TSTP Solution File: ANA032-1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : ANA032-1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n012.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 : Wed Aug 30 17:14:02 EDT 2023

% Result   : Unsatisfiable 60.55s 60.77s
% Output   : CNFRefutation 60.80s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :  336
% Syntax   : Number of formulae    :  353 (  10 unt; 326 typ;   0 def)
%            Number of atoms       :   51 (   4 equ)
%            Maximal formula atoms :    5 (   1 avg)
%            Number of connectives :   54 (  30   ~;  24   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  672 ( 279   >; 393   *;   0   +;   0  <<)
%            Number of predicates  :   88 (  86 usr;   1 prp; 0-3 aty)
%            Number of functors    :  240 ( 240 usr;  47 con; 0-18 aty)
%            Number of variables   :   37 (   2 sgn;   0   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    class_HOL_Oplus: $i > $o ).

tff(decl_23,type,
    c_in: ( $i * $i * $i ) > $o ).

tff(decl_24,type,
    c_plus: ( $i * $i * $i ) > $i ).

tff(decl_25,type,
    c_SetsAndFunctions_Oelt__set__plus: ( $i * $i * $i ) > $i ).

tff(decl_26,type,
    tc_set: $i > $i ).

tff(decl_27,type,
    c_lessequals: ( $i * $i * $i ) > $o ).

tff(decl_28,type,
    class_OrderedGroup_Ocomm__monoid__add: $i > $o ).

tff(decl_29,type,
    class_HOL_Otimes: $i > $o ).

tff(decl_30,type,
    c_times: ( $i * $i * $i ) > $i ).

tff(decl_31,type,
    c_SetsAndFunctions_Oelt__set__times: ( $i * $i * $i ) > $i ).

tff(decl_32,type,
    class_OrderedGroup_Ocomm__monoid__mult: $i > $o ).

tff(decl_33,type,
    tc_fun: ( $i * $i ) > $i ).

tff(decl_34,type,
    class_OrderedGroup_Ocancel__semigroup__add: $i > $o ).

tff(decl_35,type,
    class_OrderedGroup_Oab__group__add: $i > $o ).

tff(decl_36,type,
    class_OrderedGroup_Ocancel__ab__semigroup__add: $i > $o ).

tff(decl_37,type,
    class_OrderedGroup_Osemigroup__mult: $i > $o ).

tff(decl_38,type,
    class_OrderedGroup_Oab__semigroup__mult: $i > $o ).

tff(decl_39,type,
    class_OrderedGroup_Omonoid__mult: $i > $o ).

tff(decl_40,type,
    class_Ring__and__Field_Osemiring: $i > $o ).

tff(decl_41,type,
    class_Ring__and__Field_Ocomm__ring__1: $i > $o ).

tff(decl_42,type,
    class_Ring__and__Field_Ocomm__semiring: $i > $o ).

tff(decl_43,type,
    class_Ring__and__Field_Osemiring__0: $i > $o ).

tff(decl_44,type,
    class_Ring__and__Field_Ocomm__semiring__0: $i > $o ).

tff(decl_45,type,
    class_Ring__and__Field_Osemiring__0__cancel: $i > $o ).

tff(decl_46,type,
    class_Ring__and__Field_Oring: $i > $o ).

tff(decl_47,type,
    class_Ring__and__Field_Ocomm__semiring__0__cancel: $i > $o ).

tff(decl_48,type,
    class_Ring__and__Field_Ocomm__ring: $i > $o ).

tff(decl_49,type,
    class_Ring__and__Field_Oaxclass__0__neq__1: $i > $o ).

tff(decl_50,type,
    class_Ring__and__Field_Osemiring__1: $i > $o ).

tff(decl_51,type,
    class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).

tff(decl_52,type,
    class_Ring__and__Field_Osemiring__1__cancel: $i > $o ).

tff(decl_53,type,
    class_Ring__and__Field_Oring__1: $i > $o ).

tff(decl_54,type,
    class_Ring__and__Field_Ocomm__semiring__1__cancel: $i > $o ).

tff(decl_55,type,
    class_HOL_Ominus: $i > $o ).

tff(decl_56,type,
    class_HOL_Ozero: $i > $o ).

tff(decl_57,type,
    class_HOL_Oone: $i > $o ).

tff(decl_58,type,
    class_OrderedGroup_Osemigroup__add: $i > $o ).

tff(decl_59,type,
    class_OrderedGroup_Oab__semigroup__add: $i > $o ).

tff(decl_60,type,
    c_0: $i ).

tff(decl_61,type,
    c_Suc: $i > $i ).

tff(decl_62,type,
    c_Binomial_Obinomial: ( $i * $i ) > $i ).

tff(decl_63,type,
    tc_nat: $i ).

tff(decl_64,type,
    c_1: $i ).

tff(decl_65,type,
    c_Datatype_Oo2s: ( $i * $i ) > $i ).

tff(decl_66,type,
    c_Datatype_Ooption_OSome: ( $i * $i ) > $i ).

