%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : HEN009-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% 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 12:45:22 PM UTC 2026
% Result : Unsatisfiable 0.09s 0.46s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 22 ( 9 unt; 0 def)
% Number of atoms : 37 ( 4 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 39 ( 24 ~; 15 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 30 ( 30 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X,Y] :
( X = Y
| ~ less_equal(Y,X)
| ~ less_equal(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X] : less_equal(X,identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [X,Y,Z] :
( less_equal(divide(X,Z),Y)
| ~ less_equal(divide(X,Y),Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [X,Y,Z] :
( less_equal(divide(Z,Y),divide(Z,X))
| ~ less_equal(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [X,Y,Z] :
( less_equal(divide(X,Z),divide(Y,Z))
| ~ less_equal(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
divide(identity,a) != divide(identity,divide(identity,divide(identity,a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,plain,
! [X0,X1] :
( X0 = X1
| ~ less_equal(X1,X0)
| ~ less_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f23,plain,
! [X0] : less_equal(X0,identity),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f30,plain,
! [X0,X1,X2] :
( less_equal(divide(X0,X2),X1)
| ~ less_equal(divide(X0,X1),X2) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f31,plain,
! [X,Y] :
( ! [Z] : less_equal(divide(Z,Y),divide(Z,X))
| ~ less_equal(X,Y) ),
inference(miniscoping,[status(thm)],[f14]) ).
fof(f32,plain,
! [X0,X1,X2] :
( less_equal(divide(X2,X1),divide(X2,X0))
| ~ less_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f33,plain,
! [X,Y] :
( ! [Z] : less_equal(divide(X,Z),divide(Y,Z))
| ~ less_equal(X,Y) ),
inference(miniscoping,[status(thm)],[f15]) ).
fof(f34,plain,
! [X0,X1,X2] :
( less_equal(divide(X0,X2),divide(X1,X2))
| ~ less_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f35,plain,
divide(identity,a) != divide(identity,divide(identity,divide(identity,a))),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f85,plain,
( ~ less_equal(divide(identity,divide(identity,divide(identity,a))),divide(identity,a))
| ~ less_equal(divide(identity,a),divide(identity,divide(identity,divide(identity,a)))) ),
inference(resolution,[status(thm)],[f22,f35]) ).
fof(f113,plain,
( ~ less_equal(divide(identity,divide(identity,a)),divide(identity,divide(identity,a)))
| ~ less_equal(divide(identity,a),divide(identity,divide(identity,divide(identity,a)))) ),
inference(resolution,[status(thm)],[f85,f30]) ).
fof(f120,plain,
( ~ less_equal(identity,identity)
| ~ less_equal(divide(identity,a),divide(identity,divide(identity,divide(identity,a)))) ),
inference(resolution,[status(thm)],[f113,f34]) ).
fof(f125,plain,
~ less_equal(divide(identity,a),divide(identity,divide(identity,divide(identity,a)))),
inference(forward_subsumption_resolution,[status(thm)],[f120,f23]) ).
fof(f292,plain,
~ less_equal(divide(identity,divide(identity,a)),a),
inference(resolution,[status(thm)],[f125,f32]) ).
fof(f296,plain,
~ less_equal(divide(identity,a),divide(identity,a)),
inference(resolution,[status(thm)],[f292,f30]) ).
fof(f302,plain,
~ less_equal(identity,identity),
inference(resolution,[status(thm)],[f296,f34]) ).
fof(f307,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f302,f23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN009-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.39 % Computer : n004.cluster.edu
% 0.09/0.39 % Model : x86_64 x86_64
% 0.09/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.39 % Memory : 8046.5625MB
% 0.09/0.39 % OS : Linux 6.8.0-71-generic
% 0.09/0.39 % CPULimit : 300
% 0.09/0.39 % WCLimit : 300
% 0.09/0.39 % DateTime : Sun Sep 20 20:46:20 UTC 2026
% 0.09/0.39 % CPUTime :
% 0.09/0.40 % Drodi V4.1.1
% 0.09/0.46 % Refutation found
% 0.09/0.46 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.09/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.47 % Elapsed time: 0.075826 seconds
% 0.09/0.47 % CPU time: 0.285799 seconds
% 0.09/0.47 % Total memory used: 70.287 MB
% 0.09/0.47 % Net memory used: 69.687 MB
%------------------------------------------------------------------------------