%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : KLE170+1.002 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n002.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 12:58:27 PM UTC 2026
% Result : Theorem 30.05s 4.42s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KLE170+1.002 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.06 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.45 % Computer : n002.cluster.edu
% 0.20/0.45 % Model : x86_64 x86_64
% 0.20/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.45 % Memory : 8046.5625MB
% 0.20/0.45 % OS : Linux 6.8.0-71-generic
% 0.20/0.45 % CPULimit : 300
% 0.20/0.45 % WCLimit : 300
% 0.20/0.45 % DateTime : Sun Sep 20 22:51:46 UTC 2026
% 0.20/0.45 % CPUTime :
% 0.20/0.47 % Drodi V4.1.1
% 30.05/4.42 % Refutation found
% 30.05/4.42 % SZS status Theorem for theBenchmark: Theorem is valid
% 30.05/4.42 % SZS output start CNFRefutation for theBenchmark
% 30.05/4.42 fof(f1,axiom,(
% 30.05/4.42 (! [A,B] : addition(A,B) = addition(B,A) )),
% 30.05/4.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 30.05/4.42 fof(f2,axiom,(
% 30.05/4.42 (! [C,B,A] : addition(A,addition(B,C)) = addition(addition(A,B),C) )),
% 30.05/4.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 30.05/4.42 fof(f4,axiom,(
% 30.05/4.42 (! [A] : addition(A,A) = A )),
% 30.05/4.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 30.05/4.42 fof(f6,axiom,(
% 30.05/4.42 (! [A] : multiplication(A,one) = A )),
% 30.05/4.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 30.05/4.42 fof(f7,axiom,(
% 30.05/4.42 (! [A] : multiplication(one,A) = A )),
% 30.05/4.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 30.05/4.42 fof(f8,axiom,(
% 30.05/4.42 (! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) )),
% 30.05/4.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 30.05/4.42 fof(f9,axiom,(
% 30.05/4.42 (! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) )),
% 30.05/4.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 30.05/4.42 fof(f12,axiom,(
% 30.05/4.42 (! [A,B] :( leq(A,B)<=> addition(A,B) = B ) )),
% 30.05/4.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 30.05/4.42 fof(f13,axiom,(
% 30.05/4.42 (! [A] : leq(addition(one,multiplication(A,star(A))),star(A)) )),
% 30.05/4.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 30.05/4.42 fof(f17,conjecture,(
% 30.05/4.42 leq(multiplication(a,a),star(a)) ),
% 30.05/4.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 30.05/4.42 fof(f18,negated_conjecture,(
% 30.05/4.42 ~(leq(multiplication(a,a),star(a)) )),
% 30.05/4.42 inference(negated_conjecture,[status(cth)],[f17])).
% 30.05/4.42 fof(f19,plain,(
% 30.05/4.42 ![X0,X1]: (addition(X0,X1)=addition(X1,X0))),
% 30.05/4.42 inference(cnf_transformation,[status(thm)],[f1])).
% 30.05/4.42 fof(f20,plain,(
% 30.05/4.42 ![X0,X1,X2]: (addition(X0,addition(X1,X2))=addition(addition(X0,X1),X2))),
% 30.05/4.42 inference(cnf_transformation,[status(thm)],[f2])).
% 30.05/4.42 fof(f22,plain,(
% 30.05/4.42 ![X0]: (addition(X0,X0)=X0)),
% 30.05/4.42 inference(cnf_transformation,[status(thm)],[f4])).
% 30.05/4.42 fof(f24,plain,(
% 30.05/4.42 ![X0]: (multiplication(X0,one)=X0)),
% 30.05/4.42 inference(cnf_transformation,[status(thm)],[f6])).
% 30.05/4.42 fof(f25,plain,(
% 30.05/4.42 ![X0]: (multiplication(one,X0)=X0)),
% 30.05/4.42 inference(cnf_transformation,[status(thm)],[f7])).
% 30.05/4.42 fof(f26,plain,(
% 30.05/4.42 ![X0,X1,X2]: (multiplication(X0,addition(X1,X2))=addition(multiplication(X0,X1),multiplication(X0,X2)))),
% 30.05/4.42 inference(cnf_transformation,[status(thm)],[f8])).
% 30.05/4.42 fof(f27,plain,(
% 30.05/4.42 ![X0,X1,X2]: (multiplication(addition(X0,X1),X2)=addition(multiplication(X0,X2),multiplication(X1,X2)))),
% 30.05/4.42 inference(cnf_transformation,[status(thm)],[f9])).
