%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SET636+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 : n008.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 0.24s 0.70s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET636+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.07 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.46 % Computer : n008.cluster.edu
% 0.20/0.46 % Model : x86_64 x86_64
% 0.20/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.46 % Memory : 8046.5625MB
% 0.20/0.46 % OS : Linux 6.8.0-71-generic
% 0.20/0.46 % CPULimit : 300
% 0.20/0.46 % WCLimit : 300
% 0.20/0.46 % DateTime : Mon Sep 21 05:31:40 UTC 2026
% 0.20/0.46 % CPUTime :
% 0.20/0.50 % Drodi V4.1.1
% 0.24/0.70 % Refutation found
% 0.24/0.70 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.24/0.70 % SZS output start CNFRefutation for theBenchmark
% 0.24/0.70 fof(f1,axiom,(
% 0.24/0.70 (! [B,C,D] :( member(D,intersection(B,C))<=> ( member(D,B)& member(D,C) ) ) )),
% 0.24/0.70 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.24/0.70 fof(f2,axiom,(
% 0.24/0.70 (! [B,C] :( intersect(B,C)<=> (? [D] :( member(D,B)& member(D,C) ) )) )),
% 0.24/0.70 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.24/0.70 fof(f3,axiom,(
% 0.24/0.70 (! [B] : ~ member(B,empty_set) )),
% 0.24/0.70 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.24/0.70 fof(f4,axiom,(
% 0.24/0.70 (! [B,C] :( disjoint(B,C)<=> ~ intersect(B,C) ) )),
% 0.24/0.70 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.24/0.70 fof(f5,axiom,(
% 0.24/0.70 (! [B,C] :( B = C<=> ( subset(B,C)& subset(C,B) ) ) )),
% 0.24/0.70 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.24/0.70 fof(f6,axiom,(
% 0.24/0.70 (! [B,C] : intersection(B,C) = intersection(C,B) )),
% 0.24/0.70 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.24/0.70 fof(f7,axiom,(
% 0.24/0.70 (! [B,C] :( intersect(B,C)=> intersect(C,B) ) )),
% 0.24/0.70 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.24/0.70 fof(f8,axiom,(
% 0.24/0.70 (! [B,C] :( subset(B,C)<=> (! [D] :( member(D,B)=> member(D,C) ) )) )),
% 0.24/0.70 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.24/0.70 fof(f10,axiom,(
% 0.24/0.70 (! [B] :( empty(B)<=> (! [C] : ~ member(C,B) )) )),
% 0.24/0.70 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.24/0.70 fof(f11,axiom,(
% 0.24/0.70 (! [B,C] :( B = C<=> (! [D] :( member(D,B)<=> member(D,C) ) )) )),
% 0.24/0.70 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.24/0.70 fof(f12,conjecture,(
% 0.24/0.70 (! [B,C] :( disjoint(B,C)<=> intersection(B,C) = empty_set ) )),
% 0.24/0.70 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.24/0.70 fof(f13,negated_conjecture,(
% 0.24/0.70 ~((! [B,C] :( disjoint(B,C)<=> intersection(B,C) = empty_set ) ))),
% 0.24/0.70 inference(negated_conjecture,[status(cth)],[f12])).
% 0.24/0.70 fof(f14,plain,(
% 0.24/0.70 ![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))))),
% 0.24/0.70 inference(NNF_transformation,[status(thm)],[f1])).
% 0.24/0.70 fof(f15,plain,(
% 0.24/0.70 (![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))))),
% 0.24/0.70 inference(miniscoping,[status(thm)],[f14])).
% 0.24/0.70 fof(f16,plain,(
% 0.24/0.70 ![X0,X1,X2]: (~member(X0,intersection(X1,X2))|member(X0,X1))),
% 0.24/0.70 inference(cnf_transformation,[status(thm)],[f15])).
% 0.24/0.70 fof(f17,plain,(
% 0.24/0.70 ![X0,X1,X2]: (~member(X0,intersection(X1,X2))|member(X0,X2))),
% 0.24/0.70 inference(cnf_transformation,[status(thm)],[f15])).
% 0.24/0.70 fof(f18,plain,(
% 0.24/0.70 ![X0,X1,X2]: (member(X0,intersection(X1,X2))|~member(X0,X1)|~member(X0,X2))),
% 0.24/0.70 inference(cnf_transformation,[status(thm)],[f15])).
