%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : HEN009-3 : 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 : n019.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 0.08s 0.56s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN009-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n019.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sun Sep 20 20:46:51 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 0.08/0.56 % Refutation found
% 0.08/0.56 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.08/0.56 % SZS output start CNFRefutation for theBenchmark
% 0.08/0.56 fof(f1,axiom,(
% 0.08/0.56 (![X,Y]: (( ~ less_equal(X,Y)| divide(X,Y) = zero ) ))),
% 0.08/0.56 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.08/0.56 fof(f2,axiom,(
% 0.08/0.56 (![X,Y]: (( divide(X,Y) != zero| less_equal(X,Y) ) ))),
% 0.08/0.56 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.08/0.56 fof(f3,axiom,(
% 0.08/0.56 (![X,Y]: (less_equal(divide(X,Y),X) ))),
% 0.08/0.56 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.08/0.56 fof(f4,axiom,(
% 0.08/0.56 (![X,Z,Y]: (less_equal(divide(divide(X,Z),divide(Y,Z)),divide(divide(X,Y),Z)) ))),
% 0.08/0.56 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.08/0.56 fof(f5,axiom,(
% 0.08/0.56 (![X]: (less_equal(zero,X) ))),
% 0.08/0.56 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.08/0.56 fof(f6,axiom,(
% 0.08/0.56 (![X,Y]: (( ~ less_equal(X,Y)| ~ less_equal(Y,X)| X = Y ) ))),
% 0.08/0.56 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.08/0.56 fof(f7,axiom,(
% 0.08/0.56 (![X]: (less_equal(X,identity) ))),
% 0.08/0.56 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.08/0.56 fof(f9,hypothesis,(
% 0.08/0.56 divide(identity,a) = b ),
% 0.08/0.56 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.08/0.56 fof(f10,hypothesis,(
% 0.08/0.56 divide(identity,b) = c ),
% 0.08/0.56 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.08/0.56 fof(f11,hypothesis,(
% 0.08/0.56 divide(identity,c) = d ),
% 0.08/0.56 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.08/0.56 fof(f12,negated_conjecture,(
% 0.08/0.56 b != d ),
% 0.08/0.56 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.08/0.56 fof(f13,plain,(
% 0.08/0.56 ![X0,X1]: (~less_equal(X0,X1)|divide(X0,X1)=zero)),
% 0.08/0.56 inference(cnf_transformation,[status(thm)],[f1])).
% 0.08/0.56 fof(f14,plain,(
% 0.08/0.56 ![X0,X1]: (~divide(X0,X1)=zero|less_equal(X0,X1))),
% 0.08/0.56 inference(cnf_transformation,[status(thm)],[f2])).
% 0.08/0.56 fof(f15,plain,(
% 0.08/0.56 ![X0,X1]: (less_equal(divide(X0,X1),X0))),
% 0.08/0.56 inference(cnf_transformation,[status(thm)],[f3])).
% 0.08/0.56 fof(f16,plain,(
% 0.08/0.56 ![X0,X1,X2]: (less_equal(divide(divide(X0,X1),divide(X2,X1)),divide(divide(X0,X2),X1)))),
% 0.08/0.56 inference(cnf_transformation,[status(thm)],[f4])).
% 0.08/0.56 fof(f17,plain,(
% 0.08/0.56 ![X0]: (less_equal(zero,X0))),
% 0.08/0.56 inference(cnf_transformation,[status(thm)],[f5])).
% 0.08/0.56 fof(f18,plain,(
% 0.08/0.56 ![X0,X1]: (~less_equal(X0,X1)|~less_equal(X1,X0)|X0=X1)),
% 0.08/0.56 inference(cnf_transformation,[status(thm)],[f6])).
% 0.08/0.56 fof(f19,plain,(
% 0.08/0.56 ![X0]: (less_equal(X0,identity))),
% 0.08/0.56 inference(cnf_transformation,[status(thm)],[f7])).
% 0.08/0.56 fof(f21,plain,(
% 0.08/0.56 divide(identity,a)=b),
% 0.08/0.56 inference(cnf_transformation,[status(thm)],[f9])).
% 0.08/0.56 fof(f22,plain,(
% 0.08/0.56 divide(identity,b)=c),
% 0.08/0.56 inference(cnf_transformation,[status(thm)],[f10])).
