%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : KLE044+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n007.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 12:58:15 PM UTC 2026
% Result : Theorem 134.88s 17.45s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE044+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n007.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sun Sep 20 22:38:35 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.13/0.36 % Drodi V4.1.1
% 134.88/17.45 % Refutation found
% 134.88/17.45 % SZS status Theorem for theBenchmark: Theorem is valid
% 134.88/17.45 % SZS output start CNFRefutation for theBenchmark
% 134.88/17.45 fof(f1,axiom,(
% 134.88/17.45 (! [A,B] : addition(A,B) = addition(B,A) )),
% 134.88/17.45 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 134.88/17.45 fof(f2,axiom,(
% 134.88/17.45 (! [C,B,A] : addition(A,addition(B,C)) = addition(addition(A,B),C) )),
% 134.88/17.45 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 134.88/17.45 fof(f4,axiom,(
% 134.88/17.45 (! [A] : addition(A,A) = A )),
% 134.88/17.45 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 134.88/17.45 fof(f5,axiom,(
% 134.88/17.45 (! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C) )),
% 134.88/17.45 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 134.88/17.45 fof(f6,axiom,(
% 134.88/17.45 (! [A] : multiplication(A,one) = A )),
% 134.88/17.45 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 134.88/17.45 fof(f7,axiom,(
% 134.88/17.45 (! [A] : multiplication(one,A) = A )),
% 134.88/17.45 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 134.88/17.45 fof(f9,axiom,(
% 134.88/17.45 (! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) )),
% 134.88/17.45 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 134.88/17.45 fof(f12,axiom,(
% 134.88/17.45 (! [A,B] :( leq(A,B)<=> addition(A,B) = B ) )),
% 134.88/17.45 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 134.88/17.45 fof(f13,axiom,(
% 134.88/17.45 (! [A] : leq(addition(one,multiplication(A,star(A))),star(A)) )),
% 134.88/17.45 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 134.88/17.45 fof(f15,axiom,(
% 134.88/17.45 (! [A,B,C] :( leq(addition(multiplication(A,B),C),B)=> leq(multiplication(star(A),C),B) ) )),
% 134.88/17.45 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 134.88/17.45 fof(f17,conjecture,(
% 134.88/17.45 (! [X0] :( leq(star(addition(one,X0)),star(X0))& leq(star(X0),star(addition(one,X0))) ) )),
% 134.88/17.45 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 134.88/17.45 fof(f18,negated_conjecture,(
% 134.88/17.45 ~((! [X0] :( leq(star(addition(one,X0)),star(X0))& leq(star(X0),star(addition(one,X0))) ) ))),
% 134.88/17.45 inference(negated_conjecture,[status(cth)],[f17])).
% 134.88/17.45 fof(f19,plain,(
% 134.88/17.45 ![X0,X1]: (addition(X0,X1)=addition(X1,X0))),
% 134.88/17.45 inference(cnf_transformation,[status(thm)],[f1])).
% 134.88/17.45 fof(f20,plain,(
% 134.88/17.45 ![X0,X1,X2]: (addition(X0,addition(X1,X2))=addition(addition(X0,X1),X2))),
% 134.88/17.45 inference(cnf_transformation,[status(thm)],[f2])).
% 134.88/17.45 fof(f22,plain,(
% 134.88/17.45 ![X0]: (addition(X0,X0)=X0)),
% 134.88/17.45 inference(cnf_transformation,[status(thm)],[f4])).
% 134.88/17.45 fof(f23,plain,(
% 134.88/17.45 ![X0,X1,X2]: (multiplication(X0,multiplication(X1,X2))=multiplication(multiplication(X0,X1),X2))),
% 134.88/17.45 inference(cnf_transformation,[status(thm)],[f5])).
% 134.88/17.45 fof(f24,plain,(
% 134.88/17.45 ![X0]: (multiplication(X0,one)=X0)),
% 134.88/17.45 inference(cnf_transformation,[status(thm)],[f6])).
% 134.88/17.45 fof(f25,plain,(
% 134.88/17.45 ![X0]: (multiplication(one,X0)=X0)),
% 134.88/17.45 inference(cnf_transformation,[status(thm)],[f7])).
% 134.88/17.45 fof(f27,plain,(
% 134.88/17.45 ![X0,X1,X2]: (multiplication(addition(X0,X1),X2)=addition(multiplication(X0,X2),multiplication(X1,X2)))),
% 134.88/17.45 inference(cnf_transformation,[status(thm)],[f9])).
