TSTP Solution File: SWW225+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SWW225+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n017.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 : Fri Sep 1 00:16:37 EDT 2023
% Result : Theorem 1.26s 1.44s
% Output : CNFRefutation 1.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 212
% Syntax : Number of formulae : 250 ( 30 unt; 199 typ; 0 def)
% Number of atoms : 79 ( 21 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 52 ( 24 ~; 19 |; 2 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 304 ( 183 >; 121 *; 0 +; 0 <<)
% Number of predicates : 78 ( 76 usr; 1 prp; 0-3 aty)
% Number of functors : 123 ( 123 usr; 16 con; 0-4 aty)
% Number of variables : 69 ( 1 sgn; 40 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
hAPP: ( $i * $i ) > $i ).
tff(decl_23,type,
v_f____: $i ).
tff(decl_24,type,
c_SEQ_Osubseq: $i > $o ).
tff(decl_25,type,
tc_Nat_Onat: $i ).
tff(decl_26,type,
v_N1____: $i ).
tff(decl_27,type,
v_N2____: $i ).
tff(decl_28,type,
c_Groups_Oplus__class_Oplus: ( $i * $i * $i ) > $i ).
tff(decl_29,type,
c_Orderings_Oord__class_Oless__eq: ( $i * $i * $i ) > $o ).
tff(decl_30,type,
class_Orderings_Opreorder: $i > $o ).
tff(decl_31,type,
c_Nat_OSuc: $i > $i ).
tff(decl_32,type,
class_Groups_Oordered__ab__semigroup__add__imp__le: $i > $o ).
tff(decl_33,type,
class_Groups_Oordered__ab__semigroup__add: $i > $o ).
tff(decl_34,type,
class_Orderings_Olinorder: $i > $o ).
tff(decl_35,type,
class_Orderings_Oord: $i > $o ).
tff(decl_36,type,
tc_fun: ( $i * $i ) > $i ).
tff(decl_37,type,
class_Orderings_Oorder: $i > $o ).
tff(decl_38,type,
class_Groups_Ocancel__semigroup__add: $i > $o ).
tff(decl_39,type,
class_Groups_Ocancel__ab__semigroup__add: $i > $o ).
tff(decl_40,type,
class_Groups_Oab__semigroup__add: $i > $o ).
tff(decl_41,type,
tc_RealDef_Oreal: $i ).
tff(decl_42,type,
c_RealDef_Oreal: $i > $i ).
tff(decl_43,type,
c_SEQ_Odecseq: ( $i * $i ) > $o ).
tff(decl_44,type,
c_SEQ_Oincseq: ( $i * $i ) > $o ).
tff(decl_45,type,
c_SEQ_Omonoseq: ( $i * $i ) > $o ).
tff(decl_46,type,
c_Groups_Oone__class_Oone: $i > $i ).
tff(decl_47,type,
class_Rings_Ocomm__semiring__1: $i > $o ).
tff(decl_48,type,
class_Groups_Oone: $i > $o ).
tff(decl_49,type,
c_Orderings_Oord__class_Oless: ( $i * $i * $i ) > $o ).
tff(decl_50,type,
c_Groups_Ozero__class_Ozero: $i > $i ).
tff(decl_51,type,
class_Rings_Osemiring__1: $i > $o ).
tff(decl_52,type,
c_Nat_Osemiring__1__class_Oof__nat__aux: ( $i * $i * $i * $i ) > $i ).
tff(decl_53,type,
c_Groups_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).
tff(decl_54,type,
class_Groups_Ozero: $i > $o ).
tff(decl_55,type,
class_Groups_Ogroup__add: $i > $o ).
tff(decl_56,type,
class_Groups_Oab__group__add: $i > $o ).
tff(decl_57,type,
class_Groups_Oordered__ab__group__add: $i > $o ).
tff(decl_58,type,
hBOOL: $i > $o ).
tff(decl_59,type,
class_Groups_Olinordered__ab__group__add: $i > $o ).
tff(decl_60,type,
class_Groups_Oordered__comm__monoid__add: $i > $o ).
tff(decl_61,type,
class_Groups_Oordered__cancel__ab__semigroup__add: $i > $o ).
tff(decl_62,type,
class_Groups_Omonoid__add: $i > $o ).
tff(decl_63,type,
class_Groups_Ocomm__monoid__add: $i > $o ).
tff(decl_64,type,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct: $i > $o ).
tff(decl_65,type,
class_Rings_Olinordered__semidom: $i > $o ).
