TSTP Solution File: SEU147+2 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SEU147+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n008.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 12:35:58 EDT 2023
% Result : Theorem 4.29s 1.01s
% Output : CNFRefutation 4.29s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU147+2 : TPTP v8.1.2. Released v3.3.0.
% 0.12/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34 % Computer : n008.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.20/0.34 % WCLimit : 300
% 0.20/0.34 % DateTime : Tue May 30 09:19:08 EDT 2023
% 0.20/0.34 % CPUTime :
% 0.20/0.35 % Drodi V3.5.1
% 4.29/1.01 % Refutation found
% 4.29/1.01 % SZS status Theorem for theBenchmark: Theorem is valid
% 4.29/1.01 % SZS output start CNFRefutation for theBenchmark
% 4.29/1.01 fof(f1,axiom,(
% 4.29/1.01 (! [A,B] :( in(A,B)=> ~ in(B,A) ) )),
% 4.29/1.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.29/1.01 fof(f4,axiom,(
% 4.29/1.01 (! [A,B] : set_union2(A,B) = set_union2(B,A) )),
% 4.29/1.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.29/1.01 fof(f5,axiom,(
% 4.29/1.01 (! [A,B] : set_intersection2(A,B) = set_intersection2(B,A) )),
% 4.29/1.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.29/1.01 fof(f6,axiom,(
% 4.29/1.01 (! [A,B] :( A = B<=> ( subset(A,B)& subset(B,A) ) ) )),
% 4.29/1.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.29/1.01 fof(f8,axiom,(
% 4.29/1.01 (! [A] :( A = empty_set<=> (! [B] : ~ in(B,A) )) )),
% 4.29/1.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.29/1.01 fof(f9,axiom,(
% 4.29/1.01 (! [A,B] :( B = powerset(A)<=> (! [C] :( in(C,B)<=> subset(C,A) ) )) )),
% 4.29/1.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.29/1.01 fof(f10,axiom,(
% 4.29/1.01 (! [A,B,C] :( C = unordered_pair(A,B)<=> (! [D] :( in(D,C)<=> ( D = A| D = B ) ) )) )),
% 4.29/1.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.29/1.01 fof(f12,axiom,(
% 4.29/1.01 (! [A,B] :( subset(A,B)<=> (! [C] :( in(C,A)=> in(C,B) ) )) )),
% 4.29/1.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.29/1.01 fof(f30,lemma,(
% 4.29/1.01 (! [A] : singleton(A) != empty_set )),
% 4.29/1.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.29/1.01 fof(f31,lemma,(
% 4.29/1.01 (! [A,B] :( subset(singleton(A),B)<=> in(A,B) ) )),
% 4.29/1.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.29/1.01 fof(f32,lemma,(
% 4.29/1.01 (! [A,B] :( set_difference(A,B) = empty_set<=> subset(A,B) ) )),
% 4.29/1.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.29/1.01 fof(f33,lemma,(
% 4.29/1.01 (! [A,B,C] :( subset(A,B)=> ( in(C,A)| subset(A,set_difference(B,singleton(C))) ) ) )),
% 4.29/1.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.29/1.01 fof(f34,lemma,(
% 4.29/1.01 (! [A,B] :( subset(A,singleton(B))<=> ( A = empty_set| A = singleton(B) ) ) )),
% 4.29/1.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.29/1.01 fof(f39,lemma,(
% 4.29/1.01 (! [A,B] :( subset(A,B)=> set_union2(A,B) = B ) )),
% 4.29/1.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.29/1.01 fof(f40,lemma,(
% 4.29/1.01 (! [A,B] : subset(set_intersection2(A,B),A) )),
% 4.29/1.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.29/1.01 fof(f42,axiom,(
% 4.29/1.01 (! [A] : set_union2(A,empty_set) = A )),
% 4.29/1.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.29/1.01 fof(f43,lemma,(
% 4.29/1.01 (! [A,B,C] :( ( subset(A,B)& subset(B,C) )=> subset(A,C) ) )),
% 4.29/1.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.29/1.01 fof(f44,conjecture,(
% 4.29/1.01 powerset(empty_set) = singleton(empty_set) ),
% 4.29/1.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.29/1.01 fof(f45,negated_conjecture,(
% 4.29/1.01 ~(powerset(empty_set) = singleton(empty_set) )),
% 4.29/1.01 inference(negated_conjecture,[status(cth)],[f44])).
