TSTP Solution File: SET600+3 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SET600+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 20:39:55 EDT 2024
% Result : Theorem 0.15s 0.32s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10 % Problem : SET600+3 : TPTP v8.1.2. Released v2.2.0.
% 0.05/0.10 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.30 % Computer : n008.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Mon Apr 29 21:31:27 EDT 2024
% 0.10/0.31 % CPUTime :
% 0.15/0.31 % Drodi V3.6.0
% 0.15/0.32 % Refutation found
% 0.15/0.32 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.32 % SZS output start CNFRefutation for theBenchmark
% 0.15/0.32 fof(f1,axiom,(
% 0.15/0.32 (! [B,C,D] :( member(D,union(B,C))<=> ( member(D,B)| member(D,C) ) ) )),
% 0.15/0.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.32 fof(f2,axiom,(
% 0.15/0.32 (! [B] : ~ member(B,empty_set) )),
% 0.15/0.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.32 fof(f3,axiom,(
% 0.15/0.32 (! [B,C] :( B = C<=> ( subset(B,C)& subset(C,B) ) ) )),
% 0.15/0.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.32 fof(f5,axiom,(
% 0.15/0.32 (! [B,C] :( subset(B,C)<=> (! [D] :( member(D,B)=> member(D,C) ) )) )),
% 0.15/0.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.32 fof(f7,axiom,(
% 0.15/0.32 (! [B] :( empty(B)<=> (! [C] : ~ member(C,B) )) )),
% 0.15/0.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.32 fof(f8,axiom,(
% 0.15/0.32 (! [B,C] :( B = C<=> (! [D] :( member(D,B)<=> member(D,C) ) )) )),
% 0.15/0.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.32 fof(f9,conjecture,(
% 0.15/0.32 (! [B,C] :( union(B,C) = empty_set<=> ( B = empty_set& C = empty_set ) ) )),
% 0.15/0.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.32 fof(f10,negated_conjecture,(
% 0.15/0.32 ~((! [B,C] :( union(B,C) = empty_set<=> ( B = empty_set& C = empty_set ) ) ))),
% 0.15/0.32 inference(negated_conjecture,[status(cth)],[f9])).
% 0.15/0.32 fof(f11,plain,(
% 0.15/0.32 ![B,C,D]: ((~member(D,union(B,C))|(member(D,B)|member(D,C)))&(member(D,union(B,C))|(~member(D,B)&~member(D,C))))),
% 0.15/0.32 inference(NNF_transformation,[status(esa)],[f1])).
% 0.15/0.32 fof(f12,plain,(
% 0.15/0.32 (![B,C,D]: (~member(D,union(B,C))|(member(D,B)|member(D,C))))&(![B,C,D]: (member(D,union(B,C))|(~member(D,B)&~member(D,C))))),
% 0.15/0.32 inference(miniscoping,[status(esa)],[f11])).
% 0.15/0.32 fof(f13,plain,(
% 0.15/0.32 ![X0,X1,X2]: (~member(X0,union(X1,X2))|member(X0,X1)|member(X0,X2))),
% 0.15/0.32 inference(cnf_transformation,[status(esa)],[f12])).
% 0.15/0.32 fof(f14,plain,(
% 0.15/0.32 ![X0,X1,X2]: (member(X0,union(X1,X2))|~member(X0,X1))),
% 0.15/0.32 inference(cnf_transformation,[status(esa)],[f12])).
% 0.15/0.32 fof(f15,plain,(
% 0.15/0.32 ![X0,X1,X2]: (member(X0,union(X1,X2))|~member(X0,X2))),
% 0.15/0.32 inference(cnf_transformation,[status(esa)],[f12])).
% 0.15/0.32 fof(f16,plain,(
% 0.15/0.32 ![X0]: (~member(X0,empty_set))),
% 0.15/0.32 inference(cnf_transformation,[status(esa)],[f2])).
