%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SET047+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/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 02:11:20 PM UTC 2026
% Result : Theorem 0.08s 0.36s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET047+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n004.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 04:47:34 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 % Drodi V4.1.1
% 0.08/0.36 % Refutation found
% 0.08/0.36 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.08/0.36 % SZS output start CNFRefutation for theBenchmark
% 0.08/0.36 fof(f1,axiom,(
% 0.08/0.36 (! [X,Y] :( set_equal(X,Y)<=> (! [Z] :( element(Z,X)<=> element(Z,Y) ) )) )),
% 0.08/0.36 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.08/0.36 fof(f2,conjecture,(
% 0.08/0.36 (! [X,Y] :( set_equal(X,Y)<=> set_equal(Y,X) ) )),
% 0.08/0.36 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.08/0.36 fof(f3,negated_conjecture,(
% 0.08/0.36 ~((! [X,Y] :( set_equal(X,Y)<=> set_equal(Y,X) ) ))),
% 0.08/0.36 inference(negated_conjecture,[status(cth)],[f2])).
% 0.08/0.36 fof(f4,plain,(
% 0.08/0.36 ![X,Y]: ((~set_equal(X,Y)|(![Z]: ((~element(Z,X)|element(Z,Y))&(element(Z,X)|~element(Z,Y)))))&(set_equal(X,Y)|(?[Z]: ((~element(Z,X)|~element(Z,Y))&(element(Z,X)|element(Z,Y))))))),
% 0.08/0.36 inference(NNF_transformation,[status(thm)],[f1])).
% 0.08/0.36 fof(f5,plain,(
% 0.08/0.36 (![X,Y]: (~set_equal(X,Y)|((![Z]: (~element(Z,X)|element(Z,Y)))&(![Z]: (element(Z,X)|~element(Z,Y))))))&(![X,Y]: (set_equal(X,Y)|(?[Z]: ((~element(Z,X)|~element(Z,Y))&(element(Z,X)|element(Z,Y))))))),
% 0.08/0.36 inference(miniscoping,[status(thm)],[f4])).
% 0.08/0.36 fof(f6,plain,(
% 0.08/0.36 (![X,Y]: (~set_equal(X,Y)|((![Z]: (~element(Z,X)|element(Z,Y)))&(![Z]: (element(Z,X)|~element(Z,Y))))))&(![X,Y]: (set_equal(X,Y)|((~element(sK0_skl(Y,X),X)|~element(sK0_skl(Y,X),Y))&(element(sK0_skl(Y,X),X)|element(sK0_skl(Y,X),Y)))))),
% 0.08/0.36 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(Z,sK0_skl(Y,X))],[f5])).
% 0.08/0.36 fof(f7,plain,(
% 0.08/0.36 ![X0,X1,X2]: (~set_equal(X0,X1)|~element(X2,X0)|element(X2,X1))),
% 0.08/0.36 inference(cnf_transformation,[status(thm)],[f6])).
% 0.08/0.36 fof(f8,plain,(
% 0.08/0.36 ![X0,X1,X2]: (~set_equal(X0,X1)|element(X2,X0)|~element(X2,X1))),
% 0.08/0.36 inference(cnf_transformation,[status(thm)],[f6])).
% 0.08/0.36 fof(f9,plain,(
% 0.08/0.36 ![X0,X1]: (set_equal(X0,X1)|~element(sK0_skl(X1,X0),X0)|~element(sK0_skl(X1,X0),X1))),
% 0.08/0.36 inference(cnf_transformation,[status(thm)],[f6])).
% 0.08/0.36 fof(f10,plain,(
% 0.08/0.36 ![X0,X1]: (set_equal(X0,X1)|element(sK0_skl(X1,X0),X0)|element(sK0_skl(X1,X0),X1))),
% 0.08/0.36 inference(cnf_transformation,[status(thm)],[f6])).
% 0.08/0.36 fof(f11,plain,(
% 0.08/0.36 (?[X,Y]: (set_equal(X,Y)<~>set_equal(Y,X)))),
% 0.08/0.36 inference(pre_NNF_transformation,[status(thm)],[f3])).