% 0.08/0.56 fof(f23,plain,(
% 0.08/0.56 divide(identity,c)=d),
% 0.08/0.56 inference(cnf_transformation,[status(thm)],[f11])).
% 0.08/0.56 fof(f24,plain,(
% 0.08/0.56 ~b=d),
% 0.08/0.56 inference(cnf_transformation,[status(thm)],[f12])).
% 0.08/0.56 fof(f27,plain,(
% 0.08/0.56 ![X0,X1]: (divide(divide(X0,X1),X0)=zero)),
% 0.08/0.56 inference(resolution,[status(thm)],[f13,f15])).
% 0.08/0.56 fof(f28,plain,(
% 0.08/0.56 ![X0]: (divide(zero,X0)=zero)),
% 0.08/0.56 inference(resolution,[status(thm)],[f13,f17])).
% 0.08/0.56 fof(f29,plain,(
% 0.08/0.56 ![X0]: (divide(X0,identity)=zero)),
% 0.08/0.56 inference(resolution,[status(thm)],[f13,f19])).
% 0.08/0.56 fof(f56,plain,(
% 0.08/0.56 ![X0,X1]: (~less_equal(X0,divide(X0,X1))|X0=divide(X0,X1))),
% 0.08/0.56 inference(resolution,[status(thm)],[f18,f15])).
% 0.08/0.56 fof(f57,plain,(
% 0.08/0.56 ![X0]: (~less_equal(X0,zero)|X0=zero)),
% 0.08/0.56 inference(resolution,[status(thm)],[f18,f17])).
% 0.08/0.56 fof(f74,plain,(
% 0.08/0.56 ![X0,X1,X2]: (~less_equal(divide(divide(X0,X1),X2),divide(divide(X0,X2),divide(X1,X2)))|divide(divide(X0,X1),X2)=divide(divide(X0,X2),divide(X1,X2)))),
% 0.08/0.56 inference(resolution,[status(thm)],[f16,f18])).
% 0.08/0.56 fof(f80,plain,(
% 0.08/0.56 ![X0]: (less_equal(divide(d,divide(X0,c)),divide(divide(identity,X0),c)))),
% 0.08/0.56 inference(paramodulation,[status(thm)],[f23,f16])).
% 0.08/0.56 fof(f84,plain,(
% 0.08/0.56 ![X0,X1]: (less_equal(divide(divide(X0,X1),zero),divide(divide(X0,zero),X1)))),
% 0.08/0.56 inference(paramodulation,[status(thm)],[f28,f16])).
% 0.08/0.56 fof(f85,plain,(
% 0.08/0.56 ![X0]: (less_equal(divide(divide(X0,b),c),divide(divide(X0,identity),b)))),
% 0.08/0.56 inference(paramodulation,[status(thm)],[f22,f16])).
% 0.08/0.56 fof(f94,plain,(
% 0.08/0.56 ![X0]: (less_equal(divide(divide(identity,X0),divide(c,X0)),divide(d,X0)))),
% 0.08/0.56 inference(paramodulation,[status(thm)],[f23,f16])).
% 0.08/0.56 fof(f95,plain,(
% 0.08/0.56 ![X0]: (less_equal(divide(divide(identity,X0),divide(a,X0)),divide(b,X0)))),
% 0.08/0.56 inference(paramodulation,[status(thm)],[f21,f16])).
% 0.08/0.56 fof(f105,plain,(
% 0.08/0.56 ![X0]: (less_equal(divide(divide(X0,b),c),divide(zero,b)))),
% 0.08/0.56 inference(forward_demodulation,[status(thm)],[f29,f85])).
% 0.08/0.56 fof(f106,plain,(
% 0.08/0.56 ![X0]: (less_equal(divide(divide(X0,b),c),zero))),
% 0.08/0.56 inference(forward_demodulation,[status(thm)],[f28,f105])).
% 0.08/0.56 fof(f156,plain,(
% 0.08/0.56 ![X0]: (divide(divide(X0,b),c)=zero)),
% 0.08/0.56 inference(resolution,[status(thm)],[f106,f57])).
% 0.08/0.56 fof(f189,plain,(
% 0.08/0.56 ![X0]: (less_equal(divide(X0,b),c))),
% 0.08/0.56 inference(resolution,[status(thm)],[f156,f14])).
% 0.08/0.56 fof(f194,plain,(
% 0.08/0.56 less_equal(divide(d,divide(b,c)),zero)),
% 0.08/0.56 inference(paramodulation,[status(thm)],[f156,f80])).