tff(decl_67,type,
    c_Datatype_Ooption_ONone: $i ).

tff(decl_68,type,
    c_Main_Onot__None__eq__1: ( $i * $i ) > $i ).

tff(decl_69,type,
    c_Main_Onot__Some__eq__1: ( $i * $i ) > $i ).

tff(decl_70,type,
    c_emptyset: $i ).

tff(decl_71,type,
    c_insert: ( $i * $i * $i ) > $i ).

tff(decl_72,type,
    tc_Datatype_Ooption: $i > $i ).

tff(decl_73,type,
    c_Nat_Osize: ( $i * $i ) > $i ).

tff(decl_74,type,
    c_Pair: ( $i * $i * $i * $i ) > $i ).

tff(decl_75,type,
    tc_prod: ( $i * $i ) > $i ).

tff(decl_76,type,
    c_Sum__Type_OInl: ( $i * $i * $i ) > $i ).

tff(decl_77,type,
    tc_sum: ( $i * $i ) > $i ).

tff(decl_78,type,
    c_Sum__Type_OInr: ( $i * $i * $i ) > $i ).

tff(decl_79,type,
    c_Datatype_Othe: ( $i * $i ) > $i ).

tff(decl_80,type,
    c_Product__Type_OUnity: $i ).

tff(decl_81,type,
    c_Datatype_Ounit_Ounit__case: ( $i * $i * $i ) > $i ).

tff(decl_82,type,
    c_Datatype_Ounit_Ounit__rec: ( $i * $i * $i ) > $i ).

tff(decl_83,type,
    tc_Product__Type_Ounit: $i ).

tff(decl_84,type,
    c_Datatype__Universe_OAtom: ( $i * $i * $i ) > $i ).

tff(decl_85,type,
    c_Datatype__Universe_OScons: ( $i * $i * $i * $i ) > $i ).

tff(decl_86,type,
    c_Datatype__Universe_Odprod: ( $i * $i * $i * $i ) > $i ).

tff(decl_87,type,
    tc_Datatype__Universe_Onode: ( $i * $i ) > $i ).

tff(decl_88,type,
    c_Relation_ODomain: ( $i * $i * $i ) > $i ).

tff(decl_89,type,
    c_Datatype__Universe_Ouprod: ( $i * $i * $i * $i ) > $i ).

tff(decl_90,type,
    c_Datatype__Universe_Odsum: ( $i * $i * $i * $i ) > $i ).

tff(decl_91,type,
    c_Datatype__Universe_Ousum: ( $i * $i * $i * $i ) > $i ).

tff(decl_92,type,
    c_Datatype__Universe_OIn0: ( $i * $i * $i ) > $i ).

tff(decl_93,type,
    c_Datatype__Universe_OIn1: ( $i * $i * $i ) > $i ).

tff(decl_94,type,
    c_Datatype__Universe_OLeaf: ( $i * $i * $i ) > $i ).

tff(decl_95,type,
    c_Datatype__Universe_ONumb: ( $i * $i * $i ) > $i ).

tff(decl_96,type,
    c_Datatype__Universe_Ontrunc: ( $i * $i * $i * $i ) > $i ).

tff(decl_97,type,
    c_div: ( $i * $i * $i ) > $i ).

tff(decl_98,type,
    c_Divides_Oop_Amod: ( $i * $i * $i ) > $i ).

tff(decl_99,type,
    c_less: ( $i * $i * $i ) > $o ).

tff(decl_100,type,
    c_Divides_Oop_Advd: ( $i * $i * $i ) > $o ).

tff(decl_101,type,
    c_Equiv__Relations_Oquotient: ( $i * $i * $i ) > $i ).

tff(decl_102,type,
    c_Extraction_Osumbool_OLeft: $i ).

tff(decl_103,type,
    c_Extraction_Osumbool_Osumbool__case: ( $i * $i * $i * $i ) > $i ).

tff(decl_104,type,
    c_Extraction_Osumbool_ORight: $i ).

tff(decl_105,type,
    c_Extraction_Osumbool_Osumbool__rec: ( $i * $i * $i * $i ) > $i ).

tff(decl_106,type,
    tc_Extraction_Osumbool: $i ).

tff(decl_107,type,
    class_Orderings_Olinorder: $i > $o ).

tff(decl_108,type,
    c_Finite__Set_OFinites: $i ).

tff(decl_109,type,
    c_Finite__Set_OMax: ( $i * $i ) > $i ).

tff(decl_110,type,
    c_Orderings_Omax: ( $i * $i * $i ) > $i ).

tff(decl_111,type,
    c_Main_OMax__le__iff__1: ( $i * $i * $i ) > $i ).

tff(decl_112,type,
    c_Main_OMax__less__iff__1: ( $i * $i * $i ) > $i ).

tff(decl_113,type,
    c_Finite__Set_OMin: ( $i * $i ) > $i ).

tff(decl_114,type,
    c_Main_OMin__ge__iff__1: ( $i * $i * $i ) > $i ).

