%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ALG391-1 : 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 : n014.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 06:50:07 AM UTC 2026
% Result : Unsatisfiable 22.30s 3.71s
% Output : CNFRefutation 22.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 2
% Syntax : Number of formulae : 10 ( 4 unt; 0 def)
% Number of atoms : 20 ( 19 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 22 ( 12 ~; 10 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 4 ( 0 sgn 1 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_conjecture_0,axiom,
v_cs____ != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_1033,plain,
v_cs____ != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_conjecture_2,axiom,
! [VAR_0] :
( VAR_0 = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| c_Polynomial_Odegree(VAR_0,t_a) != c_Polynomial_Odegree(v_cs____,t_a)
| c_Polynomial_Opoly(v_cs____,hAPP(v_x,VAR_0),t_a) != c_Polynomial_Opoly(VAR_0,hAPP(v_x,VAR_0),t_a) ),
file('theBenchmark.p',cls_conjecture_2) ).
cnf(c_1036,plain,
( A = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| c_Polynomial_Odegree(A,t_a) != c_Polynomial_Odegree(v_cs____,t_a)
| c_Polynomial_Opoly(v_cs____,hAPP(v_x,A),t_a) != c_Polynomial_Opoly(A,hAPP(v_x,A),t_a) ),
inference(clausify,[status(thm)],[cls_conjecture_2]) ).
cnf(c_3143,plain,
( A = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| c_Polynomial_Odegree(v_cs____,t_a) != c_Polynomial_Odegree(A,t_a)
| c_Polynomial_Opoly(v_cs____,hAPP(v_x,A),t_a) != c_Polynomial_Opoly(A,hAPP(v_x,A),t_a) ),
inference(copy,[status(thm)],[c_1036]) ).
cnf(c_1037,plain,
( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) = A
| c_Polynomial_Odegree(v_cs____,t_a) != c_Polynomial_Odegree(A,t_a)
| c_Polynomial_Opoly(v_cs____,hAPP(v_x,A),t_a) != c_Polynomial_Opoly(A,hAPP(v_x,A),t_a) ),
inference(copy,[status(thm)],[c_3143]) ).
cnf(c_3144,plain,
( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) = v_cs____
| c_Polynomial_Odegree(v_cs____,t_a) != c_Polynomial_Odegree(v_cs____,t_a) ),
inference(xxres,[status(thm)],[c_1037]) ).
cnf(c_3145,plain,
( v_cs____ = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| c_Polynomial_Odegree(v_cs____,t_a) != c_Polynomial_Odegree(v_cs____,t_a) ),
inference(copy,[status(thm)],[c_3144]) ).
cnf(c_3146,plain,
v_cs____ = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),
inference(copy,[status(thm)],[c_3145]) ).
cnf(c_3142,plain,
$false,
inference(resolve,[status(thm)],[c_1033,c_3146]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : ALG391-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.45 % Computer : n014.cluster.edu
% 0.18/0.45 % Model : x86_64 x86_64
% 0.18/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.45 % Memory : 8046.5625MB
% 0.18/0.45 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Sat Sep 26 21:57:02 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.45 % Process 4180602 was started by sandbox on n014,
% 0.18/0.45 % Sat Sep 26 21:57:02 2026
% 0.18/0.45 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.18/0.49
% 0.18/0.49 % From the command line: assign(max_seconds, 300).
% 22.30/3.71
% 22.30/3.71 % SZS status Unsatisfiable for theBenchmark
% 22.30/3.71
% 22.30/3.71 % Proof 1 at 3.12 (+ 0.06) seconds.
% 22.30/3.71 % Length of proof is 4.
% 22.30/3.71 % Level of proof is 2.
% 22.30/3.71 % Maximum clause weight is 31.000.
% 22.30/3.71 % Given clauses 254.
% 22.30/3.71
% 22.30/3.71 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------