% 0.08/0.56 fof(f220,plain,(
% 0.08/0.56 ![X0,X1]: (~less_equal(zero,divide(divide(X0,X0),divide(X1,X0)))|divide(divide(X0,X1),X0)=divide(divide(X0,X0),divide(X1,X0)))),
% 0.08/0.56 inference(paramodulation,[status(thm)],[f27,f74])).
% 0.08/0.56 fof(f247,plain,(
% 0.08/0.56 ![X0]: (~less_equal(divide(divide(X0,identity),c),divide(divide(X0,c),d))|divide(divide(X0,identity),c)=divide(divide(X0,c),divide(identity,c)))),
% 0.08/0.56 inference(paramodulation,[status(thm)],[f23,f74])).
% 0.08/0.56 fof(f248,plain,(
% 0.08/0.56 ![X0]: (~less_equal(divide(divide(X0,identity),a),divide(divide(X0,a),b))|divide(divide(X0,identity),a)=divide(divide(X0,a),divide(identity,a)))),
% 0.08/0.56 inference(paramodulation,[status(thm)],[f21,f74])).
% 0.08/0.56 fof(f252,plain,(
% 0.08/0.56 ![X0,X1]: (~less_equal(zero,divide(divide(X0,X0),divide(X1,X0)))|zero=divide(divide(X0,X0),divide(X1,X0)))),
% 0.08/0.56 inference(forward_demodulation,[status(thm)],[f27,f220])).
% 0.08/0.56 fof(f253,plain,(
% 0.08/0.56 ![X0,X1]: (zero=divide(divide(X0,X0),divide(X1,X0)))),
% 0.08/0.56 inference(forward_subsumption_resolution,[status(thm)],[f252,f17])).
% 0.08/0.56 fof(f329,plain,(
% 0.08/0.56 ![X0]: (~less_equal(divide(zero,c),divide(divide(X0,c),d))|divide(divide(X0,identity),c)=divide(divide(X0,c),divide(identity,c)))),
% 0.08/0.56 inference(forward_demodulation,[status(thm)],[f29,f247])).
% 0.08/0.56 fof(f330,plain,(
% 0.08/0.56 ![X0]: (~less_equal(zero,divide(divide(X0,c),d))|divide(divide(X0,identity),c)=divide(divide(X0,c),divide(identity,c)))),
% 0.08/0.56 inference(forward_demodulation,[status(thm)],[f28,f329])).
% 0.08/0.56 fof(f331,plain,(
% 0.08/0.56 ![X0]: (~less_equal(zero,divide(divide(X0,c),d))|divide(zero,c)=divide(divide(X0,c),divide(identity,c)))),
% 0.08/0.56 inference(forward_demodulation,[status(thm)],[f29,f330])).
% 0.08/0.56 fof(f332,plain,(
% 0.08/0.56 ![X0]: (~less_equal(zero,divide(divide(X0,c),d))|zero=divide(divide(X0,c),divide(identity,c)))),
% 0.08/0.56 inference(forward_demodulation,[status(thm)],[f28,f331])).
% 0.08/0.56 fof(f333,plain,(
% 0.08/0.56 ![X0]: (~less_equal(zero,divide(divide(X0,c),d))|zero=divide(divide(X0,c),d))),
% 0.08/0.56 inference(forward_demodulation,[status(thm)],[f23,f332])).
% 0.08/0.56 fof(f334,plain,(
% 0.08/0.56 ![X0]: (zero=divide(divide(X0,c),d))),
% 0.08/0.56 inference(forward_subsumption_resolution,[status(thm)],[f333,f17])).
% 0.08/0.56 fof(f335,plain,(
% 0.08/0.56 ![X0]: (~less_equal(divide(zero,a),divide(divide(X0,a),b))|divide(divide(X0,identity),a)=divide(divide(X0,a),divide(identity,a)))),
% 0.08/0.56 inference(forward_demodulation,[status(thm)],[f29,f248])).
% 0.08/0.56 fof(f336,plain,(
% 0.08/0.56 ![X0]: (~less_equal(zero,divide(divide(X0,a),b))|divide(divide(X0,identity),a)=divide(divide(X0,a),divide(identity,a)))),
% 0.08/0.56 inference(forward_demodulation,[status(thm)],[f28,f335])).