% 30.05/4.42 fof(f30,plain,(
% 30.05/4.42 ![A,B]: ((~leq(A,B)|addition(A,B)=B)&(leq(A,B)|~addition(A,B)=B))),
% 30.05/4.42 inference(NNF_transformation,[status(thm)],[f12])).
% 30.05/4.42 fof(f31,plain,(
% 30.05/4.42 (![A,B]: (~leq(A,B)|addition(A,B)=B))&(![A,B]: (leq(A,B)|~addition(A,B)=B))),
% 30.05/4.42 inference(miniscoping,[status(thm)],[f30])).
% 30.05/4.42 fof(f32,plain,(
% 30.05/4.42 ![X0,X1]: (~leq(X0,X1)|addition(X0,X1)=X1)),
% 30.05/4.42 inference(cnf_transformation,[status(thm)],[f31])).
% 30.05/4.42 fof(f33,plain,(
% 30.05/4.42 ![X0,X1]: (leq(X0,X1)|~addition(X0,X1)=X1)),
% 30.05/4.42 inference(cnf_transformation,[status(thm)],[f31])).
% 30.05/4.42 fof(f34,plain,(
% 30.05/4.42 ![X0]: (leq(addition(one,multiplication(X0,star(X0))),star(X0)))),
% 30.05/4.42 inference(cnf_transformation,[status(thm)],[f13])).
% 30.05/4.42 fof(f40,plain,(
% 30.05/4.42 ~leq(multiplication(a,a),star(a))),
% 30.05/4.42 inference(cnf_transformation,[status(thm)],[f18])).
% 30.05/4.42 fof(f499,plain,(
% 30.05/4.42 ![X0,X1]: (addition(X0,addition(X0,X1))=addition(X0,X1))),
% 30.05/4.42 inference(paramodulation,[status(thm)],[f22,f20])).
% 30.05/4.42 fof(f515,plain,(
% 30.05/4.42 ![X0,X1]: (multiplication(X0,addition(one,X1))=addition(X0,multiplication(X0,X1)))),
% 30.05/4.42 inference(paramodulation,[status(thm)],[f24,f26])).
% 30.05/4.42 fof(f535,plain,(
% 30.05/4.42 ![X0,X1,X2]: (leq(multiplication(X0,X1),multiplication(X0,X2))|~multiplication(X0,addition(X1,X2))=multiplication(X0,X2))),
% 30.05/4.42 inference(paramodulation,[status(thm)],[f26,f33])).
% 30.05/4.42 fof(f564,plain,(
% 30.05/4.42 ![X0,X1]: (multiplication(addition(X0,one),X1)=addition(multiplication(X0,X1),X1))),
% 30.05/4.42 inference(paramodulation,[status(thm)],[f25,f27])).
% 30.05/4.42 fof(f861,plain,(
% 30.05/4.42 ![X0,X1]: (leq(X0,addition(X0,X1)))),
% 30.05/4.42 inference(resolution,[status(thm)],[f499,f33])).
% 30.05/4.42 fof(f924,plain,(
% 30.05/4.42 ![X0,X1,X2]: (leq(addition(X0,X1),addition(X0,addition(X1,X2))))),
% 30.05/4.42 inference(paramodulation,[status(thm)],[f20,f861])).
% 30.05/4.42 fof(f929,plain,(
% 30.05/4.42 ![X0,X1]: (leq(X0,addition(X1,X0)))),
% 30.05/4.42 inference(paramodulation,[status(thm)],[f19,f861])).
% 30.05/4.42 fof(f932,plain,(
% 30.05/4.42 ![X0,X1]: (addition(X0,addition(X1,X0))=addition(X1,X0))),
% 30.05/4.42 inference(resolution,[status(thm)],[f929,f32])).
% 30.05/4.42 fof(f938,plain,(
% 30.05/4.42 ![X0,X1,X2]: (leq(X0,addition(X1,addition(X2,X0))))),
% 30.05/4.42 inference(paramodulation,[status(thm)],[f20,f929])).
% 30.05/4.42 fof(f951,plain,(
% 30.05/4.42 ![X0,X1,X2]: (leq(X0,addition(addition(X1,X0),X2)))),
% 30.05/4.42 inference(paramodulation,[status(thm)],[f19,f938])).
% 30.05/4.42 fof(f967,plain,(
% 30.05/4.42 ![X0,X1,X2]: (leq(X0,addition(X1,addition(X0,X2))))),
% 30.05/4.42 inference(forward_demodulation,[status(thm)],[f20,f951])).
% 30.05/4.42 fof(f1183,plain,(
% 30.05/4.42 ![X0]: (addition(addition(one,multiplication(X0,star(X0))),star(X0))=star(X0))),
% 30.05/4.42 inference(resolution,[status(thm)],[f34,f32])).
