TSTP Solution File: ALG373-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : ALG373-1 : 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 : n027.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 16:07:31 EDT 2023
% Result : Unsatisfiable 0.63s 0.77s
% Output : CNFRefutation 0.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 114
% Syntax : Number of formulae : 180 ( 50 unt; 82 typ; 0 def)
% Number of atoms : 175 ( 30 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 153 ( 76 ~; 77 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 111 ( 77 >; 34 *; 0 +; 0 <<)
% Number of predicates : 49 ( 47 usr; 1 prp; 0-3 aty)
% Number of functors : 35 ( 35 usr; 5 con; 0-3 aty)
% Number of variables : 126 ( 8 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
class_RealVector_Oreal__normed__algebra: $i > $o ).
tff(decl_23,type,
tc_RealDef_Oreal: $i ).
tff(decl_24,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
tff(decl_25,type,
c_RealVector_Osko__RealVector__Xmult__right__Xpos__bounded__1__1: ( $i * $i ) > $i ).
tff(decl_26,type,
c_HOL_Oord__class_Oless: ( $i * $i * $i ) > $o ).
tff(decl_27,type,
c_RealVector_Osko__RealVector__Xmult__left__Xpos__bounded__1__1: ( $i * $i ) > $i ).
tff(decl_28,type,
class_RealVector_Oreal__normed__vector: $i > $o ).
tff(decl_29,type,
c_RealVector_Osko__RealVector__XscaleR__right__Xpos__bounded__1__1: ( $i * $i * $i ) > $i ).
tff(decl_30,type,
c_RealVector_Osko__RealVector__Xmult__Xpos__bounded__1__1: ( $i * $i ) > $i ).
tff(decl_31,type,
c_RealVector_Osko__RealVector__Xmult__left__Xnonneg__bounded__1__1: ( $i * $i ) > $i ).
tff(decl_32,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(decl_33,type,
c_RealVector_Osko__RealVector__Xmult__right__Xnonneg__bounded__1__1: ( $i * $i ) > $i ).
tff(decl_34,type,
c_RealVector_Osko__RealVector__Xmult__Xnonneg__bounded__1__1: ( $i * $i ) > $i ).
tff(decl_35,type,
c_RealVector_Osko__RealVector__XscaleR__right__Xnonneg__bounded__1__1: ( $i * $i * $i ) > $i ).
tff(decl_36,type,
class_Orderings_Olinorder: $i > $o ).
tff(decl_37,type,
class_Int_Onumber: $i > $o ).
tff(decl_38,type,
c_Int_Onumber__class_Onumber__of: ( $i * $i ) > $i ).
tff(decl_39,type,
class_Int_Oring__char__0: $i > $o ).
tff(decl_40,type,
class_Int_Onumber__ring: $i > $o ).
tff(decl_41,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
tff(decl_42,type,
c_HOL_Oabs__class_Oabs: ( $i * $i ) > $i ).
tff(decl_43,type,
class_RealVector_Oreal__algebra__1: $i > $o ).
tff(decl_44,type,
c_RealVector_Oof__real: ( $i * $i ) > $i ).
tff(decl_45,type,
c_RealVector_Onorm__class_Onorm: ( $i * $i ) > $i ).
tff(decl_46,type,
class_Ring__and__Field_Ono__zero__divisors: $i > $o ).
tff(decl_47,type,
c_HOL_Otimes__class_Otimes: ( $i * $i * $i ) > $i ).
tff(decl_48,type,
class_Ring__and__Field_Oring__no__zero__divisors: $i > $o ).
tff(decl_49,type,
class_Ring__and__Field_Oordered__ring__strict: $i > $o ).
tff(decl_50,type,
class_Ring__and__Field_Oordered__semiring__strict: $i > $o ).
tff(decl_51,type,
class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).
tff(decl_52,type,
class_OrderedGroup_Opordered__ab__group__add__abs: $i > $o ).
tff(decl_53,type,
class_Ring__and__Field_Opordered__ring__abs: $i > $o ).
tff(decl_54,type,
c_RealVector_OscaleR__class_OscaleR: ( $i * $i * $i ) > $i ).
tff(decl_55,type,
c_RealVector_Osko__RealVector__XscaleR__right__Xbounded__1__1: ( $i * $i * $i ) > $i ).
tff(decl_56,type,
c_RealVector_Osko__RealVector__Xmult__right__Xbounded__1__1: ( $i * $i ) > $i ).
tff(decl_57,type,
c_RealVector_Osko__RealVector__Xmult__left__Xbounded__1__1: ( $i * $i ) > $i ).
