%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : KLE040+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 : n014.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 0.13s 5.63s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE040+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/5.36 % Computer : n014.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
% 0.09/5.36 % CPULimit : 300
% 0.09/5.36 % WCLimit : 300
% 0.09/5.36 % DateTime : Sun Sep 20 22:40:25 UTC 2026
% 0.09/5.36 % CPUTime :
% 0.09/5.37 % Drodi V4.1.1
% 0.13/5.63 % Refutation found
% 0.13/5.63 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/5.63 % SZS output start CNFRefutation for theBenchmark
% 0.13/5.63 fof(f1,axiom,(
% 0.13/5.63 (! [A,B] : addition(A,B) = addition(B,A) )),
% 0.13/5.63 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/5.63 fof(f2,axiom,(
% 0.13/5.63 (! [C,B,A] : addition(A,addition(B,C)) = addition(addition(A,B),C) )),
% 0.13/5.63 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/5.63 fof(f4,axiom,(
% 0.13/5.63 (! [A] : addition(A,A) = A )),
% 0.13/5.63 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/5.63 fof(f6,axiom,(
% 0.13/5.63 (! [A] : multiplication(A,one) = A )),
% 0.13/5.63 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/5.63 fof(f8,axiom,(
% 0.13/5.63 (! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) )),
% 0.13/5.63 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/5.63 fof(f12,axiom,(
% 0.13/5.63 (! [A,B] :( leq(A,B)<=> addition(A,B) = B ) )),
% 0.13/5.63 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/5.63 fof(f13,axiom,(
% 0.13/5.63 (! [A] : leq(addition(one,multiplication(A,star(A))),star(A)) )),
% 0.13/5.63 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/5.63 fof(f14,axiom,(
% 0.13/5.63 (! [A] : leq(addition(one,multiplication(star(A),A)),star(A)) )),
% 0.13/5.63 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/5.63 fof(f16,axiom,(
% 0.13/5.63 (! [A,B,C] :( leq(addition(multiplication(A,B),C),A)=> leq(multiplication(C,star(B)),A) ) )),
% 0.13/5.63 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/5.63 fof(f17,conjecture,(
% 0.13/5.63 (! [X0] :( leq(multiplication(star(X0),star(X0)),star(X0))& leq(star(X0),multiplication(star(X0),star(X0))) ) )),
% 0.13/5.63 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/5.63 fof(f18,negated_conjecture,(
% 0.13/5.63 ~((! [X0] :( leq(multiplication(star(X0),star(X0)),star(X0))& leq(star(X0),multiplication(star(X0),star(X0))) ) ))),
% 0.13/5.63 inference(negated_conjecture,[status(cth)],[f17])).
% 0.13/5.63 fof(f19,plain,(
% 0.13/5.63 ![X0,X1]: (addition(X0,X1)=addition(X1,X0))),
% 0.13/5.63 inference(cnf_transformation,[status(thm)],[f1])).
% 0.13/5.63 fof(f20,plain,(
% 0.13/5.63 ![X0,X1,X2]: (addition(X0,addition(X1,X2))=addition(addition(X0,X1),X2))),
% 0.13/5.63 inference(cnf_transformation,[status(thm)],[f2])).
% 0.13/5.63 fof(f22,plain,(
% 0.13/5.63 ![X0]: (addition(X0,X0)=X0)),
% 0.13/5.63 inference(cnf_transformation,[status(thm)],[f4])).
% 0.13/5.63 fof(f24,plain,(
% 0.13/5.63 ![X0]: (multiplication(X0,one)=X0)),
% 0.13/5.63 inference(cnf_transformation,[status(thm)],[f6])).
% 0.13/5.63 fof(f26,plain,(
% 0.13/5.63 ![X0,X1,X2]: (multiplication(X0,addition(X1,X2))=addition(multiplication(X0,X1),multiplication(X0,X2)))),
% 0.13/5.63 inference(cnf_transformation,[status(thm)],[f8])).
% 0.13/5.63 fof(f30,plain,(
% 0.13/5.63 ![A,B]: ((~leq(A,B)|addition(A,B)=B)&(leq(A,B)|~addition(A,B)=B))),
% 0.13/5.63 inference(NNF_transformation,[status(thm)],[f12])).
