TSTP Solution File: SET992+1 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SET992+1 : TPTP v8.1.2. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n019.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 20:40:51 EDT 2024
% Result : Theorem 0.13s 0.37s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET992+1 : TPTP v8.1.2. Bugfixed v4.0.0.
% 0.07/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.35 % Computer : n019.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Apr 29 21:33:59 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.36 % Drodi V3.6.0
% 0.13/0.37 % Refutation found
% 0.13/0.37 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.37 % SZS output start CNFRefutation for theBenchmark
% 0.13/0.37 fof(f4,axiom,(
% 0.13/0.37 (! [A,B] :( B = singleton(A)<=> (! [C] :( in(C,B)<=> C = A ) )) )),
% 0.13/0.37 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.37 fof(f5,axiom,(
% 0.13/0.37 (! [A] :( ( relation(A)& function(A) )=> (! [B] :( B = relation_rng(A)<=> (! [C] :( in(C,B)<=> (? [D] :( in(D,relation_dom(A))& C = apply(A,D) ) )) )) )) )),
% 0.13/0.37 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.37 fof(f25,conjecture,(
% 0.13/0.37 (! [A,B] :( ( relation(B)& function(B) )=> ( relation_dom(B) = singleton(A)=> relation_rng(B) = singleton(apply(B,A)) ) ) )),
% 0.13/0.37 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.37 fof(f26,negated_conjecture,(
% 0.13/0.37 ~((! [A,B] :( ( relation(B)& function(B) )=> ( relation_dom(B) = singleton(A)=> relation_rng(B) = singleton(apply(B,A)) ) ) ))),
% 0.13/0.37 inference(negated_conjecture,[status(cth)],[f25])).
% 0.13/0.37 fof(f42,plain,(
% 0.13/0.37 ![A,B]: ((~B=singleton(A)|(![C]: ((~in(C,B)|C=A)&(in(C,B)|~C=A))))&(B=singleton(A)|(?[C]: ((~in(C,B)|~C=A)&(in(C,B)|C=A)))))),
% 0.13/0.37 inference(NNF_transformation,[status(esa)],[f4])).
% 0.13/0.37 fof(f43,plain,(
% 0.13/0.37 (![A,B]: (~B=singleton(A)|((![C]: (~in(C,B)|C=A))&(![C]: (in(C,B)|~C=A)))))&(![A,B]: (B=singleton(A)|(?[C]: ((~in(C,B)|~C=A)&(in(C,B)|C=A)))))),
% 0.13/0.37 inference(miniscoping,[status(esa)],[f42])).
% 0.13/0.37 fof(f44,plain,(
% 0.13/0.37 (![A,B]: (~B=singleton(A)|((![C]: (~in(C,B)|C=A))&(![C]: (in(C,B)|~C=A)))))&(![A,B]: (B=singleton(A)|((~in(sk0_0(B,A),B)|~sk0_0(B,A)=A)&(in(sk0_0(B,A),B)|sk0_0(B,A)=A))))),
% 0.13/0.37 inference(skolemization,[status(esa)],[f43])).
% 0.13/0.37 fof(f45,plain,(
% 0.13/0.37 ![X0,X1,X2]: (~X0=singleton(X1)|~in(X2,X0)|X2=X1)),
% 0.13/0.37 inference(cnf_transformation,[status(esa)],[f44])).
% 0.13/0.37 fof(f46,plain,(
% 0.13/0.37 ![X0,X1,X2]: (~X0=singleton(X1)|in(X2,X0)|~X2=X1)),
% 0.13/0.37 inference(cnf_transformation,[status(esa)],[f44])).
% 0.13/0.37 fof(f49,plain,(
% 0.13/0.37 ![A]: ((~relation(A)|~function(A))|(![B]: (B=relation_rng(A)<=>(![C]: (in(C,B)<=>(?[D]: (in(D,relation_dom(A))&C=apply(A,D))))))))),
% 0.13/0.37 inference(pre_NNF_transformation,[status(esa)],[f5])).
% 0.13/0.37 fof(f50,plain,(
% 0.13/0.37 ![A]: ((~relation(A)|~function(A))|(![B]: ((~B=relation_rng(A)|(![C]: ((~in(C,B)|(?[D]: (in(D,relation_dom(A))&C=apply(A,D))))&(in(C,B)|(![D]: (~in(D,relation_dom(A))|~C=apply(A,D)))))))&(B=relation_rng(A)|(?[C]: ((~in(C,B)|(![D]: (~in(D,relation_dom(A))|~C=apply(A,D))))&(in(C,B)|(?[D]: (in(D,relation_dom(A))&C=apply(A,D))))))))))),
% 0.13/0.37 inference(NNF_transformation,[status(esa)],[f49])).
