TSTP Solution File: ALG360-1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : ALG360-1 : 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 16:07:28 EDT 2023

% Result   : Unsatisfiable 33.81s 33.98s
% Output   : CNFRefutation 33.91s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :  149
% Syntax   : Number of formulae    :  233 (  73 unt; 100 typ;   0 def)
%            Number of atoms       :  226 (  90 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :  189 (  96   ~;  93   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   2 avg)
%            Maximal term depth    :    8 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  120 (  93   >;  27   *;   0   +;   0  <<)
%            Number of predicates  :   74 (  72 usr;   1 prp; 0-3 aty)
%            Number of functors    :   28 (  28 usr;   7 con; 0-3 aty)
%            Number of variables   :  170 (   4 sgn;   0   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    c_NthRoot_Osqrt: $i > $i ).

tff(decl_23,type,
    tc_RealDef_Oreal: $i ).

tff(decl_24,type,
    c_HOL_Oone__class_Oone: $i > $i ).

tff(decl_25,type,
    c_HOL_Oord__class_Oless: ( $i * $i * $i ) > $o ).

tff(decl_26,type,
    c_NthRoot_Oroot: ( $i * $i ) > $i ).

tff(decl_27,type,
    tc_nat: $i ).

tff(decl_28,type,
    c_HOL_Ozero__class_Ozero: $i > $i ).

tff(decl_29,type,
    c_lessequals: ( $i * $i * $i ) > $o ).

tff(decl_30,type,
    class_OrderedGroup_Opordered__ab__group__add__abs: $i > $o ).

tff(decl_31,type,
    c_HOL_Ouminus__class_Ouminus: ( $i * $i ) > $i ).

tff(decl_32,type,
    c_HOL_Oabs__class_Oabs: ( $i * $i ) > $i ).

tff(decl_33,type,
    class_Ring__and__Field_Oordered__ring__strict: $i > $o ).

tff(decl_34,type,
    c_HOL_Otimes__class_Otimes: ( $i * $i * $i ) > $i ).

tff(decl_35,type,
    class_Ring__and__Field_Oordered__idom: $i > $o ).

tff(decl_36,type,
    class_Ring__and__Field_Osemiring__0: $i > $o ).

tff(decl_37,type,
    class_Power_Opower: $i > $o ).

tff(decl_38,type,
    c_Power_Opower__class_Opower: ( $i * $i * $i ) > $i ).

tff(decl_39,type,
    class_Ring__and__Field_Ozero__neq__one: $i > $o ).

tff(decl_40,type,
    class_Ring__and__Field_Ono__zero__divisors: $i > $o ).

tff(decl_41,type,
    class_Ring__and__Field_Omult__zero: $i > $o ).

tff(decl_42,type,
    c_Complex_Ocomplex_OComplex: ( $i * $i ) > $i ).

tff(decl_43,type,
    c_Complex_Oii: $i ).

tff(decl_44,type,
    tc_Complex_Ocomplex: $i ).

tff(decl_45,type,
    class_OrderedGroup_Opordered__ab__group__add: $i > $o ).

tff(decl_46,type,
    class_OrderedGroup_Olordered__ab__group__add: $i > $o ).

tff(decl_47,type,
    c_HOL_Oplus__class_Oplus: ( $i * $i * $i ) > $i ).

tff(decl_48,type,
    class_RealVector_Oreal__normed__vector: $i > $o ).

tff(decl_49,type,
    c_HOL_Osgn__class_Osgn: ( $i * $i ) > $i ).

tff(decl_50,type,
    class_Ring__and__Field_Opordered__ring__abs: $i > $o ).

tff(decl_51,type,
    c_Suc: $i > $i ).

tff(decl_52,type,
    class_Ring__and__Field_Oidom: $i > $o ).

tff(decl_53,type,
    c_Ring__and__Field_Odvd__class_Odvd: ( $i * $i * $i ) > $o ).

tff(decl_54,type,
    c_HOL_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).

tff(decl_55,type,
    c_RealVector_Onorm__class_Onorm: ( $i * $i ) > $i ).

tff(decl_56,type,
    class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).

tff(decl_57,type,
    class_RealVector_Oreal__vector: $i > $o ).

tff(decl_58,type,
    c_RealVector_OscaleR__class_OscaleR: ( $i * $i * $i ) > $i ).

tff(decl_59,type,
    class_Orderings_Oorder: $i > $o ).

