TSTP Solution File: SCT044-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SCT044-1 : 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 : n007.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 14:10:51 EDT 2023
% Result : Unsatisfiable 29.41s 29.49s
% Output : CNFRefutation 29.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 63
% Number of leaves : 189
% Syntax : Number of formulae : 471 ( 148 unt; 115 typ; 0 def)
% Number of atoms : 639 ( 235 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 522 ( 239 ~; 283 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 13 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 267 ( 104 >; 163 *; 0 +; 0 <<)
% Number of predicates : 45 ( 43 usr; 1 prp; 0-9 aty)
% Number of functors : 72 ( 72 usr; 11 con; 0-7 aty)
% Number of variables : 787 ( 213 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
tc_bool: $i ).
tff(decl_23,type,
tc_fun: ( $i * $i ) > $i ).
tff(decl_24,type,
c_Lattices_Olower__semilattice__class_Oinf: $i > $i ).
tff(decl_25,type,
hAPP: ( $i * $i ) > $i ).
tff(decl_26,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(decl_27,type,
class_Lattices_Olower__semilattice: $i > $o ).
tff(decl_28,type,
class_Lattices_Olattice: $i > $o ).
tff(decl_29,type,
c_Lattices_Oupper__semilattice__class_Osup: $i > $i ).
tff(decl_30,type,
c_Orderings_Obot__class_Obot: $i > $i ).
tff(decl_31,type,
c_Fun_Ofun__upd: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_32,type,
c_Set_Oimage: ( $i * $i * $i * $i ) > $i ).
tff(decl_33,type,
c_Finite__Set_Ofinite: ( $i * $i ) > $o ).
tff(decl_34,type,
class_Lattices_Oupper__semilattice: $i > $o ).
tff(decl_35,type,
class_Orderings_Opreorder: $i > $o ).
tff(decl_36,type,
c_HOL_Oord__class_Oless: ( $i * $i * $i ) > $o ).
tff(decl_37,type,
class_Orderings_Oorder: $i > $o ).
tff(decl_38,type,
class_HOL_Oord: $i > $o ).
tff(decl_39,type,
c_HOL_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).
tff(decl_40,type,
class_Lattices_Obounded__lattice: $i > $o ).
tff(decl_41,type,
c_Fun_Oinj__on: ( $i * $i * $i * $i ) > $o ).
tff(decl_42,type,
hBOOL: $i > $o ).
tff(decl_43,type,
c_Relation_OImage: ( $i * $i * $i * $i ) > $i ).
tff(decl_44,type,
c_Set_Oinsert: ( $i * $i * $i ) > $i ).
tff(decl_45,type,
c_Finite__Set_Ofold__graph: ( $i * $i * $i * $i * $i * $i ) > $o ).
tff(decl_46,type,
c_Finite__Set_Ofun__left__comm__idem: ( $i * $i * $i ) > $o ).
tff(decl_47,type,
class_Orderings_Obot: $i > $o ).
tff(decl_48,type,
c_HOL_Ouminus__class_Ouminus: $i > $i ).
tff(decl_49,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
tff(decl_50,type,
c_Finite__Set_Ofun__left__comm: ( $i * $i * $i ) > $o ).
tff(decl_51,type,
class_Lattices_Odistrib__lattice: $i > $o ).
tff(decl_52,type,
class_Orderings_Olinorder: $i > $o ).
tff(decl_53,type,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR: ( $i * $i * $i * $i ) > $i ).
tff(decl_54,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
tff(decl_55,type,
c_Finite__Set_Osetsum: ( $i * $i * $i * $i ) > $i ).
tff(decl_56,type,
c_in: $i > $i ).
tff(decl_57,type,
class_Complete__Lattice_Ocomplete__lattice: $i > $o ).
tff(decl_58,type,
c_COMBC: ( $i * $i * $i * $i ) > $i ).
tff(decl_59,type,
class_OrderedGroup_Olordered__ab__group__add: $i > $o ).
tff(decl_60,type,
class_Lattices_Oboolean__algebra: $i > $o ).
tff(decl_61,type,
c_COMBB: ( $i * $i * $i * $i ) > $i ).
tff(decl_62,type,
c_Not: $i ).
tff(decl_63,type,
c_Collect: ( $i * $i ) > $i ).
tff(decl_64,type,
c_Set_Ovimage: ( $i * $i * $i * $i ) > $i ).
tff(decl_65,type,
c_Nitpick_Ofold__graph_H: ( $i * $i * $i * $i * $i * $i ) > $o ).
tff(decl_66,type,
class_Finite__Set_Ofinite_Ofinite: $i > $o ).
tff(decl_67,type,
c_ATP__Linkup_Osko__Set__Xbex__Un__1__3: ( $i * $i * $i * $i ) > $i ).
tff(decl_68,type,
tc_prod: ( $i * $i ) > $i ).
tff(decl_69,type,
c_Pair: ( $i * $i * $i * $i ) > $i ).
tff(decl_70,type,
class_OrderedGroup_Oab__semigroup__mult: $i > $o ).
tff(decl_71,type,
c_HOL_Otimes__class_Otimes: $i > $i ).
tff(decl_72,type,
c_fequal: $i > $i ).
tff(decl_73,type,
class_OrderedGroup_Ocomm__monoid__add: $i > $o ).
tff(decl_74,type,
c_ATP__Linkup_Osko__Finite__Set__Xsetsum__reindex__cong__1__1: ( $i * $i * $i * $i * $i * $i * $i ) > $i ).
tff(decl_75,type,
c_COMBK: ( $i * $i * $i ) > $i ).
tff(decl_76,type,
c_Typedef_Otype__definition: ( $i * $i * $i * $i * $i ) > $o ).
tff(decl_77,type,
c_Complete__Lattice_Ocomplete__lattice: ( $i * $i * $i * $i * $i * $i * $i * $i * $i ) > $o ).
tff(decl_78,type,
class_Ring__and__Field_Oidom: $i > $o ).
tff(decl_79,type,
class_Ring__and__Field_Ofield: $i > $o ).
tff(decl_80,type,
c_HOL_Oinverse__class_Odivide: $i > $i ).
tff(decl_81,type,
c_List_Olist_ONil: $i > $i ).
tff(decl_82,type,
c_List_Ofoldl: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_83,type,
tc_Arrow__Order__Mirabelle_Oalt: $i ).
tff(decl_84,type,
v_sko__Arrow__Order__Mirabelle__Xunanimity__def__1: ( $i * $i * $i ) > $i ).
tff(decl_85,type,
tc_Arrow__Order__Mirabelle_Oindi: $i ).
tff(decl_86,type,
c_Arrow__Order__Mirabelle_OProf: $i ).
tff(decl_87,type,
c_Arrow__Order__Mirabelle_Ounanimity: $i > $o ).
tff(decl_88,type,
class_Ring__and__Field_Oring: $i > $o ).
tff(decl_89,type,
v_sko__Arrow__Order__Mirabelle__XIIA__def__1: ( $i * $i * $i * $i ) > $i ).
tff(decl_90,type,
c_Arrow__Order__Mirabelle_OIIA: $i > $o ).
tff(decl_91,type,
v_sko__Arrow__Order__Mirabelle__Xthird__alt__1: ( $i * $i ) > $i ).
tff(decl_92,type,
c_List_Olist_OCons: ( $i * $i * $i ) > $i ).
tff(decl_93,type,
c_List_Odistinct: ( $i * $i ) > $o ).
tff(decl_94,type,
c_FuncSet_OPi: ( $i * $i * $i * $i ) > $i ).
tff(decl_95,type,
c_FuncSet_Osko__FuncSet__XfuncsetI__1__1: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_96,type,
tc_nat: $i ).
tff(decl_97,type,
class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).
tff(decl_98,type,
class_Ring__and__Field_Osemiring__0: $i > $o ).
tff(decl_99,type,
class_Ring__and__Field_Odivision__by__zero: $i > $o ).
tff(decl_100,type,
v_sko__Arrow__Order__Mirabelle__Xdictator__def__1: ( $i * $i ) > $i ).
tff(decl_101,type,
c_Arrow__Order__Mirabelle_Odictator: ( $i * $i ) > $o ).
tff(decl_102,type,
class_Ring__and__Field_Oordered__ring__strict: $i > $o ).
tff(decl_103,type,
class_OrderedGroup_Oab__semigroup__idem__mult: $i > $o ).
tff(decl_104,type,
c_Fun_Ooverride__on: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_105,type,
class_OrderedGroup_Ogroup__add: $i > $o ).
tff(decl_106,type,
c_ATP__Linkup_Osko__Set__XbexCI__1__1: ( $i * $i * $i ) > $i ).
tff(decl_107,type,
c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3: ( $i * $i * $i ) > $i ).
tff(decl_108,type,
c_SetInterval_Oord_OatLeastLessThan: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_109,type,
c_SetInterval_Oord_OatLeastAtMost: ( $i * $i * $i * $i ) > $i ).
tff(decl_110,type,
c_SetInterval_Oord_OgreaterThanLessThan: ( $i * $i * $i * $i ) > $i ).
tff(decl_111,type,
c_SetInterval_Oord_OgreaterThanAtMost: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_112,type,
c_ATP__Linkup_Osko__Set__XbexI__1__1: ( $i * $i * $i ) > $i ).
tff(decl_113,type,
c_FuncSet_Osko__FuncSet__XextensionalityI__1__1: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_114,type,
c_FuncSet_Oextensional: ( $i * $i * $i ) > $i ).
tff(decl_115,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
tff(decl_116,type,
c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_117,type,
c_ATP__Linkup_Osko__Set__XbexE__1__1: ( $i * $i * $i ) > $i ).
tff(decl_118,type,
c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1: ( $i * $i * $i * $i ) > $i ).
tff(decl_119,type,
c_ATP__Linkup_Osko__Set__XballE__1__1: ( $i * $i * $i ) > $i ).
tff(decl_120,type,
c_SetInterval_Oord_OatMost: ( $i * $i * $i ) > $i ).
tff(decl_121,type,
c_SetInterval_Oord_OgreaterThan: ( $i * $i * $i ) > $i ).
tff(decl_122,type,
c_SetInterval_Oord_OlessThan: ( $i * $i * $i ) > $i ).
tff(decl_123,type,
c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1: ( $i * $i * $i ) > $i ).
