%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : HEN010-2 : 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 : n014.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 1.05s 0.64s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN010-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n014.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 20 20:46:21 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.38 % Drodi V4.1.1
% 1.05/0.64 % Refutation found
% 1.05/0.64 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 1.05/0.64 % SZS output start CNFRefutation for theBenchmark
% 1.05/0.64 fof(f1,axiom,(
% 1.05/0.64 (![X,Y]: (( ~ less_equal(X,Y)| quotient(X,Y,zero) ) ))),
% 1.05/0.64 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.05/0.64 fof(f2,axiom,(
% 1.05/0.64 (![X,Y]: (( ~ quotient(X,Y,zero)| less_equal(X,Y) ) ))),
% 1.05/0.64 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.05/0.64 fof(f3,axiom,(
% 1.05/0.64 (![X,Y,Z]: (( ~ quotient(X,Y,Z)| less_equal(Z,X) ) ))),
% 1.05/0.64 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.05/0.64 fof(f4,axiom,(
% 1.05/0.64 (![X,Y,V1,Z,V2,V3,V4,V5]: (( ~ quotient(X,Y,V1)| ~ quotient(Y,Z,V2)| ~ quotient(X,Z,V3)| ~ quotient(V3,V2,V4)| ~ quotient(V1,Z,V5)| less_equal(V4,V5) ) ))),
% 1.05/0.64 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.05/0.64 fof(f5,axiom,(
% 1.05/0.64 (![X]: (less_equal(zero,X) ))),
% 1.05/0.64 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.05/0.64 fof(f6,axiom,(
% 1.05/0.64 (![X,Y]: (( ~ less_equal(X,Y)| ~ less_equal(Y,X)| X = Y ) ))),
% 1.05/0.64 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.05/0.64 fof(f7,axiom,(
% 1.05/0.64 (![X]: (less_equal(X,identity) ))),
% 1.05/0.64 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.05/0.64 fof(f8,axiom,(
% 1.05/0.64 (![X,Y]: (quotient(X,Y,divide(X,Y)) ))),
% 1.05/0.64 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.05/0.64 fof(f9,axiom,(
% 1.05/0.64 (![X,Y,Z,W]: (( ~ quotient(X,Y,Z)| ~ quotient(X,Y,W)| Z = W ) ))),
% 1.05/0.64 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.05/0.64 fof(f12,axiom,(
% 1.05/0.64 (![X]: (quotient(X,X,zero) ))),
% 1.05/0.64 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.05/0.64 fof(f13,axiom,(
% 1.05/0.64 (![X]: (quotient(X,zero,X) ))),
% 1.05/0.64 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.05/0.64 fof(f15,axiom,(
% 1.05/0.64 (![X,Y,W1,Z,W2]: (( ~ quotient(X,Y,W1)| ~ less_equal(W1,Z)| ~ quotient(X,Z,W2)| less_equal(W2,Y) ) ))),
% 1.05/0.64 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.05/0.64 fof(f17,axiom,(
% 1.05/0.64 (![X,Y,Z,W1,W2]: (( ~ less_equal(X,Y)| ~ quotient(X,Z,W1)| ~ quotient(Y,Z,W2)| less_equal(W1,W2) ) ))),
% 1.05/0.64 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.05/0.64 fof(f18,axiom,(
% 1.05/0.64 (![X,Y1,Y2,Y3]: (( ~ quotient(identity,X,Y1)| ~ quotient(identity,Y1,Y2)| ~ quotient(identity,Y2,Y3)| Y1 = Y3 ) ))),
% 1.05/0.64 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.05/0.64 fof(f19,hypothesis,(
% 1.05/0.64 quotient(identity,a,idQa) ),
% 1.05/0.64 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.05/0.64 fof(f20,hypothesis,(
% 1.05/0.64 quotient(identity,idQa,idQ_idQa) ),
% 1.05/0.64 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.05/0.64 fof(f21,hypothesis,(
% 1.05/0.64 quotient(idQa,idQ_idQa,idQa_Q__idQ_idQa) ),
% 1.05/0.64 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.05/0.64 fof(f22,negated_conjecture,(
% 1.05/0.64 idQa != idQa_Q__idQ_idQa ),
% 1.05/0.64 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.05/0.64 fof(f23,plain,(
% 1.05/0.64 ![X0,X1]: (~less_equal(X0,X1)|quotient(X0,X1,zero))),
% 1.05/0.64 inference(cnf_transformation,[status(thm)],[f1])).
% 1.05/0.64 fof(f24,plain,(
% 1.05/0.64 ![X0,X1]: (~quotient(X0,X1,zero)|less_equal(X0,X1))),
% 1.05/0.64 inference(cnf_transformation,[status(thm)],[f2])).
