TSTP Solution File: SET587+3 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SET587+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n032.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 : Wed May 31 12:34:43 EDT 2023
% Result : Theorem 0.08s 0.28s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : SET587+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.08 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.08/0.26 % Computer : n032.cluster.edu
% 0.08/0.26 % Model : x86_64 x86_64
% 0.08/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.26 % Memory : 8042.1875MB
% 0.08/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.26 % CPULimit : 300
% 0.08/0.26 % WCLimit : 300
% 0.08/0.26 % DateTime : Tue May 30 10:13:16 EDT 2023
% 0.08/0.26 % CPUTime :
% 0.08/0.27 % Drodi V3.5.1
% 0.08/0.28 % Refutation found
% 0.08/0.28 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.08/0.28 % SZS output start CNFRefutation for theBenchmark
% 0.08/0.28 fof(f2,axiom,(
% 0.08/0.28 (! [B,C,D] :( member(D,difference(B,C))<=> ( member(D,B)& ~ member(D,C) ) ) )),
% 0.08/0.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.08/0.28 fof(f3,axiom,(
% 0.08/0.28 (! [B] : ~ member(B,empty_set) )),
% 0.08/0.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.08/0.28 fof(f4,axiom,(
% 0.08/0.28 (! [B,C] :( subset(B,C)<=> (! [D] :( member(D,B)=> member(D,C) ) )) )),
% 0.08/0.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.08/0.28 fof(f5,axiom,(
% 0.08/0.28 (! [B,C] :( B = C<=> ( subset(B,C)& subset(C,B) ) ) )),
% 0.08/0.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.08/0.28 fof(f8,axiom,(
% 0.08/0.28 (! [B] :( empty(B)<=> (! [C] : ~ member(C,B) )) )),
% 0.08/0.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.08/0.28 fof(f9,conjecture,(
% 0.08/0.28 (! [B,C] :( difference(B,C) = empty_set<=> subset(B,C) ) )),
% 0.08/0.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.08/0.28 fof(f10,negated_conjecture,(
% 0.08/0.28 ~((! [B,C] :( difference(B,C) = empty_set<=> subset(B,C) ) ))),
% 0.08/0.28 inference(negated_conjecture,[status(cth)],[f9])).
% 0.08/0.28 fof(f16,plain,(
% 0.08/0.28 ![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))))),
% 0.08/0.28 inference(NNF_transformation,[status(esa)],[f2])).
% 0.08/0.28 fof(f17,plain,(
% 0.08/0.28 (![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))))),
% 0.08/0.28 inference(miniscoping,[status(esa)],[f16])).
% 0.08/0.28 fof(f18,plain,(
% 0.08/0.28 ![X0,X1,X2]: (~member(X0,difference(X1,X2))|member(X0,X1))),
% 0.08/0.28 inference(cnf_transformation,[status(esa)],[f17])).
% 0.08/0.28 fof(f19,plain,(
% 0.08/0.28 ![X0,X1,X2]: (~member(X0,difference(X1,X2))|~member(X0,X2))),
% 0.08/0.28 inference(cnf_transformation,[status(esa)],[f17])).
% 0.08/0.28 fof(f20,plain,(
% 0.08/0.28 ![X0,X1,X2]: (member(X0,difference(X1,X2))|~member(X0,X1)|member(X0,X2))),
% 0.08/0.28 inference(cnf_transformation,[status(esa)],[f17])).
% 0.08/0.28 fof(f21,plain,(
% 0.08/0.28 ![X0]: (~member(X0,empty_set))),
% 0.08/0.28 inference(cnf_transformation,[status(esa)],[f3])).
% 0.08/0.28 fof(f22,plain,(
% 0.08/0.28 ![B,C]: (subset(B,C)<=>(![D]: (~member(D,B)|member(D,C))))),
% 0.08/0.28 inference(pre_NNF_transformation,[status(esa)],[f4])).
% 0.08/0.28 fof(f23,plain,(
% 0.08/0.28 ![B,C]: ((~subset(B,C)|(![D]: (~member(D,B)|member(D,C))))&(subset(B,C)|(?[D]: (member(D,B)&~member(D,C)))))),
% 0.08/0.28 inference(NNF_transformation,[status(esa)],[f22])).
% 0.08/0.28 fof(f24,plain,(
% 0.08/0.28 (![B,C]: (~subset(B,C)|(![D]: (~member(D,B)|member(D,C)))))&(![B,C]: (subset(B,C)|(?[D]: (member(D,B)&~member(D,C)))))),
% 0.08/0.28 inference(miniscoping,[status(esa)],[f23])).
