%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SET637+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 : 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 02:12:22 PM UTC 2026
% Result : Theorem 0.11s 0.48s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET637+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
% 0.08/0.34 % Computer : n004.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Mon Sep 21 05:30:49 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.08/0.35 % Drodi V4.1.1
% 0.11/0.48 % Refutation found
% 0.11/0.48 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.48 % SZS output start CNFRefutation for theBenchmark
% 0.11/0.48 fof(f1,axiom,(
% 0.11/0.48 (! [B,C,D] :( member(D,intersection(B,C))<=> ( member(D,B)& member(D,C) ) ) )),
% 0.11/0.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.11/0.48 fof(f2,axiom,(
% 0.11/0.48 (! [B,C] :( intersect(B,C)<=> (? [D] :( member(D,B)& member(D,C) ) )) )),
% 0.11/0.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.11/0.48 fof(f3,axiom,(
% 0.11/0.48 (! [B] : ~ member(B,empty_set) )),
% 0.11/0.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.11/0.48 fof(f4,axiom,(
% 0.11/0.48 (! [B,C] :( B = C<=> (! [D] :( member(D,B)<=> member(D,C) ) )) )),
% 0.11/0.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.11/0.48 fof(f5,axiom,(
% 0.11/0.48 (! [B,C] :( not_equal(B,C)<=> B != C ) )),
% 0.11/0.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.11/0.48 fof(f7,axiom,(
% 0.11/0.48 (! [B,C] :( intersect(B,C)=> intersect(C,B) ) )),
% 0.11/0.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.11/0.48 fof(f8,axiom,(
% 0.11/0.48 (! [B] :( empty(B)<=> (! [C] : ~ member(C,B) )) )),
% 0.11/0.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.11/0.48 fof(f9,conjecture,(
% 0.11/0.48 (! [B,C] :( intersect(B,C)<=> not_equal(intersection(B,C),empty_set) ) )),
% 0.11/0.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.11/0.48 fof(f10,negated_conjecture,(
% 0.11/0.48 ~((! [B,C] :( intersect(B,C)<=> not_equal(intersection(B,C),empty_set) ) ))),
% 0.11/0.48 inference(negated_conjecture,[status(cth)],[f9])).
% 0.11/0.48 fof(f11,plain,(
% 0.11/0.48 ![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))))),
% 0.11/0.48 inference(NNF_transformation,[status(thm)],[f1])).
% 0.11/0.48 fof(f12,plain,(
% 0.11/0.48 (![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))))),
% 0.11/0.48 inference(miniscoping,[status(thm)],[f11])).
% 0.11/0.48 fof(f13,plain,(
% 0.11/0.48 ![X0,X1,X2]: (~member(X0,intersection(X1,X2))|member(X0,X1))),
% 0.11/0.48 inference(cnf_transformation,[status(thm)],[f12])).
% 0.11/0.48 fof(f14,plain,(
% 0.11/0.48 ![X0,X1,X2]: (~member(X0,intersection(X1,X2))|member(X0,X2))),
% 0.11/0.48 inference(cnf_transformation,[status(thm)],[f12])).
% 0.11/0.48 fof(f15,plain,(
% 0.11/0.48 ![X0,X1,X2]: (member(X0,intersection(X1,X2))|~member(X0,X1)|~member(X0,X2))),
% 0.11/0.48 inference(cnf_transformation,[status(thm)],[f12])).
% 0.11/0.48 fof(f16,plain,(
% 0.11/0.48 ![B,C]: ((~intersect(B,C)|(?[D]: (member(D,B)&member(D,C))))&(intersect(B,C)|(![D]: (~member(D,B)|~member(D,C)))))),
% 0.11/0.48 inference(NNF_transformation,[status(thm)],[f2])).
