TSTP Solution File: SWV820-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SWV820-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n010.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 21:48:16 EDT 2023
% Result : Unsatisfiable 41.50s 41.53s
% Output : CNFRefutation 41.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 204
% Syntax : Number of formulae : 283 ( 62 unt; 166 typ; 0 def)
% Number of atoms : 189 ( 74 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 144 ( 72 ~; 72 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 312 ( 138 >; 174 *; 0 +; 0 <<)
% Number of predicates : 59 ( 57 usr; 1 prp; 0-9 aty)
% Number of functors : 109 ( 109 usr; 28 con; 0-6 aty)
% Number of variables : 227 ( 48 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
class_Orderings_Olinorder: $i > $o ).
tff(decl_23,type,
c_in: $i > $i ).
tff(decl_24,type,
c_Finite__Set_Olinorder__class_OMax: ( $i * $i ) > $i ).
tff(decl_25,type,
hAPP: ( $i * $i ) > $i ).
tff(decl_26,type,
hBOOL: $i > $o ).
tff(decl_27,type,
tc_bool: $i ).
tff(decl_28,type,
tc_fun: ( $i * $i ) > $i ).
tff(decl_29,type,
c_Orderings_Obot__class_Obot: $i > $i ).
tff(decl_30,type,
c_Finite__Set_Ofinite: ( $i * $i ) > $o ).
tff(decl_31,type,
tc_prod: ( $i * $i ) > $i ).
tff(decl_32,type,
c_Pair: ( $i * $i ) > $i ).
tff(decl_33,type,
c_Relation_Ototal__on: ( $i * $i * $i ) > $i ).
tff(decl_34,type,
c_lessequals: $i > $i ).
tff(decl_35,type,
class_Ring__and__Field_Oring: $i > $o ).
tff(decl_36,type,
c_HOL_Oplus__class_Oplus: $i > $i ).
tff(decl_37,type,
c_HOL_Otimes__class_Otimes: $i > $i ).
tff(decl_38,type,
c_HOL_Ominus__class_Ominus: $i > $i ).
tff(decl_39,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
tff(decl_40,type,
c_HOL_Ouminus__class_Ouminus: $i > $i ).
tff(decl_41,type,
v_f: $i ).
tff(decl_42,type,
v_A: $i ).
tff(decl_43,type,
t_a: $i ).
tff(decl_44,type,
t_b: $i ).
tff(decl_45,type,
c_Set_Oimage: ( $i * $i * $i * $i ) > $i ).
tff(decl_46,type,
c_Collect: $i > $i ).
tff(decl_47,type,
c_COMBB: ( $i * $i * $i ) > $i ).
tff(decl_48,type,
c_Ex: $i > $i ).
tff(decl_49,type,
c_COMBS: ( $i * $i * $i ) > $i ).
tff(decl_50,type,
c_and: $i ).
tff(decl_51,type,
c_COMBC: ( $i * $i * $i ) > $i ).
tff(decl_52,type,
c_fequal: $i > $i ).
tff(decl_53,type,
c_Com_Ocom_OWhile: ( $i * $i ) > $i ).
tff(decl_54,type,
c_Natural_Oevalc: ( $i * $i * $i ) > $o ).
tff(decl_55,type,
c_Lattices_Oupper__semilattice__class_Osup: $i > $i ).
tff(decl_56,type,
c_Complete__Lattice_Ocomplete__lattice__class_OINFI: ( $i * $i * $i * $i ) > $i ).
tff(decl_57,type,
class_Lattices_Oboolean__algebra: $i > $o ).
tff(decl_58,type,
c_Lattices_Olower__semilattice__class_Oinf: $i > $i ).
tff(decl_59,type,
c_Com_Ocom_OSKIP: $i ).
tff(decl_60,type,
class_Orderings_Obot: $i > $o ).
tff(decl_61,type,
v_x: $i ).
tff(decl_62,type,
c_COMBK: ( $i * $i ) > $i ).
tff(decl_63,type,
c_Product__Type_OSigma: ( $i * $i * $i * $i ) > $i ).
tff(decl_64,type,
c_Finite__Set_Ofun__left__comm: ( $i * $i * $i ) > $o ).
tff(decl_65,type,
c_COMBI: $i > $i ).
tff(decl_66,type,
class_Ring__and__Field_Oidom: $i > $o ).