tff(decl_115,type,
    c_Main_OMin__gr__iff__1: ( $i * $i * $i ) > $i ).

tff(decl_116,type,
    c_Orderings_Omin: ( $i * $i * $i ) > $i ).

tff(decl_117,type,
    c_Finite__Set_Ocard: ( $i * $i ) > $i ).

tff(decl_118,type,
    c_minus: ( $i * $i * $i ) > $i ).

tff(decl_119,type,
    c_Pow: ( $i * $i ) > $i ).

tff(decl_120,type,
    c_union: ( $i * $i * $i ) > $i ).

tff(decl_121,type,
    c_Relation_Oconverse: ( $i * $i * $i ) > $i ).

tff(decl_122,type,
    c_NatArith_Oof__nat: ( $i * $i ) > $i ).

tff(decl_123,type,
    c_Fun_Oid: ( $i * $i ) > $i ).

tff(decl_124,type,
    c_GCD_Ogcd: $i > $i ).

tff(decl_125,type,
    c_UNIV: $i ).

tff(decl_126,type,
    class_Numeral_Onumber__ring: $i > $o ).

tff(decl_127,type,
    class_Ring__and__Field_Oordered__idom: $i > $o ).

tff(decl_128,type,
    c_Numeral_OMin: $i ).

tff(decl_129,type,
    c_Numeral_Onumber__of: ( $i * $i ) > $i ).

tff(decl_130,type,
    c_HOL_Oabs: ( $i * $i ) > $i ).

tff(decl_131,type,
    class_Power_Orecpower: $i > $o ).

tff(decl_132,type,
    c_Nat_Opower: ( $i * $i * $i ) > $i ).

tff(decl_133,type,
    c_Numeral_OPls: $i ).

tff(decl_134,type,
    c_Numeral_Obin__minus: $i > $i ).

tff(decl_135,type,
    c_Numeral_Obin__add: ( $i * $i ) > $i ).

tff(decl_136,type,
    c_IntDef_Oneg: ( $i * $i ) > $o ).

tff(decl_137,type,
    c_Numeral_Obit_OB1: $i ).

tff(decl_138,type,
    c_Numeral_OBit: ( $i * $i ) > $i ).

tff(decl_139,type,
    c_Numeral_Obit_OB0: $i ).

tff(decl_140,type,
    c_IntDef_Oiszero: ( $i * $i ) > $o ).

tff(decl_141,type,
    c_IntDef_Oint: $i > $i ).

tff(decl_142,type,
    tc_IntDef_Oint: $i ).

tff(decl_143,type,
    c_IntDef_Onat: $i > $i ).

tff(decl_144,type,
    c_IntDef_Oof__int: ( $i * $i ) > $i ).

tff(decl_145,type,
    c_uminus: ( $i * $i ) > $i ).

tff(decl_146,type,
    c_IntDef_OInteg: $i ).

tff(decl_147,type,
    c_IntDef_OAbs__Integ: $i > $i ).

tff(decl_148,type,
    c_IntDef_ORep__Integ: $i > $i ).

tff(decl_149,type,
    c_IntDef_OInts: $i ).

tff(decl_150,type,
    c_IntDef_ONats: $i ).

tff(decl_151,type,
    c_IntDef_Ointrel: $i ).

tff(decl_152,type,
    c_Relation_OImage: ( $i * $i * $i * $i ) > $i ).

tff(decl_153,type,
    c_IntDiv_OposDivAlg: $i > $i ).

tff(decl_154,type,
    c_IntDiv_OnegateSnd: $i > $i ).

tff(decl_155,type,
    c_fst: ( $i * $i * $i ) > $i ).

tff(decl_156,type,
    c_IntDiv_OnegDivAlg: $i > $i ).

tff(decl_157,type,
    c_snd: ( $i * $i * $i ) > $i ).

tff(decl_158,type,
    c_IntDiv_Oadjust: ( $i * $i ) > $i ).

tff(decl_159,type,
    class_LOrder_Ojoin__semilorder: $i > $o ).

tff(decl_160,type,
    c_LOrder_Ojoin: ( $i * $i * $i ) > $i ).

tff(decl_161,type,
    class_LOrder_Omeet__semilorder: $i > $o ).

tff(decl_162,type,
    c_LOrder_Omeet: ( $i * $i * $i ) > $i ).

tff(decl_163,type,
    c_List_Olist_OCons: ( $i * $i * $i ) > $i ).

tff(decl_164,type,
    tc_List_Olist: $i > $i ).

tff(decl_165,type,
    c_List_Olex: ( $i * $i ) > $i ).

tff(decl_166,type,
    c_List_Olist_ONil: $i ).

tff(decl_167,type,
    c_List_Oset: ( $i * $i ) > $i ).

tff(decl_168,type,
    c_List_Oconcat: ( $i * $i ) > $i ).

tff(decl_169,type,
    c_Main_ONil__eq__concat__conv__1: ( $i * $i ) > $i ).

