%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SET008+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/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 02:11:09 PM UTC 2026
% Result : Theorem 0.13s 0.50s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET008+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.03 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.34 % Computer : n004.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Mon Sep 21 04:41:21 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.36 % Drodi V4.1.1
% 0.13/0.50 % Refutation found
% 0.13/0.50 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.50 % SZS output start CNFRefutation for theBenchmark
% 0.13/0.50 fof(f1,axiom,(
% 0.13/0.50 (! [B,C,D] :( member(D,intersection(B,C))<=> ( member(D,B)& member(D,C) ) ) )),
% 0.13/0.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.50 fof(f2,axiom,(
% 0.13/0.50 (! [B,C,D] :( member(D,difference(B,C))<=> ( member(D,B)& ~ member(D,C) ) ) )),
% 0.13/0.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.50 fof(f3,axiom,(
% 0.13/0.50 (! [B] : ~ member(B,empty_set) )),
% 0.13/0.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.50 fof(f5,axiom,(
% 0.13/0.50 (! [B,C] : intersection(B,C) = intersection(C,B) )),
% 0.13/0.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.50 fof(f8,axiom,(
% 0.13/0.50 (! [B] :( empty(B)<=> (! [C] : ~ member(C,B) )) )),
% 0.13/0.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.50 fof(f9,axiom,(
% 0.13/0.50 (! [B,C] :( B = C<=> (! [D] :( member(D,B)<=> member(D,C) ) )) )),
% 0.13/0.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.50 fof(f10,conjecture,(
% 0.13/0.50 (! [B,C] : intersection(difference(B,C),C) = empty_set )),
% 0.13/0.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.50 fof(f11,negated_conjecture,(
% 0.13/0.50 ~((! [B,C] : intersection(difference(B,C),C) = empty_set ))),
% 0.13/0.50 inference(negated_conjecture,[status(cth)],[f10])).
% 0.13/0.50 fof(f12,plain,(
% 0.13/0.50 ![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))))),
% 0.13/0.50 inference(NNF_transformation,[status(thm)],[f1])).
% 0.13/0.50 fof(f13,plain,(
% 0.13/0.50 (![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))))),
% 0.13/0.50 inference(miniscoping,[status(thm)],[f12])).
% 0.13/0.50 fof(f14,plain,(
% 0.13/0.50 ![X0,X1,X2]: (~member(X0,intersection(X1,X2))|member(X0,X1))),
% 0.13/0.50 inference(cnf_transformation,[status(thm)],[f13])).
% 0.13/0.50 fof(f15,plain,(
% 0.13/0.50 ![X0,X1,X2]: (~member(X0,intersection(X1,X2))|member(X0,X2))),
% 0.13/0.50 inference(cnf_transformation,[status(thm)],[f13])).
% 0.13/0.50 fof(f17,plain,(
% 0.13/0.50 ![B,C,D]: ((~member(D,difference(B,C))|(member(D,B)&~member(D,C)))&(member(D,difference(B,C))|(~member(D,B)|member(D,C))))),
% 0.13/0.50 inference(NNF_transformation,[status(thm)],[f2])).
% 0.13/0.50 fof(f18,plain,(
% 0.13/0.50 (![B,C,D]: (~member(D,difference(B,C))|(member(D,B)&~member(D,C))))&(![B,C,D]: (member(D,difference(B,C))|(~member(D,B)|member(D,C))))),
% 0.13/0.50 inference(miniscoping,[status(thm)],[f17])).
% 0.13/0.50 fof(f20,plain,(
% 0.13/0.50 ![X0,X1,X2]: (~member(X0,difference(X1,X2))|~member(X0,X2))),
% 0.13/0.50 inference(cnf_transformation,[status(thm)],[f18])).
% 0.13/0.50 fof(f22,plain,(
% 0.13/0.50 ![X0]: (~member(X0,empty_set))),
% 0.13/0.50 inference(cnf_transformation,[status(thm)],[f3])).
% 0.13/0.50 fof(f28,plain,(
% 0.13/0.50 ![X0,X1]: (intersection(X0,X1)=intersection(X1,X0))),
% 0.13/0.50 inference(cnf_transformation,[status(thm)],[f5])).
% 0.13/0.50 fof(f37,plain,(
% 0.13/0.50 ![B]: ((~empty(B)|(![C]: ~member(C,B)))&(empty(B)|(?[C]: member(C,B))))),
% 0.13/0.50 inference(NNF_transformation,[status(thm)],[f8])).
% 0.13/0.50 fof(f38,plain,(
% 0.13/0.50 (![B]: (~empty(B)|(![C]: ~member(C,B))))&(![B]: (empty(B)|(?[C]: member(C,B))))),
% 0.13/0.50 inference(miniscoping,[status(thm)],[f37])).
% 0.13/0.50 fof(f39,plain,(
% 0.13/0.50 (![B]: (~empty(B)|(![C]: ~member(C,B))))&(![B]: (empty(B)|member(sK1_skl(B),B)))),
% 0.13/0.50 inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(C,sK1_skl(B))],[f38])).
% 0.13/0.50 fof(f40,plain,(
% 0.13/0.50 ![X0,X1]: (~empty(X0)|~member(X1,X0))),
% 0.13/0.50 inference(cnf_transformation,[status(thm)],[f39])).
% 0.13/0.50 fof(f41,plain,(
% 0.13/0.50 ![X0]: (empty(X0)|member(sK1_skl(X0),X0))),
% 0.13/0.50 inference(cnf_transformation,[status(thm)],[f39])).
