%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SET611+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 : n019.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 02:12:18 PM UTC 2026
% Result : Theorem 3.21s 0.88s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET611+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
% 0.09/0.34 % Computer : n019.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 05:29:05 UTC 2026
% 0.09/0.34 % CPUTime :
% 0.09/0.36 % Drodi V4.1.1
% 3.21/0.88 % Refutation found
% 3.21/0.88 % SZS status Theorem for theBenchmark: Theorem is valid
% 3.21/0.88 % SZS output start CNFRefutation for theBenchmark
% 3.21/0.88 fof(f1,axiom,(
% 3.21/0.88 (! [B,C] :( (! [D] :( member(D,B)<=> member(D,C) ))=> B = C ) )),
% 3.21/0.88 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 3.21/0.88 fof(f2,axiom,(
% 3.21/0.88 (! [B,C,D] :( member(D,intersection(B,C))<=> ( member(D,B)& member(D,C) ) ) )),
% 3.21/0.88 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 3.21/0.88 fof(f3,axiom,(
% 3.21/0.88 (! [B,C,D] :( member(D,difference(B,C))<=> ( member(D,B)& ~ member(D,C) ) ) )),
% 3.21/0.88 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 3.21/0.88 fof(f4,axiom,(
% 3.21/0.88 (! [B] : ~ member(B,empty_set) )),
% 3.21/0.88 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 3.21/0.88 fof(f6,axiom,(
% 3.21/0.88 (! [B,C] : intersection(B,C) = intersection(C,B) )),
% 3.21/0.88 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 3.21/0.88 fof(f10,axiom,(
% 3.21/0.88 (! [B] :( empty(B)<=> (! [C] : ~ member(C,B) )) )),
% 3.21/0.88 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 3.21/0.88 fof(f11,conjecture,(
% 3.21/0.88 (! [B,C] :( intersection(B,C) = empty_set<=> difference(B,C) = B ) )),
% 3.21/0.88 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 3.21/0.88 fof(f12,negated_conjecture,(
% 3.21/0.88 ~((! [B,C] :( intersection(B,C) = empty_set<=> difference(B,C) = B ) ))),
% 3.21/0.88 inference(negated_conjecture,[status(cth)],[f11])).
% 3.21/0.88 fof(f13,plain,(
% 3.21/0.88 ![B,C]: ((?[D]: (member(D,B)<~>member(D,C)))|B=C)),
% 3.21/0.88 inference(pre_NNF_transformation,[status(thm)],[f1])).
% 3.21/0.88 fof(f14,plain,(
% 3.21/0.88 ![B,C]: ((?[D]: ((member(D,B)|member(D,C))&(~member(D,B)|~member(D,C))))|B=C)),
% 3.21/0.88 inference(NNF_transformation,[status(thm)],[f13])).
% 3.21/0.88 fof(f15,plain,(
% 3.21/0.88 ![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)),
% 3.21/0.88 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(D,sK0_skl(C,B))],[f14])).
% 3.21/0.88 fof(f16,plain,(
% 3.21/0.88 ![X0,X1]: (member(sK0_skl(X0,X1),X1)|member(sK0_skl(X0,X1),X0)|X1=X0)),
% 3.21/0.88 inference(cnf_transformation,[status(thm)],[f15])).
% 3.21/0.88 fof(f17,plain,(
% 3.21/0.88 ![X0,X1]: (~member(sK0_skl(X0,X1),X1)|~member(sK0_skl(X0,X1),X0)|X1=X0)),
% 3.21/0.88 inference(cnf_transformation,[status(thm)],[f15])).
% 3.21/0.88 fof(f18,plain,(
% 3.21/0.88 ![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))))),
% 3.21/0.88 inference(NNF_transformation,[status(thm)],[f2])).
% 3.21/0.88 fof(f19,plain,(
% 3.21/0.88 (![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))))),
% 3.21/0.88 inference(miniscoping,[status(thm)],[f18])).
% 3.21/0.88 fof(f21,plain,(
% 3.21/0.88 ![X0,X1,X2]: (~member(X0,intersection(X1,X2))|member(X0,X2))),
% 3.21/0.88 inference(cnf_transformation,[status(thm)],[f19])).
% 3.21/0.88 fof(f22,plain,(
% 3.21/0.88 ![X0,X1,X2]: (member(X0,intersection(X1,X2))|~member(X0,X1)|~member(X0,X2))),
% 3.21/0.88 inference(cnf_transformation,[status(thm)],[f19])).
