TSTP Solution File: SCT084-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SCT084-1 : 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 : n022.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 14:11:08 EDT 2023
% Result : Unsatisfiable 52.12s 52.20s
% Output : CNFRefutation 52.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 170
% Syntax : Number of formulae : 368 ( 113 unt; 111 typ; 0 def)
% Number of atoms : 461 ( 131 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 415 ( 211 ~; 204 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 218 ( 96 >; 122 *; 0 +; 0 <<)
% Number of predicates : 39 ( 37 usr; 1 prp; 0-4 aty)
% Number of functors : 74 ( 74 usr; 15 con; 0-6 aty)
% Number of variables : 435 ( 117 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
class_OrderedGroup_Ogroup__add: $i > $o ).
tff(decl_23,type,
c_HOL_Ominus__class_Ominus: ( $i * $i ) > $i ).
tff(decl_24,type,
hAPP: ( $i * $i ) > $i ).
tff(decl_25,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
tff(decl_26,type,
class_Ring__and__Field_Oidom: $i > $o ).
tff(decl_27,type,
class_Int_Onumber__ring: $i > $o ).
tff(decl_28,type,
c_Set_Oimage: ( $i * $i * $i ) > $i ).
tff(decl_29,type,
tc_bool: $i ).
tff(decl_30,type,
tc_fun: ( $i * $i ) > $i ).
tff(decl_31,type,
c_Lattices_Olower__semilattice__class_Oinf: ( $i * $i ) > $i ).
tff(decl_32,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(decl_33,type,
c_Relation_OImage: ( $i * $i * $i ) > $i ).
tff(decl_34,type,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR: ( $i * $i * $i * $i ) > $i ).
tff(decl_35,type,
c_COMBB: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_36,type,
c_Orderings_Obot__class_Obot: $i > $i ).
tff(decl_37,type,
c_HOL_Ouminus__class_Ouminus: $i > $i ).
tff(decl_38,type,
c_Orderings_Otop__class_Otop: $i > $i ).
tff(decl_39,type,
c_Set_Oinsert: $i > $i ).
tff(decl_40,type,
c_Relation_Orel__comp: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_41,type,
c_COMBK: ( $i * $i * $i ) > $i ).
tff(decl_42,type,
c_Product__Type_OSigma: ( $i * $i * $i * $i ) > $i ).
tff(decl_43,type,
tc_prod: ( $i * $i ) > $i ).
tff(decl_44,type,
class_Lattices_Olattice: $i > $o ).
tff(decl_45,type,
class_Lattices_Olower__semilattice: $i > $o ).
tff(decl_46,type,
c_in: $i > $i ).
tff(decl_47,type,
hBOOL: $i > $o ).
tff(decl_48,type,
c_Complete__Lattice_Ocomplete__lattice__class_OINFI: ( $i * $i * $i * $i ) > $i ).
tff(decl_49,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
tff(decl_50,type,
c_ATP__Linkup_Osko__Fun__Ximage__INT__1__1: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_51,type,
c_Fun_Oinj__on: ( $i * $i * $i * $i ) > $o ).
tff(decl_52,type,
class_Lattices_Obounded__lattice: $i > $o ).
tff(decl_53,type,
c_Finite__Set_Ofinite: ( $i * $i ) > $o ).
tff(decl_54,type,
class_Orderings_Obot: $i > $o ).
tff(decl_55,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
tff(decl_56,type,
c_Set_Ovimage: ( $i * $i * $i ) > $i ).
tff(decl_57,type,
class_OrderedGroup_Olordered__ab__group__add: $i > $o ).
tff(decl_58,type,
class_OrderedGroup_Oordered__ab__group__add: $i > $o ).
tff(decl_59,type,
class_Lattices_Oboolean__algebra: $i > $o ).
tff(decl_60,type,
class_Orderings_Oorder: $i > $o ).
tff(decl_61,type,
c_SetInterval_Oord__class_OatLeastLessThan: ( $i * $i * $i ) > $i ).
tff(decl_62,type,
c_FuncSet_OPi: ( $i * $i * $i * $i ) > $i ).
tff(decl_63,type,
class_Complete__Lattice_Ocomplete__lattice: $i > $o ).
tff(decl_64,type,
c_Transitive__Closure_Otrancl: ( $i * $i ) > $i ).
tff(decl_65,type,
c_Relation_OId__on: ( $i * $i ) > $i ).
tff(decl_66,type,
c_Relation_Orefl__on: ( $i * $i * $i ) > $o ).
tff(decl_67,type,
class_Orderings_Olinorder: $i > $o ).
tff(decl_68,type,
t_a: $i ).
tff(decl_69,type,
v_x: $i ).
tff(decl_70,type,
class_Orderings_Opreorder: $i > $o ).
tff(decl_71,type,
c_Wellfounded_Owf: ( $i * $i ) > $o ).
tff(decl_72,type,
c_COMBC: ( $i * $i * $i * $i ) > $i ).
tff(decl_73,type,
c_Relation_ODomain: ( $i * $i * $i ) > $i ).
tff(decl_74,type,
c_Equiv__Relations_Oequiv: ( $i * $i * $i ) > $o ).
tff(decl_75,type,
c_HOL_Oord__class_Oless: $i > $i ).
tff(decl_76,type,
class_Ring__and__Field_Oordered__semidom: $i > $o ).
tff(decl_77,type,
c_Nat_Osemiring__1__class_Oof__nat: ( $i * $i ) > $i ).
tff(decl_78,type,
c_Complete__Lattice_OSup__class_OSup: ( $i * $i ) > $i ).
tff(decl_79,type,
c_Relation_ORange: ( $i * $i * $i ) > $i ).
tff(decl_80,type,
class_HOL_Ominus: $i > $o ).
tff(decl_81,type,
c_List_Osko__Equiv__Relations__XquotientE__1__1: ( $i * $i * $i * $i ) > $i ).
tff(decl_82,type,
c_Equiv__Relations_Oquotient: ( $i * $i * $i ) > $i ).
tff(decl_83,type,
c_Wellfounded_Oacc: ( $i * $i ) > $i ).
tff(decl_84,type,
class_HOL_Oord: $i > $o ).
tff(decl_85,type,
class_Orderings_Otop: $i > $o ).
tff(decl_86,type,
c_ATP__Linkup_Osko__Relation__XRange__iff__1__1: ( $i * $i * $i * $i ) > $i ).
tff(decl_87,type,
c_Pair: ( $i * $i * $i * $i ) > $i ).
