%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ALG438-1 : 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 : 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 06:50:12 AM UTC 2026
% Result : Unsatisfiable 1.48s 0.69s
% Output : CNFRefutation 1.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 3
% Syntax : Number of formulae : 10 ( 8 unt; 0 def)
% Number of atoms : 12 ( 7 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 8 ( 6 ~; 2 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-3 aty)
% Number of variables : 11 ( 0 sgn 4 !; 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_373,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(cls_conjecture_0,axiom,
c_HOL_Otimes__class_Otimes(c_Polynomial_OpCons(v_a,c_Polynomial_OpCons(v_b,v_p,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(v_a,v_q,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Polynomial_OpCons(v_b,v_p,tc_Complex_Ocomplex),v_q,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_380,plain,
c_HOL_Otimes__class_Otimes(c_Polynomial_OpCons(v_a,c_Polynomial_OpCons(v_b,v_p,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(v_a,v_q,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Polynomial_OpCons(v_b,v_p,tc_Complex_Ocomplex),v_q,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
cnf(c_381,plain,
c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(v_a,v_q,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Polynomial_OpCons(v_b,v_p,tc_Complex_Ocomplex),v_q,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != c_HOL_Otimes__class_Otimes(c_Polynomial_OpCons(v_a,c_Polynomial_OpCons(v_b,v_p,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(copy,[status(thm)],[c_380]) ).
fof(cls_mult__pCons__left_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_HOL_Otimes__class_Otimes(c_Polynomial_OpCons(VAR_1,VAR_2,VAR_0),VAR_3,tc_Polynomial_Opoly(VAR_0)) = c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(VAR_1,VAR_3,VAR_0),c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(VAR_0),c_HOL_Otimes__class_Otimes(VAR_2,VAR_3,tc_Polynomial_Opoly(VAR_0)),VAR_0),tc_Polynomial_Opoly(VAR_0))
| ~ class_Ring__and__Field_Ocomm__semiring__0(VAR_0) ),
file('theBenchmark.p',cls_mult__pCons__left_0) ).
cnf(c_427,plain,
( c_HOL_Otimes__class_Otimes(c_Polynomial_OpCons(B,C,A),D,tc_Polynomial_Opoly(A)) = c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(B,D,A),c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(C,D,tc_Polynomial_Opoly(A)),A),tc_Polynomial_Opoly(A))
| ~ class_Ring__and__Field_Ocomm__semiring__0(A) ),
inference(clausify,[status(thm)],[cls_mult__pCons__left_0]) ).
cnf(c_684,plain,
c_HOL_Otimes__class_Otimes(c_Polynomial_OpCons(A,B,tc_Complex_Ocomplex),C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(A,C,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(resolve,[status(thm)],[c_427,c_373]) ).
cnf(c_686,plain,
c_HOL_Otimes__class_Otimes(c_Polynomial_OpCons(v_a,c_Polynomial_OpCons(v_b,v_p,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(v_a,v_q,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Polynomial_OpCons(v_b,v_p,tc_Complex_Ocomplex),v_q,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(copy,[status(thm)],[c_381]) ).
cnf(c_685,plain,
$false,
inference(resolve,[status(thm)],[c_684,c_686]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : ALG438-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.43 % Computer : n006.cluster.edu
% 0.15/0.43 % Model : x86_64 x86_64
% 0.15/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.43 % Memory : 8046.5625MB
% 0.15/0.43 % OS : Linux 6.8.0-71-generic
% 0.15/0.43 % CPULimit : 300
% 0.15/0.43 % WCLimit : 300
% 0.15/0.43 % DateTime : Sat Sep 26 22:00:40 UTC 2026
% 0.15/0.44 % CPUTime :
% 0.15/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/0.44 % Process 2211392 was started by sandbox2 on n006,
% 0.15/0.44 % Sat Sep 26 22:00:40 2026
% 0.15/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.15/0.47
% 0.15/0.47 % From the command line: assign(max_seconds, 300).
% 1.48/0.69
% 1.48/0.69 % SZS status Unsatisfiable for theBenchmark
% 1.48/0.69
% 1.48/0.69 % Proof 1 at 0.21 (+ 0.01) seconds.
% 1.48/0.69 % Length of proof is 6.
% 1.48/0.69 % Level of proof is 2.
% 1.48/0.69 % Maximum clause weight is 56.000.
% 1.48/0.69 % Given clauses 148.
% 1.48/0.69
% 1.48/0.69 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------