TSTP Solution File: ALG341-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : ALG341-1 : 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 : n029.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 0.20s 0.74s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 107
% Syntax : Number of formulae : 124 ( 13 unt; 98 typ; 0 def)
% Number of atoms : 47 ( 11 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 43 ( 22 ~; 21 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 122 ( 88 >; 34 *; 0 +; 0 <<)
% Number of predicates : 63 ( 61 usr; 1 prp; 0-3 aty)
% Number of functors : 37 ( 37 usr; 10 con; 0-3 aty)
% Number of variables : 23 ( 0 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
tff(decl_23,type,
c_Power_Opower__class_Opower: ( $i * $i * $i ) > $i ).
tff(decl_24,type,
c_HOL_Oabs__class_Oabs: ( $i * $i ) > $i ).
tff(decl_25,type,
class_Ring__and__Field_Oordered__field: $i > $o ).
tff(decl_26,type,
class_Ring__and__Field_Odivision__by__zero: $i > $o ).
tff(decl_27,type,
c_HOL_Oinverse__class_Oinverse: ( $i * $i ) > $i ).
tff(decl_28,type,
c_HOL_Oinverse__class_Odivide: ( $i * $i * $i ) > $i ).
tff(decl_29,type,
class_RealVector_Oreal__vector: $i > $o ).
tff(decl_30,type,
c_HOL_Oplus__class_Oplus: ( $i * $i * $i ) > $i ).
tff(decl_31,type,
c_RealVector_OscaleR__class_OscaleR: ( $i * $i * $i ) > $i ).
tff(decl_32,type,
class_RealVector_Oreal__normed__vector: $i > $o ).
tff(decl_33,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
tff(decl_34,type,
c_HOL_Ouminus__class_Ouminus: ( $i * $i ) > $i ).
tff(decl_35,type,
class_Ring__and__Field_Ofield: $i > $o ).
tff(decl_36,type,
c_HOL_Otimes__class_Otimes: ( $i * $i * $i ) > $i ).
tff(decl_37,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
tff(decl_38,type,
class_SEQ_Obanach: $i > $o ).
tff(decl_39,type,
class_RealVector_Oreal__normed__field: $i > $o ).
tff(decl_40,type,
c_Transcendental_Oexp: ( $i * $i ) > $i ).
tff(decl_41,type,
c_HOL_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).
tff(decl_42,type,
c_RealVector_Onorm__class_Onorm: ( $i * $i ) > $i ).
tff(decl_43,type,
class_OrderedGroup_Ogroup__add: $i > $o ).
tff(decl_44,type,
class_Lattices_Oboolean__algebra: $i > $o ).
tff(decl_45,type,
class_OrderedGroup_Opordered__ab__group__add__abs: $i > $o ).
tff(decl_46,type,
class_OrderedGroup_Oordered__ab__group__add: $i > $o ).
tff(decl_47,type,
class_Ring__and__Field_Odivision__ring: $i > $o ).
tff(decl_48,type,
class_Ring__and__Field_Oring__no__zero__divisors: $i > $o ).
tff(decl_49,type,
class_Ring__and__Field_Omult__zero: $i > $o ).
tff(decl_50,type,
class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).
tff(decl_51,type,
class_RealVector_Oreal__normed__algebra: $i > $o ).
tff(decl_52,type,
class_OrderedGroup_Olordered__ab__group__add: $i > $o ).
tff(decl_53,type,
c_OrderedGroup_Olordered__ab__group__add__class_Onprt: ( $i * $i ) > $i ).
tff(decl_54,type,
class_Ring__and__Field_Oring__1__no__zero__divisors: $i > $o ).
tff(decl_55,type,
class_Ring__and__Field_Ozero__neq__one: $i > $o ).
tff(decl_56,type,
class_Ring__and__Field_Ono__zero__divisors: $i > $o ).
tff(decl_57,type,
class_Power_Opower: $i > $o ).
tff(decl_58,type,
class_Ring__and__Field_Oidom: $i > $o ).
tff(decl_59,type,
class_Int_Onumber__ring: $i > $o ).
tff(decl_60,type,
class_RealVector_Oreal__field: $i > $o ).
tff(decl_61,type,
tc_RealDef_Oreal: $i ).
tff(decl_62,type,
c_RealVector_Oof__real: ( $i * $i ) > $i ).
tff(decl_63,type,
class_Ring__and__Field_Osemiring: $i > $o ).
tff(decl_64,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(decl_65,type,
class_RealVector_Oreal__algebra__1: $i > $o ).
tff(decl_66,type,
class_OrderedGroup_Oab__semigroup__add: $i > $o ).
tff(decl_67,type,
class_OrderedGroup_Ocomm__monoid__add: $i > $o ).
tff(decl_68,type,
class_Ring__and__Field_Olordered__ring: $i > $o ).
tff(decl_69,type,
class_Ring__and__Field_Oring: $i > $o ).
tff(decl_70,type,
class_Ring__and__Field_Opordered__ring: $i > $o ).
tff(decl_71,type,
class_Nat_Osemiring__char__0: $i > $o ).
