%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SEU174+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n018.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 02:21:54 PM UTC 2026
% Result : Theorem 0.17s 0.58s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU174+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.42 % Computer : n018.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.42 % CPULimit : 300
% 0.17/0.42 % WCLimit : 300
% 0.17/0.42 % DateTime : Mon Sep 21 05:56:58 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.45 % Drodi V4.1.1
% 0.17/0.58 % Refutation found
% 0.17/0.58 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.17/0.58 % SZS output start CNFRefutation for theBenchmark
% 0.17/0.58 fof(f8,axiom,(
% 0.17/0.58 (! [A] :( A = empty_set<=> (! [B] : ~ in(B,A) )) )),
% 0.17/0.58 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.58 fof(f9,axiom,(
% 0.17/0.58 (! [A,B] :( B = powerset(A)<=> (! [C] :( in(C,B)<=> subset(C,A) ) )) )),
% 0.17/0.58 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.58 fof(f21,axiom,(
% 0.17/0.58 (! [A,B] :( element(B,powerset(powerset(A)))=> (! [C] :( element(C,powerset(powerset(A)))=> ( C = complements_of_subsets(A,B)<=> (! [D] :( element(D,powerset(A))=> ( in(D,C)<=> in(subset_complement(A,D),B) ) ) )) ) )) )),
% 0.17/0.58 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.58 fof(f34,axiom,(
% 0.17/0.58 (! [A,B] :( element(B,powerset(powerset(A)))=> element(complements_of_subsets(A,B),powerset(powerset(A))) ) )),
% 0.17/0.58 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.58 fof(f45,axiom,(
% 0.17/0.58 (! [A,B] :( element(B,powerset(powerset(A)))=> complements_of_subsets(A,complements_of_subsets(A,B)) = B ) )),
% 0.17/0.58 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.58 fof(f74,axiom,(
% 0.17/0.58 (! [A,B] :( in(A,B)=> element(A,B) ) )),
% 0.17/0.58 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.58 fof(f82,lemma,(
% 0.17/0.58 (! [A] : subset(empty_set,A) )),
% 0.17/0.58 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.58 fof(f98,conjecture,(
% 0.17/0.58 (! [A,B] :( element(B,powerset(powerset(A)))=> ~ ( B != empty_set& complements_of_subsets(A,B) = empty_set ) ) )),
% 0.17/0.58 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.58 fof(f99,negated_conjecture,(
% 0.17/0.58 ~((! [A,B] :( element(B,powerset(powerset(A)))=> ~ ( B != empty_set& complements_of_subsets(A,B) = empty_set ) ) ))),
% 0.17/0.58 inference(negated_conjecture,[status(cth)],[f98])).
% 0.17/0.58 fof(f103,axiom,(
% 0.17/0.58 (! [A,B,C] :( ( in(A,B)& element(B,powerset(C)) )=> element(A,C) ) )),
% 0.17/0.58 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.58 fof(f143,plain,(
% 0.17/0.58 ![A]: ((~A=empty_set|(![B]: ~in(B,A)))&(A=empty_set|(?[B]: in(B,A))))),
% 0.17/0.58 inference(NNF_transformation,[status(thm)],[f8])).
% 0.17/0.58 fof(f144,plain,(
% 0.17/0.58 (![A]: (~A=empty_set|(![B]: ~in(B,A))))&(![A]: (A=empty_set|(?[B]: in(B,A))))),
% 0.17/0.58 inference(miniscoping,[status(thm)],[f143])).
% 0.17/0.58 fof(f145,plain,(
% 0.17/0.58 (![A]: (~A=empty_set|(![B]: ~in(B,A))))&(![A]: (A=empty_set|in(sK1_skl(A),A)))),
% 0.17/0.58 inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(B,sK1_skl(A))],[f144])).
% 0.17/0.58 fof(f146,plain,(
% 0.17/0.58 ![X0,X1]: (~X0=empty_set|~in(X1,X0))),
% 0.17/0.58 inference(cnf_transformation,[status(thm)],[f145])).
% 0.17/0.58 fof(f147,plain,(
% 0.17/0.58 ![X0]: (X0=empty_set|in(sK1_skl(X0),X0))),
% 0.17/0.58 inference(cnf_transformation,[status(thm)],[f145])).
