_Oequiv @ SV2360 @ SV437 @ SV1530 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1042 @ SV1879 @ SV1530 @ SV1530 ) @ SV437 @ ( tc_prod @ SV1530 @ SV1530 ) )
= $true )
| ( ( ( c_Relation_OImage @ SV437 @ ( c_Set_Oinsert @ SV1042 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1530 @ tc_bool ) ) @ SV1530 ) @ SV1530 @ SV1530 )
= ( c_Relation_OImage @ SV437 @ ( c_Set_Oinsert @ SV1879 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1530 @ tc_bool ) ) @ SV1530 ) @ SV1530 @ SV1530 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5657]) ).
thf(5862,plain,
! [SV1880: $i,SV1043: $i,SV1531: $i,SV438: $i,SV2334: $i] :
( ( ( ~ ( c_Equiv__Relations_Oequiv @ SV2334 @ SV438 @ SV1531 ) )
= $true )
| ( ( ( c_in @ ( c_Pair @ SV1043 @ SV1880 @ SV1531 @ SV1531 ) @ SV438 @ ( tc_prod @ SV1531 @ SV1531 ) )
| ~ ( c_in @ SV1880 @ SV2334 @ SV1531 )
| ~ ( c_in @ SV1043 @ SV2334 @ SV1531 ) )
= $true )
| ( ( ( c_Relation_OImage @ SV438 @ ( c_Set_Oinsert @ SV1043 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1531 @ tc_bool ) ) @ SV1531 ) @ SV1531 @ SV1531 )
= ( c_Relation_OImage @ SV438 @ ( c_Set_Oinsert @ SV1880 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1531 @ tc_bool ) ) @ SV1531 ) @ SV1531 @ SV1531 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5658]) ).
thf(5863,plain,
! [SV439: $i,SV1044: $i,SV1532: $i,SV2361: $i,SV1881: $i] :
( ( ( ~ ( c_in @ SV1881 @ SV2361 @ SV1532 )
| ~ ( c_in @ SV1044 @ SV2361 @ SV1532 )
| ~ ( c_Equiv__Relations_Oequiv @ SV2361 @ SV439 @ SV1532 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1044 @ SV1881 @ SV1532 @ SV1532 ) @ SV439 @ ( tc_prod @ SV1532 @ SV1532 ) )
= $false )
| ( ( ( c_Relation_OImage @ SV439 @ ( c_Set_Oinsert @ SV1044 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1532 @ tc_bool ) ) @ SV1532 ) @ SV1532 @ SV1532 )
= ( c_Relation_OImage @ SV439 @ ( c_Set_Oinsert @ SV1881 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1532 @ tc_bool ) ) @ SV1532 ) @ SV1532 @ SV1532 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5659]) ).
thf(5864,plain,
! [SV440: $i,SV1045: $i,SV1533: $i,SV2335: $i,SV1882: $i] :
( ( ( ~ ( c_in @ SV1882 @ SV2335 @ SV1533 ) )
= $true )
| ( ( ~ ( c_in @ SV1045 @ SV2335 @ SV1533 )
| ~ ( c_Equiv__Relations_Oequiv @ SV2335 @ SV440 @ SV1533 )
| ( c_in @ ( c_Pair @ SV1045 @ SV1882 @ SV1533 @ SV1533 ) @ SV440 @ ( tc_prod @ SV1533 @ SV1533 ) ) )
= $true )
| ( ( ( c_Relation_OImage @ SV440 @ ( c_Set_Oinsert @ SV1045 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1533 @ tc_bool ) ) @ SV1533 ) @ SV1533 @ SV1533 )
= ( c_Relation_OImage @ SV440 @ ( c_Set_Oinsert @ SV1882 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1533 @ tc_bool ) ) @ SV1533 ) @ SV1533 @ SV1533 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5660]) ).
thf(5865,plain,
! [SV2131: $i,SV442: $i,SV1535: $i,SV1047: $i,SV2336: $i] :
( ( ( ~ ( c_lessequals @ SV2336 @ ( c_Product__Type_OSigma @ SV1047 @ ( c_COMBK @ SV1047 @ ( tc_fun @ SV1535 @ tc_bool ) @ SV1535 ) @ SV1535 @ SV1535 ) @ ( tc_fun @ ( tc_prod @ SV1535 @ SV1535 ) @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV442 @ SV2131 @ SV1535 @ SV1535 ) @ ( c_Transitive__Closure_Ortrancl @ SV2336 @ SV1535 ) @ ( tc_prod @ SV1535 @ SV1535 ) ) )
= $true )
| ( ( SV442 = SV2131 )
= $true )
| ( ( c_in @ SV442 @ SV1047 @ SV1535 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5661]) ).
thf(5866,plain,
! [SV446: $i,SV1883: $i,SV1539: $i,SV1051: $i,SV2255: $i] :
( ( ( c_in @ ( c_Pair @ SV2255 @ SV1051 @ SV1539 @ SV1539 ) @ ( c_Transitive__Closure_Ortrancl @ SV1883 @ SV1539 ) @ ( tc_prod @ SV1539 @ SV1539 ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV446 @ SV2255 @ SV1539 @ SV1539 ) @ SV1883 @ ( tc_prod @ SV1539 @ SV1539 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV446 @ SV1051 @ SV1539 @ SV1539 ) @ ( c_Transitive__Closure_Otrancl @ SV1883 @ SV1539 ) @ ( tc_prod @ SV1539 @ SV1539 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5662]) ).
thf(5867,plain,
! [SV447: $i,SV1884: $i,SV1540: $i,SV1052: $i,SV2256: $i] :
( ( ( c_in @ ( c_Pair @ SV2256 @ SV1052 @ SV1540 @ SV1540 ) @ SV1884 @ ( tc_prod @ SV1540 @ SV1540 ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV447 @ SV2256 @ SV1540 @ SV1540 ) @ ( c_Transitive__Closure_Ortrancl @ SV1884 @ SV1540 ) @ ( tc_prod @ SV1540 @ SV1540 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV447 @ SV1052 @ SV1540 @ SV1540 ) @ ( c_Transitive__Closure_Otrancl @ SV1884 @ SV1540 ) @ ( tc_prod @ SV1540 @ SV1540 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5663]) ).
thf(5868,plain,
! [SV1058: $i,SV1890: $i,SV1546: $i,SV453: $i,SV2337: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV2337 @ SV453 @ SV1546 @ SV1546 ) @ ( c_Transitive__Closure_Ortrancl @ SV1890 @ SV1546 ) @ ( tc_prod @ SV1546 @ SV1546 ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV2337 @ SV1058 @ SV1546 @ SV1546 ) @ ( c_Transitive__Closure_Ortrancl @ SV1890 @ SV1546 ) @ ( tc_prod @ SV1546 @ SV1546 ) )
| ~ ( c_Relation_Osingle__valued @ SV1890 @ SV1546 @ SV1546 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1058 @ SV453 @ SV1546 @ SV1546 ) @ ( c_Transitive__Closure_Ortrancl @ SV1890 @ SV1546 ) @ ( tc_prod @ SV1546 @ SV1546 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV453 @ SV1058 @ SV1546 @ SV1546 ) @ ( c_Transitive__Closure_Ortrancl @ SV1890 @ SV1546 ) @ ( tc_prod @ SV1546 @ SV1546 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5667]) ).
thf(5869,plain,
! [SV455: $i,SV1892: $i,SV1548: $i,SV1060: $i,SV2257: $i] :
( ( ( c_in @ ( c_Pair @ SV2257 @ SV1060 @ SV1548 @ SV1548 ) @ ( c_Transitive__Closure_Ortrancl @ SV1892 @ SV1548 ) @ ( tc_prod @ SV1548 @ SV1548 ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV455 @ SV2257 @ SV1548 @ SV1548 ) @ ( c_Transitive__Closure_Otrancl @ SV1892 @ SV1548 ) @ ( tc_prod @ SV1548 @ SV1548 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV455 @ SV1060 @ SV1548 @ SV1548 ) @ ( c_Transitive__Closure_Otrancl @ SV1892 @ SV1548 ) @ ( tc_prod @ SV1548 @ SV1548 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5668]) ).
thf(5870,plain,
! [SV456: $i,SV1893: $i,SV1549: $i,SV1061: $i,SV2258: $i] :
( ( ( c_in @ ( c_Pair @ SV2258 @ SV1061 @ SV1549 @ SV1549 ) @ ( c_Transitive__Closure_Otrancl @ SV1893 @ SV1549 ) @ ( tc_prod @ SV1549 @ SV1549 ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV456 @ SV2258 @ SV1549 @ SV1549 ) @ ( c_Transitive__Closure_Ortrancl @ SV1893 @ SV1549 ) @ ( tc_prod @ SV1549 @ SV1549 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV456 @ SV1061 @ SV1549 @ SV1549 ) @ ( c_Transitive__Closure_Otrancl @ SV1893 @ SV1549 ) @ ( tc_prod @ SV1549 @ SV1549 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5669]) ).
thf(5871,plain,
! [SV1898: $i,SV1554: $i,SV1066: $i,SV2362: $i,SV2338: $i,SV2134: $i,SV461: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_split @ SV461 @ SV2134 @ SV2338 @ ( tc_fun @ SV2362 @ tc_bool ) ) @ ( c_Pair @ SV1066 @ SV1554 @ SV2134 @ SV2338 ) ) @ SV1898 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ SV461 @ SV1066 ) @ SV1554 ) @ SV1898 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5670]) ).
thf(5872,plain,
! [SV470: $i,SV2136: $i,SV1902: $i,SV1075: $i] :
( ( ( c_in @ SV1075 @ ( c_Wellfounded_Oacc @ SV1902 @ SV2136 ) @ SV2136 )
= $false )
| ( ( hBOOL @ ( hAPP @ SV470 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ SV470 @ SV1902 @ SV2136 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV470 @ SV1075 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5676]) ).
thf(5873,plain,
! [SV485: $i,SV2139: $i,SV1906: $i,SV1089: $i] :
( ( ( c_in @ SV1089 @ ( c_Wellfounded_Oacc @ SV1906 @ SV2139 ) @ SV2139 )
= $false )
| ( ( hBOOL @ ( hAPP @ SV485 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ SV485 @ SV1906 @ SV2139 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV485 @ SV1089 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5680]) ).
thf(5874,plain,
! [SV518: $i,SV2266: $i,SV1574: $i,SV1119: $i] :
( ( ( c_Wellfounded_Owf @ SV1119 @ SV1574 )
= $false )
| ( ( c_in @ SV2266 @ SV518 @ SV1574 )
= $false )
| ( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 @ SV518 @ SV1119 @ SV1574 ) @ SV518 @ SV1574 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5682]) ).
thf(5875,plain,
! [SV1575: $i,SV520: $i,SV2145: $i,SV1910: $i,SV1121: $i] :
( ( ( c_Relation_Osingle__valued @ SV1121 @ SV1910 @ SV2145 )
= $false )
| ( ( ~ ( c_Relation_Osingle__valued @ SV520 @ SV1575 @ SV1910 ) )
= $true )
| ( ( c_Relation_Osingle__valued @ ( c_Relation_Orel__comp @ SV520 @ SV1121 @ SV1575 @ SV1910 @ SV2145 ) @ SV1575 @ SV2145 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5683]) ).
thf(5876,plain,
! [SV530: $i,SV2267: $i,SV1578: $i,SV1130: $i] :
( ( ( c_Wellfounded_Owf @ SV1130 @ SV1578 )
= $false )
| ( ( c_in @ SV2267 @ SV530 @ SV1578 )
= $false )
| ( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 @ SV530 @ SV1130 @ SV1578 ) @ SV530 @ SV1578 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5685]) ).
thf(5877,plain,
! [SV2146: $i,SV1914: $i,SV1133: $i,SV533: $i,SV2363: $i,SV2268: $i,SV1580: $i] :
( ( ( ~ ( c_in @ SV1580 @ SV2268 @ SV2363 )
| ! [SY6040: $i] :
( ~ ( c_Equiv__Relations_Ocongruent2 @ SY6040 @ SV533 @ SV1133 @ SV2363 @ SV1914 @ SV2146 )
| ~ ( c_Equiv__Relations_Oequiv @ SV2268 @ SY6040 @ SV2363 ) ) )
= $true )
| ( ( c_Equiv__Relations_Ocongruent @ SV533 @ ( hAPP @ SV1133 @ SV1580 ) @ SV1914 @ SV2146 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5686]) ).
thf(5878,plain,
! [SV1146: $i,SV2342: $i,SV2269: $i,SV546: $i,SV1587: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1587 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ SV546 @ SV2269 @ SV2342 ) @ SV2342 @ SV2342 ) @ SV2269 @ ( tc_prod @ SV2342 @ SV2342 ) ) )
= $true )
| ( ( ~ ( c_in @ SV1146 @ ( c_Wellfounded_Oacc @ SV2269 @ SV2342 ) @ SV2342 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV546 @ SV1587 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV546 @ SV1146 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5689]) ).
thf(5879,plain,
! [SV1147: $i,SV2270: $i,SV547: $i,SV1918: $i] :
( ( ( c_in @ ( c_Pair @ SV1918 @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ SV547 @ SV2270 ) @ t_a @ t_a ) @ SV2270 @ ( tc_prod @ t_a @ t_a ) )
= $false )
| ( ( ~ ( c_in @ SV1147 @ ( c_Wellfounded_Oacc @ SV2270 @ t_a ) @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV547 @ SV1918 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV547 @ SV1147 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5690]) ).
thf(5880,plain,
! [SV1588: $i,SV2271: $i,SV1148: $i,SV548: $i] :
( ( ( c_in @ ( c_Pair @ SV548 @ ( c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 @ SV1148 @ SV2271 @ SV1588 ) @ SV1588 @ SV1588 ) @ SV2271 @ ( tc_prod @ SV1588 @ SV1588 ) )
= $false )
| ( ( ! [SY5526: $i] :
~ ( c_in @ SY5526 @ SV1148 @ SV1588 )
| ~ ( c_Wellfounded_Owf @ SV2271 @ SV1588 ) )
= $true )
| ( ( c_in @ SV548 @ SV1148 @ SV1588 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5691]) ).
thf(5881,plain,
! [SV1151: $i,SV1591: $i,SV2149: $i,SV551: $i] :
( ( ( c_in @ ( c_Pair @ SV551 @ SV2149 @ SV1591 @ SV1591 ) @ ( c_Transitive__Closure_Ortrancl @ SV1151 @ SV1591 ) @ ( tc_prod @ SV1591 @ SV1591 ) )
= $false )
| ( ( c_in @ SV2149 @ ( c_Wellfounded_Oacc @ SV1151 @ SV1591 ) @ SV1591 )
= $false )
| ( ( c_in @ SV551 @ ( c_Wellfounded_Oacc @ SV1151 @ SV1591 ) @ SV1591 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5692]) ).
thf(5882,plain,
! [SV552: $i,SV1592: $i,SV1152: $i,SV2150: $i] :
( ( ( c_in @ SV2150 @ ( c_Wellfounded_Oacc @ SV1152 @ SV1592 ) @ SV1592 )
= $false )
| ( ( c_in @ ( c_Pair @ SV552 @ SV2150 @ SV1592 @ SV1592 ) @ ( c_Transitive__Closure_Ortrancl @ SV1152 @ SV1592 ) @ ( tc_prod @ SV1592 @ SV1592 ) )
= $false )
| ( ( c_in @ SV552 @ ( c_Wellfounded_Oacc @ SV1152 @ SV1592 ) @ SV1592 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5693]) ).
thf(5883,plain,
! [SV1153: $i,SV2151: $i,SV553: $i,SV1920: $i] :
( ( ( c_in @ ( c_Pair @ SV1920 @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ SV553 @ SV2151 ) @ t_a @ t_a ) @ SV2151 @ ( tc_prod @ t_a @ t_a ) )
= $false )
| ( ( ~ ( c_in @ SV1153 @ ( c_Wellfounded_Oacc @ SV2151 @ t_a ) @ t_a ) )
= $true )
| ( ( c_in @ SV1920 @ ( c_Wellfounded_Oacc @ SV2151 @ t_a ) @ t_a )
= $true )
| ( ( hBOOL @ ( hAPP @ SV553 @ SV1153 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5694]) ).
thf(5884,plain,
! [SV1155: $i,SV2272: $i,SV555: $i,SV1921: $i] :
( ( ( c_in @ ( c_Pair @ SV1921 @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ SV555 @ SV2272 ) @ t_a @ t_a ) @ SV2272 @ ( tc_prod @ t_a @ t_a ) )
= $false )
| ( ( ~ ( c_in @ SV1155 @ ( c_Wellfounded_Oacc @ SV2272 @ t_a ) @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV555 @ SV1921 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV555 @ SV1155 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5695]) ).
thf(5885,plain,
! [SV2343: $i,SV2273: $i,SV2152: $i,SV1922: $i,SV1594: $i,SV1156: $i,SV556: $i] :
( ( ( c_in @ ( hAPP @ ( hAPP @ SV556 @ SV1156 ) @ SV1594 ) @ ( c_Set_Oimage @ ( c_split @ SV556 @ SV1922 @ SV2152 @ SV2273 ) @ SV2343 @ ( tc_prod @ SV1922 @ SV2152 ) @ SV2273 ) @ SV2273 )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV1156 @ SV1594 @ SV1922 @ SV2152 ) @ SV2343 @ ( tc_prod @ SV1922 @ SV2152 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5696]) ).
thf(5886,plain,
! [SV1158: $i,SV2153: $i,SV558: $i,SV1924: $i] :
( ( ( c_in @ ( c_Pair @ SV1924 @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ SV558 @ SV2153 ) @ t_a @ t_a ) @ SV2153 @ ( tc_prod @ t_a @ t_a ) )
= $false )
| ( ( ~ ( c_in @ SV1158 @ ( c_Wellfounded_Oacc @ SV2153 @ t_a ) @ t_a ) )
= $true )
| ( ( c_in @ SV1924 @ ( c_Wellfounded_Oacc @ SV2153 @ t_a ) @ t_a )
= $true )
| ( ( hBOOL @ ( hAPP @ SV558 @ SV1158 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5697]) ).
thf(5887,plain,
! [SV1159: $i,SV2344: $i,SV2274: $i,SV559: $i,SV1596: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1596 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ SV559 @ SV2274 @ SV2344 ) @ SV2344 @ SV2344 ) @ SV2274 @ ( tc_prod @ SV2344 @ SV2344 ) ) )
= $true )
| ( ( ~ ( c_in @ SV1159 @ ( c_Wellfounded_Oacc @ SV2274 @ SV2344 ) @ SV2344 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV559 @ SV1596 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV559 @ SV1159 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5698]) ).
thf(5888,plain,
! [SV1597: $i,SV2275: $i,SV1160: $i,SV560: $i] :
( ( ( c_in @ ( c_Pair @ SV560 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 @ SV1160 @ SV2275 @ SV1597 ) @ SV1597 @ SV1597 ) @ SV2275 @ ( tc_prod @ SV1597 @ SV1597 ) )
= $false )
| ( ( ! [SY5538: $i] :
~ ( c_in @ SY5538 @ SV1160 @ SV1597 )
| ~ ( c_Wellfounded_Owf @ SV2275 @ SV1597 ) )
= $true )
| ( ( c_in @ SV560 @ SV1160 @ SV1597 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5699]) ).
thf(5889,plain,
! [SV2345: $i,SV2276: $i,SV2156: $i,SV1929: $i,SV1601: $i,SV1165: $i,SV565: $i] :
( ( ( c_in @ SV565 @ ( hAPP @ ( c_split @ SV1165 @ SV1601 @ SV1929 @ ( tc_fun @ SV2156 @ tc_bool ) ) @ ( c_Pair @ SV2276 @ SV2345 @ SV1601 @ SV1929 ) ) @ SV2156 )
= $true )
| ( ( ~ ( c_in @ SV565 @ ( hAPP @ ( hAPP @ SV1165 @ SV2276 ) @ SV2345 ) @ SV2156 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5702]) ).
thf(5890,plain,
! [SV2364: $i,SV2346: $i,SV2277: $i,SV2157: $i,SV1930: $i,SV1602: $i,SV1166: $i,SV566: $i] :
( ( ( ( hAPP @ ( hAPP @ SV566 @ SV1166 ) @ SV1602 )
= ( hAPP @ ( hAPP @ SV566 @ SV1930 ) @ SV2157 ) )
| ~ ( c_in @ ( c_Pair @ SV1602 @ SV2157 @ SV2277 @ SV2277 ) @ SV2346 @ ( tc_prod @ SV2277 @ SV2277 ) )
| ! [SY6041: $i] :
( ~ ( c_in @ ( c_Pair @ SV1166 @ SV1930 @ SV2364 @ SV2364 ) @ SY6041 @ ( tc_prod @ SV2364 @ SV2364 ) )
| ! [SY6042: $i] :
~ ( c_Equiv__Relations_Ocongruent2 @ SY6041 @ SV2346 @ SV566 @ SV2364 @ SV2277 @ SY6042 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5703]) ).
thf(5891,plain,
! [SV567: $i,SV2347: $i,SV2278: $i,SV1931: $i,SV1167: $i,SV1603: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1603 @ SV1167 @ SV1931 @ SV2278 ) @ SV2347 @ ( tc_prod @ SV1931 @ SV2278 ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV1603 @ SV567 @ SV1931 @ SV2278 ) @ SV2347 @ ( tc_prod @ SV1931 @ SV2278 ) )
| ~ ( c_Relation_Osingle__valued @ SV2347 @ SV1931 @ SV2278 ) )
= $true )
| ( ( SV567 = SV1167 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5704]) ).
thf(5892,plain,
! [SV2158: $i,SV568: $i,SV1168: $i,SV1932: $i,SV1604: $i,SV2279: $i] :
( ( ( c_in @ ( c_Pair @ SV2279 @ SV1604 @ SV1932 @ SV1932 ) @ SV1168 @ ( tc_prod @ SV1932 @ SV1932 ) )
= $false )
| ( ( ( hAPP @ ( c_Recdef_Ocut @ SV568 @ SV1168 @ SV1604 @ SV1932 @ SV2158 ) @ SV2279 )
= ( hAPP @ SV568 @ SV2279 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5705]) ).
thf(5893,plain,
! [SV2159: $i,SV569: $i,SV1169: $i,SV1933: $i,SV1605: $i,SV2280: $i] :
( ( ( c_in @ ( c_Pair @ SV2280 @ SV1605 @ SV1933 @ SV1933 ) @ SV1169 @ ( tc_prod @ SV1933 @ SV1933 ) )
= $false )
| ( ( ( hAPP @ ( c_Recdef_Ocut @ SV569 @ SV1169 @ SV1605 @ SV1933 @ SV2159 ) @ SV2280 )
= ( hAPP @ SV569 @ SV2280 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5706]) ).
thf(5894,plain,
! [SV572: $i,SV1936: $i,SV1608: $i,SV1172: $i,SV2281: $i] :
( ( ( c_in @ ( c_Pair @ SV2281 @ SV1172 @ SV1608 @ SV1608 ) @ SV1936 @ ( tc_prod @ SV1608 @ SV1608 ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV572 @ SV2281 @ SV1608 @ SV1608 ) @ SV1936 @ ( tc_prod @ SV1608 @ SV1608 ) )
| ~ ( c_Relation_Otrans @ SV1936 @ SV1608 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV572 @ SV1172 @ SV1608 @ SV1608 ) @ SV1936 @ ( tc_prod @ SV1608 @ SV1608 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5709]) ).
thf(5895,plain,
! [SV573: $i,SV1937: $i,SV1609: $i,SV1173: $i,SV2282: $i] :
( ( ( c_in @ ( c_Pair @ SV2282 @ SV1173 @ SV1609 @ SV1609 ) @ SV1937 @ ( tc_prod @ SV1609 @ SV1609 ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV573 @ SV2282 @ SV1609 @ SV1609 ) @ SV1937 @ ( tc_prod @ SV1609 @ SV1609 ) )
| ~ ( c_Relation_Otrans @ SV1937 @ SV1609 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV573 @ SV1173 @ SV1609 @ SV1609 ) @ SV1937 @ ( tc_prod @ SV1609 @ SV1609 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5710]) ).
thf(5896,plain,
! [SV578: $i,SV1941: $i,SV1614: $i,SV1178: $i,SV2283: $i] :
( ( ( c_in @ ( c_Pair @ SV2283 @ SV1178 @ SV1614 @ SV1614 ) @ SV1941 @ ( tc_prod @ SV1614 @ SV1614 ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV578 @ SV2283 @ SV1614 @ SV1614 ) @ ( c_Transitive__Closure_Otrancl @ SV1941 @ SV1614 ) @ ( tc_prod @ SV1614 @ SV1614 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV578 @ SV1178 @ SV1614 @ SV1614 ) @ ( c_Transitive__Closure_Otrancl @ SV1941 @ SV1614 ) @ ( tc_prod @ SV1614 @ SV1614 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5714]) ).
