%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : NUM625+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 : n002.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 01:43:23 PM UTC 2026
% Result : Theorem 17.30s 2.70s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM625+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
% 0.10/0.36 % Computer : n002.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 02:48:32 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.14/0.38 % Drodi V4.1.1
% 17.30/2.70 % Refutation found
% 17.30/2.70 % SZS status Theorem for theBenchmark: Theorem is valid
% 17.30/2.70 % SZS output start CNFRefutation for theBenchmark
% 17.30/2.70 fof(f3,axiom,(
% 17.30/2.70 (! [W0] :( aSet0(W0)=> (! [W1] :( aElementOf0(W1,W0)=> aElement0(W1) ) )) )),
% 17.30/2.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 17.30/2.70 fof(f10,definition,(
% 17.30/2.70 (! [W0] :( aSet0(W0)=> (! [W1] :( aSubsetOf0(W1,W0)<=> ( aSet0(W1)& (! [W2] :( aElementOf0(W2,W1)=> aElementOf0(W2,W0) ) )) ) )) )),
% 17.30/2.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 17.30/2.70 fof(f16,definition,(
% 17.30/2.70 (! [W0,W1] :( ( aSet0(W0)& aElement0(W1) )=> (! [W2] :( W2 = sdtmndt0(W0,W1)<=> ( aSet0(W2)& (! [W3] :( aElementOf0(W3,W2)<=> ( aElement0(W3)& aElementOf0(W3,W0)& W3 != W1 ) ) )) ) )) )),
% 17.30/2.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 17.30/2.70 fof(f23,axiom,(
% 17.30/2.70 ( aSet0(szNzAzT0)& isCountable0(szNzAzT0) ) ),
% 17.30/2.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 17.30/2.70 fof(f101,hypothesis,(
% 17.30/2.70 aSubsetOf0(xQ,szNzAzT0) ),
% 17.30/2.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 17.30/2.70 fof(f103,hypothesis,(
% 17.30/2.70 xp = szmzizndt0(xQ) ),
% 17.30/2.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 17.30/2.70 fof(f104,hypothesis,(
% 17.30/2.70 ( aSet0(xP)& xP = sdtmndt0(xQ,szmzizndt0(xQ)) ) ),
% 17.30/2.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 17.30/2.70 fof(f113,hypothesis,(
% 17.30/2.70 aElementOf0(xx,xP) ),
% 17.30/2.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 17.30/2.70 fof(f114,hypothesis,(
% 17.30/2.70 ( aElementOf0(xx,szNzAzT0)& aElementOf0(xx,xO) ) ),
% 17.30/2.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 17.30/2.70 fof(f120,hypothesis,(
% 17.30/2.70 xp = xx ),
% 17.30/2.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 17.30/2.70 fof(f129,plain,(
% 17.30/2.70 ![W0]: (~aSet0(W0)|(![W1]: (~aElementOf0(W1,W0)|aElement0(W1))))),
% 17.30/2.70 inference(pre_NNF_transformation,[status(thm)],[f3])).
% 17.30/2.70 fof(f130,plain,(
% 17.30/2.70 ![X0,X1]: (~aSet0(X0)|~aElementOf0(X1,X0)|aElement0(X1))),
% 17.30/2.70 inference(cnf_transformation,[status(thm)],[f129])).
% 17.30/2.70 fof(f147,plain,(
% 17.30/2.70 ![W0]: (~aSet0(W0)|(![W1]: (aSubsetOf0(W1,W0)<=>(aSet0(W1)&(![W2]: (~aElementOf0(W2,W1)|aElementOf0(W2,W0)))))))),
% 17.30/2.70 inference(pre_NNF_transformation,[status(thm)],[f10])).
% 17.30/2.70 fof(f148,plain,(
% 17.30/2.70 ![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))))))))),
% 17.30/2.70 inference(NNF_transformation,[status(thm)],[f147])).
% 17.30/2.70 fof(f149,plain,(
% 17.30/2.70 ![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))))))))),
% 17.30/2.70 inference(miniscoping,[status(thm)],[f148])).
% 17.30/2.70 fof(f150,plain,(
% 17.30/2.70 ![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)))))))),
% 17.30/2.70 inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(W2,sK1_skl(W1,W0))],[f149])).
% 17.30/2.70 fof(f151,plain,(
% 17.30/2.70 ![X0,X1]: (~aSet0(X0)|~aSubsetOf0(X1,X0)|aSet0(X1))),
% 17.30/2.70 inference(cnf_transformation,[status(thm)],[f150])).
% 17.30/2.70 fof(f176,plain,(
% 17.30/2.70 ![W0,W1]: ((~aSet0(W0)|~aElement0(W1))|(![W2]: (W2=sdtmndt0(W0,W1)<=>(aSet0(W2)&(![W3]: (aElementOf0(W3,W2)<=>((aElement0(W3)&aElementOf0(W3,W0))&~W3=W1)))))))),
% 17.30/2.70 inference(pre_NNF_transformation,[status(thm)],[f16])).
