%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWV616-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 02:59:39 PM UTC 2026
% Result : Unsatisfiable 10.33s 2.18s
% Output : CNFRefutation 10.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 33
% Syntax : Number of clauses : 120 ( 62 unt; 0 nHn; 61 RR)
% Number of literals : 205 ( 123 equ; 91 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 4 con; 0-3 aty)
% Number of variables : 160 ( 10 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_complex__cnj__divide_0,axiom,
c_Complex_Ocnj(c_HOL_Oinverse__class_Odivide(X1,X2,tc_Complex_Ocomplex)) = c_HOL_Oinverse__class_Odivide(c_Complex_Ocnj(X1),c_Complex_Ocnj(X2),tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complex__cnj__divide_0) ).
cnf(cls_complex__cnj__one_0,axiom,
c_Complex_Ocnj(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complex__cnj__one_0) ).
cnf(cls_inverse__eq__divide_0,axiom,
( ~ class_Ring__and__Field_Ofield(X1)
| c_HOL_Oinverse__class_Oinverse(X2,X1) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__eq__divide_0) ).
cnf(cls_right__minus__eq_1,axiom,
( ~ class_OrderedGroup_Ogroup__add(X1)
| c_HOL_Ominus__class_Ominus(X2,X2,X1) = c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__minus__eq_1) ).
cnf(cls_complex__cnj__cancel__iff_0,axiom,
( c_Complex_Ocnj(X1) != c_Complex_Ocnj(X2)
| X1 = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complex__cnj__cancel__iff_0) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ofield,axiom,
class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ofield) ).
cnf(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/sandbox/benchmark/theBenchmark.p',cls_inverse__eq__iff__eq_0) ).
cnf(cls_eq__iff__diff__eq__0_0,axiom,
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_HOL_Ominus__class_Ominus(X2,X2,X1) = c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_0) ).
cnf(cls_cnj_Odiff_0,axiom,
c_Complex_Ocnj(c_HOL_Ominus__class_Ominus(X1,X2,tc_Complex_Ocomplex)) = c_HOL_Ominus__class_Ominus(c_Complex_Ocnj(X1),c_Complex_Ocnj(X2),tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cnj_Odiff_0) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add,axiom,
class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__ring,axiom,
class_Ring__and__Field_Odivision__ring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__ring) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero,axiom,
class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero) ).
cnf(cls_inverse__inverse__eq_0,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Odivision__ring(X1)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(X2,X1),X1) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__inverse__eq_0) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add,axiom,
class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add) ).
cnf(cls_cnj_Ozero_0,axiom,
c_Complex_Ocnj(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cnj_Ozero_0) ).
cnf(cls_complex__cnj__cnj_0,axiom,
c_Complex_Ocnj(c_Complex_Ocnj(X1)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complex__cnj__cnj_0) ).
cnf(cls_diff__0__right_0,axiom,
( ~ class_OrderedGroup_Ogroup__add(X1)
| c_HOL_Ominus__class_Ominus(X2,c_HOL_Ozero__class_Ozero(X1),X1) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__0__right_0) ).
cnf(cls_inverse__zero_0,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__zero_0) ).
cnf(cls_diff__add__cancel_0,axiom,
( ~ class_OrderedGroup_Ogroup__add(X1)
| c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X2,X3,X1),X3,X1) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__cancel_0) ).
cnf(cls_inverse__eq__1__iff_0,axiom,
( c_HOL_Oinverse__class_Oinverse(X2,X1) != c_HOL_Oone__class_Oone(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| X2 = c_HOL_Oone__class_Oone(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__eq__1__iff_0) ).
