%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : KLE167+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 : 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 12:58:26 PM UTC 2026
% Result : Theorem 0.23s 0.72s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KLE167+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.44 % Computer : n007.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Sun Sep 20 22:46:21 UTC 2026
% 0.19/0.44 % CPUTime :
% 0.19/0.46 % Drodi V4.1.1
% 0.23/0.72 % Refutation found
% 0.23/0.72 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.23/0.72 % SZS output start CNFRefutation for theBenchmark
% 0.23/0.72 fof(f1,axiom,(
% 0.23/0.72 (! [A,B] : addition(A,B) = addition(B,A) )),
% 0.23/0.72 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.23/0.72 fof(f2,axiom,(
% 0.23/0.72 (! [C,B,A] : addition(A,addition(B,C)) = addition(addition(A,B),C) )),
% 0.23/0.72 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.23/0.72 fof(f3,axiom,(
% 0.23/0.72 (! [A] : addition(A,zero) = A )),
% 0.23/0.72 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.23/0.72 fof(f4,axiom,(
% 0.23/0.72 (! [A] : addition(A,A) = A )),
% 0.23/0.72 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.23/0.72 fof(f6,axiom,(
% 0.23/0.72 (! [A] : multiplication(A,one) = A )),
% 0.23/0.72 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.23/0.72 fof(f7,axiom,(
% 0.23/0.72 (! [A] : multiplication(one,A) = A )),
% 0.23/0.72 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.23/0.72 fof(f8,axiom,(
% 0.23/0.72 (! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) )),
% 0.23/0.72 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.23/0.72 fof(f10,axiom,(
% 0.23/0.72 (! [A] : multiplication(zero,A) = zero )),
% 0.23/0.72 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.23/0.72 fof(f11,axiom,(
% 0.23/0.72 (! [A] : addition(one,multiplication(A,star(A))) = star(A) )),
% 0.23/0.72 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.23/0.72 fof(f13,axiom,(
% 0.23/0.72 (! [A,B,C] :( leq(addition(multiplication(A,C),B),C)=> leq(multiplication(star(A),B),C) ) )),
% 0.23/0.72 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.23/0.72 fof(f14,axiom,(
% 0.23/0.72 (! [A,B,C] :( leq(addition(multiplication(C,A),B),C)=> leq(multiplication(B,star(A)),C) ) )),
% 0.23/0.72 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.23/0.72 fof(f18,axiom,(
% 0.23/0.72 (! [A,B] :( leq(A,B)<=> addition(A,B) = B ) )),
% 0.23/0.72 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.23/0.72 fof(f19,conjecture,(
% 0.23/0.72 (! [X0,X1] :( ( multiplication(X0,X1) = zero=> leq(multiplication(X0,star(X1)),X0) )& leq(X0,multiplication(X0,star(X1))) ) )),
% 0.23/0.72 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.23/0.72 fof(f20,negated_conjecture,(
% 0.23/0.72 ~((! [X0,X1] :( ( multiplication(X0,X1) = zero=> leq(multiplication(X0,star(X1)),X0) )& leq(X0,multiplication(X0,star(X1))) ) ))),
% 0.23/0.72 inference(negated_conjecture,[status(cth)],[f19])).
% 0.23/0.72 fof(f21,plain,(
% 0.23/0.72 ![X0,X1]: (addition(X0,X1)=addition(X1,X0))),
% 0.23/0.72 inference(cnf_transformation,[status(thm)],[f1])).
% 0.23/0.72 fof(f22,plain,(
% 0.23/0.72 ![X0,X1,X2]: (addition(X0,addition(X1,X2))=addition(addition(X0,X1),X2))),
% 0.23/0.72 inference(cnf_transformation,[status(thm)],[f2])).
% 0.23/0.72 fof(f23,plain,(
% 0.23/0.72 ![X0]: (addition(X0,zero)=X0)),
% 0.23/0.72 inference(cnf_transformation,[status(thm)],[f3])).
% 0.23/0.72 fof(f24,plain,(
% 0.23/0.72 ![X0]: (addition(X0,X0)=X0)),
% 0.23/0.72 inference(cnf_transformation,[status(thm)],[f4])).
% 0.23/0.72 fof(f26,plain,(
% 0.23/0.72 ![X0]: (multiplication(X0,one)=X0)),
% 0.23/0.72 inference(cnf_transformation,[status(thm)],[f6])).
