%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : KLE040+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 : n006.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 0.24s 16.13s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KLE040+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/15.47 % Computer : n006.cluster.edu
% 0.19/15.47 % Model : x86_64 x86_64
% 0.19/15.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/15.47 % Memory : 8046.5625MB
% 0.19/15.47 % OS : Linux 6.8.0-71-generic
% 0.19/15.47 % CPULimit : 300
% 0.19/15.47 % WCLimit : 300
% 0.19/15.47 % DateTime : Sun Sep 20 22:40:13 UTC 2026
% 0.19/15.47 % CPUTime :
% 0.19/15.48 % Drodi V4.1.1
% 0.24/16.13 % Refutation found
% 0.24/16.13 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.24/16.13 % SZS output start CNFRefutation for theBenchmark
% 0.24/16.13 fof(f1,axiom,(
% 0.24/16.13 (! [A,B] : addition(A,B) = addition(B,A) )),
% 0.24/16.13 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.24/16.13 fof(f2,axiom,(
% 0.24/16.13 (! [C,B,A] : addition(A,addition(B,C)) = addition(addition(A,B),C) )),
% 0.24/16.13 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.24/16.13 fof(f4,axiom,(
% 0.24/16.13 (! [A] : addition(A,A) = A )),
% 0.24/16.13 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.24/16.13 fof(f5,axiom,(
% 0.24/16.13 (! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C) )),
% 0.24/16.13 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.24/16.13 fof(f6,axiom,(
% 0.24/16.13 (! [A] : multiplication(A,one) = A )),
% 0.24/16.13 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.24/16.13 fof(f7,axiom,(
% 0.24/16.13 (! [A] : multiplication(one,A) = A )),
% 0.24/16.13 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.24/16.13 fof(f8,axiom,(
% 0.24/16.13 (! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) )),
% 0.24/16.13 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.24/16.13 fof(f9,axiom,(
% 0.24/16.13 (! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) )),
% 0.24/16.13 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.24/16.13 fof(f12,axiom,(
% 0.24/16.13 (! [A,B] :( leq(A,B)<=> addition(A,B) = B ) )),
% 0.24/16.13 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.24/16.13 fof(f14,axiom,(
% 0.24/16.13 (! [A] : leq(addition(one,multiplication(star(A),A)),star(A)) )),
% 0.24/16.13 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.24/16.13 fof(f16,axiom,(
% 0.24/16.13 (! [A,B,C] :( leq(addition(multiplication(A,B),C),A)=> leq(multiplication(C,star(B)),A) ) )),
% 0.24/16.13 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.24/16.13 fof(f17,conjecture,(
% 0.24/16.13 (! [X0] : multiplication(star(X0),star(X0)) = star(X0) )),
% 0.24/16.13 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.24/16.13 fof(f18,negated_conjecture,(
% 0.24/16.13 ~((! [X0] : multiplication(star(X0),star(X0)) = star(X0) ))),
% 0.24/16.13 inference(negated_conjecture,[status(cth)],[f17])).
% 0.24/16.13 fof(f19,plain,(
% 0.24/16.13 ![X0,X1]: (addition(X0,X1)=addition(X1,X0))),
% 0.24/16.13 inference(cnf_transformation,[status(thm)],[f1])).
% 0.24/16.13 fof(f20,plain,(
% 0.24/16.13 ![X0,X1,X2]: (addition(X0,addition(X1,X2))=addition(addition(X0,X1),X2))),
% 0.24/16.13 inference(cnf_transformation,[status(thm)],[f2])).
% 0.24/16.13 fof(f22,plain,(
% 0.24/16.13 ![X0]: (addition(X0,X0)=X0)),
% 0.24/16.13 inference(cnf_transformation,[status(thm)],[f4])).
% 0.24/16.13 fof(f23,plain,(
% 0.24/16.13 ![X0,X1,X2]: (multiplication(X0,multiplication(X1,X2))=multiplication(multiplication(X0,X1),X2))),
% 0.24/16.13 inference(cnf_transformation,[status(thm)],[f5])).
% 0.24/16.13 fof(f24,plain,(
% 0.24/16.13 ![X0]: (multiplication(X0,one)=X0)),
% 0.24/16.13 inference(cnf_transformation,[status(thm)],[f6])).
% 0.24/16.13 fof(f25,plain,(
% 0.24/16.13 ![X0]: (multiplication(one,X0)=X0)),
% 0.24/16.13 inference(cnf_transformation,[status(thm)],[f7])).
% 0.24/16.13 fof(f26,plain,(
% 0.24/16.13 ![X0,X1,X2]: (multiplication(X0,addition(X1,X2))=addition(multiplication(X0,X1),multiplication(X0,X2)))),
% 0.24/16.13 inference(cnf_transformation,[status(thm)],[f8])).
