TSTP Solution File: SET751+4 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SET751+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n025.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 20:40:17 EDT 2024
% Result : Theorem 123.22s 15.94s
% Output : CNFRefutation 124.05s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SET751+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% 0.08/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.35 % Computer : n025.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 21:42:41 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.37 % Drodi V3.6.0
% 123.22/15.94 % Refutation found
% 123.22/15.94 % SZS status Theorem for theBenchmark: Theorem is valid
% 123.22/15.94 % SZS output start CNFRefutation for theBenchmark
% 123.22/15.94 fof(f1,axiom,(
% 123.22/15.94 (! [A,B] :( subset(A,B)<=> (! [X] :( member(X,A)=> member(X,B) ) )) )),
% 123.22/15.94 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 123.22/15.94 fof(f3,axiom,(
% 123.22/15.94 (! [X,A] :( member(X,power_set(A))<=> subset(X,A) ) )),
% 123.22/15.94 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 123.22/15.94 fof(f8,axiom,(
% 123.22/15.94 (! [X,A] :( member(X,singleton(A))<=> X = A ) )),
% 123.22/15.94 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 123.22/15.94 fof(f22,axiom,(
% 123.22/15.94 (! [F,A,Y] :( member(Y,image2(F,A))<=> (? [X] :( member(X,A)& apply(F,X,Y) ) )) )),
% 123.22/15.94 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 123.22/15.94 fof(f29,conjecture,(
% 123.22/15.94 (! [F,A,B,X,Y] :( ( maps(F,A,B)& subset(X,A)& subset(Y,A)& subset(X,Y) )=> subset(image2(F,X),image2(F,Y)) ) )),
% 123.22/15.94 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 123.22/15.94 fof(f30,negated_conjecture,(
% 123.22/15.94 ~((! [F,A,B,X,Y] :( ( maps(F,A,B)& subset(X,A)& subset(Y,A)& subset(X,Y) )=> subset(image2(F,X),image2(F,Y)) ) ))),
% 123.22/15.94 inference(negated_conjecture,[status(cth)],[f29])).
% 123.22/15.94 fof(f31,plain,(
% 123.22/15.94 ![A,B]: (subset(A,B)<=>(![X]: (~member(X,A)|member(X,B))))),
% 123.22/15.94 inference(pre_NNF_transformation,[status(esa)],[f1])).
% 123.22/15.94 fof(f32,plain,(
% 123.22/15.94 ![A,B]: ((~subset(A,B)|(![X]: (~member(X,A)|member(X,B))))&(subset(A,B)|(?[X]: (member(X,A)&~member(X,B)))))),
% 123.22/15.94 inference(NNF_transformation,[status(esa)],[f31])).
% 123.22/15.94 fof(f33,plain,(
% 123.22/15.94 (![A,B]: (~subset(A,B)|(![X]: (~member(X,A)|member(X,B)))))&(![A,B]: (subset(A,B)|(?[X]: (member(X,A)&~member(X,B)))))),
% 123.22/15.94 inference(miniscoping,[status(esa)],[f32])).
% 123.22/15.94 fof(f34,plain,(
% 123.22/15.94 (![A,B]: (~subset(A,B)|(![X]: (~member(X,A)|member(X,B)))))&(![A,B]: (subset(A,B)|(member(sk0_0(B,A),A)&~member(sk0_0(B,A),B))))),
% 123.22/15.94 inference(skolemization,[status(esa)],[f33])).
% 123.22/15.94 fof(f35,plain,(
% 123.22/15.94 ![X0,X1,X2]: (~subset(X0,X1)|~member(X2,X0)|member(X2,X1))),
% 123.22/15.94 inference(cnf_transformation,[status(esa)],[f34])).
% 123.22/15.94 fof(f36,plain,(
% 123.22/15.94 ![X0,X1]: (subset(X0,X1)|member(sk0_0(X1,X0),X0))),
% 123.22/15.94 inference(cnf_transformation,[status(esa)],[f34])).
% 123.22/15.94 fof(f37,plain,(
% 123.22/15.94 ![X0,X1]: (subset(X0,X1)|~member(sk0_0(X1,X0),X1))),
% 123.22/15.94 inference(cnf_transformation,[status(esa)],[f34])).
% 123.22/15.94 fof(f43,plain,(
% 123.22/15.94 ![X,A]: ((~member(X,power_set(A))|subset(X,A))&(member(X,power_set(A))|~subset(X,A)))),
% 123.22/15.94 inference(NNF_transformation,[status(esa)],[f3])).
% 123.22/15.94 fof(f44,plain,(
% 123.22/15.94 (![X,A]: (~member(X,power_set(A))|subset(X,A)))&(![X,A]: (member(X,power_set(A))|~subset(X,A)))),
% 123.22/15.94 inference(miniscoping,[status(esa)],[f43])).
