TSTP Solution File: SET014+4 by Drodi---3.6.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SET014+4 : 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 : Tue Apr 30 20:38:38 EDT 2024
% Result : Theorem 0.11s 0.51s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.08 % Problem : SET014+4 : TPTP v8.1.2. Released v2.2.0.
% 0.06/0.08 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.08/0.27 % Computer : n032.cluster.edu
% 0.08/0.27 % Model : x86_64 x86_64
% 0.08/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.27 % Memory : 8042.1875MB
% 0.08/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.27 % CPULimit : 300
% 0.08/0.27 % WCLimit : 300
% 0.08/0.27 % DateTime : Mon Apr 29 21:58:05 EDT 2024
% 0.08/0.27 % CPUTime :
% 0.08/0.28 % Drodi V3.6.0
% 0.11/0.51 % Refutation found
% 0.11/0.51 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.51 % SZS output start CNFRefutation for theBenchmark
% 0.11/0.51 fof(f1,axiom,(
% 0.11/0.51 (! [A,B] :( subset(A,B)<=> (! [X] :( member(X,A)=> member(X,B) ) )) )),
% 0.11/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.11/0.51 fof(f3,axiom,(
% 0.11/0.51 (! [X,A] :( member(X,power_set(A))<=> subset(X,A) ) )),
% 0.11/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.11/0.51 fof(f5,axiom,(
% 0.11/0.51 (! [X,A,B] :( member(X,union(A,B))<=> ( member(X,A)| member(X,B) ) ) )),
% 0.11/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.11/0.51 fof(f6,axiom,(
% 0.11/0.51 (! [X] : ~ member(X,empty_set) )),
% 0.11/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.11/0.51 fof(f8,axiom,(
% 0.11/0.51 (! [X,A] :( member(X,singleton(A))<=> X = A ) )),
% 0.11/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.11/0.51 fof(f11,axiom,(
% 0.11/0.51 (! [X,A] :( member(X,product(A))<=> (! [Y] :( member(Y,A)=> member(X,Y) ) )) )),
% 0.11/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.11/0.51 fof(f12,conjecture,(
% 0.11/0.51 (! [A,X,Y] :( ( subset(X,A)& subset(Y,A) )<=> subset(union(X,Y),A) ) )),
% 0.11/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.11/0.51 fof(f13,negated_conjecture,(
% 0.11/0.51 ~((! [A,X,Y] :( ( subset(X,A)& subset(Y,A) )<=> subset(union(X,Y),A) ) ))),
% 0.11/0.51 inference(negated_conjecture,[status(cth)],[f12])).
% 0.11/0.51 fof(f14,plain,(
% 0.11/0.51 ![A,B]: (subset(A,B)<=>(![X]: (~member(X,A)|member(X,B))))),
% 0.11/0.51 inference(pre_NNF_transformation,[status(esa)],[f1])).
% 0.11/0.51 fof(f15,plain,(
% 0.11/0.51 ![A,B]: ((~subset(A,B)|(![X]: (~member(X,A)|member(X,B))))&(subset(A,B)|(?[X]: (member(X,A)&~member(X,B)))))),
% 0.11/0.51 inference(NNF_transformation,[status(esa)],[f14])).
% 0.11/0.51 fof(f16,plain,(
% 0.11/0.51 (![A,B]: (~subset(A,B)|(![X]: (~member(X,A)|member(X,B)))))&(![A,B]: (subset(A,B)|(?[X]: (member(X,A)&~member(X,B)))))),
% 0.11/0.51 inference(miniscoping,[status(esa)],[f15])).
% 0.11/0.51 fof(f17,plain,(
% 0.11/0.51 (![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))))),
% 0.11/0.51 inference(skolemization,[status(esa)],[f16])).
% 0.11/0.51 fof(f18,plain,(
% 0.11/0.51 ![X0,X1,X2]: (~subset(X0,X1)|~member(X2,X0)|member(X2,X1))),
% 0.11/0.51 inference(cnf_transformation,[status(esa)],[f17])).
% 0.11/0.51 fof(f19,plain,(
% 0.11/0.51 ![X0,X1]: (subset(X0,X1)|member(sk0_0(X1,X0),X0))),
% 0.11/0.51 inference(cnf_transformation,[status(esa)],[f17])).
% 0.11/0.51 fof(f20,plain,(
% 0.11/0.51 ![X0,X1]: (subset(X0,X1)|~member(sk0_0(X1,X0),X1))),
% 0.11/0.51 inference(cnf_transformation,[status(esa)],[f17])).
% 0.11/0.51 fof(f26,plain,(
% 0.11/0.51 ![X,A]: ((~member(X,power_set(A))|subset(X,A))&(member(X,power_set(A))|~subset(X,A)))),
% 0.11/0.51 inference(NNF_transformation,[status(esa)],[f3])).