% 0.13/0.50 fof(f42,plain,(
% 0.13/0.50 ![B,C]: ((~B=C|(![D]: ((~member(D,B)|member(D,C))&(member(D,B)|~member(D,C)))))&(B=C|(?[D]: ((~member(D,B)|~member(D,C))&(member(D,B)|member(D,C))))))),
% 0.13/0.50 inference(NNF_transformation,[status(thm)],[f9])).
% 0.13/0.50 fof(f43,plain,(
% 0.13/0.50 (![B,C]: (~B=C|((![D]: (~member(D,B)|member(D,C)))&(![D]: (member(D,B)|~member(D,C))))))&(![B,C]: (B=C|(?[D]: ((~member(D,B)|~member(D,C))&(member(D,B)|member(D,C))))))),
% 0.13/0.50 inference(miniscoping,[status(thm)],[f42])).
% 0.13/0.50 fof(f44,plain,(
% 0.13/0.50 (![B,C]: (~B=C|((![D]: (~member(D,B)|member(D,C)))&(![D]: (member(D,B)|~member(D,C))))))&(![B,C]: (B=C|((~member(sK2_skl(C,B),B)|~member(sK2_skl(C,B),C))&(member(sK2_skl(C,B),B)|member(sK2_skl(C,B),C)))))),
% 0.13/0.50 inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(D,sK2_skl(C,B))],[f43])).
% 0.13/0.50 fof(f48,plain,(
% 0.13/0.50 ![X0,X1]: (X0=X1|member(sK2_skl(X1,X0),X0)|member(sK2_skl(X1,X0),X1))),
% 0.13/0.50 inference(cnf_transformation,[status(thm)],[f44])).
% 0.13/0.50 fof(f49,plain,(
% 0.13/0.50 (?[B,C]: ~intersection(difference(B,C),C)=empty_set)),
% 0.13/0.50 inference(pre_NNF_transformation,[status(thm)],[f11])).
% 0.13/0.50 fof(f50,plain,(
% 0.13/0.50 ~intersection(difference(sK3_skl,sK4_skl),sK4_skl)=empty_set),
% 0.13/0.50 inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl,sK4_skl]),skolemize(B,sK3_skl),skolemize(C,sK4_skl)],[f49])).
% 0.13/0.50 fof(f51,plain,(
% 0.13/0.50 ~intersection(difference(sK3_skl,sK4_skl),sK4_skl)=empty_set),
% 0.13/0.50 inference(cnf_transformation,[status(thm)],[f50])).
% 0.13/0.50 fof(f54,plain,(
% 0.13/0.50 ~intersection(sK4_skl,difference(sK3_skl,sK4_skl))=empty_set),
% 0.13/0.50 inference(backward_demodulation,[status(thm)],[f28,f51])).
% 0.13/0.50 fof(f68,plain,(
% 0.13/0.50 ![X0,X1]: (empty(intersection(X0,X1))|member(sK1_skl(intersection(X0,X1)),X1))),
% 0.13/0.50 inference(resolution,[status(thm)],[f41,f15])).
% 0.13/0.50 fof(f69,plain,(
% 0.13/0.50 ![X0,X1]: (empty(intersection(X0,X1))|member(sK1_skl(intersection(X0,X1)),X0))),
% 0.13/0.50 inference(resolution,[status(thm)],[f41,f14])).
% 0.13/0.50 fof(f90,plain,(
% 0.13/0.50 ![X0]: (empty_set=X0|member(sK2_skl(X0,empty_set),X0))),
% 0.13/0.50 inference(resolution,[status(thm)],[f48,f22])).
% 0.13/0.50 fof(f121,plain,(
% 0.13/0.50 ![X0]: (empty_set=X0|~empty(X0))),
% 0.13/0.50 inference(resolution,[status(thm)],[f90,f40])).
% 0.13/0.50 fof(f141,plain,(
% 0.13/0.50 ![X0,X1,X2]: (empty(intersection(X0,difference(X1,X2)))|~member(sK1_skl(intersection(X0,difference(X1,X2))),X2))),
% 0.13/0.50 inference(resolution,[status(thm)],[f68,f20])).
% 0.13/0.50 fof(f1282,plain,(
% 0.13/0.50 ![X0,X1]: (empty(intersection(X0,difference(X1,X0)))|empty(intersection(X0,difference(X1,X0))))),
% 0.13/0.50 inference(resolution,[status(thm)],[f141,f69])).
% 0.13/0.50 fof(f1288,plain,(
% 0.13/0.50 ![X0,X1]: (empty(intersection(X0,difference(X1,X0))))),
% 0.13/0.50 inference(duplicate_literals_removal,[status(thm)],[f1282])).
% 0.13/0.50 fof(f1497,plain,(
% 0.13/0.50 ![X0,X1]: (empty_set=intersection(X0,difference(X1,X0)))),
% 0.13/0.50 inference(resolution,[status(thm)],[f1288,f121])).
% 0.13/0.50 fof(f1889,plain,(
% 0.13/0.50 ~empty_set=empty_set),
% 0.13/0.50 inference(backward_demodulation,[status(thm)],[f1497,f54])).
% 0.13/0.50 fof(f1933,plain,(
% 0.13/0.50 $false),
% 0.13/0.50 inference(trivial_equality_resolution,[status(thm)],[f1889])).
% 0.13/0.50 % SZS output end CNFRefutation for theBenchmark.p
% 0.13/0.52 % Elapsed time: 0.163143 seconds
% 0.13/0.52 % CPU time: 1.001363 seconds
% 0.13/0.52 % Total memory used: 113.184 MB
% 0.13/0.52 % Net memory used: 111.294 MB
%------------------------------------------------------------------------------