%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : NUM496+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 : n002.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 01:43:03 PM UTC 2026
% Result : Theorem 29.42s 4.14s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM496+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n002.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 : Mon Sep 21 02:37:32 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 % Drodi V4.1.1
% 29.42/4.14 % Refutation found
% 29.42/4.14 % SZS status Theorem for theBenchmark: Theorem is valid
% 29.42/4.14 % SZS output start CNFRefutation for theBenchmark
% 29.42/4.14 fof(f3,axiom,(
% 29.42/4.14 ( aNaturalNumber0(sz10)& sz10 != sz00 ) ),
% 29.42/4.14 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 29.42/4.14 fof(f5,axiom,(
% 29.42/4.14 (! [W0,W1] :( ( aNaturalNumber0(W0)& aNaturalNumber0(W1) )=> aNaturalNumber0(sdtasdt0(W0,W1)) ) )),
% 29.42/4.14 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 29.42/4.14 fof(f11,axiom,(
% 29.42/4.14 (! [W0] :( aNaturalNumber0(W0)=> ( sdtasdt0(W0,sz10) = W0& W0 = sdtasdt0(sz10,W0) ) ) )),
% 29.42/4.14 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 29.42/4.14 fof(f19,definition,(
% 29.42/4.14 (! [W0,W1] :( ( aNaturalNumber0(W0)& aNaturalNumber0(W1) )=> ( sdtlseqdt0(W0,W1)=> (! [W2] :( W2 = sdtmndt0(W1,W0)<=> ( aNaturalNumber0(W2)& sdtpldt0(W0,W2) = W1 ) ) )) ) )),
% 29.42/4.14 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 29.42/4.14 fof(f30,definition,(
% 29.42/4.14 (! [W0,W1] :( ( aNaturalNumber0(W0)& aNaturalNumber0(W1) )=> ( doDivides0(W0,W1)<=> (? [W2] :( aNaturalNumber0(W2)& W1 = sdtasdt0(W0,W2) ) )) ) )),
% 29.42/4.14 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 29.42/4.14 fof(f33,axiom,(
% 29.42/4.14 (! [W0,W1,W2] :( ( aNaturalNumber0(W0)& aNaturalNumber0(W1)& aNaturalNumber0(W2) )=> ( ( doDivides0(W0,W1)& doDivides0(W0,W2) )=> doDivides0(W0,sdtpldt0(W1,W2)) ) ) )),
% 29.42/4.14 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 29.42/4.14 fof(f39,hypothesis,(
% 29.42/4.14 ( aNaturalNumber0(xn)& aNaturalNumber0(xm)& aNaturalNumber0(xp) ) ),
% 29.42/4.14 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 29.42/4.14 fof(f42,hypothesis,(
% 29.42/4.14 sdtlseqdt0(xp,xn) ),
% 29.42/4.14 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 29.42/4.14 fof(f43,hypothesis,(
% 29.42/4.14 xr = sdtmndt0(xn,xp) ),
% 29.42/4.14 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 29.42/4.14 fof(f46,hypothesis,(
% 29.42/4.14 ( doDivides0(xp,xr)| doDivides0(xp,xm) ) ),
% 29.42/4.14 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 29.42/4.14 fof(f47,conjecture,(
% 29.42/4.14 ( doDivides0(xp,xn)| doDivides0(xp,xm) ) ),
% 29.42/4.14 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 29.42/4.14 fof(f48,negated_conjecture,(
% 29.42/4.14 ~(( doDivides0(xp,xn)| doDivides0(xp,xm) ) )),
% 29.42/4.14 inference(negated_conjecture,[status(cth)],[f47])).
% 29.42/4.14 fof(f53,plain,(
% 29.42/4.14 aNaturalNumber0(sz10)),
% 29.42/4.14 inference(cnf_transformation,[status(thm)],[f3])).
% 29.42/4.14 fof(f57,plain,(
% 29.42/4.14 ![W0,W1]: ((~aNaturalNumber0(W0)|~aNaturalNumber0(W1))|aNaturalNumber0(sdtasdt0(W0,W1)))),
% 29.42/4.14 inference(pre_NNF_transformation,[status(thm)],[f5])).
% 29.42/4.14 fof(f58,plain,(
% 29.42/4.14 ![X0,X1]: (~aNaturalNumber0(X0)|~aNaturalNumber0(X1)|aNaturalNumber0(sdtasdt0(X0,X1)))),
% 29.42/4.14 inference(cnf_transformation,[status(thm)],[f57])).
% 29.42/4.14 fof(f70,plain,(
% 29.42/4.14 ![W0]: (~aNaturalNumber0(W0)|(sdtasdt0(W0,sz10)=W0&W0=sdtasdt0(sz10,W0)))),
% 29.42/4.14 inference(pre_NNF_transformation,[status(thm)],[f11])).
