%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SET594+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n006.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 02:12:15 PM UTC 2026
% Result : Theorem 7.94s 6.51s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET594+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/5.37 % Computer : n006.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Mon Sep 21 05:27:47 UTC 2026
% 0.10/5.37 % CPUTime :
% 0.10/5.38 % Drodi V4.1.1
% 7.94/6.51 % Refutation found
% 7.94/6.51 % SZS status Theorem for theBenchmark: Theorem is valid
% 7.94/6.51 % SZS output start CNFRefutation for theBenchmark
% 7.94/6.51 fof(f1,axiom,(
% 7.94/6.51 (! [B,C] :( subset(B,C)<=> (! [D] :( member(D,B)=> member(D,C) ) )) )),
% 7.94/6.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 7.94/6.51 fof(f2,axiom,(
% 7.94/6.51 (! [B,C,D] :( member(D,union(B,C))<=> ( member(D,B)| member(D,C) ) ) )),
% 7.94/6.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 7.94/6.51 fof(f3,axiom,(
% 7.94/6.51 (! [B,C,D] :( member(D,intersection(B,C))<=> ( member(D,B)& member(D,C) ) ) )),
% 7.94/6.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 7.94/6.51 fof(f5,axiom,(
% 7.94/6.51 (! [B,C] : union(B,C) = union(C,B) )),
% 7.94/6.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 7.94/6.51 fof(f6,axiom,(
% 7.94/6.51 (! [B,C] : intersection(B,C) = intersection(C,B) )),
% 7.94/6.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 7.94/6.51 fof(f9,conjecture,(
% 7.94/6.51 (! [B,C,D] :( union(intersection(B,C),intersection(B,D)) = B=> subset(B,union(C,D)) ) )),
% 7.94/6.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 7.94/6.51 fof(f10,negated_conjecture,(
% 7.94/6.51 ~((! [B,C,D] :( union(intersection(B,C),intersection(B,D)) = B=> subset(B,union(C,D)) ) ))),
% 7.94/6.51 inference(negated_conjecture,[status(cth)],[f9])).
% 7.94/6.51 fof(f11,plain,(
% 7.94/6.51 ![B,C]: (subset(B,C)<=>(![D]: (~member(D,B)|member(D,C))))),
% 7.94/6.51 inference(pre_NNF_transformation,[status(thm)],[f1])).
% 7.94/6.51 fof(f12,plain,(
% 7.94/6.51 ![B,C]: ((~subset(B,C)|(![D]: (~member(D,B)|member(D,C))))&(subset(B,C)|(?[D]: (member(D,B)&~member(D,C)))))),
% 7.94/6.51 inference(NNF_transformation,[status(thm)],[f11])).
% 7.94/6.51 fof(f13,plain,(
% 7.94/6.51 (![B,C]: (~subset(B,C)|(![D]: (~member(D,B)|member(D,C)))))&(![B,C]: (subset(B,C)|(?[D]: (member(D,B)&~member(D,C)))))),
% 7.94/6.51 inference(miniscoping,[status(thm)],[f12])).
% 7.94/6.51 fof(f14,plain,(
% 7.94/6.51 (![B,C]: (~subset(B,C)|(![D]: (~member(D,B)|member(D,C)))))&(![B,C]: (subset(B,C)|(member(sK0_skl(C,B),B)&~member(sK0_skl(C,B),C))))),
% 7.94/6.51 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(D,sK0_skl(C,B))],[f13])).
% 7.94/6.51 fof(f16,plain,(
% 7.94/6.51 ![X0,X1]: (subset(X0,X1)|member(sK0_skl(X1,X0),X0))),
% 7.94/6.51 inference(cnf_transformation,[status(thm)],[f14])).
% 7.94/6.51 fof(f17,plain,(
% 7.94/6.51 ![X0,X1]: (subset(X0,X1)|~member(sK0_skl(X1,X0),X1))),
% 7.94/6.51 inference(cnf_transformation,[status(thm)],[f14])).
% 7.94/6.51 fof(f18,plain,(
% 7.94/6.51 ![B,C,D]: ((~member(D,union(B,C))|(member(D,B)|member(D,C)))&(member(D,union(B,C))|(~member(D,B)&~member(D,C))))),
% 7.94/6.51 inference(NNF_transformation,[status(thm)],[f2])).
% 7.94/6.51 fof(f19,plain,(
% 7.94/6.51 (![B,C,D]: (~member(D,union(B,C))|(member(D,B)|member(D,C))))&(![B,C,D]: (member(D,union(B,C))|(~member(D,B)&~member(D,C))))),
% 7.94/6.51 inference(miniscoping,[status(thm)],[f18])).
