%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : NUM501+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 : n007.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 96.62s 12.62s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM501+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n007.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 02:33:20 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 96.62/12.62 % Refutation found
% 96.62/12.62 % SZS status Theorem for theBenchmark: Theorem is valid
% 96.62/12.62 % SZS output start CNFRefutation for theBenchmark
% 96.62/12.62 fof(f5,axiom,(
% 96.62/12.62 (! [W0,W1] :( ( aNaturalNumber0(W0)& aNaturalNumber0(W1) )=> aNaturalNumber0(sdtasdt0(W0,W1)) ) )),
% 96.62/12.62 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 96.62/12.62 fof(f9,axiom,(
% 96.62/12.62 (! [W0,W1] :( ( aNaturalNumber0(W0)& aNaturalNumber0(W1) )=> sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) )),
% 96.62/12.62 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 96.62/12.62 fof(f30,definition,(
% 96.62/12.62 (! [W0,W1] :( ( aNaturalNumber0(W0)& aNaturalNumber0(W1) )=> ( doDivides0(W0,W1)<=> (? [W2] :( aNaturalNumber0(W2)& W1 = sdtasdt0(W0,W2) ) )) ) )),
% 96.62/12.62 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 96.62/12.62 fof(f32,axiom,(
% 96.62/12.62 (! [W0,W1,W2] :( ( aNaturalNumber0(W0)& aNaturalNumber0(W1)& aNaturalNumber0(W2) )=> ( ( doDivides0(W0,W1)& doDivides0(W1,W2) )=> doDivides0(W0,W2) ) ) )),
% 96.62/12.62 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 96.62/12.62 fof(f39,hypothesis,(
% 96.62/12.62 ( aNaturalNumber0(xn)& aNaturalNumber0(xm)& aNaturalNumber0(xp) ) ),
% 96.62/12.62 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 96.62/12.62 fof(f45,hypothesis,(
% 96.62/12.62 ( aNaturalNumber0(xk)& sdtasdt0(xn,xm) = sdtasdt0(xp,xk)& xk = sdtsldt0(sdtasdt0(xn,xm),xp) ) ),
% 96.62/12.62 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 96.62/12.62 fof(f48,hypothesis,(
% 96.62/12.62 ( aNaturalNumber0(xr)& (? [W0] :( aNaturalNumber0(W0)& xk = sdtasdt0(xr,W0) ))& doDivides0(xr,xk)& xr != sz00& xr != sz10& (! [W0] :( ( aNaturalNumber0(W0)& ( (? [W1] :( aNaturalNumber0(W1)& xr = sdtasdt0(W0,W1) ))| doDivides0(W0,xr) ) )=> ( W0 = sz10| W0 = xr ) ))& isPrime0(xr) ) ),
% 96.62/12.62 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 96.62/12.62 fof(f49,conjecture,(
% 96.62/12.62 ( (? [W0] :( aNaturalNumber0(W0)& sdtasdt0(xn,xm) = sdtasdt0(xr,W0) ))| doDivides0(xr,sdtasdt0(xn,xm)) ) ),
% 96.62/12.62 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 96.62/12.62 fof(f50,negated_conjecture,(
% 96.62/12.62 ~(( (? [W0] :( aNaturalNumber0(W0)& sdtasdt0(xn,xm) = sdtasdt0(xr,W0) ))| doDivides0(xr,sdtasdt0(xn,xm)) ) )),
% 96.62/12.62 inference(negated_conjecture,[status(cth)],[f49])).
% 96.62/12.62 fof(f59,plain,(
% 96.62/12.62 ![W0,W1]: ((~aNaturalNumber0(W0)|~aNaturalNumber0(W1))|aNaturalNumber0(sdtasdt0(W0,W1)))),
% 96.62/12.62 inference(pre_NNF_transformation,[status(thm)],[f5])).
% 96.62/12.62 fof(f60,plain,(
% 96.62/12.62 ![X0,X1]: (~aNaturalNumber0(X0)|~aNaturalNumber0(X1)|aNaturalNumber0(sdtasdt0(X0,X1)))),
% 96.62/12.62 inference(cnf_transformation,[status(thm)],[f59])).
% 96.62/12.62 fof(f68,plain,(
% 96.62/12.62 ![W0,W1]: ((~aNaturalNumber0(W0)|~aNaturalNumber0(W1))|sdtasdt0(W0,W1)=sdtasdt0(W1,W0))),
% 96.62/12.62 inference(pre_NNF_transformation,[status(thm)],[f9])).
% 96.62/12.62 fof(f69,plain,(
% 96.62/12.62 ![X0,X1]: (~aNaturalNumber0(X0)|~aNaturalNumber0(X1)|sdtasdt0(X0,X1)=sdtasdt0(X1,X0))),
% 96.62/12.62 inference(cnf_transformation,[status(thm)],[f68])).
% 96.62/12.62 fof(f132,plain,(
% 96.62/12.62 ![W0,W1]: ((~aNaturalNumber0(W0)|~aNaturalNumber0(W1))|(doDivides0(W0,W1)<=>(?[W2]: (aNaturalNumber0(W2)&W1=sdtasdt0(W0,W2)))))),
% 96.62/12.62 inference(pre_NNF_transformation,[status(thm)],[f30])).
