%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : NUM500+3 : 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 : n006.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 9.78s 1.88s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM500+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.39 % Computer : n006.cluster.edu
% 0.14/0.39 % Model : x86_64 x86_64
% 0.14/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.39 % Memory : 8046.5625MB
% 0.14/0.39 % OS : Linux 6.8.0-71-generic
% 0.14/0.39 % CPULimit : 300
% 0.14/0.39 % WCLimit : 300
% 0.14/0.39 % DateTime : Mon Sep 21 02:35:12 UTC 2026
% 0.14/0.39 % CPUTime :
% 0.19/0.43 % Drodi V4.1.1
% 9.78/1.88 % Refutation found
% 9.78/1.88 % SZS status Theorem for theBenchmark: Theorem is valid
% 9.78/1.88 % SZS output start CNFRefutation for theBenchmark
% 9.78/1.88 fof(f38,axiom,(
% 9.78/1.88 (! [W0] :( ( aNaturalNumber0(W0)& W0 != sz00& W0 != sz10 )=> (? [W1] :( aNaturalNumber0(W1)& doDivides0(W1,W0)& isPrime0(W1) ) )) )),
% 9.78/1.88 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 9.78/1.88 fof(f45,hypothesis,(
% 9.78/1.88 ( aNaturalNumber0(xk)& sdtasdt0(xn,xm) = sdtasdt0(xp,xk)& xk = sdtsldt0(sdtasdt0(xn,xm),xp) ) ),
% 9.78/1.88 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 9.78/1.88 fof(f46,hypothesis,(
% 9.78/1.88 ~ ( xk = sz00| xk = sz10 ) ),
% 9.78/1.88 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 9.78/1.88 fof(f48,conjecture,(
% 9.78/1.88 (? [W0] :( aNaturalNumber0(W0)& ( (? [W1] :( aNaturalNumber0(W1)& xk = sdtasdt0(W0,W1) ))| doDivides0(W0,xk) )& ( ( W0 != sz00& W0 != sz10& (! [W1] :( ( aNaturalNumber0(W1)& (? [W2] :( aNaturalNumber0(W2)& W0 = sdtasdt0(W1,W2) ))& doDivides0(W1,W0) )=> ( W1 = sz10| W1 = W0 ) ) ))| isPrime0(W0) ) ) )),
% 9.78/1.88 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 9.78/1.88 fof(f49,negated_conjecture,(
% 9.78/1.88 ~((? [W0] :( aNaturalNumber0(W0)& ( (? [W1] :( aNaturalNumber0(W1)& xk = sdtasdt0(W0,W1) ))| doDivides0(W0,xk) )& ( ( W0 != sz00& W0 != sz10& (! [W1] :( ( aNaturalNumber0(W1)& (? [W2] :( aNaturalNumber0(W2)& W0 = sdtasdt0(W1,W2) ))& doDivides0(W1,W0) )=> ( W1 = sz10| W1 = W0 ) ) ))| isPrime0(W0) ) ) ))),
% 9.78/1.88 inference(negated_conjecture,[status(cth)],[f48])).
% 9.78/1.88 fof(f163,plain,(
% 9.78/1.88 ![W0]: (((~aNaturalNumber0(W0)|W0=sz00)|W0=sz10)|(?[W1]: ((aNaturalNumber0(W1)&doDivides0(W1,W0))&isPrime0(W1))))),
% 9.78/1.88 inference(pre_NNF_transformation,[status(thm)],[f38])).
% 9.78/1.88 fof(f164,plain,(
% 9.78/1.88 ![W0]: (((~aNaturalNumber0(W0)|W0=sz00)|W0=sz10)|((aNaturalNumber0(sK3_skl(W0))&doDivides0(sK3_skl(W0),W0))&isPrime0(sK3_skl(W0))))),
% 9.78/1.88 inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl]),skolemize(W1,sK3_skl(W0))],[f163])).
% 9.78/1.88 fof(f165,plain,(
% 9.78/1.88 ![X0]: (~aNaturalNumber0(X0)|X0=sz00|X0=sz10|aNaturalNumber0(sK3_skl(X0)))),
% 9.78/1.88 inference(cnf_transformation,[status(thm)],[f164])).
% 9.78/1.88 fof(f166,plain,(
% 9.78/1.88 ![X0]: (~aNaturalNumber0(X0)|X0=sz00|X0=sz10|doDivides0(sK3_skl(X0),X0))),
% 9.78/1.88 inference(cnf_transformation,[status(thm)],[f164])).
