%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : FLD061-4 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.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 12:22:06 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.47s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 11
% Syntax : Number of formulae : 41 ( 18 unt; 0 def)
% Number of atoms : 82 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 84 ( 43 ~; 41 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 52 ( 52 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [Y,X,Z] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [X,Y] :
( ~ defined(Y)
| ~ defined(X)
| sum(X,Y,add(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [X,Z,Y] :
( ~ less_or_equal(Y,Z)
| ~ less_or_equal(X,Y)
| less_or_equal(X,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [U,V,X,Y,Z] :
( ~ sum(Y,Z,V)
| ~ sum(X,Z,U)
| ~ less_or_equal(X,Y)
| less_or_equal(U,V) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,hypothesis,
defined(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,hypothesis,
defined(c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
less_or_equal(a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
less_or_equal(c,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f35,negated_conjecture,
sum(a,c,u),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f36,negated_conjecture,
sum(d,b,v),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,negated_conjecture,
~ less_or_equal(u,v),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f44,plain,
! [X0,X1,X2] :
( ~ sum(X1,X0,X2)
| sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f64,plain,
! [Y] :
( ~ defined(Y)
| ! [X] :
( ~ defined(X)
| sum(X,Y,add(X,Y)) ) ),
inference(miniscoping,[status(thm)],[f19]) ).
fof(f65,plain,
! [X0,X1] :
( ~ defined(X1)
| ~ defined(X0)
| sum(X0,X1,add(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f69,plain,
! [Z,Y] :
( ~ less_or_equal(Y,Z)
| ! [X] :
( ~ less_or_equal(X,Y)
| less_or_equal(X,Z) ) ),
inference(miniscoping,[status(thm)],[f22]) ).
fof(f70,plain,
! [X0,X1,X2] :
( ~ less_or_equal(X2,X1)
| ~ less_or_equal(X0,X2)
| less_or_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f73,plain,
! [V,Y,Z] :
( ~ sum(Y,Z,V)
| ! [U,X] :
( ~ sum(X,Z,U)
| ~ less_or_equal(X,Y)
| less_or_equal(U,V) ) ),
inference(miniscoping,[status(thm)],[f24]) ).
fof(f74,plain,
! [X0,X1,X2,X3,X4] :
( ~ sum(X3,X4,X1)
| ~ sum(X2,X4,X0)
| ~ less_or_equal(X2,X3)
| less_or_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f73]) ).
fof(f78,plain,
defined(b),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f79,plain,
defined(c),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f83,plain,
less_or_equal(a,b),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f84,plain,
less_or_equal(c,d),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f85,plain,
sum(a,c,u),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f86,plain,
sum(d,b,v),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f87,plain,
~ less_or_equal(u,v),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f129,plain,
! [X0,X1,X2] :
( ~ sum(d,X2,X1)
| ~ sum(c,X2,X0)
| less_or_equal(X0,X1) ),
inference(resolution,[status(thm)],[f74,f84]) ).
fof(f130,plain,
! [X0,X1,X2] :
( ~ sum(b,X2,X1)
| ~ sum(a,X2,X0)
| less_or_equal(X0,X1) ),
inference(resolution,[status(thm)],[f74,f83]) ).
fof(f173,plain,
! [X0,X1,X2] :
( ~ sum(X2,c,X0)
| ~ sum(d,X2,X1)
| less_or_equal(X0,X1) ),
inference(resolution,[status(thm)],[f129,f44]) ).
fof(f178,plain,
! [X0,X1,X2] :
( ~ sum(X2,b,X1)
| ~ sum(a,X2,X0)
| less_or_equal(X0,X1) ),
inference(resolution,[status(thm)],[f130,f44]) ).
fof(f214,plain,
! [X0] :
( ~ sum(b,c,X0)
| less_or_equal(X0,v) ),
inference(resolution,[status(thm)],[f173,f86]) ).
fof(f221,plain,
! [X0] :
( ~ sum(c,b,X0)
| less_or_equal(X0,v) ),
inference(resolution,[status(thm)],[f214,f44]) ).
fof(f240,plain,
( ~ defined(b)
| ~ defined(c)
| less_or_equal(add(c,b),v) ),
inference(resolution,[status(thm)],[f221,f65]) ).
fof(f244,plain,
( ~ defined(b)
| less_or_equal(add(c,b),v) ),
inference(forward_subsumption_resolution,[status(thm)],[f240,f79]) ).
fof(f259,plain,
less_or_equal(add(c,b),v),
inference(forward_subsumption_resolution,[status(thm)],[f244,f78]) ).
fof(f264,plain,
! [X0] :
( ~ less_or_equal(X0,add(c,b))
| less_or_equal(X0,v) ),
inference(resolution,[status(thm)],[f259,f70]) ).
fof(f334,plain,
! [X0] :
( ~ sum(c,b,X0)
| less_or_equal(u,X0) ),
inference(resolution,[status(thm)],[f178,f85]) ).
fof(f345,plain,
( ~ defined(b)
| ~ defined(c)
| less_or_equal(u,add(c,b)) ),
inference(resolution,[status(thm)],[f334,f65]) ).
fof(f349,plain,
( ~ defined(b)
| less_or_equal(u,add(c,b)) ),
inference(forward_subsumption_resolution,[status(thm)],[f345,f79]) ).
fof(f355,plain,
less_or_equal(u,add(c,b)),
inference(forward_subsumption_resolution,[status(thm)],[f349,f78]) ).
fof(f360,plain,
less_or_equal(u,v),
inference(resolution,[status(thm)],[f355,f264]) ).
fof(f366,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f360,f87]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : FLD061-4 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n011.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 15:43:55 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.36 % Drodi V4.1.1
% 0.13/0.47 % Refutation found
% 0.13/0.47 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.64/0.49 % Elapsed time: 0.126236 seconds
% 0.64/0.49 % CPU time: 0.783233 seconds
% 0.64/0.49 % Total memory used: 25.103 MB
% 0.64/0.49 % Net memory used: 24.160 MB
%------------------------------------------------------------------------------