tff(decl_124,type,
c_FuncSet_Osko__FuncSet__XPi__I__1__1: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_125,type,
c_FuncSet_Osko__FuncSet__XPi__I_H__1__1: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_126,type,
c_HOL_Oundefined: $i > $i ).
tff(decl_127,type,
v_sko__Arrow__Order__Mirabelle__XIIA__def__2: $i > $i ).
tff(decl_128,type,
v_sko__Arrow__Order__Mirabelle__Xunanimity__def__2: $i > $i ).
tff(decl_129,type,
v_sko__Arrow__Order__Mirabelle__XIIA__def__3: $i > $i ).
tff(decl_130,type,
c_List_Osko__List__Xfoldl__apply__inv__1__1: ( $i * $i * $i * $i ) > $i ).
tff(decl_131,type,
v_a____: $i ).
tff(decl_132,type,
v_b____: $i ).
tff(decl_133,type,
v_P____: $i ).
tff(decl_134,type,
v_P_H____: $i > $i ).
tff(decl_135,type,
v_c____: $i ).
tff(decl_136,type,
c_Arrow__Order__Mirabelle_Obelow: $i ).
cnf(cls_Collect__mem__eq_0,axiom,
c_Collect(hAPP(c_COMBC(c_in(X1),X1,tc_fun(X1,tc_bool),tc_bool),X2),X1) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Collect__mem__eq_0) ).
cnf(cls_Collect__def_0,axiom,
c_Collect(X1,X2) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Collect__def_0) ).
cnf(cls_COMBC__def_0,axiom,
hAPP(hAPP(c_COMBC(X1,X2,X3,X4),X5),X6) = hAPP(hAPP(X1,X6),X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBC__def_0) ).
cnf(cls_insert__def_0,axiom,
c_Set_Oinsert(X1,X2,X3) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),c_Collect(hAPP(c_COMBC(c_fequal(X3),X3,X3,tc_bool),X1),X3)),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__def_0) ).
cnf(cls_Pi__I_H_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_fun(X1,X2)),X3),c_FuncSet_OPi(X4,X5,X1,X2)))
| hBOOL(hAPP(hAPP(c_in(X1),c_FuncSet_Osko__FuncSet__XPi__I_H__1__1(X4,X5,X3,X1,X2)),X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Pi__I_H_0) ).
cnf(cls_CollectI_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_Collect(X3,X1)))
| ~ hBOOL(hAPP(X3,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CollectI_0) ).
cnf(cls_singleton__conv2_0,axiom,
c_Collect(hAPP(c_fequal(X1),X2),X1) = c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singleton__conv2_0) ).
cnf(cls_funcset__image_0,axiom,
( c_lessequals(c_Set_Oimage(X1,X2,X3,X4),X5,tc_fun(X4,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X3,X4)),X1),c_FuncSet_OPi(X2,c_COMBK(X5,tc_fun(X4,tc_bool),X3),X3,X4))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_funcset__image_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_ATP__Linkup_Oequal__imp__fequal_0,axiom,
hBOOL(hAPP(hAPP(c_fequal(X1),X2),X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).
cnf(cls_image__constant__conv_1,axiom,
( c_Set_Oimage(c_COMBK(X1,X2,X3),X4,X3,X2) = c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)
| X4 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__constant__conv_1) ).
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_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_subset__empty_0,axiom,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_lessequals(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__empty_0) ).
cnf(cls_Int__absorb_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X2) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__absorb_0) ).
cnf(cls_bot__least_0,axiom,
( c_lessequals(c_Orderings_Obot__class_Obot(X1),X2,X1)
| ~ class_Orderings_Obot(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot__least_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_empty__subsetI_0,axiom,
c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__subsetI_0) ).
cnf(cls_DiffE_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_HOL_Ominus__class_Ominus(X4,X3,tc_fun(X1,tc_bool)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_DiffE_1) ).
cnf(cls_Diff__Compl_0,axiom,
c_HOL_Ominus__class_Ominus(X1,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),X3),tc_fun(X2,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X1),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__Compl_0) ).
cnf(cls_Collect__neg__eq_0,axiom,
c_Collect(hAPP(c_COMBB(c_Not,tc_bool,tc_bool,X1),X2),X1) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),c_Collect(X2,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Collect__neg__eq_0) ).
cnf(cls_xt1_I11_J_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| X3 = X2
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I11_J_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_le__funD_0,axiom,
( c_lessequals(hAPP(X2,X3),hAPP(X4,X3),X1)
| ~ class_HOL_Oord(X1)
| ~ c_lessequals(X2,X4,tc_fun(X5,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__funD_0) ).
cnf(clsarity_bool__HOL_Oord,axiom,
class_HOL_Oord(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__HOL_Oord) ).
cnf(cls_COMBB__def_0,axiom,
hAPP(hAPP(c_COMBB(X1,X2,X3,X4),X5),X6) = hAPP(X1,hAPP(X5,X6)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBB__def_0) ).
cnf(cls_less__le__not__le_1,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ c_lessequals(X2,X3,X1)
| ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
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_le__infE_0,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X2,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__infE_0) ).
cnf(clsarity_bool__Lattices_Olower__semilattice,axiom,
class_Lattices_Olower__semilattice(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olower__semilattice) ).
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_disjoint__eq__subset__Compl_0,axiom,
( c_lessequals(X2,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X3),tc_fun(X1,tc_bool))
| 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)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_disjoint__eq__subset__Compl_0) ).
cnf(cls_Int__empty__right_0,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__empty__right_0) ).
cnf(cls_Diff__eq_0,axiom,
c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X1),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__eq_0) ).
cnf(cls_Diff__empty_0,axiom,
c_HOL_Ominus__class_Ominus(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__empty_0) ).
cnf(cls_vimage__Collect__eq_0,axiom,
c_Set_Ovimage(X1,c_Collect(X2,X3),X4,X3) = c_Collect(hAPP(c_COMBB(X2,X3,tc_bool,X4),X1),X4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__Collect__eq_0) ).
cnf(cls_COMBK__def_0,axiom,
hAPP(c_COMBK(X1,X2,X3),X4) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBK__def_0) ).
cnf(cls_vimage__const_1,axiom,
( c_Set_Ovimage(c_COMBK(X1,X2,X3),X4,X3,X2) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X2),X1),X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__const_1) ).
cnf(cls_vimage__Compl_0,axiom,
c_Set_Ovimage(X1,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),X3),X4,X2) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X4,tc_bool)),c_Set_Ovimage(X1,X3,X4,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__Compl_0) ).
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_le__sup__iff_1,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X4),X2),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__sup__iff_1) ).
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_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__compl__bot_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__compl__bot_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_inf__absorb2_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) = X3
| ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X3,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__absorb2_0) ).
cnf(cls_le__infE_1,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X2,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X4),X3),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__infE_1) ).
cnf(cls_insert__Diff_0,axiom,
( c_Set_Oinsert(X1,c_HOL_Ominus__class_Ominus(X2,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X3) = X2
| ~ hBOOL(hAPP(hAPP(c_in(X3),X1),X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__Diff_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_Un__Diff__cancel_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),c_HOL_Ominus__class_Ominus(X3,X2,tc_fun(X1,tc_bool))) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Diff__cancel_0) ).
cnf(cls_CollectD_0,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X2),c_Collect(X1,X3))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CollectD_0) ).
cnf(cls_ex__in__conv_0,axiom,
~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ex__in__conv_0) ).
cnf(cls_Pi__I_0,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_fun(X1,X2)),X3),c_FuncSet_OPi(X4,X5,X1,X2)))
| hBOOL(hAPP(hAPP(c_in(X1),c_FuncSet_Osko__FuncSet__XPi__I__1__1(X4,X5,X3,X1,X2)),X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Pi__I_0) ).
cnf(cls_Collect__empty__eq_0,axiom,
( c_Collect(X1,X2) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ hBOOL(hAPP(X1,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Collect__empty__eq_0) ).
cnf(cls_rev__bexI_1,axiom,
( hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(X2,X1,X3)))
| ~ hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__bexI_1) ).
cnf(cls_CHAINED_0_01,axiom,
hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),hAPP(c_COMBC(hAPP(c_COMBC(hAPP(c_COMBB(c_Arrow__Order__Mirabelle_Obelow,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),v_P____),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_c____),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_b____)),c_Arrow__Order__Mirabelle_OProf)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0_01) ).
cnf(cls_fun__upd__apply_0,axiom,
hAPP(c_Fun_Ofun__upd(X1,X2,X3,X4,X5),X2) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__apply_0) ).
cnf(cls_Diff__cancel_0,axiom,
c_HOL_Ominus__class_Ominus(X1,X1,tc_fun(X2,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__cancel_0) ).
cnf(cls_fun__upd__idem__iff_1,axiom,
c_Fun_Ofun__upd(X1,X2,hAPP(X1,X2),X3,X4) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__idem__iff_1) ).
cnf(cls_rev__bexI_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(X2,X3,X1)),X2))
| ~ hBOOL(hAPP(X3,X4))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X4),X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__bexI_0) ).
cnf(cls_psubset__insert__iff_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X2))
| ~ c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubset__insert__iff_0) ).
cnf(clsarity_fun__Orderings_Oorder,axiom,
( class_Orderings_Oorder(tc_fun(X1,X2))
| ~ class_Orderings_Oorder(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).
cnf(cls_empty__not__insert_0,axiom,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_Set_Oinsert(X2,X3,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__not__insert_0) ).
cnf(cls_order__antisym__conv_0,axiom,
( X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X3,X1)
| ~ c_lessequals(X3,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__antisym__conv_0) ).
cnf(cls_INT__extend__simps_I4_J_0,axiom,
c_HOL_Ominus__class_Ominus(X1,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3,X2,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_INT__extend__simps_I4_J_0) ).
cnf(cls_psubset__eq_1,axiom,
~ c_HOL_Oord__class_Oless(X1,X1,tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubset__eq_1) ).
cnf(cls_sup__idem_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X2) = X2
| ~ class_Lattices_Oupper__semilattice(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__idem_0) ).
cnf(cls_inf__idem_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X2) = X2
| ~ class_Lattices_Olower__semilattice(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__idem_0) ).
cnf(cls_ball__conj__distrib_11,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X2),X4))
| ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X4,X1,X3)))
| ~ hBOOL(hAPP(X5,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X4,X5,X3))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ball__conj__distrib_11) ).