tff(decl_170,type,
    c_append: ( $i * $i * $i ) > $i ).

tff(decl_171,type,
    c_List_Orev: ( $i * $i ) > $i ).

tff(decl_172,type,
    c_List_Obutlast: ( $i * $i ) > $i ).

tff(decl_173,type,
    c_List_Olast: ( $i * $i ) > $i ).

tff(decl_174,type,
    c_List_Olists: ( $i * $i ) > $i ).

tff(decl_175,type,
    c_List_Otake: ( $i * $i * $i ) > $i ).

tff(decl_176,type,
    c_List_Odrop: ( $i * $i * $i ) > $i ).

tff(decl_177,type,
    c_List_Ochar_OChar: ( $i * $i ) > $i ).

tff(decl_178,type,
    tc_List_Ochar: $i ).

tff(decl_179,type,
    c_Main_Oconcat__eq__Nil__conv__1: ( $i * $i ) > $i ).

tff(decl_180,type,
    c_List_Orotate1: ( $i * $i ) > $i ).

tff(decl_181,type,
    c_List_Odistinct: ( $i * $i ) > $o ).

tff(decl_182,type,
    c_inter: ( $i * $i * $i ) > $i ).

tff(decl_183,type,
    c_List_Oremove1: ( $i * $i * $i ) > $i ).

tff(decl_184,type,
    c_List_Orotate: ( $i * $i * $i ) > $i ).

tff(decl_185,type,
    c_List_Osublist: ( $i * $i * $i ) > $i ).

tff(decl_186,type,
    c_List_Oupt: ( $i * $i ) > $i ).

tff(decl_187,type,
    c_List_Oreplicate: ( $i * $i * $i ) > $i ).

tff(decl_188,type,
    c_List_Ohd: ( $i * $i ) > $i ).

tff(decl_189,type,
    c_List_Otl: ( $i * $i ) > $i ).

tff(decl_190,type,
    c_List_Oitrev: ( $i * $i * $i ) > $i ).

tff(decl_191,type,
    c_List_Olist__update: ( $i * $i * $i * $i ) > $i ).

tff(decl_192,type,
    c_List_Oremdups: ( $i * $i ) > $i ).

tff(decl_193,type,
    c_List_Ozip: ( $i * $i * $i * $i ) > $i ).

tff(decl_194,type,
    c_List_Olexn: ( $i * $i * $i ) > $i ).

tff(decl_195,type,
    c_List_Olexord: ( $i * $i ) > $i ).

tff(decl_196,type,
    c_Main_Olexord__Nil__left__1: ( $i * $i ) > $i ).

tff(decl_197,type,
    c_Main_Olexord__Nil__left__2: ( $i * $i ) > $i ).

tff(decl_198,type,
    c_List_Olist__inter: ( $i * $i * $i ) > $i ).

tff(decl_199,type,
    c_List_Onth: ( $i * $i * $i ) > $i ).

tff(decl_200,type,
    c_List_Olistrel: ( $i * $i ) > $i ).

tff(decl_201,type,
    c_List_Olistset: ( $i * $i ) > $i ).

tff(decl_202,type,
    c_List_Oset__Cons: ( $i * $i * $i ) > $i ).

tff(decl_203,type,
    c_List_Onibble_ONibble9: $i ).

tff(decl_204,type,
    c_List_Onibble_Onibble__case: ( $i * $i * $i * $i * $i * $i * $i * $i * $i * $i * $i * $i * $i * $i * $i * $i * $i * $i ) > $i ).

tff(decl_205,type,
    c_List_Onibble_ONibbleA: $i ).

tff(decl_206,type,
    c_List_Onibble_ONibbleB: $i ).

tff(decl_207,type,
    c_List_Onibble_ONibbleC: $i ).

tff(decl_208,type,
    c_List_Onibble_ONibbleD: $i ).

tff(decl_209,type,
    c_List_Onibble_ONibbleE: $i ).

tff(decl_210,type,
    c_List_Onibble_ONibbleF: $i ).

tff(decl_211,type,
    c_List_Onibble_ONibble0: $i ).

tff(decl_212,type,
    c_List_Onibble_ONibble1: $i ).

tff(decl_213,type,
    c_List_Onibble_ONibble2: $i ).

tff(decl_214,type,
    c_List_Onibble_ONibble3: $i ).

tff(decl_215,type,
    c_List_Onibble_ONibble4: $i ).

tff(decl_216,type,
    c_List_Onibble_ONibble5: $i ).

tff(decl_217,type,
    c_List_Onibble_ONibble6: $i ).

tff(decl_218,type,
    c_List_Onibble_ONibble7: $i ).

tff(decl_219,type,
    c_List_Onibble_ONibble8: $i ).

tff(decl_220,type,
    c_List_Onibble_Onibble__rec: ( $i * $i * $i * $i * $i * $i * $i * $i * $i * $i * $i * $i * $i * $i * $i * $i * $i * $i ) > $i ).

tff(decl_221,type,
    tc_List_Onibble: $i ).

