%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : KLE141+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 : n009.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 12:58:23 PM UTC 2026
% Result : Theorem 2.58s 0.85s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KLE141+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.44 % Computer : n009.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Sun Sep 20 22:45:57 UTC 2026
% 0.17/0.45 % CPUTime :
% 0.17/0.46 % Drodi V4.1.1
% 2.58/0.85 % Refutation found
% 2.58/0.85 % SZS status Theorem for theBenchmark: Theorem is valid
% 2.58/0.85 % SZS output start CNFRefutation for theBenchmark
% 2.58/0.85 fof(f1,axiom,(
% 2.58/0.85 (! [A,B] : addition(A,B) = addition(B,A) )),
% 2.58/0.85 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.58/0.85 fof(f2,axiom,(
% 2.58/0.85 (! [C,B,A] : addition(A,addition(B,C)) = addition(addition(A,B),C) )),
% 2.58/0.85 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.58/0.85 fof(f3,axiom,(
% 2.58/0.85 (! [A] : addition(A,zero) = A )),
% 2.58/0.85 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.58/0.85 fof(f4,axiom,(
% 2.58/0.85 (! [A] : addition(A,A) = A )),
% 2.58/0.85 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.58/0.85 fof(f6,axiom,(
% 2.58/0.85 (! [A] : multiplication(A,one) = A )),
% 2.58/0.85 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.58/0.85 fof(f7,axiom,(
% 2.58/0.85 (! [A] : multiplication(one,A) = A )),
% 2.58/0.85 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.58/0.85 fof(f8,axiom,(
% 2.58/0.85 (! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) )),
% 2.58/0.85 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.58/0.85 fof(f9,axiom,(
% 2.58/0.85 (! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) )),
% 2.58/0.85 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.58/0.85 fof(f15,axiom,(
% 2.58/0.85 (! [A] : strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one) )),
% 2.58/0.85 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.58/0.85 fof(f16,axiom,(
% 2.58/0.85 (! [A,B,C] :( leq(C,addition(multiplication(A,C),B))=> leq(C,multiplication(strong_iteration(A),B)) ) )),
% 2.58/0.85 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.58/0.85 fof(f17,axiom,(
% 2.58/0.85 (! [A] : strong_iteration(A) = addition(star(A),multiplication(strong_iteration(A),zero)) )),
% 2.58/0.85 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.58/0.85 fof(f18,axiom,(
% 2.58/0.85 (! [A,B] :( leq(A,B)<=> addition(A,B) = B ) )),
% 2.58/0.85 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.58/0.85 fof(f19,conjecture,(
% 2.58/0.85 (! [X0] : multiplication(strong_iteration(one),X0) = strong_iteration(one) )),
% 2.58/0.85 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.58/0.85 fof(f20,negated_conjecture,(
% 2.58/0.85 ~((! [X0] : multiplication(strong_iteration(one),X0) = strong_iteration(one) ))),
% 2.58/0.85 inference(negated_conjecture,[status(cth)],[f19])).
% 2.58/0.85 fof(f21,plain,(
% 2.58/0.85 ![X0,X1]: (addition(X0,X1)=addition(X1,X0))),
% 2.58/0.85 inference(cnf_transformation,[status(thm)],[f1])).
% 2.58/0.85 fof(f22,plain,(
% 2.58/0.85 ![X0,X1,X2]: (addition(X0,addition(X1,X2))=addition(addition(X0,X1),X2))),
% 2.58/0.85 inference(cnf_transformation,[status(thm)],[f2])).
% 2.58/0.85 fof(f23,plain,(
% 2.58/0.85 ![X0]: (addition(X0,zero)=X0)),
% 2.58/0.85 inference(cnf_transformation,[status(thm)],[f3])).
% 2.58/0.85 fof(f24,plain,(
% 2.58/0.85 ![X0]: (addition(X0,X0)=X0)),
% 2.58/0.85 inference(cnf_transformation,[status(thm)],[f4])).
% 2.58/0.85 fof(f26,plain,(
% 2.58/0.85 ![X0]: (multiplication(X0,one)=X0)),
% 2.58/0.85 inference(cnf_transformation,[status(thm)],[f6])).
% 2.58/0.85 fof(f27,plain,(
% 2.58/0.85 ![X0]: (multiplication(one,X0)=X0)),
% 2.58/0.85 inference(cnf_transformation,[status(thm)],[f7])).
