%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM319+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 : n007.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 01:38:57 PM UTC 2026
% Result : Theorem 20.48s 3.13s
% Output : CNFRefutation 21.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 29 ( 16 unt; 0 def)
% Number of atoms : 68 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 75 ( 36 ~; 33 |; 4 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-1 aty)
% Number of variables : 66 ( 64 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f130,axiom,
rdn_translate(nn2,rdn_neg(rdnn(n2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f133,axiom,
rdn_translate(nn5,rdn_neg(rdnn(n5))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f135,axiom,
rdn_translate(nn7,rdn_neg(rdnn(n7))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f288,axiom,
! [X,Y,Z,RDN_X,RDN_Y,RDN_Z] :
( ( rdn_translate(Z,rdn_neg(RDN_Z))
& rdn_add_with_carry(rdnn(n0),RDN_X,RDN_Y,RDN_Z)
& rdn_translate(Y,rdn_neg(RDN_Y))
& rdn_translate(X,rdn_neg(RDN_X)) )
=> sum(X,Y,Z) ),
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(f327,axiom,
rdn_digit_add(rdnn(n2),rdnn(n5),rdnn(n7),rdnn(n0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f372,axiom,
rdn_digit_add(rdnn(n7),rdnn(n0),rdnn(n7),rdnn(n0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f402,conjecture,
? [X] : sum(nn2,nn5,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f403,negated_conjecture,
~ ? [X] : sum(nn2,nn5,X),
inference(negated_conjecture,[status(cth)],[f402]) ).
fof(f533,plain,
rdn_translate(nn2,rdn_neg(rdnn(n2))),
inference(cnf_transformation,[status(thm)],[f130]) ).
fof(f536,plain,
rdn_translate(nn5,rdn_neg(rdnn(n5))),
inference(cnf_transformation,[status(thm)],[f133]) ).
fof(f538,plain,
rdn_translate(nn7,rdn_neg(rdnn(n7))),
inference(cnf_transformation,[status(thm)],[f135]) ).
fof(f719,plain,
! [X,Y,Z,RDN_X,RDN_Y,RDN_Z] :
( sum(X,Y,Z)
| ~ rdn_translate(Z,rdn_neg(RDN_Z))
| ~ rdn_add_with_carry(rdnn(n0),RDN_X,RDN_Y,RDN_Z)
| ~ rdn_translate(Y,rdn_neg(RDN_Y))
| ~ rdn_translate(X,rdn_neg(RDN_X)) ),
inference(pre_NNF_transformation,[status(thm)],[f288]) ).
fof(f720,plain,
! [X,Y,Z] :
( sum(X,Y,Z)
| ! [RDN_Z] :
( ~ rdn_translate(Z,rdn_neg(RDN_Z))
| ! [RDN_X,RDN_Y] :
( ~ rdn_add_with_carry(rdnn(n0),RDN_X,RDN_Y,RDN_Z)
| ~ rdn_translate(Y,rdn_neg(RDN_Y))
| ~ rdn_translate(X,rdn_neg(RDN_X)) ) ) ),
inference(miniscoping,[status(thm)],[f719]) ).
fof(f721,plain,
! [X0,X1,X2,X3,X4,X5] :
( sum(X0,X2,X5)
| ~ rdn_translate(X5,rdn_neg(X4))
| ~ rdn_add_with_carry(rdnn(n0),X1,X3,X4)
| ~ rdn_translate(X2,rdn_neg(X3))
| ~ rdn_translate(X0,rdn_neg(X1)) ),
inference(cnf_transformation,[status(thm)],[f720]) ).
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(f786,plain,
rdn_digit_add(rdnn(n2),rdnn(n5),rdnn(n7),rdnn(n0)),
inference(cnf_transformation,[status(thm)],[f327]) ).
fof(f831,plain,
rdn_digit_add(rdnn(n7),rdnn(n0),rdnn(n7),rdnn(n0)),
inference(cnf_transformation,[status(thm)],[f372]) ).
fof(f861,plain,
! [X] : ~ sum(nn2,nn5,X),
inference(pre_NNF_transformation,[status(thm)],[f403]) ).
fof(f862,plain,
! [X0] : ~ sum(nn2,nn5,X0),
inference(cnf_transformation,[status(thm)],[f861]) ).
fof(f3245,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( sum(X4,X5,X6)
| ~ rdn_translate(X6,rdn_neg(rdnn(X3)))
| ~ rdn_translate(X5,rdn_neg(rdnn(X1)))
| ~ rdn_translate(X4,rdn_neg(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,f721]) ).
fof(f3602,plain,
! [X0,X1,X2,X3,X4] :
( sum(X3,nn5,X4)
| ~ rdn_translate(X4,rdn_neg(rdnn(X2)))
| ~ rdn_translate(X3,rdn_neg(rdnn(X0)))
| ~ rdn_digit_add(rdnn(X1),rdnn(n0),rdnn(X2),rdnn(n0))
| ~ rdn_digit_add(rdnn(X0),rdnn(n5),rdnn(X1),rdnn(n0)) ),
inference(resolution,[status(thm)],[f3245,f536]) ).
fof(f3661,plain,
! [X0,X1,X2] :
( sum(X1,nn5,X2)
| ~ rdn_translate(X2,rdn_neg(rdnn(X0)))
| ~ rdn_translate(X1,rdn_neg(rdnn(n2)))
| ~ rdn_digit_add(rdnn(n7),rdnn(n0),rdnn(X0),rdnn(n0)) ),
inference(resolution,[status(thm)],[f3602,f786]) ).
fof(f4151,plain,
! [X0,X1] :
( sum(X0,nn5,X1)
| ~ rdn_translate(X1,rdn_neg(rdnn(n7)))
| ~ rdn_translate(X0,rdn_neg(rdnn(n2))) ),
inference(resolution,[status(thm)],[f3661,f831]) ).
fof(f4152,plain,
! [X0] :
( sum(X0,nn5,nn7)
| ~ rdn_translate(X0,rdn_neg(rdnn(n2))) ),
inference(resolution,[status(thm)],[f4151,f538]) ).
fof(f4208,plain,
sum(nn2,nn5,nn7),
inference(resolution,[status(thm)],[f4152,f533]) ).
fof(f4209,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f4208,f862]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM319+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n007.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 02:19:51 UTC 2026
% 0.14/0.36 % CPUTime :
% 0.14/0.38 % Drodi V4.1.1
% 20.48/3.13 % Refutation found
% 20.48/3.13 % SZS status Theorem for theBenchmark: Theorem is valid
% 20.48/3.13 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.71/3.29 % Elapsed time: 2.909079 seconds
% 1.71/3.29 % CPU time: 21.922932 seconds
% 1.71/3.29 % Total memory used: 270.683 MB
% 1.71/3.29 % Net memory used: 255.233 MB
%------------------------------------------------------------------------------