% 4.29/1.01 fof(f47,lemma,(
% 4.29/1.01 (! [A,B] :( subset(A,B)=> set_intersection2(A,B) = A ) )),
% 4.29/1.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.29/1.01 fof(f50,lemma,(
% 4.29/1.01 (! [A] : subset(empty_set,A) )),
% 4.29/1.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.29/1.01 fof(f52,lemma,(
% 4.29/1.01 (! [A,B] : subset(set_difference(A,B),A) )),
% 4.29/1.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.29/1.01 fof(f57,lemma,(
% 4.29/1.01 (! [A] :( subset(A,empty_set)=> A = empty_set ) )),
% 4.29/1.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.29/1.01 fof(f60,lemma,(
% 4.29/1.01 (! [A,B] : set_difference(A,set_difference(A,B)) = set_intersection2(A,B) )),
% 4.29/1.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.29/1.01 fof(f61,axiom,(
% 4.29/1.01 (! [A] : set_difference(empty_set,A) = empty_set )),
% 4.29/1.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.29/1.01 fof(f62,lemma,(
% 4.29/1.01 (! [A,B] :( ~ ( ~ disjoint(A,B)& (! [C] : ~ in(C,set_intersection2(A,B)) ))& ~ ( (? [C] : in(C,set_intersection2(A,B)))& disjoint(A,B) ) ) )),
% 4.29/1.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.29/1.01 fof(f63,lemma,(
% 4.29/1.01 (! [A,B] :~ ( subset(A,B)& proper_subset(B,A) ) )),
% 4.29/1.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.29/1.01 fof(f68,lemma,(
% 4.29/1.01 (! [A,B] : subset(A,set_union2(A,B)) )),
% 4.29/1.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.29/1.01 fof(f69,lemma,(
% 4.29/1.01 (! [A,B] :( disjoint(A,B)<=> set_difference(A,B) = A ) )),
% 4.29/1.01 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.29/1.01 fof(f72,plain,(
% 4.29/1.01 ![A,B]: (~in(A,B)|~in(B,A))),
% 4.29/1.01 inference(pre_NNF_transformation,[status(esa)],[f1])).
% 4.29/1.01 fof(f73,plain,(
% 4.29/1.01 ![X0,X1]: (~in(X0,X1)|~in(X1,X0))),
% 4.29/1.01 inference(cnf_transformation,[status(esa)],[f72])).
% 4.29/1.01 fof(f77,plain,(
% 4.29/1.01 ![X0,X1]: (set_union2(X0,X1)=set_union2(X1,X0))),
% 4.29/1.01 inference(cnf_transformation,[status(esa)],[f4])).
% 4.29/1.01 fof(f78,plain,(
% 4.29/1.01 ![X0,X1]: (set_intersection2(X0,X1)=set_intersection2(X1,X0))),
% 4.29/1.01 inference(cnf_transformation,[status(esa)],[f5])).
% 4.29/1.01 fof(f79,plain,(
% 4.29/1.01 ![A,B]: ((~A=B|(subset(A,B)&subset(B,A)))&(A=B|(~subset(A,B)|~subset(B,A))))),
% 4.29/1.01 inference(NNF_transformation,[status(esa)],[f6])).
% 4.29/1.01 fof(f80,plain,(
% 4.29/1.01 (![A,B]: (~A=B|(subset(A,B)&subset(B,A))))&(![A,B]: (A=B|(~subset(A,B)|~subset(B,A))))),
% 4.29/1.01 inference(miniscoping,[status(esa)],[f79])).
% 4.29/1.01 fof(f81,plain,(
% 4.29/1.01 ![X0,X1]: (~X0=X1|subset(X0,X1))),
% 4.29/1.01 inference(cnf_transformation,[status(esa)],[f80])).
% 4.29/1.01 fof(f91,plain,(
% 4.29/1.01 ![A]: ((~A=empty_set|(![B]: ~in(B,A)))&(A=empty_set|(?[B]: in(B,A))))),
% 4.29/1.01 inference(NNF_transformation,[status(esa)],[f8])).
% 4.29/1.01 fof(f92,plain,(
% 4.29/1.01 (![A]: (~A=empty_set|(![B]: ~in(B,A))))&(![A]: (A=empty_set|(?[B]: in(B,A))))),
% 4.29/1.01 inference(miniscoping,[status(esa)],[f91])).
% 4.29/1.01 fof(f93,plain,(
% 4.29/1.01 (![A]: (~A=empty_set|(![B]: ~in(B,A))))&(![A]: (A=empty_set|in(sk0_1(A),A)))),
% 4.29/1.01 inference(skolemization,[status(esa)],[f92])).
% 4.29/1.01 fof(f94,plain,(
% 4.29/1.01 ![X0,X1]: (~X0=empty_set|~in(X1,X0))),
% 4.29/1.01 inference(cnf_transformation,[status(esa)],[f93])).
% 4.29/1.01 fof(f95,plain,(
% 4.29/1.01 ![X0]: (X0=empty_set|in(sk0_1(X0),X0))),
% 4.29/1.01 inference(cnf_transformation,[status(esa)],[f93])).
% 4.29/1.01 fof(f96,plain,(
% 4.29/1.01 ![A,B]: ((~B=powerset(A)|(![C]: ((~in(C,B)|subset(C,A))&(in(C,B)|~subset(C,A)))))&(B=powerset(A)|(?[C]: ((~in(C,B)|~subset(C,A))&(in(C,B)|subset(C,A))))))),
% 4.29/1.01 inference(NNF_transformation,[status(esa)],[f9])).
% 4.29/1.01 fof(f97,plain,(
% 4.29/1.01 (![A,B]: (~B=powerset(A)|((![C]: (~in(C,B)|subset(C,A)))&(![C]: (in(C,B)|~subset(C,A))))))&(![A,B]: (B=powerset(A)|(?[C]: ((~in(C,B)|~subset(C,A))&(in(C,B)|subset(C,A))))))),
% 4.29/1.01 inference(miniscoping,[status(esa)],[f96])).
% 4.29/1.01 fof(f98,plain,(
% 4.29/1.01 (![A,B]: (~B=powerset(A)|((![C]: (~in(C,B)|subset(C,A)))&(![C]: (in(C,B)|~subset(C,A))))))&(![A,B]: (B=powerset(A)|((~in(sk0_2(B,A),B)|~subset(sk0_2(B,A),A))&(in(sk0_2(B,A),B)|subset(sk0_2(B,A),A)))))),
% 4.29/1.01 inference(skolemization,[status(esa)],[f97])).