% 3.21/0.88 fof(f23,plain,(
% 3.21/0.88 ![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))))),
% 3.21/0.88 inference(NNF_transformation,[status(thm)],[f3])).
% 3.21/0.88 fof(f24,plain,(
% 3.21/0.88 (![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))))),
% 3.21/0.88 inference(miniscoping,[status(thm)],[f23])).
% 3.21/0.88 fof(f25,plain,(
% 3.21/0.88 ![X0,X1,X2]: (~member(X0,difference(X1,X2))|member(X0,X1))),
% 3.21/0.88 inference(cnf_transformation,[status(thm)],[f24])).
% 3.21/0.88 fof(f26,plain,(
% 3.21/0.88 ![X0,X1,X2]: (~member(X0,difference(X1,X2))|~member(X0,X2))),
% 3.21/0.88 inference(cnf_transformation,[status(thm)],[f24])).
% 3.21/0.88 fof(f27,plain,(
% 3.21/0.88 ![X0,X1,X2]: (member(X0,difference(X1,X2))|~member(X0,X1)|member(X0,X2))),
% 3.21/0.88 inference(cnf_transformation,[status(thm)],[f24])).
% 3.21/0.88 fof(f28,plain,(
% 3.21/0.88 ![X0]: (~member(X0,empty_set))),
% 3.21/0.88 inference(cnf_transformation,[status(thm)],[f4])).
% 3.21/0.88 fof(f34,plain,(
% 3.21/0.88 ![X0,X1]: (intersection(X0,X1)=intersection(X1,X0))),
% 3.21/0.88 inference(cnf_transformation,[status(thm)],[f6])).
% 3.21/0.88 fof(f50,plain,(
% 3.21/0.88 ![B]: ((~empty(B)|(![C]: ~member(C,B)))&(empty(B)|(?[C]: member(C,B))))),
% 3.21/0.88 inference(NNF_transformation,[status(thm)],[f10])).
% 3.21/0.88 fof(f51,plain,(
% 3.21/0.88 (![B]: (~empty(B)|(![C]: ~member(C,B))))&(![B]: (empty(B)|(?[C]: member(C,B))))),
% 3.21/0.88 inference(miniscoping,[status(thm)],[f50])).
% 3.21/0.88 fof(f52,plain,(
% 3.21/0.88 (![B]: (~empty(B)|(![C]: ~member(C,B))))&(![B]: (empty(B)|member(sK3_skl(B),B)))),
% 3.21/0.88 inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl]),skolemize(C,sK3_skl(B))],[f51])).
% 3.21/0.88 fof(f53,plain,(
% 3.21/0.88 ![X0,X1]: (~empty(X0)|~member(X1,X0))),
% 3.21/0.88 inference(cnf_transformation,[status(thm)],[f52])).
% 3.21/0.88 fof(f54,plain,(
% 3.21/0.88 ![X0]: (empty(X0)|member(sK3_skl(X0),X0))),
% 3.21/0.88 inference(cnf_transformation,[status(thm)],[f52])).
% 3.21/0.88 fof(f55,plain,(
% 3.21/0.88 (?[B,C]: (intersection(B,C)=empty_set<~>difference(B,C)=B))),
% 3.21/0.88 inference(pre_NNF_transformation,[status(thm)],[f12])).
% 3.21/0.88 fof(f56,plain,(
% 3.21/0.88 ?[B,C]: ((intersection(B,C)=empty_set|difference(B,C)=B)&(~intersection(B,C)=empty_set|~difference(B,C)=B))),
% 3.21/0.88 inference(NNF_transformation,[status(thm)],[f55])).
% 3.21/0.88 fof(f57,plain,(
% 3.21/0.88 ((intersection(sK4_skl,sK5_skl)=empty_set|difference(sK4_skl,sK5_skl)=sK4_skl)&(~intersection(sK4_skl,sK5_skl)=empty_set|~difference(sK4_skl,sK5_skl)=sK4_skl))),
% 3.21/0.88 inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl,sK5_skl]),skolemize(B,sK4_skl),skolemize(C,sK5_skl)],[f56])).
% 3.21/0.88 fof(f58,plain,(
% 3.21/0.88 intersection(sK4_skl,sK5_skl)=empty_set|difference(sK4_skl,sK5_skl)=sK4_skl),
% 3.21/0.88 inference(cnf_transformation,[status(thm)],[f57])).