% 0.24/0.70 fof(f19,plain,(
% 0.24/0.70 ![B,C]: ((~intersect(B,C)|(?[D]: (member(D,B)&member(D,C))))&(intersect(B,C)|(![D]: (~member(D,B)|~member(D,C)))))),
% 0.24/0.70 inference(NNF_transformation,[status(thm)],[f2])).
% 0.24/0.70 fof(f20,plain,(
% 0.24/0.70 (![B,C]: (~intersect(B,C)|(?[D]: (member(D,B)&member(D,C)))))&(![B,C]: (intersect(B,C)|(![D]: (~member(D,B)|~member(D,C)))))),
% 0.24/0.70 inference(miniscoping,[status(thm)],[f19])).
% 0.24/0.70 fof(f21,plain,(
% 0.24/0.70 (![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)))))),
% 0.24/0.70 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(D,sK0_skl(C,B))],[f20])).
% 0.24/0.70 fof(f22,plain,(
% 0.24/0.70 ![X0,X1]: (~intersect(X0,X1)|member(sK0_skl(X1,X0),X0))),
% 0.24/0.70 inference(cnf_transformation,[status(thm)],[f21])).
% 0.24/0.70 fof(f23,plain,(
% 0.24/0.70 ![X0,X1]: (~intersect(X0,X1)|member(sK0_skl(X1,X0),X1))),
% 0.24/0.70 inference(cnf_transformation,[status(thm)],[f21])).
% 0.24/0.70 fof(f24,plain,(
% 0.24/0.70 ![X0,X1,X2]: (intersect(X0,X1)|~member(X2,X0)|~member(X2,X1))),
% 0.24/0.70 inference(cnf_transformation,[status(thm)],[f21])).
% 0.24/0.70 fof(f25,plain,(
% 0.24/0.70 ![X0]: (~member(X0,empty_set))),
% 0.24/0.70 inference(cnf_transformation,[status(thm)],[f3])).
% 0.24/0.70 fof(f26,plain,(
% 0.24/0.70 ![B,C]: ((~disjoint(B,C)|~intersect(B,C))&(disjoint(B,C)|intersect(B,C)))),
% 0.24/0.70 inference(NNF_transformation,[status(thm)],[f4])).
% 0.24/0.70 fof(f27,plain,(
% 0.24/0.70 (![B,C]: (~disjoint(B,C)|~intersect(B,C)))&(![B,C]: (disjoint(B,C)|intersect(B,C)))),
% 0.24/0.70 inference(miniscoping,[status(thm)],[f26])).
% 0.24/0.70 fof(f28,plain,(
% 0.24/0.70 ![X0,X1]: (~disjoint(X0,X1)|~intersect(X0,X1))),
% 0.24/0.70 inference(cnf_transformation,[status(thm)],[f27])).
% 0.24/0.70 fof(f29,plain,(
% 0.24/0.70 ![X0,X1]: (disjoint(X0,X1)|intersect(X0,X1))),
% 0.24/0.70 inference(cnf_transformation,[status(thm)],[f27])).
% 0.24/0.70 fof(f30,plain,(
% 0.24/0.70 ![B,C]: ((~B=C|(subset(B,C)&subset(C,B)))&(B=C|(~subset(B,C)|~subset(C,B))))),
% 0.24/0.70 inference(NNF_transformation,[status(thm)],[f5])).
% 0.24/0.70 fof(f31,plain,(
% 0.24/0.70 (![B,C]: (~B=C|(subset(B,C)&subset(C,B))))&(![B,C]: (B=C|(~subset(B,C)|~subset(C,B))))),
% 0.24/0.70 inference(miniscoping,[status(thm)],[f30])).
% 0.24/0.70 fof(f34,plain,(
% 0.24/0.70 ![X0,X1]: (X0=X1|~subset(X0,X1)|~subset(X1,X0))),
% 0.24/0.70 inference(cnf_transformation,[status(thm)],[f31])).
% 0.24/0.70 fof(f35,plain,(
% 0.24/0.70 ![X0,X1]: (intersection(X0,X1)=intersection(X1,X0))),
% 0.24/0.70 inference(cnf_transformation,[status(thm)],[f6])).