% 9.78/1.88 fof(f167,plain,(
% 9.78/1.88 ![X0]: (~aNaturalNumber0(X0)|X0=sz00|X0=sz10|isPrime0(sK3_skl(X0)))),
% 9.78/1.88 inference(cnf_transformation,[status(thm)],[f164])).
% 9.78/1.88 fof(f207,plain,(
% 9.78/1.88 aNaturalNumber0(xk)),
% 9.78/1.88 inference(cnf_transformation,[status(thm)],[f45])).
% 9.78/1.88 fof(f210,plain,(
% 9.78/1.88 (~xk=sz00&~xk=sz10)),
% 9.78/1.88 inference(pre_NNF_transformation,[status(thm)],[f46])).
% 9.78/1.88 fof(f211,plain,(
% 9.78/1.88 ~xk=sz00),
% 9.78/1.88 inference(cnf_transformation,[status(thm)],[f210])).
% 9.78/1.88 fof(f212,plain,(
% 9.78/1.88 ~xk=sz10),
% 9.78/1.88 inference(cnf_transformation,[status(thm)],[f210])).
% 9.78/1.88 fof(f215,plain,(
% 9.78/1.88 (![W0]: ((~aNaturalNumber0(W0)|((![W1]: (~aNaturalNumber0(W1)|~xk=sdtasdt0(W0,W1)))&~doDivides0(W0,xk)))|(((W0=sz00|W0=sz10)|(?[W1]: (((aNaturalNumber0(W1)&(?[W2]: (aNaturalNumber0(W2)&W0=sdtasdt0(W1,W2))))&doDivides0(W1,W0))&(~W1=sz10&~W1=W0))))&~isPrime0(W0))))),
% 9.78/1.88 inference(pre_NNF_transformation,[status(thm)],[f49])).
% 9.78/1.88 fof(f216,definition,(
% 9.78/1.88 ![W0]: (sP2_prd(W0)<=>((![W1]: (~aNaturalNumber0(W1)|~xk=sdtasdt0(W0,W1)))&~doDivides0(W0,xk)))),
% 9.78/1.89 introduced(definition,[new_symbols(definition,[sP2_prd])],[])).
% 9.78/1.89 fof(f217,plain,(
% 9.78/1.89 ![W0]: ((~aNaturalNumber0(W0)|sP2_prd(W0))|(((W0=sz00|W0=sz10)|(?[W1]: (((aNaturalNumber0(W1)&(?[W2]: (aNaturalNumber0(W2)&W0=sdtasdt0(W1,W2))))&doDivides0(W1,W0))&(~W1=sz10&~W1=W0))))&~isPrime0(W0)))),
% 9.78/1.89 inference(formula_renaming,[status(thm)],[f215,f216])).
% 9.78/1.89 fof(f218,plain,(
% 9.78/1.89 ![W0]: ((~aNaturalNumber0(W0)|sP2_prd(W0))|(((W0=sz00|W0=sz10)|(((aNaturalNumber0(sK8_skl(W0))&(aNaturalNumber0(sK9_skl(W0))&W0=sdtasdt0(sK8_skl(W0),sK9_skl(W0))))&doDivides0(sK8_skl(W0),W0))&(~sK8_skl(W0)=sz10&~sK8_skl(W0)=W0)))&~isPrime0(W0)))),
% 9.78/1.89 inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl,sK9_skl]),skolemize(W1,sK8_skl(W0)),skolemize(W2,sK9_skl(W0))],[f217])).
% 9.78/1.89 fof(f225,plain,(
% 9.78/1.89 ![X0]: (~aNaturalNumber0(X0)|sP2_prd(X0)|~isPrime0(X0))),
% 9.78/1.89 inference(cnf_transformation,[status(thm)],[f218])).
% 9.78/1.89 fof(f246,plain,(
% 9.78/1.89 ![W0]: ((~sP2_prd(W0)|((![W1]: (~aNaturalNumber0(W1)|~xk=sdtasdt0(W0,W1)))&~doDivides0(W0,xk)))&(sP2_prd(W0)|((?[W1]: (aNaturalNumber0(W1)&xk=sdtasdt0(W0,W1)))|doDivides0(W0,xk))))),
% 9.78/1.94 inference(NNF_transformation,[status(thm)],[f216])).
% 9.78/1.94 fof(f247,plain,(
% 9.78/1.94 (![W0]: (~sP2_prd(W0)|((![W1]: (~aNaturalNumber0(W1)|~xk=sdtasdt0(W0,W1)))&~doDivides0(W0,xk))))&(![W0]: (sP2_prd(W0)|((?[W1]: (aNaturalNumber0(W1)&xk=sdtasdt0(W0,W1)))|doDivides0(W0,xk))))),
% 9.78/1.94 inference(miniscoping,[status(thm)],[f246])).