% 0.17/0.58 fof(f148,plain,(
% 0.17/0.58 ![A,B]: ((~B=powerset(A)|(![C]: ((~in(C,B)|subset(C,A))&(in(C,B)|~subset(C,A)))))&(B=powerset(A)|(?[C]: ((~in(C,B)|~subset(C,A))&(in(C,B)|subset(C,A))))))),
% 0.17/0.58 inference(NNF_transformation,[status(thm)],[f9])).
% 0.17/0.58 fof(f149,plain,(
% 0.17/0.58 (![A,B]: (~B=powerset(A)|((![C]: (~in(C,B)|subset(C,A)))&(![C]: (in(C,B)|~subset(C,A))))))&(![A,B]: (B=powerset(A)|(?[C]: ((~in(C,B)|~subset(C,A))&(in(C,B)|subset(C,A))))))),
% 0.17/0.58 inference(miniscoping,[status(thm)],[f148])).
% 0.17/0.58 fof(f150,plain,(
% 0.17/0.58 (![A,B]: (~B=powerset(A)|((![C]: (~in(C,B)|subset(C,A)))&(![C]: (in(C,B)|~subset(C,A))))))&(![A,B]: (B=powerset(A)|((~in(sK2_skl(B,A),B)|~subset(sK2_skl(B,A),A))&(in(sK2_skl(B,A),B)|subset(sK2_skl(B,A),A)))))),
% 0.17/0.58 inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(C,sK2_skl(B,A))],[f149])).
% 0.17/0.58 fof(f152,plain,(
% 0.17/0.58 ![X0,X1,X2]: (~X0=powerset(X1)|in(X2,X0)|~subset(X2,X1))),
% 0.17/0.58 inference(cnf_transformation,[status(thm)],[f150])).
% 0.17/0.58 fof(f230,plain,(
% 0.17/0.58 ![A,B]: (~element(B,powerset(powerset(A)))|(![C]: (~element(C,powerset(powerset(A)))|(C=complements_of_subsets(A,B)<=>(![D]: (~element(D,powerset(A))|(in(D,C)<=>in(subset_complement(A,D),B))))))))),
% 0.17/0.58 inference(pre_NNF_transformation,[status(thm)],[f21])).
% 0.17/0.58 fof(f231,plain,(
% 0.17/0.58 ![A,B]: (~element(B,powerset(powerset(A)))|(![C]: (~element(C,powerset(powerset(A)))|((~C=complements_of_subsets(A,B)|(![D]: (~element(D,powerset(A))|((~in(D,C)|in(subset_complement(A,D),B))&(in(D,C)|~in(subset_complement(A,D),B))))))&(C=complements_of_subsets(A,B)|(?[D]: (element(D,powerset(A))&((~in(D,C)|~in(subset_complement(A,D),B))&(in(D,C)|in(subset_complement(A,D),B))))))))))),
% 0.17/0.58 inference(NNF_transformation,[status(thm)],[f230])).
% 0.17/0.58 fof(f232,plain,(
% 0.17/0.58 ![A,B]: (~element(B,powerset(powerset(A)))|(![C]: (~element(C,powerset(powerset(A)))|((~C=complements_of_subsets(A,B)|(![D]: (~element(D,powerset(A))|((~in(D,C)|in(subset_complement(A,D),B))&(in(D,C)|~in(subset_complement(A,D),B))))))&(C=complements_of_subsets(A,B)|(element(sK16_skl(C,B,A),powerset(A))&((~in(sK16_skl(C,B,A),C)|~in(subset_complement(A,sK16_skl(C,B,A)),B))&(in(sK16_skl(C,B,A),C)|in(subset_complement(A,sK16_skl(C,B,A)),B)))))))))),
% 0.17/0.58 inference(skolemize,[status(esa),new_symbols(skolem,[sK16_skl]),skolemize(D,sK16_skl(C,B,A))],[f231])).
% 0.17/0.58 fof(f233,plain,(
% 0.17/0.58 ![X0,X1,X2,X3]: (~element(X0,powerset(powerset(X1)))|~element(X2,powerset(powerset(X1)))|~X2=complements_of_subsets(X1,X0)|~element(X3,powerset(X1))|~in(X3,X2)|in(subset_complement(X1,X3),X0))),
% 0.17/0.58 inference(cnf_transformation,[status(thm)],[f232])).
% 0.17/0.58 fof(f245,plain,(
% 0.17/0.58 ![A,B]: (~element(B,powerset(powerset(A)))|element(complements_of_subsets(A,B),powerset(powerset(A))))),
% 0.17/0.58 inference(pre_NNF_transformation,[status(thm)],[f34])).
