TSTP Solution File: ALG398-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : ALG398-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n020.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 16:07:36 EDT 2023
% Result : Unsatisfiable 1.76s 1.85s
% Output : CNFRefutation 1.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 108
% Syntax : Number of formulae : 126 ( 22 unt; 97 typ; 0 def)
% Number of atoms : 40 ( 23 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 26 ( 15 ~; 11 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 128 ( 90 >; 38 *; 0 +; 0 <<)
% Number of predicates : 72 ( 70 usr; 1 prp; 0-5 aty)
% Number of functors : 27 ( 27 usr; 7 con; 0-3 aty)
% Number of variables : 30 ( 0 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
class_Ring__and__Field_Oordered__field: $i > $o ).
tff(decl_23,type,
class_Ring__and__Field_Odivision__by__zero: $i > $o ).
tff(decl_24,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
tff(decl_25,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(decl_26,type,
c_HOL_Oinverse__class_Odivide: ( $i * $i * $i ) > $i ).
tff(decl_27,type,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le: $i > $o ).
tff(decl_28,type,
class_OrderedGroup_Ocomm__monoid__add: $i > $o ).
tff(decl_29,type,
c_HOL_Oplus__class_Oplus: ( $i * $i * $i ) > $i ).
tff(decl_30,type,
c_HOL_Oord__class_Oless: ( $i * $i * $i ) > $o ).
tff(decl_31,type,
class_Ring__and__Field_Oordered__semidom: $i > $o ).
tff(decl_32,type,
c_Power_Opower__class_Opower: ( $i * $i * $i ) > $i ).
tff(decl_33,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
tff(decl_34,type,
c_HOL_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).
tff(decl_35,type,
class_Ring__and__Field_Ofield: $i > $o ).
tff(decl_36,type,
tc_Polynomial_Opoly: $i > $i ).
tff(decl_37,type,
c_Divides_Odiv__class_Omod: ( $i * $i * $i ) > $i ).
tff(decl_38,type,
c_Polynomial_Opdivmod__rel: ( $i * $i * $i * $i * $i ) > $o ).
tff(decl_39,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
tff(decl_40,type,
c_HOL_Ouminus__class_Ouminus: ( $i * $i ) > $i ).
tff(decl_41,type,
class_RealVector_Oreal__normed__field: $i > $o ).
tff(decl_42,type,
class_RealVector_Oreal__normed__algebra: $i > $o ).
tff(decl_43,type,
c_HOL_Otimes__class_Otimes: ( $i * $i * $i ) > $i ).
tff(decl_44,type,
c_HOL_Oone__class_Oone: $i > $i ).
tff(decl_45,type,
c_HOL_Oinverse__class_Oinverse: ( $i * $i ) > $i ).
tff(decl_46,type,
class_OrderedGroup_Ogroup__add: $i > $o ).
tff(decl_47,type,
class_OrderedGroup_Opordered__comm__monoid__add: $i > $o ).
tff(decl_48,type,
class_HOL_Ozero: $i > $o ).
tff(decl_49,type,
c_Polynomial_Ocoeff: ( $i * $i * $i ) > $i ).
tff(decl_50,type,
class_Divides_Osemiring__div: $i > $o ).
tff(decl_51,type,
c_Divides_Odiv__class_Odiv: ( $i * $i * $i ) > $i ).
tff(decl_52,type,
c_Ring__and__Field_Odvd__class_Odvd: ( $i * $i * $i ) > $o ).
tff(decl_53,type,
class_Ring__and__Field_Oidom: $i > $o ).
tff(decl_54,type,
c_Polynomial_Opoly: ( $i * $i * $i ) > $i ).
tff(decl_55,type,
c_Polynomial_OpCons: ( $i * $i * $i ) > $i ).
tff(decl_56,type,
c_HOL_Oabs__class_Oabs: ( $i * $i ) > $i ).
tff(decl_57,type,
class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).
tff(decl_58,type,
class_OrderedGroup_Opordered__ab__group__add__abs: $i > $o ).
tff(decl_59,type,
class_Orderings_Olinorder: $i > $o ).
tff(decl_60,type,
class_Orderings_Opreorder: $i > $o ).
tff(decl_61,type,
class_OrderedGroup_Oab__semigroup__add: $i > $o ).
tff(decl_62,type,
c_Polynomial_Omonom: ( $i * $i * $i ) > $i ).
tff(decl_63,type,
class_Orderings_Oorder: $i > $o ).
tff(decl_64,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
tff(decl_65,type,
class_Ring__and__Field_Ocomm__ring__1: $i > $o ).
