%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM342+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 : 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 01:39:00 PM UTC 2026
% Result : Theorem 106.30s 13.93s
% Output : CNFRefutation 106.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 10
% Syntax : Number of formulae : 42 ( 17 unt; 0 def)
% Number of atoms : 103 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 115 ( 54 ~; 50 |; 8 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 98 ( 94 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
rdn_translate(n0,rdn_pos(rdnn(n0))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
rdn_translate(n4,rdn_pos(rdnn(n4))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
rdn_translate(n8,rdn_pos(rdnn(n8))),
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(f296,axiom,
! [X,Y,Z] :
( sum(Y,Z,X)
<=> difference(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(f342,axiom,
rdn_digit_add(rdnn(n4),rdnn(n0),rdnn(n4),rdnn(n0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f346,axiom,
rdn_digit_add(rdnn(n4),rdnn(n4),rdnn(n8),rdnn(n0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f382,axiom,
rdn_digit_add(rdnn(n8),rdnn(n0),rdnn(n8),rdnn(n0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f402,conjecture,
? [X,Y] :
( difference(X,Y,n0)
& sum(X,Y,n8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f403,negated_conjecture,
~ ? [X,Y] :
( difference(X,Y,n0)
& sum(X,Y,n8) ),
inference(negated_conjecture,[status(cth)],[f402]) ).
fof(f404,plain,
rdn_translate(n0,rdn_pos(rdnn(n0))),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f408,plain,
rdn_translate(n4,rdn_pos(rdnn(n4))),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f412,plain,
rdn_translate(n8,rdn_pos(rdnn(n8))),
inference(cnf_transformation,[status(thm)],[f9]) ).
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(f743,plain,
! [X,Y,Z] :
( ( ~ difference(X,Y,Z)
| sum(Y,Z,X) )
& ( difference(X,Y,Z)
| ~ sum(Y,Z,X) ) ),
inference(NNF_transformation,[status(thm)],[f296]) ).
fof(f744,plain,
( ! [X,Y,Z] :
( ~ difference(X,Y,Z)
| sum(Y,Z,X) )
& ! [X,Y,Z] :
( difference(X,Y,Z)
| ~ sum(Y,Z,X) ) ),
inference(miniscoping,[status(thm)],[f743]) ).
fof(f745,plain,
! [X0,X1,X2] :
( difference(X2,X0,X1)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f744]) ).
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(f801,plain,
rdn_digit_add(rdnn(n4),rdnn(n0),rdnn(n4),rdnn(n0)),
inference(cnf_transformation,[status(thm)],[f342]) ).
fof(f805,plain,
rdn_digit_add(rdnn(n4),rdnn(n4),rdnn(n8),rdnn(n0)),
inference(cnf_transformation,[status(thm)],[f346]) ).
fof(f841,plain,
rdn_digit_add(rdnn(n8),rdnn(n0),rdnn(n8),rdnn(n0)),
inference(cnf_transformation,[status(thm)],[f382]) ).
fof(f861,plain,
! [X,Y] :
( ~ difference(X,Y,n0)
| ~ sum(X,Y,n8) ),
inference(pre_NNF_transformation,[status(thm)],[f403]) ).
fof(f862,plain,
! [X0,X1] :
( ~ difference(X0,X1,n0)
| ~ sum(X0,X1,n8) ),
inference(cnf_transformation,[status(thm)],[f861]) ).
fof(f3241,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(f4011,plain,
! [X0,X1,X2,X3,X4] :
( sum(X2,X3,X4)
| ~ rdn_translate(X4,rdn_pos(rdnn(n8)))
| ~ rdn_translate(X3,rdn_pos(rdnn(X1)))
| ~ rdn_translate(X2,rdn_pos(rdnn(X0)))
| ~ rdn_digit_add(rdnn(X0),rdnn(X1),rdnn(n8),rdnn(n0)) ),
inference(resolution,[status(thm)],[f3241,f841]) ).
