%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ALG360-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 11:55:58 AM UTC 2026
% Result : Unsatisfiable 66.96s 10.18s
% Output : CNFRefutation 66.96s
% 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),c_NthRoot_Osqrt(X1),tc_RealDef_Oreal)
| c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),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,
( ~ c_HOL_Oord__class_Oless(X3,X2,X1)
| ~ c_lessequals(X2,X3,X1)
| ~ class_Orderings_Olinorder(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,
( ~ class_RealVector_Oreal__normed__div__algebra(X1)
| 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) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_norm__mult_0) ).
cnf(cls_norm__of__real_0,axiom,
( ~ class_RealVector_Oreal__normed__algebra__1(X1)
| c_RealVector_Onorm__class_Onorm(c_RealVector_Oof__real(X2,X1),X1) = c_HOL_Oabs__class_Oabs(X2,tc_RealDef_Oreal) ),
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,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| X2 = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X2,X3,X1),X3,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_lessequals(X1,X2,tc_RealDef_Oreal)
| X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__less__def_2) ).
cnf(cls_linorder__not__less_0,axiom,
( ~ class_Orderings_Olinorder(X1)
| c_HOL_Oord__class_Oless(X3,X2,X1)
| c_lessequals(X2,X3,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(c_HOL_Oplus__class_Oplus(X4,X2,X1),c_HOL_Oplus__class_Oplus(X4,X3,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| c_HOL_Oord__class_Oless(X2,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__left_0) ).
cnf(cls_class__semiring_Osemiring__rules_I6_J_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X1),X1) = X2 ),
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,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_HOL_Otimes__class_Otimes(X2,c_HOL_Oone__class_Oone(X1),X1) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I12_J_0) ).
cnf(cls_class__ringb_Oadd__r0__iff_0,axiom,
( X2 != c_HOL_Oplus__class_Oplus(X2,X3,X1)
| ~ class_Int_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oidom(X1)
| X3 = c_HOL_Ozero__class_Ozero(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,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| 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) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I19_J_0) ).
cnf(cls_class__semiring_Omul__c_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_HOL_Otimes__class_Otimes(X2,X3,X1) = c_HOL_Otimes__class_Otimes(X3,X2,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,
( ~ class_Ring__and__Field_Omult__zero(X1)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__zero__left_0) ).
cnf(cls_norm__zero_0,axiom,
( ~ class_RealVector_Oreal__normed__vector(X1)
| c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_norm__zero_0) ).
cnf(cls_mult__frac__frac_0,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| 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) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__frac__frac_0) ).
cnf(cls_class__semiring_Oadd__c_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_HOL_Oplus__class_Oplus(X2,X3,X1) = c_HOL_Oplus__class_Oplus(X3,X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__c_0) ).
cnf(cls_inverse__inverse__eq_0,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Odivision__ring(X1)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(X2,X1),X1) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__inverse__eq_0) ).
cnf(cls_real__sqrt__not__eq__zero_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
| c_NthRoot_Osqrt(X1) != c_HOL_Ozero__class_Ozero(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),c_NthRoot_Osqrt(X1),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__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,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| 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) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__divide__mult__cancel__right_0) ).
cnf(cls_eq__divide__imp_0,axiom,
( ~ class_Ring__and__Field_Ofield(X1)
| X3 = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X3,X2,X1),X2,X1)
| X2 = c_HOL_Ozero__class_Ozero(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,
( c_RealVector_Oof__real(X2,X1) != c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__algebra__1(X1)
| X2 = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__real__eq__0__iff_0) ).
cnf(cls_inverse__zero__imp__zero_0,axiom,
( c_HOL_Oinverse__class_Oinverse(X2,X1) != c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Odivision__ring(X1)
| X2 = 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),c_NthRoot_Osqrt(X1),tc_RealDef_Oreal)
| c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X1,tc_RealDef_Oreal) ),
inference(fof_simplification,[status(thm)],[cls_real__sqrt__ge__1__iff_0]) ).
