%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : NUM564+1 : 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 : n015.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 01:43:13 PM UTC 2026
% Result : Theorem 0.13s 0.42s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM564+1 : 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 : n015.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 02:43:21 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.13/0.37 % Drodi V4.1.1
% 0.13/0.42 % Refutation found
% 0.13/0.42 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.42 % SZS output start CNFRefutation for theBenchmark
% 0.13/0.42 fof(f5,definition,(
% 0.13/0.42 (! [W0] :( W0 = slcrc0<=> ( aSet0(W0)& ~ (? [W1] : aElementOf0(W1,W0) )) ) )),
% 0.13/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.42 fof(f10,definition,(
% 0.13/0.42 (! [W0] :( aSet0(W0)=> (! [W1] :( aSubsetOf0(W1,W0)<=> ( aSet0(W1)& (! [W2] :( aElementOf0(W2,W1)=> aElementOf0(W2,W0) ) )) ) )) )),
% 0.13/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.42 fof(f23,axiom,(
% 0.13/0.42 ( aSet0(szNzAzT0)& isCountable0(szNzAzT0) ) ),
% 0.13/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.42 fof(f24,axiom,(
% 0.13/0.42 aElementOf0(sz00,szNzAzT0) ),
% 0.13/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.42 fof(f42,axiom,(
% 0.13/0.42 (! [W0] :( aSet0(W0)=> ( sbrdtbr0(W0) = sz00<=> W0 = slcrc0 ) ) )),
% 0.13/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.42 fof(f57,definition,(
% 0.13/0.42 (! [W0,W1] :( ( aSet0(W0)& aElementOf0(W1,szNzAzT0) )=> (! [W2] :( W2 = slbdtsldtrb0(W0,W1)<=> ( aSet0(W2)& (! [W3] :( aElementOf0(W3,W2)<=> ( aSubsetOf0(W3,W0)& sbrdtbr0(W3) = W1 ) ) )) ) )) )),
% 0.13/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.42 fof(f75,hypothesis,(
% 0.13/0.42 ( aSubsetOf0(xS,szNzAzT0)& isCountable0(xS) ) ),
% 0.13/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.42 fof(f76,hypothesis,(
% 0.13/0.42 ( aFunction0(xc)& szDzozmdt0(xc) = slbdtsldtrb0(xS,xK)& aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT) ) ),
% 0.13/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.42 fof(f78,hypothesis,(
% 0.13/0.42 xK = sz00 ),
% 0.13/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.42 fof(f79,conjecture,(
% 0.13/0.42 aElementOf0(slcrc0,slbdtsldtrb0(xS,sz00)) ),
% 0.13/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.42 fof(f80,negated_conjecture,(
% 0.13/0.42 ~(aElementOf0(slcrc0,slbdtsldtrb0(xS,sz00)) )),
% 0.13/0.42 inference(negated_conjecture,[status(cth)],[f79])).
% 0.13/0.42 fof(f91,plain,(
% 0.13/0.42 ![W0]: (W0=slcrc0<=>(aSet0(W0)&(![W1]: ~aElementOf0(W1,W0))))),
% 0.13/0.42 inference(pre_NNF_transformation,[status(thm)],[f5])).
% 0.13/0.42 fof(f92,plain,(
% 0.13/0.42 ![W0]: ((~W0=slcrc0|(aSet0(W0)&(![W1]: ~aElementOf0(W1,W0))))&(W0=slcrc0|(~aSet0(W0)|(?[W1]: aElementOf0(W1,W0)))))),
% 0.13/0.42 inference(NNF_transformation,[status(thm)],[f91])).
% 0.13/0.42 fof(f93,plain,(
% 0.13/0.42 (![W0]: (~W0=slcrc0|(aSet0(W0)&(![W1]: ~aElementOf0(W1,W0)))))&(![W0]: (W0=slcrc0|(~aSet0(W0)|(?[W1]: aElementOf0(W1,W0)))))),
% 0.13/0.42 inference(miniscoping,[status(thm)],[f92])).
% 0.13/0.42 fof(f94,plain,(
% 0.13/0.42 (![W0]: (~W0=slcrc0|(aSet0(W0)&(![W1]: ~aElementOf0(W1,W0)))))&(![W0]: (W0=slcrc0|(~aSet0(W0)|aElementOf0(sK0_skl(W0),W0))))),
% 0.13/0.42 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(W1,sK0_skl(W0))],[f93])).
% 0.13/0.42 fof(f95,plain,(
% 0.13/0.42 ![X0]: (~X0=slcrc0|aSet0(X0))),
% 0.13/0.42 inference(cnf_transformation,[status(thm)],[f94])).
