%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : HEN011-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.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 12:45:24 PM UTC 2026
% Result : Unsatisfiable 1.40s 0.62s
% Output : CNFRefutation 1.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 25 ( 13 unt; 0 def)
% Number of atoms : 43 ( 6 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 46 ( 28 ~; 18 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 35 ( 35 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X,Y] : less_equal(divide(X,Y),X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Z,Y] : less_equal(divide(divide(X,Z),divide(Y,Z)),divide(divide(X,Y),Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X,Y] :
( X = Y
| ~ less_equal(Y,X)
| ~ less_equal(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X,Y,Z] :
( less_equal(X,Z)
| ~ less_equal(Y,Z)
| ~ less_equal(X,Y) ),
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(f16,axiom,
! [X] : divide(identity,divide(identity,divide(identity,X))) = divide(identity,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
divide(divide(identity,a),divide(identity,divide(identity,b))) != divide(divide(identity,b),divide(identity,divide(identity,a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,plain,
! [X0,X1] : less_equal(divide(X0,X1),X0),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f22,plain,
! [X0,X1,X2] : less_equal(divide(divide(X0,X1),divide(X2,X1)),divide(divide(X0,X2),X1)),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f24,plain,
! [X0,X1] :
( X0 = X1
| ~ less_equal(X1,X0)
| ~ less_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f30,plain,
! [X,Z] :
( less_equal(X,Z)
| ! [Y] :
( ~ less_equal(Y,Z)
| ~ less_equal(X,Y) ) ),
inference(miniscoping,[status(thm)],[f12]) ).
fof(f31,plain,
! [X0,X1,X2] :
( less_equal(X0,X2)
| ~ less_equal(X1,X2)
| ~ less_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f32,plain,
! [X0,X1,X2] :
( less_equal(divide(X0,X2),X1)
| ~ less_equal(divide(X0,X1),X2) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f37,plain,
! [X0] : divide(identity,divide(identity,divide(identity,X0))) = divide(identity,X0),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f39,plain,
divide(divide(identity,a),divide(identity,divide(identity,b))) != divide(divide(identity,b),divide(identity,divide(identity,a))),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f135,plain,
! [X0,X1] : less_equal(divide(divide(identity,X0),divide(X1,divide(identity,divide(identity,X0)))),divide(divide(identity,X1),divide(identity,divide(identity,X0)))),
inference(paramodulation,[status(thm)],[f37,f22]) ).
fof(f221,plain,
( ~ less_equal(divide(divide(identity,b),divide(identity,divide(identity,a))),divide(divide(identity,a),divide(identity,divide(identity,b))))
| ~ less_equal(divide(divide(identity,a),divide(identity,divide(identity,b))),divide(divide(identity,b),divide(identity,divide(identity,a)))) ),
inference(resolution,[status(thm)],[f39,f24]) ).
fof(f1360,plain,
( ~ less_equal(divide(divide(identity,b),divide(divide(identity,a),divide(identity,divide(identity,b)))),divide(identity,divide(identity,a)))
| ~ less_equal(divide(divide(identity,a),divide(identity,divide(identity,b))),divide(divide(identity,b),divide(identity,divide(identity,a)))) ),
inference(resolution,[status(thm)],[f221,f32]) ).
fof(f1973,plain,
! [X0] :
( ~ less_equal(X0,divide(identity,divide(identity,a)))
| ~ less_equal(divide(divide(identity,b),divide(divide(identity,a),divide(identity,divide(identity,b)))),X0)
| ~ less_equal(divide(divide(identity,a),divide(identity,divide(identity,b))),divide(divide(identity,b),divide(identity,divide(identity,a)))) ),
inference(resolution,[status(thm)],[f1360,f31]) ).
fof(f2040,plain,
( ~ less_equal(divide(divide(identity,divide(identity,a)),divide(identity,divide(identity,b))),divide(identity,divide(identity,a)))
| ~ less_equal(divide(divide(identity,a),divide(identity,divide(identity,b))),divide(divide(identity,b),divide(identity,divide(identity,a)))) ),
inference(resolution,[status(thm)],[f1973,f135]) ).
fof(f2051,plain,
~ less_equal(divide(divide(identity,a),divide(identity,divide(identity,b))),divide(divide(identity,b),divide(identity,divide(identity,a)))),
inference(forward_subsumption_resolution,[status(thm)],[f2040,f21]) ).
fof(f2052,plain,
~ less_equal(divide(divide(identity,a),divide(divide(identity,b),divide(identity,divide(identity,a)))),divide(identity,divide(identity,b))),
inference(resolution,[status(thm)],[f2051,f32]) ).
fof(f2056,plain,
! [X0] :
( ~ less_equal(X0,divide(identity,divide(identity,b)))
| ~ less_equal(divide(divide(identity,a),divide(divide(identity,b),divide(identity,divide(identity,a)))),X0) ),
inference(resolution,[status(thm)],[f2052,f31]) ).
fof(f2678,plain,
~ less_equal(divide(divide(identity,divide(identity,b)),divide(identity,divide(identity,a))),divide(identity,divide(identity,b))),
inference(resolution,[status(thm)],[f2056,f135]) ).
fof(f2689,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f2678,f21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : HEN011-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n002.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sun Sep 20 20:49:17 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.13/0.36 % Drodi V4.1.1
% 1.40/0.62 % Refutation found
% 1.40/0.62 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 1.40/0.62 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.40/0.63 % Elapsed time: 0.277542 seconds
% 1.40/0.63 % CPU time: 1.961884 seconds
% 1.40/0.63 % Total memory used: 103.032 MB
% 1.40/0.63 % Net memory used: 99.301 MB
%------------------------------------------------------------------------------