%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SEU169+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 : n015.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 02:21:53 PM UTC 2026
% Result : Theorem 0.13s 0.39s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU169+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n015.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 05:57:51 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.36 % Drodi V4.1.1
% 0.13/0.39 % Refutation found
% 0.13/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.39 % SZS output start CNFRefutation for theBenchmark
% 0.13/0.39 fof(f9,axiom,(
% 0.13/0.39 (! [A,B] :( B = powerset(A)<=> (! [C] :( in(C,B)<=> subset(C,A) ) )) )),
% 0.13/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.39 fof(f10,axiom,(
% 0.13/0.39 (! [A,B] :( ( ~ empty(A)=> ( element(B,A)<=> in(B,A) ) )& ( empty(A)=> ( element(B,A)<=> empty(B) ) ) ) )),
% 0.13/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.39 fof(f12,axiom,(
% 0.13/0.39 (! [A,B,C] :( C = set_union2(A,B)<=> (! [D] :( in(D,C)<=> ( in(D,A)| in(D,B) ) ) )) )),
% 0.13/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.39 fof(f33,axiom,(
% 0.13/0.39 (! [A] : ~ empty(powerset(A)) )),
% 0.13/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.39 fof(f47,conjecture,(
% 0.13/0.39 (! [A,B] :( element(B,powerset(A))=> (! [C] :( in(C,B)=> in(C,A) ) )) )),
% 0.13/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.39 fof(f48,negated_conjecture,(
% 0.13/0.39 ~((! [A,B] :( element(B,powerset(A))=> (! [C] :( in(C,B)=> in(C,A) ) )) ))),
% 0.13/0.39 inference(negated_conjecture,[status(cth)],[f47])).
% 0.13/0.39 fof(f62,lemma,(
% 0.13/0.39 (! [A,B] :( subset(A,B)=> set_union2(A,B) = B ) )),
% 0.13/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.39 fof(f131,plain,(
% 0.13/0.39 ![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))))))),
% 0.13/0.39 inference(NNF_transformation,[status(thm)],[f9])).
% 0.13/0.39 fof(f132,plain,(
% 0.13/0.39 (![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))))))),
% 0.13/0.39 inference(miniscoping,[status(thm)],[f131])).
% 0.13/0.39 fof(f133,plain,(
% 0.13/0.39 (![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)))))),
% 0.13/0.39 inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(C,sK2_skl(B,A))],[f132])).
% 0.13/0.39 fof(f134,plain,(
% 0.13/0.39 ![X0,X1,X2]: (~X0=powerset(X1)|~in(X2,X0)|subset(X2,X1))),
% 0.13/0.39 inference(cnf_transformation,[status(thm)],[f133])).
% 0.13/0.39 fof(f138,plain,(
% 0.13/0.39 ![A,B]: ((empty(A)|(element(B,A)<=>in(B,A)))&(~empty(A)|(element(B,A)<=>empty(B))))),
% 0.13/0.39 inference(pre_NNF_transformation,[status(thm)],[f10])).
% 0.13/0.39 fof(f139,plain,(
% 0.13/0.39 ![A,B]: ((empty(A)|((~element(B,A)|in(B,A))&(element(B,A)|~in(B,A))))&(~empty(A)|((~element(B,A)|empty(B))&(element(B,A)|~empty(B)))))),
% 0.13/0.39 inference(NNF_transformation,[status(thm)],[f138])).
% 0.13/0.39 fof(f140,plain,(
% 0.13/0.39 (![A]: (empty(A)|((![B]: (~element(B,A)|in(B,A)))&(![B]: (element(B,A)|~in(B,A))))))&(![A]: (~empty(A)|((![B]: (~element(B,A)|empty(B)))&(![B]: (element(B,A)|~empty(B))))))),
% 0.13/0.39 inference(miniscoping,[status(thm)],[f139])).
% 0.13/0.39 fof(f141,plain,(
% 0.13/0.39 ![X0,X1]: (empty(X0)|~element(X1,X0)|in(X1,X0))),
% 0.13/0.39 inference(cnf_transformation,[status(thm)],[f140])).