tff(decl_88,type,
c_ATP__Linkup_Osko__Relation__XRangeE__1__1: ( $i * $i * $i * $i ) > $i ).
tff(decl_89,type,
c_Finite__Set_Ocard: ( $i * $i ) > $i ).
tff(decl_90,type,
tc_nat: $i ).
tff(decl_91,type,
tc_Arrow__Order__Mirabelle_Oalt: $i ).
tff(decl_92,type,
c_Arrow__Order__Mirabelle_OLin: $i ).
tff(decl_93,type,
c_Arrow__Order__Mirabelle_Obelow: ( $i * $i * $i ) > $i ).
tff(decl_94,type,
c_Arrow__Order__Mirabelle_Oabove: ( $i * $i * $i ) > $i ).
tff(decl_95,type,
tc_Arrow__Order__Mirabelle_Oindi: $i ).
tff(decl_96,type,
c_Arrow__Order__Mirabelle_OProf: $i ).
tff(decl_97,type,
v_F: $i ).
tff(decl_98,type,
v_sko__local__Xpairwise__neutrality__1: ( $i * $i * $i * $i * $i * $i ) > $i ).
tff(decl_99,type,
v_sko__local__X2__1: ( $i * $i * $i * $i * $i * $i ) > $i ).
tff(decl_100,type,
v_sko__local__X3__1: ( $i * $i * $i * $i ) > $i ).
tff(decl_101,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
tff(decl_102,type,
class_HOL_Ouminus: $i > $o ).
tff(decl_103,type,
c_Relation_Ototal__on: ( $i * $i * $i ) > $o ).
tff(decl_104,type,
v_sko__local__X4__1: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_105,type,
c_HOL_OIf: $i > $i ).
tff(decl_106,type,
c_Recdef_Ocut: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_107,type,
class_Finite__Set_Ofinite_Ofinite: $i > $o ).
tff(decl_108,type,
c_Relation_Osym: ( $i * $i ) > $o ).
tff(decl_109,type,
c_Relation_OId: $i > $i ).
tff(decl_110,type,
c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__2: ( $i * $i ) > $i ).
tff(decl_111,type,
class_Ring__and__Field_Osemiring__1: $i > $o ).
tff(decl_112,type,
c_Relation_Oinv__image: ( $i * $i * $i * $i ) > $i ).
tff(decl_113,type,
class_Nat_Osemiring__char__0: $i > $o ).
tff(decl_114,type,
c_Wellfounded_Omlex__prod: ( $i * $i * $i ) > $i ).
tff(decl_115,type,
c_Arrow__Order__Mirabelle_Omkbot: ( $i * $i ) > $i ).
tff(decl_116,type,
c_Arrow__Order__Mirabelle_Omktop: ( $i * $i ) > $i ).
tff(decl_117,type,
c_ATP__Linkup_Osko__Set__Xball__UNIV__1__1: ( $i * $i ) > $i ).
tff(decl_118,type,
v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1: ( $i * $i ) > $i ).
tff(decl_119,type,
c_Wellfounded_Omeasure: ( $i * $i ) > $i ).
tff(decl_120,type,
c_Nitpick_Orefl_H: ( $i * $i ) > $o ).
tff(decl_121,type,
c_ATP__Linkup_Osko__Set__XUNIV__witness__1__1: $i > $i ).
tff(decl_122,type,
c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__1: ( $i * $i ) > $i ).
tff(decl_123,type,
c_ATP__Linkup_Osko__Set__XUNIV__eq__I__1__1: ( $i * $i ) > $i ).
tff(decl_124,type,
c_ATP__Linkup_Osko__Set__Xball__UNIV__1__2: ( $i * $i ) > $i ).
tff(decl_125,type,
v_h____: $i ).
tff(decl_126,type,
v_Lab____: $i ).
tff(decl_127,type,
v_Lba____: $i ).
tff(decl_128,type,
v_a____: $i ).
tff(decl_129,type,
v_b____: $i ).
tff(decl_130,type,
c_Arrow__Order__Mirabelle_Ounanimity: $i > $o ).
tff(decl_131,type,
v_p: $i ).
tff(decl_132,type,
c_fequal: ( $i * $i * $i ) > $o ).
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_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_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_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_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_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_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_Lab____)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0_01) ).
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_Lab____),c_Arrow__Order__Mirabelle_OLin)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0) ).
cnf(cls_inf__sup__ord_I2_J_0,axiom,
( c_lessequals(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X1),X3),X3,X1)
| ~ class_Lattices_Olattice(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I2_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_order__eq__iff_0,axiom,
( c_lessequals(X2,X2,X1)
| ~ class_Orderings_Oorder(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__iff_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_atLeastLessThan__empty_0,axiom,
( c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X3,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastLessThan__empty_0) ).
cnf(cls_inf__compl__bot_0,axiom,
( hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X1),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__greatest_0,axiom,
( c_lessequals(X2,hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3,X1),X4),X1)
| ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X2,X4,X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__greatest_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_Sup__upper_0,axiom,
( c_lessequals(X2,c_Complete__Lattice_OSup__class_OSup(X3,X1),X1)
| ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sup__upper_0) ).
cnf(cls_inf__sup__aci_I1_J_0,axiom,
( hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X1),X3) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3,X1),X2)
| ~ class_Lattices_Olattice(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I1_J_0) ).
cnf(cls_atLeastLessThan__empty__iff_0,axiom,
( ~ class_Orderings_Oorder(X1)
| c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastLessThan__empty__iff_0) ).
cnf(cls_le__iff__inf_0,axiom,
( hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X1),X3) = X2
| ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__inf_0) ).
cnf(cls_inf__le1_0,axiom,
( c_lessequals(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X1),X3),X2,X1)
| ~ class_Lattices_Olower__semilattice(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__le1_0) ).
cnf(cls_fun__diff__def_0,axiom,
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(X2,tc_fun(t_a,X1)),X3),v_x) = hAPP(c_HOL_Ominus__class_Ominus(hAPP(X2,v_x),X1),hAPP(X3,v_x))
| ~ class_HOL_Ominus(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__diff__def_0) ).
cnf(cls_Diff__insert__absorb_0,axiom,
( hAPP(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),tc_fun(X1,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))) = X3
| hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__insert__absorb_0) ).
cnf(clsarity_bool__HOL_Ominus,axiom,
class_HOL_Ominus(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__HOL_Ominus) ).
