%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ALG367-1 : 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 : n017.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 06:50:04 AM UTC 2026
% Result : Unsatisfiable 29.63s 4.29s
% Output : CNFRefutation 29.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 19 ( 9 unt; 0 def)
% Number of atoms : 33 ( 20 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 34 ( 20 ~; 14 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 2 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 25 ( 2 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_538,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_1,axiom,
! [VAR_0] :
( v_thesis____
| c_Polynomial_Odegree(VAR_0,tc_Complex_Ocomplex) != c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex)
| c_Polynomial_Opoly(VAR_0,v_q(VAR_0),tc_Complex_Ocomplex) != c_Polynomial_Opoly(v_p,c_HOL_Oplus__class_Oplus(v_z,v_q(VAR_0),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_610,plain,
( v_thesis____
| c_Polynomial_Odegree(A,tc_Complex_Ocomplex) != c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex)
| c_Polynomial_Opoly(A,v_q(A),tc_Complex_Ocomplex) != c_Polynomial_Opoly(v_p,c_HOL_Oplus__class_Oplus(v_z,v_q(A),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
cnf(c_10577,plain,
( v_thesis____
| c_Polynomial_Odegree(A,tc_Complex_Ocomplex) != c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex)
| c_Polynomial_Opoly(v_p,c_HOL_Oplus__class_Oplus(v_z,v_q(A),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_Polynomial_Opoly(A,v_q(A),tc_Complex_Ocomplex) ),
inference(copy,[status(thm)],[c_610]) ).
cnf(c_611,plain,
( v_thesis____
| c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_Polynomial_Odegree(A,tc_Complex_Ocomplex)
| c_Polynomial_Opoly(v_p,c_HOL_Oplus__class_Oplus(v_z,v_q(A),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_Polynomial_Opoly(A,v_q(A),tc_Complex_Ocomplex) ),
inference(copy,[status(thm)],[c_10577]) ).
fof(cls_conjecture_0,axiom,
~ v_thesis____,
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_612,plain,
~ v_thesis____,
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_degree__offset__poly_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( c_Polynomial_Odegree(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(VAR_1,VAR_2,VAR_0),VAR_0) = c_Polynomial_Odegree(VAR_1,VAR_0)
| ~ class_Ring__and__Field_Ocomm__semiring__0(VAR_0) ),
file('theBenchmark.p',cls_degree__offset__poly_0) ).
cnf(c_654,plain,
( c_Polynomial_Odegree(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(B,C,A),A) = c_Polynomial_Odegree(B,A)
| ~ class_Ring__and__Field_Ocomm__semiring__0(A) ),
inference(clausify,[status(thm)],[cls_degree__offset__poly_0]) ).
fof(cls_poly__offset__poly_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_Polynomial_Opoly(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(VAR_1,VAR_2,VAR_0),VAR_3,VAR_0) = c_Polynomial_Opoly(VAR_1,c_HOL_Oplus__class_Oplus(VAR_2,VAR_3,VAR_0),VAR_0)
| ~ class_Ring__and__Field_Ocomm__semiring__0(VAR_0) ),
file('theBenchmark.p',cls_poly__offset__poly_0) ).
cnf(c_655,plain,
( c_Polynomial_Opoly(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(B,C,A),D,A) = c_Polynomial_Opoly(B,c_HOL_Oplus__class_Oplus(C,D,A),A)
| ~ class_Ring__and__Field_Ocomm__semiring__0(A) ),
inference(clausify,[status(thm)],[cls_poly__offset__poly_0]) ).
cnf(c_1970,plain,
( c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_Polynomial_Odegree(A,tc_Complex_Ocomplex)
| c_Polynomial_Opoly(v_p,c_HOL_Oplus__class_Oplus(v_z,v_q(A),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_Polynomial_Opoly(A,v_q(A),tc_Complex_Ocomplex) ),
inference(resolve,[status(thm)],[c_612,c_611]) ).
cnf(c_2210,plain,
c_Polynomial_Odegree(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(A,B,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Polynomial_Odegree(A,tc_Complex_Ocomplex),
inference(resolve,[status(thm)],[c_654,c_538]) ).
cnf(c_2213,plain,
c_Polynomial_Opoly(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(A,B,tc_Complex_Ocomplex),C,tc_Complex_Ocomplex) = c_Polynomial_Opoly(A,c_HOL_Oplus__class_Oplus(B,C,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(resolve,[status(thm)],[c_655,c_538]) ).
cnf(c_10578,plain,
( c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_Polynomial_Odegree(A,tc_Complex_Ocomplex)
| c_Polynomial_Opoly(A,v_q(A),tc_Complex_Ocomplex) != c_Polynomial_Opoly(v_p,c_HOL_Oplus__class_Oplus(v_z,v_q(A),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
inference(copy,[status(thm)],[c_1970]) ).
cnf(c_10579,plain,
c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_Polynomial_Odegree(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_p,v_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(resolve,[status(thm)],[c_2213,c_10578]) ).
cnf(c_10580,plain,
c_Polynomial_Odegree(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_p,v_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),
inference(copy,[status(thm)],[c_10579]) ).
cnf(c_10576,plain,
$false,
inference(resolve,[status(thm)],[c_2210,c_10580]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : ALG367-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.41 % Computer : n017.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8046.5625MB
% 0.15/0.41 % OS : Linux 6.8.0-71-generic
% 0.15/0.41 % CPULimit : 300
% 0.15/0.41 % WCLimit : 300
% 0.15/0.41 % DateTime : Sat Sep 26 21:50:33 UTC 2026
% 0.15/0.42 % CPUTime :
% 0.15/0.42 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/0.42 % Process 1718445 was started by sandbox on n017,
% 0.15/0.42 % Sat Sep 26 21:50:33 2026
% 0.15/0.42 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.15/0.47
% 0.15/0.47 % From the command line: assign(max_seconds, 300).
% 29.63/4.29
% 29.63/4.29 % given #500 (I,wt=13): 1144 c_lessequals(A,B,tc_nat) | c_lessequals(B,A,tc_nat). [resolve(161,a,158,a)].
% 29.63/4.29
% 29.63/4.29 % given #1000 (I,wt=22): 1791 c_HOL_Oplus__class_Oplus(A,B,tc_Complex_Ocomplex) != c_HOL_Oplus__class_Oplus(A,C,tc_Complex_Ocomplex) | B = C. [copy(1790),unit_del(a,1643)].
% 29.63/4.29
% 29.63/4.29 % SZS status Unsatisfiable for theBenchmark
% 29.63/4.29
% 29.63/4.29 % Proof 1 at 3.35 (+ 0.43) seconds.
% 29.63/4.29 % Length of proof is 10.
% 29.63/4.29 % Level of proof is 3.
% 29.63/4.29 % Maximum clause weight is 42.000.
% 29.63/4.29 % Given clauses 1473.
% 29.63/4.29
% 29.63/4.29 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------