%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : HEN010-6 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n010.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 12:45:23 PM UTC 2026
% Result : Unsatisfiable 0.09s 0.41s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 24 ( 18 unt; 0 def)
% Number of atoms : 32 ( 11 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 23 ( 15 ~; 8 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 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 : 27 ( 27 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X,Y] :
( less_equal(X,Y)
| divide(X,Y) != zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y] : less_equal(divide(X,Y),X),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X] : less_equal(zero,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X,Y] :
( X = Y
| ~ less_equal(Y,X)
| ~ less_equal(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X] : divide(X,X) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [X] : divide(identity,divide(identity,divide(identity,X))) = divide(identity,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
divide(identity,a) != divide(divide(identity,a),divide(identity,divide(identity,a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,plain,
! [X0,X1] :
( less_equal(X0,X1)
| divide(X0,X1) != zero ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f19,plain,
! [X0,X1] : less_equal(divide(X0,X1),X0),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f20,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(f21,plain,
! [X0] : less_equal(zero,X0),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f22,plain,
! [X0,X1] :
( X0 = X1
| ~ less_equal(X1,X0)
| ~ less_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f26,plain,
! [X0] : divide(X0,X0) = zero,
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f33,plain,
! [X0] : divide(identity,divide(identity,divide(identity,X0))) = divide(identity,X0),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f34,plain,
divide(identity,a) != divide(divide(identity,a),divide(identity,divide(identity,a))),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f49,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)],[f33,f20]) ).
fof(f67,plain,
( ~ less_equal(divide(divide(identity,a),divide(identity,divide(identity,a))),divide(identity,a))
| ~ less_equal(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a)))) ),
inference(resolution,[status(thm)],[f22,f34]) ).
fof(f69,plain,
~ less_equal(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a)))),
inference(forward_subsumption_resolution,[status(thm)],[f67,f19]) ).
fof(f123,plain,
divide(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a)))) != zero,
inference(resolution,[status(thm)],[f69,f18]) ).
fof(f127,plain,
( ~ less_equal(zero,divide(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a)))))
| ~ less_equal(divide(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a)))),zero) ),
inference(resolution,[status(thm)],[f123,f22]) ).
fof(f129,plain,
~ less_equal(divide(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a)))),zero),
inference(forward_subsumption_resolution,[status(thm)],[f127,f21]) ).
fof(f158,plain,
! [X0] : less_equal(divide(divide(identity,X0),divide(divide(identity,X0),divide(identity,divide(identity,X0)))),zero),
inference(paramodulation,[status(thm)],[f26,f49]) ).
fof(f195,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f129,f158]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN010-6 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n010.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 20:46:42 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.09/0.41 % Refutation found
% 0.09/0.41 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.09/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.43 % Elapsed time: 0.059573 seconds
% 0.09/0.43 % CPU time: 0.202164 seconds
% 0.09/0.43 % Total memory used: 68.514 MB
% 0.09/0.43 % Net memory used: 68.141 MB
%------------------------------------------------------------------------------