%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : NUM505+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 01:43:04 PM UTC 2026
% Result : Theorem 48.51s 6.52s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM505+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n013.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % 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 02:35:24 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.13/0.36 % Drodi V4.1.1
% 48.51/6.52 % Refutation found
% 48.51/6.52 % SZS status Theorem for theBenchmark: Theorem is valid
% 48.51/6.52 % SZS output start CNFRefutation for theBenchmark
% 48.51/6.52 fof(f5,axiom,(
% 48.51/6.52 (! [W0,W1] :( ( aNaturalNumber0(W0)& aNaturalNumber0(W1) )=> aNaturalNumber0(sdtasdt0(W0,W1)) ) )),
% 48.51/6.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 48.51/6.52 fof(f20,axiom,(
% 48.51/6.52 (! [W0] :( aNaturalNumber0(W0)=> sdtlseqdt0(W0,W0) ) )),
% 48.51/6.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 48.51/6.52 fof(f23,axiom,(
% 48.51/6.52 (! [W0,W1] :( ( aNaturalNumber0(W0)& aNaturalNumber0(W1) )=> ( sdtlseqdt0(W0,W1)| ( W1 != W0& sdtlseqdt0(W1,W0) ) ) ) )),
% 48.51/6.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 48.51/6.52 fof(f31,definition,(
% 48.51/6.52 (! [W0,W1] :( ( aNaturalNumber0(W0)& aNaturalNumber0(W1) )=> ( ( W0 != sz00& doDivides0(W0,W1) )=> (! [W2] :( W2 = sdtsldt0(W1,W0)<=> ( aNaturalNumber0(W2)& W1 = sdtasdt0(W0,W2) ) ) )) ) )),
% 48.51/6.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 48.51/6.52 fof(f37,definition,(
% 48.51/6.52 (! [W0] :( aNaturalNumber0(W0)=> ( isPrime0(W0)<=> ( W0 != sz00& W0 != sz10& (! [W1] :( ( aNaturalNumber0(W1)& doDivides0(W1,W0) )=> ( W1 = sz10| W1 = W0 ) ) )) ) ) )),
% 48.51/6.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 48.51/6.52 fof(f39,hypothesis,(
% 48.51/6.52 ( aNaturalNumber0(xn)& aNaturalNumber0(xm)& aNaturalNumber0(xp) ) ),
% 48.51/6.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 48.51/6.52 fof(f41,hypothesis,(
% 48.51/6.52 ( isPrime0(xp)& doDivides0(xp,sdtasdt0(xn,xm)) ) ),
% 48.51/6.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 48.51/6.52 fof(f45,hypothesis,(
% 48.51/6.52 xk = sdtsldt0(sdtasdt0(xn,xm),xp) ),
% 48.51/6.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 48.51/6.52 fof(f50,conjecture,(
% 48.51/6.52 ( ~ sdtlseqdt0(xp,xk)=> ( xk != xp& sdtlseqdt0(xk,xp) ) ) ),
% 48.51/6.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 48.51/6.52 fof(f51,negated_conjecture,(
% 48.51/6.52 ~(( ~ sdtlseqdt0(xp,xk)=> ( xk != xp& sdtlseqdt0(xk,xp) ) ) )),
% 48.51/6.52 inference(negated_conjecture,[status(cth)],[f50])).
% 48.51/6.52 fof(f60,plain,(
% 48.51/6.52 ![W0,W1]: ((~aNaturalNumber0(W0)|~aNaturalNumber0(W1))|aNaturalNumber0(sdtasdt0(W0,W1)))),
% 48.51/6.52 inference(pre_NNF_transformation,[status(thm)],[f5])).
% 48.51/6.52 fof(f61,plain,(
% 48.51/6.52 ![X0,X1]: (~aNaturalNumber0(X0)|~aNaturalNumber0(X1)|aNaturalNumber0(sdtasdt0(X0,X1)))),
% 48.51/6.52 inference(cnf_transformation,[status(thm)],[f60])).
