%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ALG356-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/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 11:55:57 AM UTC 2026
% Result : Unsatisfiable 9.11s 1.66s
% Output : CNFRefutation 9.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 58
% Syntax : Number of clauses : 208 ( 106 unt; 18 nHn; 123 RR)
% Number of literals : 349 ( 203 equ; 143 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 16 ( 14 usr; 1 prp; 0-3 aty)
% Number of functors : 17 ( 17 usr; 3 con; 0-3 aty)
% Number of variables : 242 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
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/sandbox2/benchmark/theBenchmark.p',cls_norm__zero_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/sandbox2/benchmark/theBenchmark.p',cls_norm__of__real_0) ).
cnf(cls_complex__zero__def_0,axiom,
c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Complex_Ocomplex_OComplex(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complex__zero__def_0) ).
cnf(cls_complex__of__real__def_0,axiom,
c_RealVector_Oof__real(X1,tc_Complex_Ocomplex) = c_Complex_Ocomplex_OComplex(X1,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complex__of__real__def_0) ).
cnf(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).
cnf(cls_sgn__zero_0,axiom,
( ~ class_RealVector_Oreal__normed__vector(X1)
| c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sgn__zero_0) ).
cnf(cls_abs__not__less__zero_0,axiom,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__not__less__zero_0) ).
cnf(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1,axiom,
class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1) ).
cnf(cls_real__mult__left__cancel_0,axiom,
( c_HOL_Otimes__class_Otimes(X1,X2,tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(X1,X3,tc_RealDef_Oreal)
| X2 = X3
| X1 = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__left__cancel_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/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I12_J_0) ).
cnf(cls_sgn__1__neg_0,axiom,
( c_HOL_Osgn__class_Osgn(X2,X1) != c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sgn__1__neg_0) ).
cnf(clsarity_RealDef__Oreal__RealVector_Oreal__normed__vector,axiom,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__vector) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add__abs,axiom,
class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add__abs) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1) ).
cnf(cls_class__ring_Oneg__mul_0,axiom,
( ~ class_Int_Onumber__ring(X1)
| c_HOL_Ouminus__class_Ouminus(X2,X1) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X1),X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ring_Oneg__mul_0) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__idom,axiom,
class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__idom) ).
cnf(cls_of__real__1_0,axiom,
( ~ class_RealVector_Oreal__algebra__1(X1)
| c_RealVector_Oof__real(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X1) = c_HOL_Oone__class_Oone(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__real__1_0) ).
cnf(clsarity_RealDef__Oreal__Int_Onumber__ring,axiom,
class_Int_Onumber__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Int_Onumber__ring) ).
cnf(cls_equation__minus__iff_1,axiom,
( ~ class_OrderedGroup_Ogroup__add(X1)
| X2 = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X2,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equation__minus__iff_1) ).
cnf(cls_norm__one_0,axiom,
( ~ class_RealVector_Oreal__normed__algebra__1(X1)
| c_RealVector_Onorm__class_Onorm(c_HOL_Oone__class_Oone(X1),X1) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__one_0) ).
cnf(cls_nonzero__of__real__divide_0,axiom,
( ~ class_RealVector_Oreal__field(X1)
| X3 = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_RealVector_Oof__real(c_HOL_Oinverse__class_Odivide(X2,X3,tc_RealDef_Oreal),X1) = c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(X2,X1),c_RealVector_Oof__real(X3,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__of__real__divide_0) ).
cnf(clsarity_Complex__Ocomplex__RealVector_Oreal__algebra__1,axiom,
class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__algebra__1) ).
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/sandbox2/benchmark/theBenchmark.p',cls_real__zero__not__eq__one_0) ).
cnf(cls_inverse__1_0,axiom,
( ~ class_Ring__and__Field_Odivision__ring(X1)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(X1),X1) = c_HOL_Oone__class_Oone(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__1_0) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add,axiom,
class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add) ).
cnf(clsarity_Complex__Ocomplex__RealVector_Oreal__field,axiom,
class_RealVector_Oreal__field(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__field) ).
cnf(cls_divide__1_0,axiom,
( ~ class_Ring__and__Field_Ofield(X1)
| c_HOL_Oinverse__class_Odivide(X2,c_HOL_Oone__class_Oone(X1),X1) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__1_0) ).
cnf(cls_divide__inverse_0,axiom,
( ~ class_Ring__and__Field_Ofield(X1)
| c_HOL_Oinverse__class_Odivide(X2,X3,X1) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Oinverse__class_Oinverse(X3,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__inverse_0) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__ring,axiom,
class_Ring__and__Field_Odivision__ring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__ring) ).
cnf(cls_inverse__eq__iff__eq_0,axiom,
( c_HOL_Oinverse__class_Oinverse(X2,X1) != c_HOL_Oinverse__class_Oinverse(X3,X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Odivision__ring(X1)
| X2 = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__eq__iff__eq_0) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Odivision__ring,axiom,
class_Ring__and__Field_Odivision__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Odivision__ring) ).
cnf(cls_abs__minus__cancel_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(X2,X1),X1) = c_HOL_Oabs__class_Oabs(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__minus__cancel_0) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Ofield,axiom,
class_Ring__and__Field_Ofield(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ofield) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ofield,axiom,
class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ofield) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1) ).
cnf(cls_of__real__divide_0,axiom,
( ~ class_RealVector_Oreal__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| c_RealVector_Oof__real(c_HOL_Oinverse__class_Odivide(X2,X3,tc_RealDef_Oreal),X1) = c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(X2,X1),c_RealVector_Oof__real(X3,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__real__divide_0) ).