% 7.94/6.51 fof(f20,plain,(
% 7.94/6.51 ![X0,X1,X2]: (~member(X0,union(X1,X2))|member(X0,X1)|member(X0,X2))),
% 7.94/6.51 inference(cnf_transformation,[status(thm)],[f19])).
% 7.94/6.51 fof(f21,plain,(
% 7.94/6.51 ![X0,X1,X2]: (member(X0,union(X1,X2))|~member(X0,X1))),
% 7.94/6.51 inference(cnf_transformation,[status(thm)],[f19])).
% 7.94/6.51 fof(f22,plain,(
% 7.94/6.51 ![X0,X1,X2]: (member(X0,union(X1,X2))|~member(X0,X2))),
% 7.94/6.51 inference(cnf_transformation,[status(thm)],[f19])).
% 7.94/6.51 fof(f23,plain,(
% 7.94/6.51 ![B,C,D]: ((~member(D,intersection(B,C))|(member(D,B)&member(D,C)))&(member(D,intersection(B,C))|(~member(D,B)|~member(D,C))))),
% 7.94/6.51 inference(NNF_transformation,[status(thm)],[f3])).
% 7.94/6.51 fof(f24,plain,(
% 7.94/6.51 (![B,C,D]: (~member(D,intersection(B,C))|(member(D,B)&member(D,C))))&(![B,C,D]: (member(D,intersection(B,C))|(~member(D,B)|~member(D,C))))),
% 7.94/6.51 inference(miniscoping,[status(thm)],[f23])).
% 7.94/6.51 fof(f25,plain,(
% 7.94/6.51 ![X0,X1,X2]: (~member(X0,intersection(X1,X2))|member(X0,X1))),
% 7.94/6.51 inference(cnf_transformation,[status(thm)],[f24])).
% 7.94/6.51 fof(f33,plain,(
% 7.94/6.51 ![X0,X1]: (union(X0,X1)=union(X1,X0))),
% 7.94/6.51 inference(cnf_transformation,[status(thm)],[f5])).
% 7.94/6.51 fof(f34,plain,(
% 7.94/6.51 ![X0,X1]: (intersection(X0,X1)=intersection(X1,X0))),
% 7.94/6.51 inference(cnf_transformation,[status(thm)],[f6])).
% 7.94/6.51 fof(f43,plain,(
% 7.94/6.51 (?[B,C,D]: (union(intersection(B,C),intersection(B,D))=B&~subset(B,union(C,D))))),
% 7.94/6.51 inference(pre_NNF_transformation,[status(thm)],[f10])).
% 7.94/6.51 fof(f44,plain,(
% 7.94/6.51 (union(intersection(sK2_skl,sK3_skl),intersection(sK2_skl,sK4_skl))=sK2_skl&~subset(sK2_skl,union(sK3_skl,sK4_skl)))),
% 7.94/6.51 inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl,sK4_skl]),skolemize(B,sK2_skl),skolemize(C,sK3_skl),skolemize(D,sK4_skl)],[f43])).
% 8.39/6.53 fof(f45,plain,(
% 8.39/6.53 union(intersection(sK2_skl,sK3_skl),intersection(sK2_skl,sK4_skl))=sK2_skl),
% 8.39/6.53 inference(cnf_transformation,[status(thm)],[f44])).
% 8.39/6.53 fof(f46,plain,(
% 8.39/6.53 ~subset(sK2_skl,union(sK3_skl,sK4_skl))),
% 8.39/6.53 inference(cnf_transformation,[status(thm)],[f44])).
% 8.39/6.53 fof(f50,plain,(
% 8.39/6.53 union(intersection(sK2_skl,sK4_skl),intersection(sK2_skl,sK3_skl))=sK2_skl),
% 8.39/6.53 inference(backward_demodulation,[status(thm)],[f33,f45])).
% 8.39/6.53 fof(f51,plain,(
% 8.39/6.53 ~subset(sK2_skl,union(sK4_skl,sK3_skl))),
% 8.39/6.53 inference(backward_demodulation,[status(thm)],[f33,f46])).
% 8.39/6.53 fof(f65,plain,(
% 8.39/6.53 union(intersection(sK4_skl,sK2_skl),intersection(sK2_skl,sK3_skl))=sK2_skl),
% 8.39/6.53 inference(forward_demodulation,[status(thm)],[f34,f50])).
% 8.39/6.53 fof(f66,plain,(
% 8.39/6.53 union(intersection(sK4_skl,sK2_skl),intersection(sK3_skl,sK2_skl))=sK2_skl),
% 8.39/6.53 inference(forward_demodulation,[status(thm)],[f34,f65])).
% 8.39/6.53 fof(f67,plain,(
% 8.39/6.53 ![X0]: (~member(X0,sK2_skl)|member(X0,intersection(sK4_skl,sK2_skl))|member(X0,intersection(sK3_skl,sK2_skl)))),
% 8.39/6.53 inference(paramodulation,[status(thm)],[f66,f20])).