% 0.13/5.63 fof(f31,plain,(
% 0.13/5.63 (![A,B]: (~leq(A,B)|addition(A,B)=B))&(![A,B]: (leq(A,B)|~addition(A,B)=B))),
% 0.13/5.63 inference(miniscoping,[status(thm)],[f30])).
% 0.13/5.63 fof(f32,plain,(
% 0.13/5.63 ![X0,X1]: (~leq(X0,X1)|addition(X0,X1)=X1)),
% 0.13/5.63 inference(cnf_transformation,[status(thm)],[f31])).
% 0.13/5.63 fof(f33,plain,(
% 0.13/5.63 ![X0,X1]: (leq(X0,X1)|~addition(X0,X1)=X1)),
% 0.13/5.63 inference(cnf_transformation,[status(thm)],[f31])).
% 0.13/5.63 fof(f34,plain,(
% 0.13/5.63 ![X0]: (leq(addition(one,multiplication(X0,star(X0))),star(X0)))),
% 0.13/5.63 inference(cnf_transformation,[status(thm)],[f13])).
% 0.13/5.63 fof(f35,plain,(
% 0.13/5.63 ![X0]: (leq(addition(one,multiplication(star(X0),X0)),star(X0)))),
% 0.13/5.63 inference(cnf_transformation,[status(thm)],[f14])).
% 0.13/5.63 fof(f38,plain,(
% 0.13/5.63 ![A,B,C]: (~leq(addition(multiplication(A,B),C),A)|leq(multiplication(C,star(B)),A))),
% 0.13/5.63 inference(pre_NNF_transformation,[status(thm)],[f16])).
% 0.13/5.63 fof(f39,plain,(
% 0.13/5.63 ![X0,X1,X2]: (~leq(addition(multiplication(X0,X1),X2),X0)|leq(multiplication(X2,star(X1)),X0))),
% 0.13/5.63 inference(cnf_transformation,[status(thm)],[f38])).
% 0.13/5.63 fof(f40,plain,(
% 0.13/5.63 (?[X0]: (~leq(multiplication(star(X0),star(X0)),star(X0))|~leq(star(X0),multiplication(star(X0),star(X0)))))),
% 0.13/5.63 inference(pre_NNF_transformation,[status(thm)],[f18])).
% 0.13/5.63 fof(f41,plain,(
% 0.13/5.63 (?[X0]: ~leq(multiplication(star(X0),star(X0)),star(X0)))|(?[X0]: ~leq(star(X0),multiplication(star(X0),star(X0))))),
% 0.13/5.63 inference(miniscoping,[status(thm)],[f40])).
% 0.13/5.63 fof(f42,plain,(
% 0.13/5.63 ~leq(multiplication(star(sK0_skl),star(sK0_skl)),star(sK0_skl))|~leq(star(sK1_skl),multiplication(star(sK1_skl),star(sK1_skl)))),
% 0.13/5.63 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(X0,sK0_skl),skolemize(X0,sK1_skl)],[f41])).
% 0.13/5.63 fof(f43,plain,(
% 0.13/5.63 ~leq(multiplication(star(sK0_skl),star(sK0_skl)),star(sK0_skl))|~leq(star(sK1_skl),multiplication(star(sK1_skl),star(sK1_skl)))),
% 0.13/5.63 inference(cnf_transformation,[status(thm)],[f42])).
% 0.13/5.63 fof(f51,plain,(
% 0.13/5.63 ![X0,X1,X2]: (leq(multiplication(X0,star(X1)),X2)|~addition(addition(multiplication(X2,X1),X0),X2)=X2)),
% 0.13/5.63 inference(resolution,[status(thm)],[f39,f33])).
% 0.13/5.63 fof(f78,plain,(
% 0.13/5.63 ![X0,X1,X2]: (addition(X0,addition(X1,X2))=addition(X2,addition(X0,X1)))),
% 0.13/5.63 inference(paramodulation,[status(thm)],[f19,f20])).
% 0.13/5.63 fof(f83,plain,(
% 0.13/5.63 ![X0,X1,X2]: (addition(X0,addition(X1,X2))=addition(addition(X1,X0),X2))),
% 0.13/5.63 inference(paramodulation,[status(thm)],[f19,f20])).
