%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM321+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 : n006.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 8.05s 7.55s
% Output : CNFRefutation 8.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 12
% Syntax : Number of formulae : 44 ( 25 unt; 0 def)
% Number of atoms : 93 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 93 ( 44 ~; 40 |; 6 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-1 aty)
% Number of variables : 74 ( 72 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
rdn_translate(n3,rdn_pos(rdnn(n3))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
rdn_translate(n5,rdn_pos(rdnn(n5))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f130,axiom,
rdn_translate(nn2,rdn_neg(rdnn(n2))),
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(f269,axiom,
rdn_positive_less(rdnn(n3),rdnn(n4)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f270,axiom,
rdn_positive_less(rdnn(n4),rdnn(n5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f275,axiom,
! [X,Y,Z] :
( ( rdn_positive_less(rdnn(Y),rdnn(Z))
& rdn_positive_less(rdnn(X),rdnn(Y)) )
=> rdn_positive_less(rdnn(X),rdnn(Z)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f290,axiom,
! [X,Y,Z,RDN_X,RDN_Y,RDN_Z] :
( ( rdn_translate(Z,rdn_pos(RDN_Z))
& rdn_add_with_carry(rdnn(n0),RDN_Y,RDN_Z,RDN_X)
& rdn_positive_less(RDN_Y,RDN_X)
& rdn_translate(Y,rdn_neg(RDN_Y))
& rdn_translate(X,rdn_pos(RDN_X)) )
=> sum(X,Y,Z) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f325,axiom,
rdn_digit_add(rdnn(n2),rdnn(n3),rdnn(n5),rdnn(n0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f352,axiom,
rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f402,conjecture,
? [X] : sum(n5,nn2,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f403,negated_conjecture,
~ ? [X] : sum(n5,nn2,X),
inference(negated_conjecture,[status(cth)],[f402]) ).
fof(f407,plain,
rdn_translate(n3,rdn_pos(rdnn(n3))),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f409,plain,
rdn_translate(n5,rdn_pos(rdnn(n5))),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f533,plain,
rdn_translate(nn2,rdn_neg(rdnn(n2))),
inference(cnf_transformation,[status(thm)],[f130]) ).
fof(f671,plain,
rdn_positive_less(rdnn(n2),rdnn(n3)),
inference(cnf_transformation,[status(thm)],[f268]) ).
fof(f672,plain,
rdn_positive_less(rdnn(n3),rdnn(n4)),
inference(cnf_transformation,[status(thm)],[f269]) ).
fof(f673,plain,
rdn_positive_less(rdnn(n4),rdnn(n5)),
inference(cnf_transformation,[status(thm)],[f270]) ).
fof(f678,plain,
! [X,Y,Z] :
( rdn_positive_less(rdnn(X),rdnn(Z))
| ~ rdn_positive_less(rdnn(Y),rdnn(Z))
| ~ rdn_positive_less(rdnn(X),rdnn(Y)) ),
inference(pre_NNF_transformation,[status(thm)],[f275]) ).
fof(f679,plain,
! [X,Z] :
( rdn_positive_less(rdnn(X),rdnn(Z))
| ! [Y] :
( ~ rdn_positive_less(rdnn(Y),rdnn(Z))
| ~ rdn_positive_less(rdnn(X),rdnn(Y)) ) ),
inference(miniscoping,[status(thm)],[f678]) ).
fof(f680,plain,
! [X0,X1,X2] :
( rdn_positive_less(rdnn(X0),rdnn(X2))
| ~ rdn_positive_less(rdnn(X1),rdnn(X2))
| ~ rdn_positive_less(rdnn(X0),rdnn(X1)) ),
inference(cnf_transformation,[status(thm)],[f679]) ).
fof(f725,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_Y,RDN_Z,RDN_X)
| ~ rdn_positive_less(RDN_Y,RDN_X)
| ~ rdn_translate(Y,rdn_neg(RDN_Y))
| ~ rdn_translate(X,rdn_pos(RDN_X)) ),
inference(pre_NNF_transformation,[status(thm)],[f290]) ).
fof(f726,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_Y,RDN_Z,RDN_X)
| ~ rdn_positive_less(RDN_Y,RDN_X)
| ~ rdn_translate(Y,rdn_neg(RDN_Y))
| ~ rdn_translate(X,rdn_pos(RDN_X)) ) ) ),
inference(miniscoping,[status(thm)],[f725]) ).
fof(f727,plain,
! [X0,X1,X2,X3,X4,X5] :
( sum(X0,X2,X5)
| ~ rdn_translate(X5,rdn_pos(X4))
| ~ rdn_add_with_carry(rdnn(n0),X3,X4,X1)
| ~ rdn_positive_less(X3,X1)
| ~ rdn_translate(X2,rdn_neg(X3))
| ~ rdn_translate(X0,rdn_pos(X1)) ),
inference(cnf_transformation,[status(thm)],[f726]) ).