% 17.30/2.70 fof(f177,definition,(
% 17.30/2.70 ![W0,W1,W3]: (sP0_prd(W3,W1,W0)<=>((aElement0(W3)&aElementOf0(W3,W0))&~W3=W1))),
% 17.30/2.70 introduced(definition,[new_symbols(definition,[sP0_prd])],[])).
% 17.30/2.70 fof(f178,plain,(
% 17.30/2.70 ![W0,W1]: ((~aSet0(W0)|~aElement0(W1))|(![W2]: (W2=sdtmndt0(W0,W1)<=>(aSet0(W2)&(![W3]: (aElementOf0(W3,W2)<=>sP0_prd(W3,W1,W0)))))))),
% 17.30/2.70 inference(formula_renaming,[status(thm)],[f176,f177])).
% 17.30/2.70 fof(f179,plain,(
% 17.30/2.70 ![W0,W1]: ((~aSet0(W0)|~aElement0(W1))|(![W2]: ((~W2=sdtmndt0(W0,W1)|(aSet0(W2)&(![W3]: ((~aElementOf0(W3,W2)|sP0_prd(W3,W1,W0))&(aElementOf0(W3,W2)|~sP0_prd(W3,W1,W0))))))&(W2=sdtmndt0(W0,W1)|(~aSet0(W2)|(?[W3]: ((~aElementOf0(W3,W2)|~sP0_prd(W3,W1,W0))&(aElementOf0(W3,W2)|sP0_prd(W3,W1,W0)))))))))),
% 17.30/2.70 inference(NNF_transformation,[status(thm)],[f178])).
% 17.30/2.70 fof(f180,plain,(
% 15.93/2.73 ![W0,W1]: ((~aSet0(W0)|~aElement0(W1))|((![W2]: (~W2=sdtmndt0(W0,W1)|(aSet0(W2)&((![W3]: (~aElementOf0(W3,W2)|sP0_prd(W3,W1,W0)))&(![W3]: (aElementOf0(W3,W2)|~sP0_prd(W3,W1,W0)))))))&(![W2]: (W2=sdtmndt0(W0,W1)|(~aSet0(W2)|(?[W3]: ((~aElementOf0(W3,W2)|~sP0_prd(W3,W1,W0))&(aElementOf0(W3,W2)|sP0_prd(W3,W1,W0)))))))))),
% 15.93/2.73 inference(miniscoping,[status(thm)],[f179])).
% 15.93/2.73 fof(f181,plain,(
% 15.93/2.73 ![W0,W1]: ((~aSet0(W0)|~aElement0(W1))|((![W2]: (~W2=sdtmndt0(W0,W1)|(aSet0(W2)&((![W3]: (~aElementOf0(W3,W2)|sP0_prd(W3,W1,W0)))&(![W3]: (aElementOf0(W3,W2)|~sP0_prd(W3,W1,W0)))))))&(![W2]: (W2=sdtmndt0(W0,W1)|(~aSet0(W2)|((~aElementOf0(sK3_skl(W2,W1,W0),W2)|~sP0_prd(sK3_skl(W2,W1,W0),W1,W0))&(aElementOf0(sK3_skl(W2,W1,W0),W2)|sP0_prd(sK3_skl(W2,W1,W0),W1,W0))))))))),
% 15.93/2.73 inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl]),skolemize(W3,sK3_skl(W2,W1,W0))],[f180])).
% 15.93/2.73 fof(f183,plain,(
% 15.93/2.73 ![X0,X1,X2,X3]: (~aSet0(X0)|~aElement0(X1)|~X2=sdtmndt0(X0,X1)|~aElementOf0(X3,X2)|sP0_prd(X3,X1,X0))),
% 15.93/2.73 inference(cnf_transformation,[status(thm)],[f181])).
% 15.93/2.73 fof(f199,plain,(
% 15.93/2.73 aSet0(szNzAzT0)),
% 15.93/2.73 inference(cnf_transformation,[status(thm)],[f23])).
% 15.93/2.73 fof(f456,plain,(
% 15.93/2.73 aSubsetOf0(xQ,szNzAzT0)),
% 15.93/2.73 inference(cnf_transformation,[status(thm)],[f101])).
% 15.93/2.73 fof(f458,plain,(
% 15.93/2.73 xp=szmzizndt0(xQ)),
% 15.93/2.73 inference(cnf_transformation,[status(thm)],[f103])).
% 15.93/2.73 fof(f460,plain,(
% 15.93/2.73 xP=sdtmndt0(xQ,szmzizndt0(xQ))),
% 15.93/2.73 inference(cnf_transformation,[status(thm)],[f104])).
% 15.93/2.73 fof(f471,plain,(
% 15.93/2.73 aElementOf0(xx,xP)),
% 15.93/2.73 inference(cnf_transformation,[status(thm)],[f113])).
% 15.93/2.73 fof(f472,plain,(
% 15.93/2.73 aElementOf0(xx,szNzAzT0)),
% 15.93/2.73 inference(cnf_transformation,[status(thm)],[f114])).
% 15.93/2.73 fof(f481,plain,(
% 15.93/2.73 xp=xx),
% 15.93/2.73 inference(cnf_transformation,[status(thm)],[f120])).
