TSTP Solution File: SCT077-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SCT077-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 14:10:59 EDT 2023
% Result : Unsatisfiable 47.86s 47.91s
% Output : CNFRefutation 47.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 53
% Number of leaves : 192
% Syntax : Number of formulae : 510 ( 241 unt; 105 typ; 0 def)
% Number of atoms : 605 ( 290 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 419 ( 219 ~; 200 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 155 ( 84 >; 71 *; 0 +; 0 <<)
% Number of predicates : 35 ( 33 usr; 1 prp; 0-9 aty)
% Number of functors : 72 ( 72 usr; 21 con; 0-4 aty)
% Number of variables : 677 ( 232 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
t_b: $i ).
tff(decl_23,type,
class_Complete__Lattice_Ocomplete__lattice: $i > $o ).
tff(decl_24,type,
t_a: $i ).
tff(decl_25,type,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR: ( $i * $i ) > $i ).
tff(decl_26,type,
v_A: $i ).
tff(decl_27,type,
hAPP: ( $i * $i ) > $i ).
tff(decl_28,type,
v_f: $i ).
tff(decl_29,type,
c_Complete__Lattice_OSup__class_OSup: $i > $i ).
tff(decl_30,type,
c_Set_Oimage: ( $i * $i * $i ) > $i ).
tff(decl_31,type,
c_Complete__Lattice_Ocomplete__lattice__class_OINFI: ( $i * $i ) > $i ).
tff(decl_32,type,
c_Complete__Lattice_OInf__class_OInf: $i > $i ).
tff(decl_33,type,
tc_bool: $i ).
tff(decl_34,type,
tc_fun: ( $i * $i ) > $i ).
tff(decl_35,type,
c_lessequals: $i > $i ).
tff(decl_36,type,
c_Lattices_Oupper__semilattice__class_Osup: $i > $i ).
tff(decl_37,type,
hBOOL: $i > $o ).
tff(decl_38,type,
class_Lattices_Oupper__semilattice: $i > $o ).
tff(decl_39,type,
class_Lattices_Olattice: $i > $o ).
tff(decl_40,type,
c_Lattices_Olower__semilattice__class_Oinf: $i > $i ).
tff(decl_41,type,
class_Lattices_Olower__semilattice: $i > $o ).
tff(decl_42,type,
c_Orderings_Obot__class_Obot: $i > $i ).
tff(decl_43,type,
c_COMBB: ( $i * $i * $i ) > $i ).
tff(decl_44,type,
c_Orderings_Otop__class_Otop: $i > $i ).
tff(decl_45,type,
class_Lattices_Oboolean__algebra: $i > $o ).
tff(decl_46,type,
c_HOL_Ouminus__class_Ouminus: $i > $i ).
tff(decl_47,type,
c_Set_Oinsert: $i > $i ).
tff(decl_48,type,
c_Hilbert__Choice_OEps: ( $i * $i ) > $i ).
tff(decl_49,type,
c_in: $i > $i ).
tff(decl_50,type,
c_Set_Ovimage: ( $i * $i * $i ) > $i ).
tff(decl_51,type,
c_Collect: $i > $i ).
tff(decl_52,type,
c_Ex: $i > $i ).
tff(decl_53,type,
c_COMBS: ( $i * $i * $i ) > $i ).
tff(decl_54,type,
c_and: $i ).
tff(decl_55,type,
c_COMBC: ( $i * $i * $i ) > $i ).
tff(decl_56,type,
c_fequal: $i > $i ).
tff(decl_57,type,
class_HOL_Oord: $i > $o ).
tff(decl_58,type,
c_Hilbert__Choice_OLeastM: ( $i * $i * $i * $i ) > $i ).
tff(decl_59,type,
c_All: $i > $i ).
tff(decl_60,type,
c_implies: $i ).
tff(decl_61,type,
c_Fun_Oinj__on: ( $i * $i * $i * $i ) > $o ).
tff(decl_62,type,
class_Ring__and__Field_Osemiring__0: $i > $o ).
tff(decl_63,type,
c_HOL_Otimes__class_Otimes: $i > $i ).
tff(decl_64,type,
c_Finite__Set_Osetsum: ( $i * $i ) > $i ).
tff(decl_65,type,
c_COMBI: $i > $i ).
tff(decl_66,type,
c_Lattices_Oboolean__algebra: ( $i * $i * $i * $i * $i * $i * $i * $i * $i ) > $o ).
tff(decl_67,type,
c_Finite__Set_Ofinite: ( $i * $i ) > $o ).
tff(decl_68,type,
class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).
tff(decl_69,type,
class_Lattices_Odistrib__lattice: $i > $o ).
tff(decl_70,type,
v_x: $i ).
tff(decl_71,type,
class_Orderings_Obot: $i > $o ).
tff(decl_72,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
tff(decl_73,type,
class_Lattices_Obounded__lattice: $i > $o ).
tff(decl_74,type,
c_Complete__Lattice_Ocomplete__lattice: ( $i * $i * $i * $i * $i * $i * $i * $i * $i ) > $o ).
tff(decl_75,type,
class_Ring__and__Field_Oidom: $i > $o ).
tff(decl_76,type,
c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__2: ( $i * $i ) > $i ).
tff(decl_77,type,
c_Not: $i ).
tff(decl_78,type,
class_OrderedGroup_Olordered__ab__group__add: $i > $o ).
tff(decl_79,type,
class_Finite__Set_Ofinite_Ofinite: $i > $o ).
tff(decl_80,type,
c_Inductive_Ocomplete__lattice_Olfp: ( $i * $i * $i ) > $i ).
tff(decl_81,type,
class_Ring__and__Field_Oring: $i > $o ).
tff(decl_82,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
tff(decl_83,type,
class_OrderedGroup_Ogroup__add: $i > $o ).
tff(decl_84,type,
c_Relation_Oconverse: ( $i * $i * $i ) > $i ).
tff(decl_85,type,
class_Orderings_Oorder: $i > $o ).
tff(decl_86,type,
class_OrderedGroup_Oab__semigroup__idem__mult: $i > $o ).
tff(decl_87,type,
class_HOL_Ouminus: $i > $o ).
tff(decl_88,type,
class_Orderings_Olinorder: $i > $o ).
tff(decl_89,type,
c_HOL_Oord__class_Oless: $i > $i ).
tff(decl_90,type,
class_Orderings_Opreorder: $i > $o ).
tff(decl_91,type,
class_Ring__and__Field_Oordered__ring__strict: $i > $o ).
tff(decl_92,type,
c_HOL_Oundefined: $i > $i ).
tff(decl_93,type,
c_FuncSet_Oextensional: ( $i * $i * $i ) > $i ).
tff(decl_94,type,
class_Orderings_Otop: $i > $o ).
tff(decl_95,type,
c_ATP__Linkup_Osko__Finite__Set__Xfinite__Collect__bex__1__1: ( $i * $i * $i * $i ) > $i ).
tff(decl_96,type,
v_B: $i ).
tff(decl_97,type,
c_FuncSet_OPi: ( $i * $i * $i * $i ) > $i ).
tff(decl_98,type,
c_ATP__Linkup_Osko__Set__Xball__UNIV__1__1: ( $i * $i ) > $i ).
tff(decl_99,type,
class_OrderedGroup_Oab__semigroup__mult: $i > $o ).
tff(decl_100,type,
c_ATP__Linkup_Osko__Set__XUNIV__witness__1__1: $i > $i ).
tff(decl_101,type,
c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__1: ( $i * $i ) > $i ).
tff(decl_102,type,
c_ATP__Linkup_Osko__Set__XUNIV__eq__I__1__1: ( $i * $i ) > $i ).
tff(decl_103,type,
c_ATP__Linkup_Osko__Set__Xball__UNIV__1__2: ( $i * $i ) > $i ).
tff(decl_104,type,
v_a: $i ).
tff(decl_105,type,
c_or: $i ).
tff(decl_106,type,
c_Predicate_OPowp: ( $i * $i * $i ) > $i ).
tff(decl_107,type,
c_Hilbert__Choice_OGreatestM: ( $i * $i * $i * $i ) > $i ).
tff(decl_108,type,
c_Inductive_Ocomplete__lattice_Ogfp: ( $i * $i * $i ) > $i ).
tff(decl_109,type,
class_OrderedGroup_Ocomm__monoid__add: $i > $o ).
tff(decl_110,type,
tc_Arrow__Order__Mirabelle_Oalt: $i ).
tff(decl_111,type,
tc_prod: ( $i * $i ) > $i ).
tff(decl_112,type,
v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1: ( $i * $i ) > $i ).
tff(decl_113,type,
c_Arrow__Order__Mirabelle_OLin: $i ).
tff(decl_114,type,
c_Arrow__Order__Mirabelle_Omktop: ( $i * $i ) > $i ).
tff(decl_115,type,
c_Arrow__Order__Mirabelle_Omkbot: ( $i * $i ) > $i ).
tff(decl_116,type,
c_Arrow__Order__Mirabelle_Obelow: ( $i * $i * $i ) > $i ).
tff(decl_117,type,
v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1: $i ).
tff(decl_118,type,
c_Arrow__Order__Mirabelle_Oabove: ( $i * $i * $i ) > $i ).
tff(decl_119,type,
c_HOL_OIf: $i > $i ).
tff(decl_120,type,
v_h____: $i ).
tff(decl_121,type,
tc_Arrow__Order__Mirabelle_Oindi: $i ).
tff(decl_122,type,
tc_nat: $i ).
tff(decl_123,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
tff(decl_124,type,
v_Lba____: $i ).
tff(decl_125,type,
v_Lab____: $i ).
tff(decl_126,type,
v_n: $i ).
cnf(cls_linorder__not__less_1,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__less_1) ).
cnf(cls_bot__least_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),c_Orderings_Obot__class_Obot(X1)),X2))
| ~ class_Orderings_Obot(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot__least_0) ).
cnf(cls_linorder__neqE__nat_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X2),X1))
| X2 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE__nat_0) ).
cnf(clsarity_nat__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
cnf(clsarity_nat__Orderings_Obot,axiom,
class_Orderings_Obot(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Obot) ).
cnf(cls_order__le__less_1,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__less_1) ).
cnf(clsarity_nat__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
cnf(cls_Collect__mem__eq_0,axiom,
hAPP(c_Collect(X1),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_bool),tc_bool),c_in(X1)),X2)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Collect__mem__eq_0) ).