cnf(c_0_50,plain,
( ~ c_HOL_Oord__class_Oless(X3,X2,X1)
| ~ c_lessequals(X2,X3,X1)
| ~ class_Orderings_Olinorder(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),c_NthRoot_Osqrt(X1),tc_RealDef_Oreal)
| c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),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,
( ~ class_RealVector_Oreal__normed__div__algebra(X1)
| 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) ),
inference(fof_simplification,[status(thm)],[cls_norm__mult_0]) ).
cnf(c_0_55,plain,
( ~ class_RealVector_Oreal__normed__algebra__1(X1)
| c_RealVector_Onorm__class_Onorm(c_RealVector_Oof__real(X2,X1),X1) = c_HOL_Oabs__class_Oabs(X2,tc_RealDef_Oreal) ),
inference(fof_simplification,[status(thm)],[cls_norm__of__real_0]) ).
cnf(c_0_56,plain,
( ~ c_HOL_Oord__class_Oless(X3,X2,X1)
| ~ c_lessequals(X2,X3,X1)
| ~ class_Orderings_Olinorder(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,
( ~ class_RealVector_Oreal__normed__div__algebra(X1)
| 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) ),
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,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| X2 = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X2,X3,X1),X3,X1) ),
inference(fof_simplification,[status(thm)],[cls_divide__eq__eq_0]) ).
cnf(c_0_63,plain,
( ~ class_RealVector_Oreal__normed__algebra__1(X1)
| c_RealVector_Onorm__class_Onorm(c_RealVector_Oof__real(X2,X1),X1) = c_HOL_Oabs__class_Oabs(X2,tc_RealDef_Oreal) ),
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,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| X2 = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X2,X3,X1),X3,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_lessequals(X1,X2,tc_RealDef_Oreal)
| X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_RealDef_Oreal) ),
inference(fof_simplification,[status(thm)],[cls_real__less__def_2]) ).
cnf(c_0_76,plain,
( ~ class_Orderings_Olinorder(X1)
| c_HOL_Oord__class_Oless(X3,X2,X1)
| c_lessequals(X2,X3,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(c_HOL_Oplus__class_Oplus(X4,X2,X1),c_HOL_Oplus__class_Oplus(X4,X3,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| c_HOL_Oord__class_Oless(X2,X3,X1) ),
inference(fof_simplification,[status(thm)],[cls_add__less__cancel__left_0]) ).
cnf(c_0_79,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X1),X1) = X2 ),
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_lessequals(X1,X2,tc_RealDef_Oreal)
| X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_RealDef_Oreal) ),
c_0_75 ).
cnf(c_0_83,plain,
( ~ class_Orderings_Olinorder(X1)
| c_HOL_Oord__class_Oless(X3,X2,X1)
| c_lessequals(X2,X3,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,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_HOL_Otimes__class_Otimes(X2,c_HOL_Oone__class_Oone(X1),X1) = X2 ),
inference(fof_simplification,[status(thm)],[cls_class__semiring_Osemiring__rules_I12_J_0]) ).
cnf(c_0_86,plain,
( X2 != c_HOL_Oplus__class_Oplus(X2,X3,X1)
| ~ class_Int_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oidom(X1)
| X3 = c_HOL_Ozero__class_Ozero(X1) ),
inference(fof_simplification,[status(thm)],[cls_class__ringb_Oadd__r0__iff_0]) ).
cnf(c_0_87,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X2,X1),c_HOL_Oplus__class_Oplus(X4,X3,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| c_HOL_Oord__class_Oless(X2,X3,X1) ),
c_0_78 ).
cnf(c_0_88,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X1),X1) = X2 ),
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,
( c_HOL_Oord__class_Oless(X1,X2,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X2,X1,tc_RealDef_Oreal)
| X1 = X2 ),
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,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_HOL_Otimes__class_Otimes(X2,c_HOL_Oone__class_Oone(X1),X1) = X2 ),
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,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| 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) ),
inference(fof_simplification,[status(thm)],[cls_class__semiring_Osemiring__rules_I19_J_0]) ).