thf(5897,plain,
! [SV579: $i,SV1942: $i,SV1615: $i,SV1179: $i,SV2284: $i] :
( ( ( c_in @ ( c_Pair @ SV2284 @ SV1179 @ SV1615 @ SV1615 ) @ ( c_Transitive__Closure_Otrancl @ SV1942 @ SV1615 ) @ ( tc_prod @ SV1615 @ SV1615 ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV579 @ SV2284 @ SV1615 @ SV1615 ) @ SV1942 @ ( tc_prod @ SV1615 @ SV1615 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV579 @ SV1179 @ SV1615 @ SV1615 ) @ ( c_Transitive__Closure_Otrancl @ SV1942 @ SV1615 ) @ ( tc_prod @ SV1615 @ SV1615 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5715]) ).
thf(5898,plain,
! [SV580: $i,SV1943: $i,SV1616: $i,SV1180: $i,SV2285: $i] :
( ( ( c_in @ ( c_Pair @ SV2285 @ SV1180 @ SV1616 @ SV1616 ) @ SV1943 @ ( tc_prod @ SV1616 @ SV1616 ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV580 @ SV2285 @ SV1616 @ SV1616 ) @ ( c_Transitive__Closure_Ortrancl @ SV1943 @ SV1616 ) @ ( tc_prod @ SV1616 @ SV1616 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV580 @ SV1180 @ SV1616 @ SV1616 ) @ ( c_Transitive__Closure_Ortrancl @ SV1943 @ SV1616 ) @ ( tc_prod @ SV1616 @ SV1616 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5716]) ).
thf(5899,plain,
! [SV581: $i,SV1944: $i,SV1617: $i,SV1181: $i,SV2286: $i] :
( ( ( c_in @ ( c_Pair @ SV2286 @ SV1181 @ SV1617 @ SV1617 ) @ ( c_Transitive__Closure_Ortrancl @ SV1944 @ SV1617 ) @ ( tc_prod @ SV1617 @ SV1617 ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV581 @ SV2286 @ SV1617 @ SV1617 ) @ SV1944 @ ( tc_prod @ SV1617 @ SV1617 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV581 @ SV1181 @ SV1617 @ SV1617 ) @ ( c_Transitive__Closure_Ortrancl @ SV1944 @ SV1617 ) @ ( tc_prod @ SV1617 @ SV1617 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5717]) ).
thf(5900,plain,
! [SV583: $i,SV1946: $i,SV1619: $i,SV1183: $i,SV2287: $i] :
( ( ( c_in @ ( c_Pair @ SV2287 @ SV1183 @ SV1619 @ SV1619 ) @ ( c_Transitive__Closure_Ortrancl @ SV1946 @ SV1619 ) @ ( tc_prod @ SV1619 @ SV1619 ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV583 @ SV2287 @ SV1619 @ SV1619 ) @ ( c_Transitive__Closure_Ortrancl @ SV1946 @ SV1619 ) @ ( tc_prod @ SV1619 @ SV1619 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV583 @ SV1183 @ SV1619 @ SV1619 ) @ ( c_Transitive__Closure_Ortrancl @ SV1946 @ SV1619 ) @ ( tc_prod @ SV1619 @ SV1619 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5718]) ).
thf(5901,plain,
! [SV1947: $i,SV1622: $i,SV586: $i,SV1186: $i] :
( ( ( c_in @ ( c_Pair @ SV1186 @ SV586 @ SV1622 @ SV1622 ) @ SV1947 @ ( tc_prod @ SV1622 @ SV1622 ) )
= $false )
| ( ( ~ ( c_Wellfounded_Owf @ SV1947 @ SV1622 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV586 @ SV1186 @ SV1622 @ SV1622 ) @ SV1947 @ ( tc_prod @ SV1622 @ SV1622 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5719]) ).
thf(5902,plain,
! [SV2165: $i,SV1948: $i,SV1187: $i,SV587: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV587 @ SV1187 @ SV1948 @ SV1948 ) @ SV2165 @ ( tc_prod @ SV1948 @ SV1948 ) ) )
= $true )
| ( ( ~ ( c_Relation_Oantisym @ SV2165 @ SV1948 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1187 @ SV587 @ SV1948 @ SV1948 ) @ SV2165 @ ( tc_prod @ SV1948 @ SV1948 ) )
= $false )
| ( ( SV587 = SV1187 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5720]) ).
thf(5903,plain,
! [SV2166: $i,SV1949: $i,SV1188: $i,SV588: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV588 @ SV1188 @ SV1949 @ SV1949 ) @ SV2166 @ ( tc_prod @ SV1949 @ SV1949 ) ) )
= $true )
| ( ( ~ ( c_Relation_Oantisym @ SV2166 @ SV1949 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1188 @ SV588 @ SV1949 @ SV1949 ) @ SV2166 @ ( tc_prod @ SV1949 @ SV1949 ) )
= $false )
| ( ( SV588 = SV1188 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5721]) ).
thf(5904,plain,
! [SV589: $i,SV2288: $i,SV1950: $i,SV1623: $i,SV1189: $i] :
( ( ( c_in @ ( c_Pair @ SV1189 @ SV1623 @ SV1950 @ SV1950 ) @ SV2288 @ ( tc_prod @ SV1950 @ SV1950 ) )
= $false )
| ( ( ! [SY6028: $i] :
~ ( c_Equiv__Relations_Ocongruent @ SV2288 @ SV589 @ SV1950 @ SY6028 ) )
= $true )
| ( ( ( hAPP @ SV589 @ SV1189 )
= ( hAPP @ SV589 @ SV1623 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5722]) ).
thf(5905,plain,
! [SV2289: $i,SV2168: $i,SV1952: $i,SV1624: $i,SV1191: $i,SV591: $i] :
( ( ( ( c_Recdef_Ocut @ SV591 @ SV1191 @ SV1624 @ SV1952 @ SV2168 )
= ( c_Recdef_Ocut @ SV2289 @ SV1191 @ SV1624 @ SV1952 @ SV2168 ) )
= $false )
| ( ( ! [SY6029: $i] :
( ( ( hAPP @ SV591 @ SY6029 )
= ( hAPP @ SV2289 @ SY6029 ) )
| ~ ( c_in @ ( c_Pair @ SY6029 @ SV1624 @ SV1952 @ SV1952 ) @ SV1191 @ ( tc_prod @ SV1952 @ SV1952 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5723]) ).
thf(5906,plain,
! [SV1627: $i,SV1954: $i,SV2290: $i,SV1195: $i,SV595: $i,SV2169: $i] :
( ( ( c_in @ ( c_Pair @ ( hAPP @ SV2169 @ SV595 ) @ ( hAPP @ SV2169 @ SV1195 ) @ SV2290 @ SV2290 ) @ SV1954 @ ( tc_prod @ SV2290 @ SV2290 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV595 @ SV1195 @ SV1627 @ SV1627 ) @ ( c_Relation_Oinv__image @ SV1954 @ SV2169 @ SV2290 @ SV1627 ) @ ( tc_prod @ SV1627 @ SV1627 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5724]) ).
thf(5907,plain,
! [SV1955: $i,SV596: $i,SV2170: $i,SV2348: $i,SV1628: $i,SV1196: $i] :
( ( ( c_in @ ( c_Pair @ SV1196 @ SV1628 @ SV2348 @ SV2348 ) @ ( c_Relation_Oinv__image @ SV2170 @ SV596 @ SV1955 @ SV2348 ) @ ( tc_prod @ SV2348 @ SV2348 ) )
= $false )
| ( ( c_in @ ( c_Pair @ ( hAPP @ SV596 @ SV1196 ) @ ( hAPP @ SV596 @ SV1628 ) @ SV1955 @ SV1955 ) @ SV2170 @ ( tc_prod @ SV1955 @ SV1955 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5725]) ).
thf(5908,plain,
! [SV597: $i,SV1197: $i,SV1629: $i,SV1956: $i] :
( ( ( c_Relation_Osym @ SV1956 @ SV1629 )
= $false )
| ( ( c_in @ ( c_Pair @ SV1197 @ SV597 @ SV1629 @ SV1629 ) @ SV1956 @ ( tc_prod @ SV1629 @ SV1629 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV597 @ SV1197 @ SV1629 @ SV1629 ) @ SV1956 @ ( tc_prod @ SV1629 @ SV1629 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5726]) ).
thf(5909,plain,
! [SV598: $i,SV1198: $i,SV1630: $i,SV1957: $i] :
( ( ( c_Relation_Osym @ SV1957 @ SV1630 )
= $false )
| ( ( c_in @ ( c_Pair @ SV1198 @ SV598 @ SV1630 @ SV1630 ) @ SV1957 @ ( tc_prod @ SV1630 @ SV1630 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV598 @ SV1198 @ SV1630 @ SV1630 ) @ SV1957 @ ( tc_prod @ SV1630 @ SV1630 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5727]) ).
thf(5910,plain,
! [SV2349: $i,SV2291: $i,SV2171: $i,SV1958: $i,SV1631: $i,SV1199: $i,SV599: $i] :
( ( ( c_in @ ( c_Pair @ SV599 @ SV1199 @ SV1631 @ SV1958 ) @ ( c_Relation_Orel__comp @ SV2171 @ SV2291 @ SV1631 @ SV2349 @ SV1958 ) @ ( tc_prod @ SV1631 @ SV1958 ) )
= $true )
| ( ( ! [SY6039: $i] :
( ~ ( c_in @ ( c_Pair @ SY6039 @ SV1199 @ SV2349 @ SV1958 ) @ SV2291 @ ( tc_prod @ SV2349 @ SV1958 ) )
| ~ ( c_in @ ( c_Pair @ SV599 @ SY6039 @ SV1631 @ SV2349 ) @ SV2171 @ ( tc_prod @ SV1631 @ SV2349 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5728]) ).
thf(5911,plain,
! [SV600: $i,SV1959: $i,SV1632: $i,SV1200: $i,SV2292: $i] :
( ( ( c_in @ ( c_Pair @ SV2292 @ SV1200 @ SV1632 @ SV1632 ) @ SV1959 @ ( tc_prod @ SV1632 @ SV1632 ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV600 @ SV2292 @ SV1632 @ SV1632 ) @ SV1959 @ ( tc_prod @ SV1632 @ SV1632 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV600 @ SV1200 @ SV1632 @ SV1632 ) @ ( c_Transitive__Closure_Otrancl @ SV1959 @ SV1632 ) @ ( tc_prod @ SV1632 @ SV1632 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5729]) ).
thf(5912,plain,
! [SV601: $i,SV1960: $i,SV1633: $i,SV1201: $i,SV2293: $i] :
( ( ( c_in @ ( c_Pair @ SV2293 @ SV1201 @ SV1633 @ SV1633 ) @ ( c_Transitive__Closure_Otrancl @ SV1960 @ SV1633 ) @ ( tc_prod @ SV1633 @ SV1633 ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV601 @ SV2293 @ SV1633 @ SV1633 ) @ ( c_Transitive__Closure_Otrancl @ SV1960 @ SV1633 ) @ ( tc_prod @ SV1633 @ SV1633 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV601 @ SV1201 @ SV1633 @ SV1633 ) @ ( c_Transitive__Closure_Otrancl @ SV1960 @ SV1633 ) @ ( tc_prod @ SV1633 @ SV1633 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5730]) ).
thf(5913,plain,
! [SV1634: $i,SV1961: $i,SV1204: $i,SV604: $i] :
( ( ( SV604 = SV1204 )
= $true )
| ( ( SV604 = SV1961 )
= $true )
| ( ( c_in @ ( c_Pair @ SV604 @ SV1204 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1634 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV604 @ SV1204 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omktop @ SV1634 ) @ SV1961 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5731]) ).
thf(5914,plain,
! [SV1635: $i,SV605: $i,SV1962: $i,SV1205: $i] :
( ( ( SV1205 = SV1962 )
= $true )
| ( ( SV605 = SV1962 )
= $true )
| ( ( c_in @ ( c_Pair @ SV605 @ SV1205 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1635 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV605 @ SV1205 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omktop @ SV1635 ) @ SV1962 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5732]) ).
thf(5915,plain,
! [SV1639: $i,SV1963: $i,SV1212: $i,SV612: $i] :
( ( ( SV612 = SV1212 )
= $true )
| ( ( SV1212 = SV1963 )
= $true )
| ( ( c_in @ ( c_Pair @ SV612 @ SV1212 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1639 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV612 @ SV1212 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omkbot @ SV1639 ) @ SV1963 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5734]) ).
thf(5916,plain,
! [SV1640: $i,SV1213: $i,SV1964: $i,SV613: $i] :
( ( ( SV613 = SV1964 )
= $true )
| ( ( SV1213 = SV1964 )
= $true )
| ( ( c_in @ ( c_Pair @ SV613 @ SV1213 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ SV1640 @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV613 @ SV1213 @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( hAPP @ c_Arrow__Order__Mirabelle_Omkbot @ SV1640 ) @ SV1964 ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5735]) ).
thf(5917,plain,
! [SV1642: $i,SV2176: $i,SV1965: $i,SV617: $i,SV2294: $i,SV1217: $i] :
( ( ( ~ ( c_in @ SV1217 @ ( hAPP @ SV2294 @ SV617 ) @ SV1965 ) )
= $true )
| ( ( ~ ( c_in @ SV617 @ SV2176 @ SV1642 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV617 @ SV1217 @ SV1642 @ SV1965 ) @ ( c_Product__Type_OSigma @ SV2176 @ SV2294 @ SV1642 @ SV1965 ) @ ( tc_prod @ SV1642 @ SV1965 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5737]) ).
thf(5918,plain,
! [SV1643: $i,SV2177: $i,SV1966: $i,SV618: $i,SV2295: $i,SV1218: $i] :
( ( ( ~ ( c_in @ SV1218 @ ( hAPP @ SV2295 @ SV618 ) @ SV1966 ) )
= $true )
| ( ( ~ ( c_in @ SV618 @ SV2177 @ SV1643 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV618 @ SV1218 @ SV1643 @ SV1966 ) @ ( c_Product__Type_OSigma @ SV2177 @ SV2295 @ SV1643 @ SV1966 ) @ ( tc_prod @ SV1643 @ SV1966 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5738]) ).
thf(5919,plain,
! [SV619: $i,SV1644: $i,SV1219: $i,SV2178: $i] :
( ( ( c_in @ SV2178 @ ( c_Wellfounded_Oacc @ SV1219 @ SV1644 ) @ SV1644 )
= $false )
| ( ( c_in @ ( c_Pair @ SV619 @ SV2178 @ SV1644 @ SV1644 ) @ SV1219 @ ( tc_prod @ SV1644 @ SV1644 ) )
= $false )
| ( ( c_in @ SV619 @ ( c_Wellfounded_Oacc @ SV1219 @ SV1644 ) @ SV1644 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5739]) ).
thf(5920,plain,
! [SV620: $i,SV1645: $i,SV1220: $i,SV2179: $i] :
( ( ( c_in @ SV2179 @ ( c_Wellfounded_Oacc @ SV1220 @ SV1645 ) @ SV1645 )
= $false )
| ( ( c_in @ ( c_Pair @ SV620 @ SV2179 @ SV1645 @ SV1645 ) @ SV1220 @ ( tc_prod @ SV1645 @ SV1645 ) )
= $false )
| ( ( c_in @ SV620 @ ( c_Wellfounded_Oacc @ SV1220 @ SV1645 ) @ SV1645 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5740]) ).
thf(5921,plain,
! [SV1646: $i,SV1221: $i,SV2180: $i,SV1967: $i,SV621: $i,SV2350: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV2350 @ SV621 @ SV1967 @ SV2180 ) @ SV1221 @ ( tc_prod @ SV1967 @ SV2180 ) ) )
= $true )
| ( ( ~ ( c_in @ SV2350 @ SV1646 @ SV1967 ) )
= $true )
| ( ( c_in @ SV621 @ ( c_Relation_OImage @ SV1221 @ SV1646 @ SV1967 @ SV2180 ) @ SV2180 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5741]) ).
thf(5922,plain,
! [SV1647: $i,SV1222: $i,SV2181: $i,SV1968: $i,SV622: $i,SV2351: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV2351 @ SV622 @ SV1968 @ SV2181 ) @ SV1222 @ ( tc_prod @ SV1968 @ SV2181 ) ) )
= $true )
| ( ( ~ ( c_in @ SV2351 @ SV1647 @ SV1968 ) )
= $true )
| ( ( c_in @ SV622 @ ( c_Relation_OImage @ SV1222 @ SV1647 @ SV1968 @ SV2181 ) @ SV2181 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5742]) ).
thf(5923,plain,
! [SV1225: $i,SV2296: $i,SV1650: $i,SV625: $i,SV2183: $i] :
( ( ( c_in @ ( c_Pair @ SV2183 @ SV625 @ SV1650 @ SV1650 ) @ SV2296 @ ( tc_prod @ SV1650 @ SV1650 ) )
= $false )
| ( ( ~ ( c_Equiv__Relations_Oequiv @ SV1225 @ SV2296 @ SV1650 ) )
= $true )
| ( ( c_in @ SV625 @ SV1225 @ SV1650 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5743]) ).
thf(5924,plain,
! [SV1226: $i,SV2297: $i,SV1651: $i,SV2184: $i,SV626: $i] :
( ( ( c_in @ ( c_Pair @ SV626 @ SV2184 @ SV1651 @ SV1651 ) @ SV2297 @ ( tc_prod @ SV1651 @ SV1651 ) )
= $false )
| ( ( ~ ( c_Equiv__Relations_Oequiv @ SV1226 @ SV2297 @ SV1651 ) )
= $true )
| ( ( c_in @ SV626 @ SV1226 @ SV1651 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5744]) ).
thf(5925,plain,
! [SV1231: $i,SV2352: $i,SV1973: $i,SV2302: $i,SV631: $i,SV1656: $i] :
( ( ( c_in @ ( c_Pair @ SV1656 @ SV631 @ SV2302 @ SV1973 ) @ ( c_Product__Type_OSigma @ SV2352 @ SV1231 @ SV2302 @ SV1973 ) @ ( tc_prod @ SV2302 @ SV1973 ) )
= $false )
| ( ( c_in @ SV631 @ ( hAPP @ SV1231 @ SV1656 ) @ SV1973 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5749]) ).
thf(5926,plain,
! [SV2353: $i,SV1232: $i,SV2303: $i,SV1657: $i,SV1974: $i,SV632: $i] :
( ( ( c_in @ ( c_Pair @ SV632 @ SV1974 @ SV1657 @ SV2303 ) @ ( c_Product__Type_OSigma @ SV1232 @ SV2353 @ SV1657 @ SV2303 ) @ ( tc_prod @ SV1657 @ SV2303 ) )
= $false )
| ( ( c_in @ SV632 @ SV1232 @ SV1657 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5750]) ).
thf(5927,plain,
! [SV1975: $i,SV1233: $i,SV1658: $i,SV2365: $i,SV633: $i] :
( ( ( ~ ( c_in @ SV633 @ SV2365 @ SV1658 )
| ~ ( c_in @ SV1233 @ SV2365 @ SV1658 )
| ~ ( c_Relation_Ototal__on @ SV2365 @ SV1975 @ SV1658 ) )
= $true )
| ( ( SV1233 = SV633 )
= $true )
| ( ( c_in @ ( c_Pair @ SV1233 @ SV633 @ SV1658 @ SV1658 ) @ SV1975 @ ( tc_prod @ SV1658 @ SV1658 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV633 @ SV1233 @ SV1658 @ SV1658 ) @ SV1975 @ ( tc_prod @ SV1658 @ SV1658 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5751]) ).
thf(5928,plain,
! [SV634: $i,SV1234: $i,SV1659: $i,SV2185: $i] :
( ( ( c_Relation_Orefl__on @ SV2185 @ SV1659 @ SV1234 )
= $false )
| ( ( c_in @ SV634 @ SV2185 @ SV1234 )
= $false )
| ( ( c_in @ ( c_Pair @ SV634 @ SV634 @ SV1234 @ SV1234 ) @ SV1659 @ ( tc_prod @ SV1234 @ SV1234 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5752]) ).
thf(5929,plain,
! [SV1235: $i,SV2304: $i,SV1660: $i,SV635: $i,SV2186: $i] :
( ( ( c_in @ ( c_Pair @ SV2186 @ SV635 @ SV1660 @ SV1660 ) @ SV2304 @ ( tc_prod @ SV1660 @ SV1660 ) )
= $false )
| ( ( ~ ( c_Relation_Orefl__on @ SV1235 @ SV2304 @ SV1660 ) )
= $true )
| ( ( c_in @ SV635 @ SV1235 @ SV1660 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5753]) ).
thf(5930,plain,
! [SV1236: $i,SV2305: $i,SV1661: $i,SV2187: $i,SV636: $i] :
( ( ( c_in @ ( c_Pair @ SV636 @ SV2187 @ SV1661 @ SV1661 ) @ SV2305 @ ( tc_prod @ SV1661 @ SV1661 ) )
= $false )
| ( ( ~ ( c_Relation_Orefl__on @ SV1236 @ SV2305 @ SV1661 ) )
= $true )
| ( ( c_in @ SV636 @ SV1236 @ SV1661 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5754]) ).
thf(5931,plain,
! [SV637: $i,SV1237: $i,SV1662: $i,SV2188: $i] :
( ( ( c_Relation_Orefl__on @ SV2188 @ SV1662 @ SV1237 )
= $false )
| ( ( c_in @ SV637 @ SV2188 @ SV1237 )
= $false )
| ( ( c_in @ ( c_Pair @ SV637 @ SV637 @ SV1237 @ SV1237 ) @ SV1662 @ ( tc_prod @ SV1237 @ SV1237 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5755]) ).
thf(5932,plain,
! [SV2306: $i,SV2189: $i,SV1976: $i,SV1663: $i,SV1238: $i,SV638: $i] :
( ( ( ( c_Pair @ SV638 @ SV1238 @ SV1663 @ SV1976 )
= ( c_Pair @ SV2189 @ SV2306 @ SV1663 @ SV1976 ) )
= $false )
| ( ( SV1238 = SV2306 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5756]) ).
thf(5933,plain,
! [SV2354: $i,SV2190: $i,SV1977: $i,SV1664: $i,SV1239: $i,SV639: $i] :
( ( ( ( c_Pair @ SV639 @ SV1239 @ SV1664 @ SV1977 )
= ( c_Pair @ SV2190 @ SV2354 @ SV1664 @ SV1977 ) )
= $false )
| ( ( SV639 = SV2190 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5757]) ).
thf(5934,plain,
! [SV1680: $i,SV1983: $i,SV21: $i,SV1269: $i,SV672: $i,SV2366: $i] :
( ( ( ~ ( c_in @ SV2366 @ SV672 @ SV1269 ) )
= $true )
| ( ( c_lessequals @ SV21 @ SV1983 @ ( tc_fun @ SV1680 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( c_Product__Type_OSigma @ SV21 @ ( c_COMBK @ SV672 @ ( tc_fun @ SV1269 @ tc_bool ) @ SV1680 ) @ SV1680 @ SV1269 ) @ ( c_Product__Type_OSigma @ SV1983 @ ( c_COMBK @ SV672 @ ( tc_fun @ SV1269 @ tc_bool ) @ SV1680 ) @ SV1680 @ SV1269 ) @ ( tc_fun @ ( tc_prod @ SV1680 @ SV1269 ) @ tc_bool ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5761]) ).
thf(5935,plain,
! [SV673: $i,SV1270: $i,SV22: $i,SV2191: $i,SV1681: $i,SV2367: $i] :
( ( ( ~ ( c_in @ SV2367 @ SV1681 @ SV2191 ) )
= $true )
| ( ( c_lessequals @ ( c_Product__Type_OSigma @ SV22 @ ( c_COMBK @ SV1681 @ ( tc_fun @ SV2191 @ tc_bool ) @ SV1270 ) @ SV1270 @ SV2191 ) @ ( c_Product__Type_OSigma @ SV673 @ ( c_COMBK @ SV1681 @ ( tc_fun @ SV2191 @ tc_bool ) @ SV1270 ) @ SV1270 @ SV2191 ) @ ( tc_fun @ ( tc_prod @ SV1270 @ SV2191 ) @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV22 @ SV673 @ ( tc_fun @ SV1270 @ tc_bool ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5762]) ).
