%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM326+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n013.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 01:38:58 PM UTC 2026
% Result : Theorem 0.15s 0.40s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 15 ( 10 unt; 0 def)
% Number of atoms : 24 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 20 ( 11 ~; 7 |; 1 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-1 aty)
% Number of variables : 18 ( 16 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
rdn_translate(n5,rdn_pos(rdnn(n5))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f133,axiom,
rdn_translate(nn5,rdn_neg(rdnn(n5))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f291,axiom,
! [POS_X,NEG_X,RDN_X] :
( ( rdn_translate(NEG_X,rdn_neg(RDN_X))
& rdn_translate(POS_X,rdn_pos(RDN_X)) )
=> sum(POS_X,NEG_X,n0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f402,conjecture,
? [X] : sum(X,nn5,n0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f403,negated_conjecture,
~ ? [X] : sum(X,nn5,n0),
inference(negated_conjecture,[status(cth)],[f402]) ).
fof(f409,plain,
rdn_translate(n5,rdn_pos(rdnn(n5))),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f536,plain,
rdn_translate(nn5,rdn_neg(rdnn(n5))),
inference(cnf_transformation,[status(thm)],[f133]) ).
fof(f728,plain,
! [POS_X,NEG_X,RDN_X] :
( sum(POS_X,NEG_X,n0)
| ~ rdn_translate(NEG_X,rdn_neg(RDN_X))
| ~ rdn_translate(POS_X,rdn_pos(RDN_X)) ),
inference(pre_NNF_transformation,[status(thm)],[f291]) ).
fof(f729,plain,
! [POS_X,NEG_X] :
( sum(POS_X,NEG_X,n0)
| ! [RDN_X] :
( ~ rdn_translate(NEG_X,rdn_neg(RDN_X))
| ~ rdn_translate(POS_X,rdn_pos(RDN_X)) ) ),
inference(miniscoping,[status(thm)],[f728]) ).
fof(f730,plain,
! [X0,X1,X2] :
( sum(X0,X2,n0)
| ~ rdn_translate(X2,rdn_neg(X1))
| ~ rdn_translate(X0,rdn_pos(X1)) ),
inference(cnf_transformation,[status(thm)],[f729]) ).
fof(f861,plain,
! [X] : ~ sum(X,nn5,n0),
inference(pre_NNF_transformation,[status(thm)],[f403]) ).
fof(f862,plain,
! [X0] : ~ sum(X0,nn5,n0),
inference(cnf_transformation,[status(thm)],[f861]) ).
fof(f865,plain,
! [X0] :
( sum(X0,nn5,n0)
| ~ rdn_translate(X0,rdn_pos(rdnn(n5))) ),
inference(resolution,[status(thm)],[f730,f536]) ).
fof(f866,plain,
! [X0] : ~ rdn_translate(X0,rdn_pos(rdnn(n5))),
inference(forward_subsumption_resolution,[status(thm)],[f865,f862]) ).
fof(f867,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f409,f866]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM326+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n013.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 02:21:51 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.15/0.39 % Drodi V4.1.1
% 0.15/0.40 % Refutation found
% 0.15/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.42 % Elapsed time: 0.047872 seconds
% 0.15/0.42 % CPU time: 0.087812 seconds
% 0.15/0.42 % Total memory used: 18.324 MB
% 0.15/0.42 % Net memory used: 18.313 MB
%------------------------------------------------------------------------------