% 134.88/17.45 fof(f30,plain,(
% 134.88/17.45 ![A,B]: ((~leq(A,B)|addition(A,B)=B)&(leq(A,B)|~addition(A,B)=B))),
% 134.88/17.45 inference(NNF_transformation,[status(thm)],[f12])).
% 134.88/17.45 fof(f31,plain,(
% 134.88/17.45 (![A,B]: (~leq(A,B)|addition(A,B)=B))&(![A,B]: (leq(A,B)|~addition(A,B)=B))),
% 134.88/17.45 inference(miniscoping,[status(thm)],[f30])).
% 134.88/17.45 fof(f32,plain,(
% 134.88/17.45 ![X0,X1]: (~leq(X0,X1)|addition(X0,X1)=X1)),
% 134.88/17.45 inference(cnf_transformation,[status(thm)],[f31])).
% 134.88/17.45 fof(f33,plain,(
% 134.88/17.45 ![X0,X1]: (leq(X0,X1)|~addition(X0,X1)=X1)),
% 134.88/17.45 inference(cnf_transformation,[status(thm)],[f31])).
% 134.88/17.45 fof(f34,plain,(
% 134.88/17.45 ![X0]: (leq(addition(one,multiplication(X0,star(X0))),star(X0)))),
% 134.88/17.45 inference(cnf_transformation,[status(thm)],[f13])).
% 134.88/17.45 fof(f36,plain,(
% 134.88/17.45 ![A,B,C]: (~leq(addition(multiplication(A,B),C),B)|leq(multiplication(star(A),C),B))),
% 134.88/17.45 inference(pre_NNF_transformation,[status(thm)],[f15])).
% 134.88/17.45 fof(f37,plain,(
% 134.88/17.45 ![X0,X1,X2]: (~leq(addition(multiplication(X0,X1),X2),X1)|leq(multiplication(star(X0),X2),X1))),
% 134.88/17.45 inference(cnf_transformation,[status(thm)],[f36])).
% 134.88/17.45 fof(f40,plain,(
% 134.88/17.45 (?[X0]: (~leq(star(addition(one,X0)),star(X0))|~leq(star(X0),star(addition(one,X0)))))),
% 134.88/17.45 inference(pre_NNF_transformation,[status(thm)],[f18])).
% 134.88/17.45 fof(f41,plain,(
% 134.88/17.45 (?[X0]: ~leq(star(addition(one,X0)),star(X0)))|(?[X0]: ~leq(star(X0),star(addition(one,X0))))),
% 134.88/17.45 inference(miniscoping,[status(thm)],[f40])).
% 134.88/17.45 fof(f42,plain,(
% 134.88/17.45 ~leq(star(addition(one,sK0_skl)),star(sK0_skl))|~leq(star(sK1_skl),star(addition(one,sK1_skl)))),
% 134.88/17.45 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(X0,sK0_skl),skolemize(X0,sK1_skl)],[f41])).
% 134.88/17.45 fof(f43,plain,(
% 134.88/17.45 ~leq(star(addition(one,sK0_skl)),star(sK0_skl))|~leq(star(sK1_skl),star(addition(one,sK1_skl)))),
% 134.88/17.45 inference(cnf_transformation,[status(thm)],[f42])).
% 134.88/17.45 fof(f52,plain,(
% 134.88/17.45 ![X0,X1,X2]: (addition(X0,addition(X1,X2))=addition(X2,addition(X0,X1)))),
% 134.88/17.45 inference(paramodulation,[status(thm)],[f19,f20])).
% 134.88/17.45 fof(f58,plain,(
% 134.88/17.45 ![X0,X1]: (addition(X0,addition(X0,X1))=addition(X0,X1))),
% 134.88/17.45 inference(paramodulation,[status(thm)],[f22,f20])).
% 134.88/17.45 fof(f67,plain,(
% 134.88/17.45 ![X0,X1]: (addition(X0,addition(X1,X0))=addition(X0,X1))),
% 134.88/17.45 inference(paramodulation,[status(thm)],[f19,f58])).
% 134.88/17.45 fof(f123,plain,(
% 134.88/17.45 ![X0,X1]: (addition(X0,X1)=addition(X1,addition(X0,X1)))),
% 134.88/17.45 inference(paramodulation,[status(thm)],[f22,f52])).
% 134.88/17.45 fof(f139,plain,(
% 134.88/17.45 ![X0,X1]: (addition(X0,addition(X0,X1))=addition(X1,X0))),
% 134.88/17.45 inference(paramodulation,[status(thm)],[f22,f52])).