% 0.11/0.48 fof(f17,plain,(
% 0.11/0.48 (![B,C]: (~intersect(B,C)|(?[D]: (member(D,B)&member(D,C)))))&(![B,C]: (intersect(B,C)|(![D]: (~member(D,B)|~member(D,C)))))),
% 0.11/0.48 inference(miniscoping,[status(thm)],[f16])).
% 0.11/0.48 fof(f18,plain,(
% 0.11/0.48 (![B,C]: (~intersect(B,C)|(member(sK0_skl(C,B),B)&member(sK0_skl(C,B),C))))&(![B,C]: (intersect(B,C)|(![D]: (~member(D,B)|~member(D,C)))))),
% 0.11/0.48 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(D,sK0_skl(C,B))],[f17])).
% 0.11/0.48 fof(f19,plain,(
% 0.11/0.48 ![X0,X1]: (~intersect(X0,X1)|member(sK0_skl(X1,X0),X0))),
% 0.11/0.48 inference(cnf_transformation,[status(thm)],[f18])).
% 0.11/0.48 fof(f20,plain,(
% 0.11/0.48 ![X0,X1]: (~intersect(X0,X1)|member(sK0_skl(X1,X0),X1))),
% 0.11/0.48 inference(cnf_transformation,[status(thm)],[f18])).
% 0.11/0.48 fof(f21,plain,(
% 0.11/0.48 ![X0,X1,X2]: (intersect(X0,X1)|~member(X2,X0)|~member(X2,X1))),
% 0.11/0.48 inference(cnf_transformation,[status(thm)],[f18])).
% 0.11/0.48 fof(f22,plain,(
% 0.11/0.48 ![X0]: (~member(X0,empty_set))),
% 0.11/0.48 inference(cnf_transformation,[status(thm)],[f3])).
% 0.11/0.48 fof(f23,plain,(
% 0.11/0.48 ![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))))))),
% 0.11/0.48 inference(NNF_transformation,[status(thm)],[f4])).
% 0.11/0.48 fof(f24,plain,(
% 0.11/0.48 (![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))))))),
% 0.11/0.48 inference(miniscoping,[status(thm)],[f23])).
% 0.11/0.48 fof(f25,plain,(
% 0.11/0.48 (![B,C]: (~B=C|((![D]: (~member(D,B)|member(D,C)))&(![D]: (member(D,B)|~member(D,C))))))&(![B,C]: (B=C|((~member(sK1_skl(C,B),B)|~member(sK1_skl(C,B),C))&(member(sK1_skl(C,B),B)|member(sK1_skl(C,B),C)))))),
% 0.11/0.48 inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(D,sK1_skl(C,B))],[f24])).
% 0.11/0.48 fof(f29,plain,(
% 0.11/0.48 ![X0,X1]: (X0=X1|member(sK1_skl(X1,X0),X0)|member(sK1_skl(X1,X0),X1))),
% 0.11/0.48 inference(cnf_transformation,[status(thm)],[f25])).
% 0.11/0.48 fof(f30,plain,(
% 0.11/0.48 ![B,C]: ((~not_equal(B,C)|~B=C)&(not_equal(B,C)|B=C))),
% 0.11/0.48 inference(NNF_transformation,[status(thm)],[f5])).
% 0.11/0.48 fof(f31,plain,(
% 0.11/0.48 (![B,C]: (~not_equal(B,C)|~B=C))&(![B,C]: (not_equal(B,C)|B=C))),
% 0.11/0.48 inference(miniscoping,[status(thm)],[f30])).
% 0.11/0.48 fof(f32,plain,(
% 0.11/0.48 ![X0,X1]: (~not_equal(X0,X1)|~X0=X1)),
% 0.11/0.48 inference(cnf_transformation,[status(thm)],[f31])).
% 0.11/0.48 fof(f33,plain,(
% 0.11/0.48 ![X0,X1]: (not_equal(X0,X1)|X0=X1)),
% 0.11/0.48 inference(cnf_transformation,[status(thm)],[f31])).
