%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM330+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 : n016.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 01:38:58 PM UTC 2026
% Result : Theorem 0.09s 0.47s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 39 ( 12 unt; 3 def)
% Number of atoms : 96 ( 10 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 111 ( 54 ~; 44 |; 8 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 4 prp; 0-4 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 64 ( 60 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
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(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(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] :
( Y = n4
& X = n4
& sum(X,Y,n8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f403,negated_conjecture,
~ ? [X,Y] :
( Y = n4
& X = n4
& sum(X,Y,n8) ),
inference(negated_conjecture,[status(cth)],[f402]) ).
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(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(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] :
( Y != n4
| X != n4
| ~ sum(X,Y,n8) ),
inference(pre_NNF_transformation,[status(thm)],[f403]) ).
fof(f862,plain,
! [Y] :
( Y != n4
| ! [X] :
( X != n4
| ~ sum(X,Y,n8) ) ),
inference(miniscoping,[status(thm)],[f861]) ).
fof(f863,plain,
! [X0,X1] :
( X1 != n4
| X0 != n4
| ~ sum(X0,X1,n8) ),
inference(cnf_transformation,[status(thm)],[f862]) ).
fof(f866,plain,
~ sum(n4,n4,n8),
inference(destructive_equality_resolution,[status(thm)],[f863]) ).
fof(f1169,plain,
! [X0,X1,X2] :
( ~ rdn_translate(n8,rdn_pos(X2))
| ~ rdn_add_with_carry(rdnn(n0),X0,X1,X2)
| ~ rdn_translate(n4,rdn_pos(X1))
| ~ rdn_translate(n4,rdn_pos(X0)) ),
inference(resolution,[status(thm)],[f718,f866]) ).
fof(f1173,plain,
! [X0,X1,X2,X3] :
( ~ rdn_translate(n8,rdn_pos(rdnn(X3)))
| ~ rdn_translate(n4,rdn_pos(rdnn(X1)))
| ~ rdn_translate(n4,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,f1169]) ).
fof(f1182,plain,
! [X0] :
( ~ rdn_translate(n8,rdn_pos(rdnn(X0)))
| ~ rdn_translate(n4,rdn_pos(rdnn(n4)))
| ~ rdn_translate(n4,rdn_pos(rdnn(n4)))
| ~ rdn_digit_add(rdnn(n8),rdnn(n0),rdnn(X0),rdnn(n0)) ),
inference(resolution,[status(thm)],[f1173,f805]) ).
fof(f1200,definition,
( sQ5_spl
<=> rdn_translate(n8,rdn_pos(rdnn(n8))) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f1202,plain,
( sQ5_spl
| ~ rdn_translate(n8,rdn_pos(rdnn(n8))) ),
inference(component_clause,[status(thm)],[f1200]) ).
fof(f1204,definition,
! [X0] :
( sQ6_spl
<=> ( ~ rdn_translate(n8,rdn_pos(rdnn(X0)))
| ~ rdn_digit_add(rdnn(n8),rdnn(n0),rdnn(X0),rdnn(n0)) ) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f1205,plain,
! [X0] :
( ~ sQ6_spl
| ~ rdn_translate(n8,rdn_pos(rdnn(X0)))
| ~ rdn_digit_add(rdnn(n8),rdnn(n0),rdnn(X0),rdnn(n0)) ),
inference(component_clause,[status(thm)],[f1204]) ).
fof(f1229,definition,
( sQ13_spl
<=> rdn_translate(n4,rdn_pos(rdnn(n4))) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f1231,plain,
( sQ13_spl
| ~ rdn_translate(n4,rdn_pos(rdnn(n4))) ),
inference(component_clause,[status(thm)],[f1229]) ).
fof(f1232,plain,
( ~ sQ13_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f1182,f1204,f1229]) ).
fof(f1259,plain,
( sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1231,f408]) ).
fof(f1260,plain,
sQ13_spl,
inference(contradiction_clause,[status(thm)],[f1259]) ).
fof(f1261,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1202,f412]) ).
fof(f1262,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f1261]) ).
fof(f1688,plain,
( ~ sQ6_spl
| ~ rdn_translate(n8,rdn_pos(rdnn(n8))) ),
inference(resolution,[status(thm)],[f1205,f841]) ).
fof(f1689,plain,
( ~ sQ6_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f1688,f1200,f1204]) ).
fof(f1690,plain,
$false,
inference(sat_refutation,[status(thm)],[f1232,f1260,f1262,f1689]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM330+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n016.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 02:27:08 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 0.09/0.47 % Refutation found
% 0.09/0.47 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.49 % Elapsed time: 0.114836 seconds
% 0.09/0.49 % CPU time: 0.576666 seconds
% 0.09/0.49 % Total memory used: 111.880 MB
% 0.09/0.49 % Net memory used: 111.662 MB
%------------------------------------------------------------------------------