% 0.13/0.37 fof(f51,plain,(
% 0.13/0.37 ![A]: ((~relation(A)|~function(A))|((![B]: (~B=relation_rng(A)|((![C]: (~in(C,B)|(?[D]: (in(D,relation_dom(A))&C=apply(A,D)))))&(![C]: (in(C,B)|(![D]: (~in(D,relation_dom(A))|~C=apply(A,D))))))))&(![B]: (B=relation_rng(A)|(?[C]: ((~in(C,B)|(![D]: (~in(D,relation_dom(A))|~C=apply(A,D))))&(in(C,B)|(?[D]: (in(D,relation_dom(A))&C=apply(A,D))))))))))),
% 0.13/0.37 inference(miniscoping,[status(esa)],[f50])).
% 0.13/0.37 fof(f52,plain,(
% 0.13/0.37 ![A]: ((~relation(A)|~function(A))|((![B]: (~B=relation_rng(A)|((![C]: (~in(C,B)|(in(sk0_1(C,B,A),relation_dom(A))&C=apply(A,sk0_1(C,B,A)))))&(![C]: (in(C,B)|(![D]: (~in(D,relation_dom(A))|~C=apply(A,D))))))))&(![B]: (B=relation_rng(A)|((~in(sk0_2(B,A),B)|(![D]: (~in(D,relation_dom(A))|~sk0_2(B,A)=apply(A,D))))&(in(sk0_2(B,A),B)|(in(sk0_3(B,A),relation_dom(A))&sk0_2(B,A)=apply(A,sk0_3(B,A)))))))))),
% 0.13/0.37 inference(skolemization,[status(esa)],[f51])).
% 0.13/0.37 fof(f56,plain,(
% 0.13/0.37 ![X0,X1,X2]: (~relation(X0)|~function(X0)|X1=relation_rng(X0)|~in(sk0_2(X1,X0),X1)|~in(X2,relation_dom(X0))|~sk0_2(X1,X0)=apply(X0,X2))),
% 0.13/0.37 inference(cnf_transformation,[status(esa)],[f52])).
% 0.13/0.37 fof(f57,plain,(
% 0.13/0.37 ![X0,X1]: (~relation(X0)|~function(X0)|X1=relation_rng(X0)|in(sk0_2(X1,X0),X1)|in(sk0_3(X1,X0),relation_dom(X0)))),
% 0.13/0.37 inference(cnf_transformation,[status(esa)],[f52])).
% 0.13/0.37 fof(f58,plain,(
% 0.13/0.37 ![X0,X1]: (~relation(X0)|~function(X0)|X1=relation_rng(X0)|in(sk0_2(X1,X0),X1)|sk0_2(X1,X0)=apply(X0,sk0_3(X1,X0)))),
% 0.13/0.37 inference(cnf_transformation,[status(esa)],[f52])).
% 0.13/0.37 fof(f104,plain,(
% 0.13/0.37 (?[A,B]: ((relation(B)&function(B))&(relation_dom(B)=singleton(A)&~relation_rng(B)=singleton(apply(B,A)))))),
% 0.13/0.37 inference(pre_NNF_transformation,[status(esa)],[f26])).
% 0.13/0.38 fof(f105,plain,(
% 0.13/0.38 ?[B]: ((relation(B)&function(B))&(?[A]: (relation_dom(B)=singleton(A)&~relation_rng(B)=singleton(apply(B,A)))))),
% 0.13/0.38 inference(miniscoping,[status(esa)],[f104])).
% 0.13/0.38 fof(f106,plain,(
% 0.13/0.38 ((relation(sk0_13)&function(sk0_13))&(relation_dom(sk0_13)=singleton(sk0_14)&~relation_rng(sk0_13)=singleton(apply(sk0_13,sk0_14))))),
% 0.13/0.38 inference(skolemization,[status(esa)],[f105])).
% 0.13/0.38 fof(f107,plain,(
% 0.13/0.38 relation(sk0_13)),
% 0.13/0.38 inference(cnf_transformation,[status(esa)],[f106])).