% 0.11/0.48 fof(f35,plain,(
% 0.11/0.48 ![B,C]: (~intersect(B,C)|intersect(C,B))),
% 0.11/0.48 inference(pre_NNF_transformation,[status(thm)],[f7])).
% 0.11/0.48 fof(f36,plain,(
% 0.11/0.48 ![X0,X1]: (~intersect(X0,X1)|intersect(X1,X0))),
% 0.11/0.48 inference(cnf_transformation,[status(thm)],[f35])).
% 0.11/0.48 fof(f37,plain,(
% 0.11/0.48 ![B]: ((~empty(B)|(![C]: ~member(C,B)))&(empty(B)|(?[C]: member(C,B))))),
% 0.11/0.48 inference(NNF_transformation,[status(thm)],[f8])).
% 0.11/0.48 fof(f38,plain,(
% 0.11/0.48 (![B]: (~empty(B)|(![C]: ~member(C,B))))&(![B]: (empty(B)|(?[C]: member(C,B))))),
% 0.11/0.48 inference(miniscoping,[status(thm)],[f37])).
% 0.11/0.48 fof(f39,plain,(
% 0.11/0.48 (![B]: (~empty(B)|(![C]: ~member(C,B))))&(![B]: (empty(B)|member(sK2_skl(B),B)))),
% 0.11/0.48 inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(C,sK2_skl(B))],[f38])).
% 0.11/0.48 fof(f40,plain,(
% 0.11/0.48 ![X0,X1]: (~empty(X0)|~member(X1,X0))),
% 0.11/0.48 inference(cnf_transformation,[status(thm)],[f39])).
% 0.11/0.48 fof(f41,plain,(
% 0.11/0.48 ![X0]: (empty(X0)|member(sK2_skl(X0),X0))),
% 0.11/0.48 inference(cnf_transformation,[status(thm)],[f39])).
% 0.11/0.48 fof(f42,plain,(
% 0.11/0.48 (?[B,C]: (intersect(B,C)<~>not_equal(intersection(B,C),empty_set)))),
% 0.11/0.48 inference(pre_NNF_transformation,[status(thm)],[f10])).
% 0.11/0.48 fof(f43,plain,(
% 0.11/0.48 ?[B,C]: ((intersect(B,C)|not_equal(intersection(B,C),empty_set))&(~intersect(B,C)|~not_equal(intersection(B,C),empty_set)))),
% 0.11/0.48 inference(NNF_transformation,[status(thm)],[f42])).
% 0.11/0.48 fof(f44,plain,(
% 0.11/0.48 ((intersect(sK3_skl,sK4_skl)|not_equal(intersection(sK3_skl,sK4_skl),empty_set))&(~intersect(sK3_skl,sK4_skl)|~not_equal(intersection(sK3_skl,sK4_skl),empty_set)))),
% 0.11/0.48 inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl,sK4_skl]),skolemize(B,sK3_skl),skolemize(C,sK4_skl)],[f43])).
% 0.11/0.48 fof(f45,plain,(
% 0.11/0.48 intersect(sK3_skl,sK4_skl)|not_equal(intersection(sK3_skl,sK4_skl),empty_set)),
% 0.11/0.48 inference(cnf_transformation,[status(thm)],[f44])).
% 0.11/0.48 fof(f46,plain,(
% 0.11/0.48 ~intersect(sK3_skl,sK4_skl)|~not_equal(intersection(sK3_skl,sK4_skl),empty_set)),
% 0.11/0.48 inference(cnf_transformation,[status(thm)],[f44])).
% 0.11/0.48 fof(f47,plain,(
% 0.11/0.48 ![X0]: (~not_equal(X0,X0))),
% 0.11/0.48 inference(destructive_equality_resolution,[status(thm)],[f32])).