tff(decl_72,type,
c_Nat_Osemiring__1__class_Oof__nat: ( $i * $i ) > $i ).
tff(decl_73,type,
tc_nat: $i ).
tff(decl_74,type,
c_RealDef_Oreal: ( $i * $i ) > $i ).
tff(decl_75,type,
class_OrderedGroup_Olordered__ab__group__add__abs: $i > $o ).
tff(decl_76,type,
class_OrderedGroup_Oab__semigroup__idem__mult: $i > $o ).
tff(decl_77,type,
c_NthRoot_Osqrt: $i > $i ).
tff(decl_78,type,
class_Ring__and__Field_Oordered__ring__strict: $i > $o ).
tff(decl_79,type,
class_OrderedGroup_Ocomm__monoid__mult: $i > $o ).
tff(decl_80,type,
class_OrderedGroup_Oab__semigroup__mult: $i > $o ).
tff(decl_81,type,
class_OrderedGroup_Omonoid__add: $i > $o ).
tff(decl_82,type,
class_Ring__and__Field_Opordered__ring__abs: $i > $o ).
tff(decl_83,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
tff(decl_84,type,
class_OrderedGroup_Opordered__ab__semigroup__add: $i > $o ).
tff(decl_85,type,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le: $i > $o ).
tff(decl_86,type,
c_Transcendental_Opi: $i ).
tff(decl_87,type,
class_RealVector_Ometric__space: $i > $o ).
tff(decl_88,type,
c_RealVector_Odist__class_Odist: ( $i * $i * $i ) > $i ).
tff(decl_89,type,
class_OrderedGroup_Opordered__comm__monoid__add: $i > $o ).
tff(decl_90,type,
class_Ring__and__Field_Oordered__semidom: $i > $o ).
tff(decl_91,type,
class_Ring__and__Field_Opordered__cancel__semiring: $i > $o ).
tff(decl_92,type,
class_Ring__and__Field_Opordered__semiring: $i > $o ).
tff(decl_93,type,
class_Ring__and__Field_Ocomm__semiring: $i > $o ).
tff(decl_94,type,
class_OrderedGroup_Ocancel__ab__semigroup__add: $i > $o ).
tff(decl_95,type,
class_OrderedGroup_Ocancel__semigroup__add: $i > $o ).
tff(decl_96,type,
class_RealVector_Oreal__algebra: $i > $o ).
tff(decl_97,type,
class_OrderedGroup_Omonoid__mult: $i > $o ).
tff(decl_98,type,
class_RealVector_Odist__norm: $i > $o ).
tff(decl_99,type,
class_Ring__and__Field_Omult__mono: $i > $o ).
tff(decl_100,type,
class_Ring__and__Field_Omult__mono1: $i > $o ).
tff(decl_101,type,
c_RealVector_Osko__RealVector__XscaleR__left__Xnonneg__bounded__1__1: ( $i * $i ) > $i ).
tff(decl_102,type,
c_Transcendental_Osko__Transcendental__Xcos__is__zero__1__1: $i ).
tff(decl_103,type,
c_Complex_Osko__Complex__XRe__Xnonneg__bounded__1__1: $i ).
tff(decl_104,type,
c_RealVector_Osko__RealVector__Xmult__left__Xnonneg__bounded__1__1: ( $i * $i ) > $i ).
tff(decl_105,type,
c_RealVector_Osko__RealVector__Xdivide__Xnonneg__bounded__1__1: ( $i * $i ) > $i ).
tff(decl_106,type,
c_Transcendental_Osko__Transcendental__Xtan__total__pos__1__1: $i > $i ).
tff(decl_107,type,
c_RealVector_Osko__RealVector__Xmult__right__Xnonneg__bounded__1__1: ( $i * $i ) > $i ).
tff(decl_108,type,
c_RealVector_Osko__RealVector__Xmult__Xnonneg__bounded__1__1: ( $i * $i ) > $i ).
tff(decl_109,type,
c_Complex_Osko__Complex__XIm__Xnonneg__bounded__1__1: $i ).
tff(decl_110,type,
c_RealVector_Osko__RealVector__Xof__real__Xnonneg__bounded__1__1: ( $i * $i ) > $i ).
tff(decl_111,type,
c_Complex_Osko__Complex__Xcnj__Xnonneg__bounded__1__1: $i ).
tff(decl_112,type,
c_RealVector_Osko__RealVector__XscaleR__right__Xnonneg__bounded__1__1: ( $i * $i * $i ) > $i ).
tff(decl_113,type,
c_RealVector_Osko__RealVector__XscaleR__Xnonneg__bounded__1__1: ( $i * $i ) > $i ).
tff(decl_114,type,
class_Orderings_Olinorder: $i > $o ).
tff(decl_115,type,
class_Orderings_Oorder: $i > $o ).
tff(decl_116,type,
class_Orderings_Opreorder: $i > $o ).
tff(decl_117,type,
v_z____: $i ).
tff(decl_118,type,
tc_Complex_Ocomplex: $i ).
tff(decl_119,type,
v_r: $i ).