tff(decl_66,type,
class_Rings_Olinordered__idom: $i > $o ).
tff(decl_67,type,
v_d____: $i ).
tff(decl_68,type,
v_r: $i ).
tff(decl_69,type,
class_Rings_Ozero__neq__one: $i > $o ).
tff(decl_70,type,
c_Groups_Oabs__class_Oabs: ( $i * $i ) > $i ).
tff(decl_71,type,
c_RComplete_Onatceiling: $i > $i ).
tff(decl_72,type,
c_Int_Onumber__class_Onumber__of: ( $i * $i ) > $i ).
tff(decl_73,type,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize: ( $i * $i ) > $i ).
tff(decl_74,type,
tc_Polynomial_Opoly: $i > $i ).
tff(decl_75,type,
class_Int_Onumber: $i > $o ).
tff(decl_76,type,
class_Int_Onumber__ring: $i > $o ).
tff(decl_77,type,
class_Int_Oring__char__0: $i > $o ).
tff(decl_78,type,
class_Groups_Oordered__ab__group__add__abs: $i > $o ).
tff(decl_79,type,
tc_Int_Oint: $i ).
tff(decl_80,type,
tc_Complex_Ocomplex: $i ).
tff(decl_81,type,
v_w____: $i ).
tff(decl_82,type,
c_RealVector_Onorm__class_Onorm: ( $i * $i ) > $i ).
tff(decl_83,type,
c_RComplete_Onatfloor: $i > $i ).
tff(decl_84,type,
v_g____: $i > $i ).
tff(decl_85,type,
class_RealVector_Oreal__normed__vector: $i > $o ).
tff(decl_86,type,
v_z____: $i ).
tff(decl_87,type,
class_RealVector_Oreal__normed__algebra__1: $i > $o ).
tff(decl_88,type,
c_Nat__Numeral_Oneg: $i > $o ).
tff(decl_89,type,
c_Int_Osucc: $i > $i ).
tff(decl_90,type,
c_Complex_Oii: $i ).
tff(decl_91,type,
c_Nat__Transfer_Otsub: ( $i * $i ) > $i ).
tff(decl_92,type,
c_SEQ_OBseq: ( $i * $i ) > $o ).
tff(decl_93,type,
c_Int_OPls: $i ).
tff(decl_94,type,
c_Int_Opred: $i > $i ).
tff(decl_95,type,
c_Complex_Oexpi: $i > $i ).
tff(decl_96,type,
c_Groups_Otimes__class_Otimes: $i > $i ).
tff(decl_97,type,
c_Nat_Osemiring__1__class_Oof__nat: $i > $i ).
tff(decl_98,type,
class_RealVector_Oreal__normed__algebra: $i > $o ).
tff(decl_99,type,
class_Rings_Omult__zero: $i > $o ).
tff(decl_100,type,
class_Rings_Oring__no__zero__divisors: $i > $o ).
tff(decl_101,type,
class_Rings_Ono__zero__divisors: $i > $o ).
tff(decl_102,type,
class_Rings_Osemiring: $i > $o ).
tff(decl_103,type,
class_Rings_Ocomm__semiring: $i > $o ).
tff(decl_104,type,
class_Groups_Oab__semigroup__mult: $i > $o ).
tff(decl_105,type,
class_Nat_Osemiring__char__0: $i > $o ).
tff(decl_106,type,
class_RealVector_Oreal__normed__div__algebra: $i > $o ).
tff(decl_107,type,
class_Groups_Omonoid__mult: $i > $o ).
tff(decl_108,type,
class_Groups_Ocomm__monoid__mult: $i > $o ).
tff(decl_109,type,
class_Rings_Olinordered__ring: $i > $o ).
tff(decl_110,type,
class_Rings_Olinordered__ring__strict: $i > $o ).
tff(decl_111,type,
class_Rings_Oordered__cancel__semiring: $i > $o ).
tff(decl_112,type,
class_Rings_Oordered__ring: $i > $o ).
tff(decl_113,type,
class_Rings_Oordered__semiring: $i > $o ).
tff(decl_114,type,
class_Rings_Oordered__comm__semiring: $i > $o ).
tff(decl_115,type,
class_Rings_Olinordered__semiring__strict: $i > $o ).
tff(decl_116,type,
class_Rings_Olinordered__comm__semiring__strict: $i > $o ).
tff(decl_117,type,
class_Rings_Oring: $i > $o ).
tff(decl_118,type,
class_Rings_Oring__1: $i > $o ).
tff(decl_119,type,
class_Rings_Olinordered__semiring: $i > $o ).