tff(decl_60,type,
    class_Lattices_Oboolean__algebra: $i > $o ).

tff(decl_61,type,
    class_OrderedGroup_Ogroup__add: $i > $o ).

tff(decl_62,type,
    class_OrderedGroup_Olordered__ab__group__add__abs: $i > $o ).

tff(decl_63,type,
    c_HOL_Oinverse__class_Odivide: ( $i * $i * $i ) > $i ).

tff(decl_64,type,
    class_RealVector_Oreal__normed__field: $i > $o ).

tff(decl_65,type,
    c_HOL_Oinverse__class_Oinverse: ( $i * $i ) > $i ).

tff(decl_66,type,
    class_Ring__and__Field_Oordered__field: $i > $o ).

tff(decl_67,type,
    class_Ring__and__Field_Omult__mono1: $i > $o ).

tff(decl_68,type,
    class_Ring__and__Field_Omult__mono: $i > $o ).

tff(decl_69,type,
    class_Ring__and__Field_Opordered__ring: $i > $o ).

tff(decl_70,type,
    c_Complex_ORe: $i > $i ).

tff(decl_71,type,
    class_RealVector_Oreal__algebra__1: $i > $o ).

tff(decl_72,type,
    c_RealVector_Oof__real: ( $i * $i ) > $i ).

tff(decl_73,type,
    class_Ring__and__Field_Odivision__ring: $i > $o ).

tff(decl_74,type,
    class_Ring__and__Field_Odivision__by__zero: $i > $o ).

tff(decl_75,type,
    class_Ring__and__Field_Opordered__cancel__semiring: $i > $o ).

tff(decl_76,type,
    class_OrderedGroup_Oordered__ab__group__add: $i > $o ).

tff(decl_77,type,
    class_Ring__and__Field_Opordered__semiring: $i > $o ).

tff(decl_78,type,
    class_Ring__and__Field_Oordered__semidom: $i > $o ).

tff(decl_79,type,
    class_OrderedGroup_Oab__group__add: $i > $o ).

tff(decl_80,type,
    class_Int_Onumber__ring: $i > $o ).

tff(decl_81,type,
    class_Ring__and__Field_Ofield: $i > $o ).

tff(decl_82,type,
    class_Ring__and__Field_Ocomm__ring__1: $i > $o ).

tff(decl_83,type,
    class_OrderedGroup_Opordered__comm__monoid__add: $i > $o ).

tff(decl_84,type,
    class_Ring__and__Field_Oabs__if: $i > $o ).

tff(decl_85,type,
    class_Orderings_Olinorder: $i > $o ).

tff(decl_86,type,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le: $i > $o ).

tff(decl_87,type,
    class_OrderedGroup_Ocomm__monoid__add: $i > $o ).

tff(decl_88,type,
    class_Ring__and__Field_Olordered__ring: $i > $o ).

tff(decl_89,type,
    class_Ring__and__Field_Osgn__if: $i > $o ).

tff(decl_90,type,
    class_Orderings_Opreorder: $i > $o ).

tff(decl_91,type,
    class_Ring__and__Field_Oordered__semiring__strict: $i > $o ).

tff(decl_92,type,
    class_Ring__and__Field_Oordered__semiring: $i > $o ).

tff(decl_93,type,
    v_na____: $i ).

tff(decl_94,type,
    class_RealVector_Oreal__normed__div__algebra: $i > $o ).

tff(decl_95,type,
    class_Ring__and__Field_Oring: $i > $o ).

tff(decl_96,type,
    class_Ring__and__Field_Oring__no__zero__divisors: $i > $o ).

tff(decl_97,type,
    class_RealVector_Oreal__normed__algebra: $i > $o ).

tff(decl_98,type,
    class_RealVector_Oreal__algebra: $i > $o ).

tff(decl_99,type,
    class_Ring__and__Field_Odvd: $i > $o ).

tff(decl_100,type,
    class_Ring__and__Field_Ocomm__ring: $i > $o ).

tff(decl_101,type,
    class_OrderedGroup_Opordered__ab__semigroup__add: $i > $o ).

tff(decl_102,type,
    class_OrderedGroup_Omonoid__add: $i > $o ).

tff(decl_103,type,
    class_Ring__and__Field_Oordered__comm__semiring__strict: $i > $o ).

tff(decl_104,type,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add: $i > $o ).