% 29.42/4.14 fof(f71,plain,(
% 29.42/4.14 ![X0]: (~aNaturalNumber0(X0)|sdtasdt0(X0,sz10)=X0)),
% 29.42/4.14 inference(cnf_transformation,[status(thm)],[f70])).
% 29.42/4.14 fof(f96,plain,(
% 29.42/4.14 ![W0,W1]: ((~aNaturalNumber0(W0)|~aNaturalNumber0(W1))|(~sdtlseqdt0(W0,W1)|(![W2]: (W2=sdtmndt0(W1,W0)<=>(aNaturalNumber0(W2)&sdtpldt0(W0,W2)=W1)))))),
% 29.42/4.14 inference(pre_NNF_transformation,[status(thm)],[f19])).
% 29.42/4.14 fof(f97,plain,(
% 29.42/4.14 ![W0,W1]: ((~aNaturalNumber0(W0)|~aNaturalNumber0(W1))|(~sdtlseqdt0(W0,W1)|(![W2]: ((~W2=sdtmndt0(W1,W0)|(aNaturalNumber0(W2)&sdtpldt0(W0,W2)=W1))&(W2=sdtmndt0(W1,W0)|(~aNaturalNumber0(W2)|~sdtpldt0(W0,W2)=W1))))))),
% 29.42/4.14 inference(NNF_transformation,[status(thm)],[f96])).
% 29.42/4.14 fof(f98,plain,(
% 29.42/4.14 ![W0,W1]: ((~aNaturalNumber0(W0)|~aNaturalNumber0(W1))|(~sdtlseqdt0(W0,W1)|((![W2]: (~W2=sdtmndt0(W1,W0)|(aNaturalNumber0(W2)&sdtpldt0(W0,W2)=W1)))&(![W2]: (W2=sdtmndt0(W1,W0)|(~aNaturalNumber0(W2)|~sdtpldt0(W0,W2)=W1))))))),
% 29.42/4.14 inference(miniscoping,[status(thm)],[f97])).
% 29.42/4.14 fof(f99,plain,(
% 29.42/4.14 ![X0,X1,X2]: (~aNaturalNumber0(X0)|~aNaturalNumber0(X1)|~sdtlseqdt0(X0,X1)|~X2=sdtmndt0(X1,X0)|aNaturalNumber0(X2))),
% 29.42/4.14 inference(cnf_transformation,[status(thm)],[f98])).
% 29.42/4.14 fof(f100,plain,(
% 29.42/4.14 ![X0,X1,X2]: (~aNaturalNumber0(X0)|~aNaturalNumber0(X1)|~sdtlseqdt0(X0,X1)|~X2=sdtmndt0(X1,X0)|sdtpldt0(X0,X2)=X1)),
% 29.42/4.14 inference(cnf_transformation,[status(thm)],[f98])).
% 29.42/4.14 fof(f130,plain,(
% 29.42/4.14 ![W0,W1]: ((~aNaturalNumber0(W0)|~aNaturalNumber0(W1))|(doDivides0(W0,W1)<=>(?[W2]: (aNaturalNumber0(W2)&W1=sdtasdt0(W0,W2)))))),
% 29.42/4.14 inference(pre_NNF_transformation,[status(thm)],[f30])).
% 29.42/4.14 fof(f131,plain,(
% 29.42/4.14 ![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))))))),
% 29.42/4.14 inference(NNF_transformation,[status(thm)],[f130])).
% 29.42/4.14 fof(f132,plain,(
% 29.42/4.14 ![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))))))),
% 29.42/4.14 inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(W2,sK1_skl(W1,W0))],[f131])).
% 29.42/4.14 fof(f135,plain,(
% 29.42/4.14 ![X0,X1,X2]: (~aNaturalNumber0(X0)|~aNaturalNumber0(X1)|doDivides0(X0,X1)|~aNaturalNumber0(X2)|~X1=sdtasdt0(X0,X2))),
% 29.42/4.14 inference(cnf_transformation,[status(thm)],[f132])).
% 29.42/4.14 fof(f144,plain,(
% 29.42/4.14 ![W0,W1,W2]: (((~aNaturalNumber0(W0)|~aNaturalNumber0(W1))|~aNaturalNumber0(W2))|((~doDivides0(W0,W1)|~doDivides0(W0,W2))|doDivides0(W0,sdtpldt0(W1,W2))))),
% 29.42/4.14 inference(pre_NNF_transformation,[status(thm)],[f33])).