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/sandbox/benchmark/theBenchmark.p',cls_inverse__divide_0) ).
cnf(cls_class__ringb_Oadd__r0__iff_0,axiom,
( X2 != c_HOL_Oplus__class_Oplus(X2,X3,X1)
| ~ class_Int_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oidom(X1)
| X3 = c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_0) ).
cnf(cls_eq__divide__eq_2,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| c_HOL_Ozero__class_Ozero(X1) = c_HOL_Oinverse__class_Odivide(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__divide__eq_2) ).
cnf(cls_conjecture_0,negated_conjecture,
c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_k,tc_Complex_Ocomplex),v_n,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_n,tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(clsarity_Complex__Ocomplex__Int_Onumber__ring,axiom,
class_Int_Onumber__ring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Int_Onumber__ring) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Oidom,axiom,
class_Ring__and__Field_Oidom(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oidom) ).
cnf(cls_power__one_0,axiom,
( ~ class_OrderedGroup_Omonoid__mult(X1)
| c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X1),X2,X1) = c_HOL_Oone__class_Oone(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__one_0) ).
cnf(cls_root__unity_0,axiom,
c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(X1),X1,tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_root__unity_0) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult,axiom,
class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult) ).
cnf(cls_class__semiring_Opwr__pwr_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(X2,X3,X1),X4,X1) = c_Power_Opower__class_Opower(X2,c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Opwr__pwr_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/sandbox/benchmark/theBenchmark.p',cls_inverse__1_0) ).
cnf(cls_nat__mult__commute_0,axiom,
c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) = c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__commute_0) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1) ).
cnf(c_0_33,axiom,
c_Complex_Ocnj(c_HOL_Oinverse__class_Odivide(X1,X2,tc_Complex_Ocomplex)) = c_HOL_Oinverse__class_Odivide(c_Complex_Ocnj(X1),c_Complex_Ocnj(X2),tc_Complex_Ocomplex),
cls_complex__cnj__divide_0 ).
cnf(c_0_34,axiom,
c_Complex_Ocnj(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),
cls_complex__cnj__one_0 ).
cnf(c_0_35,plain,
( ~ class_Ring__and__Field_Ofield(X1)
| c_HOL_Oinverse__class_Oinverse(X2,X1) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),X2,X1) ),
inference(fof_simplification,[status(thm)],[cls_inverse__eq__divide_0]) ).
cnf(c_0_36,plain,
( ~ class_OrderedGroup_Ogroup__add(X1)
| c_HOL_Ominus__class_Ominus(X2,X2,X1) = c_HOL_Ozero__class_Ozero(X1) ),
inference(fof_simplification,[status(thm)],[cls_right__minus__eq_1]) ).
cnf(c_0_37,plain,
( c_Complex_Ocnj(X1) != c_Complex_Ocnj(X2)
| X1 = X2 ),
inference(fof_simplification,[status(thm)],[cls_complex__cnj__cancel__iff_0]) ).
cnf(c_0_38,plain,
c_Complex_Ocnj(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex)) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_Complex_Ocnj(X1),tc_Complex_Ocomplex),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_39,plain,
( ~ class_Ring__and__Field_Ofield(X1)
| c_HOL_Oinverse__class_Oinverse(X2,X1) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),X2,X1) ),
c_0_35 ).
cnf(c_0_40,axiom,
class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Ofield ).
cnf(c_0_41,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_42,plain,
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_HOL_Ominus__class_Ominus(X2,X2,X1) = c_HOL_Ozero__class_Ozero(X1) ),
inference(fof_simplification,[status(thm)],[cls_eq__iff__diff__eq__0_0]) ).
cnf(c_0_43,axiom,
c_Complex_Ocnj(c_HOL_Ominus__class_Ominus(X1,X2,tc_Complex_Ocomplex)) = c_HOL_Ominus__class_Ominus(c_Complex_Ocnj(X1),c_Complex_Ocnj(X2),tc_Complex_Ocomplex),
cls_cnj_Odiff_0 ).
cnf(c_0_44,plain,
( ~ class_OrderedGroup_Ogroup__add(X1)
| c_HOL_Ominus__class_Ominus(X2,X2,X1) = c_HOL_Ozero__class_Ozero(X1) ),
c_0_36 ).
cnf(c_0_45,axiom,
class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add ).
cnf(c_0_46,plain,
( c_Complex_Ocnj(X1) != c_Complex_Ocnj(X2)
| X1 = X2 ),
c_0_37 ).
cnf(c_0_47,plain,
c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_Complex_Ocnj(X1),tc_Complex_Ocomplex) = c_Complex_Ocnj(c_HOL_Oinverse__class_Oinverse(X1,tc_Complex_Ocomplex)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40])]) ).
