%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SET628+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 : n014.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 02:12:21 PM UTC 2026
% Result : Theorem 0.15s 5.41s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET628+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
% 0.09/5.38 % Computer : n014.cluster.edu
% 0.09/5.38 % Model : x86_64 x86_64
% 0.09/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.38 % Memory : 8046.5625MB
% 0.09/5.38 % OS : Linux 6.8.0-71-generic
% 0.09/5.38 % CPULimit : 300
% 0.09/5.38 % WCLimit : 300
% 0.09/5.38 % DateTime : Mon Sep 21 05:30:10 UTC 2026
% 0.09/5.38 % CPUTime :
% 0.09/5.39 % Drodi V4.1.1
% 0.15/5.41 % Refutation found
% 0.15/5.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/5.41 % SZS output start CNFRefutation for theBenchmark
% 0.15/5.41 fof(f1,axiom,(
% 0.15/5.41 (! [B,C] :( intersect(B,C)<=> (? [D] :( member(D,B)& member(D,C) ) )) )),
% 0.15/5.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/5.41 fof(f2,axiom,(
% 0.15/5.41 (! [B] : ~ member(B,empty_set) )),
% 0.15/5.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/5.41 fof(f3,axiom,(
% 0.15/5.41 (! [B,C] :( B = C<=> (! [D] :( member(D,B)<=> member(D,C) ) )) )),
% 0.15/5.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/5.41 fof(f4,axiom,(
% 0.15/5.41 (! [B,C] :( not_equal(B,C)<=> B != C ) )),
% 0.15/5.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/5.41 fof(f6,axiom,(
% 0.15/5.41 (! [B] :( empty(B)<=> (! [C] : ~ member(C,B) )) )),
% 0.15/5.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/5.41 fof(f7,conjecture,(
% 0.15/5.41 (! [B] :( intersect(B,B)<=> not_equal(B,empty_set) ) )),
% 0.15/5.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/5.41 fof(f8,negated_conjecture,(
% 0.15/5.41 ~((! [B] :( intersect(B,B)<=> not_equal(B,empty_set) ) ))),
% 0.15/5.41 inference(negated_conjecture,[status(cth)],[f7])).
% 0.15/5.41 fof(f9,plain,(
% 0.15/5.41 ![B,C]: ((~intersect(B,C)|(?[D]: (member(D,B)&member(D,C))))&(intersect(B,C)|(![D]: (~member(D,B)|~member(D,C)))))),
% 0.15/5.41 inference(NNF_transformation,[status(thm)],[f1])).
% 0.15/5.41 fof(f10,plain,(
% 0.15/5.41 (![B,C]: (~intersect(B,C)|(?[D]: (member(D,B)&member(D,C)))))&(![B,C]: (intersect(B,C)|(![D]: (~member(D,B)|~member(D,C)))))),
% 0.15/5.41 inference(miniscoping,[status(thm)],[f9])).
% 0.15/5.41 fof(f11,plain,(
% 0.15/5.41 (![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)))))),
% 0.15/5.41 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(D,sK0_skl(C,B))],[f10])).
% 0.15/5.41 fof(f13,plain,(
% 0.15/5.41 ![X0,X1]: (~intersect(X0,X1)|member(sK0_skl(X1,X0),X1))),
% 0.15/5.41 inference(cnf_transformation,[status(thm)],[f11])).
% 0.15/5.41 fof(f14,plain,(
% 0.15/5.41 ![X0,X1,X2]: (intersect(X0,X1)|~member(X2,X0)|~member(X2,X1))),
% 0.15/5.41 inference(cnf_transformation,[status(thm)],[f11])).
% 0.15/5.41 fof(f15,plain,(
% 0.15/5.41 ![X0]: (~member(X0,empty_set))),
% 0.15/5.41 inference(cnf_transformation,[status(thm)],[f2])).
