%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV627-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.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 : Sun Sep 27 09:08:51 AM UTC 2026
% Result : Unsatisfiable 5.74s 2.08s
% Output : CNFRefutation 5.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 13
% Syntax : Number of formulae : 48 ( 32 unt; 0 def)
% Number of atoms : 68 ( 37 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 53 ( 33 ~; 20 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-3 aty)
% Number of variables : 44 ( 7 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero,axiom,
class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex),
file('theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero) ).
cnf(c_45,plain,
class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero]) ).
fof(cls_power__divide_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(VAR_1,VAR_2,VAR_0),VAR_3,VAR_0) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(VAR_1,VAR_3,VAR_0),c_Power_Opower__class_Opower(VAR_2,VAR_3,VAR_0),VAR_0)
| ~ class_Ring__and__Field_Odivision__by__zero(VAR_0)
| ~ class_Ring__and__Field_Ofield(VAR_0) ),
file('theBenchmark.p',cls_power__divide_0) ).
cnf(c_49,plain,
( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(B,C,A),D,A) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(B,D,A),c_Power_Opower__class_Opower(C,D,A),A)
| ~ class_Ring__and__Field_Odivision__by__zero(A)
| ~ class_Ring__and__Field_Ofield(A) ),
inference(clausify,[status(thm)],[cls_power__divide_0]) ).
fof(cls_eq__divide__eq_4,axiom,
! [VAR_0,VAR_1] :
( c_HOL_Ozero__class_Ozero(VAR_0) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(VAR_0),VAR_1,VAR_0),VAR_1,VAR_0)
| ~ class_Ring__and__Field_Odivision__by__zero(VAR_0)
| ~ class_Ring__and__Field_Ofield(VAR_0) ),
file('theBenchmark.p',cls_eq__divide__eq_4) ).
cnf(c_61,plain,
( c_HOL_Ozero__class_Ozero(A) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),B,A),B,A)
| ~ class_Ring__and__Field_Odivision__by__zero(A)
| ~ class_Ring__and__Field_Ofield(A) ),
inference(clausify,[status(thm)],[cls_eq__divide__eq_4]) ).
fof(cls_class__semiring_Osemiring__rules_I9_J_0,axiom,
! [VAR_0,VAR_1] :
( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(VAR_0),VAR_1,VAR_0) = c_HOL_Ozero__class_Ozero(VAR_0)
| ~ class_Ring__and__Field_Ocomm__semiring__1(VAR_0) ),
file('theBenchmark.p',cls_class__semiring_Osemiring__rules_I9_J_0) ).
cnf(c_111,plain,
( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),B,A) = c_HOL_Ozero__class_Ozero(A)
| ~ class_Ring__and__Field_Ocomm__semiring__1(A) ),
inference(clausify,[status(thm)],[cls_class__semiring_Osemiring__rules_I9_J_0]) ).
fof(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1) ).
cnf(c_128,plain,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1]) ).
fof(cls_diff__self_0,axiom,
! [VAR_0,VAR_1] :
( c_HOL_Ominus__class_Ominus(VAR_1,VAR_1,VAR_0) = c_HOL_Ozero__class_Ozero(VAR_0)
| ~ class_OrderedGroup_Ogroup__add(VAR_0) ),
file('theBenchmark.p',cls_diff__self_0) ).
cnf(c_346,plain,
( c_HOL_Ominus__class_Ominus(B,B,A) = c_HOL_Ozero__class_Ozero(A)
| ~ class_OrderedGroup_Ogroup__add(A) ),
inference(clausify,[status(thm)],[cls_diff__self_0]) ).
fof(clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add,axiom,
class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex),
file('theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add) ).
cnf(c_359,plain,
class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add]) ).
fof(cls_power__one_0,axiom,
! [VAR_0,VAR_1] :
( c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(VAR_0),VAR_1,VAR_0) = c_HOL_Oone__class_Oone(VAR_0)
| ~ class_OrderedGroup_Omonoid__mult(VAR_0) ),
file('theBenchmark.p',cls_power__one_0) ).
cnf(c_444,plain,
( c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(A),B,A) = c_HOL_Oone__class_Oone(A)
| ~ class_OrderedGroup_Omonoid__mult(A) ),
inference(clausify,[status(thm)],[cls_power__one_0]) ).
fof(clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult,axiom,
class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex),
file('theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult) ).
cnf(c_447,plain,
class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult]) ).
cnf(c_527,plain,
c_HOL_Ominus__class_Ominus(A,A,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(resolve,[status(thm)],[c_359,c_346]) ).
cnf(c_658,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(resolve,[status(thm)],[c_128,c_111]) ).
fof(clsarity_Complex__Ocomplex__Ring__and__Field_Ofield,axiom,
class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
file('theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ofield) ).
cnf(c_760,plain,
class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[clsarity_Complex__Ocomplex__Ring__and__Field_Ofield]) ).
