%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : KLE038+1 : 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 : n026.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 12:58:14 PM UTC 2026
% Result : Theorem 0.22s 1.27s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KLE038+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/1.05 % Computer : n026.cluster.edu
% 0.18/1.05 % Model : x86_64 x86_64
% 0.18/1.05 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/1.05 % Memory : 8046.5625MB
% 0.18/1.05 % OS : Linux 6.8.0-71-generic
% 0.18/1.05 % CPULimit : 300
% 0.18/1.05 % WCLimit : 300
% 0.18/1.05 % DateTime : Sun Sep 20 22:42:52 UTC 2026
% 0.18/1.06 % CPUTime :
% 0.18/1.07 % Drodi V4.1.1
% 0.22/1.27 % Refutation found
% 0.22/1.27 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.22/1.27 % SZS output start CNFRefutation for theBenchmark
% 0.22/1.27 fof(f1,axiom,(
% 0.22/1.27 (! [A,B] : addition(A,B) = addition(B,A) )),
% 0.22/1.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.22/1.27 fof(f2,axiom,(
% 0.22/1.27 (! [C,B,A] : addition(A,addition(B,C)) = addition(addition(A,B),C) )),
% 0.22/1.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.22/1.27 fof(f4,axiom,(
% 0.22/1.27 (! [A] : addition(A,A) = A )),
% 0.22/1.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.22/1.27 fof(f6,axiom,(
% 0.22/1.27 (! [A] : multiplication(A,one) = A )),
% 0.22/1.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.22/1.27 fof(f7,axiom,(
% 0.22/1.27 (! [A] : multiplication(one,A) = A )),
% 0.22/1.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.22/1.27 fof(f8,axiom,(
% 0.22/1.27 (! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) )),
% 0.22/1.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.22/1.27 fof(f9,axiom,(
% 0.22/1.27 (! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) )),
% 0.22/1.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.22/1.27 fof(f12,axiom,(
% 0.22/1.27 (! [A,B] :( leq(A,B)<=> addition(A,B) = B ) )),
% 0.22/1.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.22/1.27 fof(f13,axiom,(
% 0.22/1.27 (! [A] : leq(addition(one,multiplication(A,star(A))),star(A)) )),
% 0.22/1.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.22/1.27 fof(f14,axiom,(
% 0.22/1.27 (! [A] : leq(addition(one,multiplication(star(A),A)),star(A)) )),
% 0.22/1.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.22/1.27 fof(f17,conjecture,(
% 0.22/1.27 (! [X0] : leq(X0,star(X0)) )),
% 0.22/1.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.22/1.27 fof(f18,negated_conjecture,(
% 0.22/1.27 ~((! [X0] : leq(X0,star(X0)) ))),
% 0.22/1.27 inference(negated_conjecture,[status(cth)],[f17])).
% 0.22/1.27 fof(f19,plain,(
% 0.22/1.27 ![X0,X1]: (addition(X0,X1)=addition(X1,X0))),
% 0.22/1.27 inference(cnf_transformation,[status(thm)],[f1])).
% 0.22/1.27 fof(f20,plain,(
% 0.22/1.27 ![X0,X1,X2]: (addition(X0,addition(X1,X2))=addition(addition(X0,X1),X2))),
% 0.22/1.27 inference(cnf_transformation,[status(thm)],[f2])).
% 0.22/1.27 fof(f22,plain,(
% 0.22/1.27 ![X0]: (addition(X0,X0)=X0)),
% 0.22/1.27 inference(cnf_transformation,[status(thm)],[f4])).
% 0.22/1.27 fof(f24,plain,(
% 0.22/1.27 ![X0]: (multiplication(X0,one)=X0)),
% 0.22/1.27 inference(cnf_transformation,[status(thm)],[f6])).
% 0.22/1.27 fof(f25,plain,(
% 0.22/1.27 ![X0]: (multiplication(one,X0)=X0)),
% 0.22/1.27 inference(cnf_transformation,[status(thm)],[f7])).
% 0.22/1.27 fof(f26,plain,(
% 0.22/1.27 ![X0,X1,X2]: (multiplication(X0,addition(X1,X2))=addition(multiplication(X0,X1),multiplication(X0,X2)))),
% 0.22/1.27 inference(cnf_transformation,[status(thm)],[f8])).
% 0.22/1.27 fof(f27,plain,(
% 0.22/1.27 ![X0,X1,X2]: (multiplication(addition(X0,X1),X2)=addition(multiplication(X0,X2),multiplication(X1,X2)))),
% 0.22/1.27 inference(cnf_transformation,[status(thm)],[f9])).
% 0.22/1.27 fof(f30,plain,(
% 0.22/1.27 ![A,B]: ((~leq(A,B)|addition(A,B)=B)&(leq(A,B)|~addition(A,B)=B))),
% 0.22/1.27 inference(NNF_transformation,[status(thm)],[f12])).
% 0.22/1.27 fof(f31,plain,(
% 0.22/1.27 (![A,B]: (~leq(A,B)|addition(A,B)=B))&(![A,B]: (leq(A,B)|~addition(A,B)=B))),
% 0.22/1.27 inference(miniscoping,[status(thm)],[f30])).