% 0.13/0.42 fof(f96,plain,(
% 0.13/0.42 ![X0,X1]: (~X0=slcrc0|~aElementOf0(X1,X0))),
% 0.13/0.42 inference(cnf_transformation,[status(thm)],[f94])).
% 0.13/0.42 fof(f105,plain,(
% 0.13/0.42 ![W0]: (~aSet0(W0)|(![W1]: (aSubsetOf0(W1,W0)<=>(aSet0(W1)&(![W2]: (~aElementOf0(W2,W1)|aElementOf0(W2,W0)))))))),
% 0.13/0.42 inference(pre_NNF_transformation,[status(thm)],[f10])).
% 0.13/0.42 fof(f106,plain,(
% 0.13/0.42 ![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))))))))),
% 0.13/0.42 inference(NNF_transformation,[status(thm)],[f105])).
% 0.13/0.42 fof(f107,plain,(
% 0.13/0.42 ![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))))))))),
% 0.13/0.42 inference(miniscoping,[status(thm)],[f106])).
% 0.13/0.42 fof(f108,plain,(
% 0.13/0.42 ![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)))))))),
% 0.13/0.42 inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(W2,sK1_skl(W1,W0))],[f107])).
% 0.13/0.42 fof(f109,plain,(
% 0.13/0.42 ![X0,X1]: (~aSet0(X0)|~aSubsetOf0(X1,X0)|aSet0(X1))),
% 0.13/0.42 inference(cnf_transformation,[status(thm)],[f108])).
% 0.13/0.42 fof(f111,plain,(
% 0.13/0.42 ![X0,X1]: (~aSet0(X0)|aSubsetOf0(X1,X0)|~aSet0(X1)|aElementOf0(sK1_skl(X1,X0),X1))),
% 0.13/0.42 inference(cnf_transformation,[status(thm)],[f108])).
% 0.13/0.42 fof(f157,plain,(
% 0.13/0.42 aSet0(szNzAzT0)),
% 0.13/0.42 inference(cnf_transformation,[status(thm)],[f23])).
% 0.13/0.42 fof(f159,plain,(
% 0.13/0.42 aElementOf0(sz00,szNzAzT0)),
% 0.13/0.42 inference(cnf_transformation,[status(thm)],[f24])).
% 0.13/0.42 fof(f201,plain,(
% 0.13/0.42 ![W0]: (~aSet0(W0)|(sbrdtbr0(W0)=sz00<=>W0=slcrc0))),
% 0.13/0.42 inference(pre_NNF_transformation,[status(thm)],[f42])).
% 0.13/0.42 fof(f202,plain,(
% 0.13/0.42 ![W0]: (~aSet0(W0)|((~sbrdtbr0(W0)=sz00|W0=slcrc0)&(sbrdtbr0(W0)=sz00|~W0=slcrc0)))),
% 0.13/0.42 inference(NNF_transformation,[status(thm)],[f201])).
% 0.13/0.42 fof(f204,plain,(
% 0.13/0.42 ![X0]: (~aSet0(X0)|sbrdtbr0(X0)=sz00|~X0=slcrc0)),
% 0.13/0.42 inference(cnf_transformation,[status(thm)],[f202])).
% 0.13/0.42 fof(f262,plain,(
% 0.13/0.42 ![W0,W1]: ((~aSet0(W0)|~aElementOf0(W1,szNzAzT0))|(![W2]: (W2=slbdtsldtrb0(W0,W1)<=>(aSet0(W2)&(![W3]: (aElementOf0(W3,W2)<=>(aSubsetOf0(W3,W0)&sbrdtbr0(W3)=W1)))))))),
% 0.13/0.42 inference(pre_NNF_transformation,[status(thm)],[f57])).
% 0.13/0.42 fof(f263,plain,(
% 0.13/0.42 ![W0,W1]: ((~aSet0(W0)|~aElementOf0(W1,szNzAzT0))|(![W2]: ((~W2=slbdtsldtrb0(W0,W1)|(aSet0(W2)&(![W3]: ((~aElementOf0(W3,W2)|(aSubsetOf0(W3,W0)&sbrdtbr0(W3)=W1))&(aElementOf0(W3,W2)|(~aSubsetOf0(W3,W0)|~sbrdtbr0(W3)=W1))))))&(W2=slbdtsldtrb0(W0,W1)|(~aSet0(W2)|(?[W3]: ((~aElementOf0(W3,W2)|(~aSubsetOf0(W3,W0)|~sbrdtbr0(W3)=W1))&(aElementOf0(W3,W2)|(aSubsetOf0(W3,W0)&sbrdtbr0(W3)=W1)))))))))),
% 0.13/0.42 inference(NNF_transformation,[status(thm)],[f262])).