tff(decl_222,type,
    c_List_Onull: ( $i * $i ) > $o ).

tff(decl_223,type,
    c_List_Oop_Amem: ( $i * $i * $i ) > $o ).

tff(decl_224,type,
    c_SetInterval_OlessThan: ( $i * $i ) > $i ).

tff(decl_225,type,
    c_Map_Omap__of: ( $i * $i * $i * $i ) > $i ).

tff(decl_226,type,
    class_Ring__and__Field_Oordered__semidom: $i > $o ).

tff(decl_227,type,
    c_Numeral_Obin__succ: $i > $i ).

tff(decl_228,type,
    c_Numeral_Obin__mult: ( $i * $i ) > $i ).

tff(decl_229,type,
    class_Numeral_Onumber: $i > $o ).

tff(decl_230,type,
    class_Ring__and__Field_Odivision__by__zero: $i > $o ).

tff(decl_231,type,
    class_Ring__and__Field_Ofield: $i > $o ).

tff(decl_232,type,
    c_divide: ( $i * $i * $i ) > $i ).

tff(decl_233,type,
    class_Ring__and__Field_Oordered__field: $i > $o ).

tff(decl_234,type,
    c_HOL_Oinverse: ( $i * $i ) > $i ).

tff(decl_235,type,
    class_OrderedGroup_Opordered__ab__group__add: $i > $o ).

tff(decl_236,type,
    class_Ring__and__Field_Oordered__ring__strict: $i > $o ).

tff(decl_237,type,
    c_Numeral_Obin__pred: $i > $i ).

tff(decl_238,type,
    c_Numeral_Obit_Obit__case: ( $i * $i * $i * $i ) > $i ).

tff(decl_239,type,
    c_Numeral_Obit_Obit__rec: ( $i * $i * $i * $i ) > $i ).

tff(decl_240,type,
    tc_Numeral_Obit: $i ).

tff(decl_241,type,
    class_OrderedGroup_Olordered__ab__group__abs: $i > $o ).

tff(decl_242,type,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le: $i > $o ).

tff(decl_243,type,
    class_OrderedGroup_Olordered__ab__group: $i > $o ).

tff(decl_244,type,
    c_OrderedGroup_Onprt: ( $i * $i ) > $i ).

tff(decl_245,type,
    c_OrderedGroup_Opprt: ( $i * $i ) > $i ).

tff(decl_246,type,
    class_Orderings_Oorder: $i > $o ).

tff(decl_247,type,
    c_Parity_Oeven: ( $i * $i ) > $o ).

tff(decl_248,type,
    c_Main_Osurj__pair__1: ( $i * $i * $i ) > $i ).

tff(decl_249,type,
    c_Main_Osurj__pair__2: ( $i * $i * $i ) > $i ).

tff(decl_250,type,
    c_Relation_OId: $i ).

tff(decl_251,type,
    c_Relation_Odiag: ( $i * $i ) > $i ).

tff(decl_252,type,
    c_Relation_Orel__comp: ( $i * $i * $i * $i * $i ) > $i ).

tff(decl_253,type,
    c_Relation_ORange: ( $i * $i * $i ) > $i ).

tff(decl_254,type,
    c_SetInterval_OatLeast: ( $i * $i ) > $i ).

tff(decl_255,type,
    c_SetInterval_OatMost: ( $i * $i ) > $i ).

tff(decl_256,type,
    c_SetInterval_OgreaterThan: ( $i * $i ) > $i ).

tff(decl_257,type,
    c_SetInterval_OatLeastAtMost: ( $i * $i * $i ) > $i ).

tff(decl_258,type,
    class_Orderings_Oord: $i > $o ).

tff(decl_259,type,
    c_SetInterval_OatLeastLessThan: ( $i * $i * $i ) > $i ).

tff(decl_260,type,
    c_SetInterval_OgreaterThanAtMost: ( $i * $i * $i ) > $i ).

tff(decl_261,type,
    c_SetInterval_OgreaterThanLessThan: ( $i * $i * $i ) > $i ).

tff(decl_262,type,
    c_Inter: ( $i * $i ) > $i ).

tff(decl_263,type,
    c_Main_OInter__UNIV__conv__1__1: ( $i * $i ) > $i ).

tff(decl_264,type,
    c_Main_OInter__UNIV__conv__2__1: ( $i * $i ) > $i ).

tff(decl_265,type,
    c_Main_OInter__iff__1: ( $i * $i * $i ) > $i ).

tff(decl_266,type,
    c_Union: ( $i * $i ) > $i ).

tff(decl_267,type,
    c_Main_OUnion__empty__conv__1: ( $i * $i ) > $i ).

tff(decl_268,type,
    c_Main_OUnion__iff__1: ( $i * $i * $i ) > $i ).

tff(decl_269,type,
    c_Main_Oall__not__in__conv__1: ( $i * $i ) > $i ).

tff(decl_270,type,
    c_Set_Ocontents: ( $i * $i ) > $i ).

