%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : KLE150+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 : n001.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 12:58:25 PM UTC 2026
% Result : Theorem 5.53s 1.31s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE150+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
% 0.09/0.35 % Computer : n001.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 22:52:13 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.36 % Drodi V4.1.1
% 5.53/1.31 % Refutation found
% 5.53/1.31 % SZS status Theorem for theBenchmark: Theorem is valid
% 5.53/1.31 % SZS output start CNFRefutation for theBenchmark
% 5.53/1.31 fof(f1,axiom,(
% 5.53/1.31 (! [A,B] : addition(A,B) = addition(B,A) )),
% 5.53/1.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 5.53/1.31 fof(f2,axiom,(
% 5.53/1.31 (! [C,B,A] : addition(A,addition(B,C)) = addition(addition(A,B),C) )),
% 5.53/1.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 5.53/1.31 fof(f4,axiom,(
% 5.53/1.31 (! [A] : addition(A,A) = A )),
% 5.53/1.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 5.53/1.31 fof(f5,axiom,(
% 5.53/1.31 (! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C) )),
% 5.53/1.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 5.53/1.31 fof(f10,axiom,(
% 5.53/1.31 (! [A] : multiplication(zero,A) = zero )),
% 5.53/1.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 5.53/1.31 fof(f11,axiom,(
% 5.53/1.31 (! [A] : addition(one,multiplication(A,star(A))) = star(A) )),
% 5.53/1.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 5.53/1.31 fof(f15,axiom,(
% 5.53/1.31 (! [A] : strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one) )),
% 5.53/1.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 5.53/1.31 fof(f17,axiom,(
% 5.53/1.31 (! [A] : strong_iteration(A) = addition(star(A),multiplication(strong_iteration(A),zero)) )),
% 5.53/1.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 5.53/1.31 fof(f18,axiom,(
% 5.53/1.31 (! [A,B] :( leq(A,B)<=> addition(A,B) = B ) )),
% 5.53/1.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 5.53/1.31 fof(f19,conjecture,(
% 5.53/1.31 (! [X0] :( leq(strong_iteration(multiplication(X0,zero)),addition(one,multiplication(X0,zero)))& leq(addition(one,multiplication(X0,zero)),strong_iteration(multiplication(X0,zero))) ) )),
% 5.53/1.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 5.53/1.31 fof(f20,negated_conjecture,(
% 5.53/1.31 ~((! [X0] :( leq(strong_iteration(multiplication(X0,zero)),addition(one,multiplication(X0,zero)))& leq(addition(one,multiplication(X0,zero)),strong_iteration(multiplication(X0,zero))) ) ))),
% 5.53/1.31 inference(negated_conjecture,[status(cth)],[f19])).
% 5.53/1.31 fof(f21,plain,(
% 5.53/1.31 ![X0,X1]: (addition(X0,X1)=addition(X1,X0))),
% 5.53/1.31 inference(cnf_transformation,[status(thm)],[f1])).
% 5.53/1.31 fof(f22,plain,(
% 5.53/1.31 ![X0,X1,X2]: (addition(X0,addition(X1,X2))=addition(addition(X0,X1),X2))),
% 5.53/1.31 inference(cnf_transformation,[status(thm)],[f2])).
% 5.53/1.31 fof(f24,plain,(
% 5.53/1.31 ![X0]: (addition(X0,X0)=X0)),
% 5.53/1.31 inference(cnf_transformation,[status(thm)],[f4])).
% 5.53/1.31 fof(f25,plain,(
% 5.53/1.31 ![X0,X1,X2]: (multiplication(X0,multiplication(X1,X2))=multiplication(multiplication(X0,X1),X2))),
% 5.53/1.31 inference(cnf_transformation,[status(thm)],[f5])).
% 5.53/1.31 fof(f30,plain,(
% 5.53/1.31 ![X0]: (multiplication(zero,X0)=zero)),
% 5.53/1.31 inference(cnf_transformation,[status(thm)],[f10])).
