%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : RNG099+2 : 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 : n004.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 02:05:21 PM UTC 2026
% Result : Theorem 7.85s 1.42s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG099+2 : 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 : n004.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 04:19:38 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 7.85/1.42 % Refutation found
% 7.85/1.42 % SZS status Theorem for theBenchmark: Theorem is valid
% 7.85/1.42 % SZS output start CNFRefutation for theBenchmark
% 7.85/1.42 fof(f5,axiom,(
% 7.85/1.42 (! [W0,W1] :( ( aElement0(W0)& aElement0(W1) )=> aElement0(sdtpldt0(W0,W1)) ) )),
% 7.85/1.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 7.85/1.42 fof(f6,axiom,(
% 7.85/1.42 (! [W0,W1] :( ( aElement0(W0)& aElement0(W1) )=> aElement0(sdtasdt0(W0,W1)) ) )),
% 7.85/1.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 7.85/1.42 fof(f20,axiom,(
% 7.85/1.42 (! [W0] :( aSet0(W0)=> (! [W1] :( aElementOf0(W1,W0)=> aElement0(W1) ) )) )),
% 7.85/1.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 7.85/1.42 fof(f28,hypothesis,(
% 7.85/1.42 ( aSet0(xI)& (! [W0] :( aElementOf0(W0,xI)=> ( (! [W1] :( aElementOf0(W1,xI)=> aElementOf0(sdtpldt0(W0,W1),xI) ))& (! [W1] :( aElement0(W1)=> aElementOf0(sdtasdt0(W1,W0),xI) ) )) ))& aIdeal0(xI)& aSet0(xJ)& (! [W0] :( aElementOf0(W0,xJ)=> ( (! [W1] :( aElementOf0(W1,xJ)=> aElementOf0(sdtpldt0(W0,W1),xJ) ))& (! [W1] :( aElement0(W1)=> aElementOf0(sdtasdt0(W1,W0),xJ) ) )) ))& aIdeal0(xJ) ) ),
% 7.85/1.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 7.85/1.42 fof(f30,hypothesis,(
% 7.85/1.42 ( aElement0(xx)& aElement0(xy) ) ),
% 7.85/1.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 7.85/1.42 fof(f31,hypothesis,(
% 7.85/1.42 ( aElementOf0(xa,xI)& aElementOf0(xb,xJ)& sdtpldt0(xa,xb) = sz10 ) ),
% 7.85/1.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 7.85/1.42 fof(f32,hypothesis,(
% 7.85/1.42 xw = sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)) ),
% 7.85/1.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 7.85/1.42 fof(f33,hypothesis,(
% 7.85/1.42 aElementOf0(sdtpldt0(xw,smndt0(xx)),xI) ),
% 7.85/1.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 7.85/1.42 fof(f34,hypothesis,(
% 7.85/1.42 aElementOf0(sdtpldt0(xw,smndt0(xy)),xJ) ),
% 7.85/1.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 7.85/1.42 fof(f35,conjecture,(
% 7.85/1.42 (? [W0] :( aElement0(W0)& ( aElementOf0(sdtpldt0(W0,smndt0(xx)),xI)| sdteqdtlpzmzozddtrp0(W0,xx,xI) )& ( aElementOf0(sdtpldt0(W0,smndt0(xy)),xJ)| sdteqdtlpzmzozddtrp0(W0,xy,xJ) ) ) )),
% 7.85/1.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 7.85/1.42 fof(f36,negated_conjecture,(
% 7.85/1.42 ~((? [W0] :( aElement0(W0)& ( aElementOf0(sdtpldt0(W0,smndt0(xx)),xI)| sdteqdtlpzmzozddtrp0(W0,xx,xI) )& ( aElementOf0(sdtpldt0(W0,smndt0(xy)),xJ)| sdteqdtlpzmzozddtrp0(W0,xy,xJ) ) ) ))),
% 7.85/1.42 inference(negated_conjecture,[status(cth)],[f35])).
% 7.85/1.42 fof(f44,plain,(
% 7.85/1.42 ![W0,W1]: ((~aElement0(W0)|~aElement0(W1))|aElement0(sdtpldt0(W0,W1)))),
% 7.85/1.42 inference(pre_NNF_transformation,[status(thm)],[f5])).
