%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM320+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 : n004.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 01:38:57 PM UTC 2026
% Result : Theorem 63.78s 23.52s
% Output : CNFRefutation 63.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 14
% Syntax : Number of formulae : 52 ( 23 unt; 2 def)
% Number of atoms : 124 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 143 ( 71 ~; 61 |; 6 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 3 prp; 0-4 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-1 aty)
% Number of variables : 88 ( 86 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
rdn_translate(n2,rdn_pos(rdnn(n2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f131,axiom,
rdn_translate(nn3,rdn_neg(rdnn(n3))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f133,axiom,
rdn_translate(nn5,rdn_neg(rdnn(n5))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f268,axiom,
rdn_positive_less(rdnn(n2),rdnn(n3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f269,axiom,
rdn_positive_less(rdnn(n3),rdnn(n4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f270,axiom,
rdn_positive_less(rdnn(n4),rdnn(n5)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f275,axiom,
! [X,Y,Z] :
( ( rdn_positive_less(rdnn(Y),rdnn(Z))
& rdn_positive_less(rdnn(X),rdnn(Y)) )
=> rdn_positive_less(rdnn(X),rdnn(Z)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f289,axiom,
! [X,Y,Z,RDN_X,RDN_Y,RDN_Z] :
( ( rdn_translate(Z,rdn_neg(RDN_Z))
& rdn_add_with_carry(rdnn(n0),RDN_X,RDN_Z,RDN_Y)
& rdn_positive_less(RDN_X,RDN_Y)
& rdn_translate(Y,rdn_neg(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(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,
? [Y] : sum(n2,nn5,Y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f403,negated_conjecture,
~ ? [Y] : sum(n2,nn5,Y),
inference(negated_conjecture,[status(cth)],[f402]) ).
fof(f406,plain,
rdn_translate(n2,rdn_pos(rdnn(n2))),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f534,plain,
rdn_translate(nn3,rdn_neg(rdnn(n3))),
inference(cnf_transformation,[status(thm)],[f131]) ).
fof(f536,plain,
rdn_translate(nn5,rdn_neg(rdnn(n5))),
inference(cnf_transformation,[status(thm)],[f133]) ).
fof(f671,plain,
rdn_positive_less(rdnn(n2),rdnn(n3)),
inference(cnf_transformation,[status(thm)],[f268]) ).
fof(f672,plain,
rdn_positive_less(rdnn(n3),rdnn(n4)),
inference(cnf_transformation,[status(thm)],[f269]) ).
fof(f673,plain,
rdn_positive_less(rdnn(n4),rdnn(n5)),
inference(cnf_transformation,[status(thm)],[f270]) ).
fof(f678,plain,
! [X,Y,Z] :
( rdn_positive_less(rdnn(X),rdnn(Z))
| ~ rdn_positive_less(rdnn(Y),rdnn(Z))
| ~ rdn_positive_less(rdnn(X),rdnn(Y)) ),
inference(pre_NNF_transformation,[status(thm)],[f275]) ).
fof(f679,plain,
! [X,Z] :
( rdn_positive_less(rdnn(X),rdnn(Z))
| ! [Y] :
( ~ rdn_positive_less(rdnn(Y),rdnn(Z))
| ~ rdn_positive_less(rdnn(X),rdnn(Y)) ) ),
inference(miniscoping,[status(thm)],[f678]) ).
fof(f680,plain,
! [X0,X1,X2] :
( rdn_positive_less(rdnn(X0),rdnn(X2))
| ~ rdn_positive_less(rdnn(X1),rdnn(X2))
| ~ rdn_positive_less(rdnn(X0),rdnn(X1)) ),
inference(cnf_transformation,[status(thm)],[f679]) ).
fof(f722,plain,
! [X,Y,Z,RDN_X,RDN_Y,RDN_Z] :
( sum(X,Y,Z)
| ~ rdn_translate(Z,rdn_neg(RDN_Z))
| ~ rdn_add_with_carry(rdnn(n0),RDN_X,RDN_Z,RDN_Y)
| ~ rdn_positive_less(RDN_X,RDN_Y)
| ~ rdn_translate(Y,rdn_neg(RDN_Y))
| ~ rdn_translate(X,rdn_pos(RDN_X)) ),
inference(pre_NNF_transformation,[status(thm)],[f289]) ).
