%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : NUM523+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 : n013.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 01:43:07 PM UTC 2026
% Result : Theorem 46.34s 6.55s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM523+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
% 0.15/0.42 % Computer : n013.cluster.edu
% 0.15/0.42 % Model : x86_64 x86_64
% 0.15/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.42 % Memory : 8046.5625MB
% 0.15/0.42 % OS : Linux 6.8.0-71-generic
% 0.15/0.42 % CPULimit : 300
% 0.15/0.42 % WCLimit : 300
% 0.15/0.42 % DateTime : Mon Sep 21 02:36:50 UTC 2026
% 0.15/0.42 % CPUTime :
% 0.15/0.44 % Drodi V4.1.1
% 46.34/6.55 % Refutation found
% 46.34/6.55 % SZS status Theorem for theBenchmark: Theorem is valid
% 46.34/6.55 % SZS output start CNFRefutation for theBenchmark
% 46.34/6.55 fof(f5,axiom,(
% 46.34/6.55 (! [W0,W1] :( ( aNaturalNumber0(W0)& aNaturalNumber0(W1) )=> aNaturalNumber0(sdtasdt0(W0,W1)) ) )),
% 46.34/6.55 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 46.34/6.55 fof(f30,definition,(
% 46.34/6.55 (! [W0,W1] :( ( aNaturalNumber0(W0)& aNaturalNumber0(W1) )=> ( doDivides0(W0,W1)<=> (? [W2] :( aNaturalNumber0(W2)& W1 = sdtasdt0(W0,W2) ) )) ) )),
% 46.34/6.55 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 46.34/6.55 fof(f39,axiom,(
% 46.34/6.55 (! [W0,W1,W2] :( ( aNaturalNumber0(W0)& aNaturalNumber0(W1)& aNaturalNumber0(W2) )=> ( ( isPrime0(W2)& doDivides0(W2,sdtasdt0(W0,W1)) )=> ( doDivides0(W2,W0)| doDivides0(W2,W1) ) ) ) )),
% 46.34/6.55 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 46.34/6.55 fof(f40,hypothesis,(
% 46.34/6.55 ( aNaturalNumber0(xn)& aNaturalNumber0(xm)& aNaturalNumber0(xp)& xn != sz00& xm != sz00& xp != sz00 ) ),
% 46.34/6.55 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 46.34/6.55 fof(f42,hypothesis,(
% 46.34/6.55 sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn) ),
% 46.34/6.55 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 46.34/6.55 fof(f43,hypothesis,(
% 46.34/6.55 isPrime0(xp) ),
% 46.34/6.55 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 46.34/6.55 fof(f44,conjecture,(
% 46.34/6.55 ( doDivides0(xp,sdtasdt0(xn,xn))& doDivides0(xp,xn) ) ),
% 46.34/6.55 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 46.34/6.55 fof(f45,negated_conjecture,(
% 46.34/6.55 ~(( doDivides0(xp,sdtasdt0(xn,xn))& doDivides0(xp,xn) ) )),
% 46.34/6.55 inference(negated_conjecture,[status(cth)],[f44])).
% 46.34/6.55 fof(f54,plain,(
% 46.34/6.55 ![W0,W1]: ((~aNaturalNumber0(W0)|~aNaturalNumber0(W1))|aNaturalNumber0(sdtasdt0(W0,W1)))),
% 46.34/6.55 inference(pre_NNF_transformation,[status(thm)],[f5])).
% 46.34/6.55 fof(f55,plain,(
% 46.34/6.55 ![X0,X1]: (~aNaturalNumber0(X0)|~aNaturalNumber0(X1)|aNaturalNumber0(sdtasdt0(X0,X1)))),
% 46.34/6.55 inference(cnf_transformation,[status(thm)],[f54])).
% 46.34/6.55 fof(f127,plain,(
% 46.34/6.55 ![W0,W1]: ((~aNaturalNumber0(W0)|~aNaturalNumber0(W1))|(doDivides0(W0,W1)<=>(?[W2]: (aNaturalNumber0(W2)&W1=sdtasdt0(W0,W2)))))),
% 46.34/6.55 inference(pre_NNF_transformation,[status(thm)],[f30])).
