TSTP Solution File: SWW246+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SWW246+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n022.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 00:16:43 EDT 2023
% Result : Theorem 1.72s 1.83s
% Output : CNFRefutation 1.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 152
% Syntax : Number of formulae : 166 ( 5 unt; 147 typ; 0 def)
% Number of atoms : 35 ( 7 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 32 ( 16 ~; 10 |; 1 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 235 ( 139 >; 96 *; 0 +; 0 <<)
% Number of predicates : 77 ( 75 usr; 1 prp; 0-5 aty)
% Number of functors : 72 ( 72 usr; 8 con; 0-5 aty)
% Number of variables : 28 ( 5 sgn; 19 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
hAPP: ( $i * $i ) > $i ).
tff(decl_23,type,
t_a: $i ).
tff(decl_24,type,
class_Rings_Oidom: $i > $o ).
tff(decl_25,type,
v_p: $i ).
tff(decl_26,type,
c_Polynomial_Opoly: ( $i * $i ) > $i ).
tff(decl_27,type,
c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant: ( $i * $i * $i ) > $o ).
tff(decl_28,type,
class_Groups_Ozero: $i > $o ).
tff(decl_29,type,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize: ( $i * $i ) > $i ).
tff(decl_30,type,
tc_Nat_Onat: $i ).
tff(decl_31,type,
c_Groups_Ozero__class_Ozero: $i > $i ).
tff(decl_32,type,
tc_Polynomial_Opoly: $i > $i ).
tff(decl_33,type,
class_Rings_Ocomm__semiring__0: $i > $o ).
tff(decl_34,type,
c_Polynomial_OpCons: $i > $i ).
tff(decl_35,type,
c_Groups_Oplus__class_Oplus: $i > $i ).
tff(decl_36,type,
c_Groups_Otimes__class_Otimes: $i > $i ).
tff(decl_37,type,
class_Power_Opower: $i > $o ).
tff(decl_38,type,
class_Rings_Osemiring__0: $i > $o ).
tff(decl_39,type,
c_Power_Opower__class_Opower: $i > $i ).
tff(decl_40,type,
c_Groups_Oone__class_Oone: $i > $i ).
tff(decl_41,type,
class_Rings_Ocomm__semiring__1: $i > $o ).
tff(decl_42,type,
class_Groups_Omonoid__mult: $i > $o ).
tff(decl_43,type,
class_Rings_Omult__zero: $i > $o ).
tff(decl_44,type,
class_Rings_Ono__zero__divisors: $i > $o ).
tff(decl_45,type,
class_Rings_Ozero__neq__one: $i > $o ).
tff(decl_46,type,
class_Groups_Ocomm__monoid__add: $i > $o ).
tff(decl_47,type,
class_Int_Oring__char__0: $i > $o ).
tff(decl_48,type,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct: $i > $o ).
tff(decl_49,type,
class_Rings_Oring__1__no__zero__divisors: $i > $o ).
tff(decl_50,type,
class_Groups_Ocomm__monoid__mult: $i > $o ).
tff(decl_51,type,
class_Rings_Olinordered__ring__strict: $i > $o ).
tff(decl_52,type,
c_Polynomial_Oorder: ( $i * $i * $i ) > $i ).
tff(decl_53,type,
c_Power_Opower_Opower: ( $i * $i * $i ) > $i ).
tff(decl_54,type,
class_Groups_Oab__semigroup__mult: $i > $o ).
tff(decl_55,type,
class_Groups_Oab__semigroup__add: $i > $o ).
tff(decl_56,type,
class_Groups_Ocancel__semigroup__add: $i > $o ).
tff(decl_57,type,
class_Groups_Ocancel__ab__semigroup__add: $i > $o ).
tff(decl_58,type,
class_Groups_Oone: $i > $o ).
tff(decl_59,type,
class_Groups_Omonoid__add: $i > $o ).
tff(decl_60,type,
class_Groups_Olinordered__ab__group__add: $i > $o ).
tff(decl_61,type,
c_Polynomial_Opcompose: ( $i * $i * $i ) > $i ).
tff(decl_62,type,
class_RealVector_Oreal__normed__algebra: $i > $o ).
tff(decl_63,type,
class_Rings_Ocomm__semiring: $i > $o ).
tff(decl_64,type,
class_Rings_Osemiring: $i > $o ).