tff(decl_120,type,
class_Rings_Oordered__ring__abs: $i > $o ).
tff(decl_121,type,
class_Rings_Olinordered__semiring__1: $i > $o ).
tff(decl_122,type,
class_Rings_Olinordered__semiring__1__strict: $i > $o ).
tff(decl_123,type,
c_Power_Opower__class_Opower: $i > $i ).
tff(decl_124,type,
c_Complex_Ocis: $i > $i ).
tff(decl_125,type,
class_Power_Opower: $i > $o ).
tff(decl_126,type,
class_Rings_Osemiring__0: $i > $o ).
tff(decl_127,type,
class_Rings_Ocomm__ring__1: $i > $o ).
tff(decl_128,type,
class_Rings_Oring__1__no__zero__divisors: $i > $o ).
tff(decl_129,type,
c_Power_Opower_Opower: ( $i * $i * $i ) > $i ).
tff(decl_130,type,
c_Divides_Odiv__class_Odiv: ( $i * $i * $i ) > $i ).
tff(decl_131,type,
class_Divides_Osemiring__div: $i > $o ).
tff(decl_132,type,
c_Complex_Orcis: ( $i * $i ) > $i ).
tff(decl_133,type,
c_Rings_Oinverse__class_Odivide: ( $i * $i * $i ) > $i ).
tff(decl_134,type,
class_Fields_Ofield: $i > $o ).
tff(decl_135,type,
class_Rings_Oidom: $i > $o ).
tff(decl_136,type,
class_Groups_Ocancel__comm__monoid__add: $i > $o ).
tff(decl_137,type,
class_Rings_Ocomm__semiring__0: $i > $o ).
tff(decl_138,type,
class_Rings_Ocomm__ring: $i > $o ).
tff(decl_139,type,
tc_HOL_Obool: $i ).
tff(decl_140,type,
epred1_3: ( $i * $i * $i ) > $o ).
tff(decl_141,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_142,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_143,type,
esk3_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_144,type,
esk4_2: ( $i * $i ) > $i ).
tff(decl_145,type,
esk5_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_146,type,
esk6_2: ( $i * $i ) > $i ).
tff(decl_147,type,
esk7_2: ( $i * $i ) > $i ).
tff(decl_148,type,
esk8_2: ( $i * $i ) > $i ).
tff(decl_149,type,
esk9_2: ( $i * $i ) > $i ).
tff(decl_150,type,
esk10_2: ( $i * $i ) > $i ).
tff(decl_151,type,
esk11_2: ( $i * $i ) > $i ).
tff(decl_152,type,
esk12_2: ( $i * $i ) > $i ).
tff(decl_153,type,
esk13_2: ( $i * $i ) > $i ).
tff(decl_154,type,
esk14_2: ( $i * $i ) > $i ).
tff(decl_155,type,
esk15_2: ( $i * $i ) > $i ).
tff(decl_156,type,
esk16_2: ( $i * $i ) > $i ).
tff(decl_157,type,
esk17_2: ( $i * $i ) > $i ).
tff(decl_158,type,
esk18_2: ( $i * $i ) > $i ).
tff(decl_159,type,
esk19_2: ( $i * $i ) > $i ).
tff(decl_160,type,
esk20_2: ( $i * $i ) > $i ).
tff(decl_161,type,
esk21_2: ( $i * $i ) > $i ).
tff(decl_162,type,
esk22_2: ( $i * $i ) > $i ).
tff(decl_163,type,
esk23_1: $i > $i ).
tff(decl_164,type,
esk24_2: ( $i * $i ) > $i ).
tff(decl_165,type,
esk25_3: ( $i * $i * $i ) > $i ).
tff(decl_166,type,
esk26_3: ( $i * $i * $i ) > $i ).
tff(decl_167,type,
esk27_1: $i > $i ).
tff(decl_168,type,
esk28_1: $i > $i ).
tff(decl_169,type,
esk29_2: ( $i * $i ) > $i ).
tff(decl_170,type,
esk30_1: $i > $i ).
tff(decl_171,type,
esk31_2: ( $i * $i ) > $i ).
tff(decl_172,type,
esk32_1: $i > $i ).
tff(decl_173,type,
esk33_3: ( $i * $i * $i ) > $i ).
tff(decl_174,type,
esk34_1: $i > $i ).
tff(decl_175,type,
esk35_3: ( $i * $i * $i ) > $i ).
tff(decl_176,type,
esk36_2: ( $i * $i ) > $i ).