% 0.11/0.51 fof(f27,plain,(
% 0.11/0.51 (![X,A]: (~member(X,power_set(A))|subset(X,A)))&(![X,A]: (member(X,power_set(A))|~subset(X,A)))),
% 0.11/0.51 inference(miniscoping,[status(esa)],[f26])).
% 0.11/0.51 fof(f28,plain,(
% 0.11/0.51 ![X0,X1]: (~member(X0,power_set(X1))|subset(X0,X1))),
% 0.11/0.51 inference(cnf_transformation,[status(esa)],[f27])).
% 0.11/0.51 fof(f29,plain,(
% 0.11/0.51 ![X0,X1]: (member(X0,power_set(X1))|~subset(X0,X1))),
% 0.11/0.51 inference(cnf_transformation,[status(esa)],[f27])).
% 0.11/0.51 fof(f35,plain,(
% 0.11/0.51 ![X,A,B]: ((~member(X,union(A,B))|(member(X,A)|member(X,B)))&(member(X,union(A,B))|(~member(X,A)&~member(X,B))))),
% 0.11/0.51 inference(NNF_transformation,[status(esa)],[f5])).
% 0.11/0.51 fof(f36,plain,(
% 0.11/0.51 (![X,A,B]: (~member(X,union(A,B))|(member(X,A)|member(X,B))))&(![X,A,B]: (member(X,union(A,B))|(~member(X,A)&~member(X,B))))),
% 0.11/0.51 inference(miniscoping,[status(esa)],[f35])).
% 0.11/0.51 fof(f37,plain,(
% 0.11/0.51 ![X0,X1,X2]: (~member(X0,union(X1,X2))|member(X0,X1)|member(X0,X2))),
% 0.11/0.51 inference(cnf_transformation,[status(esa)],[f36])).
% 0.11/0.51 fof(f38,plain,(
% 0.11/0.51 ![X0,X1,X2]: (member(X0,union(X1,X2))|~member(X0,X1))),
% 0.11/0.51 inference(cnf_transformation,[status(esa)],[f36])).
% 0.11/0.51 fof(f39,plain,(
% 0.11/0.51 ![X0,X1,X2]: (member(X0,union(X1,X2))|~member(X0,X2))),
% 0.11/0.51 inference(cnf_transformation,[status(esa)],[f36])).
% 0.11/0.51 fof(f40,plain,(
% 0.11/0.51 ![X0]: (~member(X0,empty_set))),
% 0.11/0.51 inference(cnf_transformation,[status(esa)],[f6])).
% 0.11/0.51 fof(f46,plain,(
% 0.11/0.51 ![X,A]: ((~member(X,singleton(A))|X=A)&(member(X,singleton(A))|~X=A))),
% 0.11/0.51 inference(NNF_transformation,[status(esa)],[f8])).
% 0.11/0.51 fof(f47,plain,(
% 0.11/0.51 (![X,A]: (~member(X,singleton(A))|X=A))&(![X,A]: (member(X,singleton(A))|~X=A))),
% 0.11/0.51 inference(miniscoping,[status(esa)],[f46])).
% 0.11/0.52 fof(f48,plain,(
% 0.11/0.52 ![X0,X1]: (~member(X0,singleton(X1))|X0=X1)),
% 0.11/0.52 inference(cnf_transformation,[status(esa)],[f47])).
% 0.11/0.52 fof(f49,plain,(
% 0.11/0.52 ![X0,X1]: (member(X0,singleton(X1))|~X0=X1)),
% 0.11/0.52 inference(cnf_transformation,[status(esa)],[f47])).
% 0.11/0.52 fof(f61,plain,(
% 0.11/0.52 ![X,A]: (member(X,product(A))<=>(![Y]: (~member(Y,A)|member(X,Y))))),
% 0.11/0.52 inference(pre_NNF_transformation,[status(esa)],[f11])).
% 0.11/0.52 fof(f62,plain,(
% 0.11/0.52 ![X,A]: ((~member(X,product(A))|(![Y]: (~member(Y,A)|member(X,Y))))&(member(X,product(A))|(?[Y]: (member(Y,A)&~member(X,Y)))))),
% 0.11/0.52 inference(NNF_transformation,[status(esa)],[f61])).
% 0.11/0.52 fof(f63,plain,(
% 0.11/0.52 (![X,A]: (~member(X,product(A))|(![Y]: (~member(Y,A)|member(X,Y)))))&(![X,A]: (member(X,product(A))|(?[Y]: (member(Y,A)&~member(X,Y)))))),
% 0.11/0.52 inference(miniscoping,[status(esa)],[f62])).
% 0.11/0.52 fof(f64,plain,(
% 0.11/0.52 (![X,A]: (~member(X,product(A))|(![Y]: (~member(Y,A)|member(X,Y)))))&(![X,A]: (member(X,product(A))|(member(sk0_2(A,X),A)&~member(X,sk0_2(A,X)))))),
% 0.11/0.52 inference(skolemization,[status(esa)],[f63])).