tff(decl_66,type,
class_Int_Onumber__ring: $i > $o ).
tff(decl_67,type,
class_Ring__and__Field_Olordered__ring: $i > $o ).
tff(decl_68,type,
class_Ring__and__Field_Oring: $i > $o ).
tff(decl_69,type,
class_Ring__and__Field_Opordered__ring: $i > $o ).
tff(decl_70,type,
class_OrderedGroup_Olordered__ab__group__add__abs: $i > $o ).
tff(decl_71,type,
class_Ring__and__Field_Oabs__if: $i > $o ).
tff(decl_72,type,
class_OrderedGroup_Olordered__ab__group__add: $i > $o ).
tff(decl_73,type,
class_Lattices_Oboolean__algebra: $i > $o ).
tff(decl_74,type,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add: $i > $o ).
tff(decl_75,type,
class_OrderedGroup_Oordered__ab__group__add: $i > $o ).
tff(decl_76,type,
class_Ring__and__Field_Ozero__neq__one: $i > $o ).
tff(decl_77,type,
class_Ring__and__Field_Oring__1__no__zero__divisors: $i > $o ).
tff(decl_78,type,
class_Ring__and__Field_Ono__zero__divisors: $i > $o ).
tff(decl_79,type,
class_Ring__and__Field_Omult__zero: $i > $o ).
tff(decl_80,type,
class_Power_Opower: $i > $o ).
tff(decl_81,type,
class_OrderedGroup_Omonoid__add: $i > $o ).
tff(decl_82,type,
class_Ring__and__Field_Oordered__semiring__strict: $i > $o ).
tff(decl_83,type,
c_Polynomial_Odegree: ( $i * $i ) > $i ).
tff(decl_84,type,
class_OrderedGroup_Opordered__ab__semigroup__add: $i > $o ).
tff(decl_85,type,
class_Ring__and__Field_Odvd: $i > $o ).
tff(decl_86,type,
class_Ring__and__Field_Ocomm__ring: $i > $o ).
tff(decl_87,type,
c_Polynomial_Osmult: ( $i * $i * $i ) > $i ).
tff(decl_88,type,
class_Divides_Oring__div: $i > $o ).
tff(decl_89,type,
class_Ring__and__Field_Ocomm__semiring__0: $i > $o ).
tff(decl_90,type,
class_Ring__and__Field_Oordered__ring__strict: $i > $o ).
tff(decl_91,type,
class_Ring__and__Field_Opordered__ring__abs: $i > $o ).
tff(decl_92,type,
class_Ring__and__Field_Oordered__semiring: $i > $o ).
tff(decl_93,type,
class_OrderedGroup_Omonoid__mult: $i > $o ).
tff(decl_94,type,
class_Ring__and__Field_Ocomm__semiring: $i > $o ).
tff(decl_95,type,
class_OrderedGroup_Ocomm__monoid__mult: $i > $o ).
tff(decl_96,type,
class_Ring__and__Field_Osemiring: $i > $o ).
tff(decl_97,type,
class_OrderedGroup_Ocancel__ab__semigroup__add: $i > $o ).
tff(decl_98,type,
class_OrderedGroup_Ocancel__semigroup__add: $i > $o ).
tff(decl_99,type,
class_RealVector_Oreal__field: $i > $o ).
tff(decl_100,type,
class_Ring__and__Field_Oring__1: $i > $o ).
tff(decl_101,type,
class_Ring__and__Field_Odivision__ring: $i > $o ).
tff(decl_102,type,
v_pa____: $i ).
tff(decl_103,type,
v_c____: $i ).
tff(decl_104,type,
tc_Complex_Ocomplex: $i ).
tff(decl_105,type,
class_Ring__and__Field_Opordered__cancel__semiring: $i > $o ).
tff(decl_106,type,
class_Ring__and__Field_Opordered__semiring: $i > $o ).
tff(decl_107,type,
class_Ring__and__Field_Omult__mono: $i > $o ).
tff(decl_108,type,
class_Ring__and__Field_Omult__mono1: $i > $o ).
tff(decl_109,type,
class_Ring__and__Field_Oordered__comm__semiring__strict: $i > $o ).
tff(decl_110,type,
v_q____: $i ).
tff(decl_111,type,
t_a: $i ).
tff(decl_112,type,
v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__lemma__2: $i > $i ).
tff(decl_113,type,
class_Ring__and__Field_Oring__no__zero__divisors: $i > $o ).
tff(decl_114,type,
class_OrderedGroup_Oab__semigroup__mult: $i > $o ).
