%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : NUM478+2 : 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 : n017.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 01:43:00 PM UTC 2026
% Result : Theorem 0.15s 5.86s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM478+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/5.37 % Computer : n017.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Mon Sep 21 02:28:47 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.39 % Drodi V4.1.1
% 0.15/5.86 % Refutation found
% 0.15/5.86 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/5.86 % SZS output start CNFRefutation for theBenchmark
% 0.15/5.86 fof(f5,axiom,(
% 0.15/5.86 (! [W0,W1] :( ( aNaturalNumber0(W0)& aNaturalNumber0(W1) )=> aNaturalNumber0(sdtasdt0(W0,W1)) ) )),
% 0.15/5.86 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/5.86 fof(f9,axiom,(
% 0.15/5.86 (! [W0,W1] :( ( aNaturalNumber0(W0)& aNaturalNumber0(W1) )=> sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) )),
% 0.15/5.86 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/5.86 fof(f10,axiom,(
% 0.15/5.86 (! [W0,W1,W2] :( ( aNaturalNumber0(W0)& aNaturalNumber0(W1)& aNaturalNumber0(W2) )=> sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ) )),
% 0.15/5.86 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/5.86 fof(f31,definition,(
% 0.15/5.86 (! [W0,W1] :( ( aNaturalNumber0(W0)& aNaturalNumber0(W1) )=> ( ( W0 != sz00& doDivides0(W0,W1) )=> (! [W2] :( W2 = sdtsldt0(W1,W0)<=> ( aNaturalNumber0(W2)& W1 = sdtasdt0(W0,W2) ) ) )) ) )),
% 0.15/5.86 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/5.86 fof(f36,hypothesis,(
% 0.15/5.86 ( aNaturalNumber0(xl)& aNaturalNumber0(xm) ) ),
% 0.15/5.86 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/5.86 fof(f37,hypothesis,(
% 0.15/5.86 ( xl != sz00& (? [W0] :( aNaturalNumber0(W0)& xm = sdtasdt0(xl,W0) ))& doDivides0(xl,xm) ) ),
% 0.15/5.86 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/5.86 fof(f38,hypothesis,(
% 0.15/5.86 aNaturalNumber0(xn) ),
% 0.15/5.86 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/5.86 fof(f39,conjecture,(
% 0.15/5.86 ( ( aNaturalNumber0(sdtsldt0(xm,xl))& xm = sdtasdt0(xl,sdtsldt0(xm,xl)) )=> ( sdtasdt0(xn,xm) = sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl)))| sdtasdt0(xn,sdtsldt0(xm,xl)) = sdtsldt0(sdtasdt0(xn,xm),xl) ) ) ),
% 0.15/5.86 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/5.86 fof(f40,negated_conjecture,(
% 0.15/5.86 ~(( ( aNaturalNumber0(sdtsldt0(xm,xl))& xm = sdtasdt0(xl,sdtsldt0(xm,xl)) )=> ( sdtasdt0(xn,xm) = sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl)))| sdtasdt0(xn,sdtsldt0(xm,xl)) = sdtsldt0(sdtasdt0(xn,xm),xl) ) ) )),
% 0.15/5.86 inference(negated_conjecture,[status(cth)],[f39])).
% 0.15/5.86 fof(f49,plain,(
% 0.15/5.86 ![W0,W1]: ((~aNaturalNumber0(W0)|~aNaturalNumber0(W1))|aNaturalNumber0(sdtasdt0(W0,W1)))),
% 0.15/5.86 inference(pre_NNF_transformation,[status(thm)],[f5])).
% 0.15/5.86 fof(f50,plain,(
% 0.15/5.86 ![X0,X1]: (~aNaturalNumber0(X0)|~aNaturalNumber0(X1)|aNaturalNumber0(sdtasdt0(X0,X1)))),
% 0.15/5.86 inference(cnf_transformation,[status(thm)],[f49])).
% 0.15/5.86 fof(f58,plain,(
% 0.15/5.86 ![W0,W1]: ((~aNaturalNumber0(W0)|~aNaturalNumber0(W1))|sdtasdt0(W0,W1)=sdtasdt0(W1,W0))),
% 0.15/5.86 inference(pre_NNF_transformation,[status(thm)],[f9])).