tff(decl_67,type,
class_Int_Onumber__ring: $i > $o ).
tff(decl_68,type,
class_Orderings_Oorder: $i > $o ).
tff(decl_69,type,
c_Orderings_Oorder__class_Omono: ( $i * $i * $i ) > $i ).
tff(decl_70,type,
c_Orderings_Oorder__class_Ostrict__mono: ( $i * $i * $i ) > $i ).
tff(decl_71,type,
class_OrderedGroup_Ogroup__add: $i > $o ).
tff(decl_72,type,
c_split: ( $i * $i * $i * $i ) > $i ).
tff(decl_73,type,
class_OrderedGroup_Opordered__ab__semigroup__add: $i > $o ).
tff(decl_74,type,
class_Lattices_Olattice: $i > $o ).
tff(decl_75,type,
c_Fun_Oinj__on: ( $i * $i * $i * $i ) > $o ).
tff(decl_76,type,
c_Fun_Ocomp: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_77,type,
class_Lattices_Odistrib__lattice: $i > $o ).
tff(decl_78,type,
class_Complete__Lattice_Ocomplete__lattice: $i > $o ).
tff(decl_79,type,
class_OrderedGroup_Ocomm__monoid__mult: $i > $o ).
tff(decl_80,type,
c_Finite__Set_Osetprod: ( $i * $i * $i * $i ) > $i ).
tff(decl_81,type,
class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).
tff(decl_82,type,
c_Fun_Oid: $i > $i ).
tff(decl_83,type,
class_OrderedGroup_Olordered__ab__group__add__join: $i > $o ).
tff(decl_84,type,
class_OrderedGroup_Olordered__ab__group__add: $i > $o ).
tff(decl_85,type,
c_Orderings_Oorder: ( $i * $i * $i ) > $o ).
tff(decl_86,type,
v_r: $i ).
tff(decl_87,type,
c_All: $i > $i ).
tff(decl_88,type,
c_implies: $i ).
tff(decl_89,type,
c_Not: $i ).
tff(decl_90,type,
c_or: $i ).
tff(decl_91,type,
class_OrderedGroup_Oordered__ab__semigroup__add: $i > $o ).
tff(decl_92,type,
class_Lattices_Oupper__semilattice: $i > $o ).
tff(decl_93,type,
c_Finite__Set_Ofun__left__comm__idem: ( $i * $i * $i ) > $o ).
tff(decl_94,type,
c_Finite__Set_Olattice_OInf__fin: ( $i * $i * $i ) > $i ).
tff(decl_95,type,
c_Complete__Lattice_Ocomplete__lattice: ( $i * $i * $i * $i * $i * $i * $i * $i * $i ) > $o ).
tff(decl_96,type,
c_Com_Ocom_OSemi: ( $i * $i ) > $i ).
tff(decl_97,type,
c_Com_Ocom_OCond: ( $i * $i * $i ) > $i ).
tff(decl_98,type,
class_OrderedGroup_Ocomm__monoid__add: $i > $o ).
tff(decl_99,type,
c_Finite__Set_Osetsum: ( $i * $i ) > $i ).
tff(decl_100,type,
c_Finite__Set_Olattice__class_OInf__fin: ( $i * $i ) > $i ).
tff(decl_101,type,
class_Ring__and__Field_Opordered__ring: $i > $o ).
tff(decl_102,type,
c_HOL_Oord__class_Oless: $i > $i ).
tff(decl_103,type,
class_Lattices_Obounded__lattice: $i > $o ).
tff(decl_104,type,
class_OrderedGroup_Osemigroup__add: $i > $o ).
tff(decl_105,type,
c_List_Ofoldl: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_106,type,
c_Lattices_Odistrib__lattice: ( $i * $i * $i * $i * $i ) > $o ).
tff(decl_107,type,
c_The: ( $i * $i ) > $i ).
tff(decl_108,type,
c_Record_Oiso__tuple__update__accessor__cong__assist: ( $i * $i * $i * $i ) > $i ).
tff(decl_109,type,
class_Orderings_Owellorder: $i > $o ).
tff(decl_110,type,
c_Orderings_Oord__class_OLeast: ( $i * $i ) > $i ).
tff(decl_111,type,
c_Suc: $i > $i ).
tff(decl_112,type,
class_Ring__and__Field_Ofield: $i > $o ).
