%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : ALG426-1 : 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 : n019.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 12:02:08 PM UTC 2026
% Result : Unsatisfiable 155.32s 23.24s
% Output : CNFRefutation 155.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 39
% Syntax : Number of clauses : 135 ( 53 unt; 8 nHn; 64 RR)
% Number of literals : 253 ( 107 equ; 123 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 17 ( 15 usr; 1 prp; 0-3 aty)
% Number of functors : 19 ( 19 usr; 3 con; 0-3 aty)
% Number of variables : 218 ( 39 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_zero__neq__one_0,axiom,
( c_HOL_Ozero__class_Ozero(X1) != c_HOL_Oone__class_Oone(X1)
| ~ class_Ring__and__Field_Ozero__neq__one(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__neq__one_0) ).
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_dvd__refl_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__refl_0) ).
cnf(cls_mult__1_0,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__mult(X1)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__1_0) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one) ).
cnf(cls_field__inverse_0,axiom,
( ~ class_Ring__and__Field_Ofield(X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X2,X1),X2,X1) = c_HOL_Oone__class_Oone(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field__inverse_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/sandbox2/benchmark/theBenchmark.p',cls_inverse__inverse__eq_0) ).
cnf(cls_dvd__minus__iff_0,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__minus__iff_0) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add,axiom,
class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add) ).
cnf(cls_dvd__mult__left_0,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X2,X4,X1),X3,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__left_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/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult) ).
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_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_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(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_dvd__0__left_0,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| X2 = c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__0__left_0) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring__1,axiom,
class_Ring__and__Field_Ocomm__ring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring__1) ).
cnf(cls_exp__minus_0,axiom,
( ~ class_RealVector_Oreal__normed__field(X1)
| ~ class_SEQ_Obanach(X1)
| c_Transcendental_Oexp(c_HOL_Ouminus__class_Ouminus(X2,X1),X1) = c_HOL_Oinverse__class_Oinverse(c_Transcendental_Oexp(X2,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp__minus_0) ).
cnf(cls_class__semiring_Osemiring__rules_I10_J_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I10_J_0) ).
cnf(cls_dvd__trans_0,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X3,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__trans_0) ).
cnf(cls_smult__eq__0__iff_1,axiom,
( ~ class_Ring__and__Field_Oidom(X1)
| c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_smult__eq__0__iff_1) ).
cnf(cls_add__poly__code_I2_J_0,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1)) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__poly__code_I2_J_0) ).
cnf(cls_degree__pCons__0_0,axiom,
( ~ class_HOL_Ozero(X1)
| c_Polynomial_Odegree(c_Polynomial_OpCons(X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1),X1) = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_degree__pCons__0_0) ).
cnf(cls_exp__not__eq__zero_0,axiom,
( c_Transcendental_Oexp(X2,X1) != c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__field(X1)
| ~ class_SEQ_Obanach(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp__not__eq__zero_0) ).
cnf(clsarity_Complex__Ocomplex__SEQ_Obanach,axiom,
class_SEQ_Obanach(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__SEQ_Obanach) ).
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_exp__add_0,axiom,
( ~ class_RealVector_Oreal__normed__field(X1)
| ~ class_SEQ_Obanach(X1)
| c_Transcendental_Oexp(c_HOL_Oplus__class_Oplus(X2,X3,X1),X1) = c_HOL_Otimes__class_Otimes(c_Transcendental_Oexp(X2,X1),c_Transcendental_Oexp(X3,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp__add_0) ).
cnf(cls_synthetic__div__unique_1,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_Polynomial_Osmult(X3,X4,X1),tc_Polynomial_Opoly(X1)) != c_Polynomial_OpCons(X5,X4,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1)
| X4 = c_Polynomial_Osynthetic__div(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synthetic__div__unique_1) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Oidom,axiom,
class_Ring__and__Field_Oidom(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oidom) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add) ).
cnf(cls_poly__pCons_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(X1)
| c_Polynomial_Opoly(c_Polynomial_OpCons(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X4,c_Polynomial_Opoly(X3,X4,X1),X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_poly__pCons_0) ).
cnf(cls_fundamental__theorem__of__algebra__alt_1,axiom,
( X1 = c_Polynomial_OpCons(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__1(X1),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex)
| c_Polynomial_Opoly(X1,v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__2(X1),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fundamental__theorem__of__algebra__alt_1) ).
cnf(clsarity_Complex__Ocomplex__HOL_Ozero,axiom,
class_HOL_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__HOL_Ozero) ).
