%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : NUM555+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 : 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 01:43:12 PM UTC 2026
% Result : Theorem 0.17s 0.54s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM555+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.44 % Computer : n009.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.45 % CPULimit : 300
% 0.17/0.45 % WCLimit : 300
% 0.17/0.45 % DateTime : Mon Sep 21 02:39:27 UTC 2026
% 0.17/0.45 % CPUTime :
% 0.17/0.49 % Drodi V4.1.1
% 0.17/0.54 % Refutation found
% 0.17/0.54 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.17/0.54 % SZS output start CNFRefutation for theBenchmark
% 0.17/0.54 fof(f16,definition,(
% 0.17/0.54 (! [W0,W1] :( ( aSet0(W0)& aElement0(W1) )=> (! [W2] :( W2 = sdtmndt0(W0,W1)<=> ( aSet0(W2)& (! [W3] :( aElementOf0(W3,W2)<=> ( aElement0(W3)& aElementOf0(W3,W0)& W3 != W1 ) ) )) ) )) )),
% 0.17/0.54 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.54 fof(f66,hypothesis,(
% 0.17/0.54 ( aSet0(xQ)& isFinite0(xQ)& sbrdtbr0(xQ) = xk ) ),
% 0.17/0.54 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.54 fof(f67,hypothesis,(
% 0.17/0.54 ( aElement0(xy)& aElementOf0(xy,xQ) ) ),
% 0.17/0.54 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.54 fof(f68,hypothesis,(
% 0.17/0.54 ~ aElementOf0(xx,xQ) ),
% 0.17/0.54 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.54 fof(f71,conjecture,(
% 0.17/0.54 ~ aElementOf0(xx,sdtmndt0(xQ,xy)) ),
% 0.17/0.54 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.54 fof(f72,negated_conjecture,(
% 0.17/0.54 ~(~ aElementOf0(xx,sdtmndt0(xQ,xy)) )),
% 0.17/0.54 inference(negated_conjecture,[status(cth)],[f71])).
% 0.17/0.54 fof(f126,plain,(
% 0.17/0.54 ![W0,W1]: ((~aSet0(W0)|~aElement0(W1))|(![W2]: (W2=sdtmndt0(W0,W1)<=>(aSet0(W2)&(![W3]: (aElementOf0(W3,W2)<=>((aElement0(W3)&aElementOf0(W3,W0))&~W3=W1)))))))),
% 0.17/0.54 inference(pre_NNF_transformation,[status(thm)],[f16])).
% 0.17/0.54 fof(f127,definition,(
% 0.17/0.54 ![W0,W1,W3]: (sP0_prd(W3,W1,W0)<=>((aElement0(W3)&aElementOf0(W3,W0))&~W3=W1))),
% 0.17/0.54 introduced(definition,[new_symbols(definition,[sP0_prd])],[])).
% 0.17/0.54 fof(f128,plain,(
% 0.17/0.54 ![W0,W1]: ((~aSet0(W0)|~aElement0(W1))|(![W2]: (W2=sdtmndt0(W0,W1)<=>(aSet0(W2)&(![W3]: (aElementOf0(W3,W2)<=>sP0_prd(W3,W1,W0)))))))),
% 0.17/0.54 inference(formula_renaming,[status(thm)],[f126,f127])).
% 0.17/0.54 fof(f129,plain,(
% 0.17/0.54 ![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)))))))))),
% 0.17/0.54 inference(NNF_transformation,[status(thm)],[f128])).
% 0.17/0.54 fof(f130,plain,(
% 0.17/0.54 ![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)))))))))),
% 0.17/0.54 inference(miniscoping,[status(thm)],[f129])).
% 0.17/0.54 fof(f131,plain,(
% 0.17/0.54 ![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))))))))),
% 0.17/0.54 inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl]),skolemize(W3,sK3_skl(W2,W1,W0))],[f130])).
% 0.17/0.54 fof(f133,plain,(
% 0.17/0.54 ![X0,X1,X2,X3]: (~aSet0(X0)|~aElement0(X1)|~X2=sdtmndt0(X0,X1)|~aElementOf0(X3,X2)|sP0_prd(X3,X1,X0))),
% 0.17/0.54 inference(cnf_transformation,[status(thm)],[f131])).
% 0.17/0.54 fof(f279,plain,(
% 0.17/0.54 aSet0(xQ)),
% 0.17/0.54 inference(cnf_transformation,[status(thm)],[f66])).
% 0.17/0.54 fof(f282,plain,(
% 0.17/0.54 aElement0(xy)),
% 0.17/0.54 inference(cnf_transformation,[status(thm)],[f67])).
% 0.17/0.54 fof(f284,plain,(
% 0.17/0.54 ~aElementOf0(xx,xQ)),
% 0.17/0.54 inference(cnf_transformation,[status(thm)],[f68])).
% 0.17/0.54 fof(f287,plain,(
% 0.17/0.54 aElementOf0(xx,sdtmndt0(xQ,xy))),
% 0.17/0.54 inference(cnf_transformation,[status(thm)],[f72])).
% 0.17/0.54 fof(f288,plain,(
% 0.17/0.54 ![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)))),
% 0.17/0.54 inference(NNF_transformation,[status(thm)],[f127])).
% 0.17/0.54 fof(f289,plain,(
% 0.17/0.54 (![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)))),
% 0.17/0.54 inference(miniscoping,[status(thm)],[f288])).
% 0.17/0.54 fof(f291,plain,(
% 0.17/0.54 ![X0,X1,X2]: (~sP0_prd(X0,X1,X2)|aElementOf0(X0,X2))),
% 0.17/0.54 inference(cnf_transformation,[status(thm)],[f289])).
% 0.17/0.54 fof(f311,plain,(
% 0.17/0.54 ![X0,X1,X2]: (~aSet0(X0)|~aElement0(X1)|~aElementOf0(X2,sdtmndt0(X0,X1))|sP0_prd(X2,X1,X0))),
% 0.17/0.54 inference(destructive_equality_resolution,[status(thm)],[f133])).
% 0.17/0.54 fof(f663,plain,(
% 0.17/0.54 ![X0,X1]: (~aSet0(X0)|~aElementOf0(X1,sdtmndt0(X0,xy))|sP0_prd(X1,xy,X0))),
% 0.17/0.54 inference(resolution,[status(thm)],[f311,f282])).
% 0.17/0.54 fof(f669,plain,(
% 0.17/0.54 ~aSet0(xQ)|sP0_prd(xx,xy,xQ)),
% 0.17/0.54 inference(resolution,[status(thm)],[f663,f287])).
% 0.17/0.54 fof(f672,plain,(
% 0.17/0.54 sP0_prd(xx,xy,xQ)),
% 0.17/0.54 inference(forward_subsumption_resolution,[status(thm)],[f669,f279])).
% 0.17/0.54 fof(f673,plain,(
% 0.17/0.54 aElementOf0(xx,xQ)),
% 0.17/0.54 inference(resolution,[status(thm)],[f672,f291])).
% 0.17/0.54 fof(f675,plain,(
% 0.17/0.54 $false),
% 0.17/0.54 inference(forward_subsumption_resolution,[status(thm)],[f673,f284])).
% 0.17/0.54 % SZS output end CNFRefutation for theBenchmark.p
% 0.26/0.62 % Elapsed time: 0.156929 seconds
% 0.26/0.62 % CPU time: 0.362220 seconds
% 0.26/0.62 % Total memory used: 56.652 MB
% 0.26/0.62 % Net memory used: 56.477 MB
%------------------------------------------------------------------------------