%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM336+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 : n013.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 0.64s 0.53s
% Output : CNFRefutation 0.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 11
% Syntax : Number of formulae : 49 ( 18 unt; 1 def)
% Number of atoms : 107 ( 11 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 104 ( 46 ~; 42 |; 9 &)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 2 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-1 aty)
% Number of variables : 87 ( 86 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
rdn_translate(n2,rdn_pos(rdnn(n2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
rdn_translate(n3,rdn_pos(rdnn(n3))),
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(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(f293,axiom,
! [X,Y,Z1,Z2] :
( ( sum(X,Y,Z2)
& sum(X,Y,Z1) )
=> Z1 = Z2 ),
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(f325,axiom,
rdn_digit_add(rdnn(n2),rdnn(n3),rdnn(n5),rdnn(n0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f352,axiom,
rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f402,conjecture,
! [X] :
( difference(X,n2,n3)
=> X = n5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f403,negated_conjecture,
~ ! [X] :
( difference(X,n2,n3)
=> X = 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(f734,plain,
! [X,Y,Z1,Z2] :
( Z1 = Z2
| ~ sum(X,Y,Z2)
| ~ sum(X,Y,Z1) ),
inference(pre_NNF_transformation,[status(thm)],[f293]) ).
fof(f735,plain,
! [Z1,Z2] :
( Z1 = Z2
| ! [X,Y] :
( ~ sum(X,Y,Z2)
| ~ sum(X,Y,Z1) ) ),
inference(miniscoping,[status(thm)],[f734]) ).
fof(f736,plain,
! [X0,X1,X2,X3] :
( X2 = X3
| ~ sum(X0,X1,X3)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f735]) ).
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(f746,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(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] :
( X != n5
& difference(X,n2,n3) ),
inference(pre_NNF_transformation,[status(thm)],[f403]) ).
fof(f862,plain,
( sK0_skl != n5
& difference(sK0_skl,n2,n3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(X,sK0_skl)],[f861]) ).
fof(f863,plain,
difference(sK0_skl,n2,n3),
inference(cnf_transformation,[status(thm)],[f862]) ).
fof(f864,plain,
sK0_skl != n5,
inference(cnf_transformation,[status(thm)],[f862]) ).
fof(f867,plain,
sum(n2,n3,sK0_skl),
inference(resolution,[status(thm)],[f746,f863]) ).
fof(f884,plain,
! [X0] :
( X0 = sK0_skl
| ~ sum(n2,n3,X0) ),
inference(resolution,[status(thm)],[f736,f867]) ).
fof(f2838,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(f2875,plain,
rdn_add_with_carry(rdnn(n0),rdnn(n2),rdnn(n3),rdnn(n5)),
inference(resolution,[status(thm)],[f2838,f784]) ).
fof(f2910,plain,
! [X0,X1,X2] :
( sum(X0,X1,X2)
| ~ rdn_translate(X2,rdn_pos(rdnn(n5)))
| ~ rdn_translate(X1,rdn_pos(rdnn(n3)))
| ~ rdn_translate(X0,rdn_pos(rdnn(n2))) ),
inference(resolution,[status(thm)],[f2875,f718]) ).
fof(f4262,plain,
! [X0,X1] :
( sum(X0,n3,X1)
| ~ rdn_translate(X1,rdn_pos(rdnn(n5)))
| ~ rdn_translate(X0,rdn_pos(rdnn(n2))) ),
inference(resolution,[status(thm)],[f2910,f407]) ).
fof(f4984,definition,
( sQ348_spl
<=> sum(n2,n3,n5) ),
introduced(definition,[new_symbols(definition,[sQ348_spl])],[split_symbol_definition]) ).
fof(f4985,plain,
( ~ sQ348_spl
| sum(n2,n3,n5) ),
inference(component_clause,[status(thm)],[f4984]) ).
fof(f4986,plain,
( sQ348_spl
| ~ sum(n2,n3,n5) ),
inference(component_clause,[status(thm)],[f4984]) ).
fof(f5031,plain,
( ~ sQ348_spl
| n5 = sK0_skl ),
inference(resolution,[status(thm)],[f4985,f884]) ).
fof(f5037,plain,
( ~ sQ348_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5031,f864]) ).
fof(f5038,plain,
~ sQ348_spl,
inference(contradiction_clause,[status(thm)],[f5037]) ).
fof(f5046,plain,
! [X0] :
( sum(X0,n3,n5)
| ~ rdn_translate(X0,rdn_pos(rdnn(n2))) ),
inference(resolution,[status(thm)],[f4262,f409]) ).
fof(f5047,plain,
sum(n2,n3,n5),
inference(resolution,[status(thm)],[f5046,f406]) ).
fof(f5048,plain,
( sQ348_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5047,f4986]) ).
fof(f5049,plain,
sQ348_spl,
inference(contradiction_clause,[status(thm)],[f5048]) ).
fof(f5050,plain,
$false,
inference(sat_refutation,[status(thm)],[f5038,f5049]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM336+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n013.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 02:22:06 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 0.64/0.53 % Refutation found
% 0.64/0.53 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.64/0.53 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.64/0.56 % Elapsed time: 0.181066 seconds
% 0.64/0.56 % CPU time: 1.031529 seconds
% 0.64/0.56 % Total memory used: 127.856 MB
% 0.64/0.56 % Net memory used: 126.607 MB
%------------------------------------------------------------------------------