% 0.23/0.72 fof(f27,plain,(
% 0.23/0.72 ![X0]: (multiplication(one,X0)=X0)),
% 0.23/0.72 inference(cnf_transformation,[status(thm)],[f7])).
% 0.23/0.72 fof(f28,plain,(
% 0.23/0.72 ![X0,X1,X2]: (multiplication(X0,addition(X1,X2))=addition(multiplication(X0,X1),multiplication(X0,X2)))),
% 0.23/0.72 inference(cnf_transformation,[status(thm)],[f8])).
% 0.23/0.72 fof(f30,plain,(
% 0.23/0.72 ![X0]: (multiplication(zero,X0)=zero)),
% 0.23/0.72 inference(cnf_transformation,[status(thm)],[f10])).
% 0.23/0.72 fof(f31,plain,(
% 0.23/0.72 ![X0]: (addition(one,multiplication(X0,star(X0)))=star(X0))),
% 0.23/0.72 inference(cnf_transformation,[status(thm)],[f11])).
% 0.23/0.72 fof(f33,plain,(
% 0.23/0.72 ![A,B,C]: (~leq(addition(multiplication(A,C),B),C)|leq(multiplication(star(A),B),C))),
% 0.23/0.72 inference(pre_NNF_transformation,[status(thm)],[f13])).
% 0.23/0.72 fof(f34,plain,(
% 0.23/0.72 ![X0,X1,X2]: (~leq(addition(multiplication(X0,X1),X2),X1)|leq(multiplication(star(X0),X2),X1))),
% 0.23/0.72 inference(cnf_transformation,[status(thm)],[f33])).
% 0.23/0.72 fof(f35,plain,(
% 0.23/0.72 ![A,B,C]: (~leq(addition(multiplication(C,A),B),C)|leq(multiplication(B,star(A)),C))),
% 0.23/0.72 inference(pre_NNF_transformation,[status(thm)],[f14])).
% 0.23/0.72 fof(f36,plain,(
% 0.23/0.72 ![X0,X1,X2]: (~leq(addition(multiplication(X0,X1),X2),X0)|leq(multiplication(X2,star(X1)),X0))),
% 0.23/0.72 inference(cnf_transformation,[status(thm)],[f35])).
% 0.23/0.72 fof(f41,plain,(
% 0.23/0.72 ![A,B]: ((~leq(A,B)|addition(A,B)=B)&(leq(A,B)|~addition(A,B)=B))),
% 0.23/0.72 inference(NNF_transformation,[status(thm)],[f18])).
% 0.23/0.72 fof(f42,plain,(
% 0.23/0.72 (![A,B]: (~leq(A,B)|addition(A,B)=B))&(![A,B]: (leq(A,B)|~addition(A,B)=B))),
% 0.23/0.72 inference(miniscoping,[status(thm)],[f41])).
% 0.23/0.72 fof(f44,plain,(
% 0.23/0.72 ![X0,X1]: (leq(X0,X1)|~addition(X0,X1)=X1)),
% 0.23/0.72 inference(cnf_transformation,[status(thm)],[f42])).
% 0.23/0.72 fof(f45,plain,(
% 0.23/0.72 (?[X0,X1]: ((multiplication(X0,X1)=zero&~leq(multiplication(X0,star(X1)),X0))|~leq(X0,multiplication(X0,star(X1)))))),
% 0.23/0.72 inference(pre_NNF_transformation,[status(thm)],[f20])).
% 0.23/0.72 fof(f46,plain,(
% 0.23/0.72 (?[X0,X1]: (multiplication(X0,X1)=zero&~leq(multiplication(X0,star(X1)),X0)))|(?[X0,X1]: ~leq(X0,multiplication(X0,star(X1))))),
% 0.23/0.72 inference(miniscoping,[status(thm)],[f45])).
% 0.23/0.72 fof(f47,plain,(
% 0.23/0.72 (multiplication(sK0_skl,sK1_skl)=zero&~leq(multiplication(sK0_skl,star(sK1_skl)),sK0_skl))|~leq(sK2_skl,multiplication(sK2_skl,star(sK3_skl)))),
% 0.23/0.72 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl,sK3_skl]),skolemize(X0,sK0_skl),skolemize(X1,sK1_skl),skolemize(X0,sK2_skl),skolemize(X1,sK3_skl)],[f46])).