% 0.13/5.63 fof(f85,plain,(
% 0.13/5.63 ![X0,X1]: (addition(X0,addition(X0,X1))=addition(X0,X1))),
% 0.13/5.63 inference(paramodulation,[status(thm)],[f22,f20])).
% 0.13/5.63 fof(f134,plain,(
% 0.13/5.63 ![X0,X1]: (multiplication(X0,addition(one,X1))=addition(X0,multiplication(X0,X1)))),
% 0.13/5.63 inference(paramodulation,[status(thm)],[f24,f26])).
% 0.13/5.63 fof(f137,plain,(
% 0.13/5.63 ![X0,X1]: (multiplication(X0,addition(X1,one))=addition(multiplication(X0,X1),X0))),
% 0.13/5.63 inference(paramodulation,[status(thm)],[f24,f26])).
% 0.13/5.63 fof(f153,plain,(
% 0.13/5.63 ![X0,X1]: (multiplication(X0,addition(X1,one))=addition(X0,multiplication(X0,X1)))),
% 0.13/5.63 inference(forward_demodulation,[status(thm)],[f19,f137])).
% 0.13/5.63 fof(f241,plain,(
% 0.13/5.63 ![X0,X1,X2]: (leq(multiplication(X0,star(X1)),X2)|~addition(multiplication(X2,X1),addition(X0,X2))=X2)),
% 0.13/5.63 inference(forward_demodulation,[status(thm)],[f20,f51])).
% 0.13/5.63 fof(f242,plain,(
% 0.13/5.63 ~addition(multiplication(star(sK0_skl),sK0_skl),addition(star(sK0_skl),star(sK0_skl)))=star(sK0_skl)|~leq(star(sK1_skl),multiplication(star(sK1_skl),star(sK1_skl)))),
% 0.13/5.63 inference(resolution,[status(thm)],[f241,f43])).
% 0.13/5.63 fof(f246,plain,(
% 0.13/5.63 ~addition(multiplication(star(sK0_skl),sK0_skl),star(sK0_skl))=star(sK0_skl)|~leq(star(sK1_skl),multiplication(star(sK1_skl),star(sK1_skl)))),
% 0.13/5.63 inference(forward_demodulation,[status(thm)],[f22,f242])).
% 0.13/5.63 fof(f247,plain,(
% 0.13/5.63 ~addition(star(sK0_skl),multiplication(star(sK0_skl),sK0_skl))=star(sK0_skl)|~leq(star(sK1_skl),multiplication(star(sK1_skl),star(sK1_skl)))),
% 0.13/5.63 inference(forward_demodulation,[status(thm)],[f19,f246])).
% 0.13/5.63 fof(f350,plain,(
% 0.13/5.63 ![X0,X1]: (addition(X0,addition(X1,X0))=addition(X0,X1))),
% 0.13/5.63 inference(paramodulation,[status(thm)],[f19,f85])).
% 0.13/5.63 fof(f373,plain,(
% 0.13/5.63 ![X0]: (addition(addition(one,multiplication(X0,star(X0))),star(X0))=star(X0))),
% 0.13/5.63 inference(resolution,[status(thm)],[f34,f32])).
% 0.13/5.63 fof(f377,plain,(
% 0.13/5.63 ![X0]: (addition(one,addition(multiplication(X0,star(X0)),star(X0)))=star(X0))),
% 0.13/5.63 inference(forward_demodulation,[status(thm)],[f20,f373])).
% 0.13/5.63 fof(f378,plain,(
% 0.13/5.63 ![X0]: (addition(one,addition(star(X0),multiplication(X0,star(X0))))=star(X0))),
% 0.13/5.63 inference(forward_demodulation,[status(thm)],[f19,f377])).
% 0.13/5.63 fof(f380,plain,(
% 0.13/5.63 ![X0]: (addition(addition(one,multiplication(star(X0),X0)),star(X0))=star(X0))),
% 0.13/5.63 inference(resolution,[status(thm)],[f35,f32])).