% 134.88/17.45 fof(f276,plain,(
% 134.88/17.45 ![X0,X1,X2]: (addition(X0,addition(addition(X0,X1),X2))=addition(addition(X1,X0),X2))),
% 134.88/17.45 inference(paramodulation,[status(thm)],[f139,f20])).
% 134.88/17.45 fof(f309,plain,(
% 134.88/17.45 ![X0,X1,X2]: (addition(X0,addition(X0,addition(X1,X2)))=addition(addition(X1,X0),X2))),
% 134.88/17.45 inference(forward_demodulation,[status(thm)],[f20,f276])).
% 134.88/17.45 fof(f310,plain,(
% 134.88/17.45 ![X0,X1,X2]: (addition(addition(X0,X1),X2)=addition(addition(X0,X2),X1))),
% 134.88/17.45 inference(forward_demodulation,[status(thm)],[f139,f309])).
% 134.88/17.45 fof(f311,plain,(
% 134.88/17.45 ![X0,X1,X2]: (addition(X0,addition(X1,X2))=addition(addition(X0,X2),X1))),
% 134.88/17.45 inference(forward_demodulation,[status(thm)],[f20,f310])).
% 134.88/17.45 fof(f343,plain,(
% 134.88/17.45 ![X0,X1]: (multiplication(addition(one,X0),X1)=addition(X1,multiplication(X0,X1)))),
% 134.88/17.45 inference(paramodulation,[status(thm)],[f25,f27])).
% 134.88/17.45 fof(f2000,plain,(
% 134.88/17.45 ![X0]: (addition(addition(one,multiplication(X0,star(X0))),star(X0))=star(X0))),
% 134.88/17.45 inference(resolution,[status(thm)],[f34,f32])).
% 134.88/17.45 fof(f2004,plain,(
% 134.88/17.45 ![X0]: (addition(one,addition(star(X0),multiplication(X0,star(X0))))=star(X0))),
% 134.88/17.45 inference(forward_demodulation,[status(thm)],[f311,f2000])).
% 134.88/17.45 fof(f2049,plain,(
% 134.88/17.45 ![X0,X1,X2]: (~leq(addition(X0,multiplication(X1,X2)),X2)|leq(multiplication(star(X1),X0),X2))),
% 134.88/17.45 inference(paramodulation,[status(thm)],[f19,f37])).
% 134.88/17.45 fof(f2365,plain,(
% 134.88/17.45 ![X0,X1]: (multiplication(addition(one,X0),X1)=addition(X1,multiplication(addition(one,X0),X1)))),
% 134.88/17.45 inference(paramodulation,[status(thm)],[f58,f343])).
% 134.88/17.45 fof(f2366,plain,(
% 134.88/17.45 ![X0,X1]: (multiplication(addition(X0,one),X1)=addition(X1,multiplication(X0,X1)))),
% 134.88/17.45 inference(paramodulation,[status(thm)],[f19,f343])).
% 134.88/17.45 fof(f2415,plain,(
% 134.88/17.45 ![X0,X1]: (addition(multiplication(X0,X1),multiplication(addition(one,X0),X1))=addition(multiplication(X0,X1),X1))),
% 134.88/17.45 inference(paramodulation,[status(thm)],[f343,f67])).
% 134.88/17.45 fof(f2416,plain,(
% 134.88/17.45 ![X0,X1]: (addition(X0,multiplication(addition(one,X1),X0))=addition(X0,multiplication(X1,X0)))),
% 134.88/17.45 inference(paramodulation,[status(thm)],[f343,f58])).
% 134.88/17.45 fof(f2451,plain,(
% 134.88/17.45 ![X0,X1]: (multiplication(addition(X0,addition(one,X0)),X1)=addition(multiplication(X0,X1),X1))),
% 134.88/17.45 inference(forward_demodulation,[status(thm)],[f27,f2415])).
% 134.88/17.45 fof(f2452,plain,(
% 134.88/17.45 ![X0,X1]: (multiplication(addition(one,X0),X1)=addition(multiplication(X0,X1),X1))),
% 134.88/17.45 inference(forward_demodulation,[status(thm)],[f123,f2451])).
% 134.88/17.45 fof(f3504,plain,(
% 134.88/17.45 ![X0,X1,X2]: (multiplication(addition(X0,one),multiplication(X1,X2))=multiplication(addition(X1,multiplication(X0,X1)),X2))),
% 134.88/17.45 inference(paramodulation,[status(thm)],[f2366,f23])).