% 3.21/0.88 fof(f59,plain,(
% 3.21/0.88 ~intersection(sK4_skl,sK5_skl)=empty_set|~difference(sK4_skl,sK5_skl)=sK4_skl),
% 3.21/0.88 inference(cnf_transformation,[status(thm)],[f57])).
% 3.21/0.88 fof(f73,plain,(
% 3.21/0.88 ![X0]: (~member(X0,sK4_skl)|~member(X0,sK5_skl)|intersection(sK4_skl,sK5_skl)=empty_set)),
% 3.21/0.88 inference(paramodulation,[status(thm)],[f58,f26])).
% 3.21/0.88 fof(f77,plain,(
% 3.21/0.88 ![X0,X1]: (empty(intersection(X0,X1))|member(sK3_skl(intersection(X0,X1)),X1))),
% 3.21/0.88 inference(resolution,[status(thm)],[f54,f21])).
% 3.21/0.88 fof(f79,plain,(
% 3.21/0.88 empty(empty_set)),
% 3.21/0.88 inference(resolution,[status(thm)],[f54,f28])).
% 3.21/0.88 fof(f167,plain,(
% 3.21/0.88 ![X0]: (member(sK0_skl(X0,empty_set),X0)|empty_set=X0)),
% 3.21/0.88 inference(resolution,[status(thm)],[f16,f28])).
% 3.21/0.88 fof(f171,plain,(
% 3.21/0.88 ![X0,X1,X2]: (member(sK0_skl(X0,X1),X0)|X1=X0|member(sK0_skl(X0,X1),difference(X1,X2))|member(sK0_skl(X0,X1),X2))),
% 3.21/0.88 inference(resolution,[status(thm)],[f16,f27])).
% 3.21/0.88 fof(f173,plain,(
% 3.21/0.88 ![X0,X1,X2]: (member(sK0_skl(X0,X1),X0)|X1=X0|member(sK0_skl(X0,X1),intersection(X1,X2))|~member(sK0_skl(X0,X1),X2))),
% 3.21/0.88 inference(resolution,[status(thm)],[f16,f22])).
% 3.21/0.88 fof(f176,plain,(
% 3.21/0.88 ![X0,X1,X2]: (member(sK0_skl(difference(X0,X1),X2),X2)|X2=difference(X0,X1)|member(sK0_skl(difference(X0,X1),X2),X0))),
% 3.21/0.88 inference(resolution,[status(thm)],[f16,f25])).
% 3.21/0.88 fof(f203,plain,(
% 3.21/0.88 ![X0]: (empty_set=X0|~empty(X0))),
% 3.21/0.88 inference(resolution,[status(thm)],[f167,f53])).
% 3.21/0.88 fof(f228,plain,(
% 3.21/0.88 ![X0]: (empty(intersection(X0,sK5_skl))|~member(sK3_skl(intersection(X0,sK5_skl)),sK4_skl)|intersection(sK4_skl,sK5_skl)=empty_set)),
% 3.21/0.88 inference(resolution,[status(thm)],[f77,f73])).
% 3.21/0.88 fof(f237,plain,(
% 3.21/0.88 ![X0,X1]: (empty(intersection(X0,X1))|member(sK3_skl(intersection(X1,X0)),X1))),
% 3.21/0.88 inference(paramodulation,[status(thm)],[f34,f77])).
% 3.21/0.88 fof(f396,plain,(
% 3.21/0.88 empty(intersection(sK4_skl,sK5_skl))|intersection(sK4_skl,sK5_skl)=empty_set|empty(intersection(sK5_skl,sK4_skl))),
% 3.21/0.88 inference(resolution,[status(thm)],[f228,f237])).
% 3.21/0.88 fof(f401,plain,(
% 3.21/0.88 empty(intersection(sK4_skl,sK5_skl))|intersection(sK4_skl,sK5_skl)=empty_set|empty(intersection(sK4_skl,sK5_skl))),
% 3.21/0.88 inference(forward_demodulation,[status(thm)],[f34,f396])).
% 3.21/0.88 fof(f402,plain,(
% 3.21/0.88 empty(intersection(sK4_skl,sK5_skl))|intersection(sK4_skl,sK5_skl)=empty_set),
% 3.21/0.88 inference(duplicate_literals_removal,[status(thm)],[f401])).