% 30.05/4.42 fof(f1188,plain,(
% 30.05/4.42 ![X0]: (addition(one,addition(multiplication(X0,star(X0)),star(X0)))=star(X0))),
% 30.05/4.42 inference(forward_demodulation,[status(thm)],[f20,f1183])).
% 30.05/4.42 fof(f1246,plain,(
% 30.05/4.42 ![X0,X1]: (addition(X0,addition(X0,X1))=addition(X1,X0))),
% 30.05/4.42 inference(paramodulation,[status(thm)],[f19,f932])).
% 30.05/4.42 fof(f1955,plain,(
% 30.05/4.42 ![X0,X1,X2]: (leq(addition(X0,X1),addition(X1,addition(X0,X2))))),
% 30.05/4.42 inference(paramodulation,[status(thm)],[f19,f924])).
% 30.05/4.42 fof(f2363,plain,(
% 30.05/4.42 ![X0,X1,X2]: (addition(addition(X0,X1),addition(X1,addition(X0,X2)))=addition(X1,addition(X0,X2)))),
% 30.05/4.42 inference(resolution,[status(thm)],[f1955,f32])).
% 30.05/4.42 fof(f2397,plain,(
% 30.05/4.42 ![X0,X1,X2]: (addition(X0,addition(X1,addition(X1,addition(X0,X2))))=addition(X1,addition(X0,X2)))),
% 30.05/4.42 inference(forward_demodulation,[status(thm)],[f20,f2363])).
% 30.05/4.42 fof(f2398,plain,(
% 30.05/4.42 ![X0,X1,X2]: (addition(X0,addition(addition(X0,X1),X2))=addition(X2,addition(X0,X1)))),
% 30.05/4.42 inference(forward_demodulation,[status(thm)],[f1246,f2397])).
% 30.05/4.42 fof(f2399,plain,(
% 30.05/4.42 ![X0,X1,X2]: (addition(X0,addition(X0,addition(X1,X2)))=addition(X2,addition(X0,X1)))),
% 30.05/4.42 inference(forward_demodulation,[status(thm)],[f20,f2398])).
% 30.05/4.42 fof(f2400,plain,(
% 30.05/4.42 ![X0,X1,X2]: (addition(addition(X0,X1),X2)=addition(X1,addition(X2,X0)))),
% 30.05/4.42 inference(forward_demodulation,[status(thm)],[f1246,f2399])).
% 30.05/4.42 fof(f5452,plain,(
% 30.05/4.42 ![X0,X1,X2]: (leq(X0,addition(X1,multiplication(X0,addition(one,X2)))))),
% 30.05/4.42 inference(paramodulation,[status(thm)],[f515,f967])).
% 30.05/4.42 fof(f6352,plain,(
% 30.05/4.42 ![X0]: (addition(addition(multiplication(X0,star(X0)),star(X0)),star(X0))=addition(one,addition(multiplication(X0,star(X0)),star(X0))))),
% 30.05/4.42 inference(paramodulation,[status(thm)],[f1188,f932])).
% 30.05/4.42 fof(f6360,plain,(
% 30.05/4.42 ![X0]: (addition(one,star(X0))=addition(one,addition(multiplication(X0,star(X0)),star(X0))))),
% 30.05/4.42 inference(paramodulation,[status(thm)],[f1188,f499])).
% 30.05/4.42 fof(f6429,plain,(
% 30.05/4.42 ![X0]: (addition(star(X0),addition(star(X0),multiplication(X0,star(X0))))=addition(one,addition(multiplication(X0,star(X0)),star(X0))))),
% 30.05/4.42 inference(forward_demodulation,[status(thm)],[f2400,f6352])).
% 30.05/4.42 fof(f6430,plain,(
% 30.05/4.42 ![X0]: (addition(multiplication(X0,star(X0)),star(X0))=addition(one,addition(multiplication(X0,star(X0)),star(X0))))),
% 30.05/4.42 inference(forward_demodulation,[status(thm)],[f1246,f6429])).
% 30.05/4.42 fof(f6431,plain,(
% 30.05/4.42 ![X0]: (addition(multiplication(X0,star(X0)),star(X0))=star(X0))),
% 30.05/4.42 inference(forward_demodulation,[status(thm)],[f1188,f6430])).
% 30.05/4.42 fof(f6437,plain,(
% 30.05/4.42 ![X0]: (addition(one,star(X0))=star(X0))),
% 30.05/4.42 inference(forward_demodulation,[status(thm)],[f1188,f6360])).
% 30.05/4.42 fof(f10023,plain,(
% 30.05/4.42 ![X0,X1,X2]: (leq(X0,addition(X1,multiplication(X0,star(X2)))))),
% 30.05/4.42 inference(paramodulation,[status(thm)],[f6437,f5452])).