% 0.13/0.42 fof(f264,plain,(
% 0.13/0.42 ![W0,W1]: ((~aSet0(W0)|~aElementOf0(W1,szNzAzT0))|((![W2]: (~W2=slbdtsldtrb0(W0,W1)|(aSet0(W2)&((![W3]: (~aElementOf0(W3,W2)|(aSubsetOf0(W3,W0)&sbrdtbr0(W3)=W1)))&(![W3]: (aElementOf0(W3,W2)|(~aSubsetOf0(W3,W0)|~sbrdtbr0(W3)=W1)))))))&(![W2]: (W2=slbdtsldtrb0(W0,W1)|(~aSet0(W2)|(?[W3]: ((~aElementOf0(W3,W2)|(~aSubsetOf0(W3,W0)|~sbrdtbr0(W3)=W1))&(aElementOf0(W3,W2)|(aSubsetOf0(W3,W0)&sbrdtbr0(W3)=W1)))))))))),
% 0.13/0.42 inference(miniscoping,[status(thm)],[f263])).
% 0.13/0.42 fof(f265,plain,(
% 0.13/0.42 ![W0,W1]: ((~aSet0(W0)|~aElementOf0(W1,szNzAzT0))|((![W2]: (~W2=slbdtsldtrb0(W0,W1)|(aSet0(W2)&((![W3]: (~aElementOf0(W3,W2)|(aSubsetOf0(W3,W0)&sbrdtbr0(W3)=W1)))&(![W3]: (aElementOf0(W3,W2)|(~aSubsetOf0(W3,W0)|~sbrdtbr0(W3)=W1)))))))&(![W2]: (W2=slbdtsldtrb0(W0,W1)|(~aSet0(W2)|((~aElementOf0(sK10_skl(W2,W1,W0),W2)|(~aSubsetOf0(sK10_skl(W2,W1,W0),W0)|~sbrdtbr0(sK10_skl(W2,W1,W0))=W1))&(aElementOf0(sK10_skl(W2,W1,W0),W2)|(aSubsetOf0(sK10_skl(W2,W1,W0),W0)&sbrdtbr0(sK10_skl(W2,W1,W0))=W1))))))))),
% 0.13/0.42 inference(skolemize,[status(esa),new_symbols(skolem,[sK10_skl]),skolemize(W3,sK10_skl(W2,W1,W0))],[f264])).
% 0.13/0.42 fof(f269,plain,(
% 0.13/0.42 ![X0,X1,X2,X3]: (~aSet0(X0)|~aElementOf0(X1,szNzAzT0)|~X2=slbdtsldtrb0(X0,X1)|aElementOf0(X3,X2)|~aSubsetOf0(X3,X0)|~sbrdtbr0(X3)=X1)),
% 0.13/0.42 inference(cnf_transformation,[status(thm)],[f265])).
% 0.13/0.42 fof(f340,plain,(
% 0.13/0.42 aSubsetOf0(xS,szNzAzT0)),
% 0.13/0.42 inference(cnf_transformation,[status(thm)],[f75])).
% 0.13/0.42 fof(f343,plain,(
% 0.13/0.42 szDzozmdt0(xc)=slbdtsldtrb0(xS,xK)),
% 0.13/0.42 inference(cnf_transformation,[status(thm)],[f76])).
% 0.13/0.42 fof(f351,plain,(
% 0.13/0.42 xK=sz00),
% 0.13/0.42 inference(cnf_transformation,[status(thm)],[f78])).
% 0.13/0.42 fof(f352,plain,(
% 0.13/0.42 ~aElementOf0(slcrc0,slbdtsldtrb0(xS,sz00))),
% 0.13/0.42 inference(cnf_transformation,[status(thm)],[f80])).
% 0.13/0.42 fof(f359,plain,(
% 0.13/0.42 aSet0(slcrc0)),
% 0.13/0.42 inference(destructive_equality_resolution,[status(thm)],[f95])).
% 0.13/0.42 fof(f360,plain,(
% 0.13/0.42 ![X0]: (~aElementOf0(X0,slcrc0))),
% 0.13/0.42 inference(destructive_equality_resolution,[status(thm)],[f96])).
% 0.13/0.42 fof(f371,plain,(
% 0.13/0.42 ~aSet0(slcrc0)|sbrdtbr0(slcrc0)=sz00),
% 0.13/0.42 inference(destructive_equality_resolution,[status(thm)],[f204])).
