%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV617-1 : 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 : n006.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 09:08:50 AM UTC 2026
% Result : Unsatisfiable 8.43s 11.54s
% Output : CNFRefutation 8.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 11
% Syntax : Number of formulae : 34 ( 23 unt; 0 def)
% Number of atoms : 47 ( 23 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 32 ( 19 ~; 13 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 6 ( 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 : 25 ( 7 sgn 9 !; 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_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_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_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_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_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]) ).
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_1143,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_1144,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_1143]) ).
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_1144]) ).
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_1145,plain,
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) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(paramod,[status(thm)],[c_787,c_775]) ).
cnf(c_1146,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_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_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(paramod,[status(thm)],[c_1089,c_1145]) ).
cnf(c_1147,plain,
c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(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_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(paramod,[status(thm)],[c_527,c_1146]) ).
cnf(c_1148,plain,
c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(paramod,[status(thm)],[c_907,c_1147]) ).
cnf(c_1142,plain,
$false,
inference(copy,[status(thm)],[c_1148]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV617-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/10.40 % Computer : n006.cluster.edu
% 0.03/10.40 % Model : x86_64 x86_64
% 0.03/10.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/10.40 % Memory : 8046.5625MB
% 0.03/10.40 % OS : Linux 6.8.0-71-generic
% 0.03/10.40 % CPULimit : 300
% 0.03/10.40 % WCLimit : 300
% 0.03/10.40 % DateTime : Sat Sep 26 14:37:24 UTC 2026
% 0.03/10.40 % CPUTime :
% 0.03/10.40 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.03/10.40 % Process 1480829 was started by sandbox on n006,
% 0.03/10.40 % Sat Sep 26 14:37:24 2026
% 0.03/10.40 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.03/10.46
% 0.03/10.46 % From the command line: assign(max_seconds, 300).
% 8.43/11.54
% 8.43/11.54 % SZS status Unsatisfiable for theBenchmark
% 8.43/11.54
% 8.43/11.54 % Proof 1 at 1.05 (+ 0.02) seconds.
% 8.43/11.54 % Length of proof is 17.
% 8.43/11.54 % Level of proof is 3.
% 8.43/11.54 % Maximum clause weight is 26.000.
% 8.43/11.54 % Given clauses 0.
% 8.43/11.54
% 8.43/11.54 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------