TSTP Solution File: SET838-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET838-1 : 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 : n004.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 14:35:50 EDT 2023
% Result : Unsatisfiable 0.19s 0.71s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 209
% Syntax : Number of formulae : 216 ( 3 unt; 205 typ; 0 def)
% Number of atoms : 19 ( 18 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 18 ( 10 ~; 8 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 416 ( 187 >; 229 *; 0 +; 0 <<)
% Number of predicates : 83 ( 81 usr; 1 prp; 0-3 aty)
% Number of functors : 124 ( 124 usr; 18 con; 0-6 aty)
% Number of variables : 8 ( 0 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_x: $i ).
tff(decl_224,type,
v_g: $i > $i ).
tff(decl_225,type,
v_f: $i > $i ).
tff(decl_226,type,
v_xa: $i > $i ).
cnf(cls_conjecture_1,negated_conjecture,
( X1 = v_x
| v_f(v_g(X1)) != X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
cnf(cls_conjecture_2,negated_conjecture,
( v_g(v_f(v_xa(X1))) = v_xa(X1)
| v_g(v_f(X1)) != X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
cnf(cls_conjecture_3,negated_conjecture,
( v_xa(X1) != X1
| v_g(v_f(X1)) != X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
cnf(cls_conjecture_0,negated_conjecture,
v_f(v_g(v_x)) = v_x,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(c_0_4,negated_conjecture,
( X1 = v_x
| v_f(v_g(X1)) != X1 ),
cls_conjecture_1 ).
cnf(c_0_5,negated_conjecture,
( v_g(v_f(v_xa(X1))) = v_xa(X1)
| v_g(v_f(X1)) != X1 ),
cls_conjecture_2 ).
cnf(c_0_6,negated_conjecture,
( v_f(v_xa(X1)) = v_x
| v_g(v_f(X1)) != X1 ),
inference(spm,[status(thm)],[c_0_4,c_0_5]) ).
cnf(c_0_7,negated_conjecture,
( v_xa(X1) != X1
| v_g(v_f(X1)) != X1 ),
cls_conjecture_3 ).
cnf(c_0_8,negated_conjecture,
( v_xa(X1) = v_g(v_x)
| v_g(v_f(X1)) != X1 ),
inference(spm,[status(thm)],[c_0_5,c_0_6]) ).
cnf(c_0_9,negated_conjecture,
v_f(v_g(v_x)) = v_x,
cls_conjecture_0 ).
cnf(c_0_10,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_8])]),c_0_9])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET838-1 : 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 : n004.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 09:18:22 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.19/0.57 start to proof: theBenchmark
% 0.19/0.71 % Version : CSE_E---1.5
% 0.19/0.71 % Problem : theBenchmark.p
% 0.19/0.71 % Proof found
% 0.19/0.71 % SZS status Theorem for theBenchmark.p
% 0.19/0.71 % SZS output start Proof
% See solution above
% 0.19/0.72 % Total time : 0.110000 s
% 0.19/0.72 % SZS output end Proof
% 0.19/0.72 % Total time : 0.132000 s
%------------------------------------------------------------------------------