% 30.05/4.42 fof(f10066,plain,(
% 30.05/4.42 ![X0,X1,X2]: (leq(X0,addition(multiplication(X0,star(X1)),X2)))),
% 30.05/4.42 inference(paramodulation,[status(thm)],[f19,f10023])).
% 30.05/4.42 fof(f10289,plain,(
% 30.05/4.42 ![X0]: (multiplication(addition(X0,one),star(X0))=star(X0))),
% 30.05/4.42 inference(paramodulation,[status(thm)],[f564,f6431])).
% 30.05/4.42 fof(f10301,plain,(
% 30.05/4.42 ![X0]: (leq(X0,star(X0)))),
% 30.05/4.42 inference(paramodulation,[status(thm)],[f6431,f10066])).
% 30.05/4.42 fof(f10405,plain,(
% 30.05/4.42 ![X0]: (addition(X0,star(X0))=star(X0))),
% 30.05/4.42 inference(resolution,[status(thm)],[f10301,f32])).
% 21.33/4.48 fof(f10478,plain,(
% 21.33/4.48 ![X0,X1]: (leq(multiplication(X0,X1),multiplication(X0,star(X1)))|~multiplication(X0,star(X1))=multiplication(X0,star(X1)))),
% 21.33/4.48 inference(paramodulation,[status(thm)],[f10405,f535])).
% 21.33/4.48 fof(f10502,plain,(
% 21.33/4.48 ![X0]: (addition(X0,star(X0))=addition(star(X0),X0))),
% 21.33/4.48 inference(paramodulation,[status(thm)],[f10405,f1246])).
% 21.33/4.48 fof(f10550,plain,(
% 21.33/4.48 ![X0,X1]: (leq(multiplication(X0,X1),multiplication(X0,star(X1))))),
% 21.33/4.48 inference(trivial_equality_resolution,[status(thm)],[f10478])).
% 21.33/4.48 fof(f10553,plain,(
% 21.33/4.48 ![X0]: (star(X0)=addition(star(X0),X0))),
% 21.33/4.48 inference(forward_demodulation,[status(thm)],[f10405,f10502])).
% 21.33/4.48 fof(f13728,plain,(
% 21.33/4.48 ![X0]: (leq(multiplication(addition(X0,one),X0),star(X0)))),
% 21.33/4.48 inference(paramodulation,[status(thm)],[f10289,f10550])).
% 21.33/4.48 fof(f14752,plain,(
% 21.33/4.48 ![X0]: (leq(addition(multiplication(X0,X0),X0),star(X0)))),
% 21.33/4.48 inference(paramodulation,[status(thm)],[f564,f13728])).
% 21.33/4.48 fof(f14806,plain,(
% 21.33/4.48 ![X0]: (leq(addition(X0,multiplication(X0,X0)),star(X0)))),
% 21.33/4.48 inference(paramodulation,[status(thm)],[f19,f14752])).
% 21.33/4.48 fof(f14842,plain,(
% 21.33/4.48 ![X0]: (addition(addition(X0,multiplication(X0,X0)),star(X0))=star(X0))),
% 21.33/4.48 inference(resolution,[status(thm)],[f14806,f32])).
% 21.33/4.48 fof(f14862,plain,(
% 21.33/4.48 ![X0]: (addition(multiplication(X0,X0),addition(star(X0),X0))=star(X0))),
% 21.33/4.48 inference(forward_demodulation,[status(thm)],[f2400,f14842])).
% 21.33/4.48 fof(f14863,plain,(
% 21.33/4.48 ![X0]: (addition(multiplication(X0,X0),star(X0))=star(X0))),
% 21.33/4.48 inference(forward_demodulation,[status(thm)],[f10553,f14862])).
% 21.33/4.48 fof(f14886,plain,(
% 21.33/4.48 ![X0]: (leq(multiplication(X0,X0),star(X0)))),
% 21.33/4.48 inference(resolution,[status(thm)],[f14863,f33])).
% 21.33/4.48 fof(f15074,plain,(
% 21.33/4.48 $false),
% 21.33/4.48 inference(backward_subsumption_resolution,[status(thm)],[f40,f14886])).
% 21.33/4.48 % SZS output end CNFRefutation for theBenchmark.p
% 21.33/4.49 % Elapsed time: 4.017256 seconds
% 21.33/4.49 % CPU time: 30.937452 seconds
% 21.33/4.49 % Total memory used: 225.106 MB
% 21.33/4.49 % Net memory used: 218.842 MB
%------------------------------------------------------------------------------