TSTP Solution File: SET834-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET834-1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n021.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 14:35:48 EDT 2023
% Result : Unsatisfiable 1.04s 1.13s
% Output : CNFRefutation 1.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 216
% Syntax : Number of formulae : 235 ( 10 unt; 206 typ; 0 def)
% Number of atoms : 55 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 51 ( 25 ~; 26 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 413 ( 184 >; 229 *; 0 +; 0 <<)
% Number of predicates : 82 ( 81 usr; 1 prp; 0-3 aty)
% Number of functors : 125 ( 125 usr; 22 con; 0-6 aty)
% Number of variables : 63 ( 6 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
c_Datatype_Oo2s: ( $i * $i ) > $i ).
tff(decl_23,type,
c_in: ( $i * $i * $i ) > $o ).
tff(decl_24,type,
c_Datatype_Ooption_OSome: ( $i * $i ) > $i ).
tff(decl_25,type,
c_Datatype_Ooption_ONone: $i ).
tff(decl_26,type,
c_Main_Onot__None__eq__iff1__1: ( $i * $i ) > $i ).
tff(decl_27,type,
c_Main_Onot__Some__eq__iff1__1: ( $i * $i ) > $i ).
tff(decl_28,type,
c_Datatype__Universe_OAtom: ( $i * $i * $i ) > $i ).
tff(decl_29,type,
c_Datatype__Universe_OScons: ( $i * $i * $i * $i ) > $i ).
tff(decl_30,type,
c_Datatype__Universe_OIn0: ( $i * $i * $i ) > $i ).
tff(decl_31,type,
c_Datatype__Universe_OIn1: ( $i * $i * $i ) > $i ).
tff(decl_32,type,
c_Datatype__Universe_OLeaf: ( $i * $i * $i ) > $i ).
tff(decl_33,type,
c_Datatype__Universe_ONumb: ( $i * $i * $i ) > $i ).
tff(decl_34,type,
c_0: $i ).
tff(decl_35,type,
tc_nat: $i ).
tff(decl_36,type,
c_Divides_Oop_Advd: ( $i * $i * $i ) > $o ).
tff(decl_37,type,
c_emptyset: $i ).
tff(decl_38,type,
c_Equiv__Relations_Oquotient: ( $i * $i * $i ) > $i ).
tff(decl_39,type,
c_Extraction_Osumbool_OLeft: $i ).
tff(decl_40,type,
c_Extraction_Osumbool_ORight: $i ).
tff(decl_41,type,
c_insert: ( $i * $i * $i ) > $i ).
tff(decl_42,type,
tc_set: $i > $i ).
tff(decl_43,type,
c_minus: ( $i * $i * $i ) > $i ).
tff(decl_44,type,
c_Finite__Set_OFinites: $i ).
tff(decl_45,type,
c_Pow: ( $i * $i ) > $i ).
tff(decl_46,type,
c_union: ( $i * $i * $i ) > $i ).
tff(decl_47,type,
c_Relation_Oconverse: ( $i * $i * $i ) > $i ).
tff(decl_48,type,
tc_prod: ( $i * $i ) > $i ).
tff(decl_49,type,
c_Pair: ( $i * $i * $i * $i ) > $i ).
tff(decl_50,type,
c_GCD_Ogcd: $i > $i ).
tff(decl_51,type,
c_UNIV: $i ).
tff(decl_52,type,
c_IntDef_Oint: $i > $i ).
tff(decl_53,type,
tc_IntDef_Oint: $i ).
tff(decl_54,type,
c_uminus: ( $i * $i ) > $i ).
tff(decl_55,type,
c_List_Olist_ONil: $i ).
tff(decl_56,type,
tc_List_Olist: $i > $i ).
tff(decl_57,type,
c_List_Olex: ( $i * $i ) > $i ).
tff(decl_58,type,
c_append: ( $i * $i * $i ) > $i ).
tff(decl_59,type,
c_List_Orev: ( $i * $i ) > $i ).
tff(decl_60,type,
c_List_Olist_OCons: ( $i * $i * $i ) > $i ).
tff(decl_61,type,
c_List_Olists: ( $i * $i ) > $i ).
tff(decl_62,type,
c_List_Ochar_OChar: ( $i * $i ) > $i ).