% 48.51/6.52 fof(f105,plain,(
% 48.51/6.52 ![W0]: (~aNaturalNumber0(W0)|sdtlseqdt0(W0,W0))),
% 48.51/6.52 inference(pre_NNF_transformation,[status(thm)],[f20])).
% 48.51/6.52 fof(f106,plain,(
% 48.51/6.52 ![X0]: (~aNaturalNumber0(X0)|sdtlseqdt0(X0,X0))),
% 48.51/6.52 inference(cnf_transformation,[status(thm)],[f105])).
% 48.51/6.52 fof(f111,plain,(
% 48.51/6.52 ![W0,W1]: ((~aNaturalNumber0(W0)|~aNaturalNumber0(W1))|(sdtlseqdt0(W0,W1)|(~W1=W0&sdtlseqdt0(W1,W0))))),
% 48.51/6.52 inference(pre_NNF_transformation,[status(thm)],[f23])).
% 48.51/6.52 fof(f113,plain,(
% 48.51/6.52 ![X0,X1]: (~aNaturalNumber0(X0)|~aNaturalNumber0(X1)|sdtlseqdt0(X0,X1)|sdtlseqdt0(X1,X0))),
% 48.51/6.52 inference(cnf_transformation,[status(thm)],[f111])).
% 48.51/6.52 fof(f139,plain,(
% 48.51/6.52 ![W0,W1]: ((~aNaturalNumber0(W0)|~aNaturalNumber0(W1))|((W0=sz00|~doDivides0(W0,W1))|(![W2]: (W2=sdtsldt0(W1,W0)<=>(aNaturalNumber0(W2)&W1=sdtasdt0(W0,W2))))))),
% 48.51/6.52 inference(pre_NNF_transformation,[status(thm)],[f31])).
% 48.51/6.52 fof(f140,plain,(
% 48.51/6.52 ![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)))))))),
% 48.51/6.52 inference(NNF_transformation,[status(thm)],[f139])).
% 48.51/6.52 fof(f141,plain,(
% 48.51/6.52 ![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)))))))),
% 48.51/6.52 inference(miniscoping,[status(thm)],[f140])).
% 48.51/6.52 fof(f142,plain,(
% 48.51/6.52 ![X0,X1,X2]: (~aNaturalNumber0(X0)|~aNaturalNumber0(X1)|X0=sz00|~doDivides0(X0,X1)|~X2=sdtsldt0(X1,X0)|aNaturalNumber0(X2))),
% 48.51/6.52 inference(cnf_transformation,[status(thm)],[f141])).
% 48.51/6.52 fof(f155,plain,(
% 48.51/6.52 ![W0]: (~aNaturalNumber0(W0)|(isPrime0(W0)<=>((~W0=sz00&~W0=sz10)&(![W1]: ((~aNaturalNumber0(W1)|~doDivides0(W1,W0))|(W1=sz10|W1=W0))))))),
% 48.51/6.52 inference(pre_NNF_transformation,[status(thm)],[f37])).
% 48.51/6.52 fof(f156,plain,(
% 48.51/6.52 ![W0]: (~aNaturalNumber0(W0)|((~isPrime0(W0)|((~W0=sz00&~W0=sz10)&(![W1]: ((~aNaturalNumber0(W1)|~doDivides0(W1,W0))|(W1=sz10|W1=W0)))))&(isPrime0(W0)|((W0=sz00|W0=sz10)|(?[W1]: ((aNaturalNumber0(W1)&doDivides0(W1,W0))&(~W1=sz10&~W1=W0)))))))),
% 48.51/6.56 inference(NNF_transformation,[status(thm)],[f155])).