% 0.15/0.32 fof(f17,plain,(
% 0.15/0.32 ![B,C]: ((~B=C|(subset(B,C)&subset(C,B)))&(B=C|(~subset(B,C)|~subset(C,B))))),
% 0.15/0.32 inference(NNF_transformation,[status(esa)],[f3])).
% 0.15/0.32 fof(f18,plain,(
% 0.15/0.32 (![B,C]: (~B=C|(subset(B,C)&subset(C,B))))&(![B,C]: (B=C|(~subset(B,C)|~subset(C,B))))),
% 0.15/0.32 inference(miniscoping,[status(esa)],[f17])).
% 0.15/0.32 fof(f21,plain,(
% 0.15/0.32 ![X0,X1]: (X0=X1|~subset(X0,X1)|~subset(X1,X0))),
% 0.15/0.32 inference(cnf_transformation,[status(esa)],[f18])).
% 0.15/0.32 fof(f23,plain,(
% 0.15/0.32 ![B,C]: (subset(B,C)<=>(![D]: (~member(D,B)|member(D,C))))),
% 0.15/0.32 inference(pre_NNF_transformation,[status(esa)],[f5])).
% 0.15/0.32 fof(f24,plain,(
% 0.15/0.32 ![B,C]: ((~subset(B,C)|(![D]: (~member(D,B)|member(D,C))))&(subset(B,C)|(?[D]: (member(D,B)&~member(D,C)))))),
% 0.15/0.32 inference(NNF_transformation,[status(esa)],[f23])).
% 0.15/0.32 fof(f25,plain,(
% 0.15/0.32 (![B,C]: (~subset(B,C)|(![D]: (~member(D,B)|member(D,C)))))&(![B,C]: (subset(B,C)|(?[D]: (member(D,B)&~member(D,C)))))),
% 0.15/0.32 inference(miniscoping,[status(esa)],[f24])).
% 0.15/0.32 fof(f26,plain,(
% 0.15/0.32 (![B,C]: (~subset(B,C)|(![D]: (~member(D,B)|member(D,C)))))&(![B,C]: (subset(B,C)|(member(sk0_0(C,B),B)&~member(sk0_0(C,B),C))))),
% 0.15/0.32 inference(skolemization,[status(esa)],[f25])).
% 0.15/0.32 fof(f28,plain,(
% 0.15/0.32 ![X0,X1]: (subset(X0,X1)|member(sk0_0(X1,X0),X0))),
% 0.15/0.32 inference(cnf_transformation,[status(esa)],[f26])).
% 0.15/0.32 fof(f31,plain,(
% 0.15/0.32 ![B]: ((~empty(B)|(![C]: ~member(C,B)))&(empty(B)|(?[C]: member(C,B))))),
% 0.15/0.32 inference(NNF_transformation,[status(esa)],[f7])).
% 0.15/0.32 fof(f32,plain,(
% 0.15/0.32 (![B]: (~empty(B)|(![C]: ~member(C,B))))&(![B]: (empty(B)|(?[C]: member(C,B))))),
% 0.15/0.32 inference(miniscoping,[status(esa)],[f31])).
% 0.15/0.32 fof(f33,plain,(
% 0.15/0.32 (![B]: (~empty(B)|(![C]: ~member(C,B))))&(![B]: (empty(B)|member(sk0_1(B),B)))),
% 0.15/0.32 inference(skolemization,[status(esa)],[f32])).
% 0.15/0.32 fof(f34,plain,(
% 0.15/0.32 ![X0,X1]: (~empty(X0)|~member(X1,X0))),
% 0.15/0.32 inference(cnf_transformation,[status(esa)],[f33])).
% 0.15/0.32 fof(f35,plain,(
% 0.15/0.32 ![X0]: (empty(X0)|member(sk0_1(X0),X0))),
% 0.15/0.32 inference(cnf_transformation,[status(esa)],[f33])).
% 0.15/0.32 fof(f36,plain,(
% 0.15/0.32 ![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))))))),
% 0.15/0.32 inference(NNF_transformation,[status(esa)],[f8])).
% 0.15/0.32 fof(f37,plain,(
% 0.15/0.32 (![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))))))),
% 0.15/0.32 inference(miniscoping,[status(esa)],[f36])).