% 0.11/0.52 fof(f65,plain,(
% 0.11/0.52 ![X0,X1,X2]: (~member(X0,product(X1))|~member(X2,X1)|member(X0,X2))),
% 0.11/0.52 inference(cnf_transformation,[status(esa)],[f64])).
% 0.11/0.52 fof(f66,plain,(
% 0.11/0.52 ![X0,X1]: (member(X0,product(X1))|member(sk0_2(X1,X0),X1))),
% 0.11/0.52 inference(cnf_transformation,[status(esa)],[f64])).
% 0.11/0.52 fof(f68,plain,(
% 0.11/0.52 (?[A,X,Y]: ((subset(X,A)&subset(Y,A))<~>subset(union(X,Y),A)))),
% 0.11/0.52 inference(pre_NNF_transformation,[status(esa)],[f13])).
% 0.11/0.52 fof(f69,plain,(
% 0.11/0.52 ?[A,X,Y]: (((subset(X,A)&subset(Y,A))|subset(union(X,Y),A))&((~subset(X,A)|~subset(Y,A))|~subset(union(X,Y),A)))),
% 0.11/0.52 inference(NNF_transformation,[status(esa)],[f68])).
% 0.11/0.52 fof(f70,plain,(
% 0.11/0.52 (((subset(sk0_4,sk0_3)&subset(sk0_5,sk0_3))|subset(union(sk0_4,sk0_5),sk0_3))&((~subset(sk0_4,sk0_3)|~subset(sk0_5,sk0_3))|~subset(union(sk0_4,sk0_5),sk0_3)))),
% 0.11/0.52 inference(skolemization,[status(esa)],[f69])).
% 0.11/0.52 fof(f71,plain,(
% 0.11/0.52 subset(sk0_4,sk0_3)|subset(union(sk0_4,sk0_5),sk0_3)),
% 0.11/0.52 inference(cnf_transformation,[status(esa)],[f70])).
% 0.11/0.52 fof(f72,plain,(
% 0.11/0.52 subset(sk0_5,sk0_3)|subset(union(sk0_4,sk0_5),sk0_3)),
% 0.11/0.52 inference(cnf_transformation,[status(esa)],[f70])).
% 0.11/0.52 fof(f73,plain,(
% 0.11/0.52 ~subset(sk0_4,sk0_3)|~subset(sk0_5,sk0_3)|~subset(union(sk0_4,sk0_5),sk0_3)),
% 0.11/0.52 inference(cnf_transformation,[status(esa)],[f70])).
% 0.11/0.52 fof(f74,plain,(
% 0.11/0.52 spl0_0 <=> subset(sk0_4,sk0_3)),
% 0.11/0.52 introduced(split_symbol_definition)).
% 0.11/0.52 fof(f75,plain,(
% 0.11/0.52 subset(sk0_4,sk0_3)|~spl0_0),
% 0.11/0.52 inference(component_clause,[status(thm)],[f74])).
% 0.11/0.52 fof(f76,plain,(
% 0.11/0.52 ~subset(sk0_4,sk0_3)|spl0_0),
% 0.11/0.52 inference(component_clause,[status(thm)],[f74])).
% 0.11/0.52 fof(f77,plain,(
% 0.11/0.52 spl0_1 <=> subset(union(sk0_4,sk0_5),sk0_3)),
% 0.11/0.52 introduced(split_symbol_definition)).
% 0.11/0.52 fof(f78,plain,(
% 0.11/0.52 subset(union(sk0_4,sk0_5),sk0_3)|~spl0_1),
% 0.11/0.52 inference(component_clause,[status(thm)],[f77])).
% 0.11/0.52 fof(f79,plain,(
% 0.11/0.52 ~subset(union(sk0_4,sk0_5),sk0_3)|spl0_1),
% 0.11/0.52 inference(component_clause,[status(thm)],[f77])).
% 0.11/0.52 fof(f80,plain,(
% 0.11/0.52 spl0_0|spl0_1),
% 0.11/0.52 inference(split_clause,[status(thm)],[f71,f74,f77])).
% 0.11/0.52 fof(f81,plain,(
% 0.11/0.52 spl0_2 <=> subset(sk0_5,sk0_3)),
% 0.11/0.52 introduced(split_symbol_definition)).
% 0.11/0.52 fof(f82,plain,(
% 0.11/0.52 subset(sk0_5,sk0_3)|~spl0_2),
% 0.11/0.52 inference(component_clause,[status(thm)],[f81])).
% 0.11/0.52 fof(f83,plain,(
% 0.11/0.52 ~subset(sk0_5,sk0_3)|spl0_2),
% 0.11/0.52 inference(component_clause,[status(thm)],[f81])).
