%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : KLE142+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 : n026.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 4.20s 1.08s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KLE142+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n026.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Sun Sep 20 22:48:52 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.45 % Drodi V4.1.1
% 4.20/1.08 % Refutation found
% 4.20/1.08 % SZS status Theorem for theBenchmark: Theorem is valid
% 4.20/1.08 % SZS output start CNFRefutation for theBenchmark
% 4.20/1.08 fof(f1,axiom,(
% 4.20/1.08 (! [A,B] : addition(A,B) = addition(B,A) )),
% 4.20/1.08 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 4.20/1.08 fof(f2,axiom,(
% 4.20/1.08 (! [C,B,A] : addition(A,addition(B,C)) = addition(addition(A,B),C) )),
% 4.20/1.08 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 4.20/1.08 fof(f3,axiom,(
% 4.20/1.08 (! [A] : addition(A,zero) = A )),
% 4.20/1.08 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 4.20/1.08 fof(f4,axiom,(
% 4.20/1.08 (! [A] : addition(A,A) = A )),
% 4.20/1.08 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 4.20/1.08 fof(f6,axiom,(
% 4.20/1.08 (! [A] : multiplication(A,one) = A )),
% 4.20/1.08 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 4.20/1.08 fof(f7,axiom,(
% 4.20/1.08 (! [A] : multiplication(one,A) = A )),
% 4.20/1.08 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 4.20/1.08 fof(f9,axiom,(
% 4.20/1.08 (! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) )),
% 4.20/1.08 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 4.20/1.08 fof(f15,axiom,(
% 4.20/1.08 (! [A] : strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one) )),
% 4.20/1.08 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 4.20/1.08 fof(f16,axiom,(
% 4.20/1.08 (! [A,B,C] :( leq(C,addition(multiplication(A,C),B))=> leq(C,multiplication(strong_iteration(A),B)) ) )),
% 4.20/1.08 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 4.20/1.08 fof(f18,axiom,(
% 4.20/1.08 (! [A,B] :( leq(A,B)<=> addition(A,B) = B ) )),
% 4.20/1.08 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 4.20/1.08 fof(f19,conjecture,(
% 4.20/1.08 (! [X0] :( leq(strong_iteration(strong_iteration(X0)),strong_iteration(one))& leq(strong_iteration(one),strong_iteration(strong_iteration(X0))) ) )),
% 4.20/1.08 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 4.20/1.08 fof(f20,negated_conjecture,(
% 4.20/1.08 ~((! [X0] :( leq(strong_iteration(strong_iteration(X0)),strong_iteration(one))& leq(strong_iteration(one),strong_iteration(strong_iteration(X0))) ) ))),
% 4.20/1.08 inference(negated_conjecture,[status(cth)],[f19])).
% 4.20/1.08 fof(f21,plain,(
% 4.20/1.08 ![X0,X1]: (addition(X0,X1)=addition(X1,X0))),
% 4.20/1.08 inference(cnf_transformation,[status(thm)],[f1])).
% 4.20/1.08 fof(f22,plain,(
% 4.20/1.08 ![X0,X1,X2]: (addition(X0,addition(X1,X2))=addition(addition(X0,X1),X2))),
% 4.20/1.08 inference(cnf_transformation,[status(thm)],[f2])).
% 4.20/1.08 fof(f23,plain,(
% 4.20/1.08 ![X0]: (addition(X0,zero)=X0)),
% 4.20/1.08 inference(cnf_transformation,[status(thm)],[f3])).
% 4.20/1.08 fof(f24,plain,(
% 4.20/1.08 ![X0]: (addition(X0,X0)=X0)),
% 4.20/1.08 inference(cnf_transformation,[status(thm)],[f4])).
% 4.20/1.08 fof(f26,plain,(
% 4.20/1.08 ![X0]: (multiplication(X0,one)=X0)),
% 4.20/1.08 inference(cnf_transformation,[status(thm)],[f6])).
% 4.20/1.08 fof(f27,plain,(
% 4.20/1.08 ![X0]: (multiplication(one,X0)=X0)),
% 4.20/1.08 inference(cnf_transformation,[status(thm)],[f7])).
