%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SET587+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 : n007.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 02:12:14 PM UTC 2026
% Result : Theorem 0.12s 0.44s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET587+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
% 0.12/0.37 % Computer : n007.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Mon Sep 21 05:25:35 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.38 % Drodi V4.1.1
% 0.12/0.44 % Refutation found
% 0.12/0.44 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.44 % SZS output start CNFRefutation for theBenchmark
% 0.12/0.44 fof(f1,axiom,(
% 0.12/0.44 (! [B,C] :( (! [D] :( member(D,B)<=> member(D,C) ))=> B = C ) )),
% 0.12/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.44 fof(f2,axiom,(
% 0.12/0.44 (! [B,C,D] :( member(D,difference(B,C))<=> ( member(D,B)& ~ member(D,C) ) ) )),
% 0.12/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.44 fof(f3,axiom,(
% 0.12/0.44 (! [B] : ~ member(B,empty_set) )),
% 0.12/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.44 fof(f4,axiom,(
% 0.12/0.44 (! [B,C] :( subset(B,C)<=> (! [D] :( member(D,B)=> member(D,C) ) )) )),
% 0.12/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.44 fof(f8,axiom,(
% 0.12/0.44 (! [B] :( empty(B)<=> (! [C] : ~ member(C,B) )) )),
% 0.12/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.44 fof(f9,conjecture,(
% 0.12/0.44 (! [B,C] :( difference(B,C) = empty_set<=> subset(B,C) ) )),
% 0.12/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.44 fof(f10,negated_conjecture,(
% 0.12/0.44 ~((! [B,C] :( difference(B,C) = empty_set<=> subset(B,C) ) ))),
% 0.12/0.44 inference(negated_conjecture,[status(cth)],[f9])).
% 0.12/0.44 fof(f11,plain,(
% 0.12/0.44 ![B,C]: ((?[D]: (member(D,B)<~>member(D,C)))|B=C)),
% 0.12/0.44 inference(pre_NNF_transformation,[status(thm)],[f1])).
% 0.12/0.44 fof(f12,plain,(
% 0.12/0.44 ![B,C]: ((?[D]: ((member(D,B)|member(D,C))&(~member(D,B)|~member(D,C))))|B=C)),
% 0.12/0.44 inference(NNF_transformation,[status(thm)],[f11])).
% 0.12/0.44 fof(f13,plain,(
% 0.12/0.44 ![B,C]: (((member(sK0_skl(C,B),B)|member(sK0_skl(C,B),C))&(~member(sK0_skl(C,B),B)|~member(sK0_skl(C,B),C)))|B=C)),
% 0.12/0.44 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(D,sK0_skl(C,B))],[f12])).
% 0.12/0.44 fof(f14,plain,(
% 0.12/0.44 ![X0,X1]: (member(sK0_skl(X0,X1),X1)|member(sK0_skl(X0,X1),X0)|X1=X0)),
% 0.12/0.44 inference(cnf_transformation,[status(thm)],[f13])).
% 0.12/0.44 fof(f16,plain,(
% 0.12/0.44 ![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))))),
% 0.12/0.44 inference(NNF_transformation,[status(thm)],[f2])).
% 0.12/0.44 fof(f17,plain,(
% 0.12/0.44 (![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))))),
% 0.12/0.44 inference(miniscoping,[status(thm)],[f16])).
% 0.12/0.44 fof(f18,plain,(
% 0.12/0.44 ![X0,X1,X2]: (~member(X0,difference(X1,X2))|member(X0,X1))),
% 0.12/0.44 inference(cnf_transformation,[status(thm)],[f17])).
% 0.12/0.44 fof(f19,plain,(
% 0.12/0.44 ![X0,X1,X2]: (~member(X0,difference(X1,X2))|~member(X0,X2))),
% 0.12/0.44 inference(cnf_transformation,[status(thm)],[f17])).
% 0.12/0.44 fof(f20,plain,(
% 0.12/0.44 ![X0,X1,X2]: (member(X0,difference(X1,X2))|~member(X0,X1)|member(X0,X2))),
% 0.12/0.44 inference(cnf_transformation,[status(thm)],[f17])).
% 0.12/0.44 fof(f21,plain,(
% 0.12/0.44 ![X0]: (~member(X0,empty_set))),
% 0.12/0.44 inference(cnf_transformation,[status(thm)],[f3])).
% 0.12/0.44 fof(f22,plain,(
% 0.12/0.44 ![B,C]: (subset(B,C)<=>(![D]: (~member(D,B)|member(D,C))))),
% 0.12/0.44 inference(pre_NNF_transformation,[status(thm)],[f4])).
% 0.12/0.44 fof(f23,plain,(
% 0.12/0.44 ![B,C]: ((~subset(B,C)|(![D]: (~member(D,B)|member(D,C))))&(subset(B,C)|(?[D]: (member(D,B)&~member(D,C)))))),
% 0.12/0.44 inference(NNF_transformation,[status(thm)],[f22])).