tff(decl_271,type,
    c_Main_Oempty__Union__conv__1: ( $i * $i ) > $i ).

tff(decl_272,type,
    c_Sum__Type_OPlus: ( $i * $i * $i * $i ) > $i ).

tff(decl_273,type,
    c_Transitive__Closure_Ortrancl: ( $i * $i ) > $i ).

tff(decl_274,type,
    c_Transitive__Closure_Otrancl: ( $i * $i ) > $i ).

tff(decl_275,type,
    c_Wellfounded__Recursion_Oacyclic: ( $i * $i ) > $o ).

tff(decl_276,type,
    c_Wellfounded__Recursion_Owf: ( $i * $i ) > $o ).

tff(decl_277,type,
    c_Wellfounded__Relations_Oless__than: $i ).

tff(decl_278,type,
    c_Main_OdprodE__1: ( $i * $i * $i * $i * $i ) > $i ).

tff(decl_279,type,
    c_Main_OdprodE__2: ( $i * $i * $i * $i * $i ) > $i ).

tff(decl_280,type,
    c_Main_OdprodE__3: ( $i * $i * $i * $i * $i ) > $i ).

tff(decl_281,type,
    c_Main_OdprodE__4: ( $i * $i * $i * $i * $i ) > $i ).

tff(decl_282,type,
    c_Main_OdsumE__1: ( $i * $i * $i * $i ) > $i ).

tff(decl_283,type,
    c_Main_OdsumE__2: ( $i * $i * $i * $i ) > $i ).

tff(decl_284,type,
    c_Main_OdsumE__3: ( $i * $i * $i * $i ) > $i ).

tff(decl_285,type,
    c_Main_OdsumE__4: ( $i * $i * $i * $i ) > $i ).

tff(decl_286,type,
    c_Main_OuprodE__1: ( $i * $i * $i * $i * $i ) > $i ).

tff(decl_287,type,
    c_Main_OuprodE__2: ( $i * $i * $i * $i * $i ) > $i ).

tff(decl_288,type,
    c_Main_OusumE__1: ( $i * $i * $i * $i ) > $i ).

tff(decl_289,type,
    c_Main_OusumE__2: ( $i * $i * $i * $i ) > $i ).

tff(decl_290,type,
    c_Main_Omod__eq__0D__dest__1: ( $i * $i ) > $i ).

tff(decl_291,type,
    c_Main_Ofinite__Union__1: ( $i * $i ) > $i ).

tff(decl_292,type,
    c_Infinite__Set_Oatmost__one: ( $i * $i ) > $o ).

tff(decl_293,type,
    c_Main_Ozmod__eq__0D__dest__1: ( $i * $i ) > $i ).

tff(decl_294,type,
    c_Main_Oin__listsI__1: ( $i * $i * $i ) > $i ).

tff(decl_295,type,
    c_Main_Olistrel__Cons1__1: ( $i * $i * $i * $i * $i ) > $i ).

tff(decl_296,type,
    c_Main_Olistrel__Cons1__2: ( $i * $i * $i * $i * $i ) > $i ).

tff(decl_297,type,
    c_Main_Olistrel__Cons2__1: ( $i * $i * $i * $i * $i ) > $i ).

tff(decl_298,type,
    c_Main_Olistrel__Cons2__2: ( $i * $i * $i * $i * $i ) > $i ).

tff(decl_299,type,
    c_List_Olenlex: ( $i * $i ) > $i ).

tff(decl_300,type,
    c_Main_ODomainE__1: ( $i * $i * $i * $i ) > $i ).

tff(decl_301,type,
    c_Main_OIdE__1: ( $i * $i ) > $i ).

tff(decl_302,type,
    c_Main_OImageE__1: ( $i * $i * $i * $i * $i ) > $i ).

tff(decl_303,type,
    c_Main_ORangeE__1: ( $i * $i * $i * $i ) > $i ).

tff(decl_304,type,
    c_Main_OconverseE__1: ( $i * $i * $i * $i ) > $i ).

tff(decl_305,type,
    c_Main_OconverseE__2: ( $i * $i * $i * $i ) > $i ).

tff(decl_306,type,
    c_Main_OdiagE__1: ( $i * $i * $i ) > $i ).

tff(decl_307,type,
    c_Main_Orel__compE__2: ( $i * $i * $i * $i * $i * $i ) > $i ).

tff(decl_308,type,
    c_Main_Orel__compE__3: ( $i * $i * $i * $i * $i * $i ) > $i ).

tff(decl_309,type,
    c_Main_Orel__compE__1: ( $i * $i * $i * $i * $i * $i ) > $i ).

tff(decl_310,type,
    c_Main_OInterI__1: ( $i * $i * $i ) > $i ).

tff(decl_311,type,
    c_Main_OUnionE__1: ( $i * $i * $i ) > $i ).

tff(decl_312,type,
    c_Main_OsubsetI__1: ( $i * $i * $i ) > $i ).

tff(decl_313,type,
    c_Main_OPlusE__1: ( $i * $i * $i * $i ) > $i ).

