%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM305+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 : n005.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 0.18s 0.58s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 12
% Syntax : Number of formulae : 42 ( 17 unt; 4 def)
% Number of atoms : 93 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 98 ( 47 ~; 41 |; 4 &)
% ( 4 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 5 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-1 aty)
% Number of variables : 54 ( 54 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
rdn_translate(n2,rdn_pos(rdnn(n2))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
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(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/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,
sum(n2,n3,n5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f403,negated_conjecture,
~ sum(n2,n3,n5),
inference(negated_conjecture,[status(cth)],[f402]) ).
fof(f406,plain,
rdn_translate(n2,rdn_pos(rdnn(n2))),
inference(cnf_transformation,[status(thm)],[f3]) ).
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(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(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,
~ sum(n2,n3,n5),
inference(cnf_transformation,[status(thm)],[f403]) ).
fof(f1181,plain,
! [X0,X1,X2] :
( ~ rdn_translate(n5,rdn_pos(X2))
| ~ rdn_add_with_carry(rdnn(n0),X0,X1,X2)
| ~ rdn_translate(n3,rdn_pos(X1))
| ~ rdn_translate(n2,rdn_pos(X0)) ),
inference(resolution,[status(thm)],[f718,f861]) ).
fof(f1185,plain,
! [X0,X1,X2,X3] :
( ~ rdn_translate(n5,rdn_pos(rdnn(X3)))
| ~ rdn_translate(n3,rdn_pos(rdnn(X1)))
| ~ rdn_translate(n2,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,f1181]) ).
fof(f1191,plain,
! [X0] :
( ~ rdn_translate(n5,rdn_pos(rdnn(X0)))
| ~ rdn_translate(n3,rdn_pos(rdnn(n3)))
| ~ rdn_translate(n2,rdn_pos(rdnn(n2)))
| ~ rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(X0),rdnn(n0)) ),
inference(resolution,[status(thm)],[f1185,f784]) ).
fof(f1210,definition,
( sQ8_spl
<=> rdn_translate(n5,rdn_pos(rdnn(n5))) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f1212,plain,
( sQ8_spl
| ~ rdn_translate(n5,rdn_pos(rdnn(n5))) ),
inference(component_clause,[status(thm)],[f1210]) ).
fof(f1214,definition,
! [X0] :
( sQ9_spl
<=> ( ~ rdn_translate(n5,rdn_pos(rdnn(X0)))
| ~ rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(X0),rdnn(n0)) ) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f1215,plain,
! [X0] :
( ~ sQ9_spl
| ~ rdn_translate(n5,rdn_pos(rdnn(X0)))
| ~ rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(X0),rdnn(n0)) ),
inference(component_clause,[status(thm)],[f1214]) ).
fof(f1233,definition,
( sQ14_spl
<=> rdn_translate(n2,rdn_pos(rdnn(n2))) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f1235,plain,
( sQ14_spl
| ~ rdn_translate(n2,rdn_pos(rdnn(n2))) ),
inference(component_clause,[status(thm)],[f1233]) ).
fof(f1236,definition,
( sQ15_spl
<=> rdn_translate(n3,rdn_pos(rdnn(n3))) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f1238,plain,
( sQ15_spl
| ~ rdn_translate(n3,rdn_pos(rdnn(n3))) ),
inference(component_clause,[status(thm)],[f1236]) ).
fof(f1239,plain,
( ~ sQ15_spl
| ~ sQ14_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f1191,f1214,f1233,f1236]) ).
fof(f1282,plain,
( sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1235,f406]) ).
fof(f1283,plain,
sQ14_spl,
inference(contradiction_clause,[status(thm)],[f1282]) ).
fof(f1284,plain,
( sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1212,f409]) ).
fof(f1285,plain,
sQ8_spl,
inference(contradiction_clause,[status(thm)],[f1284]) ).
fof(f1286,plain,
( sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1238,f407]) ).
fof(f1287,plain,
sQ15_spl,
inference(contradiction_clause,[status(thm)],[f1286]) ).
fof(f1289,plain,
( ~ sQ9_spl
| ~ rdn_translate(n5,rdn_pos(rdnn(n5))) ),
inference(resolution,[status(thm)],[f1215,f811]) ).
fof(f1290,plain,
( ~ sQ9_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f1289,f1210,f1214]) ).
fof(f1291,plain,
$false,
inference(sat_refutation,[status(thm)],[f1239,f1283,f1285,f1287,f1290]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM305+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.05 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n005.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.45 % DateTime : Mon Sep 21 02:21:19 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.50 % Drodi V4.1.1
% 0.18/0.58 % Refutation found
% 0.18/0.58 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.18/0.58 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.27/0.64 % Elapsed time: 0.176871 seconds
% 0.27/0.64 % CPU time: 0.574212 seconds
% 0.27/0.64 % Total memory used: 66.936 MB
% 0.27/0.64 % Net memory used: 66.836 MB
%------------------------------------------------------------------------------