%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SET786+1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.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 02:12:36 PM UTC 2026
% Result : Theorem 0.15s 0.39s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET786+1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n003.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 05:40:00 UTC 2026
% 0.15/0.36 % CPUTime :
% 0.15/0.37 % Drodi V4.1.1
% 0.15/0.39 % Refutation found
% 0.15/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.39 % SZS output start CNFRefutation for theBenchmark
% 0.15/0.39 fof(f1,conjecture,(
% 0.15/0.39 ~ (? [Y] :(! [X] :( element(X,Y)<=> ~ (? [Z] :( element(X,Z)& element(Z,X) ) )) ))),
% 0.15/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.39 fof(f2,negated_conjecture,(
% 0.15/0.39 ~(~ (? [Y] :(! [X] :( element(X,Y)<=> ~ (? [Z] :( element(X,Z)& element(Z,X) ) )) )))),
% 0.15/0.39 inference(negated_conjecture,[status(cth)],[f1])).
% 0.15/0.39 fof(f3,plain,(
% 0.15/0.39 ?[Y]: (![X]: (element(X,Y)<=>(![Z]: (~element(X,Z)|~element(Z,X)))))),
% 0.15/0.39 inference(pre_NNF_transformation,[status(thm)],[f2])).
% 0.15/0.39 fof(f4,plain,(
% 0.15/0.39 ?[Y]: ![X]: ((~element(X,Y)|(![Z]: (~element(X,Z)|~element(Z,X))))&(element(X,Y)|(?[Z]: (element(X,Z)&element(Z,X)))))),
% 0.15/0.39 inference(NNF_transformation,[status(thm)],[f3])).
% 0.15/0.39 fof(f5,plain,(
% 0.15/0.39 ?[Y]: ((![X]: (~element(X,Y)|(![Z]: (~element(X,Z)|~element(Z,X)))))&(![X]: (element(X,Y)|(?[Z]: (element(X,Z)&element(Z,X))))))),
% 0.15/0.39 inference(miniscoping,[status(thm)],[f4])).
% 0.15/0.39 fof(f6,plain,(
% 0.15/0.39 ((![X]: (~element(X,sK0_skl)|(![Z]: (~element(X,Z)|~element(Z,X)))))&(![X]: (element(X,sK0_skl)|(element(X,sK1_skl(X))&element(sK1_skl(X),X)))))),
% 0.15/0.39 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(Y,sK0_skl),skolemize(Z,sK1_skl(X))],[f5])).
% 0.15/0.39 fof(f7,plain,(
% 0.15/0.39 ![X0,X1]: (~element(X0,sK0_skl)|~element(X0,X1)|~element(X1,X0))),
% 0.15/0.39 inference(cnf_transformation,[status(thm)],[f6])).
% 0.15/0.39 fof(f8,plain,(
% 0.15/0.39 ![X0]: (element(X0,sK0_skl)|element(X0,sK1_skl(X0)))),
% 0.15/0.39 inference(cnf_transformation,[status(thm)],[f6])).
% 0.15/0.39 fof(f9,plain,(
% 0.15/0.39 ![X0]: (element(X0,sK0_skl)|element(sK1_skl(X0),X0))),
% 0.15/0.39 inference(cnf_transformation,[status(thm)],[f6])).
% 0.15/0.39 fof(f10,plain,(
% 0.15/0.39 ![X0]: (element(sK0_skl,sK0_skl)|~element(sK1_skl(sK0_skl),X0)|~element(X0,sK1_skl(sK0_skl)))),
% 0.15/0.39 inference(resolution,[status(thm)],[f9,f7])).
% 0.15/0.39 fof(f11,definition,(
% 0.15/0.39 sQ0_spl <=> (element(sK0_skl,sK0_skl))),
% 0.15/0.39 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.15/0.39 fof(f12,plain,(
% 0.15/0.39 element(sK0_skl,sK0_skl)|~sQ0_spl),
% 0.15/0.39 inference(component_clause,[status(thm)],[f11])).
% 0.15/0.39 fof(f14,definition,(
% 0.15/0.39 ![X0]: (sQ1_spl <=> (~element(sK1_skl(sK0_skl),X0)|~element(X0,sK1_skl(sK0_skl))))),
% 0.15/0.39 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.15/0.39 fof(f15,plain,(
% 0.15/0.39 ![X0]: (~element(sK1_skl(sK0_skl),X0)|~element(X0,sK1_skl(sK0_skl))|~sQ1_spl)),
% 0.15/0.39 inference(component_clause,[status(thm)],[f14])).
% 0.15/0.39 fof(f17,plain,(
% 0.15/0.39 sQ0_spl|sQ1_spl),
% 0.15/0.39 inference(split_clause,[status(thm)],[f10,f11,f14])).
% 0.15/0.39 fof(f18,plain,(
% 0.15/0.39 ![X0]: (~element(sK0_skl,X0)|~element(X0,sK0_skl)|~sQ0_spl)),
% 0.15/0.39 inference(resolution,[status(thm)],[f12,f7])).
% 0.15/0.39 fof(f19,plain,(
% 0.15/0.39 ~element(sK0_skl,sK0_skl)|~sQ0_spl),
% 0.15/0.39 inference(resolution,[status(thm)],[f18,f12])).
% 0.15/0.39 fof(f21,plain,(
% 0.15/0.39 $false|~sQ0_spl),
% 0.15/0.39 inference(forward_subsumption_resolution,[status(thm)],[f19,f12])).
% 0.15/0.39 fof(f22,plain,(
% 0.15/0.39 ~sQ0_spl),
% 0.15/0.39 inference(contradiction_clause,[status(thm)],[f21])).
% 0.15/0.39 fof(f23,plain,(
% 0.15/0.39 ~element(sK0_skl,sK1_skl(sK0_skl))|element(sK0_skl,sK0_skl)|~sQ1_spl),
% 0.15/0.39 inference(resolution,[status(thm)],[f15,f9])).
% 0.15/0.39 fof(f25,definition,(
% 0.15/0.39 sQ2_spl <=> (element(sK0_skl,sK1_skl(sK0_skl)))),
% 0.15/0.39 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.15/0.39 fof(f27,plain,(
% 0.15/0.39 ~element(sK0_skl,sK1_skl(sK0_skl))|sQ2_spl),
% 0.15/0.39 inference(component_clause,[status(thm)],[f25])).
% 0.15/0.39 fof(f28,plain,(
% 0.15/0.39 ~sQ2_spl|sQ0_spl|~sQ1_spl),
% 0.15/0.39 inference(split_clause,[status(thm)],[f23,f25,f11,f14])).
% 0.15/0.39 fof(f36,plain,(
% 0.15/0.39 element(sK0_skl,sK0_skl)|sQ2_spl),
% 0.15/0.39 inference(resolution,[status(thm)],[f27,f8])).
% 0.15/0.39 fof(f37,plain,(
% 0.15/0.39 sQ0_spl|sQ2_spl),
% 0.15/0.39 inference(split_clause,[status(thm)],[f36,f11,f25])).
% 0.15/0.39 fof(f38,plain,(
% 0.15/0.39 $false),
% 0.15/0.39 inference(sat_refutation,[status(thm)],[f17,f22,f28,f37])).
% 0.15/0.39 % SZS output end CNFRefutation for theBenchmark.p
% 0.15/0.42 % Elapsed time: 0.043660 seconds
% 0.15/0.42 % CPU time: 0.122490 seconds
% 0.15/0.42 % Total memory used: 16.478 MB
% 0.15/0.42 % Net memory used: 15.906 MB
%------------------------------------------------------------------------------