TSTP Solution File: SET578+3 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SET578+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n009.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 12:34:42 EDT 2023
% Result : Theorem 0.20s 0.45s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET578+3 : TPTP v8.1.2. Released v2.2.0.
% 0.06/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.33 % Computer : n009.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Tue May 30 10:11:01 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.13/0.34 % Drodi V3.5.1
% 0.20/0.45 % Refutation found
% 0.20/0.45 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.20/0.45 % SZS output start CNFRefutation for theBenchmark
% 0.20/0.45 fof(f1,axiom,(
% 0.20/0.45 (! [B,C,D] :( member(D,intersection(B,C))<=> ( member(D,B)& member(D,C) ) ) )),
% 0.20/0.45 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.20/0.45 fof(f2,axiom,(
% 0.20/0.45 (! [B,C] :( B = C<=> ( subset(B,C)& subset(C,B) ) ) )),
% 0.20/0.45 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.20/0.45 fof(f4,axiom,(
% 0.20/0.45 (! [B,C] :( subset(B,C)<=> (! [D] :( member(D,B)=> member(D,C) ) )) )),
% 0.20/0.45 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.20/0.45 fof(f6,axiom,(
% 0.20/0.45 (! [B,C] :( B = C<=> (! [D] :( member(D,B)<=> member(D,C) ) )) )),
% 0.20/0.45 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.20/0.45 fof(f7,conjecture,(
% 0.20/0.45 (! [B,C,D] :( (! [E] :( member(E,B)<=> ( member(E,C)& member(E,D) ) ))=> B = intersection(C,D) ) )),
% 0.20/0.45 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.20/0.45 fof(f8,negated_conjecture,(
% 0.20/0.45 ~((! [B,C,D] :( (! [E] :( member(E,B)<=> ( member(E,C)& member(E,D) ) ))=> B = intersection(C,D) ) ))),
% 0.20/0.45 inference(negated_conjecture,[status(cth)],[f7])).
% 0.20/0.45 fof(f9,plain,(
% 0.20/0.45 ![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))))),
% 0.20/0.45 inference(NNF_transformation,[status(esa)],[f1])).
% 0.20/0.45 fof(f10,plain,(
% 0.20/0.45 (![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))))),
% 0.20/0.45 inference(miniscoping,[status(esa)],[f9])).
% 0.20/0.45 fof(f11,plain,(
% 0.20/0.45 ![X0,X1,X2]: (~member(X0,intersection(X1,X2))|member(X0,X1))),
% 0.20/0.45 inference(cnf_transformation,[status(esa)],[f10])).
% 0.20/0.45 fof(f12,plain,(
% 0.20/0.45 ![X0,X1,X2]: (~member(X0,intersection(X1,X2))|member(X0,X2))),
% 0.20/0.45 inference(cnf_transformation,[status(esa)],[f10])).
% 0.20/0.45 fof(f13,plain,(
% 0.20/0.45 ![X0,X1,X2]: (member(X0,intersection(X1,X2))|~member(X0,X1)|~member(X0,X2))),
% 0.20/0.45 inference(cnf_transformation,[status(esa)],[f10])).
% 0.20/0.45 fof(f14,plain,(
% 0.20/0.45 ![B,C]: ((~B=C|(subset(B,C)&subset(C,B)))&(B=C|(~subset(B,C)|~subset(C,B))))),
% 0.20/0.45 inference(NNF_transformation,[status(esa)],[f2])).
% 0.20/0.45 fof(f15,plain,(
% 0.20/0.45 (![B,C]: (~B=C|(subset(B,C)&subset(C,B))))&(![B,C]: (B=C|(~subset(B,C)|~subset(C,B))))),
% 0.20/0.45 inference(miniscoping,[status(esa)],[f14])).
% 0.20/0.45 fof(f16,plain,(
% 0.20/0.45 ![X0,X1]: (~X0=X1|subset(X0,X1))),
% 0.20/0.45 inference(cnf_transformation,[status(esa)],[f15])).
% 0.20/0.45 fof(f20,plain,(
% 0.20/0.45 ![B,C]: (subset(B,C)<=>(![D]: (~member(D,B)|member(D,C))))),
% 0.20/0.45 inference(pre_NNF_transformation,[status(esa)],[f4])).
% 0.20/0.45 fof(f21,plain,(
% 0.20/0.45 ![B,C]: ((~subset(B,C)|(![D]: (~member(D,B)|member(D,C))))&(subset(B,C)|(?[D]: (member(D,B)&~member(D,C)))))),
% 0.20/0.45 inference(NNF_transformation,[status(esa)],[f20])).