% 0.11/0.52 fof(f84,plain,(
% 0.11/0.52 spl0_2|spl0_1),
% 0.11/0.52 inference(split_clause,[status(thm)],[f72,f81,f77])).
% 0.11/0.52 fof(f85,plain,(
% 0.11/0.52 ~spl0_0|~spl0_2|~spl0_1),
% 0.11/0.52 inference(split_clause,[status(thm)],[f73,f74,f81,f77])).
% 0.11/0.52 fof(f86,plain,(
% 0.11/0.52 ![X0]: (member(X0,singleton(X0)))),
% 0.11/0.52 inference(destructive_equality_resolution,[status(esa)],[f49])).
% 0.11/0.52 fof(f89,plain,(
% 0.11/0.52 ![X0,X1]: (~member(X0,union(X1,empty_set))|member(X0,X1))),
% 0.11/0.52 inference(resolution,[status(thm)],[f40,f37])).
% 0.11/0.52 fof(f90,plain,(
% 0.11/0.52 ![X0,X1]: (~subset(X0,empty_set)|~member(X1,X0))),
% 0.11/0.52 inference(resolution,[status(thm)],[f40,f18])).
% 0.11/0.52 fof(f91,plain,(
% 0.11/0.52 ![X0]: (~member(X0,union(empty_set,empty_set)))),
% 0.11/0.52 inference(resolution,[status(thm)],[f89,f40])).
% 0.11/0.52 fof(f94,plain,(
% 0.11/0.52 ![X0]: (~member(X0,union(union(empty_set,empty_set),empty_set)))),
% 0.11/0.52 inference(resolution,[status(thm)],[f91,f89])).
% 0.11/0.52 fof(f95,plain,(
% 0.11/0.52 ![X0,X1]: (~member(X0,union(X1,union(empty_set,empty_set)))|member(X0,X1))),
% 0.11/0.52 inference(resolution,[status(thm)],[f91,f37])).
% 0.11/0.52 fof(f102,plain,(
% 0.11/0.52 ![X0]: (~member(X0,union(union(union(empty_set,empty_set),empty_set),union(empty_set,empty_set))))),
% 0.11/0.52 inference(resolution,[status(thm)],[f95,f94])).
% 0.11/0.52 fof(f146,plain,(
% 0.11/0.52 ![X0,X1]: (~member(X0,power_set(empty_set))|~member(X1,X0))),
% 0.11/0.52 inference(resolution,[status(thm)],[f28,f90])).
% 0.11/0.52 fof(f149,plain,(
% 0.11/0.52 ![X0,X1]: (member(sk0_0(empty_set,X0),X0)|~member(X1,X0))),
% 0.11/0.52 inference(resolution,[status(thm)],[f19,f90])).
% 0.11/0.52 fof(f173,plain,(
% 0.11/0.52 ~member(sk0_0(sk0_3,sk0_4),sk0_3)|spl0_0),
% 0.11/0.52 inference(resolution,[status(thm)],[f76,f20])).
% 0.11/0.52 fof(f174,plain,(
% 0.11/0.52 member(sk0_0(sk0_3,sk0_4),sk0_4)|spl0_0),
% 0.11/0.52 inference(resolution,[status(thm)],[f76,f19])).
% 0.11/0.52 fof(f184,plain,(
% 0.11/0.52 ![X0]: (~subset(X0,sk0_3)|~member(sk0_0(sk0_3,sk0_4),X0)|spl0_0)),
% 0.11/0.52 inference(resolution,[status(thm)],[f173,f18])).
% 0.11/0.52 fof(f200,plain,(
% 0.11/0.52 ~member(sk0_0(sk0_3,sk0_4),union(sk0_4,sk0_5))|spl0_0|~spl0_1),
% 0.11/0.52 inference(resolution,[status(thm)],[f184,f78])).
% 0.11/0.52 fof(f210,plain,(
% 0.11/0.52 ~member(sk0_0(sk0_3,sk0_4),sk0_4)|spl0_0|~spl0_1),
% 0.11/0.52 inference(resolution,[status(thm)],[f200,f38])).
% 0.11/0.52 fof(f211,plain,(
% 0.11/0.52 $false|spl0_0|~spl0_1),
% 0.11/0.52 inference(forward_subsumption_resolution,[status(thm)],[f210,f174])).
% 0.11/0.52 fof(f212,plain,(
% 0.11/0.52 spl0_0|~spl0_1),
% 0.11/0.52 inference(contradiction_clause,[status(thm)],[f211])).
% 0.11/0.52 fof(f213,plain,(
% 0.11/0.52 ~member(sk0_0(sk0_3,sk0_5),sk0_3)|spl0_2),
% 0.11/0.52 inference(resolution,[status(thm)],[f83,f20])).