% 0.24/16.13 fof(f27,plain,(
% 0.24/16.13 ![X0,X1,X2]: (multiplication(addition(X0,X1),X2)=addition(multiplication(X0,X2),multiplication(X1,X2)))),
% 0.24/16.13 inference(cnf_transformation,[status(thm)],[f9])).
% 0.24/16.13 fof(f30,plain,(
% 0.24/16.13 ![A,B]: ((~leq(A,B)|addition(A,B)=B)&(leq(A,B)|~addition(A,B)=B))),
% 0.24/16.13 inference(NNF_transformation,[status(thm)],[f12])).
% 0.24/16.13 fof(f31,plain,(
% 0.24/16.13 (![A,B]: (~leq(A,B)|addition(A,B)=B))&(![A,B]: (leq(A,B)|~addition(A,B)=B))),
% 0.24/16.13 inference(miniscoping,[status(thm)],[f30])).
% 0.24/16.13 fof(f32,plain,(
% 0.24/16.13 ![X0,X1]: (~leq(X0,X1)|addition(X0,X1)=X1)),
% 0.24/16.13 inference(cnf_transformation,[status(thm)],[f31])).
% 0.24/16.13 fof(f33,plain,(
% 0.24/16.13 ![X0,X1]: (leq(X0,X1)|~addition(X0,X1)=X1)),
% 0.24/16.13 inference(cnf_transformation,[status(thm)],[f31])).
% 0.24/16.13 fof(f35,plain,(
% 0.24/16.13 ![X0]: (leq(addition(one,multiplication(star(X0),X0)),star(X0)))),
% 0.24/16.13 inference(cnf_transformation,[status(thm)],[f14])).
% 0.24/16.13 fof(f38,plain,(
% 0.24/16.13 ![A,B,C]: (~leq(addition(multiplication(A,B),C),A)|leq(multiplication(C,star(B)),A))),
% 0.24/16.13 inference(pre_NNF_transformation,[status(thm)],[f16])).
% 0.24/16.13 fof(f39,plain,(
% 0.24/16.13 ![X0,X1,X2]: (~leq(addition(multiplication(X0,X1),X2),X0)|leq(multiplication(X2,star(X1)),X0))),
% 0.24/16.13 inference(cnf_transformation,[status(thm)],[f38])).
% 0.24/16.13 fof(f40,plain,(
% 0.24/16.13 (?[X0]: ~multiplication(star(X0),star(X0))=star(X0))),
% 0.24/16.13 inference(pre_NNF_transformation,[status(thm)],[f18])).
% 0.24/16.13 fof(f41,plain,(
% 0.24/16.13 ~multiplication(star(sK0_skl),star(sK0_skl))=star(sK0_skl)),
% 0.24/16.13 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(X0,sK0_skl)],[f40])).
% 0.24/16.13 fof(f42,plain,(
% 0.24/16.13 ~multiplication(star(sK0_skl),star(sK0_skl))=star(sK0_skl)),
% 0.24/16.13 inference(cnf_transformation,[status(thm)],[f41])).
% 0.24/16.13 fof(f111,plain,(
% 0.24/16.13 ![X0,X1]: (addition(X0,addition(X0,X1))=addition(X0,X1))),
% 0.24/16.13 inference(paramodulation,[status(thm)],[f22,f20])).
% 0.24/16.13 fof(f127,plain,(
% 0.24/16.13 ![X0]: (leq(X0,X0))),
% 0.24/16.13 inference(resolution,[status(thm)],[f33,f22])).
% 0.24/16.13 fof(f172,plain,(
% 0.24/16.13 ![X0,X1]: (addition(X0,addition(X1,X0))=addition(X0,X1))),
% 0.24/16.13 inference(paramodulation,[status(thm)],[f19,f111])).
% 0.24/16.13 fof(f233,plain,(
% 0.24/16.13 ![X0,X1,X2,X3]: (multiplication(addition(multiplication(X0,X1),X2),X3)=addition(multiplication(X0,multiplication(X1,X3)),multiplication(X2,X3)))),
% 0.24/16.13 inference(paramodulation,[status(thm)],[f23,f27])).
% 0.24/16.13 fof(f269,plain,(
% 0.24/16.13 ![X0,X1,X2]: (multiplication(addition(multiplication(X0,X1),X0),X2)=multiplication(X0,addition(multiplication(X1,X2),X2)))),
% 0.24/16.13 inference(paramodulation,[status(thm)],[f26,f233])).
% 0.24/16.13 fof(f292,plain,(
% 0.24/16.13 ![X0,X1,X2]: (multiplication(addition(X0,multiplication(X0,X1)),X2)=multiplication(X0,addition(multiplication(X1,X2),X2)))),
% 0.24/16.13 inference(forward_demodulation,[status(thm)],[f19,f269])).