fof(f4015,plain,
! [X0,X1,X2,X3,X4] :
( sum(X2,X3,X4)
| ~ rdn_translate(X4,rdn_pos(rdnn(n4)))
| ~ rdn_translate(X3,rdn_pos(rdnn(X1)))
| ~ rdn_translate(X2,rdn_pos(rdnn(X0)))
| ~ rdn_digit_add(rdnn(X0),rdnn(X1),rdnn(n4),rdnn(n0)) ),
inference(resolution,[status(thm)],[f3241,f801]) ).
fof(f4021,plain,
! [X0,X1,X2,X3] :
( sum(X2,X3,n8)
| ~ rdn_translate(X3,rdn_pos(rdnn(X1)))
| ~ rdn_translate(X2,rdn_pos(rdnn(X0)))
| ~ rdn_digit_add(rdnn(X0),rdnn(X1),rdnn(n8),rdnn(n0)) ),
inference(resolution,[status(thm)],[f4011,f412]) ).
fof(f4026,plain,
! [X0,X1] :
( sum(X0,X1,n8)
| ~ rdn_translate(X1,rdn_pos(rdnn(n4)))
| ~ rdn_translate(X0,rdn_pos(rdnn(n4))) ),
inference(resolution,[status(thm)],[f4021,f805]) ).
fof(f4075,plain,
! [X0] :
( sum(X0,n4,n8)
| ~ rdn_translate(X0,rdn_pos(rdnn(n4))) ),
inference(resolution,[status(thm)],[f4026,f408]) ).
fof(f4076,plain,
sum(n4,n4,n8),
inference(resolution,[status(thm)],[f4075,f408]) ).
fof(f5132,plain,
! [X0,X1,X2,X3] :
( sum(X2,X3,n4)
| ~ rdn_translate(X3,rdn_pos(rdnn(X1)))
| ~ rdn_translate(X2,rdn_pos(rdnn(X0)))
| ~ rdn_digit_add(rdnn(X0),rdnn(X1),rdnn(n4),rdnn(n0)) ),
inference(resolution,[status(thm)],[f4015,f408]) ).
fof(f9549,plain,
! [X0,X1] :
( sum(X0,X1,n4)
| ~ rdn_translate(X1,rdn_pos(rdnn(n0)))
| ~ rdn_translate(X0,rdn_pos(rdnn(n4))) ),
inference(resolution,[status(thm)],[f5132,f801]) ).
fof(f9715,plain,
! [X0] :
( sum(n4,X0,n4)
| ~ rdn_translate(X0,rdn_pos(rdnn(n0))) ),
inference(resolution,[status(thm)],[f9549,f408]) ).
fof(f9716,plain,
sum(n4,n0,n4),
inference(resolution,[status(thm)],[f9715,f404]) ).
fof(f9720,plain,
difference(n4,n4,n0),
inference(resolution,[status(thm)],[f9716,f745]) ).
fof(f9721,plain,
~ sum(n4,n4,n8),
inference(resolution,[status(thm)],[f9720,f862]) ).
fof(f9723,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f9721,f4076]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM342+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.05 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.42 % Computer : n006.cluster.edu
% 0.15/0.42 % Model : x86_64 x86_64
% 0.15/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.42 % Memory : 8046.5625MB
% 0.15/0.42 % OS : Linux 6.8.0-71-generic
% 0.15/0.42 % CPULimit : 300
% 0.15/0.42 % WCLimit : 300
% 0.15/0.42 % DateTime : Mon Sep 21 02:22:57 UTC 2026
% 0.15/0.42 % CPUTime :
% 0.15/0.45 % Drodi V4.1.1
% 106.30/13.93 % Refutation found
% 106.30/13.93 % SZS status Theorem for theBenchmark: Theorem is valid
% 106.30/13.93 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 15.35/14.02 % Elapsed time: 13.579802 seconds
% 15.35/14.02 % CPU time: 107.047924 seconds
% 15.35/14.02 % Total memory used: 600.094 MB
% 15.35/14.02 % Net memory used: 536.786 MB
%------------------------------------------------------------------------------