%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : NUM617+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 01:43:22 PM UTC 2026
% Result : Theorem 0.13s 0.44s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM617+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
% 0.09/0.35 % Computer : n007.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 02:42:51 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.13/0.38 % Drodi V4.1.1
% 0.13/0.44 % Refutation found
% 0.13/0.44 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.44 % SZS output start CNFRefutation for theBenchmark
% 0.13/0.44 fof(f10,definition,(
% 0.13/0.44 (! [W0] :( aSet0(W0)=> (! [W1] :( aSubsetOf0(W1,W0)<=> ( aSet0(W1)& (! [W2] :( aElementOf0(W2,W1)=> aElementOf0(W2,W0) ) )) ) )) )),
% 0.13/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.44 fof(f23,axiom,(
% 0.13/0.44 ( aSet0(szNzAzT0)& isCountable0(szNzAzT0) ) ),
% 0.13/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.44 fof(f75,hypothesis,(
% 0.13/0.44 ( aSet0(xS)& (! [W0] :( aElementOf0(W0,xS)=> aElementOf0(W0,szNzAzT0) ))& aSubsetOf0(xS,szNzAzT0)& isCountable0(xS) ) ),
% 0.13/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.44 fof(f95,hypothesis,(
% 0.13/0.44 ( aSet0(xO)& aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))& (! [W0] :( aElementOf0(W0,sdtlbdtrb0(xd,szDzizrdt0(xd)))<=> ( aElementOf0(W0,szDzozmdt0(xd))& sdtlpdtrp0(xd,W0) = szDzizrdt0(xd) ) ))& (! [W0] :( aElementOf0(W0,xO)<=> (? [W1] :( aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd)))& sdtlpdtrp0(xe,W1) = W0 ) )))& xO = sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))) ) ),
% 0.13/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.44 fof(f98,hypothesis,(
% 0.13/0.44 ( (! [W0] :( aElementOf0(W0,xO)=> aElementOf0(W0,xS) ))& aSubsetOf0(xO,xS) ) ),
% 0.13/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.44 fof(f99,hypothesis,(
% 0.13/0.44 ( aSet0(xQ)& (! [W0] :( aElementOf0(W0,xQ)=> aElementOf0(W0,xO) ))& aSubsetOf0(xQ,xO)& sbrdtbr0(xQ) = xK& aElementOf0(xQ,slbdtsldtrb0(xO,xK)) ) ),
% 0.13/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.44 fof(f113,hypothesis,(
% 0.13/0.44 ( aElement0(xx)& aElementOf0(xx,xQ)& xx != szmzizndt0(xQ)& aElementOf0(xx,xP) ) ),
% 0.13/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.44 fof(f114,conjecture,(
% 0.13/0.44 aElementOf0(xx,szNzAzT0) ),
% 0.13/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.44 fof(f115,negated_conjecture,(
% 0.13/0.44 ~(aElementOf0(xx,szNzAzT0) )),
% 0.13/0.44 inference(negated_conjecture,[status(cth)],[f114])).
% 0.13/0.44 fof(f140,plain,(
% 0.13/0.44 ![W0]: (~aSet0(W0)|(![W1]: (aSubsetOf0(W1,W0)<=>(aSet0(W1)&(![W2]: (~aElementOf0(W2,W1)|aElementOf0(W2,W0)))))))),
% 0.13/0.44 inference(pre_NNF_transformation,[status(thm)],[f10])).
% 0.13/0.44 fof(f141,plain,(
% 0.13/0.44 ![W0]: (~aSet0(W0)|(![W1]: ((~aSubsetOf0(W1,W0)|(aSet0(W1)&(![W2]: (~aElementOf0(W2,W1)|aElementOf0(W2,W0)))))&(aSubsetOf0(W1,W0)|(~aSet0(W1)|(?[W2]: (aElementOf0(W2,W1)&~aElementOf0(W2,W0))))))))),
% 0.13/0.44 inference(NNF_transformation,[status(thm)],[f140])).
% 0.13/0.44 fof(f142,plain,(
% 0.13/0.44 ![W0]: (~aSet0(W0)|((![W1]: (~aSubsetOf0(W1,W0)|(aSet0(W1)&(![W2]: (~aElementOf0(W2,W1)|aElementOf0(W2,W0))))))&(![W1]: (aSubsetOf0(W1,W0)|(~aSet0(W1)|(?[W2]: (aElementOf0(W2,W1)&~aElementOf0(W2,W0))))))))),
% 0.13/0.44 inference(miniscoping,[status(thm)],[f141])).