cnf(clsarity_RealDef__Oreal__RealVector_Oreal__algebra__1,axiom,
class_RealVector_Oreal__algebra__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__algebra__1) ).
cnf(cls_nonzero__inverse__minus__eq_0,axiom,
( ~ class_Ring__and__Field_Odivision__ring(X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Ouminus__class_Ouminus(X2,X1),X1) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Oinverse(X2,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__inverse__minus__eq_0) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Odivision__by__zero,axiom,
class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Odivision__by__zero) ).
cnf(cls_inverse__divide_0,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1) = c_HOL_Oinverse__class_Odivide(X3,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__divide_0) ).
cnf(cls_abs__mult__self_0,axiom,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X2,X1),X1) = c_HOL_Otimes__class_Otimes(X2,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__mult__self_0) ).
cnf(clsarity_RealDef__Oreal__RealVector_Oreal__field,axiom,
class_RealVector_Oreal__field(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__field) ).
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/sandbox2/benchmark/theBenchmark.p',cls_real__mult__1_0) ).
cnf(cls_of__real__def_0,axiom,
( ~ class_RealVector_Oreal__algebra__1(X1)
| c_RealVector_Oof__real(X2,X1) = c_RealVector_OscaleR__class_OscaleR(X2,c_HOL_Oone__class_Oone(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__real__def_0) ).
cnf(cls_right__inverse__eq_1,axiom,
( ~ class_Ring__and__Field_Ofield(X1)
| c_HOL_Oinverse__class_Odivide(X2,X2,X1) = c_HOL_Oone__class_Oone(X1)
| X2 = c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__inverse__eq_1) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero,axiom,
class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero) ).
cnf(cls_Re__complex__of__real_0,axiom,
c_Complex_ORe(c_RealVector_Oof__real(X1,tc_Complex_Ocomplex)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Re__complex__of__real_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/sandbox2/benchmark/theBenchmark.p',cls_of__real__eq__0__iff_0) ).
cnf(cls_conjecture_0,negated_conjecture,
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/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(cls_real__divide__square__eq_0,axiom,
c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X1,X2,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X1,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(X2,X1,tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__divide__square__eq_0) ).
cnf(cls_divide_OscaleR_0,axiom,
( ~ class_RealVector_Oreal__normed__field(X1)
| c_HOL_Oinverse__class_Odivide(c_RealVector_OscaleR__class_OscaleR(X2,X3,X1),X4,X1) = c_RealVector_OscaleR__class_OscaleR(X2,c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide_OscaleR_0) ).
cnf(cls_norm__divide_0,axiom,
( ~ class_RealVector_Oreal__normed__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1) = c_HOL_Oinverse__class_Odivide(c_RealVector_Onorm__class_Onorm(X2,X1),c_RealVector_Onorm__class_Onorm(X3,X1),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__divide_0) ).
cnf(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__field,axiom,
class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__field) ).
cnf(cls_abs__norm__cancel_0,axiom,
( ~ class_RealVector_Oreal__normed__vector(X1)
| c_HOL_Oabs__class_Oabs(c_RealVector_Onorm__class_Onorm(X2,X1),tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__norm__cancel_0) ).
cnf(cls_norm__scaleR_0,axiom,
( ~ class_RealVector_Oreal__normed__vector(X1)
| c_RealVector_Onorm__class_Onorm(c_RealVector_OscaleR__class_OscaleR(X2,X3,X1),X1) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X3,X1),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__scaleR_0) ).
cnf(cls_complex__mod__cnj_0,axiom,
c_RealVector_Onorm__class_Onorm(c_Complex_Ocnj(X1),tc_Complex_Ocomplex) = c_RealVector_Onorm__class_Onorm(X1,tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complex__mod__cnj_0) ).
cnf(cls_nonzero__norm__divide_0,axiom,
( ~ class_RealVector_Oreal__normed__field(X1)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1) = c_HOL_Oinverse__class_Odivide(c_RealVector_Onorm__class_Onorm(X2,X1),c_RealVector_Onorm__class_Onorm(X3,X1),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__norm__divide_0) ).
cnf(cls_b_0,axiom,
v_b != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_b_0) ).
cnf(c_0_58,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_59,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_60,axiom,
c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Complex_Ocomplex_OComplex(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),
cls_complex__zero__def_0 ).
cnf(c_0_61,axiom,
c_RealVector_Oof__real(X1,tc_Complex_Ocomplex) = c_Complex_Ocomplex_OComplex(X1,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),
cls_complex__of__real__def_0 ).
cnf(c_0_62,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_58 ).
cnf(c_0_63,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector ).
cnf(c_0_64,plain,
( ~ class_RealVector_Oreal__normed__vector(X1)
| c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1) ),
inference(fof_simplification,[status(thm)],[cls_sgn__zero_0]) ).
cnf(c_0_65,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
inference(fof_simplification,[status(thm)],[cls_abs__not__less__zero_0]) ).
cnf(c_0_66,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_59 ).
cnf(c_0_67,plain,
c_RealVector_Oof__real(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(rw,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_68,axiom,
class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1 ).
cnf(c_0_69,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_62,c_0_63]) ).
cnf(c_0_70,plain,
( c_HOL_Otimes__class_Otimes(X1,X2,tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(X1,X3,tc_RealDef_Oreal)
| X2 = X3
| X1 = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(fof_simplification,[status(thm)],[cls_real__mult__left__cancel_0]) ).
cnf(c_0_71,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_72,plain,
( c_HOL_Osgn__class_Osgn(X2,X1) != c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
inference(fof_simplification,[status(thm)],[cls_sgn__1__neg_0]) ).