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/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).
cnf(cls_synthetic__div__eq__0__iff_1,axiom,
( c_Polynomial_Odegree(X2,X1) != c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1)
| c_Polynomial_Osynthetic__div(X2,X3,X1) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_synthetic__div__eq__0__iff_1) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0) ).
cnf(cls_conjecture_0,negated_conjecture,
c_Polynomial_Opoly(v_q,X1,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(cls_conjecture_1,negated_conjecture,
v_q != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
cnf(c_0_39,plain,
( c_HOL_Ozero__class_Ozero(X1) != c_HOL_Oone__class_Oone(X1)
| ~ class_Ring__and__Field_Ozero__neq__one(X1) ),
inference(fof_simplification,[status(thm)],[cls_zero__neq__one_0]) ).
cnf(c_0_40,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_41,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X2,X1) ),
inference(fof_simplification,[status(thm)],[cls_dvd__refl_0]) ).
cnf(c_0_42,plain,
( ~ class_OrderedGroup_Ocomm__monoid__mult(X1)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1) = X2 ),
inference(fof_simplification,[status(thm)],[cls_mult__1_0]) ).
cnf(c_0_43,plain,
( c_HOL_Ozero__class_Ozero(X1) != c_HOL_Oone__class_Oone(X1)
| ~ class_Ring__and__Field_Ozero__neq__one(X1) ),
c_0_39 ).
cnf(c_0_44,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one ).
cnf(c_0_45,plain,
( ~ class_Ring__and__Field_Ofield(X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X2,X1),X2,X1) = c_HOL_Oone__class_Oone(X1) ),
inference(fof_simplification,[status(thm)],[cls_field__inverse_0]) ).
cnf(c_0_46,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_47,plain,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1) ),
inference(fof_simplification,[status(thm)],[cls_dvd__minus__iff_0]) ).
cnf(c_0_48,plain,
( ~ class_OrderedGroup_Ogroup__add(X1)
| X2 = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X2,X1),X1) ),
c_0_40 ).
cnf(c_0_49,axiom,
class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add ).
cnf(c_0_50,plain,
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X2,X4,X1),X3,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1) ),
inference(fof_simplification,[status(thm)],[cls_dvd__mult__left_0]) ).
cnf(c_0_51,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X2,X1) ),
c_0_41 ).
cnf(c_0_52,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1 ).
cnf(c_0_53,plain,
( ~ class_OrderedGroup_Ocomm__monoid__mult(X1)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1) = X2 ),
c_0_42 ).
cnf(c_0_54,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult ).
cnf(c_0_55,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_56,plain,
c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_57,plain,
( ~ class_Ring__and__Field_Ofield(X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X2,X1),X2,X1) = c_HOL_Oone__class_Oone(X1) ),
c_0_45 ).
cnf(c_0_58,axiom,
class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Ofield ).
cnf(c_0_59,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_46 ).
cnf(c_0_60,axiom,
class_Ring__and__Field_Odivision__ring(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__ring ).
cnf(c_0_61,axiom,
class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero ).
cnf(c_0_62,plain,
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| X2 = c_HOL_Ozero__class_Ozero(X1) ),
inference(fof_simplification,[status(thm)],[cls_dvd__0__left_0]) ).
cnf(c_0_63,plain,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1) ),
c_0_47 ).
cnf(c_0_64,plain,
c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X1,
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_65,axiom,
class_Ring__and__Field_Ocomm__ring__1(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring__1 ).
cnf(c_0_66,plain,
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X2,X4,X1),X3,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1) ),
c_0_50 ).
cnf(c_0_67,plain,
c_Ring__and__Field_Odvd__class_Odvd(X1,X1,tc_Complex_Ocomplex),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_68,plain,
( ~ class_RealVector_Oreal__normed__field(X1)
| ~ class_SEQ_Obanach(X1)
| c_Transcendental_Oexp(c_HOL_Ouminus__class_Ouminus(X2,X1),X1) = c_HOL_Oinverse__class_Oinverse(c_Transcendental_Oexp(X2,X1),X1) ),
inference(fof_simplification,[status(thm)],[cls_exp__minus_0]) ).
cnf(c_0_69,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex) = X1,
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_70,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_55 ).
cnf(c_0_71,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X1,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| X1 = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_58])]) ).
cnf(c_0_72,plain,
c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_61])]) ).
cnf(c_0_73,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1) ),
inference(fof_simplification,[status(thm)],[cls_class__semiring_Osemiring__rules_I10_J_0]) ).