thf(5936,plain,
! [SV1282: $i,SV2195: $i,SV40: $i,SV1987: $i,SV1692: $i,SV2307: $i,SV690: $i] :
( ( ( ~ ( c_lessequals @ SV690 @ SV2307 @ ( tc_fun @ ( tc_prod @ SV1692 @ SV1987 ) @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV40 @ SV2195 @ ( tc_fun @ ( tc_prod @ SV1282 @ SV1692 ) @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( c_Relation_Orel__comp @ SV40 @ SV690 @ SV1282 @ SV1692 @ SV1987 ) @ ( c_Relation_Orel__comp @ SV2195 @ SV2307 @ SV1282 @ SV1692 @ SV1987 ) @ ( tc_fun @ ( tc_prod @ SV1282 @ SV1987 ) @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5766]) ).
thf(5937,plain,
! [SV718: $i,SV71: $i,SV2201: $i,SV2002: $i] :
( ( ( c_lessequals @ SV2002 @ SV2201 @ SV71 )
= $false )
| ( ( ~ ( c_lessequals @ SV718 @ SV2201 @ SV71 ) )
= $true )
| ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV718 @ SV2002 @ SV71 ) @ SV2201 @ SV71 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV71 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5773]) ).
thf(5938,plain,
! [SV719: $i,SV74: $i,SV2202: $i,SV2005: $i] :
( ( ( c_lessequals @ SV2005 @ SV2202 @ SV74 )
= $false )
| ( ( ~ ( c_lessequals @ SV719 @ SV2202 @ SV74 ) )
= $true )
| ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV719 @ SV2005 @ SV74 ) @ SV2202 @ SV74 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV74 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5774]) ).
thf(5939,plain,
! [SV720: $i,SV75: $i,SV2203: $i,SV2006: $i] :
( ( ( c_lessequals @ SV2006 @ SV2203 @ SV75 )
= $false )
| ( ( ~ ( c_lessequals @ SV720 @ SV2203 @ SV75 ) )
= $true )
| ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV720 @ SV2006 @ SV75 ) @ SV2203 @ SV75 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV75 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5775]) ).
thf(5940,plain,
! [SV1713: $i,SV724: $i,SV1304: $i,SV83: $i,SV2355: $i] :
( ( ( c_Equiv__Relations_Oequiv @ SV2355 @ SV83 @ SV1304 )
= $false )
| ( ( c_in @ ( c_Pair @ SV724 @ SV1713 @ SV1304 @ SV1304 ) @ SV83 @ ( tc_prod @ SV1304 @ SV1304 ) )
= $false )
| ( ( c_lessequals @ ( c_Relation_OImage @ SV83 @ ( c_Set_Oinsert @ SV724 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1304 @ tc_bool ) ) @ SV1304 ) @ SV1304 @ SV1304 ) @ ( c_Relation_OImage @ SV83 @ ( c_Set_Oinsert @ SV1713 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1304 @ tc_bool ) ) @ SV1304 ) @ SV1304 @ SV1304 ) @ ( tc_fun @ SV1304 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5776]) ).
thf(5941,plain,
! [SV1317: $i,SV2205: $i,SV103: $i,SV1724: $i,SV2015: $i,SV2310: $i,SV2368: $i,SV742: $i] :
( ( ( ~ ( c_lessequals @ SV742 @ ( c_Product__Type_OSigma @ SV2368 @ ( c_COMBK @ SV2310 @ ( tc_fun @ SV2015 @ tc_bool ) @ SV1724 ) @ SV1724 @ SV2015 ) @ ( tc_fun @ ( tc_prod @ SV1724 @ SV2015 ) @ tc_bool ) )
| ~ ( c_lessequals @ SV103 @ ( c_Product__Type_OSigma @ SV2205 @ ( c_COMBK @ SV2368 @ ( tc_fun @ SV1724 @ tc_bool ) @ SV1317 ) @ SV1317 @ SV1724 ) @ ( tc_fun @ ( tc_prod @ SV1317 @ SV1724 ) @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( c_Relation_Orel__comp @ SV103 @ SV742 @ SV1317 @ SV1724 @ SV2015 ) @ ( c_Product__Type_OSigma @ SV2205 @ ( c_COMBK @ SV2310 @ ( tc_fun @ SV2015 @ tc_bool ) @ SV1317 ) @ SV1317 @ SV2015 ) @ ( tc_fun @ ( tc_prod @ SV1317 @ SV2015 ) @ tc_bool ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5777]) ).
thf(5942,plain,
! [SV743: $i,SV1318: $i,SV104: $i] :
( ( ( c_Wellfounded_Owf @ SV104 @ SV1318 )
= $false )
| ( ( c_Wellfounded_Owf @ SV743 @ SV1318 )
= $false )
| ( ( c_lessequals @ ( c_Relation_Orel__comp @ SV104 @ SV743 @ SV1318 @ SV1318 @ SV1318 ) @ SV104 @ ( tc_fun @ ( tc_prod @ SV1318 @ SV1318 ) @ tc_bool ) )
= $false )
| ( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV104 @ SV743 @ ( tc_fun @ ( tc_prod @ SV1318 @ SV1318 ) @ tc_bool ) ) @ SV1318 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5778]) ).
thf(5943,plain,
! [SV1321: $i,SV747: $i,SV108: $i] :
( ( ( c_Wellfounded_Owf @ SV108 @ SV747 )
= $false )
| ( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV108 @ SV1321 @ ( tc_fun @ ( tc_prod @ SV747 @ SV747 ) @ tc_bool ) ) @ SV747 )
= $true )
| ( ( c_Wellfounded_Owf @ SV1321 @ SV747 )
= $false )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_ODomain @ SV108 @ SV747 @ SV747 ) @ ( c_Relation_ORange @ SV1321 @ SV747 @ SV747 ) @ ( tc_fun @ SV747 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV747 @ tc_bool ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5779]) ).
thf(5944,plain,
! [SV2017: $i,SV749: $i,SV1323: $i,SV1729: $i,SV110: $i] :
( ( ( c_Relation_Orefl__on @ SV110 @ SV1729 @ SV1323 )
= $false )
| ( ( c_Relation_Orefl__on @ SV749 @ SV2017 @ SV1323 )
= $false )
| ( ( c_Relation_Orefl__on @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV110 @ SV749 @ ( tc_fun @ SV1323 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1729 @ SV2017 @ ( tc_fun @ ( tc_prod @ SV1323 @ SV1323 ) @ tc_bool ) ) @ SV1323 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5780]) ).
thf(5945,plain,
! [SV765: $i,SV2023: $i,SV1330: $i,SV1739: $i,SV128: $i] :
( ( ( c_lessequals @ SV128 @ SV1739 @ ( tc_fun @ SV1330 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV2023 @ SV765 @ ( tc_fun @ SV1330 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV128 @ SV765 @ ( tc_fun @ SV1330 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV1739 @ SV2023 @ ( tc_fun @ SV1330 @ tc_bool ) ) @ ( tc_fun @ SV1330 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5781]) ).
thf(5946,plain,
! [SV129: $i,SV1331: $i,SV766: $i,SV2212: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV2212 @ SV766 @ ( tc_fun @ SV1331 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1331 @ tc_bool ) ) )
= $false )
| ( ( c_in @ SV129 @ SV2212 @ SV1331 )
= $false )
| ( ( c_in @ SV129 @ SV766 @ SV1331 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5782]) ).
thf(5947,plain,
! [SV141: $i,SV2027: $i,SV1745: $i] :
( ( ( c_lessequals @ SV1745 @ SV2027 @ SV141 )
= $false )
| ( ( c_lessequals @ SV2027 @ SV1745 @ SV141 )
= $false )
| ( ( SV1745 = SV2027 )
= $true )
| ( ( class_Orderings_Oorder @ SV141 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5786]) ).
thf(5948,plain,
! [SV142: $i,SV2028: $i,SV1746: $i] :
( ( ( c_lessequals @ SV1746 @ SV2028 @ SV142 )
= $false )
| ( ( c_lessequals @ SV2028 @ SV1746 @ SV142 )
= $false )
| ( ( SV1746 = SV2028 )
= $true )
| ( ( class_Orderings_Oorder @ SV142 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5787]) ).
thf(5949,plain,
! [SV144: $i,SV1748: $i,SV2030: $i] :
( ( ( c_lessequals @ SV2030 @ SV1748 @ SV144 )
= $false )
| ( ( c_lessequals @ SV1748 @ SV2030 @ SV144 )
= $false )
| ( ( SV1748 = SV2030 )
= $true )
| ( ( class_Orderings_Oorder @ SV144 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5788]) ).
thf(5950,plain,
! [SV2035: $i,SV782: $i,SV1341: $i,SV1753: $i,SV153: $i] :
( ( ( c_Relation_Orefl__on @ SV153 @ SV1753 @ SV1341 )
= $false )
| ( ( c_Relation_Orefl__on @ SV782 @ SV2035 @ SV1341 )
= $false )
| ( ( c_Relation_Orefl__on @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV153 @ SV782 @ ( tc_fun @ SV1341 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1753 @ SV2035 @ ( tc_fun @ ( tc_prod @ SV1341 @ SV1341 ) @ tc_bool ) ) @ SV1341 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5789]) ).
thf(5951,plain,
! [SV2040: $i,SV796: $i,SV1352: $i,SV1761: $i,SV170: $i] :
( ( ( c_lessequals @ SV170 @ SV1761 @ ( tc_fun @ SV1352 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV796 @ SV2040 @ ( tc_fun @ SV1352 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV170 @ SV796 @ ( tc_fun @ SV1352 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1761 @ SV2040 @ ( tc_fun @ SV1352 @ tc_bool ) ) @ ( tc_fun @ SV1352 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5794]) ).
thf(5952,plain,
! [SV2043: $i,SV174: $i,SV2217: $i,SV798: $i] :
( ( ( c_lessequals @ SV798 @ SV2217 @ SV174 )
= $false )
| ( ( ~ ( c_lessequals @ SV798 @ SV2043 @ SV174 ) )
= $true )
| ( ( c_lessequals @ SV798 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2043 @ SV2217 @ SV174 ) @ SV174 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV174 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5795]) ).
thf(5953,plain,
! [SV2044: $i,SV175: $i,SV2218: $i,SV799: $i] :
( ( ( c_lessequals @ SV799 @ SV2218 @ SV175 )
= $false )
| ( ( ~ ( c_lessequals @ SV799 @ SV2044 @ SV175 ) )
= $true )
| ( ( c_lessequals @ SV799 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2044 @ SV2218 @ SV175 ) @ SV175 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV175 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5796]) ).
thf(5954,plain,
! [SV2045: $i,SV176: $i,SV2219: $i,SV800: $i] :
( ( ( c_lessequals @ SV800 @ SV2219 @ SV176 )
= $false )
| ( ( ~ ( c_lessequals @ SV800 @ SV2045 @ SV176 ) )
= $true )
| ( ( c_lessequals @ SV800 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2045 @ SV2219 @ SV176 ) @ SV176 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV176 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5797]) ).
thf(5955,plain,
! [SV1405: $i,SV249: $i,SV2356: $i,SV2227: $i,SV863: $i] :
( ( ( c_lessequals @ SV863 @ SV2227 @ ( tc_fun @ SV2356 @ SV249 ) )
= $false )
| ( ( c_lessequals @ ( hAPP @ SV863 @ SV1405 ) @ ( hAPP @ SV2227 @ SV1405 ) @ SV249 )
= $true )
| ( ( class_HOL_Oord @ SV249 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5809]) ).
thf(5956,plain,
! [SV1433: $i,SV896: $i,SV1813: $i,SV282: $i,SV2085: $i,SV2357: $i] :
( ( ( hBOOL @ ( hAPP @ SV2357 @ SV2085 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV282 @ SV1813 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV282 @ ( hAPP @ ( c_fst @ SV896 @ SV1433 ) @ ( c_Pair @ SV1813 @ SV2085 @ SV896 @ SV1433 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5817]) ).
thf(5957,plain,
! [SV1434: $i,SV897: $i,SV2086: $i,SV283: $i,SV1814: $i,SV2369: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV2369 @ SV1814 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV283 @ SV2086 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV283 @ ( hAPP @ ( c_snd @ SV897 @ SV1434 ) @ ( c_Pair @ SV1814 @ SV2086 @ SV897 @ SV1434 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5818]) ).
thf(5958,plain,
! [SV2100: $i,SV309: $i,SV2320: $i,SV920: $i] :
( ( ( c_lessequals @ SV920 @ SV2320 @ SV309 )
= $false )
| ( ( ~ ( c_lessequals @ SV2320 @ SV2100 @ SV309 ) )
= $true )
| ( ( c_lessequals @ SV920 @ SV2100 @ SV309 )
= $true )
| ( ( class_Orderings_Oorder @ SV309 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5826]) ).
thf(5959,plain,
! [SV921: $i,SV310: $i,SV2101: $i,SV2321: $i] :
( ( ( c_lessequals @ SV2321 @ SV2101 @ SV310 )
= $false )
| ( ( ~ ( c_lessequals @ SV921 @ SV2321 @ SV310 ) )
= $true )
| ( ( c_lessequals @ SV921 @ SV2101 @ SV310 )
= $true )
| ( ( class_Orderings_Opreorder @ SV310 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5827]) ).
thf(5960,plain,
! [SV2105: $i,SV932: $i,SV1450: $i,SV1831: $i,SV323: $i] :
( ( ( c_lessequals @ SV323 @ SV1831 @ ( tc_fun @ SV1450 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV932 @ SV2105 @ ( tc_fun @ SV1450 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV323 @ SV932 @ ( tc_fun @ SV1450 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1831 @ SV2105 @ ( tc_fun @ SV1450 @ tc_bool ) ) @ ( tc_fun @ SV1450 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5832]) ).
thf(5961,plain,
! [SV2323: $i,SV2233: $i,SV333: $i,SV1459: $i,SV942: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV942 @ SV1459 @ SV333 )
= ( c_HOL_Ominus__class_Ominus @ SV2233 @ SV2323 @ SV333 ) )
= $false )
| ( ( ( c_lessequals @ SV2323 @ SV2233 @ SV333 )
| ~ ( c_lessequals @ SV1459 @ SV942 @ SV333 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV333 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5835]) ).
thf(5962,plain,
! [SV2324: $i,SV2234: $i,SV334: $i,SV1460: $i,SV943: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV943 @ SV1460 @ SV334 )
= ( c_HOL_Ominus__class_Ominus @ SV2234 @ SV2324 @ SV334 ) )
= $false )
| ( ( ( c_lessequals @ SV1460 @ SV943 @ SV334 )
| ~ ( c_lessequals @ SV2324 @ SV2234 @ SV334 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV334 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5836]) ).
thf(5963,plain,
! [SV1842: $i,SV2109: $i,SV343: $i,SV1467: $i,SV2236: $i,SV950: $i] :
( ( ( c_lessequals @ SV950 @ SV2236 @ ( tc_fun @ SV1467 @ tc_bool ) )
= $false )
| ( ( ~ ( c_lessequals @ SV343 @ SV2109 @ ( tc_fun @ ( tc_prod @ SV1467 @ SV1842 ) @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( c_Relation_OImage @ SV343 @ SV950 @ SV1467 @ SV1842 ) @ ( c_Relation_OImage @ SV2109 @ SV2236 @ SV1467 @ SV1842 ) @ ( tc_fun @ SV1842 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5837]) ).
thf(5964,plain,
! [SV2111: $i,SV2237: $i,SV955: $i,SV1471: $i,SV349: $i] :
( ( ( hBOOL @ ( hAPP @ SV349 @ SV1471 ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV955 @ SV1471 @ SV2237 @ SV2237 ) @ ( c_Transitive__Closure_Ortrancl @ SV2111 @ SV2237 ) @ ( tc_prod @ SV2237 @ SV2237 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1 @ SV349 @ SV1471 @ SV2111 @ SV2237 ) @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 @ SV349 @ SV1471 @ SV2111 @ SV2237 ) @ SV2237 @ SV2237 ) @ SV2111 @ ( tc_prod @ SV2237 @ SV2237 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV349 @ SV955 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5838]) ).
thf(5965,plain,
! [SV2112: $i,SV2238: $i,SV956: $i,SV1472: $i,SV350: $i] :
( ( ( hBOOL @ ( hAPP @ SV350 @ SV1472 ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV1472 @ SV956 @ SV2238 @ SV2238 ) @ ( c_Transitive__Closure_Ortrancl @ SV2112 @ SV2238 ) @ ( tc_prod @ SV2238 @ SV2238 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 @ SV350 @ SV1472 @ SV2112 @ SV2238 ) @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2 @ SV350 @ SV1472 @ SV2112 @ SV2238 ) @ SV2238 @ SV2238 ) @ SV2112 @ ( tc_prod @ SV2238 @ SV2238 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV350 @ SV956 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5839]) ).
thf(5966,plain,
! [SV959: $i,SV353: $i,SV2326: $i,SV1475: $i,SV1847: $i,SV2370: $i] :
( ( ( ~ ( c_Equiv__Relations_Oequiv @ SV2370 @ SV1847 @ SV1475 ) )
= $true )
| ( ( c_in @ SV2326 @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_OImage @ SV1847 @ ( c_Set_Oinsert @ SV353 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1475 @ tc_bool ) ) @ SV1475 ) @ SV1475 @ SV1475 ) @ ( c_Relation_OImage @ SV1847 @ ( c_Set_Oinsert @ SV959 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1475 @ tc_bool ) ) @ SV1475 ) @ SV1475 @ SV1475 ) @ ( tc_fun @ SV1475 @ tc_bool ) ) @ SV1475 )
= $false )
| ( ( c_in @ ( c_Pair @ SV353 @ SV959 @ SV1475 @ SV1475 ) @ SV1847 @ ( tc_prod @ SV1475 @ SV1475 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5841]) ).
thf(5967,plain,
! [SV2239: $i,SV354: $i,SV1476: $i,SV960: $i,SV1848: $i] :
( ( ( ~ ( c_lessequals @ ( c_Relation_OImage @ SV1848 @ ( c_Set_Oinsert @ SV960 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1476 @ tc_bool ) ) @ SV1476 ) @ SV1476 @ SV1476 ) @ ( c_Relation_OImage @ SV1848 @ ( c_Set_Oinsert @ SV354 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1476 @ tc_bool ) ) @ SV1476 ) @ SV1476 @ SV1476 ) @ ( tc_fun @ SV1476 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_Equiv__Relations_Oequiv @ SV2239 @ SV1848 @ SV1476 ) )
= $true )
| ( ( c_in @ SV960 @ SV2239 @ SV1476 )
= $false )
| ( ( c_in @ ( c_Pair @ SV354 @ SV960 @ SV1476 @ SV1476 ) @ SV1848 @ ( tc_prod @ SV1476 @ SV1476 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5842]) ).
thf(5968,plain,
! [SV1478: $i,SV1850: $i,SV356: $i,SV2327: $i,SV2241: $i,SV962: $i] :
( ( ( c_in @ SV962 @ SV2241 @ SV2327 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_Set_Oimage @ SV356 @ SV2241 @ SV2327 @ SV1850 ) @ SV1478 @ ( tc_fun @ SV1850 @ tc_bool ) ) )
= $true )
| ( ( c_in @ ( hAPP @ SV356 @ SV962 ) @ SV1478 @ SV1850 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5843]) ).
thf(5969,plain,
! [SV1853: $i,SV2116: $i,SV359: $i,SV1481: $i,SV965: $i,SV2371: $i] :
( ( ( ~ ( c_in @ SV2371 @ SV965 @ SV1481 ) )
= $true )
| ( ( SV359 = SV2116 )
= $true )
| ( ( ( c_Product__Type_OSigma @ SV359 @ ( c_COMBK @ SV965 @ ( tc_fun @ SV1481 @ tc_bool ) @ SV1853 ) @ SV1853 @ SV1481 )
= ( c_Product__Type_OSigma @ SV2116 @ ( c_COMBK @ SV965 @ ( tc_fun @ SV1481 @ tc_bool ) @ SV1853 ) @ SV1853 @ SV1481 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5844]) ).
thf(5970,plain,
! [SV1857: $i,SV970: $i,SV1485: $i,SV364: $i,SV2358: $i] :
( ( ( c_Equiv__Relations_Oequiv @ SV2358 @ SV364 @ SV1485 )
= $false )
| ( ( c_in @ ( c_Pair @ SV970 @ SV1857 @ SV1485 @ SV1485 ) @ SV364 @ ( tc_prod @ SV1485 @ SV1485 ) )
= $false )
| ( ( ( c_Relation_OImage @ SV364 @ ( c_Set_Oinsert @ SV970 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1485 @ tc_bool ) ) @ SV1485 ) @ SV1485 @ SV1485 )
= ( c_Relation_OImage @ SV364 @ ( c_Set_Oinsert @ SV1857 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1485 @ tc_bool ) ) @ SV1485 ) @ SV1485 @ SV1485 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5846]) ).
thf(5971,plain,
! [SV1858: $i,SV971: $i,SV1486: $i,SV365: $i,SV2359: $i] :
( ( ( c_Equiv__Relations_Oequiv @ SV2359 @ SV365 @ SV1486 )
= $false )
| ( ( c_in @ ( c_Pair @ SV971 @ SV1858 @ SV1486 @ SV1486 ) @ SV365 @ ( tc_prod @ SV1486 @ SV1486 ) )
= $false )
| ( ( ( c_Relation_OImage @ SV365 @ ( c_Set_Oinsert @ SV971 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1486 @ tc_bool ) ) @ SV1486 ) @ SV1486 @ SV1486 )
= ( c_Relation_OImage @ SV365 @ ( c_Set_Oinsert @ SV1858 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1486 @ tc_bool ) ) @ SV1486 ) @ SV1486 @ SV1486 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5847]) ).
thf(5972,plain,
! [SV389: $i,SV1496: $i,SV994: $i] :
( ( ( c_Relation_Otrans @ SV994 @ SV1496 )
= $false )
| ( ( c_Relation_Oirrefl @ SV994 @ SV1496 )
= $false )
| ( ( c_Relation_Ototal__on @ SV389 @ SV994 @ SV1496 )
= $false )
| ( ( c_Order__Relation_Ostrict__linear__order__on @ SV389 @ SV994 @ SV1496 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5848]) ).
thf(5973,plain,
! [SV2328: $i,SV1866: $i,SV1501: $i,SV2243: $i,SV2121: $i,SV1010: $i,SV405: $i] :
( ( ( c_in @ ( c_Pair @ SV405 @ SV1010 @ SV2121 @ SV2243 ) @ ( c_Relation_Orel__comp @ SV1501 @ SV1866 @ SV2121 @ SV2328 @ SV2243 ) @ ( tc_prod @ SV2121 @ SV2243 ) )
= $false )
| ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 @ SV405 @ SV1010 @ SV1501 @ SV1866 @ SV2121 @ SV2243 @ SV2328 ) @ SV1010 @ SV2328 @ SV2243 ) @ SV1866 @ ( tc_prod @ SV2328 @ SV2243 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5849]) ).
thf(5974,plain,
! [SV2329: $i,SV1867: $i,SV1502: $i,SV2244: $i,SV2122: $i,SV1011: $i,SV406: $i] :
( ( ( c_in @ ( c_Pair @ SV406 @ SV1011 @ SV2122 @ SV2244 ) @ ( c_Relation_Orel__comp @ SV1502 @ SV1867 @ SV2122 @ SV2329 @ SV2244 ) @ ( tc_prod @ SV2122 @ SV2244 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV406 @ ( c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 @ SV406 @ SV1011 @ SV1502 @ SV1867 @ SV2122 @ SV2244 @ SV2329 ) @ SV2122 @ SV2329 ) @ SV1502 @ ( tc_prod @ SV2122 @ SV2329 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5850]) ).
thf(5975,plain,
! [SV1022: $i,SV2330: $i,SV2245: $i,SV417: $i,SV1513: $i] :
( ( ( c_in @ ( c_Pair @ SV1513 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1 @ SV417 @ SV2245 @ SV2330 ) @ SV2330 @ SV2330 ) @ SV2245 @ ( tc_prod @ SV2330 @ SV2330 ) )
= $false )
| ( ( ~ ( c_Wellfounded_Owf @ SV2245 @ SV2330 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV417 @ SV1513 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV417 @ SV1022 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5851]) ).
thf(5976,plain,
! [SV1023: $i,SV2331: $i,SV2246: $i,SV418: $i,SV1514: $i] :
( ( ( c_in @ ( c_Pair @ SV1514 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1 @ SV418 @ SV2246 @ SV2331 ) @ SV2331 @ SV2331 ) @ SV2246 @ ( tc_prod @ SV2331 @ SV2331 ) )
= $false )
| ( ( ~ ( c_Wellfounded_Owf @ SV2246 @ SV2331 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV418 @ SV1514 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV418 @ SV1023 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5852]) ).
