%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SET146+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 : n026.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 02:11:39 PM UTC 2026
% Result : Theorem 0.09s 0.39s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET146+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n026.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 04:59:07 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 0.09/0.39 % Refutation found
% 0.09/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.39 % SZS output start CNFRefutation for theBenchmark
% 0.09/0.39 fof(f1,axiom,(
% 0.09/0.39 (! [B,C,D] :( member(D,intersection(B,C))<=> ( member(D,B)& member(D,C) ) ) )),
% 0.09/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.39 fof(f2,axiom,(
% 0.09/0.39 (! [B] : ~ member(B,empty_set) )),
% 0.09/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.39 fof(f3,axiom,(
% 0.09/0.39 (! [B,C] :( B = C<=> ( subset(B,C)& subset(C,B) ) ) )),
% 0.09/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.39 fof(f5,axiom,(
% 0.09/0.39 (! [B,C] :( subset(B,C)<=> (! [D] :( member(D,B)=> member(D,C) ) )) )),
% 0.09/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.39 fof(f7,axiom,(
% 0.09/0.39 (! [B] :( empty(B)<=> (! [C] : ~ member(C,B) )) )),
% 0.09/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.39 fof(f9,conjecture,(
% 0.09/0.39 (! [B] : intersection(B,empty_set) = empty_set )),
% 0.09/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.39 fof(f10,negated_conjecture,(
% 0.09/0.39 ~((! [B] : intersection(B,empty_set) = empty_set ))),
% 0.09/0.39 inference(negated_conjecture,[status(cth)],[f9])).
% 0.09/0.39 fof(f11,plain,(
% 0.09/0.39 ![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))))),
% 0.09/0.39 inference(NNF_transformation,[status(thm)],[f1])).
% 0.09/0.39 fof(f12,plain,(
% 0.09/0.39 (![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))))),
% 0.09/0.39 inference(miniscoping,[status(thm)],[f11])).
% 0.09/0.39 fof(f14,plain,(
% 0.09/0.39 ![X0,X1,X2]: (~member(X0,intersection(X1,X2))|member(X0,X2))),
% 0.09/0.39 inference(cnf_transformation,[status(thm)],[f12])).
% 0.09/0.39 fof(f16,plain,(
% 0.09/0.39 ![X0]: (~member(X0,empty_set))),
% 0.09/0.39 inference(cnf_transformation,[status(thm)],[f2])).
% 0.09/0.39 fof(f17,plain,(
% 0.09/0.39 ![B,C]: ((~B=C|(subset(B,C)&subset(C,B)))&(B=C|(~subset(B,C)|~subset(C,B))))),
% 0.09/0.39 inference(NNF_transformation,[status(thm)],[f3])).
% 0.09/0.39 fof(f18,plain,(
% 0.09/0.39 (![B,C]: (~B=C|(subset(B,C)&subset(C,B))))&(![B,C]: (B=C|(~subset(B,C)|~subset(C,B))))),
% 0.09/0.39 inference(miniscoping,[status(thm)],[f17])).
% 0.09/0.39 fof(f21,plain,(
% 0.09/0.39 ![X0,X1]: (X0=X1|~subset(X0,X1)|~subset(X1,X0))),
% 0.09/0.39 inference(cnf_transformation,[status(thm)],[f18])).
% 0.09/0.39 fof(f23,plain,(
% 0.09/0.39 ![B,C]: (subset(B,C)<=>(![D]: (~member(D,B)|member(D,C))))),
% 0.09/0.39 inference(pre_NNF_transformation,[status(thm)],[f5])).
% 0.09/0.39 fof(f24,plain,(
% 0.09/0.39 ![B,C]: ((~subset(B,C)|(![D]: (~member(D,B)|member(D,C))))&(subset(B,C)|(?[D]: (member(D,B)&~member(D,C)))))),
% 0.09/0.39 inference(NNF_transformation,[status(thm)],[f23])).
% 0.09/0.39 fof(f25,plain,(
% 0.09/0.39 (![B,C]: (~subset(B,C)|(![D]: (~member(D,B)|member(D,C)))))&(![B,C]: (subset(B,C)|(?[D]: (member(D,B)&~member(D,C)))))),
% 0.09/0.39 inference(miniscoping,[status(thm)],[f24])).
% 0.09/0.39 fof(f26,plain,(
% 0.09/0.39 (![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))))),
% 0.09/0.39 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(D,sK0_skl(C,B))],[f25])).
% 0.09/0.39 fof(f28,plain,(
% 0.09/0.39 ![X0,X1]: (subset(X0,X1)|member(sK0_skl(X1,X0),X0))),
% 0.09/0.39 inference(cnf_transformation,[status(thm)],[f26])).