% 0.08/0.28 fof(f25,plain,(
% 0.08/0.28 (![B,C]: (~subset(B,C)|(![D]: (~member(D,B)|member(D,C)))))&(![B,C]: (subset(B,C)|(member(sk0_1(C,B),B)&~member(sk0_1(C,B),C))))),
% 0.08/0.28 inference(skolemization,[status(esa)],[f24])).
% 0.08/0.28 fof(f26,plain,(
% 0.08/0.28 ![X0,X1,X2]: (~subset(X0,X1)|~member(X2,X0)|member(X2,X1))),
% 0.08/0.28 inference(cnf_transformation,[status(esa)],[f25])).
% 0.08/0.28 fof(f27,plain,(
% 0.08/0.28 ![X0,X1]: (subset(X0,X1)|member(sk0_1(X1,X0),X0))),
% 0.08/0.28 inference(cnf_transformation,[status(esa)],[f25])).
% 0.08/0.28 fof(f28,plain,(
% 0.08/0.28 ![X0,X1]: (subset(X0,X1)|~member(sk0_1(X1,X0),X1))),
% 0.08/0.28 inference(cnf_transformation,[status(esa)],[f25])).
% 0.08/0.28 fof(f29,plain,(
% 0.08/0.28 ![B,C]: ((~B=C|(subset(B,C)&subset(C,B)))&(B=C|(~subset(B,C)|~subset(C,B))))),
% 0.08/0.28 inference(NNF_transformation,[status(esa)],[f5])).
% 0.08/0.28 fof(f30,plain,(
% 0.08/0.28 (![B,C]: (~B=C|(subset(B,C)&subset(C,B))))&(![B,C]: (B=C|(~subset(B,C)|~subset(C,B))))),
% 0.08/0.28 inference(miniscoping,[status(esa)],[f29])).
% 0.08/0.28 fof(f33,plain,(
% 0.08/0.28 ![X0,X1]: (X0=X1|~subset(X0,X1)|~subset(X1,X0))),
% 0.08/0.28 inference(cnf_transformation,[status(esa)],[f30])).
% 0.08/0.28 fof(f42,plain,(
% 0.08/0.28 ![B]: ((~empty(B)|(![C]: ~member(C,B)))&(empty(B)|(?[C]: member(C,B))))),
% 0.08/0.28 inference(NNF_transformation,[status(esa)],[f8])).
% 0.08/0.28 fof(f43,plain,(
% 0.08/0.28 (![B]: (~empty(B)|(![C]: ~member(C,B))))&(![B]: (empty(B)|(?[C]: member(C,B))))),
% 0.08/0.28 inference(miniscoping,[status(esa)],[f42])).
% 0.08/0.28 fof(f44,plain,(
% 0.08/0.28 (![B]: (~empty(B)|(![C]: ~member(C,B))))&(![B]: (empty(B)|member(sk0_3(B),B)))),
% 0.08/0.28 inference(skolemization,[status(esa)],[f43])).
% 0.08/0.28 fof(f45,plain,(
% 0.08/0.28 ![X0,X1]: (~empty(X0)|~member(X1,X0))),
% 0.08/0.28 inference(cnf_transformation,[status(esa)],[f44])).
% 0.08/0.28 fof(f46,plain,(
% 0.08/0.28 ![X0]: (empty(X0)|member(sk0_3(X0),X0))),
% 0.08/0.28 inference(cnf_transformation,[status(esa)],[f44])).
% 0.08/0.28 fof(f47,plain,(
% 0.08/0.28 (?[B,C]: (difference(B,C)=empty_set<~>subset(B,C)))),
% 0.08/0.28 inference(pre_NNF_transformation,[status(esa)],[f10])).
% 0.08/0.28 fof(f48,plain,(
% 0.08/0.28 ?[B,C]: ((difference(B,C)=empty_set|subset(B,C))&(~difference(B,C)=empty_set|~subset(B,C)))),
% 0.08/0.28 inference(NNF_transformation,[status(esa)],[f47])).
% 0.08/0.28 fof(f49,plain,(
% 0.08/0.28 ((difference(sk0_4,sk0_5)=empty_set|subset(sk0_4,sk0_5))&(~difference(sk0_4,sk0_5)=empty_set|~subset(sk0_4,sk0_5)))),
% 0.08/0.28 inference(skolemization,[status(esa)],[f48])).