cnf(c_0_48,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_41 ).
cnf(c_0_49,axiom,
class_Ring__and__Field_Odivision__ring(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__ring ).
cnf(c_0_50,axiom,
class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero ).
cnf(c_0_51,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_52,plain,
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_HOL_Ominus__class_Ominus(X2,X2,X1) = c_HOL_Ozero__class_Ozero(X1) ),
c_0_42 ).
cnf(c_0_53,axiom,
class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add ).
cnf(c_0_54,plain,
c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Complex_Ocnj(c_HOL_Ominus__class_Ominus(X1,X1,tc_Complex_Ocomplex)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45])]) ).
cnf(c_0_55,axiom,
c_Complex_Ocnj(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
cls_cnj_Ozero_0 ).
cnf(c_0_56,axiom,
c_Complex_Ocnj(c_Complex_Ocnj(X1)) = X1,
cls_complex__cnj__cnj_0 ).
cnf(c_0_57,plain,
( c_Complex_Ocnj(X1) != c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)
| X1 = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) ),
inference(spm,[status(thm)],[c_0_46,c_0_34]) ).
cnf(c_0_58,plain,
c_Complex_Ocnj(c_HOL_Oinverse__class_Oinverse(X1,tc_Complex_Ocomplex)) = c_HOL_Oinverse__class_Oinverse(c_Complex_Ocnj(X1),tc_Complex_Ocomplex),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_47]),c_0_40])]) ).
cnf(c_0_59,plain,
( ~ class_OrderedGroup_Ogroup__add(X1)
| c_HOL_Ominus__class_Ominus(X2,c_HOL_Ozero__class_Ozero(X1),X1) = X2 ),
inference(fof_simplification,[status(thm)],[cls_diff__0__right_0]) ).
cnf(c_0_60,plain,
( c_HOL_Oinverse__class_Oinverse(X1,tc_Complex_Ocomplex) != c_HOL_Oinverse__class_Oinverse(X2,tc_Complex_Ocomplex)
| X1 = X2 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_50])]) ).
cnf(c_0_61,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_51 ).
cnf(c_0_62,plain,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1) ),
inference(fof_simplification,[status(thm)],[cls_inverse__zero_0]) ).
cnf(c_0_63,plain,
c_Complex_Ocnj(c_HOL_Ominus__class_Ominus(tc_nat,tc_nat,tc_Complex_Ocomplex)) = c_Complex_Ocnj(c_HOL_Ominus__class_Ominus(X1,X1,tc_Complex_Ocomplex)),
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_52]),c_0_53])]),c_0_54]) ).
cnf(c_0_64,plain,
c_Complex_Ocnj(c_HOL_Ominus__class_Ominus(tc_nat,tc_nat,tc_Complex_Ocomplex)) = c_HOL_Ominus__class_Ominus(tc_nat,tc_nat,tc_Complex_Ocomplex),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_55,c_0_54]),c_0_56]),c_0_54]) ).
cnf(c_0_65,plain,
( ~ class_OrderedGroup_Ogroup__add(X1)
| c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X2,X3,X1),X3,X1) = X2 ),
inference(fof_simplification,[status(thm)],[cls_diff__add__cancel_0]) ).
cnf(c_0_66,plain,
c_Complex_Ocnj(c_HOL_Ominus__class_Ominus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex)) = c_HOL_Ominus__class_Ominus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_Complex_Ocnj(X1),tc_Complex_Ocomplex),
inference(spm,[status(thm)],[c_0_43,c_0_34]) ).
cnf(c_0_67,plain,
( c_HOL_Oinverse__class_Oinverse(X2,X1) != c_HOL_Oone__class_Oone(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| X2 = c_HOL_Oone__class_Oone(X1) ),
inference(fof_simplification,[status(thm)],[cls_inverse__eq__1__iff_0]) ).