% 9.78/1.94 fof(f248,plain,(
% 9.78/1.94 (![W0]: (~sP2_prd(W0)|((![W1]: (~aNaturalNumber0(W1)|~xk=sdtasdt0(W0,W1)))&~doDivides0(W0,xk))))&(![W0]: (sP2_prd(W0)|((aNaturalNumber0(sK13_skl(W0))&xk=sdtasdt0(W0,sK13_skl(W0)))|doDivides0(W0,xk))))),
% 9.78/1.94 inference(skolemize,[status(esa),new_symbols(skolem,[sK13_skl]),skolemize(W1,sK13_skl(W0))],[f247])).
% 9.78/1.94 fof(f250,plain,(
% 9.78/1.94 ![X0]: (~sP2_prd(X0)|~doDivides0(X0,xk))),
% 9.78/1.94 inference(cnf_transformation,[status(thm)],[f248])).
% 9.78/1.94 fof(f3863,plain,(
% 9.78/1.94 xk=sz00|xk=sz10|aNaturalNumber0(sK3_skl(xk))),
% 9.78/1.94 inference(resolution,[status(thm)],[f165,f207])).
% 9.78/1.94 fof(f3867,plain,(
% 9.78/1.94 xk=sz10|aNaturalNumber0(sK3_skl(xk))),
% 9.78/1.94 inference(forward_subsumption_resolution,[status(thm)],[f3863,f211])).
% 9.78/1.94 fof(f3909,plain,(
% 9.78/1.94 aNaturalNumber0(sK3_skl(xk))),
% 9.78/1.94 inference(forward_subsumption_resolution,[status(thm)],[f3867,f212])).
% 9.78/1.94 fof(f4010,plain,(
% 9.78/1.94 xk=sz00|xk=sz10|isPrime0(sK3_skl(xk))),
% 9.78/1.94 inference(resolution,[status(thm)],[f167,f207])).
% 9.78/1.94 fof(f4014,plain,(
% 9.78/1.94 xk=sz10|isPrime0(sK3_skl(xk))),
% 9.78/1.94 inference(forward_subsumption_resolution,[status(thm)],[f4010,f211])).
% 9.78/1.94 fof(f4018,plain,(
% 9.78/1.94 isPrime0(sK3_skl(xk))),
% 9.78/1.94 inference(forward_subsumption_resolution,[status(thm)],[f4014,f212])).
% 9.78/1.94 fof(f4019,plain,(
% 9.78/1.94 ~aNaturalNumber0(sK3_skl(xk))|sP2_prd(sK3_skl(xk))),
% 9.78/1.94 inference(resolution,[status(thm)],[f4018,f225])).
% 9.78/1.94 fof(f4020,plain,(
% 9.78/1.94 sP2_prd(sK3_skl(xk))),
% 9.78/1.94 inference(forward_subsumption_resolution,[status(thm)],[f4019,f3909])).
% 9.78/1.94 fof(f4352,plain,(
% 9.78/1.94 xk=sz00|xk=sz10|doDivides0(sK3_skl(xk),xk)),
% 9.78/1.94 inference(resolution,[status(thm)],[f166,f207])).
% 9.78/1.94 fof(f4356,plain,(
% 9.78/1.94 xk=sz10|doDivides0(sK3_skl(xk),xk)),
% 9.78/1.94 inference(forward_subsumption_resolution,[status(thm)],[f4352,f211])).
% 9.78/1.94 fof(f4370,plain,(
% 9.78/1.94 doDivides0(sK3_skl(xk),xk)),
% 9.78/1.94 inference(forward_subsumption_resolution,[status(thm)],[f4356,f212])).
% 9.78/1.94 fof(f4371,plain,(
% 9.78/1.94 ~sP2_prd(sK3_skl(xk))),
% 9.78/1.94 inference(resolution,[status(thm)],[f4370,f250])).
% 9.78/1.94 fof(f4707,plain,(
% 9.78/1.94 $false),
% 9.78/1.94 inference(forward_subsumption_resolution,[status(thm)],[f4371,f4020])).
% 9.78/1.94 % SZS output end CNFRefutation for theBenchmark.p
% 9.78/1.94 % Elapsed time: 1.522760 seconds
% 9.78/1.94 % CPU time: 11.215449 seconds
% 9.78/1.94 % Total memory used: 172.902 MB
% 9.78/1.94 % Net memory used: 165.389 MB
%------------------------------------------------------------------------------