% 0.20/0.45 fof(f22,plain,(
% 0.20/0.45 (![B,C]: (~subset(B,C)|(![D]: (~member(D,B)|member(D,C)))))&(![B,C]: (subset(B,C)|(?[D]: (member(D,B)&~member(D,C)))))),
% 0.20/0.45 inference(miniscoping,[status(esa)],[f21])).
% 0.20/0.45 fof(f23,plain,(
% 0.20/0.45 (![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))))),
% 0.20/0.45 inference(skolemization,[status(esa)],[f22])).
% 0.20/0.45 fof(f24,plain,(
% 0.20/0.45 ![X0,X1,X2]: (~subset(X0,X1)|~member(X2,X0)|member(X2,X1))),
% 0.20/0.45 inference(cnf_transformation,[status(esa)],[f23])).
% 0.20/0.45 fof(f25,plain,(
% 0.20/0.45 ![X0,X1]: (subset(X0,X1)|member(sk0_0(X1,X0),X0))),
% 0.20/0.45 inference(cnf_transformation,[status(esa)],[f23])).
% 0.20/0.45 fof(f26,plain,(
% 0.20/0.45 ![X0,X1]: (subset(X0,X1)|~member(sk0_0(X1,X0),X1))),
% 0.20/0.45 inference(cnf_transformation,[status(esa)],[f23])).
% 0.20/0.45 fof(f28,plain,(
% 0.20/0.45 ![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))))))),
% 0.20/0.45 inference(NNF_transformation,[status(esa)],[f6])).
% 0.20/0.45 fof(f29,plain,(
% 0.20/0.45 (![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))))))),
% 0.20/0.45 inference(miniscoping,[status(esa)],[f28])).
% 0.20/0.45 fof(f30,plain,(
% 0.20/0.45 (![B,C]: (~B=C|((![D]: (~member(D,B)|member(D,C)))&(![D]: (member(D,B)|~member(D,C))))))&(![B,C]: (B=C|((~member(sk0_1(C,B),B)|~member(sk0_1(C,B),C))&(member(sk0_1(C,B),B)|member(sk0_1(C,B),C)))))),
% 0.20/0.45 inference(skolemization,[status(esa)],[f29])).
% 0.20/0.45 fof(f33,plain,(
% 0.20/0.45 ![X0,X1]: (X0=X1|~member(sk0_1(X1,X0),X0)|~member(sk0_1(X1,X0),X1))),
% 0.20/0.45 inference(cnf_transformation,[status(esa)],[f30])).
% 0.20/0.45 fof(f34,plain,(
% 0.20/0.45 ![X0,X1]: (X0=X1|member(sk0_1(X1,X0),X0)|member(sk0_1(X1,X0),X1))),
% 0.20/0.45 inference(cnf_transformation,[status(esa)],[f30])).
% 0.20/0.45 fof(f35,plain,(
% 0.20/0.45 (?[B,C,D]: ((![E]: (member(E,B)<=>(member(E,C)&member(E,D))))&~B=intersection(C,D)))),
% 0.20/0.45 inference(pre_NNF_transformation,[status(esa)],[f8])).
% 0.20/0.45 fof(f36,plain,(
% 0.20/0.45 ?[B,C,D]: ((![E]: ((~member(E,B)|(member(E,C)&member(E,D)))&(member(E,B)|(~member(E,C)|~member(E,D)))))&~B=intersection(C,D))),
% 0.20/0.45 inference(NNF_transformation,[status(esa)],[f35])).
% 0.20/0.45 fof(f37,plain,(
% 0.20/0.45 ?[B,C,D]: (((![E]: (~member(E,B)|(member(E,C)&member(E,D))))&(![E]: (member(E,B)|(~member(E,C)|~member(E,D)))))&~B=intersection(C,D))),
% 0.20/0.45 inference(miniscoping,[status(esa)],[f36])).
% 0.20/0.45 fof(f38,plain,(
% 0.20/0.45 (((![E]: (~member(E,sk0_2)|(member(E,sk0_3)&member(E,sk0_4))))&(![E]: (member(E,sk0_2)|(~member(E,sk0_3)|~member(E,sk0_4)))))&~sk0_2=intersection(sk0_3,sk0_4))),
% 0.20/0.45 inference(skolemization,[status(esa)],[f37])).