% 0.23/0.72 fof(f48,plain,(
% 0.23/0.72 multiplication(sK0_skl,sK1_skl)=zero|~leq(sK2_skl,multiplication(sK2_skl,star(sK3_skl)))),
% 0.23/0.72 inference(cnf_transformation,[status(thm)],[f47])).
% 0.23/0.72 fof(f49,plain,(
% 0.23/0.72 ~leq(multiplication(sK0_skl,star(sK1_skl)),sK0_skl)|~leq(sK2_skl,multiplication(sK2_skl,star(sK3_skl)))),
% 0.23/0.72 inference(cnf_transformation,[status(thm)],[f47])).
% 0.23/0.72 fof(f71,plain,(
% 0.23/0.72 ![X0]: (X0=addition(zero,X0))),
% 0.23/0.72 inference(paramodulation,[status(thm)],[f23,f21])).
% 0.23/0.72 fof(f82,plain,(
% 0.23/0.72 ![X0,X1,X2]: (addition(X0,addition(X1,X2))=addition(X2,addition(X0,X1)))),
% 0.23/0.72 inference(paramodulation,[status(thm)],[f21,f22])).
% 0.23/0.72 fof(f89,plain,(
% 0.23/0.72 ![X0,X1]: (addition(X0,addition(X0,X1))=addition(X0,X1))),
% 0.23/0.72 inference(paramodulation,[status(thm)],[f24,f22])).
% 0.23/0.72 fof(f102,plain,(
% 0.23/0.72 ![X0,X1]: (multiplication(X0,addition(one,X1))=addition(X0,multiplication(X0,X1)))),
% 0.23/0.72 inference(paramodulation,[status(thm)],[f26,f28])).
% 0.23/0.72 fof(f106,plain,(
% 0.23/0.72 ![X0,X1]: (multiplication(X0,addition(X1,one))=addition(multiplication(X0,X1),X0))),
% 0.23/0.72 inference(paramodulation,[status(thm)],[f26,f28])).
% 0.23/0.72 fof(f124,plain,(
% 0.23/0.72 ![X0,X1]: (multiplication(X0,addition(X1,one))=addition(X0,multiplication(X0,X1)))),
% 0.23/0.72 inference(forward_demodulation,[status(thm)],[f21,f106])).
% 0.23/0.72 fof(f148,plain,(
% 0.23/0.72 ![X0,X1,X2]: (~addition(addition(multiplication(X0,X1),X2),X0)=X0|leq(multiplication(X2,star(X1)),X0))),
% 0.23/0.72 inference(resolution,[status(thm)],[f44,f36])).
% 0.23/0.72 fof(f149,plain,(
% 0.23/0.72 ![X0,X1,X2]: (~addition(addition(multiplication(X0,X1),X2),X1)=X1|leq(multiplication(star(X0),X2),X1))),
% 0.23/0.72 inference(resolution,[status(thm)],[f44,f34])).
% 0.23/0.72 fof(f151,plain,(
% 0.23/0.72 ~addition(sK2_skl,multiplication(sK2_skl,star(sK3_skl)))=multiplication(sK2_skl,star(sK3_skl))|multiplication(sK0_skl,sK1_skl)=zero),
% 0.23/0.72 inference(resolution,[status(thm)],[f44,f48])).
% 0.23/0.72 fof(f153,plain,(
% 0.23/0.72 ![X0,X1,X2]: (~addition(multiplication(X0,X1),addition(X2,X0))=X0|leq(multiplication(X2,star(X1)),X0))),
% 0.23/0.72 inference(forward_demodulation,[status(thm)],[f22,f148])).
% 0.23/0.72 fof(f154,plain,(
% 0.23/0.72 ![X0,X1,X2]: (~addition(multiplication(X0,X1),addition(X2,X1))=X1|leq(multiplication(star(X0),X2),X1))),
% 0.23/0.72 inference(forward_demodulation,[status(thm)],[f22,f149])).
% 0.23/0.72 fof(f164,plain,(
% 0.23/0.72 ![X0,X1]: (addition(X0,addition(X1,X0))=addition(X0,X1))),
% 0.23/0.72 inference(paramodulation,[status(thm)],[f21,f89])).
% 0.23/0.72 fof(f217,plain,(
% 0.23/0.72 addition(one,zero)=star(zero)),
% 0.23/0.72 inference(paramodulation,[status(thm)],[f30,f31])).