% 7.85/1.42 fof(f45,plain,(
% 7.85/1.42 ![X0,X1]: (~aElement0(X0)|~aElement0(X1)|aElement0(sdtpldt0(X0,X1)))),
% 7.85/1.42 inference(cnf_transformation,[status(thm)],[f44])).
% 7.85/1.42 fof(f46,plain,(
% 7.85/1.42 ![W0,W1]: ((~aElement0(W0)|~aElement0(W1))|aElement0(sdtasdt0(W0,W1)))),
% 7.85/1.42 inference(pre_NNF_transformation,[status(thm)],[f6])).
% 7.85/1.42 fof(f47,plain,(
% 7.85/1.42 ![X0,X1]: (~aElement0(X0)|~aElement0(X1)|aElement0(sdtasdt0(X0,X1)))),
% 7.85/1.42 inference(cnf_transformation,[status(thm)],[f46])).
% 7.85/1.42 fof(f80,plain,(
% 7.85/1.42 ![W0]: (~aSet0(W0)|(![W1]: (~aElementOf0(W1,W0)|aElement0(W1))))),
% 7.85/1.42 inference(pre_NNF_transformation,[status(thm)],[f20])).
% 7.85/1.42 fof(f81,plain,(
% 7.85/1.42 ![X0,X1]: (~aSet0(X0)|~aElementOf0(X1,X0)|aElement0(X1))),
% 7.85/1.42 inference(cnf_transformation,[status(thm)],[f80])).
% 7.85/1.42 fof(f130,plain,(
% 7.85/1.42 ((((aSet0(xI)&(![W0]: (~aElementOf0(W0,xI)|((![W1]: (~aElementOf0(W1,xI)|aElementOf0(sdtpldt0(W0,W1),xI)))&(![W1]: (~aElement0(W1)|aElementOf0(sdtasdt0(W1,W0),xI)))))))&aIdeal0(xI))&aSet0(xJ))&(![W0]: (~aElementOf0(W0,xJ)|((![W1]: (~aElementOf0(W1,xJ)|aElementOf0(sdtpldt0(W0,W1),xJ)))&(![W1]: (~aElement0(W1)|aElementOf0(sdtasdt0(W1,W0),xJ)))))))&aIdeal0(xJ)),
% 7.85/1.42 inference(pre_NNF_transformation,[status(thm)],[f28])).
% 7.85/1.42 fof(f131,plain,(
% 7.85/1.42 aSet0(xI)),
% 7.85/1.42 inference(cnf_transformation,[status(thm)],[f130])).
% 7.85/1.42 fof(f135,plain,(
% 7.85/1.42 aSet0(xJ)),
% 7.85/1.42 inference(cnf_transformation,[status(thm)],[f130])).
% 7.85/1.42 fof(f145,plain,(
% 7.85/1.42 aElement0(xx)),
% 7.85/1.42 inference(cnf_transformation,[status(thm)],[f30])).
% 7.85/1.42 fof(f146,plain,(
% 7.85/1.42 aElement0(xy)),
% 7.85/1.42 inference(cnf_transformation,[status(thm)],[f30])).
% 7.85/1.42 fof(f147,plain,(
% 7.85/1.42 aElementOf0(xa,xI)),
% 7.85/1.42 inference(cnf_transformation,[status(thm)],[f31])).
% 7.85/1.42 fof(f148,plain,(
% 7.85/1.42 aElementOf0(xb,xJ)),
% 7.85/1.42 inference(cnf_transformation,[status(thm)],[f31])).
% 7.85/1.42 fof(f150,plain,(
% 7.85/1.42 xw=sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb))),
% 7.85/1.42 inference(cnf_transformation,[status(thm)],[f32])).
% 7.85/1.42 fof(f151,plain,(
% 7.85/1.42 aElementOf0(sdtpldt0(xw,smndt0(xx)),xI)),
% 7.85/1.42 inference(cnf_transformation,[status(thm)],[f33])).