% 0.08/0.36 fof(f12,plain,(
% 0.08/0.36 ?[X,Y]: ((set_equal(X,Y)|set_equal(Y,X))&(~set_equal(X,Y)|~set_equal(Y,X)))),
% 0.08/0.36 inference(NNF_transformation,[status(thm)],[f11])).
% 0.08/0.36 fof(f13,plain,(
% 0.08/0.36 ((set_equal(sK1_skl,sK2_skl)|set_equal(sK2_skl,sK1_skl))&(~set_equal(sK1_skl,sK2_skl)|~set_equal(sK2_skl,sK1_skl)))),
% 0.08/0.36 inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl,sK2_skl]),skolemize(X,sK1_skl),skolemize(Y,sK2_skl)],[f12])).
% 0.08/0.36 fof(f14,plain,(
% 0.08/0.36 set_equal(sK1_skl,sK2_skl)|set_equal(sK2_skl,sK1_skl)),
% 0.08/0.36 inference(cnf_transformation,[status(thm)],[f13])).
% 0.08/0.36 fof(f15,plain,(
% 0.08/0.36 ~set_equal(sK1_skl,sK2_skl)|~set_equal(sK2_skl,sK1_skl)),
% 0.08/0.36 inference(cnf_transformation,[status(thm)],[f13])).
% 0.08/0.36 fof(f16,definition,(
% 0.08/0.36 sQ0_spl <=> (set_equal(sK1_skl,sK2_skl))),
% 0.08/0.36 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.08/0.36 fof(f17,plain,(
% 0.08/0.36 set_equal(sK1_skl,sK2_skl)|~sQ0_spl),
% 0.08/0.36 inference(component_clause,[status(thm)],[f16])).
% 0.08/0.36 fof(f19,definition,(
% 0.08/0.36 sQ1_spl <=> (set_equal(sK2_skl,sK1_skl))),
% 0.08/0.36 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.08/0.36 fof(f20,plain,(
% 0.08/0.36 set_equal(sK2_skl,sK1_skl)|~sQ1_spl),
% 0.08/0.36 inference(component_clause,[status(thm)],[f19])).
% 0.08/0.36 fof(f22,plain,(
% 0.08/0.36 sQ0_spl|sQ1_spl),
% 0.08/0.36 inference(split_clause,[status(thm)],[f14,f16,f19])).
% 0.08/0.36 fof(f23,plain,(
% 0.08/0.36 ~sQ0_spl|~sQ1_spl),
% 0.08/0.36 inference(split_clause,[status(thm)],[f15,f16,f19])).
% 0.08/0.36 fof(f24,plain,(
% 0.08/0.36 ![X0,X1,X2]: (set_equal(X0,X1)|~element(sK0_skl(X1,X0),X0)|~set_equal(X1,X2)|~element(sK0_skl(X1,X0),X2))),
% 0.08/0.36 inference(resolution,[status(thm)],[f9,f8])).
% 0.08/0.36 fof(f26,plain,(
% 0.08/0.36 ![X0]: (set_equal(X0,sK2_skl)|~element(sK0_skl(sK2_skl,X0),X0)|~element(sK0_skl(sK2_skl,X0),sK1_skl)|~sQ1_spl)),
% 0.08/0.36 inference(resolution,[status(thm)],[f24,f20])).
% 0.08/0.36 fof(f35,plain,(
% 0.08/0.36 set_equal(sK1_skl,sK2_skl)|element(sK0_skl(sK2_skl,sK1_skl),sK2_skl)|set_equal(sK1_skl,sK2_skl)|~element(sK0_skl(sK2_skl,sK1_skl),sK1_skl)|~sQ1_spl),
% 0.08/0.36 inference(resolution,[status(thm)],[f10,f26])).
% 0.08/0.36 fof(f39,definition,(
% 0.08/0.37 sQ2_spl <=> (element(sK0_skl(sK1_skl,sK2_skl),sK1_skl))),
% 0.08/0.37 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.08/0.37 fof(f40,plain,(
% 0.08/0.37 element(sK0_skl(sK1_skl,sK2_skl),sK1_skl)|~sQ2_spl),
% 0.08/0.37 inference(component_clause,[status(thm)],[f39])).