% 0.11/0.52 fof(f214,plain,(
% 0.11/0.52 member(sk0_0(sk0_3,sk0_5),sk0_5)|spl0_2),
% 0.11/0.52 inference(resolution,[status(thm)],[f83,f19])).
% 0.11/0.52 fof(f224,plain,(
% 0.11/0.52 ![X0]: (~subset(X0,sk0_3)|~member(sk0_0(sk0_3,sk0_5),X0)|spl0_2)),
% 0.11/0.52 inference(resolution,[status(thm)],[f213,f18])).
% 0.11/0.52 fof(f234,plain,(
% 0.11/0.52 spl0_4 <=> member(sk0_5,power_set(sk0_3))),
% 0.11/0.52 introduced(split_symbol_definition)).
% 0.11/0.52 fof(f236,plain,(
% 0.11/0.52 ~member(sk0_5,power_set(sk0_3))|spl0_4),
% 0.11/0.52 inference(component_clause,[status(thm)],[f234])).
% 0.11/0.52 fof(f253,plain,(
% 0.11/0.52 ~member(sk0_0(sk0_3,sk0_5),union(sk0_4,sk0_5))|spl0_2|~spl0_1),
% 0.11/0.52 inference(resolution,[status(thm)],[f224,f78])).
% 0.11/0.52 fof(f266,plain,(
% 0.11/0.52 ~member(sk0_0(sk0_3,sk0_5),sk0_5)|spl0_2|~spl0_1),
% 0.11/0.52 inference(resolution,[status(thm)],[f253,f39])).
% 0.11/0.52 fof(f267,plain,(
% 0.11/0.52 $false|spl0_2|~spl0_1),
% 0.11/0.52 inference(forward_subsumption_resolution,[status(thm)],[f266,f214])).
% 0.11/0.52 fof(f268,plain,(
% 0.11/0.52 spl0_2|~spl0_1),
% 0.11/0.52 inference(contradiction_clause,[status(thm)],[f267])).
% 0.11/0.52 fof(f269,plain,(
% 0.11/0.52 ~member(sk0_0(sk0_3,union(sk0_4,sk0_5)),sk0_3)|spl0_1),
% 0.11/0.52 inference(resolution,[status(thm)],[f79,f20])).
% 0.11/0.52 fof(f270,plain,(
% 0.11/0.52 member(sk0_0(sk0_3,union(sk0_4,sk0_5)),union(sk0_4,sk0_5))|spl0_1),
% 0.11/0.52 inference(resolution,[status(thm)],[f79,f19])).
% 0.11/0.52 fof(f280,plain,(
% 0.11/0.52 ![X0]: (~subset(X0,sk0_3)|~member(sk0_0(sk0_3,union(sk0_4,sk0_5)),X0)|spl0_1)),
% 0.11/0.52 inference(resolution,[status(thm)],[f269,f18])).
% 0.11/0.52 fof(f296,plain,(
% 0.11/0.52 ~member(sk0_0(sk0_3,union(sk0_4,sk0_5)),sk0_5)|spl0_1|~spl0_2),
% 0.11/0.52 inference(resolution,[status(thm)],[f280,f82])).
% 0.11/0.52 fof(f297,plain,(
% 0.11/0.52 ~member(sk0_0(sk0_3,union(sk0_4,sk0_5)),sk0_4)|spl0_1|~spl0_0),
% 0.11/0.52 inference(resolution,[status(thm)],[f280,f75])).
% 0.11/0.52 fof(f335,plain,(
% 0.11/0.52 ![X0,X1,X2]: (~member(X0,X1)|~subset(X2,power_set(empty_set))|~member(X1,X2))),
% 0.11/0.52 inference(resolution,[status(thm)],[f146,f18])).
% 0.11/0.52 fof(f355,plain,(
% 0.11/0.52 ![X0,X1]: (member(sk0_0(empty_set,X0),X0)|~member(X1,union(X0,empty_set)))),
% 0.11/0.52 inference(resolution,[status(thm)],[f149,f89])).
% 0.11/0.52 fof(f422,plain,(
% 0.11/0.52 ![X0,X1,X2]: (~member(X0,X1)|member(X2,X0)|member(sk0_2(X1,X2),X1))),
% 0.11/0.52 inference(resolution,[status(thm)],[f65,f66])).
% 0.11/0.52 fof(f456,plain,(
% 0.11/0.52 ![X0,X1,X2]: (~member(X0,X1)|~member(X1,X2)|~member(X2,power_set(power_set(empty_set))))),
% 0.11/0.52 inference(resolution,[status(thm)],[f335,f28])).
% 0.11/0.52 fof(f808,plain,(
% 0.11/0.52 spl0_14 <=> member(sk0_0(empty_set,X0),X0)),
% 0.11/0.52 introduced(split_symbol_definition)).