% 0.13/5.63 fof(f383,plain,(
% 0.13/5.63 ![X0]: (addition(one,addition(multiplication(star(X0),X0),star(X0)))=star(X0))),
% 0.13/5.63 inference(forward_demodulation,[status(thm)],[f20,f380])).
% 0.13/5.63 fof(f384,plain,(
% 0.13/5.63 ![X0]: (addition(one,addition(star(X0),multiplication(star(X0),X0)))=star(X0))),
% 0.13/5.63 inference(forward_demodulation,[status(thm)],[f19,f383])).
% 0.13/5.63 fof(f397,plain,(
% 0.13/5.63 ~addition(star(sK0_skl),multiplication(star(sK0_skl),sK0_skl))=star(sK0_skl)|~addition(star(sK1_skl),multiplication(star(sK1_skl),star(sK1_skl)))=multiplication(star(sK1_skl),star(sK1_skl))),
% 0.13/5.63 inference(resolution,[status(thm)],[f247,f33])).
% 0.13/5.63 fof(f550,plain,(
% 0.13/5.63 ![X0,X1]: (addition(X0,X1)=addition(X1,addition(addition(X0,X1),X0)))),
% 0.13/5.63 inference(paramodulation,[status(thm)],[f22,f78])).
% 0.13/5.63 fof(f583,plain,(
% 0.13/5.63 ![X0,X1]: (addition(X0,addition(X0,X1))=addition(X1,X0))),
% 0.13/5.63 inference(paramodulation,[status(thm)],[f22,f78])).
% 0.13/5.63 fof(f615,plain,(
% 0.13/5.63 ![X0,X1]: (addition(X0,X1)=addition(X1,addition(X0,addition(X1,X0))))),
% 0.13/5.63 inference(forward_demodulation,[status(thm)],[f20,f550])).
% 0.13/5.63 fof(f616,plain,(
% 0.13/5.63 ![X0,X1]: (addition(X0,X1)=addition(X1,addition(X0,X1)))),
% 0.13/5.63 inference(forward_demodulation,[status(thm)],[f350,f615])).
% 0.13/5.63 fof(f1216,plain,(
% 0.13/5.63 ~addition(star(sK0_skl),multiplication(star(sK0_skl),sK0_skl))=star(sK0_skl)|~multiplication(star(sK1_skl),addition(one,star(sK1_skl)))=multiplication(star(sK1_skl),star(sK1_skl))),
% 0.13/5.63 inference(backward_demodulation,[status(thm)],[f134,f397])).
% 0.13/5.63 fof(f1254,plain,(
% 0.13/5.63 ~multiplication(star(sK0_skl),addition(one,sK0_skl))=star(sK0_skl)|~multiplication(star(sK1_skl),addition(one,star(sK1_skl)))=multiplication(star(sK1_skl),star(sK1_skl))),
% 0.13/5.63 inference(forward_demodulation,[status(thm)],[f134,f1216])).
% 0.13/5.63 fof(f1255,plain,(
% 0.13/5.63 ~multiplication(star(sK0_skl),addition(sK0_skl,one))=star(sK0_skl)|~multiplication(star(sK1_skl),addition(one,star(sK1_skl)))=multiplication(star(sK1_skl),star(sK1_skl))),
% 0.13/5.63 inference(forward_demodulation,[status(thm)],[f19,f1254])).
% 0.13/5.63 fof(f1667,plain,(
% 0.13/5.63 ![X0]: (addition(one,star(X0))=addition(addition(star(X0),multiplication(X0,star(X0))),one))),
% 0.13/5.63 inference(paramodulation,[status(thm)],[f378,f583])).
% 0.13/5.63 fof(f1679,plain,(
% 0.13/5.63 ![X0]: (addition(one,star(X0))=addition(multiplication(X0,star(X0)),addition(star(X0),one)))),
% 0.13/5.63 inference(forward_demodulation,[status(thm)],[f83,f1667])).
% 0.13/5.63 fof(f1680,plain,(
% 0.13/5.63 ![X0]: (addition(one,star(X0))=addition(star(X0),addition(one,multiplication(X0,star(X0)))))),
% 0.13/5.63 inference(forward_demodulation,[status(thm)],[f78,f1679])).