% 0.15/5.86 fof(f59,plain,(
% 0.15/5.86 ![X0,X1]: (~aNaturalNumber0(X0)|~aNaturalNumber0(X1)|sdtasdt0(X0,X1)=sdtasdt0(X1,X0))),
% 0.15/5.86 inference(cnf_transformation,[status(thm)],[f58])).
% 0.15/5.86 fof(f60,plain,(
% 0.15/5.86 ![W0,W1,W2]: (((~aNaturalNumber0(W0)|~aNaturalNumber0(W1))|~aNaturalNumber0(W2))|sdtasdt0(sdtasdt0(W0,W1),W2)=sdtasdt0(W0,sdtasdt0(W1,W2)))),
% 0.15/5.86 inference(pre_NNF_transformation,[status(thm)],[f10])).
% 0.15/5.86 fof(f61,plain,(
% 0.15/5.86 ![X0,X1,X2]: (~aNaturalNumber0(X0)|~aNaturalNumber0(X1)|~aNaturalNumber0(X2)|sdtasdt0(sdtasdt0(X0,X1),X2)=sdtasdt0(X0,sdtasdt0(X1,X2)))),
% 0.15/5.86 inference(cnf_transformation,[status(thm)],[f60])).
% 0.15/5.86 fof(f128,plain,(
% 0.15/5.86 ![W0,W1]: ((~aNaturalNumber0(W0)|~aNaturalNumber0(W1))|((W0=sz00|~doDivides0(W0,W1))|(![W2]: (W2=sdtsldt0(W1,W0)<=>(aNaturalNumber0(W2)&W1=sdtasdt0(W0,W2))))))),
% 0.15/5.86 inference(pre_NNF_transformation,[status(thm)],[f31])).
% 0.15/5.86 fof(f129,plain,(
% 0.15/5.86 ![W0,W1]: ((~aNaturalNumber0(W0)|~aNaturalNumber0(W1))|((W0=sz00|~doDivides0(W0,W1))|(![W2]: ((~W2=sdtsldt0(W1,W0)|(aNaturalNumber0(W2)&W1=sdtasdt0(W0,W2)))&(W2=sdtsldt0(W1,W0)|(~aNaturalNumber0(W2)|~W1=sdtasdt0(W0,W2)))))))),
% 0.15/5.86 inference(NNF_transformation,[status(thm)],[f128])).
% 0.15/5.86 fof(f130,plain,(
% 0.15/5.86 ![W0,W1]: ((~aNaturalNumber0(W0)|~aNaturalNumber0(W1))|((W0=sz00|~doDivides0(W0,W1))|((![W2]: (~W2=sdtsldt0(W1,W0)|(aNaturalNumber0(W2)&W1=sdtasdt0(W0,W2))))&(![W2]: (W2=sdtsldt0(W1,W0)|(~aNaturalNumber0(W2)|~W1=sdtasdt0(W0,W2)))))))),
% 0.15/5.86 inference(miniscoping,[status(thm)],[f129])).
% 0.15/5.86 fof(f133,plain,(
% 0.15/5.86 ![X0,X1,X2]: (~aNaturalNumber0(X0)|~aNaturalNumber0(X1)|X0=sz00|~doDivides0(X0,X1)|X2=sdtsldt0(X1,X0)|~aNaturalNumber0(X2)|~X1=sdtasdt0(X0,X2))),
% 0.15/5.86 inference(cnf_transformation,[status(thm)],[f130])).
% 0.15/5.86 fof(f142,plain,(
% 0.15/5.86 aNaturalNumber0(xl)),
% 0.15/5.86 inference(cnf_transformation,[status(thm)],[f36])).
% 0.15/5.86 fof(f144,plain,(
% 0.15/5.86 (~xl=sz00&(aNaturalNumber0(sK2_skl)&xm=sdtasdt0(xl,sK2_skl)))&doDivides0(xl,xm)),
% 0.15/5.86 inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(W0,sK2_skl)],[f37])).
% 0.15/5.86 fof(f145,plain,(
% 0.15/5.86 ~xl=sz00),
% 0.15/5.86 inference(cnf_transformation,[status(thm)],[f144])).
% 0.15/5.86 fof(f146,plain,(
% 0.15/5.86 aNaturalNumber0(sK2_skl)),
% 0.15/5.86 inference(cnf_transformation,[status(thm)],[f144])).
