%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ALG421-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.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 06:50:10 AM UTC 2026
% Result : Unsatisfiable 33.31s 5.35s
% Output : CNFRefutation 33.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of formulae : 17 ( 13 unt; 0 def)
% Number of atoms : 21 ( 12 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 10 ( 6 ~; 4 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-3 aty)
% Number of variables : 24 ( 0 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
file('theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0) ).
cnf(c_624,plain,
class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__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_625,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_conjecture_0,axiom,
c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(v_s____,v_x,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_u____,v_x,tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_Power_Opower__class_Opower(c_Polynomial_Opoly(v_r____,v_x,tc_Complex_Ocomplex),c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_637,plain,
c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(v_s____,v_x,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_u____,v_x,tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_Power_Opower__class_Opower(c_Polynomial_Opoly(v_r____,v_x,tc_Complex_Ocomplex),c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_CHAINED_0,axiom,
c_Power_Opower__class_Opower(v_r____,c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_HOL_Otimes__class_Otimes(v_s____,v_u____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
file('theBenchmark.p',cls_CHAINED_0) ).
cnf(c_638,plain,
c_Power_Opower__class_Opower(v_r____,c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_HOL_Otimes__class_Otimes(v_s____,v_u____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(clausify,[status(thm)],[cls_CHAINED_0]) ).
fof(cls_poly__power_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_Polynomial_Opoly(c_Power_Opower__class_Opower(VAR_1,VAR_2,tc_Polynomial_Opoly(VAR_0)),VAR_3,VAR_0) = c_Power_Opower__class_Opower(c_Polynomial_Opoly(VAR_1,VAR_3,VAR_0),VAR_2,VAR_0)
| ~ class_Ring__and__Field_Ocomm__semiring__1(VAR_0) ),
file('theBenchmark.p',cls_poly__power_0) ).
cnf(c_654,plain,
( c_Polynomial_Opoly(c_Power_Opower__class_Opower(B,C,tc_Polynomial_Opoly(A)),D,A) = c_Power_Opower__class_Opower(c_Polynomial_Opoly(B,D,A),C,A)
| ~ class_Ring__and__Field_Ocomm__semiring__1(A) ),
inference(clausify,[status(thm)],[cls_poly__power_0]) ).
fof(cls_poly__mult_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_Polynomial_Opoly(c_HOL_Otimes__class_Otimes(VAR_1,VAR_2,tc_Polynomial_Opoly(VAR_0)),VAR_3,VAR_0) = c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(VAR_1,VAR_3,VAR_0),c_Polynomial_Opoly(VAR_2,VAR_3,VAR_0),VAR_0)
| ~ class_Ring__and__Field_Ocomm__semiring__0(VAR_0) ),
file('theBenchmark.p',cls_poly__mult_0) ).
cnf(c_656,plain,
( c_Polynomial_Opoly(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),D,A) = c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(B,D,A),c_Polynomial_Opoly(C,D,A),A)
| ~ class_Ring__and__Field_Ocomm__semiring__0(A) ),
inference(clausify,[status(thm)],[cls_poly__mult_0]) ).
cnf(c_1608,plain,
c_Polynomial_Opoly(c_Power_Opower__class_Opower(A,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),C,tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_Polynomial_Opoly(A,C,tc_Complex_Ocomplex),B,tc_Complex_Ocomplex),
inference(resolve,[status(thm)],[c_654,c_625]) ).
cnf(c_1612,plain,
c_Polynomial_Opoly(c_HOL_Otimes__class_Otimes(A,B,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),C,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(A,C,tc_Complex_Ocomplex),c_Polynomial_Opoly(B,C,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(resolve,[status(thm)],[c_656,c_624]) ).
cnf(c_9198,plain,
c_Polynomial_Opoly(c_HOL_Otimes__class_Otimes(v_s____,v_u____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),A,tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_Polynomial_Opoly(v_r____,A,tc_Complex_Ocomplex),c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(paramod,[status(thm)],[c_638,c_1608]) ).
cnf(c_9196,plain,
c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(v_s____,A,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_u____,A,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_Polynomial_Opoly(v_r____,A,tc_Complex_Ocomplex),c_Polynomial_Odegree(v_s____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(paramod,[status(thm)],[c_1612,c_9198]) ).
cnf(c_9197,plain,
$false,
inference(resolve,[status(thm)],[c_9196,c_637]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : ALG421-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.46 % Computer : n015.cluster.edu
% 0.18/0.46 % Model : x86_64 x86_64
% 0.18/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.46 % Memory : 8046.5625MB
% 0.18/0.46 % OS : Linux 6.8.0-71-generic
% 0.18/0.46 % CPULimit : 300
% 0.18/0.46 % WCLimit : 300
% 0.18/0.46 % DateTime : Sat Sep 26 22:02:29 UTC 2026
% 0.18/0.47 % CPUTime :
% 0.18/0.47 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.47 % Process 837376 was started by sandbox2 on n015,
% 0.18/0.47 % Sat Sep 26 22:02:29 2026
% 0.18/0.47 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.23/0.52
% 0.23/0.52 % From the command line: assign(max_seconds, 300).
% 33.31/5.35
% 33.31/5.35 % given #500 (I,wt=42): 1182 c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(B)),tc_Polynomial_Opoly(B)) | c_HOL_Oord__class_Oless(C,D,tc_Polynomial_Opoly(B)) | -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,C,tc_Polynomial_Opoly(B)),c_HOL_Otimes__class_Otimes(A,D,tc_Polynomial_Opoly(B)),tc_Polynomial_Opoly(B)) | -class_Ring__and__Field_Oordered__idom(B). [resolve(91,a,89,a)].
% 33.31/5.35
% 33.31/5.35 % given #1000 (A,wt=29): 1560 c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),A,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = A. [resolve(625,a,378,a)].
% 33.31/5.35
% 33.31/5.35 % SZS status Unsatisfiable for theBenchmark
% 33.31/5.35
% 33.31/5.35 % Proof 1 at 4.16 (+ 0.61) seconds.
% 33.31/5.35 % Length of proof is 10.
% 33.31/5.35 % Level of proof is 3.
% 33.31/5.35 % Maximum clause weight is 41.000.
% 33.31/5.35 % Given clauses 1130.
% 33.31/5.35
% 33.31/5.35 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------