% 1.05/0.64 fof(f25,plain,(
% 1.05/0.64 ![X,Z]: ((![Y]: ~quotient(X,Y,Z))|less_equal(Z,X))),
% 1.05/0.64 inference(miniscoping,[status(thm)],[f3])).
% 1.05/0.64 fof(f26,plain,(
% 1.05/0.64 ![X0,X1,X2]: (~quotient(X0,X1,X2)|less_equal(X2,X0))),
% 1.05/0.64 inference(cnf_transformation,[status(thm)],[f25])).
% 1.05/0.64 fof(f27,plain,(
% 1.05/0.64 ![V4,V5]: ((![V1,Z]: ((![V2,V3]: ((![X]: ((![Y]: (~quotient(X,Y,V1)|~quotient(Y,Z,V2)))|~quotient(X,Z,V3)))|~quotient(V3,V2,V4)))|~quotient(V1,Z,V5)))|less_equal(V4,V5))),
% 1.05/0.64 inference(miniscoping,[status(thm)],[f4])).
% 1.05/0.64 fof(f28,plain,(
% 1.05/0.64 ![X0,X1,X2,X3,X4,X5,X6,X7]: (~quotient(X0,X1,X2)|~quotient(X1,X3,X4)|~quotient(X0,X3,X5)|~quotient(X5,X4,X6)|~quotient(X2,X3,X7)|less_equal(X6,X7))),
% 1.05/0.64 inference(cnf_transformation,[status(thm)],[f27])).
% 1.05/0.64 fof(f29,plain,(
% 1.05/0.64 ![X0]: (less_equal(zero,X0))),
% 1.05/0.64 inference(cnf_transformation,[status(thm)],[f5])).
% 1.05/0.64 fof(f30,plain,(
% 1.05/0.64 ![X0,X1]: (~less_equal(X0,X1)|~less_equal(X1,X0)|X0=X1)),
% 1.05/0.64 inference(cnf_transformation,[status(thm)],[f6])).
% 1.05/0.64 fof(f31,plain,(
% 1.05/0.64 ![X0]: (less_equal(X0,identity))),
% 1.05/0.64 inference(cnf_transformation,[status(thm)],[f7])).
% 1.05/0.64 fof(f32,plain,(
% 1.05/0.64 ![X0,X1]: (quotient(X0,X1,divide(X0,X1)))),
% 1.05/0.64 inference(cnf_transformation,[status(thm)],[f8])).
% 1.05/0.64 fof(f33,plain,(
% 1.05/0.64 ![Z,W]: ((![X,Y]: (~quotient(X,Y,Z)|~quotient(X,Y,W)))|Z=W)),
% 1.05/0.64 inference(miniscoping,[status(thm)],[f9])).
% 1.05/0.64 fof(f34,plain,(
% 1.05/0.64 ![X0,X1,X2,X3]: (~quotient(X0,X1,X2)|~quotient(X0,X1,X3)|X2=X3)),
% 1.05/0.64 inference(cnf_transformation,[status(thm)],[f33])).
% 1.05/0.64 fof(f37,plain,(
% 1.05/0.64 ![X0]: (quotient(X0,X0,zero))),
% 1.05/0.64 inference(cnf_transformation,[status(thm)],[f12])).
% 1.05/0.64 fof(f38,plain,(
% 1.05/0.64 ![X0]: (quotient(X0,zero,X0))),
% 1.05/0.64 inference(cnf_transformation,[status(thm)],[f13])).
% 1.05/0.64 fof(f41,plain,(
% 1.05/0.64 ![Y,W2]: ((![X,Z]: ((![W1]: (~quotient(X,Y,W1)|~less_equal(W1,Z)))|~quotient(X,Z,W2)))|less_equal(W2,Y))),
% 1.05/0.64 inference(miniscoping,[status(thm)],[f15])).
% 1.05/0.64 fof(f42,plain,(
% 1.05/0.64 ![X0,X1,X2,X3,X4]: (~quotient(X0,X1,X2)|~less_equal(X2,X3)|~quotient(X0,X3,X4)|less_equal(X4,X1))),
% 1.05/0.64 inference(cnf_transformation,[status(thm)],[f41])).
% 1.05/0.64 fof(f45,plain,(
% 1.05/0.64 ![W1,W2]: ((![Y,Z]: ((![X]: (~less_equal(X,Y)|~quotient(X,Z,W1)))|~quotient(Y,Z,W2)))|less_equal(W1,W2))),
% 1.05/0.64 inference(miniscoping,[status(thm)],[f17])).
% 1.05/0.64 fof(f46,plain,(
% 1.05/0.64 ![X0,X1,X2,X3,X4]: (~less_equal(X0,X1)|~quotient(X0,X2,X3)|~quotient(X1,X2,X4)|less_equal(X3,X4))),
% 1.05/0.64 inference(cnf_transformation,[status(thm)],[f45])).