cnf(c_0_74,plain,
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| X2 = c_HOL_Ozero__class_Ozero(X1) ),
c_0_62 ).
cnf(c_0_75,plain,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_Complex_Ocomplex)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ouminus__class_Ouminus(X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_65])]) ).
cnf(c_0_76,plain,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X3,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1) ),
inference(fof_simplification,[status(thm)],[cls_dvd__trans_0]) ).
cnf(c_0_77,plain,
c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_52])]) ).
cnf(c_0_78,plain,
( ~ class_Ring__and__Field_Oidom(X1)
| c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(fof_simplification,[status(thm)],[cls_smult__eq__0__iff_1]) ).
cnf(c_0_79,plain,
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1)) = X2 ),
inference(fof_simplification,[status(thm)],[cls_add__poly__code_I2_J_0]) ).
cnf(c_0_80,plain,
( ~ class_HOL_Ozero(X1)
| c_Polynomial_Odegree(c_Polynomial_OpCons(X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1),X1) = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(fof_simplification,[status(thm)],[cls_degree__pCons__0_0]) ).
cnf(c_0_81,plain,
( c_Transcendental_Oexp(X2,X1) != c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__field(X1)
| ~ class_SEQ_Obanach(X1) ),
inference(fof_simplification,[status(thm)],[cls_exp__not__eq__zero_0]) ).
cnf(c_0_82,plain,
( ~ class_RealVector_Oreal__normed__field(X1)
| ~ class_SEQ_Obanach(X1)
| c_Transcendental_Oexp(c_HOL_Ouminus__class_Ouminus(X2,X1),X1) = c_HOL_Oinverse__class_Oinverse(c_Transcendental_Oexp(X2,X1),X1) ),
c_0_68 ).
cnf(c_0_83,axiom,
class_SEQ_Obanach(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__SEQ_Obanach ).
cnf(c_0_84,axiom,
class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__RealVector_Oreal__normed__field ).
cnf(c_0_85,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(spm,[status(thm)],[c_0_69,c_0_70]),c_0_58])]) ).
cnf(c_0_86,plain,
( ~ class_RealVector_Oreal__normed__field(X1)
| ~ class_SEQ_Obanach(X1)
| c_Transcendental_Oexp(c_HOL_Oplus__class_Oplus(X2,X3,X1),X1) = c_HOL_Otimes__class_Otimes(c_Transcendental_Oexp(X2,X1),c_Transcendental_Oexp(X3,X1),X1) ),
inference(fof_simplification,[status(thm)],[cls_exp__add_0]) ).
cnf(c_0_87,plain,
( c_HOL_Otimes__class_Otimes(X1,c_HOL_Oinverse__class_Oinverse(X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_HOL_Oinverse__class_Oinverse(X1,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_88,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1) ),
c_0_73 ).
cnf(c_0_89,plain,
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex)
| c_HOL_Ouminus__class_Ouminus(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_74,c_0_75]),c_0_52])]) ).
cnf(c_0_90,plain,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X4,X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X3,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X1) ),
c_0_76 ).
cnf(c_0_91,plain,
c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oinverse__class_Odivide(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_70]),c_0_58])]) ).
cnf(c_0_92,plain,
( c_HOL_Oplus__class_Oplus(X2,c_Polynomial_Osmult(X3,X4,X1),tc_Polynomial_Opoly(X1)) != c_Polynomial_OpCons(X5,X4,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1)
| X4 = c_Polynomial_Osynthetic__div(X2,X3,X1) ),
inference(fof_simplification,[status(thm)],[cls_synthetic__div__unique_1]) ).
cnf(c_0_93,plain,
( ~ class_Ring__and__Field_Oidom(X1)
| c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
c_0_78 ).
cnf(c_0_94,axiom,
class_Ring__and__Field_Oidom(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Oidom ).
cnf(c_0_95,plain,
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1)) = X2 ),
c_0_79 ).
cnf(c_0_96,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add ).
cnf(c_0_97,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__0(X1)
| c_Polynomial_Opoly(c_Polynomial_OpCons(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X4,c_Polynomial_Opoly(X3,X4,X1),X1),X1) ),
inference(fof_simplification,[status(thm)],[cls_poly__pCons_0]) ).
cnf(c_0_98,plain,
( ~ class_HOL_Ozero(X1)
| c_Polynomial_Odegree(c_Polynomial_OpCons(X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X1),X1) = c_HOL_Ozero__class_Ozero(tc_nat) ),
c_0_80 ).
