TSTP Solution File: ALG360-1 by E-SAT---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E-SAT---3.1.00
% Problem  : ALG360-1 : TPTP v8.2.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n025.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 : Mon May 20 18:13:09 EDT 2024

% Result   : Unsatisfiable 44.73s 6.19s
% Output   : CNFRefutation 44.73s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   49
% Syntax   : Number of clauses     :  160 (  76 unt;  21 nHn;  96 RR)
%            Number of literals    :  292 ( 117 equ; 135 neg)
%            Maximal clause size   :    4 (   1 avg)
%            Maximal term depth    :    8 (   2 avg)
%            Number of predicates  :   17 (  15 usr;   1 prp; 0-3 aty)
%            Number of functors    :   17 (  17 usr;   5 con; 0-3 aty)
%            Number of variables   :  231 (   5 sgn)

% Comments : 
%------------------------------------------------------------------------------
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_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(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_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_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_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_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_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__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_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__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(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_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(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(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__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__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_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(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(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(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_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(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(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_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(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_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(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(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(c_0_49,plain,
    ( 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) ),
    inference(fof_simplification,[status(thm)],[cls_real__sqrt__ge__1__iff_0]) ).

cnf(c_0_50,plain,
    ( ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X2,X3,X1)
    | ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
    inference(fof_simplification,[status(thm)],[cls_linorder__not__le_1]) ).

cnf(c_0_51,plain,
    ( 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) ),
    c_0_49 ).

cnf(c_0_52,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_53,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_54,plain,
    ( 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) ),
    inference(fof_simplification,[status(thm)],[cls_norm__mult_0]) ).

cnf(c_0_55,plain,
    ( 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) ),
    inference(fof_simplification,[status(thm)],[cls_norm__of__real_0]) ).

cnf(c_0_56,plain,
    ( ~ class_Orderings_Olinorder(X1)
    | ~ c_lessequals(X2,X3,X1)
    | ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
    c_0_50 ).

cnf(c_0_57,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_51,c_0_52]),c_0_53]) ).

cnf(c_0_58,axiom,
    class_Orderings_Olinorder(tc_RealDef_Oreal),
    clsarity_RealDef__Oreal__Orderings_Olinorder ).

cnf(c_0_59,plain,
    ( 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) ),
    c_0_54 ).

cnf(c_0_60,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_61,axiom,
    class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex),
    clsarity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra ).

cnf(c_0_62,plain,
    ( 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) ),
    inference(fof_simplification,[status(thm)],[cls_divide__eq__eq_0]) ).

cnf(c_0_63,plain,
    ( 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) ),
    c_0_55 ).

cnf(c_0_64,axiom,
    class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
    clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1 ).

cnf(c_0_65,plain,
    v_b != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
    inference(fof_simplification,[status(thm)],[cls_CHAINED_0_01]) ).

cnf(c_0_66,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_56,c_0_57]),c_0_58])]) ).

cnf(c_0_67,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_68,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_69,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_59,c_0_60]),c_0_53]),c_0_61])]) ).

cnf(c_0_70,plain,
    ( 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) ),
    c_0_62 ).

cnf(c_0_71,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_63,c_0_64]) ).

cnf(c_0_72,axiom,
    class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
    clsarity_Complex__Ocomplex__Ring__and__Field_Ofield ).

cnf(c_0_73,axiom,
    class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex),
    clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero ).

cnf(c_0_74,plain,
    v_b != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
    c_0_65 ).

cnf(c_0_75,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_RealDef_Oreal)
    | X1 = X2
    | ~ c_lessequals(X1,X2,tc_RealDef_Oreal) ),
    inference(fof_simplification,[status(thm)],[cls_real__less__def_2]) ).

cnf(c_0_76,plain,
    ( c_lessequals(X2,X3,X1)
    | c_HOL_Oord__class_Oless(X3,X2,X1)
    | ~ class_Orderings_Olinorder(X1) ),
    inference(fof_simplification,[status(thm)],[cls_linorder__not__less_0]) ).

cnf(c_0_77,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),
    inference(fof_simplification,[status(thm)],[cls_conjecture_0]) ).