tff(decl_58,type,
c_RealVector_Osko__RealVector__Xmult__Xbounded__1__1: ( $i * $i ) > $i ).
tff(decl_59,type,
c_HOL_Ouminus__class_Ouminus: ( $i * $i ) > $i ).
tff(decl_60,type,
class_Ring__and__Field_Olordered__ring: $i > $o ).
tff(decl_61,type,
class_RealVector_Oreal__vector: $i > $o ).
tff(decl_62,type,
class_Ring__and__Field_Oordered__comm__semiring__strict: $i > $o ).
tff(decl_63,type,
class_Ring__and__Field_Oordered__semiring: $i > $o ).
tff(decl_64,type,
class_Ring__and__Field_Oabs__if: $i > $o ).
tff(decl_65,type,
class_OrderedGroup_Olordered__ab__group__add__abs: $i > $o ).
tff(decl_66,type,
class_OrderedGroup_Oordered__ab__group__add: $i > $o ).
tff(decl_67,type,
class_OrderedGroup_Ogroup__add: $i > $o ).
tff(decl_68,type,
class_Ring__and__Field_Oring: $i > $o ).
tff(decl_69,type,
class_Ring__and__Field_Oidom: $i > $o ).
tff(decl_70,type,
c_Complex_ORe: $i > $i ).
tff(decl_71,type,
tc_Complex_Ocomplex: $i ).
tff(decl_72,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
tff(decl_73,type,
class_OrderedGroup_Olordered__ab__group__add: $i > $o ).
tff(decl_74,type,
class_OrderedGroup_Oab__semigroup__idem__mult: $i > $o ).
tff(decl_75,type,
class_Ring__and__Field_Omult__mono1: $i > $o ).
tff(decl_76,type,
class_Ring__and__Field_Omult__mono: $i > $o ).
tff(decl_77,type,
class_Ring__and__Field_Opordered__ring: $i > $o ).
tff(decl_78,type,
class_Ring__and__Field_Opordered__cancel__semiring: $i > $o ).
tff(decl_79,type,
class_OrderedGroup_Oab__semigroup__mult: $i > $o ).
tff(decl_80,type,
class_Ring__and__Field_Opordered__semiring: $i > $o ).
tff(decl_81,type,
v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__bound__exists__1: ( $i * $i ) > $i ).
tff(decl_82,type,
class_RealVector_Oreal__algebra: $i > $o ).
tff(decl_83,type,
class_RealVector_Oreal__normed__algebra__1: $i > $o ).
tff(decl_84,type,
class_RealVector_Oreal__normed__div__algebra: $i > $o ).
tff(decl_85,type,
class_Ring__and__Field_Omult__zero: $i > $o ).
tff(decl_86,type,
class_Ring__and__Field_Ocomm__ring: $i > $o ).
tff(decl_87,type,
tc_Polynomial_Opoly: $i > $i ).
tff(decl_88,type,
c_Polynomial_Opoly: ( $i * $i * $i ) > $i ).
tff(decl_89,type,
v_r: $i ).
tff(decl_90,type,
v_p: $i ).
tff(decl_91,type,
v_sko__unknown__thm__rW8__1: ( $i * $i ) > $i ).
tff(decl_92,type,
v_sko__local__Xmth1__2: ( $i * $i ) > $i ).
tff(decl_93,type,
v_sko__local__Xmth1__1: ( $i * $i ) > $i ).
tff(decl_94,type,
class_Orderings_Oorder: $i > $o ).
tff(decl_95,type,
class_Orderings_Opreorder: $i > $o ).
tff(decl_96,type,
class_Lattices_Oboolean__algebra: $i > $o ).
tff(decl_97,type,
c_HOL_Oone__class_Oone: $i > $i ).
tff(decl_98,type,
v_xa: $i > $i ).
tff(decl_99,type,
v_x: $i > $i ).
tff(decl_100,type,
class_Ring__and__Field_Ocomm__semiring__0: $i > $o ).
tff(decl_101,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
tff(decl_102,type,
class_Ring__and__Field_Ocomm__ring__1: $i > $o ).
tff(decl_103,type,
tc_Int_Oint: $i ).
cnf(cls_xt1_I7_J_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X4,X1)
| ~ c_HOL_Oord__class_Oless(X4,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I7_J_0) ).
cnf(cls_complex__mod__minus__le__complex__mod_0,axiom,
c_lessequals(c_HOL_Ouminus__class_Ouminus(c_RealVector_Onorm__class_Onorm(X1,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,tc_Complex_Ocomplex),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complex__mod__minus__le__complex__mod_0) ).