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(f784,plain,
rdn_digit_add(rdnn(n2),rdnn(n3),rdnn(n5),rdnn(n0)),
inference(cnf_transformation,[status(thm)],[f325]) ).
fof(f811,plain,
rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0)),
inference(cnf_transformation,[status(thm)],[f352]) ).
fof(f861,plain,
! [X] : ~ sum(n5,nn2,X),
inference(pre_NNF_transformation,[status(thm)],[f403]) ).
fof(f862,plain,
! [X0] : ~ sum(n5,nn2,X0),
inference(cnf_transformation,[status(thm)],[f861]) ).
fof(f2994,plain,
! [X0] :
( rdn_positive_less(rdnn(X0),rdnn(n4))
| ~ rdn_positive_less(rdnn(X0),rdnn(n3)) ),
inference(resolution,[status(thm)],[f680,f672]) ).
fof(f2998,plain,
! [X0] :
( rdn_positive_less(rdnn(X0),rdnn(n5))
| ~ rdn_positive_less(rdnn(X0),rdnn(n4)) ),
inference(resolution,[status(thm)],[f680,f673]) ).
fof(f3083,plain,
! [X0,X1] :
( rdn_add_with_carry(rdnn(n0),rdnn(X0),rdnn(X1),rdnn(n5))
| ~ rdn_digit_add(rdnn(X0),rdnn(X1),rdnn(n5),rdnn(n0)) ),
inference(resolution,[status(thm)],[f749,f811]) ).
fof(f3433,plain,
rdn_add_with_carry(rdnn(n0),rdnn(n2),rdnn(n3),rdnn(n5)),
inference(resolution,[status(thm)],[f784,f3083]) ).
fof(f3437,plain,
! [X0,X1,X2] :
( sum(X0,X1,X2)
| ~ rdn_translate(X2,rdn_pos(rdnn(n3)))
| ~ rdn_positive_less(rdnn(n2),rdnn(n5))
| ~ rdn_translate(X1,rdn_neg(rdnn(n2)))
| ~ rdn_translate(X0,rdn_pos(rdnn(n5))) ),
inference(resolution,[status(thm)],[f3433,f727]) ).
fof(f3844,plain,
rdn_positive_less(rdnn(n2),rdnn(n4)),
inference(resolution,[status(thm)],[f2994,f671]) ).
fof(f3863,plain,
rdn_positive_less(rdnn(n2),rdnn(n5)),
inference(resolution,[status(thm)],[f2998,f3844]) ).
fof(f3867,plain,
! [X0,X1,X2] :
( sum(X0,X1,X2)
| ~ rdn_translate(X2,rdn_pos(rdnn(n3)))
| ~ rdn_translate(X1,rdn_neg(rdnn(n2)))
| ~ rdn_translate(X0,rdn_pos(rdnn(n5))) ),
inference(backward_subsumption_resolution,[status(thm)],[f3437,f3863]) ).
fof(f3929,plain,
! [X0,X1] :
( sum(X0,nn2,X1)
| ~ rdn_translate(X1,rdn_pos(rdnn(n3)))
| ~ rdn_translate(X0,rdn_pos(rdnn(n5))) ),
inference(resolution,[status(thm)],[f3867,f533]) ).
fof(f3930,plain,
! [X0] :
( sum(n5,nn2,X0)
| ~ rdn_translate(X0,rdn_pos(rdnn(n3))) ),
inference(resolution,[status(thm)],[f3929,f409]) ).
fof(f3932,plain,
! [X0] : ~ rdn_translate(X0,rdn_pos(rdnn(n3))),
inference(forward_subsumption_resolution,[status(thm)],[f3930,f862]) ).
fof(f3933,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f407,f3932]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM321+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/6.46 % Computer : n006.cluster.edu
% 0.15/6.46 % Model : x86_64 x86_64
% 0.15/6.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/6.46 % Memory : 8046.5625MB
% 0.15/6.46 % OS : Linux 6.8.0-71-generic
% 0.15/6.46 % CPULimit : 300
% 0.15/6.46 % WCLimit : 300
% 0.15/6.46 % DateTime : Mon Sep 21 02:22:05 UTC 2026
% 0.15/6.47 % CPUTime :
% 0.15/6.48 % Drodi V4.1.1
% 8.05/7.55 % Refutation found
% 8.05/7.55 % SZS status Theorem for theBenchmark: Theorem is valid
% 8.05/7.55 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 8.05/7.58 % Elapsed time: 1.101784 seconds
% 8.05/7.58 % CPU time: 8.550296 seconds
% 8.05/7.58 % Total memory used: 224.648 MB
% 8.05/7.58 % Net memory used: 217.748 MB
%------------------------------------------------------------------------------