%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWW288+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 : Thu Sep 24 03:07:34 PM UTC 2026
% Result : Theorem 0.14s 0.71s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 23 ( 11 unt; 0 def)
% Number of atoms : 38 ( 13 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 29 ( 14 ~; 11 |; 1 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 11 ( 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f14,axiom,
( ( class_Rings_Oidom(t_a)
& class_Int_Oring__char__0(t_a) )
=> v_p = c_Polynomial_OpCons(t_a,hAPP(c_Polynomial_Opoly(t_a,v_p),c_Groups_Ozero__class_Ozero(t_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,axiom,
! [V_a,T_a] :
( class_Groups_Ozero(T_a)
=> c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1012,axiom,
! [T] :
( class_Int_Oring__char__0(T)
=> class_Groups_Ozero(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1216,conjecture,
c_Polynomial_Odegree(t_a,v_p) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1217,negated_conjecture,
c_Polynomial_Odegree(t_a,v_p) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(negated_conjecture,[status(cth)],[f1216]) ).
fof(f1218,hypothesis,
class_Int_Oring__char__0(t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1219,hypothesis,
class_Rings_Oidom(t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1251,plain,
( v_p = c_Polynomial_OpCons(t_a,hAPP(c_Polynomial_Opoly(t_a,v_p),c_Groups_Ozero__class_Ozero(t_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))
| ~ class_Rings_Oidom(t_a)
| ~ class_Int_Oring__char__0(t_a) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f1252,plain,
( v_p = c_Polynomial_OpCons(t_a,hAPP(c_Polynomial_Opoly(t_a,v_p),c_Groups_Ozero__class_Ozero(t_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))
| ~ class_Rings_Oidom(t_a)
| ~ class_Int_Oring__char__0(t_a) ),
inference(cnf_transformation,[status(thm)],[f1251]) ).
fof(f1322,plain,
! [V_a,T_a] :
( c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Groups_Ozero(T_a) ),
inference(pre_NNF_transformation,[status(thm)],[f32]) ).
fof(f1323,plain,
! [T_a] :
( ! [V_a] : c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Groups_Ozero(T_a) ),
inference(miniscoping,[status(thm)],[f1322]) ).
fof(f1324,plain,
! [X0,X1] :
( c_Polynomial_Odegree(X0,c_Polynomial_OpCons(X0,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Groups_Ozero(X0) ),
inference(cnf_transformation,[status(thm)],[f1323]) ).
fof(f4522,plain,
! [T] :
( class_Groups_Ozero(T)
| ~ class_Int_Oring__char__0(T) ),
inference(pre_NNF_transformation,[status(thm)],[f1012]) ).
fof(f4523,plain,
! [X0] :
( class_Groups_Ozero(X0)
| ~ class_Int_Oring__char__0(X0) ),
inference(cnf_transformation,[status(thm)],[f4522]) ).
fof(f4831,plain,
c_Polynomial_Odegree(t_a,v_p) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(cnf_transformation,[status(thm)],[f1217]) ).
fof(f4832,plain,
class_Int_Oring__char__0(t_a),
inference(cnf_transformation,[status(thm)],[f1218]) ).
fof(f4833,plain,
class_Rings_Oidom(t_a),
inference(cnf_transformation,[status(thm)],[f1219]) ).
fof(f5054,plain,
( v_p = c_Polynomial_OpCons(t_a,hAPP(c_Polynomial_Opoly(t_a,v_p),c_Groups_Ozero__class_Ozero(t_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))
| ~ class_Int_Oring__char__0(t_a) ),
inference(forward_subsumption_resolution,[status(thm)],[f1252,f4833]) ).
fof(f5077,plain,
v_p = c_Polynomial_OpCons(t_a,hAPP(c_Polynomial_Opoly(t_a,v_p),c_Groups_Ozero__class_Ozero(t_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),
inference(backward_subsumption_resolution,[status(thm)],[f5054,f4832]) ).
fof(f5095,plain,
( c_Polynomial_Odegree(t_a,v_p) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Groups_Ozero(t_a) ),
inference(paramodulation,[status(thm)],[f5077,f1324]) ).
fof(f5105,plain,
~ class_Groups_Ozero(t_a),
inference(forward_subsumption_resolution,[status(thm)],[f5095,f4831]) ).
fof(f5294,plain,
class_Groups_Ozero(t_a),
inference(resolution,[status(thm)],[f4523,f4832]) ).
fof(f5296,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f5294,f5105]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW288+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.58 % Computer : n009.cluster.edu
% 0.10/0.58 % Model : x86_64 x86_64
% 0.10/0.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.58 % Memory : 8046.5625MB
% 0.10/0.58 % OS : Linux 6.8.0-71-generic
% 0.10/0.58 % CPULimit : 300
% 0.10/0.58 % WCLimit : 300
% 0.10/0.58 % DateTime : Mon Sep 21 09:45:58 UTC 2026
% 0.10/0.59 % CPUTime :
% 0.14/0.69 % Drodi V4.1.1
% 0.14/0.71 % Refutation found
% 0.14/0.71 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.71 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.77 % Elapsed time: 0.175156 seconds
% 0.14/0.77 % CPU time: 0.298106 seconds
% 0.14/0.77 % Total memory used: 77.418 MB
% 0.14/0.77 % Net memory used: 76.827 MB
%------------------------------------------------------------------------------