cnf(c_0_73,plain,
( ~ class_RealVector_Oreal__normed__vector(X1)
| c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1) ),
c_0_64 ).
cnf(c_0_74,axiom,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__RealVector_Oreal__normed__vector ).
cnf(c_0_75,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
c_0_65 ).
cnf(c_0_76,plain,
c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_68])]),c_0_69]) ).
cnf(c_0_77,axiom,
class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add__abs ).
cnf(c_0_78,plain,
( c_HOL_Otimes__class_Otimes(X1,X2,tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(X1,X3,tc_RealDef_Oreal)
| X2 = X3
| X1 = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
c_0_70 ).
cnf(c_0_79,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_71 ).
cnf(c_0_80,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1 ).
cnf(c_0_81,plain,
( ~ class_Int_Onumber__ring(X1)
| c_HOL_Ouminus__class_Ouminus(X2,X1) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X1),X1),X2,X1) ),
inference(fof_simplification,[status(thm)],[cls_class__ring_Oneg__mul_0]) ).
cnf(c_0_82,plain,
( c_HOL_Osgn__class_Osgn(X2,X1) != c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
c_0_72 ).
cnf(c_0_83,plain,
c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_84,axiom,
class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Oordered__idom ).
cnf(c_0_85,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_77])]) ).
cnf(c_0_86,plain,
( ~ class_RealVector_Oreal__algebra__1(X1)
| c_RealVector_Oof__real(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X1) = c_HOL_Oone__class_Oone(X1) ),
inference(fof_simplification,[status(thm)],[cls_of__real__1_0]) ).
cnf(c_0_87,plain,
( c_HOL_Otimes__class_Otimes(X2,X1,tc_RealDef_Oreal) != X2
| X2 = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| X1 = c_HOL_Oone__class_Oone(tc_RealDef_Oreal) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_80])]) ).
cnf(c_0_88,plain,
( ~ class_Int_Onumber__ring(X1)
| c_HOL_Ouminus__class_Ouminus(X2,X1) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X1),X1),X2,X1) ),
c_0_81 ).
cnf(c_0_89,axiom,
class_Int_Onumber__ring(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Int_Onumber__ring ).
cnf(c_0_90,plain,
c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_84])]),c_0_85]) ).
cnf(c_0_91,plain,
( ~ class_OrderedGroup_Ogroup__add(X1)
| X2 = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X2,X1),X1) ),
inference(fof_simplification,[status(thm)],[cls_equation__minus__iff_1]) ).
cnf(c_0_92,plain,
( ~ class_RealVector_Oreal__normed__algebra__1(X1)
| c_RealVector_Onorm__class_Onorm(c_HOL_Oone__class_Oone(X1),X1) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal) ),
inference(fof_simplification,[status(thm)],[cls_norm__one_0]) ).
cnf(c_0_93,plain,
( ~ class_RealVector_Oreal__field(X1)
| X3 = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_RealVector_Oof__real(c_HOL_Oinverse__class_Odivide(X2,X3,tc_RealDef_Oreal),X1) = c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(X2,X1),c_RealVector_Oof__real(X3,X1),X1) ),
inference(fof_simplification,[status(thm)],[cls_nonzero__of__real__divide_0]) ).
cnf(c_0_94,plain,
( ~ class_RealVector_Oreal__algebra__1(X1)
| c_RealVector_Oof__real(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X1) = c_HOL_Oone__class_Oone(X1) ),
c_0_86 ).
cnf(c_0_95,axiom,
class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__RealVector_Oreal__algebra__1 ).
cnf(c_0_96,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_97,plain,
( ~ class_Ring__and__Field_Odivision__ring(X1)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(X1),X1) = c_HOL_Oone__class_Oone(X1) ),
inference(fof_simplification,[status(thm)],[cls_inverse__1_0]) ).
cnf(c_0_98,plain,
( c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal) != c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| X1 = c_HOL_Oone__class_Oone(tc_RealDef_Oreal) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88]),c_0_89])]),c_0_90]) ).
cnf(c_0_99,plain,
( ~ class_OrderedGroup_Ogroup__add(X1)
| X2 = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X2,X1),X1) ),
c_0_91 ).
cnf(c_0_100,axiom,
class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add ).
cnf(c_0_101,plain,
( ~ class_RealVector_Oreal__normed__algebra__1(X1)
| c_RealVector_Onorm__class_Onorm(c_HOL_Oone__class_Oone(X1),X1) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal) ),
c_0_92 ).
cnf(c_0_102,plain,
( ~ class_RealVector_Oreal__field(X1)
| X3 = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_RealVector_Oof__real(c_HOL_Oinverse__class_Odivide(X2,X3,tc_RealDef_Oreal),X1) = c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(X2,X1),c_RealVector_Oof__real(X3,X1),X1) ),
c_0_93 ).
cnf(c_0_103,plain,
c_RealVector_Oof__real(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),
inference(spm,[status(thm)],[c_0_94,c_0_95]) ).
cnf(c_0_104,axiom,
class_RealVector_Oreal__field(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__RealVector_Oreal__field ).
cnf(c_0_105,plain,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal),
c_0_96 ).
cnf(c_0_106,plain,
( ~ class_Ring__and__Field_Ofield(X1)
| c_HOL_Oinverse__class_Odivide(X2,c_HOL_Oone__class_Oone(X1),X1) = X2 ),
inference(fof_simplification,[status(thm)],[cls_divide__1_0]) ).