% 0.15/0.32 fof(f38,plain,(
% 0.15/0.32 (![B,C]: (~B=C|((![D]: (~member(D,B)|member(D,C)))&(![D]: (member(D,B)|~member(D,C))))))&(![B,C]: (B=C|((~member(sk0_2(C,B),B)|~member(sk0_2(C,B),C))&(member(sk0_2(C,B),B)|member(sk0_2(C,B),C)))))),
% 0.15/0.32 inference(skolemization,[status(esa)],[f37])).
% 0.15/0.32 fof(f42,plain,(
% 0.15/0.32 ![X0,X1]: (X0=X1|member(sk0_2(X1,X0),X0)|member(sk0_2(X1,X0),X1))),
% 0.15/0.32 inference(cnf_transformation,[status(esa)],[f38])).
% 0.15/0.32 fof(f43,plain,(
% 0.15/0.32 (?[B,C]: (union(B,C)=empty_set<~>(B=empty_set&C=empty_set)))),
% 0.15/0.32 inference(pre_NNF_transformation,[status(esa)],[f10])).
% 0.15/0.32 fof(f44,plain,(
% 0.15/0.32 ?[B,C]: ((union(B,C)=empty_set|(B=empty_set&C=empty_set))&(~union(B,C)=empty_set|(~B=empty_set|~C=empty_set)))),
% 0.15/0.32 inference(NNF_transformation,[status(esa)],[f43])).
% 0.15/0.32 fof(f45,plain,(
% 0.15/0.32 ((union(sk0_3,sk0_4)=empty_set|(sk0_3=empty_set&sk0_4=empty_set))&(~union(sk0_3,sk0_4)=empty_set|(~sk0_3=empty_set|~sk0_4=empty_set)))),
% 0.15/0.32 inference(skolemization,[status(esa)],[f44])).
% 0.15/0.32 fof(f46,plain,(
% 0.15/0.32 union(sk0_3,sk0_4)=empty_set|sk0_3=empty_set),
% 0.15/0.32 inference(cnf_transformation,[status(esa)],[f45])).
% 0.15/0.32 fof(f47,plain,(
% 0.15/0.32 union(sk0_3,sk0_4)=empty_set|sk0_4=empty_set),
% 0.15/0.32 inference(cnf_transformation,[status(esa)],[f45])).
% 0.15/0.32 fof(f48,plain,(
% 0.15/0.32 ~union(sk0_3,sk0_4)=empty_set|~sk0_3=empty_set|~sk0_4=empty_set),
% 0.15/0.32 inference(cnf_transformation,[status(esa)],[f45])).
% 0.15/0.32 fof(f49,plain,(
% 0.15/0.32 spl0_0 <=> union(sk0_3,sk0_4)=empty_set),
% 0.15/0.32 introduced(split_symbol_definition)).
% 0.15/0.32 fof(f50,plain,(
% 0.15/0.32 union(sk0_3,sk0_4)=empty_set|~spl0_0),
% 0.15/0.32 inference(component_clause,[status(thm)],[f49])).
% 0.15/0.32 fof(f51,plain,(
% 0.15/0.32 ~union(sk0_3,sk0_4)=empty_set|spl0_0),
% 0.15/0.32 inference(component_clause,[status(thm)],[f49])).
% 0.15/0.32 fof(f52,plain,(
% 0.15/0.32 spl0_1 <=> sk0_3=empty_set),
% 0.15/0.32 introduced(split_symbol_definition)).
% 0.15/0.32 fof(f53,plain,(
% 0.15/0.32 sk0_3=empty_set|~spl0_1),
% 0.15/0.32 inference(component_clause,[status(thm)],[f52])).
% 0.15/0.32 fof(f55,plain,(
% 0.15/0.32 spl0_0|spl0_1),
% 0.15/0.32 inference(split_clause,[status(thm)],[f46,f49,f52])).