tff(decl_63,type,
c_Nat_Osize: ( $i * $i ) > $i ).
tff(decl_64,type,
c_less: ( $i * $i * $i ) > $o ).
tff(decl_65,type,
c_List_Oremdups: ( $i * $i ) > $i ).
tff(decl_66,type,
c_List_Oset: ( $i * $i ) > $i ).
tff(decl_67,type,
c_Suc: $i > $i ).
tff(decl_68,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(decl_69,type,
c_plus: ( $i * $i * $i ) > $i ).
tff(decl_70,type,
c_1: $i ).
tff(decl_71,type,
c_Numeral_Obit_OB0: $i ).
tff(decl_72,type,
c_Numeral_Obit_OB1: $i ).
tff(decl_73,type,
class_Orderings_Oorder: $i > $o ).
tff(decl_74,type,
c_Relation_OId: $i ).
tff(decl_75,type,
c_Relation_OImage: ( $i * $i * $i * $i ) > $i ).
tff(decl_76,type,
class_Orderings_Olinorder: $i > $o ).
tff(decl_77,type,
c_SetInterval_OatLeast: ( $i * $i ) > $i ).
tff(decl_78,type,
class_Orderings_Oord: $i > $o ).
tff(decl_79,type,
c_SetInterval_OatMost: ( $i * $i ) > $i ).
tff(decl_80,type,
c_SetInterval_OgreaterThan: ( $i * $i ) > $i ).
tff(decl_81,type,
c_SetInterval_OlessThan: ( $i * $i ) > $i ).
tff(decl_82,type,
c_inter: ( $i * $i * $i ) > $i ).
tff(decl_83,type,
c_Inter: ( $i * $i ) > $i ).
tff(decl_84,type,
c_Union: ( $i * $i ) > $i ).
tff(decl_85,type,
c_Sum__Type_OInl: ( $i * $i * $i ) > $i ).
tff(decl_86,type,
c_Sum__Type_OInr: ( $i * $i * $i ) > $i ).
tff(decl_87,type,
c_Wellfounded__Recursion_Oacyclic: ( $i * $i ) > $o ).
tff(decl_88,type,
c_Transitive__Closure_Ortrancl: ( $i * $i ) > $i ).
tff(decl_89,type,
c_Wellfounded__Recursion_Owf: ( $i * $i ) > $o ).
tff(decl_90,type,
c_Wellfounded__Relations_Oless__than: $i ).
tff(decl_91,type,
c_Datatype__Universe_Odprod: ( $i * $i * $i * $i ) > $i ).
tff(decl_92,type,
tc_Datatype__Universe_Onode: ( $i * $i ) > $i ).
tff(decl_93,type,
c_Main_OdprodE__1: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_94,type,
c_Main_OdprodE__2: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_95,type,
c_Main_OdprodE__3: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_96,type,
c_Main_OdprodE__4: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_97,type,
c_Datatype__Universe_Odsum: ( $i * $i * $i * $i ) > $i ).
tff(decl_98,type,
c_Main_OdsumE__1: ( $i * $i * $i * $i ) > $i ).
tff(decl_99,type,
c_Main_OdsumE__2: ( $i * $i * $i * $i ) > $i ).
tff(decl_100,type,
c_Main_OdsumE__3: ( $i * $i * $i * $i ) > $i ).
tff(decl_101,type,
c_Main_OdsumE__4: ( $i * $i * $i * $i ) > $i ).
tff(decl_102,type,
c_Datatype__Universe_Ouprod: ( $i * $i * $i * $i ) > $i ).
tff(decl_103,type,
c_Main_OuprodE__1: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_104,type,
c_Main_OuprodE__2: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_105,type,
c_Datatype__Universe_Ousum: ( $i * $i * $i * $i ) > $i ).
tff(decl_106,type,
c_Main_OusumE__1: ( $i * $i * $i * $i ) > $i ).
tff(decl_107,type,
c_Main_OusumE__2: ( $i * $i * $i * $i ) > $i ).
tff(decl_108,type,
c_times: ( $i * $i * $i ) > $i ).
tff(decl_109,type,
c_Divides_Oop_Amod: ( $i * $i * $i ) > $i ).
tff(decl_110,type,
c_Main_Omod__eq__0D__dest__1: ( $i * $i ) > $i ).
