%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : HEN009-6 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.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 12:45:29 PM UTC 2026
% Result : Unsatisfiable 0.14s 5.42s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN009-6 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/5.37 % Computer : n003.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Sun Sep 20 20:48:07 UTC 2026
% 0.10/5.37 % CPUTime :
% 0.10/5.38 % Drodi V4.1.1
% 0.14/5.42 % Refutation found
% 0.14/5.42 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/5.42 % SZS output start CNFRefutation for theBenchmark
% 0.14/5.42 fof(f1,axiom,(
% 0.14/5.42 (![X,Y]: (( ~ less_equal(X,Y)| divide(X,Y) = zero ) ))),
% 0.14/5.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/5.42 fof(f2,axiom,(
% 0.14/5.42 (![X,Y]: (( divide(X,Y) != zero| less_equal(X,Y) ) ))),
% 0.14/5.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/5.42 fof(f3,axiom,(
% 0.14/5.42 (![X,Y]: (less_equal(divide(X,Y),X) ))),
% 0.14/5.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/5.42 fof(f4,axiom,(
% 0.14/5.42 (![X,Z,Y]: (less_equal(divide(divide(X,Z),divide(Y,Z)),divide(divide(X,Y),Z)) ))),
% 0.14/5.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/5.42 fof(f5,axiom,(
% 0.14/5.42 (![X]: (less_equal(zero,X) ))),
% 0.14/5.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/5.42 fof(f6,axiom,(
% 0.14/5.42 (![X,Y]: (( ~ less_equal(X,Y)| ~ less_equal(Y,X)| X = Y ) ))),
% 0.14/5.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/5.42 fof(f8,axiom,(
% 0.14/5.42 (![X]: (divide(X,identity) = zero ))),
% 0.14/5.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/5.42 fof(f9,axiom,(
% 0.14/5.42 (![X]: (divide(zero,X) = zero ))),
% 0.14/5.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/5.42 fof(f10,axiom,(
% 0.14/5.42 (![X]: (divide(X,X) = zero ))),
% 0.14/5.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/5.42 fof(f11,axiom,(
% 0.14/5.42 (![X,Y,Z]: (( ~ less_equal(divide(X,Y),Z)| less_equal(divide(X,Z),Y) ) ))),
% 0.14/5.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/5.42 fof(f14,hypothesis,(
% 0.14/5.42 divide(identity,a) = b ),
% 0.14/5.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/5.42 fof(f15,hypothesis,(
% 0.14/5.42 divide(identity,b) = c ),
% 0.14/5.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/5.42 fof(f16,hypothesis,(
% 0.14/5.42 divide(identity,c) = d ),
% 0.14/5.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/5.42 fof(f17,negated_conjecture,(
% 0.14/5.42 b != d ),
% 0.14/5.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/5.42 fof(f18,plain,(
% 0.14/5.42 ![X0,X1]: (~less_equal(X0,X1)|divide(X0,X1)=zero)),
% 0.14/5.42 inference(cnf_transformation,[status(thm)],[f1])).
% 0.14/5.42 fof(f19,plain,(
% 0.14/5.42 ![X0,X1]: (~divide(X0,X1)=zero|less_equal(X0,X1))),
% 0.14/5.42 inference(cnf_transformation,[status(thm)],[f2])).
% 0.14/5.42 fof(f20,plain,(
% 0.14/5.42 ![X0,X1]: (less_equal(divide(X0,X1),X0))),
% 0.14/5.42 inference(cnf_transformation,[status(thm)],[f3])).
% 0.14/5.42 fof(f21,plain,(
% 0.14/5.42 ![X0,X1,X2]: (less_equal(divide(divide(X0,X1),divide(X2,X1)),divide(divide(X0,X2),X1)))),
% 0.14/5.42 inference(cnf_transformation,[status(thm)],[f4])).
% 0.14/5.42 fof(f22,plain,(
% 0.14/5.42 ![X0]: (less_equal(zero,X0))),
% 0.14/5.42 inference(cnf_transformation,[status(thm)],[f5])).
% 0.14/5.42 fof(f23,plain,(
% 0.14/5.42 ![X0,X1]: (~less_equal(X0,X1)|~less_equal(X1,X0)|X0=X1)),
% 0.14/5.42 inference(cnf_transformation,[status(thm)],[f6])).
% 0.14/5.42 fof(f25,plain,(
% 0.14/5.42 ![X0]: (divide(X0,identity)=zero)),
% 0.14/5.42 inference(cnf_transformation,[status(thm)],[f8])).
% 0.14/5.42 fof(f26,plain,(
% 0.14/5.42 ![X0]: (divide(zero,X0)=zero)),
% 0.14/5.42 inference(cnf_transformation,[status(thm)],[f9])).