% 0.15/5.86 fof(f147,plain,(
% 0.15/5.86 xm=sdtasdt0(xl,sK2_skl)),
% 0.15/5.86 inference(cnf_transformation,[status(thm)],[f144])).
% 0.15/5.86 fof(f148,plain,(
% 0.15/5.86 doDivides0(xl,xm)),
% 0.15/5.86 inference(cnf_transformation,[status(thm)],[f144])).
% 0.15/5.86 fof(f149,plain,(
% 0.15/5.86 aNaturalNumber0(xn)),
% 0.15/5.86 inference(cnf_transformation,[status(thm)],[f38])).
% 0.15/5.86 fof(f150,plain,(
% 0.15/5.86 ((aNaturalNumber0(sdtsldt0(xm,xl))&xm=sdtasdt0(xl,sdtsldt0(xm,xl)))&(~sdtasdt0(xn,xm)=sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl)))&~sdtasdt0(xn,sdtsldt0(xm,xl))=sdtsldt0(sdtasdt0(xn,xm),xl)))),
% 0.15/5.86 inference(pre_NNF_transformation,[status(thm)],[f40])).
% 0.15/5.86 fof(f151,plain,(
% 0.15/5.86 aNaturalNumber0(sdtsldt0(xm,xl))),
% 0.15/5.86 inference(cnf_transformation,[status(thm)],[f150])).
% 0.15/5.86 fof(f152,plain,(
% 0.15/5.86 xm=sdtasdt0(xl,sdtsldt0(xm,xl))),
% 0.15/5.86 inference(cnf_transformation,[status(thm)],[f150])).
% 0.15/5.86 fof(f153,plain,(
% 0.15/5.86 ~sdtasdt0(xn,xm)=sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl)))),
% 0.15/5.86 inference(cnf_transformation,[status(thm)],[f150])).
% 0.15/5.86 fof(f164,plain,(
% 0.15/5.86 ![X0,X1]: (~aNaturalNumber0(X0)|~aNaturalNumber0(sdtasdt0(X0,X1))|X0=sz00|~doDivides0(X0,sdtasdt0(X0,X1))|X1=sdtsldt0(sdtasdt0(X0,X1),X0)|~aNaturalNumber0(X1))),
% 0.15/5.86 inference(destructive_equality_resolution,[status(thm)],[f133])).
% 0.15/5.86 fof(f171,plain,(
% 0.15/5.86 ![X0,X1]: (~aNaturalNumber0(X0)|~aNaturalNumber0(X1)|sdtasdt0(sdtasdt0(X0,X1),sdtsldt0(xm,xl))=sdtasdt0(X0,sdtasdt0(X1,sdtsldt0(xm,xl))))),
% 0.15/5.86 inference(resolution,[status(thm)],[f61,f151])).
% 0.15/5.86 fof(f172,plain,(
% 0.15/5.86 ![X0,X1]: (~aNaturalNumber0(X0)|X0=sz00|~doDivides0(X0,sdtasdt0(X0,X1))|X1=sdtsldt0(sdtasdt0(X0,X1),X0)|~aNaturalNumber0(X1))),
% 0.15/5.86 inference(forward_subsumption_resolution,[status(thm)],[f164,f50])).
% 0.15/5.86 fof(f174,definition,(
% 0.15/5.86 sQ0_spl <=> (aNaturalNumber0(xl))),
% 0.15/5.86 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.15/5.86 fof(f176,plain,(
% 0.15/5.86 ~aNaturalNumber0(xl)|sQ0_spl),
% 0.15/5.86 inference(component_clause,[status(thm)],[f174])).
% 0.15/5.86 fof(f177,definition,(
% 0.15/5.86 sQ1_spl <=> (xl=sz00)),
% 0.15/5.86 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.15/5.86 fof(f178,plain,(
% 0.15/5.86 xl=sz00|~sQ1_spl),
% 0.15/5.86 inference(component_clause,[status(thm)],[f177])).
% 0.15/5.86 fof(f180,definition,(
% 0.15/5.86 sQ2_spl <=> (doDivides0(xl,xm))),
% 0.15/5.86 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.15/5.86 fof(f182,plain,(
% 0.15/5.86 ~doDivides0(xl,xm)|sQ2_spl),
% 0.15/5.86 inference(component_clause,[status(thm)],[f180])).