% 96.62/12.62 fof(f133,plain,(
% 96.62/12.62 ![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))))))),
% 96.62/12.62 inference(NNF_transformation,[status(thm)],[f132])).
% 96.62/12.62 fof(f134,plain,(
% 96.62/12.62 ![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))))))),
% 96.62/12.62 inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(W2,sK1_skl(W1,W0))],[f133])).
% 96.62/12.62 fof(f137,plain,(
% 96.62/12.62 ![X0,X1,X2]: (~aNaturalNumber0(X0)|~aNaturalNumber0(X1)|doDivides0(X0,X1)|~aNaturalNumber0(X2)|~X1=sdtasdt0(X0,X2))),
% 96.62/12.62 inference(cnf_transformation,[status(thm)],[f134])).
% 96.62/12.62 fof(f144,plain,(
% 96.62/12.62 ![W0,W1,W2]: (((~aNaturalNumber0(W0)|~aNaturalNumber0(W1))|~aNaturalNumber0(W2))|((~doDivides0(W0,W1)|~doDivides0(W1,W2))|doDivides0(W0,W2)))),
% 96.62/12.62 inference(pre_NNF_transformation,[status(thm)],[f32])).
% 96.62/12.62 fof(f145,plain,(
% 96.62/12.62 ![X0,X1,X2]: (~aNaturalNumber0(X0)|~aNaturalNumber0(X1)|~aNaturalNumber0(X2)|~doDivides0(X0,X1)|~doDivides0(X1,X2)|doDivides0(X0,X2))),
% 96.62/12.62 inference(cnf_transformation,[status(thm)],[f144])).
% 96.62/12.67 fof(f169,plain,(
% 96.62/12.67 aNaturalNumber0(xn)),
% 96.62/12.67 inference(cnf_transformation,[status(thm)],[f39])).
% 96.62/12.67 fof(f170,plain,(
% 96.62/12.67 aNaturalNumber0(xm)),
% 96.62/12.67 inference(cnf_transformation,[status(thm)],[f39])).
% 96.62/12.67 fof(f171,plain,(
% 96.62/12.67 aNaturalNumber0(xp)),
% 96.62/12.67 inference(cnf_transformation,[status(thm)],[f39])).
% 96.62/12.67 fof(f208,plain,(
% 96.62/12.67 aNaturalNumber0(xk)),
% 96.62/12.67 inference(cnf_transformation,[status(thm)],[f45])).
% 96.62/12.67 fof(f209,plain,(
% 96.62/12.67 sdtasdt0(xn,xm)=sdtasdt0(xp,xk)),
% 96.62/12.67 inference(cnf_transformation,[status(thm)],[f45])).
% 96.62/12.67 fof(f216,plain,(
% 96.62/12.67 (((((aNaturalNumber0(xr)&(?[W0]: (aNaturalNumber0(W0)&xk=sdtasdt0(xr,W0))))&doDivides0(xr,xk))&~xr=sz00)&~xr=sz10)&(![W0]: ((~aNaturalNumber0(W0)|((![W1]: (~aNaturalNumber0(W1)|~xr=sdtasdt0(W0,W1)))&~doDivides0(W0,xr)))|(W0=sz10|W0=xr))))&isPrime0(xr)),
% 96.62/12.67 inference(pre_NNF_transformation,[status(thm)],[f48])).
% 96.62/12.67 fof(f217,plain,(
% 96.62/12.67 (((((aNaturalNumber0(xr)&(aNaturalNumber0(sK8_skl)&xk=sdtasdt0(xr,sK8_skl)))&doDivides0(xr,xk))&~xr=sz00)&~xr=sz10)&(![W0]: ((~aNaturalNumber0(W0)|((![W1]: (~aNaturalNumber0(W1)|~xr=sdtasdt0(W0,W1)))&~doDivides0(W0,xr)))|(W0=sz10|W0=xr))))&isPrime0(xr)),
% 96.62/12.67 inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl]),skolemize(W0,sK8_skl)],[f216])).
% 96.62/12.67 fof(f218,plain,(
% 96.62/12.67 aNaturalNumber0(xr)),
% 96.62/12.67 inference(cnf_transformation,[status(thm)],[f217])).
% 96.62/12.67 fof(f221,plain,(
% 96.62/12.67 doDivides0(xr,xk)),
% 96.62/12.67 inference(cnf_transformation,[status(thm)],[f217])).
% 96.62/12.67 fof(f227,plain,(
% 96.62/12.67 ((![W0]: (~aNaturalNumber0(W0)|~sdtasdt0(xn,xm)=sdtasdt0(xr,W0)))&~doDivides0(xr,sdtasdt0(xn,xm)))),
% 96.62/12.67 inference(pre_NNF_transformation,[status(thm)],[f50])).
% 96.62/12.67 fof(f229,plain,(
% 96.62/12.67 ~doDivides0(xr,sdtasdt0(xn,xm))),
% 96.62/12.67 inference(cnf_transformation,[status(thm)],[f227])).