% 0.13/0.38 fof(f108,plain,(
% 0.13/0.38 function(sk0_13)),
% 0.13/0.38 inference(cnf_transformation,[status(esa)],[f106])).
% 0.13/0.38 fof(f109,plain,(
% 0.13/0.38 relation_dom(sk0_13)=singleton(sk0_14)),
% 0.13/0.38 inference(cnf_transformation,[status(esa)],[f106])).
% 0.13/0.38 fof(f110,plain,(
% 0.13/0.38 ~relation_rng(sk0_13)=singleton(apply(sk0_13,sk0_14))),
% 0.13/0.38 inference(cnf_transformation,[status(esa)],[f106])).
% 0.13/0.38 fof(f138,plain,(
% 0.13/0.38 ![X0,X1]: (~in(X0,singleton(X1))|X0=X1)),
% 0.13/0.38 inference(destructive_equality_resolution,[status(esa)],[f45])).
% 0.13/0.38 fof(f139,plain,(
% 0.13/0.38 ![X0]: (in(X0,singleton(X0)))),
% 0.13/0.38 inference(destructive_equality_resolution,[status(esa)],[f46])).
% 0.13/0.38 fof(f175,plain,(
% 0.13/0.38 spl0_4 <=> relation(sk0_13)),
% 0.13/0.38 introduced(split_symbol_definition)).
% 0.13/0.38 fof(f177,plain,(
% 0.13/0.38 ~relation(sk0_13)|spl0_4),
% 0.13/0.38 inference(component_clause,[status(thm)],[f175])).
% 0.13/0.38 fof(f180,plain,(
% 0.13/0.38 $false|spl0_4),
% 0.13/0.38 inference(forward_subsumption_resolution,[status(thm)],[f177,f107])).
% 0.13/0.38 fof(f181,plain,(
% 0.13/0.38 spl0_4),
% 0.13/0.38 inference(contradiction_clause,[status(thm)],[f180])).
% 0.13/0.38 fof(f192,plain,(
% 0.13/0.38 spl0_5 <=> function(sk0_13)),
% 0.13/0.38 introduced(split_symbol_definition)).
% 0.13/0.38 fof(f194,plain,(
% 0.13/0.38 ~function(sk0_13)|spl0_5),
% 0.13/0.38 inference(component_clause,[status(thm)],[f192])).
% 0.13/0.38 fof(f200,plain,(
% 0.13/0.38 $false|spl0_5),
% 0.13/0.38 inference(forward_subsumption_resolution,[status(thm)],[f194,f108])).
% 0.13/0.38 fof(f201,plain,(
% 0.13/0.38 spl0_5),
% 0.13/0.38 inference(contradiction_clause,[status(thm)],[f200])).
% 0.13/0.38 fof(f316,plain,(
% 0.13/0.38 spl0_17 <=> X0=relation_rng(sk0_13)|in(sk0_2(X0,sk0_13),X0)|in(sk0_3(X0,sk0_13),singleton(sk0_14))),
% 0.13/0.38 introduced(split_symbol_definition)).
% 0.13/0.38 fof(f317,plain,(
% 0.13/0.38 ![X0]: (X0=relation_rng(sk0_13)|in(sk0_2(X0,sk0_13),X0)|in(sk0_3(X0,sk0_13),singleton(sk0_14))|~spl0_17)),
% 0.13/0.38 inference(component_clause,[status(thm)],[f316])).
% 0.13/0.38 fof(f319,plain,(
% 0.13/0.38 ![X0]: (~relation(sk0_13)|~function(sk0_13)|X0=relation_rng(sk0_13)|in(sk0_2(X0,sk0_13),X0)|in(sk0_3(X0,sk0_13),singleton(sk0_14)))),
% 0.13/0.38 inference(paramodulation,[status(thm)],[f109,f57])).
% 0.13/0.38 fof(f320,plain,(
% 0.13/0.38 ~spl0_4|~spl0_5|spl0_17),
% 0.13/0.38 inference(split_clause,[status(thm)],[f319,f175,f192,f316])).
% 0.13/0.38 fof(f366,plain,(
% 0.13/0.38 ![X0]: (X0=relation_rng(sk0_13)|in(sk0_2(X0,sk0_13),X0)|sk0_3(X0,sk0_13)=sk0_14|~spl0_17)),
% 0.13/0.38 inference(resolution,[status(thm)],[f317,f138])).