% 0.24/16.13 fof(f293,plain,(
% 0.24/16.13 ![X0,X1,X2]: (multiplication(addition(X0,multiplication(X0,X1)),X2)=multiplication(X0,addition(X2,multiplication(X1,X2))))),
% 0.24/16.13 inference(forward_demodulation,[status(thm)],[f19,f292])).
% 0.24/16.13 fof(f320,plain,(
% 0.24/16.13 ![X0,X1]: (addition(X0,multiplication(X0,X1))=multiplication(X0,addition(one,multiplication(X1,one))))),
% 0.24/16.13 inference(paramodulation,[status(thm)],[f24,f293])).
% 0.24/16.13 fof(f327,plain,(
% 0.24/16.13 ![X0,X1]: (multiplication(addition(one,X0),X1)=multiplication(one,addition(X1,multiplication(X0,X1))))),
% 0.24/16.13 inference(paramodulation,[status(thm)],[f25,f293])).
% 0.24/16.13 fof(f368,plain,(
% 0.24/16.13 ![X0,X1]: (addition(X0,multiplication(X0,X1))=multiplication(X0,addition(one,X1)))),
% 0.24/16.13 inference(forward_demodulation,[status(thm)],[f24,f320])).
% 0.24/16.13 fof(f382,plain,(
% 0.24/16.13 ![X0,X1]: (multiplication(addition(one,X0),X1)=addition(X1,multiplication(X0,X1)))),
% 0.24/16.13 inference(forward_demodulation,[status(thm)],[f25,f327])).
% 0.24/16.13 fof(f432,plain,(
% 0.24/16.13 ![X0,X1]: (addition(X0,multiplication(X0,X1))=multiplication(X0,addition(X1,one)))),
% 0.24/16.13 inference(paramodulation,[status(thm)],[f19,f368])).
% 0.24/16.13 fof(f494,plain,(
% 0.24/16.13 ![X0,X1]: (multiplication(addition(X0,one),X1)=addition(X1,multiplication(X0,X1)))),
% 0.24/16.13 inference(paramodulation,[status(thm)],[f19,f382])).
% 0.24/16.13 fof(f1087,plain,(
% 0.24/16.13 ![X0]: (addition(addition(one,multiplication(star(X0),X0)),star(X0))=star(X0))),
% 0.24/16.13 inference(resolution,[status(thm)],[f35,f32])).
% 0.24/16.13 fof(f1090,plain,(
% 0.24/16.13 ![X0]: (addition(one,addition(multiplication(star(X0),X0),star(X0)))=star(X0))),
% 0.24/16.13 inference(forward_demodulation,[status(thm)],[f20,f1087])).
% 0.24/16.13 fof(f1091,plain,(
% 0.24/16.13 ![X0]: (addition(one,addition(star(X0),multiplication(star(X0),X0)))=star(X0))),
% 0.24/16.13 inference(forward_demodulation,[status(thm)],[f19,f1090])).
% 0.24/16.13 fof(f1092,plain,(
% 0.24/16.13 ![X0]: (addition(one,multiplication(star(X0),addition(X0,one)))=star(X0))),
% 0.24/16.13 inference(forward_demodulation,[status(thm)],[f432,f1091])).
% 0.24/16.13 fof(f1134,plain,(
% 0.24/16.13 ![X0,X1,X2]: (~leq(multiplication(X0,addition(X1,X2)),X0)|leq(multiplication(multiplication(X0,X2),star(X1)),X0))),
% 0.24/16.13 inference(paramodulation,[status(thm)],[f26,f39])).
% 0.24/16.13 fof(f1161,plain,(
% 0.24/16.13 ![X0,X1,X2]: (~leq(multiplication(X0,addition(X1,X2)),X0)|leq(multiplication(X0,multiplication(X2,star(X1))),X0))),
% 0.24/16.13 inference(forward_demodulation,[status(thm)],[f23,f1134])).
% 0.24/16.13 fof(f1261,plain,(
% 0.24/16.13 ![X0]: (addition(one,star(X0))=addition(one,multiplication(star(X0),addition(X0,one))))),
% 0.24/16.13 inference(paramodulation,[status(thm)],[f1092,f111])).
% 0.24/16.13 fof(f1268,plain,(
% 0.24/16.13 ![X0]: (addition(one,star(X0))=star(X0))),
% 0.24/16.13 inference(forward_demodulation,[status(thm)],[f1092,f1261])).
% 0.24/16.13 fof(f1446,plain,(
% 0.24/16.13 ![X0]: (addition(multiplication(star(X0),addition(X0,one)),star(X0))=addition(multiplication(star(X0),addition(X0,one)),one))),
% 0.24/16.15 inference(paramodulation,[status(thm)],[f1092,f172])).