tff(decl_65,type,
class_Rings_Ocomm__ring__1: $i > $o ).
tff(decl_66,type,
c_Polynomial_Omonom: ( $i * $i * $i ) > $i ).
tff(decl_67,type,
class_Rings_Oring__no__zero__divisors: $i > $o ).
tff(decl_68,type,
tc_fun: ( $i * $i ) > $i ).
tff(decl_69,type,
c_COMBB: ( $i * $i * $i ) > $i ).
tff(decl_70,type,
c_COMBK: ( $i * $i ) > $i ).
tff(decl_71,type,
c_COMBC: ( $i * $i * $i * $i ) > $i ).
tff(decl_72,type,
c_Polynomial_Opoly__rec: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_73,type,
c_Polynomial_Ocoeff: ( $i * $i ) > $i ).
tff(decl_74,type,
c_If: $i > $i ).
tff(decl_75,type,
c_fequal: $i > $i ).
tff(decl_76,type,
c_Polynomial_Osmult: $i > $i ).
tff(decl_77,type,
c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly: ( $i * $i * $i ) > $i ).
tff(decl_78,type,
c_COMBS: ( $i * $i * $i ) > $i ).
tff(decl_79,type,
tc_Int_Oint: $i ).
tff(decl_80,type,
c_Polynomial_Osynthetic__div: ( $i * $i * $i ) > $i ).
tff(decl_81,type,
c_Polynomial_OAbs__poly: ( $i * $i ) > $i ).
tff(decl_82,type,
c_Polynomial_Odegree: ( $i * $i ) > $i ).
tff(decl_83,type,
c_Nat_Onat_Onat__case: ( $i * $i * $i ) > $i ).
tff(decl_84,type,
c_Groups_Ominus__class_Ominus: $i > $i ).
tff(decl_85,type,
class_Groups_Oab__group__add: $i > $o ).
tff(decl_86,type,
class_Rings_Ocomm__ring: $i > $o ).
tff(decl_87,type,
class_Groups_Ogroup__add: $i > $o ).
tff(decl_88,type,
class_Rings_Oring: $i > $o ).
tff(decl_89,type,
tc_HOL_Obool: $i ).
tff(decl_90,type,
class_Rings_Oring__1: $i > $o ).
tff(decl_91,type,
c_Groups_Ouminus__class_Ouminus: $i > $i ).
tff(decl_92,type,
class_Fields_Ofield: $i > $o ).
tff(decl_93,type,
c_Polynomial_Opoly__gcd: ( $i * $i * $i ) > $i ).
tff(decl_94,type,
c_Nat_OSuc: $i ).
tff(decl_95,type,
class_Groups_Ominus: $i > $o ).
tff(decl_96,type,
class_Lattices_Oboolean__algebra: $i > $o ).
tff(decl_97,type,
class_Groups_Ouminus: $i > $o ).
tff(decl_98,type,
c_COMBI: $i > $i ).
tff(decl_99,type,
class_Lattices_Oab__semigroup__idem__mult: $i > $o ).
tff(decl_100,type,
c_Rings_Odvd__class_Odvd: $i > $i ).
tff(decl_101,type,
hBOOL: $i > $o ).
tff(decl_102,type,
c_Rings_Oinverse__class_Oinverse: $i > $i ).
tff(decl_103,type,
class_Rings_Odivision__ring__inverse__zero: $i > $o ).
tff(decl_104,type,
class_Rings_Odvd: $i > $o ).
tff(decl_105,type,
class_Rings_Odivision__ring: $i > $o ).
tff(decl_106,type,
class_Fields_Ofield__inverse__zero: $i > $o ).
tff(decl_107,type,
c_fNot: $i ).
tff(decl_108,type,
c_Orderings_Oord__class_OLeast: ( $i * $i ) > $i ).
tff(decl_109,type,
class_RealVector_Oreal__normed__field: $i > $o ).
tff(decl_110,type,
c_Deriv_Oderiv: ( $i * $i * $i * $i ) > $o ).
tff(decl_111,type,
c_Divides_Odiv__class_Omod: ( $i * $i * $i ) > $i ).
tff(decl_112,type,
class_Orderings_Owellorder: $i > $o ).
tff(decl_113,type,
class_Divides_Osemiring__div: $i > $o ).
tff(decl_114,type,
class_Divides_Oring__div: $i > $o ).