% 0.23/0.72 fof(f218,plain,(
% 0.23/0.72 ![X0]: (addition(one,star(X0))=addition(one,multiplication(X0,star(X0))))),
% 0.23/0.72 inference(paramodulation,[status(thm)],[f31,f89])).
% 0.23/0.72 fof(f220,plain,(
% 0.23/0.72 one=star(zero)),
% 0.23/0.72 inference(forward_demodulation,[status(thm)],[f23,f217])).
% 0.23/0.72 fof(f221,plain,(
% 0.23/0.72 ![X0]: (addition(one,star(X0))=star(X0))),
% 0.23/0.72 inference(forward_demodulation,[status(thm)],[f31,f218])).
% 0.23/0.72 fof(f424,plain,(
% 0.23/0.72 ![X0,X1]: (addition(X0,X1)=addition(X1,addition(addition(X0,X1),X0)))),
% 0.23/0.72 inference(paramodulation,[status(thm)],[f24,f82])).
% 0.23/0.72 fof(f503,plain,(
% 0.23/0.72 ![X0,X1]: (addition(X0,X1)=addition(X1,addition(X0,addition(X1,X0))))),
% 0.23/0.72 inference(forward_demodulation,[status(thm)],[f22,f424])).
% 0.23/0.72 fof(f504,plain,(
% 0.23/0.72 ![X0,X1]: (addition(X0,X1)=addition(X1,addition(X0,X1)))),
% 0.23/0.73 inference(forward_demodulation,[status(thm)],[f164,f503])).
% 0.23/0.73 fof(f1180,plain,(
% 0.23/0.73 ![X0,X1,X2]: (~addition(X0,addition(multiplication(X0,X1),X2))=X0|leq(multiplication(X2,star(X1)),X0))),
% 0.23/0.73 inference(forward_demodulation,[status(thm)],[f82,f153])).
% 0.23/0.73 fof(f1181,plain,(
% 0.23/0.73 ~addition(sK0_skl,addition(multiplication(sK0_skl,sK1_skl),sK0_skl))=sK0_skl|~leq(sK2_skl,multiplication(sK2_skl,star(sK3_skl)))),
% 0.23/0.73 inference(resolution,[status(thm)],[f1180,f49])).
% 0.23/0.73 fof(f1190,plain,(
% 0.23/0.73 ~addition(multiplication(sK0_skl,sK1_skl),sK0_skl)=sK0_skl|~leq(sK2_skl,multiplication(sK2_skl,star(sK3_skl)))),
% 0.23/0.73 inference(forward_demodulation,[status(thm)],[f504,f1181])).
% 0.23/0.73 fof(f1191,plain,(
% 0.23/0.73 ~addition(sK0_skl,multiplication(sK0_skl,sK1_skl))=sK0_skl|~leq(sK2_skl,multiplication(sK2_skl,star(sK3_skl)))),
% 0.23/0.73 inference(forward_demodulation,[status(thm)],[f21,f1190])).
% 0.23/0.73 fof(f1203,plain,(
% 0.23/0.73 ![X0,X1,X2]: (~addition(X0,addition(multiplication(X1,X0),X2))=X0|leq(multiplication(star(X1),X2),X0))),
% 0.23/0.73 inference(forward_demodulation,[status(thm)],[f82,f154])).
% 0.23/0.73 fof(f1209,plain,(
% 0.23/0.73 ![X0,X1]: (~addition(X0,addition(multiplication(zero,X0),X1))=X0|leq(multiplication(one,X1),X0))),
% 0.23/0.73 inference(paramodulation,[status(thm)],[f220,f1203])).
% 0.23/0.73 fof(f1215,plain,(
% 0.23/0.73 ![X0,X1]: (~addition(X0,addition(zero,X1))=X0|leq(multiplication(one,X1),X0))),
% 0.23/0.73 inference(forward_demodulation,[status(thm)],[f30,f1209])).
% 0.23/0.73 fof(f1216,plain,(
% 0.23/0.73 ![X0,X1]: (~addition(X0,X1)=X0|leq(multiplication(one,X1),X0))),
% 0.23/0.73 inference(forward_demodulation,[status(thm)],[f71,f1215])).
% 0.23/0.73 fof(f1217,plain,(
% 0.23/0.73 ![X0,X1]: (~addition(X0,X1)=X0|leq(X1,X0))),
% 0.23/0.73 inference(forward_demodulation,[status(thm)],[f27,f1216])).