% 0.13/0.42 fof(f385,plain,(
% 0.13/0.42 ![X0,X1]: (~aSet0(X0)|~aElementOf0(sbrdtbr0(X1),szNzAzT0)|aElementOf0(X1,slbdtsldtrb0(X0,sbrdtbr0(X1)))|~aSubsetOf0(X1,X0))),
% 0.13/0.42 inference(destructive_equality_resolution,[status(thm)],[f269])).
% 0.13/0.42 fof(f410,plain,(
% 0.13/0.42 ![X0]: (~aSet0(X0)|aSubsetOf0(slcrc0,X0)|aElementOf0(sK1_skl(slcrc0,X0),slcrc0))),
% 0.13/0.42 inference(resolution,[status(thm)],[f111,f359])).
% 0.13/0.42 fof(f411,plain,(
% 0.13/0.42 ![X0]: (~aSet0(X0)|aSubsetOf0(slcrc0,X0))),
% 0.13/0.42 inference(forward_subsumption_resolution,[status(thm)],[f410,f360])).
% 0.13/0.42 fof(f416,plain,(
% 0.13/0.42 ~aSet0(szNzAzT0)|aSet0(xS)),
% 0.13/0.42 inference(resolution,[status(thm)],[f340,f109])).
% 0.13/0.43 fof(f418,plain,(
% 0.13/0.43 aSet0(xS)),
% 0.13/0.43 inference(forward_subsumption_resolution,[status(thm)],[f416,f157])).
% 0.13/0.43 fof(f419,plain,(
% 0.13/0.43 sbrdtbr0(slcrc0)=sz00),
% 0.13/0.43 inference(forward_subsumption_resolution,[status(thm)],[f371,f359])).
% 0.13/0.43 fof(f448,plain,(
% 0.13/0.43 ~aElementOf0(slcrc0,szDzozmdt0(xc))),
% 0.13/0.43 inference(backward_demodulation,[status(thm)],[f449,f352])).
% 0.13/0.43 fof(f449,plain,(
% 0.13/0.43 szDzozmdt0(xc)=slbdtsldtrb0(xS,sz00)),
% 0.13/0.43 inference(forward_demodulation,[status(thm)],[f351,f343])).
% 0.13/0.43 fof(f1352,plain,(
% 0.13/0.43 ![X0]: (~aSet0(X0)|~aElementOf0(sz00,szNzAzT0)|aElementOf0(slcrc0,slbdtsldtrb0(X0,sbrdtbr0(slcrc0)))|~aSubsetOf0(slcrc0,X0))),
% 0.13/0.43 inference(paramodulation,[status(thm)],[f419,f385])).
% 0.13/0.43 fof(f1355,plain,(
% 0.13/0.43 ![X0]: (~aSet0(X0)|~aElementOf0(sz00,szNzAzT0)|aElementOf0(slcrc0,slbdtsldtrb0(X0,sz00))|~aSubsetOf0(slcrc0,X0))),
% 0.13/0.43 inference(forward_demodulation,[status(thm)],[f419,f1352])).
% 0.13/0.43 fof(f1356,plain,(
% 0.13/0.43 ![X0]: (~aSet0(X0)|aElementOf0(slcrc0,slbdtsldtrb0(X0,sz00))|~aSubsetOf0(slcrc0,X0))),
% 0.13/0.43 inference(forward_subsumption_resolution,[status(thm)],[f1355,f159])).
% 0.13/0.43 fof(f1391,plain,(
% 0.13/0.43 ![X0]: (~aSet0(X0)|aElementOf0(slcrc0,slbdtsldtrb0(X0,sz00)))),
% 0.13/0.43 inference(forward_subsumption_resolution,[status(thm)],[f1356,f411])).
% 0.13/0.43 fof(f1398,plain,(
% 0.13/0.43 ~aSet0(xS)|aElementOf0(slcrc0,szDzozmdt0(xc))),
% 0.13/0.43 inference(paramodulation,[status(thm)],[f449,f1391])).
% 0.13/0.43 fof(f1404,plain,(
% 0.13/0.43 aElementOf0(slcrc0,szDzozmdt0(xc))),
% 0.13/0.43 inference(forward_subsumption_resolution,[status(thm)],[f1398,f418])).
% 0.13/0.43 fof(f1414,plain,(
% 0.13/0.43 $false),
% 0.13/0.43 inference(forward_subsumption_resolution,[status(thm)],[f1404,f448])).
% 0.13/0.43 % SZS output end CNFRefutation for theBenchmark.p
% 0.13/0.45 % Elapsed time: 0.078609 seconds
% 0.13/0.45 % CPU time: 0.328003 seconds
% 0.13/0.45 % Total memory used: 111.902 MB
% 0.13/0.45 % Net memory used: 111.497 MB
%------------------------------------------------------------------------------