% 5.53/1.31 fof(f31,plain,(
% 5.53/1.31 ![X0]: (addition(one,multiplication(X0,star(X0)))=star(X0))),
% 5.53/1.31 inference(cnf_transformation,[status(thm)],[f11])).
% 5.53/1.31 fof(f37,plain,(
% 5.53/1.31 ![X0]: (strong_iteration(X0)=addition(multiplication(X0,strong_iteration(X0)),one))),
% 5.53/1.31 inference(cnf_transformation,[status(thm)],[f15])).
% 5.53/1.31 fof(f40,plain,(
% 5.53/1.31 ![X0]: (strong_iteration(X0)=addition(star(X0),multiplication(strong_iteration(X0),zero)))),
% 5.53/1.31 inference(cnf_transformation,[status(thm)],[f17])).
% 5.53/1.31 fof(f41,plain,(
% 5.53/1.31 ![A,B]: ((~leq(A,B)|addition(A,B)=B)&(leq(A,B)|~addition(A,B)=B))),
% 5.53/1.31 inference(NNF_transformation,[status(thm)],[f18])).
% 5.53/1.31 fof(f42,plain,(
% 5.53/1.31 (![A,B]: (~leq(A,B)|addition(A,B)=B))&(![A,B]: (leq(A,B)|~addition(A,B)=B))),
% 5.53/1.31 inference(miniscoping,[status(thm)],[f41])).
% 5.53/1.31 fof(f44,plain,(
% 5.53/1.31 ![X0,X1]: (leq(X0,X1)|~addition(X0,X1)=X1)),
% 5.53/1.31 inference(cnf_transformation,[status(thm)],[f42])).
% 5.53/1.31 fof(f45,plain,(
% 5.53/1.31 (?[X0]: (~leq(strong_iteration(multiplication(X0,zero)),addition(one,multiplication(X0,zero)))|~leq(addition(one,multiplication(X0,zero)),strong_iteration(multiplication(X0,zero)))))),
% 5.53/1.31 inference(pre_NNF_transformation,[status(thm)],[f20])).
% 5.53/1.31 fof(f46,plain,(
% 5.53/1.31 (?[X0]: ~leq(strong_iteration(multiplication(X0,zero)),addition(one,multiplication(X0,zero))))|(?[X0]: ~leq(addition(one,multiplication(X0,zero)),strong_iteration(multiplication(X0,zero))))),
% 5.53/1.31 inference(miniscoping,[status(thm)],[f45])).
% 5.53/1.31 fof(f47,plain,(
% 5.53/1.31 ~leq(strong_iteration(multiplication(sK0_skl,zero)),addition(one,multiplication(sK0_skl,zero)))|~leq(addition(one,multiplication(sK1_skl,zero)),strong_iteration(multiplication(sK1_skl,zero)))),
% 5.53/1.32 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(X0,sK0_skl),skolemize(X0,sK1_skl)],[f46])).
% 5.53/1.32 fof(f48,plain,(
% 5.53/1.32 ~leq(strong_iteration(multiplication(sK0_skl,zero)),addition(one,multiplication(sK0_skl,zero)))|~leq(addition(one,multiplication(sK1_skl,zero)),strong_iteration(multiplication(sK1_skl,zero)))),
% 5.53/1.32 inference(cnf_transformation,[status(thm)],[f47])).
% 5.53/1.32 fof(f49,plain,(
% 5.53/1.32 ![X0]: (strong_iteration(X0)=addition(one,multiplication(X0,strong_iteration(X0))))),
% 5.53/1.32 inference(forward_demodulation,[status(thm)],[f21,f37])).
% 5.53/1.32 fof(f71,plain,(
% 5.53/1.32 ![X0]: (leq(X0,X0))),
% 5.53/1.32 inference(resolution,[status(thm)],[f44,f24])).
% 5.53/1.32 fof(f115,plain,(
% 5.53/1.32 ![X0,X1]: (addition(X0,addition(X0,X1))=addition(X0,X1))),
% 5.53/1.32 inference(paramodulation,[status(thm)],[f24,f22])).