tff(decl_113,type,
c_HOL_Oinverse__class_Odivide: $i > $i ).
tff(decl_114,type,
class_Lattices_Olower__semilattice: $i > $o ).
tff(decl_115,type,
class_Ring__and__Field_Odivision__by__zero: $i > $o ).
tff(decl_116,type,
c_Orderings_Oorder_Ostrict__mono: ( $i * $i * $i ) > $i ).
tff(decl_117,type,
c_Orderings_Oorder_Omono: ( $i * $i * $i ) > $i ).
tff(decl_118,type,
c_Product__Type_Oscomp: ( $i * $i * $i * $i * $i * $i ) > $i ).
tff(decl_119,type,
class_Orderings_Opreorder: $i > $o ).
tff(decl_120,type,
c_Hilbert__Choice_OEps: ( $i * $i ) > $i ).
tff(decl_121,type,
class_OrderedGroup_Oab__semigroup__mult: $i > $o ).
tff(decl_122,type,
c_Lattices_Oboolean__algebra: ( $i * $i * $i * $i * $i * $i * $i * $i * $i ) > $o ).
tff(decl_123,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
tff(decl_124,type,
class_OrderedGroup_Oab__semigroup__add: $i > $o ).
tff(decl_125,type,
class_OrderedGroup_Olordered__ab__group__add__meet: $i > $o ).
tff(decl_126,type,
class_Ring__and__Field_Osemiring__0: $i > $o ).
tff(decl_127,type,
c_List_Omap: ( $i * $i * $i * $i ) > $i ).
tff(decl_128,type,
c_Finite__Set_Olattice__class_OSup__fin: ( $i * $i ) > $i ).
tff(decl_129,type,
class_Ring__and__Field_Osemiring: $i > $o ).
tff(decl_130,type,
tc_nat: $i ).
tff(decl_131,type,
class_OrderedGroup_Ocancel__ab__semigroup__add: $i > $o ).
tff(decl_132,type,
class_OrderedGroup_Ocancel__semigroup__add: $i > $o ).
tff(decl_133,type,
c_HOL_Oinduct__forall: ( $i * $i ) > $i ).
tff(decl_134,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
tff(decl_135,type,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add: $i > $o ).
tff(decl_136,type,
c_Recdef_Ocut: ( $i * $i ) > $i ).
tff(decl_137,type,
c_Finite__Set_Olattice_OSup__fin: ( $i * $i * $i ) > $i ).
tff(decl_138,type,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le: $i > $o ).
tff(decl_139,type,
c_Relation_Oantisym: ( $i * $i ) > $i ).
tff(decl_140,type,
class_OrderedGroup_Oab__semigroup__idem__mult: $i > $o ).
tff(decl_141,type,
class_HOL_Ouminus: $i > $o ).
tff(decl_142,type,
c_Fun_Ofcomp: ( $i * $i * $i ) > $i ).
tff(decl_143,type,
c_Relation_Otrans: ( $i * $i ) > $i ).
tff(decl_144,type,
c_Relation_Osym: ( $i * $i ) > $i ).
tff(decl_145,type,
class_Ring__and__Field_Oordered__ring__strict: $i > $o ).
tff(decl_146,type,
class_Finite__Set_Ofinite_Ofinite: $i > $o ).
tff(decl_147,type,
c_Finite__Set_Olinorder__class_OMin: ( $i * $i ) > $i ).
tff(decl_148,type,
class_Ring__and__Field_Ocomm__semiring: $i > $o ).
tff(decl_149,type,
c_Finite__Set_Olinorder_OMax: ( $i * $i * $i ) > $i ).
tff(decl_150,type,
c_OrderedGroup_Oordered__ab__semigroup__add: ( $i * $i * $i * $i ) > $o ).
tff(decl_151,type,
c_Finite__Set_Olinorder_OMin: ( $i * $i * $i ) > $i ).
tff(decl_152,type,
v_B: $i ).
tff(decl_153,type,
c_Predicate_OPowp: ( $i * $i * $i ) > $i ).
tff(decl_154,type,
c_List_Ofilter: ( $i * $i * $i ) > $i ).
tff(decl_155,type,
c_HOL_Oinduct__conj: $i ).
tff(decl_156,type,
c_ATP__Linkup_Osko__FunDef__Xfundef__ex1__uniqueness__1__1: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_157,type,
c_FunDef_OTHE__default: $i > $i ).