% 0.08/0.28 fof(f50,plain,(
% 0.08/0.28 difference(sk0_4,sk0_5)=empty_set|subset(sk0_4,sk0_5)),
% 0.08/0.28 inference(cnf_transformation,[status(esa)],[f49])).
% 0.08/0.28 fof(f51,plain,(
% 0.08/0.28 ~difference(sk0_4,sk0_5)=empty_set|~subset(sk0_4,sk0_5)),
% 0.08/0.28 inference(cnf_transformation,[status(esa)],[f49])).
% 0.08/0.28 fof(f52,plain,(
% 0.08/0.28 spl0_0 <=> difference(sk0_4,sk0_5)=empty_set),
% 0.08/0.28 introduced(split_symbol_definition)).
% 0.08/0.28 fof(f53,plain,(
% 0.08/0.28 difference(sk0_4,sk0_5)=empty_set|~spl0_0),
% 0.08/0.28 inference(component_clause,[status(thm)],[f52])).
% 0.08/0.28 fof(f55,plain,(
% 0.08/0.28 spl0_1 <=> subset(sk0_4,sk0_5)),
% 0.08/0.28 introduced(split_symbol_definition)).
% 0.08/0.28 fof(f56,plain,(
% 0.08/0.28 subset(sk0_4,sk0_5)|~spl0_1),
% 0.08/0.28 inference(component_clause,[status(thm)],[f55])).
% 0.08/0.28 fof(f58,plain,(
% 0.08/0.28 spl0_0|spl0_1),
% 0.08/0.28 inference(split_clause,[status(thm)],[f50,f52,f55])).
% 0.08/0.28 fof(f59,plain,(
% 0.08/0.28 ~spl0_0|~spl0_1),
% 0.08/0.28 inference(split_clause,[status(thm)],[f51,f52,f55])).
% 0.08/0.28 fof(f62,plain,(
% 0.08/0.28 ![X0,X1,X2]: (~empty(difference(X0,X1))|~member(X2,X0)|member(X2,X1))),
% 0.08/0.28 inference(resolution,[status(thm)],[f45,f20])).
% 0.08/0.28 fof(f63,plain,(
% 0.08/0.28 ![X0,X1]: (empty(difference(X0,X1))|~member(sk0_3(difference(X0,X1)),X1))),
% 0.08/0.28 inference(resolution,[status(thm)],[f46,f19])).
% 0.08/0.28 fof(f64,plain,(
% 0.08/0.28 ![X0,X1]: (empty(difference(X0,X1))|member(sk0_3(difference(X0,X1)),X0))),
% 0.08/0.28 inference(resolution,[status(thm)],[f46,f18])).
% 0.08/0.28 fof(f65,plain,(
% 0.08/0.28 empty(empty_set)),
% 0.08/0.28 inference(resolution,[status(thm)],[f46,f21])).
% 0.08/0.28 fof(f67,plain,(
% 0.08/0.28 ![X0]: (empty(difference(X0,X0))|empty(difference(X0,X0)))),
% 0.08/0.28 inference(resolution,[status(thm)],[f64,f63])).
% 0.08/0.28 fof(f68,plain,(
% 0.08/0.28 ![X0]: (empty(difference(X0,X0)))),
% 0.08/0.28 inference(duplicate_literals_removal,[status(esa)],[f67])).
% 0.08/0.28 fof(f71,plain,(
% 0.08/0.28 ![X0]: (empty(difference(empty_set,X0)))),
% 0.08/0.28 inference(resolution,[status(thm)],[f64,f21])).
% 0.08/0.28 fof(f72,plain,(
% 0.08/0.28 ![X0,X1]: (empty(difference(X0,X1))|~empty(X0))),
% 0.08/0.28 inference(resolution,[status(thm)],[f64,f45])).
% 0.08/0.28 fof(f81,plain,(
% 0.08/0.28 ![X0]: (subset(empty_set,X0))),
% 0.08/0.28 inference(resolution,[status(thm)],[f27,f21])).
% 0.08/0.28 fof(f82,plain,(
% 0.08/0.28 ![X0,X1]: (subset(X0,X1)|~empty(X0))),
% 0.08/0.28 inference(resolution,[status(thm)],[f27,f45])).
% 0.08/0.28 fof(f84,plain,(
% 0.08/0.28 ![X0]: (X0=empty_set|~subset(X0,empty_set))),
% 0.08/0.28 inference(resolution,[status(thm)],[f81,f33])).