cnf(cls_conjecture_0,negated_conjecture,
~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_r,tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(cls_real__le__linear_0,axiom,
( c_lessequals(X1,X2,tc_RealDef_Oreal)
| c_lessequals(X2,X1,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__le__linear_0) ).
cnf(cls_real__le__antisym_0,axiom,
( X1 = X2
| ~ c_lessequals(X2,X1,tc_RealDef_Oreal)
| ~ c_lessequals(X1,X2,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__le__antisym_0) ).
cnf(cls_CHAINED_0,axiom,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_z____,tc_Complex_Ocomplex),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0) ).
cnf(cls_real__le__trans_0,axiom,
( c_lessequals(X1,X2,tc_RealDef_Oreal)
| ~ c_lessequals(X3,X2,tc_RealDef_Oreal)
| ~ c_lessequals(X1,X3,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__le__trans_0) ).
cnf(cls_zero__le__iff__nprt__id_0,axiom,
( c_OrderedGroup_Olordered__ab__group__add__class_Onprt(X2,X1) = X2
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__iff__nprt__id_0) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add,axiom,
class_OrderedGroup_Olordered__ab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add) ).
cnf(cls_CHAINED_0_01,axiom,
c_lessequals(c_RealVector_Onorm__class_Onorm(v_z____,tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0_01) ).
cnf(cls_zero__le__iff__zero__nprt_1,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| c_OrderedGroup_Olordered__ab__group__add__class_Onprt(X2,X1) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__iff__zero__nprt_1) ).
cnf(c_0_9,negated_conjecture,
~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_r,tc_RealDef_Oreal),
cls_conjecture_0 ).
cnf(c_0_10,axiom,
( c_lessequals(X1,X2,tc_RealDef_Oreal)
| c_lessequals(X2,X1,tc_RealDef_Oreal) ),
cls_real__le__linear_0 ).
cnf(c_0_11,axiom,
( X1 = X2
| ~ c_lessequals(X2,X1,tc_RealDef_Oreal)
| ~ c_lessequals(X1,X2,tc_RealDef_Oreal) ),
cls_real__le__antisym_0 ).
cnf(c_0_12,axiom,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_z____,tc_Complex_Ocomplex),tc_RealDef_Oreal),
cls_CHAINED_0 ).
cnf(c_0_13,axiom,
( c_lessequals(X1,X2,tc_RealDef_Oreal)
| ~ c_lessequals(X3,X2,tc_RealDef_Oreal)
| ~ c_lessequals(X1,X3,tc_RealDef_Oreal) ),
cls_real__le__trans_0 ).
cnf(c_0_14,negated_conjecture,
c_lessequals(v_r,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_15,axiom,
( c_OrderedGroup_Olordered__ab__group__add__class_Onprt(X2,X1) = X2
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_zero__le__iff__nprt__id_0 ).
cnf(c_0_16,axiom,
class_OrderedGroup_Olordered__ab__group__add(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add ).
cnf(c_0_17,axiom,
c_lessequals(c_RealVector_Onorm__class_Onorm(v_z____,tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal),
cls_CHAINED_0_01 ).
cnf(c_0_18,plain,
( c_RealVector_Onorm__class_Onorm(v_z____,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(v_z____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_19,negated_conjecture,
( c_lessequals(X1,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(X1,v_r,tc_RealDef_Oreal) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_20,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| c_OrderedGroup_Olordered__ab__group__add__class_Onprt(X2,X1) != c_HOL_Ozero__class_Ozero(X1) ),
cls_zero__le__iff__zero__nprt_1 ).
cnf(c_0_21,negated_conjecture,
c_OrderedGroup_Olordered__ab__group__add__class_Onprt(v_r,tc_RealDef_Oreal) = v_r,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_14]),c_0_16])]) ).
cnf(c_0_22,plain,
( c_RealVector_Onorm__class_Onorm(v_z____,tc_Complex_Ocomplex) = v_r
| ~ c_lessequals(v_r,c_RealVector_Onorm__class_Onorm(v_z____,tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
inference(spm,[status(thm)],[c_0_11,c_0_17]) ).
cnf(c_0_23,negated_conjecture,
c_RealVector_Onorm__class_Onorm(v_z____,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_17])]) ).
cnf(c_0_24,negated_conjecture,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != v_r,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_16])]),c_0_9]) ).
cnf(c_0_25,plain,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_23]),c_0_23]),c_0_14])]),c_0_24]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ALG341-1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n029.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 : Mon Aug 28 04:18:26 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.58 start to proof: theBenchmark
% 0.20/0.74 % Version : CSE_E---1.5
% 0.20/0.74 % Problem : theBenchmark.p
% 0.20/0.74 % Proof found
% 0.20/0.74 % SZS status Theorem for theBenchmark.p
% 0.20/0.74 % SZS output start Proof
% See solution above
% 0.20/0.75 % Total time : 0.142000 s
% 0.20/0.75 % SZS output end Proof
% 0.20/0.75 % Total time : 0.158000 s
%------------------------------------------------------------------------------