tff(decl_158,type,
c_ATP__Linkup_Osko__FunDef__Xfundef__ex1__existence__1__1: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_159,type,
c_ATP__Linkup_Osko__FunDef__Xfundef__ex1__iff__1__1: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_160,type,
c_ATP__Linkup_Osko__FunDef__Xfundef__default__value__1__1: ( $i * $i * $i * $i ) > $i ).
tff(decl_161,type,
class_HOL_Oord: $i > $o ).
tff(decl_162,type,
c_Hilbert__Choice_OGreatestM: ( $i * $i * $i * $i ) > $i ).
tff(decl_163,type,
c_Recdef_Owfrec: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_164,type,
c_Recdef_Owfrec__rel: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_165,type,
c_Natural_Oevaln: $i ).
tff(decl_166,type,
c_Natural_Osko__Natural__Xevaln__max2__1__1: ( $i * $i * $i * $i * $i * $i ) > $i ).
tff(decl_167,type,
v_P: $i ).
tff(decl_168,type,
c_Hoare__Mirabelle_Otriple_Otriple: ( $i * $i * $i * $i ) > $i ).
tff(decl_169,type,
c_Hoare__Mirabelle_Otriple_Otriple__rec: ( $i * $i * $i * $i ) > $i ).
tff(decl_170,type,
c_Recdef_Oadm__wf: ( $i * $i * $i * $i ) > $o ).
tff(decl_171,type,
v_upd: $i ).
tff(decl_172,type,
v_acc: $i ).
tff(decl_173,type,
c_Hilbert__Choice_OLeastM: ( $i * $i * $i * $i ) > $i ).
tff(decl_174,type,
c_List_Osko__List__Xfoldl__apply__inv__1__1: ( $i * $i * $i * $i ) > $i ).
tff(decl_175,type,
c_List_Olistsp: ( $i * $i * $i ) > $i ).
tff(decl_176,type,
c_Orderings_Oord_OLeast: ( $i * $i * $i ) > $i ).
tff(decl_177,type,
v_Q: $i ).
tff(decl_178,type,
t_c: $i ).
tff(decl_179,type,
v_R: $i ).
tff(decl_180,type,
c_Hoare__Mirabelle_Otriple__valid: ( $i * $i ) > $i ).
tff(decl_181,type,
tc_Com_Ocom: $i ).
tff(decl_182,type,
tc_Com_Ostate: $i ).
tff(decl_183,type,
c_Hoare__Mirabelle_Otriple_Otriple__case: ( $i * $i * $i ) > $i ).
tff(decl_184,type,
v_n: $i ).
tff(decl_185,type,
v_xa: $i ).
tff(decl_186,type,
v_c: $i ).
tff(decl_187,type,
v_xb: $i ).
cnf(cls_Collect__neg__eq_0,axiom,
hAPP(c_Collect(X1),hAPP(hAPP(c_COMBB(tc_bool,tc_bool,X1),c_Not),X2)) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),hAPP(c_Collect(X1),X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Collect__neg__eq_0) ).
cnf(cls_Collect__def_0,axiom,
hAPP(c_Collect(X1),X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Collect__def_0) ).
cnf(cls_inf__sup__aci_I5_J_0,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X2)
| ~ class_Lattices_Olattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I5_J_0) ).
cnf(clsarity_bool__Lattices_Olattice,axiom,
class_Lattices_Olattice(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olattice) ).
cnf(cls_fun__Compl__def_0,axiom,
( hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(t_a,X1)),X2),v_x) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(X2,v_x))
| ~ class_HOL_Ouminus(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__Compl__def_0) ).
cnf(clsarity_bool__HOL_Ouminus,axiom,
class_HOL_Ouminus(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__HOL_Ouminus) ).
cnf(cls_COMBB__def_0,axiom,
hAPP(hAPP(hAPP(c_COMBB(X1,X2,X3),X4),X5),X6) = hAPP(X4,hAPP(X5,X6)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBB__def_0) ).
cnf(cls_sup__eq__bot__eq1_0,axiom,
( X2 = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Obounded__lattice(X1)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) != c_Orderings_Obot__class_Obot(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__eq__bot__eq1_0) ).
cnf(clsarity_bool__Lattices_Obounded__lattice,axiom,
class_Lattices_Obounded__lattice(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Obounded__lattice) ).
cnf(cls_COMBK__def_0,axiom,
hAPP(hAPP(c_COMBK(X1,X2),X3),X4) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBK__def_0) ).
cnf(cls_compl__inf_0,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3))
| ~ class_Lattices_Oboolean__algebra(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compl__inf_0) ).
cnf(clsarity_bool__Lattices_Oboolean__algebra,axiom,
class_Lattices_Oboolean__algebra(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oboolean__algebra) ).
