%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWV626-1 : 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 : 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 02:59:40 PM UTC 2026
% Result : Unsatisfiable 5.15s 1.22s
% Output : CNFRefutation 5.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 18
% Syntax : Number of clauses : 68 ( 31 unt; 4 nHn; 24 RR)
% Number of literals : 123 ( 71 equ; 60 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 4 con; 0-3 aty)
% Number of variables : 121 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
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_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/sandbox/benchmark/theBenchmark.p',cls_divide__1_0) ).
cnf(cls_class__semiring_Osemiring__rules_I33_J_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_Power_Opower__class_Opower(X2,c_HOL_Oone__class_Oone(tc_nat),X1) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I33_J_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(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_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/sandbox/benchmark/theBenchmark.p',cls_right__inverse__eq_1) ).
cnf(cls_root__nonzero_0,axiom,
c_FFT__Mirabelle_Oroot(X1) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_root__nonzero_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__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(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_power__one__over_0,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),X2,X1),X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__one__over_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_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/sandbox/benchmark/theBenchmark.p',cls_divide__inverse_0) ).
cnf(cls_class__semiring_Opwr__mul_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X2,X4,X1),c_Power_Opower__class_Opower(X3,X4,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Opwr__mul_0) ).
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_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),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_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),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_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),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_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),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(cls_power__divide_0,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X2,X3,X1),X4,X1) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X2,X4,X1),c_Power_Opower__class_Opower(X3,X4,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__divide_0) ).
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_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(c_0_18,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_19,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_20,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_Power_Opower__class_Opower(X2,c_HOL_Oone__class_Oone(tc_nat),X1) = X2 ),
inference(fof_simplification,[status(thm)],[cls_class__semiring_Osemiring__rules_I33_J_0]) ).
cnf(c_0_21,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_22,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_18 ).
cnf(c_0_23,axiom,
class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Ofield ).
cnf(c_0_24,plain,
( ~ class_Ring__and__Field_Ofield(X1)
| c_HOL_Oinverse__class_Odivide(X2,c_HOL_Oone__class_Oone(X1),X1) = X2 ),
c_0_19 ).
cnf(c_0_25,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_26,plain,
c_FFT__Mirabelle_Oroot(X1) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(fof_simplification,[status(thm)],[cls_root__nonzero_0]) ).
cnf(c_0_27,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_28,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_Power_Opower__class_Opower(X2,c_HOL_Oone__class_Oone(tc_nat),X1) = X2 ),
c_0_20 ).
cnf(c_0_29,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1 ).
cnf(c_0_30,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_21 ).
cnf(c_0_31,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(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_32,plain,
c_HOL_Oinverse__class_Odivide(X1,c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X1,
inference(spm,[status(thm)],[c_0_24,c_0_23]) ).
cnf(c_0_33,axiom,
class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero ).
cnf(c_0_34,plain,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),X2,X1),X3,X1) ),
inference(fof_simplification,[status(thm)],[cls_power__one__over_0]) ).
cnf(c_0_35,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_25 ).
cnf(c_0_36,plain,
c_FFT__Mirabelle_Oroot(X1) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
c_0_26 ).
cnf(c_0_37,plain,
c_FFT__Mirabelle_Oroot(c_HOL_Oone__class_Oone(tc_nat)) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29])]) ).
cnf(c_0_38,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_39,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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]),c_0_23]),c_0_33])]) ).
cnf(c_0_40,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_41,plain,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),c_Power_Opower__class_Opower(X2,X3,X1),X1) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),X2,X1),X3,X1) ),
c_0_34 ).
cnf(c_0_42,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_HOL_Oinverse__class_Odivide(X1,X1,tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) ),
inference(spm,[status(thm)],[c_0_35,c_0_23]) ).
cnf(c_0_43,plain,
c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_44,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_38 ).
cnf(c_0_45,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_39,c_0_30]),c_0_23]),c_0_33])]) ).
cnf(c_0_46,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_40 ).
cnf(c_0_47,plain,
c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_31]),c_0_23]),c_0_33])]),c_0_43]) ).
cnf(c_0_48,plain,
( c_HOL_Oinverse__class_Odivide(X2,X1,tc_Complex_Ocomplex) != c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)
| c_HOL_Oinverse__class_Odivide(X1,X2,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_44,c_0_45]),c_0_23]),c_0_33])]) ).
cnf(c_0_49,plain,
c_HOL_Oinverse__class_Odivide(X1,c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_23])]) ).
