%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : KLE151+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n010.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 12:58:25 PM UTC 2026
% Result : Theorem 0.22s 5.74s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : KLE151+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/5.47 % Computer : n010.cluster.edu
% 0.17/5.47 % Model : x86_64 x86_64
% 0.17/5.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/5.47 % Memory : 8046.5625MB
% 0.17/5.47 % OS : Linux 6.8.0-71-generic
% 0.17/5.47 % CPULimit : 300
% 0.17/5.47 % WCLimit : 300
% 0.17/5.47 % DateTime : Sun Sep 20 22:47:01 UTC 2026
% 0.17/5.48 % CPUTime :
% 0.17/5.49 % Drodi V4.1.1
% 0.22/5.74 % Refutation found
% 0.22/5.74 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.22/5.74 % SZS output start CNFRefutation for theBenchmark
% 0.22/5.74 fof(f1,axiom,(
% 0.22/5.74 (! [A,B] : addition(A,B) = addition(B,A) )),
% 0.22/5.74 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.22/5.74 fof(f2,axiom,(
% 0.22/5.74 (! [C,B,A] : addition(A,addition(B,C)) = addition(addition(A,B),C) )),
% 0.22/5.74 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.22/5.74 fof(f4,axiom,(
% 0.22/5.74 (! [A] : addition(A,A) = A )),
% 0.22/5.74 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.22/5.74 fof(f5,axiom,(
% 0.22/5.74 (! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C) )),
% 0.22/5.74 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.22/5.74 fof(f6,axiom,(
% 0.22/5.74 (! [A] : multiplication(A,one) = A )),
% 0.22/5.74 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.22/5.74 fof(f7,axiom,(
% 0.22/5.74 (! [A] : multiplication(one,A) = A )),
% 0.22/5.74 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.22/5.74 fof(f8,axiom,(
% 0.22/5.74 (! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) )),
% 0.22/5.74 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.22/5.74 fof(f9,axiom,(
% 0.22/5.74 (! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) )),
% 0.22/5.74 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.22/5.74 fof(f15,axiom,(
% 0.22/5.74 (! [A] : strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one) )),
% 0.22/5.74 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.22/5.74 fof(f16,axiom,(
% 0.22/5.74 (! [A,B,C] :( leq(C,addition(multiplication(A,C),B))=> leq(C,multiplication(strong_iteration(A),B)) ) )),
% 0.22/5.74 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.22/5.74 fof(f18,axiom,(
% 0.22/5.74 (! [A,B] :( leq(A,B)<=> addition(A,B) = B ) )),
% 0.22/5.74 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.22/5.74 fof(f19,conjecture,(
% 0.22/5.74 (! [X0,X1] : leq(multiplication(X0,strong_iteration(multiplication(X1,X0))),multiplication(strong_iteration(multiplication(X0,X1)),X0)) )),
% 0.22/5.74 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.22/5.74 fof(f20,negated_conjecture,(
% 0.22/5.74 ~((! [X0,X1] : leq(multiplication(X0,strong_iteration(multiplication(X1,X0))),multiplication(strong_iteration(multiplication(X0,X1)),X0)) ))),
% 0.22/5.74 inference(negated_conjecture,[status(cth)],[f19])).
% 0.22/5.74 fof(f21,plain,(
% 0.22/5.74 ![X0,X1]: (addition(X0,X1)=addition(X1,X0))),
% 0.22/5.74 inference(cnf_transformation,[status(thm)],[f1])).
% 0.22/5.74 fof(f22,plain,(
% 0.22/5.74 ![X0,X1,X2]: (addition(X0,addition(X1,X2))=addition(addition(X0,X1),X2))),
% 0.22/5.74 inference(cnf_transformation,[status(thm)],[f2])).
% 0.22/5.74 fof(f24,plain,(
% 0.22/5.74 ![X0]: (addition(X0,X0)=X0)),
% 0.22/5.74 inference(cnf_transformation,[status(thm)],[f4])).
% 0.22/5.74 fof(f25,plain,(
% 0.22/5.74 ![X0,X1,X2]: (multiplication(X0,multiplication(X1,X2))=multiplication(multiplication(X0,X1),X2))),
% 0.22/5.74 inference(cnf_transformation,[status(thm)],[f5])).
% 0.22/5.74 fof(f26,plain,(
% 0.22/5.74 ![X0]: (multiplication(X0,one)=X0)),
% 0.22/5.74 inference(cnf_transformation,[status(thm)],[f6])).