% 0.15/5.41 fof(f16,plain,(
% 0.15/5.41 ![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))))))),
% 0.15/5.41 inference(NNF_transformation,[status(thm)],[f3])).
% 0.15/5.41 fof(f17,plain,(
% 0.15/5.41 (![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))))))),
% 0.15/5.41 inference(miniscoping,[status(thm)],[f16])).
% 0.15/5.41 fof(f18,plain,(
% 0.15/5.41 (![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)))))),
% 0.15/5.41 inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(D,sK1_skl(C,B))],[f17])).
% 0.15/5.41 fof(f22,plain,(
% 0.15/5.41 ![X0,X1]: (X0=X1|member(sK1_skl(X1,X0),X0)|member(sK1_skl(X1,X0),X1))),
% 0.15/5.41 inference(cnf_transformation,[status(thm)],[f18])).
% 0.15/5.41 fof(f23,plain,(
% 0.15/5.41 ![B,C]: ((~not_equal(B,C)|~B=C)&(not_equal(B,C)|B=C))),
% 0.15/5.41 inference(NNF_transformation,[status(thm)],[f4])).
% 0.15/5.41 fof(f24,plain,(
% 0.15/5.41 (![B,C]: (~not_equal(B,C)|~B=C))&(![B,C]: (not_equal(B,C)|B=C))),
% 0.15/5.41 inference(miniscoping,[status(thm)],[f23])).
% 0.15/5.41 fof(f25,plain,(
% 0.15/5.41 ![X0,X1]: (~not_equal(X0,X1)|~X0=X1)),
% 0.15/5.41 inference(cnf_transformation,[status(thm)],[f24])).
% 0.15/5.41 fof(f26,plain,(
% 0.15/5.41 ![X0,X1]: (not_equal(X0,X1)|X0=X1)),
% 0.15/5.41 inference(cnf_transformation,[status(thm)],[f24])).
% 0.15/5.41 fof(f29,plain,(
% 0.15/5.41 ![B]: ((~empty(B)|(![C]: ~member(C,B)))&(empty(B)|(?[C]: member(C,B))))),
% 0.15/5.41 inference(NNF_transformation,[status(thm)],[f6])).
% 0.15/5.41 fof(f30,plain,(
% 0.15/5.41 (![B]: (~empty(B)|(![C]: ~member(C,B))))&(![B]: (empty(B)|(?[C]: member(C,B))))),
% 0.15/5.41 inference(miniscoping,[status(thm)],[f29])).
% 0.15/5.41 fof(f31,plain,(
% 0.15/5.41 (![B]: (~empty(B)|(![C]: ~member(C,B))))&(![B]: (empty(B)|member(sK2_skl(B),B)))),
% 0.15/5.41 inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(C,sK2_skl(B))],[f30])).
% 0.15/5.41 fof(f32,plain,(
% 0.15/5.41 ![X0,X1]: (~empty(X0)|~member(X1,X0))),
% 0.15/5.41 inference(cnf_transformation,[status(thm)],[f31])).
% 0.15/5.41 fof(f33,plain,(
% 0.15/5.41 ![X0]: (empty(X0)|member(sK2_skl(X0),X0))),
% 0.15/5.41 inference(cnf_transformation,[status(thm)],[f31])).
% 0.15/5.41 fof(f34,plain,(
% 0.15/5.41 (?[B]: (intersect(B,B)<~>not_equal(B,empty_set)))),
% 0.15/5.41 inference(pre_NNF_transformation,[status(thm)],[f8])).
% 0.15/5.41 fof(f35,plain,(
% 0.15/5.41 ?[B]: ((intersect(B,B)|not_equal(B,empty_set))&(~intersect(B,B)|~not_equal(B,empty_set)))),
% 0.15/5.41 inference(NNF_transformation,[status(thm)],[f34])).