tff(decl_115,type,
class_OrderedGroup_Oab__semigroup__idem__mult: $i > $o ).
tff(decl_116,type,
v_x: $i ).
tff(decl_117,type,
class_OrderedGroup_Ocancel__comm__monoid__add: $i > $o ).
tff(decl_118,type,
tc_nat: $i ).
cnf(cls_conjecture_0,negated_conjecture,
c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex) != c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(cls_pqc0_0,axiom,
c_Polynomial_Opoly(v_pa____,v_c____,tc_Complex_Ocomplex) = c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pqc0_0) ).
cnf(cls_class__semiring_Omul__c_0,axiom,
( c_HOL_Otimes__class_Otimes(X2,X3,X1) = c_HOL_Otimes__class_Otimes(X3,X2,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__c_0) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1) ).
cnf(cls_complex__divide__def_0,axiom,
c_HOL_Oinverse__class_Odivide(X1,X2,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Oinverse__class_Oinverse(X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complex__divide__def_0) ).
cnf(cls_poly__smult_0,axiom,
( c_Polynomial_Opoly(c_Polynomial_Osmult(X2,X3,X1),X4,X1) = c_HOL_Otimes__class_Otimes(X2,c_Polynomial_Opoly(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_poly__smult_0) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0) ).
cnf(cls_divide__eq__eq_0,axiom,
( X2 = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X2,X3,X1),X3,X1)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq_0) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ofield,axiom,
class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ofield) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero,axiom,
class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero) ).
cnf(cls_pc0_0,axiom,
c_Polynomial_Opoly(v_pa____,v_c____,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pc0_0) ).
cnf(c_0_11,negated_conjecture,
c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex) != c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
cls_conjecture_0 ).
cnf(c_0_12,axiom,
c_Polynomial_Opoly(v_pa____,v_c____,tc_Complex_Ocomplex) = c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),
cls_pqc0_0 ).
cnf(c_0_13,axiom,
( c_HOL_Otimes__class_Otimes(X2,X3,X1) = c_HOL_Otimes__class_Otimes(X3,X2,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Omul__c_0 ).
cnf(c_0_14,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1 ).
cnf(c_0_15,negated_conjecture,
c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_pa____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_pa____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_11,c_0_12]),c_0_12]) ).
cnf(c_0_16,plain,
c_HOL_Otimes__class_Otimes(X1,X2,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(X2,X1,tc_Complex_Ocomplex),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_17,axiom,
c_HOL_Oinverse__class_Odivide(X1,X2,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Oinverse__class_Oinverse(X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
cls_complex__divide__def_0 ).
cnf(c_0_18,negated_conjecture,
c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(v_pa____,v_c____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_pa____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex),
inference(rw,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_19,axiom,
( c_Polynomial_Opoly(c_Polynomial_Osmult(X2,X3,X1),X4,X1) = c_HOL_Otimes__class_Otimes(X2,c_Polynomial_Opoly(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
cls_poly__smult_0 ).
cnf(c_0_20,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X1,tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(X2,X1,tc_Complex_Ocomplex),
inference(spm,[status(thm)],[c_0_17,c_0_16]) ).
cnf(c_0_21,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0 ).
cnf(c_0_22,axiom,
( X2 = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X2,X3,X1),X3,X1)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
cls_divide__eq__eq_0 ).
cnf(c_0_23,axiom,
class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Ofield ).
cnf(c_0_24,axiom,
class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero ).
cnf(c_0_25,negated_conjecture,
c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(v_pa____,v_c____,tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_pa____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]),c_0_21])]) ).
cnf(c_0_26,plain,
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Oinverse__class_Odivide(X2,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X2
| X1 = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24])]),c_0_16]) ).
cnf(c_0_27,axiom,
c_Polynomial_Opoly(v_pa____,v_c____,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
cls_pc0_0 ).
cnf(c_0_28,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ALG398-1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.15/0.34 % Computer : n020.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Mon Aug 28 05:19:44 EDT 2023
% 0.15/0.34 % CPUTime :
% 0.19/0.57 start to proof: theBenchmark
% 1.76/1.85 % Version : CSE_E---1.5
% 1.76/1.85 % Problem : theBenchmark.p
% 1.76/1.85 % Proof found
% 1.76/1.85 % SZS status Theorem for theBenchmark.p
% 1.76/1.85 % SZS output start Proof
% See solution above
% 1.76/1.86 % Total time : 1.248000 s
% 1.76/1.86 % SZS output end Proof
% 1.76/1.86 % Total time : 1.277000 s
%------------------------------------------------------------------------------