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_diff__eq_0,axiom,
( hAPP(c_HOL_Ominus__class_Ominus(X2,X1),X3) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3))
| ~ class_Lattices_Oboolean__algebra(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__eq_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(cls_inf__sup__aci_I4_J_0,axiom,
( hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X1),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X1),X3)) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X1),X3)
| ~ class_Lattices_Olattice(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I4_J_0) ).
cnf(cls_inf__sup__aci_I3_J_0,axiom,
( hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X1),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3,X1),X4)) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3,X1),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X1),X4))
| ~ class_Lattices_Olattice(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I3_J_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)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__neq__le__trans_0) ).
cnf(cls_top__greatest_0,axiom,
( c_lessequals(X2,c_Orderings_Otop__class_Otop(X1),X1)
| ~ class_Orderings_Otop(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_top__greatest_0) ).
cnf(cls_order__eq__iff_2,axiom,
( X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X3,X2,X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__iff_2) ).
cnf(cls_inf__sup__ord_I1_J_0,axiom,
( c_lessequals(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X1),X3),X2,X1)
| ~ class_Lattices_Olattice(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I1_J_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_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_xt1_I7_J_0,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X4,X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I7_J_0) ).
cnf(cls_const__Lin__Prof_0,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))),c_COMBK(X1,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi)),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X1),c_Arrow__Order__Mirabelle_OLin)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_const__Lin__Prof_0) ).
cnf(cls_empty__not__insert_0,axiom,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__not__insert_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_bex__UNIV_0,axiom,
( hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__1(X1,X2)))
| ~ hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bex__UNIV_0) ).
cnf(cls_UNIV__I_0,axiom,
hBOOL(hAPP(hAPP(c_in(X1),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UNIV__I_0) ).
cnf(cls_Lin__irrefl_0,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Lin__irrefl_0) ).
cnf(cls_bex__UNIV_2,axiom,
( hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__2(X1,X2)))
| ~ hBOOL(hAPP(X1,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bex__UNIV_2) ).
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_less__le__not__le_1,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ c_lessequals(X2,X3,X1)
| ~ 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_le__iff__inf_1,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Lattices_Olower__semilattice(X1)
| hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X1),X3) != X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__inf_1) ).
cnf(cls_compl__inf__bot_0,axiom,
( hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X1),X2) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_compl__inf__bot_0) ).
cnf(cls_less__le__not__le_2,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| c_lessequals(X3,X2,X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__le__not__le_2) ).
cnf(cls_xt1_I6_J_0,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X4,X1)
| ~ c_lessequals(X4,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).
cnf(cls_inf__absorb2_0,axiom,
( hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X1),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_inf__sup__aci_I2_J_0,axiom,
( hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X1),X3),X1),X4) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X1),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3,X1),X4))
| ~ class_Lattices_Olattice(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I2_J_0) ).
cnf(cls_le__infE_0,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X2,hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3,X1),X4),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__infE_0) ).
cnf(cls_inf__bot__right_0,axiom,
( hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X1),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_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(c_0_59,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(X3,X2)) ),
cls_mem__def_1 ).
cnf(c_0_60,axiom,
hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2)),
cls_top1I_0 ).
cnf(c_0_61,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_62,axiom,
class_Orderings_Otop(tc_bool),
clsarity_bool__Orderings_Otop ).
cnf(c_0_63,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_64,plain,
hBOOL(hAPP(hAPP(c_in(X1),X2),c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)))),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_65,axiom,
hAPP(c_COMBK(X1,X2,X3),X4) = X1,
cls_COMBK__def_0 ).
cnf(c_0_66,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_61,c_0_62]) ).
cnf(c_0_67,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_63,c_0_64]) ).
cnf(c_0_68,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),c_COMBK(X3,X4,X5)))
| ~ hBOOL(X3) ),
inference(spm,[status(thm)],[c_0_59,c_0_65]) ).
cnf(c_0_69,plain,
hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),v_x) = c_Orderings_Otop__class_Otop(tc_bool),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_70,plain,
( c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) = c_COMBK(X2,X3,X4)
| ~ hBOOL(X2) ),
inference(spm,[status(thm)],[c_0_63,c_0_68]) ).
cnf(c_0_71,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X2),X1)) ),
cls_mem__def_0 ).
cnf(c_0_72,axiom,
hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_Lab____)),
cls_CHAINED_0_01 ).
cnf(c_0_73,plain,
( X1 = c_Orderings_Otop__class_Otop(tc_bool)
| ~ hBOOL(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_65]) ).
cnf(c_0_74,plain,
hBOOL(hAPP(v_Lab____,c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_75,plain,
c_Orderings_Otop__class_Otop(tc_bool) = hAPP(v_Lab____,c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_76,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 ).
cnf(c_0_77,axiom,
( c_lessequals(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X1),X3),X3,X1)
| ~ class_Lattices_Olattice(X1) ),
cls_inf__sup__ord_I2_J_0 ).
cnf(c_0_78,axiom,
class_Lattices_Olattice(tc_bool),
clsarity_bool__Lattices_Olattice ).
cnf(c_0_79,plain,
( X1 = hAPP(v_Lab____,c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ hBOOL(X1) ),
inference(rw,[status(thm)],[c_0_73,c_0_75]) ).
cnf(c_0_80,axiom,
( c_lessequals(X2,X2,X1)
| ~ class_Orderings_Oorder(X1) ),
cls_order__eq__iff_0 ).
cnf(c_0_81,axiom,
class_Orderings_Oorder(tc_bool),
clsarity_bool__Orderings_Oorder ).
cnf(c_0_82,plain,
hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lab____)),
inference(spm,[status(thm)],[c_0_71,c_0_76]) ).
cnf(c_0_83,axiom,
( c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X3,X2,X1) ),
cls_atLeastLessThan__empty_0 ).
cnf(c_0_84,plain,
c_lessequals(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,tc_bool),X2),X2,tc_bool),
inference(spm,[status(thm)],[c_0_77,c_0_78]) ).
cnf(c_0_85,plain,
( X1 = X2
| ~ hBOOL(X1)
| ~ hBOOL(X2) ),
inference(spm,[status(thm)],[c_0_79,c_0_79]) ).
cnf(c_0_86,axiom,
( hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X1),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_87,axiom,
class_Lattices_Oboolean__algebra(tc_bool),
clsarity_bool__Lattices_Oboolean__algebra ).
cnf(c_0_88,axiom,
( c_lessequals(X2,hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3,X1),X4),X1)
| ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X2,X4,X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_inf__greatest_0 ).
cnf(c_0_89,plain,
c_lessequals(X1,X1,tc_bool),
inference(spm,[status(thm)],[c_0_80,c_0_81]) ).
cnf(c_0_90,axiom,
class_Lattices_Olower__semilattice(tc_bool),
clsarity_bool__Lattices_Olower__semilattice ).
