%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM301+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 : n016.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 0.21s 0.59s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 18 ( 12 unt; 0 def)
% Number of atoms : 33 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 32 ( 17 ~; 12 |; 2 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-1 aty)
% Number of variables : 25 ( 23 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f130,axiom,
rdn_translate(nn2,rdn_neg(rdnn(n2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f131,axiom,
rdn_translate(nn3,rdn_neg(rdnn(n3))),
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(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(f402,conjecture,
? [X] : less(X,nn2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f403,negated_conjecture,
~ ? [X] : less(X,nn2),
inference(negated_conjecture,[status(cth)],[f402]) ).
fof(f533,plain,
rdn_translate(nn2,rdn_neg(rdnn(n2))),
inference(cnf_transformation,[status(thm)],[f130]) ).
fof(f534,plain,
rdn_translate(nn3,rdn_neg(rdnn(n3))),
inference(cnf_transformation,[status(thm)],[f131]) ).
fof(f671,plain,
rdn_positive_less(rdnn(n2),rdnn(n3)),
inference(cnf_transformation,[status(thm)],[f268]) ).
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(f861,plain,
! [X] : ~ less(X,nn2),
inference(pre_NNF_transformation,[status(thm)],[f403]) ).
fof(f862,plain,
! [X0] : ~ less(X0,nn2),
inference(cnf_transformation,[status(thm)],[f861]) ).
fof(f872,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(f873,plain,
! [X0,X1] :
( ~ rdn_positive_less(rdnn(n2),X1)
| ~ rdn_translate(X0,rdn_neg(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f872,f862]) ).
fof(f934,plain,
! [X0] : ~ rdn_translate(X0,rdn_neg(rdnn(n3))),
inference(resolution,[status(thm)],[f671,f873]) ).
fof(f937,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f534,f934]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM301+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.46 % Computer : n016.cluster.edu
% 0.18/0.46 % Model : x86_64 x86_64
% 0.18/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.46 % Memory : 8046.5625MB
% 0.18/0.46 % OS : Linux 6.8.0-71-generic
% 0.18/0.46 % CPULimit : 300
% 0.18/0.47 % WCLimit : 300
% 0.18/0.47 % DateTime : Mon Sep 21 02:25:53 UTC 2026
% 0.18/0.47 % CPUTime :
% 0.18/0.52 % Drodi V4.1.1
% 0.21/0.59 % Refutation found
% 0.21/0.59 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.21/0.59 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.21/0.64 % Elapsed time: 0.153195 seconds
% 0.21/0.64 % CPU time: 0.256540 seconds
% 0.21/0.64 % Total memory used: 41.809 MB
% 0.21/0.64 % Net memory used: 41.767 MB
%------------------------------------------------------------------------------