cnf(c_0_99,axiom,
( X1 = c_Polynomial_OpCons(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__1(X1),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex)
| c_Polynomial_Opoly(X1,v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__2(X1),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
cls_fundamental__theorem__of__algebra__alt_1 ).
cnf(c_0_100,axiom,
class_HOL_Ozero(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__HOL_Ozero ).
cnf(c_0_101,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_102,plain,
( c_Transcendental_Oexp(X2,X1) != c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__field(X1)
| ~ class_SEQ_Obanach(X1) ),
c_0_81 ).
cnf(c_0_103,plain,
c_Transcendental_Oexp(c_HOL_Ouminus__class_Ouminus(X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_Transcendental_Oexp(X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(rw,[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_104,plain,
( ~ class_RealVector_Oreal__normed__field(X1)
| ~ class_SEQ_Obanach(X1)
| c_Transcendental_Oexp(c_HOL_Oplus__class_Oplus(X2,X3,X1),X1) = c_HOL_Otimes__class_Otimes(c_Transcendental_Oexp(X2,X1),c_Transcendental_Oexp(X3,X1),X1) ),
c_0_86 ).
cnf(c_0_105,plain,
( c_HOL_Oinverse__class_Odivide(X1,X1,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_HOL_Oinverse__class_Oinverse(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_87,c_0_70]),c_0_58])]) ).
cnf(c_0_106,plain,
c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(spm,[status(thm)],[c_0_88,c_0_52]) ).
cnf(c_0_107,plain,
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex)
| X1 = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_75]),c_0_64]) ).
cnf(c_0_108,plain,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_Complex_Ocomplex)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oinverse__class_Odivide(X2,X3,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_52])]) ).
cnf(c_0_109,plain,
( c_Polynomial_Odegree(X2,X1) != c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1)
| c_Polynomial_Osynthetic__div(X2,X3,X1) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(fof_simplification,[status(thm)],[cls_synthetic__div__eq__0__iff_1]) ).
cnf(c_0_110,plain,
( c_HOL_Oplus__class_Oplus(X2,c_Polynomial_Osmult(X3,X4,X1),tc_Polynomial_Opoly(X1)) != c_Polynomial_OpCons(X5,X4,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1)
| X4 = c_Polynomial_Osynthetic__div(X2,X3,X1) ),
c_0_92 ).
cnf(c_0_111,plain,
c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(spm,[status(thm)],[c_0_93,c_0_94]) ).
cnf(c_0_112,plain,
c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = X1,
inference(spm,[status(thm)],[c_0_95,c_0_96]) ).
cnf(c_0_113,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0 ).
cnf(c_0_114,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__0(X1)
| c_Polynomial_Opoly(c_Polynomial_OpCons(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X4,c_Polynomial_Opoly(X3,X4,X1),X1),X1) ),
c_0_97 ).
cnf(c_0_115,plain,
( c_Polynomial_Odegree(X1,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Polynomial_Opoly(X1,v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__2(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_98,c_0_99]),c_0_100])]) ).
cnf(c_0_116,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_101 ).
cnf(c_0_117,plain,
c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_Transcendental_Oexp(X1,tc_Complex_Ocomplex),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_102,c_0_103]),c_0_83]),c_0_84])]) ).
cnf(c_0_118,plain,
c_Transcendental_Oexp(c_HOL_Oplus__class_Oplus(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_Transcendental_Oexp(X1,tc_Complex_Ocomplex),c_Transcendental_Oexp(X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_83]),c_0_84])]) ).
cnf(c_0_119,plain,
( c_HOL_Oinverse__class_Odivide(X2,X2,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_HOL_Oinverse__class_Odivide(X1,X2,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_70,c_0_105]),c_0_106]),c_0_58])]) ).
cnf(c_0_120,plain,
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex)
| c_HOL_Oinverse__class_Odivide(X1,X2,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(spm,[status(thm)],[c_0_107,c_0_108]) ).
cnf(c_0_121,plain,
( c_Polynomial_Odegree(X2,X1) != c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1)
| c_Polynomial_Osynthetic__div(X2,X3,X1) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
c_0_109 ).
cnf(c_0_122,plain,
c_Polynomial_Osynthetic__div(c_Polynomial_OpCons(X1,X2,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X2,
inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_111]),c_0_112]),c_0_113])])]) ).
