%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : KLE139+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 : 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 12:58:23 PM UTC 2026
% Result : Theorem 55.55s 12.50s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE139+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
% 0.09/5.36 % Computer : n010.cluster.edu
% 0.09/5.36 % Model : x86_64 x86_64
% 0.09/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.36 % Memory : 8046.5625MB
% 0.09/5.36 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Sun Sep 20 22:46:16 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.38 % Drodi V4.1.1
% 55.55/12.50 % Refutation found
% 55.55/12.50 % SZS status Theorem for theBenchmark: Theorem is valid
% 55.55/12.50 % SZS output start CNFRefutation for theBenchmark
% 55.55/12.50 fof(f1,axiom,(
% 55.55/12.50 (! [A,B] : addition(A,B) = addition(B,A) )),
% 55.55/12.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 55.55/12.50 fof(f2,axiom,(
% 55.55/12.50 (! [C,B,A] : addition(A,addition(B,C)) = addition(addition(A,B),C) )),
% 55.55/12.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 55.55/12.50 fof(f4,axiom,(
% 55.55/12.50 (! [A] : addition(A,A) = A )),
% 55.55/12.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 55.55/12.50 fof(f5,axiom,(
% 55.55/12.50 (! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C) )),
% 55.55/12.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 55.55/12.50 fof(f9,axiom,(
% 55.55/12.50 (! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) )),
% 55.55/12.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 55.55/12.50 fof(f10,axiom,(
% 55.55/12.50 (! [A] : multiplication(zero,A) = zero )),
% 55.55/12.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 55.55/12.50 fof(f12,axiom,(
% 55.55/12.50 (! [A] : addition(one,multiplication(star(A),A)) = star(A) )),
% 55.55/12.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 55.55/12.50 fof(f17,axiom,(
% 55.55/12.50 (! [A] : strong_iteration(A) = addition(star(A),multiplication(strong_iteration(A),zero)) )),
% 55.55/12.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 55.55/12.50 fof(f18,axiom,(
% 55.55/12.50 (! [A,B] :( leq(A,B)<=> addition(A,B) = B ) )),
% 55.55/12.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 55.55/12.50 fof(f19,conjecture,(
% 55.55/12.50 (! [X0] :( leq(strong_iteration(X0),addition(multiplication(strong_iteration(X0),X0),one))& leq(addition(multiplication(strong_iteration(X0),X0),one),strong_iteration(X0)) ) )),
% 55.55/12.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 55.55/12.50 fof(f20,negated_conjecture,(
% 55.55/12.50 ~((! [X0] :( leq(strong_iteration(X0),addition(multiplication(strong_iteration(X0),X0),one))& leq(addition(multiplication(strong_iteration(X0),X0),one),strong_iteration(X0)) ) ))),
% 55.55/12.50 inference(negated_conjecture,[status(cth)],[f19])).
% 55.55/12.50 fof(f21,plain,(
% 55.55/12.50 ![X0,X1]: (addition(X0,X1)=addition(X1,X0))),
% 55.55/12.50 inference(cnf_transformation,[status(thm)],[f1])).
% 55.55/12.50 fof(f22,plain,(
% 55.55/12.50 ![X0,X1,X2]: (addition(X0,addition(X1,X2))=addition(addition(X0,X1),X2))),
% 55.55/12.50 inference(cnf_transformation,[status(thm)],[f2])).
% 55.55/12.50 fof(f24,plain,(
% 55.55/12.50 ![X0]: (addition(X0,X0)=X0)),
% 55.55/12.50 inference(cnf_transformation,[status(thm)],[f4])).
% 55.55/12.50 fof(f25,plain,(
% 55.55/12.50 ![X0,X1,X2]: (multiplication(X0,multiplication(X1,X2))=multiplication(multiplication(X0,X1),X2))),
% 55.55/12.50 inference(cnf_transformation,[status(thm)],[f5])).