% 4.29/1.01 fof(f99,plain,(
% 4.29/1.01 ![X0,X1,X2]: (~X0=powerset(X1)|~in(X2,X0)|subset(X2,X1))),
% 4.29/1.01 inference(cnf_transformation,[status(esa)],[f98])).
% 4.29/1.01 fof(f100,plain,(
% 4.29/1.01 ![X0,X1,X2]: (~X0=powerset(X1)|in(X2,X0)|~subset(X2,X1))),
% 4.29/1.01 inference(cnf_transformation,[status(esa)],[f98])).
% 4.29/1.01 fof(f101,plain,(
% 4.29/1.01 ![X0,X1]: (X0=powerset(X1)|~in(sk0_2(X0,X1),X0)|~subset(sk0_2(X0,X1),X1))),
% 4.29/1.01 inference(cnf_transformation,[status(esa)],[f98])).
% 4.29/1.01 fof(f102,plain,(
% 4.29/1.01 ![X0,X1]: (X0=powerset(X1)|in(sk0_2(X0,X1),X0)|subset(sk0_2(X0,X1),X1))),
% 4.29/1.01 inference(cnf_transformation,[status(esa)],[f98])).
% 4.29/1.01 fof(f103,plain,(
% 4.29/1.01 ![A,B,C]: ((~C=unordered_pair(A,B)|(![D]: ((~in(D,C)|(D=A|D=B))&(in(D,C)|(~D=A&~D=B)))))&(C=unordered_pair(A,B)|(?[D]: ((~in(D,C)|(~D=A&~D=B))&(in(D,C)|(D=A|D=B))))))),
% 4.29/1.01 inference(NNF_transformation,[status(esa)],[f10])).
% 4.29/1.01 fof(f104,plain,(
% 4.29/1.01 (![A,B,C]: (~C=unordered_pair(A,B)|((![D]: (~in(D,C)|(D=A|D=B)))&(![D]: (in(D,C)|(~D=A&~D=B))))))&(![A,B,C]: (C=unordered_pair(A,B)|(?[D]: ((~in(D,C)|(~D=A&~D=B))&(in(D,C)|(D=A|D=B))))))),
% 4.29/1.01 inference(miniscoping,[status(esa)],[f103])).
% 4.29/1.01 fof(f105,plain,(
% 4.29/1.01 (![A,B,C]: (~C=unordered_pair(A,B)|((![D]: (~in(D,C)|(D=A|D=B)))&(![D]: (in(D,C)|(~D=A&~D=B))))))&(![A,B,C]: (C=unordered_pair(A,B)|((~in(sk0_3(C,B,A),C)|(~sk0_3(C,B,A)=A&~sk0_3(C,B,A)=B))&(in(sk0_3(C,B,A),C)|(sk0_3(C,B,A)=A|sk0_3(C,B,A)=B)))))),
% 4.29/1.01 inference(skolemization,[status(esa)],[f104])).
% 4.29/1.01 fof(f107,plain,(
% 4.29/1.01 ![X0,X1,X2,X3]: (~X0=unordered_pair(X1,X2)|in(X3,X0)|~X3=X1)),
% 4.29/1.01 inference(cnf_transformation,[status(esa)],[f105])).
% 4.29/1.01 fof(f108,plain,(
% 4.29/1.01 ![X0,X1,X2,X3]: (~X0=unordered_pair(X1,X2)|in(X3,X0)|~X3=X2)),
% 4.29/1.01 inference(cnf_transformation,[status(esa)],[f105])).
% 4.29/1.01 fof(f121,plain,(
% 4.29/1.01 ![A,B]: (subset(A,B)<=>(![C]: (~in(C,A)|in(C,B))))),
% 4.29/1.01 inference(pre_NNF_transformation,[status(esa)],[f12])).
% 4.29/1.01 fof(f122,plain,(
% 4.29/1.01 ![A,B]: ((~subset(A,B)|(![C]: (~in(C,A)|in(C,B))))&(subset(A,B)|(?[C]: (in(C,A)&~in(C,B)))))),
% 4.29/1.01 inference(NNF_transformation,[status(esa)],[f121])).
% 4.29/1.01 fof(f123,plain,(
% 4.29/1.01 (![A,B]: (~subset(A,B)|(![C]: (~in(C,A)|in(C,B)))))&(![A,B]: (subset(A,B)|(?[C]: (in(C,A)&~in(C,B)))))),
% 4.29/1.01 inference(miniscoping,[status(esa)],[f122])).
% 4.29/1.01 fof(f124,plain,(
% 4.29/1.01 (![A,B]: (~subset(A,B)|(![C]: (~in(C,A)|in(C,B)))))&(![A,B]: (subset(A,B)|(in(sk0_5(B,A),A)&~in(sk0_5(B,A),B))))),
% 4.29/1.01 inference(skolemization,[status(esa)],[f123])).
% 4.29/1.01 fof(f125,plain,(
% 4.29/1.01 ![X0,X1,X2]: (~subset(X0,X1)|~in(X2,X0)|in(X2,X1))),
% 4.29/1.01 inference(cnf_transformation,[status(esa)],[f124])).