% 1.05/0.64 fof(f47,plain,(
% 1.05/0.64 ![Y1,Y3]: ((![Y2]: (((![X]: ~quotient(identity,X,Y1))|~quotient(identity,Y1,Y2))|~quotient(identity,Y2,Y3)))|Y1=Y3)),
% 1.05/0.64 inference(miniscoping,[status(thm)],[f18])).
% 1.05/0.64 fof(f48,plain,(
% 1.05/0.64 ![X0,X1,X2,X3]: (~quotient(identity,X0,X1)|~quotient(identity,X1,X2)|~quotient(identity,X2,X3)|X1=X3)),
% 1.05/0.64 inference(cnf_transformation,[status(thm)],[f47])).
% 1.05/0.64 fof(f49,plain,(
% 1.05/0.64 quotient(identity,a,idQa)),
% 1.05/0.64 inference(cnf_transformation,[status(thm)],[f19])).
% 1.05/0.64 fof(f50,plain,(
% 1.05/0.64 quotient(identity,idQa,idQ_idQa)),
% 1.05/0.64 inference(cnf_transformation,[status(thm)],[f20])).
% 1.05/0.64 fof(f51,plain,(
% 1.05/0.64 quotient(idQa,idQ_idQa,idQa_Q__idQ_idQa)),
% 1.05/0.64 inference(cnf_transformation,[status(thm)],[f21])).
% 1.05/0.64 fof(f52,plain,(
% 1.05/0.64 ~idQa=idQa_Q__idQ_idQa),
% 1.05/0.64 inference(cnf_transformation,[status(thm)],[f22])).
% 1.05/0.64 fof(f56,plain,(
% 1.05/0.64 ![X0]: (less_equal(X0,X0))),
% 1.05/0.64 inference(resolution,[status(thm)],[f24,f37])).
% 1.05/0.64 fof(f57,plain,(
% 1.05/0.64 less_equal(idQa_Q__idQ_idQa,idQa)),
% 1.05/0.64 inference(resolution,[status(thm)],[f26,f51])).
% 1.05/0.64 fof(f71,plain,(
% 1.05/0.64 ~less_equal(idQa,idQa_Q__idQ_idQa)|idQa_Q__idQ_idQa=idQa),
% 1.05/0.64 inference(resolution,[status(thm)],[f30,f57])).
% 1.05/0.64 fof(f72,plain,(
% 1.05/0.64 ![X0]: (~less_equal(X0,zero)|zero=X0)),
% 1.05/0.64 inference(resolution,[status(thm)],[f30,f29])).
% 1.05/0.64 fof(f75,plain,(
% 1.05/0.64 ~less_equal(idQa,idQa_Q__idQ_idQa)),
% 1.05/0.64 inference(forward_subsumption_resolution,[status(thm)],[f71,f52])).
% 1.05/0.64 fof(f76,plain,(
% 1.05/0.64 ![X0,X1,X2,X3,X4,X5,X6]: (~quotient(X0,X1,X2)|~quotient(X3,X1,X4)|~quotient(X4,X2,X5)|~quotient(divide(X3,X0),X1,X6)|less_equal(X5,X6))),
% 1.05/0.64 inference(resolution,[status(thm)],[f32,f28])).
% 1.05/0.64 fof(f119,plain,(
% 1.05/0.64 ![X0,X1]: (~quotient(X0,zero,X1)|X0=X1)),
% 1.05/0.64 inference(resolution,[status(thm)],[f34,f38])).
% 1.05/0.64 fof(f134,plain,(
% 1.05/0.64 ![X0,X1,X2,X3]: (~less_equal(divide(X0,X1),X2)|~quotient(X0,X2,X3)|less_equal(X3,X1))),
% 1.05/0.64 inference(resolution,[status(thm)],[f42,f32])).
% 1.05/0.64 fof(f165,plain,(
% 1.05/0.64 ![X0]: (X0=divide(X0,zero))),
% 1.05/0.64 inference(resolution,[status(thm)],[f119,f32])).
% 1.05/0.64 fof(f205,plain,(
% 1.05/0.64 ![X0,X1,X2,X3]: (~quotient(X0,X1,X2)|~quotient(identity,X1,X3)|less_equal(X2,X3))),
% 1.05/0.64 inference(resolution,[status(thm)],[f46,f31])).
% 1.05/0.64 fof(f208,plain,(
% 1.05/0.64 ![X0,X1]: (~quotient(identity,idQa,X0)|~quotient(identity,X0,X1)|idQa=X1)),
% 1.05/0.64 inference(resolution,[status(thm)],[f48,f49])).