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/sandbox/benchmark/theBenchmark.p',cls_double__compl_0) ).
cnf(cls_inf__sup__absorb_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)) = X2
| ~ class_Lattices_Olattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__absorb_0) ).
cnf(cls_Collect__imp__eq_0,axiom,
hAPP(c_Collect(X1),hAPP(hAPP(c_COMBS(X1,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),X1),c_implies),X2)),X3)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),hAPP(c_Collect(X1),X2))),hAPP(c_Collect(X1),X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Collect__imp__eq_0) ).
cnf(cls_sup1CI_0,axiom,
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),X4))
| ~ hBOOL(hAPP(X3,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1CI_0) ).
cnf(cls_id__apply_0,axiom,
hAPP(c_Fun_Oid(X1),X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_id__apply_0) ).
cnf(cls_COMBS__def_0,axiom,
hAPP(hAPP(hAPP(c_COMBS(X1,X2,X3),X4),X5),X6) = hAPP(hAPP(X4,X6),hAPP(X5,X6)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBS__def_0) ).
cnf(cls_Collect__mem__eq_0,axiom,
hAPP(c_Collect(X1),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_bool),tc_bool),c_in(X1)),X2)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Collect__mem__eq_0) ).
cnf(cls_Suc__leD_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Suc(X1)),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__leD_0) ).
cnf(cls_le__refl_0,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X1),X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__refl_0) ).
cnf(cls_order__eq__iff_2,axiom,
( X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_2) ).
cnf(cls_inf__sup__ord_I4_J_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X2)))
| ~ class_Lattices_Olattice(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I4_J_0) ).
cnf(cls_le__sup__iff_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X4)),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__sup__iff_0) ).
cnf(cls_le__bool__def__raw_0,axiom,
c_lessequals(tc_bool) = c_implies,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__bool__def__raw_0) ).
cnf(clsarity_bool__Lattices_Oupper__semilattice,axiom,
class_Lattices_Oupper__semilattice(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oupper__semilattice) ).
cnf(cls_sup__Un__eq_0,axiom,
hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(hAPP(c_COMBC(t_a,tc_fun(t_a,tc_bool),tc_bool),c_in(t_a)),X1)),hAPP(hAPP(c_COMBC(t_a,tc_fun(t_a,tc_bool),tc_bool),c_in(t_a)),X2)),v_x) = hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),X1),X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__Un__eq_0) ).
cnf(cls_not__less__eq__eq_1,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Suc(X2)),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq__eq_1) ).
cnf(clsarity_bool__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).
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/sandbox/benchmark/theBenchmark.p',cls_ComplI_0) ).
cnf(cls_Un__empty__right_0,axiom,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty__right_0) ).
cnf(cls_linorder__linear_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__linear_0) ).
cnf(clsarity_nat__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
cnf(cls_inf__absorb2_0,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) = X3
| ~ class_Lattices_Olower__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__absorb2_0) ).
cnf(clsarity_nat__Lattices_Olower__semilattice,axiom,
class_Lattices_Olower__semilattice(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olower__semilattice) ).
cnf(cls_le__iff__inf_1,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Lattices_Olower__semilattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) != X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__inf_1) ).
cnf(cls_n__not__Suc__n_0,axiom,
X1 != c_Suc(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_n__not__Suc__n_0) ).
cnf(cls_not__less__eq__eq_0,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Suc(X1)),X2))
| hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X2),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq__eq_0) ).
cnf(c_0_38,axiom,
hAPP(c_Collect(X1),hAPP(hAPP(c_COMBB(tc_bool,tc_bool,X1),c_Not),X2)) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),hAPP(c_Collect(X1),X2)),
cls_Collect__neg__eq_0 ).
cnf(c_0_39,axiom,
hAPP(c_Collect(X1),X2) = X2,
cls_Collect__def_0 ).
cnf(c_0_40,axiom,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X2)
| ~ class_Lattices_Olattice(X1) ),
cls_inf__sup__aci_I5_J_0 ).
