%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : HEN010-4 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n017.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 0.15s 1.30s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 13
% Syntax : Number of formulae : 52 ( 30 unt; 0 def)
% Number of atoms : 76 ( 36 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 53 ( 29 ~; 24 |; 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 : 71 ( 71 !; 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(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(f7,axiom,
! [X] : less_equal(X,identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X] : divide(zero,X) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X] : divide(X,X) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
divide(a,zero) = a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [X,Y,Z] :
( less_equal(divide(Z,Y),divide(Z,X))
| ~ less_equal(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [X,Y,Z] :
( less_equal(divide(X,Z),divide(Y,Z))
| ~ less_equal(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [X] : divide(identity,divide(identity,divide(identity,X))) = divide(identity,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,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] :
( divide(X0,X1) = zero
| ~ less_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f19,plain,
! [X0,X1] :
( less_equal(X0,X1)
| divide(X0,X1) != zero ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f21,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(f22,plain,
! [X0] : less_equal(zero,X0),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f23,plain,
! [X0,X1] :
( X0 = X1
| ~ less_equal(X1,X0)
| ~ less_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f24,plain,
! [X0] : less_equal(X0,identity),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f26,plain,
! [X0] : divide(zero,X0) = zero,
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f27,plain,
! [X0] : divide(X0,X0) = zero,
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f28,plain,
divide(a,zero) = a,
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f32,plain,
! [X,Y] :
( ! [Z] : less_equal(divide(Z,Y),divide(Z,X))
| ~ less_equal(X,Y) ),
inference(miniscoping,[status(thm)],[f14]) ).
fof(f33,plain,
! [X0,X1,X2] :
( less_equal(divide(X2,X1),divide(X2,X0))
| ~ less_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f34,plain,
! [X,Y] :
( ! [Z] : less_equal(divide(X,Z),divide(Y,Z))
| ~ less_equal(X,Y) ),
inference(miniscoping,[status(thm)],[f15]) ).
fof(f35,plain,
! [X0,X1,X2] :
( less_equal(divide(X0,X2),divide(X1,X2))
| ~ less_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f36,plain,
! [X0] : divide(identity,divide(identity,divide(identity,X0))) = divide(identity,X0),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f37,plain,
divide(identity,a) != divide(divide(identity,a),divide(identity,divide(identity,a))),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f40,plain,
divide(identity,divide(identity,zero)) = divide(identity,identity),
inference(paramodulation,[status(thm)],[f27,f36]) ).
fof(f41,plain,
divide(identity,divide(identity,zero)) = zero,
inference(forward_demodulation,[status(thm)],[f27,f40]) ).
fof(f76,plain,
! [X0] :
( identity = X0
| ~ less_equal(identity,X0) ),
inference(resolution,[status(thm)],[f23,f24]) ).
fof(f79,plain,
! [X0] :
( divide(identity,X0) != zero
| identity = X0 ),
inference(resolution,[status(thm)],[f76,f19]) ).
fof(f80,plain,
identity = divide(identity,zero),
inference(resolution,[status(thm)],[f79,f41]) ).
fof(f104,plain,
! [X0,X1,X2] :
( divide(divide(X0,X1),X2) = divide(divide(X0,X2),divide(X1,X2))
| ~ less_equal(divide(divide(X0,X1),X2),divide(divide(X0,X2),divide(X1,X2))) ),
inference(resolution,[status(thm)],[f21,f23]) ).
fof(f111,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)],[f36,f21]) ).
fof(f116,plain,
! [X0,X1] : less_equal(divide(divide(X0,X1),zero),divide(divide(X0,zero),X1)),
inference(paramodulation,[status(thm)],[f26,f21]) ).
fof(f165,plain,
! [X0,X1] :
( divide(divide(identity,X0),divide(identity,divide(identity,X1))) = divide(divide(identity,X1),divide(X0,divide(identity,divide(identity,X1))))
| ~ less_equal(divide(divide(identity,X0),divide(identity,divide(identity,X1))),divide(divide(identity,X1),divide(X0,divide(identity,divide(identity,X1))))) ),
inference(resolution,[status(thm)],[f111,f23]) ).
fof(f308,plain,
! [X0,X1] : less_equal(divide(X0,X1),divide(X0,zero)),
inference(resolution,[status(thm)],[f33,f22]) ).
fof(f432,plain,
! [X0,X1] : less_equal(divide(X0,X1),divide(identity,X1)),
inference(resolution,[status(thm)],[f35,f24]) ).