% 0.14/5.42 fof(f27,plain,(
% 0.14/5.42 ![X0]: (divide(X0,X0)=zero)),
% 0.14/5.42 inference(cnf_transformation,[status(thm)],[f10])).
% 0.14/5.42 fof(f28,plain,(
% 0.14/5.42 ![X0,X1,X2]: (~less_equal(divide(X0,X1),X2)|less_equal(divide(X0,X2),X1))),
% 0.14/5.42 inference(cnf_transformation,[status(thm)],[f11])).
% 0.14/5.42 fof(f32,plain,(
% 0.14/5.42 divide(identity,a)=b),
% 0.14/5.42 inference(cnf_transformation,[status(thm)],[f14])).
% 0.14/5.42 fof(f33,plain,(
% 0.14/5.42 divide(identity,b)=c),
% 0.14/5.42 inference(cnf_transformation,[status(thm)],[f15])).
% 0.14/5.42 fof(f34,plain,(
% 0.14/5.42 divide(identity,c)=d),
% 0.14/5.42 inference(cnf_transformation,[status(thm)],[f16])).
% 0.14/5.42 fof(f35,plain,(
% 0.14/5.42 ~b=d),
% 0.14/5.42 inference(cnf_transformation,[status(thm)],[f17])).
% 0.14/5.42 fof(f64,plain,(
% 0.14/5.42 ![X0]: (less_equal(X0,X0))),
% 0.14/5.42 inference(resolution,[status(thm)],[f19,f27])).
% 0.14/5.42 fof(f84,plain,(
% 0.14/5.42 ![X0]: (less_equal(divide(b,divide(X0,a)),divide(divide(identity,X0),a)))),
% 0.14/5.42 inference(paramodulation,[status(thm)],[f32,f21])).
% 0.14/5.42 fof(f89,plain,(
% 0.14/5.42 ![X0]: (less_equal(divide(divide(X0,b),c),divide(divide(X0,identity),b)))),
% 0.14/5.42 inference(paramodulation,[status(thm)],[f33,f21])).
% 0.14/5.42 fof(f91,plain,(
% 0.14/5.42 ![X0]: (less_equal(divide(divide(X0,a),b),divide(divide(X0,identity),a)))),
% 0.14/5.42 inference(paramodulation,[status(thm)],[f32,f21])).
% 0.14/5.42 fof(f116,plain,(
% 0.14/5.42 ![X0]: (less_equal(divide(divide(X0,b),c),divide(zero,b)))),
% 0.14/5.42 inference(forward_demodulation,[status(thm)],[f25,f89])).
% 0.14/5.42 fof(f117,plain,(
% 0.14/5.42 ![X0]: (less_equal(divide(divide(X0,b),c),zero))),
% 0.14/5.42 inference(forward_demodulation,[status(thm)],[f26,f116])).
% 0.14/5.42 fof(f120,plain,(
% 0.14/5.42 ![X0]: (less_equal(divide(divide(X0,a),b),divide(zero,a)))),
% 0.14/5.42 inference(forward_demodulation,[status(thm)],[f25,f91])).
% 0.14/5.42 fof(f121,plain,(
% 0.14/5.42 ![X0]: (less_equal(divide(divide(X0,a),b),zero))),
% 0.14/5.42 inference(forward_demodulation,[status(thm)],[f26,f120])).
% 0.14/5.42 fof(f160,plain,(
% 0.14/5.42 ![X0,X1]: (~less_equal(X0,divide(X0,X1))|X0=divide(X0,X1))),
% 0.14/5.42 inference(resolution,[status(thm)],[f23,f20])).
% 0.14/5.42 fof(f161,plain,(
% 0.14/5.42 ![X0]: (~less_equal(X0,zero)|X0=zero)),
% 0.14/5.42 inference(resolution,[status(thm)],[f23,f22])).
% 0.14/5.42 fof(f183,plain,(
% 0.14/5.42 ![X0]: (divide(divide(X0,b),c)=zero)),
% 0.14/5.42 inference(resolution,[status(thm)],[f117,f161])).
% 0.14/5.42 fof(f197,plain,(
% 0.14/5.42 ![X0]: (less_equal(divide(X0,b),c))),
% 0.14/5.42 inference(resolution,[status(thm)],[f183,f19])).
% 0.14/5.42 fof(f267,plain,(
% 0.14/5.42 ![X0]: (divide(divide(X0,a),b)=zero)),
% 0.14/5.42 inference(resolution,[status(thm)],[f121,f161])).
% 0.14/5.42 fof(f281,plain,(
% 0.14/5.42 ![X0]: (less_equal(divide(X0,a),b))),
% 0.14/5.42 inference(resolution,[status(thm)],[f267,f19])).
% 0.14/5.42 fof(f310,plain,(
% 0.14/5.42 ![X0]: (less_equal(divide(X0,b),a))),
% 0.14/5.42 inference(resolution,[status(thm)],[f28,f281])).