cnf(c_0_91,axiom,
( c_lessequals(X2,c_Complete__Lattice_OSup__class_OSup(X3,X1),X1)
| ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
cls_Sup__upper_0 ).
cnf(c_0_92,plain,
hBOOL(hAPP(hAPP(c_in(X1),v_Lab____),c_Arrow__Order__Mirabelle_OLin)),
inference(spm,[status(thm)],[c_0_59,c_0_82]) ).
cnf(c_0_93,axiom,
( hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X1),X3) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3,X1),X2)
| ~ class_Lattices_Olattice(X1) ),
cls_inf__sup__aci_I1_J_0 ).
cnf(c_0_94,axiom,
( ~ class_Orderings_Oorder(X1)
| c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X1) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3)) ),
cls_atLeastLessThan__empty__iff_0 ).
cnf(c_0_95,plain,
c_SetInterval_Oord__class_OatLeastLessThan(X1,hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,tc_bool),X1),tc_bool) = c_Orderings_Obot__class_Obot(tc_fun(tc_bool,tc_bool)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_81])]) ).
cnf(c_0_96,axiom,
( hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X1),X3) = X2
| ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_le__iff__inf_0 ).
cnf(c_0_97,axiom,
( c_lessequals(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X1),X3),X2,X1)
| ~ class_Lattices_Olower__semilattice(X1) ),
cls_inf__le1_0 ).
cnf(c_0_98,axiom,
( hAPP(hAPP(c_HOL_Ominus__class_Ominus(X2,tc_fun(t_a,X1)),X3),v_x) = hAPP(c_HOL_Ominus__class_Ominus(hAPP(X2,v_x),X1),hAPP(X3,v_x))
| ~ class_HOL_Ominus(X1) ),
cls_fun__diff__def_0 ).
cnf(c_0_99,axiom,
( hAPP(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),tc_fun(X1,tc_bool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))) = X3
| hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
cls_Diff__insert__absorb_0 ).
cnf(c_0_100,axiom,
class_HOL_Ominus(tc_bool),
clsarity_bool__HOL_Ominus ).
cnf(c_0_101,plain,
( X1 = hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lab____)
| ~ hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_85,c_0_82]) ).
cnf(c_0_102,axiom,
hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X2)),
cls_insert__code_1 ).
cnf(c_0_103,axiom,
( hAPP(c_HOL_Ominus__class_Ominus(X2,X1),X3) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3))
| ~ class_Lattices_Oboolean__algebra(X1) ),
cls_diff__eq_0 ).
cnf(c_0_104,plain,
hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,tc_bool),hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X1)) = c_Orderings_Obot__class_Obot(tc_bool),
inference(spm,[status(thm)],[c_0_86,c_0_87]) ).
cnf(c_0_105,plain,
( c_lessequals(X1,hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,tc_bool),X1),tc_bool)
| ~ c_lessequals(X1,X2,tc_bool) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_90])]) ).
cnf(c_0_106,plain,
( c_lessequals(v_Lab____,c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,X1),X1)
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(spm,[status(thm)],[c_0_91,c_0_92]) ).
cnf(c_0_107,axiom,
class_Complete__Lattice_Ocomplete__lattice(tc_bool),
clsarity_bool__Complete__Lattice_Ocomplete__lattice ).
cnf(c_0_108,plain,
hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,tc_bool),X2) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,tc_bool),X1),
inference(spm,[status(thm)],[c_0_93,c_0_78]) ).
cnf(c_0_109,plain,
~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_bool),X1),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,tc_bool),X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_95]),c_0_81])]) ).
cnf(c_0_110,plain,
( hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X2),X3),X2),X1) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X2),X3)
| ~ class_Lattices_Olower__semilattice(X2) ),
inference(spm,[status(thm)],[c_0_96,c_0_97]) ).
cnf(c_0_111,plain,
( hAPP(c_HOL_Ominus__class_Ominus(hAPP(hAPP(hAPP(c_Set_Oinsert(t_a),X1),X2),v_x),tc_bool),hAPP(hAPP(hAPP(c_Set_Oinsert(t_a),X1),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),v_x)) = hAPP(X2,v_x)
| hBOOL(hAPP(hAPP(c_in(t_a),X1),X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_99]),c_0_100])]) ).
cnf(c_0_112,plain,
hAPP(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X2) = hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lab____),
inference(spm,[status(thm)],[c_0_101,c_0_102]) ).
cnf(c_0_113,plain,
hAPP(c_HOL_Ominus__class_Ominus(X1,tc_bool),X1) = c_Orderings_Obot__class_Obot(tc_bool),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_104]),c_0_87])]) ).
cnf(c_0_114,axiom,
( hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X1),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X1),X3)) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X1),X3)
| ~ class_Lattices_Olattice(X1) ),
cls_inf__sup__aci_I4_J_0 ).
cnf(c_0_115,axiom,
( hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X1),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3,X1),X4)) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3,X1),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X1),X4))
| ~ class_Lattices_Olattice(X1) ),
cls_inf__sup__aci_I3_J_0 ).
cnf(c_0_116,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_order__neq__le__trans_0 ).
cnf(c_0_117,plain,
c_lessequals(v_Lab____,hAPP(c_Lattices_Olower__semilattice__class_Oinf(v_Lab____,tc_bool),c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_bool)),tc_bool),
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_106]),c_0_107])]),c_0_108]) ).
cnf(c_0_118,plain,
~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_bool),X1),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,tc_bool),X2))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_110]),c_0_90])]) ).
cnf(c_0_119,plain,
( c_Orderings_Obot__class_Obot(tc_bool) = hAPP(X1,v_x)
| hBOOL(hAPP(hAPP(c_in(t_a),v_x),X1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_112]),c_0_112]),c_0_113]) ).
cnf(c_0_120,axiom,
( c_lessequals(X2,c_Orderings_Otop__class_Otop(X1),X1)
| ~ class_Orderings_Otop(X1) ),
cls_top__greatest_0 ).
cnf(c_0_121,axiom,
( X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X3,X2,X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_order__eq__iff_2 ).
cnf(c_0_122,axiom,
( c_lessequals(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X1),X3),X2,X1)
| ~ class_Lattices_Olattice(X1) ),
cls_inf__sup__ord_I1_J_0 ).
cnf(c_0_123,plain,
( hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X2),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3,X2),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X2),X4))) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3,X2),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X2),X4))
| ~ class_Lattices_Olattice(X2) ),
inference(spm,[status(thm)],[c_0_114,c_0_115]) ).