thf(5977,plain,
! [SV1024: $i,SV2332: $i,SV2247: $i,SV419: $i,SV1515: $i] :
( ( ( c_in @ ( c_Pair @ SV1515 @ ( c_List_Osko__Recdef__Xtfl__wf__induct__1__1 @ SV419 @ SV2247 @ SV2332 ) @ SV2332 @ SV2332 ) @ SV2247 @ ( tc_prod @ SV2332 @ SV2332 ) )
= $false )
| ( ( ~ ( c_Wellfounded_Owf @ SV2247 @ SV2332 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV419 @ SV1515 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV419 @ SV1024 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5853]) ).
thf(5978,plain,
! [SV1025: $i,SV2333: $i,SV2248: $i,SV420: $i,SV1516: $i] :
( ( ( c_in @ ( c_Pair @ SV1516 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1 @ SV420 @ SV2248 @ SV2333 ) @ SV2333 @ SV2333 ) @ SV2248 @ ( tc_prod @ SV2333 @ SV2333 ) )
= $false )
| ( ( ~ ( c_Wellfounded_Owf @ SV2248 @ SV2333 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV420 @ SV1516 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV420 @ SV1025 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5854]) ).
thf(5979,plain,
! [SV2123: $i,SV2249: $i,SV1029: $i,SV1520: $i,SV424: $i] :
( ( ( hBOOL @ ( hAPP @ SV424 @ SV1520 ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV1029 @ SV1520 @ SV2249 @ SV2249 ) @ ( c_Transitive__Closure_Ortrancl @ SV2123 @ SV2249 ) @ ( tc_prod @ SV2249 @ SV2249 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV424 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 @ SV424 @ SV1520 @ SV2123 @ SV2249 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV424 @ SV1029 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5855]) ).
thf(5980,plain,
! [SV2124: $i,SV2250: $i,SV1030: $i,SV1521: $i,SV425: $i] :
( ( ( hBOOL @ ( hAPP @ SV425 @ SV1521 ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV1030 @ SV1521 @ SV2250 @ SV2250 ) @ ( c_Transitive__Closure_Ortrancl @ SV2124 @ SV2250 ) @ ( tc_prod @ SV2250 @ SV2250 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 @ SV425 @ SV1521 @ SV2124 @ SV2250 ) @ SV1521 @ SV2250 @ SV2250 ) @ ( c_Transitive__Closure_Ortrancl @ SV2124 @ SV2250 ) @ ( tc_prod @ SV2250 @ SV2250 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV425 @ SV1030 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5856]) ).
thf(5981,plain,
! [SV2125: $i,SV2251: $i,SV1031: $i,SV1522: $i,SV426: $i] :
( ( ( hBOOL @ ( hAPP @ SV426 @ SV1522 ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV1522 @ SV1031 @ SV2251 @ SV2251 ) @ ( c_Transitive__Closure_Ortrancl @ SV2125 @ SV2251 ) @ ( tc_prod @ SV2251 @ SV2251 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1522 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 @ SV426 @ SV1522 @ SV2125 @ SV2251 ) @ SV2251 @ SV2251 ) @ ( c_Transitive__Closure_Ortrancl @ SV2125 @ SV2251 ) @ ( tc_prod @ SV2251 @ SV2251 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV426 @ SV1031 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5857]) ).
thf(5982,plain,
! [SV2126: $i,SV2252: $i,SV1032: $i,SV1523: $i,SV427: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV427 @ SV1523 ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV1523 @ SV1032 @ SV2252 @ SV2252 ) @ ( c_Transitive__Closure_Ortrancl @ SV2126 @ SV2252 ) @ ( tc_prod @ SV2252 @ SV2252 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV427 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2 @ SV427 @ SV1523 @ SV2126 @ SV2252 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV427 @ SV1032 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5858]) ).
thf(5983,plain,
! [SV2127: $i,SV2253: $i,SV1034: $i,SV1525: $i,SV429: $i] :
( ( ( hBOOL @ ( hAPP @ SV429 @ SV1525 ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV1525 @ SV1034 @ SV2253 @ SV2253 ) @ ( c_Transitive__Closure_Ortrancl @ SV2127 @ SV2253 ) @ ( tc_prod @ SV2253 @ SV2253 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV429 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 @ SV429 @ SV1525 @ SV2127 @ SV2253 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV429 @ SV1034 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5859]) ).
thf(5984,plain,
! [SV2128: $i,SV2254: $i,SV1036: $i,SV1527: $i,SV431: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV431 @ SV1527 ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV1036 @ SV1527 @ SV2254 @ SV2254 ) @ ( c_Transitive__Closure_Ortrancl @ SV2128 @ SV2254 ) @ ( tc_prod @ SV2254 @ SV2254 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV431 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1 @ SV431 @ SV1527 @ SV2128 @ SV2254 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV431 @ SV1036 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5860]) ).
thf(5985,plain,
! [SV1042: $i,SV437: $i,SV1530: $i,SV2360: $i,SV1879: $i] :
( ( ( ~ ( c_in @ SV1879 @ SV2360 @ SV1530 ) )
= $true )
| ( ( ~ ( c_Equiv__Relations_Oequiv @ SV2360 @ SV437 @ SV1530 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1042 @ SV1879 @ SV1530 @ SV1530 ) @ SV437 @ ( tc_prod @ SV1530 @ SV1530 ) )
= $true )
| ( ( ( c_Relation_OImage @ SV437 @ ( c_Set_Oinsert @ SV1042 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1530 @ tc_bool ) ) @ SV1530 ) @ SV1530 @ SV1530 )
= ( c_Relation_OImage @ SV437 @ ( c_Set_Oinsert @ SV1879 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1530 @ tc_bool ) ) @ SV1530 ) @ SV1530 @ SV1530 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5861]) ).
thf(5986,plain,
! [SV1880: $i,SV1043: $i,SV1531: $i,SV438: $i,SV2334: $i] :
( ( ( c_Equiv__Relations_Oequiv @ SV2334 @ SV438 @ SV1531 )
= $false )
| ( ( ( c_in @ ( c_Pair @ SV1043 @ SV1880 @ SV1531 @ SV1531 ) @ SV438 @ ( tc_prod @ SV1531 @ SV1531 ) )
| ~ ( c_in @ SV1880 @ SV2334 @ SV1531 )
| ~ ( c_in @ SV1043 @ SV2334 @ SV1531 ) )
= $true )
| ( ( ( c_Relation_OImage @ SV438 @ ( c_Set_Oinsert @ SV1043 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1531 @ tc_bool ) ) @ SV1531 ) @ SV1531 @ SV1531 )
= ( c_Relation_OImage @ SV438 @ ( c_Set_Oinsert @ SV1880 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1531 @ tc_bool ) ) @ SV1531 ) @ SV1531 @ SV1531 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5862]) ).
thf(5987,plain,
! [SV439: $i,SV1044: $i,SV1532: $i,SV2361: $i,SV1881: $i] :
( ( ( ~ ( c_in @ SV1881 @ SV2361 @ SV1532 ) )
= $true )
| ( ( ~ ( c_in @ SV1044 @ SV2361 @ SV1532 )
| ~ ( c_Equiv__Relations_Oequiv @ SV2361 @ SV439 @ SV1532 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1044 @ SV1881 @ SV1532 @ SV1532 ) @ SV439 @ ( tc_prod @ SV1532 @ SV1532 ) )
= $false )
| ( ( ( c_Relation_OImage @ SV439 @ ( c_Set_Oinsert @ SV1044 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1532 @ tc_bool ) ) @ SV1532 ) @ SV1532 @ SV1532 )
= ( c_Relation_OImage @ SV439 @ ( c_Set_Oinsert @ SV1881 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1532 @ tc_bool ) ) @ SV1532 ) @ SV1532 @ SV1532 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5863]) ).
thf(5988,plain,
! [SV440: $i,SV1045: $i,SV1533: $i,SV2335: $i,SV1882: $i] :
( ( ( c_in @ SV1882 @ SV2335 @ SV1533 )
= $false )
| ( ( ~ ( c_in @ SV1045 @ SV2335 @ SV1533 )
| ~ ( c_Equiv__Relations_Oequiv @ SV2335 @ SV440 @ SV1533 )
| ( c_in @ ( c_Pair @ SV1045 @ SV1882 @ SV1533 @ SV1533 ) @ SV440 @ ( tc_prod @ SV1533 @ SV1533 ) ) )
= $true )
| ( ( ( c_Relation_OImage @ SV440 @ ( c_Set_Oinsert @ SV1045 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1533 @ tc_bool ) ) @ SV1533 ) @ SV1533 @ SV1533 )
= ( c_Relation_OImage @ SV440 @ ( c_Set_Oinsert @ SV1882 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1533 @ tc_bool ) ) @ SV1533 ) @ SV1533 @ SV1533 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5864]) ).
thf(5989,plain,
! [SV2131: $i,SV442: $i,SV1535: $i,SV1047: $i,SV2336: $i] :
( ( ( c_lessequals @ SV2336 @ ( c_Product__Type_OSigma @ SV1047 @ ( c_COMBK @ SV1047 @ ( tc_fun @ SV1535 @ tc_bool ) @ SV1535 ) @ SV1535 @ SV1535 ) @ ( tc_fun @ ( tc_prod @ SV1535 @ SV1535 ) @ tc_bool ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV442 @ SV2131 @ SV1535 @ SV1535 ) @ ( c_Transitive__Closure_Ortrancl @ SV2336 @ SV1535 ) @ ( tc_prod @ SV1535 @ SV1535 ) ) )
= $true )
| ( ( SV442 = SV2131 )
= $true )
| ( ( c_in @ SV442 @ SV1047 @ SV1535 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5865]) ).
thf(5990,plain,
! [SV1051: $i,SV1883: $i,SV1539: $i,SV2255: $i,SV446: $i] :
( ( ( c_in @ ( c_Pair @ SV446 @ SV2255 @ SV1539 @ SV1539 ) @ SV1883 @ ( tc_prod @ SV1539 @ SV1539 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV2255 @ SV1051 @ SV1539 @ SV1539 ) @ ( c_Transitive__Closure_Ortrancl @ SV1883 @ SV1539 ) @ ( tc_prod @ SV1539 @ SV1539 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV446 @ SV1051 @ SV1539 @ SV1539 ) @ ( c_Transitive__Closure_Otrancl @ SV1883 @ SV1539 ) @ ( tc_prod @ SV1539 @ SV1539 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5866]) ).
thf(5991,plain,
! [SV1052: $i,SV1884: $i,SV1540: $i,SV2256: $i,SV447: $i] :
( ( ( c_in @ ( c_Pair @ SV447 @ SV2256 @ SV1540 @ SV1540 ) @ ( c_Transitive__Closure_Ortrancl @ SV1884 @ SV1540 ) @ ( tc_prod @ SV1540 @ SV1540 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV2256 @ SV1052 @ SV1540 @ SV1540 ) @ SV1884 @ ( tc_prod @ SV1540 @ SV1540 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV447 @ SV1052 @ SV1540 @ SV1540 ) @ ( c_Transitive__Closure_Otrancl @ SV1884 @ SV1540 ) @ ( tc_prod @ SV1540 @ SV1540 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5867]) ).
thf(5992,plain,
! [SV1058: $i,SV1890: $i,SV1546: $i,SV453: $i,SV2337: $i] :
( ( ( c_in @ ( c_Pair @ SV2337 @ SV453 @ SV1546 @ SV1546 ) @ ( c_Transitive__Closure_Ortrancl @ SV1890 @ SV1546 ) @ ( tc_prod @ SV1546 @ SV1546 ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV2337 @ SV1058 @ SV1546 @ SV1546 ) @ ( c_Transitive__Closure_Ortrancl @ SV1890 @ SV1546 ) @ ( tc_prod @ SV1546 @ SV1546 ) )
| ~ ( c_Relation_Osingle__valued @ SV1890 @ SV1546 @ SV1546 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1058 @ SV453 @ SV1546 @ SV1546 ) @ ( c_Transitive__Closure_Ortrancl @ SV1890 @ SV1546 ) @ ( tc_prod @ SV1546 @ SV1546 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV453 @ SV1058 @ SV1546 @ SV1546 ) @ ( c_Transitive__Closure_Ortrancl @ SV1890 @ SV1546 ) @ ( tc_prod @ SV1546 @ SV1546 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5868]) ).
thf(5993,plain,
! [SV1060: $i,SV1892: $i,SV1548: $i,SV2257: $i,SV455: $i] :
( ( ( c_in @ ( c_Pair @ SV455 @ SV2257 @ SV1548 @ SV1548 ) @ ( c_Transitive__Closure_Otrancl @ SV1892 @ SV1548 ) @ ( tc_prod @ SV1548 @ SV1548 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV2257 @ SV1060 @ SV1548 @ SV1548 ) @ ( c_Transitive__Closure_Ortrancl @ SV1892 @ SV1548 ) @ ( tc_prod @ SV1548 @ SV1548 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV455 @ SV1060 @ SV1548 @ SV1548 ) @ ( c_Transitive__Closure_Otrancl @ SV1892 @ SV1548 ) @ ( tc_prod @ SV1548 @ SV1548 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5869]) ).
thf(5994,plain,
! [SV1061: $i,SV1893: $i,SV1549: $i,SV2258: $i,SV456: $i] :
( ( ( c_in @ ( c_Pair @ SV456 @ SV2258 @ SV1549 @ SV1549 ) @ ( c_Transitive__Closure_Ortrancl @ SV1893 @ SV1549 ) @ ( tc_prod @ SV1549 @ SV1549 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV2258 @ SV1061 @ SV1549 @ SV1549 ) @ ( c_Transitive__Closure_Otrancl @ SV1893 @ SV1549 ) @ ( tc_prod @ SV1549 @ SV1549 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV456 @ SV1061 @ SV1549 @ SV1549 ) @ ( c_Transitive__Closure_Otrancl @ SV1893 @ SV1549 ) @ ( tc_prod @ SV1549 @ SV1549 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5870]) ).
thf(5995,plain,
! [SV1898: $i,SV1554: $i,SV1066: $i,SV2362: $i,SV2338: $i,SV2134: $i,SV461: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_split @ SV461 @ SV2134 @ SV2338 @ ( tc_fun @ SV2362 @ tc_bool ) ) @ ( c_Pair @ SV1066 @ SV1554 @ SV2134 @ SV2338 ) ) @ SV1898 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ SV461 @ SV1066 ) @ SV1554 ) @ SV1898 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5871]) ).
thf(5996,plain,
! [SV2145: $i,SV1121: $i,SV1910: $i,SV1575: $i,SV520: $i] :
( ( ( c_Relation_Osingle__valued @ SV520 @ SV1575 @ SV1910 )
= $false )
| ( ( c_Relation_Osingle__valued @ SV1121 @ SV1910 @ SV2145 )
= $false )
| ( ( c_Relation_Osingle__valued @ ( c_Relation_Orel__comp @ SV520 @ SV1121 @ SV1575 @ SV1910 @ SV2145 ) @ SV1575 @ SV2145 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5875]) ).
thf(5997,plain,
! [SV2146: $i,SV1914: $i,SV1133: $i,SV533: $i,SV2363: $i,SV2268: $i,SV1580: $i] :
( ( ( ~ ( c_in @ SV1580 @ SV2268 @ SV2363 ) )
= $true )
| ( ( ! [SY6040: $i] :
( ~ ( c_Equiv__Relations_Ocongruent2 @ SY6040 @ SV533 @ SV1133 @ SV2363 @ SV1914 @ SV2146 )
| ~ ( c_Equiv__Relations_Oequiv @ SV2268 @ SY6040 @ SV2363 ) ) )
= $true )
| ( ( c_Equiv__Relations_Ocongruent @ SV533 @ ( hAPP @ SV1133 @ SV1580 ) @ SV1914 @ SV2146 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5877]) ).
thf(5998,plain,
! [SV1146: $i,SV2342: $i,SV2269: $i,SV546: $i,SV1587: $i] :
( ( ( c_in @ ( c_Pair @ SV1587 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ SV546 @ SV2269 @ SV2342 ) @ SV2342 @ SV2342 ) @ SV2269 @ ( tc_prod @ SV2342 @ SV2342 ) )
= $false )
| ( ( ~ ( c_in @ SV1146 @ ( c_Wellfounded_Oacc @ SV2269 @ SV2342 ) @ SV2342 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV546 @ SV1587 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV546 @ SV1146 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5878]) ).
thf(5999,plain,
! [SV547: $i,SV1918: $i,SV2270: $i,SV1147: $i] :
( ( ( c_in @ SV1147 @ ( c_Wellfounded_Oacc @ SV2270 @ t_a ) @ t_a )
= $false )
| ( ( c_in @ ( c_Pair @ SV1918 @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ SV547 @ SV2270 ) @ t_a @ t_a ) @ SV2270 @ ( tc_prod @ t_a @ t_a ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV547 @ SV1918 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV547 @ SV1147 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5879]) ).
thf(6000,plain,
! [SV548: $i,SV2271: $i,SV1588: $i,SV1148: $i] :
( ( ( ! [SY5526: $i] :
~ ( c_in @ SY5526 @ SV1148 @ SV1588 ) )
= $true )
| ( ( ~ ( c_Wellfounded_Owf @ SV2271 @ SV1588 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV548 @ ( c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 @ SV1148 @ SV2271 @ SV1588 ) @ SV1588 @ SV1588 ) @ SV2271 @ ( tc_prod @ SV1588 @ SV1588 ) )
= $false )
| ( ( c_in @ SV548 @ SV1148 @ SV1588 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5880]) ).
thf(6001,plain,
! [SV553: $i,SV1920: $i,SV2151: $i,SV1153: $i] :
( ( ( c_in @ SV1153 @ ( c_Wellfounded_Oacc @ SV2151 @ t_a ) @ t_a )
= $false )
| ( ( c_in @ ( c_Pair @ SV1920 @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ SV553 @ SV2151 ) @ t_a @ t_a ) @ SV2151 @ ( tc_prod @ t_a @ t_a ) )
= $false )
| ( ( c_in @ SV1920 @ ( c_Wellfounded_Oacc @ SV2151 @ t_a ) @ t_a )
= $true )
| ( ( hBOOL @ ( hAPP @ SV553 @ SV1153 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5883]) ).
thf(6002,plain,
! [SV555: $i,SV1921: $i,SV2272: $i,SV1155: $i] :
( ( ( c_in @ SV1155 @ ( c_Wellfounded_Oacc @ SV2272 @ t_a ) @ t_a )
= $false )
| ( ( c_in @ ( c_Pair @ SV1921 @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ SV555 @ SV2272 ) @ t_a @ t_a ) @ SV2272 @ ( tc_prod @ t_a @ t_a ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV555 @ SV1921 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV555 @ SV1155 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5884]) ).
thf(6003,plain,
! [SV2273: $i,SV556: $i,SV2343: $i,SV2152: $i,SV1922: $i,SV1594: $i,SV1156: $i] :
( ( ( c_in @ ( c_Pair @ SV1156 @ SV1594 @ SV1922 @ SV2152 ) @ SV2343 @ ( tc_prod @ SV1922 @ SV2152 ) )
= $false )
| ( ( c_in @ ( hAPP @ ( hAPP @ SV556 @ SV1156 ) @ SV1594 ) @ ( c_Set_Oimage @ ( c_split @ SV556 @ SV1922 @ SV2152 @ SV2273 ) @ SV2343 @ ( tc_prod @ SV1922 @ SV2152 ) @ SV2273 ) @ SV2273 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5885]) ).
thf(6004,plain,
! [SV558: $i,SV1924: $i,SV2153: $i,SV1158: $i] :
( ( ( c_in @ SV1158 @ ( c_Wellfounded_Oacc @ SV2153 @ t_a ) @ t_a )
= $false )
| ( ( c_in @ ( c_Pair @ SV1924 @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ SV558 @ SV2153 ) @ t_a @ t_a ) @ SV2153 @ ( tc_prod @ t_a @ t_a ) )
= $false )
| ( ( c_in @ SV1924 @ ( c_Wellfounded_Oacc @ SV2153 @ t_a ) @ t_a )
= $true )
| ( ( hBOOL @ ( hAPP @ SV558 @ SV1158 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5886]) ).
thf(6005,plain,
! [SV1159: $i,SV2344: $i,SV2274: $i,SV559: $i,SV1596: $i] :
( ( ( c_in @ ( c_Pair @ SV1596 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ SV559 @ SV2274 @ SV2344 ) @ SV2344 @ SV2344 ) @ SV2274 @ ( tc_prod @ SV2344 @ SV2344 ) )
= $false )
| ( ( ~ ( c_in @ SV1159 @ ( c_Wellfounded_Oacc @ SV2274 @ SV2344 ) @ SV2344 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV559 @ SV1596 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV559 @ SV1159 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5887]) ).
thf(6006,plain,
! [SV560: $i,SV2275: $i,SV1597: $i,SV1160: $i] :
( ( ( ! [SY5538: $i] :
~ ( c_in @ SY5538 @ SV1160 @ SV1597 ) )
= $true )
| ( ( ~ ( c_Wellfounded_Owf @ SV2275 @ SV1597 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV560 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 @ SV1160 @ SV2275 @ SV1597 ) @ SV1597 @ SV1597 ) @ SV2275 @ ( tc_prod @ SV1597 @ SV1597 ) )
= $false )
| ( ( c_in @ SV560 @ SV1160 @ SV1597 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5888]) ).
thf(6007,plain,
! [SV1929: $i,SV1601: $i,SV2156: $i,SV2345: $i,SV2276: $i,SV1165: $i,SV565: $i] :
( ( ( c_in @ SV565 @ ( hAPP @ ( hAPP @ SV1165 @ SV2276 ) @ SV2345 ) @ SV2156 )
= $false )
| ( ( c_in @ SV565 @ ( hAPP @ ( c_split @ SV1165 @ SV1601 @ SV1929 @ ( tc_fun @ SV2156 @ tc_bool ) ) @ ( c_Pair @ SV2276 @ SV2345 @ SV1601 @ SV1929 ) ) @ SV2156 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5889]) ).
thf(6008,plain,
! [SV2364: $i,SV2346: $i,SV2277: $i,SV2157: $i,SV1930: $i,SV1602: $i,SV1166: $i,SV566: $i] :
( ( ( ( hAPP @ ( hAPP @ SV566 @ SV1166 ) @ SV1602 )
= ( hAPP @ ( hAPP @ SV566 @ SV1930 ) @ SV2157 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV1602 @ SV2157 @ SV2277 @ SV2277 ) @ SV2346 @ ( tc_prod @ SV2277 @ SV2277 ) )
| ! [SY6041: $i] :
( ~ ( c_in @ ( c_Pair @ SV1166 @ SV1930 @ SV2364 @ SV2364 ) @ SY6041 @ ( tc_prod @ SV2364 @ SV2364 ) )
| ! [SY6042: $i] :
~ ( c_Equiv__Relations_Ocongruent2 @ SY6041 @ SV2346 @ SV566 @ SV2364 @ SV2277 @ SY6042 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5890]) ).
thf(6009,plain,
! [SV567: $i,SV2347: $i,SV2278: $i,SV1931: $i,SV1167: $i,SV1603: $i] :
( ( ( c_in @ ( c_Pair @ SV1603 @ SV1167 @ SV1931 @ SV2278 ) @ SV2347 @ ( tc_prod @ SV1931 @ SV2278 ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV1603 @ SV567 @ SV1931 @ SV2278 ) @ SV2347 @ ( tc_prod @ SV1931 @ SV2278 ) )
| ~ ( c_Relation_Osingle__valued @ SV2347 @ SV1931 @ SV2278 ) )
= $true )
| ( ( SV567 = SV1167 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5891]) ).
thf(6010,plain,
! [SV1172: $i,SV1936: $i,SV1608: $i,SV2281: $i,SV572: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV572 @ SV2281 @ SV1608 @ SV1608 ) @ SV1936 @ ( tc_prod @ SV1608 @ SV1608 ) ) )
= $true )
| ( ( ~ ( c_Relation_Otrans @ SV1936 @ SV1608 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV2281 @ SV1172 @ SV1608 @ SV1608 ) @ SV1936 @ ( tc_prod @ SV1608 @ SV1608 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV572 @ SV1172 @ SV1608 @ SV1608 ) @ SV1936 @ ( tc_prod @ SV1608 @ SV1608 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5894]) ).