tff(decl_314,type,
    c_Main_OPlusE__2: ( $i * $i * $i * $i ) > $i ).

tff(decl_315,type,
    c_Relation_Otrans: ( $i * $i ) > $o ).

tff(decl_316,type,
    c_Wellfounded__Relations_Olex__prod: ( $i * $i * $i * $i ) > $i ).

tff(decl_317,type,
    class_Finite__Set_Ofinite: $i > $o ).

tff(decl_318,type,
    class_LOrder_Olorder: $i > $o ).

tff(decl_319,type,
    class_OrderedGroup_Opordered__ab__semigroup__add: $i > $o ).

tff(decl_320,type,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add: $i > $o ).

tff(decl_321,type,
    class_OrderedGroup_Oordered__cancel__ab__semigroup__add: $i > $o ).

tff(decl_322,type,
    class_Ring__and__Field_Opordered__semiring: $i > $o ).

tff(decl_323,type,
    class_Ring__and__Field_Opordered__cancel__semiring: $i > $o ).

tff(decl_324,type,
    class_Ring__and__Field_Oordered__semiring__strict: $i > $o ).

tff(decl_325,type,
    class_Ring__and__Field_Opordered__comm__semiring: $i > $o ).

tff(decl_326,type,
    class_Ring__and__Field_Opordered__cancel__comm__semiring: $i > $o ).

tff(decl_327,type,
    class_Ring__and__Field_Oordered__comm__semiring__strict: $i > $o ).

tff(decl_328,type,
    class_Ring__and__Field_Oaxclass__abs__if: $i > $o ).

tff(decl_329,type,
    class_Ring__and__Field_Opordered__ring: $i > $o ).

tff(decl_330,type,
    class_OrderedGroup_Olordered__ab__group__meet: $i > $o ).

tff(decl_331,type,
    class_OrderedGroup_Olordered__ab__group__join: $i > $o ).

tff(decl_332,type,
    class_Ring__and__Field_Olordered__ring: $i > $o ).

tff(decl_333,type,
    class_Ring__and__Field_Oaxclass__no__zero__divisors: $i > $o ).

tff(decl_334,type,
    class_Ring__and__Field_Oidom: $i > $o ).

tff(decl_335,type,
    class_Divides_Odiv: $i > $o ).

tff(decl_336,type,
    class_Nat_Opower: $i > $o ).

tff(decl_337,type,
    class_Parity_Oeven__odd: $i > $o ).

tff(decl_338,type,
    tc_bool: $i ).

tff(decl_339,type,
    class_Wellfounded__Recursion_Owellorder: $i > $o ).

tff(decl_340,type,
    class_HOL_Oinverse: $i > $o ).

tff(decl_341,type,
    class_Ring__and__Field_Opordered__comm__ring: $i > $o ).

tff(decl_342,type,
    v_x: $i ).

tff(decl_343,type,
    v_b: $i > $i ).

tff(decl_344,type,
    t_b: $i ).

tff(decl_345,type,
    v_c: $i ).

tff(decl_346,type,
    v_g: $i > $i ).

tff(decl_347,type,
    v_f: $i > $i ).

cnf(clsrel_Ring__and__Field_Oordered__idom_17,axiom,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_17) ).

cnf(tfree_tcs,negated_conjecture,
    class_Ring__and__Field_Oordered__idom(t_b),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_tcs) ).

cnf(cls_conjecture_1,negated_conjecture,
    ~ c_lessequals(c_times(c_HOL_Oabs(v_b(v_x),t_b),c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_c,c_times(c_HOL_Oabs(v_f(v_x),t_b),c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).

cnf(cls_OrderedGroup_Omult__ac__2_0,axiom,
    ( c_times(X2,X3,X1) = c_times(X3,X2,X1)
    | ~ class_OrderedGroup_Oab__semigroup__mult(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Omult__ac__2_0) ).

cnf(cls_Ring__and__Field_Opordered__semiring__class_Omult__left__mono_0,axiom,
    ( c_lessequals(c_times(X4,X2,X1),c_times(X4,X3,X1),X1)
    | ~ class_Ring__and__Field_Opordered__semiring(X1)
    | ~ c_lessequals(X2,X3,X1)
    | ~ c_lessequals(c_0,X4,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Opordered__semiring__class_Omult__left__mono_0) ).

cnf(cls_OrderedGroup_Omult__ac__3_0,axiom,
    ( c_times(X2,c_times(X3,X4,X1),X1) = c_times(X3,c_times(X2,X4,X1),X1)
    | ~ class_OrderedGroup_Oab__semigroup__mult(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Omult__ac__3_0) ).

cnf(cls_conjecture_0,negated_conjecture,
    c_lessequals(c_HOL_Oabs(v_b(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).

cnf(cls_OrderedGroup_Oabs__ge__zero_0,axiom,
    ( c_lessequals(c_0,c_HOL_Oabs(X2,X1),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-1.ax',cls_OrderedGroup_Oabs__ge__zero_0) ).