% 134.88/17.45 fof(f4737,plain,(
% 134.88/17.45 ![X0,X1,X2]: (leq(multiplication(star(X0),X1),X2)|~addition(addition(X1,multiplication(X0,X2)),X2)=X2)),
% 134.88/17.45 inference(resolution,[status(thm)],[f2049,f33])).
% 134.88/17.45 fof(f4780,plain,(
% 134.88/17.45 ![X0,X1,X2]: (leq(multiplication(star(X0),X1),X2)|~addition(X1,addition(X2,multiplication(X0,X2)))=X2)),
% 134.88/17.45 inference(forward_demodulation,[status(thm)],[f311,f4737])).
% 134.88/17.45 fof(f6412,plain,(
% 134.88/17.45 ![X0]: (addition(one,addition(star(X0),multiplication(X0,star(X0))))=addition(addition(star(X0),multiplication(X0,star(X0))),star(X0)))),
% 134.88/17.45 inference(paramodulation,[status(thm)],[f2004,f123])).
% 134.88/17.45 fof(f6416,plain,(
% 134.88/17.45 ![X0]: (addition(one,star(X0))=addition(one,addition(star(X0),multiplication(X0,star(X0)))))),
% 134.88/17.45 inference(paramodulation,[status(thm)],[f2004,f58])).
% 134.88/17.45 fof(f6445,plain,(
% 134.88/17.45 ![X0]: (star(X0)=addition(addition(star(X0),multiplication(X0,star(X0))),star(X0)))),
% 134.88/17.45 inference(forward_demodulation,[status(thm)],[f2004,f6412])).
% 134.88/17.45 fof(f6446,plain,(
% 134.88/17.45 ![X0]: (star(X0)=addition(star(X0),addition(star(X0),multiplication(X0,star(X0)))))),
% 134.88/17.45 inference(forward_demodulation,[status(thm)],[f311,f6445])).
% 134.88/17.45 fof(f6447,plain,(
% 134.88/17.45 ![X0]: (star(X0)=addition(multiplication(X0,star(X0)),star(X0)))),
% 134.88/17.45 inference(forward_demodulation,[status(thm)],[f139,f6446])).
% 134.88/17.45 fof(f6458,plain,(
% 134.88/17.45 ![X0]: (addition(one,star(X0))=star(X0))),
% 134.88/17.45 inference(forward_demodulation,[status(thm)],[f2004,f6416])).
% 134.88/17.45 fof(f6487,plain,(
% 134.88/17.45 ![X0,X1]: (addition(one,addition(star(X0),X1))=addition(star(X0),X1))),
% 134.88/17.45 inference(paramodulation,[status(thm)],[f6458,f20])).
% 134.88/17.45 fof(f6607,plain,(
% 134.88/17.45 ![X0]: (star(X0)=multiplication(addition(one,X0),star(X0)))),
% 134.88/17.45 inference(paramodulation,[status(thm)],[f2452,f6447])).
% 134.88/17.45 fof(f6669,plain,(
% 134.88/17.45 ![X0]: (star(multiplication(addition(one,X0),one))=multiplication(addition(one,multiplication(X0,one)),star(multiplication(addition(one,X0),one))))),
% 134.88/17.45 inference(paramodulation,[status(thm)],[f2416,f6607])).
% 134.88/17.45 fof(f6727,plain,(
% 134.88/17.45 ![X0]: (star(addition(one,X0))=multiplication(addition(one,multiplication(X0,one)),star(multiplication(addition(one,X0),one))))),
% 134.88/17.45 inference(forward_demodulation,[status(thm)],[f24,f6669])).
% 134.88/17.45 fof(f6728,plain,(
% 134.88/17.45 ![X0]: (star(addition(one,X0))=multiplication(addition(X0,one),multiplication(one,star(multiplication(addition(one,X0),one)))))),
% 134.88/17.45 inference(forward_demodulation,[status(thm)],[f3504,f6727])).
% 134.88/17.45 fof(f6729,plain,(
% 134.88/17.45 ![X0]: (star(addition(one,X0))=multiplication(addition(X0,one),star(multiplication(addition(one,X0),one))))),
% 134.88/17.45 inference(forward_demodulation,[status(thm)],[f25,f6728])).