cnf(cls_ord_OlessThan__iff_1,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_SetInterval_Oord_OlessThan(X3,X4,X1)))
| ~ hBOOL(hAPP(hAPP(X3,X2),X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ord_OlessThan__iff_1) ).
cnf(cls_sup__absorb1_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) = X2
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ c_lessequals(X3,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__absorb1_0) ).
cnf(cls_inf__bot__right_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),c_Orderings_Obot__class_Obot(X1)) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Obounded__lattice(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__bot__right_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_sup__bot__right_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),c_Orderings_Obot__class_Obot(X1)) = X2
| ~ class_Lattices_Obounded__lattice(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__bot__right_0) ).
cnf(c_0_74,axiom,
c_Collect(hAPP(c_COMBC(c_in(X1),X1,tc_fun(X1,tc_bool),tc_bool),X2),X1) = X2,
cls_Collect__mem__eq_0 ).
cnf(c_0_75,axiom,
c_Collect(X1,X2) = X1,
cls_Collect__def_0 ).
cnf(c_0_76,axiom,
hAPP(hAPP(c_COMBC(X1,X2,X3,X4),X5),X6) = hAPP(hAPP(X1,X6),X5),
cls_COMBC__def_0 ).
cnf(c_0_77,plain,
hAPP(c_COMBC(c_in(X1),X1,tc_fun(X1,tc_bool),tc_bool),X2) = X2,
inference(rw,[status(thm)],[c_0_74,c_0_75]) ).
cnf(c_0_78,axiom,
c_Set_Oinsert(X1,X2,X3) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),c_Collect(hAPP(c_COMBC(c_fequal(X3),X3,X3,tc_bool),X1),X3)),X2),
cls_insert__def_0 ).
cnf(c_0_79,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_fun(X1,X2)),X3),c_FuncSet_OPi(X4,X5,X1,X2)))
| hBOOL(hAPP(hAPP(c_in(X1),c_FuncSet_Osko__FuncSet__XPi__I_H__1__1(X4,X5,X3,X1,X2)),X4)) ),
cls_Pi__I_H_0 ).
cnf(c_0_80,plain,
hAPP(hAPP(c_in(X1),X2),X3) = hAPP(X3,X2),
inference(spm,[status(thm)],[c_0_76,c_0_77]) ).
cnf(c_0_81,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_Collect(X3,X1)))
| ~ hBOOL(hAPP(X3,X2)) ),
cls_CollectI_0 ).
cnf(c_0_82,axiom,
c_Collect(hAPP(c_fequal(X1),X2),X1) = c_Set_Oinsert(X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),
cls_singleton__conv2_0 ).
cnf(c_0_83,plain,
c_Set_Oinsert(X1,X2,X3) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),hAPP(c_COMBC(c_fequal(X3),X3,X3,tc_bool),X1)),X2),
inference(rw,[status(thm)],[c_0_78,c_0_75]) ).
cnf(c_0_84,axiom,
( c_lessequals(c_Set_Oimage(X1,X2,X3,X4),X5,tc_fun(X4,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(X3,X4)),X1),c_FuncSet_OPi(X2,c_COMBK(X5,tc_fun(X4,tc_bool),X3),X3,X4))) ),
cls_funcset__image_0 ).
cnf(c_0_85,axiom,
~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2)),
cls_bot1E_0 ).
cnf(c_0_86,plain,
( hBOOL(hAPP(X1,c_FuncSet_Osko__FuncSet__XPi__I_H__1__1(X1,X2,X3,X4,X5)))
| hBOOL(hAPP(c_FuncSet_OPi(X1,X2,X4,X5),X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_79,c_0_80]),c_0_80]) ).
cnf(c_0_87,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(X3,X2)) ),
inference(rw,[status(thm)],[c_0_81,c_0_75]) ).
cnf(c_0_88,axiom,
hBOOL(hAPP(hAPP(c_fequal(X1),X2),X2)),
cls_ATP__Linkup_Oequal__imp__fequal_0 ).
cnf(c_0_89,axiom,
( c_Set_Oimage(c_COMBK(X1,X2,X3),X4,X3,X2) = c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)
| X4 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
cls_image__constant__conv_1 ).
cnf(c_0_90,plain,
hAPP(c_fequal(X1),X2) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(c_COMBC(c_fequal(X1),X1,X1,tc_bool),X2)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_82,c_0_75]),c_0_83]) ).
cnf(c_0_91,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_92,plain,
( c_lessequals(c_Set_Oimage(X1,X2,X3,X4),X5,tc_fun(X4,tc_bool))
| ~ hBOOL(hAPP(c_FuncSet_OPi(X2,c_COMBK(X5,tc_fun(X4,tc_bool),X3),X3,X4),X1)) ),
inference(rw,[status(thm)],[c_0_84,c_0_80]) ).
cnf(c_0_93,plain,
hBOOL(hAPP(c_FuncSet_OPi(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,X3,X4),X5)),
inference(spm,[status(thm)],[c_0_85,c_0_86]) ).
cnf(c_0_94,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_95,plain,
hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(c_fequal(X3),X2))),
inference(spm,[status(thm)],[c_0_87,c_0_88]) ).
cnf(c_0_96,plain,
( X4 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| c_Set_Oimage(c_COMBK(X1,X2,X3),X4,X3,X2) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X2,tc_bool)),hAPP(c_COMBC(c_fequal(X2),X2,X2,tc_bool),X1)),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))) ),
inference(rw,[status(thm)],[c_0_89,c_0_83]) ).
cnf(c_0_97,plain,
hAPP(c_COMBC(c_fequal(X1),X1,X1,tc_bool),X2) = hAPP(c_fequal(X1),X2),
inference(rw,[status(thm)],[c_0_90,c_0_91]) ).
cnf(c_0_98,axiom,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ c_lessequals(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
cls_subset__empty_0 ).
cnf(c_0_99,plain,
c_lessequals(c_Set_Oimage(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3,X4),X5,tc_fun(X4,tc_bool)),
inference(spm,[status(thm)],[c_0_92,c_0_93]) ).
cnf(c_0_100,plain,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),hAPP(c_fequal(X2),X3)),X4) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X3),X4)) ),
inference(spm,[status(thm)],[c_0_94,c_0_95]) ).
cnf(c_0_101,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X2) = X2,
cls_Int__absorb_0 ).
cnf(c_0_102,plain,
( c_Set_Oimage(c_COMBK(X1,X2,X3),X4,X3,X2) = hAPP(c_fequal(X2),X1)
| X4 = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_96,c_0_97]),c_0_91]) ).
cnf(c_0_103,plain,
c_Set_Oimage(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3,X4) = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool)),
inference(spm,[status(thm)],[c_0_98,c_0_99]) ).
cnf(c_0_104,plain,
hAPP(c_fequal(X1),X2) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_101]),c_0_95])]) ).
cnf(c_0_105,axiom,
( c_lessequals(c_Orderings_Obot__class_Obot(X1),X2,X1)
| ~ class_Orderings_Obot(X1) ),
cls_bot__least_0 ).
cnf(c_0_106,axiom,
class_Orderings_Obot(tc_bool),
clsarity_bool__Orderings_Obot ).
cnf(c_0_107,axiom,
c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)),
cls_empty__subsetI_0 ).
cnf(c_0_108,plain,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_103]),c_0_104]) ).
cnf(c_0_109,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_HOL_Ominus__class_Ominus(X4,X3,tc_fun(X1,tc_bool)))) ),
cls_DiffE_1 ).
cnf(c_0_110,axiom,
c_HOL_Ominus__class_Ominus(X1,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),X3),tc_fun(X2,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X2,tc_bool)),X1),X3),
cls_Diff__Compl_0 ).
cnf(c_0_111,axiom,
c_Collect(hAPP(c_COMBB(c_Not,tc_bool,tc_bool,X1),X2),X1) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),c_Collect(X2,X1)),
cls_Collect__neg__eq_0 ).
cnf(c_0_112,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| X3 = X2
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_xt1_I11_J_0 ).
cnf(c_0_113,plain,
c_lessequals(c_Orderings_Obot__class_Obot(tc_bool),X1,tc_bool),
inference(spm,[status(thm)],[c_0_105,c_0_106]) ).
cnf(c_0_114,axiom,
class_Orderings_Oorder(tc_bool),
clsarity_bool__Orderings_Oorder ).
cnf(c_0_115,axiom,
( c_lessequals(hAPP(X2,X3),hAPP(X4,X3),X1)
| ~ class_HOL_Oord(X1)
| ~ c_lessequals(X2,X4,tc_fun(X5,X1)) ),
cls_le__funD_0 ).
cnf(c_0_116,plain,
c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,tc_fun(X3,tc_bool)),
inference(spm,[status(thm)],[c_0_107,c_0_108]) ).
cnf(c_0_117,axiom,
class_HOL_Oord(tc_bool),
clsarity_bool__HOL_Oord ).
cnf(c_0_118,plain,
( ~ hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X4))) ),
inference(spm,[status(thm)],[c_0_109,c_0_110]) ).
cnf(c_0_119,axiom,
hAPP(hAPP(c_COMBB(X1,X2,X3,X4),X5),X6) = hAPP(X1,hAPP(X5,X6)),
cls_COMBB__def_0 ).
cnf(c_0_120,plain,
hAPP(c_COMBB(c_Not,tc_bool,tc_bool,X1),X2) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_111,c_0_75]),c_0_75]) ).
cnf(c_0_121,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ c_lessequals(X2,X3,X1)
| ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
cls_less__le__not__le_1 ).
cnf(c_0_122,plain,
( c_Orderings_Obot__class_Obot(tc_bool) = X1
| c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_bool),X1,tc_bool) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_113]),c_0_114])]) ).
cnf(c_0_123,axiom,
class_Orderings_Opreorder(tc_bool),
clsarity_bool__Orderings_Opreorder ).
cnf(c_0_124,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X2,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X3),X4),X1) ),
cls_le__infE_0 ).
cnf(c_0_125,plain,
c_lessequals(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2),hAPP(X3,X2),tc_bool),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_116]),c_0_117])]) ).
cnf(c_0_126,axiom,
class_Lattices_Olower__semilattice(tc_bool),
clsarity_bool__Lattices_Olower__semilattice ).
cnf(c_0_127,plain,
( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X3),X4)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_118,c_0_80]),c_0_80]) ).
cnf(c_0_128,plain,
hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2),X3) = hAPP(c_Not,hAPP(X2,X3)),
inference(spm,[status(thm)],[c_0_119,c_0_120]) ).