% 0.12/0.44 fof(f24,plain,(
% 0.12/0.44 (![B,C]: (~subset(B,C)|(![D]: (~member(D,B)|member(D,C)))))&(![B,C]: (subset(B,C)|(?[D]: (member(D,B)&~member(D,C)))))),
% 0.12/0.44 inference(miniscoping,[status(thm)],[f23])).
% 0.12/0.44 fof(f25,plain,(
% 0.12/0.44 (![B,C]: (~subset(B,C)|(![D]: (~member(D,B)|member(D,C)))))&(![B,C]: (subset(B,C)|(member(sK1_skl(C,B),B)&~member(sK1_skl(C,B),C))))),
% 0.12/0.44 inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(D,sK1_skl(C,B))],[f24])).
% 0.12/0.44 fof(f26,plain,(
% 0.12/0.44 ![X0,X1,X2]: (~subset(X0,X1)|~member(X2,X0)|member(X2,X1))),
% 0.12/0.44 inference(cnf_transformation,[status(thm)],[f25])).
% 0.12/0.44 fof(f27,plain,(
% 0.12/0.44 ![X0,X1]: (subset(X0,X1)|member(sK1_skl(X1,X0),X0))),
% 0.12/0.44 inference(cnf_transformation,[status(thm)],[f25])).
% 0.12/0.44 fof(f28,plain,(
% 0.12/0.44 ![X0,X1]: (subset(X0,X1)|~member(sK1_skl(X1,X0),X1))),
% 0.12/0.44 inference(cnf_transformation,[status(thm)],[f25])).
% 0.12/0.44 fof(f42,plain,(
% 0.12/0.44 ![B]: ((~empty(B)|(![C]: ~member(C,B)))&(empty(B)|(?[C]: member(C,B))))),
% 0.12/0.44 inference(NNF_transformation,[status(thm)],[f8])).
% 0.12/0.44 fof(f43,plain,(
% 0.12/0.44 (![B]: (~empty(B)|(![C]: ~member(C,B))))&(![B]: (empty(B)|(?[C]: member(C,B))))),
% 0.12/0.44 inference(miniscoping,[status(thm)],[f42])).
% 0.12/0.44 fof(f44,plain,(
% 0.12/0.44 (![B]: (~empty(B)|(![C]: ~member(C,B))))&(![B]: (empty(B)|member(sK3_skl(B),B)))),
% 0.12/0.44 inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl]),skolemize(C,sK3_skl(B))],[f43])).
% 0.12/0.44 fof(f45,plain,(
% 0.12/0.44 ![X0,X1]: (~empty(X0)|~member(X1,X0))),
% 0.12/0.44 inference(cnf_transformation,[status(thm)],[f44])).
% 0.12/0.44 fof(f46,plain,(
% 0.12/0.44 ![X0]: (empty(X0)|member(sK3_skl(X0),X0))),
% 0.12/0.44 inference(cnf_transformation,[status(thm)],[f44])).
% 0.12/0.44 fof(f47,plain,(
% 0.12/0.44 (?[B,C]: (difference(B,C)=empty_set<~>subset(B,C)))),
% 0.12/0.44 inference(pre_NNF_transformation,[status(thm)],[f10])).
% 0.12/0.44 fof(f48,plain,(
% 0.12/0.44 ?[B,C]: ((difference(B,C)=empty_set|subset(B,C))&(~difference(B,C)=empty_set|~subset(B,C)))),
% 0.12/0.44 inference(NNF_transformation,[status(thm)],[f47])).
% 0.12/0.44 fof(f49,plain,(
% 0.12/0.44 ((difference(sK4_skl,sK5_skl)=empty_set|subset(sK4_skl,sK5_skl))&(~difference(sK4_skl,sK5_skl)=empty_set|~subset(sK4_skl,sK5_skl)))),
% 0.12/0.44 inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl,sK5_skl]),skolemize(B,sK4_skl),skolemize(C,sK5_skl)],[f48])).
% 0.12/0.44 fof(f50,plain,(
% 0.12/0.44 difference(sK4_skl,sK5_skl)=empty_set|subset(sK4_skl,sK5_skl)),
% 0.12/0.44 inference(cnf_transformation,[status(thm)],[f49])).
% 0.12/0.44 fof(f51,plain,(
% 0.12/0.44 ~difference(sK4_skl,sK5_skl)=empty_set|~subset(sK4_skl,sK5_skl)),
% 0.12/0.44 inference(cnf_transformation,[status(thm)],[f49])).
% 0.12/0.44 fof(f54,plain,(
% 0.12/0.44 ![X0]: (~member(X0,sK4_skl)|member(X0,sK5_skl)|difference(sK4_skl,sK5_skl)=empty_set)),
% 0.12/0.44 inference(resolution,[status(thm)],[f26,f50])).
