TSTP Solution File: ALG340-1 by CSE_E---1.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : ALG340-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n006.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 16:07:24 EDT 2023
% Result : Unsatisfiable 0.19s 0.69s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 77
% Syntax : Number of formulae : 88 ( 9 unt; 70 typ; 0 def)
% Number of atoms : 27 ( 5 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 22 ( 13 ~; 9 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 84 ( 67 >; 17 *; 0 +; 0 <<)
% Number of predicates : 56 ( 54 usr; 1 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 3 con; 0-3 aty)
% Number of variables : 16 ( 5 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_HOL_Oinverse__class_Odivide: ( $i * $i * $i ) > $i ).
tff(decl_26,type,
c_HOL_Oord__class_Oless: ( $i * $i * $i ) > $o ).
tff(decl_27,type,
class_Ring__and__Field_Oordered__ring__strict: $i > $o ).
tff(decl_28,type,
c_HOL_Otimes__class_Otimes: ( $i * $i * $i ) > $i ).
tff(decl_29,type,
class_OrderedGroup_Olordered__ab__group__add: $i > $o ).
tff(decl_30,type,
c_HOL_Oplus__class_Oplus: ( $i * $i * $i ) > $i ).
tff(decl_31,type,
class_Ring__and__Field_Oordered__semidom: $i > $o ).
tff(decl_32,type,
class_Ring__and__Field_Oordered__semiring__strict: $i > $o ).
tff(decl_33,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
tff(decl_34,type,
c_HOL_Osgn__class_Osgn: ( $i * $i ) > $i ).
tff(decl_35,type,
c_Power_Opower__class_Opower: ( $i * $i * $i ) > $i ).
tff(decl_36,type,
class_OrderedGroup_Opordered__comm__monoid__add: $i > $o ).
tff(decl_37,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(decl_38,type,
class_RealVector_Oreal__normed__algebra: $i > $o ).
tff(decl_39,type,
c_RealVector_Onorm__class_Onorm: ( $i * $i ) > $i ).
tff(decl_40,type,
tc_RealDef_Oreal: $i ).
tff(decl_41,type,
class_OrderedGroup_Opordered__ab__semigroup__add: $i > $o ).
tff(decl_42,type,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le: $i > $o ).
tff(decl_43,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
tff(decl_44,type,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add: $i > $o ).
tff(decl_45,type,
class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).
tff(decl_46,type,
class_OrderedGroup_Ocomm__monoid__add: $i > $o ).
tff(decl_47,type,
class_Ring__and__Field_Oidom: $i > $o ).
tff(decl_48,type,
class_Int_Onumber__ring: $i > $o ).
tff(decl_49,type,
class_OrderedGroup_Omonoid__add: $i > $o ).
tff(decl_50,type,
class_RealVector_Oreal__normed__vector: $i > $o ).
tff(decl_51,type,
class_RealVector_Oreal__normed__field: $i > $o ).
tff(decl_52,type,
class_Ring__and__Field_Ofield: $i > $o ).
tff(decl_53,type,
class_Ring__and__Field_Oordered__comm__semiring__strict: $i > $o ).
tff(decl_54,type,
class_Ring__and__Field_Opordered__cancel__semiring: $i > $o ).
tff(decl_55,type,
class_Ring__and__Field_Opordered__semiring: $i > $o ).
tff(decl_56,type,
class_Ring__and__Field_Opordered__ring: $i > $o ).
tff(decl_57,type,
class_Ring__and__Field_Omult__mono: $i > $o ).
tff(decl_58,type,
class_Ring__and__Field_Omult__mono1: $i > $o ).
tff(decl_59,type,
c_RealDef_Oreal__of__preal: $i > $i ).
tff(decl_60,type,
c_Transcendental_Oln: $i > $i ).
tff(decl_61,type,
class_Ring__and__Field_Ono__zero__divisors: $i > $o ).
tff(decl_62,type,
class_Ring__and__Field_Oring__no__zero__divisors: $i > $o ).
tff(decl_63,type,
class_Ring__and__Field_Ozero__neq__one: $i > $o ).
tff(decl_64,type,
class_Ring__and__Field_Omult__zero: $i > $o ).
tff(decl_65,type,
class_Power_Opower: $i > $o ).
tff(decl_66,type,
class_Ring__and__Field_Oring__1__no__zero__divisors: $i > $o ).
tff(decl_67,type,
class_Ring__and__Field_Osgn__if: $i > $o ).
tff(decl_68,type,
class_Ring__and__Field_Osemiring: $i > $o ).