% 0.22/1.27 fof(f32,plain,(
% 0.22/1.27 ![X0,X1]: (~leq(X0,X1)|addition(X0,X1)=X1)),
% 0.22/1.27 inference(cnf_transformation,[status(thm)],[f31])).
% 0.22/1.27 fof(f33,plain,(
% 0.22/1.27 ![X0,X1]: (leq(X0,X1)|~addition(X0,X1)=X1)),
% 0.22/1.27 inference(cnf_transformation,[status(thm)],[f31])).
% 0.22/1.27 fof(f34,plain,(
% 0.22/1.27 ![X0]: (leq(addition(one,multiplication(X0,star(X0))),star(X0)))),
% 0.22/1.27 inference(cnf_transformation,[status(thm)],[f13])).
% 0.22/1.27 fof(f35,plain,(
% 0.22/1.27 ![X0]: (leq(addition(one,multiplication(star(X0),X0)),star(X0)))),
% 0.22/1.27 inference(cnf_transformation,[status(thm)],[f14])).
% 0.22/1.27 fof(f40,plain,(
% 0.22/1.27 (?[X0]: ~leq(X0,star(X0)))),
% 0.22/1.27 inference(pre_NNF_transformation,[status(thm)],[f18])).
% 0.22/1.27 fof(f41,plain,(
% 0.22/1.27 ~leq(sK0_skl,star(sK0_skl))),
% 0.22/1.27 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(X0,sK0_skl)],[f40])).
% 0.22/1.27 fof(f42,plain,(
% 0.22/1.27 ~leq(sK0_skl,star(sK0_skl))),
% 0.22/1.27 inference(cnf_transformation,[status(thm)],[f41])).
% 0.22/1.27 fof(f65,plain,(
% 0.22/1.27 ![X0,X1]: (leq(X0,X1)|~addition(X1,X0)=X1)),
% 0.22/1.27 inference(paramodulation,[status(thm)],[f19,f33])).
% 0.22/1.27 fof(f161,plain,(
% 0.22/1.27 ~addition(star(sK0_skl),sK0_skl)=star(sK0_skl)),
% 0.22/1.27 inference(resolution,[status(thm)],[f65,f42])).
% 0.22/1.27 fof(f170,plain,(
% 0.22/1.27 ![X0,X1,X2]: (addition(X0,addition(X1,X2))=addition(addition(X1,X0),X2))),
% 0.22/1.27 inference(paramodulation,[status(thm)],[f19,f20])).
% 0.22/1.27 fof(f172,plain,(
% 0.22/1.27 ![X0,X1]: (addition(X0,addition(X0,X1))=addition(X0,X1))),
% 0.22/1.27 inference(paramodulation,[status(thm)],[f22,f20])).
% 0.22/1.27 fof(f215,plain,(
% 0.22/1.27 ![X0,X1]: (multiplication(X0,addition(X1,one))=addition(multiplication(X0,X1),X0))),
% 0.22/1.27 inference(paramodulation,[status(thm)],[f24,f26])).
% 0.22/1.27 fof(f240,plain,(
% 0.22/1.27 ~addition(sK0_skl,star(sK0_skl))=star(sK0_skl)),
% 0.22/1.27 inference(paramodulation,[status(thm)],[f19,f161])).
% 0.22/1.27 fof(f374,plain,(
% 0.22/1.27 ![X0]: (addition(addition(one,multiplication(X0,star(X0))),star(X0))=star(X0))),
% 0.22/1.27 inference(resolution,[status(thm)],[f34,f32])).
% 0.22/1.27 fof(f379,plain,(
% 0.22/1.27 ![X0]: (addition(one,addition(multiplication(X0,star(X0)),star(X0)))=star(X0))),
% 0.22/1.27 inference(forward_demodulation,[status(thm)],[f20,f374])).
% 0.22/1.27 fof(f382,plain,(
% 0.22/1.27 ![X0]: (addition(addition(one,multiplication(star(X0),X0)),star(X0))=star(X0))),
% 0.22/1.27 inference(resolution,[status(thm)],[f35,f32])).
% 0.22/1.27 fof(f386,plain,(
% 0.22/1.27 ![X0]: (addition(one,addition(multiplication(star(X0),X0),star(X0)))=star(X0))),
% 0.22/1.27 inference(forward_demodulation,[status(thm)],[f20,f382])).
% 0.22/1.27 fof(f458,plain,(
% 0.22/1.27 ![X0,X1]: (leq(X0,addition(X0,X1)))),
% 0.22/1.27 inference(resolution,[status(thm)],[f172,f33])).
% 0.22/1.27 fof(f467,plain,(
% 0.22/1.27 ![X0,X1]: (addition(X0,addition(X1,X0))=addition(X0,X1))),
% 0.22/1.27 inference(paramodulation,[status(thm)],[f19,f172])).
% 0.22/1.27 fof(f493,plain,(
% 0.22/1.27 ![X0,X1,X2]: (leq(multiplication(X0,X1),multiplication(addition(X0,X2),X1)))),
% 0.22/1.27 inference(paramodulation,[status(thm)],[f27,f458])).