cnf(c_0_107,plain,
( ~ class_Ring__and__Field_Ofield(X1)
| c_HOL_Oinverse__class_Odivide(X2,X3,X1) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Oinverse__class_Oinverse(X3,X1),X1) ),
inference(fof_simplification,[status(thm)],[cls_divide__inverse_0]) ).
cnf(c_0_108,plain,
( ~ class_Ring__and__Field_Odivision__ring(X1)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(X1),X1) = c_HOL_Oone__class_Oone(X1) ),
c_0_97 ).
cnf(c_0_109,axiom,
class_Ring__and__Field_Odivision__ring(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__ring ).
cnf(c_0_110,plain,
( c_HOL_Oinverse__class_Oinverse(X2,X1) != c_HOL_Oinverse__class_Oinverse(X3,X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Odivision__ring(X1)
| X2 = X3 ),
inference(fof_simplification,[status(thm)],[cls_inverse__eq__iff__eq_0]) ).
cnf(c_0_111,axiom,
class_Ring__and__Field_Odivision__ring(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Odivision__ring ).
cnf(c_0_112,plain,
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(X2,X1),X1) = c_HOL_Oabs__class_Oabs(X2,X1) ),
inference(fof_simplification,[status(thm)],[cls_abs__minus__cancel_0]) ).
cnf(c_0_113,plain,
( X1 != c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_99]),c_0_100])]) ).
cnf(c_0_114,plain,
c_RealVector_Onorm__class_Onorm(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal),
inference(spm,[status(thm)],[c_0_101,c_0_68]) ).
cnf(c_0_115,plain,
c_RealVector_Oof__real(c_HOL_Oinverse__class_Odivide(X1,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(X1,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_103]),c_0_104])]),c_0_105]) ).
cnf(c_0_116,plain,
( ~ class_Ring__and__Field_Ofield(X1)
| c_HOL_Oinverse__class_Odivide(X2,c_HOL_Oone__class_Oone(X1),X1) = X2 ),
c_0_106 ).
cnf(c_0_117,axiom,
class_Ring__and__Field_Ofield(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Ofield ).
cnf(c_0_118,plain,
( ~ class_Ring__and__Field_Ofield(X1)
| c_HOL_Oinverse__class_Odivide(X2,X3,X1) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Oinverse__class_Oinverse(X3,X1),X1) ),
c_0_107 ).
cnf(c_0_119,plain,
c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),
inference(spm,[status(thm)],[c_0_108,c_0_109]) ).
cnf(c_0_120,axiom,
class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Ofield ).
cnf(c_0_121,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1 ).
cnf(c_0_122,plain,
( ~ class_RealVector_Oreal__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| c_RealVector_Oof__real(c_HOL_Oinverse__class_Odivide(X2,X3,tc_RealDef_Oreal),X1) = c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(X2,X1),c_RealVector_Oof__real(X3,X1),X1) ),
inference(fof_simplification,[status(thm)],[cls_of__real__divide_0]) ).
cnf(c_0_123,axiom,
class_RealVector_Oreal__algebra__1(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__RealVector_Oreal__algebra__1 ).
cnf(c_0_124,plain,
( ~ class_Ring__and__Field_Odivision__ring(X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Ouminus__class_Ouminus(X2,X1),X1) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Oinverse(X2,X1),X1) ),
inference(fof_simplification,[status(thm)],[cls_nonzero__inverse__minus__eq_0]) ).
cnf(c_0_125,plain,
( c_HOL_Oinverse__class_Oinverse(X2,X1) != c_HOL_Oinverse__class_Oinverse(X3,X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Odivision__ring(X1)
| X2 = X3 ),
c_0_110 ).
cnf(c_0_126,plain,
c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal),
inference(spm,[status(thm)],[c_0_108,c_0_111]) ).
cnf(c_0_127,axiom,
class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Odivision__by__zero ).
cnf(c_0_128,plain,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1) = c_HOL_Oinverse__class_Odivide(X3,X2,X1) ),
inference(fof_simplification,[status(thm)],[cls_inverse__divide_0]) ).
cnf(c_0_129,plain,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X2,X1),X1) = c_HOL_Otimes__class_Otimes(X2,X2,X1) ),
inference(fof_simplification,[status(thm)],[cls_abs__mult__self_0]) ).
cnf(c_0_130,plain,
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(X2,X1),X1) = c_HOL_Oabs__class_Oabs(X2,X1) ),
c_0_112 ).
cnf(c_0_131,plain,
c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal),
inference(er,[status(thm)],[c_0_113]) ).
cnf(c_0_132,plain,
c_HOL_Oabs__class_Oabs(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal),
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_103]),c_0_68])]),c_0_114]) ).
cnf(c_0_133,plain,
c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(X1,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_RealVector_Oof__real(X1,tc_Complex_Ocomplex),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_116]),c_0_117])]) ).
cnf(c_0_134,plain,
c_HOL_Oinverse__class_Odivide(X1,c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_119]),c_0_120])]) ).
cnf(c_0_135,plain,
c_HOL_Otimes__class_Otimes(X1,c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X1,
inference(spm,[status(thm)],[c_0_79,c_0_121]) ).
cnf(c_0_136,plain,
( ~ class_RealVector_Oreal__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| c_RealVector_Oof__real(c_HOL_Oinverse__class_Odivide(X2,X3,tc_RealDef_Oreal),X1) = c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(X2,X1),c_RealVector_Oof__real(X3,X1),X1) ),
c_0_122 ).
cnf(c_0_137,plain,
c_RealVector_Oof__real(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal),
inference(spm,[status(thm)],[c_0_94,c_0_123]) ).