% 0.22/5.74 fof(f27,plain,(
% 0.22/5.74 ![X0]: (multiplication(one,X0)=X0)),
% 0.22/5.74 inference(cnf_transformation,[status(thm)],[f7])).
% 0.22/5.74 fof(f28,plain,(
% 0.22/5.74 ![X0,X1,X2]: (multiplication(X0,addition(X1,X2))=addition(multiplication(X0,X1),multiplication(X0,X2)))),
% 0.22/5.74 inference(cnf_transformation,[status(thm)],[f8])).
% 0.22/5.74 fof(f29,plain,(
% 0.22/5.74 ![X0,X1,X2]: (multiplication(addition(X0,X1),X2)=addition(multiplication(X0,X2),multiplication(X1,X2)))),
% 0.22/5.74 inference(cnf_transformation,[status(thm)],[f9])).
% 0.22/5.74 fof(f37,plain,(
% 0.22/5.74 ![X0]: (strong_iteration(X0)=addition(multiplication(X0,strong_iteration(X0)),one))),
% 0.22/5.74 inference(cnf_transformation,[status(thm)],[f15])).
% 0.22/5.74 fof(f38,plain,(
% 0.22/5.74 ![A,B,C]: (~leq(C,addition(multiplication(A,C),B))|leq(C,multiplication(strong_iteration(A),B)))),
% 0.22/5.74 inference(pre_NNF_transformation,[status(thm)],[f16])).
% 0.22/5.74 fof(f39,plain,(
% 0.22/5.74 ![X0,X1,X2]: (~leq(X0,addition(multiplication(X1,X0),X2))|leq(X0,multiplication(strong_iteration(X1),X2)))),
% 0.22/5.74 inference(cnf_transformation,[status(thm)],[f38])).
% 0.22/5.74 fof(f41,plain,(
% 0.22/5.74 ![A,B]: ((~leq(A,B)|addition(A,B)=B)&(leq(A,B)|~addition(A,B)=B))),
% 0.22/5.74 inference(NNF_transformation,[status(thm)],[f18])).
% 0.22/5.74 fof(f42,plain,(
% 0.22/5.74 (![A,B]: (~leq(A,B)|addition(A,B)=B))&(![A,B]: (leq(A,B)|~addition(A,B)=B))),
% 0.22/5.74 inference(miniscoping,[status(thm)],[f41])).
% 0.22/5.74 fof(f44,plain,(
% 0.22/5.74 ![X0,X1]: (leq(X0,X1)|~addition(X0,X1)=X1)),
% 0.22/5.74 inference(cnf_transformation,[status(thm)],[f42])).
% 0.22/5.74 fof(f45,plain,(
% 0.22/5.74 (?[X0,X1]: ~leq(multiplication(X0,strong_iteration(multiplication(X1,X0))),multiplication(strong_iteration(multiplication(X0,X1)),X0)))),
% 0.22/5.74 inference(pre_NNF_transformation,[status(thm)],[f20])).
% 0.22/5.74 fof(f46,plain,(
% 0.22/5.74 ~leq(multiplication(sK0_skl,strong_iteration(multiplication(sK1_skl,sK0_skl))),multiplication(strong_iteration(multiplication(sK0_skl,sK1_skl)),sK0_skl))),
% 0.22/5.74 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(X0,sK0_skl),skolemize(X1,sK1_skl)],[f45])).
% 0.22/5.74 fof(f47,plain,(
% 0.22/5.74 ~leq(multiplication(sK0_skl,strong_iteration(multiplication(sK1_skl,sK0_skl))),multiplication(strong_iteration(multiplication(sK0_skl,sK1_skl)),sK0_skl))),
% 0.22/5.74 inference(cnf_transformation,[status(thm)],[f46])).
% 0.22/5.74 fof(f48,plain,(
% 0.22/5.74 ![X0]: (strong_iteration(X0)=addition(one,multiplication(X0,strong_iteration(X0))))),
% 0.22/5.74 inference(forward_demodulation,[status(thm)],[f21,f37])).
% 0.22/5.74 fof(f54,plain,(
% 0.22/5.74 ![X0,X1,X2]: (~addition(X0,addition(multiplication(X1,X0),X2))=addition(multiplication(X1,X0),X2)|leq(X0,multiplication(strong_iteration(X1),X2)))),
% 0.22/5.74 inference(resolution,[status(thm)],[f44,f39])).