% 0.17/0.58 fof(f246,plain,(
% 0.17/0.58 ![X0,X1]: (~element(X0,powerset(powerset(X1)))|element(complements_of_subsets(X1,X0),powerset(powerset(X1))))),
% 0.17/0.58 inference(cnf_transformation,[status(thm)],[f245])).
% 0.17/0.58 fof(f264,plain,(
% 0.17/0.58 ![A,B]: (~element(B,powerset(powerset(A)))|complements_of_subsets(A,complements_of_subsets(A,B))=B)),
% 0.17/0.58 inference(pre_NNF_transformation,[status(thm)],[f45])).
% 0.17/0.58 fof(f265,plain,(
% 0.17/0.58 ![X0,X1]: (~element(X0,powerset(powerset(X1)))|complements_of_subsets(X1,complements_of_subsets(X1,X0))=X0)),
% 0.17/0.58 inference(cnf_transformation,[status(thm)],[f264])).
% 0.17/0.58 fof(f346,plain,(
% 0.17/0.58 ![A,B]: (~in(A,B)|element(A,B))),
% 0.17/0.58 inference(pre_NNF_transformation,[status(thm)],[f74])).
% 0.17/0.58 fof(f347,plain,(
% 0.17/0.58 ![X0,X1]: (~in(X0,X1)|element(X0,X1))),
% 0.17/0.58 inference(cnf_transformation,[status(thm)],[f346])).
% 0.17/0.58 fof(f365,plain,(
% 0.17/0.58 ![X0]: (subset(empty_set,X0))),
% 0.17/0.58 inference(cnf_transformation,[status(thm)],[f82])).
% 0.17/0.59 fof(f412,plain,(
% 0.17/0.59 (?[A,B]: (element(B,powerset(powerset(A)))&(~B=empty_set&complements_of_subsets(A,B)=empty_set)))),
% 0.17/0.59 inference(pre_NNF_transformation,[status(thm)],[f99])).
% 0.17/0.59 fof(f413,plain,(
% 0.17/0.59 (element(sK27_skl,powerset(powerset(sK26_skl)))&(~sK27_skl=empty_set&complements_of_subsets(sK26_skl,sK27_skl)=empty_set))),
% 0.17/0.59 inference(skolemize,[status(esa),new_symbols(skolem,[sK26_skl,sK27_skl]),skolemize(A,sK26_skl),skolemize(B,sK27_skl)],[f412])).
% 0.17/0.59 fof(f414,plain,(
% 0.17/0.59 element(sK27_skl,powerset(powerset(sK26_skl)))),
% 0.17/0.59 inference(cnf_transformation,[status(thm)],[f413])).
% 0.17/0.59 fof(f415,plain,(
% 0.17/0.59 ~sK27_skl=empty_set),
% 0.17/0.59 inference(cnf_transformation,[status(thm)],[f413])).
% 0.17/0.59 fof(f416,plain,(
% 0.17/0.59 complements_of_subsets(sK26_skl,sK27_skl)=empty_set),
% 0.17/0.59 inference(cnf_transformation,[status(thm)],[f413])).
% 0.17/0.59 fof(f421,plain,(
% 0.17/0.59 ![A,B,C]: ((~in(A,B)|~element(B,powerset(C)))|element(A,C))),
% 0.17/0.59 inference(pre_NNF_transformation,[status(thm)],[f103])).
% 0.17/0.59 fof(f422,plain,(
% 0.17/0.59 ![A,C]: ((![B]: (~in(A,B)|~element(B,powerset(C))))|element(A,C))),
% 0.17/0.59 inference(miniscoping,[status(thm)],[f421])).
% 0.17/0.59 fof(f423,plain,(
% 0.17/0.59 ![X0,X1,X2]: (~in(X0,X1)|~element(X1,powerset(X2))|element(X0,X2))),
% 0.17/0.59 inference(cnf_transformation,[status(thm)],[f422])).
% 0.17/0.59 fof(f491,plain,(
% 0.17/0.59 ![X0]: (~in(X0,empty_set))),
% 0.17/0.59 inference(destructive_equality_resolution,[status(thm)],[f146])).
