%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM344+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 : 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 01:39:00 PM UTC 2026
% Result : Theorem 0.19s 0.45s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 39 ( 10 unt; 2 def)
% Number of atoms : 85 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 89 ( 43 ~; 35 |; 6 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 3 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-1 aty)
% Number of variables : 68 ( 64 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
rdn_translate(n0,rdn_pos(rdnn(n0))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
rdn_translate(n1,rdn_pos(rdnn(n1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f129,axiom,
rdn_translate(nn1,rdn_neg(rdnn(n1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f282,axiom,
! [X,Y,RDN_X,RDN_Y] :
( ( rdn_translate(Y,rdn_pos(RDN_Y))
& rdn_translate(X,rdn_neg(RDN_X)) )
=> less(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f291,axiom,
! [POS_X,NEG_X,RDN_X] :
( ( rdn_translate(NEG_X,rdn_neg(RDN_X))
& rdn_translate(POS_X,rdn_pos(RDN_X)) )
=> sum(POS_X,NEG_X,n0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f292,axiom,
! [X,Y,Z,RDN_X,RDN_Y] :
( ( sum(Y,X,Z)
& rdn_translate(Y,rdn_pos(RDN_Y))
& rdn_translate(X,rdn_neg(RDN_X)) )
=> sum(X,Y,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f402,conjecture,
? [X,Y] :
( less(X,Y)
& sum(X,n1,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f403,negated_conjecture,
~ ? [X,Y] :
( less(X,Y)
& sum(X,n1,Y) ),
inference(negated_conjecture,[status(cth)],[f402]) ).
fof(f404,plain,
rdn_translate(n0,rdn_pos(rdnn(n0))),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f405,plain,
rdn_translate(n1,rdn_pos(rdnn(n1))),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f532,plain,
rdn_translate(nn1,rdn_neg(rdnn(n1))),
inference(cnf_transformation,[status(thm)],[f129]) ).
fof(f697,plain,
! [X,Y,RDN_X,RDN_Y] :
( less(X,Y)
| ~ rdn_translate(Y,rdn_pos(RDN_Y))
| ~ rdn_translate(X,rdn_neg(RDN_X)) ),
inference(pre_NNF_transformation,[status(thm)],[f282]) ).
fof(f698,plain,
! [X,Y] :
( less(X,Y)
| ! [RDN_Y] : ~ rdn_translate(Y,rdn_pos(RDN_Y))
| ! [RDN_X] : ~ rdn_translate(X,rdn_neg(RDN_X)) ),
inference(miniscoping,[status(thm)],[f697]) ).
fof(f699,plain,
! [X0,X1,X2,X3] :
( less(X0,X2)
| ~ rdn_translate(X2,rdn_pos(X3))
| ~ rdn_translate(X0,rdn_neg(X1)) ),
inference(cnf_transformation,[status(thm)],[f698]) ).
fof(f728,plain,
! [POS_X,NEG_X,RDN_X] :
( sum(POS_X,NEG_X,n0)
| ~ rdn_translate(NEG_X,rdn_neg(RDN_X))
| ~ rdn_translate(POS_X,rdn_pos(RDN_X)) ),
inference(pre_NNF_transformation,[status(thm)],[f291]) ).
fof(f729,plain,
! [POS_X,NEG_X] :
( sum(POS_X,NEG_X,n0)
| ! [RDN_X] :
( ~ rdn_translate(NEG_X,rdn_neg(RDN_X))
| ~ rdn_translate(POS_X,rdn_pos(RDN_X)) ) ),
inference(miniscoping,[status(thm)],[f728]) ).
fof(f730,plain,
! [X0,X1,X2] :
( sum(X0,X2,n0)
| ~ rdn_translate(X2,rdn_neg(X1))
| ~ rdn_translate(X0,rdn_pos(X1)) ),
inference(cnf_transformation,[status(thm)],[f729]) ).
fof(f731,plain,
! [X,Y,Z,RDN_X,RDN_Y] :
( sum(X,Y,Z)
| ~ sum(Y,X,Z)
| ~ rdn_translate(Y,rdn_pos(RDN_Y))
| ~ rdn_translate(X,rdn_neg(RDN_X)) ),
inference(pre_NNF_transformation,[status(thm)],[f292]) ).
fof(f732,plain,
! [X,Y,Z] :
( sum(X,Y,Z)
| ~ sum(Y,X,Z)
| ! [RDN_Y] : ~ rdn_translate(Y,rdn_pos(RDN_Y))
| ! [RDN_X] : ~ rdn_translate(X,rdn_neg(RDN_X)) ),
inference(miniscoping,[status(thm)],[f731]) ).