% 0.13/0.39 fof(f154,plain,(
% 0.13/0.39 ![A,B,C]: ((~C=set_union2(A,B)|(![D]: ((~in(D,C)|(in(D,A)|in(D,B)))&(in(D,C)|(~in(D,A)&~in(D,B))))))&(C=set_union2(A,B)|(?[D]: ((~in(D,C)|(~in(D,A)&~in(D,B)))&(in(D,C)|(in(D,A)|in(D,B)))))))),
% 0.13/0.39 inference(NNF_transformation,[status(thm)],[f12])).
% 0.13/0.39 fof(f155,plain,(
% 0.13/0.39 (![A,B,C]: (~C=set_union2(A,B)|((![D]: (~in(D,C)|(in(D,A)|in(D,B))))&(![D]: (in(D,C)|(~in(D,A)&~in(D,B)))))))&(![A,B,C]: (C=set_union2(A,B)|(?[D]: ((~in(D,C)|(~in(D,A)&~in(D,B)))&(in(D,C)|(in(D,A)|in(D,B)))))))),
% 0.13/0.39 inference(miniscoping,[status(thm)],[f154])).
% 0.13/0.39 fof(f156,plain,(
% 0.13/0.39 (![A,B,C]: (~C=set_union2(A,B)|((![D]: (~in(D,C)|(in(D,A)|in(D,B))))&(![D]: (in(D,C)|(~in(D,A)&~in(D,B)))))))&(![A,B,C]: (C=set_union2(A,B)|((~in(sK4_skl(C,B,A),C)|(~in(sK4_skl(C,B,A),A)&~in(sK4_skl(C,B,A),B)))&(in(sK4_skl(C,B,A),C)|(in(sK4_skl(C,B,A),A)|in(sK4_skl(C,B,A),B))))))),
% 0.13/0.39 inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl]),skolemize(D,sK4_skl(C,B,A))],[f155])).
% 0.13/0.39 fof(f158,plain,(
% 0.13/0.39 ![X0,X1,X2,X3]: (~X0=set_union2(X1,X2)|in(X3,X0)|~in(X3,X1))),
% 0.13/0.39 inference(cnf_transformation,[status(thm)],[f156])).
% 0.13/0.39 fof(f218,plain,(
% 0.13/0.39 ![X0]: (~empty(powerset(X0)))),
% 0.13/0.39 inference(cnf_transformation,[status(thm)],[f33])).
% 0.13/0.39 fof(f248,plain,(
% 0.13/0.39 (?[A,B]: (element(B,powerset(A))&(?[C]: (in(C,B)&~in(C,A)))))),
% 0.13/0.39 inference(pre_NNF_transformation,[status(thm)],[f48])).
% 0.13/0.39 fof(f249,plain,(
% 0.13/0.39 (element(sK18_skl,powerset(sK17_skl))&(in(sK19_skl,sK18_skl)&~in(sK19_skl,sK17_skl)))),
% 0.13/0.39 inference(skolemize,[status(esa),new_symbols(skolem,[sK17_skl,sK18_skl,sK19_skl]),skolemize(A,sK17_skl),skolemize(B,sK18_skl),skolemize(C,sK19_skl)],[f248])).
% 0.13/0.39 fof(f250,plain,(
% 0.13/0.39 element(sK18_skl,powerset(sK17_skl))),
% 0.13/0.39 inference(cnf_transformation,[status(thm)],[f249])).
% 0.13/0.39 fof(f251,plain,(
% 0.13/0.39 in(sK19_skl,sK18_skl)),
% 0.13/0.39 inference(cnf_transformation,[status(thm)],[f249])).
% 0.13/0.39 fof(f252,plain,(
% 0.13/0.39 ~in(sK19_skl,sK17_skl)),
% 0.13/0.39 inference(cnf_transformation,[status(thm)],[f249])).
% 0.13/0.39 fof(f294,plain,(
% 0.13/0.39 ![A,B]: (~subset(A,B)|set_union2(A,B)=B)),
% 0.13/0.39 inference(pre_NNF_transformation,[status(thm)],[f62])).
% 0.13/0.39 fof(f295,plain,(
% 0.13/0.39 ![X0,X1]: (~subset(X0,X1)|set_union2(X0,X1)=X1)),
% 0.13/0.39 inference(cnf_transformation,[status(thm)],[f294])).