% 134.88/17.45 fof(f6730,plain,(
% 134.88/17.45 ![X0]: (star(addition(one,X0))=multiplication(addition(X0,one),star(addition(one,X0))))),
% 134.88/17.45 inference(forward_demodulation,[status(thm)],[f24,f6729])).
% 134.88/17.45 fof(f42358,plain,(
% 134.88/17.45 ![X0,X1]: (leq(star(X0),X1)|~addition(one,addition(X1,multiplication(X0,X1)))=X1)),
% 134.88/17.45 inference(paramodulation,[status(thm)],[f24,f4780])).
% 134.88/17.45 fof(f42427,plain,(
% 134.88/17.45 ~addition(one,addition(star(addition(one,sK1_skl)),multiplication(sK1_skl,star(addition(one,sK1_skl)))))=star(addition(one,sK1_skl))|~leq(star(addition(one,sK0_skl)),star(sK0_skl))),
% 134.88/17.45 inference(resolution,[status(thm)],[f42358,f43])).
% 134.88/17.45 fof(f42454,plain,(
% 134.88/17.45 ~addition(star(addition(one,sK1_skl)),multiplication(sK1_skl,star(addition(one,sK1_skl))))=star(addition(one,sK1_skl))|~leq(star(addition(one,sK0_skl)),star(sK0_skl))),
% 134.88/17.45 inference(forward_demodulation,[status(thm)],[f6487,f42427])).
% 134.88/17.45 fof(f48707,plain,(
% 134.88/17.45 ~addition(star(addition(one,sK1_skl)),multiplication(sK1_skl,star(addition(one,sK1_skl))))=star(addition(one,sK1_skl))|~addition(one,addition(star(sK0_skl),multiplication(addition(one,sK0_skl),star(sK0_skl))))=star(sK0_skl)),
% 134.88/17.45 inference(resolution,[status(thm)],[f42454,f42358])).
% 134.88/17.45 fof(f48709,plain,(
% 134.88/17.45 ~addition(star(addition(one,sK1_skl)),multiplication(sK1_skl,star(addition(one,sK1_skl))))=star(addition(one,sK1_skl))|~addition(star(sK0_skl),multiplication(addition(one,sK0_skl),star(sK0_skl)))=star(sK0_skl)),
% 134.88/17.45 inference(forward_demodulation,[status(thm)],[f6487,f48707])).
% 134.88/17.45 fof(f48710,plain,(
% 134.88/17.45 ~addition(star(addition(one,sK1_skl)),multiplication(sK1_skl,star(addition(one,sK1_skl))))=star(addition(one,sK1_skl))|~multiplication(addition(one,sK0_skl),star(sK0_skl))=star(sK0_skl)),
% 134.88/17.45 inference(forward_demodulation,[status(thm)],[f2365,f48709])).
% 134.88/17.45 fof(f48711,plain,(
% 134.88/17.45 ~addition(star(addition(one,sK1_skl)),multiplication(sK1_skl,star(addition(one,sK1_skl))))=star(addition(one,sK1_skl))|~star(sK0_skl)=star(sK0_skl)),
% 134.88/17.45 inference(forward_demodulation,[status(thm)],[f6607,f48710])).
% 134.88/17.45 fof(f48712,plain,(
% 134.88/17.45 ~addition(star(addition(one,sK1_skl)),multiplication(sK1_skl,star(addition(one,sK1_skl))))=star(addition(one,sK1_skl))),
% 105.42/17.54 inference(trivial_equality_resolution,[status(thm)],[f48711])).
% 105.42/17.54 fof(f48715,plain,(
% 105.42/17.54 ~multiplication(addition(sK1_skl,one),star(addition(one,sK1_skl)))=star(addition(one,sK1_skl))),
% 105.42/17.54 inference(paramodulation,[status(thm)],[f2366,f48712])).
% 105.42/17.54 fof(f48717,plain,(
% 105.42/17.54 ~star(addition(one,sK1_skl))=star(addition(one,sK1_skl))),
% 105.42/17.54 inference(forward_demodulation,[status(thm)],[f6730,f48715])).
% 105.42/17.54 fof(f48718,plain,(
% 105.42/17.54 $false),
% 105.42/17.54 inference(trivial_equality_resolution,[status(thm)],[f48717])).
% 105.42/17.54 % SZS output end CNFRefutation for theBenchmark.p
% 105.42/17.57 % Elapsed time: 17.206669 seconds
% 105.42/17.57 % CPU time: 136.009177 seconds
% 105.42/17.57 % Total memory used: 702.528 MB
% 105.42/17.57 % Net memory used: 678.562 MB
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