tff(decl_177,type,
esk37_3: ( $i * $i * $i ) > $i ).
tff(decl_178,type,
esk38_2: ( $i * $i ) > $i ).
tff(decl_179,type,
esk39_3: ( $i * $i * $i ) > $i ).
tff(decl_180,type,
esk40_2: ( $i * $i ) > $i ).
tff(decl_181,type,
esk41_3: ( $i * $i * $i ) > $i ).
tff(decl_182,type,
esk42_2: ( $i * $i ) > $i ).
tff(decl_183,type,
esk43_1: $i > $i ).
tff(decl_184,type,
esk44_0: $i ).
tff(decl_185,type,
esk45_0: $i ).
tff(decl_186,type,
esk46_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_187,type,
esk47_2: ( $i * $i ) > $i ).
tff(decl_188,type,
esk48_3: ( $i * $i * $i ) > $i ).
tff(decl_189,type,
esk49_2: ( $i * $i ) > $i ).
tff(decl_190,type,
esk50_3: ( $i * $i * $i ) > $i ).
tff(decl_191,type,
esk51_2: ( $i * $i ) > $i ).
tff(decl_192,type,
esk52_3: ( $i * $i * $i ) > $i ).
tff(decl_193,type,
esk53_2: ( $i * $i ) > $i ).
tff(decl_194,type,
esk54_3: ( $i * $i * $i ) > $i ).
tff(decl_195,type,
esk55_1: $i > $i ).
tff(decl_196,type,
esk56_1: $i > $i ).
tff(decl_197,type,
esk57_1: $i > $i ).
tff(decl_198,type,
esk58_1: $i > $i ).
tff(decl_199,type,
esk59_2: ( $i * $i ) > $i ).
tff(decl_200,type,
esk60_2: ( $i * $i ) > $i ).
tff(decl_201,type,
esk61_2: ( $i * $i ) > $i ).
tff(decl_202,type,
esk62_1: $i > $i ).
tff(decl_203,type,
esk63_2: ( $i * $i ) > $i ).
tff(decl_204,type,
esk64_3: ( $i * $i * $i ) > $i ).
tff(decl_205,type,
esk65_3: ( $i * $i * $i ) > $i ).
tff(decl_206,type,
esk66_1: $i > $i ).
tff(decl_207,type,
esk67_1: $i > $i ).
tff(decl_208,type,
esk68_2: ( $i * $i ) > $i ).
tff(decl_209,type,
esk69_2: ( $i * $i ) > $i ).
tff(decl_210,type,
esk70_2: ( $i * $i ) > $i ).
tff(decl_211,type,
esk71_2: ( $i * $i ) > $i ).
tff(decl_212,type,
esk72_2: ( $i * $i ) > $i ).
tff(decl_213,type,
esk73_3: ( $i * $i * $i ) > $i ).
tff(decl_214,type,
esk74_3: ( $i * $i * $i ) > $i ).
tff(decl_215,type,
esk75_3: ( $i * $i * $i ) > $i ).
tff(decl_216,type,
esk76_2: ( $i * $i ) > $i ).
tff(decl_217,type,
esk77_3: ( $i * $i * $i ) > $i ).
tff(decl_218,type,
esk78_3: ( $i * $i * $i ) > $i ).
tff(decl_219,type,
esk79_3: ( $i * $i * $i ) > $i ).
tff(decl_220,type,
esk80_3: ( $i * $i * $i ) > $i ).
fof(fact_real__of__nat__Suc,axiom,
! [X6] : hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(X6)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X6),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__Suc) ).
fof(fact_Suc__eq__plus1,axiom,
! [X6] : c_Nat_OSuc(X6) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X6,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__eq__plus1) ).
fof(conj_0,conjecture,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(fact_not__less__eq__eq,axiom,
! [X19,X18] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X19)
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X19),X18) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__eq__eq) ).
fof(fact_nat__less__real__le,axiom,
! [X18,X19] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X18)
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X19),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X18)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__less__real__le) ).
fof(fact_real__eq__of__nat,axiom,
c_RealDef_Oreal(tc_Nat_Onat) = c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__eq__of__nat) ).
fof(fact_Suc__le__lessD,axiom,
! [X6,X7] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X7),X6)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X7,X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__le__lessD) ).
fof(fact_nat__add__commute,axiom,
! [X6,X7] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X7,X6) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X6,X7),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__commute) ).
fof(fact_le__antisym,axiom,
! [X6,X7] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,X6)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X6,X7)
=> X7 = X6 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__antisym) ).