cnf(c_0_138,axiom,
class_RealVector_Oreal__field(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__RealVector_Oreal__field ).
cnf(c_0_139,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_140,plain,
( ~ class_Ring__and__Field_Odivision__ring(X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Ouminus__class_Ouminus(X2,X1),X1) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Oinverse(X2,X1),X1) ),
c_0_124 ).
cnf(c_0_141,plain,
( ~ class_RealVector_Oreal__algebra__1(X1)
| c_RealVector_Oof__real(X2,X1) = c_RealVector_OscaleR__class_OscaleR(X2,c_HOL_Oone__class_Oone(X1),X1) ),
inference(fof_simplification,[status(thm)],[cls_of__real__def_0]) ).
cnf(c_0_142,plain,
( ~ class_Ring__and__Field_Ofield(X1)
| c_HOL_Oinverse__class_Odivide(X2,X2,X1) = c_HOL_Oone__class_Oone(X1)
| X2 = c_HOL_Ozero__class_Ozero(X1) ),
inference(fof_simplification,[status(thm)],[cls_right__inverse__eq_1]) ).
cnf(c_0_143,axiom,
class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero ).
cnf(c_0_144,plain,
( c_HOL_Oinverse__class_Oinverse(X1,tc_RealDef_Oreal) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal)
| c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_126]),c_0_111]),c_0_127])]) ).
cnf(c_0_145,plain,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1) = c_HOL_Oinverse__class_Odivide(X3,X2,X1) ),
c_0_128 ).
cnf(c_0_146,plain,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X2,X1),X1) = c_HOL_Otimes__class_Otimes(X2,X2,X1) ),
c_0_129 ).
cnf(c_0_147,plain,
c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),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_130,c_0_131]),c_0_132]),c_0_77])]) ).
cnf(c_0_148,axiom,
c_Complex_ORe(c_RealVector_Oof__real(X1,tc_Complex_Ocomplex)) = X1,
cls_Re__complex__of__real_0 ).
cnf(c_0_149,plain,
c_RealVector_Oof__real(c_HOL_Oinverse__class_Odivide(X1,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_Complex_Ocomplex) = c_RealVector_Oof__real(X1,tc_Complex_Ocomplex),
inference(rw,[status(thm)],[c_0_115,c_0_133]) ).
cnf(c_0_150,plain,
c_HOL_Oinverse__class_Odivide(X1,c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X1,
inference(rw,[status(thm)],[c_0_134,c_0_135]) ).
cnf(c_0_151,plain,
c_RealVector_Oof__real(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X1,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Oof__real(X1,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_137]),c_0_138]),c_0_127])]) ).
cnf(c_0_152,plain,
c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X1,tc_RealDef_Oreal) = c_HOL_Oinverse__class_Oinverse(X1,tc_RealDef_Oreal),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_118]),c_0_117])]) ).
cnf(c_0_153,plain,
c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Oinverse(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_131]),c_0_126]),c_0_111])]),c_0_90]) ).
cnf(c_0_154,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_155,negated_conjecture,
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),
inference(fof_simplification,[status(thm)],[cls_conjecture_0]) ).
cnf(c_0_156,plain,
( ~ class_RealVector_Oreal__algebra__1(X1)
| c_RealVector_Oof__real(X2,X1) = c_RealVector_OscaleR__class_OscaleR(X2,c_HOL_Oone__class_Oone(X1),X1) ),
c_0_141 ).
cnf(c_0_157,plain,
( ~ class_Ring__and__Field_Ofield(X1)
| c_HOL_Oinverse__class_Odivide(X2,X2,X1) = c_HOL_Oone__class_Oone(X1)
| X2 = c_HOL_Ozero__class_Ozero(X1) ),
c_0_142 ).
cnf(c_0_158,plain,
( c_HOL_Oinverse__class_Oinverse(X1,tc_Complex_Ocomplex) != c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)
| c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_119]),c_0_109]),c_0_143])]) ).
cnf(c_0_159,plain,
( c_HOL_Oinverse__class_Odivide(X2,X1,tc_RealDef_Oreal) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal)
| c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(X1,X2,tc_RealDef_Oreal) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_145]),c_0_117]),c_0_127])]) ).
cnf(c_0_160,axiom,
c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X1,X2,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X1,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(X2,X1,tc_RealDef_Oreal),
cls_real__divide__square__eq_0 ).
cnf(c_0_161,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),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_146,c_0_147]),c_0_139]),c_0_84])]) ).
cnf(c_0_162,plain,
c_HOL_Oinverse__class_Odivide(X1,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_148,c_0_149]),c_0_148]) ).
cnf(c_0_163,plain,
c_RealVector_Oof__real(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X1,tc_RealDef_Oreal),tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_RealVector_Oof__real(X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_103]),c_0_104]),c_0_143])]) ).
cnf(c_0_164,plain,
c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Oinverse(X1,tc_Complex_Ocomplex),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_145,c_0_150]),c_0_120]),c_0_143])]) ).
cnf(c_0_165,plain,
c_RealVector_Oof__real(c_HOL_Oinverse__class_Oinverse(X1,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Oinverse(c_RealVector_Oof__real(X1,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_151,c_0_152]),c_0_152]) ).
cnf(c_0_166,plain,
c_HOL_Oinverse__class_Oinverse(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(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_99,c_0_153]),c_0_100])]) ).
cnf(c_0_167,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_154 ).
cnf(c_0_168,negated_conjecture,
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),
c_0_155 ).