cnf(c_0_124,plain,
hAPP(c_Lattices_Olower__semilattice__class_Oinf(v_Lab____,tc_bool),c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_bool)) = v_Lab____,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_117]),c_0_81])]),c_0_118]) ).
cnf(c_0_125,plain,
( c_Orderings_Obot__class_Obot(tc_bool) = hAPP(X1,v_x)
| hBOOL(hAPP(X1,v_x)) ),
inference(spm,[status(thm)],[c_0_71,c_0_119]) ).
cnf(c_0_126,plain,
c_lessequals(X1,c_Orderings_Otop__class_Otop(tc_bool),tc_bool),
inference(spm,[status(thm)],[c_0_120,c_0_62]) ).
cnf(c_0_127,plain,
( hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X2),X3) = X1
| ~ class_Orderings_Oorder(X2)
| ~ class_Lattices_Olattice(X2)
| ~ c_lessequals(X1,hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X2),X3),X2) ),
inference(spm,[status(thm)],[c_0_121,c_0_122]) ).
cnf(c_0_128,plain,
hAPP(c_Lattices_Olower__semilattice__class_Oinf(v_Lab____,tc_bool),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,tc_bool),v_Lab____)) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,tc_bool),v_Lab____),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_124]),c_0_78])]) ).
cnf(c_0_129,axiom,
( c_lessequals(c_Orderings_Obot__class_Obot(X1),X2,X1)
| ~ class_Orderings_Obot(X1) ),
cls_bot__least_0 ).
cnf(c_0_130,plain,
( c_Orderings_Obot__class_Obot(tc_bool) = X1
| hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_125,c_0_65]) ).
cnf(c_0_131,axiom,
class_Orderings_Obot(tc_bool),
clsarity_bool__Orderings_Obot ).
cnf(c_0_132,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_133,plain,
hBOOL(hAPP(hAPP(c_in(X1),c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_Lab____)),
inference(spm,[status(thm)],[c_0_59,c_0_74]) ).
cnf(c_0_134,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X4,X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X4),X3)) ),
cls_xt1_I7_J_0 ).
cnf(c_0_135,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_116,c_0_126]),c_0_81])]) ).
cnf(c_0_136,plain,
( hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,tc_bool),v_Lab____) = v_Lab____
| ~ c_lessequals(v_Lab____,hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,tc_bool),v_Lab____),tc_bool) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_128]),c_0_81]),c_0_78])]) ).
cnf(c_0_137,plain,
( hBOOL(X1)
| c_lessequals(X1,X2,tc_bool) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_130]),c_0_131])]) ).
cnf(c_0_138,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))),c_COMBK(X1,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi)),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X1),c_Arrow__Order__Mirabelle_OLin)) ),
cls_const__Lin__Prof_0 ).
cnf(c_0_139,axiom,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),
cls_empty__not__insert_0 ).
cnf(c_0_140,plain,
hAPP(hAPP(c_Set_Oinsert(X1),c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_Lab____) = v_Lab____,
inference(spm,[status(thm)],[c_0_132,c_0_133]) ).
cnf(c_0_141,plain,
( X1 = c_Orderings_Otop__class_Otop(tc_bool)
| hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_bool),X2),c_Orderings_Otop__class_Otop(tc_bool)))
| ~ c_lessequals(X2,X1,tc_bool) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_135]),c_0_81])]) ).
cnf(c_0_142,plain,
c_lessequals(c_Orderings_Obot__class_Obot(tc_bool),X1,tc_bool),
inference(spm,[status(thm)],[c_0_129,c_0_131]) ).
cnf(c_0_143,axiom,
~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2)),
cls_bot1E_0 ).
cnf(c_0_144,plain,
( hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,tc_bool),v_Lab____) = v_Lab____
| hBOOL(v_Lab____) ),
inference(spm,[status(thm)],[c_0_136,c_0_137]) ).
cnf(c_0_145,axiom,
( hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__1(X1,X2)))
| ~ hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(hAPP(c_in(X2),X3),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)))) ),
cls_bex__UNIV_0 ).
cnf(c_0_146,axiom,
hBOOL(hAPP(hAPP(c_in(X1),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)))),
cls_UNIV__I_0 ).
cnf(c_0_147,plain,
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))),c_COMBK(v_Lab____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi)),c_Arrow__Order__Mirabelle_OProf)),
inference(spm,[status(thm)],[c_0_138,c_0_92]) ).
cnf(c_0_148,plain,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != v_Lab____,
inference(spm,[status(thm)],[c_0_139,c_0_140]) ).
cnf(c_0_149,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_141,c_0_142]) ).
cnf(c_0_150,axiom,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X3))
| ~ hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),X3),c_Arrow__Order__Mirabelle_OLin)) ),
cls_Lin__irrefl_0 ).
cnf(c_0_151,plain,
( ~ hBOOL(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))
| ~ hBOOL(hAPP(X2,X3))
| ~ hBOOL(X2) ),
inference(spm,[status(thm)],[c_0_143,c_0_85]) ).
cnf(c_0_152,plain,
( v_Lab____ = X1
| hBOOL(v_Lab____)
| ~ c_lessequals(X1,v_Lab____,tc_bool) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_144]),c_0_81]),c_0_78])]) ).
cnf(c_0_153,plain,
( hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__1(X1,X2)))
| ~ hBOOL(hAPP(X1,X3)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_145,c_0_146])]) ).
cnf(c_0_154,axiom,
( hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__2(X1,X2)))
| ~ hBOOL(hAPP(X1,X3)) ),
cls_bex__UNIV_2 ).
cnf(c_0_155,plain,
hBOOL(hAPP(c_Arrow__Order__Mirabelle_OProf,c_COMBK(v_Lab____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi))),
inference(spm,[status(thm)],[c_0_71,c_0_147]) ).
cnf(c_0_156,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_157,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ c_lessequals(X2,X3,X1)
| ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X3),X2)) ),
cls_less__le__not__le_1 ).
cnf(c_0_158,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_148,c_0_149]),c_0_149]) ).
cnf(c_0_159,axiom,
class_Orderings_Opreorder(tc_bool),
clsarity_bool__Orderings_Opreorder ).
cnf(c_0_160,plain,
( ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X1,X2,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_Lab____))
| ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(X2,X1,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_Lab____)) ),
inference(spm,[status(thm)],[c_0_150,c_0_92]) ).
cnf(c_0_161,plain,
( ~ hBOOL(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)))
| ~ hBOOL(hAPP(c_in(X2),X3)) ),
inference(spm,[status(thm)],[c_0_151,c_0_64]) ).
