TSTP Solution File: ALG373-1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% 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
%------------------------------------------------------------------------------