% 0.20/0.45 fof(f39,plain,(
% 0.20/0.45 ![X0]: (~member(X0,sk0_2)|member(X0,sk0_3))),
% 0.20/0.45 inference(cnf_transformation,[status(esa)],[f38])).
% 0.20/0.45 fof(f40,plain,(
% 0.20/0.45 ![X0]: (~member(X0,sk0_2)|member(X0,sk0_4))),
% 0.20/0.45 inference(cnf_transformation,[status(esa)],[f38])).
% 0.20/0.45 fof(f41,plain,(
% 0.20/0.45 ![X0]: (member(X0,sk0_2)|~member(X0,sk0_3)|~member(X0,sk0_4))),
% 0.20/0.45 inference(cnf_transformation,[status(esa)],[f38])).
% 0.20/0.45 fof(f42,plain,(
% 0.20/0.45 ~sk0_2=intersection(sk0_3,sk0_4)),
% 0.20/0.45 inference(cnf_transformation,[status(esa)],[f38])).
% 0.20/0.45 fof(f43,plain,(
% 0.20/0.45 ![X0]: (subset(X0,X0))),
% 0.20/0.45 inference(destructive_equality_resolution,[status(esa)],[f16])).
% 0.20/0.45 fof(f63,plain,(
% 0.20/0.45 ![X0]: (subset(sk0_4,X0)|member(sk0_0(X0,sk0_4),sk0_2)|~member(sk0_0(X0,sk0_4),sk0_3))),
% 0.20/0.45 inference(resolution,[status(thm)],[f25,f41])).
% 0.20/0.45 fof(f81,plain,(
% 0.20/0.45 ![X0]: (subset(X0,sk0_4)|~member(sk0_0(sk0_4,X0),sk0_2))),
% 0.20/0.45 inference(resolution,[status(thm)],[f26,f40])).
% 0.20/0.45 fof(f91,plain,(
% 0.20/0.45 ![X0,X1]: (~subset(sk0_4,X0)|member(X1,X0)|~member(X1,sk0_2))),
% 0.20/0.45 inference(resolution,[status(thm)],[f24,f40])).
% 0.20/0.45 fof(f92,plain,(
% 0.20/0.45 ![X0,X1]: (~subset(sk0_3,X0)|member(X1,X0)|~member(X1,sk0_2))),
% 0.20/0.45 inference(resolution,[status(thm)],[f24,f39])).
% 0.20/0.45 fof(f96,plain,(
% 0.20/0.45 spl0_3 <=> ~member(sk0_0(X0,sk0_4),sk0_2)|subset(sk0_4,X0)|member(sk0_0(X0,sk0_4),sk0_2)),
% 0.20/0.45 introduced(split_symbol_definition)).
% 0.20/0.45 fof(f104,plain,(
% 0.20/0.45 spl0_4 <=> subset(sk0_4,sk0_4)),
% 0.20/0.45 introduced(split_symbol_definition)).
% 0.20/0.45 fof(f106,plain,(
% 0.20/0.45 ~subset(sk0_4,sk0_4)|spl0_4),
% 0.20/0.45 inference(component_clause,[status(thm)],[f104])).
% 0.20/0.45 fof(f107,plain,(
% 0.20/0.45 spl0_5 <=> ~member(X0,sk0_2)|member(X0,sk0_2)|~member(X0,sk0_3)),
% 0.20/0.45 introduced(split_symbol_definition)).
% 0.20/0.45 fof(f110,plain,(
% 0.20/0.45 ![X0]: (~subset(sk0_4,sk0_4)|~member(X0,sk0_2)|member(X0,sk0_2)|~member(X0,sk0_3))),
% 0.20/0.45 inference(resolution,[status(thm)],[f91,f41])).
% 0.20/0.45 fof(f111,plain,(
% 0.20/0.45 ~spl0_4|spl0_5),
% 0.20/0.45 inference(split_clause,[status(thm)],[f110,f104,f107])).
% 0.20/0.45 fof(f113,plain,(
% 0.20/0.45 $false|spl0_4),
% 0.20/0.45 inference(forward_subsumption_resolution,[status(thm)],[f106,f43])).
% 0.20/0.45 fof(f114,plain,(
% 0.20/0.45 spl0_4),
% 0.20/0.45 inference(contradiction_clause,[status(thm)],[f113])).
% 0.20/0.45 fof(f115,plain,(
% 0.20/0.45 spl0_6 <=> subset(sk0_3,sk0_3)),
% 0.20/0.45 introduced(split_symbol_definition)).