% 0.08/0.28 fof(f86,plain,(
% 0.08/0.28 ![X0,X1]: (~empty(X0)|X1=X0|~subset(X1,X0))),
% 0.08/0.28 inference(resolution,[status(thm)],[f82,f33])).
% 0.08/0.28 fof(f87,plain,(
% 0.08/0.28 ![X0]: (X0=empty_set|~empty(X0))),
% 0.08/0.28 inference(resolution,[status(thm)],[f84,f82])).
% 0.08/0.28 fof(f88,plain,(
% 0.08/0.28 ![X0]: (difference(empty_set,X0)=empty_set)),
% 0.08/0.28 inference(resolution,[status(thm)],[f87,f71])).
% 0.08/0.28 fof(f89,plain,(
% 0.08/0.28 ![X0,X1]: (difference(X0,X1)=empty_set|~empty(X0))),
% 0.08/0.28 inference(resolution,[status(thm)],[f87,f72])).
% 0.08/0.28 fof(f90,plain,(
% 0.08/0.28 ![X0]: (difference(X0,X0)=empty_set)),
% 0.08/0.28 inference(resolution,[status(thm)],[f87,f68])).
% 0.08/0.28 fof(f98,plain,(
% 0.08/0.28 spl0_2 <=> empty(empty_set)),
% 0.08/0.28 introduced(split_symbol_definition)).
% 0.08/0.28 fof(f100,plain,(
% 0.08/0.28 ~empty(empty_set)|spl0_2),
% 0.08/0.28 inference(component_clause,[status(thm)],[f98])).
% 0.08/0.28 fof(f114,plain,(
% 0.08/0.28 spl0_4 <=> ~member(X0,X1)|member(X0,X1)),
% 0.08/0.28 introduced(split_symbol_definition)).
% 0.08/0.28 fof(f117,plain,(
% 0.08/0.28 ![X0,X1]: (~empty(empty_set)|~member(X0,X1)|member(X0,X1))),
% 0.08/0.28 inference(paramodulation,[status(thm)],[f90,f62])).
% 0.08/0.28 fof(f118,plain,(
% 0.08/0.28 ~spl0_2|spl0_4),
% 0.08/0.28 inference(split_clause,[status(thm)],[f117,f98,f114])).
% 0.08/0.28 fof(f144,plain,(
% 0.08/0.28 spl0_7 <=> ~member(X0,empty_set)|member(X0,X1)),
% 0.08/0.28 introduced(split_symbol_definition)).
% 0.08/0.28 fof(f147,plain,(
% 0.08/0.28 ![X0,X1]: (~empty(empty_set)|~member(X0,empty_set)|member(X0,X1))),
% 0.08/0.28 inference(paramodulation,[status(thm)],[f88,f62])).
% 0.08/0.28 fof(f148,plain,(
% 0.08/0.28 ~spl0_2|spl0_7),
% 0.08/0.28 inference(split_clause,[status(thm)],[f147,f98,f144])).
% 0.08/0.28 fof(f151,plain,(
% 0.08/0.28 $false|spl0_2),
% 0.08/0.28 inference(forward_subsumption_resolution,[status(thm)],[f100,f65])).
% 0.08/0.28 fof(f152,plain,(
% 0.08/0.28 spl0_2),
% 0.08/0.28 inference(contradiction_clause,[status(thm)],[f151])).
% 0.08/0.28 fof(f154,plain,(
% 0.08/0.28 ![X0,X1]: (~empty(X0)|X1=X0|~empty(X1))),
% 0.08/0.28 inference(resolution,[status(thm)],[f86,f82])).
% 0.08/0.28 fof(f155,plain,(
% 0.08/0.28 ![X0,X1,X2]: (~empty(X0)|difference(X1,X2)=X0|~empty(X1))),
% 0.08/0.28 inference(resolution,[status(thm)],[f154,f72])).
% 0.08/0.28 fof(f157,plain,(
% 0.08/0.28 spl0_8 <=> empty_set=empty_set),
% 0.08/0.28 introduced(split_symbol_definition)).
% 0.08/0.28 fof(f160,plain,(
% 0.08/0.28 empty_set=empty_set|~empty(empty_set)),
% 0.08/0.28 inference(paramodulation,[status(thm)],[f88,f89])).
% 0.08/0.28 fof(f161,plain,(
% 0.08/0.28 spl0_8|~spl0_2),
% 0.08/0.28 inference(split_clause,[status(thm)],[f160,f157,f98])).