cnf(c_0_78,plain,
    ( 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) ),
    inference(fof_simplification,[status(thm)],[cls_add__less__cancel__left_0]) ).

cnf(c_0_79,plain,
    ( c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X1),X1) = X2
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(fof_simplification,[status(thm)],[cls_class__semiring_Osemiring__rules_I6_J_0]) ).

cnf(c_0_80,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_66,c_0_67]),c_0_68]) ).

cnf(c_0_81,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_69,c_0_70]),c_0_71]),c_0_72]),c_0_73])]),c_0_74]) ).

cnf(c_0_82,plain,
    ( c_HOL_Oord__class_Oless(X1,X2,tc_RealDef_Oreal)
    | X1 = X2
    | ~ c_lessequals(X1,X2,tc_RealDef_Oreal) ),
    c_0_75 ).

cnf(c_0_83,plain,
    ( c_lessequals(X2,X3,X1)
    | c_HOL_Oord__class_Oless(X3,X2,X1)
    | ~ class_Orderings_Olinorder(X1) ),
    c_0_76 ).

cnf(c_0_84,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),
    c_0_77 ).

cnf(c_0_85,plain,
    ( c_HOL_Otimes__class_Otimes(X2,c_HOL_Oone__class_Oone(X1),X1) = X2
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(fof_simplification,[status(thm)],[cls_class__semiring_Osemiring__rules_I12_J_0]) ).

cnf(c_0_86,plain,
    ( 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) ),
    inference(fof_simplification,[status(thm)],[cls_class__ringb_Oadd__r0__iff_0]) ).

cnf(c_0_87,plain,
    ( 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) ),
    c_0_78 ).

cnf(c_0_88,plain,
    ( c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X1),X1) = X2
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    c_0_79 ).

cnf(c_0_89,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_80,c_0_81]) ).

cnf(c_0_90,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_82,c_0_83]),c_0_58])]) ).

cnf(c_0_91,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_84,c_0_60]),c_0_53]) ).

cnf(c_0_92,plain,
    ( c_HOL_Otimes__class_Otimes(X2,c_HOL_Oone__class_Oone(X1),X1) = X2
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    c_0_85 ).

cnf(c_0_93,axiom,
    class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
    clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1 ).

cnf(c_0_94,plain,
    ( 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) ),
    inference(fof_simplification,[status(thm)],[cls_class__semiring_Osemiring__rules_I19_J_0]) ).

cnf(c_0_95,plain,
    ( c_HOL_Otimes__class_Otimes(X2,X3,X1) = c_HOL_Otimes__class_Otimes(X3,X2,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(fof_simplification,[status(thm)],[cls_class__semiring_Omul__c_0]) ).

cnf(c_0_96,plain,
    ( 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) ),
    c_0_86 ).

cnf(c_0_97,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_98,axiom,
    class_Int_Onumber__ring(tc_Complex_Ocomplex),
    clsarity_Complex__Ocomplex__Int_Onumber__ring ).

cnf(c_0_99,axiom,
    class_Ring__and__Field_Oidom(tc_Complex_Ocomplex),
    clsarity_Complex__Ocomplex__Ring__and__Field_Oidom ).

cnf(c_0_100,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_87,c_0_88]) ).

cnf(c_0_101,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_89,c_0_90]) ).

cnf(c_0_102,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_103,axiom,
    class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal),
    clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1 ).

cnf(c_0_104,plain,
    ( 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) ),
    inference(fof_simplification,[status(thm)],[cls_mult__zero__left_0]) ).

cnf(c_0_105,plain,
    ( 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) ),
    inference(fof_simplification,[status(thm)],[cls_norm__zero_0]) ).

cnf(c_0_106,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_91,c_0_92]),c_0_93])]) ).

cnf(c_0_107,plain,
    ( 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) ),
    c_0_94 ).

cnf(c_0_108,plain,
    ( 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) ),
    inference(fof_simplification,[status(thm)],[cls_mult__frac__frac_0]) ).