thf(6011,plain,
! [SV1173: $i,SV1937: $i,SV1609: $i,SV2282: $i,SV573: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV573 @ SV2282 @ SV1609 @ SV1609 ) @ SV1937 @ ( tc_prod @ SV1609 @ SV1609 ) ) )
= $true )
| ( ( ~ ( c_Relation_Otrans @ SV1937 @ SV1609 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV2282 @ SV1173 @ SV1609 @ SV1609 ) @ SV1937 @ ( tc_prod @ SV1609 @ SV1609 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV573 @ SV1173 @ SV1609 @ SV1609 ) @ SV1937 @ ( tc_prod @ SV1609 @ SV1609 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5895]) ).
thf(6012,plain,
! [SV1178: $i,SV1941: $i,SV1614: $i,SV2283: $i,SV578: $i] :
( ( ( c_in @ ( c_Pair @ SV578 @ SV2283 @ SV1614 @ SV1614 ) @ ( c_Transitive__Closure_Otrancl @ SV1941 @ SV1614 ) @ ( tc_prod @ SV1614 @ SV1614 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV2283 @ SV1178 @ SV1614 @ SV1614 ) @ SV1941 @ ( tc_prod @ SV1614 @ SV1614 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV578 @ SV1178 @ SV1614 @ SV1614 ) @ ( c_Transitive__Closure_Otrancl @ SV1941 @ SV1614 ) @ ( tc_prod @ SV1614 @ SV1614 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5896]) ).
thf(6013,plain,
! [SV1179: $i,SV1942: $i,SV1615: $i,SV2284: $i,SV579: $i] :
( ( ( c_in @ ( c_Pair @ SV579 @ SV2284 @ SV1615 @ SV1615 ) @ SV1942 @ ( tc_prod @ SV1615 @ SV1615 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV2284 @ SV1179 @ SV1615 @ SV1615 ) @ ( c_Transitive__Closure_Otrancl @ SV1942 @ SV1615 ) @ ( tc_prod @ SV1615 @ SV1615 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV579 @ SV1179 @ SV1615 @ SV1615 ) @ ( c_Transitive__Closure_Otrancl @ SV1942 @ SV1615 ) @ ( tc_prod @ SV1615 @ SV1615 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5897]) ).
thf(6014,plain,
! [SV1180: $i,SV1943: $i,SV1616: $i,SV2285: $i,SV580: $i] :
( ( ( c_in @ ( c_Pair @ SV580 @ SV2285 @ SV1616 @ SV1616 ) @ ( c_Transitive__Closure_Ortrancl @ SV1943 @ SV1616 ) @ ( tc_prod @ SV1616 @ SV1616 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV2285 @ SV1180 @ SV1616 @ SV1616 ) @ SV1943 @ ( tc_prod @ SV1616 @ SV1616 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV580 @ SV1180 @ SV1616 @ SV1616 ) @ ( c_Transitive__Closure_Ortrancl @ SV1943 @ SV1616 ) @ ( tc_prod @ SV1616 @ SV1616 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5898]) ).
thf(6015,plain,
! [SV1181: $i,SV1944: $i,SV1617: $i,SV2286: $i,SV581: $i] :
( ( ( c_in @ ( c_Pair @ SV581 @ SV2286 @ SV1617 @ SV1617 ) @ SV1944 @ ( tc_prod @ SV1617 @ SV1617 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV2286 @ SV1181 @ SV1617 @ SV1617 ) @ ( c_Transitive__Closure_Ortrancl @ SV1944 @ SV1617 ) @ ( tc_prod @ SV1617 @ SV1617 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV581 @ SV1181 @ SV1617 @ SV1617 ) @ ( c_Transitive__Closure_Ortrancl @ SV1944 @ SV1617 ) @ ( tc_prod @ SV1617 @ SV1617 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5899]) ).
thf(6016,plain,
! [SV1183: $i,SV1946: $i,SV1619: $i,SV2287: $i,SV583: $i] :
( ( ( c_in @ ( c_Pair @ SV583 @ SV2287 @ SV1619 @ SV1619 ) @ ( c_Transitive__Closure_Ortrancl @ SV1946 @ SV1619 ) @ ( tc_prod @ SV1619 @ SV1619 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV2287 @ SV1183 @ SV1619 @ SV1619 ) @ ( c_Transitive__Closure_Ortrancl @ SV1946 @ SV1619 ) @ ( tc_prod @ SV1619 @ SV1619 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV583 @ SV1183 @ SV1619 @ SV1619 ) @ ( c_Transitive__Closure_Ortrancl @ SV1946 @ SV1619 ) @ ( tc_prod @ SV1619 @ SV1619 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5900]) ).
thf(6017,plain,
! [SV586: $i,SV1186: $i,SV1622: $i,SV1947: $i] :
( ( ( c_Wellfounded_Owf @ SV1947 @ SV1622 )
= $false )
| ( ( c_in @ ( c_Pair @ SV1186 @ SV586 @ SV1622 @ SV1622 ) @ SV1947 @ ( tc_prod @ SV1622 @ SV1622 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV586 @ SV1186 @ SV1622 @ SV1622 ) @ SV1947 @ ( tc_prod @ SV1622 @ SV1622 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5901]) ).
thf(6018,plain,
! [SV2165: $i,SV1948: $i,SV1187: $i,SV587: $i] :
( ( ( c_in @ ( c_Pair @ SV587 @ SV1187 @ SV1948 @ SV1948 ) @ SV2165 @ ( tc_prod @ SV1948 @ SV1948 ) )
= $false )
| ( ( ~ ( c_Relation_Oantisym @ SV2165 @ SV1948 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1187 @ SV587 @ SV1948 @ SV1948 ) @ SV2165 @ ( tc_prod @ SV1948 @ SV1948 ) )
= $false )
| ( ( SV587 = SV1187 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5902]) ).
thf(6019,plain,
! [SV2166: $i,SV1949: $i,SV1188: $i,SV588: $i] :
( ( ( c_in @ ( c_Pair @ SV588 @ SV1188 @ SV1949 @ SV1949 ) @ SV2166 @ ( tc_prod @ SV1949 @ SV1949 ) )
= $false )
| ( ( ~ ( c_Relation_Oantisym @ SV2166 @ SV1949 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1188 @ SV588 @ SV1949 @ SV1949 ) @ SV2166 @ ( tc_prod @ SV1949 @ SV1949 ) )
= $false )
| ( ( SV588 = SV1188 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5903]) ).
thf(6020,plain,
! [SV1623: $i,SV1189: $i,SV2372: $i,SV1950: $i,SV589: $i,SV2288: $i] :
( ( ( ~ ( c_Equiv__Relations_Ocongruent @ SV2288 @ SV589 @ SV1950 @ SV2372 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1189 @ SV1623 @ SV1950 @ SV1950 ) @ SV2288 @ ( tc_prod @ SV1950 @ SV1950 ) )
= $false )
| ( ( ( hAPP @ SV589 @ SV1189 )
= ( hAPP @ SV589 @ SV1623 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5904]) ).
thf(6021,plain,
! [SV2168: $i,SV1191: $i,SV1952: $i,SV1624: $i,SV2289: $i,SV2373: $i,SV591: $i] :
( ( ( ( ( hAPP @ SV591 @ SV2373 )
= ( hAPP @ SV2289 @ SV2373 ) )
| ~ ( c_in @ ( c_Pair @ SV2373 @ SV1624 @ SV1952 @ SV1952 ) @ SV1191 @ ( tc_prod @ SV1952 @ SV1952 ) ) )
= $true )
| ( ( ( c_Recdef_Ocut @ SV591 @ SV1191 @ SV1624 @ SV1952 @ SV2168 )
= ( c_Recdef_Ocut @ SV2289 @ SV1191 @ SV1624 @ SV1952 @ SV2168 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5905]) ).
thf(6022,plain,
! [SV2171: $i,SV1631: $i,SV599: $i,SV2291: $i,SV1958: $i,SV2349: $i,SV1199: $i,SV2374: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV2374 @ SV1199 @ SV2349 @ SV1958 ) @ SV2291 @ ( tc_prod @ SV2349 @ SV1958 ) )
| ~ ( c_in @ ( c_Pair @ SV599 @ SV2374 @ SV1631 @ SV2349 ) @ SV2171 @ ( tc_prod @ SV1631 @ SV2349 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV599 @ SV1199 @ SV1631 @ SV1958 ) @ ( c_Relation_Orel__comp @ SV2171 @ SV2291 @ SV1631 @ SV2349 @ SV1958 ) @ ( tc_prod @ SV1631 @ SV1958 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5910]) ).
thf(6023,plain,
! [SV1200: $i,SV1959: $i,SV1632: $i,SV2292: $i,SV600: $i] :
( ( ( c_in @ ( c_Pair @ SV600 @ SV2292 @ SV1632 @ SV1632 ) @ SV1959 @ ( tc_prod @ SV1632 @ SV1632 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV2292 @ SV1200 @ SV1632 @ SV1632 ) @ SV1959 @ ( tc_prod @ SV1632 @ SV1632 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV600 @ SV1200 @ SV1632 @ SV1632 ) @ ( c_Transitive__Closure_Otrancl @ SV1959 @ SV1632 ) @ ( tc_prod @ SV1632 @ SV1632 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5911]) ).
thf(6024,plain,
! [SV1201: $i,SV1960: $i,SV1633: $i,SV2293: $i,SV601: $i] :
( ( ( c_in @ ( c_Pair @ SV601 @ SV2293 @ SV1633 @ SV1633 ) @ ( c_Transitive__Closure_Otrancl @ SV1960 @ SV1633 ) @ ( tc_prod @ SV1633 @ SV1633 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV2293 @ SV1201 @ SV1633 @ SV1633 ) @ ( c_Transitive__Closure_Otrancl @ SV1960 @ SV1633 ) @ ( tc_prod @ SV1633 @ SV1633 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV601 @ SV1201 @ SV1633 @ SV1633 ) @ ( c_Transitive__Closure_Otrancl @ SV1960 @ SV1633 ) @ ( tc_prod @ SV1633 @ SV1633 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5912]) ).
thf(6025,plain,
! [SV1642: $i,SV2176: $i,SV1965: $i,SV617: $i,SV2294: $i,SV1217: $i] :
( ( ( c_in @ SV1217 @ ( hAPP @ SV2294 @ SV617 ) @ SV1965 )
= $false )
| ( ( ~ ( c_in @ SV617 @ SV2176 @ SV1642 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV617 @ SV1217 @ SV1642 @ SV1965 ) @ ( c_Product__Type_OSigma @ SV2176 @ SV2294 @ SV1642 @ SV1965 ) @ ( tc_prod @ SV1642 @ SV1965 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5917]) ).
thf(6026,plain,
! [SV1643: $i,SV2177: $i,SV1966: $i,SV618: $i,SV2295: $i,SV1218: $i] :
( ( ( c_in @ SV1218 @ ( hAPP @ SV2295 @ SV618 ) @ SV1966 )
= $false )
| ( ( ~ ( c_in @ SV618 @ SV2177 @ SV1643 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV618 @ SV1218 @ SV1643 @ SV1966 ) @ ( c_Product__Type_OSigma @ SV2177 @ SV2295 @ SV1643 @ SV1966 ) @ ( tc_prod @ SV1643 @ SV1966 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5918]) ).
thf(6027,plain,
! [SV1646: $i,SV1221: $i,SV2180: $i,SV1967: $i,SV621: $i,SV2350: $i] :
( ( ( c_in @ ( c_Pair @ SV2350 @ SV621 @ SV1967 @ SV2180 ) @ SV1221 @ ( tc_prod @ SV1967 @ SV2180 ) )
= $false )
| ( ( ~ ( c_in @ SV2350 @ SV1646 @ SV1967 ) )
= $true )
| ( ( c_in @ SV621 @ ( c_Relation_OImage @ SV1221 @ SV1646 @ SV1967 @ SV2180 ) @ SV2180 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5921]) ).
thf(6028,plain,
! [SV1647: $i,SV1222: $i,SV2181: $i,SV1968: $i,SV622: $i,SV2351: $i] :
( ( ( c_in @ ( c_Pair @ SV2351 @ SV622 @ SV1968 @ SV2181 ) @ SV1222 @ ( tc_prod @ SV1968 @ SV2181 ) )
= $false )
| ( ( ~ ( c_in @ SV2351 @ SV1647 @ SV1968 ) )
= $true )
| ( ( c_in @ SV622 @ ( c_Relation_OImage @ SV1222 @ SV1647 @ SV1968 @ SV2181 ) @ SV2181 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5922]) ).
thf(6029,plain,
! [SV625: $i,SV2183: $i,SV1650: $i,SV2296: $i,SV1225: $i] :
( ( ( c_Equiv__Relations_Oequiv @ SV1225 @ SV2296 @ SV1650 )
= $false )
| ( ( c_in @ ( c_Pair @ SV2183 @ SV625 @ SV1650 @ SV1650 ) @ SV2296 @ ( tc_prod @ SV1650 @ SV1650 ) )
= $false )
| ( ( c_in @ SV625 @ SV1225 @ SV1650 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5923]) ).
thf(6030,plain,
! [SV2184: $i,SV626: $i,SV1651: $i,SV2297: $i,SV1226: $i] :
( ( ( c_Equiv__Relations_Oequiv @ SV1226 @ SV2297 @ SV1651 )
= $false )
| ( ( c_in @ ( c_Pair @ SV626 @ SV2184 @ SV1651 @ SV1651 ) @ SV2297 @ ( tc_prod @ SV1651 @ SV1651 ) )
= $false )
| ( ( c_in @ SV626 @ SV1226 @ SV1651 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5924]) ).
thf(6031,plain,
! [SV1975: $i,SV1233: $i,SV1658: $i,SV2365: $i,SV633: $i] :
( ( ( ~ ( c_in @ SV633 @ SV2365 @ SV1658 ) )
= $true )
| ( ( ~ ( c_in @ SV1233 @ SV2365 @ SV1658 )
| ~ ( c_Relation_Ototal__on @ SV2365 @ SV1975 @ SV1658 ) )
= $true )
| ( ( SV1233 = SV633 )
= $true )
| ( ( c_in @ ( c_Pair @ SV1233 @ SV633 @ SV1658 @ SV1658 ) @ SV1975 @ ( tc_prod @ SV1658 @ SV1658 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV633 @ SV1233 @ SV1658 @ SV1658 ) @ SV1975 @ ( tc_prod @ SV1658 @ SV1658 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5927]) ).
thf(6032,plain,
! [SV635: $i,SV2186: $i,SV1660: $i,SV2304: $i,SV1235: $i] :
( ( ( c_Relation_Orefl__on @ SV1235 @ SV2304 @ SV1660 )
= $false )
| ( ( c_in @ ( c_Pair @ SV2186 @ SV635 @ SV1660 @ SV1660 ) @ SV2304 @ ( tc_prod @ SV1660 @ SV1660 ) )
= $false )
| ( ( c_in @ SV635 @ SV1235 @ SV1660 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5929]) ).
thf(6033,plain,
! [SV2187: $i,SV636: $i,SV1661: $i,SV2305: $i,SV1236: $i] :
( ( ( c_Relation_Orefl__on @ SV1236 @ SV2305 @ SV1661 )
= $false )
| ( ( c_in @ ( c_Pair @ SV636 @ SV2187 @ SV1661 @ SV1661 ) @ SV2305 @ ( tc_prod @ SV1661 @ SV1661 ) )
= $false )
| ( ( c_in @ SV636 @ SV1236 @ SV1661 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5930]) ).
thf(6034,plain,
! [SV1680: $i,SV1983: $i,SV21: $i,SV1269: $i,SV672: $i,SV2366: $i] :
( ( ( c_in @ SV2366 @ SV672 @ SV1269 )
= $false )
| ( ( c_lessequals @ SV21 @ SV1983 @ ( tc_fun @ SV1680 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( c_Product__Type_OSigma @ SV21 @ ( c_COMBK @ SV672 @ ( tc_fun @ SV1269 @ tc_bool ) @ SV1680 ) @ SV1680 @ SV1269 ) @ ( c_Product__Type_OSigma @ SV1983 @ ( c_COMBK @ SV672 @ ( tc_fun @ SV1269 @ tc_bool ) @ SV1680 ) @ SV1680 @ SV1269 ) @ ( tc_fun @ ( tc_prod @ SV1680 @ SV1269 ) @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5934]) ).
thf(6035,plain,
! [SV673: $i,SV1270: $i,SV22: $i,SV2191: $i,SV1681: $i,SV2367: $i] :
( ( ( c_in @ SV2367 @ SV1681 @ SV2191 )
= $false )
| ( ( c_lessequals @ ( c_Product__Type_OSigma @ SV22 @ ( c_COMBK @ SV1681 @ ( tc_fun @ SV2191 @ tc_bool ) @ SV1270 ) @ SV1270 @ SV2191 ) @ ( c_Product__Type_OSigma @ SV673 @ ( c_COMBK @ SV1681 @ ( tc_fun @ SV2191 @ tc_bool ) @ SV1270 ) @ SV1270 @ SV2191 ) @ ( tc_fun @ ( tc_prod @ SV1270 @ SV2191 ) @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV22 @ SV673 @ ( tc_fun @ SV1270 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5935]) ).
thf(6036,plain,
! [SV1282: $i,SV2195: $i,SV40: $i,SV1987: $i,SV1692: $i,SV2307: $i,SV690: $i] :
( ( ( c_lessequals @ SV690 @ SV2307 @ ( tc_fun @ ( tc_prod @ SV1692 @ SV1987 ) @ tc_bool ) )
= $false )
| ( ( ~ ( c_lessequals @ SV40 @ SV2195 @ ( tc_fun @ ( tc_prod @ SV1282 @ SV1692 ) @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( c_Relation_Orel__comp @ SV40 @ SV690 @ SV1282 @ SV1692 @ SV1987 ) @ ( c_Relation_Orel__comp @ SV2195 @ SV2307 @ SV1282 @ SV1692 @ SV1987 ) @ ( tc_fun @ ( tc_prod @ SV1282 @ SV1987 ) @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5936]) ).
thf(6037,plain,
! [SV2002: $i,SV71: $i,SV2201: $i,SV718: $i] :
( ( ( c_lessequals @ SV718 @ SV2201 @ SV71 )
= $false )
| ( ( c_lessequals @ SV2002 @ SV2201 @ SV71 )
= $false )
| ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV718 @ SV2002 @ SV71 ) @ SV2201 @ SV71 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV71 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5937]) ).
thf(6038,plain,
! [SV2005: $i,SV74: $i,SV2202: $i,SV719: $i] :
( ( ( c_lessequals @ SV719 @ SV2202 @ SV74 )
= $false )
| ( ( c_lessequals @ SV2005 @ SV2202 @ SV74 )
= $false )
| ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV719 @ SV2005 @ SV74 ) @ SV2202 @ SV74 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV74 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5938]) ).
thf(6039,plain,
! [SV2006: $i,SV75: $i,SV2203: $i,SV720: $i] :
( ( ( c_lessequals @ SV720 @ SV2203 @ SV75 )
= $false )
| ( ( c_lessequals @ SV2006 @ SV2203 @ SV75 )
= $false )
| ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV720 @ SV2006 @ SV75 ) @ SV2203 @ SV75 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV75 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5939]) ).
thf(6040,plain,
! [SV1317: $i,SV2205: $i,SV103: $i,SV1724: $i,SV2015: $i,SV2310: $i,SV2368: $i,SV742: $i] :
( ( ( ~ ( c_lessequals @ SV742 @ ( c_Product__Type_OSigma @ SV2368 @ ( c_COMBK @ SV2310 @ ( tc_fun @ SV2015 @ tc_bool ) @ SV1724 ) @ SV1724 @ SV2015 ) @ ( tc_fun @ ( tc_prod @ SV1724 @ SV2015 ) @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV103 @ ( c_Product__Type_OSigma @ SV2205 @ ( c_COMBK @ SV2368 @ ( tc_fun @ SV1724 @ tc_bool ) @ SV1317 ) @ SV1317 @ SV1724 ) @ ( tc_fun @ ( tc_prod @ SV1317 @ SV1724 ) @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( c_Relation_Orel__comp @ SV103 @ SV742 @ SV1317 @ SV1724 @ SV2015 ) @ ( c_Product__Type_OSigma @ SV2205 @ ( c_COMBK @ SV2310 @ ( tc_fun @ SV2015 @ tc_bool ) @ SV1317 ) @ SV1317 @ SV2015 ) @ ( tc_fun @ ( tc_prod @ SV1317 @ SV2015 ) @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5941]) ).
thf(6041,plain,
! [SV2217: $i,SV174: $i,SV2043: $i,SV798: $i] :
( ( ( c_lessequals @ SV798 @ SV2043 @ SV174 )
= $false )
| ( ( c_lessequals @ SV798 @ SV2217 @ SV174 )
= $false )
| ( ( c_lessequals @ SV798 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2043 @ SV2217 @ SV174 ) @ SV174 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV174 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5952]) ).
thf(6042,plain,
! [SV2218: $i,SV175: $i,SV2044: $i,SV799: $i] :
( ( ( c_lessequals @ SV799 @ SV2044 @ SV175 )
= $false )
| ( ( c_lessequals @ SV799 @ SV2218 @ SV175 )
= $false )
| ( ( c_lessequals @ SV799 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2044 @ SV2218 @ SV175 ) @ SV175 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV175 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5953]) ).
thf(6043,plain,
! [SV2219: $i,SV176: $i,SV2045: $i,SV800: $i] :
( ( ( c_lessequals @ SV800 @ SV2045 @ SV176 )
= $false )
| ( ( c_lessequals @ SV800 @ SV2219 @ SV176 )
= $false )
| ( ( c_lessequals @ SV800 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2045 @ SV2219 @ SV176 ) @ SV176 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV176 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5954]) ).
thf(6044,plain,
! [SV1433: $i,SV896: $i,SV2085: $i,SV2357: $i,SV1813: $i,SV282: $i] :
( ( ( hBOOL @ ( hAPP @ SV282 @ SV1813 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV2357 @ SV2085 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV282 @ ( hAPP @ ( c_fst @ SV896 @ SV1433 ) @ ( c_Pair @ SV1813 @ SV2085 @ SV896 @ SV1433 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5956]) ).
thf(6045,plain,
! [SV1434: $i,SV897: $i,SV2086: $i,SV283: $i,SV1814: $i,SV2369: $i] :
( ( ( hBOOL @ ( hAPP @ SV2369 @ SV1814 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV283 @ SV2086 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV283 @ ( hAPP @ ( c_snd @ SV897 @ SV1434 ) @ ( c_Pair @ SV1814 @ SV2086 @ SV897 @ SV1434 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5957]) ).
thf(6046,plain,
! [SV920: $i,SV309: $i,SV2100: $i,SV2320: $i] :
( ( ( c_lessequals @ SV2320 @ SV2100 @ SV309 )
= $false )
| ( ( c_lessequals @ SV920 @ SV2320 @ SV309 )
= $false )
| ( ( c_lessequals @ SV920 @ SV2100 @ SV309 )
= $true )
| ( ( class_Orderings_Oorder @ SV309 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5958]) ).
thf(6047,plain,
! [SV2101: $i,SV310: $i,SV2321: $i,SV921: $i] :
( ( ( c_lessequals @ SV921 @ SV2321 @ SV310 )
= $false )
| ( ( c_lessequals @ SV2321 @ SV2101 @ SV310 )
= $false )
| ( ( c_lessequals @ SV921 @ SV2101 @ SV310 )
= $true )
| ( ( class_Orderings_Opreorder @ SV310 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5959]) ).
thf(6048,plain,
! [SV942: $i,SV1459: $i,SV333: $i,SV2233: $i,SV2323: $i] :
( ( ( c_lessequals @ SV2323 @ SV2233 @ SV333 )
= $true )
| ( ( ~ ( c_lessequals @ SV1459 @ SV942 @ SV333 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV942 @ SV1459 @ SV333 )
= ( c_HOL_Ominus__class_Ominus @ SV2233 @ SV2323 @ SV333 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV333 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5961]) ).
thf(6049,plain,
! [SV2234: $i,SV2324: $i,SV334: $i,SV943: $i,SV1460: $i] :
( ( ( c_lessequals @ SV1460 @ SV943 @ SV334 )
= $true )
| ( ( ~ ( c_lessequals @ SV2324 @ SV2234 @ SV334 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV943 @ SV1460 @ SV334 )
= ( c_HOL_Ominus__class_Ominus @ SV2234 @ SV2324 @ SV334 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV334 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5962]) ).