cnf(cls_Collect__def_0,axiom,
hAPP(c_Collect(X1),X2) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Collect__def_0) ).
cnf(cls_order__eq__iff_2,axiom,
( X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__iff_2) ).
cnf(cls_COMBC__def_0,axiom,
hAPP(hAPP(hAPP(c_COMBC(X1,X2,X3),X4),X5),X6) = hAPP(hAPP(X4,X6),X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBC__def_0) ).
cnf(cls_inf__sup__ord_I1_J_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),X2))
| ~ class_Lattices_Olattice(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I1_J_0) ).
cnf(clsarity_nat__Lattices_Olattice,axiom,
class_Lattices_Olattice(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olattice) ).
cnf(cls_UNIV__eq__I_0,axiom,
( c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) = X2
| ~ hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Set__XUNIV__eq__I__1__1(X2,X1)),X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UNIV__eq__I_0) ).
cnf(cls_le__iff__inf_1,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Lattices_Olower__semilattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) != X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__inf_1) ).
cnf(clsarity_nat__Lattices_Olower__semilattice,axiom,
class_Lattices_Olower__semilattice(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olower__semilattice) ).
cnf(cls_top__fun__eq_0,axiom,
( hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,X1)),v_x) = c_Orderings_Otop__class_Otop(X1)
| ~ class_Orderings_Otop(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_top__fun__eq_0) ).
cnf(clsarity_bool__Orderings_Otop,axiom,
class_Orderings_Otop(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Otop) ).
cnf(cls_sup__top__left_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),c_Orderings_Otop__class_Otop(X1)),X2) = c_Orderings_Otop__class_Otop(X1)
| ~ class_Lattices_Obounded__lattice(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__top__left_0) ).
cnf(clsarity_bool__Lattices_Obounded__lattice,axiom,
class_Lattices_Obounded__lattice(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Obounded__lattice) ).
cnf(cls_top1I_0,axiom,
hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_top1I_0) ).
cnf(cls_Collect__neg__eq_0,axiom,
hAPP(c_Collect(X1),hAPP(hAPP(c_COMBB(tc_bool,tc_bool,X1),c_Not),X2)) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),hAPP(c_Collect(X1),X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Collect__neg__eq_0) ).
cnf(clsarity_bool__Orderings_Obot,axiom,
class_Orderings_Obot(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Obot) ).
cnf(cls_Compl__empty__eq_0,axiom,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Compl__empty__eq_0) ).
cnf(cls_ComplI_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X3)))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ComplI_0) ).
cnf(cls_bot__fun__eq_0,axiom,
( hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,X1)),v_x) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Orderings_Obot(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot__fun__eq_0) ).
cnf(cls_COMBB__def_0,axiom,
hAPP(hAPP(hAPP(c_COMBB(X1,X2,X3),X4),X5),X6) = hAPP(X4,hAPP(X5,X6)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBB__def_0) ).
cnf(cls_compl__top__eq_0,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),c_Orderings_Otop__class_Otop(X1)) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_compl__top__eq_0) ).
cnf(clsarity_bool__Lattices_Oboolean__algebra,axiom,
class_Lattices_Oboolean__algebra(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oboolean__algebra) ).
cnf(cls_exE__some_0,axiom,
( hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X1,X3)))
| ~ hBOOL(hAPP(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exE__some_0) ).
cnf(cls_bot1E_0,axiom,
~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot1E_0) ).
cnf(cls_insert__absorb_0,axiom,
( hAPP(hAPP(c_Set_Oinsert(X1),X2),X3) = X3
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__absorb_0) ).
cnf(cls_Collect__disj__eq_0,axiom,
hAPP(c_Collect(X1),hAPP(hAPP(c_COMBS(X1,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),X1),c_or),X2)),X3)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(c_Collect(X1),X2)),hAPP(c_Collect(X1),X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Collect__disj__eq_0) ).
cnf(cls_mem__def_0,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X2),X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mem__def_0) ).
cnf(cls_CHAINED_0_01,axiom,
hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_Lab____),c_Arrow__Order__Mirabelle_OLin)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0_01) ).
cnf(cls_inf__top__right_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),c_Orderings_Otop__class_Otop(X1)) = X2
| ~ class_Lattices_Obounded__lattice(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__top__right_0) ).
cnf(cls_sup1CI_1,axiom,
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),X4))
| ~ hBOOL(hAPP(X2,X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup1CI_1) ).
cnf(cls_COMBS__def_0,axiom,
hAPP(hAPP(hAPP(c_COMBS(X1,X2,X3),X4),X5),X6) = hAPP(hAPP(X4,X6),hAPP(X5,X6)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBS__def_0) ).
cnf(cls_insert__code_1,axiom,
hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__code_1) ).
cnf(cls_sup__commute_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X2)
| ~ class_Lattices_Oupper__semilattice(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__commute_0) ).
cnf(clsarity_bool__Lattices_Oupper__semilattice,axiom,
class_Lattices_Oupper__semilattice(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oupper__semilattice) ).
cnf(cls_sup__bot__left_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),c_Orderings_Obot__class_Obot(X1)),X2) = X2
| ~ class_Lattices_Obounded__lattice(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__bot__left_0) ).
cnf(cls_inf__sup__distrib1_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X4))
| ~ class_Lattices_Odistrib__lattice(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__distrib1_0) ).
cnf(clsarity_bool__Lattices_Odistrib__lattice,axiom,
class_Lattices_Odistrib__lattice(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Odistrib__lattice) ).
cnf(cls_sup__absorb1_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) = X2
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__absorb1_0) ).
cnf(clsarity_nat__Lattices_Oupper__semilattice,axiom,
class_Lattices_Oupper__semilattice(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Lattices_Oupper__semilattice) ).
cnf(cls_sup__ge2_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X2)))
| ~ class_Lattices_Oupper__semilattice(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__ge2_0) ).
cnf(cls_sup__inf__distrib1_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X4))
| ~ class_Lattices_Odistrib__lattice(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__inf__distrib1_0) ).
cnf(clsarity_nat__Lattices_Odistrib__lattice,axiom,
class_Lattices_Odistrib__lattice(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Lattices_Odistrib__lattice) ).
cnf(cls_less__le__not__le_1,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__le__not__le_1) ).
cnf(clsarity_bool__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).
cnf(cls_vimage__Collect__eq_0,axiom,
hAPP(c_Set_Ovimage(X1,X2,X3),hAPP(c_Collect(X3),X4)) = hAPP(c_Collect(X2),hAPP(hAPP(c_COMBB(X3,tc_bool,X2),X4),X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__Collect__eq_0) ).
cnf(cls_compl__sup_0,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3))
| ~ class_Lattices_Oboolean__algebra(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_compl__sup_0) ).
cnf(cls_fun__Compl__def_0,axiom,
( hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(t_a,X1)),X2),v_x) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(X2,v_x))
| ~ class_HOL_Ouminus(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__Compl__def_0) ).
cnf(clsarity_bool__HOL_Ouminus,axiom,
class_HOL_Ouminus(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__HOL_Ouminus) ).
cnf(cls_double__complement_0,axiom,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__complement_0) ).
cnf(cls_vimage__ident_0,axiom,
hAPP(c_Set_Ovimage(c_COMBI(X1),X1,X1),X2) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__ident_0) ).
cnf(cls_Compl__UNIV__eq_0,axiom,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Compl__UNIV__eq_0) ).
cnf(cls_sup__top__right_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),c_Orderings_Otop__class_Otop(X1)) = c_Orderings_Otop__class_Otop(X1)
| ~ class_Lattices_Obounded__lattice(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__top__right_0) ).
cnf(cls_order__neq__le__trans_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__neq__le__trans_0) ).
cnf(clsarity_bool__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).
cnf(cls_COMBI__def_0,axiom,
hAPP(c_COMBI(X1),X2) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBI__def_0) ).
cnf(cls_CHAINED_0,axiom,
hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_Lba____),c_Arrow__Order__Mirabelle_OLin)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0) ).
cnf(cls_Un__empty__right_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty__right_0) ).
cnf(cls_Collect__imp__eq_0,axiom,
hAPP(c_Collect(X1),hAPP(hAPP(c_COMBS(X1,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),X1),c_implies),X2)),X3)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),hAPP(c_Collect(X1),X2))),hAPP(c_Collect(X1),X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Collect__imp__eq_0) ).
cnf(cls_sup1CI_0,axiom,
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),X4))
| ~ hBOOL(hAPP(X3,X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup1CI_0) ).
cnf(cls_Compl__eq__Compl__iff_0,axiom,
( X2 = X3
| hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2) != hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Compl__eq__Compl__iff_0) ).
cnf(cls_Collect__empty__eq_0,axiom,
( hAPP(c_Collect(X1),X2) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ hBOOL(hAPP(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Collect__empty__eq_0) ).
cnf(cls_Un__empty__left_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),X2) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty__left_0) ).
cnf(cls_mem__def_1,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(X3,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mem__def_1) ).
cnf(cls_compl__bot__eq_0,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),c_Orderings_Obot__class_Obot(X1)) = c_Orderings_Otop__class_Otop(X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_compl__bot__eq_0) ).
cnf(cls_double__compl_0,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)) = X2
| ~ class_Lattices_Oboolean__algebra(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__compl_0) ).
cnf(cls_less__not__refl_0,axiom,
~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__not__refl_0) ).
cnf(cls_not__leE_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__leE_0) ).
cnf(cls_inf__sup__aci_I1_J_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X2)
| ~ class_Lattices_Olattice(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I1_J_0) ).
cnf(clsarity_bool__Lattices_Olattice,axiom,
class_Lattices_Olattice(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olattice) ).
cnf(cls_ComplD_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X3))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ComplD_0) ).
cnf(cls_inf__sup__aci_I2_J_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4))
| ~ class_Lattices_Olattice(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I2_J_0) ).
cnf(cls_disjoint__iff__not__equal_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X4),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_disjoint__iff__not__equal_0) ).
cnf(cls_inf__sup__absorb_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)) = X2
| ~ class_Lattices_Olattice(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__absorb_0) ).
cnf(cls_top__greatest_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_Orderings_Otop__class_Otop(X1)))
| ~ class_Orderings_Otop(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_top__greatest_0) ).
cnf(cls_Sup__insert_0,axiom,
( hAPP(c_Complete__Lattice_OSup__class_OSup(X1),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(c_Complete__Lattice_OSup__class_OSup(X1),X3))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sup__insert_0) ).