% 5.53/1.32 fof(f128,plain,(
% 5.53/1.32 ![X0,X1]: (addition(one,multiplication(X0,multiplication(X1,star(multiplication(X0,X1)))))=star(multiplication(X0,X1)))),
% 5.53/1.32 inference(paramodulation,[status(thm)],[f25,f31])).
% 5.53/1.32 fof(f132,plain,(
% 5.53/1.32 ![X0,X1]: (leq(X0,addition(X0,X1)))),
% 5.53/1.32 inference(resolution,[status(thm)],[f115,f44])).
% 5.53/1.32 fof(f434,plain,(
% 5.53/1.32 ![X0,X1]: (strong_iteration(multiplication(X0,X1))=addition(one,multiplication(X0,multiplication(X1,strong_iteration(multiplication(X0,X1))))))),
% 5.53/1.32 inference(paramodulation,[status(thm)],[f25,f49])).
% 5.53/1.32 fof(f1926,plain,(
% 5.53/1.32 ![X0]: (leq(star(X0),strong_iteration(X0)))),
% 5.53/1.32 inference(paramodulation,[status(thm)],[f40,f132])).
% 5.53/1.32 fof(f4349,plain,(
% 5.53/1.32 ![X0]: (addition(one,multiplication(X0,zero))=star(multiplication(X0,zero)))),
% 5.53/1.32 inference(paramodulation,[status(thm)],[f30,f128])).
% 5.53/1.32 fof(f4408,plain,(
% 5.53/1.32 ~leq(strong_iteration(multiplication(sK0_skl,zero)),addition(one,multiplication(sK0_skl,zero)))|~leq(star(multiplication(sK1_skl,zero)),strong_iteration(multiplication(sK1_skl,zero)))),
% 5.53/1.32 inference(backward_demodulation,[status(thm)],[f4349,f48])).
% 5.53/1.32 fof(f4477,plain,(
% 5.53/1.32 ~leq(strong_iteration(multiplication(sK0_skl,zero)),star(multiplication(sK0_skl,zero)))|~leq(star(multiplication(sK1_skl,zero)),strong_iteration(multiplication(sK1_skl,zero)))),
% 5.53/1.32 inference(forward_demodulation,[status(thm)],[f4349,f4408])).
% 5.53/1.32 fof(f4478,plain,(
% 5.53/1.32 ~leq(strong_iteration(multiplication(sK0_skl,zero)),star(multiplication(sK0_skl,zero)))),
% 5.53/1.32 inference(forward_subsumption_resolution,[status(thm)],[f4477,f1926])).
% 5.53/1.32 fof(f5709,plain,(
% 5.53/1.32 ![X0]: (strong_iteration(multiplication(X0,zero))=addition(one,multiplication(X0,zero)))),
% 5.53/1.32 inference(paramodulation,[status(thm)],[f30,f434])).
% 5.53/1.32 fof(f5769,plain,(
% 5.53/1.32 ~leq(star(multiplication(sK0_skl,zero)),star(multiplication(sK0_skl,zero)))),
% 5.53/1.32 inference(backward_demodulation,[status(thm)],[f5770,f4478])).
% 5.53/1.32 fof(f5770,plain,(
% 5.53/1.32 ![X0]: (strong_iteration(multiplication(X0,zero))=star(multiplication(X0,zero)))),
% 5.53/1.32 inference(forward_demodulation,[status(thm)],[f4349,f5709])).
% 5.53/1.32 fof(f5840,plain,(
% 5.53/1.32 $false),
% 5.53/1.32 inference(forward_subsumption_resolution,[status(thm)],[f5769,f71])).
% 5.53/1.32 % SZS output end CNFRefutation for theBenchmark.p
% 1.02/1.34 % Elapsed time: 0.966050 seconds
% 1.02/1.34 % CPU time: 7.356009 seconds
% 1.02/1.34 % Total memory used: 135.334 MB
% 1.02/1.34 % Net memory used: 133.134 MB
%------------------------------------------------------------------------------