cnf(c_0_95,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_HOL_Otimes__class_Otimes(X2,X3,X1) = c_HOL_Otimes__class_Otimes(X3,X2,X1) ),
inference(fof_simplification,[status(thm)],[cls_class__semiring_Omul__c_0]) ).
cnf(c_0_96,plain,
( X2 != c_HOL_Oplus__class_Oplus(X2,X3,X1)
| ~ class_Int_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oidom(X1)
| X3 = c_HOL_Ozero__class_Ozero(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(X3,c_HOL_Oplus__class_Oplus(X3,X2,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
inference(spm,[status(thm)],[c_0_87,c_0_88]) ).
cnf(c_0_101,plain,
( 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)
| 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) ),
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,
( ~ class_Ring__and__Field_Omult__zero(X1)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1) ),
inference(fof_simplification,[status(thm)],[cls_mult__zero__left_0]) ).
cnf(c_0_105,plain,
( ~ class_RealVector_Oreal__normed__vector(X1)
| c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
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,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| 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) ),
c_0_94 ).
cnf(c_0_108,plain,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| 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) ),
inference(fof_simplification,[status(thm)],[cls_mult__frac__frac_0]) ).
cnf(c_0_109,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_HOL_Otimes__class_Otimes(X2,X3,X1) = c_HOL_Otimes__class_Otimes(X3,X2,X1) ),
c_0_95 ).
cnf(c_0_110,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_HOL_Oplus__class_Oplus(X2,X3,X1) = c_HOL_Oplus__class_Oplus(X3,X2,X1) ),
inference(fof_simplification,[status(thm)],[cls_class__semiring_Oadd__c_0]) ).
cnf(c_0_111,plain,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Odivision__ring(X1)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(X2,X1),X1) = X2 ),
inference(fof_simplification,[status(thm)],[cls_inverse__inverse__eq_0]) ).
cnf(c_0_112,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
| c_NthRoot_Osqrt(X1) != c_HOL_Ozero__class_Ozero(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),c_NthRoot_Osqrt(X1),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__gt__0__iff_0]) ).
cnf(c_0_114,plain,
( c_Complex_Ocomplex_OComplex(c_HOL_Oplus__class_Oplus(X2,X1,tc_RealDef_Oreal),X3) != c_Complex_Ocomplex_OComplex(X2,X3)
| c_RealVector_Oof__real(X1,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
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_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),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) = c_HOL_Oone__class_Oone(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,
( ~ class_Ring__and__Field_Omult__zero(X1)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(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,
( ~ class_RealVector_Oreal__normed__vector(X1)
| c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
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,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| 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) ),
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,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| 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) ),
inference(fof_simplification,[status(thm)],[cls_mult__divide__mult__cancel__right_0]) ).
cnf(c_0_126,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_HOL_Oplus__class_Oplus(X2,X3,X1) = c_HOL_Oplus__class_Oplus(X3,X2,X1) ),
c_0_110 ).
cnf(c_0_127,plain,
( ~ class_Ring__and__Field_Ofield(X1)
| X3 = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X3,X2,X1),X2,X1)
| X2 = c_HOL_Ozero__class_Ozero(X1) ),
inference(fof_simplification,[status(thm)],[cls_eq__divide__imp_0]) ).
cnf(c_0_128,plain,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Odivision__ring(X1)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(X2,X1),X1) = X2 ),
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_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
| c_NthRoot_Osqrt(X1) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
c_0_112 ).
cnf(c_0_131,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(X1),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal) ),
c_0_113 ).