% 0.08/0.56 fof(f337,plain,(
% 0.08/0.56 ![X0]: (~less_equal(zero,divide(divide(X0,a),b))|divide(zero,a)=divide(divide(X0,a),divide(identity,a)))),
% 0.08/0.56 inference(forward_demodulation,[status(thm)],[f29,f336])).
% 0.08/0.56 fof(f338,plain,(
% 0.08/0.56 ![X0]: (~less_equal(zero,divide(divide(X0,a),b))|zero=divide(divide(X0,a),divide(identity,a)))),
% 0.08/0.56 inference(forward_demodulation,[status(thm)],[f28,f337])).
% 0.08/0.56 fof(f339,plain,(
% 0.08/0.56 ![X0]: (~less_equal(zero,divide(divide(X0,a),b))|zero=divide(divide(X0,a),b))),
% 0.08/0.56 inference(forward_demodulation,[status(thm)],[f21,f338])).
% 0.08/0.56 fof(f340,plain,(
% 0.08/0.56 ![X0]: (zero=divide(divide(X0,a),b))),
% 0.08/0.56 inference(forward_subsumption_resolution,[status(thm)],[f339,f17])).
% 0.08/0.56 fof(f429,plain,(
% 0.08/0.56 ![X0]: (less_equal(divide(X0,c),d))),
% 0.08/0.56 inference(resolution,[status(thm)],[f334,f14])).
% 0.08/0.56 fof(f476,plain,(
% 0.08/0.56 ![X0]: (less_equal(divide(X0,a),b))),
% 0.08/0.56 inference(resolution,[status(thm)],[f340,f14])).
% 0.08/0.56 fof(f480,plain,(
% 0.08/0.56 zero=divide(b,b)),
% 0.08/0.57 inference(paramodulation,[status(thm)],[f21,f340])).
% 0.08/0.57 fof(f565,plain,(
% 0.08/0.57 ![X0]: (~less_equal(b,divide(X0,a))|b=divide(X0,a))),
% 0.08/0.57 inference(resolution,[status(thm)],[f476,f18])).
% 0.08/0.57 fof(f574,plain,(
% 0.08/0.57 divide(d,divide(b,c))=zero),
% 0.08/0.57 inference(resolution,[status(thm)],[f194,f57])).
% 0.08/0.57 fof(f579,plain,(
% 0.08/0.57 less_equal(d,divide(b,c))),
% 0.08/0.57 inference(resolution,[status(thm)],[f574,f14])).
% 0.08/0.57 fof(f609,plain,(
% 0.08/0.57 ~less_equal(divide(b,c),d)|divide(b,c)=d),
% 0.08/0.57 inference(resolution,[status(thm)],[f579,f18])).
% 0.08/0.57 fof(f611,plain,(
% 0.08/0.57 divide(b,c)=d),
% 0.08/0.57 inference(forward_subsumption_resolution,[status(thm)],[f609,f429])).
% 0.08/0.57 fof(f626,plain,(
% 0.08/0.57 ~less_equal(b,d)|b=divide(b,c)),
% 0.08/0.57 inference(paramodulation,[status(thm)],[f611,f56])).
% 0.08/0.57 fof(f641,plain,(
% 0.08/0.57 ~less_equal(b,d)|b=d),
% 0.08/0.57 inference(forward_demodulation,[status(thm)],[f611,f626])).
% 0.08/0.57 fof(f642,plain,(
% 0.08/0.57 ~less_equal(b,d)),
% 0.08/0.57 inference(forward_subsumption_resolution,[status(thm)],[f641,f24])).
% 0.08/0.57 fof(f666,plain,(
% 0.08/0.57 less_equal(divide(c,divide(a,b)),divide(b,b))),
% 0.08/0.57 inference(paramodulation,[status(thm)],[f22,f95])).
% 0.08/0.57 fof(f674,plain,(
% 0.08/0.57 less_equal(divide(c,divide(a,b)),zero)),
% 0.08/0.57 inference(forward_demodulation,[status(thm)],[f480,f666])).
% 0.08/0.57 fof(f718,plain,(
% 0.08/0.57 ![X0,X1]: (less_equal(divide(X0,X0),divide(X1,X0)))),
% 0.08/0.57 inference(resolution,[status(thm)],[f253,f14])).
% 0.08/0.57 fof(f791,plain,(
% 0.08/0.57 ![X0]: (divide(X0,X0)=divide(divide(X0,X0),X0))),
% 0.08/0.57 inference(resolution,[status(thm)],[f718,f56])).