cnf(c_0_123,plain,
( c_Polynomial_Odegree(c_Polynomial_OpCons(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__2(c_Polynomial_OpCons(X1,X2,tc_Complex_Ocomplex)),c_Polynomial_Opoly(X2,v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__2(c_Polynomial_OpCons(X1,X2,tc_Complex_Ocomplex)),tc_Complex_Ocomplex),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_114,c_0_115]),c_0_113])]) ).
cnf(c_0_124,negated_conjecture,
c_Polynomial_Opoly(v_q,X1,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
cls_conjecture_0 ).
cnf(c_0_125,plain,
c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X1,
inference(spm,[status(thm)],[c_0_116,c_0_52]) ).
cnf(c_0_126,negated_conjecture,
v_q != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(fof_simplification,[status(thm)],[cls_conjecture_1]) ).
cnf(c_0_127,plain,
c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Transcendental_Oexp(X1,tc_Complex_Ocomplex),c_Transcendental_Oexp(X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(spm,[status(thm)],[c_0_117,c_0_118]) ).
cnf(c_0_128,plain,
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex)
| c_HOL_Oinverse__class_Odivide(X1,X2,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(spm,[status(thm)],[c_0_119,c_0_120]) ).
cnf(c_0_129,plain,
( c_Polynomial_Odegree(c_Polynomial_OpCons(X2,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_122]),c_0_113])]) ).
cnf(c_0_130,negated_conjecture,
( X1 = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Polynomial_Odegree(c_Polynomial_OpCons(X1,v_q,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_124]),c_0_106]),c_0_125]) ).
cnf(c_0_131,negated_conjecture,
v_q != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
c_0_126 ).
cnf(c_0_132,plain,
~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Transcendental_Oexp(X1,tc_Complex_Ocomplex),c_Transcendental_Oexp(X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(spm,[status(thm)],[c_0_127,c_0_128]) ).
cnf(c_0_133,negated_conjecture,
X1 = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_130]),c_0_131]) ).
cnf(c_0_134,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_132,c_0_133]),c_0_67])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG426-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.35 % Computer : n019.cluster.edu
% 0.11/0.35 % Model : x86_64 x86_64
% 0.11/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.35 % Memory : 8046.5625MB
% 0.11/0.35 % OS : Linux 6.8.0-71-generic
% 0.11/0.35 % CPULimit : 300
% 0.11/0.35 % WCLimit : 300
% 0.11/0.35 % DateTime : Mon Sep 21 13:20:49 UTC 2026
% 0.11/0.35 % CPUTime :
% 0.11/0.35 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.42 Running first-order theorem proving
% 0.14/0.42 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
% 155.32/23.24 % Version: 3.5.1
% 155.32/23.24 % Preprocessing class: FSLMSMSSSSSNFFN.
% 155.32/23.24 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 155.32/23.24 % Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 900s (3) cores
% 155.32/23.24 % Starting new_bool_3 with 600s (2) cores
% 155.32/23.24 % Starting new_bool_1 with 600s (2) cores
% 155.32/23.24 % Starting sh5l with 300s (1) cores
% 155.32/23.24 % G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with pid 2668270 completed with status 0
% 155.32/23.24 % Result found by G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y
% 155.32/23.24 % Preprocessing class: FSLMSMSSSSSNFFN.
% 155.32/23.24 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 155.32/23.24 % Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 900s (3) cores
% 155.32/23.24 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 155.32/23.24 % No SInE strategy applied
% 155.32/23.24 % Search class: FGHSS-FSLM32-DFFFFFNN
% 155.32/23.24 % Scheduled 7 strats onto 3 cores with 900 seconds (900 total)
% 155.32/23.24 % Starting SubtermCWHack with 82s (1) cores
% 155.32/23.24 % Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 91s (1) cores
% 155.32/23.24 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 82s (1) cores
% 155.32/23.24 % G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with pid 2668275 completed with status 0
% 155.32/23.24 % Result found by G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y
% 155.32/23.24 % Preprocessing class: FSLMSMSSSSSNFFN.
% 155.32/23.24 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 155.32/23.24 % Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 900s (3) cores
% 155.32/23.24 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 155.32/23.24 % No SInE strategy applied
% 155.32/23.24 % Search class: FGHSS-FSLM32-DFFFFFNN
% 155.32/23.24 % Scheduled 7 strats onto 3 cores with 900 seconds (900 total)
% 155.32/23.24 % Starting SubtermCWHack with 82s (1) cores
% 155.32/23.24 % Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 91s (1) cores
% 155.32/23.24 % Preprocessing time : 0.014 s
% 155.32/23.24 % Presaturation interreduction done
% 155.32/23.24
% 155.32/23.24 % Proof found!