cnf(c_0_162,plain,
( v_Lab____ = X1
| hBOOL(v_Lab____)
| hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_152,c_0_137]) ).
cnf(c_0_163,plain,
hBOOL(hAPP(v_Lab____,c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__1(v_Lab____,X1))),
inference(spm,[status(thm)],[c_0_153,c_0_74]) ).
cnf(c_0_164,plain,
hBOOL(hAPP(c_Arrow__Order__Mirabelle_OProf,c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__2(c_Arrow__Order__Mirabelle_OProf,X1))),
inference(spm,[status(thm)],[c_0_154,c_0_155]) ).
cnf(c_0_165,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Lattices_Olower__semilattice(X1)
| hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X1),X3) != X2 ),
cls_le__iff__inf_1 ).
cnf(c_0_166,axiom,
( hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X1),X2) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Oboolean__algebra(X1) ),
cls_compl__inf__bot_0 ).
cnf(c_0_167,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_156,c_0_87]) ).
cnf(c_0_168,plain,
hAPP(v_Lab____,c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) = hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lab____),
inference(spm,[status(thm)],[c_0_101,c_0_74]) ).
cnf(c_0_169,plain,
~ c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Obot__class_Obot(tc_bool),tc_bool),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_157,c_0_158]),c_0_159])]) ).
cnf(c_0_170,plain,
~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_Lab____)),
inference(spm,[status(thm)],[c_0_160,c_0_133]) ).
cnf(c_0_171,plain,
( hBOOL(v_Lab____)
| ~ hBOOL(hAPP(c_in(X1),X2)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_161,c_0_162]),c_0_148]) ).
cnf(c_0_172,plain,
hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__1(v_Lab____,X2)),v_Lab____)),
inference(spm,[status(thm)],[c_0_59,c_0_163]) ).
cnf(c_0_173,plain,
c_SetInterval_Oord__class_OatLeastLessThan(c_Orderings_Otop__class_Otop(tc_bool),X1,tc_bool) = c_Orderings_Obot__class_Obot(tc_fun(tc_bool,tc_bool)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_126]),c_0_81])]) ).
cnf(c_0_174,plain,
hBOOL(hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__2(c_Arrow__Order__Mirabelle_OProf,X2)),c_Arrow__Order__Mirabelle_OProf)),
inference(spm,[status(thm)],[c_0_59,c_0_164]) ).
cnf(c_0_175,plain,
( c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X2,X1)
| hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2) != c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Oboolean__algebra(X1)
| ~ class_Lattices_Olower__semilattice(X1) ),
inference(spm,[status(thm)],[c_0_165,c_0_166]) ).
cnf(c_0_176,plain,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)) = hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lab____),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_167,c_0_75]),c_0_168]) ).
cnf(c_0_177,plain,
~ c_lessequals(hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lab____),c_Orderings_Obot__class_Obot(tc_bool),tc_bool),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_169,c_0_75]),c_0_168]) ).
cnf(c_0_178,plain,
hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_Lab____) = c_Orderings_Obot__class_Obot(tc_bool),
inference(spm,[status(thm)],[c_0_170,c_0_130]) ).
cnf(c_0_179,plain,
( hAPP(c_in(X1),X2) = v_Lab____
| hBOOL(v_Lab____) ),
inference(spm,[status(thm)],[c_0_171,c_0_162]) ).
cnf(c_0_180,plain,
hAPP(hAPP(c_in(X1),c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__1(v_Lab____,X2)),v_Lab____) = hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lab____),
inference(spm,[status(thm)],[c_0_101,c_0_172]) ).
cnf(c_0_181,plain,
~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_173]),c_0_81])]) ).
cnf(c_0_182,axiom,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X1),X2),X3))
| c_lessequals(X3,X2,X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_less__le__not__le_2 ).
cnf(c_0_183,plain,
hAPP(hAPP(c_Set_Oinsert(X1),c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__2(c_Arrow__Order__Mirabelle_OProf,X2)),c_Arrow__Order__Mirabelle_OProf) = c_Arrow__Order__Mirabelle_OProf,
inference(spm,[status(thm)],[c_0_132,c_0_174]) ).
cnf(c_0_184,plain,
c_Orderings_Obot__class_Obot(tc_bool) != hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lab____),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_175,c_0_176]),c_0_87]),c_0_90])]),c_0_177]) ).
cnf(c_0_185,plain,
( c_Orderings_Obot__class_Obot(tc_bool) = hAPP(v_Lab____,v_Lab____)
| hBOOL(v_Lab____) ),
inference(spm,[status(thm)],[c_0_178,c_0_179]) ).
cnf(c_0_186,plain,
( hAPP(v_Lab____,v_Lab____) = hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lab____)
| hBOOL(v_Lab____) ),
inference(spm,[status(thm)],[c_0_180,c_0_179]) ).
cnf(c_0_187,plain,
~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_bool),hAPP(v_Lab____,c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),X1)),
inference(spm,[status(thm)],[c_0_181,c_0_75]) ).
cnf(c_0_188,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_bool),X1),c_Orderings_Otop__class_Otop(tc_bool)))
| c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),X1,tc_bool) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_182,c_0_126]),c_0_159])]) ).
cnf(c_0_189,plain,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_Arrow__Order__Mirabelle_OProf,
inference(spm,[status(thm)],[c_0_139,c_0_183]) ).
cnf(c_0_190,plain,
( X1 = hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lab____)
| c_Orderings_Obot__class_Obot(tc_bool) = X1 ),
inference(spm,[status(thm)],[c_0_101,c_0_130]) ).
cnf(c_0_191,plain,
hBOOL(v_Lab____),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_184,c_0_185]),c_0_186]) ).
cnf(c_0_192,plain,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_bool),X1),X2))
| ~ hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_187,c_0_79]) ).
cnf(c_0_193,plain,
( hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_bool),X1),hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lab____)))
| c_lessequals(hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lab____),X1,tc_bool) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_188,c_0_75]),c_0_75]),c_0_168]),c_0_168]) ).
cnf(c_0_194,plain,
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lab____)
| c_Orderings_Obot__class_Obot(tc_bool) != c_Arrow__Order__Mirabelle_OProf ),
inference(spm,[status(thm)],[c_0_189,c_0_190]) ).
cnf(c_0_195,plain,
hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lab____) = v_Lab____,
inference(spm,[status(thm)],[c_0_101,c_0_191]) ).
cnf(c_0_196,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_132,c_0_92]) ).
cnf(c_0_197,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X4,X1)
| ~ c_lessequals(X4,X3,X1) ),
cls_xt1_I6_J_0 ).