% 46.34/6.55 fof(f128,plain,(
% 46.34/6.55 ![W0,W1]: ((~aNaturalNumber0(W0)|~aNaturalNumber0(W1))|((~doDivides0(W0,W1)|(?[W2]: (aNaturalNumber0(W2)&W1=sdtasdt0(W0,W2))))&(doDivides0(W0,W1)|(![W2]: (~aNaturalNumber0(W2)|~W1=sdtasdt0(W0,W2))))))),
% 46.34/6.55 inference(NNF_transformation,[status(thm)],[f127])).
% 46.34/6.55 fof(f129,plain,(
% 46.34/6.55 ![W0,W1]: ((~aNaturalNumber0(W0)|~aNaturalNumber0(W1))|((~doDivides0(W0,W1)|(aNaturalNumber0(sK1_skl(W1,W0))&W1=sdtasdt0(W0,sK1_skl(W1,W0))))&(doDivides0(W0,W1)|(![W2]: (~aNaturalNumber0(W2)|~W1=sdtasdt0(W0,W2))))))),
% 46.34/6.55 inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(W2,sK1_skl(W1,W0))],[f128])).
% 46.34/6.55 fof(f132,plain,(
% 46.34/6.55 ![X0,X1,X2]: (~aNaturalNumber0(X0)|~aNaturalNumber0(X1)|doDivides0(X0,X1)|~aNaturalNumber0(X2)|~X1=sdtasdt0(X0,X2))),
% 46.34/6.55 inference(cnf_transformation,[status(thm)],[f129])).
% 46.34/6.55 fof(f164,plain,(
% 46.34/6.55 ![W0,W1,W2]: (((~aNaturalNumber0(W0)|~aNaturalNumber0(W1))|~aNaturalNumber0(W2))|((~isPrime0(W2)|~doDivides0(W2,sdtasdt0(W0,W1)))|(doDivides0(W2,W0)|doDivides0(W2,W1))))),
% 46.34/6.55 inference(pre_NNF_transformation,[status(thm)],[f39])).
% 46.34/6.55 fof(f165,plain,(
% 46.34/6.55 ![X0,X1,X2]: (~aNaturalNumber0(X0)|~aNaturalNumber0(X1)|~aNaturalNumber0(X2)|~isPrime0(X2)|~doDivides0(X2,sdtasdt0(X0,X1))|doDivides0(X2,X0)|doDivides0(X2,X1))),
% 46.34/6.55 inference(cnf_transformation,[status(thm)],[f164])).
% 46.34/6.55 fof(f166,plain,(
% 46.34/6.55 aNaturalNumber0(xn)),
% 46.34/6.55 inference(cnf_transformation,[status(thm)],[f40])).
% 46.34/6.55 fof(f167,plain,(
% 46.34/6.55 aNaturalNumber0(xm)),
% 46.34/6.55 inference(cnf_transformation,[status(thm)],[f40])).
% 46.34/6.55 fof(f168,plain,(
% 46.34/6.55 aNaturalNumber0(xp)),
% 46.34/6.55 inference(cnf_transformation,[status(thm)],[f40])).
% 46.34/6.55 fof(f174,plain,(
% 46.34/6.55 sdtasdt0(xp,sdtasdt0(xm,xm))=sdtasdt0(xn,xn)),
% 46.34/6.55 inference(cnf_transformation,[status(thm)],[f42])).
% 46.34/6.55 fof(f175,plain,(
% 46.34/6.55 isPrime0(xp)),
% 46.34/6.55 inference(cnf_transformation,[status(thm)],[f43])).
% 46.34/6.55 fof(f176,plain,(
% 46.34/6.55 (~doDivides0(xp,sdtasdt0(xn,xn))|~doDivides0(xp,xn))),
% 46.34/6.55 inference(pre_NNF_transformation,[status(thm)],[f45])).
% 46.34/6.55 fof(f177,plain,(
% 46.34/6.55 ~doDivides0(xp,sdtasdt0(xn,xn))|~doDivides0(xp,xn)),
% 46.34/6.55 inference(cnf_transformation,[status(thm)],[f176])).
