%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : NUM584+3 : 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 : n017.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 01:43:16 PM UTC 2026
% Result : Theorem 0.21s 5.56s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM584+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/5.48 % Computer : n017.cluster.edu
% 0.17/5.48 % Model : x86_64 x86_64
% 0.17/5.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/5.48 % Memory : 8046.5625MB
% 0.17/5.48 % OS : Linux 6.8.0-71-generic
% 0.17/5.48 % CPULimit : 300
% 0.17/5.48 % WCLimit : 300
% 0.17/5.48 % DateTime : Mon Sep 21 02:37:47 UTC 2026
% 0.17/5.49 % CPUTime :
% 0.21/5.50 % Drodi V4.1.1
% 0.21/5.56 % Refutation found
% 0.21/5.56 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.21/5.56 % SZS output start CNFRefutation for theBenchmark
% 0.21/5.56 fof(f87,hypothesis,(
% 0.21/5.56 ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))& (! [W0] :( aElementOf0(W0,sdtlpdtrp0(xN,xi))=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0) ))& aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))& (! [W0] :( aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))<=> ( aElement0(W0)& ( aElementOf0(W0,xQ)| W0 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) ))& sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = xK ) ),
% 0.21/5.56 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.21/5.56 fof(f88,hypothesis,(
% 0.21/5.56 ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))& (! [W0] :( aElementOf0(W0,sdtlpdtrp0(xN,xi))=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0) ))& aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))& (! [W0] :( aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))<=> ( aElement0(W0)& ( aElementOf0(W0,xQ)| W0 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) ))& (! [W0] :( aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))=> aElementOf0(W0,xS) ))& aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS) ) ),
% 0.21/5.56 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.21/5.56 fof(f89,conjecture,(
% 0.21/5.56 ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))& (! [W0] :( aElementOf0(W0,sdtlpdtrp0(xN,xi))=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0) ) ))=> ( ( aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))& (! [W0] :( aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))<=> ( aElement0(W0)& ( aElementOf0(W0,xQ)| W0 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) ) ))=> ( ( ( (! [W0] :( aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))=> aElementOf0(W0,xS) ))| aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS) )& sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = xK )| aElementOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),slbdtsldtrb0(xS,xK)) ) ) ) ),
% 0.21/5.56 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.21/5.56 fof(f90,negated_conjecture,(
% 0.21/5.57 ~(( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))& (! [W0] :( aElementOf0(W0,sdtlpdtrp0(xN,xi))=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0) ) ))=> ( ( aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))& (! [W0] :( aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))<=> ( aElement0(W0)& ( aElementOf0(W0,xQ)| W0 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) ) ))=> ( ( ( (! [W0] :( aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))=> aElementOf0(W0,xS) ))| aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS) )& sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = xK )| aElementOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),slbdtsldtrb0(xS,xK)) ) ) ) )),
% 0.21/5.57 inference(negated_conjecture,[status(cth)],[f89])).
% 0.21/5.57 fof(f437,plain,(
% 0.21/5.57 (((aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))&(![W0]: (~aElementOf0(W0,sdtlpdtrp0(xN,xi))|sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0))))&aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))))&(![W0]: (aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))<=>(aElement0(W0)&(aElementOf0(W0,xQ)|W0=szmzizndt0(sdtlpdtrp0(xN,xi)))))))&sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))=xK),
% 0.21/5.57 inference(pre_NNF_transformation,[status(thm)],[f87])).
% 0.21/5.57 fof(f438,plain,(
% 0.21/5.57 (((aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))&(![W0]: (~aElementOf0(W0,sdtlpdtrp0(xN,xi))|sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0))))&aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))))&(![W0]: ((~aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))|(aElement0(W0)&(aElementOf0(W0,xQ)|W0=szmzizndt0(sdtlpdtrp0(xN,xi)))))&(aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))|(~aElement0(W0)|(~aElementOf0(W0,xQ)&~W0=szmzizndt0(sdtlpdtrp0(xN,xi))))))))&sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))=xK),
% 0.21/5.57 inference(NNF_transformation,[status(thm)],[f437])).
% 0.21/5.57 fof(f439,plain,(
% 0.21/5.57 (((aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))&(![W0]: (~aElementOf0(W0,sdtlpdtrp0(xN,xi))|sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0))))&aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))))&((![W0]: (~aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))|(aElement0(W0)&(aElementOf0(W0,xQ)|W0=szmzizndt0(sdtlpdtrp0(xN,xi))))))&(![W0]: (aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))|(~aElement0(W0)|(~aElementOf0(W0,xQ)&~W0=szmzizndt0(sdtlpdtrp0(xN,xi))))))))&sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))=xK),
% 0.21/5.57 inference(miniscoping,[status(thm)],[f438])).
% 0.21/5.57 fof(f447,plain,(
% 0.21/5.57 sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))=xK),
% 0.21/5.57 inference(cnf_transformation,[status(thm)],[f439])).
% 0.21/5.57 fof(f448,plain,(
% 0.21/5.57 ((((aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))&(![W0]: (~aElementOf0(W0,sdtlpdtrp0(xN,xi))|sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0))))&aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))))&(![W0]: (aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))<=>(aElement0(W0)&(aElementOf0(W0,xQ)|W0=szmzizndt0(sdtlpdtrp0(xN,xi)))))))&(![W0]: (~aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))|aElementOf0(W0,xS))))&aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS)),
% 0.21/5.57 inference(pre_NNF_transformation,[status(thm)],[f88])).
