%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ALG348-1 : 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 06:50:03 AM UTC 2026
% Result : Unsatisfiable 19.86s 2.97s
% Output : CNFRefutation 19.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 3
% Syntax : Number of formulae : 8 ( 6 unt; 0 def)
% Number of atoms : 10 ( 5 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 6 ( 4 ~; 2 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 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_1564,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_Polynomial_Opoly(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_p,v_a,tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex) != c_Polynomial_Opoly(v_p,c_HOL_Oplus__class_Oplus(v_a,v_x,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_1587,plain,
c_Polynomial_Opoly(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(v_p,v_a,tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex) != c_Polynomial_Opoly(v_p,c_HOL_Oplus__class_Oplus(v_a,v_x,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[cls_conjecture_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_1596,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_7163,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_1596,c_1564]) ).
cnf(c_7164,plain,
$false,
inference(resolve,[status(thm)],[c_7163,c_1587]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG348-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n006.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 21:53:50 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.38 % Process 2197184 was started by sandbox2 on n006,
% 0.10/0.38 % Sat Sep 26 21:53:50 2026
% 0.10/0.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.41
% 0.10/0.41 % From the command line: assign(max_seconds, 300).
% 19.86/2.97
% 19.86/2.97 % given #500 (I,wt=29): 1506 c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(C,B,tc_RealDef_Oreal),tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(A,C,tc_RealDef_Oreal) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),B,tc_RealDef_Oreal). [resolve(42,a,56,a)].
% 19.86/2.97
% 19.86/2.97 % SZS status Unsatisfiable for theBenchmark
% 19.86/2.97
% 19.86/2.97 % Proof 1 at 2.46 (+ 0.09) seconds.
% 19.86/2.97 % Length of proof is 5.
% 19.86/2.97 % Level of proof is 2.
% 19.86/2.97 % Maximum clause weight is 32.000.
% 19.86/2.97 % Given clauses 587.
% 19.86/2.97
% 19.86/2.97 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------