% 0.24/0.70 fof(f36,plain,(
% 0.24/0.70 ![B,C]: (~intersect(B,C)|intersect(C,B))),
% 0.24/0.70 inference(pre_NNF_transformation,[status(thm)],[f7])).
% 0.24/0.70 fof(f37,plain,(
% 0.24/0.70 ![X0,X1]: (~intersect(X0,X1)|intersect(X1,X0))),
% 0.24/0.70 inference(cnf_transformation,[status(thm)],[f36])).
% 0.24/0.70 fof(f38,plain,(
% 0.24/0.70 ![B,C]: (subset(B,C)<=>(![D]: (~member(D,B)|member(D,C))))),
% 0.24/0.70 inference(pre_NNF_transformation,[status(thm)],[f8])).
% 0.24/0.70 fof(f39,plain,(
% 0.24/0.70 ![B,C]: ((~subset(B,C)|(![D]: (~member(D,B)|member(D,C))))&(subset(B,C)|(?[D]: (member(D,B)&~member(D,C)))))),
% 0.24/0.70 inference(NNF_transformation,[status(thm)],[f38])).
% 0.24/0.70 fof(f40,plain,(
% 0.24/0.70 (![B,C]: (~subset(B,C)|(![D]: (~member(D,B)|member(D,C)))))&(![B,C]: (subset(B,C)|(?[D]: (member(D,B)&~member(D,C)))))),
% 0.24/0.70 inference(miniscoping,[status(thm)],[f39])).
% 0.24/0.70 fof(f41,plain,(
% 0.24/0.70 (![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))))),
% 0.24/0.70 inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(D,sK1_skl(C,B))],[f40])).
% 0.24/0.70 fof(f43,plain,(
% 0.24/0.70 ![X0,X1]: (subset(X0,X1)|member(sK1_skl(X1,X0),X0))),
% 0.24/0.70 inference(cnf_transformation,[status(thm)],[f41])).
% 0.24/0.70 fof(f44,plain,(
% 0.24/0.70 ![X0,X1]: (subset(X0,X1)|~member(sK1_skl(X1,X0),X1))),
% 0.24/0.70 inference(cnf_transformation,[status(thm)],[f41])).
% 0.24/0.70 fof(f46,plain,(
% 0.24/0.70 ![B]: ((~empty(B)|(![C]: ~member(C,B)))&(empty(B)|(?[C]: member(C,B))))),
% 0.24/0.70 inference(NNF_transformation,[status(thm)],[f10])).
% 0.24/0.70 fof(f47,plain,(
% 0.24/0.70 (![B]: (~empty(B)|(![C]: ~member(C,B))))&(![B]: (empty(B)|(?[C]: member(C,B))))),
% 0.24/0.70 inference(miniscoping,[status(thm)],[f46])).
% 0.24/0.70 fof(f48,plain,(
% 0.24/0.70 (![B]: (~empty(B)|(![C]: ~member(C,B))))&(![B]: (empty(B)|member(sK2_skl(B),B)))),
% 0.24/0.70 inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(C,sK2_skl(B))],[f47])).
% 0.24/0.70 fof(f49,plain,(
% 0.24/0.70 ![X0,X1]: (~empty(X0)|~member(X1,X0))),
% 0.24/0.70 inference(cnf_transformation,[status(thm)],[f48])).
% 0.24/0.70 fof(f50,plain,(
% 0.24/0.70 ![X0]: (empty(X0)|member(sK2_skl(X0),X0))),
% 0.24/0.70 inference(cnf_transformation,[status(thm)],[f48])).
% 0.24/0.70 fof(f51,plain,(
% 0.24/0.70 ![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))))))),
% 0.24/0.70 inference(NNF_transformation,[status(thm)],[f11])).
% 0.24/0.70 fof(f52,plain,(
% 0.24/0.70 (![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))))))),
% 0.24/0.70 inference(miniscoping,[status(thm)],[f51])).
% 0.24/0.70 fof(f53,plain,(
% 0.24/0.70 (![B,C]: (~B=C|((![D]: (~member(D,B)|member(D,C)))&(![D]: (member(D,B)|~member(D,C))))))&(![B,C]: (B=C|((~member(sK3_skl(C,B),B)|~member(sK3_skl(C,B),C))&(member(sK3_skl(C,B),B)|member(sK3_skl(C,B),C)))))),
% 0.24/0.70 inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl]),skolemize(D,sK3_skl(C,B))],[f52])).