% 4.29/1.01 fof(f168,plain,(
% 4.29/1.01 ![X0]: (~singleton(X0)=empty_set)),
% 4.29/1.01 inference(cnf_transformation,[status(esa)],[f30])).
% 4.29/1.01 fof(f169,plain,(
% 4.29/1.01 ![A,B]: ((~subset(singleton(A),B)|in(A,B))&(subset(singleton(A),B)|~in(A,B)))),
% 4.29/1.01 inference(NNF_transformation,[status(esa)],[f31])).
% 4.29/1.01 fof(f170,plain,(
% 4.29/1.01 (![A,B]: (~subset(singleton(A),B)|in(A,B)))&(![A,B]: (subset(singleton(A),B)|~in(A,B)))),
% 4.29/1.01 inference(miniscoping,[status(esa)],[f169])).
% 4.29/1.01 fof(f172,plain,(
% 4.29/1.01 ![X0,X1]: (subset(singleton(X0),X1)|~in(X0,X1))),
% 4.29/1.01 inference(cnf_transformation,[status(esa)],[f170])).
% 4.29/1.01 fof(f173,plain,(
% 4.29/1.01 ![A,B]: ((~set_difference(A,B)=empty_set|subset(A,B))&(set_difference(A,B)=empty_set|~subset(A,B)))),
% 4.29/1.01 inference(NNF_transformation,[status(esa)],[f32])).
% 4.29/1.01 fof(f174,plain,(
% 4.29/1.01 (![A,B]: (~set_difference(A,B)=empty_set|subset(A,B)))&(![A,B]: (set_difference(A,B)=empty_set|~subset(A,B)))),
% 4.29/1.01 inference(miniscoping,[status(esa)],[f173])).
% 4.29/1.01 fof(f175,plain,(
% 4.29/1.01 ![X0,X1]: (~set_difference(X0,X1)=empty_set|subset(X0,X1))),
% 4.29/1.01 inference(cnf_transformation,[status(esa)],[f174])).
% 4.29/1.01 fof(f176,plain,(
% 4.29/1.01 ![X0,X1]: (set_difference(X0,X1)=empty_set|~subset(X0,X1))),
% 4.29/1.01 inference(cnf_transformation,[status(esa)],[f174])).
% 4.29/1.01 fof(f177,plain,(
% 4.29/1.01 ![A,B,C]: (~subset(A,B)|(in(C,A)|subset(A,set_difference(B,singleton(C)))))),
% 4.29/1.01 inference(pre_NNF_transformation,[status(esa)],[f33])).
% 4.29/1.01 fof(f178,plain,(
% 4.29/1.01 ![A,B]: (~subset(A,B)|(![C]: (in(C,A)|subset(A,set_difference(B,singleton(C))))))),
% 4.29/1.01 inference(miniscoping,[status(esa)],[f177])).
% 4.29/1.01 fof(f179,plain,(
% 4.29/1.01 ![X0,X1,X2]: (~subset(X0,X1)|in(X2,X0)|subset(X0,set_difference(X1,singleton(X2))))),
% 4.29/1.01 inference(cnf_transformation,[status(esa)],[f178])).
% 4.29/1.01 fof(f180,plain,(
% 4.29/1.01 ![A,B]: ((~subset(A,singleton(B))|(A=empty_set|A=singleton(B)))&(subset(A,singleton(B))|(~A=empty_set&~A=singleton(B))))),
% 4.29/1.01 inference(NNF_transformation,[status(esa)],[f34])).
% 4.29/1.01 fof(f181,plain,(
% 4.29/1.01 (![A,B]: (~subset(A,singleton(B))|(A=empty_set|A=singleton(B))))&(![A,B]: (subset(A,singleton(B))|(~A=empty_set&~A=singleton(B))))),
% 4.29/1.01 inference(miniscoping,[status(esa)],[f180])).
% 4.29/1.01 fof(f182,plain,(
% 4.29/1.01 ![X0,X1]: (~subset(X0,singleton(X1))|X0=empty_set|X0=singleton(X1))),
% 4.29/1.01 inference(cnf_transformation,[status(esa)],[f181])).
% 4.29/1.01 fof(f193,plain,(
% 4.29/1.01 ![A,B]: (~subset(A,B)|set_union2(A,B)=B)),
% 4.29/1.01 inference(pre_NNF_transformation,[status(esa)],[f39])).
% 4.29/1.01 fof(f194,plain,(
% 4.29/1.01 ![X0,X1]: (~subset(X0,X1)|set_union2(X0,X1)=X1)),
% 4.29/1.01 inference(cnf_transformation,[status(esa)],[f193])).
% 4.29/1.01 fof(f195,plain,(
% 4.29/1.01 ![X0,X1]: (subset(set_intersection2(X0,X1),X0))),
% 4.29/1.01 inference(cnf_transformation,[status(esa)],[f40])).
% 4.29/1.01 fof(f198,plain,(
% 4.29/1.01 ![X0]: (set_union2(X0,empty_set)=X0)),
% 4.29/1.01 inference(cnf_transformation,[status(esa)],[f42])).
% 4.29/1.01 fof(f199,plain,(
% 4.29/1.01 ![A,B,C]: ((~subset(A,B)|~subset(B,C))|subset(A,C))),
% 4.29/1.01 inference(pre_NNF_transformation,[status(esa)],[f43])).