cnf(clsarity_RealDef__Oreal__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Orderings_Oorder) ).
cnf(cls_linorder__not__less_0,axiom,
( c_lessequals(X2,X3,X1)
| c_HOL_Oord__class_Oless(X3,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__less_0) ).
cnf(clsarity_RealDef__Oreal__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Orderings_Olinorder) ).
cnf(cls_abs__of__nonneg_0,axiom,
( c_HOL_Oabs__class_Oabs(X2,X1) = X2
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__of__nonneg_0) ).
cnf(cls_rp_0,axiom,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_r,tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rp_0) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add__abs,axiom,
class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add__abs) ).
cnf(cls_linorder__neq__iff_1,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).
cnf(cls_equation__minus__iff_1,axiom,
( X2 = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X2,X1),X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equation__minus__iff_1) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add,axiom,
class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add) ).
cnf(cls_conjecture_2,negated_conjecture,
~ c_HOL_Oord__class_Oless(v_x(X1),X1,tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
cnf(cls_abs__ge__minus__self_0,axiom,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Oabs__class_Oabs(X2,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__ge__minus__self_0) ).
cnf(cls_conjecture_1,negated_conjecture,
c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_xa(X1),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(v_x(X1),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
cnf(cls_xt1_I8_J_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1)
| ~ c_lessequals(X4,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I8_J_0) ).
cnf(cls_minus__less__iff_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X3,X1),X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__less__iff_1) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add,axiom,
class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add) ).
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_abs__norm__cancel_0,axiom,
( c_HOL_Oabs__class_Oabs(c_RealVector_Onorm__class_Onorm(X2,X1),tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(X2,X1)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__norm__cancel_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_neg__equal__zero_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Oordered__ab__group__add(X1)
| c_HOL_Ouminus__class_Ouminus(X2,X1) != X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__equal__zero_0) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Oordered__ab__group__add,axiom,
class_OrderedGroup_Oordered__ab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oordered__ab__group__add) ).
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_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_abs__minus__le__zero_0,axiom,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Oabs__class_Oabs(X2,X1),X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__minus__le__zero_0) ).
cnf(cls_real__less__def_2,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_RealDef_Oreal)
| X1 = X2
| ~ c_lessequals(X1,X2,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__less__def_2) ).
cnf(cls_neg__less__iff__less_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__less__iff__less_1) ).
cnf(cls_CHAINED_0,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ouminus__class_Ouminus(X2,tc_RealDef_Oreal)
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(X1,tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0) ).
cnf(cls_mth1_1,axiom,
c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_sko__local__Xmth1__2(v_p,v_r),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(v_sko__local__Xmth1__1(v_p,v_r),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mth1_1) ).
cnf(cls_mth1_0,axiom,
c_lessequals(c_RealVector_Onorm__class_Onorm(v_sko__local__Xmth1__2(v_p,v_r),tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mth1_0) ).
cnf(cls_less__minus__self__iff_1,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ouminus__class_Ouminus(X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__minus__self__iff_1) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__idom,axiom,
class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__idom) ).
cnf(c_0_32,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X4,X1)
| ~ c_HOL_Oord__class_Oless(X4,X3,X1) ),
cls_xt1_I7_J_0 ).
cnf(c_0_33,axiom,
c_lessequals(c_HOL_Ouminus__class_Ouminus(c_RealVector_Onorm__class_Onorm(X1,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,tc_Complex_Ocomplex),tc_RealDef_Oreal),
cls_complex__mod__minus__le__complex__mod_0 ).
cnf(c_0_34,axiom,
class_Orderings_Oorder(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Orderings_Oorder ).
cnf(c_0_35,axiom,
( c_lessequals(X2,X3,X1)
| c_HOL_Oord__class_Oless(X3,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
cls_linorder__not__less_0 ).
cnf(c_0_36,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Orderings_Olinorder ).
cnf(c_0_37,axiom,
( c_HOL_Oabs__class_Oabs(X2,X1) = X2
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_abs__of__nonneg_0 ).
cnf(c_0_38,axiom,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_r,tc_RealDef_Oreal),
cls_rp_0 ).
cnf(c_0_39,axiom,
class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add__abs ).
cnf(c_0_40,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X2,X1) ),
cls_linorder__neq__iff_1 ).
cnf(c_0_41,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(c_RealVector_Onorm__class_Onorm(X1,tc_Complex_Ocomplex),tc_RealDef_Oreal),X2,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(X1,tc_Complex_Ocomplex),X2,tc_RealDef_Oreal) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34])]) ).