% 0.13/5.63 fof(f1681,plain,(
% 0.13/5.63 ![X0]: (addition(one,star(X0))=addition(one,addition(multiplication(X0,star(X0)),star(X0))))),
% 0.13/5.63 inference(forward_demodulation,[status(thm)],[f78,f1680])).
% 0.13/5.63 fof(f1682,plain,(
% 0.13/5.63 ![X0]: (addition(one,star(X0))=addition(one,addition(star(X0),multiplication(X0,star(X0)))))),
% 0.13/5.63 inference(forward_demodulation,[status(thm)],[f19,f1681])).
% 0.13/5.63 fof(f1683,plain,(
% 0.13/5.63 ![X0]: (addition(one,star(X0))=star(X0))),
% 0.13/5.63 inference(forward_demodulation,[status(thm)],[f378,f1682])).
% 0.13/5.63 fof(f1777,plain,(
% 0.13/5.63 ~multiplication(star(sK0_skl),addition(sK0_skl,one))=star(sK0_skl)|~multiplication(star(sK1_skl),star(sK1_skl))=multiplication(star(sK1_skl),star(sK1_skl))),
% 0.13/5.63 inference(backward_demodulation,[status(thm)],[f1683,f1255])).
% 0.13/5.63 fof(f1790,plain,(
% 0.13/5.63 ~multiplication(star(sK0_skl),addition(sK0_skl,one))=star(sK0_skl)),
% 0.13/5.63 inference(trivial_equality_resolution,[status(thm)],[f1777])).
% 0.13/5.63 fof(f2011,plain,(
% 0.13/5.63 ![X0]: (addition(one,multiplication(star(X0),addition(X0,one)))=star(X0))),
% 0.13/5.63 inference(forward_demodulation,[status(thm)],[f153,f384])).
% 0.13/5.63 fof(f2022,plain,(
% 0.13/5.63 ![X0]: (addition(one,multiplication(star(X0),addition(X0,one)))=addition(multiplication(star(X0),addition(X0,one)),star(X0)))),
% 0.13/5.63 inference(paramodulation,[status(thm)],[f2011,f616])).
% 0.13/5.63 fof(f2038,plain,(
% 0.13/5.63 ![X0]: (star(X0)=addition(multiplication(star(X0),addition(X0,one)),star(X0)))),
% 0.13/5.63 inference(forward_demodulation,[status(thm)],[f2011,f2022])).
% 0.13/5.63 fof(f2039,plain,(
% 0.13/5.63 ![X0]: (star(X0)=addition(star(X0),multiplication(star(X0),addition(X0,one))))),
% 0.13/5.63 inference(forward_demodulation,[status(thm)],[f19,f2038])).
% 0.13/5.63 fof(f2040,plain,(
% 0.13/5.63 ![X0]: (star(X0)=multiplication(star(X0),addition(addition(X0,one),one)))),
% 0.13/5.63 inference(forward_demodulation,[status(thm)],[f153,f2039])).
% 0.13/5.63 fof(f2041,plain,(
% 0.13/5.63 ![X0]: (star(X0)=multiplication(star(X0),addition(one,addition(X0,one))))),
% 0.13/5.63 inference(forward_demodulation,[status(thm)],[f83,f2040])).
% 0.13/5.63 fof(f2042,plain,(
% 0.13/5.63 ![X0]: (star(X0)=multiplication(star(X0),addition(X0,one)))),
% 0.13/5.63 inference(forward_demodulation,[status(thm)],[f616,f2041])).
% 0.13/5.63 fof(f3523,plain,(
% 0.13/5.63 ~star(sK0_skl)=star(sK0_skl)),
% 0.13/5.63 inference(backward_demodulation,[status(thm)],[f2042,f1790])).
% 0.13/5.63 fof(f3585,plain,(
% 0.13/5.63 $false),
% 0.13/5.63 inference(trivial_equality_resolution,[status(thm)],[f3523])).
% 0.13/5.63 % SZS output end CNFRefutation for theBenchmark.p
% 0.13/5.65 % Elapsed time: 0.270623 seconds
% 0.13/5.65 % CPU time: 1.936175 seconds
% 0.13/5.65 % Total memory used: 91.846 MB
% 0.13/5.65 % Net memory used: 90.646 MB
%------------------------------------------------------------------------------