% 0.24/16.15 fof(f1492,plain,(
% 0.24/16.15 ![X0]: (addition(star(X0),multiplication(star(X0),addition(X0,one)))=addition(multiplication(star(X0),addition(X0,one)),one))),
% 0.24/16.15 inference(forward_demodulation,[status(thm)],[f19,f1446])).
% 0.24/16.15 fof(f1493,plain,(
% 0.24/16.15 ![X0]: (multiplication(star(X0),addition(addition(X0,one),one))=addition(multiplication(star(X0),addition(X0,one)),one))),
% 0.24/16.15 inference(forward_demodulation,[status(thm)],[f432,f1492])).
% 0.24/16.15 fof(f1494,plain,(
% 0.24/16.15 ![X0]: (multiplication(star(X0),addition(X0,addition(one,one)))=addition(multiplication(star(X0),addition(X0,one)),one))),
% 0.24/16.15 inference(forward_demodulation,[status(thm)],[f20,f1493])).
% 0.24/16.15 fof(f1495,plain,(
% 0.24/16.15 ![X0]: (multiplication(star(X0),addition(X0,one))=addition(multiplication(star(X0),addition(X0,one)),one))),
% 0.24/16.15 inference(forward_demodulation,[status(thm)],[f22,f1494])).
% 0.24/16.15 fof(f1496,plain,(
% 0.24/16.15 ![X0]: (multiplication(star(X0),addition(X0,one))=addition(one,multiplication(star(X0),addition(X0,one))))),
% 0.24/16.15 inference(forward_demodulation,[status(thm)],[f19,f1495])).
% 0.24/16.15 fof(f1497,plain,(
% 0.24/16.15 ![X0]: (multiplication(star(X0),addition(X0,one))=star(X0))),
% 0.24/16.15 inference(forward_demodulation,[status(thm)],[f1092,f1496])).
% 0.24/16.15 fof(f1984,plain,(
% 0.24/16.15 ![X0]: (~leq(star(X0),star(X0))|leq(multiplication(star(X0),multiplication(one,star(X0))),star(X0)))),
% 0.24/16.15 inference(paramodulation,[status(thm)],[f1497,f1161])).
% 0.24/16.15 fof(f2015,plain,(
% 0.24/16.15 ![X0]: (~leq(star(X0),star(X0))|leq(multiplication(star(X0),star(X0)),star(X0)))),
% 0.24/16.15 inference(forward_demodulation,[status(thm)],[f25,f1984])).
% 0.24/16.15 fof(f2016,plain,(
% 0.24/16.15 ![X0]: (leq(multiplication(star(X0),star(X0)),star(X0)))),
% 0.24/16.15 inference(forward_subsumption_resolution,[status(thm)],[f2015,f127])).
% 0.24/16.15 fof(f4104,plain,(
% 0.24/16.15 ![X0]: (addition(multiplication(star(X0),star(X0)),star(X0))=star(X0))),
% 0.24/16.15 inference(resolution,[status(thm)],[f2016,f32])).
% 0.24/16.15 fof(f4108,plain,(
% 0.24/16.15 ![X0]: (addition(star(X0),multiplication(star(X0),star(X0)))=star(X0))),
% 0.24/16.15 inference(forward_demodulation,[status(thm)],[f19,f4104])).
% 0.24/16.15 fof(f4109,plain,(
% 0.24/16.15 ![X0]: (multiplication(addition(star(X0),one),star(X0))=star(X0))),
% 0.24/16.15 inference(forward_demodulation,[status(thm)],[f494,f4108])).
% 0.24/16.15 fof(f4110,plain,(
% 0.24/16.15 ![X0]: (multiplication(addition(one,star(X0)),star(X0))=star(X0))),
% 0.24/16.15 inference(forward_demodulation,[status(thm)],[f19,f4109])).
% 0.24/16.15 fof(f4111,plain,(
% 0.24/16.15 ![X0]: (multiplication(star(X0),star(X0))=star(X0))),
% 0.24/16.15 inference(forward_demodulation,[status(thm)],[f1268,f4110])).
% 0.24/16.15 fof(f4121,plain,(
% 0.24/16.15 ~star(sK0_skl)=star(sK0_skl)),
% 0.24/16.15 inference(backward_demodulation,[status(thm)],[f4111,f42])).
% 0.24/16.15 fof(f4166,plain,(
% 0.24/16.15 $false),
% 0.24/16.15 inference(trivial_equality_resolution,[status(thm)],[f4121])).
% 0.24/16.15 % SZS output end CNFRefutation for theBenchmark.p
% 0.24/16.16 % Elapsed time: 0.674120 seconds
% 0.24/16.16 % CPU time: 5.195558 seconds
% 0.24/16.16 % Total memory used: 106.781 MB
% 0.24/16.16 % Net memory used: 105.212 MB
%------------------------------------------------------------------------------