tff(decl_105,type,
    class_OrderedGroup_Omonoid__mult: $i > $o ).

tff(decl_106,type,
    class_RealVector_Oreal__normed__algebra__1: $i > $o ).

tff(decl_107,type,
    class_Ring__and__Field_Oring__1__no__zero__divisors: $i > $o ).

tff(decl_108,type,
    class_RealVector_Oreal__field: $i > $o ).

tff(decl_109,type,
    c_Complex_Oexpi: $i > $i ).

tff(decl_110,type,
    v_b: $i ).

tff(decl_111,type,
    class_Ring__and__Field_Oring__1: $i > $o ).

tff(decl_112,type,
    v_sko__local__XIH__1: ( $i * $i ) > $i ).

tff(decl_113,type,
    v_v____: $i ).

tff(decl_114,type,
    class_OrderedGroup_Ocancel__semigroup__add: $i > $o ).

tff(decl_115,type,
    class_OrderedGroup_Ocancel__ab__semigroup__add: $i > $o ).

tff(decl_116,type,
    class_Ring__and__Field_Ocomm__semiring: $i > $o ).

tff(decl_117,type,
    class_OrderedGroup_Oab__semigroup__mult: $i > $o ).

tff(decl_118,type,
    class_OrderedGroup_Ocomm__monoid__mult: $i > $o ).

tff(decl_119,type,
    class_OrderedGroup_Oab__semigroup__idem__mult: $i > $o ).

tff(decl_120,type,
    class_OrderedGroup_Oab__semigroup__add: $i > $o ).

tff(decl_121,type,
    class_Ring__and__Field_Osemiring: $i > $o ).

cnf(cls_real__sqrt__ge__1__iff_0,axiom,
    ( c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
    | ~ c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(X1),tc_RealDef_Oreal) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__ge__1__iff_0) ).

cnf(cls_le__real__sqrt__sumsq_0,axiom,
    c_lessequals(X1,c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X2,X2,tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__real__sqrt__sumsq_0) ).

cnf(cls_real__mult__1_0,axiom,
    c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X1,tc_RealDef_Oreal) = X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__mult__1_0) ).

cnf(cls_linorder__not__le_1,axiom,
    ( ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X2,X3,X1)
    | ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__le_1) ).

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_norm__mult_0,axiom,
    ( c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(X2,X3,X1),X1) = c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(X2,X1),c_RealVector_Onorm__class_Onorm(X3,X1),tc_RealDef_Oreal)
    | ~ class_RealVector_Oreal__normed__div__algebra(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_norm__mult_0) ).

cnf(cls_th0_0,axiom,
    c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_th0_0) ).

cnf(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra,axiom,
    class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra) ).

cnf(cls_norm__of__real_0,axiom,
    ( c_RealVector_Onorm__class_Onorm(c_RealVector_Oof__real(X2,X1),X1) = c_HOL_Oabs__class_Oabs(X2,tc_RealDef_Oreal)
    | ~ class_RealVector_Oreal__normed__algebra__1(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_norm__of__real_0) ).

cnf(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1,axiom,
    class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1) ).

cnf(cls_real__sqrt__mult_0,axiom,
    c_NthRoot_Osqrt(c_HOL_Otimes__class_Otimes(X1,X2,tc_RealDef_Oreal)) = c_HOL_Otimes__class_Otimes(c_NthRoot_Osqrt(X1),c_NthRoot_Osqrt(X2),tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__mult_0) ).

cnf(cls_real__sqrt__abs2_0,axiom,
    c_NthRoot_Osqrt(c_HOL_Otimes__class_Otimes(X1,X1,tc_RealDef_Oreal)) = c_HOL_Oabs__class_Oabs(X1,tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__abs2_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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero) ).

cnf(cls_CHAINED_0_01,axiom,
    v_b != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0_01) ).