% 15.93/2.73 fof(f482,plain,(
% 15.93/2.73 ![W0,W1,W3]: ((~sP0_prd(W3,W1,W0)|((aElement0(W3)&aElementOf0(W3,W0))&~W3=W1))&(sP0_prd(W3,W1,W0)|((~aElement0(W3)|~aElementOf0(W3,W0))|W3=W1)))),
% 15.93/2.73 inference(NNF_transformation,[status(thm)],[f177])).
% 15.93/2.73 fof(f483,plain,(
% 15.93/2.73 (![W0,W1,W3]: (~sP0_prd(W3,W1,W0)|((aElement0(W3)&aElementOf0(W3,W0))&~W3=W1)))&(![W0,W1,W3]: (sP0_prd(W3,W1,W0)|((~aElement0(W3)|~aElementOf0(W3,W0))|W3=W1)))),
% 15.93/2.73 inference(miniscoping,[status(thm)],[f482])).
% 15.93/2.73 fof(f486,plain,(
% 15.93/2.73 ![X0,X1,X2]: (~sP0_prd(X0,X1,X2)|~X0=X1)),
% 15.93/2.73 inference(cnf_transformation,[status(thm)],[f483])).
% 15.93/2.73 fof(f505,plain,(
% 15.93/2.73 ![X0,X1,X2]: (~aSet0(X0)|~aElement0(X1)|~aElementOf0(X2,sdtmndt0(X0,X1))|sP0_prd(X2,X1,X0))),
% 15.93/2.73 inference(destructive_equality_resolution,[status(thm)],[f183])).
% 15.93/2.73 fof(f542,plain,(
% 15.93/2.73 xP=sdtmndt0(xQ,xp)),
% 15.93/2.73 inference(forward_demodulation,[status(thm)],[f458,f460])).
% 15.93/2.73 fof(f547,plain,(
% 15.93/2.73 aElementOf0(xp,szNzAzT0)),
% 15.93/2.73 inference(backward_demodulation,[status(thm)],[f481,f472])).
% 15.93/2.73 fof(f548,plain,(
% 15.93/2.73 aElementOf0(xp,xP)),
% 15.93/2.73 inference(backward_demodulation,[status(thm)],[f481,f471])).
% 15.93/2.73 fof(f549,plain,(
% 15.93/2.73 ![X0,X1]: (~sP0_prd(X0,X0,X1))),
% 15.93/2.73 inference(destructive_equality_resolution,[status(thm)],[f486])).
% 15.93/2.73 fof(f558,plain,(
% 15.93/2.73 ![X0]: (~aSubsetOf0(X0,szNzAzT0)|aSet0(X0))),
% 15.93/2.73 inference(resolution,[status(thm)],[f199,f151])).
% 15.93/2.73 fof(f559,plain,(
% 15.93/2.73 ![X0]: (~aElementOf0(X0,szNzAzT0)|aElement0(X0))),
% 15.93/2.73 inference(resolution,[status(thm)],[f199,f130])).
% 15.93/2.73 fof(f657,plain,(
% 15.93/2.73 ![X0]: (~aSet0(xQ)|~aElement0(xp)|~aElementOf0(X0,xP)|sP0_prd(X0,xp,xQ))),
% 15.93/2.73 inference(paramodulation,[status(thm)],[f542,f505])).
% 15.93/2.73 fof(f673,plain,(
% 15.93/2.73 aSet0(xQ)),
% 15.93/2.73 inference(resolution,[status(thm)],[f558,f456])).
% 15.93/2.73 fof(f677,plain,(
% 15.93/2.73 ![X0]: (~aElement0(xp)|~aElementOf0(X0,xP)|sP0_prd(X0,xp,xQ))),
% 15.93/2.73 inference(backward_subsumption_resolution,[status(thm)],[f657,f673])).
% 15.93/2.73 fof(f726,plain,(
% 15.93/2.73 aElement0(xp)),
% 15.93/2.73 inference(resolution,[status(thm)],[f559,f547])).
% 15.93/2.73 fof(f733,plain,(
% 15.93/2.73 ![X0]: (~aElementOf0(X0,xP)|sP0_prd(X0,xp,xQ))),
% 15.93/2.73 inference(backward_subsumption_resolution,[status(thm)],[f677,f726])).
% 15.93/2.73 fof(f2661,plain,(
% 15.93/2.73 sP0_prd(xp,xp,xQ)),
% 15.93/2.73 inference(resolution,[status(thm)],[f733,f548])).
% 15.93/2.73 fof(f2664,plain,(
% 15.93/2.73 $false),
% 15.93/2.73 inference(forward_subsumption_resolution,[status(thm)],[f2661,f549])).
% 15.93/2.73 % SZS output end CNFRefutation for theBenchmark.p
% 15.93/2.75 % Elapsed time: 2.371682 seconds
% 15.93/2.75 % CPU time: 18.382895 seconds
% 15.93/2.75 % Total memory used: 296.250 MB
% 15.93/2.75 % Net memory used: 282.044 MB
%------------------------------------------------------------------------------