cnf(c_0_109,plain,
    ( c_HOL_Otimes__class_Otimes(X2,X3,X1) = c_HOL_Otimes__class_Otimes(X3,X2,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    c_0_95 ).

cnf(c_0_110,plain,
    ( c_HOL_Oplus__class_Oplus(X2,X3,X1) = c_HOL_Oplus__class_Oplus(X3,X2,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    inference(fof_simplification,[status(thm)],[cls_class__semiring_Oadd__c_0]) ).

cnf(c_0_111,plain,
    ( 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) ),
    inference(fof_simplification,[status(thm)],[cls_inverse__inverse__eq_0]) ).

cnf(c_0_112,plain,
    ( 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) ),
    inference(fof_simplification,[status(thm)],[cls_real__sqrt__not__eq__zero_0]) ).

cnf(c_0_113,plain,
    ( 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) ),
    inference(fof_simplification,[status(thm)],[cls_real__sqrt__gt__0__iff_0]) ).

cnf(c_0_114,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_96,c_0_97]),c_0_98]),c_0_99])]) ).

cnf(c_0_115,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_100,c_0_101]),c_0_102]),c_0_103])]) ).

cnf(c_0_116,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_117,plain,
    ( 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) ),
    c_0_104 ).

cnf(c_0_118,axiom,
    class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex),
    clsarity_Complex__Ocomplex__Ring__and__Field_Omult__zero ).

cnf(c_0_119,plain,
    ( 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) ),
    c_0_105 ).

cnf(c_0_120,axiom,
    class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
    clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector ).

cnf(c_0_121,plain,
    c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal),
    inference(fof_simplification,[status(thm)],[cls_real__zero__not__eq__one_0]) ).

cnf(c_0_122,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_106,c_0_107]),c_0_93])]) ).

cnf(c_0_123,plain,
    ( 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) ),
    c_0_108 ).

cnf(c_0_124,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_109,c_0_93]) ).

cnf(c_0_125,plain,
    ( 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) ),
    inference(fof_simplification,[status(thm)],[cls_mult__divide__mult__cancel__right_0]) ).

cnf(c_0_126,plain,
    ( c_HOL_Oplus__class_Oplus(X2,X3,X1) = c_HOL_Oplus__class_Oplus(X3,X2,X1)
    | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
    c_0_110 ).

cnf(c_0_127,plain,
    ( 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) ),
    inference(fof_simplification,[status(thm)],[cls_eq__divide__imp_0]) ).

cnf(c_0_128,plain,
    ( 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) ),
    c_0_111 ).

cnf(c_0_129,axiom,
    class_Ring__and__Field_Odivision__ring(tc_Complex_Ocomplex),
    clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__ring ).

cnf(c_0_130,plain,
    ( 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) ),
    c_0_112 ).

cnf(c_0_131,plain,
    ( 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) ),
    c_0_113 ).

cnf(c_0_132,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_114,c_0_115]) ).

cnf(c_0_133,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_116,c_0_117]),c_0_118])]) ).

cnf(c_0_134,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_119,c_0_120]) ).

cnf(c_0_135,plain,
    c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal),
    c_0_121 ).

cnf(c_0_136,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_122,c_0_123]),c_0_72]),c_0_73])]),c_0_124]) ).

cnf(c_0_137,plain,
    ( 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) ),
    c_0_125 ).

cnf(c_0_138,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_126,c_0_93]) ).

cnf(c_0_139,plain,
    ( 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) ),
    c_0_127 ).

cnf(c_0_140,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_116,c_0_128]),c_0_73]),c_0_129])]) ).

cnf(c_0_141,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_142,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_130,c_0_68]) ).

cnf(c_0_143,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_59,c_0_61]) ).

cnf(c_0_144,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_131,c_0_68]) ).

cnf(c_0_145,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_60,c_0_132]),c_0_133]),c_0_134]),c_0_135]) ).

cnf(c_0_146,plain,
    ( 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) ),
    inference(fof_simplification,[status(thm)],[cls_of__real__eq__0__iff_0]) ).

cnf(c_0_147,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_136,c_0_137]),c_0_72]),c_0_73])]),c_0_138]) ).