cnf(c_0_68,plain,
( c_HOL_Oinverse__class_Oinverse(c_Complex_Ocnj(X1),tc_Complex_Ocomplex) != c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)
| c_HOL_Oinverse__class_Oinverse(X1,tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_69,plain,
( ~ class_OrderedGroup_Ogroup__add(X1)
| c_HOL_Ominus__class_Ominus(X2,c_HOL_Ozero__class_Ozero(X1),X1) = X2 ),
c_0_59 ).
cnf(c_0_70,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_71,plain,
c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X1,
inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_49]),c_0_50])])]) ).
cnf(c_0_72,plain,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1) ),
c_0_62 ).
cnf(c_0_73,plain,
c_Complex_Ocnj(c_HOL_Ominus__class_Ominus(X1,X1,tc_Complex_Ocomplex)) = c_HOL_Ominus__class_Ominus(tc_nat,tc_nat,tc_Complex_Ocomplex),
inference(rw,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_74,plain,
c_HOL_Ominus__class_Ominus(tc_nat,tc_nat,tc_Complex_Ocomplex) = c_HOL_Ominus__class_Ominus(X1,X1,tc_Complex_Ocomplex),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_54]),c_0_54]),c_0_56]) ).
cnf(c_0_75,plain,
( X2 != c_HOL_Oplus__class_Oplus(X2,X3,X1)
| ~ class_Int_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oidom(X1)
| X3 = c_HOL_Ozero__class_Ozero(X1) ),
inference(fof_simplification,[status(thm)],[cls_class__ringb_Oadd__r0__iff_0]) ).
cnf(c_0_76,plain,
( ~ class_OrderedGroup_Ogroup__add(X1)
| c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X2,X3,X1),X3,X1) = X2 ),
c_0_65 ).
cnf(c_0_77,plain,
( c_HOL_Ominus__class_Ominus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_Complex_Ocnj(X1),tc_Complex_Ocomplex) != c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)
| c_HOL_Ominus__class_Ominus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) ),
inference(spm,[status(thm)],[c_0_57,c_0_66]) ).
cnf(c_0_78,plain,
c_Complex_Ocnj(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex)) = c_HOL_Ominus__class_Ominus(c_Complex_Ocnj(X1),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(spm,[status(thm)],[c_0_43,c_0_34]) ).
cnf(c_0_79,plain,
( c_HOL_Oinverse__class_Oinverse(X2,X1) != c_HOL_Oone__class_Oone(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| X2 = c_HOL_Oone__class_Oone(X1) ),
c_0_67 ).
cnf(c_0_80,plain,
( c_HOL_Oinverse__class_Oinverse(X1,tc_Complex_Ocomplex) != c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)
| c_HOL_Oinverse__class_Oinverse(c_Complex_Ocnj(X1),tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) ),
inference(spm,[status(thm)],[c_0_68,c_0_56]) ).
cnf(c_0_81,plain,
c_HOL_Ominus__class_Ominus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_69]),c_0_34]),c_0_55]),c_0_45])]) ).
cnf(c_0_82,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_70 ).
cnf(c_0_83,plain,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| c_HOL_Ozero__class_Ozero(X1) = c_HOL_Oinverse__class_Odivide(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
inference(fof_simplification,[status(thm)],[cls_eq__divide__eq_2]) ).
cnf(c_0_84,plain,
c_HOL_Oinverse__class_Oinverse(c_HOL_Ominus__class_Ominus(tc_nat,tc_nat,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ominus__class_Ominus(tc_nat,tc_nat,tc_Complex_Ocomplex),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_54]),c_0_73]),c_0_54]),c_0_73]),c_0_50])]) ).
cnf(c_0_85,plain,
c_HOL_Ominus__class_Ominus(X1,X1,tc_Complex_Ocomplex) = c_HOL_Ominus__class_Ominus(X2,X2,tc_Complex_Ocomplex),
inference(spm,[status(thm)],[c_0_74,c_0_74]) ).
cnf(c_0_86,negated_conjecture,
c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_k,tc_Complex_Ocomplex),v_n,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_n,tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(fof_simplification,[status(thm)],[cls_conjecture_0]) ).
cnf(c_0_87,plain,
( X2 != c_HOL_Oplus__class_Oplus(X2,X3,X1)
| ~ class_Int_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oidom(X1)
| X3 = c_HOL_Ozero__class_Ozero(X1) ),
c_0_75 ).