% 0.15/5.86 fof(f197,plain,(
% 0.15/5.86 ![X0]: (~aNaturalNumber0(X0)|sdtasdt0(X0,xl)=sdtasdt0(xl,X0))),
% 0.15/5.86 inference(resolution,[status(thm)],[f142,f59])).
% 0.15/5.86 fof(f225,plain,(
% 0.15/5.86 ~aNaturalNumber0(xl)|xl=sz00|~doDivides0(xl,xm)|sK2_skl=sdtsldt0(sdtasdt0(xl,sK2_skl),xl)|~aNaturalNumber0(sK2_skl)),
% 0.15/5.86 inference(paramodulation,[status(thm)],[f147,f172])).
% 0.15/5.86 fof(f226,definition,(
% 0.15/5.86 sQ5_spl <=> (sK2_skl=sdtsldt0(sdtasdt0(xl,sK2_skl),xl))),
% 0.15/5.86 introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition])).
% 0.15/5.86 fof(f227,plain,(
% 0.15/5.86 sK2_skl=sdtsldt0(sdtasdt0(xl,sK2_skl),xl)|~sQ5_spl),
% 0.15/5.86 inference(component_clause,[status(thm)],[f226])).
% 0.15/5.86 fof(f229,definition,(
% 0.15/5.86 sQ6_spl <=> (aNaturalNumber0(sK2_skl))),
% 0.15/5.86 introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition])).
% 0.15/5.86 fof(f231,plain,(
% 0.15/5.86 ~aNaturalNumber0(sK2_skl)|sQ6_spl),
% 0.15/5.86 inference(component_clause,[status(thm)],[f229])).
% 0.15/5.86 fof(f232,plain,(
% 0.15/5.86 ~sQ0_spl|sQ1_spl|~sQ2_spl|sQ5_spl|~sQ6_spl),
% 0.15/5.86 inference(split_clause,[status(thm)],[f225,f174,f177,f180,f226,f229])).
% 0.15/5.86 fof(f252,plain,(
% 0.15/5.86 $false|sQ0_spl),
% 0.15/5.86 inference(forward_subsumption_resolution,[status(thm)],[f176,f142])).
% 0.15/5.86 fof(f253,plain,(
% 0.15/5.86 sQ0_spl),
% 0.15/5.86 inference(contradiction_clause,[status(thm)],[f252])).
% 0.15/5.86 fof(f254,plain,(
% 0.15/5.86 $false|~sQ1_spl),
% 0.15/5.87 inference(forward_subsumption_resolution,[status(thm)],[f178,f145])).
% 0.15/5.87 fof(f255,plain,(
% 0.15/5.87 ~sQ1_spl),
% 0.15/5.87 inference(contradiction_clause,[status(thm)],[f254])).
% 0.15/5.87 fof(f337,plain,(
% 0.15/5.87 $false|sQ6_spl),
% 0.15/5.87 inference(forward_subsumption_resolution,[status(thm)],[f231,f146])).
% 0.15/5.87 fof(f338,plain,(
% 0.15/5.87 sQ6_spl),
% 0.15/5.87 inference(contradiction_clause,[status(thm)],[f337])).
% 0.15/5.87 fof(f921,plain,(
% 0.15/5.87 ![X0]: (~aNaturalNumber0(X0)|sdtasdt0(sdtasdt0(X0,xn),sdtsldt0(xm,xl))=sdtasdt0(X0,sdtasdt0(xn,sdtsldt0(xm,xl))))),
% 0.15/5.87 inference(resolution,[status(thm)],[f171,f149])).
% 0.15/5.87 fof(f926,plain,(
% 0.15/5.87 ![X0]: (~aNaturalNumber0(X0)|sdtasdt0(sdtasdt0(X0,xl),sdtsldt0(xm,xl))=sdtasdt0(X0,sdtasdt0(xl,sdtsldt0(xm,xl))))),
% 0.15/5.87 inference(resolution,[status(thm)],[f171,f142])).
% 0.15/5.87 fof(f927,plain,(
% 0.15/5.87 ![X0]: (~aNaturalNumber0(X0)|sdtasdt0(sdtasdt0(X0,xl),sdtsldt0(xm,xl))=sdtasdt0(X0,xm))),
% 0.15/5.87 inference(forward_demodulation,[status(thm)],[f152,f926])).