% 48.51/6.56 fof(f157,plain,(
% 48.51/6.56 ![W0]: (~aNaturalNumber0(W0)|((~isPrime0(W0)|((~W0=sz00&~W0=sz10)&(![W1]: ((~aNaturalNumber0(W1)|~doDivides0(W1,W0))|(W1=sz10|W1=W0)))))&(isPrime0(W0)|((W0=sz00|W0=sz10)|((aNaturalNumber0(sK2_skl(W0))&doDivides0(sK2_skl(W0),W0))&(~sK2_skl(W0)=sz10&~sK2_skl(W0)=W0))))))),
% 48.51/6.56 inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(W1,sK2_skl(W0))],[f156])).
% 48.51/6.56 fof(f158,plain,(
% 48.51/6.56 ![X0]: (~aNaturalNumber0(X0)|~isPrime0(X0)|~X0=sz00)),
% 48.51/6.56 inference(cnf_transformation,[status(thm)],[f157])).
% 48.51/6.56 fof(f170,plain,(
% 48.51/6.56 aNaturalNumber0(xn)),
% 48.51/6.56 inference(cnf_transformation,[status(thm)],[f39])).
% 48.51/6.56 fof(f171,plain,(
% 48.51/6.56 aNaturalNumber0(xm)),
% 48.51/6.56 inference(cnf_transformation,[status(thm)],[f39])).
% 48.51/6.56 fof(f172,plain,(
% 48.51/6.56 aNaturalNumber0(xp)),
% 48.51/6.56 inference(cnf_transformation,[status(thm)],[f39])).
% 48.51/6.56 fof(f175,plain,(
% 48.51/6.56 isPrime0(xp)),
% 48.51/6.56 inference(cnf_transformation,[status(thm)],[f41])).
% 48.51/6.56 fof(f176,plain,(
% 48.51/6.56 doDivides0(xp,sdtasdt0(xn,xm))),
% 48.51/6.56 inference(cnf_transformation,[status(thm)],[f41])).
% 48.51/6.56 fof(f183,plain,(
% 48.51/6.56 xk=sdtsldt0(sdtasdt0(xn,xm),xp)),
% 48.51/6.56 inference(cnf_transformation,[status(thm)],[f45])).
% 48.51/6.56 fof(f194,plain,(
% 48.51/6.56 (~sdtlseqdt0(xp,xk)&(xk=xp|~sdtlseqdt0(xk,xp)))),
% 48.51/6.56 inference(pre_NNF_transformation,[status(thm)],[f51])).
% 48.51/6.56 fof(f195,plain,(
% 48.51/6.56 ~sdtlseqdt0(xp,xk)),
% 48.51/6.56 inference(cnf_transformation,[status(thm)],[f194])).
% 48.51/6.56 fof(f196,plain,(
% 48.51/6.56 xk=xp|~sdtlseqdt0(xk,xp)),
% 48.51/6.56 inference(cnf_transformation,[status(thm)],[f194])).
% 48.51/6.56 fof(f199,plain,(
% 48.51/6.56 sdtlseqdt0(xp,xp)),
% 48.51/6.56 inference(resolution,[status(thm)],[f106,f172])).
% 48.51/6.56 fof(f200,plain,(
% 48.51/6.56 ![X0]: (~aNaturalNumber0(X0)|sdtlseqdt0(xp,X0)|sdtlseqdt0(X0,xp))),
% 48.51/6.56 inference(resolution,[status(thm)],[f113,f172])).
% 48.51/6.56 fof(f282,plain,(
% 48.51/6.56 ![X0]: (~aNaturalNumber0(X0)|aNaturalNumber0(sdtasdt0(xn,X0)))),
% 48.51/6.56 inference(resolution,[status(thm)],[f61,f170])).
% 48.51/6.56 fof(f987,plain,(
% 48.51/6.56 ~aNaturalNumber0(xp)|~xp=sz00),
% 48.51/6.56 inference(resolution,[status(thm)],[f158,f175])).