% 0.11/0.52 fof(f809,plain,(
% 0.11/0.52 ![X0]: (member(sk0_0(empty_set,X0),X0)|~spl0_14)),
% 0.11/0.52 inference(component_clause,[status(thm)],[f808])).
% 0.11/0.52 fof(f811,plain,(
% 0.11/0.52 spl0_15 <=> ~member(X1,empty_set)),
% 0.11/0.52 introduced(split_symbol_definition)).
% 0.11/0.52 fof(f814,plain,(
% 0.11/0.52 ![X0,X1]: (member(sk0_0(empty_set,X0),X0)|~member(X1,empty_set))),
% 0.11/0.52 inference(resolution,[status(thm)],[f355,f39])).
% 0.11/0.52 fof(f815,plain,(
% 0.11/0.52 spl0_14|spl0_15),
% 0.11/0.52 inference(split_clause,[status(thm)],[f814,f808,f811])).
% 0.11/0.52 fof(f937,plain,(
% 0.11/0.52 ![X0,X1]: (member(X0,X1)|member(sk0_2(singleton(X1),X0),singleton(X1)))),
% 0.11/0.52 inference(resolution,[status(thm)],[f422,f86])).
% 0.11/0.52 fof(f954,plain,(
% 0.11/0.52 ![X0,X1]: (member(X0,X1)|sk0_2(singleton(X1),X0)=X1)),
% 0.11/0.52 inference(resolution,[status(thm)],[f937,f48])).
% 0.11/0.52 fof(f1039,plain,(
% 0.11/0.52 ![X0]: (sk0_2(singleton(empty_set),X0)=empty_set)),
% 0.11/0.52 inference(resolution,[status(thm)],[f954,f40])).
% 0.11/0.52 fof(f1044,plain,(
% 0.11/0.52 ![X0,X1]: (sk0_2(singleton(X0),X1)=X0|member(sk0_0(empty_set,X0),X0))),
% 0.11/0.52 inference(resolution,[status(thm)],[f954,f149])).
% 0.11/0.52 fof(f1045,plain,(
% 0.11/0.52 spl0_19 <=> member(X0,empty_set)),
% 0.11/0.52 introduced(split_symbol_definition)).
% 0.11/0.52 fof(f1046,plain,(
% 0.11/0.52 ![X0]: (member(X0,empty_set)|~spl0_19)),
% 0.11/0.52 inference(component_clause,[status(thm)],[f1045])).
% 0.11/0.52 fof(f1048,plain,(
% 0.11/0.52 spl0_20 <=> member(empty_set,singleton(empty_set))),
% 0.11/0.52 introduced(split_symbol_definition)).
% 0.11/0.52 fof(f1051,plain,(
% 0.11/0.52 ![X0]: (member(X0,empty_set)|member(empty_set,singleton(empty_set)))),
% 0.11/0.52 inference(paramodulation,[status(thm)],[f1039,f937])).
% 0.11/0.52 fof(f1052,plain,(
% 0.11/0.52 spl0_19|spl0_20),
% 0.11/0.52 inference(split_clause,[status(thm)],[f1051,f1045,f1048])).
% 0.11/0.52 fof(f1054,plain,(
% 0.11/0.52 $false|~spl0_19),
% 0.11/0.52 inference(forward_subsumption_resolution,[status(thm)],[f1046,f40])).
% 0.11/0.52 fof(f1055,plain,(
% 0.11/0.52 ~spl0_19),
% 0.11/0.52 inference(contradiction_clause,[status(thm)],[f1054])).
% 0.11/0.52 fof(f1103,plain,(
% 0.11/0.52 spl0_31 <=> sk0_2(singleton(power_set(empty_set)),X0)=power_set(empty_set)),
% 0.11/0.52 introduced(split_symbol_definition)).
% 0.11/0.52 fof(f1104,plain,(
% 0.11/0.52 ![X0]: (sk0_2(singleton(power_set(empty_set)),X0)=power_set(empty_set)|~spl0_31)),
% 0.11/0.52 inference(component_clause,[status(thm)],[f1103])).
% 0.11/0.52 fof(f1106,plain,(
% 0.11/0.52 spl0_32 <=> ~member(X1,sk0_0(empty_set,power_set(empty_set)))),
% 0.11/0.52 introduced(split_symbol_definition)).
% 0.11/0.52 fof(f1107,plain,(
% 0.11/0.52 ![X0]: (~member(X0,sk0_0(empty_set,power_set(empty_set)))|~spl0_32)),
% 0.11/0.52 inference(component_clause,[status(thm)],[f1106])).
% 0.11/0.52 fof(f1109,plain,(
% 0.11/0.52 ![X0,X1]: (sk0_2(singleton(power_set(empty_set)),X0)=power_set(empty_set)|~member(X1,sk0_0(empty_set,power_set(empty_set))))),
% 0.11/0.52 inference(resolution,[status(thm)],[f1044,f146])).