% 2.58/0.85 fof(f28,plain,(
% 2.58/0.85 ![X0,X1,X2]: (multiplication(X0,addition(X1,X2))=addition(multiplication(X0,X1),multiplication(X0,X2)))),
% 2.58/0.85 inference(cnf_transformation,[status(thm)],[f8])).
% 2.58/0.85 fof(f29,plain,(
% 2.58/0.85 ![X0,X1,X2]: (multiplication(addition(X0,X1),X2)=addition(multiplication(X0,X2),multiplication(X1,X2)))),
% 2.58/0.85 inference(cnf_transformation,[status(thm)],[f9])).
% 2.58/0.85 fof(f37,plain,(
% 2.58/0.85 ![X0]: (strong_iteration(X0)=addition(multiplication(X0,strong_iteration(X0)),one))),
% 2.58/0.85 inference(cnf_transformation,[status(thm)],[f15])).
% 2.58/0.85 fof(f38,plain,(
% 2.58/0.85 ![A,B,C]: (~leq(C,addition(multiplication(A,C),B))|leq(C,multiplication(strong_iteration(A),B)))),
% 2.58/0.85 inference(pre_NNF_transformation,[status(thm)],[f16])).
% 2.58/0.85 fof(f39,plain,(
% 2.58/0.85 ![X0,X1,X2]: (~leq(X0,addition(multiplication(X1,X0),X2))|leq(X0,multiplication(strong_iteration(X1),X2)))),
% 2.58/0.85 inference(cnf_transformation,[status(thm)],[f38])).
% 2.58/0.85 fof(f40,plain,(
% 2.58/0.85 ![X0]: (strong_iteration(X0)=addition(star(X0),multiplication(strong_iteration(X0),zero)))),
% 2.58/0.85 inference(cnf_transformation,[status(thm)],[f17])).
% 2.58/0.85 fof(f41,plain,(
% 2.58/0.85 ![A,B]: ((~leq(A,B)|addition(A,B)=B)&(leq(A,B)|~addition(A,B)=B))),
% 2.58/0.85 inference(NNF_transformation,[status(thm)],[f18])).
% 2.58/0.85 fof(f42,plain,(
% 2.58/0.85 (![A,B]: (~leq(A,B)|addition(A,B)=B))&(![A,B]: (leq(A,B)|~addition(A,B)=B))),
% 2.58/0.85 inference(miniscoping,[status(thm)],[f41])).
% 2.58/0.85 fof(f43,plain,(
% 2.58/0.85 ![X0,X1]: (~leq(X0,X1)|addition(X0,X1)=X1)),
% 2.58/0.85 inference(cnf_transformation,[status(thm)],[f42])).
% 2.58/0.85 fof(f44,plain,(
% 2.58/0.85 ![X0,X1]: (leq(X0,X1)|~addition(X0,X1)=X1)),
% 2.58/0.85 inference(cnf_transformation,[status(thm)],[f42])).
% 2.58/0.85 fof(f45,plain,(
% 2.58/0.85 (?[X0]: ~multiplication(strong_iteration(one),X0)=strong_iteration(one))),
% 2.58/0.85 inference(pre_NNF_transformation,[status(thm)],[f20])).
% 2.58/0.85 fof(f46,plain,(
% 2.58/0.85 ~multiplication(strong_iteration(one),sK0_skl)=strong_iteration(one)),
% 2.58/0.85 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(X0,sK0_skl)],[f45])).
% 2.58/0.85 fof(f47,plain,(
% 2.58/0.85 ~multiplication(strong_iteration(one),sK0_skl)=strong_iteration(one)),
% 2.58/0.85 inference(cnf_transformation,[status(thm)],[f46])).
% 2.58/0.85 fof(f64,plain,(
% 2.58/0.85 ![X0,X1]: (~leq(X0,addition(X0,X1))|leq(X0,multiplication(strong_iteration(one),X1)))),
% 2.58/0.85 inference(paramodulation,[status(thm)],[f27,f39])).
% 2.58/0.85 fof(f186,plain,(
% 2.58/0.85 ![X0]: (strong_iteration(X0)=addition(one,multiplication(X0,strong_iteration(X0))))),
% 2.58/0.85 inference(paramodulation,[status(thm)],[f37,f21])).
% 2.58/0.85 fof(f302,plain,(
% 2.58/0.85 ![X0,X1]: (addition(X0,addition(X0,X1))=addition(X0,X1))),
% 2.58/0.85 inference(paramodulation,[status(thm)],[f24,f22])).