cnf(c_0_50,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X2,X4,X1),c_Power_Opower__class_Opower(X3,X4,X1),X1) ),
inference(fof_simplification,[status(thm)],[cls_class__semiring_Opwr__mul_0]) ).
cnf(c_0_51,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(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_22]),c_0_23])]) ).
cnf(c_0_52,plain,
( c_HOL_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)
| c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_53,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X2,X4,X1),c_Power_Opower__class_Opower(X3,X4,X1),X1) ),
c_0_50 ).
cnf(c_0_54,plain,
c_HOL_Otimes__class_Otimes(X1,c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_51]),c_0_32]),c_0_23])]) ).
cnf(c_0_55,negated_conjecture,
c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),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_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),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_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),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_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),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_56,plain,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X2,X3,X1),X4,X1) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X2,X4,X1),c_Power_Opower__class_Opower(X3,X4,X1),X1) ),
inference(fof_simplification,[status(thm)],[cls_power__divide_0]) ).
cnf(c_0_57,plain,
( c_Power_Opower__class_Opower(X2,X1,tc_Complex_Ocomplex) != c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)
| c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex),c_Power_Opower__class_Opower(X2,X1,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_52,c_0_53]),c_0_54]),c_0_29])]) ).
cnf(c_0_58,negated_conjecture,
c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),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_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),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_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),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_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
c_0_55 ).
cnf(c_0_59,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_60,plain,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X2,X3,X1),X4,X1) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X2,X4,X1),c_Power_Opower__class_Opower(X3,X4,X1),X1) ),
c_0_56 ).
cnf(c_0_61,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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_27]),c_0_32]) ).
cnf(c_0_62,negated_conjecture,
c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),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_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_k,tc_Complex_Ocomplex),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_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_k,tc_Complex_Ocomplex),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_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_k,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),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(spm,[status(thm)],[c_0_58,c_0_41]),c_0_31]),c_0_31]),c_0_31]),c_0_31]),c_0_23]),c_0_33])]) ).
cnf(c_0_63,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_59 ).
cnf(c_0_64,plain,
c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(X1,tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(X1,X2,tc_Complex_Ocomplex),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_60,c_0_61]),c_0_31]),c_0_31]),c_0_23]),c_0_33])]) ).
cnf(c_0_65,negated_conjecture,
c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(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),tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_k,tc_Complex_Ocomplex),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_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),tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_k,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_29])]),c_0_64]),c_0_64]) ).
cnf(c_0_66,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_67,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_63]),c_0_66]),c_0_29])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV626-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n019.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 09:14:49 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.15/1.22 % Version: 3.5.1
% 5.15/1.22 % Preprocessing class: FMLSSMSSSSSNFFN.
% 5.15/1.22 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 5.15/1.22 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 900s (3) cores
% 5.15/1.22 % Starting new_bool_3 with 600s (2) cores
% 5.15/1.22 % Starting new_bool_1 with 600s (2) cores
% 5.15/1.22 % Starting sh5l with 300s (1) cores
% 5.15/1.22 % new_bool_1 with pid 2220928 completed with status 0
% 5.15/1.22 % Result found by new_bool_1
% 5.15/1.22 % Preprocessing class: FMLSSMSSSSSNFFN.
% 5.15/1.22 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 5.15/1.22 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 900s (3) cores
% 5.15/1.22 % Starting new_bool_3 with 600s (2) cores
% 5.15/1.22 % Starting new_bool_1 with 600s (2) cores
% 5.15/1.22 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 5.15/1.22 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 5.15/1.22 % Search class: FGHSM-FSLM32-DFFFFFNN
% 5.15/1.22 % Scheduled 13 strats onto 2 cores with 600 seconds (600 total)
% 5.15/1.22 % Starting SubtermCWHack with 55s (1) cores
% 5.15/1.22 % Starting new_bool_1 with 61s (1) cores
% 5.15/1.22 % new_bool_1 with pid 2220933 completed with status 0
% 5.15/1.22 % Result found by new_bool_1
% 5.15/1.22 % Preprocessing class: FMLSSMSSSSSNFFN.
% 5.15/1.22 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 5.15/1.22 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 900s (3) cores
% 5.15/1.22 % Starting new_bool_3 with 600s (2) cores
% 5.15/1.22 % Starting new_bool_1 with 600s (2) cores
% 5.15/1.22 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 5.15/1.22 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 5.15/1.22 % Search class: FGHSM-FSLM32-DFFFFFNN
% 5.15/1.22 % Scheduled 13 strats onto 2 cores with 600 seconds (600 total)
% 5.15/1.22 % Starting SubtermCWHack with 55s (1) cores
% 5.15/1.22 % Starting new_bool_1 with 61s (1) cores
% 5.15/1.22 % Preprocessing time : 0.007 s
% 5.15/1.22 % Presaturation interreduction done
% 5.15/1.22
% 5.15/1.22 % Proof found!