cnf(c_0_88,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X2,tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex) = X1,
inference(spm,[status(thm)],[c_0_76,c_0_45]) ).
cnf(c_0_89,axiom,
class_Int_Onumber__ring(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Int_Onumber__ring ).
cnf(c_0_90,axiom,
class_Ring__and__Field_Oidom(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Oidom ).
cnf(c_0_91,plain,
( c_HOL_Ominus__class_Ominus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(c_Complex_Ocnj(X1),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)
| c_HOL_Ominus__class_Ominus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) ),
inference(spm,[status(thm)],[c_0_77,c_0_78]) ).
cnf(c_0_92,plain,
( c_HOL_Oinverse__class_Oinverse(X1,tc_Complex_Ocomplex) != c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)
| c_Complex_Ocnj(X1) = 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_79,c_0_80]),c_0_40]),c_0_50])]) ).
cnf(c_0_93,plain,
c_HOL_Ominus__class_Ominus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(X1,X1,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_81,c_0_44]),c_0_45])]) ).
cnf(c_0_94,plain,
c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Odivide(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(X2,X1,tc_Complex_Ocomplex),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_82]),c_0_40]),c_0_50])]) ).
cnf(c_0_95,plain,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| c_HOL_Ozero__class_Ozero(X1) = c_HOL_Oinverse__class_Odivide(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
c_0_83 ).
cnf(c_0_96,plain,
c_HOL_Oinverse__class_Oinverse(c_HOL_Ominus__class_Ominus(X1,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ominus__class_Ominus(X1,X1,tc_Complex_Ocomplex),
inference(spm,[status(thm)],[c_0_84,c_0_85]) ).
cnf(c_0_97,plain,
( ~ class_OrderedGroup_Omonoid__mult(X1)
| c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X1),X2,X1) = c_HOL_Oone__class_Oone(X1) ),
inference(fof_simplification,[status(thm)],[cls_power__one_0]) ).
cnf(c_0_98,negated_conjecture,
c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_k,tc_Complex_Ocomplex),v_n,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_n,tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
c_0_86 ).
cnf(c_0_99,axiom,
c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(X1),X1,tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),
cls_root__unity_0 ).
cnf(c_0_100,plain,
( c_HOL_Ominus__class_Ominus(X2,X1,tc_Complex_Ocomplex) != X2
| X1 = c_HOL_Ominus__class_Ominus(tc_nat,tc_nat,tc_Complex_Ocomplex) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88]),c_0_54]),c_0_73]),c_0_89]),c_0_90])]) ).
cnf(c_0_101,plain,
( c_HOL_Oinverse__class_Oinverse(X1,tc_Complex_Ocomplex) != c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)
| c_HOL_Ominus__class_Ominus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),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_91,c_0_92]),c_0_93])]) ).
cnf(c_0_102,plain,
c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(tc_nat,tc_nat,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex) = c_HOL_Ominus__class_Ominus(tc_nat,tc_nat,tc_Complex_Ocomplex),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_95]),c_0_54]),c_0_73]),c_0_96]),c_0_54]),c_0_73]),c_0_40]),c_0_50])]) ).
cnf(c_0_103,plain,
( ~ class_OrderedGroup_Omonoid__mult(X1)
| c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X1),X2,X1) = c_HOL_Oone__class_Oone(X1) ),
c_0_97 ).
cnf(c_0_104,axiom,
class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult ).
cnf(c_0_105,negated_conjecture,
c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_k,tc_Complex_Ocomplex),v_n,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(rw,[status(thm)],[c_0_98,c_0_99]) ).
cnf(c_0_106,plain,
( c_HOL_Oinverse__class_Oinverse(X1,tc_Complex_Ocomplex) != c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)
| c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ominus__class_Ominus(tc_nat,tc_nat,tc_Complex_Ocomplex) ),
inference(spm,[status(thm)],[c_0_100,c_0_101]) ).