% 0.11/0.52 fof(f1110,plain,(
% 0.11/0.52 spl0_31|spl0_32),
% 0.11/0.52 inference(split_clause,[status(thm)],[f1109,f1103,f1106])).
% 0.11/0.52 fof(f1322,plain,(
% 0.11/0.52 $false|~spl0_14),
% 0.11/0.52 inference(resolution,[status(thm)],[f809,f102])).
% 0.11/0.52 fof(f1323,plain,(
% 0.11/0.52 ~spl0_14),
% 0.11/0.52 inference(contradiction_clause,[status(thm)],[f1322])).
% 0.11/0.52 fof(f1328,plain,(
% 0.11/0.52 spl0_40 <=> member(X0,power_set(empty_set))),
% 0.11/0.52 introduced(split_symbol_definition)).
% 0.11/0.52 fof(f1329,plain,(
% 0.11/0.52 ![X0]: (member(X0,power_set(empty_set))|~spl0_40)),
% 0.11/0.52 inference(component_clause,[status(thm)],[f1328])).
% 0.11/0.52 fof(f1331,plain,(
% 0.11/0.52 spl0_41 <=> member(power_set(empty_set),singleton(power_set(empty_set)))),
% 0.11/0.52 introduced(split_symbol_definition)).
% 0.11/0.52 fof(f1334,plain,(
% 0.11/0.52 ![X0]: (member(X0,power_set(empty_set))|member(power_set(empty_set),singleton(power_set(empty_set)))|~spl0_31)),
% 0.11/0.52 inference(paramodulation,[status(thm)],[f1104,f937])).
% 0.11/0.52 fof(f1335,plain,(
% 0.11/0.52 spl0_40|spl0_41|~spl0_31),
% 0.11/0.52 inference(split_clause,[status(thm)],[f1334,f1328,f1331,f1103])).
% 0.11/0.52 fof(f1337,plain,(
% 0.11/0.52 ~subset(sk0_5,sk0_3)|spl0_4),
% 0.11/0.52 inference(resolution,[status(thm)],[f236,f29])).
% 0.11/0.52 fof(f1338,plain,(
% 0.11/0.52 ~spl0_2|spl0_4),
% 0.11/0.52 inference(split_clause,[status(thm)],[f1337,f81,f234])).
% 0.11/0.52 fof(f1353,plain,(
% 0.11/0.52 ![X0,X1]: (~subset(X0,sk0_0(empty_set,power_set(empty_set)))|~member(X1,X0)|~spl0_32)),
% 0.11/0.52 inference(resolution,[status(thm)],[f1107,f18])).
% 0.11/0.52 fof(f1429,plain,(
% 0.11/0.52 ![X0,X1]: (~member(X0,X1)|~member(X1,power_set(sk0_0(empty_set,power_set(empty_set))))|~spl0_32)),
% 0.11/0.52 inference(resolution,[status(thm)],[f1353,f28])).
% 0.11/0.52 fof(f1465,plain,(
% 0.11/0.52 spl0_42 <=> member(sk0_0(sk0_3,union(sk0_4,sk0_5)),sk0_4)),
% 0.11/0.52 introduced(split_symbol_definition)).
% 0.11/0.52 fof(f1466,plain,(
% 0.11/0.52 member(sk0_0(sk0_3,union(sk0_4,sk0_5)),sk0_4)|~spl0_42),
% 0.11/0.52 inference(component_clause,[status(thm)],[f1465])).
% 0.11/0.52 fof(f1478,plain,(
% 0.11/0.52 spl0_45 <=> member(sk0_0(sk0_3,union(sk0_4,sk0_5)),sk0_5)),
% 0.11/0.52 introduced(split_symbol_definition)).
% 0.11/0.52 fof(f1479,plain,(
% 0.11/0.52 member(sk0_0(sk0_3,union(sk0_4,sk0_5)),sk0_5)|~spl0_45),
% 0.11/0.53 inference(component_clause,[status(thm)],[f1478])).
% 0.11/0.53 fof(f1555,plain,(
% 0.11/0.53 spl0_48 <=> sk0_2(singleton(power_set(sk0_0(empty_set,power_set(empty_set)))),X0)=power_set(sk0_0(empty_set,power_set(empty_set)))),
% 0.11/0.53 introduced(split_symbol_definition)).
% 0.11/0.53 fof(f1558,plain,(
% 0.11/0.53 spl0_49 <=> ~member(X1,sk0_0(empty_set,power_set(sk0_0(empty_set,power_set(empty_set)))))),
% 0.11/0.53 introduced(split_symbol_definition)).
% 0.11/0.53 fof(f1561,plain,(
% 0.11/0.53 ![X0,X1]: (sk0_2(singleton(power_set(sk0_0(empty_set,power_set(empty_set)))),X0)=power_set(sk0_0(empty_set,power_set(empty_set)))|~member(X1,sk0_0(empty_set,power_set(sk0_0(empty_set,power_set(empty_set)))))|~spl0_32)),
% 0.11/0.53 inference(resolution,[status(thm)],[f1044,f1429])).