tff(decl_115,type,
c_Rings_Oinverse__class_Odivide: $i > $i ).
tff(decl_116,type,
c_Nat_Osemiring__1__class_Oof__nat: ( $i * $i ) > $i ).
tff(decl_117,type,
class_Nat_Osemiring__char__0: $i > $o ).
tff(decl_118,type,
class_Rings_Osemiring__1: $i > $o ).
tff(decl_119,type,
class_RealVector_Oreal__field: $i > $o ).
tff(decl_120,type,
c_Nat_Osemiring__1__class_Oof__nat__aux: ( $i * $i * $i * $i ) > $i ).
tff(decl_121,type,
c_Polynomial_Opdivmod__rel: ( $i * $i * $i * $i * $i ) > $o ).
tff(decl_122,type,
c_Orderings_Oord__class_Oless: ( $i * $i * $i ) > $o ).
tff(decl_123,type,
c_Transcendental_Odiffs: ( $i * $i * $i ) > $i ).
tff(decl_124,type,
class_Rings_Olinordered__semidom: $i > $o ).
tff(decl_125,type,
class_Rings_Olinordered__comm__semiring__strict: $i > $o ).
tff(decl_126,type,
class_Rings_Olinordered__semiring__strict: $i > $o ).
tff(decl_127,type,
class_Rings_Olinordered__ring: $i > $o ).
tff(decl_128,type,
class_Groups_Oordered__comm__monoid__add: $i > $o ).
tff(decl_129,type,
class_Rings_Olinordered__idom: $i > $o ).
tff(decl_130,type,
class_Groups_Oordered__ab__group__add: $i > $o ).
tff(decl_131,type,
class_Groups_Oordered__ab__semigroup__add__imp__le: $i > $o ).
tff(decl_132,type,
class_Groups_Oordered__cancel__ab__semigroup__add: $i > $o ).
tff(decl_133,type,
class_Orderings_Opreorder: $i > $o ).
tff(decl_134,type,
class_Orderings_Olinorder: $i > $o ).
tff(decl_135,type,
class_Orderings_Oorder: $i > $o ).
tff(decl_136,type,
class_Orderings_Oord: $i > $o ).
tff(decl_137,type,
class_Fields_Olinordered__field__inverse__zero: $i > $o ).
tff(decl_138,type,
class_Fields_Olinordered__field: $i > $o ).
tff(decl_139,type,
class_Rings_Oordered__ring: $i > $o ).
tff(decl_140,type,
c_fconj: $i ).
tff(decl_141,type,
c_Orderings_Oorder_Ostrict__mono: ( $i * $i * $i * $i ) > $o ).
tff(decl_142,type,
c_Orderings_Oorder_Omono: ( $i * $i * $i * $i ) > $o ).
tff(decl_143,type,
c_Polynomial_Opos__poly: ( $i * $i ) > $o ).
tff(decl_144,type,
c_Divides_Odiv__class_Odiv: ( $i * $i * $i ) > $i ).
tff(decl_145,type,
c_Groups_Osgn__class_Osgn: ( $i * $i ) > $i ).
tff(decl_146,type,
c_Orderings_Oord__class_Oless__eq: ( $i * $i * $i ) > $o ).
tff(decl_147,type,
class_Groups_Ocancel__comm__monoid__add: $i > $o ).
tff(decl_148,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_149,type,
esk2_1: $i > $i ).
tff(decl_150,type,
esk3_1: $i > $i ).
tff(decl_151,type,
esk4_3: ( $i * $i * $i ) > $i ).
tff(decl_152,type,
esk5_3: ( $i * $i * $i ) > $i ).
tff(decl_153,type,
esk6_3: ( $i * $i * $i ) > $i ).
tff(decl_154,type,
esk7_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_155,type,
esk8_2: ( $i * $i ) > $i ).
tff(decl_156,type,
esk9_2: ( $i * $i ) > $i ).
tff(decl_157,type,
esk10_2: ( $i * $i ) > $i ).
tff(decl_158,type,
esk11_1: $i > $i ).
tff(decl_159,type,
esk12_2: ( $i * $i ) > $i ).
tff(decl_160,type,
esk13_3: ( $i * $i * $i ) > $i ).
tff(decl_161,type,
esk14_3: ( $i * $i * $i ) > $i ).
tff(decl_162,type,
esk15_3: ( $i * $i * $i ) > $i ).
