%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : KLE142+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 : 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 0.12s 0.42s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE142+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n009.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sun Sep 20 22:46:12 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 0.12/0.42 % Refutation found
% 0.12/0.42 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.42 % SZS output start CNFRefutation for theBenchmark
% 0.12/0.42 fof(f1,axiom,(
% 0.12/0.42 (! [A,B] : addition(A,B) = addition(B,A) )),
% 0.12/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.42 fof(f2,axiom,(
% 0.12/0.42 (! [C,B,A] : addition(A,addition(B,C)) = addition(addition(A,B),C) )),
% 0.12/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.42 fof(f4,axiom,(
% 0.12/0.42 (! [A] : addition(A,A) = A )),
% 0.12/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.42 fof(f6,axiom,(
% 0.12/0.42 (! [A] : multiplication(A,one) = A )),
% 0.12/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.42 fof(f7,axiom,(
% 0.12/0.42 (! [A] : multiplication(one,A) = A )),
% 0.12/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.42 fof(f9,axiom,(
% 0.12/0.42 (! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) )),
% 0.12/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.42 fof(f15,axiom,(
% 0.12/0.42 (! [A] : strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one) )),
% 0.12/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.42 fof(f16,axiom,(
% 0.12/0.42 (! [A,B,C] :( leq(C,addition(multiplication(A,C),B))=> leq(C,multiplication(strong_iteration(A),B)) ) )),
% 0.12/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.42 fof(f18,axiom,(
% 0.12/0.42 (! [A,B] :( leq(A,B)<=> addition(A,B) = B ) )),
% 0.12/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.42 fof(f19,conjecture,(
% 0.12/0.42 (! [X0] : strong_iteration(strong_iteration(X0)) = strong_iteration(one) )),
% 0.12/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.42 fof(f20,negated_conjecture,(
% 0.12/0.42 ~((! [X0] : strong_iteration(strong_iteration(X0)) = strong_iteration(one) ))),
% 0.12/0.42 inference(negated_conjecture,[status(cth)],[f19])).
% 0.12/0.42 fof(f21,plain,(
% 0.12/0.42 ![X0,X1]: (addition(X0,X1)=addition(X1,X0))),
% 0.12/0.42 inference(cnf_transformation,[status(thm)],[f1])).
% 0.12/0.42 fof(f22,plain,(
% 0.12/0.42 ![X0,X1,X2]: (addition(X0,addition(X1,X2))=addition(addition(X0,X1),X2))),
% 0.12/0.42 inference(cnf_transformation,[status(thm)],[f2])).
% 0.12/0.42 fof(f24,plain,(
% 0.12/0.42 ![X0]: (addition(X0,X0)=X0)),
% 0.12/0.42 inference(cnf_transformation,[status(thm)],[f4])).
% 0.12/0.42 fof(f26,plain,(
% 0.12/0.42 ![X0]: (multiplication(X0,one)=X0)),
% 0.12/0.42 inference(cnf_transformation,[status(thm)],[f6])).
% 0.12/0.42 fof(f27,plain,(
% 0.12/0.42 ![X0]: (multiplication(one,X0)=X0)),
% 0.12/0.42 inference(cnf_transformation,[status(thm)],[f7])).
% 0.12/0.42 fof(f29,plain,(
% 0.12/0.42 ![X0,X1,X2]: (multiplication(addition(X0,X1),X2)=addition(multiplication(X0,X2),multiplication(X1,X2)))),
% 0.12/0.42 inference(cnf_transformation,[status(thm)],[f9])).
% 0.12/0.42 fof(f37,plain,(
% 0.12/0.42 ![X0]: (strong_iteration(X0)=addition(multiplication(X0,strong_iteration(X0)),one))),
% 0.12/0.42 inference(cnf_transformation,[status(thm)],[f15])).
% 0.12/0.42 fof(f38,plain,(
% 0.12/0.42 ![A,B,C]: (~leq(C,addition(multiplication(A,C),B))|leq(C,multiplication(strong_iteration(A),B)))),
% 0.12/0.42 inference(pre_NNF_transformation,[status(thm)],[f16])).