% 0.13/0.44 fof(f143,plain,(
% 0.13/0.44 ![W0]: (~aSet0(W0)|((![W1]: (~aSubsetOf0(W1,W0)|(aSet0(W1)&(![W2]: (~aElementOf0(W2,W1)|aElementOf0(W2,W0))))))&(![W1]: (aSubsetOf0(W1,W0)|(~aSet0(W1)|(aElementOf0(sK1_skl(W1,W0),W1)&~aElementOf0(sK1_skl(W1,W0),W0)))))))),
% 0.13/0.44 inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(W2,sK1_skl(W1,W0))],[f142])).
% 0.13/0.44 fof(f145,plain,(
% 0.13/0.44 ![X0,X1,X2]: (~aSet0(X0)|~aSubsetOf0(X1,X0)|~aElementOf0(X2,X1)|aElementOf0(X2,X0))),
% 0.13/0.45 inference(cnf_transformation,[status(thm)],[f143])).
% 0.13/0.45 fof(f192,plain,(
% 0.13/0.45 aSet0(szNzAzT0)),
% 0.13/0.45 inference(cnf_transformation,[status(thm)],[f23])).
% 0.13/0.45 fof(f375,plain,(
% 0.13/0.45 ((aSet0(xS)&(![W0]: (~aElementOf0(W0,xS)|aElementOf0(W0,szNzAzT0))))&aSubsetOf0(xS,szNzAzT0))&isCountable0(xS)),
% 0.13/0.45 inference(pre_NNF_transformation,[status(thm)],[f75])).
% 0.13/0.45 fof(f376,plain,(
% 0.13/0.45 aSet0(xS)),
% 0.13/0.45 inference(cnf_transformation,[status(thm)],[f375])).
% 0.13/0.45 fof(f378,plain,(
% 0.13/0.45 aSubsetOf0(xS,szNzAzT0)),
% 0.13/0.45 inference(cnf_transformation,[status(thm)],[f375])).
% 0.13/0.45 fof(f578,plain,(
% 0.13/0.45 (((aSet0(xO)&aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd))))&(![W0]: ((~aElementOf0(W0,sdtlbdtrb0(xd,szDzizrdt0(xd)))|(aElementOf0(W0,szDzozmdt0(xd))&sdtlpdtrp0(xd,W0)=szDzizrdt0(xd)))&(aElementOf0(W0,sdtlbdtrb0(xd,szDzizrdt0(xd)))|(~aElementOf0(W0,szDzozmdt0(xd))|~sdtlpdtrp0(xd,W0)=szDzizrdt0(xd))))))&(![W0]: ((~aElementOf0(W0,xO)|(?[W1]: (aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd)))&sdtlpdtrp0(xe,W1)=W0)))&(aElementOf0(W0,xO)|(![W1]: (~aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd)))|~sdtlpdtrp0(xe,W1)=W0))))))&xO=sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),
% 0.13/0.46 inference(NNF_transformation,[status(thm)],[f95])).
% 0.13/0.46 fof(f579,plain,(
% 0.13/0.46 (((aSet0(xO)&aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd))))&((![W0]: (~aElementOf0(W0,sdtlbdtrb0(xd,szDzizrdt0(xd)))|(aElementOf0(W0,szDzozmdt0(xd))&sdtlpdtrp0(xd,W0)=szDzizrdt0(xd))))&(![W0]: (aElementOf0(W0,sdtlbdtrb0(xd,szDzizrdt0(xd)))|(~aElementOf0(W0,szDzozmdt0(xd))|~sdtlpdtrp0(xd,W0)=szDzizrdt0(xd))))))&((![W0]: (~aElementOf0(W0,xO)|(?[W1]: (aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd)))&sdtlpdtrp0(xe,W1)=W0))))&(![W0]: (aElementOf0(W0,xO)|(![W1]: (~aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd)))|~sdtlpdtrp0(xe,W1)=W0))))))&xO=sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),
% 0.13/0.46 inference(miniscoping,[status(thm)],[f578])).
% 0.13/0.46 fof(f580,plain,(
% 0.13/0.46 (((aSet0(xO)&aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd))))&((![W0]: (~aElementOf0(W0,sdtlbdtrb0(xd,szDzizrdt0(xd)))|(aElementOf0(W0,szDzozmdt0(xd))&sdtlpdtrp0(xd,W0)=szDzizrdt0(xd))))&(![W0]: (aElementOf0(W0,sdtlbdtrb0(xd,szDzizrdt0(xd)))|(~aElementOf0(W0,szDzozmdt0(xd))|~sdtlpdtrp0(xd,W0)=szDzizrdt0(xd))))))&((![W0]: (~aElementOf0(W0,xO)|(aElementOf0(sK34_skl(W0),sdtlbdtrb0(xd,szDzizrdt0(xd)))&sdtlpdtrp0(xe,sK34_skl(W0))=W0)))&(![W0]: (aElementOf0(W0,xO)|(![W1]: (~aElementOf0(W1,sdtlbdtrb0(xd,szDzizrdt0(xd)))|~sdtlpdtrp0(xe,W1)=W0))))))&xO=sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),
% 0.13/0.46 inference(skolemize,[status(esa),new_symbols(skolem,[sK34_skl]),skolemize(W1,sK34_skl(W0))],[f579])).