% 0.13/0.39 fof(f425,plain,(
% 0.13/0.39 ![X0,X1]: (~in(X0,powerset(X1))|subset(X0,X1))),
% 0.13/0.39 inference(destructive_equality_resolution,[status(thm)],[f134])).
% 0.13/0.39 fof(f431,plain,(
% 0.13/0.39 ![X0,X1,X2]: (in(X0,set_union2(X1,X2))|~in(X0,X1))),
% 0.13/0.39 inference(destructive_equality_resolution,[status(thm)],[f158])).
% 0.13/0.39 fof(f452,definition,(
% 0.13/0.39 sQ0_spl <=> (empty(powerset(sK17_skl)))),
% 0.13/0.39 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.13/0.39 fof(f453,plain,(
% 0.13/0.39 empty(powerset(sK17_skl))|~sQ0_spl),
% 0.13/0.39 inference(component_clause,[status(thm)],[f452])).
% 0.13/0.39 fof(f459,plain,(
% 0.13/0.39 empty(powerset(sK17_skl))|in(sK18_skl,powerset(sK17_skl))),
% 0.13/0.39 inference(resolution,[status(thm)],[f141,f250])).
% 0.13/0.39 fof(f460,definition,(
% 0.13/0.39 sQ2_spl <=> (in(sK18_skl,powerset(sK17_skl)))),
% 0.13/0.39 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.13/0.39 fof(f461,plain,(
% 0.13/0.39 in(sK18_skl,powerset(sK17_skl))|~sQ2_spl),
% 0.13/0.39 inference(component_clause,[status(thm)],[f460])).
% 0.13/0.39 fof(f463,plain,(
% 0.13/0.39 sQ0_spl|sQ2_spl),
% 0.13/0.39 inference(split_clause,[status(thm)],[f459,f452,f460])).
% 0.13/0.39 fof(f465,plain,(
% 0.13/0.39 subset(sK18_skl,sK17_skl)|~sQ2_spl),
% 0.13/0.39 inference(resolution,[status(thm)],[f461,f425])).
% 0.13/0.39 fof(f479,plain,(
% 0.13/0.39 $false|~sQ0_spl),
% 0.13/0.39 inference(forward_subsumption_resolution,[status(thm)],[f453,f218])).
% 0.13/0.39 fof(f480,plain,(
% 0.13/0.39 ~sQ0_spl),
% 0.13/0.39 inference(contradiction_clause,[status(thm)],[f479])).
% 0.13/0.39 fof(f1086,plain,(
% 0.13/0.39 set_union2(sK18_skl,sK17_skl)=sK17_skl|~sQ2_spl),
% 0.13/0.39 inference(resolution,[status(thm)],[f295,f465])).
% 0.13/0.39 fof(f1177,plain,(
% 0.13/0.39 ![X0]: (in(sK19_skl,set_union2(sK18_skl,X0)))),
% 0.13/0.39 inference(resolution,[status(thm)],[f431,f251])).
% 0.13/0.39 fof(f1217,plain,(
% 0.13/0.39 in(sK19_skl,sK17_skl)|~sQ2_spl),
% 0.13/0.39 inference(paramodulation,[status(thm)],[f1086,f1177])).
% 0.13/0.39 fof(f1226,plain,(
% 0.13/0.39 $false|~sQ2_spl),
% 0.13/0.39 inference(forward_subsumption_resolution,[status(thm)],[f1217,f252])).
% 0.13/0.39 fof(f1227,plain,(
% 0.13/0.39 ~sQ2_spl),
% 0.13/0.39 inference(contradiction_clause,[status(thm)],[f1226])).
% 0.13/0.39 fof(f1228,plain,(
% 0.13/0.39 $false),
% 0.13/0.39 inference(sat_refutation,[status(thm)],[f463,f480,f1227])).
% 0.13/0.39 % SZS output end CNFRefutation for theBenchmark.p
% 0.13/0.42 % Elapsed time: 0.062961 seconds
% 0.13/0.42 % CPU time: 0.231827 seconds
% 0.13/0.42 % Total memory used: 109.683 MB
% 0.13/0.42 % Net memory used: 109.372 MB
%------------------------------------------------------------------------------