%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV629-1 : 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 : n020.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 0.62s 0.47s
% Output : CNFRefutation 0.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 12 ( 10 unt; 0 def)
% Number of atoms : 14 ( 9 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 6 ( 4 ~; 2 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-3 aty)
% Number of variables : 7 ( 0 sgn 3 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_power__one__right_0,axiom,
! [VAR_0,VAR_1] :
( c_Power_Opower__class_Opower(VAR_1,c_HOL_Oone__class_Oone(tc_nat),VAR_0) = VAR_1
| ~ class_OrderedGroup_Omonoid__mult(VAR_0) ),
file('theBenchmark.p',cls_power__one__right_0) ).
cnf(c_162,plain,
( c_Power_Opower__class_Opower(B,c_HOL_Oone__class_Oone(tc_nat),A) = B
| ~ class_OrderedGroup_Omonoid__mult(A) ),
inference(clausify,[status(thm)],[cls_power__one__right_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_165,plain,
class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult]) ).
cnf(c_179,plain,
c_Power_Opower__class_Opower(A,c_HOL_Oone__class_Oone(tc_nat),tc_Complex_Ocomplex) = A,
inference(resolve,[status(thm)],[c_165,c_162]) ).
fof(cls_conjecture_0,axiom,
c_FFT__Mirabelle_Oroot(c_HOL_Oone__class_Oone(tc_nat)) != c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_289,plain,
c_FFT__Mirabelle_Oroot(c_HOL_Oone__class_Oone(tc_nat)) != c_HOL_Oone__class_Oone(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_299,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_640,plain,
c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = c_FFT__Mirabelle_Oroot(c_HOL_Oone__class_Oone(tc_nat)),
inference(paramod,[status(thm)],[c_299,c_179]) ).
cnf(c_641,plain,
c_FFT__Mirabelle_Oroot(c_HOL_Oone__class_Oone(tc_nat)) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),
inference(copy,[status(thm)],[c_640]) ).
cnf(c_639,plain,
$false,
inference(resolve,[status(thm)],[c_289,c_641]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV629-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n020.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 14:39:49 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 1799291 was started by sandbox on n020,
% 0.09/0.36 % Sat Sep 26 14:39:49 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.38
% 0.09/0.38 % From the command line: assign(max_seconds, 300).
% 0.62/0.47
% 0.62/0.47 % SZS status Unsatisfiable for theBenchmark
% 0.62/0.47
% 0.62/0.47 % Proof 1 at 0.08 (+ 0.01) seconds.
% 0.62/0.47 % Length of proof is 6.
% 0.62/0.47 % Level of proof is 2.
% 0.62/0.47 % Maximum clause weight is 23.000.
% 0.62/0.47 % Given clauses 54.
% 0.62/0.47
% 0.62/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------