%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM310+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 : n003.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 01:38:56 PM UTC 2026
% Result : Theorem 12.62s 2.03s
% Output : CNFRefutation 12.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 13
% Syntax : Number of formulae : 54 ( 21 unt; 0 def)
% Number of atoms : 136 ( 12 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 157 ( 75 ~; 64 |; 12 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 135 ( 135 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
rdn_translate(n3,rdn_pos(rdnn(n3))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
rdn_translate(n6,rdn_pos(rdnn(n6))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,axiom,
rdn_translate(n36,rdn_pos(rdn(rdnn(n6),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(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/sandbox/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/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(f287,axiom,
! [X,Y,Z,RDN_X,RDN_Y,RDN_Z] :
( ( rdn_translate(Z,rdn_pos(RDN_Z))
& rdn_add_with_carry(rdnn(n0),RDN_X,RDN_Y,RDN_Z)
& rdn_translate(Y,rdn_pos(RDN_Y))
& rdn_translate(X,rdn_pos(RDN_X)) )
=> sum(X,Y,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f294,axiom,
! [X1,X2,Y,Z] :
( ( sum(X2,Y,Z)
& sum(X1,Y,Z) )
=> X1 = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f297,axiom,
! [C,D1,D2,RD,ID] :
( ( rdn_digit_add(rdnn(ID),rdnn(C),rdnn(RD),rdnn(n0))
& rdn_digit_add(rdnn(D1),rdnn(D2),rdnn(ID),rdnn(n0)) )
=> rdn_add_with_carry(rdnn(C),rdnn(D1),rdnn(D2),rdnn(RD)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f335,axiom,
rdn_digit_add(rdnn(n3),rdnn(n3),rdnn(n6),rdnn(n0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f362,axiom,
rdn_digit_add(rdnn(n6),rdnn(n0),rdnn(n6),rdnn(n0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f402,conjecture,
~ sum(n2,n3,n6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f403,negated_conjecture,
~ ~ sum(n2,n3,n6),
inference(negated_conjecture,[status(cth)],[f402]) ).
fof(f407,plain,
rdn_translate(n3,rdn_pos(rdnn(n3))),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f410,plain,
rdn_translate(n6,rdn_pos(rdnn(n6))),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f440,plain,
rdn_translate(n36,rdn_pos(rdn(rdnn(n6),rdnn(n3)))),
inference(cnf_transformation,[status(thm)],[f37]) ).
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(f716,plain,
! [X,Y,Z,RDN_X,RDN_Y,RDN_Z] :
( sum(X,Y,Z)
| ~ rdn_translate(Z,rdn_pos(RDN_Z))
| ~ rdn_add_with_carry(rdnn(n0),RDN_X,RDN_Y,RDN_Z)
| ~ rdn_translate(Y,rdn_pos(RDN_Y))
| ~ rdn_translate(X,rdn_pos(RDN_X)) ),
inference(pre_NNF_transformation,[status(thm)],[f287]) ).
fof(f717,plain,
! [X,Y,Z] :
( sum(X,Y,Z)
| ! [RDN_Z] :
( ~ rdn_translate(Z,rdn_pos(RDN_Z))
| ! [RDN_X,RDN_Y] :
( ~ rdn_add_with_carry(rdnn(n0),RDN_X,RDN_Y,RDN_Z)
| ~ rdn_translate(Y,rdn_pos(RDN_Y))
| ~ rdn_translate(X,rdn_pos(RDN_X)) ) ) ),
inference(miniscoping,[status(thm)],[f716]) ).
fof(f718,plain,
! [X0,X1,X2,X3,X4,X5] :
( sum(X0,X2,X5)
| ~ rdn_translate(X5,rdn_pos(X4))
| ~ rdn_add_with_carry(rdnn(n0),X1,X3,X4)
| ~ rdn_translate(X2,rdn_pos(X3))
| ~ rdn_translate(X0,rdn_pos(X1)) ),
inference(cnf_transformation,[status(thm)],[f717]) ).
fof(f737,plain,
! [X1,X2,Y,Z] :
( X1 = X2
| ~ sum(X2,Y,Z)
| ~ sum(X1,Y,Z) ),
inference(pre_NNF_transformation,[status(thm)],[f294]) ).
fof(f738,plain,
! [X1,X2] :
( X1 = X2
| ! [Y,Z] :
( ~ sum(X2,Y,Z)
| ~ sum(X1,Y,Z) ) ),
inference(miniscoping,[status(thm)],[f737]) ).
fof(f739,plain,
! [X0,X1,X2,X3] :
( X0 = X3
| ~ sum(X3,X1,X2)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f738]) ).
fof(f747,plain,
! [C,D1,D2,RD,ID] :
( rdn_add_with_carry(rdnn(C),rdnn(D1),rdnn(D2),rdnn(RD))
| ~ rdn_digit_add(rdnn(ID),rdnn(C),rdnn(RD),rdnn(n0))
| ~ rdn_digit_add(rdnn(D1),rdnn(D2),rdnn(ID),rdnn(n0)) ),
inference(pre_NNF_transformation,[status(thm)],[f297]) ).
fof(f748,plain,
! [C,D1,D2,RD] :
( rdn_add_with_carry(rdnn(C),rdnn(D1),rdnn(D2),rdnn(RD))
| ! [ID] :
( ~ rdn_digit_add(rdnn(ID),rdnn(C),rdnn(RD),rdnn(n0))
| ~ rdn_digit_add(rdnn(D1),rdnn(D2),rdnn(ID),rdnn(n0)) ) ),
inference(miniscoping,[status(thm)],[f747]) ).