cnf(cls_insert__absorb2_0,axiom,
hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)) = hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__absorb2_0) ).
cnf(cls_Sup__UNIV_0,axiom,
( hAPP(c_Complete__Lattice_OSup__class_OSup(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool))) = c_Orderings_Otop__class_Otop(X1)
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sup__UNIV_0) ).
cnf(cls_Int__UNIV__right_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool))) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__UNIV__right_0) ).
cnf(cls_xt1_I7_J_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I7_J_0) ).
cnf(clsarity_bool__Complete__Lattice_Ocomplete__lattice,axiom,
class_Complete__Lattice_Ocomplete__lattice(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Complete__Lattice_Ocomplete__lattice) ).
cnf(c_0_87,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2)) ),
cls_linorder__not__less_1 ).
cnf(c_0_88,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),c_Orderings_Obot__class_Obot(X1)),X2))
| ~ class_Orderings_Obot(X1) ),
cls_bot__least_0 ).
cnf(c_0_89,plain,
( ~ class_Orderings_Olinorder(X1)
| ~ class_Orderings_Obot(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),c_Orderings_Obot__class_Obot(X1))) ),
inference(spm,[status(thm)],[c_0_87,c_0_88]) ).
cnf(c_0_90,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X2))
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X2),X1))
| X2 = X1 ),
cls_linorder__neqE__nat_0 ).
cnf(c_0_91,axiom,
class_Orderings_Olinorder(tc_nat),
clsarity_nat__Orderings_Olinorder ).
cnf(c_0_92,axiom,
class_Orderings_Obot(tc_nat),
clsarity_nat__Orderings_Obot ).
cnf(c_0_93,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3)) ),
cls_order__le__less_1 ).
cnf(c_0_94,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_nat)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Orderings_Obot__class_Obot(tc_nat)),X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_91]),c_0_92])]) ).
cnf(c_0_95,axiom,
class_Orderings_Oorder(tc_nat),
clsarity_nat__Orderings_Oorder ).
cnf(c_0_96,axiom,
hAPP(c_Collect(X1),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_bool),tc_bool),c_in(X1)),X2)) = X2,
cls_Collect__mem__eq_0 ).
cnf(c_0_97,axiom,
hAPP(c_Collect(X1),X2) = X2,
cls_Collect__def_0 ).
cnf(c_0_98,axiom,
( X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
cls_order__eq__iff_2 ).
cnf(c_0_99,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_nat)
| hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Orderings_Obot__class_Obot(tc_nat)),X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_94]),c_0_95])]) ).
cnf(c_0_100,axiom,
hAPP(hAPP(hAPP(c_COMBC(X1,X2,X3),X4),X5),X6) = hAPP(hAPP(X4,X6),X5),
cls_COMBC__def_0 ).
cnf(c_0_101,plain,
hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_bool),tc_bool),c_in(X1)),X2) = X2,
inference(rw,[status(thm)],[c_0_96,c_0_97]) ).
cnf(c_0_102,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_nat)
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X1),c_Orderings_Obot__class_Obot(tc_nat))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_99]),c_0_95])]) ).
cnf(c_0_103,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),X2))
| ~ class_Lattices_Olattice(X1) ),
cls_inf__sup__ord_I1_J_0 ).
cnf(c_0_104,axiom,
class_Lattices_Olattice(tc_nat),
clsarity_nat__Lattices_Olattice ).
cnf(c_0_105,axiom,
( c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) = X2
| ~ hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Set__XUNIV__eq__I__1__1(X2,X1)),X2)) ),
cls_UNIV__eq__I_0 ).
cnf(c_0_106,plain,
hAPP(hAPP(c_in(X1),X2),X3) = hAPP(X3,X2),
inference(spm,[status(thm)],[c_0_100,c_0_101]) ).
cnf(c_0_107,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Lattices_Olower__semilattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) != X2 ),
cls_le__iff__inf_1 ).
cnf(c_0_108,plain,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),c_Orderings_Obot__class_Obot(tc_nat)),X1) = c_Orderings_Obot__class_Obot(tc_nat),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_103]),c_0_104])]) ).
cnf(c_0_109,axiom,
class_Lattices_Olower__semilattice(tc_nat),
clsarity_nat__Lattices_Olower__semilattice ).
cnf(c_0_110,plain,
( c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) = X2
| ~ hBOOL(hAPP(X2,c_ATP__Linkup_Osko__Set__XUNIV__eq__I__1__1(X2,X1))) ),
inference(rw,[status(thm)],[c_0_105,c_0_106]) ).
cnf(c_0_111,plain,
hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Orderings_Obot__class_Obot(tc_nat)),X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_108]),c_0_109])]) ).
cnf(c_0_112,axiom,
( hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,X1)),v_x) = c_Orderings_Otop__class_Otop(X1)
| ~ class_Orderings_Otop(X1) ),
cls_top__fun__eq_0 ).
cnf(c_0_113,axiom,
class_Orderings_Otop(tc_bool),
clsarity_bool__Orderings_Otop ).
cnf(c_0_114,plain,
c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) = hAPP(c_lessequals(tc_nat),c_Orderings_Obot__class_Obot(tc_nat)),
inference(spm,[status(thm)],[c_0_110,c_0_111]) ).
cnf(c_0_115,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),c_Orderings_Otop__class_Otop(X1)),X2) = c_Orderings_Otop__class_Otop(X1)
| ~ class_Lattices_Obounded__lattice(X1) ),
cls_sup__top__left_0 ).
cnf(c_0_116,axiom,
class_Lattices_Obounded__lattice(tc_bool),
clsarity_bool__Lattices_Obounded__lattice ).
cnf(c_0_117,axiom,
hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2)),
cls_top1I_0 ).
cnf(c_0_118,plain,
hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,tc_bool)),v_x) = c_Orderings_Otop__class_Otop(tc_bool),
inference(spm,[status(thm)],[c_0_112,c_0_113]) ).
cnf(c_0_119,axiom,
hAPP(c_Collect(X1),hAPP(hAPP(c_COMBB(tc_bool,tc_bool,X1),c_Not),X2)) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),hAPP(c_Collect(X1),X2)),
cls_Collect__neg__eq_0 ).
cnf(c_0_120,axiom,
class_Orderings_Obot(tc_bool),
clsarity_bool__Orderings_Obot ).
cnf(c_0_121,plain,
( hAPP(c_lessequals(tc_nat),c_Orderings_Obot__class_Obot(tc_nat)) = X1
| ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__XUNIV__eq__I__1__1(X1,X2))) ),
inference(rw,[status(thm)],[c_0_110,c_0_114]) ).
cnf(c_0_122,plain,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),X1) = c_Orderings_Otop__class_Otop(tc_bool),
inference(spm,[status(thm)],[c_0_115,c_0_116]) ).
cnf(c_0_123,plain,
hBOOL(c_Orderings_Otop__class_Otop(tc_bool)),
inference(spm,[status(thm)],[c_0_117,c_0_118]) ).
cnf(c_0_124,axiom,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),
cls_Compl__empty__eq_0 ).
cnf(c_0_125,plain,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2) = hAPP(hAPP(c_COMBB(tc_bool,tc_bool,X1),c_Not),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_119,c_0_97]),c_0_97]) ).
cnf(c_0_126,plain,
hBOOL(hAPP(hAPP(c_lessequals(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),X1)),
inference(spm,[status(thm)],[c_0_88,c_0_120]) ).
cnf(c_0_127,plain,
hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) = hAPP(c_lessequals(tc_nat),c_Orderings_Obot__class_Obot(tc_nat)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_122]),c_0_123])]) ).
cnf(c_0_128,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X3)))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
cls_ComplI_0 ).
cnf(c_0_129,axiom,
( hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,X1)),v_x) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Orderings_Obot(X1) ),
cls_bot__fun__eq_0 ).
cnf(c_0_130,plain,
hAPP(hAPP(c_COMBB(tc_bool,tc_bool,X1),c_Not),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),
inference(rw,[status(thm)],[c_0_124,c_0_125]) ).
cnf(c_0_131,plain,
hAPP(c_lessequals(tc_nat),c_Orderings_Obot__class_Obot(tc_nat)) = hAPP(c_lessequals(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),
inference(spm,[status(thm)],[c_0_121,c_0_126]) ).
cnf(c_0_132,plain,
hAPP(hAPP(c_lessequals(tc_nat),c_Orderings_Obot__class_Obot(tc_nat)),X1) = c_Orderings_Otop__class_Otop(tc_bool),
inference(rw,[status(thm)],[c_0_122,c_0_127]) ).
cnf(c_0_133,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(hAPP(c_COMBB(tc_bool,tc_bool,X1),c_Not),X3)))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(rw,[status(thm)],[c_0_128,c_0_125]) ).
cnf(c_0_134,axiom,
hAPP(hAPP(hAPP(c_COMBB(X1,X2,X3),X4),X5),X6) = hAPP(X4,hAPP(X5,X6)),
cls_COMBB__def_0 ).
cnf(c_0_135,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),c_Orderings_Otop__class_Otop(X1)) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
cls_compl__top__eq_0 ).
cnf(c_0_136,axiom,
class_Lattices_Oboolean__algebra(tc_bool),
clsarity_bool__Lattices_Oboolean__algebra ).
cnf(c_0_137,axiom,
( hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X1,X3)))
| ~ hBOOL(hAPP(X1,X2)) ),
cls_exE__some_0 ).
cnf(c_0_138,plain,
hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),v_x) = c_Orderings_Obot__class_Obot(tc_bool),
inference(spm,[status(thm)],[c_0_129,c_0_120]) ).
cnf(c_0_139,axiom,
~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2)),
cls_bot1E_0 ).
cnf(c_0_140,axiom,
( hAPP(hAPP(c_Set_Oinsert(X1),X2),X3) = X3
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
cls_insert__absorb_0 ).
cnf(c_0_141,plain,
hAPP(hAPP(c_COMBB(tc_bool,tc_bool,X1),c_Not),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))) = hAPP(c_lessequals(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_130,c_0_114]),c_0_131]) ).
cnf(c_0_142,plain,
hAPP(hAPP(c_lessequals(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),X1) = c_Orderings_Otop__class_Otop(tc_bool),
inference(rw,[status(thm)],[c_0_132,c_0_131]) ).