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_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(cls_conjecture_0,negated_conjecture,
    ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_b,c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).

cnf(cls_add__less__cancel__left_0,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X2,X1),c_HOL_Oplus__class_Oplus(X4,X3,X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__left_0) ).

cnf(cls_class__semiring_Osemiring__rules_I6_J_0,axiom,
    ( c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X1),X1) = X2
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).

cnf(cls_class__semiring_Osemiring__rules_I12_J_0,axiom,
    ( c_HOL_Otimes__class_Otimes(X2,c_HOL_Oone__class_Oone(X1),X1) = X2
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I12_J_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/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1) ).

cnf(cls_class__ringb_Oadd__r0__iff_0,axiom,
    ( X3 = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Oidom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | X2 != c_HOL_Oplus__class_Oplus(X2,X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_0) ).

cnf(cls_Complex__add__complex__of__real_0,axiom,
    c_HOL_Oplus__class_Oplus(c_Complex_Ocomplex_OComplex(X1,X2),c_RealVector_Oof__real(X3,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Complex_Ocomplex_OComplex(c_HOL_Oplus__class_Oplus(X1,X3,tc_RealDef_Oreal),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Complex__add__complex__of__real_0) ).

cnf(clsarity_Complex__Ocomplex__Int_Onumber__ring,axiom,
    class_Int_Onumber__ring(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Int_Onumber__ring) ).

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(clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add__imp__le,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).

cnf(clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1,axiom,
    class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1) ).

cnf(cls_class__semiring_Osemiring__rules_I19_J_0,axiom,
    ( c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1) = c_HOL_Otimes__class_Otimes(X3,c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I19_J_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/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__c_0) ).

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/sandbox/benchmark/theBenchmark.p',cls_complex__divide__def_0) ).

cnf(cls_mult__zero__left_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Omult__zero(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__zero__left_0) ).

cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Omult__zero,axiom,
    class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Omult__zero) ).

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_mult__frac__frac_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_HOL_Oinverse__class_Odivide(X4,X5,X1),X1) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X3,X5,X1),X1)
    | ~ class_Ring__and__Field_Ofield(X1)
    | ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__frac__frac_0) ).

cnf(cls_class__semiring_Oadd__c_0,axiom,
    ( c_HOL_Oplus__class_Oplus(X2,X3,X1) = c_HOL_Oplus__class_Oplus(X3,X2,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__c_0) ).

cnf(cls_inverse__inverse__eq_0,axiom,
    ( c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(X2,X1),X1) = X2
    | ~ class_Ring__and__Field_Odivision__ring(X1)
    | ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__inverse__eq_0) ).

cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__ring,axiom,
    class_Ring__and__Field_Odivision__ring(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__ring) ).

cnf(cls_real__sqrt__not__eq__zero_0,axiom,
    ( c_NthRoot_Osqrt(X1) != c_HOL_Ozero__class_Ozero(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_real__sqrt__not__eq__zero_0) ).

cnf(cls_real__sqrt__gt__0__iff_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(X1),tc_RealDef_Oreal) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__gt__0__iff_0) ).

cnf(cls_real__zero__not__eq__one_0,axiom,
    c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__zero__not__eq__one_0) ).

cnf(cls_mult__divide__mult__cancel__right_0,axiom,
    ( c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1) = c_HOL_Oinverse__class_Odivide(X2,X4,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/sandbox/benchmark/theBenchmark.p',cls_mult__divide__mult__cancel__right_0) ).

cnf(cls_eq__divide__imp_0,axiom,
    ( X2 = c_HOL_Ozero__class_Ozero(X1)
    | X3 = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X3,X2,X1),X2,X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__divide__imp_0) ).

cnf(cls_v_0,axiom,
    c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_v_0) ).

cnf(cls_of__real__eq__0__iff_0,axiom,
    ( X2 = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
    | ~ class_RealVector_Oreal__algebra__1(X1)
    | c_RealVector_Oof__real(X2,X1) != c_HOL_Ozero__class_Ozero(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__real__eq__0__iff_0) ).

cnf(clsarity_Complex__Ocomplex__RealVector_Oreal__algebra__1,axiom,
    class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__algebra__1) ).

cnf(cls_inverse__zero__imp__zero_0,axiom,
    ( X2 = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Odivision__ring(X1)
    | c_HOL_Oinverse__class_Oinverse(X2,X1) != c_HOL_Ozero__class_Ozero(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__zero__imp__zero_0) ).

cnf(c_0_49,axiom,
    ( c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
    | ~ c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(X1),tc_RealDef_Oreal) ),
    cls_real__sqrt__ge__1__iff_0 ).

cnf(c_0_50,axiom,
    c_lessequals(X1,c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X2,X2,tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_RealDef_Oreal),
    cls_le__real__sqrt__sumsq_0 ).

cnf(c_0_51,axiom,
    c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X1,tc_RealDef_Oreal) = X1,
    cls_real__mult__1_0 ).