fof(fact_termination__basic__simps_I2_J,axiom,
! [X23,X26,X4] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,X26)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X23,X26)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I2_J) ).
fof(fact__096N1_A_L_AN2_A_060_061_Af_A_IN1_A_L_AN2_J_096,axiom,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____),hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096N1_A_L_AN2_A_060_061_Af_A_IN1_A_L_AN2_J_096) ).
fof(fact_nat__add__assoc,axiom,
! [X15,X6,X7] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X7,X6),X15) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X7,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X6,X15)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__assoc) ).
fof(fact_real__le__refl,axiom,
! [X33] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X33,X33),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__le__refl) ).
fof(c_0_13,plain,
! [X369] : hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(X369)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X369),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(variable_rename,[status(thm)],[fact_real__of__nat__Suc]) ).
fof(c_0_14,plain,
! [X1002] : c_Nat_OSuc(X1002) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1002,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[fact_Suc__eq__plus1]) ).
fof(c_0_15,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_0])]) ).
cnf(c_0_16,plain,
hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(X1)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_17,plain,
c_Nat_OSuc(X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_18,plain,
! [X19,X18] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X19)
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X19),X18) ),
inference(fof_simplification,[status(thm)],[fact_not__less__eq__eq]) ).
cnf(c_0_19,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_20,plain,
! [X405,X406] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X406,X405)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X406),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X405)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X406),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X405))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X406,X405) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__real__le])]) ).
cnf(c_0_21,plain,
hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(rw,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_22,plain,
c_RealDef_Oreal(tc_Nat_Onat) = c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[fact_real__eq__of__nat]) ).
fof(c_0_23,plain,
! [X966,X967] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X967),X966)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X967,X966) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__le__lessD])]) ).
fof(c_0_24,plain,
! [X162,X163] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X163,X162)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X162),X163) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X162),X163)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X163,X162) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])]) ).
cnf(c_0_25,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_17]),c_0_17]) ).
cnf(c_0_26,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_27,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_22]),c_0_22]) ).
fof(c_0_28,plain,
! [X303,X304] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X304,X303) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X303,X304),
inference(variable_rename,[status(thm)],[fact_nat__add__commute]) ).
fof(c_0_29,plain,
! [X150,X151] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X151,X150)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X150,X151)
| X151 = X150 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__antisym])]) ).
cnf(c_0_30,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_31,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_32,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_22]),c_0_22]) ).
cnf(c_0_33,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_22]),c_0_27]),c_0_22]) ).
cnf(c_0_34,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
fof(c_0_35,plain,
! [X834,X835,X836] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X836,X835)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X836,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X834,X835)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I2_J])]) ).
cnf(c_0_36,plain,
( X1 = X2
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_37,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____),hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),
inference(split_conjunct,[status(thm)],[fact__096N1_A_L_AN2_A_060_061_Af_A_IN1_A_L_AN2_J_096]) ).
cnf(c_0_38,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2) ),
inference(rw,[status(thm)],[c_0_30,c_0_17]) ).
cnf(c_0_39,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1) ),
inference(rw,[status(thm)],[c_0_31,c_0_17]) ).
cnf(c_0_40,negated_conjecture,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]) ).
cnf(c_0_41,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_42,plain,
( hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_43,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_44,negated_conjecture,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____),hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
fof(c_0_45,plain,
! [X297,X298,X299] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X299,X298),X297) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X299,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X298,X297)),
inference(variable_rename,[status(thm)],[fact_nat__add__assoc]) ).
fof(c_0_46,plain,
! [X340] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X340,X340),
inference(variable_rename,[status(thm)],[fact_real__le__refl]) ).
cnf(c_0_47,plain,
hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_44]) ).
cnf(c_0_48,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_49,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X1),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_50,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_47]),c_0_48]),c_0_48]),c_0_49])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SWW225+1 : TPTP v8.1.2. Released v5.2.0.
% 0.12/0.14 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.36 % Computer : n017.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sun Aug 27 18:35:42 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.60 start to proof: theBenchmark
% 1.26/1.44 % Version : CSE_E---1.5
% 1.26/1.44 % Problem : theBenchmark.p
% 1.26/1.44 % Proof found
% 1.26/1.44 % SZS status Theorem for theBenchmark.p
% 1.26/1.44 % SZS output start Proof
% See solution above
% 1.26/1.45 % Total time : 0.787000 s
% 1.26/1.45 % SZS output end Proof
% 1.26/1.45 % Total time : 0.828000 s
%------------------------------------------------------------------------------