%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : NUM482+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 : n009.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 01:43:01 PM UTC 2026
% Result : Theorem 0.09s 0.40s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM482+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n009.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 02:33:43 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.09/0.40 % Refutation found
% 0.09/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.40 % SZS output start CNFRefutation for theBenchmark
% 0.09/0.40 fof(f3,axiom,(
% 0.09/0.40 ( aNaturalNumber0(sz10)& sz10 != sz00 ) ),
% 0.09/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.40 fof(f11,axiom,(
% 0.09/0.40 (! [W0] :( aNaturalNumber0(W0)=> ( sdtasdt0(W0,sz10) = W0& W0 = sdtasdt0(sz10,W0) ) ) )),
% 0.09/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.40 fof(f38,hypothesis,(
% 0.09/0.40 aNaturalNumber0(xk) ),
% 0.09/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.40 fof(f41,conjecture,(
% 0.09/0.40 ( ( (! [W0] :( ( aNaturalNumber0(W0)& ( (? [W1] :( aNaturalNumber0(W1)& xk = sdtasdt0(W0,W1) ))| doDivides0(W0,xk) ) )=> ( W0 = sz10| W0 = xk ) ))& isPrime0(xk) )=> (? [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) ) ) )) ),
% 0.09/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.40 fof(f42,negated_conjecture,(
% 0.09/0.40 ~(( ( (! [W0] :( ( aNaturalNumber0(W0)& ( (? [W1] :( aNaturalNumber0(W1)& xk = sdtasdt0(W0,W1) ))| doDivides0(W0,xk) ) )=> ( W0 = sz10| W0 = xk ) ))& isPrime0(xk) )=> (? [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) ) ) )) )),
% 0.09/0.40 inference(negated_conjecture,[status(cth)],[f41])).
% 0.09/0.40 fof(f47,plain,(
% 0.09/0.40 aNaturalNumber0(sz10)),
% 0.09/0.40 inference(cnf_transformation,[status(thm)],[f3])).
% 0.09/0.40 fof(f64,plain,(
% 0.09/0.40 ![W0]: (~aNaturalNumber0(W0)|(sdtasdt0(W0,sz10)=W0&W0=sdtasdt0(sz10,W0)))),
% 0.09/0.40 inference(pre_NNF_transformation,[status(thm)],[f11])).
% 0.09/0.40 fof(f65,plain,(
% 0.09/0.40 ![X0]: (~aNaturalNumber0(X0)|sdtasdt0(X0,sz10)=X0)),
% 0.09/0.40 inference(cnf_transformation,[status(thm)],[f64])).
% 0.09/0.40 fof(f156,plain,(
% 0.09/0.40 aNaturalNumber0(xk)),
% 0.09/0.40 inference(cnf_transformation,[status(thm)],[f38])).
% 0.09/0.40 fof(f170,plain,(
% 0.09/0.40 (((![W0]: ((~aNaturalNumber0(W0)|((![W1]: (~aNaturalNumber0(W1)|~xk=sdtasdt0(W0,W1)))&~doDivides0(W0,xk)))|(W0=sz10|W0=xk)))&isPrime0(xk))&(![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)))))),
% 0.09/0.40 inference(pre_NNF_transformation,[status(thm)],[f42])).
% 0.09/0.40 fof(f171,definition,(
% 0.09/0.40 ![W0]: (sP0_prd(W0)<=>((![W1]: (~aNaturalNumber0(W1)|~xk=sdtasdt0(W0,W1)))&~doDivides0(W0,xk)))),
% 0.09/0.40 introduced(definition,[new_symbols(definition,[sP0_prd])],[])).
% 0.09/0.40 fof(f172,plain,(
% 0.09/0.40 ((![W0]: ((~aNaturalNumber0(W0)|((![W1]: (~aNaturalNumber0(W1)|~xk=sdtasdt0(W0,W1)))&~doDivides0(W0,xk)))|(W0=sz10|W0=xk)))&isPrime0(xk))&(![W0]: ((~aNaturalNumber0(W0)|sP0_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))))),
% 0.09/0.40 inference(formula_renaming,[status(thm)],[f170,f171])).