cnf(c_0_41,axiom,
class_Lattices_Olattice(tc_bool),
clsarity_bool__Lattices_Olattice ).
cnf(c_0_42,axiom,
( hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(t_a,X1)),X2),v_x) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(X2,v_x))
| ~ class_HOL_Ouminus(X1) ),
cls_fun__Compl__def_0 ).
cnf(c_0_43,axiom,
class_HOL_Ouminus(tc_bool),
clsarity_bool__HOL_Ouminus ).
cnf(c_0_44,plain,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),X2) = hAPP(hAPP(c_COMBB(tc_bool,tc_bool,X1),c_Not),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_39]),c_0_39]) ).
cnf(c_0_45,axiom,
hAPP(hAPP(hAPP(c_COMBB(X1,X2,X3),X4),X5),X6) = hAPP(X4,hAPP(X5,X6)),
cls_COMBB__def_0 ).
cnf(c_0_46,axiom,
( X2 = c_Orderings_Obot__class_Obot(X1)
| ~ class_Lattices_Obounded__lattice(X1)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) != c_Orderings_Obot__class_Obot(X1) ),
cls_sup__eq__bot__eq1_0 ).
cnf(c_0_47,plain,
hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X1),X2) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X2),X1),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_48,axiom,
class_Lattices_Obounded__lattice(tc_bool),
clsarity_bool__Lattices_Obounded__lattice ).
cnf(c_0_49,plain,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),hAPP(X1,v_x)) = hAPP(c_Not,hAPP(X1,v_x)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_44]),c_0_45]) ).
cnf(c_0_50,axiom,
hAPP(hAPP(c_COMBK(X1,X2),X3),X4) = X3,
cls_COMBK__def_0 ).
cnf(c_0_51,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_bool)
| hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X2),X1) != c_Orderings_Obot__class_Obot(tc_bool) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_48])]) ).
cnf(c_0_52,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3))
| ~ class_Lattices_Oboolean__algebra(X1) ),
cls_compl__inf_0 ).
cnf(c_0_53,plain,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_bool),X1) = hAPP(c_Not,X1),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_54,axiom,
class_Lattices_Oboolean__algebra(tc_bool),
clsarity_bool__Lattices_Oboolean__algebra ).
cnf(c_0_55,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_56,plain,
( hAPP(c_Not,X1) = c_Orderings_Obot__class_Obot(tc_bool)
| hAPP(c_Not,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),X2),X1)) != c_Orderings_Obot__class_Obot(tc_bool) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_53]),c_0_53]),c_0_54])]) ).
cnf(c_0_57,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)) = X2
| ~ class_Lattices_Olattice(X1) ),
cls_inf__sup__absorb_0 ).
cnf(c_0_58,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_55,c_0_54]) ).
cnf(c_0_59,plain,
( hAPP(c_Not,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X1),X2)) = c_Orderings_Obot__class_Obot(tc_bool)
| hAPP(c_Not,X1) != c_Orderings_Obot__class_Obot(tc_bool) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_41])]) ).
cnf(c_0_60,plain,
hAPP(c_Not,hAPP(c_Not,X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_58,c_0_53]),c_0_53]) ).
cnf(c_0_61,axiom,
hAPP(c_Collect(X1),hAPP(hAPP(c_COMBS(X1,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),X1),c_implies),X2)),X3)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X1,tc_bool)),hAPP(c_Collect(X1),X2))),hAPP(c_Collect(X1),X3)),
cls_Collect__imp__eq_0 ).
cnf(c_0_62,plain,
( hAPP(c_Not,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(c_Not,X1)),X2)) = c_Orderings_Obot__class_Obot(tc_bool)
| X1 != c_Orderings_Obot__class_Obot(tc_bool) ),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_63,axiom,
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),X3),X4))
| ~ hBOOL(hAPP(X3,X4)) ),
cls_sup1CI_0 ).
cnf(c_0_64,axiom,
hAPP(c_Fun_Oid(X1),X2) = X2,
cls_id__apply_0 ).
cnf(c_0_65,axiom,
hAPP(hAPP(hAPP(c_COMBS(X1,X2,X3),X4),X5),X6) = hAPP(hAPP(X4,X6),hAPP(X5,X6)),
cls_COMBS__def_0 ).
