%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : RNG123+1 : 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 : n011.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 02:05:24 PM UTC 2026
% Result : Theorem 15.89s 2.52s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG123+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n011.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Sep 21 04:21:55 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.14/0.39 % Drodi V4.1.1
% 15.89/2.52 % Refutation found
% 15.89/2.52 % SZS status Theorem for theBenchmark: Theorem is valid
% 15.89/2.52 % SZS output start CNFRefutation for theBenchmark
% 15.89/2.52 fof(f24,definition,(
% 15.89/2.52 (! [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) ) )) ) )) ) )),
% 15.89/2.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 15.89/2.52 fof(f42,hypothesis,(
% 15.89/2.52 ( aIdeal0(xI)& xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) ) ),
% 15.89/2.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 15.89/2.52 fof(f45,hypothesis,(
% 15.89/2.52 ( aElementOf0(xu,xI)& xu != sz00& (! [W0] :( ( aElementOf0(W0,xI)& W0 != sz00 )=> ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu)) ) )) ),
% 15.89/2.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 15.89/2.52 fof(f50,hypothesis,(
% 15.89/2.52 ( aElement0(xq)& aElement0(xr)& xb = sdtpldt0(sdtasdt0(xq,xu),xr)& ( xr = sz00| iLess0(sbrdtbr0(xr),sbrdtbr0(xu)) ) ) ),
% 15.89/2.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 15.89/2.52 fof(f51,hypothesis,(
% 15.89/2.52 xr != sz00 ),
% 15.89/2.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 15.89/2.52 fof(f52,hypothesis,(
% 15.89/2.52 aElementOf0(smndt0(sdtasdt0(xq,xu)),xI) ),
% 15.89/2.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 15.89/2.52 fof(f53,hypothesis,(
% 15.89/2.52 aElementOf0(xb,xI) ),
% 15.89/2.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 15.89/2.52 fof(f54,hypothesis,(
% 15.89/2.52 xr = sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb) ),
% 15.89/2.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 15.89/2.52 fof(f130,plain,(
% 15.89/2.52 ![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))))))))),
% 15.89/2.52 inference(pre_NNF_transformation,[status(thm)],[f24])).
% 15.89/2.52 fof(f131,plain,(
% 15.89/2.52 ![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)))))))))),
% 15.89/2.52 inference(NNF_transformation,[status(thm)],[f130])).
% 15.89/2.52 fof(f132,plain,(
% 15.89/2.52 (![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)))))))))),
% 15.89/2.52 inference(miniscoping,[status(thm)],[f131])).
% 15.89/2.52 fof(f133,plain,(
% 15.89/2.52 (![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)))))))),
% 15.89/2.52 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))],[f132])).
% 15.89/2.52 fof(f135,plain,(
% 15.89/2.52 ![X0,X1,X2]: (~aIdeal0(X0)|~aElementOf0(X1,X0)|~aElementOf0(X2,X0)|aElementOf0(sdtpldt0(X1,X2),X0))),
% 15.89/2.52 inference(cnf_transformation,[status(thm)],[f133])).
% 15.89/2.52 fof(f213,plain,(
% 15.89/2.52 aIdeal0(xI)),
% 15.89/2.52 inference(cnf_transformation,[status(thm)],[f42])).
% 15.89/2.52 fof(f222,plain,(
% 15.89/2.52 (aElementOf0(xu,xI)&~xu=sz00)&(![W0]: ((~aElementOf0(W0,xI)|W0=sz00)|~iLess0(sbrdtbr0(W0),sbrdtbr0(xu))))),
% 15.89/2.52 inference(pre_NNF_transformation,[status(thm)],[f45])).
% 15.89/2.52 fof(f225,plain,(
% 15.89/2.52 ![X0]: (~aElementOf0(X0,xI)|X0=sz00|~iLess0(sbrdtbr0(X0),sbrdtbr0(xu)))),
% 15.89/2.52 inference(cnf_transformation,[status(thm)],[f222])).
% 15.89/2.52 fof(f237,plain,(
% 15.89/2.52 xr=sz00|iLess0(sbrdtbr0(xr),sbrdtbr0(xu))),
% 15.89/2.52 inference(cnf_transformation,[status(thm)],[f50])).
% 15.89/2.52 fof(f238,plain,(
% 15.89/2.52 ~xr=sz00),
% 15.89/2.52 inference(cnf_transformation,[status(thm)],[f51])).
% 15.89/2.52 fof(f239,plain,(
% 15.89/2.52 aElementOf0(smndt0(sdtasdt0(xq,xu)),xI)),
% 15.89/2.52 inference(cnf_transformation,[status(thm)],[f52])).
% 15.89/2.54 fof(f240,plain,(
% 15.89/2.54 aElementOf0(xb,xI)),
% 15.89/2.54 inference(cnf_transformation,[status(thm)],[f53])).
% 15.89/2.54 fof(f241,plain,(
% 15.89/2.54 xr=sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb)),
% 15.89/2.54 inference(cnf_transformation,[status(thm)],[f54])).
% 15.89/2.54 fof(f274,definition,(
% 15.89/2.54 sQ4_spl <=> (xr=sz00)),
% 15.89/2.54 introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition])).
% 15.89/2.54 fof(f275,plain,(
% 15.89/2.54 xr=sz00|~sQ4_spl),
% 15.89/2.54 inference(component_clause,[status(thm)],[f274])).