cnf(c_0_148,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_139,c_0_116]),c_0_72])]),c_0_140]),c_0_124]) ).

cnf(c_0_149,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_141,c_0_126]),c_0_93])]) ).

cnf(c_0_150,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_142,c_0_81]),c_0_143]) ).

cnf(c_0_151,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_144,c_0_81]),c_0_143]),c_0_145])]) ).

cnf(c_0_152,plain,
    ( 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) ),
    inference(fof_simplification,[status(thm)],[cls_inverse__zero__imp__zero_0]) ).

cnf(c_0_153,plain,
    ( 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) ),
    c_0_146 ).

cnf(c_0_154,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_147,c_0_148]),c_0_149])]) ).

cnf(c_0_155,axiom,
    class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex),
    clsarity_Complex__Ocomplex__RealVector_Oreal__algebra__1 ).

cnf(c_0_156,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_150,c_0_151])]) ).

cnf(c_0_157,plain,
    ( 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) ),
    c_0_152 ).

cnf(c_0_158,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_153,c_0_154]),c_0_155])]),c_0_156]) ).

cnf(c_0_159,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_157,c_0_158]),c_0_129])]),c_0_74]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem    : ALG360-1 : TPTP v8.2.0. Released v4.1.0.
% 0.06/0.13  % Command    : run_E %s %d THM
% 0.12/0.33  % Computer : n025.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % 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   : Sat May 18 23:52:08 EDT 2024
% 0.12/0.34  % CPUTime    : 
% 0.18/0.46  Running first-order model finding
% 0.18/0.46  Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --satauto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 44.73/6.19  # Version: 3.1.0
% 44.73/6.19  # Preprocessing class: FMLMSMSSSSSNFFN.
% 44.73/6.19  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 44.73/6.19  # Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4c with 1500s (5) cores
% 44.73/6.19  # Starting new_bool_3 with 300s (1) cores
% 44.73/6.19  # Starting new_bool_1 with 300s (1) cores
% 44.73/6.19  # Starting sh5l with 300s (1) cores
% 44.73/6.19  # G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4c with pid 6255 completed with status 0
% 44.73/6.19  # Result found by G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4c
% 44.73/6.19  # Preprocessing class: FMLMSMSSSSSNFFN.
% 44.73/6.19  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 44.73/6.19  # Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4c with 1500s (5) cores
% 44.73/6.19  # No SInE strategy applied
% 44.73/6.19  # Search class: FGHSM-SSLM32-DFFFFFNN
% 44.73/6.19  # Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 44.73/6.19  # Starting G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_RG_S04AN with 113s (1) cores
% 44.73/6.19  # Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4c with 151s (1) cores
% 44.73/6.19  # Starting G-E--_208_B07_F1_SE_CS_SP_PS_S4d with 113s (1) cores
% 44.73/6.19  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 113s (1) cores
% 44.73/6.19  # Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 113s (1) cores
% 44.73/6.19  # G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4c with pid 6263 completed with status 0
% 44.73/6.19  # Result found by G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4c
% 44.73/6.19  # Preprocessing class: FMLMSMSSSSSNFFN.
% 44.73/6.19  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 44.73/6.19  # Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4c with 1500s (5) cores
% 44.73/6.19  # No SInE strategy applied
% 44.73/6.19  # Search class: FGHSM-SSLM32-DFFFFFNN
% 44.73/6.19  # Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 44.73/6.19  # Starting G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_RG_S04AN with 113s (1) cores
% 44.73/6.19  # Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4c with 151s (1) cores
% 44.73/6.19  # Preprocessing time       : 0.011 s
% 44.73/6.19  
% 44.73/6.19  # Proof found!