% 0.24/0.70 fof(f57,plain,(
% 0.24/0.70 ![X0,X1]: (X0=X1|member(sK3_skl(X1,X0),X0)|member(sK3_skl(X1,X0),X1))),
% 0.24/0.70 inference(cnf_transformation,[status(thm)],[f53])).
% 0.24/0.70 fof(f58,plain,(
% 0.24/0.70 (?[B,C]: (disjoint(B,C)<~>intersection(B,C)=empty_set))),
% 0.24/0.70 inference(pre_NNF_transformation,[status(thm)],[f13])).
% 0.24/0.70 fof(f59,plain,(
% 0.24/0.70 ?[B,C]: ((disjoint(B,C)|intersection(B,C)=empty_set)&(~disjoint(B,C)|~intersection(B,C)=empty_set))),
% 0.24/0.70 inference(NNF_transformation,[status(thm)],[f58])).
% 0.24/0.70 fof(f60,plain,(
% 0.24/0.70 ((disjoint(sK4_skl,sK5_skl)|intersection(sK4_skl,sK5_skl)=empty_set)&(~disjoint(sK4_skl,sK5_skl)|~intersection(sK4_skl,sK5_skl)=empty_set))),
% 0.24/0.70 inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl,sK5_skl]),skolemize(B,sK4_skl),skolemize(C,sK5_skl)],[f59])).
% 0.24/0.70 fof(f61,plain,(
% 0.24/0.70 disjoint(sK4_skl,sK5_skl)|intersection(sK4_skl,sK5_skl)=empty_set),
% 0.24/0.70 inference(cnf_transformation,[status(thm)],[f60])).
% 0.24/0.70 fof(f62,plain,(
% 0.24/0.70 ~disjoint(sK4_skl,sK5_skl)|~intersection(sK4_skl,sK5_skl)=empty_set),
% 0.24/0.70 inference(cnf_transformation,[status(thm)],[f60])).
% 0.24/0.70 fof(f63,definition,(
% 0.24/0.70 sQ0_spl <=> (disjoint(sK4_skl,sK5_skl))),
% 0.24/0.70 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.24/0.70 fof(f66,definition,(
% 0.24/0.70 sQ1_spl <=> (intersection(sK4_skl,sK5_skl)=empty_set)),
% 0.24/0.70 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.24/0.70 fof(f67,plain,(
% 0.24/0.70 intersection(sK4_skl,sK5_skl)=empty_set|~sQ1_spl),
% 0.24/0.70 inference(component_clause,[status(thm)],[f66])).
% 0.24/0.70 fof(f69,plain,(
% 0.24/0.70 sQ0_spl|sQ1_spl),
% 0.24/0.70 inference(split_clause,[status(thm)],[f61,f63,f66])).
% 0.24/0.70 fof(f70,plain,(
% 0.24/0.70 ~sQ0_spl|~sQ1_spl),
% 0.24/0.70 inference(split_clause,[status(thm)],[f62,f63,f66])).
% 0.24/0.70 fof(f84,plain,(
% 0.24/0.70 ![X0,X1]: (member(sK0_skl(X0,X1),X1)|disjoint(X1,X0))),
% 0.24/0.70 inference(resolution,[status(thm)],[f22,f29])).
% 0.24/0.70 fof(f85,plain,(
% 0.24/0.70 ![X0,X1]: (intersect(X0,X1)|disjoint(X1,X0))),
% 0.24/0.70 inference(resolution,[status(thm)],[f37,f29])).
% 0.24/0.70 fof(f88,plain,(
% 0.24/0.70 ![X0,X1]: (disjoint(X0,X1)|~disjoint(X1,X0))),
% 0.24/0.70 inference(resolution,[status(thm)],[f85,f28])).
% 0.24/0.70 fof(f89,plain,(
% 0.24/0.70 ![X0,X1]: (empty(intersection(X0,X1))|member(sK2_skl(intersection(X0,X1)),X1))),
% 0.24/0.70 inference(resolution,[status(thm)],[f50,f17])).
% 0.24/0.70 fof(f90,plain,(
% 0.24/0.70 ![X0,X1]: (empty(intersection(X0,X1))|member(sK2_skl(intersection(X0,X1)),X0))),
% 0.24/0.70 inference(resolution,[status(thm)],[f50,f16])).