% 0.15/0.32 fof(f56,plain,(
% 0.15/0.32 spl0_2 <=> sk0_4=empty_set),
% 0.15/0.32 introduced(split_symbol_definition)).
% 0.15/0.32 fof(f57,plain,(
% 0.15/0.32 sk0_4=empty_set|~spl0_2),
% 0.15/0.32 inference(component_clause,[status(thm)],[f56])).
% 0.15/0.32 fof(f59,plain,(
% 0.15/0.32 spl0_0|spl0_2),
% 0.15/0.32 inference(split_clause,[status(thm)],[f47,f49,f56])).
% 0.15/0.32 fof(f60,plain,(
% 0.15/0.32 ~spl0_0|~spl0_1|~spl0_2),
% 0.15/0.32 inference(split_clause,[status(thm)],[f48,f49,f52,f56])).
% 0.15/0.32 fof(f70,plain,(
% 0.15/0.32 ![X0,X1,X2]: (~empty(union(X0,X1))|~member(X2,X0))),
% 0.15/0.32 inference(resolution,[status(thm)],[f34,f14])).
% 0.15/0.32 fof(f75,plain,(
% 0.15/0.32 ![X0,X1]: (empty(union(X0,X1))|member(sk0_1(union(X0,X1)),X0)|member(sk0_1(union(X0,X1)),X1))),
% 0.15/0.32 inference(resolution,[status(thm)],[f35,f13])).
% 0.15/0.32 fof(f76,plain,(
% 0.15/0.32 empty(empty_set)),
% 0.15/0.32 inference(resolution,[status(thm)],[f35,f16])).
% 0.15/0.32 fof(f78,plain,(
% 0.15/0.32 ![X0]: (empty(union(X0,empty_set))|member(sk0_1(union(X0,empty_set)),X0))),
% 0.15/0.32 inference(resolution,[status(thm)],[f75,f16])).
% 0.15/0.32 fof(f83,plain,(
% 0.15/0.32 ![X0]: (subset(empty_set,X0))),
% 0.15/0.32 inference(resolution,[status(thm)],[f28,f16])).
% 0.15/0.32 fof(f84,plain,(
% 0.15/0.32 ![X0,X1]: (subset(X0,X1)|~empty(X0))),
% 0.15/0.32 inference(resolution,[status(thm)],[f28,f34])).
% 0.15/0.32 fof(f85,plain,(
% 0.15/0.32 ![X0]: (X0=empty_set|~subset(X0,empty_set))),
% 0.15/0.32 inference(resolution,[status(thm)],[f83,f21])).
% 0.15/0.32 fof(f87,plain,(
% 0.15/0.32 ![X0]: (X0=empty_set|~empty(X0))),
% 0.15/0.32 inference(resolution,[status(thm)],[f85,f84])).
% 0.15/0.32 fof(f100,plain,(
% 0.15/0.32 ![X0]: (X0=empty_set|member(sk0_2(empty_set,X0),X0))),
% 0.15/0.32 inference(resolution,[status(thm)],[f42,f16])).
% 0.15/0.32 fof(f119,plain,(
% 0.15/0.32 empty(union(empty_set,empty_set))),
% 0.15/0.32 inference(resolution,[status(thm)],[f78,f16])).
% 0.15/0.32 fof(f164,plain,(
% 0.15/0.32 spl0_8 <=> empty(empty_set)),
% 0.15/0.32 introduced(split_symbol_definition)).
% 0.15/0.32 fof(f166,plain,(
% 0.15/0.32 ~empty(empty_set)|spl0_8),
% 0.15/0.32 inference(component_clause,[status(thm)],[f164])).
% 0.15/0.32 fof(f167,plain,(
% 0.15/0.32 spl0_9 <=> ~member(X0,sk0_3)),
% 0.15/0.32 introduced(split_symbol_definition)).
% 0.15/0.32 fof(f168,plain,(
% 0.15/0.32 ![X0]: (~member(X0,sk0_3)|~spl0_9)),
% 0.15/0.32 inference(component_clause,[status(thm)],[f167])).
