%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : RNG111+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 : n016.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 02:05:23 PM UTC 2026
% Result : Theorem 0.09s 0.39s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG111+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 : n016.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 04:25:07 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.09/0.39 % Refutation found
% 0.09/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.39 % SZS output start CNFRefutation for theBenchmark
% 0.09/0.39 fof(f45,conjecture,(
% 0.09/0.39 (! [W0] :( ( aElementOf0(W0,xI)& W0 != sz00 )=> ( (! [W1] :( ( aElementOf0(W1,xI)& W1 != sz00 )=> ( iLess0(sbrdtbr0(W1),sbrdtbr0(W0))=> (? [W2] :( aElementOf0(W2,xI)& W2 != sz00& (! [W3] :( ( aElementOf0(W3,xI)& W3 != sz00 )=> ~ iLess0(sbrdtbr0(W3),sbrdtbr0(W2)) ) )) )) ))=> (? [W1] :( aElementOf0(W1,xI)& W1 != sz00& (! [W2] :( ( aElementOf0(W2,xI)& W2 != sz00 )=> ~ iLess0(sbrdtbr0(W2),sbrdtbr0(W1)) ) )) )) ) )),
% 0.09/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.39 fof(f46,negated_conjecture,(
% 0.09/0.39 ~((! [W0] :( ( aElementOf0(W0,xI)& W0 != sz00 )=> ( (! [W1] :( ( aElementOf0(W1,xI)& W1 != sz00 )=> ( iLess0(sbrdtbr0(W1),sbrdtbr0(W0))=> (? [W2] :( aElementOf0(W2,xI)& W2 != sz00& (! [W3] :( ( aElementOf0(W3,xI)& W3 != sz00 )=> ~ iLess0(sbrdtbr0(W3),sbrdtbr0(W2)) ) )) )) ))=> (? [W1] :( aElementOf0(W1,xI)& W1 != sz00& (! [W2] :( ( aElementOf0(W2,xI)& W2 != sz00 )=> ~ iLess0(sbrdtbr0(W2),sbrdtbr0(W1)) ) )) )) ) ))),
% 0.09/0.39 inference(negated_conjecture,[status(cth)],[f45])).
% 0.09/0.39 fof(f212,plain,(
% 0.09/0.39 (?[W0]: ((aElementOf0(W0,xI)&~W0=sz00)&((![W1]: ((~aElementOf0(W1,xI)|W1=sz00)|(~iLess0(sbrdtbr0(W1),sbrdtbr0(W0))|(?[W2]: ((aElementOf0(W2,xI)&~W2=sz00)&(![W3]: ((~aElementOf0(W3,xI)|W3=sz00)|~iLess0(sbrdtbr0(W3),sbrdtbr0(W2)))))))))&(![W1]: ((~aElementOf0(W1,xI)|W1=sz00)|(?[W2]: ((aElementOf0(W2,xI)&~W2=sz00)&iLess0(sbrdtbr0(W2),sbrdtbr0(W1)))))))))),
% 0.09/0.39 inference(pre_NNF_transformation,[status(thm)],[f46])).
% 0.09/0.39 fof(f213,plain,(
% 0.09/0.39 ((aElementOf0(sK21_skl,xI)&~sK21_skl=sz00)&((![W1]: ((~aElementOf0(W1,xI)|W1=sz00)|(~iLess0(sbrdtbr0(W1),sbrdtbr0(sK21_skl))|((aElementOf0(sK22_skl(W1),xI)&~sK22_skl(W1)=sz00)&(![W3]: ((~aElementOf0(W3,xI)|W3=sz00)|~iLess0(sbrdtbr0(W3),sbrdtbr0(sK22_skl(W1)))))))))&(![W1]: ((~aElementOf0(W1,xI)|W1=sz00)|((aElementOf0(sK23_skl(W1),xI)&~sK23_skl(W1)=sz00)&iLess0(sbrdtbr0(sK23_skl(W1)),sbrdtbr0(W1)))))))),
% 0.09/0.39 inference(skolemize,[status(esa),new_symbols(skolem,[sK21_skl,sK22_skl,sK23_skl]),skolemize(W0,sK21_skl),skolemize(W2,sK22_skl(W1)),skolemize(W2,sK23_skl(W1))],[f212])).
% 0.09/0.39 fof(f214,plain,(
% 0.09/0.39 aElementOf0(sK21_skl,xI)),
% 0.09/0.39 inference(cnf_transformation,[status(thm)],[f213])).
% 0.09/0.39 fof(f215,plain,(
% 0.09/0.39 ~sK21_skl=sz00),
% 0.09/0.39 inference(cnf_transformation,[status(thm)],[f213])).
% 0.09/0.39 fof(f216,plain,(
% 0.09/0.39 ![X0]: (~aElementOf0(X0,xI)|X0=sz00|~iLess0(sbrdtbr0(X0),sbrdtbr0(sK21_skl))|aElementOf0(sK22_skl(X0),xI))),
% 0.09/0.39 inference(cnf_transformation,[status(thm)],[f213])).