% 29.42/4.14 fof(f145,plain,(
% 29.42/4.14 ![X0,X1,X2]: (~aNaturalNumber0(X0)|~aNaturalNumber0(X1)|~aNaturalNumber0(X2)|~doDivides0(X0,X1)|~doDivides0(X0,X2)|doDivides0(X0,sdtpldt0(X1,X2)))),
% 29.42/4.14 inference(cnf_transformation,[status(thm)],[f144])).
% 29.42/4.14 fof(f167,plain,(
% 29.42/4.14 aNaturalNumber0(xn)),
% 29.42/4.14 inference(cnf_transformation,[status(thm)],[f39])).
% 29.42/4.14 fof(f169,plain,(
% 29.42/4.14 aNaturalNumber0(xp)),
% 29.42/4.14 inference(cnf_transformation,[status(thm)],[f39])).
% 29.42/4.14 fof(f174,plain,(
% 29.42/4.14 sdtlseqdt0(xp,xn)),
% 29.42/4.14 inference(cnf_transformation,[status(thm)],[f42])).
% 29.42/4.14 fof(f175,plain,(
% 29.42/4.14 xr=sdtmndt0(xn,xp)),
% 29.42/4.14 inference(cnf_transformation,[status(thm)],[f43])).
% 29.42/4.14 fof(f179,plain,(
% 29.42/4.14 doDivides0(xp,xr)|doDivides0(xp,xm)),
% 29.42/4.14 inference(cnf_transformation,[status(thm)],[f46])).
% 29.42/4.14 fof(f180,plain,(
% 29.42/4.14 (~doDivides0(xp,xn)&~doDivides0(xp,xm))),
% 29.42/4.14 inference(pre_NNF_transformation,[status(thm)],[f48])).
% 29.42/4.14 fof(f181,plain,(
% 29.42/4.14 ~doDivides0(xp,xn)),
% 29.42/4.14 inference(cnf_transformation,[status(thm)],[f180])).
% 29.42/4.14 fof(f182,plain,(
% 29.42/4.14 ~doDivides0(xp,xm)),
% 29.42/4.14 inference(cnf_transformation,[status(thm)],[f180])).
% 29.42/4.14 fof(f184,plain,(
% 29.42/4.14 ![X0,X1]: (~aNaturalNumber0(X0)|~aNaturalNumber0(X1)|~sdtlseqdt0(X0,X1)|aNaturalNumber0(sdtmndt0(X1,X0)))),
% 29.42/4.14 inference(destructive_equality_resolution,[status(thm)],[f99])).
% 29.42/4.14 fof(f185,plain,(
% 29.42/4.14 ![X0,X1]: (~aNaturalNumber0(X0)|~aNaturalNumber0(X1)|~sdtlseqdt0(X0,X1)|sdtpldt0(X0,sdtmndt0(X1,X0))=X1)),
% 29.42/4.14 inference(destructive_equality_resolution,[status(thm)],[f100])).
% 29.42/4.14 fof(f189,plain,(
% 29.42/4.14 ![X0,X1]: (~aNaturalNumber0(X0)|~aNaturalNumber0(sdtasdt0(X0,X1))|doDivides0(X0,sdtasdt0(X0,X1))|~aNaturalNumber0(X1))),
% 29.42/4.14 inference(destructive_equality_resolution,[status(thm)],[f135])).
% 29.42/4.14 fof(f195,plain,(
% 29.42/4.14 ![X0,X1]: (~aNaturalNumber0(X0)|doDivides0(X0,sdtasdt0(X0,X1))|~aNaturalNumber0(X1))),
% 29.42/4.14 inference(backward_subsumption_resolution,[status(thm)],[f189,f58])).
% 29.42/4.14 fof(f313,plain,(
% 29.42/4.14 sdtasdt0(xp,sz10)=xp),
% 29.42/4.14 inference(resolution,[status(thm)],[f71,f169])).
% 29.42/4.14 fof(f515,plain,(
% 29.42/4.14 ~aNaturalNumber0(xp)|doDivides0(xp,xp)|~aNaturalNumber0(sz10)),
% 29.42/4.14 inference(paramodulation,[status(thm)],[f313,f195])).
% 29.42/4.14 fof(f519,plain,(
% 29.42/4.14 doDivides0(xp,xp)|~aNaturalNumber0(sz10)),
% 29.42/4.14 inference(forward_subsumption_resolution,[status(thm)],[f515,f169])).
% 29.42/4.14 fof(f652,plain,(
% 29.42/4.14 ~aNaturalNumber0(xp)|~aNaturalNumber0(xn)|aNaturalNumber0(sdtmndt0(xn,xp))),
% 29.42/4.14 inference(resolution,[status(thm)],[f184,f174])).