% 0.15/0.32 fof(f170,plain,(
% 0.15/0.32 ![X0]: (~empty(empty_set)|~member(X0,sk0_3)|~spl0_0)),
% 0.15/0.32 inference(paramodulation,[status(thm)],[f50,f70])).
% 0.15/0.32 fof(f171,plain,(
% 0.15/0.32 ~spl0_8|spl0_9|~spl0_0),
% 0.15/0.32 inference(split_clause,[status(thm)],[f170,f164,f167,f49])).
% 0.15/0.32 fof(f178,plain,(
% 0.15/0.32 ![X0]: (member(X0,empty_set)|~member(X0,sk0_4)|~spl0_0)),
% 0.15/0.32 inference(paramodulation,[status(thm)],[f50,f15])).
% 0.15/0.32 fof(f179,plain,(
% 0.15/0.32 ![X0]: (~member(X0,sk0_4)|~spl0_0)),
% 0.15/0.32 inference(forward_subsumption_resolution,[status(thm)],[f178,f16])).
% 0.15/0.32 fof(f182,plain,(
% 0.15/0.32 $false|spl0_8),
% 0.15/0.32 inference(forward_subsumption_resolution,[status(thm)],[f166,f76])).
% 0.15/0.32 fof(f183,plain,(
% 0.15/0.32 spl0_8),
% 0.15/0.32 inference(contradiction_clause,[status(thm)],[f182])).
% 0.15/0.32 fof(f184,plain,(
% 0.15/0.32 ~union(empty_set,sk0_4)=empty_set|~spl0_1|spl0_0),
% 0.15/0.32 inference(forward_demodulation,[status(thm)],[f53,f51])).
% 0.15/0.32 fof(f185,plain,(
% 0.15/0.32 ~union(empty_set,empty_set)=empty_set|~spl0_2|~spl0_1|spl0_0),
% 0.15/0.32 inference(forward_demodulation,[status(thm)],[f57,f184])).
% 0.15/0.32 fof(f205,plain,(
% 0.15/0.32 union(empty_set,empty_set)=empty_set),
% 0.15/0.32 inference(resolution,[status(thm)],[f119,f87])).
% 0.15/0.32 fof(f206,plain,(
% 0.15/0.32 $false|~spl0_2|~spl0_1|spl0_0),
% 0.15/0.32 inference(forward_subsumption_resolution,[status(thm)],[f205,f185])).
% 0.15/0.32 fof(f207,plain,(
% 0.15/0.32 ~spl0_2|~spl0_1|spl0_0),
% 0.15/0.32 inference(contradiction_clause,[status(thm)],[f206])).
% 0.15/0.32 fof(f208,plain,(
% 0.15/0.32 sk0_3=empty_set|~spl0_9),
% 0.15/0.32 inference(resolution,[status(thm)],[f168,f100])).
% 0.15/0.32 fof(f209,plain,(
% 0.15/0.32 spl0_1|~spl0_9),
% 0.15/0.32 inference(split_clause,[status(thm)],[f208,f52,f167])).
% 0.15/0.32 fof(f253,plain,(
% 0.15/0.32 sk0_4=empty_set|~spl0_0),
% 0.15/0.32 inference(resolution,[status(thm)],[f179,f100])).
% 0.15/0.32 fof(f254,plain,(
% 0.15/0.32 spl0_2|~spl0_0),
% 0.15/0.32 inference(split_clause,[status(thm)],[f253,f56,f49])).
% 0.15/0.32 fof(f264,plain,(
% 0.15/0.32 $false),
% 0.15/0.32 inference(sat_refutation,[status(thm)],[f55,f59,f60,f171,f183,f207,f209,f254])).
% 0.15/0.32 % SZS output end CNFRefutation for theBenchmark.p
% 0.15/0.33 % Elapsed time: 0.017539 seconds
% 0.15/0.33 % CPU time: 0.039159 seconds
% 0.15/0.33 % Total memory used: 14.966 MB
% 0.15/0.33 % Net memory used: 14.923 MB
%------------------------------------------------------------------------------