% 0.24/0.70 fof(f92,plain,(
% 0.24/0.70 ![X0,X1]: (empty(X0)|member(sK2_skl(X0),intersection(X1,X0))|~member(sK2_skl(X0),X1))),
% 0.24/0.70 inference(resolution,[status(thm)],[f50,f18])).
% 0.24/0.70 fof(f95,plain,(
% 0.24/0.70 ![X0,X1]: (member(sK0_skl(X0,X1),X0)|disjoint(X1,X0))),
% 0.24/0.70 inference(resolution,[status(thm)],[f23,f29])).
% 0.24/0.70 fof(f102,plain,(
% 0.24/0.70 ![X0,X1,X2]: (disjoint(X0,X1)|member(sK0_skl(X1,X0),intersection(X2,X0))|~member(sK0_skl(X1,X0),X2))),
% 0.24/0.70 inference(resolution,[status(thm)],[f84,f18])).
% 0.24/0.70 fof(f107,plain,(
% 0.24/0.70 ![X0]: (empty(intersection(X0,empty_set)))),
% 0.24/0.70 inference(resolution,[status(thm)],[f89,f25])).
% 0.24/0.70 fof(f108,plain,(
% 0.24/0.70 ![X0,X1,X2]: (empty(intersection(X0,X1))|intersect(X2,X1)|~member(sK2_skl(intersection(X0,X1)),X2))),
% 0.24/0.70 inference(resolution,[status(thm)],[f89,f24])).
% 0.24/0.70 fof(f113,definition,(
% 0.24/0.70 sQ2_spl <=> (empty(intersection(sK4_skl,sK5_skl)))),
% 0.24/0.70 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.24/0.70 fof(f114,plain,(
% 0.24/0.70 empty(intersection(sK4_skl,sK5_skl))|~sQ2_spl),
% 0.24/0.70 inference(component_clause,[status(thm)],[f113])).
% 0.24/0.70 fof(f115,plain,(
% 0.24/0.70 ~empty(intersection(sK4_skl,sK5_skl))|sQ2_spl),
% 0.24/0.70 inference(component_clause,[status(thm)],[f113])).
% 0.24/0.70 fof(f121,plain,(
% 0.24/0.70 ![X0,X1]: (~member(X0,intersection(X1,empty_set)))),
% 0.24/0.70 inference(resolution,[status(thm)],[f107,f49])).
% 0.24/0.70 fof(f122,plain,(
% 0.24/0.70 ![X0]: (empty(intersection(empty_set,X0)))),
% 0.24/0.70 inference(paramodulation,[status(thm)],[f35,f107])).
% 0.24/0.70 fof(f124,plain,(
% 0.24/0.70 ![X0,X1]: (~member(X0,intersection(empty_set,X1)))),
% 0.24/0.70 inference(resolution,[status(thm)],[f122,f49])).
% 0.24/0.70 fof(f156,plain,(
% 0.24/0.70 ![X0]: (empty(X0)|member(sK2_skl(X0),intersection(X0,X0))|empty(X0))),
% 0.24/0.70 inference(resolution,[status(thm)],[f92,f50])).
% 0.24/0.70 fof(f159,plain,(
% 0.24/0.70 ![X0]: (empty(X0)|member(sK2_skl(X0),intersection(X0,X0)))),
% 0.24/0.70 inference(duplicate_literals_removal,[status(thm)],[f156])).
% 0.24/0.70 fof(f170,plain,(
% 0.24/0.70 ![X0,X1]: (subset(intersection(empty_set,X0),X1))),
% 0.24/0.70 inference(resolution,[status(thm)],[f43,f124])).
% 0.24/0.70 fof(f171,plain,(
% 0.24/0.70 ![X0,X1]: (subset(intersection(X0,empty_set),X1))),
% 0.24/0.70 inference(resolution,[status(thm)],[f43,f121])).
% 0.24/0.70 fof(f172,plain,(
% 0.24/0.70 ![X0,X1,X2]: (subset(intersection(X0,X1),X2)|member(sK1_skl(X2,intersection(X0,X1)),X1))),
% 0.24/0.70 inference(resolution,[status(thm)],[f43,f17])).