cnf(c_0_52,axiom,
    ( ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X2,X3,X1)
    | ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
    cls_linorder__not__le_1 ).

cnf(c_0_53,plain,
    c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X1,X1,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_51]) ).

cnf(c_0_54,axiom,
    class_Orderings_Olinorder(tc_RealDef_Oreal),
    clsarity_RealDef__Oreal__Orderings_Olinorder ).

cnf(c_0_55,axiom,
    ( c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(X2,X3,X1),X1) = c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(X2,X1),c_RealVector_Onorm__class_Onorm(X3,X1),tc_RealDef_Oreal)
    | ~ class_RealVector_Oreal__normed__div__algebra(X1) ),
    cls_norm__mult_0 ).

cnf(c_0_56,axiom,
    c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal),
    cls_th0_0 ).

cnf(c_0_57,axiom,
    class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex),
    clsarity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra ).

cnf(c_0_58,axiom,
    ( c_RealVector_Onorm__class_Onorm(c_RealVector_Oof__real(X2,X1),X1) = c_HOL_Oabs__class_Oabs(X2,tc_RealDef_Oreal)
    | ~ class_RealVector_Oreal__normed__algebra__1(X1) ),
    cls_norm__of__real_0 ).

cnf(c_0_59,axiom,
    class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
    clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1 ).

cnf(c_0_60,plain,
    ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X1,X1,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_54])]) ).

cnf(c_0_61,axiom,
    c_NthRoot_Osqrt(c_HOL_Otimes__class_Otimes(X1,X2,tc_RealDef_Oreal)) = c_HOL_Otimes__class_Otimes(c_NthRoot_Osqrt(X1),c_NthRoot_Osqrt(X2),tc_RealDef_Oreal),
    cls_real__sqrt__mult_0 ).

cnf(c_0_62,axiom,
    c_NthRoot_Osqrt(c_HOL_Otimes__class_Otimes(X1,X1,tc_RealDef_Oreal)) = c_HOL_Oabs__class_Oabs(X1,tc_RealDef_Oreal),
    cls_real__sqrt__abs2_0 ).

cnf(c_0_63,plain,
    c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_RealVector_Onorm__class_Onorm(X1,tc_Complex_Ocomplex),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_51]),c_0_57])]) ).

cnf(c_0_64,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_65,plain,
    c_RealVector_Onorm__class_Onorm(c_RealVector_Oof__real(X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oabs__class_Oabs(X1,tc_RealDef_Oreal),
    inference(spm,[status(thm)],[c_0_58,c_0_59]) ).

cnf(c_0_66,axiom,
    class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
    clsarity_Complex__Ocomplex__Ring__and__Field_Ofield ).

cnf(c_0_67,axiom,
    class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex),
    clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero ).

cnf(c_0_68,axiom,
    v_b != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
    cls_CHAINED_0_01 ).

cnf(c_0_69,plain,
    ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(X1,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_62]) ).

cnf(c_0_70,plain,
    c_HOL_Oabs__class_Oabs(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_65]),c_0_66]),c_0_67])]),c_0_68]) ).

cnf(c_0_71,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_72,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_73,negated_conjecture,
    ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_b,c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
    cls_conjecture_0 ).

cnf(c_0_74,axiom,
    ( c_HOL_Oord__class_Oless(X2,X3,X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X2,X1),c_HOL_Oplus__class_Oplus(X4,X3,X1),X1) ),
    cls_add__less__cancel__left_0 ).

cnf(c_0_75,axiom,
    ( c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X1),X1) = X2
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Osemiring__rules_I6_J_0 ).

cnf(c_0_76,plain,
    ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),
    inference(spm,[status(thm)],[c_0_69,c_0_70]) ).

cnf(c_0_77,plain,
    ( X1 = X2
    | c_HOL_Oord__class_Oless(X2,X1,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_71,c_0_72]),c_0_54])]) ).

cnf(c_0_78,negated_conjecture,
    ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_b,c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_73,c_0_56]),c_0_51]) ).

cnf(c_0_79,axiom,
    ( c_HOL_Otimes__class_Otimes(X2,c_HOL_Oone__class_Oone(X1),X1) = X2
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Osemiring__rules_I12_J_0 ).

cnf(c_0_80,axiom,
    class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
    clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1 ).