% 0.13/0.38 fof(f386,plain,(
% 0.13/0.38 ![X0]: (singleton(X0)=relation_rng(sk0_13)|sk0_3(singleton(X0),sk0_13)=sk0_14|sk0_2(singleton(X0),sk0_13)=X0|~spl0_17)),
% 0.13/0.38 inference(resolution,[status(thm)],[f366,f138])).
% 0.13/0.38 fof(f424,plain,(
% 0.13/0.38 spl0_28 <=> singleton(X0)=relation_rng(sk0_13)|in(sk0_2(singleton(X0),sk0_13),singleton(X0))|sk0_2(singleton(X0),sk0_13)=apply(sk0_13,sk0_14)|singleton(X0)=relation_rng(sk0_13)|sk0_2(singleton(X0),sk0_13)=X0),
% 0.13/0.38 introduced(split_symbol_definition)).
% 0.13/0.38 fof(f425,plain,(
% 0.13/0.38 ![X0]: (singleton(X0)=relation_rng(sk0_13)|in(sk0_2(singleton(X0),sk0_13),singleton(X0))|sk0_2(singleton(X0),sk0_13)=apply(sk0_13,sk0_14)|singleton(X0)=relation_rng(sk0_13)|sk0_2(singleton(X0),sk0_13)=X0|~spl0_28)),
% 0.13/0.38 inference(component_clause,[status(thm)],[f424])).
% 0.13/0.38 fof(f427,plain,(
% 0.13/0.38 ![X0]: (~relation(sk0_13)|~function(sk0_13)|singleton(X0)=relation_rng(sk0_13)|in(sk0_2(singleton(X0),sk0_13),singleton(X0))|sk0_2(singleton(X0),sk0_13)=apply(sk0_13,sk0_14)|singleton(X0)=relation_rng(sk0_13)|sk0_2(singleton(X0),sk0_13)=X0|~spl0_17)),
% 0.13/0.38 inference(paramodulation,[status(thm)],[f386,f58])).
% 0.13/0.38 fof(f428,plain,(
% 0.13/0.38 ~spl0_4|~spl0_5|spl0_28|~spl0_17),
% 0.13/0.38 inference(split_clause,[status(thm)],[f427,f175,f192,f424,f316])).
% 0.13/0.38 fof(f429,plain,(
% 0.13/0.38 spl0_29 <=> in(sk0_14,relation_dom(sk0_13))),
% 0.13/0.38 introduced(split_symbol_definition)).
% 0.13/0.38 fof(f431,plain,(
% 0.13/0.38 ~in(sk0_14,relation_dom(sk0_13))|spl0_29),
% 0.13/0.38 inference(component_clause,[status(thm)],[f429])).
% 0.13/0.38 fof(f436,plain,(
% 0.13/0.38 ![X0]: (singleton(X0)=relation_rng(sk0_13)|in(sk0_2(singleton(X0),sk0_13),singleton(X0))|sk0_2(singleton(X0),sk0_13)=apply(sk0_13,sk0_14)|sk0_2(singleton(X0),sk0_13)=X0|~spl0_28)),
% 0.13/0.38 inference(duplicate_literals_removal,[status(esa)],[f425])).
% 0.13/0.38 fof(f437,plain,(
% 0.13/0.38 ![X0]: (singleton(X0)=relation_rng(sk0_13)|sk0_2(singleton(X0),sk0_13)=apply(sk0_13,sk0_14)|sk0_2(singleton(X0),sk0_13)=X0|~spl0_28)),
% 0.13/0.38 inference(forward_subsumption_resolution,[status(thm)],[f436,f138])).
% 0.13/0.38 fof(f532,plain,(
% 0.13/0.38 ![X0]: (singleton(X0)=relation_rng(sk0_13)|~apply(sk0_13,sk0_14)=X0|sk0_2(singleton(X0),sk0_13)=X0|~spl0_28)),
% 0.13/0.38 inference(equality_factoring,[status(esa)],[f437])).
% 0.13/0.38 fof(f533,plain,(
% 0.13/0.38 singleton(apply(sk0_13,sk0_14))=relation_rng(sk0_13)|sk0_2(singleton(apply(sk0_13,sk0_14)),sk0_13)=apply(sk0_13,sk0_14)|~spl0_28),
% 0.13/0.38 inference(destructive_equality_resolution,[status(esa)],[f532])).
% 0.13/0.38 fof(f534,plain,(
% 0.13/0.38 sk0_2(singleton(apply(sk0_13,sk0_14)),sk0_13)=apply(sk0_13,sk0_14)|~spl0_28),
% 0.13/0.38 inference(forward_subsumption_resolution,[status(thm)],[f533,f110])).