% 4.29/1.01 fof(f200,plain,(
% 4.29/1.01 ![A,C]: ((![B]: (~subset(A,B)|~subset(B,C)))|subset(A,C))),
% 4.29/1.01 inference(miniscoping,[status(esa)],[f199])).
% 4.29/1.01 fof(f201,plain,(
% 4.29/1.01 ![X0,X1,X2]: (~subset(X0,X1)|~subset(X1,X2)|subset(X0,X2))),
% 4.29/1.01 inference(cnf_transformation,[status(esa)],[f200])).
% 4.29/1.01 fof(f202,plain,(
% 4.29/1.01 ~powerset(empty_set)=singleton(empty_set)),
% 4.29/1.01 inference(cnf_transformation,[status(esa)],[f45])).
% 4.29/1.01 fof(f206,plain,(
% 4.29/1.01 ![A,B]: (~subset(A,B)|set_intersection2(A,B)=A)),
% 4.29/1.01 inference(pre_NNF_transformation,[status(esa)],[f47])).
% 4.29/1.01 fof(f207,plain,(
% 4.29/1.01 ![X0,X1]: (~subset(X0,X1)|set_intersection2(X0,X1)=X0)),
% 4.29/1.01 inference(cnf_transformation,[status(esa)],[f206])).
% 4.29/1.01 fof(f214,plain,(
% 4.29/1.01 ![X0]: (subset(empty_set,X0))),
% 4.29/1.01 inference(cnf_transformation,[status(esa)],[f50])).
% 4.29/1.01 fof(f218,plain,(
% 4.29/1.01 ![X0,X1]: (subset(set_difference(X0,X1),X0))),
% 4.29/1.01 inference(cnf_transformation,[status(esa)],[f52])).
% 4.29/1.01 fof(f231,plain,(
% 4.29/1.01 ![A]: (~subset(A,empty_set)|A=empty_set)),
% 4.29/1.01 inference(pre_NNF_transformation,[status(esa)],[f57])).
% 4.29/1.01 fof(f232,plain,(
% 4.29/1.01 ![X0]: (~subset(X0,empty_set)|X0=empty_set)),
% 4.29/1.01 inference(cnf_transformation,[status(esa)],[f231])).
% 4.29/1.01 fof(f236,plain,(
% 4.29/1.01 ![X0,X1]: (set_difference(X0,set_difference(X0,X1))=set_intersection2(X0,X1))),
% 4.29/1.01 inference(cnf_transformation,[status(esa)],[f60])).
% 4.29/1.01 fof(f237,plain,(
% 4.29/1.01 ![X0]: (set_difference(empty_set,X0)=empty_set)),
% 4.29/1.01 inference(cnf_transformation,[status(esa)],[f61])).
% 4.29/1.01 fof(f238,plain,(
% 4.29/1.01 ![A,B]: ((disjoint(A,B)|(?[C]: in(C,set_intersection2(A,B))))&((![C]: ~in(C,set_intersection2(A,B)))|~disjoint(A,B)))),
% 4.29/1.01 inference(pre_NNF_transformation,[status(esa)],[f62])).
% 4.29/1.01 fof(f239,plain,(
% 4.29/1.01 (![A,B]: (disjoint(A,B)|(?[C]: in(C,set_intersection2(A,B)))))&(![A,B]: ((![C]: ~in(C,set_intersection2(A,B)))|~disjoint(A,B)))),
% 4.29/1.01 inference(miniscoping,[status(esa)],[f238])).
% 4.29/1.01 fof(f240,plain,(
% 4.29/1.01 (![A,B]: (disjoint(A,B)|in(sk0_12(B,A),set_intersection2(A,B))))&(![A,B]: ((![C]: ~in(C,set_intersection2(A,B)))|~disjoint(A,B)))),
% 4.29/1.01 inference(skolemization,[status(esa)],[f239])).
% 4.29/1.01 fof(f242,plain,(
% 4.29/1.01 ![X0,X1,X2]: (~in(X0,set_intersection2(X1,X2))|~disjoint(X1,X2))),
% 4.29/1.01 inference(cnf_transformation,[status(esa)],[f240])).
% 4.29/1.01 fof(f243,plain,(
% 4.29/1.01 ![A,B]: (~subset(A,B)|~proper_subset(B,A))),
% 4.29/1.01 inference(pre_NNF_transformation,[status(esa)],[f63])).
% 4.29/1.01 fof(f244,plain,(
% 4.29/1.01 ![X0,X1]: (~subset(X0,X1)|~proper_subset(X1,X0))),
% 4.29/1.01 inference(cnf_transformation,[status(esa)],[f243])).
% 4.29/1.01 fof(f254,plain,(
% 4.29/1.01 ![X0,X1]: (subset(X0,set_union2(X0,X1)))),
% 4.29/1.01 inference(cnf_transformation,[status(esa)],[f68])).
% 4.29/1.01 fof(f255,plain,(
% 4.29/1.01 ![A,B]: ((~disjoint(A,B)|set_difference(A,B)=A)&(disjoint(A,B)|~set_difference(A,B)=A))),
% 4.29/1.01 inference(NNF_transformation,[status(esa)],[f69])).
% 4.29/1.01 fof(f256,plain,(
% 4.29/1.01 (![A,B]: (~disjoint(A,B)|set_difference(A,B)=A))&(![A,B]: (disjoint(A,B)|~set_difference(A,B)=A))),
% 4.29/1.01 inference(miniscoping,[status(esa)],[f255])).