% 1.05/0.64 fof(f399,plain,(
% 1.05/0.64 ![X0,X1,X2,X3]: (~quotient(X0,idQ_idQa,X1)|~quotient(X1,idQa_Q__idQ_idQa,X2)|~quotient(divide(X0,idQa),idQ_idQa,X3)|less_equal(X2,X3))),
% 1.05/0.64 inference(resolution,[status(thm)],[f76,f51])).
% 1.05/0.64 fof(f469,plain,(
% 1.05/0.64 ![X0,X1,X2]: (~quotient(divide(X0,idQ_idQa),idQa_Q__idQ_idQa,X1)|~quotient(divide(X0,idQa),idQ_idQa,X2)|less_equal(X1,X2))),
% 1.05/0.64 inference(resolution,[status(thm)],[f399,f32])).
% 1.05/0.64 fof(f816,plain,(
% 1.05/0.64 ![X0,X1,X2]: (~quotient(X0,divide(X0,X1),X2)|less_equal(X2,X1))),
% 1.05/0.64 inference(resolution,[status(thm)],[f134,f56])).
% 1.05/0.64 fof(f965,plain,(
% 1.05/0.64 ![X0,X1,X2]: (~quotient(identity,X0,X1)|less_equal(divide(X2,X0),X1))),
% 1.05/0.64 inference(resolution,[status(thm)],[f205,f32])).
% 1.05/0.64 fof(f1057,plain,(
% 1.05/0.64 ![X0]: (~quotient(identity,idQ_idQa,X0)|idQa=X0)),
% 1.05/0.65 inference(resolution,[status(thm)],[f208,f50])).
% 1.05/0.65 fof(f1085,plain,(
% 1.05/0.65 idQa=divide(identity,idQ_idQa)),
% 1.05/0.65 inference(resolution,[status(thm)],[f1057,f32])).
% 1.05/0.65 fof(f1247,plain,(
% 1.05/0.65 ![X0,X1]: (less_equal(divide(X0,divide(X0,X1)),X1))),
% 1.05/0.65 inference(resolution,[status(thm)],[f816,f32])).
% 1.05/0.65 fof(f1415,plain,(
% 1.05/0.65 ![X0,X1]: (~quotient(divide(X0,idQa),idQ_idQa,X1)|less_equal(divide(divide(X0,idQ_idQa),idQa_Q__idQ_idQa),X1))),
% 1.05/0.65 inference(resolution,[status(thm)],[f469,f32])).
% 1.05/0.65 fof(f2179,plain,(
% 1.05/0.65 ![X0]: (less_equal(divide(X0,idQa),idQ_idQa))),
% 1.05/0.65 inference(resolution,[status(thm)],[f965,f50])).
% 1.05/0.65 fof(f2266,plain,(
% 1.05/0.65 ![X0]: (quotient(divide(X0,idQa),idQ_idQa,zero))),
% 1.05/0.65 inference(resolution,[status(thm)],[f2179,f23])).
% 1.05/0.65 fof(f3139,plain,(
% 1.05/0.65 ![X0]: (less_equal(divide(divide(X0,idQ_idQa),idQa_Q__idQ_idQa),zero))),
% 1.05/0.65 inference(resolution,[status(thm)],[f1415,f2266])).
% 1.05/0.65 fof(f3465,plain,(
% 1.05/0.65 less_equal(divide(idQa,idQa_Q__idQ_idQa),zero)),
% 1.05/0.65 inference(paramodulation,[status(thm)],[f1085,f3139])).
% 1.05/0.65 fof(f3484,plain,(
% 1.05/0.65 zero=divide(idQa,idQa_Q__idQ_idQa)),
% 1.05/0.65 inference(resolution,[status(thm)],[f3465,f72])).
% 1.05/0.65 fof(f3532,plain,(
% 1.05/0.65 less_equal(divide(idQa,zero),idQa_Q__idQ_idQa)),
% 1.05/0.65 inference(paramodulation,[status(thm)],[f3484,f1247])).
% 1.05/0.65 fof(f3564,plain,(
% 1.05/0.65 less_equal(idQa,idQa_Q__idQ_idQa)),
% 1.05/0.65 inference(forward_demodulation,[status(thm)],[f165,f3532])).
% 1.05/0.65 fof(f3565,plain,(
% 1.05/0.65 $false),
% 1.05/0.65 inference(forward_subsumption_resolution,[status(thm)],[f3564,f75])).
% 1.05/0.65 % SZS output end CNFRefutation for theBenchmark.p
% 1.05/0.68 % Elapsed time: 0.287908 seconds
% 1.05/0.68 % CPU time: 2.010493 seconds
% 1.05/0.68 % Total memory used: 62.594 MB
% 1.05/0.68 % Net memory used: 58.439 MB
%------------------------------------------------------------------------------