% 0.09/0.39 fof(f31,plain,(
% 0.09/0.39 ![B]: ((~empty(B)|(![C]: ~member(C,B)))&(empty(B)|(?[C]: member(C,B))))),
% 0.09/0.40 inference(NNF_transformation,[status(thm)],[f7])).
% 0.09/0.40 fof(f32,plain,(
% 0.09/0.40 (![B]: (~empty(B)|(![C]: ~member(C,B))))&(![B]: (empty(B)|(?[C]: member(C,B))))),
% 0.09/0.40 inference(miniscoping,[status(thm)],[f31])).
% 0.09/0.40 fof(f33,plain,(
% 0.09/0.40 (![B]: (~empty(B)|(![C]: ~member(C,B))))&(![B]: (empty(B)|member(sK1_skl(B),B)))),
% 0.09/0.40 inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(C,sK1_skl(B))],[f32])).
% 0.09/0.40 fof(f34,plain,(
% 0.09/0.40 ![X0,X1]: (~empty(X0)|~member(X1,X0))),
% 0.09/0.40 inference(cnf_transformation,[status(thm)],[f33])).
% 0.09/0.40 fof(f35,plain,(
% 0.09/0.40 ![X0]: (empty(X0)|member(sK1_skl(X0),X0))),
% 0.09/0.40 inference(cnf_transformation,[status(thm)],[f33])).
% 0.09/0.40 fof(f43,plain,(
% 0.09/0.40 (?[B]: ~intersection(B,empty_set)=empty_set)),
% 0.09/0.40 inference(pre_NNF_transformation,[status(thm)],[f10])).
% 0.09/0.40 fof(f44,plain,(
% 0.09/0.40 ~intersection(sK3_skl,empty_set)=empty_set),
% 0.09/0.40 inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl]),skolemize(B,sK3_skl)],[f43])).
% 0.09/0.40 fof(f45,plain,(
% 0.09/0.40 ~intersection(sK3_skl,empty_set)=empty_set),
% 0.09/0.40 inference(cnf_transformation,[status(thm)],[f44])).
% 0.09/0.40 fof(f59,plain,(
% 0.09/0.40 ![X0,X1]: (empty(intersection(X0,X1))|member(sK1_skl(intersection(X0,X1)),X1))),
% 0.09/0.40 inference(resolution,[status(thm)],[f35,f14])).
% 0.09/0.40 fof(f66,plain,(
% 0.09/0.40 ![X0]: (subset(empty_set,X0))),
% 0.09/0.40 inference(resolution,[status(thm)],[f28,f16])).
% 0.09/0.40 fof(f68,plain,(
% 0.09/0.40 ![X0]: (X0=empty_set|~subset(X0,empty_set))),
% 0.09/0.40 inference(resolution,[status(thm)],[f66,f21])).
% 0.09/0.40 fof(f77,plain,(
% 0.09/0.40 ![X0]: (empty(intersection(X0,empty_set)))),
% 0.09/0.40 inference(resolution,[status(thm)],[f59,f16])).
% 0.09/0.40 fof(f81,plain,(
% 0.09/0.40 ![X0,X1]: (~member(X0,intersection(X1,empty_set)))),
% 0.09/0.40 inference(resolution,[status(thm)],[f77,f34])).
% 0.09/0.40 fof(f93,plain,(
% 0.09/0.40 ![X0,X1]: (subset(intersection(X0,empty_set),X1))),
% 0.09/0.40 inference(resolution,[status(thm)],[f81,f28])).
% 0.09/0.40 fof(f105,plain,(
% 0.09/0.40 ![X0]: (intersection(X0,empty_set)=empty_set)),
% 0.09/0.40 inference(resolution,[status(thm)],[f93,f68])).
% 0.09/0.40 fof(f110,plain,(
% 0.09/0.40 ~empty_set=empty_set),
% 0.09/0.40 inference(backward_demodulation,[status(thm)],[f105,f45])).
% 0.09/0.40 fof(f119,plain,(
% 0.09/0.40 $false),
% 0.09/0.40 inference(trivial_equality_resolution,[status(thm)],[f110])).
% 0.09/0.40 % SZS output end CNFRefutation for theBenchmark.p
% 0.09/0.42 % Elapsed time: 0.046250 seconds
% 0.09/0.42 % CPU time: 0.146393 seconds
% 0.09/0.42 % Total memory used: 76.407 MB
% 0.09/0.42 % Net memory used: 76.081 MB
%------------------------------------------------------------------------------