cnf(c_0_143,plain,
( hBOOL(hAPP(c_Not,hAPP(X1,X2)))
| hBOOL(hAPP(X1,X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_133,c_0_106]),c_0_134]),c_0_106]) ).
cnf(c_0_144,plain,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) = c_Orderings_Obot__class_Obot(tc_bool),
inference(spm,[status(thm)],[c_0_135,c_0_136]) ).
cnf(c_0_145,plain,
~ hBOOL(c_Orderings_Obot__class_Obot(tc_bool)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_138]),c_0_139]) ).
cnf(c_0_146,axiom,
hAPP(c_Collect(X1),hAPP(hAPP(c_COMBS(X1,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),X1),c_or),X2)),X3)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(c_Collect(X1),X2)),hAPP(c_Collect(X1),X3)),
cls_Collect__disj__eq_0 ).
cnf(c_0_147,plain,
( hAPP(hAPP(c_Set_Oinsert(X1),X2),X3) = X3
| ~ hBOOL(hAPP(X3,X2)) ),
inference(rw,[status(thm)],[c_0_140,c_0_106]) ).
cnf(c_0_148,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X2),X1)) ),
cls_mem__def_0 ).
cnf(c_0_149,axiom,
hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_Lab____),c_Arrow__Order__Mirabelle_OLin)),
cls_CHAINED_0_01 ).
cnf(c_0_150,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),c_Orderings_Otop__class_Otop(X1)) = X2
| ~ class_Lattices_Obounded__lattice(X1) ),
cls_inf__top__right_0 ).
cnf(c_0_151,plain,
hAPP(c_Not,hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2)) = c_Orderings_Otop__class_Otop(tc_bool),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_141]),c_0_142]) ).
cnf(c_0_152,axiom,
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),X4))
| ~ hBOOL(hAPP(X2,X4)) ),
cls_sup1CI_1 ).
cnf(c_0_153,plain,
hBOOL(hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool))),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_144]),c_0_145]) ).
cnf(c_0_154,axiom,
hAPP(hAPP(hAPP(c_COMBS(X1,X2,X3),X4),X5),X6) = hAPP(hAPP(X4,X6),hAPP(X5,X6)),
cls_COMBS__def_0 ).
cnf(c_0_155,plain,
hAPP(hAPP(c_COMBS(X1,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),X1),c_or),X2)),X3) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_146,c_0_97]),c_0_97]),c_0_97]) ).
cnf(c_0_156,axiom,
hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X2)),
cls_insert__code_1 ).
cnf(c_0_157,plain,
( hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(c_in(X3),X4)) = hAPP(c_in(X3),X4)
| ~ hBOOL(hAPP(X2,X4)) ),
inference(spm,[status(thm)],[c_0_147,c_0_106]) ).
cnf(c_0_158,plain,
hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lab____)),
inference(spm,[status(thm)],[c_0_148,c_0_149]) ).
cnf(c_0_159,plain,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X1),c_Orderings_Otop__class_Otop(tc_bool)) = X1,
inference(spm,[status(thm)],[c_0_150,c_0_116]) ).
cnf(c_0_160,plain,
c_Orderings_Otop__class_Otop(tc_bool) = hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool)),
inference(spm,[status(thm)],[c_0_151,c_0_138]) ).
cnf(c_0_161,plain,
hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) = hAPP(c_lessequals(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),
inference(rw,[status(thm)],[c_0_127,c_0_131]) ).
cnf(c_0_162,plain,
hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),c_Not),X2),c_Orderings_Obot__class_Obot(tc_bool))),
inference(spm,[status(thm)],[c_0_152,c_0_153]) ).
cnf(c_0_163,plain,
hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),X4) = hAPP(hAPP(c_or,hAPP(X2,X4)),hAPP(X3,X4)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_154,c_0_155]),c_0_134]) ).
cnf(c_0_164,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X2)
| ~ class_Lattices_Oupper__semilattice(X1) ),
cls_sup__commute_0 ).
cnf(c_0_165,axiom,
class_Lattices_Oupper__semilattice(tc_bool),
clsarity_bool__Lattices_Oupper__semilattice ).
cnf(c_0_166,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),c_Orderings_Obot__class_Obot(X1)),X2) = X2
| ~ class_Lattices_Obounded__lattice(X1) ),
cls_sup__bot__left_0 ).
cnf(c_0_167,plain,
hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X2),X3),X4)),X5),X3)),
inference(spm,[status(thm)],[c_0_152,c_0_156]) ).
cnf(c_0_168,plain,
hAPP(hAPP(c_Set_Oinsert(X1),c_Arrow__Order__Mirabelle_OLin),hAPP(c_in(X2),v_Lab____)) = hAPP(c_in(X2),v_Lab____),
inference(spm,[status(thm)],[c_0_157,c_0_158]) ).
cnf(c_0_169,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X4))
| ~ class_Lattices_Odistrib__lattice(X1) ),
cls_inf__sup__distrib1_0 ).
cnf(c_0_170,plain,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X1),hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool))) = X1,
inference(rw,[status(thm)],[c_0_159,c_0_160]) ).
cnf(c_0_171,plain,
hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool))) = hAPP(c_lessequals(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),
inference(rw,[status(thm)],[c_0_161,c_0_160]) ).
cnf(c_0_172,axiom,
class_Lattices_Odistrib__lattice(tc_bool),
clsarity_bool__Lattices_Odistrib__lattice ).
cnf(c_0_173,plain,
hBOOL(hAPP(hAPP(c_or,hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool))),hAPP(X1,c_Orderings_Obot__class_Obot(tc_bool)))),
inference(rw,[status(thm)],[c_0_162,c_0_163]) ).
cnf(c_0_174,plain,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X1),X2) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X2),X1),
inference(spm,[status(thm)],[c_0_164,c_0_165]) ).
cnf(c_0_175,plain,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),X1) = X1,
inference(spm,[status(thm)],[c_0_166,c_0_116]) ).
cnf(c_0_176,plain,
hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(c_in(X2),v_Lab____)),X3),c_Arrow__Order__Mirabelle_OLin)),
inference(spm,[status(thm)],[c_0_167,c_0_168]) ).
cnf(c_0_177,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) = X2
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2)) ),
cls_sup__absorb1_0 ).
cnf(c_0_178,axiom,
class_Lattices_Oupper__semilattice(tc_nat),
clsarity_nat__Lattices_Oupper__semilattice ).
cnf(c_0_179,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X2)))
| ~ class_Lattices_Oupper__semilattice(X1) ),
cls_sup__ge2_0 ).
cnf(c_0_180,plain,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X1),X2)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_169,c_0_170]),c_0_171]),c_0_142]),c_0_160]),c_0_170]),c_0_172])]) ).
cnf(c_0_181,plain,
( hAPP(c_lessequals(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)) = X1
| ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__XUNIV__eq__I__1__1(X1,X2))) ),
inference(rw,[status(thm)],[c_0_121,c_0_131]) ).
cnf(c_0_182,plain,
hBOOL(hAPP(hAPP(c_or,hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool))),X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_173,c_0_174]),c_0_175]) ).
cnf(c_0_183,plain,
hBOOL(hAPP(hAPP(c_or,hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lab____)),hAPP(X1,c_Arrow__Order__Mirabelle_OLin))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_176,c_0_163]),c_0_106]) ).
cnf(c_0_184,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X4))
| ~ class_Lattices_Odistrib__lattice(X1) ),
cls_sup__inf__distrib1_0 ).
cnf(c_0_185,plain,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),X1),c_Orderings_Obot__class_Obot(tc_nat)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_177,c_0_111]),c_0_178])]) ).
cnf(c_0_186,axiom,
class_Lattices_Odistrib__lattice(tc_nat),
clsarity_nat__Lattices_Odistrib__lattice ).
cnf(c_0_187,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2)) ),
cls_less__le__not__le_1 ).
cnf(c_0_188,plain,
hBOOL(hAPP(hAPP(c_lessequals(tc_bool),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X1),X2)),X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_179,c_0_180]),c_0_165])]) ).
cnf(c_0_189,axiom,
class_Orderings_Opreorder(tc_bool),
clsarity_bool__Orderings_Opreorder ).
cnf(c_0_190,plain,
hAPP(c_lessequals(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)) = hAPP(c_or,hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool))),
inference(spm,[status(thm)],[c_0_181,c_0_182]) ).
cnf(c_0_191,plain,
hBOOL(hAPP(hAPP(c_or,hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lab____)),hAPP(X1,hAPP(X2,c_Arrow__Order__Mirabelle_OLin)))),
inference(spm,[status(thm)],[c_0_183,c_0_134]) ).
cnf(c_0_192,plain,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),X1),X2)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_184,c_0_185]),c_0_108]),c_0_185]),c_0_186])]) ).
cnf(c_0_193,axiom,
hAPP(c_Set_Ovimage(X1,X2,X3),hAPP(c_Collect(X3),X4)) = hAPP(c_Collect(X2),hAPP(hAPP(c_COMBB(X3,tc_bool,X2),X4),X1)),
cls_vimage__Collect__eq_0 ).
cnf(c_0_194,plain,
~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_bool),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X1),X2))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_187,c_0_188]),c_0_189])]) ).
cnf(c_0_195,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3))
| ~ class_Lattices_Oboolean__algebra(X1) ),
cls_compl__sup_0 ).
cnf(c_0_196,axiom,
( hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(t_a,X1)),X2),v_x) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(X2,v_x))
| ~ class_HOL_Ouminus(X1) ),
cls_fun__Compl__def_0 ).
cnf(c_0_197,axiom,
class_HOL_Ouminus(tc_bool),
clsarity_bool__HOL_Ouminus ).
cnf(c_0_198,plain,
( hAPP(c_or,hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool))) = X1
| ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__XUNIV__eq__I__1__1(X1,X2))) ),
inference(rw,[status(thm)],[c_0_181,c_0_190]) ).
cnf(c_0_199,plain,
hBOOL(hAPP(hAPP(c_or,hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lab____)),X1)),
inference(spm,[status(thm)],[c_0_191,c_0_192]) ).
cnf(c_0_200,axiom,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2)) = X2,
cls_double__complement_0 ).
cnf(c_0_201,axiom,
hAPP(c_Set_Ovimage(c_COMBI(X1),X1,X1),X2) = X2,
cls_vimage__ident_0 ).