cnf(c_0_42,axiom,
( X2 = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X2,X1),X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_equation__minus__iff_1 ).
cnf(c_0_43,axiom,
class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add ).
cnf(c_0_44,negated_conjecture,
~ c_HOL_Oord__class_Oless(v_x(X1),X1,tc_RealDef_Oreal),
cls_conjecture_2 ).
cnf(c_0_45,plain,
( c_lessequals(X1,X2,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X2,X1,tc_RealDef_Oreal) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_46,axiom,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Oabs__class_Oabs(X2,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
cls_abs__ge__minus__self_0 ).
cnf(c_0_47,plain,
c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal) = v_r,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39])]) ).
cnf(c_0_48,plain,
~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(X1,tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(c_RealVector_Onorm__class_Onorm(X1,tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_36])]) ).
cnf(c_0_49,negated_conjecture,
c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_xa(X1),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(v_x(X1),tc_RealDef_Oreal),
cls_conjecture_1 ).
cnf(c_0_50,plain,
c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),tc_RealDef_Oreal) = X1,
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_51,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1)
| ~ c_lessequals(X4,X3,X1) ),
cls_xt1_I8_J_0 ).
cnf(c_0_52,negated_conjecture,
c_lessequals(X1,v_x(X1),tc_RealDef_Oreal),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_53,plain,
c_lessequals(c_HOL_Ouminus__class_Ouminus(v_r,tc_RealDef_Oreal),v_r,tc_RealDef_Oreal),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_39])]) ).
cnf(c_0_54,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X3,X1),X2,X1) ),
cls_minus__less__iff_1 ).
cnf(c_0_55,axiom,
class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add ).
cnf(c_0_56,negated_conjecture,
~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(v_x(X1),tc_RealDef_Oreal),v_x(X1),tc_RealDef_Oreal),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_50]) ).
cnf(c_0_57,negated_conjecture,
( c_HOL_Oord__class_Oless(X1,v_x(X2),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_RealDef_Oreal) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_34])]) ).
cnf(c_0_58,plain,
( c_HOL_Oord__class_Oless(X1,v_r,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ouminus__class_Ouminus(v_r,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_53]),c_0_34])]) ).
cnf(c_0_59,plain,
( c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(X2,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_45]),c_0_55])]) ).
cnf(c_0_60,negated_conjecture,
~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(v_x(X1),tc_RealDef_Oreal),X1,tc_RealDef_Oreal),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_61,plain,
( c_lessequals(X1,v_r,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),v_r,tc_RealDef_Oreal) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_50]) ).
cnf(c_0_62,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_63,negated_conjecture,
c_lessequals(v_x(v_r),v_r,tc_RealDef_Oreal),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_64,negated_conjecture,
c_lessequals(v_x(X1),c_HOL_Ouminus__class_Ouminus(v_x(X1),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_49]),c_0_50]) ).
cnf(c_0_65,negated_conjecture,
v_x(v_r) = v_r,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_52])]) ).
cnf(c_0_66,plain,
( c_HOL_Ouminus__class_Ouminus(v_r,tc_RealDef_Oreal) = v_r
| ~ c_lessequals(v_r,c_HOL_Ouminus__class_Ouminus(v_r,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(spm,[status(thm)],[c_0_62,c_0_53]) ).
cnf(c_0_67,negated_conjecture,
c_lessequals(v_r,c_HOL_Ouminus__class_Ouminus(v_r,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_68,axiom,
( c_HOL_Oabs__class_Oabs(c_RealVector_Onorm__class_Onorm(X2,X1),tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(X2,X1)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
cls_abs__norm__cancel_0 ).
cnf(c_0_69,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector ).
cnf(c_0_70,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Oordered__ab__group__add(X1)
| c_HOL_Ouminus__class_Ouminus(X2,X1) != X2 ),
cls_neg__equal__zero_0 ).
cnf(c_0_71,plain,
c_HOL_Ouminus__class_Ouminus(v_r,tc_RealDef_Oreal) = v_r,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_66,c_0_67])]) ).
cnf(c_0_72,axiom,
class_OrderedGroup_Oordered__ab__group__add(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__OrderedGroup_Oordered__ab__group__add ).
cnf(c_0_73,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_74,axiom,
( c_lessequals(X1,X2,tc_RealDef_Oreal)
| c_lessequals(X2,X1,tc_RealDef_Oreal) ),
cls_real__le__linear_0 ).
cnf(c_0_75,axiom,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Oabs__class_Oabs(X2,X1),X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
cls_abs__minus__le__zero_0 ).