fof(cls_conjecture_0,axiom,
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_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_775,plain,
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_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_root__unity_0,axiom,
! [VAR_0] : c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(VAR_0),VAR_0,tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),
file('theBenchmark.p',cls_root__unity_0) ).
cnf(c_787,plain,
c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(A),A,tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[cls_root__unity_0]) ).
fof(cls_divide__1_0,axiom,
! [VAR_0,VAR_1] :
( c_HOL_Oinverse__class_Odivide(VAR_1,c_HOL_Oone__class_Oone(VAR_0),VAR_0) = VAR_1
| ~ class_Ring__and__Field_Ofield(VAR_0) ),
file('theBenchmark.p',cls_divide__1_0) ).
cnf(c_790,plain,
( c_HOL_Oinverse__class_Odivide(B,c_HOL_Oone__class_Oone(A),A) = B
| ~ class_Ring__and__Field_Ofield(A) ),
inference(clausify,[status(thm)],[cls_divide__1_0]) ).
cnf(c_893,plain,
( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(A,B,tc_Complex_Ocomplex),C,tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(A,C,tc_Complex_Ocomplex),c_Power_Opower__class_Opower(B,C,tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex) ),
inference(resolve,[status(thm)],[c_49,c_45]) ).
cnf(c_894,plain,
c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(A,B,tc_Complex_Ocomplex),C,tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(A,C,tc_Complex_Ocomplex),c_Power_Opower__class_Opower(B,C,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(resolve,[status(thm)],[c_760,c_893]) ).
cnf(c_906,plain,
( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex),A,tc_Complex_Ocomplex)
| ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex) ),
inference(resolve,[status(thm)],[c_61,c_45]) ).
cnf(c_1784,plain,
( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex)
| ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex) ),
inference(paramod,[status(thm)],[c_658,c_906]) ).
cnf(c_1785,plain,
( c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex) ),
inference(copy,[status(thm)],[c_1784]) ).
cnf(c_907,plain,
c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(resolve,[status(thm)],[c_760,c_1785]) ).
cnf(c_1089,plain,
c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),
inference(resolve,[status(thm)],[c_444,c_447]) ).
cnf(c_1786,plain,
c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),v_n,tc_Complex_Ocomplex),c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_n,tc_Complex_Ocomplex),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_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(paramod,[status(thm)],[c_894,c_775]) ).
cnf(c_1787,plain,
c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_n,tc_Complex_Ocomplex),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_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(paramod,[status(thm)],[c_1089,c_1786]) ).
cnf(c_1788,plain,
c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),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_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(paramod,[status(thm)],[c_787,c_1787]) ).
cnf(c_1789,plain,
c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),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_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(paramod,[status(thm)],[c_894,c_1788]) ).
cnf(c_1790,plain,
c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),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_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(paramod,[status(thm)],[c_1089,c_1789]) ).
cnf(c_1791,plain,
c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),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_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(paramod,[status(thm)],[c_1089,c_1790]) ).
cnf(c_1792,plain,
c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(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_Odivide(c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),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_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(paramod,[status(thm)],[c_894,c_1791]) ).
cnf(c_1162,plain,
c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(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_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),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_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(paramod,[status(thm)],[c_1089,c_1792]) ).
cnf(c_1782,plain,
c_HOL_Oinverse__class_Odivide(A,c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = A,
inference(resolve,[status(thm)],[c_790,c_760]) ).
cnf(c_1793,plain,
c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),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_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(paramod,[status(thm)],[c_1782,c_1162]) ).
cnf(c_1794,plain,
c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),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_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(paramod,[status(thm)],[c_527,c_1793]) ).
cnf(c_1795,plain,
c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(paramod,[status(thm)],[c_907,c_1794]) ).
cnf(c_1783,plain,
$false,
inference(copy,[status(thm)],[c_1795]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV627-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.41 % Computer : n013.cluster.edu
% 0.09/0.41 % Model : x86_64 x86_64
% 0.09/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.41 % Memory : 8046.5625MB
% 0.09/0.41 % OS : Linux 6.8.0-71-generic
% 0.09/0.41 % CPULimit : 300
% 0.09/0.41 % WCLimit : 300
% 0.09/0.41 % DateTime : Sat Sep 26 14:38:21 UTC 2026
% 0.09/0.41 % CPUTime :
% 0.09/0.41 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.41 % Process 2958224 was started by sandbox on n013,
% 0.09/0.41 % Sat Sep 26 14:38:21 2026
% 0.09/0.41 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.43
% 0.11/0.43 % From the command line: assign(max_seconds, 300).
% 5.74/2.08
% 5.74/2.08 % SZS status Unsatisfiable for theBenchmark
% 5.74/2.08
% 5.74/2.08 % Proof 1 at 0.69 (+ 0.05) seconds.
% 5.74/2.08 % Length of proof is 23.
% 5.74/2.08 % Level of proof is 4.
% 5.74/2.08 % Maximum clause weight is 69.000.
% 5.74/2.08 % Given clauses 228.
% 5.74/2.08
% 5.74/2.08 % SZS output start CNFRefutation for theBenchmark
% See solution above
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