%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM292+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 : 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 : Thu Sep 24 01:38:54 PM UTC 2026
% Result : Theorem 12.59s 2.12s
% Output : CNFRefutation 12.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 26 ( 13 unt; 0 def)
% Number of atoms : 48 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 41 ( 19 ~; 17 |; 2 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 37 ( 37 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
rdn_translate(n2,rdn_pos(rdnn(n2))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
rdn_translate(n13,rdn_pos(rdn(rdnn(n3),rdnn(n1)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f257,axiom,
rdn_non_zero_digit(rdnn(n1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f278,axiom,
! [D,Db,Ob] :
( rdn_non_zero(Ob)
=> rdn_positive_less(rdnn(D),rdn(rdnn(Db),Ob)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f279,axiom,
! [X] :
( rdn_non_zero_digit(rdnn(X))
=> rdn_non_zero(rdnn(X)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f281,axiom,
! [X,Y,RDN_X,RDN_Y] :
( ( rdn_positive_less(RDN_X,RDN_Y)
& rdn_translate(Y,rdn_pos(RDN_Y))
& rdn_translate(X,rdn_pos(RDN_X)) )
=> less(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f402,conjecture,
less(n2,n13),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f403,negated_conjecture,
~ less(n2,n13),
inference(negated_conjecture,[status(cth)],[f402]) ).
fof(f406,plain,
rdn_translate(n2,rdn_pos(rdnn(n2))),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f417,plain,
rdn_translate(n13,rdn_pos(rdn(rdnn(n3),rdnn(n1)))),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f660,plain,
rdn_non_zero_digit(rdnn(n1)),
inference(cnf_transformation,[status(thm)],[f257]) ).
fof(f686,plain,
! [D,Db,Ob] :
( rdn_positive_less(rdnn(D),rdn(rdnn(Db),Ob))
| ~ rdn_non_zero(Ob) ),
inference(pre_NNF_transformation,[status(thm)],[f278]) ).
fof(f687,plain,
! [Ob] :
( ! [D,Db] : rdn_positive_less(rdnn(D),rdn(rdnn(Db),Ob))
| ~ rdn_non_zero(Ob) ),
inference(miniscoping,[status(thm)],[f686]) ).
fof(f688,plain,
! [X0,X1,X2] :
( rdn_positive_less(rdnn(X1),rdn(rdnn(X2),X0))
| ~ rdn_non_zero(X0) ),
inference(cnf_transformation,[status(thm)],[f687]) ).
fof(f689,plain,
! [X] :
( rdn_non_zero(rdnn(X))
| ~ rdn_non_zero_digit(rdnn(X)) ),
inference(pre_NNF_transformation,[status(thm)],[f279]) ).
fof(f690,plain,
! [X0] :
( rdn_non_zero(rdnn(X0))
| ~ rdn_non_zero_digit(rdnn(X0)) ),
inference(cnf_transformation,[status(thm)],[f689]) ).
fof(f694,plain,
! [X,Y,RDN_X,RDN_Y] :
( less(X,Y)
| ~ rdn_positive_less(RDN_X,RDN_Y)
| ~ rdn_translate(Y,rdn_pos(RDN_Y))
| ~ rdn_translate(X,rdn_pos(RDN_X)) ),
inference(pre_NNF_transformation,[status(thm)],[f281]) ).
fof(f695,plain,
! [X,Y] :
( less(X,Y)
| ! [RDN_X,RDN_Y] :
( ~ rdn_positive_less(RDN_X,RDN_Y)
| ~ rdn_translate(Y,rdn_pos(RDN_Y))
| ~ rdn_translate(X,rdn_pos(RDN_X)) ) ),
inference(miniscoping,[status(thm)],[f694]) ).
fof(f696,plain,
! [X0,X1,X2,X3] :
( less(X0,X2)
| ~ rdn_positive_less(X1,X3)
| ~ rdn_translate(X2,rdn_pos(X3))
| ~ rdn_translate(X0,rdn_pos(X1)) ),
inference(cnf_transformation,[status(thm)],[f695]) ).
fof(f861,plain,
~ less(n2,n13),
inference(cnf_transformation,[status(thm)],[f403]) ).
fof(f864,plain,
! [X0,X1] :
( less(X0,n13)
| ~ rdn_positive_less(X1,rdn(rdnn(n3),rdnn(n1)))
| ~ rdn_translate(X0,rdn_pos(X1)) ),
inference(resolution,[status(thm)],[f696,f417]) ).
fof(f1367,plain,
rdn_non_zero(rdnn(n1)),
inference(resolution,[status(thm)],[f690,f660]) ).
fof(f11509,plain,
! [X0,X1] : rdn_positive_less(rdnn(X0),rdn(rdnn(X1),rdnn(n1))),
inference(resolution,[status(thm)],[f688,f1367]) ).
fof(f13500,plain,
! [X0,X1] :
( less(X0,n13)
| ~ rdn_translate(X0,rdn_pos(rdnn(X1))) ),
inference(resolution,[status(thm)],[f11509,f864]) ).
fof(f16039,plain,
less(n2,n13),
inference(resolution,[status(thm)],[f13500,f406]) ).
fof(f16049,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f16039,f861]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM292+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n005.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 21 02:20:34 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.39 % Drodi V4.1.1
% 12.59/2.12 % Refutation found
% 12.59/2.12 % SZS status Theorem for theBenchmark: Theorem is valid
% 12.59/2.12 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 12.59/2.16 % Elapsed time: 1.780377 seconds
% 12.59/2.16 % CPU time: 13.669543 seconds
% 12.59/2.16 % Total memory used: 325.526 MB
% 12.59/2.16 % Net memory used: 318.660 MB
%------------------------------------------------------------------------------