% 55.55/12.50 fof(f29,plain,(
% 55.55/12.50 ![X0,X1,X2]: (multiplication(addition(X0,X1),X2)=addition(multiplication(X0,X2),multiplication(X1,X2)))),
% 55.55/12.50 inference(cnf_transformation,[status(thm)],[f9])).
% 55.55/12.50 fof(f30,plain,(
% 55.55/12.50 ![X0]: (multiplication(zero,X0)=zero)),
% 55.55/12.50 inference(cnf_transformation,[status(thm)],[f10])).
% 55.55/12.50 fof(f32,plain,(
% 55.55/12.50 ![X0]: (addition(one,multiplication(star(X0),X0))=star(X0))),
% 55.55/12.50 inference(cnf_transformation,[status(thm)],[f12])).
% 55.55/12.50 fof(f40,plain,(
% 55.55/12.50 ![X0]: (strong_iteration(X0)=addition(star(X0),multiplication(strong_iteration(X0),zero)))),
% 55.55/12.50 inference(cnf_transformation,[status(thm)],[f17])).
% 55.55/12.50 fof(f41,plain,(
% 55.55/12.50 ![A,B]: ((~leq(A,B)|addition(A,B)=B)&(leq(A,B)|~addition(A,B)=B))),
% 55.55/12.50 inference(NNF_transformation,[status(thm)],[f18])).
% 55.55/12.50 fof(f42,plain,(
% 55.55/12.50 (![A,B]: (~leq(A,B)|addition(A,B)=B))&(![A,B]: (leq(A,B)|~addition(A,B)=B))),
% 55.55/12.50 inference(miniscoping,[status(thm)],[f41])).
% 55.55/12.50 fof(f44,plain,(
% 55.55/12.50 ![X0,X1]: (leq(X0,X1)|~addition(X0,X1)=X1)),
% 55.55/12.50 inference(cnf_transformation,[status(thm)],[f42])).
% 55.55/12.50 fof(f45,plain,(
% 55.55/12.50 (?[X0]: (~leq(strong_iteration(X0),addition(multiplication(strong_iteration(X0),X0),one))|~leq(addition(multiplication(strong_iteration(X0),X0),one),strong_iteration(X0))))),
% 55.55/12.50 inference(pre_NNF_transformation,[status(thm)],[f20])).
% 55.55/12.50 fof(f46,plain,(
% 55.55/12.50 (?[X0]: ~leq(strong_iteration(X0),addition(multiplication(strong_iteration(X0),X0),one)))|(?[X0]: ~leq(addition(multiplication(strong_iteration(X0),X0),one),strong_iteration(X0)))),
% 55.55/12.50 inference(miniscoping,[status(thm)],[f45])).
% 55.55/12.50 fof(f47,plain,(
% 55.55/12.50 ~leq(strong_iteration(sK0_skl),addition(multiplication(strong_iteration(sK0_skl),sK0_skl),one))|~leq(addition(multiplication(strong_iteration(sK1_skl),sK1_skl),one),strong_iteration(sK1_skl))),
% 56.35/12.56 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(X0,sK0_skl),skolemize(X0,sK1_skl)],[f46])).
% 56.35/12.56 fof(f48,plain,(
% 56.35/12.56 ~leq(strong_iteration(sK0_skl),addition(multiplication(strong_iteration(sK0_skl),sK0_skl),one))|~leq(addition(multiplication(strong_iteration(sK1_skl),sK1_skl),one),strong_iteration(sK1_skl))),
% 56.35/12.56 inference(cnf_transformation,[status(thm)],[f47])).
% 56.35/12.56 fof(f55,plain,(
% 56.35/12.56 ~leq(strong_iteration(sK0_skl),addition(one,multiplication(strong_iteration(sK0_skl),sK0_skl)))|~leq(addition(multiplication(strong_iteration(sK1_skl),sK1_skl),one),strong_iteration(sK1_skl))),
% 56.35/12.56 inference(paramodulation,[status(thm)],[f21,f48])).
