%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ALG424-1 : 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 : n005.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 21.43s 3.22s
% Output : CNFRefutation 21.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 20 ( 12 unt; 0 def)
% Number of atoms : 36 ( 23 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 35 ( 19 ~; 16 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-3 aty)
% Number of variables : 9 ( 0 sgn 3 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_conjecture_0,axiom,
~ c_Ring__and__Field_Odvd__class_Odvd(v_pa____,c_Power_Opower__class_Opower(v_qa____,v_na____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_502,plain,
~ c_Ring__and__Field_Odvd__class_Odvd(v_pa____,c_Power_Opower__class_Opower(v_qa____,v_na____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_CHAINED_0_03,axiom,
( c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(v_pa____,c_Power_Opower__class_Opower(v_qa____,v_na____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
file('theBenchmark.p',cls_CHAINED_0_03) ).
cnf(c_503,plain,
( c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(v_pa____,c_Power_Opower__class_Opower(v_qa____,v_na____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
inference(clausify,[status(thm)],[cls_CHAINED_0_03]) ).
cnf(c_504,plain,
c_Polynomial_Oorder(v_a____,v_pa____,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(resolve,[status(thm)],[c_502,c_503]) ).
fof(cls_CHAINED_0_02,axiom,
c_Polynomial_Opoly(v_pa____,v_a____,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('theBenchmark.p',cls_CHAINED_0_02) ).
cnf(c_505,plain,
c_Polynomial_Opoly(v_pa____,v_a____,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[cls_CHAINED_0_02]) ).
fof(cls_CHAINED_0_01,axiom,
! [VAR_0,VAR_1,VAR_2] :
( c_Polynomial_Opoly(VAR_2,VAR_1,VAR_0) != c_HOL_Ozero__class_Ozero(VAR_0)
| VAR_2 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(VAR_0))
| c_Polynomial_Oorder(VAR_1,VAR_2,VAR_0) != c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Ring__and__Field_Oidom(VAR_0) ),
file('theBenchmark.p',cls_CHAINED_0_01) ).
cnf(c_506,plain,
( c_Polynomial_Opoly(C,B,A) != c_HOL_Ozero__class_Ozero(A)
| C = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A))
| c_Polynomial_Oorder(B,C,A) != c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Ring__and__Field_Oidom(A) ),
inference(clausify,[status(thm)],[cls_CHAINED_0_01]) ).
cnf(c_507,plain,
( c_Polynomial_Opoly(C,B,A) != c_HOL_Ozero__class_Ozero(A)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)) = C
| c_Polynomial_Oorder(B,C,A) != c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Ring__and__Field_Oidom(A) ),
inference(copy,[status(thm)],[c_506]) ).
fof(cls_CHAINED_0,axiom,
v_pa____ != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
file('theBenchmark.p',cls_CHAINED_0) ).
cnf(c_510,plain,
v_pa____ != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(clausify,[status(thm)],[cls_CHAINED_0]) ).
cnf(c_511,plain,
c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_pa____,
inference(copy,[status(thm)],[c_510]) ).
fof(clsarity_Complex__Ocomplex__Ring__and__Field_Oidom,axiom,
class_Ring__and__Field_Oidom(tc_Complex_Ocomplex),
file('theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oidom) ).
cnf(c_1299,plain,
class_Ring__and__Field_Oidom(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[clsarity_Complex__Ocomplex__Ring__and__Field_Oidom]) ).
cnf(c_1759,plain,
( c_Polynomial_Opoly(v_pa____,v_a____,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_pa____
| ~ class_Ring__and__Field_Oidom(tc_Complex_Ocomplex) ),
inference(resolve,[status(thm)],[c_507,c_504]) ).
cnf(c_1760,plain,
( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_pa____
| ~ class_Ring__and__Field_Oidom(tc_Complex_Ocomplex) ),
inference(paramod,[status(thm)],[c_505,c_1759]) ).
cnf(c_1761,plain,
( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_pa____
| ~ class_Ring__and__Field_Oidom(tc_Complex_Ocomplex) ),
inference(copy,[status(thm)],[c_1760]) ).
cnf(c_1762,plain,
c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_pa____,
inference(resolve,[status(thm)],[c_1299,c_1761]) ).
cnf(c_1758,plain,
$false,
inference(resolve,[status(thm)],[c_511,c_1762]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : ALG424-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.44 % Computer : n005.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Sat Sep 26 21:59:32 UTC 2026
% 0.17/0.45 % CPUTime :
% 0.17/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.45 % Process 3190827 was started by sandbox on n005,
% 0.17/0.45 % Sat Sep 26 21:59:32 2026
% 0.17/0.45 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.26/0.51
% 0.26/0.51 % From the command line: assign(max_seconds, 300).
% 21.43/3.22
% 21.43/3.22 % SZS status Unsatisfiable for theBenchmark
% 21.43/3.22
% 21.43/3.22 % Proof 1 at 2.62 (+ 0.05) seconds.
% 21.43/3.22 % Length of proof is 10.
% 21.43/3.22 % Level of proof is 2.
% 21.43/3.22 % Maximum clause weight is 27.000.
% 21.43/3.22 % Given clauses 11.
% 21.43/3.22
% 21.43/3.22 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------