% 7.85/1.42 fof(f152,plain,(
% 7.85/1.42 aElementOf0(sdtpldt0(xw,smndt0(xy)),xJ)),
% 7.85/1.42 inference(cnf_transformation,[status(thm)],[f34])).
% 7.85/1.42 fof(f153,plain,(
% 7.85/1.42 (![W0]: ((~aElement0(W0)|(~aElementOf0(sdtpldt0(W0,smndt0(xx)),xI)&~sdteqdtlpzmzozddtrp0(W0,xx,xI)))|(~aElementOf0(sdtpldt0(W0,smndt0(xy)),xJ)&~sdteqdtlpzmzozddtrp0(W0,xy,xJ))))),
% 7.85/1.42 inference(pre_NNF_transformation,[status(thm)],[f36])).
% 7.85/1.42 fof(f154,definition,(
% 7.85/1.42 ![W0]: (sP2_prd(W0)<=>(~aElementOf0(sdtpldt0(W0,smndt0(xx)),xI)&~sdteqdtlpzmzozddtrp0(W0,xx,xI)))),
% 7.85/1.42 introduced(definition,[new_symbols(definition,[sP2_prd])],[])).
% 7.85/1.42 fof(f155,plain,(
% 7.85/1.42 ![W0]: ((~aElement0(W0)|sP2_prd(W0))|(~aElementOf0(sdtpldt0(W0,smndt0(xy)),xJ)&~sdteqdtlpzmzozddtrp0(W0,xy,xJ)))),
% 7.85/1.42 inference(formula_renaming,[status(thm)],[f153,f154])).
% 7.85/1.42 fof(f156,plain,(
% 7.85/1.42 ![X0]: (~aElement0(X0)|sP2_prd(X0)|~aElementOf0(sdtpldt0(X0,smndt0(xy)),xJ))),
% 7.85/1.42 inference(cnf_transformation,[status(thm)],[f155])).
% 7.85/1.42 fof(f169,plain,(
% 7.85/1.42 ![W0]: ((~sP2_prd(W0)|(~aElementOf0(sdtpldt0(W0,smndt0(xx)),xI)&~sdteqdtlpzmzozddtrp0(W0,xx,xI)))&(sP2_prd(W0)|(aElementOf0(sdtpldt0(W0,smndt0(xx)),xI)|sdteqdtlpzmzozddtrp0(W0,xx,xI))))),
% 7.85/1.42 inference(NNF_transformation,[status(thm)],[f154])).
% 7.85/1.42 fof(f170,plain,(
% 7.85/1.42 (![W0]: (~sP2_prd(W0)|(~aElementOf0(sdtpldt0(W0,smndt0(xx)),xI)&~sdteqdtlpzmzozddtrp0(W0,xx,xI))))&(![W0]: (sP2_prd(W0)|(aElementOf0(sdtpldt0(W0,smndt0(xx)),xI)|sdteqdtlpzmzozddtrp0(W0,xx,xI))))),
% 7.85/1.42 inference(miniscoping,[status(thm)],[f169])).
% 7.85/1.42 fof(f171,plain,(
% 7.85/1.42 ![X0]: (~sP2_prd(X0)|~aElementOf0(sdtpldt0(X0,smndt0(xx)),xI))),
% 7.85/1.42 inference(cnf_transformation,[status(thm)],[f170])).
% 7.85/1.42 fof(f299,definition,(
% 7.85/1.42 sQ14_spl <=> (aElement0(xx))),
% 7.85/1.42 introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition])).
% 7.85/1.42 fof(f301,plain,(
% 7.85/1.42 ~aElement0(xx)|sQ14_spl),
% 7.85/1.42 inference(component_clause,[status(thm)],[f299])).
% 7.85/1.42 fof(f310,definition,(
% 7.85/1.42 sQ16_spl <=> (aElement0(xa))),
% 7.85/1.42 introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition])).
% 7.85/1.42 fof(f312,plain,(
% 7.85/1.42 ~aElement0(xa)|sQ16_spl),
% 7.85/1.42 inference(component_clause,[status(thm)],[f310])).