% 0.20/0.45 fof(f117,plain,(
% 0.20/0.45 ~subset(sk0_3,sk0_3)|spl0_6),
% 0.20/0.45 inference(component_clause,[status(thm)],[f115])).
% 0.20/0.45 fof(f118,plain,(
% 0.20/0.45 ![X0]: (~subset(sk0_3,sk0_3)|~member(sk0_0(X0,sk0_4),sk0_2)|subset(sk0_4,X0)|member(sk0_0(X0,sk0_4),sk0_2))),
% 0.20/0.45 inference(resolution,[status(thm)],[f92,f63])).
% 0.20/0.45 fof(f119,plain,(
% 0.20/0.45 ~spl0_6|spl0_3),
% 0.20/0.45 inference(split_clause,[status(thm)],[f118,f115,f96])).
% 0.20/0.45 fof(f129,plain,(
% 0.20/0.45 $false|spl0_6),
% 0.20/0.45 inference(forward_subsumption_resolution,[status(thm)],[f117,f43])).
% 0.20/0.45 fof(f130,plain,(
% 0.20/0.45 spl0_6),
% 0.20/0.45 inference(contradiction_clause,[status(thm)],[f129])).
% 0.20/0.45 fof(f170,plain,(
% 0.20/0.45 spl0_14 <=> subset(sk0_2,sk0_4)),
% 0.20/0.45 introduced(split_symbol_definition)).
% 0.20/0.45 fof(f173,plain,(
% 0.20/0.45 subset(sk0_2,sk0_4)|subset(sk0_2,sk0_4)),
% 0.20/0.45 inference(resolution,[status(thm)],[f81,f25])).
% 0.20/0.45 fof(f174,plain,(
% 0.20/0.45 spl0_14),
% 0.20/0.45 inference(split_clause,[status(thm)],[f173,f170])).
% 0.20/0.45 fof(f188,plain,(
% 0.20/0.45 spl0_16 <=> member(sk0_1(intersection(sk0_3,sk0_4),sk0_2),sk0_2)),
% 0.20/0.45 introduced(split_symbol_definition)).
% 0.20/0.45 fof(f191,plain,(
% 0.20/0.45 spl0_17 <=> member(sk0_1(intersection(sk0_3,sk0_4),sk0_2),intersection(sk0_3,sk0_4))),
% 0.20/0.45 introduced(split_symbol_definition)).
% 0.20/0.45 fof(f192,plain,(
% 0.20/0.45 member(sk0_1(intersection(sk0_3,sk0_4),sk0_2),intersection(sk0_3,sk0_4))|~spl0_17),
% 0.20/0.45 inference(component_clause,[status(thm)],[f191])).
% 0.20/0.45 fof(f193,plain,(
% 0.20/0.45 ~member(sk0_1(intersection(sk0_3,sk0_4),sk0_2),intersection(sk0_3,sk0_4))|spl0_17),
% 0.20/0.45 inference(component_clause,[status(thm)],[f191])).
% 0.20/0.45 fof(f194,plain,(
% 0.20/0.45 ~member(sk0_1(intersection(sk0_3,sk0_4),sk0_2),sk0_2)|~member(sk0_1(intersection(sk0_3,sk0_4),sk0_2),intersection(sk0_3,sk0_4))),
% 0.20/0.45 inference(resolution,[status(thm)],[f33,f42])).
% 0.20/0.45 fof(f195,plain,(
% 0.20/0.45 ~spl0_16|~spl0_17),
% 0.20/0.45 inference(split_clause,[status(thm)],[f194,f188,f191])).
% 0.20/0.45 fof(f204,plain,(
% 0.20/0.45 member(sk0_1(intersection(sk0_3,sk0_4),sk0_2),sk0_2)|member(sk0_1(intersection(sk0_3,sk0_4),sk0_2),intersection(sk0_3,sk0_4))),
% 0.20/0.45 inference(resolution,[status(thm)],[f34,f42])).
% 0.20/0.45 fof(f205,plain,(
% 0.20/0.45 spl0_16|spl0_17),
% 0.20/0.45 inference(split_clause,[status(thm)],[f204,f188,f191])).
% 0.20/0.45 fof(f396,plain,(
% 0.20/0.45 member(sk0_1(intersection(sk0_3,sk0_4),sk0_2),sk0_4)|~spl0_17),
% 0.20/0.45 inference(resolution,[status(thm)],[f192,f12])).
% 0.20/0.45 fof(f397,plain,(
% 0.20/0.45 member(sk0_1(intersection(sk0_3,sk0_4),sk0_2),sk0_3)|~spl0_17),
% 0.20/0.45 inference(resolution,[status(thm)],[f192,f11])).