% 0.22/5.74 fof(f60,plain,(
% 0.22/5.74 ~addition(multiplication(sK0_skl,strong_iteration(multiplication(sK1_skl,sK0_skl))),addition(multiplication(multiplication(sK0_skl,sK1_skl),multiplication(sK0_skl,strong_iteration(multiplication(sK1_skl,sK0_skl)))),sK0_skl))=addition(multiplication(multiplication(sK0_skl,sK1_skl),multiplication(sK0_skl,strong_iteration(multiplication(sK1_skl,sK0_skl)))),sK0_skl)),
% 0.22/5.74 inference(resolution,[status(thm)],[f54,f47])).
% 0.22/5.74 fof(f62,plain,(
% 0.22/5.74 ~addition(multiplication(sK0_skl,strong_iteration(multiplication(sK1_skl,sK0_skl))),addition(sK0_skl,multiplication(multiplication(sK0_skl,sK1_skl),multiplication(sK0_skl,strong_iteration(multiplication(sK1_skl,sK0_skl))))))=addition(multiplication(multiplication(sK0_skl,sK1_skl),multiplication(sK0_skl,strong_iteration(multiplication(sK1_skl,sK0_skl)))),sK0_skl)),
% 0.22/5.74 inference(forward_demodulation,[status(thm)],[f21,f60])).
% 0.22/5.74 fof(f63,plain,(
% 0.22/5.74 ~addition(multiplication(sK0_skl,strong_iteration(multiplication(sK1_skl,sK0_skl))),addition(sK0_skl,multiplication(sK0_skl,multiplication(sK1_skl,multiplication(sK0_skl,strong_iteration(multiplication(sK1_skl,sK0_skl)))))))=addition(multiplication(multiplication(sK0_skl,sK1_skl),multiplication(sK0_skl,strong_iteration(multiplication(sK1_skl,sK0_skl)))),sK0_skl)),
% 0.22/5.74 inference(forward_demodulation,[status(thm)],[f25,f62])).
% 0.22/5.74 fof(f64,plain,(
% 0.22/5.74 ~addition(multiplication(sK0_skl,strong_iteration(multiplication(sK1_skl,sK0_skl))),addition(sK0_skl,multiplication(sK0_skl,multiplication(sK1_skl,multiplication(sK0_skl,strong_iteration(multiplication(sK1_skl,sK0_skl)))))))=addition(sK0_skl,multiplication(multiplication(sK0_skl,sK1_skl),multiplication(sK0_skl,strong_iteration(multiplication(sK1_skl,sK0_skl)))))),
% 0.22/5.74 inference(forward_demodulation,[status(thm)],[f21,f63])).
% 0.22/5.74 fof(f65,plain,(
% 0.22/5.74 ~addition(multiplication(sK0_skl,strong_iteration(multiplication(sK1_skl,sK0_skl))),addition(sK0_skl,multiplication(sK0_skl,multiplication(sK1_skl,multiplication(sK0_skl,strong_iteration(multiplication(sK1_skl,sK0_skl)))))))=addition(sK0_skl,multiplication(sK0_skl,multiplication(sK1_skl,multiplication(sK0_skl,strong_iteration(multiplication(sK1_skl,sK0_skl))))))),
% 0.22/5.74 inference(forward_demodulation,[status(thm)],[f25,f64])).
% 0.22/5.74 fof(f106,plain,(
% 0.22/5.74 ![X0,X1,X2]: (addition(X0,addition(X1,X2))=addition(X2,addition(X0,X1)))),
% 0.22/5.74 inference(paramodulation,[status(thm)],[f21,f22])).
% 0.22/5.74 fof(f113,plain,(
% 0.22/5.74 ![X0,X1]: (addition(X0,addition(X0,X1))=addition(X0,X1))),
% 0.22/5.74 inference(paramodulation,[status(thm)],[f24,f22])).
% 0.22/5.74 fof(f118,plain,(
% 0.22/5.74 ~addition(sK0_skl,addition(multiplication(sK0_skl,multiplication(sK1_skl,multiplication(sK0_skl,strong_iteration(multiplication(sK1_skl,sK0_skl))))),multiplication(sK0_skl,strong_iteration(multiplication(sK1_skl,sK0_skl)))))=addition(sK0_skl,multiplication(sK0_skl,multiplication(sK1_skl,multiplication(sK0_skl,strong_iteration(multiplication(sK1_skl,sK0_skl))))))),
% 0.22/5.74 inference(backward_demodulation,[status(thm)],[f106,f65])).