cnf(c_0_202,plain,
hAPP(c_Set_Ovimage(X1,X2,X3),X4) = hAPP(hAPP(c_COMBB(X3,tc_bool,X2),X4),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_193,c_0_97]),c_0_97]) ).
cnf(c_0_203,plain,
~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_bool),hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X1)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X1),X2)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_194,c_0_195]),c_0_136])]) ).
cnf(c_0_204,plain,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),hAPP(X1,v_x)) = hAPP(c_Not,hAPP(X1,v_x)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_196,c_0_197]),c_0_125]),c_0_134]) ).
cnf(c_0_205,plain,
hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool))) = hAPP(c_or,hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool))),
inference(rw,[status(thm)],[c_0_171,c_0_190]) ).
cnf(c_0_206,plain,
hAPP(c_or,hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool))) = hAPP(c_or,hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lab____)),
inference(spm,[status(thm)],[c_0_198,c_0_199]) ).
cnf(c_0_207,axiom,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
cls_Compl__UNIV__eq_0 ).
cnf(c_0_208,plain,
hAPP(hAPP(c_COMBB(tc_bool,tc_bool,X1),c_Not),hAPP(hAPP(c_COMBB(tc_bool,tc_bool,X1),c_Not),X2)) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_200,c_0_125]),c_0_125]) ).
cnf(c_0_209,plain,
hAPP(hAPP(c_COMBB(X1,tc_bool,X1),X2),c_COMBI(X1)) = X2,
inference(rw,[status(thm)],[c_0_201,c_0_202]) ).
cnf(c_0_210,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),c_Orderings_Otop__class_Otop(X1)) = c_Orderings_Otop__class_Otop(X1)
| ~ class_Lattices_Obounded__lattice(X1) ),
cls_sup__top__right_0 ).
cnf(c_0_211,plain,
~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_bool),hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X1)),hAPP(c_Not,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X1),v_x)))),
inference(spm,[status(thm)],[c_0_203,c_0_204]) ).
cnf(c_0_212,plain,
hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool))) = hAPP(c_or,hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lab____)),
inference(rw,[status(thm)],[c_0_205,c_0_206]) ).
cnf(c_0_213,plain,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool))) = c_Orderings_Obot__class_Obot(tc_bool),
inference(rw,[status(thm)],[c_0_144,c_0_160]) ).
cnf(c_0_214,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
cls_order__neq__le__trans_0 ).
cnf(c_0_215,axiom,
class_Orderings_Oorder(tc_bool),
clsarity_bool__Orderings_Oorder ).
cnf(c_0_216,plain,
hAPP(hAPP(c_COMBB(tc_bool,tc_bool,X1),c_Not),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
inference(rw,[status(thm)],[c_0_207,c_0_125]) ).
cnf(c_0_217,axiom,
hAPP(c_COMBI(X1),X2) = X2,
cls_COMBI__def_0 ).
cnf(c_0_218,plain,
c_COMBI(tc_bool) = hAPP(hAPP(c_COMBB(tc_bool,tc_bool,tc_bool),c_Not),c_Not),
inference(spm,[status(thm)],[c_0_208,c_0_209]) ).
cnf(c_0_219,axiom,
hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_Lba____),c_Arrow__Order__Mirabelle_OLin)),
cls_CHAINED_0 ).
cnf(c_0_220,plain,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X1),c_Orderings_Otop__class_Otop(tc_bool)) = c_Orderings_Otop__class_Otop(tc_bool),
inference(spm,[status(thm)],[c_0_210,c_0_116]) ).
cnf(c_0_221,plain,
~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),hAPP(c_Not,hAPP(hAPP(c_or,hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lab____)),v_x)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_211,c_0_212]),c_0_213]) ).
cnf(c_0_222,plain,
( c_Orderings_Obot__class_Obot(tc_bool) = X1
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_214,c_0_126]),c_0_215])]) ).
cnf(c_0_223,plain,
hAPP(hAPP(c_COMBB(tc_bool,tc_bool,X1),c_Not),hAPP(c_lessequals(tc_bool),c_Orderings_Obot__class_Obot(tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_216,c_0_114]),c_0_131]) ).
cnf(c_0_224,plain,
hAPP(c_Not,hAPP(c_Not,X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_217,c_0_218]),c_0_134]) ).
cnf(c_0_225,plain,
hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lba____)),
inference(spm,[status(thm)],[c_0_148,c_0_219]) ).
cnf(c_0_226,plain,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X1),hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool))) = hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_220,c_0_160]),c_0_160]) ).
cnf(c_0_227,plain,
c_Orderings_Obot__class_Obot(tc_bool) = hAPP(c_Not,hAPP(hAPP(c_or,hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lab____)),v_x)),
inference(spm,[status(thm)],[c_0_221,c_0_222]) ).
cnf(c_0_228,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))) = X2,
cls_Un__empty__right_0 ).
cnf(c_0_229,plain,
hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2) = c_Orderings_Obot__class_Obot(tc_bool),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_223]),c_0_142]),c_0_160]),c_0_224]) ).
cnf(c_0_230,plain,
hAPP(hAPP(c_Set_Oinsert(X1),c_Arrow__Order__Mirabelle_OLin),hAPP(c_in(X2),v_Lba____)) = hAPP(c_in(X2),v_Lba____),
inference(spm,[status(thm)],[c_0_157,c_0_225]) ).
cnf(c_0_231,plain,
hAPP(hAPP(c_or,hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lab____)),X1) = hAPP(hAPP(c_or,hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lab____)),v_x),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_164,c_0_212]),c_0_226]),c_0_165])]),c_0_227]),c_0_224]) ).
cnf(c_0_232,plain,
hAPP(hAPP(c_or,hAPP(X1,X2)),hAPP(c_Not,hAPP(hAPP(c_or,hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lab____)),v_x))) = hAPP(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_163,c_0_228]),c_0_229]),c_0_227]) ).
cnf(c_0_233,plain,
hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(c_in(X2),v_Lba____)),X3),c_Arrow__Order__Mirabelle_OLin)),
inference(spm,[status(thm)],[c_0_167,c_0_230]) ).
cnf(c_0_234,plain,
c_Orderings_Otop__class_Otop(tc_bool) = hAPP(hAPP(c_or,hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lab____)),v_x),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_160,c_0_227]),c_0_224]) ).
cnf(c_0_235,plain,
hAPP(hAPP(c_or,hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lab____)),v_x) = hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lab____),
inference(spm,[status(thm)],[c_0_231,c_0_232]) ).
cnf(c_0_236,plain,
hBOOL(hAPP(hAPP(c_or,hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lba____)),hAPP(X1,c_Arrow__Order__Mirabelle_OLin))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_233,c_0_163]),c_0_106]) ).
cnf(c_0_237,plain,
c_Orderings_Otop__class_Otop(tc_bool) = hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lab____),
inference(rw,[status(thm)],[c_0_234,c_0_235]) ).
cnf(c_0_238,plain,
hBOOL(hAPP(hAPP(c_or,hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lba____)),hAPP(X1,hAPP(X2,c_Arrow__Order__Mirabelle_OLin)))),
inference(spm,[status(thm)],[c_0_236,c_0_134]) ).
cnf(c_0_239,axiom,
hAPP(c_Collect(X1),hAPP(hAPP(c_COMBS(X1,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),X1),c_implies),X2)),X3)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),hAPP(c_Collect(X1),X2))),hAPP(c_Collect(X1),X3)),
cls_Collect__imp__eq_0 ).
cnf(c_0_240,plain,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X1),hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lab____)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_150,c_0_237]),c_0_116])]) ).
cnf(c_0_241,plain,
hAPP(hAPP(c_or,hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lab____)),X1) = hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lab____),
inference(rw,[status(thm)],[c_0_231,c_0_235]) ).
cnf(c_0_242,plain,
( hAPP(c_or,hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lab____)) = X1
| ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__XUNIV__eq__I__1__1(X1,X2))) ),
inference(rw,[status(thm)],[c_0_198,c_0_206]) ).
cnf(c_0_243,plain,
hBOOL(hAPP(hAPP(c_or,hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lba____)),X1)),
inference(spm,[status(thm)],[c_0_238,c_0_192]) ).
cnf(c_0_244,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(c_COMBB(X2,tc_bool,X2),X3)),X4),c_COMBI(X2)))
| ~ hBOOL(X3) ),
inference(spm,[status(thm)],[c_0_152,c_0_209]) ).
cnf(c_0_245,axiom,
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),X4))
| ~ hBOOL(hAPP(X3,X4)) ),
cls_sup1CI_0 ).
cnf(c_0_246,plain,
hAPP(hAPP(c_COMBS(X1,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),X1),c_implies),X2)),X3) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(hAPP(c_COMBB(tc_bool,tc_bool,X1),c_Not),X2)),X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_239,c_0_97]),c_0_125]),c_0_97]),c_0_97]) ).
cnf(c_0_247,plain,
hAPP(hAPP(c_or,X1),hAPP(c_Not,hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lab____))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_232,c_0_240]),c_0_241]) ).
cnf(c_0_248,plain,
hAPP(c_or,hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lab____)) = hAPP(c_or,hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lba____)),
inference(spm,[status(thm)],[c_0_242,c_0_243]) ).
cnf(c_0_249,plain,
hAPP(hAPP(c_COMBB(tc_bool,tc_bool,X1),c_Not),hAPP(c_or,hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool)))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
inference(rw,[status(thm)],[c_0_223,c_0_190]) ).
cnf(c_0_250,plain,
( hBOOL(hAPP(hAPP(c_or,X1),hAPP(X2,c_COMBI(X3))))
| ~ hBOOL(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_244,c_0_163]),c_0_209]) ).
cnf(c_0_251,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),hAPP(c_COMBB(X3,tc_bool,X3),X4)),c_COMBI(X3)))
| ~ hBOOL(X4) ),
inference(spm,[status(thm)],[c_0_245,c_0_209]) ).
cnf(c_0_252,plain,
hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(hAPP(c_COMBB(tc_bool,tc_bool,X1),c_Not),X2)),X3),X4) = hAPP(hAPP(c_implies,hAPP(X2,X4)),hAPP(X3,X4)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_154,c_0_246]),c_0_134]) ).
cnf(c_0_253,plain,
hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lab____) = hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lba____),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_247,c_0_248]),c_0_247]) ).
cnf(c_0_254,plain,
hAPP(hAPP(c_COMBB(tc_bool,tc_bool,X1),c_Not),hAPP(c_or,hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lab____))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
inference(rw,[status(thm)],[c_0_249,c_0_206]) ).