% 0.08/0.28 fof(f167,plain,(
% 0.08/0.28 spl0_9 <=> ~empty(X0)|empty_set=X0),
% 0.08/0.28 introduced(split_symbol_definition)).
% 0.08/0.28 fof(f170,plain,(
% 0.08/0.28 ![X0]: (~empty(X0)|empty_set=X0|~empty(empty_set))),
% 0.08/0.28 inference(paramodulation,[status(thm)],[f88,f155])).
% 0.08/0.28 fof(f171,plain,(
% 0.08/0.28 spl0_9|~spl0_2),
% 0.08/0.28 inference(split_clause,[status(thm)],[f170,f167,f98])).
% 0.08/0.28 fof(f201,plain,(
% 0.08/0.28 spl0_11 <=> empty(difference(sk0_4,sk0_5))),
% 0.08/0.28 introduced(split_symbol_definition)).
% 0.08/0.28 fof(f202,plain,(
% 0.08/0.28 empty(difference(sk0_4,sk0_5))|~spl0_11),
% 0.08/0.28 inference(component_clause,[status(thm)],[f201])).
% 0.08/0.28 fof(f219,plain,(
% 0.08/0.28 ![X0]: (member(X0,empty_set)|~member(X0,sk0_4)|member(X0,sk0_5)|~spl0_0)),
% 0.08/0.28 inference(paramodulation,[status(thm)],[f53,f20])).
% 0.08/0.28 fof(f220,plain,(
% 0.08/0.28 ![X0]: (~member(X0,sk0_4)|member(X0,sk0_5)|~spl0_0)),
% 0.08/0.28 inference(forward_subsumption_resolution,[status(thm)],[f219,f21])).
% 0.08/0.28 fof(f231,plain,(
% 0.08/0.28 ![X0]: (~member(X0,sk0_4)|member(X0,sk0_5)|~spl0_1)),
% 0.08/0.28 inference(resolution,[status(thm)],[f56,f26])).
% 0.08/0.28 fof(f243,plain,(
% 0.08/0.28 ![X0]: (member(sk0_3(difference(sk0_4,X0)),sk0_5)|empty(difference(sk0_4,X0))|~spl0_1)),
% 0.08/0.28 inference(resolution,[status(thm)],[f231,f64])).
% 0.08/0.28 fof(f258,plain,(
% 0.08/0.28 empty(difference(sk0_4,sk0_5))|empty(difference(sk0_4,sk0_5))|~spl0_1),
% 0.08/0.28 inference(resolution,[status(thm)],[f243,f63])).
% 0.08/0.28 fof(f259,plain,(
% 0.08/0.28 spl0_11|~spl0_1),
% 0.08/0.28 inference(split_clause,[status(thm)],[f258,f201,f55])).
% 0.08/0.28 fof(f272,plain,(
% 0.08/0.28 difference(sk0_4,sk0_5)=empty_set|~spl0_11),
% 0.08/0.28 inference(resolution,[status(thm)],[f202,f87])).
% 0.08/0.28 fof(f273,plain,(
% 0.08/0.28 spl0_0|~spl0_11),
% 0.08/0.28 inference(split_clause,[status(thm)],[f272,f52,f201])).
% 0.08/0.28 fof(f302,plain,(
% 0.08/0.28 ![X0]: (member(sk0_1(X0,sk0_4),sk0_5)|subset(sk0_4,X0)|~spl0_0)),
% 0.08/0.28 inference(resolution,[status(thm)],[f220,f27])).
% 0.08/0.28 fof(f311,plain,(
% 0.08/0.28 subset(sk0_4,sk0_5)|subset(sk0_4,sk0_5)|~spl0_0),
% 0.08/0.28 inference(resolution,[status(thm)],[f302,f28])).
% 0.08/0.28 fof(f312,plain,(
% 0.08/0.28 spl0_1|~spl0_0),
% 0.08/0.28 inference(split_clause,[status(thm)],[f311,f55,f52])).
% 0.08/0.28 fof(f315,plain,(
% 0.08/0.28 $false),
% 0.08/0.28 inference(sat_refutation,[status(thm)],[f58,f59,f118,f148,f152,f161,f171,f259,f273,f312])).
% 0.08/0.28 % SZS output end CNFRefutation for theBenchmark.p
% 0.12/0.50 % Elapsed time: 0.013516 seconds
% 0.12/0.50 % CPU time: 0.037295 seconds
% 0.12/0.50 % Memory used: 11.689 MB
%------------------------------------------------------------------------------