% 4.20/1.08 fof(f29,plain,(
% 4.20/1.08 ![X0,X1,X2]: (multiplication(addition(X0,X1),X2)=addition(multiplication(X0,X2),multiplication(X1,X2)))),
% 4.20/1.08 inference(cnf_transformation,[status(thm)],[f9])).
% 4.20/1.08 fof(f37,plain,(
% 4.20/1.08 ![X0]: (strong_iteration(X0)=addition(multiplication(X0,strong_iteration(X0)),one))),
% 4.20/1.08 inference(cnf_transformation,[status(thm)],[f15])).
% 4.20/1.08 fof(f38,plain,(
% 4.20/1.08 ![A,B,C]: (~leq(C,addition(multiplication(A,C),B))|leq(C,multiplication(strong_iteration(A),B)))),
% 4.20/1.08 inference(pre_NNF_transformation,[status(thm)],[f16])).
% 4.20/1.08 fof(f39,plain,(
% 4.20/1.08 ![X0,X1,X2]: (~leq(X0,addition(multiplication(X1,X0),X2))|leq(X0,multiplication(strong_iteration(X1),X2)))),
% 4.20/1.08 inference(cnf_transformation,[status(thm)],[f38])).
% 4.20/1.08 fof(f41,plain,(
% 4.20/1.08 ![A,B]: ((~leq(A,B)|addition(A,B)=B)&(leq(A,B)|~addition(A,B)=B))),
% 4.20/1.08 inference(NNF_transformation,[status(thm)],[f18])).
% 4.20/1.08 fof(f42,plain,(
% 4.20/1.08 (![A,B]: (~leq(A,B)|addition(A,B)=B))&(![A,B]: (leq(A,B)|~addition(A,B)=B))),
% 4.20/1.08 inference(miniscoping,[status(thm)],[f41])).
% 4.20/1.08 fof(f43,plain,(
% 4.20/1.08 ![X0,X1]: (~leq(X0,X1)|addition(X0,X1)=X1)),
% 4.20/1.08 inference(cnf_transformation,[status(thm)],[f42])).
% 4.20/1.08 fof(f44,plain,(
% 4.20/1.08 ![X0,X1]: (leq(X0,X1)|~addition(X0,X1)=X1)),
% 4.20/1.08 inference(cnf_transformation,[status(thm)],[f42])).
% 4.20/1.08 fof(f45,plain,(
% 4.20/1.08 (?[X0]: (~leq(strong_iteration(strong_iteration(X0)),strong_iteration(one))|~leq(strong_iteration(one),strong_iteration(strong_iteration(X0)))))),
% 4.20/1.08 inference(pre_NNF_transformation,[status(thm)],[f20])).
% 4.20/1.08 fof(f46,plain,(
% 4.20/1.08 (?[X0]: ~leq(strong_iteration(strong_iteration(X0)),strong_iteration(one)))|(?[X0]: ~leq(strong_iteration(one),strong_iteration(strong_iteration(X0))))),
% 4.20/1.08 inference(miniscoping,[status(thm)],[f45])).
% 4.20/1.08 fof(f47,plain,(
% 4.20/1.08 ~leq(strong_iteration(strong_iteration(sK0_skl)),strong_iteration(one))|~leq(strong_iteration(one),strong_iteration(strong_iteration(sK1_skl)))),
% 4.20/1.08 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(X0,sK0_skl),skolemize(X0,sK1_skl)],[f46])).
% 4.20/1.08 fof(f48,plain,(
% 4.20/1.08 ~leq(strong_iteration(strong_iteration(sK0_skl)),strong_iteration(one))|~leq(strong_iteration(one),strong_iteration(strong_iteration(sK1_skl)))),
% 4.20/1.08 inference(cnf_transformation,[status(thm)],[f47])).
% 4.20/1.08 fof(f49,definition,(
% 4.20/1.08 sQ0_spl <=> (leq(strong_iteration(strong_iteration(sK0_skl)),strong_iteration(one)))),
% 4.20/1.08 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 4.20/1.08 fof(f51,plain,(
% 4.20/1.08 ~leq(strong_iteration(strong_iteration(sK0_skl)),strong_iteration(one))|sQ0_spl),
% 4.20/1.08 inference(component_clause,[status(thm)],[f49])).