% 0.23/0.73 fof(f1279,plain,(
% 0.23/0.73 ~multiplication(sK2_skl,addition(one,star(sK3_skl)))=multiplication(sK2_skl,star(sK3_skl))|multiplication(sK0_skl,sK1_skl)=zero),
% 0.23/0.73 inference(backward_demodulation,[status(thm)],[f102,f151])).
% 0.23/0.73 fof(f1319,plain,(
% 0.23/0.73 ~multiplication(sK2_skl,star(sK3_skl))=multiplication(sK2_skl,star(sK3_skl))|multiplication(sK0_skl,sK1_skl)=zero),
% 0.23/0.73 inference(forward_demodulation,[status(thm)],[f221,f1279])).
% 0.23/0.73 fof(f1320,plain,(
% 0.23/0.73 multiplication(sK0_skl,sK1_skl)=zero),
% 0.23/0.73 inference(trivial_equality_resolution,[status(thm)],[f1319])).
% 0.23/0.73 fof(f1642,plain,(
% 0.23/0.73 multiplication(sK0_skl,addition(sK1_skl,one))=addition(sK0_skl,zero)),
% 0.23/0.73 inference(paramodulation,[status(thm)],[f1320,f124])).
% 0.23/0.73 fof(f1665,plain,(
% 0.23/0.73 multiplication(sK0_skl,addition(sK1_skl,one))=sK0_skl),
% 0.23/0.73 inference(forward_demodulation,[status(thm)],[f23,f1642])).
% 0.23/0.73 fof(f2121,plain,(
% 0.23/0.73 ~multiplication(sK0_skl,addition(sK1_skl,one))=sK0_skl|~leq(sK2_skl,multiplication(sK2_skl,star(sK3_skl)))),
% 0.23/0.73 inference(forward_demodulation,[status(thm)],[f124,f1191])).
% 0.23/0.73 fof(f2122,plain,(
% 0.23/0.73 ~sK0_skl=sK0_skl|~leq(sK2_skl,multiplication(sK2_skl,star(sK3_skl)))),
% 0.23/0.73 inference(forward_demodulation,[status(thm)],[f1665,f2121])).
% 0.23/0.73 fof(f2123,plain,(
% 0.23/0.73 ~leq(sK2_skl,multiplication(sK2_skl,star(sK3_skl)))),
% 0.23/0.73 inference(trivial_equality_resolution,[status(thm)],[f2122])).
% 0.23/0.73 fof(f2124,plain,(
% 0.23/0.73 ~addition(multiplication(sK2_skl,star(sK3_skl)),sK2_skl)=multiplication(sK2_skl,star(sK3_skl))),
% 0.23/0.73 inference(resolution,[status(thm)],[f2123,f1217])).
% 0.23/0.73 fof(f2126,plain,(
% 0.23/0.73 ~addition(sK2_skl,multiplication(sK2_skl,star(sK3_skl)))=multiplication(sK2_skl,star(sK3_skl))),
% 0.23/0.73 inference(forward_demodulation,[status(thm)],[f21,f2124])).
% 0.23/0.73 fof(f2127,plain,(
% 0.23/0.73 ~multiplication(sK2_skl,addition(star(sK3_skl),one))=multiplication(sK2_skl,star(sK3_skl))),
% 0.23/0.73 inference(forward_demodulation,[status(thm)],[f124,f2126])).
% 0.23/0.73 fof(f2128,plain,(
% 0.23/0.73 ~multiplication(sK2_skl,addition(one,star(sK3_skl)))=multiplication(sK2_skl,star(sK3_skl))),
% 0.23/0.73 inference(forward_demodulation,[status(thm)],[f21,f2127])).
% 0.23/0.73 fof(f2129,plain,(
% 0.23/0.73 ~multiplication(sK2_skl,star(sK3_skl))=multiplication(sK2_skl,star(sK3_skl))),
% 0.23/0.73 inference(forward_demodulation,[status(thm)],[f221,f2128])).
% 0.23/0.73 fof(f2130,plain,(
% 0.23/0.73 $false),
% 0.23/0.73 inference(trivial_equality_resolution,[status(thm)],[f2129])).
% 0.23/0.73 % SZS output end CNFRefutation for theBenchmark.p
% 0.43/0.74 % Elapsed time: 0.278935 seconds
% 0.43/0.74 % CPU time: 1.788131 seconds
% 0.43/0.74 % Total memory used: 83.608 MB
% 0.43/0.74 % Net memory used: 82.718 MB
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