%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : RNG088+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 02:05:19 PM UTC 2026
% Result : Theorem 0.13s 0.49s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG088+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n002.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 04:21:32 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.13/0.38 % Drodi V4.1.1
% 0.13/0.49 % Refutation found
% 0.13/0.49 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.49 % SZS output start CNFRefutation for theBenchmark
% 0.13/0.49 fof(f24,definition,(
% 0.13/0.49 (! [W0] :( aIdeal0(W0)<=> ( aSet0(W0)& (! [W1] :( aElementOf0(W1,W0)=> ( (! [W2] :( aElementOf0(W2,W0)=> aElementOf0(sdtpldt0(W1,W2),W0) ))& (! [W2] :( aElement0(W2)=> aElementOf0(sdtasdt0(W2,W1),W0) ) )) ) )) ) )),
% 0.13/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.49 fof(f25,hypothesis,(
% 0.13/0.49 ( aIdeal0(xI)& aIdeal0(xJ) ) ),
% 0.13/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.49 fof(f27,hypothesis,(
% 0.13/0.49 ( aElementOf0(xk,xI)& aElementOf0(xl,xJ)& xx = sdtpldt0(xk,xl) ) ),
% 0.13/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.49 fof(f28,hypothesis,(
% 0.13/0.49 ( aElementOf0(xm,xI)& aElementOf0(xn,xJ)& xy = sdtpldt0(xm,xn) ) ),
% 0.13/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.49 fof(f29,conjecture,(
% 0.13/0.49 ( aElementOf0(sdtpldt0(xk,xm),xI)& aElementOf0(sdtpldt0(xl,xn),xJ) ) ),
% 0.13/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.49 fof(f30,negated_conjecture,(
% 0.13/0.49 ~(( aElementOf0(sdtpldt0(xk,xm),xI)& aElementOf0(sdtpldt0(xl,xn),xJ) ) )),
% 0.13/0.49 inference(negated_conjecture,[status(cth)],[f29])).
% 0.13/0.49 fof(f104,plain,(
% 0.13/0.49 ![W0]: (aIdeal0(W0)<=>(aSet0(W0)&(![W1]: (~aElementOf0(W1,W0)|((![W2]: (~aElementOf0(W2,W0)|aElementOf0(sdtpldt0(W1,W2),W0)))&(![W2]: (~aElement0(W2)|aElementOf0(sdtasdt0(W2,W1),W0))))))))),
% 0.13/0.49 inference(pre_NNF_transformation,[status(thm)],[f24])).
% 0.13/0.49 fof(f105,plain,(
% 0.13/0.49 ![W0]: ((~aIdeal0(W0)|(aSet0(W0)&(![W1]: (~aElementOf0(W1,W0)|((![W2]: (~aElementOf0(W2,W0)|aElementOf0(sdtpldt0(W1,W2),W0)))&(![W2]: (~aElement0(W2)|aElementOf0(sdtasdt0(W2,W1),W0))))))))&(aIdeal0(W0)|(~aSet0(W0)|(?[W1]: (aElementOf0(W1,W0)&((?[W2]: (aElementOf0(W2,W0)&~aElementOf0(sdtpldt0(W1,W2),W0)))|(?[W2]: (aElement0(W2)&~aElementOf0(sdtasdt0(W2,W1),W0)))))))))),
% 0.13/0.49 inference(NNF_transformation,[status(thm)],[f104])).
% 0.13/0.49 fof(f106,plain,(
% 0.13/0.49 (![W0]: (~aIdeal0(W0)|(aSet0(W0)&(![W1]: (~aElementOf0(W1,W0)|((![W2]: (~aElementOf0(W2,W0)|aElementOf0(sdtpldt0(W1,W2),W0)))&(![W2]: (~aElement0(W2)|aElementOf0(sdtasdt0(W2,W1),W0)))))))))&(![W0]: (aIdeal0(W0)|(~aSet0(W0)|(?[W1]: (aElementOf0(W1,W0)&((?[W2]: (aElementOf0(W2,W0)&~aElementOf0(sdtpldt0(W1,W2),W0)))|(?[W2]: (aElement0(W2)&~aElementOf0(sdtasdt0(W2,W1),W0)))))))))),
% 0.13/0.49 inference(miniscoping,[status(thm)],[f105])).
% 0.13/0.49 fof(f107,plain,(
% 0.13/0.49 (![W0]: (~aIdeal0(W0)|(aSet0(W0)&(![W1]: (~aElementOf0(W1,W0)|((![W2]: (~aElementOf0(W2,W0)|aElementOf0(sdtpldt0(W1,W2),W0)))&(![W2]: (~aElement0(W2)|aElementOf0(sdtasdt0(W2,W1),W0)))))))))&(![W0]: (aIdeal0(W0)|(~aSet0(W0)|(aElementOf0(sK8_skl(W0),W0)&((aElementOf0(sK9_skl(W0),W0)&~aElementOf0(sdtpldt0(sK8_skl(W0),sK9_skl(W0)),W0))|(aElement0(sK10_skl(W0))&~aElementOf0(sdtasdt0(sK10_skl(W0),sK8_skl(W0)),W0)))))))),
% 0.13/0.49 inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl,sK9_skl,sK10_skl]),skolemize(W1,sK8_skl(W0)),skolemize(W2,sK9_skl(W0)),skolemize(W2,sK10_skl(W0))],[f106])).