tff(decl_111,type,
c_Main_Ofinite__Union__1: ( $i * $i ) > $i ).
tff(decl_112,type,
c_Infinite__Set_Oatmost__one: ( $i * $i ) > $o ).
tff(decl_113,type,
c_Main_Ozmod__eq__0D__dest__1: ( $i * $i ) > $i ).
tff(decl_114,type,
c_List_Odistinct: ( $i * $i ) > $o ).
tff(decl_115,type,
c_Main_Oin__listsI__1: ( $i * $i * $i ) > $i ).
tff(decl_116,type,
c_List_Olistrel: ( $i * $i ) > $i ).
tff(decl_117,type,
c_Main_Olistrel__Cons1__1: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_118,type,
c_Main_Olistrel__Cons1__2: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_119,type,
c_Main_Olistrel__Cons2__1: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_120,type,
c_Main_Olistrel__Cons2__2: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_121,type,
c_List_Olenlex: ( $i * $i ) > $i ).
tff(decl_122,type,
c_Relation_ODomain: ( $i * $i * $i ) > $i ).
tff(decl_123,type,
c_Main_ODomainE__1: ( $i * $i * $i * $i ) > $i ).
tff(decl_124,type,
c_Main_OIdE__1: ( $i * $i ) > $i ).
tff(decl_125,type,
c_Main_OImageE__1: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_126,type,
c_Relation_ORange: ( $i * $i * $i ) > $i ).
tff(decl_127,type,
c_Main_ORangeE__1: ( $i * $i * $i * $i ) > $i ).
tff(decl_128,type,
c_Main_OconverseE__1: ( $i * $i * $i * $i ) > $i ).
tff(decl_129,type,
c_Main_OconverseE__2: ( $i * $i * $i * $i ) > $i ).
tff(decl_130,type,
c_Relation_Odiag: ( $i * $i ) > $i ).
tff(decl_131,type,
c_Main_OdiagE__1: ( $i * $i * $i ) > $i ).
tff(decl_132,type,
c_Relation_Orel__comp: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_133,type,
c_Main_Orel__compE__2: ( $i * $i * $i * $i * $i * $i ) > $i ).
tff(decl_134,type,
c_Main_Orel__compE__3: ( $i * $i * $i * $i * $i * $i ) > $i ).
tff(decl_135,type,
c_Main_Orel__compE__1: ( $i * $i * $i * $i * $i * $i ) > $i ).
tff(decl_136,type,
c_SetInterval_OatLeastAtMost: ( $i * $i * $i ) > $i ).
tff(decl_137,type,
c_SetInterval_OatLeastLessThan: ( $i * $i * $i ) > $i ).
tff(decl_138,type,
c_SetInterval_OgreaterThanAtMost: ( $i * $i * $i ) > $i ).
tff(decl_139,type,
c_SetInterval_OgreaterThanLessThan: ( $i * $i * $i ) > $i ).
tff(decl_140,type,
c_Main_OInterI__1: ( $i * $i * $i ) > $i ).
tff(decl_141,type,
c_Main_OUnionE__1: ( $i * $i * $i ) > $i ).
tff(decl_142,type,
c_Main_OsubsetI__1: ( $i * $i * $i ) > $i ).
tff(decl_143,type,
c_Sum__Type_OPlus: ( $i * $i * $i * $i ) > $i ).
tff(decl_144,type,
tc_sum: ( $i * $i ) > $i ).
tff(decl_145,type,
c_Main_OPlusE__1: ( $i * $i * $i * $i ) > $i ).
tff(decl_146,type,
c_Main_OPlusE__2: ( $i * $i * $i * $i ) > $i ).
tff(decl_147,type,
c_Transitive__Closure_Otrancl: ( $i * $i ) > $i ).
tff(decl_148,type,
c_Relation_Otrans: ( $i * $i ) > $o ).
tff(decl_149,type,
c_Wellfounded__Relations_Olex__prod: ( $i * $i * $i * $i ) > $i ).
tff(decl_150,type,
tc_Datatype_Ooption: $i > $i ).
tff(decl_151,type,
class_Finite__Set_Ofinite: $i > $o ).
tff(decl_152,type,
class_HOL_Ominus: $i > $o ).
tff(decl_153,type,
class_HOL_Oone: $i > $o ).