% 48.51/6.56 fof(f989,plain,(
% 48.51/6.56 ~xp=sz00),
% 48.51/6.56 inference(forward_subsumption_resolution,[status(thm)],[f987,f172])).
% 48.51/6.56 fof(f3571,plain,(
% 48.51/6.56 aNaturalNumber0(sdtasdt0(xn,xm))),
% 48.51/6.56 inference(resolution,[status(thm)],[f282,f171])).
% 48.51/6.56 fof(f13331,plain,(
% 48.51/6.56 ![X0]: (~aNaturalNumber0(xp)|~aNaturalNumber0(sdtasdt0(xn,xm))|xp=sz00|~X0=sdtsldt0(sdtasdt0(xn,xm),xp)|aNaturalNumber0(X0))),
% 48.51/6.56 inference(resolution,[status(thm)],[f142,f176])).
% 48.51/6.56 fof(f13334,plain,(
% 48.51/6.56 ![X0]: (~aNaturalNumber0(xp)|~aNaturalNumber0(sdtasdt0(xn,xm))|xp=sz00|~X0=xk|aNaturalNumber0(X0))),
% 48.51/6.56 inference(forward_demodulation,[status(thm)],[f183,f13331])).
% 48.51/6.56 fof(f13335,plain,(
% 48.51/6.56 ![X0]: (~aNaturalNumber0(sdtasdt0(xn,xm))|xp=sz00|~X0=xk|aNaturalNumber0(X0))),
% 48.51/6.56 inference(forward_subsumption_resolution,[status(thm)],[f13334,f172])).
% 48.51/6.56 fof(f38496,plain,(
% 48.51/6.56 ![X0]: (xp=sz00|~X0=xk|aNaturalNumber0(X0))),
% 48.51/6.56 inference(forward_subsumption_resolution,[status(thm)],[f13335,f3571])).
% 48.51/6.56 fof(f38497,plain,(
% 48.51/6.56 xp=sz00|aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xp))),
% 48.51/6.56 inference(resolution,[status(thm)],[f38496,f183])).
% 48.51/6.56 fof(f38499,plain,(
% 48.51/6.56 xp=sz00|aNaturalNumber0(xk)),
% 48.51/6.56 inference(forward_demodulation,[status(thm)],[f183,f38497])).
% 48.51/6.56 fof(f38500,plain,(
% 48.51/6.56 aNaturalNumber0(xk)),
% 48.51/6.56 inference(forward_subsumption_resolution,[status(thm)],[f38499,f989])).
% 48.51/6.56 fof(f38590,plain,(
% 48.51/6.56 sdtlseqdt0(xp,xk)|sdtlseqdt0(xk,xp)),
% 48.51/6.56 inference(resolution,[status(thm)],[f38500,f200])).
% 48.51/6.56 fof(f38611,plain,(
% 48.51/6.56 sdtlseqdt0(xk,xp)),
% 48.51/6.56 inference(forward_subsumption_resolution,[status(thm)],[f38590,f195])).
% 48.51/6.56 fof(f38612,plain,(
% 48.51/6.56 xk=xp),
% 48.51/6.56 inference(backward_subsumption_resolution,[status(thm)],[f196,f38611])).
% 48.51/6.56 fof(f38678,plain,(
% 48.51/6.56 ~sdtlseqdt0(xp,xp)),
% 48.51/6.56 inference(backward_demodulation,[status(thm)],[f38612,f195])).
% 48.51/6.56 fof(f38680,plain,(
% 48.51/6.56 $false),
% 48.51/6.56 inference(forward_subsumption_resolution,[status(thm)],[f38678,f199])).
% 48.51/6.56 % SZS output end CNFRefutation for theBenchmark.p
% 3.98/7.54 % Elapsed time: 7.183683 seconds
% 3.98/7.54 % CPU time: 49.925724 seconds
% 3.98/7.54 % Total memory used: 357.910 MB
% 3.98/7.54 % Net memory used: 335.447 MB
%------------------------------------------------------------------------------