%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM303+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 : n009.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 0.12s 0.47s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 28 ( 13 unt; 0 def)
% Number of atoms : 62 ( 9 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 66 ( 32 ~; 24 |; 7 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 48 ( 48 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f22,axiom,
rdn_translate(n21,rdn_pos(rdn(rdnn(n1),rdnn(n2)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,axiom,
rdn_translate(n31,rdn_pos(rdn(rdnn(n1),rdnn(n3)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f268,axiom,
rdn_positive_less(rdnn(n2),rdnn(n3)),
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(f284,axiom,
! [X,Y] :
( less(X,Y)
<=> ( Y != X
& ~ less(Y,X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f402,conjecture,
n31 != n21,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f403,negated_conjecture,
~ ( n31 != n21 ),
inference(negated_conjecture,[status(cth)],[f402]) ).
fof(f425,plain,
rdn_translate(n21,rdn_pos(rdn(rdnn(n1),rdnn(n2)))),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f435,plain,
rdn_translate(n31,rdn_pos(rdn(rdnn(n1),rdnn(n3)))),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f671,plain,
rdn_positive_less(rdnn(n2),rdnn(n3)),
inference(cnf_transformation,[status(thm)],[f268]) ).
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(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(f706,plain,
! [X0,X1] :
( X1 != X0
| ~ less(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f704]) ).
fof(f861,plain,
n31 = n21,
inference(cnf_transformation,[status(thm)],[f403]) ).
fof(f862,plain,
! [X0] : ~ less(X0,X0),
inference(destructive_equality_resolution,[status(thm)],[f706]) ).
fof(f864,plain,
rdn_translate(n21,rdn_pos(rdn(rdnn(n1),rdnn(n3)))),
inference(forward_demodulation,[status(thm)],[f861,f435]) ).
fof(f1354,plain,
! [X0,X1] :
( less(X0,n21)
| ~ rdn_positive_less(X1,rdn(rdnn(n1),rdnn(n3)))
| ~ rdn_translate(X0,rdn_pos(X1)) ),
inference(resolution,[status(thm)],[f696,f864]) ).
fof(f1357,plain,
! [X0,X1,X2] :
( ~ rdn_positive_less(X2,rdnn(n3))
| less(X0,n21)
| ~ rdn_translate(X0,rdn_pos(rdn(rdnn(X1),X2))) ),
inference(resolution,[status(thm)],[f1354,f683]) ).
fof(f1648,plain,
( ~ rdn_positive_less(rdnn(n2),rdnn(n3))
| less(n21,n21) ),
inference(resolution,[status(thm)],[f1357,f425]) ).
fof(f1659,plain,
~ rdn_positive_less(rdnn(n2),rdnn(n3)),
inference(forward_subsumption_resolution,[status(thm)],[f1648,f862]) ).
fof(f2113,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f1659,f671]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM303+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.34 % Computer : n009.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Mon Sep 21 02:21:27 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.12/0.36 % Drodi V4.1.1
% 0.12/0.47 % Refutation found
% 0.12/0.47 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.17/0.53 % Elapsed time: 0.163834 seconds
% 0.17/0.53 % CPU time: 0.449255 seconds
% 0.17/0.53 % Total memory used: 127.381 MB
% 0.17/0.53 % Net memory used: 126.919 MB
%------------------------------------------------------------------------------