tff(decl_154,type,
class_Ring__and__Field_Osemiring: $i > $o ).
tff(decl_155,type,
class_Ring__and__Field_Ocomm__semiring: $i > $o ).
tff(decl_156,type,
class_OrderedGroup_Ocomm__monoid__add: $i > $o ).
tff(decl_157,type,
class_Ring__and__Field_Osemiring__0: $i > $o ).
tff(decl_158,type,
class_Ring__and__Field_Ocomm__semiring__0: $i > $o ).
tff(decl_159,type,
class_OrderedGroup_Ocancel__semigroup__add: $i > $o ).
tff(decl_160,type,
class_OrderedGroup_Ocancel__ab__semigroup__add: $i > $o ).
tff(decl_161,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
tff(decl_162,type,
class_Ring__and__Field_Osemiring__0__cancel: $i > $o ).
tff(decl_163,type,
class_Ring__and__Field_Oring: $i > $o ).
tff(decl_164,type,
class_HOL_Oplus: $i > $o ).
tff(decl_165,type,
class_Ring__and__Field_Ocomm__semiring__0__cancel: $i > $o ).
tff(decl_166,type,
class_Ring__and__Field_Ocomm__ring: $i > $o ).
tff(decl_167,type,
class_Ring__and__Field_Oaxclass__0__neq__1: $i > $o ).
tff(decl_168,type,
class_OrderedGroup_Omonoid__mult: $i > $o ).
tff(decl_169,type,
class_OrderedGroup_Ocomm__monoid__mult: $i > $o ).
tff(decl_170,type,
class_Ring__and__Field_Osemiring__1: $i > $o ).
tff(decl_171,type,
class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).
tff(decl_172,type,
class_Ring__and__Field_Osemiring__1__cancel: $i > $o ).
tff(decl_173,type,
class_Ring__and__Field_Oring__1: $i > $o ).
tff(decl_174,type,
class_Ring__and__Field_Ocomm__semiring__1__cancel: $i > $o ).
tff(decl_175,type,
class_HOL_Otimes: $i > $o ).
tff(decl_176,type,
class_Ring__and__Field_Ocomm__ring__1: $i > $o ).
tff(decl_177,type,
class_LOrder_Omeet__semilorder: $i > $o ).
tff(decl_178,type,
class_LOrder_Ojoin__semilorder: $i > $o ).
tff(decl_179,type,
class_LOrder_Olorder: $i > $o ).
tff(decl_180,type,
class_OrderedGroup_Opordered__ab__semigroup__add: $i > $o ).
tff(decl_181,type,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add: $i > $o ).
tff(decl_182,type,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le: $i > $o ).
tff(decl_183,type,
class_OrderedGroup_Oordered__cancel__ab__semigroup__add: $i > $o ).
tff(decl_184,type,
class_HOL_Ozero: $i > $o ).
tff(decl_185,type,
class_Ring__and__Field_Opordered__semiring: $i > $o ).
tff(decl_186,type,
class_Ring__and__Field_Opordered__cancel__semiring: $i > $o ).
tff(decl_187,type,
class_Ring__and__Field_Oordered__semiring__strict: $i > $o ).
tff(decl_188,type,
class_Ring__and__Field_Opordered__comm__semiring: $i > $o ).
tff(decl_189,type,
class_Ring__and__Field_Opordered__cancel__comm__semiring: $i > $o ).
tff(decl_190,type,
class_Ring__and__Field_Oordered__comm__semiring__strict: $i > $o ).
tff(decl_191,type,
class_Ring__and__Field_Oaxclass__abs__if: $i > $o ).
tff(decl_192,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
tff(decl_193,type,
class_OrderedGroup_Olordered__ab__group: $i > $o ).
tff(decl_194,type,
class_Ring__and__Field_Opordered__ring: $i > $o ).
tff(decl_195,type,
class_OrderedGroup_Olordered__ab__group__abs: $i > $o ).
tff(decl_196,type,
class_OrderedGroup_Olordered__ab__group__meet: $i > $o ).
tff(decl_197,type,
class_OrderedGroup_Olordered__ab__group__join: $i > $o ).
tff(decl_198,type,
class_Ring__and__Field_Olordered__ring: $i > $o ).
tff(decl_199,type,
class_Ring__and__Field_Oaxclass__no__zero__divisors: $i > $o ).