% 7.85/1.42 fof(f313,definition,(
% 7.85/1.42 sQ17_spl <=> (aElement0(xb))),
% 7.85/1.42 introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition])).
% 7.85/1.42 fof(f315,plain,(
% 7.85/1.42 ~aElement0(xb)|sQ17_spl),
% 7.85/1.42 inference(component_clause,[status(thm)],[f313])).
% 7.85/1.42 fof(f333,definition,(
% 7.85/1.42 sQ18_spl <=> (aElement0(xy))),
% 7.85/1.42 introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition])).
% 7.85/1.42 fof(f335,plain,(
% 7.85/1.42 ~aElement0(xy)|sQ18_spl),
% 7.85/1.42 inference(component_clause,[status(thm)],[f333])).
% 7.85/1.42 fof(f383,plain,(
% 7.85/1.42 $false|sQ14_spl),
% 7.85/1.42 inference(forward_subsumption_resolution,[status(thm)],[f301,f145])).
% 7.85/1.42 fof(f384,plain,(
% 7.85/1.42 sQ14_spl),
% 7.85/1.42 inference(contradiction_clause,[status(thm)],[f383])).
% 7.85/1.42 fof(f415,plain,(
% 7.85/1.42 $false|sQ18_spl),
% 7.85/1.42 inference(forward_subsumption_resolution,[status(thm)],[f335,f146])).
% 7.85/1.42 fof(f416,plain,(
% 7.85/1.42 sQ18_spl),
% 7.85/1.42 inference(contradiction_clause,[status(thm)],[f415])).
% 7.85/1.42 fof(f793,plain,(
% 7.85/1.42 ![X0]: (~aElementOf0(X0,xJ)|aElement0(X0))),
% 7.85/1.42 inference(resolution,[status(thm)],[f81,f135])).
% 7.85/1.42 fof(f794,plain,(
% 7.85/1.42 ![X0]: (~aElementOf0(X0,xI)|aElement0(X0))),
% 7.85/1.42 inference(resolution,[status(thm)],[f81,f131])).
% 7.85/1.42 fof(f796,plain,(
% 7.85/1.42 aElement0(xb)),
% 7.85/1.42 inference(resolution,[status(thm)],[f793,f148])).
% 7.85/1.42 fof(f850,plain,(
% 7.85/1.42 aElement0(xa)),
% 7.85/1.42 inference(resolution,[status(thm)],[f794,f147])).
% 7.85/1.42 fof(f2808,plain,(
% 7.85/1.42 $false|sQ17_spl),
% 7.85/1.42 inference(forward_subsumption_resolution,[status(thm)],[f315,f796])).
% 7.85/1.42 fof(f2809,plain,(
% 7.85/1.42 sQ17_spl),
% 7.85/1.42 inference(contradiction_clause,[status(thm)],[f2808])).
% 7.85/1.42 fof(f2810,plain,(
% 7.85/1.42 $false|sQ16_spl),
% 7.85/1.42 inference(forward_subsumption_resolution,[status(thm)],[f312,f850])).
% 7.85/1.42 fof(f2811,plain,(
% 7.85/1.42 sQ16_spl),
% 7.85/1.42 inference(contradiction_clause,[status(thm)],[f2810])).
% 7.85/1.42 fof(f6193,plain,(
% 7.85/1.42 ~aElement0(sdtasdt0(xy,xa))|~aElement0(sdtasdt0(xx,xb))|aElement0(xw)),
% 7.85/1.44 inference(paramodulation,[status(thm)],[f150,f45])).
% 7.85/1.44 fof(f6197,definition,(
% 7.85/1.44 sQ227_spl <=> (aElement0(sdtasdt0(xy,xa)))),
% 7.85/1.44 introduced(definition,[new_symbols(definition,[sQ227_spl])],[split_symbol_definition])).
% 7.85/1.44 fof(f6199,plain,(
% 7.85/1.44 ~aElement0(sdtasdt0(xy,xa))|sQ227_spl),
% 7.85/1.44 inference(component_clause,[status(thm)],[f6197])).
