%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM299+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.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 01:38:55 PM UTC 2026
% Result : Theorem 0.11s 0.50s
% Output : CNFRefutation 0.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 30 ( 14 unt; 0 def)
% Number of atoms : 71 ( 5 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 78 ( 37 ~; 30 |; 8 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-1 aty)
% Number of variables : 46 ( 46 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f130,axiom,
rdn_translate(nn2,rdn_neg(rdnn(n2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f132,axiom,
rdn_translate(nn4,rdn_neg(rdnn(n4))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f268,axiom,
rdn_positive_less(rdnn(n2),rdnn(n3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f269,axiom,
rdn_positive_less(rdnn(n3),rdnn(n4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f275,axiom,
! [X,Y,Z] :
( ( rdn_positive_less(rdnn(Y),rdnn(Z))
& rdn_positive_less(rdnn(X),rdnn(Y)) )
=> rdn_positive_less(rdnn(X),rdnn(Z)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f283,axiom,
! [X,Y,RDN_X,RDN_Y] :
( ( rdn_positive_less(RDN_Y,RDN_X)
& rdn_translate(Y,rdn_neg(RDN_Y))
& rdn_translate(X,rdn_neg(RDN_X)) )
=> less(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f284,axiom,
! [X,Y] :
( less(X,Y)
<=> ( Y != X
& ~ less(Y,X) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f402,conjecture,
~ less(nn2,nn4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f403,negated_conjecture,
~ ~ less(nn2,nn4),
inference(negated_conjecture,[status(cth)],[f402]) ).
fof(f533,plain,
rdn_translate(nn2,rdn_neg(rdnn(n2))),
inference(cnf_transformation,[status(thm)],[f130]) ).
fof(f535,plain,
rdn_translate(nn4,rdn_neg(rdnn(n4))),
inference(cnf_transformation,[status(thm)],[f132]) ).
fof(f671,plain,
rdn_positive_less(rdnn(n2),rdnn(n3)),
inference(cnf_transformation,[status(thm)],[f268]) ).
fof(f672,plain,
rdn_positive_less(rdnn(n3),rdnn(n4)),
inference(cnf_transformation,[status(thm)],[f269]) ).
fof(f678,plain,
! [X,Y,Z] :
( rdn_positive_less(rdnn(X),rdnn(Z))
| ~ rdn_positive_less(rdnn(Y),rdnn(Z))
| ~ rdn_positive_less(rdnn(X),rdnn(Y)) ),
inference(pre_NNF_transformation,[status(thm)],[f275]) ).
fof(f679,plain,
! [X,Z] :
( rdn_positive_less(rdnn(X),rdnn(Z))
| ! [Y] :
( ~ rdn_positive_less(rdnn(Y),rdnn(Z))
| ~ rdn_positive_less(rdnn(X),rdnn(Y)) ) ),
inference(miniscoping,[status(thm)],[f678]) ).
fof(f680,plain,
! [X0,X1,X2] :
( rdn_positive_less(rdnn(X0),rdnn(X2))
| ~ rdn_positive_less(rdnn(X1),rdnn(X2))
| ~ rdn_positive_less(rdnn(X0),rdnn(X1)) ),
inference(cnf_transformation,[status(thm)],[f679]) ).
fof(f700,plain,
! [X,Y,RDN_X,RDN_Y] :
( less(X,Y)
| ~ rdn_positive_less(RDN_Y,RDN_X)
| ~ rdn_translate(Y,rdn_neg(RDN_Y))
| ~ rdn_translate(X,rdn_neg(RDN_X)) ),
inference(pre_NNF_transformation,[status(thm)],[f283]) ).
fof(f701,plain,
! [X,Y] :
( less(X,Y)
| ! [RDN_X,RDN_Y] :
( ~ rdn_positive_less(RDN_Y,RDN_X)
| ~ rdn_translate(Y,rdn_neg(RDN_Y))
| ~ rdn_translate(X,rdn_neg(RDN_X)) ) ),
inference(miniscoping,[status(thm)],[f700]) ).
fof(f702,plain,
! [X0,X1,X2,X3] :
( less(X0,X2)
| ~ rdn_positive_less(X3,X1)
| ~ rdn_translate(X2,rdn_neg(X3))
| ~ rdn_translate(X0,rdn_neg(X1)) ),
inference(cnf_transformation,[status(thm)],[f701]) ).
fof(f703,plain,
! [X,Y] :
( ( Y = X
| less(Y,X)
| less(X,Y) )
& ( ( Y != X
& ~ less(Y,X) )
| ~ less(X,Y) ) ),
inference(NNF_transformation,[status(thm)],[f284]) ).
fof(f704,plain,
( ! [X,Y] :
( Y = X
| less(Y,X)
| less(X,Y) )
& ! [X,Y] :
( ( Y != X
& ~ less(Y,X) )
| ~ less(X,Y) ) ),
inference(miniscoping,[status(thm)],[f703]) ).
fof(f705,plain,
! [X0,X1] :
( ~ less(X1,X0)
| ~ less(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f704]) ).
fof(f861,plain,
less(nn2,nn4),
inference(cnf_transformation,[status(thm)],[f403]) ).
fof(f867,plain,
! [X0,X1] :
( less(X0,nn2)
| ~ rdn_positive_less(rdnn(n2),X1)
| ~ rdn_translate(X0,rdn_neg(X1)) ),
inference(resolution,[status(thm)],[f702,f533]) ).
fof(f871,plain,
~ less(nn4,nn2),
inference(resolution,[status(thm)],[f705,f861]) ).
fof(f909,plain,
! [X0,X1,X2] :
( less(X2,nn2)
| ~ rdn_translate(X2,rdn_neg(rdnn(X1)))
| ~ rdn_positive_less(rdnn(X0),rdnn(X1))
| ~ rdn_positive_less(rdnn(n2),rdnn(X0)) ),
inference(resolution,[status(thm)],[f680,f867]) ).
fof(f920,plain,
! [X0,X1] :
( less(X1,nn2)
| ~ rdn_translate(X1,rdn_neg(rdnn(X0)))
| ~ rdn_positive_less(rdnn(n3),rdnn(X0)) ),
inference(resolution,[status(thm)],[f909,f671]) ).
fof(f926,plain,
! [X0] :
( less(X0,nn2)
| ~ rdn_translate(X0,rdn_neg(rdnn(n4))) ),
inference(resolution,[status(thm)],[f920,f672]) ).
fof(f934,plain,
less(nn4,nn2),
inference(resolution,[status(thm)],[f926,f535]) ).
fof(f935,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f934,f871]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM299+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n026.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 02:23:52 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.39 % Drodi V4.1.1
% 0.11/0.50 % Refutation found
% 0.11/0.50 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.53/0.54 % Elapsed time: 0.153997 seconds
% 0.53/0.54 % CPU time: 0.884859 seconds
% 0.53/0.54 % Total memory used: 117.765 MB
% 0.53/0.54 % Net memory used: 117.418 MB
%------------------------------------------------------------------------------