%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : HEN012-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 0.16s 0.47s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 24 ( 16 unt; 0 def)
% Number of atoms : 34 ( 12 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 22 ( 12 ~; 10 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 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 : 38 ( 38 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] :
( divide(X,Y) = zero
| ~ less_equal(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
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(f8,negated_conjecture,
~ less_equal(a,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,plain,
! [X0,X1] :
( divide(X0,X1) = zero
| ~ less_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f10,plain,
! [X0,X1] :
( less_equal(X0,X1)
| divide(X0,X1) != zero ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f11,plain,
! [X0,X1] : less_equal(divide(X0,X1),X0),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f12,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(f13,plain,
! [X0] : less_equal(zero,X0),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f14,plain,
! [X0,X1] :
( X0 = X1
| ~ less_equal(X1,X0)
| ~ less_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f16,plain,
~ less_equal(a,a),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f17,plain,
! [X0] :
( zero = X0
| ~ less_equal(X0,zero) ),
inference(resolution,[status(thm)],[f13,f14]) ).
fof(f24,plain,
! [X0,X1] : divide(divide(X0,X1),X0) = zero,
inference(resolution,[status(thm)],[f11,f9]) ).
fof(f25,plain,
! [X0,X1] :
( divide(X0,X1) = X0
| ~ less_equal(X0,divide(X0,X1)) ),
inference(resolution,[status(thm)],[f11,f14]) ).
fof(f60,plain,
! [X0,X1] : less_equal(divide(divide(X0,X0),divide(X1,X0)),zero),
inference(paramodulation,[status(thm)],[f24,f12]) ).
fof(f83,plain,
! [X0,X1] : zero = divide(divide(X0,X0),divide(X1,X0)),
inference(resolution,[status(thm)],[f60,f17]) ).
fof(f97,plain,
! [X0,X1] : less_equal(divide(X0,X0),divide(X1,X0)),
inference(resolution,[status(thm)],[f83,f10]) ).
fof(f120,plain,
! [X0] : divide(divide(X0,X0),X0) = divide(X0,X0),
inference(resolution,[status(thm)],[f97,f25]) ).
fof(f130,plain,
! [X0] : zero = divide(X0,X0),
inference(forward_demodulation,[status(thm)],[f24,f120]) ).
fof(f135,plain,
! [X0] : less_equal(X0,X0),
inference(resolution,[status(thm)],[f130,f10]) ).
fof(f158,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f16,f135]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : HEN012-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.44 % Computer : n009.cluster.edu
% 0.16/0.44 % Model : x86_64 x86_64
% 0.16/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.44 % Memory : 8046.5625MB
% 0.16/0.44 % OS : Linux 6.8.0-71-generic
% 0.16/0.44 % CPULimit : 300
% 0.16/0.44 % WCLimit : 300
% 0.16/0.44 % DateTime : Sun Sep 20 20:46:43 UTC 2026
% 0.16/0.44 % CPUTime :
% 0.16/0.45 % Drodi V4.1.1
% 0.16/0.47 % Refutation found
% 0.16/0.47 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.16/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.16/0.50 % Elapsed time: 0.047518 seconds
% 0.16/0.50 % CPU time: 0.125268 seconds
% 0.16/0.50 % Total memory used: 13.927 MB
% 0.16/0.50 % Net memory used: 13.825 MB
%------------------------------------------------------------------------------