% 0.15/5.41 fof(f36,plain,(
% 0.15/5.41 ((intersect(sK3_skl,sK3_skl)|not_equal(sK3_skl,empty_set))&(~intersect(sK3_skl,sK3_skl)|~not_equal(sK3_skl,empty_set)))),
% 0.15/5.41 inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl]),skolemize(B,sK3_skl)],[f35])).
% 0.15/5.41 fof(f37,plain,(
% 0.15/5.41 intersect(sK3_skl,sK3_skl)|not_equal(sK3_skl,empty_set)),
% 0.15/5.41 inference(cnf_transformation,[status(thm)],[f36])).
% 0.15/5.41 fof(f38,plain,(
% 0.15/5.41 ~intersect(sK3_skl,sK3_skl)|~not_equal(sK3_skl,empty_set)),
% 0.15/5.41 inference(cnf_transformation,[status(thm)],[f36])).
% 0.15/5.41 fof(f39,plain,(
% 0.15/5.41 ![X0]: (~not_equal(X0,X0))),
% 0.15/5.41 inference(destructive_equality_resolution,[status(thm)],[f25])).
% 0.15/5.41 fof(f41,plain,(
% 0.15/5.41 sK3_skl=empty_set|~intersect(sK3_skl,sK3_skl)),
% 0.15/5.41 inference(resolution,[status(thm)],[f26,f38])).
% 0.15/5.41 fof(f45,plain,(
% 0.15/5.41 ![X0]: (empty(X0)|intersect(X0,X0))),
% 0.15/5.41 inference(resolution,[status(thm)],[f33,f14])).
% 0.15/5.41 fof(f52,plain,(
% 0.15/5.41 ![X0]: (empty_set=X0|member(sK1_skl(X0,empty_set),X0))),
% 0.15/5.41 inference(resolution,[status(thm)],[f22,f15])).
% 0.15/5.41 fof(f66,plain,(
% 0.15/5.41 empty(sK3_skl)|sK3_skl=empty_set),
% 0.15/5.41 inference(resolution,[status(thm)],[f45,f41])).
% 0.15/5.41 fof(f76,plain,(
% 0.15/5.41 ![X0]: (empty_set=X0|~empty(X0))),
% 0.15/5.41 inference(resolution,[status(thm)],[f52,f32])).
% 0.15/5.41 fof(f82,plain,(
% 0.15/5.41 sK3_skl=empty_set),
% 0.15/5.41 inference(backward_subsumption_resolution,[status(thm)],[f66,f76])).
% 0.15/5.41 fof(f88,plain,(
% 0.15/5.41 ![X0]: (~member(X0,sK3_skl))),
% 0.15/5.41 inference(backward_demodulation,[status(thm)],[f82,f15])).
% 0.15/5.41 fof(f90,plain,(
% 0.15/5.41 intersect(sK3_skl,sK3_skl)|not_equal(sK3_skl,sK3_skl)),
% 0.15/5.41 inference(backward_demodulation,[status(thm)],[f82,f37])).
% 0.15/5.41 fof(f92,plain,(
% 0.15/5.41 intersect(sK3_skl,sK3_skl)),
% 0.15/5.41 inference(forward_subsumption_resolution,[status(thm)],[f90,f39])).
% 0.15/5.41 fof(f98,plain,(
% 0.15/5.41 member(sK0_skl(sK3_skl,sK3_skl),sK3_skl)),
% 0.15/5.41 inference(resolution,[status(thm)],[f92,f13])).
% 0.15/5.41 fof(f101,plain,(
% 0.15/5.41 $false),
% 0.15/5.41 inference(forward_subsumption_resolution,[status(thm)],[f98,f88])).
% 0.15/5.41 % SZS output end CNFRefutation for theBenchmark.p
% 0.15/5.44 % Elapsed time: 0.051382 seconds
% 0.15/5.44 % CPU time: 0.147168 seconds
% 0.15/5.44 % Total memory used: 80.065 MB
% 0.15/5.44 % Net memory used: 79.615 MB
%------------------------------------------------------------------------------