% 0.17/0.59 fof(f493,plain,(
% 0.17/0.59 ![X0,X1]: (in(X0,powerset(X1))|~subset(X0,X1))),
% 0.17/0.59 inference(destructive_equality_resolution,[status(thm)],[f152])).
% 0.17/0.59 fof(f511,plain,(
% 0.17/0.59 ![X0,X1,X2]: (~element(X0,powerset(powerset(X1)))|~element(complements_of_subsets(X1,X0),powerset(powerset(X1)))|~element(X2,powerset(X1))|~in(X2,complements_of_subsets(X1,X0))|in(subset_complement(X1,X2),X0))),
% 0.17/0.59 inference(destructive_equality_resolution,[status(thm)],[f233])).
% 0.17/0.59 fof(f521,plain,(
% 0.17/0.59 ![X0]: (in(empty_set,powerset(X0)))),
% 0.17/0.59 inference(resolution,[status(thm)],[f493,f365])).
% 0.17/0.59 fof(f535,plain,(
% 0.17/0.59 ![X0]: (element(empty_set,powerset(X0)))),
% 0.17/0.59 inference(resolution,[status(thm)],[f521,f347])).
% 0.17/0.59 fof(f554,plain,(
% 0.17/0.59 ![X0,X1,X2]: (~element(X0,powerset(powerset(X1)))|~element(X2,powerset(X1))|~in(X2,complements_of_subsets(X1,X0))|in(subset_complement(X1,X2),X0))),
% 0.17/0.59 inference(backward_subsumption_resolution,[status(thm)],[f511,f246])).
% 0.17/0.59 fof(f560,plain,(
% 0.17/0.59 complements_of_subsets(sK26_skl,complements_of_subsets(sK26_skl,sK27_skl))=sK27_skl),
% 0.17/0.59 inference(resolution,[status(thm)],[f265,f414])).
% 0.17/0.59 fof(f562,plain,(
% 0.17/0.59 complements_of_subsets(sK26_skl,empty_set)=sK27_skl),
% 0.17/0.59 inference(forward_demodulation,[status(thm)],[f416,f560])).
% 0.17/0.59 fof(f624,plain,(
% 0.17/0.59 ![X0]: (~in(X0,sK27_skl)|element(X0,powerset(sK26_skl)))),
% 0.17/0.59 inference(resolution,[status(thm)],[f423,f414])).
% 0.17/0.59 fof(f731,plain,(
% 0.17/0.59 ![X0]: (~element(empty_set,powerset(powerset(sK26_skl)))|~element(X0,powerset(sK26_skl))|~in(X0,sK27_skl)|in(subset_complement(sK26_skl,X0),empty_set))),
% 0.17/0.59 inference(paramodulation,[status(thm)],[f562,f554])).
% 0.17/0.59 fof(f735,plain,(
% 0.17/0.59 ![X0]: (~element(X0,powerset(sK26_skl))|~in(X0,sK27_skl)|in(subset_complement(sK26_skl,X0),empty_set))),
% 0.17/0.59 inference(forward_subsumption_resolution,[status(thm)],[f731,f535])).
% 0.17/0.59 fof(f1012,plain,(
% 0.17/0.59 ![X0]: (~in(X0,sK27_skl)|in(subset_complement(sK26_skl,X0),empty_set))),
% 0.17/0.59 inference(forward_subsumption_resolution,[status(thm)],[f735,f624])).
% 0.17/0.59 fof(f1014,plain,(
% 0.17/0.59 in(subset_complement(sK26_skl,sK1_skl(sK27_skl)),empty_set)|sK27_skl=empty_set),
% 0.17/0.59 inference(resolution,[status(thm)],[f1012,f147])).
% 0.17/0.59 fof(f1018,plain,(
% 0.17/0.59 sK27_skl=empty_set),
% 0.17/0.59 inference(forward_subsumption_resolution,[status(thm)],[f1014,f491])).
% 0.17/0.59 fof(f1021,plain,(
% 0.17/0.59 $false),
% 0.17/0.59 inference(forward_subsumption_resolution,[status(thm)],[f1018,f415])).
% 0.17/0.59 % SZS output end CNFRefutation for theBenchmark.p
% 0.26/0.61 % Elapsed time: 0.164790 seconds
% 0.26/0.61 % CPU time: 0.955872 seconds
% 0.26/0.61 % Total memory used: 119.064 MB
% 0.26/0.61 % Net memory used: 117.800 MB
%------------------------------------------------------------------------------