% 0.13/0.49 fof(f109,plain,(
% 0.13/0.49 ![X0,X1,X2]: (~aIdeal0(X0)|~aElementOf0(X1,X0)|~aElementOf0(X2,X0)|aElementOf0(sdtpldt0(X1,X2),X0))),
% 0.13/0.49 inference(cnf_transformation,[status(thm)],[f107])).
% 0.13/0.49 fof(f116,plain,(
% 0.13/0.49 aIdeal0(xI)),
% 0.13/0.49 inference(cnf_transformation,[status(thm)],[f25])).
% 0.13/0.49 fof(f117,plain,(
% 0.13/0.49 aIdeal0(xJ)),
% 0.13/0.49 inference(cnf_transformation,[status(thm)],[f25])).
% 0.13/0.49 fof(f121,plain,(
% 0.13/0.49 aElementOf0(xk,xI)),
% 0.13/0.49 inference(cnf_transformation,[status(thm)],[f27])).
% 0.13/0.49 fof(f122,plain,(
% 0.13/0.49 aElementOf0(xl,xJ)),
% 0.13/0.49 inference(cnf_transformation,[status(thm)],[f27])).
% 0.13/0.49 fof(f124,plain,(
% 0.13/0.49 aElementOf0(xm,xI)),
% 0.13/0.49 inference(cnf_transformation,[status(thm)],[f28])).
% 0.13/0.49 fof(f125,plain,(
% 0.13/0.49 aElementOf0(xn,xJ)),
% 0.13/0.49 inference(cnf_transformation,[status(thm)],[f28])).
% 0.13/0.49 fof(f127,plain,(
% 0.13/0.49 (~aElementOf0(sdtpldt0(xk,xm),xI)|~aElementOf0(sdtpldt0(xl,xn),xJ))),
% 0.13/0.49 inference(pre_NNF_transformation,[status(thm)],[f30])).
% 0.13/0.49 fof(f128,plain,(
% 0.13/0.49 ~aElementOf0(sdtpldt0(xk,xm),xI)|~aElementOf0(sdtpldt0(xl,xn),xJ)),
% 0.13/0.49 inference(cnf_transformation,[status(thm)],[f127])).
% 0.13/0.49 fof(f140,definition,(
% 0.13/0.49 sQ0_spl <=> (aElementOf0(sdtpldt0(xk,xm),xI))),
% 0.13/0.49 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.13/0.49 fof(f142,plain,(
% 0.13/0.49 ~aElementOf0(sdtpldt0(xk,xm),xI)|sQ0_spl),
% 0.13/0.49 inference(component_clause,[status(thm)],[f140])).
% 0.13/0.49 fof(f143,definition,(
% 0.13/0.49 sQ1_spl <=> (aElementOf0(sdtpldt0(xl,xn),xJ))),
% 0.13/0.49 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.13/0.49 fof(f145,plain,(
% 0.13/0.49 ~aElementOf0(sdtpldt0(xl,xn),xJ)|sQ1_spl),
% 0.13/0.49 inference(component_clause,[status(thm)],[f143])).
% 0.13/0.49 fof(f146,plain,(
% 0.13/0.49 ~sQ0_spl|~sQ1_spl),
% 0.13/0.49 inference(split_clause,[status(thm)],[f128,f140,f143])).
% 0.13/0.49 fof(f1373,plain,(
% 0.13/0.49 ![X0]: (~aIdeal0(xJ)|~aElementOf0(X0,xJ)|aElementOf0(sdtpldt0(xl,X0),xJ))),
% 0.13/0.49 inference(resolution,[status(thm)],[f109,f122])).
% 0.13/0.49 fof(f1374,plain,(
% 0.13/0.49 ![X0]: (~aIdeal0(xI)|~aElementOf0(X0,xI)|aElementOf0(sdtpldt0(xk,X0),xI))),
% 0.13/0.49 inference(resolution,[status(thm)],[f109,f121])).
% 0.13/0.49 fof(f1375,definition,(
% 0.13/0.49 sQ45_spl <=> (aIdeal0(xJ))),
% 0.13/0.49 introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition])).
% 0.13/0.49 fof(f1377,plain,(
% 0.13/0.49 ~aIdeal0(xJ)|sQ45_spl),
% 0.13/0.49 inference(component_clause,[status(thm)],[f1375])).