% 7.85/1.44 fof(f6200,definition,(
% 7.85/1.44 sQ228_spl <=> (aElement0(sdtasdt0(xx,xb)))),
% 7.85/1.44 introduced(definition,[new_symbols(definition,[sQ228_spl])],[split_symbol_definition])).
% 7.85/1.44 fof(f6202,plain,(
% 7.85/1.44 ~aElement0(sdtasdt0(xx,xb))|sQ228_spl),
% 7.85/1.44 inference(component_clause,[status(thm)],[f6200])).
% 7.85/1.44 fof(f6204,definition,(
% 7.85/1.44 sQ229_spl <=> (aElement0(xw))),
% 7.85/1.44 introduced(definition,[new_symbols(definition,[sQ229_spl])],[split_symbol_definition])).
% 7.85/1.44 fof(f6207,plain,(
% 7.85/1.44 ~sQ227_spl|~sQ228_spl|sQ229_spl),
% 7.85/1.44 inference(split_clause,[status(thm)],[f6193,f6197,f6200,f6204])).
% 7.85/1.44 fof(f6209,plain,(
% 7.85/1.44 ~aElement0(xx)|~aElement0(xb)|sQ228_spl),
% 7.85/1.44 inference(resolution,[status(thm)],[f6202,f47])).
% 7.85/1.44 fof(f6210,plain,(
% 7.85/1.44 ~sQ14_spl|~sQ17_spl|sQ228_spl),
% 7.85/1.44 inference(split_clause,[status(thm)],[f6209,f299,f313,f6200])).
% 7.85/1.44 fof(f6211,plain,(
% 7.85/1.44 ~aElement0(xy)|~aElement0(xa)|sQ227_spl),
% 7.85/1.44 inference(resolution,[status(thm)],[f6199,f47])).
% 7.85/1.44 fof(f6212,plain,(
% 7.85/1.44 ~sQ18_spl|~sQ16_spl|sQ227_spl),
% 7.85/1.44 inference(split_clause,[status(thm)],[f6211,f333,f310,f6197])).
% 7.85/1.44 fof(f6416,definition,(
% 7.85/1.44 sQ250_spl <=> (sP2_prd(xw))),
% 7.85/1.44 introduced(definition,[new_symbols(definition,[sQ250_spl])],[split_symbol_definition])).
% 7.85/1.44 fof(f6417,plain,(
% 7.85/1.44 sP2_prd(xw)|~sQ250_spl),
% 7.85/1.44 inference(component_clause,[status(thm)],[f6416])).
% 7.85/1.44 fof(f6975,plain,(
% 7.85/1.44 ~sP2_prd(xw)),
% 7.85/1.44 inference(resolution,[status(thm)],[f151,f171])).
% 7.85/1.44 fof(f6980,plain,(
% 7.85/1.44 $false|~sQ250_spl),
% 7.85/1.44 inference(forward_subsumption_resolution,[status(thm)],[f6975,f6417])).
% 7.85/1.44 fof(f6981,plain,(
% 7.85/1.44 ~sQ250_spl),
% 7.85/1.44 inference(contradiction_clause,[status(thm)],[f6980])).
% 7.85/1.44 fof(f6986,plain,(
% 7.85/1.44 ~aElement0(xw)|sP2_prd(xw)),
% 7.85/1.44 inference(resolution,[status(thm)],[f152,f156])).
% 7.85/1.44 fof(f6991,plain,(
% 7.85/1.44 ~sQ229_spl|sQ250_spl),
% 7.85/1.44 inference(split_clause,[status(thm)],[f6986,f6204,f6416])).
% 7.85/1.44 fof(f6993,plain,(
% 7.85/1.44 $false),
% 7.85/1.44 inference(sat_refutation,[status(thm)],[f384,f416,f2809,f2811,f6207,f6210,f6212,f6981,f6991])).
% 7.85/1.44 % SZS output end CNFRefutation for theBenchmark.p
% 7.85/1.44 % Elapsed time: 1.070685 seconds
% 7.85/1.44 % CPU time: 8.197192 seconds
% 7.85/1.44 % Total memory used: 225.144 MB
% 7.85/1.44 % Net memory used: 215.200 MB
%------------------------------------------------------------------------------