cnf(c_0_129,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_130,axiom,
( c_lessequals(X2,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X3),tc_fun(X1,tc_bool))
| 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)) ),
cls_disjoint__eq__subset__Compl_0 ).
cnf(c_0_131,axiom,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
cls_Int__empty__right_0 ).
cnf(c_0_132,plain,
( c_Orderings_Obot__class_Obot(tc_bool) = X1
| ~ c_lessequals(X1,c_Orderings_Obot__class_Obot(tc_bool),tc_bool) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_122]),c_0_123])]) ).
cnf(c_0_133,plain,
c_lessequals(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2),X3,tc_bool),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_125]),c_0_126])]) ).
cnf(c_0_134,plain,
( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),X4))
| ~ hBOOL(hAPP(c_Not,hAPP(X3,X4))) ),
inference(rw,[status(thm)],[c_0_127,c_0_128]) ).
cnf(c_0_135,axiom,
c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X3,tc_bool)),X1),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),X2)),
cls_Diff__eq_0 ).
cnf(c_0_136,axiom,
c_HOL_Ominus__class_Ominus(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X1,
cls_Diff__empty_0 ).
cnf(c_0_137,plain,
( hBOOL(hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2),X3))
| hBOOL(hAPP(X2,X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_129,c_0_80]),c_0_80]) ).
cnf(c_0_138,axiom,
c_Set_Ovimage(X1,c_Collect(X2,X3),X4,X3) = c_Collect(hAPP(c_COMBB(X2,X3,tc_bool,X4),X1),X4),
cls_vimage__Collect__eq_0 ).
cnf(c_0_139,plain,
c_lessequals(X1,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))),tc_fun(X2,tc_bool)),
inference(spm,[status(thm)],[c_0_130,c_0_131]) ).
cnf(c_0_140,plain,
hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2) = c_Orderings_Obot__class_Obot(tc_bool),
inference(spm,[status(thm)],[c_0_132,c_0_133]) ).
cnf(c_0_141,plain,
( ~ hBOOL(hAPP(c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)),X4))
| ~ hBOOL(hAPP(c_Not,hAPP(c_Not,hAPP(X2,X4)))) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_135]),c_0_128]) ).
cnf(c_0_142,plain,
c_HOL_Ominus__class_Ominus(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X3,tc_bool)) = X1,
inference(spm,[status(thm)],[c_0_136,c_0_108]) ).
cnf(c_0_143,plain,
( hBOOL(hAPP(c_Not,hAPP(X1,X2)))
| hBOOL(hAPP(X1,X2)) ),
inference(rw,[status(thm)],[c_0_137,c_0_128]) ).
cnf(c_0_144,axiom,
hAPP(c_COMBK(X1,X2,X3),X4) = X1,
cls_COMBK__def_0 ).
cnf(c_0_145,axiom,
( c_Set_Ovimage(c_COMBK(X1,X2,X3),X4,X3,X2) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X2),X1),X4)) ),
cls_vimage__const_1 ).
cnf(c_0_146,plain,
c_Set_Ovimage(X1,X2,X4,X3) = hAPP(c_COMBB(X2,X3,tc_bool,X4),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_138,c_0_75]),c_0_75]) ).
cnf(c_0_147,axiom,
c_Set_Ovimage(X1,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),X3),X4,X2) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X4,tc_bool)),c_Set_Ovimage(X1,X3,X4,X2)),
cls_vimage__Compl_0 ).
cnf(c_0_148,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_149,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X4),X2),X3,X1) ),
cls_le__sup__iff_1 ).
cnf(c_0_150,plain,
c_lessequals(hAPP(X1,X2),hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool)),tc_bool),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_139]),c_0_128]),c_0_140]),c_0_117])]) ).
cnf(c_0_151,axiom,
class_Lattices_Oupper__semilattice(tc_bool),
clsarity_bool__Lattices_Oupper__semilattice ).
cnf(c_0_152,plain,
( ~ hBOOL(hAPP(c_Not,hAPP(c_Not,hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2))))
| ~ hBOOL(hAPP(X3,X2)) ),
inference(spm,[status(thm)],[c_0_141,c_0_142]) ).
cnf(c_0_153,plain,
( hBOOL(hAPP(c_Not,X1))
| hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_143,c_0_144]) ).
cnf(c_0_154,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_155,plain,
( hAPP(c_COMBB(X4,X2,tc_bool,X3),c_COMBK(X1,X2,X3)) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| hBOOL(hAPP(hAPP(c_in(X2),X1),X4)) ),
inference(rw,[status(thm)],[c_0_145,c_0_146]) ).
cnf(c_0_156,plain,
hAPP(c_COMBB(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X2,tc_bool)),X3),X2,tc_bool,X4),X1) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X4,tc_bool)),hAPP(c_COMBB(X3,X2,tc_bool,X4),X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_147,c_0_146]),c_0_146]) ).
cnf(c_0_157,plain,
hAPP(c_Not,hAPP(c_Not,hAPP(X1,X2))) = hAPP(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_148]),c_0_128]) ).
cnf(c_0_158,plain,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))) = X2,
inference(spm,[status(thm)],[c_0_91,c_0_108]) ).
cnf(c_0_159,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
cls_inf__compl__bot_0 ).
cnf(c_0_160,axiom,
class_Lattices_Oboolean__algebra(tc_bool),
clsarity_bool__Lattices_Oboolean__algebra ).
cnf(c_0_161,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) = X3
| ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X3,X2,X1) ),
cls_inf__absorb2_0 ).
cnf(c_0_162,plain,
c_lessequals(X1,hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool)),tc_bool),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_149,c_0_150]),c_0_151])]) ).
cnf(c_0_163,plain,
( hBOOL(hAPP(c_Not,hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2)))
| ~ hBOOL(hAPP(X3,X2)) ),
inference(spm,[status(thm)],[c_0_152,c_0_153]) ).
cnf(c_0_164,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X2,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X4),X3),X1) ),
cls_le__infE_1 ).
cnf(c_0_165,axiom,
( c_Set_Oinsert(X1,c_HOL_Ominus__class_Ominus(X2,c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X3),tc_fun(X3,tc_bool)),X3) = X2
| ~ hBOOL(hAPP(hAPP(c_in(X3),X1),X2)) ),
cls_insert__Diff_0 ).
cnf(c_0_166,plain,
( ~ hBOOL(hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2),X3))
| ~ hBOOL(hAPP(X2,X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_154,c_0_80]),c_0_80]) ).
cnf(c_0_167,plain,
( hAPP(c_COMBB(X1,X2,tc_bool,X3),c_COMBK(X4,X2,X3)) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| hBOOL(hAPP(X1,X4)) ),
inference(rw,[status(thm)],[c_0_155,c_0_80]) ).
cnf(c_0_168,plain,
hAPP(c_COMBB(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(tc_bool,tc_bool)),c_Not),tc_bool,tc_bool,X1),X2) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_156,c_0_120]),c_0_148]) ).
cnf(c_0_169,plain,
hAPP(c_Not,hAPP(c_Not,X1)) = X1,
inference(spm,[status(thm)],[c_0_157,c_0_158]) ).
cnf(c_0_170,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_94,c_0_80]),c_0_80]) ).
cnf(c_0_171,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_172,plain,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X1),hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X1)) = c_Orderings_Obot__class_Obot(tc_bool),
inference(spm,[status(thm)],[c_0_159,c_0_160]) ).
cnf(c_0_173,plain,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool))),X1) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_161,c_0_162]),c_0_126])]) ).
cnf(c_0_174,plain,
( hBOOL(hAPP(c_Not,hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2)))
| ~ hBOOL(X3) ),
inference(spm,[status(thm)],[c_0_163,c_0_144]) ).
cnf(c_0_175,plain,
c_lessequals(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2),X2,tc_bool),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_164,c_0_125]),c_0_126])]) ).
cnf(c_0_176,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),hAPP(c_COMBC(c_fequal(X3),X3,X3,tc_bool),X1)),c_HOL_Ominus__class_Ominus(X2,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),hAPP(c_COMBC(c_fequal(X3),X3,X3,tc_bool),X1)),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))),tc_fun(X3,tc_bool))) = X2
| ~ hBOOL(hAPP(hAPP(c_in(X3),X1),X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_165,c_0_83]),c_0_83]) ).
cnf(c_0_177,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),c_HOL_Ominus__class_Ominus(X3,X2,tc_fun(X1,tc_bool))) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),
cls_Un__Diff__cancel_0 ).
cnf(c_0_178,plain,
( ~ hBOOL(hAPP(c_Not,hAPP(X1,X2)))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(rw,[status(thm)],[c_0_166,c_0_128]) ).
cnf(c_0_179,plain,
( c_COMBK(X1,tc_bool,X2) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| hBOOL(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_167,c_0_168]),c_0_128]),c_0_169]) ).
cnf(c_0_180,plain,
( c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X3,tc_bool)),X2),X4))
| ~ hBOOL(hAPP(X1,X4)) ),
inference(spm,[status(thm)],[c_0_170,c_0_135]) ).
cnf(c_0_181,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_171,c_0_160]) ).
cnf(c_0_182,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(spm,[status(thm)],[c_0_172,c_0_173]) ).
cnf(c_0_183,plain,
hBOOL(hAPP(c_Not,hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2))),
inference(spm,[status(thm)],[c_0_174,c_0_93]) ).
cnf(c_0_184,plain,
hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool)) = c_Orderings_Obot__class_Obot(tc_bool),
inference(spm,[status(thm)],[c_0_132,c_0_175]) ).
cnf(c_0_185,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(c_fequal(X1),X2)),X3) = X3
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_176,c_0_97]),c_0_97]),c_0_91]),c_0_177]) ).
cnf(c_0_186,plain,
( ~ hBOOL(hAPP(c_Not,X1))
| ~ hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_178,c_0_144]) ).
cnf(c_0_187,plain,
( c_Orderings_Obot__class_Obot(tc_bool) = X1
| hBOOL(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_179]),c_0_140]) ).
cnf(c_0_188,plain,
( hBOOL(hAPP(X1,X2))
| c_HOL_Ominus__class_Ominus(X3,X1,tc_fun(X4,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_bool))
| ~ hBOOL(hAPP(X3,X2)) ),
inference(spm,[status(thm)],[c_0_180,c_0_137]) ).