% 29.42/4.14 fof(f658,plain,(
% 29.42/4.14 ~aNaturalNumber0(xp)|~aNaturalNumber0(xn)|aNaturalNumber0(xr)),
% 29.42/4.14 inference(forward_demodulation,[status(thm)],[f175,f652])).
% 29.42/4.14 fof(f659,plain,(
% 29.42/4.14 ~aNaturalNumber0(xn)|aNaturalNumber0(xr)),
% 29.42/4.14 inference(forward_subsumption_resolution,[status(thm)],[f658,f169])).
% 29.42/4.14 fof(f665,plain,(
% 29.42/4.14 ~aNaturalNumber0(xp)|~aNaturalNumber0(xn)|sdtpldt0(xp,sdtmndt0(xn,xp))=xn),
% 29.42/4.14 inference(resolution,[status(thm)],[f185,f174])).
% 29.42/4.14 fof(f671,plain,(
% 29.42/4.14 ~aNaturalNumber0(xp)|~aNaturalNumber0(xn)|sdtpldt0(xp,xr)=xn),
% 29.42/4.14 inference(forward_demodulation,[status(thm)],[f175,f665])).
% 29.42/4.14 fof(f672,plain,(
% 29.42/4.14 ~aNaturalNumber0(xn)|sdtpldt0(xp,xr)=xn),
% 29.42/4.14 inference(forward_subsumption_resolution,[status(thm)],[f671,f169])).
% 29.42/4.16 fof(f1003,plain,(
% 29.42/4.16 aNaturalNumber0(xr)),
% 29.42/4.16 inference(forward_subsumption_resolution,[status(thm)],[f659,f167])).
% 29.42/4.16 fof(f1789,plain,(
% 29.42/4.16 doDivides0(xp,xr)),
% 29.42/4.16 inference(forward_subsumption_resolution,[status(thm)],[f179,f182])).
% 29.42/4.16 fof(f1798,plain,(
% 29.42/4.16 ![X0]: (~aNaturalNumber0(xp)|~aNaturalNumber0(X0)|~aNaturalNumber0(xr)|~doDivides0(xp,X0)|doDivides0(xp,sdtpldt0(X0,xr)))),
% 29.42/4.16 inference(resolution,[status(thm)],[f1789,f145])).
% 29.42/4.16 fof(f1808,plain,(
% 29.42/4.16 ![X0]: (~aNaturalNumber0(X0)|~aNaturalNumber0(xr)|~doDivides0(xp,X0)|doDivides0(xp,sdtpldt0(X0,xr)))),
% 29.42/4.16 inference(forward_subsumption_resolution,[status(thm)],[f1798,f169])).
% 29.42/4.16 fof(f4026,plain,(
% 29.42/4.16 ![X0]: (~aNaturalNumber0(X0)|~doDivides0(xp,X0)|doDivides0(xp,sdtpldt0(X0,xr)))),
% 29.42/4.16 inference(forward_subsumption_resolution,[status(thm)],[f1808,f1003])).
% 29.42/4.16 fof(f4178,plain,(
% 29.42/4.16 doDivides0(xp,xp)),
% 29.42/4.16 inference(forward_subsumption_resolution,[status(thm)],[f519,f53])).
% 29.42/4.16 fof(f4179,plain,(
% 29.42/4.16 ~aNaturalNumber0(xp)|doDivides0(xp,sdtpldt0(xp,xr))),
% 29.42/4.16 inference(resolution,[status(thm)],[f4178,f4026])).
% 29.42/4.16 fof(f4191,plain,(
% 29.42/4.16 doDivides0(xp,sdtpldt0(xp,xr))),
% 29.42/4.16 inference(forward_subsumption_resolution,[status(thm)],[f4179,f169])).
% 29.42/4.16 fof(f10197,plain,(
% 29.42/4.16 doDivides0(xp,xn)),
% 29.42/4.16 inference(backward_demodulation,[status(thm)],[f10198,f4191])).
% 29.42/4.16 fof(f10198,plain,(
% 29.42/4.16 sdtpldt0(xp,xr)=xn),
% 29.42/4.16 inference(forward_subsumption_resolution,[status(thm)],[f672,f167])).
% 29.42/4.16 fof(f10202,plain,(
% 29.42/4.16 $false),
% 29.42/4.16 inference(forward_subsumption_resolution,[status(thm)],[f10197,f181])).
% 29.42/4.16 % SZS output end CNFRefutation for theBenchmark.p
% 29.42/4.18 % Elapsed time: 3.811322 seconds
% 29.42/4.18 % CPU time: 29.911820 seconds
% 29.42/4.18 % Total memory used: 310.688 MB
% 29.42/4.18 % Net memory used: 292.211 MB
%------------------------------------------------------------------------------