cnf(c_0_132,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)
| 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) ),
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,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| 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) ),
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,
( ~ class_Ring__and__Field_Ofield(X1)
| X3 = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X3,X2,X1),X2,X1)
| X2 = c_HOL_Ozero__class_Ozero(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_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_Oabs__class_Oabs(X1,tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(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_Oabs__class_Oabs(X1,tc_RealDef_Oreal),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_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,
( c_RealVector_Oof__real(X2,X1) != c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__algebra__1(X1)
| X2 = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(fof_simplification,[status(thm)],[cls_of__real__eq__0__iff_0]) ).
cnf(c_0_147,negated_conjecture,
( ~ 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)
| 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) ),
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_Oinverse__class_Oinverse(X1,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_HOL_Otimes__class_Otimes(X1,c_HOL_Oinverse__class_Odivide(X2,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X2 ),
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_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)
| c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(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,
( c_HOL_Oinverse__class_Oinverse(X2,X1) != c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Odivision__ring(X1)
| X2 = c_HOL_Ozero__class_Ozero(X1) ),
inference(fof_simplification,[status(thm)],[cls_inverse__zero__imp__zero_0]) ).
cnf(c_0_153,plain,
( c_RealVector_Oof__real(X2,X1) != c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__algebra__1(X1)
| X2 = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
c_0_146 ).
cnf(c_0_154,negated_conjecture,
( c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| 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) ),
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,
( c_HOL_Oinverse__class_Oinverse(X2,X1) != c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Odivision__ring(X1)
| X2 = 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
% 0.00/0.03 % Problem : ALG360-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n016.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 21 13:22:08 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 66.96/10.18 % Version: 3.5.1
% 66.96/10.18 % Preprocessing class: FMLMSMSSSSSNFFN.
% 66.96/10.18 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 66.96/10.18 % Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4c with 1500s (5) cores
% 66.96/10.18 % Starting new_bool_3 with 300s (1) cores
% 66.96/10.18 % Starting new_bool_1 with 300s (1) cores
% 66.96/10.18 % Starting sh5l with 300s (1) cores
% 66.96/10.18 % G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4c with pid 2507555 completed with status 0
% 66.96/10.18 % Result found by G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4c
% 66.96/10.18 % Preprocessing class: FMLMSMSSSSSNFFN.
% 66.96/10.18 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 66.96/10.18 % Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4c with 1500s (5) cores
% 66.96/10.18 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 66.96/10.18 % No SInE strategy applied
% 66.96/10.18 % Search class: FGHSM-SSLM32-DFFFFFNN
% 66.96/10.18 % Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 66.96/10.18 % Starting SubtermCWHack with 136s (1) cores
% 66.96/10.18 % Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4c with 151s (1) cores
% 66.96/10.18 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2mI with 113s (1) cores
% 66.96/10.18 % Starting G-E--_208_B07_F1_SE_CS_SP_PS_S4d with 113s (1) cores
% 66.96/10.18 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 113s (1) cores
% 66.96/10.18 % G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4c with pid 2507563 completed with status 0
% 66.96/10.18 % Result found by G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4c
% 66.96/10.18 % Preprocessing class: FMLMSMSSSSSNFFN.
% 66.96/10.18 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 66.96/10.18 % Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4c with 1500s (5) cores
% 66.96/10.18 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 66.96/10.18 % No SInE strategy applied
% 66.96/10.18 % Search class: FGHSM-SSLM32-DFFFFFNN
% 66.96/10.18 % Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 66.96/10.18 % Starting SubtermCWHack with 136s (1) cores
% 66.96/10.18 % Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4c with 151s (1) cores
% 66.96/10.18 % Preprocessing time : 0.014 s
% 66.96/10.18
% 66.96/10.18 % Proof found!