% 123.22/15.94 fof(f45,plain,(
% 123.22/15.94 ![X0,X1]: (~member(X0,power_set(X1))|subset(X0,X1))),
% 123.22/15.94 inference(cnf_transformation,[status(esa)],[f44])).
% 123.22/15.94 fof(f46,plain,(
% 123.22/15.94 ![X0,X1]: (member(X0,power_set(X1))|~subset(X0,X1))),
% 123.22/15.94 inference(cnf_transformation,[status(esa)],[f44])).
% 123.22/15.94 fof(f63,plain,(
% 123.22/15.94 ![X,A]: ((~member(X,singleton(A))|X=A)&(member(X,singleton(A))|~X=A))),
% 123.22/15.94 inference(NNF_transformation,[status(esa)],[f8])).
% 123.22/15.94 fof(f64,plain,(
% 123.22/15.94 (![X,A]: (~member(X,singleton(A))|X=A))&(![X,A]: (member(X,singleton(A))|~X=A))),
% 123.22/15.94 inference(miniscoping,[status(esa)],[f63])).
% 123.22/15.94 fof(f65,plain,(
% 123.22/15.94 ![X0,X1]: (~member(X0,singleton(X1))|X0=X1)),
% 123.22/15.94 inference(cnf_transformation,[status(esa)],[f64])).
% 123.22/15.94 fof(f66,plain,(
% 123.22/15.94 ![X0,X1]: (member(X0,singleton(X1))|~X0=X1)),
% 123.22/15.94 inference(cnf_transformation,[status(esa)],[f64])).
% 123.22/15.94 fof(f176,plain,(
% 123.22/15.94 ![F,A,Y]: ((~member(Y,image2(F,A))|(?[X]: (member(X,A)&apply(F,X,Y))))&(member(Y,image2(F,A))|(![X]: (~member(X,A)|~apply(F,X,Y)))))),
% 123.22/15.94 inference(NNF_transformation,[status(esa)],[f22])).
% 123.22/15.94 fof(f177,plain,(
% 123.22/15.94 (![F,A,Y]: (~member(Y,image2(F,A))|(?[X]: (member(X,A)&apply(F,X,Y)))))&(![F,A,Y]: (member(Y,image2(F,A))|(![X]: (~member(X,A)|~apply(F,X,Y)))))),
% 123.22/15.94 inference(miniscoping,[status(esa)],[f176])).
% 123.22/15.94 fof(f178,plain,(
% 123.22/15.94 (![F,A,Y]: (~member(Y,image2(F,A))|(member(sk0_23(Y,A,F),A)&apply(F,sk0_23(Y,A,F),Y))))&(![F,A,Y]: (member(Y,image2(F,A))|(![X]: (~member(X,A)|~apply(F,X,Y)))))),
% 123.22/15.94 inference(skolemization,[status(esa)],[f177])).
% 123.22/15.94 fof(f179,plain,(
% 123.22/15.94 ![X0,X1,X2]: (~member(X0,image2(X1,X2))|member(sk0_23(X0,X2,X1),X2))),
% 123.22/15.94 inference(cnf_transformation,[status(esa)],[f178])).
% 123.22/15.94 fof(f180,plain,(
% 123.22/15.95 ![X0,X1,X2]: (~member(X0,image2(X1,X2))|apply(X1,sk0_23(X0,X2,X1),X0))),
% 123.22/15.95 inference(cnf_transformation,[status(esa)],[f178])).
% 123.22/15.95 fof(f181,plain,(
% 123.22/15.95 ![X0,X1,X2,X3]: (member(X0,image2(X1,X2))|~member(X3,X2)|~apply(X1,X3,X0))),
% 123.22/15.95 inference(cnf_transformation,[status(esa)],[f178])).
% 123.22/15.95 fof(f244,plain,(
% 123.22/15.95 (?[F,A,B,X,Y]: ((((maps(F,A,B)&subset(X,A))&subset(Y,A))&subset(X,Y))&~subset(image2(F,X),image2(F,Y))))),
% 123.22/15.95 inference(pre_NNF_transformation,[status(esa)],[f30])).
% 123.22/15.95 fof(f245,plain,(
% 123.22/15.95 ?[F,X,Y]: (((?[A]: (((?[B]: maps(F,A,B))&subset(X,A))&subset(Y,A)))&subset(X,Y))&~subset(image2(F,X),image2(F,Y)))),
% 123.22/15.95 inference(miniscoping,[status(esa)],[f244])).
% 123.22/15.95 fof(f246,plain,(
% 123.22/15.95 ((((maps(sk0_39,sk0_42,sk0_43)&subset(sk0_40,sk0_42))&subset(sk0_41,sk0_42))&subset(sk0_40,sk0_41))&~subset(image2(sk0_39,sk0_40),image2(sk0_39,sk0_41)))),
% 123.22/15.95 inference(skolemization,[status(esa)],[f245])).