% 56.35/12.56 fof(f57,plain,(
% 56.35/12.56 ![X0]: (leq(X0,X0))),
% 56.35/12.56 inference(resolution,[status(thm)],[f44,f24])).
% 56.35/12.56 fof(f92,plain,(
% 56.35/12.56 ![X0,X1]: (addition(one,addition(multiplication(star(X0),X0),X1))=addition(star(X0),X1))),
% 56.35/12.56 inference(paramodulation,[status(thm)],[f32,f22])).
% 56.35/12.56 fof(f1805,plain,(
% 56.35/12.56 ![X0,X1]: (addition(one,multiplication(addition(star(X0),X1),X0))=addition(star(X0),multiplication(X1,X0)))),
% 56.35/12.56 inference(paramodulation,[status(thm)],[f29,f92])).
% 56.35/12.56 fof(f57364,plain,(
% 56.35/12.56 ![X0]: (addition(one,multiplication(strong_iteration(X0),X0))=addition(star(X0),multiplication(multiplication(strong_iteration(X0),zero),X0)))),
% 56.35/12.56 inference(paramodulation,[status(thm)],[f40,f1805])).
% 56.35/12.56 fof(f57571,plain,(
% 56.35/12.56 ![X0]: (addition(one,multiplication(strong_iteration(X0),X0))=addition(star(X0),multiplication(strong_iteration(X0),multiplication(zero,X0))))),
% 56.35/12.56 inference(forward_demodulation,[status(thm)],[f25,f57364])).
% 56.35/12.56 fof(f57572,plain,(
% 56.35/12.56 ![X0]: (addition(one,multiplication(strong_iteration(X0),X0))=addition(star(X0),multiplication(strong_iteration(X0),zero)))),
% 56.35/12.56 inference(forward_demodulation,[status(thm)],[f30,f57571])).
% 56.35/12.56 fof(f57573,plain,(
% 56.35/12.56 ![X0]: (addition(one,multiplication(strong_iteration(X0),X0))=strong_iteration(X0))),
% 56.35/12.56 inference(forward_demodulation,[status(thm)],[f40,f57572])).
% 56.35/12.56 fof(f73941,plain,(
% 56.35/12.56 ~leq(strong_iteration(sK0_skl),strong_iteration(sK0_skl))|~leq(addition(multiplication(strong_iteration(sK1_skl),sK1_skl),one),strong_iteration(sK1_skl))),
% 56.35/12.56 inference(backward_demodulation,[status(thm)],[f57573,f55])).
% 56.35/12.56 fof(f74108,plain,(
% 56.35/12.56 ~leq(addition(multiplication(strong_iteration(sK1_skl),sK1_skl),one),strong_iteration(sK1_skl))),
% 56.35/12.56 inference(forward_subsumption_resolution,[status(thm)],[f73941,f57])).
% 56.35/12.56 fof(f74293,plain,(
% 56.35/12.56 ~leq(addition(one,multiplication(strong_iteration(sK1_skl),sK1_skl)),strong_iteration(sK1_skl))),
% 56.35/12.56 inference(paramodulation,[status(thm)],[f21,f74108])).
% 56.35/12.56 fof(f74295,plain,(
% 56.35/12.56 ~leq(strong_iteration(sK1_skl),strong_iteration(sK1_skl))),
% 56.35/12.56 inference(forward_demodulation,[status(thm)],[f57573,f74293])).
% 56.35/12.56 fof(f74296,plain,(
% 56.35/12.56 $false),
% 56.35/12.56 inference(forward_subsumption_resolution,[status(thm)],[f74295,f57])).
% 56.35/12.56 % SZS output end CNFRefutation for theBenchmark.p
% 56.35/12.60 % Elapsed time: 7.214882 seconds
% 56.35/12.60 % CPU time: 56.923900 seconds
% 56.35/12.60 % Total memory used: 453.224 MB
% 56.35/12.60 % Net memory used: 442.337 MB
%------------------------------------------------------------------------------