% 4.20/1.08 fof(f52,definition,(
% 4.20/1.08 sQ1_spl <=> (leq(strong_iteration(one),strong_iteration(strong_iteration(sK1_skl))))),
% 4.20/1.08 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 4.20/1.08 fof(f54,plain,(
% 4.20/1.08 ~leq(strong_iteration(one),strong_iteration(strong_iteration(sK1_skl)))|sQ1_spl),
% 4.20/1.08 inference(component_clause,[status(thm)],[f52])).
% 4.20/1.08 fof(f55,plain,(
% 4.20/1.08 ~sQ0_spl|~sQ1_spl),
% 4.20/1.08 inference(split_clause,[status(thm)],[f48,f49,f52])).
% 4.20/1.08 fof(f110,plain,(
% 4.20/1.08 ![X0,X1]: (addition(X0,addition(X0,X1))=addition(X0,X1))),
% 4.20/1.08 inference(paramodulation,[status(thm)],[f24,f22])).
% 4.20/1.08 fof(f119,plain,(
% 4.20/1.08 ![X0,X1]: (leq(X0,addition(X0,X1)))),
% 4.20/1.08 inference(resolution,[status(thm)],[f110,f44])).
% 4.20/1.08 fof(f126,plain,(
% 4.20/1.08 ![X0,X1]: (addition(X0,addition(X1,X0))=addition(X0,X1))),
% 4.20/1.08 inference(paramodulation,[status(thm)],[f21,f110])).
% 4.20/1.08 fof(f150,plain,(
% 4.20/1.08 ![X0,X1]: (leq(X0,addition(X1,X0)))),
% 4.20/1.08 inference(paramodulation,[status(thm)],[f21,f119])).
% 4.20/1.08 fof(f153,plain,(
% 4.20/1.08 ![X0,X1]: (addition(X0,addition(X1,X0))=addition(X1,X0))),
% 4.20/1.08 inference(resolution,[status(thm)],[f150,f43])).
% 4.20/1.08 fof(f154,plain,(
% 4.20/1.08 ![X0,X1,X2]: (leq(X0,addition(X1,addition(X2,X0))))),
% 4.20/1.08 inference(paramodulation,[status(thm)],[f22,f150])).
% 4.20/1.08 fof(f212,plain,(
% 4.20/1.08 ![X0,X1]: (addition(X0,addition(X0,X1))=addition(X1,X0))),
% 4.20/1.08 inference(paramodulation,[status(thm)],[f21,f153])).
% 4.20/1.08 fof(f281,plain,(
% 4.20/1.08 ![X0,X1,X2]: (addition(X0,addition(addition(X0,X1),X2))=addition(addition(X1,X0),X2))),
% 4.20/1.08 inference(paramodulation,[status(thm)],[f212,f22])).
% 4.20/1.08 fof(f314,plain,(
% 4.20/1.08 ![X0,X1,X2]: (addition(X0,addition(X0,addition(X1,X2)))=addition(addition(X1,X0),X2))),
% 4.20/1.08 inference(forward_demodulation,[status(thm)],[f22,f281])).
% 4.20/1.08 fof(f315,plain,(
% 4.20/1.08 ![X0,X1,X2]: (addition(addition(X0,X1),X2)=addition(addition(X0,X2),X1))),
% 4.20/1.08 inference(forward_demodulation,[status(thm)],[f212,f314])).
% 4.20/1.08 fof(f316,plain,(
% 4.20/1.08 ![X0,X1,X2]: (addition(X0,addition(X1,X2))=addition(addition(X0,X2),X1))),
% 4.20/1.08 inference(forward_demodulation,[status(thm)],[f22,f315])).
% 4.20/1.08 fof(f2075,plain,(
% 4.20/1.08 ![X0,X1]: (multiplication(addition(one,X0),X1)=addition(X1,multiplication(X0,X1)))),
% 4.20/1.08 inference(paramodulation,[status(thm)],[f27,f29])).
% 4.20/1.08 fof(f2392,plain,(
% 4.20/1.08 ![X0,X1]: (addition(multiplication(X0,X1),multiplication(addition(one,X0),X1))=addition(multiplication(X0,X1),X1))),
% 4.20/1.08 inference(paramodulation,[status(thm)],[f2075,f126])).