% 0.08/0.57 fof(f816,plain,(
% 0.08/0.57 ![X0]: (divide(X0,X0)=zero)),
% 0.08/0.57 inference(forward_demodulation,[status(thm)],[f27,f791])).
% 0.08/0.57 fof(f1161,plain,(
% 0.08/0.57 divide(c,divide(a,b))=zero),
% 0.08/0.57 inference(resolution,[status(thm)],[f674,f57])).
% 0.08/0.57 fof(f1166,plain,(
% 0.08/0.57 less_equal(c,divide(a,b))),
% 0.08/0.57 inference(resolution,[status(thm)],[f1161,f14])).
% 0.08/0.57 fof(f1205,plain,(
% 0.08/0.57 ~less_equal(divide(a,b),c)|divide(a,b)=c),
% 0.08/0.57 inference(resolution,[status(thm)],[f1166,f18])).
% 0.08/0.57 fof(f1207,plain,(
% 0.08/0.57 divide(a,b)=c),
% 0.08/0.57 inference(forward_subsumption_resolution,[status(thm)],[f1205,f189])).
% 0.08/0.57 fof(f1229,plain,(
% 0.08/0.57 divide(c,a)=zero),
% 0.08/0.57 inference(paramodulation,[status(thm)],[f1207,f27])).
% 0.08/0.57 fof(f1306,plain,(
% 0.08/0.57 less_equal(divide(divide(identity,a),zero),divide(d,a))),
% 0.08/0.57 inference(paramodulation,[status(thm)],[f1229,f94])).
% 0.08/0.57 fof(f1328,plain,(
% 0.08/0.57 less_equal(divide(b,zero),divide(d,a))),
% 0.08/0.57 inference(forward_demodulation,[status(thm)],[f21,f1306])).
% 0.08/0.57 fof(f1624,plain,(
% 0.08/0.57 ![X0]: (less_equal(divide(divide(X0,divide(X0,zero)),zero),zero))),
% 0.08/0.57 inference(paramodulation,[status(thm)],[f816,f84])).
% 0.08/0.57 fof(f3178,plain,(
% 0.08/0.57 ![X0]: (divide(divide(X0,divide(X0,zero)),zero)=zero)),
% 0.08/0.57 inference(resolution,[status(thm)],[f1624,f57])).
% 0.08/0.57 fof(f3196,plain,(
% 0.08/0.57 ![X0]: (less_equal(divide(X0,divide(X0,zero)),zero))),
% 0.08/0.57 inference(resolution,[status(thm)],[f3178,f14])).
% 0.08/0.57 fof(f3278,plain,(
% 0.08/0.57 ![X0]: (divide(X0,divide(X0,zero))=zero)),
% 0.08/0.57 inference(resolution,[status(thm)],[f3196,f57])).
% 0.08/0.57 fof(f3295,plain,(
% 0.08/0.57 ![X0]: (less_equal(X0,divide(X0,zero)))),
% 0.08/0.57 inference(resolution,[status(thm)],[f3278,f14])).
% 0.08/0.57 fof(f3443,plain,(
% 0.08/0.57 ![X0]: (X0=divide(X0,zero))),
% 0.08/0.57 inference(resolution,[status(thm)],[f3295,f56])).
% 0.08/0.57 fof(f4684,plain,(
% 0.08/0.57 less_equal(b,divide(d,a))),
% 0.08/0.57 inference(backward_demodulation,[status(thm)],[f3443,f1328])).
% 0.08/0.57 fof(f5018,plain,(
% 0.08/0.57 b=divide(d,a)),
% 0.08/0.57 inference(resolution,[status(thm)],[f4684,f565])).
% 0.08/0.57 fof(f5056,plain,(
% 0.08/0.57 less_equal(b,d)),
% 0.08/0.57 inference(paramodulation,[status(thm)],[f5018,f15])).
% 0.08/0.57 fof(f5085,plain,(
% 0.08/0.57 $false),
% 0.08/0.57 inference(forward_subsumption_resolution,[status(thm)],[f5056,f642])).
% 0.08/0.57 % SZS output end CNFRefutation for theBenchmark.p
% 0.77/0.57 % Elapsed time: 0.208779 seconds
% 0.77/0.57 % CPU time: 1.448286 seconds
% 0.77/0.57 % Total memory used: 97.043 MB
% 0.77/0.57 % Net memory used: 95.757 MB
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