cnf(c_0_255,plain,
( hAPP(c_or,hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lba____)) = X1
| ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__XUNIV__eq__I__1__1(X1,X2))) ),
inference(rw,[status(thm)],[c_0_242,c_0_248]) ).
cnf(c_0_256,plain,
( hBOOL(hAPP(hAPP(c_or,X1),X2))
| ~ hBOOL(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_250,c_0_106]),c_0_217]) ).
cnf(c_0_257,plain,
( hBOOL(hAPP(hAPP(c_implies,hAPP(X1,c_COMBI(X2))),X3))
| ~ hBOOL(X3) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_251,c_0_252]),c_0_209]) ).
cnf(c_0_258,axiom,
( X2 = X3
| hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2) != hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X3) ),
cls_Compl__eq__Compl__iff_0 ).
cnf(c_0_259,axiom,
( hAPP(c_Collect(X1),X2) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ hBOOL(hAPP(X2,X3)) ),
cls_Collect__empty__eq_0 ).
cnf(c_0_260,plain,
hAPP(hAPP(c_or,hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lba____)),X1) = hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lba____),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_241,c_0_248]),c_0_253]) ).
cnf(c_0_261,plain,
hAPP(hAPP(c_COMBB(tc_bool,tc_bool,X1),c_Not),hAPP(c_or,hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lba____))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
inference(rw,[status(thm)],[c_0_254,c_0_248]) ).
cnf(c_0_262,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),X2) = X2,
cls_Un__empty__left_0 ).
cnf(c_0_263,plain,
( hAPP(c_or,hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lba____)) = hAPP(c_or,X1)
| ~ hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_255,c_0_256]) ).
cnf(c_0_264,plain,
( hBOOL(hAPP(hAPP(c_implies,X1),X2))
| ~ hBOOL(X2) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_257,c_0_106]),c_0_217]) ).
cnf(c_0_265,plain,
( X1 = X2
| hAPP(hAPP(c_COMBB(tc_bool,tc_bool,X3),c_Not),X1) != hAPP(hAPP(c_COMBB(tc_bool,tc_bool,X3),c_Not),X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_258,c_0_125]),c_0_125]) ).
cnf(c_0_266,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(X3,X2)) ),
cls_mem__def_1 ).
cnf(c_0_267,plain,
( X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ hBOOL(hAPP(X1,X3)) ),
inference(rw,[status(thm)],[c_0_259,c_0_97]) ).
cnf(c_0_268,plain,
hAPP(hAPP(c_implies,hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lba____)),hAPP(X1,X2)) = hAPP(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_252,c_0_260]),c_0_261]),c_0_262]) ).
cnf(c_0_269,plain,
( hAPP(c_or,hAPP(hAPP(c_implies,X1),X2)) = hAPP(c_or,hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lba____))
| ~ hBOOL(X2) ),
inference(spm,[status(thm)],[c_0_263,c_0_264]) ).
cnf(c_0_270,plain,
( X1 = hAPP(hAPP(c_COMBB(tc_bool,tc_bool,tc_bool),c_Not),c_Not)
| hAPP(hAPP(c_COMBB(tc_bool,tc_bool,tc_bool),c_Not),X1) != c_Not ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_265,c_0_209]),c_0_218]) ).
cnf(c_0_271,plain,
hBOOL(hAPP(hAPP(c_in(X1),X2),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)))),
inference(spm,[status(thm)],[c_0_266,c_0_117]) ).
cnf(c_0_272,plain,
( hAPP(hAPP(c_COMBB(X1,X2,X3),X4),X5) != c_Orderings_Obot__class_Obot(tc_fun(X6,tc_bool))
| ~ hBOOL(hAPP(X4,hAPP(X5,X7))) ),
inference(spm,[status(thm)],[c_0_267,c_0_134]) ).
cnf(c_0_273,plain,
hAPP(hAPP(c_implies,hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lba____)),X1) = X1,
inference(spm,[status(thm)],[c_0_268,c_0_224]) ).
cnf(c_0_274,plain,
( hAPP(hAPP(c_implies,X1),X2) = hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lba____)
| ~ hBOOL(X2) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_247,c_0_269]),c_0_247]) ).
cnf(c_0_275,plain,
( hAPP(hAPP(c_COMBB(tc_bool,tc_bool,tc_bool),c_Not),c_Not) = c_Orderings_Obot__class_Obot(tc_fun(tc_bool,tc_bool))
| c_Orderings_Otop__class_Otop(tc_fun(tc_bool,tc_bool)) != c_Not ),
inference(spm,[status(thm)],[c_0_270,c_0_130]) ).
cnf(c_0_276,plain,
c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) = c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),
inference(spm,[status(thm)],[c_0_105,c_0_271]) ).
cnf(c_0_277,plain,
( hAPP(hAPP(c_COMBB(X1,X2,X3),X4),c_Not) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool))
| ~ hBOOL(hAPP(X4,X6)) ),
inference(spm,[status(thm)],[c_0_272,c_0_224]) ).
cnf(c_0_278,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),c_Orderings_Obot__class_Obot(X1)) = c_Orderings_Otop__class_Otop(X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
cls_compl__bot__eq_0 ).
cnf(c_0_279,plain,
( hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lba____) = X1
| ~ hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_273,c_0_274]) ).
cnf(c_0_280,plain,
( hBOOL(hAPP(c_Not,X1))
| hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_143,c_0_185]) ).
cnf(c_0_281,plain,
( hAPP(hAPP(c_COMBB(tc_bool,tc_bool,tc_bool),c_Not),c_Not) = c_Orderings_Obot__class_Obot(tc_fun(tc_bool,tc_bool))
| c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) != c_Not ),
inference(spm,[status(thm)],[c_0_275,c_0_276]) ).
cnf(c_0_282,plain,
hAPP(hAPP(c_COMBB(X1,X2,X3),c_Not),c_Not) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),
inference(spm,[status(thm)],[c_0_277,c_0_153]) ).
cnf(c_0_283,plain,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)) = c_Orderings_Otop__class_Otop(tc_bool),
inference(spm,[status(thm)],[c_0_278,c_0_136]) ).
cnf(c_0_284,plain,
( hAPP(c_Not,X1) = hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lba____)
| hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_279,c_0_280]) ).
cnf(c_0_285,plain,
hAPP(c_lessequals(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)) != c_Not,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_281,c_0_114]),c_0_131]),c_0_282]) ).
cnf(c_0_286,plain,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)) = hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool)),
inference(rw,[status(thm)],[c_0_283,c_0_160]) ).
cnf(c_0_287,plain,
( hAPP(c_Not,X1) = hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lba____)
| hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lba____) = X1 ),
inference(spm,[status(thm)],[c_0_279,c_0_284]) ).
cnf(c_0_288,plain,
hAPP(c_or,hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool))) != c_Not,
inference(rw,[status(thm)],[c_0_285,c_0_190]) ).
cnf(c_0_289,plain,
hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),c_HOL_Ouminus__class_Ouminus(tc_bool)),c_Orderings_Obot__class_Obot(tc_bool))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_245,c_0_286]),c_0_153])]) ).
cnf(c_0_290,plain,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_Arrow__Order__Mirabelle_OLin,
inference(spm,[status(thm)],[c_0_267,c_0_225]) ).
cnf(c_0_291,plain,
( hAPP(c_Not,hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lba____)) = X1
| hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lba____) = X1 ),
inference(spm,[status(thm)],[c_0_224,c_0_287]) ).
cnf(c_0_292,plain,
hAPP(c_or,hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lab____)) != c_Not,
inference(rw,[status(thm)],[c_0_288,c_0_206]) ).
cnf(c_0_293,plain,
hBOOL(hAPP(hAPP(c_in(X1),v_Lab____),c_Arrow__Order__Mirabelle_OLin)),
inference(spm,[status(thm)],[c_0_266,c_0_158]) ).
cnf(c_0_294,plain,
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_HOL_Ouminus__class_Ouminus(tc_bool)
| ~ hBOOL(c_Orderings_Otop__class_Otop(tc_bool)) ),
inference(spm,[status(thm)],[c_0_267,c_0_283]) ).
cnf(c_0_295,plain,
hBOOL(hAPP(hAPP(c_or,hAPP(X1,c_Orderings_Obot__class_Obot(tc_bool))),hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_289,c_0_163]),c_0_283]),c_0_160]) ).
cnf(c_0_296,plain,
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lba____)
| hAPP(c_Not,hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lba____)) != c_Arrow__Order__Mirabelle_OLin ),
inference(spm,[status(thm)],[c_0_290,c_0_291]) ).
cnf(c_0_297,plain,
hAPP(c_or,hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lba____)) != c_Not,
inference(rw,[status(thm)],[c_0_292,c_0_248]) ).
cnf(c_0_298,plain,
hAPP(hAPP(c_Set_Oinsert(X1),v_Lab____),c_Arrow__Order__Mirabelle_OLin) = c_Arrow__Order__Mirabelle_OLin,
inference(spm,[status(thm)],[c_0_140,c_0_293]) ).
cnf(c_0_299,plain,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_HOL_Ouminus__class_Ouminus(tc_bool),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_294,c_0_123])]) ).
cnf(c_0_300,plain,
hAPP(c_or,hAPP(X1,c_Orderings_Obot__class_Obot(tc_bool))) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
inference(spm,[status(thm)],[c_0_267,c_0_295]) ).
cnf(c_0_301,plain,
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lba____)
| hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lba____) = X2
| X2 != c_Arrow__Order__Mirabelle_OLin ),
inference(spm,[status(thm)],[c_0_296,c_0_291]) ).
cnf(c_0_302,plain,
( hAPP(c_or,hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lba____)) = hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lba____)
| hAPP(c_Not,hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lba____)) != c_Not ),
inference(spm,[status(thm)],[c_0_297,c_0_291]) ).
cnf(c_0_303,plain,
( hBOOL(hAPP(c_Not,c_Arrow__Order__Mirabelle_OLin))
| hBOOL(c_Arrow__Order__Mirabelle_OLin) ),
inference(spm,[status(thm)],[c_0_143,c_0_298]) ).
cnf(c_0_304,plain,
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_Not
| ~ hBOOL(X2) ),
inference(spm,[status(thm)],[c_0_267,c_0_224]) ).