% 96.62/12.67 fof(f258,plain,(
% 96.62/12.67 ![X0,X2]: (~aNaturalNumber0(X0)|~aNaturalNumber0(sdtasdt0(X0,X2))|doDivides0(X0,sdtasdt0(X0,X2))|~aNaturalNumber0(X2))),
% 96.62/12.67 inference(destructive_equality_resolution,[status(thm)],[f137])).
% 96.62/12.67 fof(f259,plain,(
% 96.62/12.67 ![X0,X1]: (~aNaturalNumber0(X0)|doDivides0(X0,sdtasdt0(X0,X1))|~aNaturalNumber0(X1))),
% 96.62/12.67 inference(forward_subsumption_resolution,[status(thm)],[f258,f60])).
% 96.62/12.67 fof(f356,plain,(
% 96.62/12.67 ![X0]: (~aNaturalNumber0(xr)|~aNaturalNumber0(X0)|~aNaturalNumber0(sdtasdt0(xn,xm))|~doDivides0(xr,X0)|~doDivides0(X0,sdtasdt0(xn,xm)))),
% 96.62/12.67 inference(resolution,[status(thm)],[f145,f229])).
% 96.62/12.67 fof(f357,plain,(
% 96.62/12.67 ![X0]: (~aNaturalNumber0(X0)|~aNaturalNumber0(sdtasdt0(xn,xm))|~doDivides0(xr,X0)|~doDivides0(X0,sdtasdt0(xn,xm)))),
% 96.62/12.67 inference(forward_subsumption_resolution,[status(thm)],[f356,f218])).
% 96.62/12.67 fof(f681,plain,(
% 96.62/12.67 ![X0]: (~aNaturalNumber0(X0)|aNaturalNumber0(sdtasdt0(X0,xm)))),
% 96.62/12.67 inference(resolution,[status(thm)],[f170,f60])).
% 96.62/12.67 fof(f691,plain,(
% 96.62/12.67 aNaturalNumber0(sdtasdt0(xn,xm))),
% 96.62/12.67 inference(resolution,[status(thm)],[f681,f169])).
% 96.62/12.67 fof(f698,plain,(
% 96.62/12.67 ![X0]: (~aNaturalNumber0(X0)|~doDivides0(xr,X0)|~doDivides0(X0,sdtasdt0(xn,xm)))),
% 96.62/12.67 inference(backward_subsumption_resolution,[status(thm)],[f357,f691])).
% 96.62/12.67 fof(f819,plain,(
% 96.62/12.67 ~aNaturalNumber0(xk)|~doDivides0(xk,sdtasdt0(xn,xm))),
% 96.62/12.67 inference(resolution,[status(thm)],[f698,f221])).
% 96.62/12.67 fof(f822,plain,(
% 96.62/12.67 ~doDivides0(xk,sdtasdt0(xn,xm))),
% 96.62/12.67 inference(forward_subsumption_resolution,[status(thm)],[f819,f208])).
% 96.62/12.67 fof(f5359,plain,(
% 96.62/12.67 ![X0]: (~aNaturalNumber0(X0)|sdtasdt0(X0,xp)=sdtasdt0(xp,X0))),
% 96.62/12.67 inference(resolution,[status(thm)],[f171,f69])).
% 96.62/12.67 fof(f6272,plain,(
% 96.62/12.67 sdtasdt0(xk,xp)=sdtasdt0(xp,xk)),
% 96.62/12.67 inference(resolution,[status(thm)],[f208,f5359])).
% 96.62/12.67 fof(f6446,plain,(
% 96.62/12.67 sdtasdt0(xn,xm)=sdtasdt0(xk,xp)),
% 96.62/12.67 inference(backward_demodulation,[status(thm)],[f6272,f209])).
% 96.62/12.67 fof(f6517,plain,(
% 96.62/12.67 ~doDivides0(xk,sdtasdt0(xk,xp))),
% 96.62/12.67 inference(backward_demodulation,[status(thm)],[f6446,f822])).
% 96.62/12.67 fof(f6667,plain,(
% 96.62/12.67 ~aNaturalNumber0(xk)|~aNaturalNumber0(xp)),
% 96.62/12.67 inference(resolution,[status(thm)],[f6517,f259])).
% 96.62/12.67 fof(f6670,plain,(
% 96.62/12.67 ~aNaturalNumber0(xp)),
% 96.62/12.67 inference(forward_subsumption_resolution,[status(thm)],[f6667,f208])).
% 96.62/12.67 fof(f6671,plain,(
% 96.62/12.67 $false),
% 96.62/12.67 inference(backward_subsumption_resolution,[status(thm)],[f171,f6670])).
% 96.62/12.67 % SZS output end CNFRefutation for theBenchmark.p
% 96.62/12.70 % Elapsed time: 12.312631 seconds
% 96.62/12.70 % CPU time: 97.267409 seconds
% 96.62/12.70 % Total memory used: 555.758 MB
% 96.62/12.70 % Net memory used: 513.074 MB
%------------------------------------------------------------------------------