% 0.22/5.74 fof(f121,plain,(
% 0.22/5.74 ~addition(sK0_skl,addition(multiplication(sK0_skl,strong_iteration(multiplication(sK1_skl,sK0_skl))),multiplication(sK0_skl,multiplication(sK1_skl,multiplication(sK0_skl,strong_iteration(multiplication(sK1_skl,sK0_skl)))))))=addition(sK0_skl,multiplication(sK0_skl,multiplication(sK1_skl,multiplication(sK0_skl,strong_iteration(multiplication(sK1_skl,sK0_skl))))))),
% 0.22/5.74 inference(forward_demodulation,[status(thm)],[f21,f118])).
% 0.22/5.74 fof(f122,plain,(
% 0.22/5.74 ~addition(sK0_skl,multiplication(sK0_skl,addition(strong_iteration(multiplication(sK1_skl,sK0_skl)),multiplication(sK1_skl,multiplication(sK0_skl,strong_iteration(multiplication(sK1_skl,sK0_skl)))))))=addition(sK0_skl,multiplication(sK0_skl,multiplication(sK1_skl,multiplication(sK0_skl,strong_iteration(multiplication(sK1_skl,sK0_skl))))))),
% 0.22/5.74 inference(forward_demodulation,[status(thm)],[f28,f121])).
% 0.22/5.74 fof(f139,plain,(
% 0.22/5.74 ![X0,X1]: (multiplication(X0,addition(one,X1))=addition(X0,multiplication(X0,X1)))),
% 0.22/5.74 inference(paramodulation,[status(thm)],[f26,f28])).
% 0.22/5.74 fof(f163,plain,(
% 0.22/5.74 ![X0,X1,X2,X3]: (multiplication(addition(multiplication(X0,X1),X2),X3)=addition(multiplication(X0,multiplication(X1,X3)),multiplication(X2,X3)))),
% 0.22/5.74 inference(paramodulation,[status(thm)],[f25,f29])).
% 0.22/5.74 fof(f226,plain,(
% 0.22/5.74 ![X0,X1,X2]: (multiplication(addition(multiplication(X0,X1),one),X2)=addition(multiplication(X0,multiplication(X1,X2)),X2))),
% 0.22/5.74 inference(paramodulation,[status(thm)],[f27,f163])).
% 0.22/5.74 fof(f245,plain,(
% 0.22/5.74 ![X0,X1,X2]: (multiplication(addition(one,multiplication(X0,X1)),X2)=addition(multiplication(X0,multiplication(X1,X2)),X2))),
% 0.22/5.74 inference(forward_demodulation,[status(thm)],[f21,f226])).
% 0.22/5.74 fof(f246,plain,(
% 0.22/5.74 ~addition(sK0_skl,multiplication(sK0_skl,multiplication(addition(one,multiplication(sK1_skl,sK0_skl)),strong_iteration(multiplication(sK1_skl,sK0_skl)))))=addition(sK0_skl,multiplication(sK0_skl,multiplication(sK1_skl,multiplication(sK0_skl,strong_iteration(multiplication(sK1_skl,sK0_skl))))))),
% 0.22/5.74 inference(backward_demodulation,[status(thm)],[f247,f122])).
% 0.22/5.74 fof(f247,plain,(
% 0.22/5.74 ![X0,X1,X2]: (multiplication(addition(one,multiplication(X0,X1)),X2)=addition(X2,multiplication(X0,multiplication(X1,X2))))),
% 0.22/5.74 inference(forward_demodulation,[status(thm)],[f21,f245])).
% 0.22/5.74 fof(f355,plain,(
% 0.22/5.74 ![X0,X1]: (addition(X0,addition(X1,X0))=addition(X0,X1))),
% 0.22/5.74 inference(paramodulation,[status(thm)],[f21,f113])).
% 0.22/5.74 fof(f554,plain,(
% 0.22/5.74 ![X0,X1]: (strong_iteration(multiplication(X0,X1))=addition(one,multiplication(X0,multiplication(X1,strong_iteration(multiplication(X0,X1))))))),
% 0.22/5.74 inference(paramodulation,[status(thm)],[f25,f48])).
% 0.22/5.74 fof(f558,plain,(
% 0.22/5.74 ![X0]: (addition(one,strong_iteration(X0))=addition(one,multiplication(X0,strong_iteration(X0))))),
% 0.22/5.74 inference(paramodulation,[status(thm)],[f48,f113])).
% 0.22/5.74 fof(f568,plain,(
% 0.22/5.74 ![X0]: (addition(one,strong_iteration(X0))=strong_iteration(X0))),
% 0.22/5.74 inference(forward_demodulation,[status(thm)],[f48,f558])).