% 0.09/0.40 fof(f173,plain,(
% 0.09/0.40 ((![W0]: ((~aNaturalNumber0(W0)|((![W1]: (~aNaturalNumber0(W1)|~xk=sdtasdt0(W0,W1)))&~doDivides0(W0,xk)))|(W0=sz10|W0=xk)))&isPrime0(xk))&(![W0]: ((~aNaturalNumber0(W0)|sP0_prd(W0))|(((W0=sz00|W0=sz10)|(((aNaturalNumber0(sK5_skl(W0))&(aNaturalNumber0(sK6_skl(W0))&W0=sdtasdt0(sK5_skl(W0),sK6_skl(W0))))&doDivides0(sK5_skl(W0),W0))&(~sK5_skl(W0)=sz10&~sK5_skl(W0)=W0)))&~isPrime0(W0))))),
% 0.09/0.40 inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl,sK6_skl]),skolemize(W1,sK5_skl(W0)),skolemize(W2,sK6_skl(W0))],[f172])).
% 0.09/0.40 fof(f176,plain,(
% 0.09/0.40 isPrime0(xk)),
% 0.09/0.40 inference(cnf_transformation,[status(thm)],[f173])).
% 0.09/0.40 fof(f183,plain,(
% 0.09/0.40 ![X0]: (~aNaturalNumber0(X0)|sP0_prd(X0)|~isPrime0(X0))),
% 0.09/0.40 inference(cnf_transformation,[status(thm)],[f173])).
% 0.09/0.40 fof(f184,plain,(
% 0.09/0.40 ![W0]: ((~sP0_prd(W0)|((![W1]: (~aNaturalNumber0(W1)|~xk=sdtasdt0(W0,W1)))&~doDivides0(W0,xk)))&(sP0_prd(W0)|((?[W1]: (aNaturalNumber0(W1)&xk=sdtasdt0(W0,W1)))|doDivides0(W0,xk))))),
% 0.09/0.41 inference(NNF_transformation,[status(thm)],[f171])).
% 0.09/0.41 fof(f185,plain,(
% 0.09/0.41 (![W0]: (~sP0_prd(W0)|((![W1]: (~aNaturalNumber0(W1)|~xk=sdtasdt0(W0,W1)))&~doDivides0(W0,xk))))&(![W0]: (sP0_prd(W0)|((?[W1]: (aNaturalNumber0(W1)&xk=sdtasdt0(W0,W1)))|doDivides0(W0,xk))))),
% 0.09/0.41 inference(miniscoping,[status(thm)],[f184])).
% 0.09/0.41 fof(f186,plain,(
% 0.09/0.41 (![W0]: (~sP0_prd(W0)|((![W1]: (~aNaturalNumber0(W1)|~xk=sdtasdt0(W0,W1)))&~doDivides0(W0,xk))))&(![W0]: (sP0_prd(W0)|((aNaturalNumber0(sK7_skl(W0))&xk=sdtasdt0(W0,sK7_skl(W0)))|doDivides0(W0,xk))))),
% 0.09/0.41 inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl]),skolemize(W1,sK7_skl(W0))],[f185])).
% 0.09/0.41 fof(f187,plain,(
% 0.09/0.41 ![X0,X1]: (~sP0_prd(X0)|~aNaturalNumber0(X1)|~xk=sdtasdt0(X0,X1))),
% 0.09/0.41 inference(cnf_transformation,[status(thm)],[f186])).
% 0.09/0.41 fof(f206,plain,(
% 0.09/0.41 sP0_prd(xk)|~isPrime0(xk)),
% 0.09/0.41 inference(resolution,[status(thm)],[f156,f183])).
% 0.09/0.41 fof(f207,plain,(
% 0.09/0.41 sP0_prd(xk)),
% 0.09/0.41 inference(forward_subsumption_resolution,[status(thm)],[f206,f176])).
% 0.09/0.41 fof(f210,plain,(
% 0.09/0.41 sdtasdt0(xk,sz10)=xk),
% 0.09/0.41 inference(resolution,[status(thm)],[f65,f156])).
% 0.09/0.41 fof(f227,plain,(
% 0.09/0.41 ~sP0_prd(xk)|~aNaturalNumber0(sz10)),
% 0.09/0.41 inference(resolution,[status(thm)],[f210,f187])).
% 0.09/0.41 fof(f230,plain,(
% 0.09/0.41 ~aNaturalNumber0(sz10)),
% 0.09/0.41 inference(forward_subsumption_resolution,[status(thm)],[f227,f207])).
% 0.09/0.41 fof(f233,plain,(
% 0.09/0.41 $false),
% 0.09/0.41 inference(forward_subsumption_resolution,[status(thm)],[f230,f47])).
% 0.09/0.41 % SZS output end CNFRefutation for theBenchmark.p
% 0.09/0.43 % Elapsed time: 0.059105 seconds
% 0.09/0.43 % CPU time: 0.214772 seconds
% 0.09/0.43 % Total memory used: 82.212 MB
% 0.09/0.43 % Net memory used: 81.965 MB
%------------------------------------------------------------------------------