% 0.15/5.87 fof(f1055,plain,(
% 0.15/5.87 $false|sQ2_spl),
% 0.15/5.87 inference(forward_subsumption_resolution,[status(thm)],[f182,f148])).
% 0.15/5.87 fof(f1056,plain,(
% 0.15/5.87 sQ2_spl),
% 0.15/5.87 inference(contradiction_clause,[status(thm)],[f1055])).
% 0.15/5.87 fof(f1057,plain,(
% 0.15/5.87 sK2_skl=sdtsldt0(xm,xl)|~sQ5_spl),
% 0.15/5.87 inference(forward_demodulation,[status(thm)],[f147,f227])).
% 0.15/5.87 fof(f1074,plain,(
% 0.15/5.87 sdtasdt0(xn,xl)=sdtasdt0(xl,xn)),
% 0.15/5.87 inference(resolution,[status(thm)],[f197,f149])).
% 0.15/5.87 fof(f1970,plain,(
% 0.15/5.87 sdtasdt0(sdtasdt0(xl,xn),sdtsldt0(xm,xl))=sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl)))),
% 0.15/5.87 inference(resolution,[status(thm)],[f921,f142])).
% 0.15/5.87 fof(f1983,plain,(
% 0.15/5.87 sdtasdt0(sdtasdt0(xn,xl),sdtsldt0(xm,xl))=sdtasdt0(xn,xm)),
% 0.15/5.87 inference(resolution,[status(thm)],[f927,f149])).
% 0.15/5.87 fof(f2107,plain,(
% 0.15/5.87 ~sdtasdt0(xn,xm)=sdtasdt0(xl,sdtasdt0(xn,sK2_skl))|~sQ5_spl),
% 0.15/5.87 inference(backward_demodulation,[status(thm)],[f1057,f153])).
% 0.15/5.87 fof(f3339,plain,(
% 0.15/5.87 sdtasdt0(sdtasdt0(xl,xn),sK2_skl)=sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl)))|~sQ5_spl),
% 0.15/5.87 inference(forward_demodulation,[status(thm)],[f1057,f1970])).
% 0.15/5.87 fof(f3340,plain,(
% 0.15/5.87 sdtasdt0(sdtasdt0(xl,xn),sK2_skl)=sdtasdt0(xl,sdtasdt0(xn,sK2_skl))|~sQ5_spl),
% 0.15/5.87 inference(forward_demodulation,[status(thm)],[f1057,f3339])).
% 0.15/5.87 fof(f3521,plain,(
% 0.15/5.87 sdtasdt0(sdtasdt0(xl,xn),sdtsldt0(xm,xl))=sdtasdt0(xn,xm)),
% 0.15/5.87 inference(forward_demodulation,[status(thm)],[f1074,f1983])).
% 0.15/5.87 fof(f3522,plain,(
% 0.15/5.87 sdtasdt0(xn,xm)=sdtasdt0(xl,sdtasdt0(xn,sK2_skl))|~sQ5_spl),
% 0.15/5.87 inference(backward_demodulation,[status(thm)],[f3523,f3340])).
% 0.15/5.87 fof(f3523,plain,(
% 0.15/5.87 sdtasdt0(sdtasdt0(xl,xn),sK2_skl)=sdtasdt0(xn,xm)|~sQ5_spl),
% 0.15/5.87 inference(forward_demodulation,[status(thm)],[f1057,f3521])).
% 0.15/5.87 fof(f3530,plain,(
% 0.15/5.87 $false|~sQ5_spl),
% 0.15/5.87 inference(forward_subsumption_resolution,[status(thm)],[f3522,f2107])).
% 0.15/5.87 fof(f3531,plain,(
% 0.15/5.87 ~sQ5_spl),
% 0.15/5.87 inference(contradiction_clause,[status(thm)],[f3530])).
% 0.15/5.87 fof(f3532,plain,(
% 0.15/5.87 $false),
% 0.15/5.87 inference(sat_refutation,[status(thm)],[f232,f253,f255,f338,f1056,f3531])).
% 0.15/5.87 % SZS output end CNFRefutation for theBenchmark.p
% 0.15/5.88 % Elapsed time: 0.487116 seconds
% 0.15/5.88 % CPU time: 3.623955 seconds
% 0.15/5.88 % Total memory used: 154.165 MB
% 0.15/5.88 % Net memory used: 149.891 MB
%------------------------------------------------------------------------------