% 0.13/0.46 fof(f581,plain,(
% 0.13/0.46 aSet0(xO)),
% 0.13/0.46 inference(cnf_transformation,[status(thm)],[f580])).
% 0.13/0.46 fof(f600,plain,(
% 0.13/0.46 (![W0]: (~aElementOf0(W0,xO)|aElementOf0(W0,xS)))&aSubsetOf0(xO,xS)),
% 0.13/0.46 inference(pre_NNF_transformation,[status(thm)],[f98])).
% 0.13/0.46 fof(f602,plain,(
% 0.13/0.46 aSubsetOf0(xO,xS)),
% 0.13/0.46 inference(cnf_transformation,[status(thm)],[f600])).
% 0.13/0.46 fof(f603,plain,(
% 0.13/0.46 (((aSet0(xQ)&(![W0]: (~aElementOf0(W0,xQ)|aElementOf0(W0,xO))))&aSubsetOf0(xQ,xO))&sbrdtbr0(xQ)=xK)&aElementOf0(xQ,slbdtsldtrb0(xO,xK))),
% 0.13/0.46 inference(pre_NNF_transformation,[status(thm)],[f99])).
% 0.13/0.46 fof(f606,plain,(
% 0.13/0.46 aSubsetOf0(xQ,xO)),
% 0.13/0.46 inference(cnf_transformation,[status(thm)],[f603])).
% 0.13/0.46 fof(f656,plain,(
% 0.13/0.46 aElementOf0(xx,xQ)),
% 0.13/0.46 inference(cnf_transformation,[status(thm)],[f113])).
% 0.13/0.46 fof(f659,plain,(
% 0.13/0.46 ~aElementOf0(xx,szNzAzT0)),
% 0.13/0.46 inference(cnf_transformation,[status(thm)],[f115])).
% 0.13/0.46 fof(f882,plain,(
% 0.13/0.46 ![X0]: (~aSet0(X0)|~aSubsetOf0(xQ,X0)|aElementOf0(xx,X0))),
% 0.13/0.46 inference(resolution,[status(thm)],[f145,f656])).
% 0.13/0.46 fof(f933,plain,(
% 0.13/0.46 ~aSet0(xO)|aElementOf0(xx,xO)),
% 0.13/0.46 inference(resolution,[status(thm)],[f606,f882])).
% 0.13/0.46 fof(f937,plain,(
% 0.13/0.46 aElementOf0(xx,xO)),
% 0.13/0.46 inference(forward_subsumption_resolution,[status(thm)],[f933,f581])).
% 0.13/0.46 fof(f939,plain,(
% 0.13/0.46 ![X0]: (~aSet0(X0)|~aSubsetOf0(xO,X0)|aElementOf0(xx,X0))),
% 0.13/0.46 inference(resolution,[status(thm)],[f937,f145])).
% 0.13/0.46 fof(f942,plain,(
% 0.13/0.46 ~aSet0(xS)|aElementOf0(xx,xS)),
% 0.13/0.46 inference(resolution,[status(thm)],[f939,f602])).
% 0.13/0.46 fof(f943,plain,(
% 0.13/0.46 aElementOf0(xx,xS)),
% 0.13/0.46 inference(forward_subsumption_resolution,[status(thm)],[f942,f376])).
% 0.13/0.46 fof(f944,plain,(
% 0.13/0.46 ![X0]: (~aSet0(X0)|~aSubsetOf0(xS,X0)|aElementOf0(xx,X0))),
% 0.13/0.46 inference(resolution,[status(thm)],[f943,f145])).
% 0.13/0.46 fof(f947,plain,(
% 0.13/0.46 ~aSet0(szNzAzT0)|aElementOf0(xx,szNzAzT0)),
% 0.13/0.46 inference(resolution,[status(thm)],[f944,f378])).
% 0.13/0.46 fof(f948,plain,(
% 0.13/0.46 aElementOf0(xx,szNzAzT0)),
% 0.13/0.46 inference(forward_subsumption_resolution,[status(thm)],[f947,f192])).
% 0.13/0.46 fof(f949,plain,(
% 0.13/0.46 $false),
% 0.13/0.46 inference(forward_subsumption_resolution,[status(thm)],[f948,f659])).
% 0.13/0.46 % SZS output end CNFRefutation for theBenchmark.p
% 0.13/0.47 % Elapsed time: 0.109937 seconds
% 0.13/0.47 % CPU time: 0.482326 seconds
% 0.13/0.47 % Total memory used: 129.274 MB
% 0.13/0.47 % Net memory used: 128.612 MB
%------------------------------------------------------------------------------