tff(decl_200,type,
class_Ring__and__Field_Oordered__ring__strict: $i > $o ).
tff(decl_201,type,
class_Ring__and__Field_Oordered__semidom: $i > $o ).
tff(decl_202,type,
class_Ring__and__Field_Oidom: $i > $o ).
tff(decl_203,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
tff(decl_204,type,
class_Numeral_Onumber: $i > $o ).
tff(decl_205,type,
class_OrderedGroup_Osemigroup__add: $i > $o ).
tff(decl_206,type,
class_Numeral_Onumber__ring: $i > $o ).
tff(decl_207,type,
class_Divides_Odiv: $i > $o ).
tff(decl_208,type,
class_Nat_Opower: $i > $o ).
tff(decl_209,type,
class_Power_Orecpower: $i > $o ).
tff(decl_210,type,
class_Parity_Oeven__odd: $i > $o ).
tff(decl_211,type,
class_OrderedGroup_Oab__semigroup__add: $i > $o ).
tff(decl_212,type,
class_OrderedGroup_Osemigroup__mult: $i > $o ).
tff(decl_213,type,
class_OrderedGroup_Oab__semigroup__mult: $i > $o ).
tff(decl_214,type,
tc_Product__Type_Ounit: $i ).
tff(decl_215,type,
tc_bool: $i ).
tff(decl_216,type,
tc_fun: ( $i * $i ) > $i ).
tff(decl_217,type,
class_Wellfounded__Recursion_Owellorder: $i > $o ).
tff(decl_218,type,
class_Ring__and__Field_Odivision__by__zero: $i > $o ).
tff(decl_219,type,
class_HOL_Oinverse: $i > $o ).
tff(decl_220,type,
class_Ring__and__Field_Ofield: $i > $o ).
tff(decl_221,type,
class_Ring__and__Field_Oordered__field: $i > $o ).
tff(decl_222,type,
class_Ring__and__Field_Opordered__comm__ring: $i > $o ).
tff(decl_223,type,
v_Y: $i ).
tff(decl_224,type,
v_X: $i ).
tff(decl_225,type,
t_a: $i ).
tff(decl_226,type,
v_Z: $i ).
tff(decl_227,type,
v_x: $i ).
cnf(cls_Set_OsubsetI_1,axiom,
( c_lessequals(X1,X2,tc_set(X3))
| ~ c_in(c_Main_OsubsetI__1(X1,X2,X3),X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-0.ax',cls_Set_OsubsetI_1) ).
cnf(cls_Set_OUnCI_0,axiom,
( c_in(X1,c_union(X4,X2,X3),X3)
| ~ c_in(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-2.ax',cls_Set_OUnCI_0) ).
cnf(cls_Set_OsubsetI_0,axiom,
( c_in(c_Main_OsubsetI__1(X1,X2,X3),X1,X3)
| c_lessequals(X1,X2,tc_set(X3)) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-0.ax',cls_Set_OsubsetI_0) ).
cnf(cls_Set_OUnCI_1,axiom,
( c_in(X1,c_union(X2,X4,X3),X3)
| ~ c_in(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-2.ax',cls_Set_OUnCI_1) ).
cnf(cls_conjecture_5,negated_conjecture,
( c_lessequals(v_X,X1,tc_set(t_a))
| ~ c_lessequals(v_Z,X1,tc_set(t_a))
| ~ c_lessequals(v_Y,X1,tc_set(t_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_5) ).
cnf(cls_Set_OsubsetD_0,axiom,
( c_in(X1,X4,X3)
| ~ c_in(X1,X2,X3)
| ~ c_lessequals(X2,X4,tc_set(X3)) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-0.ax',cls_Set_OsubsetD_0) ).
cnf(cls_Set_OUnE_0,axiom,
( c_in(X1,X3,X4)
| c_in(X1,X2,X4)
| ~ c_in(X1,c_union(X2,X3,X4),X4) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-2.ax',cls_Set_OUnE_0) ).