fof(f723,plain,
! [X,Y,Z] :
( sum(X,Y,Z)
| ! [RDN_Z] :
( ~ rdn_translate(Z,rdn_neg(RDN_Z))
| ! [RDN_X,RDN_Y] :
( ~ rdn_add_with_carry(rdnn(n0),RDN_X,RDN_Z,RDN_Y)
| ~ rdn_positive_less(RDN_X,RDN_Y)
| ~ rdn_translate(Y,rdn_neg(RDN_Y))
| ~ rdn_translate(X,rdn_pos(RDN_X)) ) ) ),
inference(miniscoping,[status(thm)],[f722]) ).
fof(f724,plain,
! [X0,X1,X2,X3,X4,X5] :
( sum(X0,X2,X5)
| ~ rdn_translate(X5,rdn_neg(X4))
| ~ rdn_add_with_carry(rdnn(n0),X1,X4,X3)
| ~ rdn_positive_less(X1,X3)
| ~ rdn_translate(X2,rdn_neg(X3))
| ~ rdn_translate(X0,rdn_pos(X1)) ),
inference(cnf_transformation,[status(thm)],[f723]) ).
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,
! [Y] : ~ sum(n2,nn5,Y),
inference(pre_NNF_transformation,[status(thm)],[f403]) ).
fof(f862,plain,
! [X0] : ~ sum(n2,nn5,X0),
inference(cnf_transformation,[status(thm)],[f861]) ).
fof(f11336,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ rdn_digit_add(rdnn(X6),rdnn(n0),rdnn(X3),rdnn(n0))
| ~ rdn_digit_add(rdnn(X1),rdnn(X5),rdnn(X6),rdnn(n0))
| sum(X0,X2,X4)
| ~ rdn_translate(X4,rdn_neg(rdnn(X5)))
| ~ rdn_positive_less(rdnn(X1),rdnn(X3))
| ~ rdn_translate(X2,rdn_neg(rdnn(X3)))
| ~ rdn_translate(X0,rdn_pos(rdnn(X1))) ),
inference(resolution,[status(thm)],[f724,f749]) ).
fof(f13179,plain,
! [X0,X1,X2,X3,X4] :
( ~ rdn_digit_add(rdnn(X4),rdnn(n0),rdnn(X1),rdnn(n0))
| ~ rdn_digit_add(rdnn(X0),rdnn(X3),rdnn(X4),rdnn(n0))
| ~ rdn_translate(X2,rdn_neg(rdnn(X3)))
| ~ rdn_positive_less(rdnn(X0),rdnn(X1))
| ~ rdn_translate(nn5,rdn_neg(rdnn(X1)))
| ~ rdn_translate(n2,rdn_pos(rdnn(X0))) ),
inference(resolution,[status(thm)],[f11336,f862]) ).
fof(f13188,plain,
! [X0,X1,X2,X3] :
( ~ rdn_digit_add(rdnn(X3),rdnn(n0),rdnn(n5),rdnn(n0))
| ~ rdn_digit_add(rdnn(X0),rdnn(X2),rdnn(X3),rdnn(n0))
| ~ rdn_translate(X1,rdn_neg(rdnn(X2)))
| ~ rdn_positive_less(rdnn(X0),rdnn(n5))
| ~ rdn_translate(n2,rdn_pos(rdnn(X0))) ),
inference(resolution,[status(thm)],[f13179,f536]) ).
fof(f13226,plain,
! [X0,X1,X2] :
( ~ rdn_digit_add(rdnn(X0),rdnn(X2),rdnn(n5),rdnn(n0))
| ~ rdn_translate(X1,rdn_neg(rdnn(X2)))
| ~ rdn_positive_less(rdnn(X0),rdnn(n5))
| ~ rdn_translate(n2,rdn_pos(rdnn(X0))) ),
inference(resolution,[status(thm)],[f13188,f811]) ).
fof(f13278,plain,
! [X0,X1] :
( ~ rdn_digit_add(rdnn(n2),rdnn(X1),rdnn(n5),rdnn(n0))
| ~ rdn_translate(X0,rdn_neg(rdnn(X1)))
| ~ rdn_positive_less(rdnn(n2),rdnn(n5)) ),
inference(resolution,[status(thm)],[f13226,f406]) ).