% 0.12/0.42 fof(f39,plain,(
% 0.12/0.42 ![X0,X1,X2]: (~leq(X0,addition(multiplication(X1,X0),X2))|leq(X0,multiplication(strong_iteration(X1),X2)))),
% 0.12/0.42 inference(cnf_transformation,[status(thm)],[f38])).
% 0.12/0.42 fof(f41,plain,(
% 0.12/0.42 ![A,B]: ((~leq(A,B)|addition(A,B)=B)&(leq(A,B)|~addition(A,B)=B))),
% 0.12/0.42 inference(NNF_transformation,[status(thm)],[f18])).
% 0.12/0.42 fof(f42,plain,(
% 0.12/0.42 (![A,B]: (~leq(A,B)|addition(A,B)=B))&(![A,B]: (leq(A,B)|~addition(A,B)=B))),
% 0.12/0.42 inference(miniscoping,[status(thm)],[f41])).
% 0.12/0.42 fof(f43,plain,(
% 0.12/0.42 ![X0,X1]: (~leq(X0,X1)|addition(X0,X1)=X1)),
% 0.12/0.42 inference(cnf_transformation,[status(thm)],[f42])).
% 0.12/0.42 fof(f44,plain,(
% 0.12/0.42 ![X0,X1]: (leq(X0,X1)|~addition(X0,X1)=X1)),
% 0.12/0.42 inference(cnf_transformation,[status(thm)],[f42])).
% 0.12/0.42 fof(f45,plain,(
% 0.12/0.42 (?[X0]: ~strong_iteration(strong_iteration(X0))=strong_iteration(one))),
% 0.12/0.42 inference(pre_NNF_transformation,[status(thm)],[f20])).
% 0.12/0.42 fof(f46,plain,(
% 0.12/0.42 ~strong_iteration(strong_iteration(sK0_skl))=strong_iteration(one)),
% 0.12/0.42 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(X0,sK0_skl)],[f45])).
% 0.12/0.42 fof(f47,plain,(
% 0.12/0.42 ~strong_iteration(strong_iteration(sK0_skl))=strong_iteration(one)),
% 0.12/0.42 inference(cnf_transformation,[status(thm)],[f46])).
% 0.12/0.42 fof(f50,plain,(
% 0.12/0.42 ![X0,X1]: (~leq(X0,addition(X0,X1))|leq(X0,multiplication(strong_iteration(one),X1)))),
% 0.12/0.43 inference(paramodulation,[status(thm)],[f27,f39])).
% 0.12/0.43 fof(f104,plain,(
% 0.12/0.43 ![X0]: (strong_iteration(X0)=addition(one,multiplication(X0,strong_iteration(X0))))),
% 0.12/0.43 inference(paramodulation,[status(thm)],[f37,f21])).
% 0.12/0.43 fof(f215,plain,(
% 0.12/0.43 ![X0,X1]: (addition(X0,addition(X0,X1))=addition(X0,X1))),
% 0.12/0.43 inference(paramodulation,[status(thm)],[f24,f22])).
% 0.12/0.43 fof(f226,plain,(
% 0.12/0.43 ![X0,X1]: (leq(X0,addition(X0,X1)))),
% 0.12/0.43 inference(resolution,[status(thm)],[f215,f44])).
% 0.12/0.43 fof(f235,plain,(
% 0.12/0.43 ![X0]: (addition(one,strong_iteration(X0))=addition(one,multiplication(X0,strong_iteration(X0))))),
% 0.12/0.43 inference(paramodulation,[status(thm)],[f104,f215])).
% 0.12/0.43 fof(f250,plain,(
% 0.12/0.43 ![X0,X1]: (leq(X0,multiplication(strong_iteration(one),X1)))),
% 0.12/0.43 inference(backward_subsumption_resolution,[status(thm)],[f50,f226])).
% 0.12/0.43 fof(f261,plain,(
% 0.12/0.43 ![X0]: (addition(one,strong_iteration(X0))=strong_iteration(X0))),
% 0.12/0.43 inference(forward_demodulation,[status(thm)],[f104,f235])).