% 0.24/0.70 fof(f173,plain,(
% 0.24/0.70 ![X0,X1,X2]: (subset(intersection(X0,X1),X2)|member(sK1_skl(X2,intersection(X0,X1)),X0))),
% 0.24/0.70 inference(resolution,[status(thm)],[f43,f16])).
% 0.24/0.70 fof(f174,plain,(
% 0.24/0.70 ![X0]: (subset(empty_set,X0))),
% 0.24/0.70 inference(resolution,[status(thm)],[f43,f25])).
% 0.24/0.70 fof(f180,plain,(
% 0.24/0.70 ![X0]: (X0=empty_set|~subset(X0,empty_set))),
% 0.24/0.70 inference(resolution,[status(thm)],[f174,f34])).
% 0.24/0.70 fof(f196,plain,(
% 0.24/0.70 ![X0]: (intersection(empty_set,X0)=empty_set)),
% 0.24/0.70 inference(resolution,[status(thm)],[f180,f170])).
% 0.24/0.70 fof(f197,plain,(
% 0.24/0.70 ![X0]: (intersection(X0,empty_set)=empty_set)),
% 0.24/0.70 inference(resolution,[status(thm)],[f180,f171])).
% 0.24/0.70 fof(f212,plain,(
% 0.24/0.70 ![X0]: (empty(intersection(empty_set,X0))|member(sK2_skl(empty_set),empty_set))),
% 0.24/0.70 inference(paramodulation,[status(thm)],[f196,f90])).
% 0.24/0.70 fof(f218,definition,(
% 0.24/0.70 ![X0]: (sQ5_spl <=> (empty(intersection(empty_set,X0))))),
% 0.24/0.70 introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition])).
% 0.24/0.70 fof(f221,definition,(
% 0.24/0.70 sQ6_spl <=> (member(sK2_skl(empty_set),empty_set))),
% 0.24/0.70 introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition])).
% 0.24/0.70 fof(f222,plain,(
% 0.24/0.70 member(sK2_skl(empty_set),empty_set)|~sQ6_spl),
% 0.24/0.70 inference(component_clause,[status(thm)],[f221])).
% 0.24/0.70 fof(f224,plain,(
% 0.24/0.70 sQ5_spl|sQ6_spl),
% 0.24/0.70 inference(split_clause,[status(thm)],[f212,f218,f221])).
% 0.24/0.70 fof(f237,plain,(
% 0.24/0.70 ![X0]: (empty(intersection(X0,empty_set))|member(sK2_skl(empty_set),empty_set))),
% 0.24/0.70 inference(paramodulation,[status(thm)],[f197,f89])).
% 0.24/0.70 fof(f243,definition,(
% 0.24/0.70 ![X0]: (sQ7_spl <=> (empty(intersection(X0,empty_set))))),
% 0.24/0.70 introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition])).
% 0.24/0.70 fof(f246,plain,(
% 0.24/0.70 sQ7_spl|sQ6_spl),
% 0.24/0.70 inference(split_clause,[status(thm)],[f237,f243,f221])).
% 0.24/0.70 fof(f247,plain,(
% 0.24/0.70 $false|~sQ6_spl),
% 0.24/0.70 inference(forward_subsumption_resolution,[status(thm)],[f222,f25])).
% 0.24/0.70 fof(f248,plain,(
% 0.24/0.70 ~sQ6_spl),
% 0.24/0.70 inference(contradiction_clause,[status(thm)],[f247])).
% 0.24/0.70 fof(f250,plain,(
% 0.24/0.70 ![X0,X1]: (subset(intersection(X0,X1),X1)|subset(intersection(X0,X1),X1))),
% 0.24/0.70 inference(resolution,[status(thm)],[f172,f44])).
% 0.24/0.70 fof(f261,plain,(
% 0.24/0.70 ![X0,X1]: (subset(intersection(X0,X1),X1))),
% 0.24/0.70 inference(duplicate_literals_removal,[status(thm)],[f250])).
% 0.24/0.70 fof(f266,plain,(
% 0.24/0.70 ![X0,X1]: (subset(intersection(X0,X1),X0)|subset(intersection(X0,X1),X0))),
% 0.24/0.70 inference(resolution,[status(thm)],[f173,f44])).