% 46.34/6.55 fof(f178,definition,(
% 46.34/6.55 sQ0_spl <=> (doDivides0(xp,sdtasdt0(xn,xn)))),
% 46.34/6.55 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 46.34/6.55 fof(f179,plain,(
% 46.34/6.55 doDivides0(xp,sdtasdt0(xn,xn))|~sQ0_spl),
% 46.34/6.55 inference(component_clause,[status(thm)],[f178])).
% 46.34/6.55 fof(f181,definition,(
% 46.34/6.55 sQ1_spl <=> (doDivides0(xp,xn))),
% 46.34/6.55 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 46.34/6.55 fof(f184,plain,(
% 46.34/6.55 ~sQ0_spl|~sQ1_spl),
% 46.34/6.55 inference(split_clause,[status(thm)],[f177,f178,f181])).
% 46.34/6.55 fof(f188,plain,(
% 46.34/6.55 ![X0]: (~aNaturalNumber0(X0)|aNaturalNumber0(sdtasdt0(xn,X0)))),
% 46.34/6.55 inference(resolution,[status(thm)],[f55,f166])).
% 46.34/6.55 fof(f198,plain,(
% 46.34/6.55 aNaturalNumber0(sdtasdt0(xn,xn))),
% 46.34/6.55 inference(resolution,[status(thm)],[f188,f166])).
% 46.34/6.55 fof(f294,plain,(
% 46.34/6.55 ![X0]: (~aNaturalNumber0(X0)|aNaturalNumber0(sdtasdt0(xm,X0)))),
% 46.34/6.55 inference(resolution,[status(thm)],[f167,f55])).
% 46.34/6.55 fof(f683,plain,(
% 46.34/6.55 aNaturalNumber0(sdtasdt0(xm,xm))),
% 46.34/6.55 inference(resolution,[status(thm)],[f294,f167])).
% 46.34/6.55 fof(f808,definition,(
% 46.34/6.55 sQ2_spl <=> (aNaturalNumber0(xp))),
% 46.34/6.55 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 46.34/6.55 fof(f810,plain,(
% 46.34/6.55 ~aNaturalNumber0(xp)|sQ2_spl),
% 46.34/6.55 inference(component_clause,[status(thm)],[f808])).
% 46.34/6.55 fof(f814,definition,(
% 46.34/6.55 sQ4_spl <=> (aNaturalNumber0(sdtasdt0(xn,xn)))),
% 46.34/6.55 introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition])).
% 46.34/6.55 fof(f816,plain,(
% 46.34/6.55 ~aNaturalNumber0(sdtasdt0(xn,xn))|sQ4_spl),
% 46.34/6.55 inference(component_clause,[status(thm)],[f814])).
% 46.34/6.55 fof(f819,plain,(
% 46.34/6.55 $false|sQ4_spl),
% 46.34/6.55 inference(forward_subsumption_resolution,[status(thm)],[f816,f198])).
% 46.34/6.55 fof(f820,plain,(
% 46.34/6.55 sQ4_spl),
% 46.34/6.55 inference(contradiction_clause,[status(thm)],[f819])).
% 46.34/6.55 fof(f827,definition,(
% 46.34/6.55 sQ6_spl <=> (aNaturalNumber0(xn))),
% 46.34/6.55 introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition])).
% 46.34/6.55 fof(f829,plain,(
% 46.34/6.55 ~aNaturalNumber0(xn)|sQ6_spl),
% 46.34/6.55 inference(component_clause,[status(thm)],[f827])).
% 46.34/6.55 fof(f831,plain,(
% 46.34/6.55 $false|sQ2_spl),
% 46.34/6.55 inference(forward_subsumption_resolution,[status(thm)],[f810,f168])).
% 46.34/6.55 fof(f832,plain,(
% 46.34/6.55 sQ2_spl),
% 46.34/6.55 inference(contradiction_clause,[status(thm)],[f831])).
% 46.34/6.55 fof(f833,plain,(
% 46.34/6.55 $false|sQ6_spl),
% 46.34/6.55 inference(forward_subsumption_resolution,[status(thm)],[f829,f166])).