fof(f733,plain,
! [X0,X1,X2,X3,X4] :
( sum(X0,X2,X4)
| ~ sum(X2,X0,X4)
| ~ rdn_translate(X2,rdn_pos(X3))
| ~ rdn_translate(X0,rdn_neg(X1)) ),
inference(cnf_transformation,[status(thm)],[f732]) ).
fof(f861,plain,
! [X,Y] :
( ~ less(X,Y)
| ~ sum(X,n1,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f403]) ).
fof(f862,plain,
! [X0,X1] :
( ~ less(X0,X1)
| ~ sum(X0,n1,X1) ),
inference(cnf_transformation,[status(thm)],[f861]) ).
fof(f878,plain,
! [X0,X1,X2] :
( sum(nn1,X0,X2)
| ~ sum(X0,nn1,X2)
| ~ rdn_translate(X0,rdn_pos(X1)) ),
inference(resolution,[status(thm)],[f532,f733]) ).
fof(f879,plain,
! [X0] :
( sum(X0,nn1,n0)
| ~ rdn_translate(X0,rdn_pos(rdnn(n1))) ),
inference(resolution,[status(thm)],[f532,f730]) ).
fof(f881,plain,
! [X0,X1] :
( less(nn1,X0)
| ~ rdn_translate(X0,rdn_pos(X1)) ),
inference(resolution,[status(thm)],[f532,f699]) ).
fof(f903,plain,
! [X0,X1] :
( ~ sum(nn1,n1,X0)
| ~ rdn_translate(X0,rdn_pos(X1)) ),
inference(resolution,[status(thm)],[f881,f862]) ).
fof(f999,plain,
sum(n1,nn1,n0),
inference(resolution,[status(thm)],[f879,f405]) ).
fof(f1000,plain,
! [X0] :
( sum(nn1,n1,n0)
| ~ rdn_translate(n1,rdn_pos(X0)) ),
inference(resolution,[status(thm)],[f999,f878]) ).
fof(f1004,definition,
! [X0] :
( sQ5_spl
<=> ~ rdn_translate(n1,rdn_pos(X0)) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f1005,plain,
! [X0] :
( ~ sQ5_spl
| ~ rdn_translate(n1,rdn_pos(X0)) ),
inference(component_clause,[status(thm)],[f1004]) ).
fof(f1007,definition,
( sQ6_spl
<=> sum(nn1,n1,n0) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f1008,plain,
( ~ sQ6_spl
| sum(nn1,n1,n0) ),
inference(component_clause,[status(thm)],[f1007]) ).
fof(f1010,plain,
( sQ6_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f1000,f1004,f1007]) ).
fof(f1011,plain,
( ~ sQ5_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f405,f1005]) ).
fof(f1012,plain,
~ sQ5_spl,
inference(contradiction_clause,[status(thm)],[f1011]) ).
fof(f1013,plain,
! [X0] :
( ~ sQ6_spl
| ~ rdn_translate(n0,rdn_pos(X0)) ),
inference(resolution,[status(thm)],[f1008,f903]) ).
fof(f1031,plain,
( ~ sQ6_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f404,f1013]) ).
fof(f1032,plain,
~ sQ6_spl,
inference(contradiction_clause,[status(thm)],[f1031]) ).
fof(f1033,plain,
$false,
inference(sat_refutation,[status(thm)],[f1010,f1012,f1032]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM344+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.05 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.41 % Computer : n004.cluster.edu
% 0.16/0.41 % Model : x86_64 x86_64
% 0.16/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.41 % Memory : 8046.5625MB
% 0.16/0.41 % OS : Linux 6.8.0-71-generic
% 0.16/0.41 % CPULimit : 300
% 0.16/0.41 % WCLimit : 300
% 0.16/0.41 % DateTime : Mon Sep 21 02:22:49 UTC 2026
% 0.16/0.41 % CPUTime :
% 0.19/0.44 % Drodi V4.1.1
% 0.19/0.45 % Refutation found
% 0.19/0.45 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.19/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.19/0.53 % Elapsed time: 0.109473 seconds
% 0.19/0.53 % CPU time: 0.142071 seconds
% 0.19/0.53 % Total memory used: 15.730 MB
% 0.19/0.53 % Net memory used: 15.707 MB
%------------------------------------------------------------------------------