cnf(cls_conjecture_2,negated_conjecture,
c_in(v_x,v_X,t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
cnf(cls_conjecture_4,negated_conjecture,
~ c_in(v_x,v_Y,t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
cnf(cls_conjecture_3,negated_conjecture,
~ c_in(v_x,v_Z,t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
cnf(c_0_10,axiom,
( c_lessequals(X1,X2,tc_set(X3))
| ~ c_in(c_Main_OsubsetI__1(X1,X2,X3),X2,X3) ),
cls_Set_OsubsetI_1 ).
cnf(c_0_11,axiom,
( c_in(X1,c_union(X4,X2,X3),X3)
| ~ c_in(X1,X2,X3) ),
cls_Set_OUnCI_0 ).
cnf(c_0_12,plain,
( c_lessequals(X1,c_union(X2,X3,X4),tc_set(X4))
| ~ c_in(c_Main_OsubsetI__1(X1,c_union(X2,X3,X4),X4),X3,X4) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_13,axiom,
( c_in(c_Main_OsubsetI__1(X1,X2,X3),X1,X3)
| c_lessequals(X1,X2,tc_set(X3)) ),
cls_Set_OsubsetI_0 ).
cnf(c_0_14,axiom,
( c_in(X1,c_union(X2,X4,X3),X3)
| ~ c_in(X1,X2,X3) ),
cls_Set_OUnCI_1 ).
cnf(c_0_15,negated_conjecture,
( c_lessequals(v_X,X1,tc_set(t_a))
| ~ c_lessequals(v_Z,X1,tc_set(t_a))
| ~ c_lessequals(v_Y,X1,tc_set(t_a)) ),
cls_conjecture_5 ).
cnf(c_0_16,plain,
c_lessequals(X1,c_union(X2,X1,X3),tc_set(X3)),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_17,plain,
( c_lessequals(X1,c_union(X2,X3,X4),tc_set(X4))
| ~ c_in(c_Main_OsubsetI__1(X1,c_union(X2,X3,X4),X4),X2,X4) ),
inference(spm,[status(thm)],[c_0_10,c_0_14]) ).
cnf(c_0_18,negated_conjecture,
( c_lessequals(v_X,c_union(X1,v_Z,t_a),tc_set(t_a))
| ~ c_lessequals(v_Y,c_union(X1,v_Z,t_a),tc_set(t_a)) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_19,plain,
c_lessequals(X1,c_union(X1,X2,X3),tc_set(X3)),
inference(spm,[status(thm)],[c_0_17,c_0_13]) ).
cnf(c_0_20,axiom,
( c_in(X1,X4,X3)
| ~ c_in(X1,X2,X3)
| ~ c_lessequals(X2,X4,tc_set(X3)) ),
cls_Set_OsubsetD_0 ).
cnf(c_0_21,negated_conjecture,
c_lessequals(v_X,c_union(v_Y,v_Z,t_a),tc_set(t_a)),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_22,axiom,
( c_in(X1,X3,X4)
| c_in(X1,X2,X4)
| ~ c_in(X1,c_union(X2,X3,X4),X4) ),
cls_Set_OUnE_0 ).
cnf(c_0_23,negated_conjecture,
( c_in(X1,c_union(v_Y,v_Z,t_a),t_a)
| ~ c_in(X1,v_X,t_a) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_24,negated_conjecture,
( c_in(X1,v_Y,t_a)
| c_in(X1,v_Z,t_a)
| ~ c_in(X1,v_X,t_a) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_25,negated_conjecture,
c_in(v_x,v_X,t_a),
cls_conjecture_2 ).
cnf(c_0_26,negated_conjecture,
~ c_in(v_x,v_Y,t_a),
cls_conjecture_4 ).
cnf(c_0_27,negated_conjecture,
~ c_in(v_x,v_Z,t_a),
cls_conjecture_3 ).
cnf(c_0_28,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]),c_0_27]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET834-1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35 % Computer : n021.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % 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 : Sat Aug 26 09:29:41 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.19/0.57 start to proof: theBenchmark
% 1.04/1.13 % Version : CSE_E---1.5
% 1.04/1.13 % Problem : theBenchmark.p
% 1.04/1.13 % Proof found
% 1.04/1.13 % SZS status Theorem for theBenchmark.p
% 1.04/1.13 % SZS output start Proof
% See solution above
% 1.04/1.15 % Total time : 0.537000 s
% 1.04/1.15 % SZS output end Proof
% 1.04/1.15 % Total time : 0.559000 s
%------------------------------------------------------------------------------