cnf(c_0_107,plain,
c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X1,X1,tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex) = c_HOL_Ominus__class_Ominus(X1,X1,tc_Complex_Ocomplex),
inference(spm,[status(thm)],[c_0_102,c_0_85]) ).
cnf(c_0_108,plain,
c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),
inference(spm,[status(thm)],[c_0_103,c_0_104]) ).
cnf(c_0_109,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(X2,X3,X1),X4,X1) = c_Power_Opower__class_Opower(X2,c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),X1) ),
inference(fof_simplification,[status(thm)],[cls_class__semiring_Opwr__pwr_0]) ).
cnf(c_0_110,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_111,negated_conjecture,
c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_k,tc_Complex_Ocomplex),v_n,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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_106]),c_0_107]),c_0_108]),c_0_74]),c_0_107])]) ).
cnf(c_0_112,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(X2,X3,X1),X4,X1) = c_Power_Opower__class_Opower(X2,c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),X1) ),
c_0_109 ).
cnf(c_0_113,axiom,
c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) = c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),
cls_nat__mult__commute_0 ).
cnf(c_0_114,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1 ).
cnf(c_0_115,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_110 ).
cnf(c_0_116,negated_conjecture,
c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),c_HOL_Otimes__class_Otimes(v_n,v_k,tc_nat),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_111,c_0_112]),c_0_113]),c_0_114])]) ).
cnf(c_0_117,plain,
c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(X1),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),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_112,c_0_99]),c_0_108]),c_0_114])]) ).
cnf(c_0_118,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_115,c_0_49]) ).
cnf(c_0_119,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_116,c_0_117]),c_0_118])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV616-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n010.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Mon Sep 21 09:14:54 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.33/2.18 % Version: 3.5.1
% 10.33/2.18 % Preprocessing class: FMLSSMSSSSSNFFN.
% 10.33/2.18 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 10.33/2.18 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 900s (3) cores
% 10.33/2.18 % Starting new_bool_3 with 600s (2) cores
% 10.33/2.18 % Starting new_bool_1 with 600s (2) cores
% 10.33/2.18 % Starting sh5l with 300s (1) cores
% 10.33/2.18 % G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with pid 554695 completed with status 0
% 10.33/2.18 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d
% 10.33/2.18 % Preprocessing class: FMLSSMSSSSSNFFN.
% 10.33/2.18 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 10.33/2.18 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 900s (3) cores
% 10.33/2.18 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 10.33/2.18 % No SInE strategy applied
% 10.33/2.18 % Search class: FGHSM-SSLM32-MFFFFFNN
% 10.33/2.18 % Scheduled 7 strats onto 3 cores with 900 seconds (900 total)
% 10.33/2.18 % Starting SubtermCWHack with 82s (1) cores
% 10.33/2.18 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 91s (1) cores
% 10.33/2.18 % Starting G-E--_208_C12_11_nc_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 82s (1) cores
% 10.33/2.18 % G-E--_208_C12_11_nc_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with pid 554701 completed with status 0
% 10.33/2.18 % Result found by G-E--_208_C12_11_nc_F1_SE_CS_SP_PS_S5PRR_RG_S04AN
% 10.33/2.18 % Preprocessing class: FMLSSMSSSSSNFFN.
% 10.33/2.18 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 10.33/2.18 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 900s (3) cores
% 10.33/2.18 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 10.33/2.18 % No SInE strategy applied
% 10.33/2.18 % Search class: FGHSM-SSLM32-MFFFFFNN
% 10.33/2.18 % Scheduled 7 strats onto 3 cores with 900 seconds (900 total)
% 10.33/2.18 % Starting SubtermCWHack with 82s (1) cores
% 10.33/2.18 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 91s (1) cores
% 10.33/2.18 % Starting G-E--_208_C12_11_nc_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 82s (1) cores
% 10.33/2.18 % Preprocessing time : 0.013 s
% 10.33/2.18 % Presaturation interreduction done
% 10.33/2.18
% 10.33/2.18 % Proof found!
