%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM294+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 : n011.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 0.11s 0.58s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 23 ( 12 unt; 0 def)
% Number of atoms : 45 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 44 ( 22 ~; 18 |; 2 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 50 ( 48 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f13,axiom,
rdn_translate(n12,rdn_pos(rdn(rdnn(n2),rdnn(n1)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,axiom,
rdn_translate(n22,rdn_pos(rdn(rdnn(n2),rdnn(n2)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f267,axiom,
rdn_positive_less(rdnn(n1),rdnn(n2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f276,axiom,
! [Ds,Os,Db,Ob] :
( rdn_positive_less(Os,Ob)
=> rdn_positive_less(rdn(rdnn(Ds),Os),rdn(rdnn(Db),Ob)) ),
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,
? [X] : less(n12,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f403,negated_conjecture,
~ ? [X] : less(n12,X),
inference(negated_conjecture,[status(cth)],[f402]) ).
fof(f416,plain,
rdn_translate(n12,rdn_pos(rdn(rdnn(n2),rdnn(n1)))),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f426,plain,
rdn_translate(n22,rdn_pos(rdn(rdnn(n2),rdnn(n2)))),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f670,plain,
rdn_positive_less(rdnn(n1),rdnn(n2)),
inference(cnf_transformation,[status(thm)],[f267]) ).
fof(f681,plain,
! [Ds,Os,Db,Ob] :
( rdn_positive_less(rdn(rdnn(Ds),Os),rdn(rdnn(Db),Ob))
| ~ rdn_positive_less(Os,Ob) ),
inference(pre_NNF_transformation,[status(thm)],[f276]) ).
fof(f682,plain,
! [Os,Ob] :
( ! [Ds,Db] : rdn_positive_less(rdn(rdnn(Ds),Os),rdn(rdnn(Db),Ob))
| ~ rdn_positive_less(Os,Ob) ),
inference(miniscoping,[status(thm)],[f681]) ).
fof(f683,plain,
! [X0,X1,X2,X3] :
( rdn_positive_less(rdn(rdnn(X2),X0),rdn(rdnn(X3),X1))
| ~ rdn_positive_less(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f682]) ).
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,
! [X] : ~ less(n12,X),
inference(pre_NNF_transformation,[status(thm)],[f403]) ).
fof(f862,plain,
! [X0] : ~ less(n12,X0),
inference(cnf_transformation,[status(thm)],[f861]) ).
fof(f881,plain,
! [X0,X1,X2,X3,X4,X5] :
( less(X2,X4)
| ~ rdn_translate(X4,rdn_pos(rdn(rdnn(X5),X1)))
| ~ rdn_translate(X2,rdn_pos(rdn(rdnn(X3),X0)))
| ~ rdn_positive_less(X0,X1) ),
inference(resolution,[status(thm)],[f683,f696]) ).
fof(f889,plain,
! [X0,X1,X2,X3] :
( less(X0,X2)
| ~ rdn_translate(X2,rdn_pos(rdn(rdnn(X3),rdnn(n2))))
| ~ rdn_translate(X0,rdn_pos(rdn(rdnn(X1),rdnn(n1)))) ),
inference(resolution,[status(thm)],[f881,f670]) ).
fof(f893,plain,
! [X0,X1] :
( less(n12,X0)
| ~ rdn_translate(X0,rdn_pos(rdn(rdnn(X1),rdnn(n2)))) ),
inference(resolution,[status(thm)],[f889,f416]) ).
fof(f894,plain,
! [X0,X1] : ~ rdn_translate(X0,rdn_pos(rdn(rdnn(X1),rdnn(n2)))),
inference(forward_subsumption_resolution,[status(thm)],[f893,f862]) ).
fof(f896,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f426,f894]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM294+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.38 % Computer : n011.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 21 02:21:10 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.40 % Drodi V4.1.1
% 0.11/0.58 % Refutation found
% 0.11/0.58 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.58 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.16/0.61 % Elapsed time: 0.213548 seconds
% 1.16/0.61 % CPU time: 1.385193 seconds
% 1.16/0.61 % Total memory used: 125.207 MB
% 1.16/0.61 % Net memory used: 124.385 MB
%------------------------------------------------------------------------------