% 0.20/0.45 fof(f415,plain,(
% 0.20/0.45 spl0_28 <=> member(sk0_1(intersection(sk0_3,sk0_4),sk0_2),sk0_3)),
% 0.20/0.45 introduced(split_symbol_definition)).
% 0.20/0.45 fof(f417,plain,(
% 0.20/0.45 ~member(sk0_1(intersection(sk0_3,sk0_4),sk0_2),sk0_3)|spl0_28),
% 0.20/0.45 inference(component_clause,[status(thm)],[f415])).
% 0.20/0.45 fof(f418,plain,(
% 0.20/0.45 member(sk0_1(intersection(sk0_3,sk0_4),sk0_2),sk0_2)|~member(sk0_1(intersection(sk0_3,sk0_4),sk0_2),sk0_3)|~spl0_17),
% 0.20/0.45 inference(resolution,[status(thm)],[f396,f41])).
% 0.20/0.45 fof(f419,plain,(
% 0.20/0.45 spl0_16|~spl0_28|~spl0_17),
% 0.20/0.45 inference(split_clause,[status(thm)],[f418,f188,f415,f191])).
% 0.20/0.45 fof(f433,plain,(
% 0.20/0.45 spl0_29 <=> member(sk0_1(intersection(sk0_3,sk0_4),sk0_2),sk0_4)),
% 0.20/0.45 introduced(split_symbol_definition)).
% 0.20/0.45 fof(f435,plain,(
% 0.20/0.45 ~member(sk0_1(intersection(sk0_3,sk0_4),sk0_2),sk0_4)|spl0_29),
% 0.20/0.45 inference(component_clause,[status(thm)],[f433])).
% 0.20/0.45 fof(f436,plain,(
% 0.20/0.45 ~member(sk0_1(intersection(sk0_3,sk0_4),sk0_2),sk0_3)|~member(sk0_1(intersection(sk0_3,sk0_4),sk0_2),sk0_4)|spl0_17),
% 0.20/0.45 inference(resolution,[status(thm)],[f193,f13])).
% 0.20/0.45 fof(f437,plain,(
% 0.20/0.45 ~spl0_28|~spl0_29|spl0_17),
% 0.20/0.45 inference(split_clause,[status(thm)],[f436,f415,f433,f191])).
% 0.20/0.45 fof(f463,plain,(
% 0.20/0.45 ~subset(sk0_3,sk0_3)|~member(sk0_1(intersection(sk0_3,sk0_4),sk0_2),sk0_2)|spl0_28),
% 0.20/0.45 inference(resolution,[status(thm)],[f417,f92])).
% 0.20/0.45 fof(f464,plain,(
% 0.20/0.45 ~spl0_6|~spl0_16|spl0_28),
% 0.20/0.45 inference(split_clause,[status(thm)],[f463,f115,f188,f415])).
% 0.20/0.45 fof(f516,plain,(
% 0.20/0.45 $false|spl0_28|~spl0_17),
% 0.20/0.45 inference(forward_subsumption_resolution,[status(thm)],[f397,f417])).
% 0.20/0.45 fof(f517,plain,(
% 0.20/0.45 spl0_28|~spl0_17),
% 0.20/0.45 inference(contradiction_clause,[status(thm)],[f516])).
% 0.20/0.45 fof(f540,plain,(
% 0.20/0.45 ~subset(sk0_4,sk0_4)|~member(sk0_1(intersection(sk0_3,sk0_4),sk0_2),sk0_2)|spl0_29),
% 0.20/0.45 inference(resolution,[status(thm)],[f435,f91])).
% 0.20/0.45 fof(f541,plain,(
% 0.20/0.45 ~spl0_4|~spl0_16|spl0_29),
% 0.20/0.45 inference(split_clause,[status(thm)],[f540,f104,f188,f433])).
% 0.20/0.45 fof(f554,plain,(
% 0.20/0.45 $false),
% 0.20/0.45 inference(sat_refutation,[status(thm)],[f111,f114,f119,f130,f174,f195,f205,f419,f437,f464,f517,f541])).
% 0.20/0.45 % SZS output end CNFRefutation for theBenchmark.p
% 0.20/0.46 % Elapsed time: 0.122658 seconds
% 0.20/0.46 % CPU time: 0.860514 seconds
% 0.20/0.46 % Memory used: 65.974 MB
%------------------------------------------------------------------------------