% 0.08/0.37 fof(f42,definition,(
% 0.08/0.37 sQ3_spl <=> (element(sK0_skl(sK1_skl,sK2_skl),sK2_skl))),
% 0.08/0.37 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 0.08/0.37 fof(f44,plain,(
% 0.08/0.37 ~element(sK0_skl(sK1_skl,sK2_skl),sK2_skl)|sQ3_spl),
% 0.08/0.37 inference(component_clause,[status(thm)],[f42])).
% 0.08/0.37 fof(f46,definition,(
% 0.08/0.37 sQ4_spl <=> (element(sK0_skl(sK2_skl,sK1_skl),sK2_skl))),
% 0.08/0.37 introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition])).
% 0.08/0.37 fof(f47,plain,(
% 0.08/0.37 element(sK0_skl(sK2_skl,sK1_skl),sK2_skl)|~sQ4_spl),
% 0.08/0.37 inference(component_clause,[status(thm)],[f46])).
% 0.08/0.37 fof(f49,definition,(
% 0.08/0.37 sQ5_spl <=> (element(sK0_skl(sK2_skl,sK1_skl),sK1_skl))),
% 0.08/0.37 introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition])).
% 0.08/0.37 fof(f51,plain,(
% 0.08/0.37 ~element(sK0_skl(sK2_skl,sK1_skl),sK1_skl)|sQ5_spl),
% 0.08/0.37 inference(component_clause,[status(thm)],[f49])).
% 0.08/0.37 fof(f52,plain,(
% 0.08/0.37 sQ0_spl|sQ4_spl|~sQ5_spl|~sQ1_spl),
% 0.08/0.37 inference(split_clause,[status(thm)],[f35,f16,f46,f49,f19])).
% 0.08/0.37 fof(f55,plain,(
% 0.08/0.37 ![X0]: (set_equal(X0,sK1_skl)|~element(sK0_skl(sK1_skl,X0),X0)|~element(sK0_skl(sK1_skl,X0),sK2_skl)|~sQ0_spl)),
% 0.08/0.37 inference(resolution,[status(thm)],[f17,f24])).
% 0.08/0.37 fof(f70,plain,(
% 0.08/0.37 set_equal(sK2_skl,sK1_skl)|~element(sK0_skl(sK1_skl,sK2_skl),sK2_skl)|set_equal(sK2_skl,sK1_skl)|element(sK0_skl(sK1_skl,sK2_skl),sK1_skl)|~sQ0_spl),
% 0.08/0.37 inference(resolution,[status(thm)],[f55,f10])).
% 0.08/0.37 fof(f73,plain,(
% 0.08/0.37 sQ1_spl|~sQ3_spl|sQ2_spl|~sQ0_spl),
% 0.08/0.37 inference(split_clause,[status(thm)],[f70,f19,f42,f39,f16])).
% 0.08/0.37 fof(f74,plain,(
% 0.08/0.37 set_equal(sK2_skl,sK1_skl)|element(sK0_skl(sK1_skl,sK2_skl),sK1_skl)|sQ3_spl),
% 0.08/0.37 inference(resolution,[status(thm)],[f44,f10])).
% 0.08/0.37 fof(f76,plain,(
% 0.08/0.37 ![X0]: (~set_equal(X0,sK2_skl)|~element(sK0_skl(sK1_skl,sK2_skl),X0)|sQ3_spl)),
% 0.08/0.37 inference(resolution,[status(thm)],[f44,f7])).
% 0.08/0.37 fof(f77,plain,(
% 0.08/0.37 sQ1_spl|sQ2_spl|sQ3_spl),
% 0.08/0.37 inference(split_clause,[status(thm)],[f74,f19,f39,f42])).