cnf(c_0_189,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(spm,[status(thm)],[c_0_181,c_0_182]) ).
cnf(c_0_190,plain,
hBOOL(hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool))),
inference(spm,[status(thm)],[c_0_183,c_0_184]) ).
cnf(c_0_191,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(c_fequal(X1),X2)),X3) = X3
| ~ hBOOL(hAPP(X3,X2)) ),
inference(rw,[status(thm)],[c_0_185,c_0_80]) ).
cnf(c_0_192,plain,
( c_Orderings_Obot__class_Obot(tc_bool) = hAPP(c_Not,X1)
| ~ hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_186,c_0_187]) ).
cnf(c_0_193,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X2),c_Collect(X1,X3))) ),
cls_CollectD_0 ).
cnf(c_0_194,axiom,
~ hBOOL(hAPP(hAPP(c_in(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))),
cls_ex__in__conv_0 ).
cnf(c_0_195,axiom,
( hBOOL(hAPP(hAPP(c_in(tc_fun(X1,X2)),X3),c_FuncSet_OPi(X4,X5,X1,X2)))
| hBOOL(hAPP(hAPP(c_in(X1),c_FuncSet_Osko__FuncSet__XPi__I__1__1(X4,X5,X3,X1,X2)),X4)) ),
cls_Pi__I_0 ).
cnf(c_0_196,plain,
( hBOOL(hAPP(X1,c_Orderings_Obot__class_Obot(tc_bool)))
| c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(tc_bool),X1,tc_fun(X2,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_188,c_0_189]),c_0_190])]) ).
cnf(c_0_197,plain,
~ hBOOL(c_Orderings_Obot__class_Obot(tc_bool)),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_191,c_0_184]),c_0_158]),c_0_104]) ).
cnf(c_0_198,plain,
( c_Orderings_Obot__class_Obot(tc_bool) = hAPP(c_Not,X1)
| c_Orderings_Obot__class_Obot(tc_bool) = X1 ),
inference(spm,[status(thm)],[c_0_192,c_0_187]) ).
cnf(c_0_199,plain,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X2),X1)) ),
inference(rw,[status(thm)],[c_0_193,c_0_75]) ).
cnf(c_0_200,plain,
hBOOL(hAPP(hAPP(c_in(tc_fun(X1,X2)),X3),c_FuncSet_OPi(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X4,X1,X2))),
inference(spm,[status(thm)],[c_0_194,c_0_195]) ).
cnf(c_0_201,plain,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_HOL_Ouminus__class_Ouminus(tc_bool),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_196,c_0_142]),c_0_140]),c_0_197]) ).
cnf(c_0_202,plain,
( hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool)) = X1
| c_Orderings_Obot__class_Obot(tc_bool) = X1 ),
inference(spm,[status(thm)],[c_0_169,c_0_198]) ).
cnf(c_0_203,plain,
hBOOL(hAPP(c_FuncSet_OPi(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,X1,X3),X4)),
inference(spm,[status(thm)],[c_0_199,c_0_200]) ).
cnf(c_0_204,axiom,
( c_Collect(X1,X2) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ hBOOL(hAPP(X1,X3)) ),
cls_Collect__empty__eq_0 ).
cnf(c_0_205,plain,
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_bool)
| c_HOL_Ouminus__class_Ouminus(tc_bool) != hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool)) ),
inference(spm,[status(thm)],[c_0_201,c_0_202]) ).
cnf(c_0_206,axiom,
( hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(X2,X1,X3)))
| ~ hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X2)) ),
cls_rev__bexI_1 ).
cnf(c_0_207,plain,
hBOOL(hAPP(hAPP(c_in(X1),X2),c_FuncSet_OPi(c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),X4,X3,X5))),
inference(spm,[status(thm)],[c_0_87,c_0_203]) ).
cnf(c_0_208,axiom,
hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),hAPP(c_COMBC(hAPP(c_COMBC(hAPP(c_COMBB(c_Arrow__Order__Mirabelle_Obelow,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),v_P____),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_c____),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_b____)),c_Arrow__Order__Mirabelle_OProf)),
cls_CHAINED_0_01 ).
cnf(c_0_209,plain,
( X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ hBOOL(hAPP(X1,X3)) ),
inference(rw,[status(thm)],[c_0_204,c_0_75]) ).
cnf(c_0_210,plain,
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_Orderings_Obot__class_Obot(tc_bool)
| c_HOL_Ouminus__class_Ouminus(tc_bool) = c_Orderings_Obot__class_Obot(tc_bool) ),
inference(spm,[status(thm)],[c_0_205,c_0_202]) ).
cnf(c_0_211,plain,
( hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(c_FuncSet_OPi(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3,X2,X4),X1,X5)))
| ~ hBOOL(hAPP(X1,X6)) ),
inference(spm,[status(thm)],[c_0_206,c_0_207]) ).
cnf(c_0_212,plain,
hBOOL(hAPP(c_Arrow__Order__Mirabelle_OProf,hAPP(c_COMBC(hAPP(c_COMBC(hAPP(c_COMBB(c_Arrow__Order__Mirabelle_Obelow,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),v_P____),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_c____),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_b____))),
inference(spm,[status(thm)],[c_0_199,c_0_208]) ).
cnf(c_0_213,plain,
( c_HOL_Ouminus__class_Ouminus(tc_bool) = c_Orderings_Obot__class_Obot(tc_bool)
| X1 != c_Orderings_Obot__class_Obot(tc_bool)
| ~ hBOOL(hAPP(X1,X2)) ),
inference(spm,[status(thm)],[c_0_209,c_0_210]) ).
cnf(c_0_214,plain,
hBOOL(hAPP(c_Arrow__Order__Mirabelle_OProf,c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(c_FuncSet_OPi(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,X1,X3),c_Arrow__Order__Mirabelle_OProf,X4))),
inference(spm,[status(thm)],[c_0_211,c_0_212]) ).
cnf(c_0_215,plain,
( c_HOL_Ouminus__class_Ouminus(tc_bool) = c_Orderings_Obot__class_Obot(tc_bool)
| c_Orderings_Obot__class_Obot(tc_bool) != c_Arrow__Order__Mirabelle_OProf ),
inference(spm,[status(thm)],[c_0_213,c_0_214]) ).
cnf(c_0_216,plain,
( X1 = X2
| hBOOL(X1)
| hBOOL(X2) ),
inference(spm,[status(thm)],[c_0_187,c_0_187]) ).
cnf(c_0_217,plain,
( c_HOL_Ouminus__class_Ouminus(tc_bool) = X1
| hBOOL(X1)
| X1 != c_Arrow__Order__Mirabelle_OProf ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_215,c_0_216]),c_0_197]) ).
cnf(c_0_218,plain,
( c_HOL_Ouminus__class_Ouminus(tc_bool) = c_Arrow__Order__Mirabelle_OProf
| hBOOL(c_Arrow__Order__Mirabelle_OProf) ),
inference(er,[status(thm)],[c_0_217]) ).
cnf(c_0_219,plain,
( hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool)) = hAPP(c_Arrow__Order__Mirabelle_OProf,c_Orderings_Obot__class_Obot(tc_bool))
| hBOOL(c_Arrow__Order__Mirabelle_OProf) ),
inference(spm,[status(thm)],[c_0_189,c_0_218]) ).
cnf(c_0_220,plain,
( hAPP(c_Not,X1) = hAPP(c_Arrow__Order__Mirabelle_OProf,X1)
| hBOOL(c_Arrow__Order__Mirabelle_OProf)
| hBOOL(X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_219,c_0_216]),c_0_197]) ).
cnf(c_0_221,plain,
( hAPP(c_Arrow__Order__Mirabelle_OProf,hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool))) = c_Orderings_Obot__class_Obot(tc_bool)
| hBOOL(c_Arrow__Order__Mirabelle_OProf) ),
inference(spm,[status(thm)],[c_0_182,c_0_218]) ).
cnf(c_0_222,plain,
( hAPP(c_Arrow__Order__Mirabelle_OProf,hAPP(c_Not,X1)) = X1
| hBOOL(c_Arrow__Order__Mirabelle_OProf)
| ~ hBOOL(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_186,c_0_220]),c_0_169]) ).
cnf(c_0_223,plain,
( c_HOL_Ominus__class_Ominus(X1,X2,tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(c_Not,hAPP(X2,X4)))
| ~ hBOOL(hAPP(X1,X4)) ),
inference(rw,[status(thm)],[c_0_180,c_0_128]) ).
cnf(c_0_224,plain,
( hAPP(c_Arrow__Order__Mirabelle_OProf,hAPP(c_Arrow__Order__Mirabelle_OProf,X1)) = X1
| hBOOL(c_Arrow__Order__Mirabelle_OProf) ),
inference(spm,[status(thm)],[c_0_181,c_0_218]) ).
cnf(c_0_225,plain,
( hAPP(c_Arrow__Order__Mirabelle_OProf,hAPP(c_Not,X1)) = X1
| hBOOL(c_Arrow__Order__Mirabelle_OProf) ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_221,c_0_216]),c_0_197]),c_0_222]) ).
cnf(c_0_226,axiom,
hAPP(c_Fun_Ofun__upd(X1,X2,X3,X4,X5),X2) = X3,
cls_fun__upd__apply_0 ).
cnf(c_0_227,plain,
( c_HOL_Ominus__class_Ominus(X1,c_Not,tc_fun(X2,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ hBOOL(hAPP(X1,X3))
| ~ hBOOL(X3) ),
inference(spm,[status(thm)],[c_0_223,c_0_169]) ).
cnf(c_0_228,plain,
( hAPP(c_Not,X1) = hAPP(c_Arrow__Order__Mirabelle_OProf,X1)
| hBOOL(c_Arrow__Order__Mirabelle_OProf) ),
inference(spm,[status(thm)],[c_0_224,c_0_225]) ).
cnf(c_0_229,axiom,
c_HOL_Ominus__class_Ominus(X1,X1,tc_fun(X2,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
cls_Diff__cancel_0 ).
cnf(c_0_230,plain,
( hBOOL(hAPP(X1,X2))
| c_HOL_Ominus__class_Ominus(c_Fun_Ofun__upd(X3,X2,X4,X5,X6),X1,tc_fun(X7,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_bool))
| ~ hBOOL(X4) ),
inference(spm,[status(thm)],[c_0_188,c_0_226]) ).