% 2.58/0.85 fof(f313,plain,(
% 2.58/0.85 ![X0,X1]: (leq(X0,addition(X0,X1)))),
% 2.58/0.85 inference(resolution,[status(thm)],[f302,f44])).
% 2.58/0.85 fof(f320,plain,(
% 2.58/0.85 ![X0]: (addition(multiplication(X0,strong_iteration(X0)),strong_iteration(X0))=addition(multiplication(X0,strong_iteration(X0)),one))),
% 2.58/0.85 inference(paramodulation,[status(thm)],[f37,f302])).
% 2.58/0.85 fof(f323,plain,(
% 2.58/0.85 ![X0]: (addition(one,strong_iteration(X0))=addition(one,multiplication(X0,strong_iteration(X0))))),
% 2.58/0.85 inference(paramodulation,[status(thm)],[f186,f302])).
% 2.58/0.85 fof(f328,plain,(
% 2.58/0.85 ![X0,X1]: (addition(X0,addition(X1,X0))=addition(X0,X1))),
% 2.58/0.85 inference(paramodulation,[status(thm)],[f21,f302])).
% 2.58/0.85 fof(f340,plain,(
% 2.58/0.85 ![X0,X1]: (leq(X0,multiplication(strong_iteration(one),X1)))),
% 2.58/0.85 inference(backward_subsumption_resolution,[status(thm)],[f64,f313])).
% 2.58/0.85 fof(f347,plain,(
% 2.58/0.85 ![X0]: (addition(multiplication(X0,strong_iteration(X0)),strong_iteration(X0))=strong_iteration(X0))),
% 2.58/0.85 inference(forward_demodulation,[status(thm)],[f37,f320])).
% 2.58/0.85 fof(f352,plain,(
% 2.58/0.85 ![X0]: (addition(one,strong_iteration(X0))=strong_iteration(X0))),
% 2.58/0.85 inference(forward_demodulation,[status(thm)],[f186,f323])).
% 2.58/0.85 fof(f410,plain,(
% 2.58/0.85 ![X0,X1]: (multiplication(X0,addition(X1,one))=addition(multiplication(X0,X1),X0))),
% 2.58/0.85 inference(paramodulation,[status(thm)],[f26,f28])).
% 2.58/0.85 fof(f443,plain,(
% 2.58/0.85 ![X0,X1]: (multiplication(addition(one,X0),X1)=addition(X1,multiplication(X0,X1)))),
% 2.58/0.85 inference(paramodulation,[status(thm)],[f27,f29])).
% 2.58/0.85 fof(f498,plain,(
% 2.58/0.85 ![X0,X1]: (addition(X0,multiplication(strong_iteration(one),X1))=multiplication(strong_iteration(one),X1))),
% 2.58/0.85 inference(resolution,[status(thm)],[f340,f43])).
% 2.58/0.85 fof(f499,plain,(
% 2.58/0.85 ![X0]: (leq(X0,strong_iteration(one)))),
% 2.58/0.85 inference(paramodulation,[status(thm)],[f26,f340])).
% 2.58/0.85 fof(f503,plain,(
% 2.58/0.85 ![X0]: (addition(X0,strong_iteration(one))=strong_iteration(one))),
% 2.58/0.85 inference(resolution,[status(thm)],[f499,f43])).
% 2.58/0.85 fof(f579,plain,(
% 2.58/0.85 ![X0]: (addition(strong_iteration(X0),multiplication(X0,strong_iteration(X0)))=strong_iteration(X0))),
% 2.58/0.85 inference(paramodulation,[status(thm)],[f21,f347])).
% 2.58/0.85 fof(f850,plain,(
% 2.58/0.85 ![X0]: (multiplication(addition(one,X0),strong_iteration(X0))=strong_iteration(X0))),
% 2.58/0.85 inference(paramodulation,[status(thm)],[f579,f443])).
% 2.58/0.85 fof(f1002,plain,(
% 2.58/0.85 ![X0]: (addition(strong_iteration(X0),strong_iteration(X0))=addition(strong_iteration(X0),one))),
% 2.58/0.85 inference(paramodulation,[status(thm)],[f352,f328])).
% 2.58/0.85 fof(f1046,plain,(
% 2.58/0.85 ![X0]: (strong_iteration(X0)=addition(strong_iteration(X0),one))),
% 2.58/0.85 inference(forward_demodulation,[status(thm)],[f24,f1002])).