thf(6050,plain,
! [SV2236: $i,SV950: $i,SV1842: $i,SV1467: $i,SV2109: $i,SV343: $i] :
( ( ( c_lessequals @ SV343 @ SV2109 @ ( tc_fun @ ( tc_prod @ SV1467 @ SV1842 ) @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV950 @ SV2236 @ ( tc_fun @ SV1467 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( c_Relation_OImage @ SV343 @ SV950 @ SV1467 @ SV1842 ) @ ( c_Relation_OImage @ SV2109 @ SV2236 @ SV1467 @ SV1842 ) @ ( tc_fun @ SV1842 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5963]) ).
thf(6051,plain,
! [SV349: $i,SV2111: $i,SV2237: $i,SV1471: $i,SV955: $i] :
( ( ( c_in @ ( c_Pair @ SV955 @ SV1471 @ SV2237 @ SV2237 ) @ ( c_Transitive__Closure_Ortrancl @ SV2111 @ SV2237 ) @ ( tc_prod @ SV2237 @ SV2237 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV349 @ SV1471 ) )
= $false )
| ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1 @ SV349 @ SV1471 @ SV2111 @ SV2237 ) @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 @ SV349 @ SV1471 @ SV2111 @ SV2237 ) @ SV2237 @ SV2237 ) @ SV2111 @ ( tc_prod @ SV2237 @ SV2237 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV349 @ SV955 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5964]) ).
thf(6052,plain,
! [SV350: $i,SV2112: $i,SV2238: $i,SV956: $i,SV1472: $i] :
( ( ( c_in @ ( c_Pair @ SV1472 @ SV956 @ SV2238 @ SV2238 ) @ ( c_Transitive__Closure_Ortrancl @ SV2112 @ SV2238 ) @ ( tc_prod @ SV2238 @ SV2238 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV350 @ SV1472 ) )
= $false )
| ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 @ SV350 @ SV1472 @ SV2112 @ SV2238 ) @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2 @ SV350 @ SV1472 @ SV2112 @ SV2238 ) @ SV2238 @ SV2238 ) @ SV2112 @ ( tc_prod @ SV2238 @ SV2238 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV350 @ SV956 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5965]) ).
thf(6053,plain,
! [SV959: $i,SV353: $i,SV2326: $i,SV1475: $i,SV1847: $i,SV2370: $i] :
( ( ( c_Equiv__Relations_Oequiv @ SV2370 @ SV1847 @ SV1475 )
= $false )
| ( ( c_in @ SV2326 @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_OImage @ SV1847 @ ( c_Set_Oinsert @ SV353 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1475 @ tc_bool ) ) @ SV1475 ) @ SV1475 @ SV1475 ) @ ( c_Relation_OImage @ SV1847 @ ( c_Set_Oinsert @ SV959 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1475 @ tc_bool ) ) @ SV1475 ) @ SV1475 @ SV1475 ) @ ( tc_fun @ SV1475 @ tc_bool ) ) @ SV1475 )
= $false )
| ( ( c_in @ ( c_Pair @ SV353 @ SV959 @ SV1475 @ SV1475 ) @ SV1847 @ ( tc_prod @ SV1475 @ SV1475 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5966]) ).
thf(6054,plain,
! [SV2239: $i,SV354: $i,SV1476: $i,SV960: $i,SV1848: $i] :
( ( ( c_lessequals @ ( c_Relation_OImage @ SV1848 @ ( c_Set_Oinsert @ SV960 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1476 @ tc_bool ) ) @ SV1476 ) @ SV1476 @ SV1476 ) @ ( c_Relation_OImage @ SV1848 @ ( c_Set_Oinsert @ SV354 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1476 @ tc_bool ) ) @ SV1476 ) @ SV1476 @ SV1476 ) @ ( tc_fun @ SV1476 @ tc_bool ) )
= $false )
| ( ( ~ ( c_Equiv__Relations_Oequiv @ SV2239 @ SV1848 @ SV1476 ) )
= $true )
| ( ( c_in @ SV960 @ SV2239 @ SV1476 )
= $false )
| ( ( c_in @ ( c_Pair @ SV354 @ SV960 @ SV1476 @ SV1476 ) @ SV1848 @ ( tc_prod @ SV1476 @ SV1476 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5967]) ).
thf(6055,plain,
! [SV962: $i,SV1478: $i,SV1850: $i,SV2327: $i,SV2241: $i,SV356: $i] :
( ( ( c_lessequals @ ( c_Set_Oimage @ SV356 @ SV2241 @ SV2327 @ SV1850 ) @ SV1478 @ ( tc_fun @ SV1850 @ tc_bool ) )
= $false )
| ( ( c_in @ SV962 @ SV2241 @ SV2327 )
= $false )
| ( ( c_in @ ( hAPP @ SV356 @ SV962 ) @ SV1478 @ SV1850 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5968]) ).
thf(6056,plain,
! [SV1853: $i,SV2116: $i,SV359: $i,SV1481: $i,SV965: $i,SV2371: $i] :
( ( ( c_in @ SV2371 @ SV965 @ SV1481 )
= $false )
| ( ( SV359 = SV2116 )
= $true )
| ( ( ( c_Product__Type_OSigma @ SV359 @ ( c_COMBK @ SV965 @ ( tc_fun @ SV1481 @ tc_bool ) @ SV1853 ) @ SV1853 @ SV1481 )
= ( c_Product__Type_OSigma @ SV2116 @ ( c_COMBK @ SV965 @ ( tc_fun @ SV1481 @ tc_bool ) @ SV1853 ) @ SV1853 @ SV1481 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5969]) ).
thf(6057,plain,
! [SV1022: $i,SV417: $i,SV1513: $i,SV2330: $i,SV2245: $i] :
( ( ( c_Wellfounded_Owf @ SV2245 @ SV2330 )
= $false )
| ( ( c_in @ ( c_Pair @ SV1513 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1 @ SV417 @ SV2245 @ SV2330 ) @ SV2330 @ SV2330 ) @ SV2245 @ ( tc_prod @ SV2330 @ SV2330 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV417 @ SV1513 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV417 @ SV1022 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5975]) ).
thf(6058,plain,
! [SV1023: $i,SV418: $i,SV1514: $i,SV2331: $i,SV2246: $i] :
( ( ( c_Wellfounded_Owf @ SV2246 @ SV2331 )
= $false )
| ( ( c_in @ ( c_Pair @ SV1514 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1 @ SV418 @ SV2246 @ SV2331 ) @ SV2331 @ SV2331 ) @ SV2246 @ ( tc_prod @ SV2331 @ SV2331 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV418 @ SV1514 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV418 @ SV1023 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5976]) ).
thf(6059,plain,
! [SV1024: $i,SV419: $i,SV1515: $i,SV2332: $i,SV2247: $i] :
( ( ( c_Wellfounded_Owf @ SV2247 @ SV2332 )
= $false )
| ( ( c_in @ ( c_Pair @ SV1515 @ ( c_List_Osko__Recdef__Xtfl__wf__induct__1__1 @ SV419 @ SV2247 @ SV2332 ) @ SV2332 @ SV2332 ) @ SV2247 @ ( tc_prod @ SV2332 @ SV2332 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV419 @ SV1515 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV419 @ SV1024 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5977]) ).
thf(6060,plain,
! [SV1025: $i,SV420: $i,SV1516: $i,SV2333: $i,SV2248: $i] :
( ( ( c_Wellfounded_Owf @ SV2248 @ SV2333 )
= $false )
| ( ( c_in @ ( c_Pair @ SV1516 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1 @ SV420 @ SV2248 @ SV2333 ) @ SV2333 @ SV2333 ) @ SV2248 @ ( tc_prod @ SV2333 @ SV2333 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV420 @ SV1516 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV420 @ SV1025 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5978]) ).
thf(6061,plain,
! [SV424: $i,SV2123: $i,SV2249: $i,SV1520: $i,SV1029: $i] :
( ( ( c_in @ ( c_Pair @ SV1029 @ SV1520 @ SV2249 @ SV2249 ) @ ( c_Transitive__Closure_Ortrancl @ SV2123 @ SV2249 ) @ ( tc_prod @ SV2249 @ SV2249 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV424 @ SV1520 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV424 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 @ SV424 @ SV1520 @ SV2123 @ SV2249 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV424 @ SV1029 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5979]) ).
thf(6062,plain,
! [SV425: $i,SV2124: $i,SV2250: $i,SV1521: $i,SV1030: $i] :
( ( ( c_in @ ( c_Pair @ SV1030 @ SV1521 @ SV2250 @ SV2250 ) @ ( c_Transitive__Closure_Ortrancl @ SV2124 @ SV2250 ) @ ( tc_prod @ SV2250 @ SV2250 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV425 @ SV1521 ) )
= $false )
| ( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 @ SV425 @ SV1521 @ SV2124 @ SV2250 ) @ SV1521 @ SV2250 @ SV2250 ) @ ( c_Transitive__Closure_Ortrancl @ SV2124 @ SV2250 ) @ ( tc_prod @ SV2250 @ SV2250 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV425 @ SV1030 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5980]) ).
thf(6063,plain,
! [SV426: $i,SV2125: $i,SV2251: $i,SV1031: $i,SV1522: $i] :
( ( ( c_in @ ( c_Pair @ SV1522 @ SV1031 @ SV2251 @ SV2251 ) @ ( c_Transitive__Closure_Ortrancl @ SV2125 @ SV2251 ) @ ( tc_prod @ SV2251 @ SV2251 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV426 @ SV1522 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1522 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 @ SV426 @ SV1522 @ SV2125 @ SV2251 ) @ SV2251 @ SV2251 ) @ ( c_Transitive__Closure_Ortrancl @ SV2125 @ SV2251 ) @ ( tc_prod @ SV2251 @ SV2251 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV426 @ SV1031 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5981]) ).
thf(6064,plain,
! [SV2126: $i,SV2252: $i,SV1032: $i,SV1523: $i,SV427: $i] :
( ( ( hBOOL @ ( hAPP @ SV427 @ SV1523 ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV1523 @ SV1032 @ SV2252 @ SV2252 ) @ ( c_Transitive__Closure_Ortrancl @ SV2126 @ SV2252 ) @ ( tc_prod @ SV2252 @ SV2252 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV427 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2 @ SV427 @ SV1523 @ SV2126 @ SV2252 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV427 @ SV1032 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5982]) ).
thf(6065,plain,
! [SV429: $i,SV2127: $i,SV2253: $i,SV1034: $i,SV1525: $i] :
( ( ( c_in @ ( c_Pair @ SV1525 @ SV1034 @ SV2253 @ SV2253 ) @ ( c_Transitive__Closure_Ortrancl @ SV2127 @ SV2253 ) @ ( tc_prod @ SV2253 @ SV2253 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV429 @ SV1525 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV429 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 @ SV429 @ SV1525 @ SV2127 @ SV2253 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV429 @ SV1034 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5983]) ).
thf(6066,plain,
! [SV2128: $i,SV2254: $i,SV1036: $i,SV1527: $i,SV431: $i] :
( ( ( hBOOL @ ( hAPP @ SV431 @ SV1527 ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV1036 @ SV1527 @ SV2254 @ SV2254 ) @ ( c_Transitive__Closure_Ortrancl @ SV2128 @ SV2254 ) @ ( tc_prod @ SV2254 @ SV2254 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV431 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1 @ SV431 @ SV1527 @ SV2128 @ SV2254 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV431 @ SV1036 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5984]) ).
thf(6067,plain,
! [SV1042: $i,SV437: $i,SV1530: $i,SV2360: $i,SV1879: $i] :
( ( ( c_in @ SV1879 @ SV2360 @ SV1530 )
= $false )
| ( ( ~ ( c_Equiv__Relations_Oequiv @ SV2360 @ SV437 @ SV1530 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1042 @ SV1879 @ SV1530 @ SV1530 ) @ SV437 @ ( tc_prod @ SV1530 @ SV1530 ) )
= $true )
| ( ( ( c_Relation_OImage @ SV437 @ ( c_Set_Oinsert @ SV1042 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1530 @ tc_bool ) ) @ SV1530 ) @ SV1530 @ SV1530 )
= ( c_Relation_OImage @ SV437 @ ( c_Set_Oinsert @ SV1879 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1530 @ tc_bool ) ) @ SV1530 ) @ SV1530 @ SV1530 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5985]) ).
thf(6068,plain,
! [SV2334: $i,SV438: $i,SV1531: $i,SV1880: $i,SV1043: $i] :
( ( ( c_in @ ( c_Pair @ SV1043 @ SV1880 @ SV1531 @ SV1531 ) @ SV438 @ ( tc_prod @ SV1531 @ SV1531 ) )
= $true )
| ( ( ~ ( c_in @ SV1880 @ SV2334 @ SV1531 )
| ~ ( c_in @ SV1043 @ SV2334 @ SV1531 ) )
= $true )
| ( ( c_Equiv__Relations_Oequiv @ SV2334 @ SV438 @ SV1531 )
= $false )
| ( ( ( c_Relation_OImage @ SV438 @ ( c_Set_Oinsert @ SV1043 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1531 @ tc_bool ) ) @ SV1531 ) @ SV1531 @ SV1531 )
= ( c_Relation_OImage @ SV438 @ ( c_Set_Oinsert @ SV1880 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1531 @ tc_bool ) ) @ SV1531 ) @ SV1531 @ SV1531 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5986]) ).
thf(6069,plain,
! [SV439: $i,SV1044: $i,SV1532: $i,SV2361: $i,SV1881: $i] :
( ( ( c_in @ SV1881 @ SV2361 @ SV1532 )
= $false )
| ( ( ~ ( c_in @ SV1044 @ SV2361 @ SV1532 )
| ~ ( c_Equiv__Relations_Oequiv @ SV2361 @ SV439 @ SV1532 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1044 @ SV1881 @ SV1532 @ SV1532 ) @ SV439 @ ( tc_prod @ SV1532 @ SV1532 ) )
= $false )
| ( ( ( c_Relation_OImage @ SV439 @ ( c_Set_Oinsert @ SV1044 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1532 @ tc_bool ) ) @ SV1532 ) @ SV1532 @ SV1532 )
= ( c_Relation_OImage @ SV439 @ ( c_Set_Oinsert @ SV1881 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1532 @ tc_bool ) ) @ SV1532 ) @ SV1532 @ SV1532 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5987]) ).
thf(6070,plain,
! [SV1882: $i,SV440: $i,SV1533: $i,SV2335: $i,SV1045: $i] :
( ( ( ~ ( c_in @ SV1045 @ SV2335 @ SV1533 ) )
= $true )
| ( ( ~ ( c_Equiv__Relations_Oequiv @ SV2335 @ SV440 @ SV1533 )
| ( c_in @ ( c_Pair @ SV1045 @ SV1882 @ SV1533 @ SV1533 ) @ SV440 @ ( tc_prod @ SV1533 @ SV1533 ) ) )
= $true )
| ( ( c_in @ SV1882 @ SV2335 @ SV1533 )
= $false )
| ( ( ( c_Relation_OImage @ SV440 @ ( c_Set_Oinsert @ SV1045 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1533 @ tc_bool ) ) @ SV1533 ) @ SV1533 @ SV1533 )
= ( c_Relation_OImage @ SV440 @ ( c_Set_Oinsert @ SV1882 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1533 @ tc_bool ) ) @ SV1533 ) @ SV1533 @ SV1533 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5988]) ).
thf(6071,plain,
! [SV1047: $i,SV2336: $i,SV1535: $i,SV2131: $i,SV442: $i] :
( ( ( c_in @ ( c_Pair @ SV442 @ SV2131 @ SV1535 @ SV1535 ) @ ( c_Transitive__Closure_Ortrancl @ SV2336 @ SV1535 ) @ ( tc_prod @ SV1535 @ SV1535 ) )
= $false )
| ( ( c_lessequals @ SV2336 @ ( c_Product__Type_OSigma @ SV1047 @ ( c_COMBK @ SV1047 @ ( tc_fun @ SV1535 @ tc_bool ) @ SV1535 ) @ SV1535 @ SV1535 ) @ ( tc_fun @ ( tc_prod @ SV1535 @ SV1535 ) @ tc_bool ) )
= $false )
| ( ( SV442 = SV2131 )
= $true )
| ( ( c_in @ SV442 @ SV1047 @ SV1535 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5989]) ).
thf(6072,plain,
! [SV453: $i,SV1890: $i,SV1546: $i,SV1058: $i,SV2337: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV2337 @ SV1058 @ SV1546 @ SV1546 ) @ ( c_Transitive__Closure_Ortrancl @ SV1890 @ SV1546 ) @ ( tc_prod @ SV1546 @ SV1546 ) ) )
= $true )
| ( ( ~ ( c_Relation_Osingle__valued @ SV1890 @ SV1546 @ SV1546 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV2337 @ SV453 @ SV1546 @ SV1546 ) @ ( c_Transitive__Closure_Ortrancl @ SV1890 @ SV1546 ) @ ( tc_prod @ SV1546 @ SV1546 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1058 @ SV453 @ SV1546 @ SV1546 ) @ ( c_Transitive__Closure_Ortrancl @ SV1890 @ SV1546 ) @ ( tc_prod @ SV1546 @ SV1546 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV453 @ SV1058 @ SV1546 @ SV1546 ) @ ( c_Transitive__Closure_Ortrancl @ SV1890 @ SV1546 ) @ ( tc_prod @ SV1546 @ SV1546 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5992]) ).
thf(6073,plain,
! [SV2146: $i,SV1914: $i,SV1133: $i,SV533: $i,SV2363: $i,SV2268: $i,SV1580: $i] :
( ( ( c_in @ SV1580 @ SV2268 @ SV2363 )
= $false )
| ( ( ! [SY6040: $i] :
( ~ ( c_Equiv__Relations_Ocongruent2 @ SY6040 @ SV533 @ SV1133 @ SV2363 @ SV1914 @ SV2146 )
| ~ ( c_Equiv__Relations_Oequiv @ SV2268 @ SY6040 @ SV2363 ) ) )
= $true )
| ( ( c_Equiv__Relations_Ocongruent @ SV533 @ ( hAPP @ SV1133 @ SV1580 ) @ SV1914 @ SV2146 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5997]) ).
thf(6074,plain,
! [SV546: $i,SV1587: $i,SV2342: $i,SV2269: $i,SV1146: $i] :
( ( ( c_in @ SV1146 @ ( c_Wellfounded_Oacc @ SV2269 @ SV2342 ) @ SV2342 )
= $false )
| ( ( c_in @ ( c_Pair @ SV1587 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ SV546 @ SV2269 @ SV2342 ) @ SV2342 @ SV2342 ) @ SV2269 @ ( tc_prod @ SV2342 @ SV2342 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV546 @ SV1587 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV546 @ SV1146 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5998]) ).
thf(6075,plain,
! [SV548: $i,SV2271: $i,SV1588: $i,SV1148: $i,SV2375: $i] :
( ( ( ~ ( c_in @ SV2375 @ SV1148 @ SV1588 ) )
= $true )
| ( ( ~ ( c_Wellfounded_Owf @ SV2271 @ SV1588 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV548 @ ( c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 @ SV1148 @ SV2271 @ SV1588 ) @ SV1588 @ SV1588 ) @ SV2271 @ ( tc_prod @ SV1588 @ SV1588 ) )
= $false )
| ( ( c_in @ SV548 @ SV1148 @ SV1588 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[6000]) ).
thf(6076,plain,
! [SV559: $i,SV1596: $i,SV2344: $i,SV2274: $i,SV1159: $i] :
( ( ( c_in @ SV1159 @ ( c_Wellfounded_Oacc @ SV2274 @ SV2344 ) @ SV2344 )
= $false )
| ( ( c_in @ ( c_Pair @ SV1596 @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ SV559 @ SV2274 @ SV2344 ) @ SV2344 @ SV2344 ) @ SV2274 @ ( tc_prod @ SV2344 @ SV2344 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV559 @ SV1596 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV559 @ SV1159 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6005]) ).
thf(6077,plain,
! [SV560: $i,SV2275: $i,SV1597: $i,SV1160: $i,SV2376: $i] :
( ( ( ~ ( c_in @ SV2376 @ SV1160 @ SV1597 ) )
= $true )
| ( ( ~ ( c_Wellfounded_Owf @ SV2275 @ SV1597 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV560 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 @ SV1160 @ SV2275 @ SV1597 ) @ SV1597 @ SV1597 ) @ SV2275 @ ( tc_prod @ SV1597 @ SV1597 ) )
= $false )
| ( ( c_in @ SV560 @ SV1160 @ SV1597 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[6006]) ).
thf(6078,plain,
! [SV566: $i,SV2364: $i,SV1930: $i,SV1166: $i,SV2346: $i,SV2277: $i,SV2157: $i,SV1602: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1602 @ SV2157 @ SV2277 @ SV2277 ) @ SV2346 @ ( tc_prod @ SV2277 @ SV2277 ) ) )
= $true )
| ( ( ! [SY6041: $i] :
( ~ ( c_in @ ( c_Pair @ SV1166 @ SV1930 @ SV2364 @ SV2364 ) @ SY6041 @ ( tc_prod @ SV2364 @ SV2364 ) )
| ! [SY6042: $i] :
~ ( c_Equiv__Relations_Ocongruent2 @ SY6041 @ SV2346 @ SV566 @ SV2364 @ SV2277 @ SY6042 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ SV566 @ SV1166 ) @ SV1602 )
= ( hAPP @ ( hAPP @ SV566 @ SV1930 ) @ SV2157 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6008]) ).
thf(6079,plain,
! [SV1167: $i,SV2347: $i,SV2278: $i,SV1931: $i,SV567: $i,SV1603: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1603 @ SV567 @ SV1931 @ SV2278 ) @ SV2347 @ ( tc_prod @ SV1931 @ SV2278 ) ) )
= $true )
| ( ( ~ ( c_Relation_Osingle__valued @ SV2347 @ SV1931 @ SV2278 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1603 @ SV1167 @ SV1931 @ SV2278 ) @ SV2347 @ ( tc_prod @ SV1931 @ SV2278 ) )
= $false )
| ( ( SV567 = SV1167 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6009]) ).
thf(6080,plain,
! [SV1172: $i,SV1936: $i,SV1608: $i,SV2281: $i,SV572: $i] :
( ( ( c_in @ ( c_Pair @ SV572 @ SV2281 @ SV1608 @ SV1608 ) @ SV1936 @ ( tc_prod @ SV1608 @ SV1608 ) )
= $false )
| ( ( ~ ( c_Relation_Otrans @ SV1936 @ SV1608 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV2281 @ SV1172 @ SV1608 @ SV1608 ) @ SV1936 @ ( tc_prod @ SV1608 @ SV1608 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV572 @ SV1172 @ SV1608 @ SV1608 ) @ SV1936 @ ( tc_prod @ SV1608 @ SV1608 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6010]) ).
thf(6081,plain,
! [SV1173: $i,SV1937: $i,SV1609: $i,SV2282: $i,SV573: $i] :
( ( ( c_in @ ( c_Pair @ SV573 @ SV2282 @ SV1609 @ SV1609 ) @ SV1937 @ ( tc_prod @ SV1609 @ SV1609 ) )
= $false )
| ( ( ~ ( c_Relation_Otrans @ SV1937 @ SV1609 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV2282 @ SV1173 @ SV1609 @ SV1609 ) @ SV1937 @ ( tc_prod @ SV1609 @ SV1609 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV573 @ SV1173 @ SV1609 @ SV1609 ) @ SV1937 @ ( tc_prod @ SV1609 @ SV1609 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6011]) ).
thf(6082,plain,
! [SV1187: $i,SV587: $i,SV1948: $i,SV2165: $i] :
( ( ( c_Relation_Oantisym @ SV2165 @ SV1948 )
= $false )
| ( ( c_in @ ( c_Pair @ SV587 @ SV1187 @ SV1948 @ SV1948 ) @ SV2165 @ ( tc_prod @ SV1948 @ SV1948 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1187 @ SV587 @ SV1948 @ SV1948 ) @ SV2165 @ ( tc_prod @ SV1948 @ SV1948 ) )
= $false )
| ( ( SV587 = SV1187 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6018]) ).
thf(6083,plain,
! [SV1188: $i,SV588: $i,SV1949: $i,SV2166: $i] :
( ( ( c_Relation_Oantisym @ SV2166 @ SV1949 )
= $false )
| ( ( c_in @ ( c_Pair @ SV588 @ SV1188 @ SV1949 @ SV1949 ) @ SV2166 @ ( tc_prod @ SV1949 @ SV1949 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1188 @ SV588 @ SV1949 @ SV1949 ) @ SV2166 @ ( tc_prod @ SV1949 @ SV1949 ) )
= $false )
| ( ( SV588 = SV1188 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6019]) ).