% 8.39/6.53 fof(f71,plain,(
% 8.39/6.53 ![X0]: (subset(sK2_skl,X0)|member(sK0_skl(X0,sK2_skl),intersection(sK4_skl,sK2_skl))|member(sK0_skl(X0,sK2_skl),intersection(sK3_skl,sK2_skl)))),
% 8.39/6.53 inference(resolution,[status(thm)],[f16,f67])).
% 8.39/6.53 fof(f81,plain,(
% 8.39/6.53 ![X0]: (subset(sK2_skl,X0)|member(sK0_skl(X0,sK2_skl),intersection(sK4_skl,sK2_skl))|member(sK0_skl(X0,sK2_skl),sK3_skl))),
% 8.39/6.53 inference(resolution,[status(thm)],[f71,f25])).
% 8.39/6.53 fof(f94,plain,(
% 8.39/6.53 ![X0]: (subset(sK2_skl,X0)|member(sK0_skl(X0,sK2_skl),sK3_skl)|member(sK0_skl(X0,sK2_skl),sK4_skl))),
% 8.39/6.53 inference(resolution,[status(thm)],[f81,f25])).
% 8.39/6.53 fof(f107,plain,(
% 8.39/6.53 ![X0,X1]: (subset(sK2_skl,X0)|member(sK0_skl(X0,sK2_skl),sK4_skl)|member(sK0_skl(X0,sK2_skl),union(X1,sK3_skl)))),
% 8.39/6.53 inference(resolution,[status(thm)],[f94,f22])).
% 8.39/6.53 fof(f116,plain,(
% 8.39/6.53 ![X0]: (subset(sK2_skl,union(X0,sK3_skl))|member(sK0_skl(union(X0,sK3_skl),sK2_skl),sK4_skl)|subset(sK2_skl,union(X0,sK3_skl)))),
% 8.39/6.53 inference(resolution,[status(thm)],[f107,f17])).
% 8.39/6.53 fof(f123,plain,(
% 8.39/6.53 ![X0]: (subset(sK2_skl,union(X0,sK3_skl))|member(sK0_skl(union(X0,sK3_skl),sK2_skl),sK4_skl))),
% 8.39/6.53 inference(duplicate_literals_removal,[status(thm)],[f116])).
% 8.39/6.53 fof(f126,plain,(
% 8.39/6.53 ![X0,X1]: (subset(sK2_skl,union(X0,sK3_skl))|member(sK0_skl(union(X0,sK3_skl),sK2_skl),union(sK4_skl,X1)))),
% 8.39/6.53 inference(resolution,[status(thm)],[f123,f21])).
% 8.39/6.53 fof(f3823,plain,(
% 8.39/6.53 subset(sK2_skl,union(sK4_skl,sK3_skl))|subset(sK2_skl,union(sK4_skl,sK3_skl))),
% 8.39/6.53 inference(resolution,[status(thm)],[f126,f17])).
% 8.39/6.53 fof(f3838,definition,(
% 8.39/6.53 sQ52_spl <=> (subset(sK2_skl,union(sK4_skl,sK3_skl)))),
% 8.39/6.53 introduced(definition,[new_symbols(definition,[sQ52_spl])],[split_symbol_definition])).
% 8.39/6.53 fof(f3839,plain,(
% 8.39/6.53 subset(sK2_skl,union(sK4_skl,sK3_skl))|~sQ52_spl),
% 8.39/6.53 inference(component_clause,[status(thm)],[f3838])).
% 8.39/6.53 fof(f3841,plain,(
% 8.39/6.53 sQ52_spl),
% 8.39/6.53 inference(split_clause,[status(thm)],[f3823,f3838])).
% 8.39/6.53 fof(f3846,plain,(
% 8.39/6.53 $false|~sQ52_spl),
% 8.39/6.53 inference(forward_subsumption_resolution,[status(thm)],[f3839,f51])).
% 8.39/6.53 fof(f3847,plain,(
% 8.39/6.53 ~sQ52_spl),
% 8.39/6.53 inference(contradiction_clause,[status(thm)],[f3846])).
% 8.39/6.53 fof(f3848,plain,(
% 8.39/6.53 $false),
% 8.39/6.53 inference(sat_refutation,[status(thm)],[f3841,f3847])).
% 8.39/6.53 % SZS output end CNFRefutation for theBenchmark.p
% 8.39/6.54 % Elapsed time: 1.154902 seconds
% 8.39/6.54 % CPU time: 8.899161 seconds
% 8.39/6.54 % Total memory used: 185.143 MB
% 8.39/6.54 % Net memory used: 173.105 MB
%------------------------------------------------------------------------------