% 44.73/6.19  # SZS status Unsatisfiable
% 44.73/6.19  # SZS output start CNFRefutation
% See solution above
% 44.73/6.19  # Parsed axioms                        : 1197
% 44.73/6.19  # Removed by relevancy pruning/SinE    : 0
% 44.73/6.19  # Initial clauses                      : 1197
% 44.73/6.19  # Removed in clause preprocessing      : 0
% 44.73/6.19  # Initial clauses in saturation        : 1197
% 44.73/6.19  # Processed clauses                    : 51220
% 44.73/6.19  # ...of these trivial                  : 999
% 44.73/6.19  # ...subsumed                          : 43630
% 44.73/6.19  # ...remaining for further processing  : 6591
% 44.73/6.19  # Other redundant clauses eliminated   : 246
% 44.73/6.19  # Clauses deleted for lack of memory   : 0
% 44.73/6.19  # Backward-subsumed                    : 142
% 44.73/6.19  # Backward-rewritten                   : 845
% 44.73/6.19  # Generated clauses                    : 454286
% 44.73/6.19  # ...of the previous two non-redundant : 425662
% 44.73/6.19  # ...aggressively subsumed             : 0
% 44.73/6.19  # Contextual simplify-reflections      : 14
% 44.73/6.19  # Paramodulations                      : 453899
% 44.73/6.19  # Factorizations                       : 19
% 44.73/6.19  # NegExts                              : 0
% 44.73/6.19  # Equation resolutions                 : 368
% 44.73/6.19  # Disequality decompositions           : 0
% 44.73/6.19  # Total rewrite steps                  : 491501
% 44.73/6.19  # ...of those cached                   : 479956
% 44.73/6.19  # Propositional unsat checks           : 0
% 44.73/6.19  #    Propositional check models        : 0
% 44.73/6.19  #    Propositional check unsatisfiable : 0
% 44.73/6.19  #    Propositional clauses             : 0
% 44.73/6.19  #    Propositional clauses after purity: 0
% 44.73/6.19  #    Propositional unsat core size     : 0
% 44.73/6.19  #    Propositional preprocessing time  : 0.000
% 44.73/6.19  #    Propositional encoding time       : 0.000
% 44.73/6.19  #    Propositional solver time         : 0.000
% 44.73/6.19  #    Success case prop preproc time    : 0.000
% 44.73/6.19  #    Success case prop encoding time   : 0.000
% 44.73/6.19  #    Success case prop solver time     : 0.000
% 44.73/6.19  # Current number of processed clauses  : 5604
% 44.73/6.19  #    Positive orientable unit clauses  : 746
% 44.73/6.19  #    Positive unorientable unit clauses: 25
% 44.73/6.19  #    Negative unit clauses             : 1903
% 44.73/6.19  #    Non-unit-clauses                  : 2930
% 44.73/6.19  # Current number of unprocessed clauses: 373700
% 44.73/6.19  # ...number of literals in the above   : 1115619
% 44.73/6.19  # Current number of archived formulas  : 0
% 44.73/6.19  # Current number of archived clauses   : 987
% 44.73/6.19  # Clause-clause subsumption calls (NU) : 752477
% 44.73/6.19  # Rec. Clause-clause subsumption calls : 304754
% 44.73/6.19  # Non-unit clause-clause subsumptions  : 4119
% 44.73/6.19  # Unit Clause-clause subsumption calls : 241676
% 44.73/6.19  # Rewrite failures with RHS unbound    : 4
% 44.73/6.19  # BW rewrite match attempts            : 6464
% 44.73/6.19  # BW rewrite match successes           : 1882
% 44.73/6.19  # Condensation attempts                : 0
% 44.73/6.19  # Condensation successes               : 0
% 44.73/6.19  # Termbank termtop insertions          : 8689251
% 44.73/6.19  # Search garbage collected termcells   : 2336
% 44.73/6.19  
% 44.73/6.19  # -------------------------------------------------
% 44.73/6.19  # User time                : 5.347 s
% 44.73/6.19  # System time              : 0.206 s
% 44.73/6.19  # Total time               : 5.553 s
% 44.73/6.19  # Maximum resident set size: 4076 pages
% 44.73/6.19  
% 44.73/6.19  # -------------------------------------------------
% 44.73/6.19  # User time                : 27.075 s
% 44.73/6.19  # System time              : 0.837 s
% 44.73/6.19  # Total time               : 27.913 s
% 44.73/6.19  # Maximum resident set size: 2548 pages
% 44.73/6.19  % E---3.1 exiting
%------------------------------------------------------------------------------