% 46.34/6.55 fof(f834,plain,(
% 46.34/6.55 sQ6_spl),
% 46.34/6.55 inference(contradiction_clause,[status(thm)],[f833])).
% 46.34/6.55 fof(f7481,definition,(
% 46.34/6.55 sQ655_spl <=> (isPrime0(xp))),
% 46.34/6.55 introduced(definition,[new_symbols(definition,[sQ655_spl])],[split_symbol_definition])).
% 46.34/6.55 fof(f7483,plain,(
% 46.34/6.55 ~isPrime0(xp)|sQ655_spl),
% 46.34/6.55 inference(component_clause,[status(thm)],[f7481])).
% 46.34/6.55 fof(f7496,plain,(
% 46.34/6.55 $false|sQ655_spl),
% 46.34/6.55 inference(forward_subsumption_resolution,[status(thm)],[f7483,f175])).
% 46.34/6.55 fof(f7497,plain,(
% 46.34/6.55 sQ655_spl),
% 46.34/6.55 inference(contradiction_clause,[status(thm)],[f7496])).
% 46.34/6.55 fof(f8624,plain,(
% 46.34/6.55 ~aNaturalNumber0(xn)|~aNaturalNumber0(xn)|~aNaturalNumber0(xp)|~isPrime0(xp)|doDivides0(xp,xn)|doDivides0(xp,xn)|~sQ0_spl),
% 46.34/6.55 inference(resolution,[status(thm)],[f165,f179])).
% 46.34/6.55 fof(f8630,plain,(
% 46.34/6.55 ~sQ6_spl|~sQ2_spl|~sQ655_spl|sQ1_spl|~sQ0_spl),
% 46.34/6.55 inference(split_clause,[status(thm)],[f8624,f827,f808,f7481,f181,f178])).
% 46.34/6.55 fof(f9122,plain,(
% 46.34/6.55 ~aNaturalNumber0(xp)|~aNaturalNumber0(sdtasdt0(xn,xn))|doDivides0(xp,sdtasdt0(xn,xn))|~aNaturalNumber0(sdtasdt0(xm,xm))),
% 46.34/6.55 inference(resolution,[status(thm)],[f174,f132])).
% 46.34/6.55 fof(f9132,definition,(
% 46.34/6.55 sQ812_spl <=> (aNaturalNumber0(sdtasdt0(xm,xm)))),
% 46.34/6.55 introduced(definition,[new_symbols(definition,[sQ812_spl])],[split_symbol_definition])).
% 46.34/6.55 fof(f9134,plain,(
% 46.34/6.55 ~aNaturalNumber0(sdtasdt0(xm,xm))|sQ812_spl),
% 46.34/6.55 inference(component_clause,[status(thm)],[f9132])).
% 46.34/6.55 fof(f9135,plain,(
% 46.34/6.55 ~sQ2_spl|~sQ4_spl|sQ0_spl|~sQ812_spl),
% 46.34/6.55 inference(split_clause,[status(thm)],[f9122,f808,f814,f178,f9132])).
% 46.34/6.55 fof(f19778,plain,(
% 46.34/6.55 $false|sQ812_spl),
% 46.34/6.55 inference(forward_subsumption_resolution,[status(thm)],[f683,f9134])).
% 46.34/6.55 fof(f19779,plain,(
% 46.34/6.55 sQ812_spl),
% 46.34/6.55 inference(contradiction_clause,[status(thm)],[f19778])).
% 46.34/6.55 fof(f19780,plain,(
% 46.34/6.55 $false),
% 46.34/6.55 inference(sat_refutation,[status(thm)],[f184,f820,f832,f834,f7497,f8630,f9135,f19779])).
% 46.34/6.59 % SZS output end CNFRefutation for theBenchmark.p
% 46.34/6.61 % Elapsed time: 6.165244 seconds
% 46.34/6.61 % CPU time: 48.397626 seconds
% 46.34/6.61 % Total memory used: 293.021 MB
% 46.34/6.61 % Net memory used: 277.620 MB
%------------------------------------------------------------------------------