% 0.24/0.70 fof(f277,plain,(
% 0.24/0.70 ![X0,X1]: (subset(intersection(X0,X1),X0))),
% 0.24/0.70 inference(duplicate_literals_removal,[status(thm)],[f266])).
% 0.24/0.70 fof(f284,plain,(
% 0.24/0.70 ![X0,X1]: (X0=intersection(X1,X0)|~subset(X0,intersection(X1,X0)))),
% 0.24/0.70 inference(resolution,[status(thm)],[f261,f34])).
% 0.24/0.70 fof(f292,plain,(
% 0.24/0.70 ![X0,X1]: (X0=intersection(X0,X1)|~subset(X0,intersection(X0,X1)))),
% 0.24/0.70 inference(resolution,[status(thm)],[f277,f34])).
% 0.24/0.70 fof(f319,plain,(
% 0.24/0.70 ![X0]: (X0=empty_set|member(sK3_skl(empty_set,X0),X0))),
% 0.24/0.70 inference(resolution,[status(thm)],[f57,f25])).
% 0.24/0.70 fof(f374,plain,(
% 0.24/0.70 empty(empty_set)|member(sK2_skl(empty_set),empty_set)),
% 0.24/0.70 inference(paramodulation,[status(thm)],[f196,f159])).
% 0.24/0.70 fof(f378,definition,(
% 0.24/0.70 sQ10_spl <=> (empty(empty_set))),
% 0.24/0.70 introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition])).
% 0.24/0.70 fof(f381,plain,(
% 0.24/0.70 sQ10_spl|sQ6_spl),
% 0.24/0.70 inference(split_clause,[status(thm)],[f374,f378,f221])).
% 0.24/0.70 fof(f519,plain,(
% 0.24/0.70 ![X0]: (empty_set=intersection(X0,empty_set)|~subset(empty_set,empty_set))),
% 0.24/0.70 inference(paramodulation,[status(thm)],[f197,f284])).
% 0.24/0.70 fof(f530,definition,(
% 0.24/0.70 ![X0]: (sQ15_spl <=> (empty_set=intersection(X0,empty_set)))),
% 0.24/0.70 introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition])).
% 0.24/0.70 fof(f533,definition,(
% 0.24/0.70 sQ16_spl <=> (subset(empty_set,empty_set))),
% 0.24/0.70 introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition])).
% 0.24/0.70 fof(f535,plain,(
% 0.24/0.70 ~subset(empty_set,empty_set)|sQ16_spl),
% 0.24/0.70 inference(component_clause,[status(thm)],[f533])).
% 0.24/0.70 fof(f536,plain,(
% 0.24/0.70 sQ15_spl|~sQ16_spl),
% 0.24/0.70 inference(split_clause,[status(thm)],[f519,f530,f533])).
% 0.24/0.70 fof(f577,plain,(
% 0.24/0.70 ![X0]: (empty_set=intersection(empty_set,X0)|~subset(empty_set,empty_set))),
% 0.24/0.70 inference(paramodulation,[status(thm)],[f196,f292])).
% 0.24/0.70 fof(f588,definition,(
% 0.24/0.70 ![X0]: (sQ19_spl <=> (empty_set=intersection(empty_set,X0)))),
% 0.24/0.70 introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition])).
% 0.24/0.72 fof(f591,plain,(
% 0.24/0.72 sQ19_spl|~sQ16_spl),
% 0.24/0.72 inference(split_clause,[status(thm)],[f577,f588,f533])).
% 0.24/0.72 fof(f593,plain,(
% 0.24/0.72 $false|sQ16_spl),
% 0.24/0.72 inference(forward_subsumption_resolution,[status(thm)],[f535,f174])).
% 0.24/0.72 fof(f594,plain,(
% 0.24/0.72 sQ16_spl),
% 0.24/0.72 inference(contradiction_clause,[status(thm)],[f593])).
% 0.24/0.72 fof(f1043,plain,(
% 0.24/0.72 ![X0]: (disjoint(sK5_skl,X0)|member(sK0_skl(X0,sK5_skl),empty_set)|~member(sK0_skl(X0,sK5_skl),sK4_skl)|~sQ1_spl)),
% 0.24/0.72 inference(paramodulation,[status(thm)],[f67,f102])).