% 0.09/0.39 fof(f217,plain,(
% 0.09/0.39 ![X0]: (~aElementOf0(X0,xI)|X0=sz00|~iLess0(sbrdtbr0(X0),sbrdtbr0(sK21_skl))|~sK22_skl(X0)=sz00)),
% 0.09/0.39 inference(cnf_transformation,[status(thm)],[f213])).
% 0.09/0.39 fof(f218,plain,(
% 0.09/0.39 ![X0,X1]: (~aElementOf0(X0,xI)|X0=sz00|~iLess0(sbrdtbr0(X0),sbrdtbr0(sK21_skl))|~aElementOf0(X1,xI)|X1=sz00|~iLess0(sbrdtbr0(X1),sbrdtbr0(sK22_skl(X0))))),
% 0.09/0.39 inference(cnf_transformation,[status(thm)],[f213])).
% 0.09/0.39 fof(f219,plain,(
% 0.09/0.39 ![X0]: (~aElementOf0(X0,xI)|X0=sz00|aElementOf0(sK23_skl(X0),xI))),
% 0.09/0.39 inference(cnf_transformation,[status(thm)],[f213])).
% 0.09/0.39 fof(f220,plain,(
% 0.09/0.39 ![X0]: (~aElementOf0(X0,xI)|X0=sz00|~sK23_skl(X0)=sz00)),
% 0.09/0.39 inference(cnf_transformation,[status(thm)],[f213])).
% 0.09/0.39 fof(f221,plain,(
% 0.09/0.39 ![X0]: (~aElementOf0(X0,xI)|X0=sz00|iLess0(sbrdtbr0(sK23_skl(X0)),sbrdtbr0(X0)))),
% 0.09/0.39 inference(cnf_transformation,[status(thm)],[f213])).
% 0.09/0.39 fof(f259,plain,(
% 0.09/0.39 sK21_skl=sz00|~sK23_skl(sK21_skl)=sz00),
% 0.09/0.39 inference(resolution,[status(thm)],[f220,f214])).
% 0.09/0.39 fof(f260,definition,(
% 0.09/0.39 sQ2_spl <=> (sK21_skl=sz00)),
% 0.09/0.39 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.09/0.39 fof(f261,plain,(
% 0.09/0.39 sK21_skl=sz00|~sQ2_spl),
% 0.09/0.39 inference(component_clause,[status(thm)],[f260])).
% 0.09/0.39 fof(f263,definition,(
% 0.09/0.39 sQ3_spl <=> (sK23_skl(sK21_skl)=sz00)),
% 0.09/0.39 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 0.09/0.39 fof(f266,plain,(
% 0.09/0.39 sQ2_spl|~sQ3_spl),
% 0.09/0.39 inference(split_clause,[status(thm)],[f259,f260,f263])).
% 0.09/0.39 fof(f267,plain,(
% 0.09/0.39 $false|~sQ2_spl),
% 0.09/0.39 inference(forward_subsumption_resolution,[status(thm)],[f261,f215])).
% 0.09/0.39 fof(f268,plain,(
% 0.09/0.39 ~sQ2_spl),
% 0.09/0.39 inference(contradiction_clause,[status(thm)],[f267])).
% 0.09/0.39 fof(f366,plain,(
% 0.09/0.39 sK21_skl=sz00|aElementOf0(sK23_skl(sK21_skl),xI)),
% 0.09/0.39 inference(resolution,[status(thm)],[f219,f214])).
% 0.09/0.39 fof(f370,definition,(
% 0.09/0.39 sQ4_spl <=> (aElementOf0(sK23_skl(sK21_skl),xI))),
% 0.09/0.39 introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition])).
% 0.09/0.39 fof(f373,plain,(
% 0.09/0.39 sQ2_spl|sQ4_spl),
% 0.09/0.39 inference(split_clause,[status(thm)],[f366,f260,f370])).
% 0.09/0.39 fof(f390,plain,(
% 0.09/0.39 ~aElementOf0(sK21_skl,xI)|sK21_skl=sz00|~aElementOf0(sK23_skl(sK21_skl),xI)|sK23_skl(sK21_skl)=sz00|~sK22_skl(sK23_skl(sK21_skl))=sz00),
% 0.09/0.39 inference(resolution,[status(thm)],[f221,f217])).
% 0.09/0.39 fof(f396,definition,(
% 0.09/0.39 sQ7_spl <=> (aElementOf0(sK21_skl,xI))),
% 0.09/0.39 introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition])).
% 0.09/0.39 fof(f398,plain,(
% 0.09/0.39 ~aElementOf0(sK21_skl,xI)|sQ7_spl),
% 0.09/0.39 inference(component_clause,[status(thm)],[f396])).