cnf(c_0_305,plain,
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lba____)
| c_HOL_Ouminus__class_Ouminus(tc_bool) != hAPP(c_Not,hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lba____)) ),
inference(spm,[status(thm)],[c_0_299,c_0_291]) ).
cnf(c_0_306,plain,
hAPP(c_or,X1) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_300,c_0_174]),c_0_175]) ).
cnf(c_0_307,plain,
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lba____)
| hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lba____) = c_Arrow__Order__Mirabelle_OLin ),
inference(er,[status(thm)],[c_0_301]) ).
cnf(c_0_308,plain,
( hAPP(c_or,hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lba____)) = hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lba____)
| hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lba____) = X1
| X1 != c_Not ),
inference(spm,[status(thm)],[c_0_302,c_0_291]) ).
cnf(c_0_309,plain,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_Not,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_267,c_0_303]),c_0_304]) ).
cnf(c_0_310,plain,
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lba____)
| c_HOL_Ouminus__class_Ouminus(tc_bool) = hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lba____) ),
inference(spm,[status(thm)],[c_0_305,c_0_291]) ).
cnf(c_0_311,plain,
( hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lba____) = c_Arrow__Order__Mirabelle_OLin
| hAPP(c_or,X1) != hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lba____) ),
inference(spm,[status(thm)],[c_0_306,c_0_307]) ).
cnf(c_0_312,plain,
( hAPP(c_or,hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lba____)) = hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lba____)
| hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lba____) = c_Not ),
inference(er,[status(thm)],[c_0_308]) ).
cnf(c_0_313,plain,
( hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lba____) = c_Arrow__Order__Mirabelle_OLin
| hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lba____) != c_Not ),
inference(spm,[status(thm)],[c_0_309,c_0_307]) ).
cnf(c_0_314,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)) = X2
| ~ class_Lattices_Oboolean__algebra(X1) ),
cls_double__compl_0 ).
cnf(c_0_315,plain,
( c_HOL_Ouminus__class_Ouminus(tc_bool) = hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lba____)
| hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lba____) != c_Arrow__Order__Mirabelle_OLin ),
inference(spm,[status(thm)],[c_0_290,c_0_310]) ).
cnf(c_0_316,plain,
hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lba____) = c_Arrow__Order__Mirabelle_OLin,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_311,c_0_312]),c_0_313]) ).
cnf(c_0_317,axiom,
~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X1),X1)),
cls_less__not__refl_0 ).
cnf(c_0_318,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
cls_not__leE_0 ).
cnf(c_0_319,plain,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X1)) = X1,
inference(spm,[status(thm)],[c_0_314,c_0_136]) ).
cnf(c_0_320,plain,
c_HOL_Ouminus__class_Ouminus(tc_bool) = c_Arrow__Order__Mirabelle_OLin,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_315,c_0_316]),c_0_316])]) ).
cnf(c_0_321,plain,
hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X1),X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_317,c_0_318]),c_0_91])]) ).
cnf(c_0_322,plain,
hAPP(hAPP(hAPP(c_COMBS(X1,X2,X3),X4),c_Collect(X5)),X6) = hAPP(hAPP(X4,X6),X6),
inference(spm,[status(thm)],[c_0_154,c_0_97]) ).
cnf(c_0_323,plain,
hAPP(c_Arrow__Order__Mirabelle_OLin,hAPP(c_Arrow__Order__Mirabelle_OLin,X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_319,c_0_320]),c_0_320]) ).
cnf(c_0_324,plain,
hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lab____) = c_Arrow__Order__Mirabelle_OLin,
inference(rw,[status(thm)],[c_0_253,c_0_316]) ).
cnf(c_0_325,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X2)
| ~ class_Lattices_Olattice(X1) ),
cls_inf__sup__aci_I1_J_0 ).
cnf(c_0_326,axiom,
class_Lattices_Olattice(tc_bool),
clsarity_bool__Lattices_Olattice ).
cnf(c_0_327,plain,
hBOOL(hAPP(hAPP(hAPP(c_COMBS(X1,X2,X3),c_lessequals(tc_nat)),c_Collect(X4)),X5)),
inference(spm,[status(thm)],[c_0_321,c_0_322]) ).
cnf(c_0_328,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X3))) ),
cls_ComplD_0 ).
cnf(c_0_329,plain,
hBOOL(hAPP(hAPP(c_in(X1),v_Lba____),c_Arrow__Order__Mirabelle_OLin)),
inference(spm,[status(thm)],[c_0_266,c_0_225]) ).
cnf(c_0_330,plain,
hBOOL(hAPP(hAPP(c_or,X1),hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_295,c_0_174]),c_0_175]) ).
cnf(c_0_331,plain,
( hAPP(c_or,c_Arrow__Order__Mirabelle_OLin) = c_Arrow__Order__Mirabelle_OLin
| c_Not = c_Arrow__Order__Mirabelle_OLin ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_312,c_0_316]),c_0_316]),c_0_316]) ).
cnf(c_0_332,plain,
hAPP(c_Arrow__Order__Mirabelle_OLin,c_Arrow__Order__Mirabelle_OLin) = v_Lab____,
inference(spm,[status(thm)],[c_0_323,c_0_324]) ).
cnf(c_0_333,plain,
~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_bool),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X2),X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_194,c_0_325]),c_0_326])]) ).
cnf(c_0_334,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)),X4) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4))
| ~ class_Lattices_Olattice(X1) ),
cls_inf__sup__aci_I2_J_0 ).
cnf(c_0_335,plain,
hAPP(hAPP(c_COMBS(X1,X2,X3),c_lessequals(tc_nat)),c_Collect(X4)) = hAPP(c_lessequals(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),
inference(spm,[status(thm)],[c_0_181,c_0_327]) ).
cnf(c_0_336,plain,
hAPP(hAPP(c_lessequals(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),X1) = hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool)),
inference(rw,[status(thm)],[c_0_142,c_0_160]) ).
cnf(c_0_337,plain,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(hAPP(c_COMBB(tc_bool,tc_bool,X1),c_Not),X3)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(rw,[status(thm)],[c_0_328,c_0_125]) ).
cnf(c_0_338,plain,
hBOOL(hAPP(hAPP(c_in(X1),c_Arrow__Order__Mirabelle_OLin),hAPP(c_in(X2),v_Lba____))),
inference(spm,[status(thm)],[c_0_266,c_0_329]) ).
cnf(c_0_339,plain,
( c_Arrow__Order__Mirabelle_OLin = X1
| ~ hBOOL(X1) ),
inference(rw,[status(thm)],[c_0_279,c_0_316]) ).
cnf(c_0_340,plain,
( c_Not = c_Arrow__Order__Mirabelle_OLin
| hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,c_Arrow__Order__Mirabelle_OLin)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_330,c_0_331]),c_0_227]),c_0_241]),c_0_253]),c_0_316]),c_0_224]) ).
cnf(c_0_341,plain,
v_Lab____ = v_Lba____,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_323,c_0_316]),c_0_332]) ).
cnf(c_0_342,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X4),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) ),
cls_disjoint__iff__not__equal_0 ).
cnf(c_0_343,plain,
~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_bool),X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X3),X1)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_333,c_0_334]),c_0_326])]) ).
cnf(c_0_344,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)) = X2
| ~ class_Lattices_Olattice(X1) ),
cls_inf__sup__absorb_0 ).
cnf(c_0_345,plain,
hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool)) = hAPP(hAPP(c_lessequals(tc_nat),X1),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_154,c_0_335]),c_0_336]),c_0_97]) ).
cnf(c_0_346,plain,
~ hBOOL(hAPP(hAPP(c_in(X1),c_Arrow__Order__Mirabelle_OLin),hAPP(hAPP(c_COMBB(tc_bool,tc_bool,X1),c_Not),hAPP(c_in(X2),v_Lba____)))),
inference(spm,[status(thm)],[c_0_337,c_0_338]) ).
cnf(c_0_347,plain,
( hAPP(c_Arrow__Order__Mirabelle_OLin,c_Arrow__Order__Mirabelle_OLin) = c_Arrow__Order__Mirabelle_OLin
| c_Not = c_Arrow__Order__Mirabelle_OLin ),
inference(spm,[status(thm)],[c_0_339,c_0_340]) ).
cnf(c_0_348,plain,
hAPP(c_Arrow__Order__Mirabelle_OLin,c_Arrow__Order__Mirabelle_OLin) = v_Lba____,
inference(rw,[status(thm)],[c_0_332,c_0_341]) ).
cnf(c_0_349,plain,
hBOOL(c_Arrow__Order__Mirabelle_OLin),
inference(rw,[status(thm)],[c_0_225,c_0_316]) ).
cnf(c_0_350,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ hBOOL(hAPP(X2,X4))
| ~ hBOOL(hAPP(X3,X4)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_342,c_0_106]),c_0_106]) ).
cnf(c_0_351,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),c_Orderings_Otop__class_Otop(X1)))
| ~ class_Orderings_Otop(X1) ),
cls_top__greatest_0 ).
cnf(c_0_352,plain,
~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_bool),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X1),X2)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X3),X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_343,c_0_344]),c_0_326])]) ).
cnf(c_0_353,plain,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X1),hAPP(hAPP(c_lessequals(tc_nat),X2),X2)) = X1,
inference(spm,[status(thm)],[c_0_170,c_0_345]) ).
cnf(c_0_354,axiom,
( hAPP(c_Complete__Lattice_OSup__class_OSup(X1),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(c_Complete__Lattice_OSup__class_OSup(X1),X3))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
cls_Sup__insert_0 ).
cnf(c_0_355,axiom,
hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)) = hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),
cls_insert__absorb2_0 ).
cnf(c_0_356,axiom,
( hAPP(c_Complete__Lattice_OSup__class_OSup(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool))) = c_Orderings_Otop__class_Otop(X1)
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
cls_Sup__UNIV_0 ).
cnf(c_0_357,plain,
~ hBOOL(hAPP(c_Not,hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lba____))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_346,c_0_106]),c_0_134]),c_0_106]) ).
cnf(c_0_358,plain,
( c_Not = c_Arrow__Order__Mirabelle_OLin
| v_Lba____ = c_Arrow__Order__Mirabelle_OLin ),
inference(spm,[status(thm)],[c_0_347,c_0_348]) ).
cnf(c_0_359,plain,
( c_Not = c_Arrow__Order__Mirabelle_OLin
| hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_256,c_0_331]),c_0_349])]) ).