tff(decl_163,type,
esk16_3: ( $i * $i * $i ) > $i ).
tff(decl_164,type,
esk17_2: ( $i * $i ) > $i ).
tff(decl_165,type,
esk18_1: $i > $i ).
tff(decl_166,type,
esk19_3: ( $i * $i * $i ) > $i ).
tff(decl_167,type,
esk20_3: ( $i * $i * $i ) > $i ).
tff(decl_168,type,
esk21_3: ( $i * $i * $i ) > $i ).
fof(fact__C0_C,axiom,
( class_Rings_Oidom(t_a)
=> ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(t_a,t_a,c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__C0_C) ).
fof(fact_constant__def,axiom,
! [X2,X15,X5] :
( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X5,X15,X2)
<=> ! [X3,X16] : hAPP(X2,X3) = hAPP(X2,X16) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_constant__def) ).
fof(fact_poly__0,axiom,
! [X6,X9] :
( class_Rings_Ocomm__semiring__0(X9)
=> hAPP(c_Polynomial_Opoly(X9,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X9))),X6) = c_Groups_Ozero__class_Ozero(X9) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__0) ).
fof(tfree_0,hypothesis,
class_Rings_Oidom(t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_0) ).
fof(clrel_Rings_Oidom__Rings_Ocomm__semiring__0,axiom,
! [X95] :
( class_Rings_Oidom(X95)
=> class_Rings_Ocomm__semiring__0(X95) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clrel_Rings_Oidom__Rings_Ocomm__semiring__0) ).
fof(c_0_5,plain,
( class_Rings_Oidom(t_a)
=> ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(t_a,t_a,c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))) ),
inference(fof_simplification,[status(thm)],[fact__C0_C]) ).
fof(c_0_6,plain,
( ~ class_Rings_Oidom(t_a)
| ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(t_a,t_a,c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))) ),
inference(fof_nnf,[status(thm)],[c_0_5]) ).
fof(c_0_7,plain,
! [X156,X157,X158,X159,X160,X161,X164,X165] :
( ( ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X158,X157,X156)
| hAPP(X156,X159) = hAPP(X156,X160) )
& ( hAPP(X161,esk2_1(X161)) != hAPP(X161,esk3_1(X161))
| c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X165,X164,X161) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_constant__def])])])])]) ).
fof(c_0_8,plain,
! [X116,X117] :
( ~ class_Rings_Ocomm__semiring__0(X117)
| hAPP(c_Polynomial_Opoly(X117,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X117))),X116) = c_Groups_Ozero__class_Ozero(X117) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__0])]) ).
cnf(c_0_9,plain,
( ~ class_Rings_Oidom(t_a)
| ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(t_a,t_a,c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,hypothesis,
class_Rings_Oidom(t_a),
inference(split_conjunct,[status(thm)],[tfree_0]) ).
cnf(c_0_11,plain,
( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X2,X3,X1)
| hAPP(X1,esk2_1(X1)) != hAPP(X1,esk3_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,plain,
( hAPP(c_Polynomial_Opoly(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(t_a,t_a,c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_9,c_0_10])]) ).
cnf(c_0_14,plain,
( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X1,X2,c_Polynomial_Opoly(X3,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3))))
| ~ class_Rings_Ocomm__semiring__0(X3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_12]) ).
fof(c_0_15,plain,
! [X3043] :
( ~ class_Rings_Oidom(X3043)
| class_Rings_Ocomm__semiring__0(X3043) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[clrel_Rings_Oidom__Rings_Ocomm__semiring__0])]) ).
cnf(c_0_16,plain,
~ class_Rings_Ocomm__semiring__0(t_a),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_17,plain,
( class_Rings_Ocomm__semiring__0(X1)
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_18,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_10])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWW246+1 : TPTP v8.1.2. Released v5.2.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n022.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Aug 27 21:34:54 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.55 start to proof: theBenchmark
% 1.72/1.83 % Version : CSE_E---1.5
% 1.72/1.83 % Problem : theBenchmark.p
% 1.72/1.83 % Proof found
% 1.72/1.83 % SZS status Theorem for theBenchmark.p
% 1.72/1.83 % SZS output start Proof
% See solution above
% 1.72/1.84 % Total time : 1.238000 s
% 1.72/1.84 % SZS output end Proof
% 1.72/1.84 % Total time : 1.282000 s
%------------------------------------------------------------------------------