thf(6084,plain,
! [SV1623: $i,SV1189: $i,SV2372: $i,SV1950: $i,SV589: $i,SV2288: $i] :
( ( ( c_Equiv__Relations_Ocongruent @ SV2288 @ SV589 @ SV1950 @ SV2372 )
= $false )
| ( ( c_in @ ( c_Pair @ SV1189 @ SV1623 @ SV1950 @ SV1950 ) @ SV2288 @ ( tc_prod @ SV1950 @ SV1950 ) )
= $false )
| ( ( ( hAPP @ SV589 @ SV1189 )
= ( hAPP @ SV589 @ SV1623 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6020]) ).
thf(6085,plain,
! [SV2168: $i,SV1191: $i,SV1952: $i,SV1624: $i,SV2289: $i,SV2373: $i,SV591: $i] :
( ( ( ( hAPP @ SV591 @ SV2373 )
= ( hAPP @ SV2289 @ SV2373 ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV2373 @ SV1624 @ SV1952 @ SV1952 ) @ SV1191 @ ( tc_prod @ SV1952 @ SV1952 ) ) )
= $true )
| ( ( ( c_Recdef_Ocut @ SV591 @ SV1191 @ SV1624 @ SV1952 @ SV2168 )
= ( c_Recdef_Ocut @ SV2289 @ SV1191 @ SV1624 @ SV1952 @ SV2168 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6021]) ).
thf(6086,plain,
! [SV2171: $i,SV1631: $i,SV599: $i,SV2291: $i,SV1958: $i,SV2349: $i,SV1199: $i,SV2374: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV2374 @ SV1199 @ SV2349 @ SV1958 ) @ SV2291 @ ( tc_prod @ SV2349 @ SV1958 ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ SV599 @ SV2374 @ SV1631 @ SV2349 ) @ SV2171 @ ( tc_prod @ SV1631 @ SV2349 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV599 @ SV1199 @ SV1631 @ SV1958 ) @ ( c_Relation_Orel__comp @ SV2171 @ SV2291 @ SV1631 @ SV2349 @ SV1958 ) @ ( tc_prod @ SV1631 @ SV1958 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6022]) ).
thf(6087,plain,
! [SV1965: $i,SV2294: $i,SV1217: $i,SV1642: $i,SV2176: $i,SV617: $i] :
( ( ( c_in @ SV617 @ SV2176 @ SV1642 )
= $false )
| ( ( c_in @ SV1217 @ ( hAPP @ SV2294 @ SV617 ) @ SV1965 )
= $false )
| ( ( c_in @ ( c_Pair @ SV617 @ SV1217 @ SV1642 @ SV1965 ) @ ( c_Product__Type_OSigma @ SV2176 @ SV2294 @ SV1642 @ SV1965 ) @ ( tc_prod @ SV1642 @ SV1965 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6025]) ).
thf(6088,plain,
! [SV1966: $i,SV2295: $i,SV1218: $i,SV1643: $i,SV2177: $i,SV618: $i] :
( ( ( c_in @ SV618 @ SV2177 @ SV1643 )
= $false )
| ( ( c_in @ SV1218 @ ( hAPP @ SV2295 @ SV618 ) @ SV1966 )
= $false )
| ( ( c_in @ ( c_Pair @ SV618 @ SV1218 @ SV1643 @ SV1966 ) @ ( c_Product__Type_OSigma @ SV2177 @ SV2295 @ SV1643 @ SV1966 ) @ ( tc_prod @ SV1643 @ SV1966 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6026]) ).
thf(6089,plain,
! [SV1221: $i,SV2180: $i,SV621: $i,SV1967: $i,SV1646: $i,SV2350: $i] :
( ( ( c_in @ SV2350 @ SV1646 @ SV1967 )
= $false )
| ( ( c_in @ ( c_Pair @ SV2350 @ SV621 @ SV1967 @ SV2180 ) @ SV1221 @ ( tc_prod @ SV1967 @ SV2180 ) )
= $false )
| ( ( c_in @ SV621 @ ( c_Relation_OImage @ SV1221 @ SV1646 @ SV1967 @ SV2180 ) @ SV2180 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6027]) ).
thf(6090,plain,
! [SV1222: $i,SV2181: $i,SV622: $i,SV1968: $i,SV1647: $i,SV2351: $i] :
( ( ( c_in @ SV2351 @ SV1647 @ SV1968 )
= $false )
| ( ( c_in @ ( c_Pair @ SV2351 @ SV622 @ SV1968 @ SV2181 ) @ SV1222 @ ( tc_prod @ SV1968 @ SV2181 ) )
= $false )
| ( ( c_in @ SV622 @ ( c_Relation_OImage @ SV1222 @ SV1647 @ SV1968 @ SV2181 ) @ SV2181 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6028]) ).
thf(6091,plain,
! [SV1975: $i,SV1233: $i,SV1658: $i,SV2365: $i,SV633: $i] :
( ( ( c_in @ SV633 @ SV2365 @ SV1658 )
= $false )
| ( ( ~ ( c_in @ SV1233 @ SV2365 @ SV1658 )
| ~ ( c_Relation_Ototal__on @ SV2365 @ SV1975 @ SV1658 ) )
= $true )
| ( ( SV1233 = SV633 )
= $true )
| ( ( c_in @ ( c_Pair @ SV1233 @ SV633 @ SV1658 @ SV1658 ) @ SV1975 @ ( tc_prod @ SV1658 @ SV1658 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV633 @ SV1233 @ SV1658 @ SV1658 ) @ SV1975 @ ( tc_prod @ SV1658 @ SV1658 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6031]) ).
thf(6092,plain,
! [SV1987: $i,SV2307: $i,SV690: $i,SV1692: $i,SV1282: $i,SV2195: $i,SV40: $i] :
( ( ( c_lessequals @ SV40 @ SV2195 @ ( tc_fun @ ( tc_prod @ SV1282 @ SV1692 ) @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV690 @ SV2307 @ ( tc_fun @ ( tc_prod @ SV1692 @ SV1987 ) @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( c_Relation_Orel__comp @ SV40 @ SV690 @ SV1282 @ SV1692 @ SV1987 ) @ ( c_Relation_Orel__comp @ SV2195 @ SV2307 @ SV1282 @ SV1692 @ SV1987 ) @ ( tc_fun @ ( tc_prod @ SV1282 @ SV1987 ) @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6036]) ).
thf(6093,plain,
! [SV1317: $i,SV2205: $i,SV103: $i,SV1724: $i,SV2015: $i,SV2310: $i,SV2368: $i,SV742: $i] :
( ( ( c_lessequals @ SV742 @ ( c_Product__Type_OSigma @ SV2368 @ ( c_COMBK @ SV2310 @ ( tc_fun @ SV2015 @ tc_bool ) @ SV1724 ) @ SV1724 @ SV2015 ) @ ( tc_fun @ ( tc_prod @ SV1724 @ SV2015 ) @ tc_bool ) )
= $false )
| ( ( ~ ( c_lessequals @ SV103 @ ( c_Product__Type_OSigma @ SV2205 @ ( c_COMBK @ SV2368 @ ( tc_fun @ SV1724 @ tc_bool ) @ SV1317 ) @ SV1317 @ SV1724 ) @ ( tc_fun @ ( tc_prod @ SV1317 @ SV1724 ) @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( c_Relation_Orel__comp @ SV103 @ SV742 @ SV1317 @ SV1724 @ SV2015 ) @ ( c_Product__Type_OSigma @ SV2205 @ ( c_COMBK @ SV2310 @ ( tc_fun @ SV2015 @ tc_bool ) @ SV1317 ) @ SV1317 @ SV2015 ) @ ( tc_fun @ ( tc_prod @ SV1317 @ SV2015 ) @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6040]) ).
thf(6094,plain,
! [SV2233: $i,SV2323: $i,SV333: $i,SV942: $i,SV1459: $i] :
( ( ( c_lessequals @ SV1459 @ SV942 @ SV333 )
= $false )
| ( ( c_lessequals @ SV2323 @ SV2233 @ SV333 )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV942 @ SV1459 @ SV333 )
= ( c_HOL_Ominus__class_Ominus @ SV2233 @ SV2323 @ SV333 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV333 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6048]) ).
thf(6095,plain,
! [SV943: $i,SV1460: $i,SV334: $i,SV2234: $i,SV2324: $i] :
( ( ( c_lessequals @ SV2324 @ SV2234 @ SV334 )
= $false )
| ( ( c_lessequals @ SV1460 @ SV943 @ SV334 )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV943 @ SV1460 @ SV334 )
= ( c_HOL_Ominus__class_Ominus @ SV2234 @ SV2324 @ SV334 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV334 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6049]) ).
thf(6096,plain,
! [SV354: $i,SV960: $i,SV1476: $i,SV1848: $i,SV2239: $i] :
( ( ( c_Equiv__Relations_Oequiv @ SV2239 @ SV1848 @ SV1476 )
= $false )
| ( ( c_lessequals @ ( c_Relation_OImage @ SV1848 @ ( c_Set_Oinsert @ SV960 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1476 @ tc_bool ) ) @ SV1476 ) @ SV1476 @ SV1476 ) @ ( c_Relation_OImage @ SV1848 @ ( c_Set_Oinsert @ SV354 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1476 @ tc_bool ) ) @ SV1476 ) @ SV1476 @ SV1476 ) @ ( tc_fun @ SV1476 @ tc_bool ) )
= $false )
| ( ( c_in @ SV960 @ SV2239 @ SV1476 )
= $false )
| ( ( c_in @ ( c_Pair @ SV354 @ SV960 @ SV1476 @ SV1476 ) @ SV1848 @ ( tc_prod @ SV1476 @ SV1476 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6054]) ).
thf(6097,plain,
! [SV427: $i,SV2126: $i,SV2252: $i,SV1032: $i,SV1523: $i] :
( ( ( c_in @ ( c_Pair @ SV1523 @ SV1032 @ SV2252 @ SV2252 ) @ ( c_Transitive__Closure_Ortrancl @ SV2126 @ SV2252 ) @ ( tc_prod @ SV2252 @ SV2252 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV427 @ SV1523 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV427 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2 @ SV427 @ SV1523 @ SV2126 @ SV2252 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV427 @ SV1032 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6064]) ).
thf(6098,plain,
! [SV431: $i,SV2128: $i,SV2254: $i,SV1527: $i,SV1036: $i] :
( ( ( c_in @ ( c_Pair @ SV1036 @ SV1527 @ SV2254 @ SV2254 ) @ ( c_Transitive__Closure_Ortrancl @ SV2128 @ SV2254 ) @ ( tc_prod @ SV2254 @ SV2254 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV431 @ SV1527 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV431 @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1 @ SV431 @ SV1527 @ SV2128 @ SV2254 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV431 @ SV1036 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6066]) ).
thf(6099,plain,
! [SV1042: $i,SV1879: $i,SV1530: $i,SV437: $i,SV2360: $i] :
( ( ( c_Equiv__Relations_Oequiv @ SV2360 @ SV437 @ SV1530 )
= $false )
| ( ( c_in @ SV1879 @ SV2360 @ SV1530 )
= $false )
| ( ( c_in @ ( c_Pair @ SV1042 @ SV1879 @ SV1530 @ SV1530 ) @ SV437 @ ( tc_prod @ SV1530 @ SV1530 ) )
= $true )
| ( ( ( c_Relation_OImage @ SV437 @ ( c_Set_Oinsert @ SV1042 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1530 @ tc_bool ) ) @ SV1530 ) @ SV1530 @ SV1530 )
= ( c_Relation_OImage @ SV437 @ ( c_Set_Oinsert @ SV1879 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1530 @ tc_bool ) ) @ SV1530 ) @ SV1530 @ SV1530 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6067]) ).
thf(6100,plain,
! [SV438: $i,SV1043: $i,SV1531: $i,SV2334: $i,SV1880: $i] :
( ( ( ~ ( c_in @ SV1880 @ SV2334 @ SV1531 ) )
= $true )
| ( ( ~ ( c_in @ SV1043 @ SV2334 @ SV1531 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1043 @ SV1880 @ SV1531 @ SV1531 ) @ SV438 @ ( tc_prod @ SV1531 @ SV1531 ) )
= $true )
| ( ( c_Equiv__Relations_Oequiv @ SV2334 @ SV438 @ SV1531 )
= $false )
| ( ( ( c_Relation_OImage @ SV438 @ ( c_Set_Oinsert @ SV1043 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1531 @ tc_bool ) ) @ SV1531 ) @ SV1531 @ SV1531 )
= ( c_Relation_OImage @ SV438 @ ( c_Set_Oinsert @ SV1880 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1531 @ tc_bool ) ) @ SV1531 ) @ SV1531 @ SV1531 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6068]) ).
thf(6101,plain,
! [SV1881: $i,SV439: $i,SV1532: $i,SV2361: $i,SV1044: $i] :
( ( ( ~ ( c_in @ SV1044 @ SV2361 @ SV1532 ) )
= $true )
| ( ( ~ ( c_Equiv__Relations_Oequiv @ SV2361 @ SV439 @ SV1532 ) )
= $true )
| ( ( c_in @ SV1881 @ SV2361 @ SV1532 )
= $false )
| ( ( c_in @ ( c_Pair @ SV1044 @ SV1881 @ SV1532 @ SV1532 ) @ SV439 @ ( tc_prod @ SV1532 @ SV1532 ) )
= $false )
| ( ( ( c_Relation_OImage @ SV439 @ ( c_Set_Oinsert @ SV1044 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1532 @ tc_bool ) ) @ SV1532 ) @ SV1532 @ SV1532 )
= ( c_Relation_OImage @ SV439 @ ( c_Set_Oinsert @ SV1881 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1532 @ tc_bool ) ) @ SV1532 ) @ SV1532 @ SV1532 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6069]) ).
thf(6102,plain,
! [SV1882: $i,SV440: $i,SV1533: $i,SV2335: $i,SV1045: $i] :
( ( ( c_in @ SV1045 @ SV2335 @ SV1533 )
= $false )
| ( ( ~ ( c_Equiv__Relations_Oequiv @ SV2335 @ SV440 @ SV1533 )
| ( c_in @ ( c_Pair @ SV1045 @ SV1882 @ SV1533 @ SV1533 ) @ SV440 @ ( tc_prod @ SV1533 @ SV1533 ) ) )
= $true )
| ( ( c_in @ SV1882 @ SV2335 @ SV1533 )
= $false )
| ( ( ( c_Relation_OImage @ SV440 @ ( c_Set_Oinsert @ SV1045 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1533 @ tc_bool ) ) @ SV1533 ) @ SV1533 @ SV1533 )
= ( c_Relation_OImage @ SV440 @ ( c_Set_Oinsert @ SV1882 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1533 @ tc_bool ) ) @ SV1533 ) @ SV1533 @ SV1533 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6070]) ).
thf(6103,plain,
! [SV453: $i,SV1890: $i,SV1546: $i,SV1058: $i,SV2337: $i] :
( ( ( c_in @ ( c_Pair @ SV2337 @ SV1058 @ SV1546 @ SV1546 ) @ ( c_Transitive__Closure_Ortrancl @ SV1890 @ SV1546 ) @ ( tc_prod @ SV1546 @ SV1546 ) )
= $false )
| ( ( ~ ( c_Relation_Osingle__valued @ SV1890 @ SV1546 @ SV1546 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV2337 @ SV453 @ SV1546 @ SV1546 ) @ ( c_Transitive__Closure_Ortrancl @ SV1890 @ SV1546 ) @ ( tc_prod @ SV1546 @ SV1546 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1058 @ SV453 @ SV1546 @ SV1546 ) @ ( c_Transitive__Closure_Ortrancl @ SV1890 @ SV1546 ) @ ( tc_prod @ SV1546 @ SV1546 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV453 @ SV1058 @ SV1546 @ SV1546 ) @ ( c_Transitive__Closure_Ortrancl @ SV1890 @ SV1546 ) @ ( tc_prod @ SV1546 @ SV1546 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6072]) ).
thf(6104,plain,
! [SV1580: $i,SV2268: $i,SV2146: $i,SV1914: $i,SV2363: $i,SV1133: $i,SV533: $i,SV2377: $i] :
( ( ( ~ ( c_Equiv__Relations_Ocongruent2 @ SV2377 @ SV533 @ SV1133 @ SV2363 @ SV1914 @ SV2146 )
| ~ ( c_Equiv__Relations_Oequiv @ SV2268 @ SV2377 @ SV2363 ) )
= $true )
| ( ( c_in @ SV1580 @ SV2268 @ SV2363 )
= $false )
| ( ( c_Equiv__Relations_Ocongruent @ SV533 @ ( hAPP @ SV1133 @ SV1580 ) @ SV1914 @ SV2146 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6073]) ).
thf(6105,plain,
! [SV548: $i,SV2271: $i,SV1588: $i,SV1148: $i,SV2375: $i] :
( ( ( c_in @ SV2375 @ SV1148 @ SV1588 )
= $false )
| ( ( ~ ( c_Wellfounded_Owf @ SV2271 @ SV1588 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV548 @ ( c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 @ SV1148 @ SV2271 @ SV1588 ) @ SV1588 @ SV1588 ) @ SV2271 @ ( tc_prod @ SV1588 @ SV1588 ) )
= $false )
| ( ( c_in @ SV548 @ SV1148 @ SV1588 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6075]) ).
thf(6106,plain,
! [SV560: $i,SV2275: $i,SV1597: $i,SV1160: $i,SV2376: $i] :
( ( ( c_in @ SV2376 @ SV1160 @ SV1597 )
= $false )
| ( ( ~ ( c_Wellfounded_Owf @ SV2275 @ SV1597 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV560 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 @ SV1160 @ SV2275 @ SV1597 ) @ SV1597 @ SV1597 ) @ SV2275 @ ( tc_prod @ SV1597 @ SV1597 ) )
= $false )
| ( ( c_in @ SV560 @ SV1160 @ SV1597 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6077]) ).
thf(6107,plain,
! [SV566: $i,SV2364: $i,SV1930: $i,SV1166: $i,SV2346: $i,SV2277: $i,SV2157: $i,SV1602: $i] :
( ( ( c_in @ ( c_Pair @ SV1602 @ SV2157 @ SV2277 @ SV2277 ) @ SV2346 @ ( tc_prod @ SV2277 @ SV2277 ) )
= $false )
| ( ( ! [SY6041: $i] :
( ~ ( c_in @ ( c_Pair @ SV1166 @ SV1930 @ SV2364 @ SV2364 ) @ SY6041 @ ( tc_prod @ SV2364 @ SV2364 ) )
| ! [SY6042: $i] :
~ ( c_Equiv__Relations_Ocongruent2 @ SY6041 @ SV2346 @ SV566 @ SV2364 @ SV2277 @ SY6042 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ SV566 @ SV1166 ) @ SV1602 )
= ( hAPP @ ( hAPP @ SV566 @ SV1930 ) @ SV2157 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6078]) ).
thf(6108,plain,
! [SV1167: $i,SV2347: $i,SV2278: $i,SV1931: $i,SV567: $i,SV1603: $i] :
( ( ( c_in @ ( c_Pair @ SV1603 @ SV567 @ SV1931 @ SV2278 ) @ SV2347 @ ( tc_prod @ SV1931 @ SV2278 ) )
= $false )
| ( ( ~ ( c_Relation_Osingle__valued @ SV2347 @ SV1931 @ SV2278 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1603 @ SV1167 @ SV1931 @ SV2278 ) @ SV2347 @ ( tc_prod @ SV1931 @ SV2278 ) )
= $false )
| ( ( SV567 = SV1167 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6079]) ).
thf(6109,plain,
! [SV1172: $i,SV2281: $i,SV572: $i,SV1608: $i,SV1936: $i] :
( ( ( c_Relation_Otrans @ SV1936 @ SV1608 )
= $false )
| ( ( c_in @ ( c_Pair @ SV572 @ SV2281 @ SV1608 @ SV1608 ) @ SV1936 @ ( tc_prod @ SV1608 @ SV1608 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV2281 @ SV1172 @ SV1608 @ SV1608 ) @ SV1936 @ ( tc_prod @ SV1608 @ SV1608 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV572 @ SV1172 @ SV1608 @ SV1608 ) @ SV1936 @ ( tc_prod @ SV1608 @ SV1608 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6080]) ).
thf(6110,plain,
! [SV1173: $i,SV2282: $i,SV573: $i,SV1609: $i,SV1937: $i] :
( ( ( c_Relation_Otrans @ SV1937 @ SV1609 )
= $false )
| ( ( c_in @ ( c_Pair @ SV573 @ SV2282 @ SV1609 @ SV1609 ) @ SV1937 @ ( tc_prod @ SV1609 @ SV1609 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV2282 @ SV1173 @ SV1609 @ SV1609 ) @ SV1937 @ ( tc_prod @ SV1609 @ SV1609 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV573 @ SV1173 @ SV1609 @ SV1609 ) @ SV1937 @ ( tc_prod @ SV1609 @ SV1609 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6081]) ).
thf(6111,plain,
! [SV2168: $i,SV2289: $i,SV591: $i,SV1191: $i,SV1952: $i,SV1624: $i,SV2373: $i] :
( ( ( c_in @ ( c_Pair @ SV2373 @ SV1624 @ SV1952 @ SV1952 ) @ SV1191 @ ( tc_prod @ SV1952 @ SV1952 ) )
= $false )
| ( ( ( hAPP @ SV591 @ SV2373 )
= ( hAPP @ SV2289 @ SV2373 ) )
= $true )
| ( ( ( c_Recdef_Ocut @ SV591 @ SV1191 @ SV1624 @ SV1952 @ SV2168 )
= ( c_Recdef_Ocut @ SV2289 @ SV1191 @ SV1624 @ SV1952 @ SV2168 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6085]) ).
thf(6112,plain,
! [SV2171: $i,SV1631: $i,SV599: $i,SV2291: $i,SV1958: $i,SV2349: $i,SV1199: $i,SV2374: $i] :
( ( ( c_in @ ( c_Pair @ SV2374 @ SV1199 @ SV2349 @ SV1958 ) @ SV2291 @ ( tc_prod @ SV2349 @ SV1958 ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ SV599 @ SV2374 @ SV1631 @ SV2349 ) @ SV2171 @ ( tc_prod @ SV1631 @ SV2349 ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV599 @ SV1199 @ SV1631 @ SV1958 ) @ ( c_Relation_Orel__comp @ SV2171 @ SV2291 @ SV1631 @ SV2349 @ SV1958 ) @ ( tc_prod @ SV1631 @ SV1958 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6086]) ).
thf(6113,plain,
! [SV633: $i,SV1975: $i,SV1658: $i,SV2365: $i,SV1233: $i] :
( ( ( ~ ( c_in @ SV1233 @ SV2365 @ SV1658 ) )
= $true )
| ( ( ~ ( c_Relation_Ototal__on @ SV2365 @ SV1975 @ SV1658 ) )
= $true )
| ( ( c_in @ SV633 @ SV2365 @ SV1658 )
= $false )
| ( ( SV1233 = SV633 )
= $true )
| ( ( c_in @ ( c_Pair @ SV1233 @ SV633 @ SV1658 @ SV1658 ) @ SV1975 @ ( tc_prod @ SV1658 @ SV1658 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV633 @ SV1233 @ SV1658 @ SV1658 ) @ SV1975 @ ( tc_prod @ SV1658 @ SV1658 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6091]) ).
thf(6114,plain,
! [SV2015: $i,SV2310: $i,SV742: $i,SV1317: $i,SV1724: $i,SV2368: $i,SV2205: $i,SV103: $i] :
( ( ( c_lessequals @ SV103 @ ( c_Product__Type_OSigma @ SV2205 @ ( c_COMBK @ SV2368 @ ( tc_fun @ SV1724 @ tc_bool ) @ SV1317 ) @ SV1317 @ SV1724 ) @ ( tc_fun @ ( tc_prod @ SV1317 @ SV1724 ) @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV742 @ ( c_Product__Type_OSigma @ SV2368 @ ( c_COMBK @ SV2310 @ ( tc_fun @ SV2015 @ tc_bool ) @ SV1724 ) @ SV1724 @ SV2015 ) @ ( tc_fun @ ( tc_prod @ SV1724 @ SV2015 ) @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( c_Relation_Orel__comp @ SV103 @ SV742 @ SV1317 @ SV1724 @ SV2015 ) @ ( c_Product__Type_OSigma @ SV2205 @ ( c_COMBK @ SV2310 @ ( tc_fun @ SV2015 @ tc_bool ) @ SV1317 ) @ SV1317 @ SV2015 ) @ ( tc_fun @ ( tc_prod @ SV1317 @ SV2015 ) @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6093]) ).