% 3.21/0.88 fof(f403,plain,(
% 3.21/0.88 intersection(sK4_skl,sK5_skl)=empty_set),
% 3.21/0.88 inference(forward_subsumption_resolution,[status(thm)],[f402,f203])).
% 3.21/0.88 fof(f418,plain,(
% 3.21/0.88 ~empty_set=empty_set|~difference(sK4_skl,sK5_skl)=sK4_skl),
% 3.21/0.88 inference(backward_demodulation,[status(thm)],[f403,f59])).
% 3.21/0.88 fof(f426,plain,(
% 3.21/0.88 ~difference(sK4_skl,sK5_skl)=sK4_skl),
% 3.21/0.88 inference(trivial_equality_resolution,[status(thm)],[f418])).
% 3.21/0.88 fof(f1268,plain,(
% 3.21/0.88 ![X0,X1]: (X0=difference(X0,X1)|~member(sK0_skl(difference(X0,X1),X0),difference(X0,X1))|X0=difference(X0,X1))),
% 3.21/0.88 inference(resolution,[status(thm)],[f176,f17])).
% 3.21/0.88 fof(f1313,plain,(
% 3.21/0.88 ![X0,X1]: (X0=difference(X0,X1)|~member(sK0_skl(difference(X0,X1),X0),difference(X0,X1)))),
% 3.21/0.88 inference(duplicate_literals_removal,[status(thm)],[f1268])).
% 3.21/0.88 fof(f2415,plain,(
% 3.21/0.88 ![X0,X1]: (X0=difference(X0,X1)|X0=difference(X0,X1)|member(sK0_skl(difference(X0,X1),X0),X1))),
% 3.21/0.88 inference(resolution,[status(thm)],[f1313,f171])).
% 3.21/0.88 fof(f2431,plain,(
% 3.21/0.88 ![X0,X1]: (X0=difference(X0,X1)|member(sK0_skl(difference(X0,X1),X0),X1))),
% 3.21/0.88 inference(duplicate_literals_removal,[status(thm)],[f2415])).
% 3.21/0.88 fof(f2445,plain,(
% 3.21/0.88 ![X0,X1]: (X0=difference(X0,X1)|member(sK0_skl(difference(X0,X1),X0),difference(X0,X1))|X0=difference(X0,X1)|member(sK0_skl(difference(X0,X1),X0),intersection(X0,X1)))),
% 3.21/0.88 inference(resolution,[status(thm)],[f2431,f173])).
% 3.21/0.88 fof(f2462,plain,(
% 3.21/0.88 ![X0,X1]: (X0=difference(X0,X1)|member(sK0_skl(difference(X0,X1),X0),difference(X0,X1))|member(sK0_skl(difference(X0,X1),X0),intersection(X0,X1)))),
% 3.21/0.88 inference(duplicate_literals_removal,[status(thm)],[f2445])).
% 3.21/0.88 fof(f2463,plain,(
% 3.21/0.88 ![X0,X1]: (X0=difference(X0,X1)|member(sK0_skl(difference(X0,X1),X0),intersection(X0,X1)))),
% 3.21/0.88 inference(forward_subsumption_resolution,[status(thm)],[f2462,f1313])).
% 3.21/0.88 fof(f3044,plain,(
% 3.21/0.88 ![X0,X1]: (X0=difference(X0,X1)|~empty(intersection(X0,X1)))),
% 3.21/0.88 inference(resolution,[status(thm)],[f2463,f53])).
% 3.21/0.88 fof(f3066,plain,(
% 3.21/0.88 sK4_skl=difference(sK4_skl,sK5_skl)|~empty(empty_set)),
% 3.21/0.88 inference(paramodulation,[status(thm)],[f403,f3044])).
% 3.21/0.88 fof(f3072,plain,(
% 3.21/0.88 ~empty(empty_set)),
% 3.21/0.88 inference(forward_subsumption_resolution,[status(thm)],[f3066,f426])).
% 3.21/0.88 fof(f3074,plain,(
% 3.21/0.88 $false),
% 3.21/0.88 inference(forward_subsumption_resolution,[status(thm)],[f3072,f79])).
% 3.21/0.88 % SZS output end CNFRefutation for theBenchmark.p
% 3.21/0.90 % Elapsed time: 0.544120 seconds
% 3.21/0.90 % CPU time: 4.028456 seconds
% 3.21/0.90 % Total memory used: 152.609 MB
% 3.21/0.90 % Net memory used: 144.490 MB
%------------------------------------------------------------------------------