% 4.29/1.01 fof(f258,plain,(
% 4.29/1.01 ![X0,X1]: (disjoint(X0,X1)|~set_difference(X0,X1)=X0)),
% 4.29/1.01 inference(cnf_transformation,[status(esa)],[f256])).
% 4.29/1.01 fof(f264,plain,(
% 4.29/1.01 ![X0]: (subset(X0,X0))),
% 4.29/1.01 inference(destructive_equality_resolution,[status(esa)],[f81])).
% 4.29/1.01 fof(f268,plain,(
% 4.29/1.01 ![X0]: (~in(X0,empty_set))),
% 4.29/1.01 inference(destructive_equality_resolution,[status(esa)],[f94])).
% 4.29/1.01 fof(f269,plain,(
% 4.29/1.01 ![X0,X1]: (~in(X0,powerset(X1))|subset(X0,X1))),
% 4.29/1.01 inference(destructive_equality_resolution,[status(esa)],[f99])).
% 4.29/1.01 fof(f270,plain,(
% 4.29/1.01 ![X0,X1]: (in(X0,powerset(X1))|~subset(X0,X1))),
% 4.29/1.01 inference(destructive_equality_resolution,[status(esa)],[f100])).
% 4.29/1.01 fof(f272,plain,(
% 4.29/1.01 ![X0,X1]: (in(X0,unordered_pair(X0,X1)))),
% 4.29/1.01 inference(destructive_equality_resolution,[status(esa)],[f107])).
% 4.29/1.01 fof(f273,plain,(
% 4.29/1.01 ![X0,X1]: (in(X0,unordered_pair(X1,X0)))),
% 4.29/1.01 inference(destructive_equality_resolution,[status(esa)],[f108])).
% 4.29/1.01 fof(f287,plain,(
% 4.29/1.01 ![X0]: (in(empty_set,powerset(X0)))),
% 4.29/1.01 inference(resolution,[status(thm)],[f270,f214])).
% 4.29/1.01 fof(f289,plain,(
% 4.29/1.01 ![X0]: (subset(singleton(empty_set),powerset(X0)))),
% 4.29/1.01 inference(resolution,[status(thm)],[f172,f287])).
% 4.29/1.01 fof(f300,plain,(
% 4.29/1.01 spl0_0 <=> empty_set=empty_set),
% 4.29/1.01 introduced(split_symbol_definition)).
% 4.29/1.01 fof(f303,plain,(
% 4.29/1.01 spl0_1 <=> empty_set=singleton(X0)),
% 4.29/1.01 introduced(split_symbol_definition)).
% 4.29/1.01 fof(f304,plain,(
% 4.29/1.01 ![X0]: (empty_set=singleton(X0)|~spl0_1)),
% 4.29/1.01 inference(component_clause,[status(thm)],[f303])).
% 4.29/1.01 fof(f306,plain,(
% 4.29/1.01 ![X0]: (empty_set=empty_set|empty_set=singleton(X0))),
% 4.29/1.01 inference(resolution,[status(thm)],[f182,f214])).
% 4.29/1.01 fof(f307,plain,(
% 4.29/1.01 spl0_0|spl0_1),
% 4.29/1.01 inference(split_clause,[status(thm)],[f306,f300,f303])).
% 4.29/1.01 fof(f309,plain,(
% 4.29/1.01 ![X0,X1]: (in(X0,X1)|subset(X1,set_difference(X1,singleton(X0))))),
% 4.29/1.01 inference(resolution,[status(thm)],[f264,f179])).
% 4.29/1.01 fof(f310,plain,(
% 4.29/1.01 ![X0]: (set_difference(X0,X0)=empty_set)),
% 4.29/1.01 inference(resolution,[status(thm)],[f264,f176])).
% 4.29/1.01 fof(f311,plain,(
% 4.29/1.01 ![X0]: (in(X0,powerset(X0)))),
% 4.29/1.01 inference(resolution,[status(thm)],[f264,f270])).
% 4.29/1.01 fof(f313,plain,(
% 4.29/1.01 spl0_2 <=> subset(X0,X0)),
% 4.29/1.01 introduced(split_symbol_definition)).
% 4.29/1.01 fof(f316,plain,(
% 4.29/1.01 ![X0]: (~empty_set=empty_set|subset(X0,X0))),
% 4.29/1.01 inference(paramodulation,[status(thm)],[f310,f175])).
% 4.29/1.01 fof(f317,plain,(
% 4.29/1.01 ~spl0_0|spl0_2),
% 4.29/1.01 inference(split_clause,[status(thm)],[f316,f300,f313])).
% 4.29/1.01 fof(f318,plain,(
% 4.29/1.01 $false|~spl0_1),
% 4.29/1.01 inference(forward_subsumption_resolution,[status(thm)],[f304,f168])).
% 4.29/1.01 fof(f319,plain,(
% 4.29/1.01 ~spl0_1),
% 4.29/1.01 inference(contradiction_clause,[status(thm)],[f318])).
% 4.29/1.01 fof(f321,plain,(
% 4.29/1.01 ![X0]: (subset(singleton(X0),powerset(X0)))),
% 4.29/1.01 inference(resolution,[status(thm)],[f311,f172])).
% 4.29/1.01 fof(f322,plain,(
% 4.29/1.01 ![X0,X1]: (subset(singleton(X0),unordered_pair(X0,X1)))),
% 4.29/1.01 inference(resolution,[status(thm)],[f272,f172])).