% 0.11/0.53 fof(f1562,plain,(
% 0.11/0.53 spl0_48|spl0_49|~spl0_32),
% 0.11/0.53 inference(split_clause,[status(thm)],[f1561,f1555,f1558,f1106])).
% 0.11/0.53 fof(f1655,plain,(
% 0.11/0.53 spl0_50 <=> ~member(X0,X1)|~member(X1,sk0_0(empty_set,power_set(power_set(empty_set))))),
% 0.11/0.53 introduced(split_symbol_definition)).
% 0.11/0.53 fof(f1658,plain,(
% 0.11/0.53 spl0_51 <=> sk0_2(singleton(power_set(power_set(empty_set))),X2)=power_set(power_set(empty_set))),
% 0.11/0.53 introduced(split_symbol_definition)).
% 0.11/0.53 fof(f1661,plain,(
% 0.11/0.53 ![X0,X1,X2]: (~member(X0,X1)|~member(X1,sk0_0(empty_set,power_set(power_set(empty_set))))|sk0_2(singleton(power_set(power_set(empty_set))),X2)=power_set(power_set(empty_set)))),
% 0.11/0.53 inference(resolution,[status(thm)],[f456,f1044])).
% 0.11/0.53 fof(f1662,plain,(
% 0.11/0.53 spl0_50|spl0_51),
% 0.11/0.53 inference(split_clause,[status(thm)],[f1661,f1655,f1658])).
% 0.11/0.53 fof(f1955,plain,(
% 0.11/0.53 ![X0,X1]: (~member(X0,X1)|~spl0_40)),
% 0.11/0.53 inference(backward_subsumption_resolution,[status(thm)],[f146,f1329])).
% 0.11/0.53 fof(f1970,plain,(
% 0.11/0.53 ![X0,X1]: (member(sk0_2(X0,X1),X0)|~spl0_40)),
% 0.11/0.53 inference(backward_subsumption_resolution,[status(thm)],[f66,f1955])).
% 0.11/0.53 fof(f1971,plain,(
% 0.11/0.53 $false|~spl0_40),
% 0.11/0.53 inference(forward_subsumption_resolution,[status(thm)],[f1970,f1955])).
% 0.11/0.53 fof(f1972,plain,(
% 0.11/0.53 ~spl0_40),
% 0.11/0.53 inference(contradiction_clause,[status(thm)],[f1971])).
% 0.11/0.53 fof(f1995,plain,(
% 0.11/0.53 member(sk0_0(sk0_3,union(sk0_4,sk0_5)),sk0_4)|member(sk0_0(sk0_3,union(sk0_4,sk0_5)),sk0_5)|spl0_1),
% 0.11/0.53 inference(resolution,[status(thm)],[f37,f270])).
% 0.11/0.53 fof(f1996,plain,(
% 0.11/0.53 spl0_42|spl0_45|spl0_1),
% 0.11/0.53 inference(split_clause,[status(thm)],[f1995,f1465,f1478,f77])).
% 0.11/0.53 fof(f1997,plain,(
% 0.11/0.53 $false|spl0_1|~spl0_0|~spl0_42),
% 0.11/0.53 inference(forward_subsumption_resolution,[status(thm)],[f1466,f297])).
% 0.11/0.53 fof(f1998,plain,(
% 0.11/0.53 spl0_1|~spl0_0|~spl0_42),
% 0.11/0.53 inference(contradiction_clause,[status(thm)],[f1997])).
% 0.11/0.53 fof(f1999,plain,(
% 0.11/0.53 $false|spl0_1|~spl0_2|~spl0_45),
% 0.11/0.53 inference(forward_subsumption_resolution,[status(thm)],[f1479,f296])).
% 0.11/0.53 fof(f2000,plain,(
% 0.11/0.53 spl0_1|~spl0_2|~spl0_45),
% 0.11/0.53 inference(contradiction_clause,[status(thm)],[f1999])).
% 0.11/0.53 fof(f2001,plain,(
% 0.11/0.53 $false),
% 0.11/0.53 inference(sat_refutation,[status(thm)],[f80,f84,f85,f212,f268,f815,f1052,f1055,f1110,f1323,f1335,f1338,f1562,f1662,f1972,f1996,f1998,f2000])).
% 0.11/0.53 % SZS output end CNFRefutation for theBenchmark.p
% 1.83/0.53 % Elapsed time: 0.254731 seconds
% 1.83/0.53 % CPU time: 1.926506 seconds
% 1.83/0.53 % Total memory used: 84.162 MB
% 1.83/0.53 % Net memory used: 82.394 MB
%------------------------------------------------------------------------------