cnf(c_0_66,plain,
hAPP(hAPP(c_COMBS(X1,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),X1),c_implies),X2)),X3) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(hAPP(c_COMBB(tc_bool,tc_bool,X1),c_Not),X2)),X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_61,c_0_39]),c_0_44]),c_0_39]),c_0_39]) ).
cnf(c_0_67,axiom,
hAPP(c_Collect(X1),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_bool),tc_bool),c_in(X1)),X2)) = X2,
cls_Collect__mem__eq_0 ).
cnf(c_0_68,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Suc(X1)),X2)) ),
cls_Suc__leD_0 ).
cnf(c_0_69,axiom,
hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X1),X1)),
cls_le__refl_0 ).
cnf(c_0_70,axiom,
( X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3)) ),
cls_order__eq__iff_2 ).
cnf(c_0_71,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X3),X2)))
| ~ class_Lattices_Olattice(X1) ),
cls_inf__sup__ord_I4_J_0 ).
cnf(c_0_72,plain,
hAPP(c_Not,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool))),X1)) = c_Orderings_Obot__class_Obot(tc_bool),
inference(er,[status(thm)],[c_0_62]) ).
cnf(c_0_73,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Lattices_Oupper__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X4)),X3)) ),
cls_le__sup__iff_0 ).
cnf(c_0_74,axiom,
c_lessequals(tc_bool) = c_implies,
cls_le__bool__def__raw_0 ).
cnf(c_0_75,axiom,
class_Lattices_Oupper__semilattice(tc_bool),
clsarity_bool__Lattices_Oupper__semilattice ).
cnf(c_0_76,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),X2),c_Fun_Oid(X3)),X4))
| ~ hBOOL(X4) ),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_77,plain,
hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X1,tc_bool)),hAPP(hAPP(c_COMBB(tc_bool,tc_bool,X1),c_Not),X2)),X3),X4) = hAPP(hAPP(c_implies,hAPP(X2,X4)),hAPP(X3,X4)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_45]) ).
cnf(c_0_78,axiom,
hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(hAPP(c_COMBC(t_a,tc_fun(t_a,tc_bool),tc_bool),c_in(t_a)),X1)),hAPP(hAPP(c_COMBC(t_a,tc_fun(t_a,tc_bool),tc_bool),c_in(t_a)),X2)),v_x) = hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),X1),X2)),
cls_sup__Un__eq_0 ).
cnf(c_0_79,plain,
hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_bool),tc_bool),c_in(X1)),X2) = X2,
inference(rw,[status(thm)],[c_0_67,c_0_39]) ).
cnf(c_0_80,axiom,
( ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Suc(X2)),X1)) ),
cls_not__less__eq__eq_1 ).
cnf(c_0_81,plain,
hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X1),c_Suc(X1))),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_82,plain,
( hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3) = X3
| ~ class_Lattices_Olattice(X1)
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1),X2),X3)),X3)) ),
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_83,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(spm,[status(thm)],[c_0_60,c_0_72]) ).
cnf(c_0_84,axiom,
class_Orderings_Oorder(tc_bool),
clsarity_bool__Orderings_Oorder ).
cnf(c_0_85,plain,
( hBOOL(hAPP(hAPP(c_implies,X1),X2))
| ~ hBOOL(hAPP(hAPP(c_implies,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),X1),X3)),X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_75])]) ).
cnf(c_0_86,plain,
( hBOOL(hAPP(hAPP(c_implies,hAPP(X1,X2)),X2))
| ~ hBOOL(X2) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_64]) ).
cnf(c_0_87,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_88,plain,
hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),X1),X2)) = hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),X1),X2),v_x),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_78,c_0_79]),c_0_79]) ).
cnf(c_0_89,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_90,plain,
~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Suc(c_Suc(X1))),X1)),
inference(spm,[status(thm)],[c_0_80,c_0_81]) ).
cnf(c_0_91,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
cls_linorder__linear_0 ).
cnf(c_0_92,axiom,
class_Orderings_Olinorder(tc_nat),
clsarity_nat__Orderings_Olinorder ).
cnf(c_0_93,plain,
( hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool)) = X1
| ~ hBOOL(hAPP(hAPP(c_implies,hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool))),X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_41]),c_0_84]),c_0_74])]) ).