cnf(c_0_360,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),c_Collect(X2)),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ hBOOL(hAPP(X3,X4))
| ~ hBOOL(X4) ),
inference(spm,[status(thm)],[c_0_350,c_0_97]) ).
cnf(c_0_361,plain,
hBOOL(hAPP(hAPP(c_lessequals(tc_bool),X1),c_Orderings_Otop__class_Otop(tc_bool))),
inference(spm,[status(thm)],[c_0_351,c_0_113]) ).
cnf(c_0_362,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool))) = X2,
cls_Int__UNIV__right_0 ).
cnf(c_0_363,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X3)) ),
cls_xt1_I7_J_0 ).
cnf(c_0_364,plain,
~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_bool),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(c_lessequals(tc_nat),X1),X1)),X2)),X3)),
inference(spm,[status(thm)],[c_0_352,c_0_353]) ).
cnf(c_0_365,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),hAPP(c_Complete__Lattice_OSup__class_OSup(X1),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))) = hAPP(c_Complete__Lattice_OSup__class_OSup(X1),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(spm,[status(thm)],[c_0_354,c_0_355]) ).
cnf(c_0_366,plain,
hAPP(hAPP(c_lessequals(tc_nat),X1),X1) = hAPP(hAPP(c_or,hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lab____)),v_x),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_345,c_0_227]),c_0_224]) ).
cnf(c_0_367,axiom,
class_Complete__Lattice_Ocomplete__lattice(tc_bool),
clsarity_bool__Complete__Lattice_Ocomplete__lattice ).
cnf(c_0_368,plain,
( c_Complete__Lattice_OSup__class_OSup(X1) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ hBOOL(c_Orderings_Otop__class_Otop(X1))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(spm,[status(thm)],[c_0_267,c_0_356]) ).
cnf(c_0_369,plain,
( c_Not = c_Arrow__Order__Mirabelle_OLin
| ~ hBOOL(hAPP(c_Not,v_Lba____)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_357,c_0_358]),c_0_332]),c_0_341]) ).
cnf(c_0_370,plain,
( c_Not = c_Arrow__Order__Mirabelle_OLin
| hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_359,c_0_323]) ).
cnf(c_0_371,plain,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),c_Collect(X2)),hAPP(c_lessequals(tc_bool),X3)) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_360,c_0_361]),c_0_123])]) ).
cnf(c_0_372,plain,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),hAPP(c_lessequals(tc_bool),c_Orderings_Obot__class_Obot(tc_bool))) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_362,c_0_114]),c_0_131]) ).
cnf(c_0_373,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),X1))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_bool),X2),X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_363,c_0_126]),c_0_215])]) ).
cnf(c_0_374,plain,
( X1 = c_Orderings_Otop__class_Otop(tc_bool)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_bool),X1),c_Orderings_Otop__class_Otop(tc_bool))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_214,c_0_361]),c_0_215])]) ).
cnf(c_0_375,plain,
~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_bool),hAPP(c_Complete__Lattice_OSup__class_OSup(tc_bool),hAPP(hAPP(c_Set_Oinsert(tc_bool),hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lab____)),X1))),X2)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_364,c_0_365]),c_0_366]),c_0_241]),c_0_367])]) ).
cnf(c_0_376,plain,
( hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Collect(X3)) = c_Collect(X3)
| ~ hBOOL(X2) ),
inference(spm,[status(thm)],[c_0_147,c_0_97]) ).
cnf(c_0_377,plain,
c_Complete__Lattice_OSup__class_OSup(tc_bool) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_368,c_0_123]),c_0_367])]) ).
cnf(c_0_378,plain,
( hAPP(c_Not,X1) = c_Arrow__Order__Mirabelle_OLin
| hBOOL(X1) ),
inference(rw,[status(thm)],[c_0_284,c_0_316]) ).
cnf(c_0_379,plain,
c_Not = c_Arrow__Order__Mirabelle_OLin,
inference(spm,[status(thm)],[c_0_369,c_0_370]) ).
cnf(c_0_380,plain,
c_Collect(X1) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
inference(spm,[status(thm)],[c_0_371,c_0_372]) ).
cnf(c_0_381,plain,
( X1 = c_Orderings_Otop__class_Otop(tc_bool)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_Orderings_Otop__class_Otop(tc_bool))) ),
inference(spm,[status(thm)],[c_0_373,c_0_374]) ).
cnf(c_0_382,plain,
~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_bool),hAPP(c_Complete__Lattice_OSup__class_OSup(tc_bool),c_Collect(X1))),X2)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_375,c_0_376]),c_0_158])]) ).
cnf(c_0_383,plain,
( X1 = c_Orderings_Otop__class_Otop(X2)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X2),X1),c_Orderings_Otop__class_Otop(X2)))
| ~ class_Orderings_Otop(X2)
| ~ class_Orderings_Oorder(X2) ),
inference(spm,[status(thm)],[c_0_214,c_0_351]) ).
cnf(c_0_384,plain,
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lba____)
| c_Complete__Lattice_OSup__class_OSup(tc_bool) != hAPP(c_Not,hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lba____)) ),
inference(spm,[status(thm)],[c_0_377,c_0_291]) ).
cnf(c_0_385,plain,
( hAPP(c_Arrow__Order__Mirabelle_OLin,X1) = c_Arrow__Order__Mirabelle_OLin
| hBOOL(X1) ),
inference(rw,[status(thm)],[c_0_378,c_0_379]) ).
cnf(c_0_386,plain,
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lba____)
| c_Collect(X2) != hAPP(c_Not,hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lba____)) ),
inference(spm,[status(thm)],[c_0_380,c_0_291]) ).
cnf(c_0_387,plain,
hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_Orderings_Otop__class_Otop(tc_bool))),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_290,c_0_381]),c_0_381]) ).
cnf(c_0_388,plain,
~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_bool),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X1),X2)),X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_333,c_0_344]),c_0_326])]) ).
cnf(c_0_389,plain,
hAPP(c_Complete__Lattice_OSup__class_OSup(tc_bool),c_Collect(X1)) = hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lab____),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_382,c_0_383]),c_0_160]),c_0_227]),c_0_241]),c_0_224]),c_0_113]),c_0_215])]) ).
cnf(c_0_390,plain,
c_Complete__Lattice_OSup__class_OSup(tc_bool) != hAPP(c_Not,c_Arrow__Order__Mirabelle_OLin),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_384,c_0_316]),c_0_316]),c_0_290]) ).
cnf(c_0_391,plain,
( hAPP(c_Arrow__Order__Mirabelle_OLin,X1) = c_Arrow__Order__Mirabelle_OLin
| c_Arrow__Order__Mirabelle_OLin = X1 ),
inference(spm,[status(thm)],[c_0_339,c_0_385]) ).
cnf(c_0_392,plain,
c_Collect(X1) != hAPP(c_Not,c_Arrow__Order__Mirabelle_OLin),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_386,c_0_316]),c_0_316]),c_0_290]) ).
cnf(c_0_393,plain,
hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool)))),
inference(spm,[status(thm)],[c_0_387,c_0_160]) ).
cnf(c_0_394,plain,
~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_bool),hAPP(c_Complete__Lattice_OSup__class_OSup(tc_bool),hAPP(hAPP(c_Set_Oinsert(tc_bool),X1),X2))),X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_388,c_0_365]),c_0_367])]) ).
cnf(c_0_395,plain,
hAPP(hAPP(c_Set_Oinsert(X1),c_Collect(X2)),c_Complete__Lattice_OSup__class_OSup(tc_bool)) = c_Complete__Lattice_OSup__class_OSup(tc_bool),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_147,c_0_389]),c_0_158])]) ).
cnf(c_0_396,plain,
c_Complete__Lattice_OSup__class_OSup(tc_bool) != v_Lba____,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_390,c_0_379]),c_0_332]),c_0_341]) ).
cnf(c_0_397,plain,
( c_Arrow__Order__Mirabelle_OLin = X1
| v_Lba____ = X1 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_323,c_0_391]),c_0_332]),c_0_341]) ).
cnf(c_0_398,plain,
c_Collect(X1) != v_Lba____,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_392,c_0_379]),c_0_332]),c_0_341]) ).
cnf(c_0_399,plain,
hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_bool),v_Lba____),c_Arrow__Order__Mirabelle_OLin)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_393,c_0_379]),c_0_227]),c_0_379]),c_0_241]),c_0_341]),c_0_316]),c_0_332]),c_0_341]),c_0_227]),c_0_379]),c_0_241]),c_0_341]),c_0_316]),c_0_332]),c_0_341]),c_0_316]) ).
cnf(c_0_400,plain,
~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_bool),hAPP(c_Complete__Lattice_OSup__class_OSup(tc_bool),c_Complete__Lattice_OSup__class_OSup(tc_bool))),c_Collect(X1))),
inference(spm,[status(thm)],[c_0_394,c_0_395]) ).
cnf(c_0_401,plain,
c_Complete__Lattice_OSup__class_OSup(tc_bool) = c_Arrow__Order__Mirabelle_OLin,
inference(spm,[status(thm)],[c_0_396,c_0_397]) ).
cnf(c_0_402,plain,
c_Collect(X1) = c_Arrow__Order__Mirabelle_OLin,
inference(spm,[status(thm)],[c_0_398,c_0_397]) ).
cnf(c_0_403,plain,
hAPP(hAPP(c_HOL_Oord__class_Oless(tc_bool),v_Lba____),c_Arrow__Order__Mirabelle_OLin) = c_Arrow__Order__Mirabelle_OLin,
inference(spm,[status(thm)],[c_0_339,c_0_399]) ).
cnf(c_0_404,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_400,c_0_401]),c_0_332]),c_0_341]),c_0_402]),c_0_403]),c_0_349])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SCT077-1 : TPTP v8.1.2. Released v4.1.0.
% 0.11/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n009.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Aug 24 15:14:06 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.57 start to proof: theBenchmark
% 47.86/47.91 % Version : CSE_E---1.5
% 47.86/47.91 % Problem : theBenchmark.p
% 47.86/47.91 % Proof found
% 47.86/47.91 % SZS status Theorem for theBenchmark.p
% 47.86/47.91 % SZS output start Proof
% See solution above
% 47.95/47.93 % Total time : 47.320000 s
% 47.95/47.93 % SZS output end Proof
% 47.95/47.93 % Total time : 47.339000 s
%------------------------------------------------------------------------------