% 4.20/1.08 fof(f2425,plain,(
% 4.20/1.08 ![X0,X1]: (multiplication(addition(X0,addition(one,X0)),X1)=addition(multiplication(X0,X1),X1))),
% 4.20/1.08 inference(forward_demodulation,[status(thm)],[f29,f2392])).
% 4.20/1.08 fof(f2426,plain,(
% 4.20/1.08 ![X0,X1]: (multiplication(addition(one,X0),X1)=addition(multiplication(X0,X1),X1))),
% 4.20/1.08 inference(forward_demodulation,[status(thm)],[f153,f2425])).
% 4.20/1.08 fof(f5265,plain,(
% 4.20/1.08 ![X0]: (addition(one,strong_iteration(X0))=addition(multiplication(X0,strong_iteration(X0)),one))),
% 4.20/1.08 inference(paramodulation,[status(thm)],[f37,f153])).
% 4.20/1.08 fof(f5294,plain,(
% 4.20/1.08 ![X0]: (addition(one,strong_iteration(X0))=strong_iteration(X0))),
% 4.20/1.08 inference(forward_demodulation,[status(thm)],[f37,f5265])).
% 4.20/1.08 fof(f5582,plain,(
% 4.20/1.08 ![X0,X1,X2]: (~leq(X0,addition(addition(multiplication(X1,X0),X0),X2))|leq(X0,multiplication(strong_iteration(addition(one,X1)),X2)))),
% 4.20/1.09 inference(paramodulation,[status(thm)],[f2426,f39])).
% 4.20/1.09 fof(f5598,plain,(
% 4.20/1.09 ![X0,X1,X2]: (~leq(X0,addition(multiplication(X1,X0),addition(X2,X0)))|leq(X0,multiplication(strong_iteration(addition(one,X1)),X2)))),
% 4.20/1.09 inference(forward_demodulation,[status(thm)],[f316,f5582])).
% 4.20/1.09 fof(f5599,plain,(
% 4.20/1.09 ![X0,X1,X2]: (leq(X0,multiplication(strong_iteration(addition(one,X1)),X2)))),
% 4.20/1.09 inference(forward_subsumption_resolution,[status(thm)],[f5598,f154])).
% 4.20/1.09 fof(f5679,plain,(
% 4.20/1.09 ![X0,X1]: (leq(X0,strong_iteration(addition(one,X1))))),
% 4.20/1.09 inference(paramodulation,[status(thm)],[f26,f5599])).
% 4.20/1.09 fof(f5706,plain,(
% 4.20/1.09 ![X0,X1]: (leq(X0,strong_iteration(strong_iteration(X1))))),
% 4.20/1.09 inference(paramodulation,[status(thm)],[f5294,f5679])).
% 4.20/1.09 fof(f5722,plain,(
% 4.20/1.09 ![X0]: (leq(X0,strong_iteration(one)))),
% 4.20/1.09 inference(paramodulation,[status(thm)],[f23,f5679])).
% 4.20/1.09 fof(f5726,plain,(
% 4.20/1.09 $false|sQ0_spl),
% 4.20/1.09 inference(backward_subsumption_resolution,[status(thm)],[f51,f5722])).
% 4.20/1.09 fof(f5727,plain,(
% 4.20/1.09 sQ0_spl),
% 4.20/1.09 inference(contradiction_clause,[status(thm)],[f5726])).
% 4.20/1.09 fof(f5728,plain,(
% 4.20/1.09 $false|sQ1_spl),
% 4.20/1.09 inference(forward_subsumption_resolution,[status(thm)],[f54,f5706])).
% 4.20/1.09 fof(f5729,plain,(
% 4.20/1.09 sQ1_spl),
% 4.20/1.09 inference(contradiction_clause,[status(thm)],[f5728])).
% 4.20/1.09 fof(f5730,plain,(
% 4.20/1.09 $false),
% 4.20/1.09 inference(sat_refutation,[status(thm)],[f55,f5727,f5729])).
% 4.20/1.09 % SZS output end CNFRefutation for theBenchmark.p
% 4.20/1.11 % Elapsed time: 0.663418 seconds
% 4.20/1.11 % CPU time: 4.912120 seconds
% 4.20/1.11 % Total memory used: 103.896 MB
% 4.20/1.11 % Net memory used: 101.963 MB
%------------------------------------------------------------------------------