cnf(c_0_94,plain,
( hBOOL(hAPP(hAPP(c_implies,X1),X2))
| ~ hBOOL(X2) ),
inference(spm,[status(thm)],[c_0_85,c_0_86]) ).
cnf(c_0_95,plain,
( hBOOL(hAPP(hAPP(c_in(X1),X2),hAPP(hAPP(c_COMBB(tc_bool,tc_bool,X1),c_Not),X3)))
| hBOOL(hAPP(hAPP(c_in(X1),X2),X3)) ),
inference(rw,[status(thm)],[c_0_87,c_0_44]) ).
cnf(c_0_96,plain,
hAPP(hAPP(c_in(t_a),v_x),X1) = hAPP(X1,v_x),
inference(spm,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_97,axiom,
( hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) = X3
| ~ class_Lattices_Olower__semilattice(X1)
| ~ hBOOL(hAPP(hAPP(c_lessequals(X1),X3),X2)) ),
cls_inf__absorb2_0 ).
cnf(c_0_98,plain,
hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X1),c_Suc(c_Suc(X1)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_92])]) ).
cnf(c_0_99,axiom,
class_Lattices_Olower__semilattice(tc_nat),
clsarity_nat__Lattices_Olower__semilattice ).
cnf(c_0_100,plain,
( hAPP(c_Not,c_Orderings_Obot__class_Obot(tc_bool)) = X1
| ~ hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_93,c_0_94]) ).
cnf(c_0_101,plain,
( hBOOL(hAPP(c_Not,hAPP(X1,v_x)))
| hBOOL(hAPP(X1,v_x)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_45]),c_0_96]) ).
cnf(c_0_102,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(X1),X2),X3))
| ~ class_Lattices_Olower__semilattice(X1)
| hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X1),X2),X3) != X2 ),
cls_le__iff__inf_1 ).
cnf(c_0_103,plain,
hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),c_Suc(c_Suc(X1))),X1) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98]),c_0_99])]) ).
cnf(c_0_104,axiom,
X1 != c_Suc(X1),
cls_n__not__Suc__n_0 ).
cnf(c_0_105,plain,
( X1 = X2
| ~ hBOOL(X2)
| ~ hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_100,c_0_100]) ).
cnf(c_0_106,plain,
( c_Orderings_Obot__class_Obot(tc_bool) = X1
| ~ hBOOL(hAPP(c_Not,X1)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_100]),c_0_60]) ).
cnf(c_0_107,plain,
( hBOOL(hAPP(c_Not,X1))
| hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_101,c_0_50]) ).
cnf(c_0_108,plain,
c_Suc(c_Suc(X1)) != X1,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_103]),c_0_99])]),c_0_90]) ).
cnf(c_0_109,plain,
( ~ hBOOL(c_Suc(X1))
| ~ hBOOL(X1) ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_105])]) ).
cnf(c_0_110,plain,
( c_Orderings_Obot__class_Obot(tc_bool) = X1
| hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_106,c_0_107]) ).
cnf(c_0_111,plain,
( ~ hBOOL(c_Suc(c_Suc(X1)))
| ~ hBOOL(X1) ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_105])]) ).
cnf(c_0_112,plain,
( c_Suc(X1) = c_Orderings_Obot__class_Obot(tc_bool)
| ~ hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_109,c_0_110]) ).
cnf(c_0_113,plain,
( ~ hBOOL(c_Suc(c_Orderings_Obot__class_Obot(tc_bool)))
| ~ hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_111,c_0_112]) ).
cnf(c_0_114,axiom,
( hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Suc(X1)),X2))
| hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X2),X1)) ),
cls_not__less__eq__eq_0 ).
cnf(c_0_115,plain,
~ hBOOL(X1),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_110]),c_0_104]) ).
cnf(c_0_116,plain,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_114,c_0_115]),c_0_115]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWV820-1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34 % Computer : n010.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue Aug 29 10:42:33 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.61 start to proof: theBenchmark
% 41.50/41.53 % Version : CSE_E---1.5
% 41.50/41.53 % Problem : theBenchmark.p
% 41.50/41.53 % Proof found
% 41.50/41.53 % SZS status Theorem for theBenchmark.p
% 41.50/41.53 % SZS output start Proof
% See solution above
% 41.50/41.54 % Total time : 40.884000 s
% 41.50/41.54 % SZS output end Proof
% 41.50/41.54 % Total time : 40.920000 s
%------------------------------------------------------------------------------