%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ALG434-1 : 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 : n016.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 06:50:11 AM UTC 2026
% Result : Unsatisfiable 0.34s 15.59s
% Output : CNFRefutation 0.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 11 ( 8 unt; 0 def)
% Number of atoms : 16 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 12 ( 7 ~; 5 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-3 aty)
% Number of variables : 10 ( 3 sgn 4 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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_409,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_Ring__and__Field_Odvd__class_Odvd(v_p,c_Polynomial_Osmult(v_a,v_q,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_412,plain,
~ c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Polynomial_Osmult(v_a,v_q,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_CHAINED_0_01,axiom,
c_Ring__and__Field_Odvd__class_Odvd(v_p,v_q,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
file('theBenchmark.p',cls_CHAINED_0_01) ).
cnf(c_413,plain,
c_Ring__and__Field_Odvd__class_Odvd(v_p,v_q,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(clausify,[status(thm)],[cls_CHAINED_0_01]) ).
fof(cls_dvd__smult_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(VAR_1,VAR_3,tc_Polynomial_Opoly(VAR_0))
| c_Ring__and__Field_Odvd__class_Odvd(VAR_1,c_Polynomial_Osmult(VAR_2,VAR_3,VAR_0),tc_Polynomial_Opoly(VAR_0))
| ~ class_Ring__and__Field_Ocomm__semiring__1(VAR_0) ),
file('theBenchmark.p',cls_dvd__smult_0) ).
cnf(c_422,plain,
( ~ c_Ring__and__Field_Odvd__class_Odvd(B,D,tc_Polynomial_Opoly(A))
| c_Ring__and__Field_Odvd__class_Odvd(B,c_Polynomial_Osmult(C,D,A),tc_Polynomial_Opoly(A))
| ~ class_Ring__and__Field_Ocomm__semiring__1(A) ),
inference(clausify,[status(thm)],[cls_dvd__smult_0]) ).
cnf(c_917,plain,
( c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Polynomial_Osmult(A,v_q,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
inference(resolve,[status(thm)],[c_422,c_413]) ).
cnf(c_915,plain,
c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Polynomial_Osmult(A,v_q,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(resolve,[status(thm)],[c_409,c_917]) ).
cnf(c_916,plain,
$false,
inference(resolve,[status(thm)],[c_915,c_412]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG434-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/5.38 % Computer : n016.cluster.edu
% 0.09/5.38 % Model : x86_64 x86_64
% 0.09/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.38 % Memory : 8046.5625MB
% 0.09/5.38 % OS : Linux 6.8.0-71-generic
% 0.08/15.44 % CPULimit : 300
% 0.08/15.44 % WCLimit : 300
% 0.08/15.44 % DateTime : Sat Sep 26 21:59:44 UTC 2026
% 0.08/15.44 % CPUTime :
% 0.08/15.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/15.44 % Process 3639950 was started by sandbox on n013,
% 0.08/15.44 % Sat Sep 26 21:59:44 2026
% 0.08/15.44 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/15.45
% 0.08/15.45 % From the command line: assign(max_seconds, 300).
% 0.34/15.59
% 0.34/15.59 % SZS status Unsatisfiable for theBenchmark
% 0.34/15.59
% 0.34/15.59 % Proof 1 at 0.11 (+ 0.01) seconds.
% 0.34/15.59 % Length of proof is 6.
% 0.34/15.59 % Level of proof is 2.
% 0.34/15.59 % Maximum clause weight is 19.000.
% 0.34/15.59 % Given clauses 73.
% 0.34/15.59
% 0.34/15.59 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------