% 0.22/5.74 fof(f1220,plain,(
% 0.22/5.74 ![X0,X1]: (multiplication(X0,strong_iteration(X1))=addition(X0,multiplication(X0,strong_iteration(X1))))),
% 0.22/5.74 inference(paramodulation,[status(thm)],[f568,f139])).
% 0.22/5.74 fof(f2123,plain,(
% 0.22/5.74 ![X0,X1,X2]: (multiplication(X0,strong_iteration(multiplication(X1,X2)))=addition(X0,multiplication(X0,multiplication(X1,multiplication(X2,strong_iteration(multiplication(X1,X2)))))))),
% 0.22/5.74 inference(paramodulation,[status(thm)],[f554,f139])).
% 0.22/5.74 fof(f2128,plain,(
% 0.22/5.74 ![X0,X1]: (addition(multiplication(X0,multiplication(X1,strong_iteration(multiplication(X0,X1)))),strong_iteration(multiplication(X0,X1)))=addition(multiplication(X0,multiplication(X1,strong_iteration(multiplication(X0,X1)))),one))),
% 0.22/5.74 inference(paramodulation,[status(thm)],[f554,f355])).
% 0.22/5.74 fof(f2155,plain,(
% 0.22/5.74 ~addition(sK0_skl,multiplication(sK0_skl,multiplication(addition(one,multiplication(sK1_skl,sK0_skl)),strong_iteration(multiplication(sK1_skl,sK0_skl)))))=multiplication(sK0_skl,strong_iteration(multiplication(sK1_skl,sK0_skl)))),
% 0.22/5.74 inference(backward_demodulation,[status(thm)],[f2123,f246])).
% 0.22/5.75 fof(f2159,plain,(
% 0.22/5.75 ![X0,X1]: (addition(strong_iteration(multiplication(X0,X1)),multiplication(X0,multiplication(X1,strong_iteration(multiplication(X0,X1)))))=addition(multiplication(X0,multiplication(X1,strong_iteration(multiplication(X0,X1)))),one))),
% 0.22/5.75 inference(forward_demodulation,[status(thm)],[f21,f2128])).
% 0.22/5.75 fof(f2160,plain,(
% 0.22/5.75 ![X0,X1]: (multiplication(addition(one,multiplication(X0,X1)),strong_iteration(multiplication(X0,X1)))=addition(multiplication(X0,multiplication(X1,strong_iteration(multiplication(X0,X1)))),one))),
% 0.22/5.75 inference(forward_demodulation,[status(thm)],[f247,f2159])).
% 0.22/5.75 fof(f2161,plain,(
% 0.22/5.75 ![X0,X1]: (multiplication(addition(one,multiplication(X0,X1)),strong_iteration(multiplication(X0,X1)))=addition(one,multiplication(X0,multiplication(X1,strong_iteration(multiplication(X0,X1))))))),
% 0.22/5.75 inference(forward_demodulation,[status(thm)],[f21,f2160])).
% 0.22/5.75 fof(f2162,plain,(
% 0.22/5.75 ![X0,X1]: (multiplication(addition(one,multiplication(X0,X1)),strong_iteration(multiplication(X0,X1)))=strong_iteration(multiplication(X0,X1)))),
% 0.22/5.75 inference(forward_demodulation,[status(thm)],[f554,f2161])).
% 0.22/5.75 fof(f2164,plain,(
% 0.22/5.75 ~addition(sK0_skl,multiplication(sK0_skl,strong_iteration(multiplication(sK1_skl,sK0_skl))))=multiplication(sK0_skl,strong_iteration(multiplication(sK1_skl,sK0_skl)))),
% 0.22/5.75 inference(forward_demodulation,[status(thm)],[f2162,f2155])).
% 0.22/5.75 fof(f2165,plain,(
% 0.22/5.75 ~multiplication(sK0_skl,strong_iteration(multiplication(sK1_skl,sK0_skl)))=multiplication(sK0_skl,strong_iteration(multiplication(sK1_skl,sK0_skl)))),
% 0.22/5.75 inference(forward_demodulation,[status(thm)],[f1220,f2164])).
% 0.22/5.75 fof(f2166,plain,(
% 0.22/5.75 $false),
% 0.22/5.75 inference(trivial_equality_resolution,[status(thm)],[f2165])).
% 0.22/5.75 % SZS output end CNFRefutation for theBenchmark.p
% 0.22/5.80 % Elapsed time: 0.304547 seconds
% 0.22/5.80 % CPU time: 2.007935 seconds
% 0.22/5.80 % Total memory used: 89.078 MB
% 0.22/5.80 % Net memory used: 88.173 MB
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