% 0.22/1.27 fof(f499,plain,(
% 0.22/1.27 ![X0,X1]: (leq(X0,addition(X1,X0)))),
% 0.22/1.27 inference(paramodulation,[status(thm)],[f19,f458])).
% 0.22/1.27 fof(f502,plain,(
% 0.22/1.27 ![X0,X1]: (addition(X0,addition(X1,X0))=addition(X1,X0))),
% 0.22/1.27 inference(resolution,[status(thm)],[f499,f32])).
% 0.22/1.27 fof(f1461,plain,(
% 0.22/1.27 ![X0,X1]: (leq(X0,multiplication(addition(one,X1),X0)))),
% 0.22/1.27 inference(paramodulation,[status(thm)],[f25,f493])).
% 0.22/1.27 fof(f2613,plain,(
% 0.22/1.27 ![X0,X1]: (leq(X0,multiplication(star(X1),X0)))),
% 0.22/1.27 inference(paramodulation,[status(thm)],[f379,f1461])).
% 0.22/1.27 fof(f2653,plain,(
% 0.22/1.27 ![X0]: (addition(one,star(X0))=addition(one,addition(multiplication(X0,star(X0)),star(X0))))),
% 0.22/1.27 inference(paramodulation,[status(thm)],[f379,f172])).
% 0.22/1.27 fof(f2702,plain,(
% 0.22/1.27 ![X0]: (addition(one,star(X0))=star(X0))),
% 0.22/1.27 inference(forward_demodulation,[status(thm)],[f379,f2653])).
% 0.22/1.27 fof(f2783,plain,(
% 0.22/1.27 ![X0]: (addition(one,multiplication(star(X0),addition(X0,one)))=star(X0))),
% 0.22/1.27 inference(forward_demodulation,[status(thm)],[f215,f386])).
% 0.22/1.27 fof(f2821,plain,(
% 0.22/1.27 ![X0]: (addition(multiplication(star(X0),addition(X0,one)),star(X0))=addition(one,multiplication(star(X0),addition(X0,one))))),
% 0.22/1.27 inference(paramodulation,[status(thm)],[f2783,f502])).
% 0.22/1.27 fof(f2855,plain,(
% 0.22/1.27 ![X0]: (multiplication(star(X0),addition(addition(X0,one),one))=addition(one,multiplication(star(X0),addition(X0,one))))),
% 0.22/1.27 inference(forward_demodulation,[status(thm)],[f215,f2821])).
% 0.22/1.27 fof(f2856,plain,(
% 0.22/1.27 ![X0]: (multiplication(star(X0),addition(one,addition(X0,one)))=addition(one,multiplication(star(X0),addition(X0,one))))),
% 0.22/1.27 inference(forward_demodulation,[status(thm)],[f170,f2855])).
% 0.22/1.27 fof(f2857,plain,(
% 0.22/1.27 ![X0]: (multiplication(star(X0),addition(one,X0))=addition(one,multiplication(star(X0),addition(X0,one))))),
% 0.22/1.27 inference(forward_demodulation,[status(thm)],[f467,f2856])).
% 0.22/1.27 fof(f2858,plain,(
% 0.22/1.27 ![X0]: (multiplication(star(X0),addition(one,X0))=star(X0))),
% 0.22/1.27 inference(forward_demodulation,[status(thm)],[f2783,f2857])).
% 0.22/1.27 fof(f3356,plain,(
% 0.22/1.27 ![X0]: (leq(addition(one,X0),star(X0)))),
% 0.22/1.27 inference(paramodulation,[status(thm)],[f2858,f2613])).
% 0.22/1.27 fof(f3421,plain,(
% 0.22/1.27 ![X0]: (addition(addition(one,X0),star(X0))=star(X0))),
% 0.22/1.27 inference(resolution,[status(thm)],[f3356,f32])).
% 0.22/1.27 fof(f3438,plain,(
% 0.22/1.27 ![X0]: (addition(X0,addition(one,star(X0)))=star(X0))),
% 0.22/1.27 inference(forward_demodulation,[status(thm)],[f170,f3421])).
% 0.22/1.27 fof(f3439,plain,(
% 0.22/1.27 ![X0]: (addition(X0,star(X0))=star(X0))),
% 0.22/1.27 inference(forward_demodulation,[status(thm)],[f2702,f3438])).
% 0.22/1.27 fof(f3446,plain,(
% 0.22/1.27 ~star(sK0_skl)=star(sK0_skl)),
% 0.22/1.27 inference(backward_demodulation,[status(thm)],[f3439,f240])).
% 0.22/1.28 fof(f3509,plain,(
% 0.22/1.28 $false),
% 0.22/1.28 inference(trivial_equality_resolution,[status(thm)],[f3446])).
% 0.22/1.28 % SZS output end CNFRefutation for theBenchmark.p
% 0.22/1.32 % Elapsed time: 0.245276 seconds
% 0.22/1.32 % CPU time: 1.407484 seconds
% 0.22/1.32 % Total memory used: 78.053 MB
% 0.22/1.32 % Net memory used: 77.439 MB
%------------------------------------------------------------------------------