fof(f749,plain,
! [X0,X1,X2,X3,X4] :
( rdn_add_with_carry(rdnn(X3),rdnn(X0),rdnn(X1),rdnn(X4))
| ~ rdn_digit_add(rdnn(X2),rdnn(X3),rdnn(X4),rdnn(n0))
| ~ rdn_digit_add(rdnn(X0),rdnn(X1),rdnn(X2),rdnn(n0)) ),
inference(cnf_transformation,[status(thm)],[f748]) ).
fof(f794,plain,
rdn_digit_add(rdnn(n3),rdnn(n3),rdnn(n6),rdnn(n0)),
inference(cnf_transformation,[status(thm)],[f335]) ).
fof(f821,plain,
rdn_digit_add(rdnn(n6),rdnn(n0),rdnn(n6),rdnn(n0)),
inference(cnf_transformation,[status(thm)],[f362]) ).
fof(f861,plain,
sum(n2,n3,n6),
inference(cnf_transformation,[status(thm)],[f403]) ).
fof(f862,plain,
! [X0] : ~ less(X0,X0),
inference(destructive_equality_resolution,[status(thm)],[f706]) ).
fof(f865,plain,
! [X0] :
( X0 = n2
| ~ sum(X0,n3,n6) ),
inference(resolution,[status(thm)],[f739,f861]) ).
fof(f2122,plain,
! [X0,X1,X2] :
( ~ rdn_positive_less(X1,X2)
| ~ rdn_translate(X0,rdn_pos(X2))
| ~ rdn_translate(X0,rdn_pos(X1)) ),
inference(resolution,[status(thm)],[f696,f862]) ).
fof(f2167,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( sum(X4,X5,X6)
| ~ rdn_translate(X6,rdn_pos(rdnn(X3)))
| ~ rdn_translate(X5,rdn_pos(rdnn(X1)))
| ~ rdn_translate(X4,rdn_pos(rdnn(X0)))
| ~ rdn_digit_add(rdnn(X2),rdnn(n0),rdnn(X3),rdnn(n0))
| ~ rdn_digit_add(rdnn(X0),rdnn(X1),rdnn(X2),rdnn(n0)) ),
inference(resolution,[status(thm)],[f749,f718]) ).
fof(f3612,plain,
! [X0,X1,X2,X3,X4] :
( ~ rdn_positive_less(X2,X4)
| ~ rdn_translate(X0,rdn_pos(rdn(rdnn(X3),X4)))
| ~ rdn_translate(X0,rdn_pos(rdn(rdnn(X1),X2))) ),
inference(resolution,[status(thm)],[f2122,f683]) ).
fof(f3848,plain,
! [X0,X1,X2,X3,X4] :
( sum(X2,X3,X4)
| ~ rdn_translate(X4,rdn_pos(rdnn(n6)))
| ~ rdn_translate(X3,rdn_pos(rdnn(X1)))
| ~ rdn_translate(X2,rdn_pos(rdnn(X0)))
| ~ rdn_digit_add(rdnn(X0),rdnn(X1),rdnn(n6),rdnn(n0)) ),
inference(resolution,[status(thm)],[f2167,f821]) ).
fof(f3872,plain,
! [X0,X1,X2,X3] :
( sum(X2,X3,n6)
| ~ rdn_translate(X3,rdn_pos(rdnn(X1)))
| ~ rdn_translate(X2,rdn_pos(rdnn(X0)))
| ~ rdn_digit_add(rdnn(X0),rdnn(X1),rdnn(n6),rdnn(n0)) ),
inference(resolution,[status(thm)],[f3848,f410]) ).
fof(f3904,plain,
! [X0,X1,X2] :
( ~ rdn_translate(X0,rdn_pos(rdn(rdnn(X2),rdnn(n3))))
| ~ rdn_translate(X0,rdn_pos(rdn(rdnn(X1),rdnn(n2)))) ),
inference(resolution,[status(thm)],[f3612,f671]) ).
fof(f4609,plain,
! [X0,X1] :
( sum(X0,X1,n6)
| ~ rdn_translate(X1,rdn_pos(rdnn(n3)))
| ~ rdn_translate(X0,rdn_pos(rdnn(n3))) ),
inference(resolution,[status(thm)],[f3872,f794]) ).
fof(f4850,plain,
! [X0] : ~ rdn_translate(n36,rdn_pos(rdn(rdnn(X0),rdnn(n2)))),
inference(resolution,[status(thm)],[f3904,f440]) ).
fof(f5462,plain,
! [X0] :
( sum(X0,n3,n6)
| ~ rdn_translate(X0,rdn_pos(rdnn(n3))) ),
inference(resolution,[status(thm)],[f4609,f407]) ).
fof(f9515,plain,
sum(n3,n3,n6),
inference(resolution,[status(thm)],[f5462,f407]) ).
fof(f9518,plain,
n3 = n2,
inference(resolution,[status(thm)],[f9515,f865]) ).
fof(f9601,plain,
rdn_translate(n36,rdn_pos(rdn(rdnn(n6),rdnn(n2)))),
inference(backward_demodulation,[status(thm)],[f9518,f440]) ).
fof(f9745,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f9601,f4850]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM310+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.37 % Computer : n003.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Mon Sep 21 02:23:15 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.39 % Drodi V4.1.1
% 12.62/2.03 % Refutation found
% 12.62/2.03 % SZS status Theorem for theBenchmark: Theorem is valid
% 12.62/2.03 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 12.62/2.08 % Elapsed time: 1.695992 seconds
% 12.62/2.08 % CPU time: 13.092835 seconds
% 12.62/2.08 % Total memory used: 212.879 MB
% 12.62/2.08 % Net memory used: 202.207 MB
%------------------------------------------------------------------------------