% 123.22/15.95 fof(f250,plain,(
% 123.22/15.95 subset(sk0_40,sk0_41)),
% 123.22/15.95 inference(cnf_transformation,[status(esa)],[f246])).
% 123.22/15.95 fof(f251,plain,(
% 123.22/15.95 ~subset(image2(sk0_39,sk0_40),image2(sk0_39,sk0_41))),
% 123.22/15.95 inference(cnf_transformation,[status(esa)],[f246])).
% 123.22/15.95 fof(f265,plain,(
% 123.22/15.95 ![X0]: (member(X0,singleton(X0)))),
% 123.22/15.95 inference(destructive_equality_resolution,[status(esa)],[f66])).
% 123.22/15.95 fof(f270,plain,(
% 123.22/15.95 ![X0,X1]: (subset(singleton(X0),X1)|sk0_0(X1,singleton(X0))=X0)),
% 123.22/15.95 inference(resolution,[status(thm)],[f36,f65])).
% 123.22/15.95 fof(f275,plain,(
% 123.22/15.95 ![X0,X1,X2]: (subset(X0,X1)|~subset(X2,power_set(X1))|~member(X0,X2))),
% 123.22/15.95 inference(resolution,[status(thm)],[f45,f35])).
% 123.22/15.95 fof(f276,plain,(
% 123.22/15.95 ~member(sk0_0(image2(sk0_39,sk0_41),image2(sk0_39,sk0_40)),image2(sk0_39,sk0_41))),
% 123.22/15.95 inference(resolution,[status(thm)],[f37,f251])).
% 123.22/15.95 fof(f291,plain,(
% 123.22/15.95 ![X0]: (~member(X0,sk0_41)|~apply(sk0_39,X0,sk0_0(image2(sk0_39,sk0_41),image2(sk0_39,sk0_40))))),
% 123.22/15.95 inference(resolution,[status(thm)],[f276,f181])).
% 123.22/15.95 fof(f427,plain,(
% 123.22/15.95 ![X0,X1,X2]: (subset(X0,X1)|~member(X0,X2)|~member(sk0_0(power_set(X1),X2),power_set(X1)))),
% 123.22/15.95 inference(resolution,[status(thm)],[f275,f37])).
% 123.22/15.95 fof(f443,plain,(
% 123.22/15.95 ![X0,X1,X2]: (subset(X0,X1)|~member(X0,X2)|~subset(sk0_0(power_set(X1),X2),X1))),
% 123.22/15.95 inference(resolution,[status(thm)],[f427,f46])).
% 123.22/15.95 fof(f651,plain,(
% 123.22/15.95 ![X0,X1,X2]: (sk0_0(power_set(X0),singleton(X1))=X1|subset(X2,X0)|~member(X2,singleton(X1)))),
% 123.22/15.95 inference(resolution,[status(thm)],[f270,f275])).
% 123.22/15.95 fof(f687,plain,(
% 123.22/15.95 ![X0,X1,X2]: (member(sk0_23(sk0_0(X0,image2(X1,X2)),X2,X1),X2)|subset(image2(X1,X2),X0))),
% 123.22/15.95 inference(resolution,[status(thm)],[f179,f36])).
% 123.22/15.95 fof(f926,plain,(
% 123.22/15.95 spl0_62 <=> subset(image2(sk0_39,sk0_40),image2(sk0_39,sk0_41))),
% 123.22/15.95 introduced(split_symbol_definition)).
% 123.22/15.95 fof(f1222,plain,(
% 123.22/15.95 ![X0,X1]: (sk0_0(power_set(X0),singleton(X1))=X1|subset(X1,X0))),
% 123.22/15.95 inference(resolution,[status(thm)],[f651,f265])).
% 123.22/15.95 fof(f1225,plain,(
% 123.22/15.95 sk0_0(power_set(image2(sk0_39,sk0_41)),singleton(image2(sk0_39,sk0_40)))=image2(sk0_39,sk0_40)),
% 123.22/15.95 inference(resolution,[status(thm)],[f1222,f251])).
% 123.22/15.95 fof(f1781,plain,(
% 123.22/15.95 spl0_87 <=> subset(X0,image2(sk0_39,sk0_41))|~member(X0,singleton(image2(sk0_39,sk0_40)))),
% 123.22/15.95 introduced(split_symbol_definition)).
% 123.22/15.95 fof(f1782,plain,(
% 123.22/15.95 ![X0]: (subset(X0,image2(sk0_39,sk0_41))|~member(X0,singleton(image2(sk0_39,sk0_40)))|~spl0_87)),
% 123.22/15.95 inference(component_clause,[status(thm)],[f1781])).