% 0.08/0.37 fof(f80,plain,(
% 0.08/0.37 set_equal(sK1_skl,sK2_skl)|~element(sK0_skl(sK2_skl,sK1_skl),sK1_skl)|~sQ4_spl),
% 0.08/0.37 inference(resolution,[status(thm)],[f47,f9])).
% 0.08/0.37 fof(f81,plain,(
% 0.08/0.37 sQ0_spl|~sQ5_spl|~sQ4_spl),
% 0.08/0.37 inference(split_clause,[status(thm)],[f80,f16,f49,f46])).
% 0.08/0.37 fof(f84,plain,(
% 0.08/0.37 set_equal(sK2_skl,sK1_skl)|~element(sK0_skl(sK1_skl,sK2_skl),sK2_skl)|~sQ2_spl),
% 0.08/0.37 inference(resolution,[status(thm)],[f40,f9])).
% 0.08/0.37 fof(f85,plain,(
% 0.08/0.37 sQ1_spl|~sQ3_spl|~sQ2_spl),
% 0.08/0.37 inference(split_clause,[status(thm)],[f84,f19,f42,f39])).
% 0.08/0.37 fof(f96,plain,(
% 0.08/0.37 set_equal(sK1_skl,sK2_skl)|element(sK0_skl(sK2_skl,sK1_skl),sK2_skl)|sQ5_spl),
% 0.08/0.37 inference(resolution,[status(thm)],[f51,f10])).
% 0.08/0.37 fof(f98,plain,(
% 0.08/0.37 ![X0]: (~set_equal(X0,sK1_skl)|~element(sK0_skl(sK2_skl,sK1_skl),X0)|sQ5_spl)),
% 0.08/0.37 inference(resolution,[status(thm)],[f51,f7])).
% 0.08/0.37 fof(f99,plain,(
% 0.08/0.37 sQ0_spl|sQ4_spl|sQ5_spl),
% 0.08/0.37 inference(split_clause,[status(thm)],[f96,f16,f46,f49])).
% 0.08/0.37 fof(f108,plain,(
% 0.08/0.37 ~element(sK0_skl(sK1_skl,sK2_skl),sK1_skl)|sQ3_spl|~sQ0_spl),
% 0.08/0.37 inference(resolution,[status(thm)],[f76,f17])).
% 0.08/0.37 fof(f109,plain,(
% 0.08/0.37 $false|~sQ2_spl|sQ3_spl|~sQ0_spl),
% 0.08/0.37 inference(forward_subsumption_resolution,[status(thm)],[f108,f40])).
% 0.08/0.37 fof(f110,plain,(
% 0.08/0.37 ~sQ2_spl|sQ3_spl|~sQ0_spl),
% 0.08/0.37 inference(contradiction_clause,[status(thm)],[f109])).
% 0.08/0.37 fof(f119,plain,(
% 0.08/0.37 ~element(sK0_skl(sK2_skl,sK1_skl),sK2_skl)|sQ5_spl|~sQ1_spl),
% 0.08/0.37 inference(resolution,[status(thm)],[f98,f20])).
% 0.08/0.37 fof(f120,plain,(
% 0.08/0.37 $false|~sQ4_spl|sQ5_spl|~sQ1_spl),
% 0.08/0.37 inference(forward_subsumption_resolution,[status(thm)],[f119,f47])).
% 0.08/0.37 fof(f121,plain,(
% 0.08/0.37 ~sQ4_spl|sQ5_spl|~sQ1_spl),
% 0.08/0.37 inference(contradiction_clause,[status(thm)],[f120])).
% 0.08/0.37 fof(f122,plain,(
% 0.08/0.37 $false),
% 0.08/0.37 inference(sat_refutation,[status(thm)],[f22,f23,f52,f73,f77,f81,f85,f99,f110,f121])).
% 0.08/0.37 % SZS output end CNFRefutation for theBenchmark.p
% 0.12/0.39 % Elapsed time: 0.032622 seconds
% 0.12/0.39 % CPU time: 0.060533 seconds
% 0.12/0.39 % Total memory used: 3.939 MB
% 0.12/0.39 % Net memory used: 3.876 MB
%------------------------------------------------------------------------------