cnf(c_0_198,plain,
( c_lessequals(hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lab____),X1,tc_bool)
| ~ hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_192,c_0_193]) ).
cnf(c_0_199,plain,
c_lessequals(X1,hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lab____),tc_bool),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_126,c_0_75]),c_0_168]) ).
cnf(c_0_200,plain,
c_Orderings_Obot__class_Obot(tc_bool) != c_Arrow__Order__Mirabelle_OProf,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_194,c_0_195]),c_0_148]) ).
cnf(c_0_201,plain,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_Arrow__Order__Mirabelle_OLin,
inference(spm,[status(thm)],[c_0_139,c_0_196]) ).
cnf(c_0_202,plain,
( c_lessequals(X1,hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X3),X1),X3)
| ~ class_Orderings_Oorder(X3)
| ~ class_Lattices_Olower__semilattice(X3)
| ~ c_lessequals(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_88,c_0_80]) ).
cnf(c_0_203,plain,
( c_lessequals(X1,X2,tc_bool)
| ~ hBOOL(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_197,c_0_198]),c_0_81]),c_0_199])]) ).
cnf(c_0_204,axiom,
( hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X1),X3) = X3
| ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X3,X2,X1) ),
cls_inf__absorb2_0 ).
cnf(c_0_205,axiom,
( hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X1),X3),X1),X4) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X1),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3,X1),X4))
| ~ class_Lattices_Olattice(X1) ),
cls_inf__sup__aci_I2_J_0 ).
cnf(c_0_206,plain,
( hBOOL(X1)
| X1 != c_Arrow__Order__Mirabelle_OProf ),
inference(spm,[status(thm)],[c_0_200,c_0_130]) ).
cnf(c_0_207,plain,
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = hAPP(c_Arrow__Order__Mirabelle_OLin,v_Lab____)
| c_Orderings_Obot__class_Obot(tc_bool) != c_Arrow__Order__Mirabelle_OLin ),
inference(spm,[status(thm)],[c_0_201,c_0_190]) ).
cnf(c_0_208,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X2,hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3,X1),X4),X1) ),
cls_le__infE_0 ).
cnf(c_0_209,axiom,
( hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,X1),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_210,plain,
( c_lessequals(X1,hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,tc_bool),X1),tc_bool)
| ~ hBOOL(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_202,c_0_203]),c_0_81]),c_0_90])]) ).
cnf(c_0_211,plain,
( hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,tc_bool),X2) = X2
| ~ hBOOL(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_204,c_0_203]),c_0_90])]) ).
cnf(c_0_212,plain,
( c_lessequals(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X2),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X3,X2),X4)),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X2),X3),X2)
| ~ class_Lattices_Olattice(X2) ),
inference(spm,[status(thm)],[c_0_122,c_0_205]) ).
cnf(c_0_213,plain,
( X1 = v_Lab____
| ~ hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_85,c_0_191]) ).
cnf(c_0_214,plain,
hBOOL(c_Arrow__Order__Mirabelle_OProf),
inference(er,[status(thm)],[c_0_206]) ).
cnf(c_0_215,plain,
c_Orderings_Obot__class_Obot(tc_bool) != c_Arrow__Order__Mirabelle_OLin,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_207,c_0_195]),c_0_148]) ).
cnf(c_0_216,plain,
( c_lessequals(X1,X2,X3)
| ~ class_Lattices_Obounded__lattice(X3)
| ~ class_Lattices_Olower__semilattice(X3)
| ~ c_lessequals(X1,c_Orderings_Obot__class_Obot(X3),X3) ),
inference(spm,[status(thm)],[c_0_208,c_0_209]) ).
cnf(c_0_217,plain,
( c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X1),c_Orderings_Obot__class_Obot(tc_bool),tc_bool)
| ~ hBOOL(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_210,c_0_86]),c_0_87])]) ).
cnf(c_0_218,axiom,
class_Lattices_Obounded__lattice(tc_bool),
clsarity_bool__Lattices_Obounded__lattice ).
cnf(c_0_219,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_220,plain,
( hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X1) = hAPP(c_HOL_Ominus__class_Ominus(X2,tc_bool),X1)
| ~ hBOOL(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_211]),c_0_87])]) ).
cnf(c_0_221,plain,
c_lessequals(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,tc_bool),v_Lab____),hAPP(c_Lattices_Olower__semilattice__class_Oinf(v_Lab____,tc_bool),X1),tc_bool),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_212,c_0_128]),c_0_78])]) ).
cnf(c_0_222,plain,
hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,tc_bool),X2),tc_bool),X3) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,tc_bool),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X2,tc_bool),X3)),
inference(spm,[status(thm)],[c_0_205,c_0_78]) ).
cnf(c_0_223,plain,
hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,tc_bool),hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,tc_bool),X2)) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,tc_bool),X2),
inference(spm,[status(thm)],[c_0_114,c_0_78]) ).
cnf(c_0_224,plain,
hBOOL(c_Orderings_Otop__class_Otop(tc_bool)),
inference(spm,[status(thm)],[c_0_60,c_0_66]) ).
cnf(c_0_225,plain,
v_Lab____ = c_Arrow__Order__Mirabelle_OProf,
inference(spm,[status(thm)],[c_0_213,c_0_214]) ).
cnf(c_0_226,plain,
( hBOOL(X1)
| X1 != c_Arrow__Order__Mirabelle_OLin ),
inference(spm,[status(thm)],[c_0_215,c_0_130]) ).
cnf(c_0_227,plain,
( c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X1),X2,tc_bool)
| ~ hBOOL(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_216,c_0_217]),c_0_218]),c_0_90])]) ).
cnf(c_0_228,plain,
( hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),hAPP(c_HOL_Ominus__class_Ominus(X1,tc_bool),X2)) = X2
| ~ hBOOL(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_219,c_0_220]),c_0_87])]) ).
cnf(c_0_229,plain,
( hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X1),X3) = hAPP(c_HOL_Ominus__class_Ominus(X3,X1),X2)
| ~ class_Lattices_Oboolean__algebra(X1)
| ~ class_Lattices_Olattice(X1) ),
inference(spm,[status(thm)],[c_0_93,c_0_103]) ).
cnf(c_0_230,plain,
hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,tc_bool),hAPP(c_Lattices_Olower__semilattice__class_Oinf(v_Lab____,tc_bool),X1)) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,tc_bool),v_Lab____),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_221]),c_0_222]),c_0_223]),c_0_90])]) ).