cnf(c_0_81,axiom,
    ( X3 = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Oidom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | X2 != c_HOL_Oplus__class_Oplus(X2,X3,X1) ),
    cls_class__ringb_Oadd__r0__iff_0 ).

cnf(c_0_82,axiom,
    c_HOL_Oplus__class_Oplus(c_Complex_Ocomplex_OComplex(X1,X2),c_RealVector_Oof__real(X3,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Complex_Ocomplex_OComplex(c_HOL_Oplus__class_Oplus(X1,X3,tc_RealDef_Oreal),X2),
    cls_Complex__add__complex__of__real_0 ).

cnf(c_0_83,axiom,
    class_Int_Onumber__ring(tc_Complex_Ocomplex),
    clsarity_Complex__Ocomplex__Int_Onumber__ring ).

cnf(c_0_84,axiom,
    class_Ring__and__Field_Oidom(tc_Complex_Ocomplex),
    clsarity_Complex__Ocomplex__Ring__and__Field_Oidom ).

cnf(c_0_85,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
    | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
    | ~ c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X3,X2,X1),X1) ),
    inference(spm,[status(thm)],[c_0_74,c_0_75]) ).

cnf(c_0_86,plain,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_RealDef_Oreal) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal)
    | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
    inference(spm,[status(thm)],[c_0_76,c_0_77]) ).

cnf(c_0_87,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
    clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add__imp__le ).

cnf(c_0_88,axiom,
    class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal),
    clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1 ).

cnf(c_0_89,negated_conjecture,
    ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_b,c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_80])]) ).

cnf(c_0_90,axiom,
    ( c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1) = c_HOL_Otimes__class_Otimes(X3,c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Osemiring__rules_I19_J_0 ).

cnf(c_0_91,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_92,plain,
    ( c_RealVector_Oof__real(X1,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
    | c_Complex_Ocomplex_OComplex(c_HOL_Oplus__class_Oplus(X2,X1,tc_RealDef_Oreal),X3) != c_Complex_Ocomplex_OComplex(X2,X3) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_83]),c_0_84])]) ).

cnf(c_0_93,plain,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_RealDef_Oreal) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_87]),c_0_88])]) ).

cnf(c_0_94,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_95,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Omult__zero(X1) ),
    cls_mult__zero__left_0 ).

cnf(c_0_96,axiom,
    class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex),
    clsarity_Complex__Ocomplex__Ring__and__Field_Omult__zero ).

cnf(c_0_97,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_98,axiom,
    class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
    clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector ).

cnf(c_0_99,negated_conjecture,
    ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_b,c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_80])]) ).

cnf(c_0_100,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X2,X3,X1),c_HOL_Oinverse__class_Odivide(X4,X5,X1),X1) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X3,X5,X1),X1)
    | ~ class_Ring__and__Field_Ofield(X1)
    | ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
    cls_mult__frac__frac_0 ).

cnf(c_0_101,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_91,c_0_80]) ).

cnf(c_0_102,axiom,
    ( c_HOL_Oplus__class_Oplus(X2,X3,X1) = c_HOL_Oplus__class_Oplus(X3,X2,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    cls_class__semiring_Oadd__c_0 ).

cnf(c_0_103,axiom,
    ( c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(X2,X1),X1) = X2
    | ~ class_Ring__and__Field_Odivision__ring(X1)
    | ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
    cls_inverse__inverse__eq_0 ).

cnf(c_0_104,axiom,
    class_Ring__and__Field_Odivision__ring(tc_Complex_Ocomplex),
    clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__ring ).

cnf(c_0_105,axiom,
    ( c_NthRoot_Osqrt(X1) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal) ),
    cls_real__sqrt__not__eq__zero_0 ).

cnf(c_0_106,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(X1),tc_RealDef_Oreal) ),
    cls_real__sqrt__gt__0__iff_0 ).

cnf(c_0_107,plain,
    ( c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
    inference(spm,[status(thm)],[c_0_92,c_0_93]) ).

cnf(c_0_108,plain,
    c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_95]),c_0_96])]) ).

cnf(c_0_109,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_97,c_0_98]) ).

cnf(c_0_110,axiom,
    c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal),
    cls_real__zero__not__eq__one_0 ).

cnf(c_0_111,negated_conjecture,
    ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_b,c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_b,c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),
    inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_100]),c_0_66]),c_0_67])]),c_0_101]) ).