cnf(c_0_169,plain,
( ~ class_RealVector_Oreal__algebra__1(X3)
| ~ class_Ring__and__Field_Ofield(X3)
| X2 = c_HOL_Ozero__class_Ozero(X3)
| c_RealVector_OscaleR__class_OscaleR(X1,c_HOL_Oinverse__class_Odivide(X2,X2,X3),X3) = c_RealVector_Oof__real(X1,X3) ),
inference(spm,[status(thm)],[c_0_156,c_0_157]) ).
cnf(c_0_170,plain,
( ~ class_RealVector_Oreal__normed__field(X1)
| c_HOL_Oinverse__class_Odivide(c_RealVector_OscaleR__class_OscaleR(X2,X3,X1),X4,X1) = c_RealVector_OscaleR__class_OscaleR(X2,c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1) ),
inference(fof_simplification,[status(thm)],[cls_divide_OscaleR_0]) ).
cnf(c_0_171,plain,
( c_HOL_Oinverse__class_Odivide(X2,X1,tc_Complex_Ocomplex) != c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)
| c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(X1,X2,tc_Complex_Ocomplex) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_158,c_0_145]),c_0_120]),c_0_143])]) ).
cnf(c_0_172,plain,
( c_RealVector_Oof__real(c_HOL_Oinverse__class_Odivide(X2,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal)
| c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(X1,tc_RealDef_Oreal),c_RealVector_Oof__real(X2,tc_RealDef_Oreal),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_159,c_0_136]),c_0_138]),c_0_127])]) ).
cnf(c_0_173,plain,
c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_160,c_0_161]),c_0_161]),c_0_162]) ).
cnf(c_0_174,plain,
c_RealVector_Oof__real(c_HOL_Oinverse__class_Oinverse(X1,tc_RealDef_Oreal),tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Oinverse(c_RealVector_Oof__real(X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_163,c_0_152]),c_0_164]) ).
cnf(c_0_175,plain,
c_HOL_Oinverse__class_Oinverse(c_RealVector_Oof__real(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_RealVector_Oof__real(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(spm,[status(thm)],[c_0_165,c_0_166]) ).
cnf(c_0_176,plain,
( c_HOL_Oinverse__class_Oinverse(c_RealVector_Oof__real(X1,tc_RealDef_Oreal),tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_HOL_Oinverse__class_Oinverse(X1,tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_167,c_0_165]),c_0_123])]) ).
cnf(c_0_177,plain,
( ~ class_RealVector_Oreal__normed__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1) = c_HOL_Oinverse__class_Odivide(c_RealVector_Onorm__class_Onorm(X2,X1),c_RealVector_Onorm__class_Onorm(X3,X1),tc_RealDef_Oreal) ),
inference(fof_simplification,[status(thm)],[cls_norm__divide_0]) ).
cnf(c_0_178,negated_conjecture,
( c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Odivide(c_RealVector_OscaleR__class_OscaleR(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(X1,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal)
| X1 = 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_168,c_0_169]),c_0_120]),c_0_95])]) ).
cnf(c_0_179,plain,
( ~ class_RealVector_Oreal__normed__field(X1)
| c_HOL_Oinverse__class_Odivide(c_RealVector_OscaleR__class_OscaleR(X2,X3,X1),X4,X1) = c_RealVector_OscaleR__class_OscaleR(X2,c_HOL_Oinverse__class_Odivide(X3,X4,X1),X1) ),
c_0_170 ).
cnf(c_0_180,axiom,
class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__RealVector_Oreal__normed__field ).
cnf(c_0_181,plain,
( c_RealVector_Oof__real(c_HOL_Oinverse__class_Odivide(X2,X1,tc_RealDef_Oreal),tc_Complex_Ocomplex) != c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)
| c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(X1,tc_Complex_Ocomplex),c_RealVector_Oof__real(X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_171,c_0_136]),c_0_104]),c_0_143])]) ).
cnf(c_0_182,plain,
c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_RealVector_Oof__real(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_172,c_0_173]),c_0_137])]) ).
cnf(c_0_183,plain,
( c_HOL_Oinverse__class_Oinverse(c_RealVector_Oof__real(X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_HOL_Oinverse__class_Oinverse(X1,tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_167,c_0_174]),c_0_95])]) ).
cnf(c_0_184,plain,
c_HOL_Oinverse__class_Oinverse(c_RealVector_Oof__real(c_RealVector_Oof__real(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_RealVector_Oof__real(c_RealVector_Oof__real(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_Complex_Ocomplex),
inference(spm,[status(thm)],[c_0_174,c_0_175]) ).
cnf(c_0_185,plain,
c_RealVector_Oof__real(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_176,c_0_175]),c_0_166]),c_0_90]) ).
cnf(c_0_186,plain,
( ~ class_RealVector_Oreal__normed__vector(X1)
| c_HOL_Oabs__class_Oabs(c_RealVector_Onorm__class_Onorm(X2,X1),tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(X2,X1) ),
inference(fof_simplification,[status(thm)],[cls_abs__norm__cancel_0]) ).
cnf(c_0_187,plain,
( ~ class_RealVector_Oreal__normed__field(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1) = c_HOL_Oinverse__class_Odivide(c_RealVector_Onorm__class_Onorm(X2,X1),c_RealVector_Onorm__class_Onorm(X3,X1),tc_RealDef_Oreal) ),
c_0_177 ).
cnf(c_0_188,negated_conjecture,
( c_RealVector_Onorm__class_Onorm(c_RealVector_OscaleR__class_OscaleR(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oinverse__class_Odivide(X1,X1,tc_Complex_Ocomplex),v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal)
| X1 = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_178,c_0_179]),c_0_180])]) ).