% 2.58/0.85 fof(f1078,plain,(
% 2.58/0.85 ![X0,X1]: (addition(strong_iteration(X0),addition(one,X1))=addition(strong_iteration(X0),X1))),
% 2.58/0.85 inference(paramodulation,[status(thm)],[f1046,f22])).
% 2.58/0.85 fof(f1331,plain,(
% 2.58/0.85 ![X0]: (multiplication(addition(one,X0),addition(strong_iteration(X0),one))=addition(strong_iteration(X0),addition(one,X0)))),
% 2.58/0.86 inference(paramodulation,[status(thm)],[f850,f410])).
% 2.58/0.86 fof(f1346,plain,(
% 2.58/0.86 ![X0]: (multiplication(addition(one,X0),strong_iteration(X0))=addition(strong_iteration(X0),addition(one,X0)))),
% 2.58/0.86 inference(forward_demodulation,[status(thm)],[f1046,f1331])).
% 2.58/0.86 fof(f1347,plain,(
% 2.58/0.86 ![X0]: (strong_iteration(X0)=addition(strong_iteration(X0),addition(one,X0)))),
% 2.58/0.86 inference(forward_demodulation,[status(thm)],[f850,f1346])).
% 2.58/0.86 fof(f1348,plain,(
% 2.58/0.86 ![X0]: (strong_iteration(X0)=addition(strong_iteration(X0),X0))),
% 2.58/0.86 inference(forward_demodulation,[status(thm)],[f1078,f1347])).
% 2.58/0.86 fof(f1361,plain,(
% 2.58/0.86 strong_iteration(strong_iteration(one))=strong_iteration(one)),
% 2.58/0.86 inference(paramodulation,[status(thm)],[f503,f1348])).
% 2.58/0.86 fof(f1649,plain,(
% 2.58/0.86 strong_iteration(strong_iteration(one))=addition(star(strong_iteration(one)),multiplication(strong_iteration(one),zero))),
% 2.58/0.86 inference(paramodulation,[status(thm)],[f1361,f40])).
% 2.58/0.86 fof(f1665,plain,(
% 2.58/0.86 strong_iteration(one)=addition(star(strong_iteration(one)),multiplication(strong_iteration(one),zero))),
% 2.58/0.86 inference(forward_demodulation,[status(thm)],[f1361,f1649])).
% 2.58/0.86 fof(f1666,plain,(
% 2.58/0.86 strong_iteration(one)=multiplication(strong_iteration(one),zero)),
% 2.58/0.86 inference(forward_demodulation,[status(thm)],[f498,f1665])).
% 2.58/0.86 fof(f1685,plain,(
% 2.58/0.86 ![X0]: (multiplication(strong_iteration(one),addition(X0,zero))=addition(multiplication(strong_iteration(one),X0),strong_iteration(one)))),
% 2.58/0.86 inference(paramodulation,[status(thm)],[f1666,f28])).
% 2.58/0.86 fof(f1707,plain,(
% 2.58/0.86 ![X0]: (multiplication(strong_iteration(one),X0)=addition(multiplication(strong_iteration(one),X0),strong_iteration(one)))),
% 2.58/0.86 inference(forward_demodulation,[status(thm)],[f23,f1685])).
% 2.58/0.86 fof(f1709,plain,(
% 2.58/0.86 ~strong_iteration(one)=strong_iteration(one)),
% 2.58/0.86 inference(backward_demodulation,[status(thm)],[f1716,f47])).
% 2.58/0.86 fof(f1716,plain,(
% 2.58/0.86 ![X0]: (multiplication(strong_iteration(one),X0)=strong_iteration(one))),
% 2.58/0.86 inference(forward_demodulation,[status(thm)],[f503,f1707])).
% 2.58/0.86 fof(f1728,plain,(
% 2.58/0.86 $false),
% 2.58/0.86 inference(trivial_equality_resolution,[status(thm)],[f1709])).
% 2.58/0.86 % SZS output end CNFRefutation for theBenchmark.p
% 2.58/0.88 % Elapsed time: 0.416218 seconds
% 2.58/0.88 % CPU time: 2.948797 seconds
% 2.58/0.88 % Total memory used: 93.968 MB
% 2.58/0.88 % Net memory used: 92.725 MB
%------------------------------------------------------------------------------