% 0.13/0.38 fof(f555,plain,(
% 0.13/0.38 ~in(sk0_14,singleton(sk0_14))|spl0_29),
% 0.13/0.38 inference(forward_demodulation,[status(thm)],[f109,f431])).
% 0.13/0.38 fof(f556,plain,(
% 0.13/0.38 $false|spl0_29),
% 0.13/0.38 inference(forward_subsumption_resolution,[status(thm)],[f555,f139])).
% 0.13/0.38 fof(f557,plain,(
% 0.13/0.38 spl0_29),
% 0.13/0.38 inference(contradiction_clause,[status(thm)],[f556])).
% 0.13/0.38 fof(f562,plain,(
% 0.13/0.38 spl0_42 <=> singleton(apply(sk0_13,sk0_14))=relation_rng(sk0_13)),
% 0.13/0.38 introduced(split_symbol_definition)).
% 0.13/0.38 fof(f563,plain,(
% 0.13/0.38 singleton(apply(sk0_13,sk0_14))=relation_rng(sk0_13)|~spl0_42),
% 0.13/0.38 inference(component_clause,[status(thm)],[f562])).
% 0.13/0.38 fof(f565,plain,(
% 0.13/0.38 spl0_43 <=> in(sk0_2(singleton(apply(sk0_13,sk0_14)),sk0_13),singleton(apply(sk0_13,sk0_14)))),
% 0.13/0.38 introduced(split_symbol_definition)).
% 0.13/0.38 fof(f567,plain,(
% 0.13/0.38 ~in(sk0_2(singleton(apply(sk0_13,sk0_14)),sk0_13),singleton(apply(sk0_13,sk0_14)))|spl0_43),
% 0.13/0.38 inference(component_clause,[status(thm)],[f565])).
% 0.13/0.38 fof(f568,plain,(
% 0.13/0.38 ~relation(sk0_13)|~function(sk0_13)|singleton(apply(sk0_13,sk0_14))=relation_rng(sk0_13)|~in(sk0_2(singleton(apply(sk0_13,sk0_14)),sk0_13),singleton(apply(sk0_13,sk0_14)))|~in(sk0_14,relation_dom(sk0_13))|~spl0_28),
% 0.13/0.38 inference(resolution,[status(thm)],[f534,f56])).
% 0.13/0.38 fof(f569,plain,(
% 0.13/0.38 ~spl0_4|~spl0_5|spl0_42|~spl0_43|~spl0_29|~spl0_28),
% 0.13/0.38 inference(split_clause,[status(thm)],[f568,f175,f192,f562,f565,f429,f424])).
% 0.13/0.38 fof(f596,plain,(
% 0.13/0.38 ~in(apply(sk0_13,sk0_14),singleton(apply(sk0_13,sk0_14)))|~spl0_28|spl0_43),
% 0.13/0.38 inference(forward_demodulation,[status(thm)],[f534,f567])).
% 0.13/0.38 fof(f597,plain,(
% 0.13/0.38 $false|~spl0_28|spl0_43),
% 0.13/0.38 inference(forward_subsumption_resolution,[status(thm)],[f596,f139])).
% 0.13/0.38 fof(f598,plain,(
% 0.13/0.38 ~spl0_28|spl0_43),
% 0.13/0.38 inference(contradiction_clause,[status(thm)],[f597])).
% 0.13/0.38 fof(f599,plain,(
% 0.13/0.38 $false|~spl0_42),
% 0.13/0.38 inference(forward_subsumption_resolution,[status(thm)],[f563,f110])).
% 0.13/0.38 fof(f600,plain,(
% 0.13/0.38 ~spl0_42),
% 0.13/0.38 inference(contradiction_clause,[status(thm)],[f599])).
% 0.13/0.38 fof(f601,plain,(
% 0.13/0.38 $false),
% 0.13/0.38 inference(sat_refutation,[status(thm)],[f181,f201,f320,f428,f557,f569,f598,f600])).
% 0.13/0.38 % SZS output end CNFRefutation for theBenchmark.p
% 0.13/0.38 % Elapsed time: 0.027973 seconds
% 0.13/0.38 % CPU time: 0.087985 seconds
% 0.13/0.38 % Total memory used: 18.111 MB
% 0.13/0.38 % Net memory used: 18.027 MB
%------------------------------------------------------------------------------