cnf(c_0_231,plain,
( hBOOL(c_Arrow__Order__Mirabelle_OProf)
| ~ hBOOL(hAPP(c_Arrow__Order__Mirabelle_OProf,X1))
| ~ hBOOL(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_227,c_0_228]),c_0_229])]) ).
cnf(c_0_232,plain,
( hBOOL(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))
| hBOOL(X2)
| ~ hBOOL(hAPP(X2,X3)) ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_209,c_0_216])]) ).
cnf(c_0_233,plain,
( c_Fun_Ofun__upd(X1,X2,X3,X4,X5) != c_Orderings_Obot__class_Obot(tc_fun(X6,tc_bool))
| ~ hBOOL(X3) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_230,c_0_136]),c_0_85]) ).
cnf(c_0_234,plain,
( c_Orderings_Obot__class_Obot(tc_bool) = hAPP(c_Arrow__Order__Mirabelle_OProf,X1)
| hBOOL(c_Arrow__Order__Mirabelle_OProf)
| ~ hBOOL(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_231,c_0_202]),c_0_190])]) ).
cnf(c_0_235,plain,
( hBOOL(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))
| hBOOL(c_Arrow__Order__Mirabelle_OProf) ),
inference(spm,[status(thm)],[c_0_232,c_0_214]) ).
cnf(c_0_236,plain,
c_Fun_Ofun__upd(X1,X2,hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool)),X3,X4) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_bool)),
inference(spm,[status(thm)],[c_0_233,c_0_190]) ).
cnf(c_0_237,axiom,
c_Fun_Ofun__upd(X1,X2,hAPP(X1,X2),X3,X4) = X1,
cls_fun__upd__idem__iff_1 ).
cnf(c_0_238,plain,
( hAPP(c_Arrow__Order__Mirabelle_OProf,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))) = c_Orderings_Obot__class_Obot(tc_bool)
| hBOOL(c_Arrow__Order__Mirabelle_OProf) ),
inference(spm,[status(thm)],[c_0_234,c_0_235]) ).
cnf(c_0_239,plain,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_Not,
inference(spm,[status(thm)],[c_0_236,c_0_237]) ).
cnf(c_0_240,plain,
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = hAPP(c_Arrow__Order__Mirabelle_OProf,c_Orderings_Obot__class_Obot(tc_bool))
| hBOOL(c_Arrow__Order__Mirabelle_OProf) ),
inference(spm,[status(thm)],[c_0_224,c_0_238]) ).
cnf(c_0_241,plain,
( hBOOL(c_Arrow__Order__Mirabelle_OProf)
| hAPP(c_Arrow__Order__Mirabelle_OProf,c_Orderings_Obot__class_Obot(tc_bool)) != c_Not ),
inference(spm,[status(thm)],[c_0_239,c_0_240]) ).
cnf(c_0_242,plain,
( hBOOL(c_Arrow__Order__Mirabelle_OProf)
| hBOOL(X1)
| hAPP(c_Arrow__Order__Mirabelle_OProf,X1) != c_Not ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_241,c_0_216]),c_0_197]) ).
cnf(c_0_243,plain,
( c_Orderings_Obot__class_Obot(tc_bool) = X1
| ~ hBOOL(hAPP(c_Not,X1)) ),
inference(spm,[status(thm)],[c_0_197,c_0_198]) ).
cnf(c_0_244,plain,
( hBOOL(hAPP(c_Arrow__Order__Mirabelle_OProf,X1))
| hBOOL(c_Arrow__Order__Mirabelle_OProf)
| X1 != c_Not ),
inference(spm,[status(thm)],[c_0_242,c_0_224]) ).
cnf(c_0_245,plain,
( c_Orderings_Obot__class_Obot(tc_bool) = X1
| hBOOL(c_Arrow__Order__Mirabelle_OProf)
| ~ hBOOL(hAPP(c_Arrow__Order__Mirabelle_OProf,X1)) ),
inference(spm,[status(thm)],[c_0_243,c_0_228]) ).
cnf(c_0_246,plain,
( hBOOL(hAPP(c_Arrow__Order__Mirabelle_OProf,c_Not))
| hBOOL(c_Arrow__Order__Mirabelle_OProf) ),
inference(er,[status(thm)],[c_0_244]) ).
cnf(c_0_247,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(X2,X3,X1)),X2))
| ~ hBOOL(hAPP(X3,X4))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X4),X2)) ),
cls_rev__bexI_0 ).
cnf(c_0_248,plain,
( c_HOL_Ouminus__class_Ouminus(tc_bool) = c_Orderings_Obot__class_Obot(tc_bool)
| c_Orderings_Obot__class_Obot(tc_bool) != c_Not ),
inference(spm,[status(thm)],[c_0_239,c_0_210]) ).
cnf(c_0_249,plain,
( c_Orderings_Obot__class_Obot(tc_bool) = c_Not
| hBOOL(c_Arrow__Order__Mirabelle_OProf) ),
inference(spm,[status(thm)],[c_0_245,c_0_246]) ).
cnf(c_0_250,plain,
( hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(X1,X2,X3)))
| ~ hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(X2,X4)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_247,c_0_80]),c_0_80]) ).
cnf(c_0_251,plain,
( c_HOL_Ouminus__class_Ouminus(tc_bool) = c_Not
| hBOOL(c_Arrow__Order__Mirabelle_OProf) ),
inference(spm,[status(thm)],[c_0_248,c_0_249]) ).
cnf(c_0_252,plain,
( hBOOL(hAPP(c_Not,c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(c_Not,X1,X2)))
| ~ hBOOL(hAPP(X1,c_Orderings_Obot__class_Obot(tc_bool))) ),
inference(spm,[status(thm)],[c_0_250,c_0_190]) ).
cnf(c_0_253,plain,
( hBOOL(c_Arrow__Order__Mirabelle_OProf)
| c_HOL_Ouminus__class_Ouminus(tc_bool) != hAPP(c_Arrow__Order__Mirabelle_OProf,c_Orderings_Obot__class_Obot(tc_bool)) ),
inference(spm,[status(thm)],[c_0_201,c_0_240]) ).
cnf(c_0_254,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X2))
| ~ c_HOL_Oord__class_Oless(X1,c_Set_Oinsert(X4,X2,X3),tc_fun(X3,tc_bool)) ),
cls_psubset__insert__iff_0 ).
cnf(c_0_255,axiom,
( class_Orderings_Oorder(tc_fun(X1,X2))
| ~ class_Orderings_Oorder(X2) ),
clsarity_fun__Orderings_Oorder ).
cnf(c_0_256,axiom,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_Set_Oinsert(X2,X3,X1),
cls_empty__not__insert_0 ).
cnf(c_0_257,axiom,
( X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X3,X1)
| ~ c_lessequals(X3,X2,X1) ),
cls_order__antisym__conv_0 ).
cnf(c_0_258,plain,
( c_Not = c_Arrow__Order__Mirabelle_OProf
| hBOOL(c_Arrow__Order__Mirabelle_OProf) ),
inference(spm,[status(thm)],[c_0_218,c_0_251]) ).
cnf(c_0_259,plain,
( hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(X2,X1,X3)))
| ~ hBOOL(hAPP(X2,X4))
| ~ hBOOL(hAPP(X1,X4)) ),
inference(rw,[status(thm)],[c_0_206,c_0_80]) ).
cnf(c_0_260,plain,
hBOOL(hAPP(c_Not,c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(c_Not,c_HOL_Ouminus__class_Ouminus(tc_bool),X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_252,c_0_189]),c_0_190])]) ).
cnf(c_0_261,plain,
( hBOOL(c_Arrow__Order__Mirabelle_OProf)
| hAPP(c_Arrow__Order__Mirabelle_OProf,c_Orderings_Obot__class_Obot(tc_bool)) != c_Arrow__Order__Mirabelle_OProf ),
inference(spm,[status(thm)],[c_0_253,c_0_218]) ).
cnf(c_0_262,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X2))
| ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),hAPP(c_COMBC(c_fequal(X3),X3,X3,tc_bool),X4)),X2),tc_fun(X3,tc_bool)) ),
inference(rw,[status(thm)],[c_0_254,c_0_83]) ).
cnf(c_0_263,plain,
class_Orderings_Oorder(tc_fun(X1,tc_bool)),
inference(spm,[status(thm)],[c_0_255,c_0_114]) ).
cnf(c_0_264,plain,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(c_COMBC(c_fequal(X1),X1,X1,tc_bool),X2)),X3),
inference(rw,[status(thm)],[c_0_256,c_0_83]) ).
cnf(c_0_265,plain,
( hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool)) = X1
| ~ c_lessequals(hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool)),X1,tc_bool) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_257,c_0_162]),c_0_114])]) ).
cnf(c_0_266,plain,
( c_Orderings_Obot__class_Obot(tc_bool) = hAPP(c_Not,c_Arrow__Order__Mirabelle_OProf)
| c_Not = c_Arrow__Order__Mirabelle_OProf ),
inference(spm,[status(thm)],[c_0_192,c_0_258]) ).
cnf(c_0_267,plain,
( hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(c_Not,X1,X2)))
| ~ hBOOL(hAPP(X1,c_Orderings_Obot__class_Obot(tc_bool))) ),
inference(spm,[status(thm)],[c_0_259,c_0_190]) ).
cnf(c_0_268,plain,
~ hBOOL(c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(c_Not,c_HOL_Ouminus__class_Ouminus(tc_bool),X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_227,c_0_260]),c_0_229])]) ).
cnf(c_0_269,plain,
( hBOOL(c_Arrow__Order__Mirabelle_OProf)
| hBOOL(X1)
| hAPP(c_Arrow__Order__Mirabelle_OProf,X1) != c_Arrow__Order__Mirabelle_OProf ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_261,c_0_216]),c_0_197]) ).
cnf(c_0_270,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_fun(X3,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X4),X2))
| ~ c_HOL_Oord__class_Oless(X1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X3,tc_bool)),hAPP(c_fequal(X3),X4)),X2),tc_fun(X3,tc_bool)) ),
inference(rw,[status(thm)],[c_0_262,c_0_97]) ).
cnf(c_0_271,plain,
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = X2
| c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_107]),c_0_263])]) ).
cnf(c_0_272,plain,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(c_fequal(X1),X2)),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
inference(rw,[status(thm)],[c_0_264,c_0_97]) ).