% 15.89/2.54 fof(f277,definition,(
% 15.89/2.54 sQ5_spl <=> (iLess0(sbrdtbr0(xr),sbrdtbr0(xu)))),
% 15.89/2.54 introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition])).
% 15.89/2.54 fof(f278,plain,(
% 15.89/2.54 iLess0(sbrdtbr0(xr),sbrdtbr0(xu))|~sQ5_spl),
% 15.89/2.54 inference(component_clause,[status(thm)],[f277])).
% 15.89/2.54 fof(f280,plain,(
% 15.89/2.54 sQ4_spl|sQ5_spl),
% 15.89/2.54 inference(split_clause,[status(thm)],[f237,f274,f277])).
% 15.89/2.54 fof(f294,plain,(
% 15.89/2.54 $false|~sQ4_spl),
% 15.89/2.54 inference(forward_subsumption_resolution,[status(thm)],[f275,f238])).
% 15.89/2.54 fof(f295,plain,(
% 15.89/2.54 ~sQ4_spl),
% 15.89/2.54 inference(contradiction_clause,[status(thm)],[f294])).
% 15.89/2.54 fof(f2805,plain,(
% 15.89/2.54 ![X0,X1]: (~aElementOf0(X0,xI)|~aElementOf0(X1,xI)|aElementOf0(sdtpldt0(X0,X1),xI))),
% 15.89/2.54 inference(resolution,[status(thm)],[f135,f213])).
% 15.89/2.54 fof(f10186,plain,(
% 15.89/2.54 ~aElementOf0(xr,xI)|xr=sz00|~sQ5_spl),
% 15.89/2.54 inference(resolution,[status(thm)],[f225,f278])).
% 15.89/2.54 fof(f10187,definition,(
% 15.89/2.54 sQ481_spl <=> (aElementOf0(xr,xI))),
% 15.89/2.54 introduced(definition,[new_symbols(definition,[sQ481_spl])],[split_symbol_definition])).
% 15.89/2.54 fof(f10190,plain,(
% 15.89/2.54 ~sQ481_spl|sQ4_spl|~sQ5_spl),
% 15.89/2.54 inference(split_clause,[status(thm)],[f10186,f10187,f274,f277])).
% 15.89/2.54 fof(f10769,definition,(
% 15.89/2.54 sQ504_spl <=> (aElementOf0(xb,xI))),
% 15.89/2.54 introduced(definition,[new_symbols(definition,[sQ504_spl])],[split_symbol_definition])).
% 15.89/2.54 fof(f10771,plain,(
% 15.89/2.54 ~aElementOf0(xb,xI)|sQ504_spl),
% 15.89/2.54 inference(component_clause,[status(thm)],[f10769])).
% 15.89/2.54 fof(f10775,plain,(
% 15.89/2.54 $false|sQ504_spl),
% 15.89/2.54 inference(forward_subsumption_resolution,[status(thm)],[f10771,f240])).
% 15.89/2.54 fof(f10776,plain,(
% 15.89/2.54 sQ504_spl),
% 15.89/2.54 inference(contradiction_clause,[status(thm)],[f10775])).
% 15.89/2.54 fof(f15599,plain,(
% 15.89/2.54 ~aElementOf0(smndt0(sdtasdt0(xq,xu)),xI)|~aElementOf0(xb,xI)|aElementOf0(xr,xI)),
% 15.89/2.54 inference(paramodulation,[status(thm)],[f241,f2805])).
% 15.89/2.54 fof(f15601,definition,(
% 15.89/2.54 sQ786_spl <=> (aElementOf0(smndt0(sdtasdt0(xq,xu)),xI))),
% 15.89/2.54 introduced(definition,[new_symbols(definition,[sQ786_spl])],[split_symbol_definition])).
% 15.89/2.54 fof(f15603,plain,(
% 15.89/2.54 ~aElementOf0(smndt0(sdtasdt0(xq,xu)),xI)|sQ786_spl),
% 15.89/2.54 inference(component_clause,[status(thm)],[f15601])).
% 15.89/2.54 fof(f15604,plain,(
% 15.89/2.54 ~sQ786_spl|~sQ504_spl|sQ481_spl),
% 15.89/2.54 inference(split_clause,[status(thm)],[f15599,f15601,f10769,f10187])).
% 15.89/2.54 fof(f15606,plain,(
% 15.89/2.54 $false|sQ786_spl),
% 15.89/2.54 inference(forward_subsumption_resolution,[status(thm)],[f15603,f239])).
% 15.89/2.54 fof(f15607,plain,(
% 15.89/2.54 sQ786_spl),
% 15.89/2.54 inference(contradiction_clause,[status(thm)],[f15606])).
% 15.89/2.54 fof(f15608,plain,(
% 15.89/2.54 $false),
% 15.89/2.54 inference(sat_refutation,[status(thm)],[f280,f295,f10190,f10776,f15604,f15607])).
% 15.89/2.54 % SZS output end CNFRefutation for theBenchmark.p
% 2.79/2.56 % Elapsed time: 2.172538 seconds
% 2.79/2.56 % CPU time: 16.900744 seconds
% 2.79/2.56 % Total memory used: 327.071 MB
% 2.79/2.56 % Net memory used: 308.876 MB
%------------------------------------------------------------------------------