% 0.14/5.42 fof(f312,plain,(
% 0.14/5.42 ![X0]: (less_equal(divide(X0,c),b))),
% 0.14/5.42 inference(resolution,[status(thm)],[f28,f197])).
% 0.14/5.42 fof(f315,plain,(
% 0.14/5.42 ![X0,X1]: (less_equal(divide(X0,divide(X0,X1)),X1))),
% 0.14/5.42 inference(resolution,[status(thm)],[f28,f64])).
% 0.14/5.42 fof(f354,plain,(
% 0.14/5.42 less_equal(c,a)),
% 0.14/5.42 inference(paramodulation,[status(thm)],[f33,f310])).
% 0.14/5.42 fof(f358,plain,(
% 0.14/5.42 divide(c,a)=zero),
% 0.14/5.42 inference(resolution,[status(thm)],[f354,f18])).
% 0.14/5.42 fof(f395,plain,(
% 0.14/5.42 less_equal(divide(b,zero),divide(divide(identity,c),a))),
% 0.14/5.42 inference(paramodulation,[status(thm)],[f358,f84])).
% 0.14/5.42 fof(f405,plain,(
% 0.14/5.42 less_equal(divide(b,zero),divide(d,a))),
% 0.14/5.42 inference(forward_demodulation,[status(thm)],[f34,f395])).
% 0.14/5.42 fof(f678,plain,(
% 0.14/5.42 less_equal(d,b)),
% 0.14/5.42 inference(paramodulation,[status(thm)],[f34,f312])).
% 0.14/5.42 fof(f681,plain,(
% 0.14/5.42 ~less_equal(b,d)|b=d),
% 0.14/5.42 inference(resolution,[status(thm)],[f678,f23])).
% 0.14/5.42 fof(f682,plain,(
% 0.14/5.42 divide(d,b)=zero),
% 0.14/5.42 inference(resolution,[status(thm)],[f678,f18])).
% 0.14/5.42 fof(f683,plain,(
% 0.14/5.42 ~less_equal(b,d)),
% 0.14/5.42 inference(forward_subsumption_resolution,[status(thm)],[f681,f35])).
% 0.14/5.42 fof(f691,plain,(
% 0.14/5.42 ![X0]: (~less_equal(zero,X0)|less_equal(divide(d,X0),b))),
% 0.14/5.42 inference(paramodulation,[status(thm)],[f682,f28])).
% 0.14/5.42 fof(f701,plain,(
% 0.14/5.42 ![X0]: (less_equal(divide(d,X0),b))),
% 0.14/5.42 inference(forward_subsumption_resolution,[status(thm)],[f691,f22])).
% 0.14/5.42 fof(f715,plain,(
% 0.14/5.42 ![X0]: (divide(X0,divide(X0,zero))=zero)),
% 0.14/5.42 inference(resolution,[status(thm)],[f315,f161])).
% 0.14/5.42 fof(f781,plain,(
% 0.14/5.42 ![X0]: (less_equal(X0,divide(X0,zero)))),
% 0.14/5.42 inference(resolution,[status(thm)],[f715,f19])).
% 0.14/5.42 fof(f836,plain,(
% 0.14/5.42 ![X0]: (X0=divide(X0,zero))),
% 0.14/5.42 inference(resolution,[status(thm)],[f781,f160])).
% 0.14/5.42 fof(f1426,plain,(
% 0.14/5.42 less_equal(b,divide(d,a))),
% 0.14/5.42 inference(forward_demodulation,[status(thm)],[f836,f405])).
% 0.14/5.42 fof(f1429,plain,(
% 0.14/5.42 ~less_equal(divide(d,a),b)|divide(d,a)=b),
% 0.14/5.42 inference(resolution,[status(thm)],[f1426,f23])).
% 0.14/5.42 fof(f1431,plain,(
% 0.14/5.42 divide(d,a)=b),
% 0.14/5.42 inference(forward_subsumption_resolution,[status(thm)],[f1429,f701])).
% 0.14/5.42 fof(f1550,plain,(
% 0.14/5.42 less_equal(b,d)),
% 0.14/5.42 inference(paramodulation,[status(thm)],[f1431,f20])).
% 0.14/5.42 fof(f1561,plain,(
% 0.14/5.42 $false),
% 0.14/5.42 inference(forward_subsumption_resolution,[status(thm)],[f1550,f683])).
% 0.14/5.42 % SZS output end CNFRefutation for theBenchmark.p
% 0.14/5.44 % Elapsed time: 0.060984 seconds
% 0.14/5.44 % CPU time: 0.279725 seconds
% 0.14/5.44 % Total memory used: 68.509 MB
% 0.14/5.44 % Net memory used: 68.125 MB
%------------------------------------------------------------------------------