cnf(c_0_189,plain,
c_HOL_Oinverse__class_Odivide(c_RealVector_Oof__real(c_RealVector_Oof__real(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_Complex_Ocomplex),c_RealVector_Oof__real(c_RealVector_Oof__real(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_181,c_0_182]),c_0_103])]) ).
cnf(c_0_190,plain,
c_RealVector_Oof__real(c_RealVector_Oof__real(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_183,c_0_184]),c_0_175]),c_0_185]) ).
cnf(c_0_191,plain,
( ~ class_RealVector_Oreal__normed__vector(X1)
| c_RealVector_Onorm__class_Onorm(c_RealVector_OscaleR__class_OscaleR(X2,X3,X1),X1) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X3,X1),tc_RealDef_Oreal) ),
inference(fof_simplification,[status(thm)],[cls_norm__scaleR_0]) ).
cnf(c_0_192,plain,
( ~ class_RealVector_Oreal__normed__vector(X1)
| c_HOL_Oabs__class_Oabs(c_RealVector_Onorm__class_Onorm(X2,X1),tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(X2,X1) ),
c_0_186 ).
cnf(c_0_193,axiom,
c_RealVector_Onorm__class_Onorm(c_Complex_Ocnj(X1),tc_Complex_Ocomplex) = c_RealVector_Onorm__class_Onorm(X1,tc_Complex_Ocomplex),
cls_complex__mod__cnj_0 ).
cnf(c_0_194,plain,
c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,tc_Complex_Ocomplex),tc_RealDef_Oreal),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_187,c_0_114]),c_0_180]),c_0_143])]) ).
cnf(c_0_195,negated_conjecture,
c_RealVector_Onorm__class_Onorm(c_RealVector_OscaleR__class_OscaleR(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_188,c_0_189]),c_0_164]),c_0_190]) ).
cnf(c_0_196,plain,
( ~ class_RealVector_Oreal__normed__vector(X1)
| c_RealVector_Onorm__class_Onorm(c_RealVector_OscaleR__class_OscaleR(X2,X3,X1),X1) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X3,X1),tc_RealDef_Oreal) ),
c_0_191 ).
cnf(c_0_197,plain,
c_HOL_Oabs__class_Oabs(c_RealVector_Onorm__class_Onorm(X1,tc_Complex_Ocomplex),tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(X1,tc_Complex_Ocomplex),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_192,c_0_193]),c_0_63])]) ).
cnf(c_0_198,plain,
c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Oinverse(X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Oinverse(c_RealVector_Onorm__class_Onorm(X1,tc_Complex_Ocomplex),tc_RealDef_Oreal),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_194,c_0_152]),c_0_164]) ).
cnf(c_0_199,negated_conjecture,
c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),c_HOL_Oinverse__class_Oinverse(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_195,c_0_196]),c_0_197]),c_0_198]),c_0_63])]) ).
cnf(c_0_200,plain,
( ~ class_RealVector_Oreal__normed__field(X1)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1) = c_HOL_Oinverse__class_Odivide(c_RealVector_Onorm__class_Onorm(X2,X1),c_RealVector_Onorm__class_Onorm(X3,X1),tc_RealDef_Oreal) ),
inference(fof_simplification,[status(thm)],[cls_nonzero__norm__divide_0]) ).
cnf(c_0_201,plain,
v_b != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(fof_simplification,[status(thm)],[cls_b_0]) ).
cnf(c_0_202,negated_conjecture,
c_HOL_Oinverse__class_Odivide(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),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(spm,[status(thm)],[c_0_199,c_0_118]),c_0_117])]) ).
cnf(c_0_203,plain,
( ~ class_RealVector_Oreal__normed__field(X1)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Odivide(X2,X3,X1),X1) = c_HOL_Oinverse__class_Odivide(c_RealVector_Onorm__class_Onorm(X2,X1),c_RealVector_Onorm__class_Onorm(X3,X1),tc_RealDef_Oreal) ),
c_0_200 ).
cnf(c_0_204,plain,
v_b != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
c_0_201 ).
cnf(c_0_205,negated_conjecture,
c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Odivide(v_b,v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_202,c_0_203]),c_0_180])]),c_0_204]) ).
cnf(c_0_206,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Odivide(X1,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_157]),c_0_120])]) ).
cnf(c_0_207,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_205,c_0_206]),c_0_204]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG356-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n016.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 13:21:53 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.41 Running first-order theorem proving
% 0.15/0.41 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 9.11/1.66 % Version: 3.5.1
% 9.11/1.66 % Preprocessing class: FMLMSMSSSSSNFFN.
% 9.11/1.66 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 9.11/1.66 % Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4c with 1500s (5) cores
% 9.11/1.66 % Starting new_bool_3 with 300s (1) cores
% 9.11/1.66 % Starting new_bool_1 with 300s (1) cores
% 9.11/1.66 % Starting sh5l with 300s (1) cores
% 9.11/1.66 % G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4c with pid 2506824 completed with status 0
% 9.11/1.66 % Result found by G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4c
% 9.11/1.66 % Preprocessing class: FMLMSMSSSSSNFFN.