cnf(clsrel_Ring__and__Field_Oordered__idom_42,axiom,
    ( class_Ring__and__Field_Opordered__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_42) ).

cnf(clsrel_Ring__and__Field_Oordered__idom_50,axiom,
    ( class_OrderedGroup_Olordered__ab__group__abs(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_50) ).

cnf(c_0_10,axiom,
    ( class_OrderedGroup_Oab__semigroup__mult(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    clsrel_Ring__and__Field_Oordered__idom_17 ).

cnf(c_0_11,negated_conjecture,
    class_Ring__and__Field_Oordered__idom(t_b),
    tfree_tcs ).

cnf(c_0_12,negated_conjecture,
    ~ c_lessequals(c_times(c_HOL_Oabs(v_b(v_x),t_b),c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_c,c_times(c_HOL_Oabs(v_f(v_x),t_b),c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b),
    cls_conjecture_1 ).

cnf(c_0_13,axiom,
    ( c_times(X2,X3,X1) = c_times(X3,X2,X1)
    | ~ class_OrderedGroup_Oab__semigroup__mult(X1) ),
    cls_OrderedGroup_Omult__ac__2_0 ).

cnf(c_0_14,negated_conjecture,
    class_OrderedGroup_Oab__semigroup__mult(t_b),
    inference(spm,[status(thm)],[c_0_10,c_0_11]) ).

cnf(c_0_15,axiom,
    ( c_lessequals(c_times(X4,X2,X1),c_times(X4,X3,X1),X1)
    | ~ class_Ring__and__Field_Opordered__semiring(X1)
    | ~ c_lessequals(X2,X3,X1)
    | ~ c_lessequals(c_0,X4,X1) ),
    cls_Ring__and__Field_Opordered__semiring__class_Omult__left__mono_0 ).

cnf(c_0_16,axiom,
    ( c_times(X2,c_times(X3,X4,X1),X1) = c_times(X3,c_times(X2,X4,X1),X1)
    | ~ class_OrderedGroup_Oab__semigroup__mult(X1) ),
    cls_OrderedGroup_Omult__ac__3_0 ).

cnf(c_0_17,negated_conjecture,
    ~ c_lessequals(c_times(c_HOL_Oabs(v_f(v_x),t_b),c_HOL_Oabs(v_b(v_x),t_b),t_b),c_times(v_c,c_times(c_HOL_Oabs(v_f(v_x),t_b),c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14])]) ).

cnf(c_0_18,plain,
    ( c_lessequals(c_times(X1,X2,X3),c_times(X4,c_times(X1,X5,X3),X3),X3)
    | ~ class_Ring__and__Field_Opordered__semiring(X3)
    | ~ class_OrderedGroup_Oab__semigroup__mult(X3)
    | ~ c_lessequals(X2,c_times(X4,X5,X3),X3)
    | ~ c_lessequals(c_0,X1,X3) ),
    inference(spm,[status(thm)],[c_0_15,c_0_16]) ).

cnf(c_0_19,negated_conjecture,
    c_lessequals(c_HOL_Oabs(v_b(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),
    cls_conjecture_0 ).

cnf(c_0_20,negated_conjecture,
    ( ~ class_Ring__and__Field_Opordered__semiring(t_b)
    | ~ c_lessequals(c_0,c_HOL_Oabs(v_f(v_x),t_b),t_b) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_14]),c_0_19])]) ).

cnf(c_0_21,axiom,
    ( c_lessequals(c_0,c_HOL_Oabs(X2,X1),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    cls_OrderedGroup_Oabs__ge__zero_0 ).

cnf(c_0_22,negated_conjecture,
    ( ~ class_Ring__and__Field_Opordered__semiring(t_b)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(t_b) ),
    inference(spm,[status(thm)],[c_0_20,c_0_21]) ).

cnf(c_0_23,axiom,
    ( class_Ring__and__Field_Opordered__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    clsrel_Ring__and__Field_Oordered__idom_42 ).

cnf(c_0_24,negated_conjecture,
    ~ class_OrderedGroup_Olordered__ab__group__abs(t_b),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_11])]) ).

cnf(c_0_25,axiom,
    ( class_OrderedGroup_Olordered__ab__group__abs(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    clsrel_Ring__and__Field_Oordered__idom_50 ).

cnf(c_0_26,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_11])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : ANA032-1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34  % Computer : n012.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   : Fri Aug 25 18:02:11 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.19/0.56  start to proof: theBenchmark
% 60.55/60.77  % Version  : CSE_E---1.5
% 60.55/60.77  % Problem  : theBenchmark.p
% 60.55/60.77  % Proof found
% 60.55/60.77  % SZS status Theorem for theBenchmark.p
% 60.55/60.77  % SZS output start Proof
% See solution above
% 60.80/60.78  % Total time : 60.150000 s
% 60.80/60.78  % SZS output end Proof
% 60.80/60.79  % Total time : 60.209000 s
%------------------------------------------------------------------------------