% 0.24/0.72 fof(f1049,plain,(
% 0.24/0.72 ![X0]: (disjoint(sK5_skl,X0)|~member(sK0_skl(X0,sK5_skl),sK4_skl)|~sQ1_spl)),
% 0.24/0.72 inference(forward_subsumption_resolution,[status(thm)],[f1043,f25])).
% 0.24/0.72 fof(f1244,plain,(
% 0.24/0.72 ![X0,X1]: (empty(intersection(X0,X1))|intersect(X0,X1)|empty(intersection(X0,X1)))),
% 0.24/0.72 inference(resolution,[status(thm)],[f108,f90])).
% 0.24/0.72 fof(f1255,plain,(
% 0.24/0.72 ![X0,X1]: (empty(intersection(X0,X1))|intersect(X0,X1))),
% 0.24/0.72 inference(duplicate_literals_removal,[status(thm)],[f1244])).
% 0.24/0.72 fof(f1272,plain,(
% 0.24/0.72 disjoint(sK5_skl,sK4_skl)|disjoint(sK5_skl,sK4_skl)|~sQ1_spl),
% 0.24/0.72 inference(resolution,[status(thm)],[f1049,f95])).
% 0.24/0.72 fof(f1273,definition,(
% 0.24/0.72 sQ36_spl <=> (disjoint(sK5_skl,sK4_skl))),
% 0.24/0.72 introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition])).
% 0.24/0.72 fof(f1274,plain,(
% 0.24/0.72 disjoint(sK5_skl,sK4_skl)|~sQ36_spl),
% 0.24/0.72 inference(component_clause,[status(thm)],[f1273])).
% 0.24/0.72 fof(f1277,plain,(
% 0.24/0.72 sQ36_spl|~sQ1_spl),
% 0.24/0.72 inference(split_clause,[status(thm)],[f1272,f1273,f66])).
% 0.24/0.72 fof(f1278,plain,(
% 0.24/0.72 disjoint(sK4_skl,sK5_skl)|~sQ36_spl),
% 0.24/0.72 inference(resolution,[status(thm)],[f1274,f88])).
% 0.24/0.72 fof(f1321,plain,(
% 0.24/0.72 ![X0]: (~member(X0,intersection(sK4_skl,sK5_skl))|~sQ2_spl)),
% 0.24/0.72 inference(resolution,[status(thm)],[f114,f49])).
% 0.24/0.72 fof(f1334,plain,(
% 0.24/0.72 intersection(sK4_skl,sK5_skl)=empty_set|~sQ2_spl),
% 0.24/0.72 inference(resolution,[status(thm)],[f1321,f319])).
% 0.24/0.72 fof(f1369,plain,(
% 0.24/0.72 sQ1_spl|~sQ2_spl),
% 0.24/0.72 inference(split_clause,[status(thm)],[f1334,f66,f113])).
% 0.24/0.72 fof(f1372,plain,(
% 0.24/0.72 sQ0_spl|~sQ36_spl),
% 0.24/0.72 inference(split_clause,[status(thm)],[f1278,f63,f1273])).
% 0.24/0.72 fof(f1434,plain,(
% 0.24/0.72 intersect(sK4_skl,sK5_skl)|sQ2_spl),
% 0.24/0.72 inference(resolution,[status(thm)],[f1255,f115])).
% 0.24/0.72 fof(f1451,plain,(
% 0.24/0.72 ~disjoint(sK4_skl,sK5_skl)|sQ2_spl),
% 0.24/0.72 inference(resolution,[status(thm)],[f1434,f28])).
% 0.24/0.72 fof(f1452,plain,(
% 0.24/0.72 ~sQ0_spl|sQ2_spl),
% 0.24/0.72 inference(split_clause,[status(thm)],[f1451,f63,f113])).
% 0.24/0.72 fof(f1453,plain,(
% 0.24/0.72 $false),
% 0.24/0.72 inference(sat_refutation,[status(thm)],[f69,f70,f224,f246,f248,f381,f536,f591,f594,f1277,f1369,f1372,f1452])).
% 0.24/0.72 % SZS output end CNFRefutation for theBenchmark.p
% 0.24/0.75 % Elapsed time: 0.263140 seconds
% 0.24/0.75 % CPU time: 1.332955 seconds
% 0.24/0.75 % Total memory used: 113.175 MB
% 0.24/0.75 % Net memory used: 111.392 MB
%------------------------------------------------------------------------------