cnf(c_0_76,negated_conjecture,
c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(v_x(X1),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(v_x(X1),tc_RealDef_Oreal),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_49]),c_0_69])]) ).
cnf(c_0_77,plain,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = v_r,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_72])]) ).
cnf(c_0_78,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_RealDef_Oreal)
| X1 = X2
| ~ c_lessequals(X1,X2,tc_RealDef_Oreal) ),
cls_real__less__def_2 ).
cnf(c_0_79,plain,
( c_lessequals(X1,X2,tc_RealDef_Oreal)
| c_lessequals(X3,X1,tc_RealDef_Oreal)
| ~ c_lessequals(X3,X2,tc_RealDef_Oreal) ),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_80,negated_conjecture,
c_lessequals(v_x(X1),v_r,tc_RealDef_Oreal),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_50]),c_0_77]),c_0_39])]) ).
cnf(c_0_81,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
cls_neg__less__iff__less_1 ).
cnf(c_0_82,negated_conjecture,
( v_x(X1) = X1
| ~ c_lessequals(v_x(X1),X1,tc_RealDef_Oreal) ),
inference(spm,[status(thm)],[c_0_44,c_0_78]) ).
cnf(c_0_83,negated_conjecture,
( c_lessequals(v_x(X1),X2,tc_RealDef_Oreal)
| c_lessequals(X2,v_r,tc_RealDef_Oreal) ),
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
cnf(c_0_84,negated_conjecture,
~ c_HOL_Oord__class_Oless(X1,v_x(c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal)),tc_RealDef_Oreal),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_81]),c_0_55])]) ).
cnf(c_0_85,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ouminus__class_Ouminus(X2,tc_RealDef_Oreal)
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(X1,tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal) ),
cls_CHAINED_0 ).
cnf(c_0_86,axiom,
c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_sko__local__Xmth1__2(v_p,v_r),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(v_sko__local__Xmth1__1(v_p,v_r),tc_RealDef_Oreal),
cls_mth1_1 ).
cnf(c_0_87,axiom,
c_lessequals(c_RealVector_Onorm__class_Onorm(v_sko__local__Xmth1__2(v_p,v_r),tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal),
cls_mth1_0 ).
cnf(c_0_88,negated_conjecture,
( v_x(X1) = X1
| c_lessequals(X1,v_r,tc_RealDef_Oreal) ),
inference(spm,[status(thm)],[c_0_82,c_0_83]) ).
cnf(c_0_89,negated_conjecture,
~ c_HOL_Oord__class_Oless(X1,c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(spm,[status(thm)],[c_0_84,c_0_57]) ).
cnf(c_0_90,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ouminus__class_Ouminus(X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_less__minus__self__iff_1 ).
cnf(c_0_91,axiom,
class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Oordered__idom ).
cnf(c_0_92,plain,
( c_HOL_Oord__class_Oless(X1,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Ouminus__class_Ouminus(v_sko__local__Xmth1__1(v_p,v_r),tc_RealDef_Oreal) != c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_87])]) ).
cnf(c_0_93,negated_conjecture,
c_lessequals(X1,v_r,tc_RealDef_Oreal),
inference(spm,[status(thm)],[c_0_80,c_0_88]) ).
cnf(c_0_94,negated_conjecture,
~ c_HOL_Oord__class_Oless(X1,v_r,tc_RealDef_Oreal),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_91]),c_0_77])]) ).
cnf(c_0_95,plain,
c_HOL_Oord__class_Oless(v_sko__local__Xmth1__1(v_p,v_r),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(er,[status(thm)],[c_0_92]) ).
cnf(c_0_96,negated_conjecture,
~ c_HOL_Oord__class_Oless(X1,X2,tc_RealDef_Oreal),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_93]),c_0_34])]),c_0_94]) ).
cnf(c_0_97,plain,
$false,
inference(sr,[status(thm)],[c_0_95,c_0_96]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ALG373-1 : 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
% 0.12/0.34 % Computer : n027.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 06:18:21 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.18/0.55 start to proof: theBenchmark
% 0.63/0.77 % Version : CSE_E---1.5
% 0.63/0.77 % Problem : theBenchmark.p
% 0.63/0.77 % Proof found
% 0.63/0.77 % SZS status Theorem for theBenchmark.p
% 0.63/0.77 % SZS output start Proof
% See solution above
% 0.63/0.78 % Total time : 0.190000 s
% 0.63/0.78 % SZS output end Proof
% 0.63/0.78 % Total time : 0.203000 s
%------------------------------------------------------------------------------