% 0.11/0.48 fof(f58,plain,(
% 0.11/0.48 ![X0,X1]: (empty(intersection(X0,X1))|member(sK2_skl(intersection(X0,X1)),X1))),
% 0.11/0.48 inference(resolution,[status(thm)],[f41,f14])).
% 0.11/0.48 fof(f59,plain,(
% 0.11/0.48 ![X0,X1]: (empty(intersection(X0,X1))|member(sK2_skl(intersection(X0,X1)),X0))),
% 0.11/0.48 inference(resolution,[status(thm)],[f41,f13])).
% 0.11/0.48 fof(f66,plain,(
% 0.11/0.48 ![X0]: (empty_set=X0|member(sK1_skl(X0,empty_set),X0))),
% 0.11/0.48 inference(resolution,[status(thm)],[f29,f22])).
% 0.11/0.48 fof(f80,plain,(
% 0.11/0.48 ![X0,X1,X2]: (X0=X1|member(sK1_skl(X1,X0),X0)|member(sK1_skl(X1,X0),intersection(X2,X1))|~member(sK1_skl(X1,X0),X2))),
% 0.11/0.48 inference(resolution,[status(thm)],[f29,f15])).
% 0.11/0.48 fof(f86,plain,(
% 0.11/0.48 ![X0,X1]: (empty_set=X0|intersect(X1,X0)|~member(sK1_skl(X0,empty_set),X1))),
% 0.11/0.48 inference(resolution,[status(thm)],[f66,f21])).
% 0.11/0.48 fof(f98,plain,(
% 0.11/0.48 ![X0,X1,X2]: (empty(intersection(X0,X1))|intersect(X2,X1)|~member(sK2_skl(intersection(X0,X1)),X2))),
% 0.11/0.48 inference(resolution,[status(thm)],[f58,f21])).
% 0.11/0.48 fof(f512,plain,(
% 0.11/0.48 ![X0]: (empty_set=X0|member(sK1_skl(X0,empty_set),empty_set)|member(sK1_skl(X0,empty_set),intersection(X0,X0))|empty_set=X0)),
% 0.11/0.48 inference(resolution,[status(thm)],[f80,f66])).
% 0.11/0.48 fof(f541,plain,(
% 0.11/0.48 ![X0]: (empty_set=X0|member(sK1_skl(X0,empty_set),empty_set)|member(sK1_skl(X0,empty_set),intersection(X0,X0)))),
% 0.11/0.48 inference(duplicate_literals_removal,[status(thm)],[f512])).
% 0.11/0.48 fof(f542,plain,(
% 0.11/0.48 ![X0]: (empty_set=X0|member(sK1_skl(X0,empty_set),intersection(X0,X0)))),
% 0.11/0.48 inference(forward_subsumption_resolution,[status(thm)],[f541,f22])).
% 0.11/0.48 fof(f612,plain,(
% 0.11/0.48 ![X0]: (empty_set=X0|intersect(intersection(X0,X0),X0)|empty_set=X0)),
% 0.11/0.48 inference(resolution,[status(thm)],[f86,f542])).
% 0.11/0.48 fof(f626,plain,(
% 0.11/0.48 ![X0]: (empty_set=X0|intersect(intersection(X0,X0),X0))),
% 0.11/0.48 inference(duplicate_literals_removal,[status(thm)],[f612])).
% 0.11/0.48 fof(f637,plain,(
% 0.11/0.48 ![X0]: (empty_set=X0|intersect(X0,intersection(X0,X0)))),
% 0.11/0.48 inference(resolution,[status(thm)],[f626,f36])).
% 0.11/0.48 fof(f678,plain,(
% 0.11/0.48 ![X0]: (empty_set=X0|member(sK0_skl(intersection(X0,X0),X0),X0))),
% 0.11/0.48 inference(resolution,[status(thm)],[f637,f19])).
% 0.11/0.48 fof(f872,plain,(
% 0.11/0.48 ![X0,X1]: (empty(intersection(X0,X1))|intersect(X0,X1)|empty(intersection(X0,X1)))),
% 0.11/0.48 inference(resolution,[status(thm)],[f98,f59])).