% 155.32/23.24 % SZS status Unsatisfiable
% 155.32/23.24 % SZS output start CNFRefutation
% See solution above
% 155.32/23.24 % Parsed axioms : 728
% 155.32/23.24 % Removed by relevancy pruning/SinE : 0
% 155.32/23.24 % Initial clauses : 728
% 155.32/23.24 % Removed in clause preprocessing : 0
% 155.32/23.24 % Initial clauses in saturation : 728
% 155.32/23.24 % Processed clauses : 57824
% 155.32/23.24 % ...of these trivial : 454
% 155.32/23.24 % ...subsumed : 48409
% 155.32/23.24 % ...remaining for further processing : 8961
% 155.32/23.24 % Other redundant clauses eliminated : 25644
% 155.32/23.24 % Clauses deleted for lack of memory : 0
% 155.32/23.24 % Backward-subsumed : 307
% 155.32/23.24 % Backward-rewritten : 7096
% 155.32/23.24 % Generated clauses : 924288
% 155.32/23.24 % ...of the previous two non-redundant : 846016
% 155.32/23.24 % ...aggressively subsumed : 0
% 155.32/23.24 % Contextual simplify-reflections : 89
% 155.32/23.24 % Paramodulations : 898564
% 155.32/23.24 % Factorizations : 14
% 155.32/23.24 % NegExts : 0
% 155.32/23.24 % Equation resolutions : 25710
% 155.32/23.24 % Disequality decompositions : 0
% 155.32/23.24 % Total rewrite steps : 810374
% 155.32/23.24 % ...of those cached : 759246
% 155.32/23.24 % Propositional unsat checks : 1
% 155.32/23.24 % Propositional check models : 0
% 155.32/23.24 % Propositional check unsatisfiable : 0
% 155.32/23.24 % Propositional clauses : 0
% 155.32/23.24 % Propositional clauses after purity: 0
% 155.32/23.24 % Propositional unsat core size : 0
% 155.32/23.24 % Propositional preprocessing time : 0.000
% 155.32/23.24 % Propositional encoding time : 0.245
% 155.32/23.24 % Propositional solver time : 0.145
% 155.32/23.24 % Success case prop preproc time : 0.000
% 155.32/23.24 % Success case prop encoding time : 0.000
% 155.32/23.24 % Success case prop solver time : 0.000
% 155.32/23.24 % Current number of processed clauses : 898
% 155.32/23.24 % Positive orientable unit clauses : 46
% 155.32/23.24 % Positive unorientable unit clauses: 1
% 155.32/23.24 % Negative unit clauses : 0
% 155.32/23.24 % Non-unit-clauses : 851
% 155.32/23.24 % Current number of unprocessed clauses: 787629
% 155.32/23.24 % ...number of literals in the above : 3141691
% 155.32/23.24 % Current number of archived formulas : 0
% 155.32/23.24 % Current number of archived clauses : 8063
% 155.32/23.24 % Clause-clause subsumption calls (NU) : 10727140
% 155.32/23.24 % Rec. Clause-clause subsumption calls : 6374523
% 155.32/23.24 % Non-unit clause-clause subsumptions : 33644
% 155.32/23.24 % Unit Clause-clause subsumption calls : 261894
% 155.32/23.24 % Rewrite failures with RHS unbound : 3
% 155.32/23.24 % BW rewrite match attempts : 32004
% 155.32/23.24 % BW rewrite match successes : 7591
% 155.32/23.24 % Condensation attempts : 0
% 155.32/23.24 % Condensation successes : 0
% 155.32/23.24 % Termbank termtop insertions : 23962562
% 155.32/23.24 % Search garbage collected termcells : 1157
% 155.32/23.24
% 155.32/23.24 % -------------------------------------------------
% 155.32/23.24 % User time : 21.592 s
% 155.32/23.24 % System time : 0.594 s
% 155.32/23.24 % Total time : 22.186 s
% 155.32/23.24 % Maximum resident set size: 4928 pages
% 155.32/23.24
% 155.32/23.24 % -------------------------------------------------
% 155.32/23.24 % User time : 64.779 s
% 155.32/23.24 % System time : 1.973 s
% 155.32/23.24 % Total time : 66.753 s
% 155.32/23.24 % Maximum resident set size: 5376 pages
% 155.32/23.24 % E exiting
%------------------------------------------------------------------------------