% 0.09/0.39 fof(f399,definition,(
% 0.09/0.39 sQ8_spl <=> (sK22_skl(sK23_skl(sK21_skl))=sz00)),
% 0.09/0.39 introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition])).
% 0.09/0.39 fof(f402,plain,(
% 0.09/0.39 ~sQ7_spl|sQ2_spl|~sQ4_spl|sQ3_spl|~sQ8_spl),
% 0.09/0.39 inference(split_clause,[status(thm)],[f390,f396,f260,f370,f263,f399])).
% 0.09/0.39 fof(f403,plain,(
% 0.09/0.39 $false|sQ7_spl),
% 0.09/0.39 inference(forward_subsumption_resolution,[status(thm)],[f398,f214])).
% 0.09/0.39 fof(f404,plain,(
% 0.09/0.39 sQ7_spl),
% 0.09/0.39 inference(contradiction_clause,[status(thm)],[f403])).
% 0.09/0.39 fof(f405,plain,(
% 0.09/0.39 ~aElementOf0(sK23_skl(sK21_skl),xI)|sK23_skl(sK21_skl)=sz00|aElementOf0(sK22_skl(sK23_skl(sK21_skl)),xI)|~aElementOf0(sK21_skl,xI)|sK21_skl=sz00),
% 0.09/0.39 inference(resolution,[status(thm)],[f216,f221])).
% 0.09/0.39 fof(f406,definition,(
% 0.09/0.39 sQ9_spl <=> (aElementOf0(sK22_skl(sK23_skl(sK21_skl)),xI))),
% 0.09/0.39 introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition])).
% 0.09/0.39 fof(f409,plain,(
% 0.09/0.39 ~sQ4_spl|sQ3_spl|sQ9_spl|~sQ7_spl|sQ2_spl),
% 0.09/0.39 inference(split_clause,[status(thm)],[f405,f370,f263,f406,f396,f260])).
% 0.09/0.39 fof(f410,plain,(
% 0.09/0.39 ![X0]: (~aElementOf0(X0,xI)|X0=sz00|~iLess0(sbrdtbr0(X0),sbrdtbr0(sK21_skl))|~aElementOf0(sK23_skl(sK22_skl(X0)),xI)|sK23_skl(sK22_skl(X0))=sz00|~aElementOf0(sK22_skl(X0),xI)|sK22_skl(X0)=sz00)),
% 0.09/0.39 inference(resolution,[status(thm)],[f218,f221])).
% 0.09/0.39 fof(f411,plain,(
% 0.09/0.39 ![X0]: (~aElementOf0(X0,xI)|X0=sz00|~iLess0(sbrdtbr0(X0),sbrdtbr0(sK21_skl))|sK23_skl(sK22_skl(X0))=sz00|~aElementOf0(sK22_skl(X0),xI)|sK22_skl(X0)=sz00)),
% 0.09/0.39 inference(forward_subsumption_resolution,[status(thm)],[f410,f219])).
% 0.09/0.39 fof(f420,plain,(
% 0.09/0.39 ![X0]: (~aElementOf0(X0,xI)|X0=sz00|~iLess0(sbrdtbr0(X0),sbrdtbr0(sK21_skl))|~aElementOf0(sK22_skl(X0),xI)|sK22_skl(X0)=sz00)),
% 0.09/0.39 inference(forward_subsumption_resolution,[status(thm)],[f411,f220])).
% 0.09/0.39 fof(f421,plain,(
% 0.09/0.39 ~aElementOf0(sK23_skl(sK21_skl),xI)|sK23_skl(sK21_skl)=sz00|~aElementOf0(sK22_skl(sK23_skl(sK21_skl)),xI)|sK22_skl(sK23_skl(sK21_skl))=sz00|~aElementOf0(sK21_skl,xI)|sK21_skl=sz00),
% 0.09/0.39 inference(resolution,[status(thm)],[f420,f221])).
% 0.09/0.39 fof(f422,plain,(
% 0.09/0.39 ~sQ4_spl|sQ3_spl|~sQ9_spl|sQ8_spl|~sQ7_spl|sQ2_spl),
% 0.09/0.39 inference(split_clause,[status(thm)],[f421,f370,f263,f406,f399,f396,f260])).
% 0.09/0.39 fof(f423,plain,(
% 0.09/0.39 $false),
% 0.09/0.39 inference(sat_refutation,[status(thm)],[f266,f268,f373,f402,f404,f409,f422])).
% 0.09/0.39 % SZS output end CNFRefutation for theBenchmark.p
% 0.09/0.43 % Elapsed time: 0.049951 seconds
% 0.09/0.43 % CPU time: 0.159363 seconds
% 0.09/0.43 % Total memory used: 106.963 MB
% 0.09/0.43 % Net memory used: 106.772 MB
%------------------------------------------------------------------------------