% 66.96/10.18 % SZS status Unsatisfiable
% 66.96/10.18 % SZS output start CNFRefutation
% See solution above
% 66.96/10.19 % Parsed axioms : 1197
% 66.96/10.19 % Removed by relevancy pruning/SinE : 0
% 66.96/10.19 % Initial clauses : 1197
% 66.96/10.19 % Removed in clause preprocessing : 0
% 66.96/10.19 % Initial clauses in saturation : 1197
% 66.96/10.19 % Processed clauses : 51220
% 66.96/10.19 % ...of these trivial : 1010
% 66.96/10.19 % ...subsumed : 43620
% 66.96/10.19 % ...remaining for further processing : 6590
% 66.96/10.19 % Other redundant clauses eliminated : 246
% 66.96/10.19 % Clauses deleted for lack of memory : 0
% 66.96/10.19 % Backward-subsumed : 141
% 66.96/10.19 % Backward-rewritten : 845
% 66.96/10.19 % Generated clauses : 454178
% 66.96/10.19 % ...of the previous two non-redundant : 425557
% 66.96/10.19 % ...aggressively subsumed : 0
% 66.96/10.19 % Contextual simplify-reflections : 14
% 66.96/10.19 % Paramodulations : 453791
% 66.96/10.19 % Factorizations : 19
% 66.96/10.19 % NegExts : 0
% 66.96/10.19 % Equation resolutions : 368
% 66.96/10.19 % Disequality decompositions : 0
% 66.96/10.19 % Total rewrite steps : 491260
% 66.96/10.19 % ...of those cached : 479721
% 66.96/10.19 % Propositional unsat checks : 0
% 66.96/10.19 % Propositional check models : 0
% 66.96/10.19 % Propositional check unsatisfiable : 0
% 66.96/10.19 % Propositional clauses : 0
% 66.96/10.19 % Propositional clauses after purity: 0
% 66.96/10.19 % Propositional unsat core size : 0
% 66.96/10.19 % Propositional preprocessing time : 0.000
% 66.96/10.19 % Propositional encoding time : 0.000
% 66.96/10.19 % Propositional solver time : 0.000
% 66.96/10.19 % Success case prop preproc time : 0.000
% 66.96/10.19 % Success case prop encoding time : 0.000
% 66.96/10.19 % Success case prop solver time : 0.000
% 66.96/10.19 % Current number of processed clauses : 5604
% 66.96/10.19 % Positive orientable unit clauses : 746
% 66.96/10.19 % Positive unorientable unit clauses: 25
% 66.96/10.19 % Negative unit clauses : 1903
% 66.96/10.19 % Non-unit-clauses : 2930
% 66.96/10.19 % Current number of unprocessed clauses: 373609
% 66.96/10.19 % ...number of literals in the above : 1115009
% 66.96/10.19 % Current number of archived formulas : 0
% 66.96/10.19 % Current number of archived clauses : 986
% 66.96/10.19 % Clause-clause subsumption calls (NU) : 677752
% 66.96/10.19 % Rec. Clause-clause subsumption calls : 300603
% 66.96/10.19 % Non-unit clause-clause subsumptions : 4119
% 66.96/10.19 % Unit Clause-clause subsumption calls : 220646
% 66.96/10.19 % Rewrite failures with RHS unbound : 4
% 66.96/10.19 % BW rewrite match attempts : 6468
% 66.96/10.19 % BW rewrite match successes : 1884
% 66.96/10.19 % Condensation attempts : 0
% 66.96/10.19 % Condensation successes : 0
% 66.96/10.19 % Termbank termtop insertions : 8691929
% 66.96/10.19 % Search garbage collected termcells : 2336
% 66.96/10.19
% 66.96/10.19 % -------------------------------------------------
% 66.96/10.19 % User time : 9.172 s
% 66.96/10.19 % System time : 0.301 s
% 66.96/10.19 % Total time : 9.473 s
% 66.96/10.19 % Maximum resident set size: 5988 pages
% 66.96/10.19
% 66.96/10.19 % -------------------------------------------------
% 66.96/10.19 % User time : 45.965 s
% 66.96/10.19 % System time : 1.526 s
% 66.96/10.19 % Total time : 47.491 s
% 66.96/10.19 % Maximum resident set size: 5632 pages
% 66.96/10.19 % E exiting
%------------------------------------------------------------------------------