% 4.29/1.01 fof(f323,plain,(
% 4.29/1.01 ![X0,X1]: (subset(singleton(X0),unordered_pair(X1,X0)))),
% 4.29/1.01 inference(resolution,[status(thm)],[f273,f172])).
% 4.29/1.01 fof(f324,plain,(
% 4.29/1.01 ![X0,X1]: (set_intersection2(singleton(X0),X1)=empty_set|set_intersection2(singleton(X0),X1)=singleton(X0))),
% 4.29/1.01 inference(resolution,[status(thm)],[f195,f182])).
% 4.29/1.01 fof(f325,plain,(
% 4.29/1.01 ![X0]: (set_intersection2(empty_set,X0)=empty_set)),
% 4.29/1.01 inference(resolution,[status(thm)],[f195,f232])).
% 4.29/1.01 fof(f327,plain,(
% 4.29/1.01 ![X0,X1]: (set_difference(set_intersection2(X0,X1),X0)=empty_set)),
% 4.29/1.01 inference(resolution,[status(thm)],[f195,f176])).
% 4.29/1.01 fof(f328,plain,(
% 4.29/1.01 ![X0,X1]: (in(set_intersection2(X0,X1),powerset(X0)))),
% 4.29/1.01 inference(resolution,[status(thm)],[f195,f270])).
% 4.29/1.01 fof(f333,plain,(
% 4.29/1.01 ![X0,X1]: (set_difference(set_difference(X0,X1),X0)=empty_set)),
% 4.29/1.01 inference(resolution,[status(thm)],[f218,f176])).
% 4.29/1.01 fof(f344,plain,(
% 4.29/1.01 ![X0,X1]: (set_difference(X0,set_union2(X0,X1))=empty_set)),
% 4.29/1.01 inference(resolution,[status(thm)],[f254,f176])).
% 4.29/1.01 fof(f345,plain,(
% 4.29/1.01 ![X0,X1]: (in(X0,powerset(set_union2(X0,X1))))),
% 4.29/1.01 inference(resolution,[status(thm)],[f254,f270])).
% 4.29/1.01 fof(f359,plain,(
% 4.29/1.01 ![X0]: (set_difference(singleton(X0),powerset(X0))=empty_set)),
% 4.29/1.01 inference(resolution,[status(thm)],[f321,f176])).
% 4.29/1.01 fof(f363,plain,(
% 4.29/1.01 ![X0,X1]: (set_difference(singleton(X0),unordered_pair(X0,X1))=empty_set)),
% 4.29/1.01 inference(resolution,[status(thm)],[f322,f176])).
% 4.29/1.01 fof(f369,plain,(
% 4.29/1.01 ![X0,X1]: (set_difference(singleton(X0),unordered_pair(X1,X0))=empty_set)),
% 4.29/1.01 inference(resolution,[status(thm)],[f323,f176])).
% 4.29/1.01 fof(f375,plain,(
% 4.29/1.01 spl0_3 <=> subset(empty_set,X0)),
% 4.29/1.01 introduced(split_symbol_definition)).
% 4.29/1.01 fof(f378,plain,(
% 4.29/1.01 ![X0]: (~empty_set=empty_set|subset(empty_set,X0))),
% 4.29/1.01 inference(paramodulation,[status(thm)],[f237,f175])).
% 4.29/1.01 fof(f379,plain,(
% 4.29/1.01 ~spl0_0|spl0_3),
% 4.29/1.01 inference(split_clause,[status(thm)],[f378,f300,f375])).
% 4.29/1.01 fof(f386,plain,(
% 4.29/1.01 spl0_4 <=> subset(set_intersection2(X0,X1),X0)),
% 4.29/1.01 introduced(split_symbol_definition)).
% 4.29/1.01 fof(f389,plain,(
% 4.29/1.01 ![X0,X1]: (~empty_set=empty_set|subset(set_intersection2(X0,X1),X0))),
% 4.29/1.01 inference(paramodulation,[status(thm)],[f327,f175])).
% 4.29/1.01 fof(f390,plain,(
% 4.29/1.01 ~spl0_0|spl0_4),
% 4.29/1.01 inference(split_clause,[status(thm)],[f389,f300,f386])).
% 4.29/1.01 fof(f394,plain,(
% 4.29/1.01 ![X0,X1]: (subset(singleton(set_intersection2(X0,X1)),powerset(X0)))),
% 4.29/1.01 inference(resolution,[status(thm)],[f328,f172])).
% 4.29/1.01 fof(f409,plain,(
% 4.29/1.01 spl0_5 <=> subset(X0,set_union2(X0,X1))),
% 4.29/1.01 introduced(split_symbol_definition)).
% 4.29/1.01 fof(f412,plain,(
% 4.29/1.01 ![X0,X1]: (~empty_set=empty_set|subset(X0,set_union2(X0,X1)))),
% 4.29/1.01 inference(paramodulation,[status(thm)],[f344,f175])).
% 4.29/1.01 fof(f413,plain,(
% 4.29/1.01 ~spl0_0|spl0_5),
% 4.29/1.01 inference(split_clause,[status(thm)],[f412,f300,f409])).
% 4.29/1.01 fof(f417,plain,(
% 4.29/1.01 ![X0,X1]: (subset(singleton(X0),powerset(set_union2(X0,X1))))),
% 4.29/1.01 inference(resolution,[status(thm)],[f345,f172])).