cnf(c_0_273,plain,
( c_Orderings_Obot__class_Obot(tc_bool) = X1
| X1 = X2
| ~ c_lessequals(X1,X2,tc_bool) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_265,c_0_198]),c_0_169]),c_0_169]) ).
cnf(c_0_274,plain,
( c_Not = c_Arrow__Order__Mirabelle_OProf
| c_lessequals(X1,c_Arrow__Order__Mirabelle_OProf,tc_bool) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_162,c_0_266]),c_0_169]) ).
cnf(c_0_275,plain,
hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(c_Not,c_HOL_Ouminus__class_Ouminus(tc_bool),X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_267,c_0_189]),c_0_190])]) ).
cnf(c_0_276,plain,
c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1(c_Not,c_HOL_Ouminus__class_Ouminus(tc_bool),X1) = c_Orderings_Obot__class_Obot(tc_bool),
inference(spm,[status(thm)],[c_0_268,c_0_187]) ).
cnf(c_0_277,plain,
( hBOOL(hAPP(c_Arrow__Order__Mirabelle_OProf,X1))
| hBOOL(c_Arrow__Order__Mirabelle_OProf)
| X1 != c_Arrow__Order__Mirabelle_OProf ),
inference(spm,[status(thm)],[c_0_269,c_0_224]) ).
cnf(c_0_278,plain,
( c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X3),X2)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_270,c_0_271]),c_0_272]) ).
cnf(c_0_279,plain,
c_Fun_Ofun__upd(c_Not,hAPP(c_Not,X1),X1,X2,X3) = c_Not,
inference(spm,[status(thm)],[c_0_237,c_0_169]) ).
cnf(c_0_280,plain,
( c_Orderings_Obot__class_Obot(tc_bool) = X1
| c_Not = c_Arrow__Order__Mirabelle_OProf
| X1 = c_Arrow__Order__Mirabelle_OProf ),
inference(spm,[status(thm)],[c_0_273,c_0_274]) ).
cnf(c_0_281,plain,
( c_HOL_Ominus__class_Ominus(X1,c_HOL_Ouminus__class_Ouminus(tc_bool),tc_fun(X2,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ hBOOL(hAPP(X1,hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X3)))
| ~ hBOOL(hAPP(c_Not,X3)) ),
inference(spm,[status(thm)],[c_0_223,c_0_181]) ).
cnf(c_0_282,plain,
( hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X1))
| hBOOL(X1) ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_275,c_0_216]),c_0_276]),c_0_197]) ).
cnf(c_0_283,plain,
( hBOOL(hAPP(c_Arrow__Order__Mirabelle_OProf,c_Arrow__Order__Mirabelle_OProf))
| hBOOL(c_Arrow__Order__Mirabelle_OProf) ),
inference(er,[status(thm)],[c_0_277]) ).
cnf(c_0_284,plain,
( c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool))
| ~ hBOOL(hAPP(X2,X3)) ),
inference(rw,[status(thm)],[c_0_278,c_0_80]) ).
cnf(c_0_285,axiom,
c_HOL_Ominus__class_Ominus(X1,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3,X2,tc_fun(X4,tc_bool)),tc_fun(X4,tc_bool)) = X1,
cls_INT__extend__simps_I4_J_0 ).
cnf(c_0_286,plain,
( c_Orderings_Obot__class_Obot(tc_bool) = c_Not
| c_Not = c_Arrow__Order__Mirabelle_OProf ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_279,c_0_280]),c_0_279])]) ).
cnf(c_0_287,plain,
( hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X1))
| ~ hBOOL(hAPP(c_Not,X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_281,c_0_282]),c_0_229])]) ).
cnf(c_0_288,plain,
( hBOOL(hAPP(c_Arrow__Order__Mirabelle_OProf,c_Orderings_Obot__class_Obot(tc_bool)))
| hBOOL(c_Arrow__Order__Mirabelle_OProf) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_219]),c_0_197]) ).
cnf(c_0_289,plain,
( c_Orderings_Obot__class_Obot(tc_bool) = hAPP(c_Arrow__Order__Mirabelle_OProf,hAPP(c_Arrow__Order__Mirabelle_OProf,c_Arrow__Order__Mirabelle_OProf))
| hBOOL(c_Arrow__Order__Mirabelle_OProf) ),
inference(spm,[status(thm)],[c_0_234,c_0_283]) ).
cnf(c_0_290,plain,
c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),c_Arrow__Order__Mirabelle_OProf,tc_fun(X1,tc_bool)),
inference(spm,[status(thm)],[c_0_284,c_0_214]) ).
cnf(c_0_291,plain,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,X1,tc_fun(X3,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool)),
inference(spm,[status(thm)],[c_0_229,c_0_285]) ).
cnf(c_0_292,plain,
( c_Not = c_Arrow__Order__Mirabelle_OProf
| X1 = c_Arrow__Order__Mirabelle_OProf
| c_Not = X1 ),
inference(spm,[status(thm)],[c_0_280,c_0_286]) ).
cnf(c_0_293,plain,
( hBOOL(c_Arrow__Order__Mirabelle_OProf)
| ~ hBOOL(c_Not) ),
inference(spm,[status(thm)],[c_0_231,c_0_246]) ).
cnf(c_0_294,plain,
( hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X1))
| hBOOL(c_Arrow__Order__Mirabelle_OProf)
| ~ hBOOL(hAPP(c_Arrow__Order__Mirabelle_OProf,X1)) ),
inference(spm,[status(thm)],[c_0_287,c_0_228]) ).
cnf(c_0_295,plain,
( hBOOL(hAPP(c_Arrow__Order__Mirabelle_OProf,hAPP(c_Arrow__Order__Mirabelle_OProf,hAPP(c_Arrow__Order__Mirabelle_OProf,c_Arrow__Order__Mirabelle_OProf))))
| hBOOL(c_Arrow__Order__Mirabelle_OProf) ),
inference(spm,[status(thm)],[c_0_288,c_0_289]) ).
cnf(c_0_296,plain,
c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),c_Arrow__Order__Mirabelle_OProf,tc_fun(X2,tc_bool)),
inference(spm,[status(thm)],[c_0_290,c_0_108]) ).
cnf(c_0_297,plain,
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_Arrow__Order__Mirabelle_OProf
| c_Not = c_Arrow__Order__Mirabelle_OProf ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_291,c_0_292]),c_0_291]),c_0_239]) ).
cnf(c_0_298,axiom,
~ c_HOL_Oord__class_Oless(X1,X1,tc_fun(X2,tc_bool)),
cls_psubset__eq_1 ).
cnf(c_0_299,plain,
( c_HOL_Ouminus__class_Ouminus(tc_bool) = c_Orderings_Obot__class_Obot(tc_bool)
| hBOOL(c_Arrow__Order__Mirabelle_OProf) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_235,c_0_210]),c_0_197]) ).
cnf(c_0_300,plain,
( X1 = c_Not
| hBOOL(c_Arrow__Order__Mirabelle_OProf)
| hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_293,c_0_216]) ).
cnf(c_0_301,plain,
( hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),hAPP(c_Arrow__Order__Mirabelle_OProf,hAPP(c_Arrow__Order__Mirabelle_OProf,c_Arrow__Order__Mirabelle_OProf))))
| hBOOL(c_Arrow__Order__Mirabelle_OProf) ),
inference(spm,[status(thm)],[c_0_294,c_0_295]) ).
cnf(c_0_302,plain,
c_Not = c_Arrow__Order__Mirabelle_OProf,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_296,c_0_297]),c_0_298]) ).
cnf(c_0_303,plain,
( hBOOL(c_Arrow__Order__Mirabelle_OProf)
| hAPP(c_Arrow__Order__Mirabelle_OProf,c_Orderings_Obot__class_Obot(tc_bool)) != c_Orderings_Obot__class_Obot(tc_bool) ),
inference(spm,[status(thm)],[c_0_253,c_0_299]) ).
cnf(c_0_304,plain,
( hAPP(c_Not,X1) = c_Not
| hBOOL(c_Arrow__Order__Mirabelle_OProf)
| ~ hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_186,c_0_300]) ).
cnf(c_0_305,plain,
( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_bool),hAPP(c_Arrow__Order__Mirabelle_OProf,hAPP(c_Arrow__Order__Mirabelle_OProf,c_Arrow__Order__Mirabelle_OProf))))
| hBOOL(c_Arrow__Order__Mirabelle_OProf) ),
inference(spm,[status(thm)],[c_0_301,c_0_299]) ).
cnf(c_0_306,plain,
hAPP(c_Arrow__Order__Mirabelle_OProf,hAPP(c_Arrow__Order__Mirabelle_OProf,X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_169,c_0_302]),c_0_302]) ).
cnf(c_0_307,plain,
( hBOOL(c_Arrow__Order__Mirabelle_OProf)
| hBOOL(X1)
| hAPP(c_Arrow__Order__Mirabelle_OProf,X1) != X1 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_303,c_0_216]),c_0_197]) ).
cnf(c_0_308,plain,
( hAPP(c_Arrow__Order__Mirabelle_OProf,X1) = c_Arrow__Order__Mirabelle_OProf
| hBOOL(c_Arrow__Order__Mirabelle_OProf)
| ~ hBOOL(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_304,c_0_302]),c_0_302]) ).
cnf(c_0_309,plain,
( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_bool),c_Arrow__Order__Mirabelle_OProf))
| hBOOL(c_Arrow__Order__Mirabelle_OProf) ),
inference(spm,[status(thm)],[c_0_305,c_0_306]) ).
cnf(c_0_310,plain,
( hBOOL(hAPP(c_Arrow__Order__Mirabelle_OProf,X1))
| hBOOL(c_Arrow__Order__Mirabelle_OProf)
| hAPP(c_Arrow__Order__Mirabelle_OProf,X1) != X1 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_307,c_0_225]),c_0_302]),c_0_302]) ).
cnf(c_0_311,plain,
( hAPP(c_Arrow__Order__Mirabelle_OProf,hAPP(c_Orderings_Obot__class_Obot(tc_bool),c_Arrow__Order__Mirabelle_OProf)) = c_Arrow__Order__Mirabelle_OProf
| hBOOL(c_Arrow__Order__Mirabelle_OProf) ),
inference(spm,[status(thm)],[c_0_308,c_0_309]) ).