% 0.12/0.44 fof(f57,plain,(
% 0.12/0.44 ![X0,X1]: (empty(difference(X0,X1))|~member(sK3_skl(difference(X0,X1)),X1))),
% 0.12/0.44 inference(resolution,[status(thm)],[f46,f19])).
% 0.12/0.44 fof(f58,plain,(
% 0.12/0.44 ![X0,X1]: (empty(difference(X0,X1))|member(sK3_skl(difference(X0,X1)),X0))),
% 0.12/0.44 inference(resolution,[status(thm)],[f46,f18])).
% 0.12/0.44 fof(f62,plain,(
% 0.12/0.44 ![X0]: (member(sK0_skl(X0,empty_set),X0)|empty_set=X0)),
% 0.12/0.44 inference(resolution,[status(thm)],[f14,f21])).
% 0.12/0.44 fof(f84,plain,(
% 0.12/0.44 ![X0,X1,X2]: (subset(X0,X1)|member(sK1_skl(X1,X0),difference(X0,X2))|member(sK1_skl(X1,X0),X2))),
% 0.12/0.44 inference(resolution,[status(thm)],[f27,f20])).
% 0.12/0.44 fof(f102,plain,(
% 0.12/0.44 ![X0]: (empty(difference(sK4_skl,X0))|member(sK3_skl(difference(sK4_skl,X0)),sK5_skl)|difference(sK4_skl,sK5_skl)=empty_set)),
% 0.12/0.44 inference(resolution,[status(thm)],[f58,f54])).
% 0.12/0.44 fof(f118,plain,(
% 0.12/0.44 ![X0]: (empty_set=X0|~empty(X0))),
% 0.12/0.44 inference(resolution,[status(thm)],[f62,f45])).
% 0.12/0.44 fof(f469,plain,(
% 0.12/0.44 empty(difference(sK4_skl,sK5_skl))|difference(sK4_skl,sK5_skl)=empty_set|empty(difference(sK4_skl,sK5_skl))),
% 0.12/0.44 inference(resolution,[status(thm)],[f102,f57])).
% 0.12/0.44 fof(f473,plain,(
% 0.12/0.44 empty(difference(sK4_skl,sK5_skl))|difference(sK4_skl,sK5_skl)=empty_set),
% 0.12/0.44 inference(duplicate_literals_removal,[status(thm)],[f469])).
% 0.12/0.44 fof(f474,plain,(
% 0.12/0.44 difference(sK4_skl,sK5_skl)=empty_set),
% 0.12/0.44 inference(forward_subsumption_resolution,[status(thm)],[f473,f118])).
% 0.12/0.44 fof(f582,plain,(
% 0.12/0.44 ~empty_set=empty_set|~subset(sK4_skl,sK5_skl)),
% 0.12/0.44 inference(backward_demodulation,[status(thm)],[f474,f51])).
% 0.12/0.44 fof(f592,plain,(
% 0.12/0.44 ![X0]: (subset(sK4_skl,X0)|member(sK1_skl(X0,sK4_skl),empty_set)|member(sK1_skl(X0,sK4_skl),sK5_skl))),
% 0.12/0.44 inference(paramodulation,[status(thm)],[f474,f84])).
% 0.12/0.44 fof(f608,plain,(
% 0.12/0.44 ~subset(sK4_skl,sK5_skl)),
% 0.12/0.44 inference(trivial_equality_resolution,[status(thm)],[f582])).
% 0.12/0.44 fof(f622,plain,(
% 0.12/0.44 ![X0]: (subset(sK4_skl,X0)|member(sK1_skl(X0,sK4_skl),sK5_skl))),
% 0.12/0.44 inference(forward_subsumption_resolution,[status(thm)],[f592,f21])).
% 0.12/0.44 fof(f897,plain,(
% 0.12/0.44 subset(sK4_skl,sK5_skl)|subset(sK4_skl,sK5_skl)),
% 0.12/0.44 inference(resolution,[status(thm)],[f622,f28])).
% 0.12/0.44 fof(f900,plain,(
% 0.12/0.44 subset(sK4_skl,sK5_skl)),
% 0.12/0.44 inference(duplicate_literals_removal,[status(thm)],[f897])).
% 0.12/0.44 fof(f901,plain,(
% 0.12/0.44 $false),
% 0.12/0.44 inference(forward_subsumption_resolution,[status(thm)],[f900,f608])).
% 0.12/0.44 % SZS output end CNFRefutation for theBenchmark.p
% 0.12/0.47 % Elapsed time: 0.081910 seconds
% 0.12/0.47 % CPU time: 0.371126 seconds
% 0.12/0.47 % Total memory used: 85.563 MB
% 0.12/0.47 % Net memory used: 84.618 MB
%------------------------------------------------------------------------------