% 0.13/0.49 fof(f1382,definition,(
% 0.13/0.49 sQ47_spl <=> (aIdeal0(xI))),
% 0.13/0.49 introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition])).
% 0.13/0.49 fof(f1384,plain,(
% 0.13/0.49 ~aIdeal0(xI)|sQ47_spl),
% 0.13/0.49 inference(component_clause,[status(thm)],[f1382])).
% 0.13/0.49 fof(f1389,definition,(
% 0.13/0.49 ![X0]: (sQ49_spl <=> (~aElementOf0(X0,xJ)|aElementOf0(sdtpldt0(xl,X0),xJ)))),
% 0.13/0.49 introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition])).
% 0.13/0.49 fof(f1390,plain,(
% 0.13/0.49 ![X0]: (~aElementOf0(X0,xJ)|aElementOf0(sdtpldt0(xl,X0),xJ)|~sQ49_spl)),
% 0.13/0.49 inference(component_clause,[status(thm)],[f1389])).
% 0.13/0.49 fof(f1392,plain,(
% 0.13/0.49 ~sQ45_spl|sQ49_spl),
% 0.13/0.49 inference(split_clause,[status(thm)],[f1373,f1375,f1389])).
% 0.13/0.49 fof(f1393,definition,(
% 0.13/0.49 ![X0]: (sQ50_spl <=> (~aElementOf0(X0,xI)|aElementOf0(sdtpldt0(xk,X0),xI)))),
% 0.13/0.49 introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition])).
% 0.13/0.49 fof(f1394,plain,(
% 0.13/0.49 ![X0]: (~aElementOf0(X0,xI)|aElementOf0(sdtpldt0(xk,X0),xI)|~sQ50_spl)),
% 0.13/0.49 inference(component_clause,[status(thm)],[f1393])).
% 0.13/0.50 fof(f1396,plain,(
% 0.13/0.50 ~sQ47_spl|sQ50_spl),
% 0.13/0.50 inference(split_clause,[status(thm)],[f1374,f1382,f1393])).
% 0.13/0.50 fof(f1397,plain,(
% 0.13/0.50 $false|sQ47_spl),
% 0.13/0.50 inference(forward_subsumption_resolution,[status(thm)],[f1384,f116])).
% 0.13/0.50 fof(f1398,plain,(
% 0.13/0.50 sQ47_spl),
% 0.13/0.50 inference(contradiction_clause,[status(thm)],[f1397])).
% 0.13/0.50 fof(f1399,plain,(
% 0.13/0.50 $false|sQ45_spl),
% 0.13/0.50 inference(forward_subsumption_resolution,[status(thm)],[f1377,f117])).
% 0.13/0.50 fof(f1400,plain,(
% 0.13/0.50 sQ45_spl),
% 0.13/0.50 inference(contradiction_clause,[status(thm)],[f1399])).
% 0.13/0.50 fof(f1443,plain,(
% 0.13/0.50 aElementOf0(sdtpldt0(xk,xm),xI)|~sQ50_spl),
% 0.13/0.50 inference(resolution,[status(thm)],[f1394,f124])).
% 0.13/0.50 fof(f1445,plain,(
% 0.13/0.50 $false|sQ0_spl|~sQ50_spl),
% 0.13/0.50 inference(forward_subsumption_resolution,[status(thm)],[f1443,f142])).
% 0.13/0.50 fof(f1446,plain,(
% 0.13/0.50 sQ0_spl|~sQ50_spl),
% 0.13/0.50 inference(contradiction_clause,[status(thm)],[f1445])).
% 0.13/0.50 fof(f1587,plain,(
% 0.13/0.50 aElementOf0(sdtpldt0(xl,xn),xJ)|~sQ49_spl),
% 0.13/0.50 inference(resolution,[status(thm)],[f1390,f125])).
% 0.13/0.50 fof(f1589,plain,(
% 0.13/0.50 $false|sQ1_spl|~sQ49_spl),
% 0.13/0.50 inference(forward_subsumption_resolution,[status(thm)],[f1587,f145])).
% 0.13/0.50 fof(f1590,plain,(
% 0.13/0.50 sQ1_spl|~sQ49_spl),
% 0.13/0.50 inference(contradiction_clause,[status(thm)],[f1589])).
% 0.13/0.50 fof(f1591,plain,(
% 0.13/0.50 $false),
% 0.13/0.50 inference(sat_refutation,[status(thm)],[f146,f1392,f1396,f1398,f1400,f1446,f1590])).
% 0.13/0.50 % SZS output end CNFRefutation for theBenchmark.p
% 0.13/0.50 % Elapsed time: 0.128176 seconds
% 0.13/0.50 % CPU time: 0.694973 seconds
% 0.13/0.50 % Total memory used: 115.258 MB
% 0.13/0.50 % Net memory used: 114.101 MB
%------------------------------------------------------------------------------