%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : HEN009-6 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : 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 12:45:22 PM UTC 2026
% Result : Unsatisfiable 0.11s 0.40s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 14
% Syntax : Number of formulae : 63 ( 50 unt; 0 def)
% Number of atoms : 78 ( 31 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 33 ( 18 ~; 15 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 60 ( 60 !; 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,axiom,
! [X] : divide(X,identity) = zero,
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,
! [X,Y,Z] :
( less_equal(divide(X,Z),Y)
| ~ less_equal(divide(X,Y),Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,hypothesis,
divide(identity,a) = b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,hypothesis,
divide(identity,b) = c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,hypothesis,
divide(identity,c) = d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
b != d,
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(f20,plain,
! [X0,X1] : less_equal(divide(X0,X1),X0),
inference(cnf_transformation,[status(thm)],[f3]) ).
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(f25,plain,
! [X0] : divide(X0,identity) = zero,
inference(cnf_transformation,[status(thm)],[f8]) ).
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,
! [X0,X1,X2] :
( less_equal(divide(X0,X2),X1)
| ~ less_equal(divide(X0,X1),X2) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f32,plain,
divide(identity,a) = b,
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f33,plain,
divide(identity,b) = c,
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f34,plain,
divide(identity,c) = d,
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f35,plain,
b != d,
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f64,plain,
! [X0] : less_equal(X0,X0),
inference(resolution,[status(thm)],[f19,f27]) ).
fof(f84,plain,
! [X0] : less_equal(divide(b,divide(X0,a)),divide(divide(identity,X0),a)),
inference(paramodulation,[status(thm)],[f32,f21]) ).
fof(f89,plain,
! [X0] : less_equal(divide(divide(X0,b),c),divide(divide(X0,identity),b)),
inference(paramodulation,[status(thm)],[f33,f21]) ).
fof(f91,plain,
! [X0] : less_equal(divide(divide(X0,a),b),divide(divide(X0,identity),a)),
inference(paramodulation,[status(thm)],[f32,f21]) ).
fof(f116,plain,
! [X0] : less_equal(divide(divide(X0,b),c),divide(zero,b)),
inference(forward_demodulation,[status(thm)],[f25,f89]) ).
fof(f117,plain,
! [X0] : less_equal(divide(divide(X0,b),c),zero),
inference(forward_demodulation,[status(thm)],[f26,f116]) ).
fof(f120,plain,
! [X0] : less_equal(divide(divide(X0,a),b),divide(zero,a)),
inference(forward_demodulation,[status(thm)],[f25,f91]) ).
fof(f121,plain,
! [X0] : less_equal(divide(divide(X0,a),b),zero),
inference(forward_demodulation,[status(thm)],[f26,f120]) ).
fof(f160,plain,
! [X0,X1] :
( X0 = divide(X0,X1)
| ~ less_equal(X0,divide(X0,X1)) ),
inference(resolution,[status(thm)],[f23,f20]) ).
fof(f161,plain,
! [X0] :
( X0 = zero
| ~ less_equal(X0,zero) ),
inference(resolution,[status(thm)],[f23,f22]) ).
fof(f183,plain,
! [X0] : divide(divide(X0,b),c) = zero,
inference(resolution,[status(thm)],[f117,f161]) ).
fof(f197,plain,
! [X0] : less_equal(divide(X0,b),c),
inference(resolution,[status(thm)],[f183,f19]) ).
fof(f267,plain,
! [X0] : divide(divide(X0,a),b) = zero,
inference(resolution,[status(thm)],[f121,f161]) ).
fof(f281,plain,
! [X0] : less_equal(divide(X0,a),b),
inference(resolution,[status(thm)],[f267,f19]) ).
fof(f310,plain,
! [X0] : less_equal(divide(X0,b),a),
inference(resolution,[status(thm)],[f28,f281]) ).
fof(f312,plain,
! [X0] : less_equal(divide(X0,c),b),
inference(resolution,[status(thm)],[f28,f197]) ).
fof(f315,plain,
! [X0,X1] : less_equal(divide(X0,divide(X0,X1)),X1),
inference(resolution,[status(thm)],[f28,f64]) ).
fof(f354,plain,
less_equal(c,a),
inference(paramodulation,[status(thm)],[f33,f310]) ).
fof(f358,plain,
divide(c,a) = zero,
inference(resolution,[status(thm)],[f354,f18]) ).
fof(f395,plain,
less_equal(divide(b,zero),divide(divide(identity,c),a)),
inference(paramodulation,[status(thm)],[f358,f84]) ).
fof(f405,plain,
less_equal(divide(b,zero),divide(d,a)),
inference(forward_demodulation,[status(thm)],[f34,f395]) ).
fof(f678,plain,
less_equal(d,b),
inference(paramodulation,[status(thm)],[f34,f312]) ).
fof(f681,plain,
( b = d
| ~ less_equal(b,d) ),
inference(resolution,[status(thm)],[f678,f23]) ).
fof(f682,plain,
divide(d,b) = zero,
inference(resolution,[status(thm)],[f678,f18]) ).
fof(f683,plain,
~ less_equal(b,d),
inference(forward_subsumption_resolution,[status(thm)],[f681,f35]) ).
fof(f691,plain,
! [X0] :
( less_equal(divide(d,X0),b)
| ~ less_equal(zero,X0) ),
inference(paramodulation,[status(thm)],[f682,f28]) ).
fof(f701,plain,
! [X0] : less_equal(divide(d,X0),b),
inference(forward_subsumption_resolution,[status(thm)],[f691,f22]) ).
fof(f715,plain,
! [X0] : divide(X0,divide(X0,zero)) = zero,
inference(resolution,[status(thm)],[f315,f161]) ).
fof(f781,plain,
! [X0] : less_equal(X0,divide(X0,zero)),
inference(resolution,[status(thm)],[f715,f19]) ).
fof(f836,plain,
! [X0] : X0 = divide(X0,zero),
inference(resolution,[status(thm)],[f781,f160]) ).
fof(f1426,plain,
less_equal(b,divide(d,a)),
inference(forward_demodulation,[status(thm)],[f836,f405]) ).
fof(f1429,plain,
( divide(d,a) = b
| ~ less_equal(divide(d,a),b) ),
inference(resolution,[status(thm)],[f1426,f23]) ).
fof(f1431,plain,
divide(d,a) = b,
inference(forward_subsumption_resolution,[status(thm)],[f1429,f701]) ).
fof(f1550,plain,
less_equal(b,d),
inference(paramodulation,[status(thm)],[f1431,f20]) ).
fof(f1561,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f1550,f683]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : HEN009-6 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n009.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Sun Sep 20 20:46:28 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.11/0.36 % Drodi V4.1.1
% 0.11/0.40 % Refutation found
% 0.11/0.40 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.11/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.43 % Elapsed time: 0.063829 seconds
% 0.11/0.43 % CPU time: 0.291829 seconds
% 0.11/0.43 % Total memory used: 71.247 MB
% 0.11/0.43 % Net memory used: 70.848 MB
%------------------------------------------------------------------------------