% 0.21/5.57 fof(f449,plain,(
% 0.21/5.57 ((((aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))&(![W0]: (~aElementOf0(W0,sdtlpdtrp0(xN,xi))|sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0))))&aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))))&(![W0]: ((~aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))|(aElement0(W0)&(aElementOf0(W0,xQ)|W0=szmzizndt0(sdtlpdtrp0(xN,xi)))))&(aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))|(~aElement0(W0)|(~aElementOf0(W0,xQ)&~W0=szmzizndt0(sdtlpdtrp0(xN,xi))))))))&(![W0]: (~aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))|aElementOf0(W0,xS))))&aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS)),
% 0.21/5.57 inference(NNF_transformation,[status(thm)],[f448])).
% 0.21/5.57 fof(f450,plain,(
% 0.21/5.57 ((((aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))&(![W0]: (~aElementOf0(W0,sdtlpdtrp0(xN,xi))|sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0))))&aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))))&((![W0]: (~aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))|(aElement0(W0)&(aElementOf0(W0,xQ)|W0=szmzizndt0(sdtlpdtrp0(xN,xi))))))&(![W0]: (aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))|(~aElement0(W0)|(~aElementOf0(W0,xQ)&~W0=szmzizndt0(sdtlpdtrp0(xN,xi))))))))&(![W0]: (~aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))|aElementOf0(W0,xS))))&aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS)),
% 0.21/5.57 inference(miniscoping,[status(thm)],[f449])).
% 0.21/5.57 fof(f459,plain,(
% 0.21/5.57 aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS)),
% 0.21/5.57 inference(cnf_transformation,[status(thm)],[f450])).
% 0.21/5.57 fof(f460,plain,(
% 0.21/5.57 ((aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))&(![W0]: (~aElementOf0(W0,sdtlpdtrp0(xN,xi))|sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0))))&((aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))&(![W0]: (aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))<=>(aElement0(W0)&(aElementOf0(W0,xQ)|W0=szmzizndt0(sdtlpdtrp0(xN,xi)))))))&((((?[W0]: (aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))&~aElementOf0(W0,xS)))&~aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS))|~sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))=xK)&~aElementOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),slbdtsldtrb0(xS,xK)))))),
% 0.21/5.57 inference(pre_NNF_transformation,[status(thm)],[f90])).
% 0.21/5.57 fof(f461,plain,(
% 0.21/5.57 (aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))&(![W0]: (~aElementOf0(W0,sdtlpdtrp0(xN,xi))|sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0))))&((aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))&(![W0]: ((~aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))|(aElement0(W0)&(aElementOf0(W0,xQ)|W0=szmzizndt0(sdtlpdtrp0(xN,xi)))))&(aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))|(~aElement0(W0)|(~aElementOf0(W0,xQ)&~W0=szmzizndt0(sdtlpdtrp0(xN,xi))))))))&((((?[W0]: (aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))&~aElementOf0(W0,xS)))&~aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS))|~sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))=xK)&~aElementOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),slbdtsldtrb0(xS,xK))))),
% 0.21/5.58 inference(NNF_transformation,[status(thm)],[f460])).
% 0.21/5.58 fof(f462,plain,(
% 0.21/5.58 (aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))&(![W0]: (~aElementOf0(W0,sdtlpdtrp0(xN,xi))|sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0))))&((aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))&((![W0]: (~aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))|(aElement0(W0)&(aElementOf0(W0,xQ)|W0=szmzizndt0(sdtlpdtrp0(xN,xi))))))&(![W0]: (aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))|(~aElement0(W0)|(~aElementOf0(W0,xQ)&~W0=szmzizndt0(sdtlpdtrp0(xN,xi))))))))&((((?[W0]: (aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))&~aElementOf0(W0,xS)))&~aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS))|~sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))=xK)&~aElementOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),slbdtsldtrb0(xS,xK))))),
% 0.21/5.58 inference(miniscoping,[status(thm)],[f461])).
% 0.21/5.58 fof(f463,plain,(
% 0.21/5.58 (aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))&(![W0]: (~aElementOf0(W0,sdtlpdtrp0(xN,xi))|sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W0))))&((aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))&((![W0]: (~aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))|(aElement0(W0)&(aElementOf0(W0,xQ)|W0=szmzizndt0(sdtlpdtrp0(xN,xi))))))&(![W0]: (aElementOf0(W0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))|(~aElement0(W0)|(~aElementOf0(W0,xQ)&~W0=szmzizndt0(sdtlpdtrp0(xN,xi))))))))&((((aElementOf0(sK24_skl,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))&~aElementOf0(sK24_skl,xS))&~aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS))|~sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))=xK)&~aElementOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),slbdtsldtrb0(xS,xK))))),
% 0.21/5.58 inference(skolemize,[status(esa),new_symbols(skolem,[sK24_skl]),skolemize(W0,sK24_skl)],[f462])).
% 0.21/5.58 fof(f473,plain,(
% 0.21/5.58 ~aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS)|~sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))=xK),
% 0.21/5.58 inference(cnf_transformation,[status(thm)],[f463])).
% 0.21/5.58 fof(f610,plain,(
% 0.21/5.58 ~aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS)|~xK=xK),
% 0.21/5.58 inference(forward_demodulation,[status(thm)],[f447,f473])).
% 0.21/5.58 fof(f611,plain,(
% 0.21/5.58 ~aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS)),
% 0.21/5.58 inference(trivial_equality_resolution,[status(thm)],[f610])).
% 0.21/5.58 fof(f612,plain,(
% 0.21/5.58 $false),
% 0.21/5.58 inference(forward_subsumption_resolution,[status(thm)],[f611,f459])).
% 0.21/5.58 % SZS output end CNFRefutation for theBenchmark.p
% 0.21/5.60 % Elapsed time: 0.105429 seconds
% 0.21/5.60 % CPU time: 0.378231 seconds
% 0.21/5.60 % Total memory used: 82.624 MB
% 0.21/5.60 % Net memory used: 82.306 MB
%------------------------------------------------------------------------------