tff(decl_69,type,
class_OrderedGroup_Oab__semigroup__add: $i > $o ).
tff(decl_70,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
tff(decl_71,type,
class_OrderedGroup_Oab__semigroup__idem__mult: $i > $o ).
tff(decl_72,type,
class_OrderedGroup_Ocomm__monoid__mult: $i > $o ).
tff(decl_73,type,
class_OrderedGroup_Oab__semigroup__mult: $i > $o ).
tff(decl_74,type,
class_Ring__and__Field_Ocomm__semiring: $i > $o ).
tff(decl_75,type,
class_OrderedGroup_Ocancel__ab__semigroup__add: $i > $o ).
tff(decl_76,type,
class_OrderedGroup_Ocancel__semigroup__add: $i > $o ).
tff(decl_77,type,
class_RealVector_Oreal__normed__div__algebra: $i > $o ).
tff(decl_78,type,
class_OrderedGroup_Omonoid__mult: $i > $o ).
tff(decl_79,type,
class_Ring__and__Field_Oordered__semiring: $i > $o ).
tff(decl_80,type,
c_RComplete_Osko__RComplete__XRats__dense__in__nn__real__1__1: ( $i * $i ) > $i ).
tff(decl_81,type,
class_Orderings_Oorder: $i > $o ).
tff(decl_82,type,
class_Orderings_Olinorder: $i > $o ).
tff(decl_83,type,
class_Orderings_Opreorder: $i > $o ).
tff(decl_84,type,
class_Ring__and__Field_Ocomm__semiring__0: $i > $o ).
tff(decl_85,type,
tc_Polynomial_Opoly: $i > $i ).
tff(decl_86,type,
c_Polynomial_Opoly: ( $i * $i * $i ) > $i ).
tff(decl_87,type,
v_x: $i > $i ).
tff(decl_88,type,
tc_Complex_Ocomplex: $i ).
tff(decl_89,type,
v_r: $i ).
tff(decl_90,type,
class_OrderedGroup_Ocancel__comm__monoid__add: $i > $o ).
tff(decl_91,type,
class_Ring__and__Field_Ocomm__ring__1: $i > $o ).
cnf(cls_conjecture_1,negated_conjecture,
( ~ c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_x(X1),tc_Complex_Ocomplex),tc_Complex_Ocomplex),X1,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
cnf(cls_real__less__def_0,axiom,
( c_lessequals(X1,X2,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__less__def_0) ).
cnf(cls_norm__zero_0,axiom,
( c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_norm__zero_0) ).
cnf(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).
cnf(cls_order__root_1,axiom,
( c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oidom(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__root_1) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Oidom,axiom,
class_Ring__and__Field_Oidom(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oidom) ).
cnf(cls_real__of__preal__zero__less_0,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal__of__preal(X1),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__of__preal__zero__less_0) ).
cnf(c_0_7,negated_conjecture,
( ~ c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_x(X1),tc_Complex_Ocomplex),tc_Complex_Ocomplex),X1,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal) ),
cls_conjecture_1 ).
cnf(c_0_8,axiom,
( c_lessequals(X1,X2,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_RealDef_Oreal) ),
cls_real__less__def_0 ).
cnf(c_0_9,axiom,
( c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
cls_norm__zero_0 ).
cnf(c_0_10,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector ).
cnf(c_0_11,negated_conjecture,
( ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_x(X1),tc_Complex_Ocomplex),tc_Complex_Ocomplex),X1,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal) ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_12,axiom,
( c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oidom(X1) ),
cls_order__root_1 ).
cnf(c_0_13,plain,
c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_14,axiom,
class_Ring__and__Field_Oidom(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Oidom ).
cnf(c_0_15,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal__of__preal(X1),tc_RealDef_Oreal),
cls_real__of__preal__zero__less_0 ).
cnf(c_0_16,negated_conjecture,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13]),c_0_14])]) ).
cnf(c_0_17,plain,
$false,
inference(sr,[status(thm)],[c_0_15,c_0_16]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ALG340-1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34 % Computer : n006.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 : Mon Aug 28 04:45:21 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.56 start to proof: theBenchmark
% 0.19/0.69 % Version : CSE_E---1.5
% 0.19/0.69 % Problem : theBenchmark.p
% 0.19/0.69 % Proof found
% 0.19/0.69 % SZS status Theorem for theBenchmark.p
% 0.19/0.69 % SZS output start Proof
% See solution above
% 0.19/0.70 % Total time : 0.110000 s
% 0.19/0.70 % SZS output end Proof
% 0.19/0.70 % Total time : 0.126000 s
%------------------------------------------------------------------------------