% 0.11/0.48 fof(f882,plain,(
% 0.11/0.48 ![X0,X1]: (empty(intersection(X0,X1))|intersect(X0,X1))),
% 0.11/0.48 inference(duplicate_literals_removal,[status(thm)],[f872])).
% 0.11/0.48 fof(f888,plain,(
% 0.11/0.48 ![X0,X1,X2]: (intersect(X0,X1)|~member(X2,intersection(X0,X1)))),
% 0.11/0.48 inference(resolution,[status(thm)],[f882,f40])).
% 0.11/0.48 fof(f914,plain,(
% 0.11/0.48 ![X0,X1]: (intersect(X0,X1)|empty_set=intersection(X0,X1))),
% 0.11/0.48 inference(resolution,[status(thm)],[f888,f678])).
% 0.11/0.48 fof(f962,plain,(
% 0.11/0.48 empty_set=intersection(sK3_skl,sK4_skl)|~not_equal(intersection(sK3_skl,sK4_skl),empty_set)),
% 0.11/0.48 inference(resolution,[status(thm)],[f914,f46])).
% 0.11/0.48 fof(f967,plain,(
% 0.11/0.48 intersect(sK3_skl,sK4_skl)|not_equal(empty_set,empty_set)),
% 0.11/0.48 inference(backward_demodulation,[status(thm)],[f968,f45])).
% 0.11/0.48 fof(f968,plain,(
% 0.11/0.48 empty_set=intersection(sK3_skl,sK4_skl)),
% 0.11/0.48 inference(forward_subsumption_resolution,[status(thm)],[f962,f33])).
% 0.11/0.48 fof(f969,plain,(
% 0.11/0.48 intersect(sK3_skl,sK4_skl)),
% 0.11/0.48 inference(forward_subsumption_resolution,[status(thm)],[f967,f47])).
% 0.11/0.48 fof(f970,plain,(
% 0.11/0.48 member(sK0_skl(sK4_skl,sK3_skl),sK4_skl)),
% 0.11/0.48 inference(resolution,[status(thm)],[f969,f20])).
% 0.11/0.48 fof(f971,plain,(
% 0.11/0.48 member(sK0_skl(sK4_skl,sK3_skl),sK3_skl)),
% 0.11/0.48 inference(resolution,[status(thm)],[f969,f19])).
% 0.11/0.48 fof(f974,plain,(
% 0.11/0.48 ![X0]: (member(sK0_skl(sK4_skl,sK3_skl),intersection(X0,sK4_skl))|~member(sK0_skl(sK4_skl,sK3_skl),X0))),
% 0.11/0.48 inference(resolution,[status(thm)],[f970,f15])).
% 0.11/0.48 fof(f1299,plain,(
% 0.11/0.48 member(sK0_skl(sK4_skl,sK3_skl),intersection(sK3_skl,sK4_skl))),
% 0.11/0.48 inference(resolution,[status(thm)],[f974,f971])).
% 0.11/0.48 fof(f1301,plain,(
% 0.11/0.48 member(sK0_skl(sK4_skl,sK3_skl),empty_set)),
% 0.11/0.48 inference(forward_demodulation,[status(thm)],[f968,f1299])).
% 0.11/0.48 fof(f1302,plain,(
% 0.11/0.48 $false),
% 0.11/0.48 inference(forward_subsumption_resolution,[status(thm)],[f1301,f22])).
% 0.11/0.48 % SZS output end CNFRefutation for theBenchmark.p
% 0.11/0.49 % Elapsed time: 0.139147 seconds
% 0.11/0.49 % CPU time: 0.947690 seconds
% 0.11/0.49 % Total memory used: 115.724 MB
% 0.11/0.49 % Net memory used: 113.361 MB
%------------------------------------------------------------------------------