%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM334+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 : n017.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 01:38:59 PM UTC 2026
% Result : Theorem 0.02s 0.43s
% Output : CNFRefutation 0.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 15
% Syntax : Number of formulae : 53 ( 21 unt; 5 def)
% Number of atoms : 115 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 116 ( 54 ~; 48 |; 6 &)
% ( 6 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 11 ( 10 usr; 6 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-1 aty)
% Number of variables : 69 ( 69 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
rdn_translate(n2,rdn_pos(rdnn(n2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
rdn_translate(n5,rdn_pos(rdnn(n5))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
rdn_translate(n7,rdn_pos(rdnn(n7))),
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(f302,axiom,
rdn_digit_add(rdnn(n0),rdnn(n0),rdnn(n0),rdnn(n0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f354,axiom,
rdn_digit_add(rdnn(n5),rdnn(n2),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,
difference(n7,n5,n2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f403,negated_conjecture,
~ difference(n7,n5,n2),
inference(negated_conjecture,[status(cth)],[f402]) ).
fof(f406,plain,
rdn_translate(n2,rdn_pos(rdnn(n2))),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f409,plain,
rdn_translate(n5,rdn_pos(rdnn(n5))),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f411,plain,
rdn_translate(n7,rdn_pos(rdnn(n7))),
inference(cnf_transformation,[status(thm)],[f8]) ).
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(f761,plain,
rdn_digit_add(rdnn(n0),rdnn(n0),rdnn(n0),rdnn(n0)),
inference(cnf_transformation,[status(thm)],[f302]) ).
fof(f813,plain,
rdn_digit_add(rdnn(n5),rdnn(n2),rdnn(n7),rdnn(n0)),
inference(cnf_transformation,[status(thm)],[f354]) ).
fof(f831,plain,
rdn_digit_add(rdnn(n7),rdnn(n0),rdnn(n7),rdnn(n0)),
inference(cnf_transformation,[status(thm)],[f372]) ).
fof(f861,plain,
~ difference(n7,n5,n2),
inference(cnf_transformation,[status(thm)],[f403]) ).
fof(f864,plain,
~ sum(n5,n2,n7),
inference(resolution,[status(thm)],[f745,f861]) ).
fof(f1155,plain,
! [X0,X1,X2] :
( ~ rdn_translate(n7,rdn_pos(X2))
| ~ rdn_add_with_carry(rdnn(n0),X0,X1,X2)
| ~ rdn_translate(n2,rdn_pos(X1))
| ~ rdn_translate(n5,rdn_pos(X0)) ),
inference(resolution,[status(thm)],[f718,f864]) ).
fof(f1186,plain,
! [X0,X1,X2,X3] :
( ~ rdn_translate(n7,rdn_pos(rdnn(X3)))
| ~ rdn_translate(n2,rdn_pos(rdnn(X1)))
| ~ rdn_translate(n5,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,f1155]) ).
fof(f1198,plain,
! [X0] :
( ~ rdn_translate(n7,rdn_pos(rdnn(X0)))
| ~ rdn_translate(n2,rdn_pos(rdnn(n2)))
| ~ rdn_translate(n5,rdn_pos(rdnn(n5)))
| ~ rdn_digit_add(rdnn(n7),rdnn(n0),rdnn(X0),rdnn(n0)) ),
inference(resolution,[status(thm)],[f1186,f813]) ).
fof(f1218,definition,
( sQ8_spl
<=> rdn_translate(n7,rdn_pos(rdnn(n7))) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f1220,plain,
( sQ8_spl
| ~ rdn_translate(n7,rdn_pos(rdnn(n7))) ),
inference(component_clause,[status(thm)],[f1218]) ).
fof(f1222,definition,
! [X0] :
( sQ9_spl
<=> ( ~ rdn_translate(n7,rdn_pos(rdnn(X0)))
| ~ rdn_digit_add(rdnn(n7),rdnn(n0),rdnn(X0),rdnn(n0)) ) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f1223,plain,
! [X0] :
( ~ sQ9_spl
| ~ rdn_translate(n7,rdn_pos(rdnn(X0)))
| ~ rdn_digit_add(rdnn(n7),rdnn(n0),rdnn(X0),rdnn(n0)) ),
inference(component_clause,[status(thm)],[f1222]) ).
fof(f1226,definition,
( sQ10_spl
<=> rdn_translate(n5,rdn_pos(rdnn(n5))) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f1228,plain,
( sQ10_spl
| ~ rdn_translate(n5,rdn_pos(rdnn(n5))) ),
inference(component_clause,[status(thm)],[f1226]) ).
fof(f1229,definition,
( sQ11_spl
<=> rdn_translate(n2,rdn_pos(rdnn(n2))) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f1231,plain,
( sQ11_spl
| ~ rdn_translate(n2,rdn_pos(rdnn(n2))) ),
inference(component_clause,[status(thm)],[f1229]) ).
fof(f1232,plain,
( ~ sQ11_spl
| ~ sQ10_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f1198,f1222,f1226,f1229]) ).
fof(f1288,plain,
( sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1220,f411]) ).
fof(f1289,plain,
sQ8_spl,
inference(contradiction_clause,[status(thm)],[f1288]) ).
fof(f1292,plain,
( sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1228,f409]) ).
fof(f1293,plain,
sQ10_spl,
inference(contradiction_clause,[status(thm)],[f1292]) ).
fof(f1481,definition,
( sQ57_spl
<=> rdn_digit_add(rdnn(n0),rdnn(n0),rdnn(n0),rdnn(n0)) ),
introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition]) ).
fof(f1483,plain,
( sQ57_spl
| ~ rdn_digit_add(rdnn(n0),rdnn(n0),rdnn(n0),rdnn(n0)) ),
inference(component_clause,[status(thm)],[f1481]) ).
fof(f1537,plain,
( sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1231,f406]) ).
fof(f1538,plain,
sQ11_spl,
inference(contradiction_clause,[status(thm)],[f1537]) ).
fof(f1681,plain,
( sQ57_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1483,f761]) ).
fof(f1682,plain,
sQ57_spl,
inference(contradiction_clause,[status(thm)],[f1681]) ).
fof(f1683,plain,
( ~ sQ9_spl
| ~ rdn_translate(n7,rdn_pos(rdnn(n7))) ),
inference(resolution,[status(thm)],[f1223,f831]) ).
fof(f1684,plain,
( ~ sQ9_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f1683,f1218,f1222]) ).
fof(f1685,plain,
$false,
inference(sat_refutation,[status(thm)],[f1232,f1289,f1293,f1538,f1682,f1684]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM334+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n017.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 21 02:17:57 UTC 2026
% 0.02/0.36 % CPUTime :
% 0.02/0.38 % Drodi V4.1.1
% 0.02/0.43 % Refutation found
% 0.02/0.43 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.02/0.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.02/0.45 % Elapsed time: 0.087104 seconds
% 0.02/0.45 % CPU time: 0.375395 seconds
% 0.02/0.45 % Total memory used: 100.982 MB
% 0.02/0.45 % Net memory used: 100.681 MB
%------------------------------------------------------------------------------