% 123.22/15.95 fof(f1786,plain,(
% 123.22/15.95 ![X0]: (subset(X0,image2(sk0_39,sk0_41))|~member(X0,singleton(image2(sk0_39,sk0_40)))|~subset(image2(sk0_39,sk0_40),image2(sk0_39,sk0_41)))),
% 123.22/15.95 inference(paramodulation,[status(thm)],[f1225,f443])).
% 123.22/15.95 fof(f1787,plain,(
% 123.22/15.95 spl0_87|~spl0_62),
% 123.22/15.95 inference(split_clause,[status(thm)],[f1786,f1781,f926])).
% 123.22/15.95 fof(f1974,plain,(
% 123.22/15.95 ![X0,X1,X2]: (apply(X0,sk0_23(sk0_0(X1,image2(X0,X2)),X2,X0),sk0_0(X1,image2(X0,X2)))|subset(image2(X0,X2),X1))),
% 123.22/15.95 inference(resolution,[status(thm)],[f180,f36])).
% 123.22/15.95 fof(f2104,plain,(
% 123.22/15.95 subset(image2(sk0_39,sk0_40),image2(sk0_39,sk0_41))|~spl0_87),
% 123.22/15.95 inference(resolution,[status(thm)],[f1782,f265])).
% 123.22/15.95 fof(f2105,plain,(
% 123.22/15.95 $false|~spl0_87),
% 123.22/15.95 inference(forward_subsumption_resolution,[status(thm)],[f2104,f251])).
% 123.22/15.95 fof(f2106,plain,(
% 123.22/15.95 ~spl0_87),
% 123.22/15.95 inference(contradiction_clause,[status(thm)],[f2105])).
% 123.22/15.95 fof(f22526,plain,(
% 123.22/15.95 member(sk0_23(sk0_0(image2(sk0_39,sk0_41),image2(sk0_39,sk0_40)),sk0_40,sk0_39),sk0_40)),
% 124.05/16.01 inference(resolution,[status(thm)],[f687,f251])).
% 124.05/16.01 fof(f22595,plain,(
% 124.05/16.01 spl0_355 <=> member(sk0_23(sk0_0(image2(sk0_39,sk0_41),image2(sk0_39,sk0_40)),sk0_40,sk0_39),sk0_41)),
% 124.05/16.01 introduced(split_symbol_definition)).
% 124.05/16.01 fof(f22597,plain,(
% 124.05/16.01 ~member(sk0_23(sk0_0(image2(sk0_39,sk0_41),image2(sk0_39,sk0_40)),sk0_40,sk0_39),sk0_41)|spl0_355),
% 124.05/16.01 inference(component_clause,[status(thm)],[f22595])).
% 124.05/16.01 fof(f22598,plain,(
% 124.05/16.01 subset(image2(sk0_39,sk0_40),image2(sk0_39,sk0_41))|~member(sk0_23(sk0_0(image2(sk0_39,sk0_41),image2(sk0_39,sk0_40)),sk0_40,sk0_39),sk0_41)),
% 124.05/16.01 inference(resolution,[status(thm)],[f1974,f291])).
% 124.05/16.01 fof(f22599,plain,(
% 124.05/16.01 spl0_62|~spl0_355),
% 124.05/16.01 inference(split_clause,[status(thm)],[f22598,f926,f22595])).
% 124.05/16.01 fof(f22769,plain,(
% 124.05/16.01 ![X0]: (~subset(X0,sk0_41)|~member(sk0_23(sk0_0(image2(sk0_39,sk0_41),image2(sk0_39,sk0_40)),sk0_40,sk0_39),X0)|spl0_355)),
% 124.05/16.01 inference(resolution,[status(thm)],[f22597,f35])).
% 124.05/16.01 fof(f24887,plain,(
% 124.05/16.01 ~subset(sk0_40,sk0_41)|spl0_355),
% 124.05/16.01 inference(resolution,[status(thm)],[f22769,f22526])).
% 124.05/16.01 fof(f24888,plain,(
% 124.05/16.01 $false|spl0_355),
% 124.05/16.01 inference(forward_subsumption_resolution,[status(thm)],[f24887,f250])).
% 124.05/16.01 fof(f24889,plain,(
% 124.05/16.01 spl0_355),
% 124.05/16.01 inference(contradiction_clause,[status(thm)],[f24888])).
% 124.05/16.01 fof(f24890,plain,(
% 124.05/16.01 $false),
% 124.05/16.01 inference(sat_refutation,[status(thm)],[f1787,f2106,f22599,f24889])).
% 124.05/16.01 % SZS output end CNFRefutation for theBenchmark.p
% 124.46/16.11 % Elapsed time: 15.740923 seconds
% 124.46/16.11 % CPU time: 124.323986 seconds
% 124.46/16.11 % Total memory used: 487.759 MB
% 124.46/16.11 % Net memory used: 448.259 MB
%------------------------------------------------------------------------------