cnf(c_0_312,plain,
( hBOOL(c_Arrow__Order__Mirabelle_OProf)
| X1 != hAPP(c_Arrow__Order__Mirabelle_OProf,c_Orderings_Obot__class_Obot(tc_bool))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(spm,[status(thm)],[c_0_209,c_0_240]) ).
cnf(c_0_313,plain,
( hBOOL(c_Arrow__Order__Mirabelle_OProf)
| hAPP(c_Orderings_Obot__class_Obot(tc_bool),c_Arrow__Order__Mirabelle_OProf) != c_Arrow__Order__Mirabelle_OProf ),
inference(spm,[status(thm)],[c_0_310,c_0_311]) ).
cnf(c_0_314,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X2) = X2
| ~ class_Lattices_Oupper__semilattice(X1) ),
cls_sup__idem_0 ).
cnf(c_0_315,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X2) = X2
| ~ class_Lattices_Olower__semilattice(X1) ),
cls_inf__idem_0 ).
cnf(c_0_316,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X2),X4))
| ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X4,X1,X3)))
| ~ hBOOL(hAPP(X5,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X4,X5,X3))) ),
cls_ball__conj__distrib_11 ).
cnf(c_0_317,plain,
( hBOOL(c_Arrow__Order__Mirabelle_OProf)
| ~ hBOOL(hAPP(hAPP(c_Arrow__Order__Mirabelle_OProf,c_Orderings_Obot__class_Obot(tc_bool)),X1)) ),
inference(er,[status(thm)],[c_0_312]) ).
cnf(c_0_318,plain,
( c_Orderings_Obot__class_Obot(tc_bool) = hAPP(c_Arrow__Order__Mirabelle_OProf,X1)
| c_Orderings_Obot__class_Obot(tc_bool) = X1 ),
inference(rw,[status(thm)],[c_0_198,c_0_302]) ).
cnf(c_0_319,plain,
( hBOOL(c_Arrow__Order__Mirabelle_OProf)
| hBOOL(X1)
| hAPP(X1,c_Arrow__Order__Mirabelle_OProf) != c_Arrow__Order__Mirabelle_OProf ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_313,c_0_216]),c_0_197]) ).
cnf(c_0_320,plain,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X1),X1) = X1,
inference(spm,[status(thm)],[c_0_314,c_0_151]) ).
cnf(c_0_321,plain,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X1),X1) = X1,
inference(spm,[status(thm)],[c_0_315,c_0_126]) ).
cnf(c_0_322,plain,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X4,X3,X5)))
| ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X4,X1,X5)))
| ~ hBOOL(hAPP(X4,X2)) ),
inference(rw,[status(thm)],[c_0_316,c_0_80]) ).
cnf(c_0_323,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_SetInterval_Oord_OlessThan(X3,X4,X1)))
| ~ hBOOL(hAPP(hAPP(X3,X2),X4)) ),
cls_ord_OlessThan__iff_1 ).
cnf(c_0_324,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) = X2
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ c_lessequals(X3,X2,X1) ),
cls_sup__absorb1_0 ).
cnf(c_0_325,plain,
( c_Orderings_Obot__class_Obot(tc_bool) = X1
| hBOOL(c_Arrow__Order__Mirabelle_OProf)
| ~ hBOOL(hAPP(X1,X2)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_317,c_0_318]),c_0_306]) ).
cnf(c_0_326,plain,
( hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Arrow__Order__Mirabelle_OProf))
| hBOOL(c_Arrow__Order__Mirabelle_OProf) ),
inference(spm,[status(thm)],[c_0_319,c_0_320]) ).
cnf(c_0_327,plain,
( hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),c_Arrow__Order__Mirabelle_OProf))
| hBOOL(c_Arrow__Order__Mirabelle_OProf) ),
inference(spm,[status(thm)],[c_0_319,c_0_321]) ).
cnf(c_0_328,plain,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X3,X1,X4)))
| ~ hBOOL(hAPP(X3,X2)) ),
inference(spm,[status(thm)],[c_0_322,c_0_203]) ).
cnf(c_0_329,plain,
( hBOOL(hAPP(c_SetInterval_Oord_OlessThan(X1,X2,X3),X4))
| ~ hBOOL(hAPP(hAPP(X1,X4),X2)) ),
inference(rw,[status(thm)],[c_0_323,c_0_80]) ).
cnf(c_0_330,plain,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool))),X1) = hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_324,c_0_162]),c_0_151])]) ).
cnf(c_0_331,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),c_Orderings_Obot__class_Obot(X1)) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Obounded__lattice(X1) ),
cls_inf__bot__right_0 ).
cnf(c_0_332,axiom,
class_Lattices_Obounded__lattice(tc_bool),
clsarity_bool__Lattices_Obounded__lattice ).
cnf(c_0_333,plain,
( c_Orderings_Obot__class_Obot(tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(tc_bool)
| hBOOL(c_Arrow__Order__Mirabelle_OProf) ),
inference(spm,[status(thm)],[c_0_325,c_0_326]) ).
cnf(c_0_334,plain,
( c_Orderings_Obot__class_Obot(tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(tc_bool)
| hBOOL(c_Arrow__Order__Mirabelle_OProf) ),
inference(spm,[status(thm)],[c_0_325,c_0_327]) ).
cnf(c_0_335,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),c_Orderings_Obot__class_Obot(X1)) = X2
| ~ class_Lattices_Obounded__lattice(X1) ),
cls_sup__bot__right_0 ).
cnf(c_0_336,plain,
( hBOOL(c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(X1,c_Not,X2))
| hBOOL(hAPP(c_Not,X3))
| ~ hBOOL(hAPP(X1,X3)) ),
inference(spm,[status(thm)],[c_0_328,c_0_153]) ).
cnf(c_0_337,plain,
hBOOL(hAPP(c_SetInterval_Oord_OlessThan(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X1,X2),hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_329,c_0_330]),c_0_190])]) ).
cnf(c_0_338,plain,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X1),c_Orderings_Obot__class_Obot(tc_bool)) = c_Orderings_Obot__class_Obot(tc_bool),
inference(spm,[status(thm)],[c_0_331,c_0_332]) ).
cnf(c_0_339,plain,
( c_Lattices_Olower__semilattice__class_Oinf(tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(tc_bool)
| hBOOL(c_Arrow__Order__Mirabelle_OProf) ),
inference(spm,[status(thm)],[c_0_333,c_0_334]) ).
cnf(c_0_340,plain,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X1),c_Orderings_Obot__class_Obot(tc_bool)) = X1,
inference(spm,[status(thm)],[c_0_335,c_0_332]) ).
cnf(c_0_341,plain,
hBOOL(c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3(c_SetInterval_Oord_OlessThan(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X1,X2),c_Not,X3)),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_336,c_0_337]),c_0_169]),c_0_197]) ).
cnf(c_0_342,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_bool)
| hBOOL(c_Arrow__Order__Mirabelle_OProf) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_338,c_0_339]),c_0_340]) ).
cnf(c_0_343,plain,
( hBOOL(hAPP(X1,X2))
| c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X2),X1,tc_fun(X3,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_bool))
| ~ hBOOL(X2) ),
inference(spm,[status(thm)],[c_0_188,c_0_321]) ).
cnf(c_0_344,plain,
( c_Orderings_Obot__class_Obot(tc_bool) = hAPP(c_Arrow__Order__Mirabelle_OProf,X1)
| ~ hBOOL(X1) ),
inference(rw,[status(thm)],[c_0_192,c_0_302]) ).
cnf(c_0_345,plain,
hBOOL(c_Arrow__Order__Mirabelle_OProf),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_341,c_0_342]),c_0_197]) ).
cnf(c_0_346,plain,
( hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X1) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| ~ hBOOL(X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_343,c_0_136]),c_0_85]) ).
cnf(c_0_347,plain,
( hAPP(c_Arrow__Order__Mirabelle_OProf,c_Orderings_Obot__class_Obot(tc_bool)) = X1
| c_Orderings_Obot__class_Obot(tc_bool) = X1 ),
inference(rw,[status(thm)],[c_0_202,c_0_302]) ).
cnf(c_0_348,plain,
c_Orderings_Obot__class_Obot(tc_bool) = hAPP(c_Arrow__Order__Mirabelle_OProf,c_Arrow__Order__Mirabelle_OProf),
inference(spm,[status(thm)],[c_0_344,c_0_345]) ).
cnf(c_0_349,plain,
hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool))) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
inference(spm,[status(thm)],[c_0_346,c_0_190]) ).
cnf(c_0_350,plain,
( hAPP(c_Arrow__Order__Mirabelle_OProf,c_Arrow__Order__Mirabelle_OProf) = X1
| c_Arrow__Order__Mirabelle_OProf = X1 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_347,c_0_348]),c_0_306]),c_0_348]) ).
cnf(c_0_351,plain,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_Arrow__Order__Mirabelle_OProf,
inference(rw,[status(thm)],[c_0_239,c_0_302]) ).
cnf(c_0_352,plain,
hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),c_Arrow__Order__Mirabelle_OProf) != hAPP(c_Arrow__Order__Mirabelle_OProf,c_Arrow__Order__Mirabelle_OProf),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_349,c_0_350]),c_0_302]),c_0_348]),c_0_306]),c_0_351]) ).
cnf(c_0_353,plain,
hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),c_Arrow__Order__Mirabelle_OProf) = c_Arrow__Order__Mirabelle_OProf,
inference(spm,[status(thm)],[c_0_352,c_0_350]) ).
cnf(c_0_354,plain,
hAPP(c_Arrow__Order__Mirabelle_OProf,c_Arrow__Order__Mirabelle_OProf) != c_Arrow__Order__Mirabelle_OProf,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_351,c_0_350]),c_0_351]) ).
cnf(c_0_355,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_321,c_0_353]),c_0_354]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SCT044-1 : TPTP v8.1.2. Released v4.1.0.
% 0.07/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.34 % Computer : n007.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Thu Aug 24 15:22:55 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.21/0.57 start to proof: theBenchmark
% 29.41/29.49 % Version : CSE_E---1.5
% 29.41/29.49 % Problem : theBenchmark.p
% 29.41/29.49 % Proof found
% 29.41/29.49 % SZS status Theorem for theBenchmark.p
% 29.41/29.49 % SZS output start Proof
% See solution above
% 29.53/29.51 % Total time : 28.892000 s
% 29.53/29.51 % SZS output end Proof
% 29.53/29.51 % Total time : 28.918000 s
%------------------------------------------------------------------------------