% 5.15/1.22 % SZS status Unsatisfiable
% 5.15/1.22 % SZS output start CNFRefutation
% See solution above
% 5.15/1.22 % Parsed axioms : 1041
% 5.15/1.22 % Removed by relevancy pruning/SinE : 667
% 5.15/1.22 % Initial clauses : 374
% 5.15/1.22 % Removed in clause preprocessing : 0
% 5.15/1.22 % Initial clauses in saturation : 374
% 5.15/1.22 % Processed clauses : 4647
% 5.15/1.22 % ...of these trivial : 100
% 5.15/1.22 % ...subsumed : 3121
% 5.15/1.22 % ...remaining for further processing : 1426
% 5.15/1.22 % Other redundant clauses eliminated : 220
% 5.15/1.22 % Clauses deleted for lack of memory : 0
% 5.15/1.22 % Backward-subsumed : 46
% 5.15/1.22 % Backward-rewritten : 105
% 5.15/1.22 % Generated clauses : 25969
% 5.15/1.22 % ...of the previous two non-redundant : 22130
% 5.15/1.22 % ...aggressively subsumed : 0
% 5.15/1.22 % Contextual simplify-reflections : 1
% 5.15/1.22 % Paramodulations : 25721
% 5.15/1.22 % Factorizations : 15
% 5.15/1.22 % NegExts : 0
% 5.15/1.22 % Equation resolutions : 233
% 5.15/1.22 % Disequality decompositions : 0
% 5.15/1.22 % Total rewrite steps : 26215
% 5.15/1.22 % ...of those cached : 25179
% 5.15/1.22 % Propositional unsat checks : 0
% 5.15/1.22 % Propositional check models : 0
% 5.15/1.22 % Propositional check unsatisfiable : 0
% 5.15/1.22 % Propositional clauses : 0
% 5.15/1.22 % Propositional clauses after purity: 0
% 5.15/1.22 % Propositional unsat core size : 0
% 5.15/1.22 % Propositional preprocessing time : 0.000
% 5.15/1.22 % Propositional encoding time : 0.000
% 5.15/1.22 % Propositional solver time : 0.000
% 5.15/1.22 % Success case prop preproc time : 0.000
% 5.15/1.22 % Success case prop encoding time : 0.000
% 5.15/1.22 % Success case prop solver time : 0.000
% 5.15/1.22 % Current number of processed clauses : 962
% 5.15/1.22 % Positive orientable unit clauses : 126
% 5.15/1.22 % Positive unorientable unit clauses: 5
% 5.15/1.22 % Negative unit clauses : 104
% 5.15/1.22 % Non-unit-clauses : 727
% 5.15/1.22 % Current number of unprocessed clauses: 17740
% 5.15/1.22 % ...number of literals in the above : 58251
% 5.15/1.22 % Current number of archived formulas : 0
% 5.15/1.22 % Current number of archived clauses : 462
% 5.15/1.22 % Clause-clause subsumption calls (NU) : 102626
% 5.15/1.22 % Rec. Clause-clause subsumption calls : 36070
% 5.15/1.22 % Non-unit clause-clause subsumptions : 1830
% 5.15/1.22 % Unit Clause-clause subsumption calls : 8058
% 5.15/1.22 % Rewrite failures with RHS unbound : 0
% 5.15/1.22 % BW rewrite match attempts : 747
% 5.15/1.22 % BW rewrite match successes : 122
% 5.15/1.22 % Condensation attempts : 0
% 5.15/1.22 % Condensation successes : 0
% 5.15/1.22 % Termbank termtop insertions : 436496
% 5.15/1.22 % Search garbage collected termcells : 2876
% 5.15/1.22
% 5.15/1.22 % -------------------------------------------------
% 5.15/1.22 % User time : 0.711 s
% 5.15/1.22 % System time : 0.027 s
% 5.15/1.22 % Total time : 0.738 s
% 5.15/1.22 % Maximum resident set size: 5112 pages
% 5.15/1.22
% 5.15/1.22 % -------------------------------------------------
% 5.15/1.22 % User time : 1.404 s
% 5.15/1.22 % System time : 0.070 s
% 5.15/1.22 % Total time : 1.474 s
% 5.15/1.22 % Maximum resident set size: 5632 pages
% 5.15/1.22 % E exiting
%------------------------------------------------------------------------------