thf(6115,plain,
! [SV438: $i,SV1043: $i,SV1531: $i,SV2334: $i,SV1880: $i] :
( ( ( c_in @ SV1880 @ SV2334 @ SV1531 )
= $false )
| ( ( ~ ( c_in @ SV1043 @ SV2334 @ SV1531 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1043 @ SV1880 @ SV1531 @ SV1531 ) @ SV438 @ ( tc_prod @ SV1531 @ SV1531 ) )
= $true )
| ( ( c_Equiv__Relations_Oequiv @ SV2334 @ SV438 @ SV1531 )
= $false )
| ( ( ( c_Relation_OImage @ SV438 @ ( c_Set_Oinsert @ SV1043 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1531 @ tc_bool ) ) @ SV1531 ) @ SV1531 @ SV1531 )
= ( c_Relation_OImage @ SV438 @ ( c_Set_Oinsert @ SV1880 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1531 @ tc_bool ) ) @ SV1531 ) @ SV1531 @ SV1531 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6100]) ).
thf(6116,plain,
! [SV1881: $i,SV439: $i,SV1532: $i,SV2361: $i,SV1044: $i] :
( ( ( c_in @ SV1044 @ SV2361 @ SV1532 )
= $false )
| ( ( ~ ( c_Equiv__Relations_Oequiv @ SV2361 @ SV439 @ SV1532 ) )
= $true )
| ( ( c_in @ SV1881 @ SV2361 @ SV1532 )
= $false )
| ( ( c_in @ ( c_Pair @ SV1044 @ SV1881 @ SV1532 @ SV1532 ) @ SV439 @ ( tc_prod @ SV1532 @ SV1532 ) )
= $false )
| ( ( ( c_Relation_OImage @ SV439 @ ( c_Set_Oinsert @ SV1044 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1532 @ tc_bool ) ) @ SV1532 ) @ SV1532 @ SV1532 )
= ( c_Relation_OImage @ SV439 @ ( c_Set_Oinsert @ SV1881 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1532 @ tc_bool ) ) @ SV1532 ) @ SV1532 @ SV1532 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6101]) ).
thf(6117,plain,
! [SV1882: $i,SV1045: $i,SV1533: $i,SV440: $i,SV2335: $i] :
( ( ( ~ ( c_Equiv__Relations_Oequiv @ SV2335 @ SV440 @ SV1533 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1045 @ SV1882 @ SV1533 @ SV1533 ) @ SV440 @ ( tc_prod @ SV1533 @ SV1533 ) )
= $true )
| ( ( c_in @ SV1045 @ SV2335 @ SV1533 )
= $false )
| ( ( c_in @ SV1882 @ SV2335 @ SV1533 )
= $false )
| ( ( ( c_Relation_OImage @ SV440 @ ( c_Set_Oinsert @ SV1045 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1533 @ tc_bool ) ) @ SV1533 ) @ SV1533 @ SV1533 )
= ( c_Relation_OImage @ SV440 @ ( c_Set_Oinsert @ SV1882 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1533 @ tc_bool ) ) @ SV1533 ) @ SV1533 @ SV1533 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6102]) ).
thf(6118,plain,
! [SV453: $i,SV1058: $i,SV2337: $i,SV1546: $i,SV1890: $i] :
( ( ( c_Relation_Osingle__valued @ SV1890 @ SV1546 @ SV1546 )
= $false )
| ( ( c_in @ ( c_Pair @ SV2337 @ SV1058 @ SV1546 @ SV1546 ) @ ( c_Transitive__Closure_Ortrancl @ SV1890 @ SV1546 ) @ ( tc_prod @ SV1546 @ SV1546 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV2337 @ SV453 @ SV1546 @ SV1546 ) @ ( c_Transitive__Closure_Ortrancl @ SV1890 @ SV1546 ) @ ( tc_prod @ SV1546 @ SV1546 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1058 @ SV453 @ SV1546 @ SV1546 ) @ ( c_Transitive__Closure_Ortrancl @ SV1890 @ SV1546 ) @ ( tc_prod @ SV1546 @ SV1546 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV453 @ SV1058 @ SV1546 @ SV1546 ) @ ( c_Transitive__Closure_Ortrancl @ SV1890 @ SV1546 ) @ ( tc_prod @ SV1546 @ SV1546 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6103]) ).
thf(6119,plain,
! [SV1580: $i,SV2268: $i,SV2146: $i,SV1914: $i,SV2363: $i,SV1133: $i,SV533: $i,SV2377: $i] :
( ( ( ~ ( c_Equiv__Relations_Ocongruent2 @ SV2377 @ SV533 @ SV1133 @ SV2363 @ SV1914 @ SV2146 ) )
= $true )
| ( ( ~ ( c_Equiv__Relations_Oequiv @ SV2268 @ SV2377 @ SV2363 ) )
= $true )
| ( ( c_in @ SV1580 @ SV2268 @ SV2363 )
= $false )
| ( ( c_Equiv__Relations_Ocongruent @ SV533 @ ( hAPP @ SV1133 @ SV1580 ) @ SV1914 @ SV2146 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6104]) ).
thf(6120,plain,
! [SV548: $i,SV1148: $i,SV2375: $i,SV1588: $i,SV2271: $i] :
( ( ( c_Wellfounded_Owf @ SV2271 @ SV1588 )
= $false )
| ( ( c_in @ SV2375 @ SV1148 @ SV1588 )
= $false )
| ( ( c_in @ ( c_Pair @ SV548 @ ( c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 @ SV1148 @ SV2271 @ SV1588 ) @ SV1588 @ SV1588 ) @ SV2271 @ ( tc_prod @ SV1588 @ SV1588 ) )
= $false )
| ( ( c_in @ SV548 @ SV1148 @ SV1588 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6105]) ).
thf(6121,plain,
! [SV560: $i,SV1160: $i,SV2376: $i,SV1597: $i,SV2275: $i] :
( ( ( c_Wellfounded_Owf @ SV2275 @ SV1597 )
= $false )
| ( ( c_in @ SV2376 @ SV1160 @ SV1597 )
= $false )
| ( ( c_in @ ( c_Pair @ SV560 @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 @ SV1160 @ SV2275 @ SV1597 ) @ SV1597 @ SV1597 ) @ SV2275 @ ( tc_prod @ SV1597 @ SV1597 ) )
= $false )
| ( ( c_in @ SV560 @ SV1160 @ SV1597 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6106]) ).
thf(6122,plain,
! [SV2157: $i,SV1602: $i,SV2277: $i,SV566: $i,SV2346: $i,SV2378: $i,SV2364: $i,SV1930: $i,SV1166: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1166 @ SV1930 @ SV2364 @ SV2364 ) @ SV2378 @ ( tc_prod @ SV2364 @ SV2364 ) )
| ! [SY6043: $i] :
~ ( c_Equiv__Relations_Ocongruent2 @ SV2378 @ SV2346 @ SV566 @ SV2364 @ SV2277 @ SY6043 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1602 @ SV2157 @ SV2277 @ SV2277 ) @ SV2346 @ ( tc_prod @ SV2277 @ SV2277 ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV566 @ SV1166 ) @ SV1602 )
= ( hAPP @ ( hAPP @ SV566 @ SV1930 ) @ SV2157 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6107]) ).
thf(6123,plain,
! [SV1167: $i,SV567: $i,SV1603: $i,SV2278: $i,SV1931: $i,SV2347: $i] :
( ( ( c_Relation_Osingle__valued @ SV2347 @ SV1931 @ SV2278 )
= $false )
| ( ( c_in @ ( c_Pair @ SV1603 @ SV567 @ SV1931 @ SV2278 ) @ SV2347 @ ( tc_prod @ SV1931 @ SV2278 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1603 @ SV1167 @ SV1931 @ SV2278 ) @ SV2347 @ ( tc_prod @ SV1931 @ SV2278 ) )
= $false )
| ( ( SV567 = SV1167 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6108]) ).
thf(6124,plain,
! [SV2291: $i,SV1958: $i,SV1199: $i,SV2171: $i,SV2349: $i,SV1631: $i,SV2374: $i,SV599: $i] :
( ( ( c_in @ ( c_Pair @ SV599 @ SV2374 @ SV1631 @ SV2349 ) @ SV2171 @ ( tc_prod @ SV1631 @ SV2349 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV2374 @ SV1199 @ SV2349 @ SV1958 ) @ SV2291 @ ( tc_prod @ SV2349 @ SV1958 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV599 @ SV1199 @ SV1631 @ SV1958 ) @ ( c_Relation_Orel__comp @ SV2171 @ SV2291 @ SV1631 @ SV2349 @ SV1958 ) @ ( tc_prod @ SV1631 @ SV1958 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6112]) ).
thf(6125,plain,
! [SV633: $i,SV1975: $i,SV1658: $i,SV2365: $i,SV1233: $i] :
( ( ( c_in @ SV1233 @ SV2365 @ SV1658 )
= $false )
| ( ( ~ ( c_Relation_Ototal__on @ SV2365 @ SV1975 @ SV1658 ) )
= $true )
| ( ( c_in @ SV633 @ SV2365 @ SV1658 )
= $false )
| ( ( SV1233 = SV633 )
= $true )
| ( ( c_in @ ( c_Pair @ SV1233 @ SV633 @ SV1658 @ SV1658 ) @ SV1975 @ ( tc_prod @ SV1658 @ SV1658 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV633 @ SV1233 @ SV1658 @ SV1658 ) @ SV1975 @ ( tc_prod @ SV1658 @ SV1658 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6113]) ).
thf(6126,plain,
! [SV438: $i,SV1880: $i,SV1531: $i,SV2334: $i,SV1043: $i] :
( ( ( c_in @ SV1043 @ SV2334 @ SV1531 )
= $false )
| ( ( c_in @ SV1880 @ SV2334 @ SV1531 )
= $false )
| ( ( c_in @ ( c_Pair @ SV1043 @ SV1880 @ SV1531 @ SV1531 ) @ SV438 @ ( tc_prod @ SV1531 @ SV1531 ) )
= $true )
| ( ( c_Equiv__Relations_Oequiv @ SV2334 @ SV438 @ SV1531 )
= $false )
| ( ( ( c_Relation_OImage @ SV438 @ ( c_Set_Oinsert @ SV1043 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1531 @ tc_bool ) ) @ SV1531 ) @ SV1531 @ SV1531 )
= ( c_Relation_OImage @ SV438 @ ( c_Set_Oinsert @ SV1880 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1531 @ tc_bool ) ) @ SV1531 ) @ SV1531 @ SV1531 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6115]) ).
thf(6127,plain,
! [SV1881: $i,SV1044: $i,SV1532: $i,SV439: $i,SV2361: $i] :
( ( ( c_Equiv__Relations_Oequiv @ SV2361 @ SV439 @ SV1532 )
= $false )
| ( ( c_in @ SV1044 @ SV2361 @ SV1532 )
= $false )
| ( ( c_in @ SV1881 @ SV2361 @ SV1532 )
= $false )
| ( ( c_in @ ( c_Pair @ SV1044 @ SV1881 @ SV1532 @ SV1532 ) @ SV439 @ ( tc_prod @ SV1532 @ SV1532 ) )
= $false )
| ( ( ( c_Relation_OImage @ SV439 @ ( c_Set_Oinsert @ SV1044 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1532 @ tc_bool ) ) @ SV1532 ) @ SV1532 @ SV1532 )
= ( c_Relation_OImage @ SV439 @ ( c_Set_Oinsert @ SV1881 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1532 @ tc_bool ) ) @ SV1532 ) @ SV1532 @ SV1532 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6116]) ).
thf(6128,plain,
! [SV1882: $i,SV1045: $i,SV1533: $i,SV440: $i,SV2335: $i] :
( ( ( c_Equiv__Relations_Oequiv @ SV2335 @ SV440 @ SV1533 )
= $false )
| ( ( c_in @ ( c_Pair @ SV1045 @ SV1882 @ SV1533 @ SV1533 ) @ SV440 @ ( tc_prod @ SV1533 @ SV1533 ) )
= $true )
| ( ( c_in @ SV1045 @ SV2335 @ SV1533 )
= $false )
| ( ( c_in @ SV1882 @ SV2335 @ SV1533 )
= $false )
| ( ( ( c_Relation_OImage @ SV440 @ ( c_Set_Oinsert @ SV1045 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1533 @ tc_bool ) ) @ SV1533 ) @ SV1533 @ SV1533 )
= ( c_Relation_OImage @ SV440 @ ( c_Set_Oinsert @ SV1882 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1533 @ tc_bool ) ) @ SV1533 ) @ SV1533 @ SV1533 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6117]) ).
thf(6129,plain,
! [SV1580: $i,SV2268: $i,SV2146: $i,SV1914: $i,SV2363: $i,SV1133: $i,SV533: $i,SV2377: $i] :
( ( ( c_Equiv__Relations_Ocongruent2 @ SV2377 @ SV533 @ SV1133 @ SV2363 @ SV1914 @ SV2146 )
= $false )
| ( ( ~ ( c_Equiv__Relations_Oequiv @ SV2268 @ SV2377 @ SV2363 ) )
= $true )
| ( ( c_in @ SV1580 @ SV2268 @ SV2363 )
= $false )
| ( ( c_Equiv__Relations_Ocongruent @ SV533 @ ( hAPP @ SV1133 @ SV1580 ) @ SV1914 @ SV2146 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6119]) ).
thf(6130,plain,
! [SV2157: $i,SV1602: $i,SV2277: $i,SV566: $i,SV2346: $i,SV2378: $i,SV2364: $i,SV1930: $i,SV1166: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV1166 @ SV1930 @ SV2364 @ SV2364 ) @ SV2378 @ ( tc_prod @ SV2364 @ SV2364 ) ) )
= $true )
| ( ( ! [SY6043: $i] :
~ ( c_Equiv__Relations_Ocongruent2 @ SV2378 @ SV2346 @ SV566 @ SV2364 @ SV2277 @ SY6043 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1602 @ SV2157 @ SV2277 @ SV2277 ) @ SV2346 @ ( tc_prod @ SV2277 @ SV2277 ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV566 @ SV1166 ) @ SV1602 )
= ( hAPP @ ( hAPP @ SV566 @ SV1930 ) @ SV2157 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6122]) ).
thf(6131,plain,
! [SV633: $i,SV1233: $i,SV1658: $i,SV1975: $i,SV2365: $i] :
( ( ( c_Relation_Ototal__on @ SV2365 @ SV1975 @ SV1658 )
= $false )
| ( ( c_in @ SV1233 @ SV2365 @ SV1658 )
= $false )
| ( ( c_in @ SV633 @ SV2365 @ SV1658 )
= $false )
| ( ( SV1233 = SV633 )
= $true )
| ( ( c_in @ ( c_Pair @ SV1233 @ SV633 @ SV1658 @ SV1658 ) @ SV1975 @ ( tc_prod @ SV1658 @ SV1658 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV633 @ SV1233 @ SV1658 @ SV1658 ) @ SV1975 @ ( tc_prod @ SV1658 @ SV1658 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6125]) ).
thf(6132,plain,
! [SV1580: $i,SV2146: $i,SV1914: $i,SV1133: $i,SV533: $i,SV2363: $i,SV2377: $i,SV2268: $i] :
( ( ( c_Equiv__Relations_Oequiv @ SV2268 @ SV2377 @ SV2363 )
= $false )
| ( ( c_Equiv__Relations_Ocongruent2 @ SV2377 @ SV533 @ SV1133 @ SV2363 @ SV1914 @ SV2146 )
= $false )
| ( ( c_in @ SV1580 @ SV2268 @ SV2363 )
= $false )
| ( ( c_Equiv__Relations_Ocongruent @ SV533 @ ( hAPP @ SV1133 @ SV1580 ) @ SV1914 @ SV2146 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6129]) ).
thf(6133,plain,
! [SV2157: $i,SV1602: $i,SV2277: $i,SV566: $i,SV2346: $i,SV2378: $i,SV2364: $i,SV1930: $i,SV1166: $i] :
( ( ( c_in @ ( c_Pair @ SV1166 @ SV1930 @ SV2364 @ SV2364 ) @ SV2378 @ ( tc_prod @ SV2364 @ SV2364 ) )
= $false )
| ( ( ! [SY6043: $i] :
~ ( c_Equiv__Relations_Ocongruent2 @ SV2378 @ SV2346 @ SV566 @ SV2364 @ SV2277 @ SY6043 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1602 @ SV2157 @ SV2277 @ SV2277 ) @ SV2346 @ ( tc_prod @ SV2277 @ SV2277 ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV566 @ SV1166 ) @ SV1602 )
= ( hAPP @ ( hAPP @ SV566 @ SV1930 ) @ SV2157 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6130]) ).
thf(6134,plain,
! [SV2157: $i,SV1602: $i,SV1930: $i,SV1166: $i,SV2379: $i,SV2277: $i,SV2364: $i,SV566: $i,SV2346: $i,SV2378: $i] :
( ( ( ~ ( c_Equiv__Relations_Ocongruent2 @ SV2378 @ SV2346 @ SV566 @ SV2364 @ SV2277 @ SV2379 ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV1166 @ SV1930 @ SV2364 @ SV2364 ) @ SV2378 @ ( tc_prod @ SV2364 @ SV2364 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1602 @ SV2157 @ SV2277 @ SV2277 ) @ SV2346 @ ( tc_prod @ SV2277 @ SV2277 ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV566 @ SV1166 ) @ SV1602 )
= ( hAPP @ ( hAPP @ SV566 @ SV1930 ) @ SV2157 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6133]) ).
thf(6135,plain,
! [SV2157: $i,SV1602: $i,SV1930: $i,SV1166: $i,SV2379: $i,SV2277: $i,SV2364: $i,SV566: $i,SV2346: $i,SV2378: $i] :
( ( ( c_Equiv__Relations_Ocongruent2 @ SV2378 @ SV2346 @ SV566 @ SV2364 @ SV2277 @ SV2379 )
= $false )
| ( ( c_in @ ( c_Pair @ SV1166 @ SV1930 @ SV2364 @ SV2364 ) @ SV2378 @ ( tc_prod @ SV2364 @ SV2364 ) )
= $false )
| ( ( c_in @ ( c_Pair @ SV1602 @ SV2157 @ SV2277 @ SV2277 ) @ SV2346 @ ( tc_prod @ SV2277 @ SV2277 ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV566 @ SV1166 ) @ SV1602 )
= ( hAPP @ ( hAPP @ SV566 @ SV1930 ) @ SV2157 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6134]) ).
thf(6136,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[2022,6135,6132,6131,6128,6127,6126,6124,6123,6121,6120,6118,6114,6111,6110,6109,6099,6098,6097,6096,6095,6094,6092,6090,6089,6088,6087,6084,6083,6082,6076,6074,6071,6065,6063,6062,6061,6060,6059,6058,6057,6056,6055,6053,6052,6051,6050,6047,6046,6045,6044,6043,6042,6041,6039,6038,6037,6035,6034,6033,6032,6030,6029,6024,6023,6017,6016,6015,6014,6013,6012,6007,6004,6003,6002,6001,5999,5996,5995,5994,5993,5991,5990,5974,5973,5972,5971,5970,5960,5955,5951,5950,5949,5948,5947,5946,5945,5944,5943,5942,5940,5933,5932,5931,5928,5926,5925,5920,5919,5916,5915,5914,5913,5909,5908,5907,5906,5893,5892,5882,5881,5876,5874,5873,5872,5845,5840,5834,5833,5831,5830,5829,5828,5825,5824,5823,5822,5821,5820,5819,5816,5815,5814,5813,5812,5811,5810,5808,5807,5806,5805,5804,5803,5802,5801,5800,5799,5798,5793,5792,5791,5790,5785,5784,5783,5772,5771,5770,5769,5768,5767,5765,5764,5763,5760,5759,5758,5748,5747,5746,5745,5736,5733,5713,5712,5711,5708,5707,5701,5700,5688,5687,5684,5681,5679,5678,5677,5675,5674,5673,5672,5671,5666,5665,5664,5656,5655,5648,5647,5646,5641,5640,5639,5638,5635,5634,5632,5631,5626,5625,5623,5620,5616,5615,5613,5612,5611,5604,5602,5601,5586,5585,5584,5583,5582,5573,5564,5563,5562,5561,5560,5559,5558,5546,5545,5544,5540,5539,5535,5532,5529,5526,5525,5518,5517,5516,5510,5509,5485,5465,5463,5457,5452,5439,5436,5432,5426,5415,5413,5412,5400,5399,5398,5397,5394,5392,5391,5380,5376,5374,5362,5360,5357,5356,5355,5349,5345,5344,5343,5339,5338,5337,5323,5320,5313,5312,5310,5300,5299,5291,5290,5284,5283,5282,5281,5277,5276,5271,5270,5266,5264,5263,5261,5260,5251,5250,5249,5248,5241,5240,5238,5231,5230,5213,5208,5207,5206,5205,5204,5201,5200,5196,5195,5183,5182,5181,5180,5174,5173,5165,5164,5163,5159,5158,5157,5156,5140,5131,5128,5116,5115,5070,5069,5068,5066,5065,5063,5061,5054,5053,5052,5050,5044,5023,5022,4989,4986,4985,4983,4974,4973,4972,4971,4951,4949,4947,4945,4916,4915,4914,4913,4912,4911,4909,4904,4893,4876,4872,4870,4869,4868,4867,4866,4865,4852,4851,4850,4849,4848,4842,4840,4839,4836,4833,4832,4828,4827,4825,4822,4821,4815,4814,4813,4809,4807,4799,4794,4786,4779,4776,4775,4774,4772,4769,4768,4767,4766,4765,4762,4761,4754,4753,4748,4743,4742,4740,4737,4736,4735,4719,4718,4717,4716,4715,4714,4713,4712,4711,4681,4678,4630,4626,4621,4609,4608,4604,4602,4600,4599,4598,4594,4593,4592,4591,4590,4586,4583,4582,4579,4577,4546,4516,4515,4514,4507,4498,4497,4496,4495,4494,4493,4457,4454,4453,4446,4445,4431,4427,4421,4420,4415,4414,4413,4412,4384,4376,4371,4368,4350,4341,4327,4322,4321,4300,4299,4294,4288,4287,4284,4283,4282,4281,4263,4262,4261,4254,4233,4232,4227,4226,4221,4217,4216,4215,4201,4196,4195,4194,4193,4192,4191,4190,4189,4188,4152,4146,4142,4123,4122,4077,4076,4066,4063,4043,4042,4008,4006,3963,3949,3909,3877,3872,3853,3852,3851,3846,3845,3843,3820,3817,3816,3812,3810,3809,3805,3793,3792,3775,3772,3771,3765,3764,3736,3714,3690,3682,3681,3675,3666,3665,3651,3647,3646,3644,3643,3613,3601,3591,3590,3551,3550,3491,3490,3484,3483,3477,3472,3468,3464,3462,3456,3455,3453,3451,3450,3448,3447,3444,3443,3435,3432,3429,3420,3388,3351,3350,3349,3348,3330,3329,3326,3325,3324,3323,3282,3268,3267,3256,3127,3115,3082,3081,3080,3063,3062,3055,3054,3005,2999,2997,2968,2967,2961,2828,2822,2814,2798,2785,2678,2646,2644,2499,2496,2471,2469,2460,2306,2302,2301,2300,2299,2298,2297,2296,2295,2294,2293,2292,2291,2290,2289,2288,2287,2286,2285,2275,2174,2173]) ).
thf(6137,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[6136]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SCT100-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.19 % Computer : n015.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Oct 6 14:25:13 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.20 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 223.21/45.22 .....
% 223.21/45.22
% 223.21/45.22 No.of.Axioms: 677
% 223.21/45.22
% 223.21/45.22 Length.of.Defs: 0
% 223.21/45.22
% 223.21/45.22 Contains.Choice.Funs: false
% 223.21/45.22 ......................................................................................................................................................................................................................................................................................................................................................................................
% 223.21/45.22
% 223.21/45.22 ********************************
% 223.21/45.22 * All subproblems solved! *
% 223.21/45.22 ********************************
% 223.21/45.22 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:2,axioms:677,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:69,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:6136,loop_count:0,foatp_calls:1,translation:fof_experiment)
% 223.21/45.22
% 223.21/45.22 %**** Beginning of derivation protocol ****
% 223.21/45.22 % SZS output start CNFRefutation
% See solution above
% 223.21/45.24
% 223.21/45.24 %**** End of derivation protocol ****
% 223.21/45.24 %**** no. of clauses in derivation: 6137 ****
% 223.21/45.24 %**** clause counter: 6136 ****
% 223.21/45.24
% 223.21/45.24 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:2,axioms:677,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:69,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:6136,loop_count:0,foatp_calls:1,translation:fof_experiment)
%------------------------------------------------------------------------------