cnf(c_0_112,axiom,
    ( c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1) = c_HOL_Oinverse__class_Odivide(X2,X4,X1)
    | X3 = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Ofield(X1)
    | ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
    cls_mult__divide__mult__cancel__right_0 ).

cnf(c_0_113,plain,
    c_HOL_Oplus__class_Oplus(X1,X2,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(X2,X1,tc_Complex_Ocomplex),
    inference(spm,[status(thm)],[c_0_102,c_0_80]) ).

cnf(c_0_114,axiom,
    ( X2 = c_HOL_Ozero__class_Ozero(X1)
    | X3 = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X3,X2,X1),X2,X1)
    | ~ class_Ring__and__Field_Ofield(X1) ),
    cls_eq__divide__imp_0 ).

cnf(c_0_115,plain,
    c_HOL_Oinverse__class_Odivide(X1,c_HOL_Oinverse__class_Oinverse(X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(X1,X2,tc_Complex_Ocomplex),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_103]),c_0_67]),c_0_104])]) ).

cnf(c_0_116,axiom,
    c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),
    cls_v_0 ).

cnf(c_0_117,plain,
    ( c_HOL_Oabs__class_Oabs(X1,tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X1,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
    inference(spm,[status(thm)],[c_0_105,c_0_62]) ).

cnf(c_0_118,plain,
    c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(X1,tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(X2,tc_Complex_Ocomplex),tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
    inference(spm,[status(thm)],[c_0_55,c_0_57]) ).

cnf(c_0_119,plain,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X1,X1,tc_RealDef_Oreal),tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(X1,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
    inference(spm,[status(thm)],[c_0_106,c_0_62]) ).

cnf(c_0_120,plain,
    c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_RealDef_Oreal),
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_107]),c_0_108]),c_0_109]),c_0_110]) ).

cnf(c_0_121,negated_conjecture,
    ( c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
    | ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_b,c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
    inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_112]),c_0_66]),c_0_67])]),c_0_113]) ).

cnf(c_0_122,plain,
    ( c_HOL_Otimes__class_Otimes(X1,c_HOL_Oinverse__class_Odivide(X2,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X2
    | c_HOL_Oinverse__class_Oinverse(X1,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_94]),c_0_66])]),c_0_115]),c_0_101]) ).

cnf(c_0_123,plain,
    c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(v_v____,v_na____,tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_102]),c_0_80])]) ).

cnf(c_0_124,plain,
    ( c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(v_b,v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_70]),c_0_118]) ).

cnf(c_0_125,plain,
    c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(v_b,v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_70]),c_0_118]),c_0_120])]) ).

cnf(c_0_126,axiom,
    ( X2 = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
    | ~ class_RealVector_Oreal__algebra__1(X1)
    | c_RealVector_Oof__real(X2,X1) != c_HOL_Ozero__class_Ozero(X1) ),
    cls_of__real__eq__0__iff_0 ).

cnf(c_0_127,negated_conjecture,
    ( c_RealVector_Oof__real(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
    | c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_122]),c_0_123])]) ).

cnf(c_0_128,axiom,
    class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex),
    clsarity_Complex__Ocomplex__RealVector_Oreal__algebra__1 ).

cnf(c_0_129,plain,
    c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_124,c_0_125])]) ).

cnf(c_0_130,axiom,
    ( X2 = c_HOL_Ozero__class_Ozero(X1)
    | ~ class_Ring__and__Field_Odivision__ring(X1)
    | c_HOL_Oinverse__class_Oinverse(X2,X1) != c_HOL_Ozero__class_Ozero(X1) ),
    cls_inverse__zero__imp__zero_0 ).

cnf(c_0_131,negated_conjecture,
    c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_127]),c_0_128])]),c_0_129]) ).

cnf(c_0_132,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_131]),c_0_104])]),c_0_68]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : ALG360-1 : 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 : 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 06:01:21 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.19/0.57  start to proof: theBenchmark
% 33.81/33.98  % Version  : CSE_E---1.5
% 33.81/33.98  % Problem  : theBenchmark.p
% 33.81/33.98  % Proof found
% 33.81/33.98  % SZS status Theorem for theBenchmark.p
% 33.81/33.98  % SZS output start Proof
% See solution above
% 33.91/34.00  % Total time : 33.315000 s
% 33.91/34.00  % SZS output end Proof
% 33.91/34.00  % Total time : 33.336000 s
%------------------------------------------------------------------------------