fof(f440,plain,
! [X0,X1] : divide(divide(X0,X1),divide(identity,X1)) = zero,
inference(resolution,[status(thm)],[f432,f18]) ).
fof(f604,plain,
! [X0] :
( divide(divide(X0,a),zero) = divide(divide(X0,zero),divide(a,zero))
| ~ less_equal(divide(divide(X0,a),zero),divide(divide(X0,zero),a)) ),
inference(paramodulation,[status(thm)],[f28,f104]) ).
fof(f716,plain,
! [X0] :
( divide(divide(X0,a),zero) = divide(divide(X0,zero),a)
| ~ less_equal(divide(divide(X0,a),zero),divide(divide(X0,zero),a)) ),
inference(forward_demodulation,[status(thm)],[f28,f604]) ).
fof(f718,plain,
! [X0] : divide(divide(X0,a),zero) = divide(divide(X0,zero),a),
inference(forward_subsumption_resolution,[status(thm)],[f716,f116]) ).
fof(f1200,plain,
! [X0] :
( divide(divide(identity,divide(identity,divide(identity,X0))),divide(identity,divide(identity,X0))) = divide(divide(identity,X0),divide(divide(identity,divide(identity,X0)),divide(identity,divide(identity,X0))))
| ~ less_equal(divide(divide(identity,divide(identity,divide(identity,X0))),divide(identity,divide(identity,X0))),divide(divide(identity,X0),zero)) ),
inference(paramodulation,[status(thm)],[f27,f165]) ).
fof(f1293,plain,
! [X0] :
( divide(divide(identity,divide(identity,divide(identity,X0))),divide(identity,divide(identity,X0))) = divide(divide(identity,X0),divide(divide(identity,divide(identity,X0)),divide(identity,divide(identity,X0))))
| ~ less_equal(divide(divide(identity,X0),divide(identity,divide(identity,X0))),divide(divide(identity,X0),zero)) ),
inference(forward_demodulation,[status(thm)],[f36,f1200]) ).
fof(f1294,plain,
! [X0] :
( divide(divide(identity,X0),divide(identity,divide(identity,X0))) = divide(divide(identity,X0),divide(divide(identity,divide(identity,X0)),divide(identity,divide(identity,X0))))
| ~ less_equal(divide(divide(identity,X0),divide(identity,divide(identity,X0))),divide(divide(identity,X0),zero)) ),
inference(forward_demodulation,[status(thm)],[f36,f1293]) ).
fof(f1295,plain,
! [X0] :
( divide(divide(identity,X0),divide(identity,divide(identity,X0))) = divide(divide(identity,X0),zero)
| ~ less_equal(divide(divide(identity,X0),divide(identity,divide(identity,X0))),divide(divide(identity,X0),zero)) ),
inference(forward_demodulation,[status(thm)],[f440,f1294]) ).
fof(f1296,plain,
divide(identity,a) != divide(divide(identity,a),zero),
inference(backward_demodulation,[status(thm)],[f1299,f37]) ).
fof(f1299,plain,
! [X0] : divide(divide(identity,X0),divide(identity,divide(identity,X0))) = divide(divide(identity,X0),zero),
inference(forward_subsumption_resolution,[status(thm)],[f1295,f308]) ).
fof(f1331,plain,
divide(identity,a) != divide(divide(identity,zero),a),
inference(forward_demodulation,[status(thm)],[f718,f1296]) ).
fof(f1332,plain,
divide(identity,a) != divide(identity,a),
inference(forward_demodulation,[status(thm)],[f80,f1331]) ).
fof(f1333,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f1332]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN010-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/1.19 % Computer : n017.cluster.edu
% 0.11/1.19 % Model : x86_64 x86_64
% 0.11/1.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/1.19 % Memory : 8046.5625MB
% 0.11/1.19 % OS : Linux 6.8.0-71-generic
% 0.11/1.19 % CPULimit : 300
% 0.11/1.19 % WCLimit : 300
% 0.11/1.19 % DateTime : Sun Sep 20 20:41:43 UTC 2026
% 0.11/1.19 % CPUTime :
% 0.15/1.25 % Drodi V4.1.1
% 0.15/1.30 % Refutation found
% 0.15/1.30 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.15/1.30 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/1.32 % Elapsed time: 0.126587 seconds
% 0.15/1.32 % CPU time: 0.433465 seconds
% 0.15/1.32 % Total memory used: 74.828 MB
% 0.15/1.32 % Net memory used: 74.079 MB
%------------------------------------------------------------------------------