fof(f13279,definition,
( sQ901_spl
<=> rdn_positive_less(rdnn(n2),rdnn(n5)) ),
introduced(definition,[new_symbols(definition,[sQ901_spl])],[split_symbol_definition]) ).
fof(f13281,plain,
( sQ901_spl
| ~ rdn_positive_less(rdnn(n2),rdnn(n5)) ),
inference(component_clause,[status(thm)],[f13279]) ).
fof(f13282,definition,
! [X0,X1] :
( sQ902_spl
<=> ( ~ rdn_digit_add(rdnn(n2),rdnn(X1),rdnn(n5),rdnn(n0))
| ~ rdn_translate(X0,rdn_neg(rdnn(X1))) ) ),
introduced(definition,[new_symbols(definition,[sQ902_spl])],[split_symbol_definition]) ).
fof(f13283,plain,
! [X0,X1] :
( ~ sQ902_spl
| ~ rdn_digit_add(rdnn(n2),rdnn(X1),rdnn(n5),rdnn(n0))
| ~ rdn_translate(X0,rdn_neg(rdnn(X1))) ),
inference(component_clause,[status(thm)],[f13282]) ).
fof(f13285,plain,
( sQ902_spl
| ~ sQ901_spl ),
inference(split_clause,[status(thm)],[f13278,f13279,f13282]) ).
fof(f13293,plain,
! [X0] :
( sQ901_spl
| ~ rdn_positive_less(rdnn(X0),rdnn(n5))
| ~ rdn_positive_less(rdnn(n2),rdnn(X0)) ),
inference(resolution,[status(thm)],[f13281,f680]) ).
fof(f13294,plain,
! [X0] :
( ~ sQ902_spl
| ~ rdn_translate(X0,rdn_neg(rdnn(n3))) ),
inference(resolution,[status(thm)],[f13283,f784]) ).
fof(f13303,plain,
( ~ sQ902_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f534,f13294]) ).
fof(f13304,plain,
~ sQ902_spl,
inference(contradiction_clause,[status(thm)],[f13303]) ).
fof(f13307,plain,
( sQ901_spl
| ~ rdn_positive_less(rdnn(n3),rdnn(n5)) ),
inference(resolution,[status(thm)],[f13293,f671]) ).
fof(f13322,plain,
! [X0] :
( sQ901_spl
| ~ rdn_positive_less(rdnn(X0),rdnn(n5))
| ~ rdn_positive_less(rdnn(n3),rdnn(X0)) ),
inference(resolution,[status(thm)],[f13307,f680]) ).
fof(f13352,plain,
( sQ901_spl
| ~ rdn_positive_less(rdnn(n4),rdnn(n5)) ),
inference(resolution,[status(thm)],[f13322,f672]) ).
fof(f13354,plain,
( sQ901_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f13352,f673]) ).
fof(f13355,plain,
sQ901_spl,
inference(contradiction_clause,[status(thm)],[f13354]) ).
fof(f13356,plain,
$false,
inference(sat_refutation,[status(thm)],[f13285,f13304,f13355]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM320+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/15.38 % Computer : n004.cluster.edu
% 0.10/15.38 % Model : x86_64 x86_64
% 0.10/15.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/15.38 % Memory : 8046.5625MB
% 0.10/15.38 % OS : Linux 6.8.0-71-generic
% 0.10/15.38 % CPULimit : 300
% 0.10/15.38 % WCLimit : 300
% 0.10/15.38 % DateTime : Mon Sep 21 02:22:06 UTC 2026
% 0.10/15.38 % CPUTime :
% 0.13/15.40 % Drodi V4.1.1
% 63.78/23.52 % Refutation found
% 63.78/23.52 % SZS status Theorem for theBenchmark: Theorem is valid
% 63.78/23.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 15.13/23.64 % Elapsed time: 8.244794 seconds
% 15.13/23.64 % CPU time: 64.576846 seconds
% 15.13/23.64 % Total memory used: 441.343 MB
% 15.13/23.64 % Net memory used: 419.341 MB
%------------------------------------------------------------------------------