% 0.12/0.43 fof(f316,plain,(
% 0.12/0.43 ![X0]: (leq(X0,strong_iteration(one)))),
% 0.12/0.43 inference(paramodulation,[status(thm)],[f26,f250])).
% 0.12/0.43 fof(f375,plain,(
% 0.12/0.43 ![X0,X1]: (multiplication(addition(one,X0),X1)=addition(X1,multiplication(X0,X1)))),
% 0.12/0.43 inference(paramodulation,[status(thm)],[f27,f29])).
% 0.12/0.43 fof(f402,plain,(
% 0.12/0.43 ![X0]: (addition(X0,strong_iteration(one))=strong_iteration(one))),
% 0.12/0.43 inference(resolution,[status(thm)],[f316,f43])).
% 0.12/0.43 fof(f408,plain,(
% 0.12/0.43 ![X0]: (addition(strong_iteration(one),X0)=strong_iteration(one))),
% 0.12/0.43 inference(paramodulation,[status(thm)],[f21,f402])).
% 0.12/0.43 fof(f531,plain,(
% 0.12/0.43 ![X0,X1,X2]: (~leq(X0,addition(addition(X0,multiplication(X1,X0)),X2))|leq(X0,multiplication(strong_iteration(addition(one,X1)),X2)))),
% 0.12/0.43 inference(paramodulation,[status(thm)],[f375,f39])).
% 0.12/0.43 fof(f563,plain,(
% 0.12/0.43 ![X0,X1,X2]: (~leq(X0,addition(X0,addition(multiplication(X1,X0),X2)))|leq(X0,multiplication(strong_iteration(addition(one,X1)),X2)))),
% 0.12/0.43 inference(forward_demodulation,[status(thm)],[f22,f531])).
% 0.12/0.43 fof(f564,plain,(
% 0.12/0.43 ![X0,X1,X2]: (leq(X0,multiplication(strong_iteration(addition(one,X1)),X2)))),
% 0.12/0.43 inference(forward_subsumption_resolution,[status(thm)],[f563,f226])).
% 0.12/0.43 fof(f592,plain,(
% 0.12/0.43 ![X0,X1]: (leq(X0,strong_iteration(addition(one,X1))))),
% 0.12/0.43 inference(paramodulation,[status(thm)],[f26,f564])).
% 0.12/0.43 fof(f605,plain,(
% 0.12/0.43 ![X0,X1]: (leq(X0,strong_iteration(strong_iteration(X1))))),
% 0.12/0.43 inference(paramodulation,[status(thm)],[f261,f592])).
% 0.12/0.43 fof(f616,plain,(
% 0.12/0.43 ![X0,X1]: (addition(X0,strong_iteration(strong_iteration(X1)))=strong_iteration(strong_iteration(X1)))),
% 0.12/0.43 inference(resolution,[status(thm)],[f605,f43])).
% 0.12/0.43 fof(f661,plain,(
% 0.12/0.43 ![X0]: (strong_iteration(one)=strong_iteration(strong_iteration(X0)))),
% 0.12/0.43 inference(paramodulation,[status(thm)],[f408,f616])).
% 0.12/0.43 fof(f689,plain,(
% 0.12/0.43 ~strong_iteration(one)=strong_iteration(one)),
% 0.12/0.43 inference(backward_demodulation,[status(thm)],[f661,f47])).
% 0.12/0.43 fof(f730,plain,(
% 0.12/0.43 $false),
% 0.12/0.43 inference(trivial_equality_resolution,[status(thm)],[f689])).
% 0.12/0.43 % SZS output end CNFRefutation for theBenchmark.p
% 0.12/0.44 % Elapsed time: 0.079193 seconds
% 0.12/0.44 % CPU time: 0.366307 seconds
% 0.12/0.44 % Total memory used: 71.915 MB
% 0.12/0.44 % Net memory used: 71.501 MB
%------------------------------------------------------------------------------