cnf(c_0_231,plain,
hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X1),tc_bool),X2) = hAPP(c_HOL_Ominus__class_Ominus(X2,tc_bool),X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_108]),c_0_87])]) ).
cnf(c_0_232,plain,
hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,tc_bool),hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X2)) = hAPP(c_HOL_Ominus__class_Ominus(X1,tc_bool),X2),
inference(spm,[status(thm)],[c_0_103,c_0_87]) ).
cnf(c_0_233,plain,
hBOOL(hAPP(hAPP(c_in(X1),c_Orderings_Obot__class_Obot(tc_bool)),c_HOL_Ouminus__class_Ouminus(tc_bool))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_167]),c_0_224])]) ).
cnf(c_0_234,plain,
( X1 = c_Arrow__Order__Mirabelle_OProf
| ~ hBOOL(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_101,c_0_195]),c_0_225]) ).
cnf(c_0_235,plain,
hBOOL(c_Arrow__Order__Mirabelle_OLin),
inference(er,[status(thm)],[c_0_226]) ).
cnf(c_0_236,plain,
( c_lessequals(X1,X2,tc_bool)
| ~ hBOOL(hAPP(c_HOL_Ominus__class_Ominus(X3,tc_bool),X1))
| ~ hBOOL(X3) ),
inference(spm,[status(thm)],[c_0_227,c_0_228]) ).
cnf(c_0_237,plain,
hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_HOL_Ominus__class_Ominus(v_Lab____,tc_bool),X1),tc_bool),X1) = hAPP(c_HOL_Ominus__class_Ominus(v_Lab____,tc_bool),X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_229,c_0_230]),c_0_231]),c_0_232]),c_0_87]),c_0_78])]) ).
cnf(c_0_238,plain,
hAPP(hAPP(c_Set_Oinsert(X1),c_Orderings_Obot__class_Obot(tc_bool)),c_HOL_Ouminus__class_Ouminus(tc_bool)) = c_HOL_Ouminus__class_Ouminus(tc_bool),
inference(spm,[status(thm)],[c_0_132,c_0_233]) ).
cnf(c_0_239,plain,
c_Arrow__Order__Mirabelle_OProf = c_Arrow__Order__Mirabelle_OLin,
inference(spm,[status(thm)],[c_0_234,c_0_235]) ).
cnf(c_0_240,plain,
( c_lessequals(X1,X2,tc_bool)
| ~ hBOOL(hAPP(c_HOL_Ominus__class_Ominus(v_Lab____,tc_bool),X1)) ),
inference(spm,[status(thm)],[c_0_236,c_0_237]) ).
cnf(c_0_241,plain,
( hAPP(c_HOL_Ominus__class_Ominus(X1,X2),hAPP(c_HOL_Ouminus__class_Ouminus(X2),X3)) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1,X2),X3)
| ~ class_Lattices_Oboolean__algebra(X2) ),
inference(spm,[status(thm)],[c_0_103,c_0_219]) ).
cnf(c_0_242,plain,
c_HOL_Ouminus__class_Ouminus(tc_bool) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
inference(spm,[status(thm)],[c_0_139,c_0_238]) ).
cnf(c_0_243,plain,
( c_Orderings_Obot__class_Obot(tc_bool) = X1
| X1 = c_Arrow__Order__Mirabelle_OLin ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_190,c_0_195]),c_0_225]),c_0_239]) ).
cnf(c_0_244,plain,
( X1 = X2
| ~ hBOOL(X1)
| ~ c_lessequals(X1,X2,tc_bool) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_203]),c_0_81])]) ).
cnf(c_0_245,plain,
~ c_lessequals(v_Lab____,c_Orderings_Obot__class_Obot(tc_bool),tc_bool),
inference(rw,[status(thm)],[c_0_177,c_0_195]) ).
cnf(c_0_246,plain,
( c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X1),X2,tc_bool)
| ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(v_Lab____,tc_bool),X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_240,c_0_241]),c_0_87])]) ).
cnf(c_0_247,plain,
c_HOL_Ouminus__class_Ouminus(tc_bool) != c_Orderings_Obot__class_Obot(tc_bool),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_242,c_0_243]),c_0_201]) ).
cnf(c_0_248,plain,
( c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_bool) = v_Lab____
| ~ hBOOL(v_Lab____) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_244,c_0_106]),c_0_107])]) ).
cnf(c_0_249,plain,
~ c_lessequals(c_Arrow__Order__Mirabelle_OProf,c_Orderings_Obot__class_Obot(tc_bool),tc_bool),
inference(rw,[status(thm)],[c_0_245,c_0_225]) ).
cnf(c_0_250,plain,
( c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_bool)),X1,tc_bool)
| ~ hBOOL(v_Lab____) ),
inference(spm,[status(thm)],[c_0_246,c_0_124]) ).
cnf(c_0_251,plain,
c_HOL_Ouminus__class_Ouminus(tc_bool) = c_Arrow__Order__Mirabelle_OLin,
inference(spm,[status(thm)],[c_0_247,c_0_243]) ).
cnf(c_0_252,plain,
c_Complete__Lattice_OSup__class_OSup(c_Arrow__Order__Mirabelle_OLin,tc_bool) = v_Lab____,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_248,c_0_191])]) ).
cnf(c_0_253,plain,
hAPP(c_Arrow__Order__Mirabelle_OLin,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)],[c_0_195,c_0_225]),c_0_225]),c_0_239]),c_0_239]) ).
cnf(c_0_254,plain,
~ c_lessequals(c_Arrow__Order__Mirabelle_OLin,c_Orderings_Obot__class_Obot(tc_bool),tc_bool),
inference(rw,[status(thm)],[c_0_249,c_0_239]) ).
cnf(c_0_255,plain,
c_lessequals(c_Arrow__Order__Mirabelle_OLin,X1,tc_bool),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_250,c_0_191])]),c_0_251]),c_0_252]),c_0_225]),c_0_239]),c_0_253]) ).
cnf(c_0_256,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_254,c_0_255])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SCT084-1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.14 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n022.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
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Aug 24 16:09:55 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.58 start to proof: theBenchmark
% 52.12/52.20 % Version : CSE_E---1.5
% 52.12/52.20 % Problem : theBenchmark.p
% 52.12/52.20 % Proof found
% 52.12/52.20 % SZS status Theorem for theBenchmark.p
% 52.12/52.20 % SZS output start Proof
% See solution above
% 52.12/52.22 % Total time : 51.585000 s
% 52.12/52.22 % SZS output end Proof
% 52.12/52.22 % Total time : 51.617000 s
%------------------------------------------------------------------------------