% 9.11/1.66 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 9.11/1.66 % Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4c with 1500s (5) cores
% 9.11/1.66 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 9.11/1.66 % SinE strategy is gf600_h_gu_R05_F100_L20000
% 9.11/1.66 % Search class: FGHSM-SSLM32-MFFFFFNN
% 9.11/1.66 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 9.11/1.66 % Starting SubtermCWHack with 136s (1) cores
% 9.11/1.66 % Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4c with 151s (1) cores
% 9.11/1.66 % Starting G-E--_208_C12_11_nc_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 9.11/1.66 % Starting G-E--_208_C12_02_nc_F1_SE_CS_SP_PS_S5PRR_RG_S070I with 136s (1) cores
% 9.11/1.66 % Starting G-E--_208_C47_F1_SE_CS_SP_PS_S0Y with 136s (1) cores
% 9.11/1.66 % G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4c with pid 2506844 completed with status 0
% 9.11/1.66 % Result found by G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4c
% 9.11/1.66 % Preprocessing class: FMLMSMSSSSSNFFN.
% 9.11/1.66 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 9.11/1.66 % Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4c with 1500s (5) cores
% 9.11/1.66 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 9.11/1.66 % SinE strategy is gf600_h_gu_R05_F100_L20000
% 9.11/1.66 % Search class: FGHSM-SSLM32-MFFFFFNN
% 9.11/1.66 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 9.11/1.66 % Starting SubtermCWHack with 136s (1) cores
% 9.11/1.66 % Starting G-E--_008_C45_F1_PI_AE_Q4_CS_SP_S4c with 151s (1) cores
% 9.11/1.66 % Preprocessing time : 0.014 s
% 9.11/1.66
% 9.11/1.66 % Proof found!
% 9.11/1.66 % SZS status Unsatisfiable
% 9.11/1.66 % SZS output start CNFRefutation
% See solution above
% 9.11/1.66 % Parsed axioms : 1206
% 9.11/1.66 % Removed by relevancy pruning/SinE : 51
% 9.11/1.66 % Initial clauses : 1155
% 9.11/1.66 % Removed in clause preprocessing : 0
% 9.11/1.66 % Initial clauses in saturation : 1155
% 9.11/1.66 % Processed clauses : 8505
% 9.11/1.66 % ...of these trivial : 418
% 9.11/1.66 % ...subsumed : 6090
% 9.11/1.66 % ...remaining for further processing : 1997
% 9.11/1.66 % Other redundant clauses eliminated : 54
% 9.11/1.66 % Clauses deleted for lack of memory : 0
% 9.11/1.66 % Backward-subsumed : 15
% 9.11/1.66 % Backward-rewritten : 164
% 9.11/1.66 % Generated clauses : 63401
% 9.11/1.66 % ...of the previous two non-redundant : 56970
% 9.11/1.66 % ...aggressively subsumed : 0
% 9.11/1.66 % Contextual simplify-reflections : 3
% 9.11/1.66 % Paramodulations : 63231
% 9.11/1.66 % Factorizations : 6
% 9.11/1.66 % NegExts : 0
% 9.11/1.66 % Equation resolutions : 164
% 9.11/1.66 % Disequality decompositions : 0
% 9.11/1.66 % Total rewrite steps : 55986
% 9.11/1.66 % ...of those cached : 54028
% 9.11/1.66 % Propositional unsat checks : 0
% 9.11/1.66 % Propositional check models : 0
% 9.11/1.66 % Propositional check unsatisfiable : 0
% 9.11/1.66 % Propositional clauses : 0
% 9.11/1.66 % Propositional clauses after purity: 0
% 9.11/1.66 % Propositional unsat core size : 0
% 9.11/1.66 % Propositional preprocessing time : 0.000
% 9.11/1.66 % Propositional encoding time : 0.000
% 9.11/1.66 % Propositional solver time : 0.000
% 9.11/1.66 % Success case prop preproc time : 0.000
% 9.11/1.66 % Success case prop encoding time : 0.000
% 9.11/1.66 % Success case prop solver time : 0.000
% 9.11/1.66 % Current number of processed clauses : 1818
% 9.11/1.66 % Positive orientable unit clauses : 404
% 9.11/1.66 % Positive unorientable unit clauses: 8
% 9.11/1.66 % Negative unit clauses : 172
% 9.11/1.66 % Non-unit-clauses : 1234
% 9.11/1.66 % Current number of unprocessed clauses: 49329
% 9.11/1.66 % ...number of literals in the above : 165654
% 9.11/1.66 % Current number of archived formulas : 0
% 9.11/1.66 % Current number of archived clauses : 179
% 9.11/1.66 % Clause-clause subsumption calls (NU) : 293592
% 9.11/1.66 % Rec. Clause-clause subsumption calls : 133423
% 9.11/1.66 % Non-unit clause-clause subsumptions : 1565
% 9.11/1.66 % Unit Clause-clause subsumption calls : 69518
% 9.11/1.66 % Rewrite failures with RHS unbound : 0
% 9.11/1.66 % BW rewrite match attempts : 976
% 9.11/1.66 % BW rewrite match successes : 114
% 9.11/1.66 % Condensation attempts : 0
% 9.11/1.66 % Condensation successes : 0
% 9.11/1.66 % Termbank termtop insertions : 1040611
% 9.11/1.66 % Search garbage collected termcells : 2554
% 9.11/1.66
% 9.11/1.66 % -------------------------------------------------
% 9.11/1.66 % User time : 1.111 s
% 9.11/1.66 % System time : 0.055 s
% 9.11/1.66 % Total time : 1.166 s
% 9.11/1.66 % Maximum resident set size: 6264 pages
% 9.11/1.66
% 9.11/1.66 % -------------------------------------------------
% 9.11/1.66 % User time : 5.574 s
% 9.11/1.66 % System time : 0.235 s
% 9.11/1.66 % Total time : 5.810 s
% 9.11/1.66 % Maximum resident set size: 5632 pages
% 9.11/1.66 % E exiting
%------------------------------------------------------------------------------