% 10.33/2.18 % SZS status Unsatisfiable
% 10.33/2.18 % SZS output start CNFRefutation
% See solution above
% 10.33/2.18 % Parsed axioms : 1041
% 10.33/2.18 % Removed by relevancy pruning/SinE : 0
% 10.33/2.18 % Initial clauses : 1041
% 10.33/2.18 % Removed in clause preprocessing : 0
% 10.33/2.18 % Initial clauses in saturation : 1041
% 10.33/2.18 % Processed clauses : 8334
% 10.33/2.18 % ...of these trivial : 108
% 10.33/2.18 % ...subsumed : 5607
% 10.33/2.18 % ...remaining for further processing : 2619
% 10.33/2.18 % Other redundant clauses eliminated : 329
% 10.33/2.18 % Clauses deleted for lack of memory : 0
% 10.33/2.18 % Backward-subsumed : 54
% 10.33/2.18 % Backward-rewritten : 236
% 10.33/2.18 % Generated clauses : 36220
% 10.33/2.18 % ...of the previous two non-redundant : 32633
% 10.33/2.18 % ...aggressively subsumed : 0
% 10.33/2.18 % Contextual simplify-reflections : 0
% 10.33/2.18 % Paramodulations : 35883
% 10.33/2.18 % Factorizations : 2
% 10.33/2.18 % NegExts : 0
% 10.33/2.18 % Equation resolutions : 335
% 10.33/2.18 % Disequality decompositions : 0
% 10.33/2.18 % Total rewrite steps : 33860
% 10.33/2.18 % ...of those cached : 32874
% 10.33/2.18 % Propositional unsat checks : 0
% 10.33/2.18 % Propositional check models : 0
% 10.33/2.18 % Propositional check unsatisfiable : 0
% 10.33/2.18 % Propositional clauses : 0
% 10.33/2.18 % Propositional clauses after purity: 0
% 10.33/2.18 % Propositional unsat core size : 0
% 10.33/2.18 % Propositional preprocessing time : 0.000
% 10.33/2.18 % Propositional encoding time : 0.000
% 10.33/2.18 % Propositional solver time : 0.000
% 10.33/2.18 % Success case prop preproc time : 0.000
% 10.33/2.18 % Success case prop encoding time : 0.000
% 10.33/2.18 % Success case prop solver time : 0.000
% 10.33/2.18 % Current number of processed clauses : 1425
% 10.33/2.18 % Positive orientable unit clauses : 244
% 10.33/2.18 % Positive unorientable unit clauses: 7
% 10.33/2.18 % Negative unit clauses : 88
% 10.33/2.18 % Non-unit-clauses : 1086
% 10.33/2.18 % Current number of unprocessed clauses: 25817
% 10.33/2.18 % ...number of literals in the above : 90216
% 10.33/2.18 % Current number of archived formulas : 0
% 10.33/2.18 % Current number of archived clauses : 1194
% 10.33/2.18 % Clause-clause subsumption calls (NU) : 379470
% 10.33/2.18 % Rec. Clause-clause subsumption calls : 149086
% 10.33/2.18 % Non-unit clause-clause subsumptions : 2188
% 10.33/2.18 % Unit Clause-clause subsumption calls : 15384
% 10.33/2.18 % Rewrite failures with RHS unbound : 0
% 10.33/2.18 % BW rewrite match attempts : 1049
% 10.33/2.18 % BW rewrite match successes : 185
% 10.33/2.18 % Condensation attempts : 0
% 10.33/2.18 % Condensation successes : 0
% 10.33/2.18 % Termbank termtop insertions : 579803
% 10.33/2.18 % Search garbage collected termcells : 2058
% 10.33/2.18
% 10.33/2.18 % -------------------------------------------------
% 10.33/2.18 % User time : 1.357 s
% 10.33/2.18 % System time : 0.049 s
% 10.33/2.18 % Total time : 1.406 s
% 10.33/2.18 % Maximum resident set size: 5624 pages
% 10.33/2.18
% 10.33/2.18 % -------------------------------------------------
% 10.33/2.18 % User time : 4.294 s
% 10.33/2.18 % System time : 0.160 s
% 10.33/2.18 % Total time : 4.453 s
% 10.33/2.18 % Maximum resident set size: 5632 pages
% 10.33/2.18 % E exiting
%------------------------------------------------------------------------------