% 4.29/1.01 fof(f431,plain,(
% 4.29/1.01 spl0_6 <=> subset(singleton(X0),powerset(X0))),
% 4.29/1.01 introduced(split_symbol_definition)).
% 4.29/1.01 fof(f434,plain,(
% 4.29/1.01 ![X0]: (~empty_set=empty_set|subset(singleton(X0),powerset(X0)))),
% 4.29/1.01 inference(paramodulation,[status(thm)],[f359,f175])).
% 4.29/1.01 fof(f435,plain,(
% 4.29/1.01 ~spl0_0|spl0_6),
% 4.29/1.01 inference(split_clause,[status(thm)],[f434,f300,f431])).
% 4.29/1.01 fof(f441,plain,(
% 4.29/1.01 ![X0,X1,X2]: (in(X0,X1)|in(X2,X1)|subset(X1,set_difference(set_difference(X1,singleton(X0)),singleton(X2))))),
% 4.29/1.01 inference(resolution,[status(thm)],[f309,f179])).
% 4.29/1.01 fof(f442,plain,(
% 4.29/1.01 ![X0,X1]: (in(X0,X1)|set_difference(X1,set_difference(X1,singleton(X0)))=empty_set)),
% 4.29/1.01 inference(resolution,[status(thm)],[f309,f176])).
% 4.29/1.01 fof(f443,plain,(
% 4.29/1.01 ![X0,X1]: (in(X0,X1)|set_intersection2(X1,singleton(X0))=empty_set)),
% 4.29/1.01 inference(forward_demodulation,[status(thm)],[f236,f442])).
% 4.29/1.01 fof(f444,plain,(
% 4.29/1.01 ![X0,X1]: (in(X0,X1)|in(X1,powerset(set_difference(X1,singleton(X0)))))),
% 4.29/1.01 inference(resolution,[status(thm)],[f309,f270])).
% 4.29/1.01 fof(f445,plain,(
% 4.29/1.01 ![X0,X1]: (in(X0,set_intersection2(singleton(X0),X1))|subset(set_intersection2(singleton(X0),X1),empty_set))),
% 4.29/1.01 inference(paramodulation,[status(thm)],[f327,f309])).
% 4.29/1.01 fof(f446,plain,(
% 4.29/1.01 spl0_7 <=> in(X0,empty_set)),
% 4.29/1.01 introduced(split_symbol_definition)).
% 4.29/1.01 fof(f447,plain,(
% 4.29/1.01 ![X0]: (in(X0,empty_set)|~spl0_7)),
% 4.29/1.01 inference(component_clause,[status(thm)],[f446])).
% 4.29/1.01 fof(f449,plain,(
% 4.29/1.01 spl0_8 <=> subset(empty_set,empty_set)),
% 4.29/1.01 introduced(split_symbol_definition)).
% 4.29/1.01 fof(f452,plain,(
% 4.29/1.01 ![X0]: (in(X0,empty_set)|subset(empty_set,empty_set))),
% 4.29/1.01 inference(paramodulation,[status(thm)],[f237,f309])).
% 4.29/1.01 fof(f453,plain,(
% 4.29/1.01 spl0_7|spl0_8),
% 4.29/1.01 inference(split_clause,[status(thm)],[f452,f446,f449])).
% 4.29/1.01 fof(f455,plain,(
% 4.29/1.01 $false|~spl0_7),
% 4.29/1.01 inference(forward_subsumption_resolution,[status(thm)],[f447,f268])).
% 4.29/1.01 fof(f456,plain,(
% 4.29/1.01 ~spl0_7),
% 4.29/1.01 inference(contradiction_clause,[status(thm)],[f455])).
% 4.29/1.01 fof(f482,plain,(
% 4.29/1.01 ![X0,X1]: (set_difference(singleton(set_intersection2(X0,X1)),powerset(X0))=empty_set)),
% 4.29/1.01 inference(resolution,[status(thm)],[f394,f176])).
% 4.29/1.01 fof(f499,plain,(
% 4.29/1.01 ![X0,X1]: (set_difference(singleton(X0),powerset(set_union2(X0,X1)))=empty_set)),
% 4.29/1.01 inference(resolution,[status(thm)],[f417,f176])).
% 4.29/1.01 fof(f520,plain,(
% 4.29/1.01 ![X0,X1]: (set_intersection2(powerset(X0),singleton(X1))=empty_set|subset(X1,X0))),
% 4.29/1.01 inference(resolution,[status(thm)],[f443,f269])).
% 4.29/1.01 fof(f521,plain,(
% 4.29/1.01 ![X0,X1]: (set_intersection2(singleton(X0),powerset(X1))=empty_set|subset(X0,X1))),
% 4.29/1.01 inference(forward_demodulation,[status(thm)],[f78,f520])).
% 4.29/1.01 fof(f667,plain,(
% 4.29/1.01 spl0_11 <=> subset(singleton(set_intersection2(X0,X1)),powerset(X0))),
% 4.29/1.01 introduced(split_symbol_definition)).
% 4.29/1.01 fof(f670,plain,(
% 4.29/1.01 ![X0,X1]: (~empty_set=empty_set|subset(singleton(set_intersection2(X0,X1)),powerset(X0)))),
% 4.29/1.01 inference(paramodulation,[status(thm)],[f482,f175])).
% 4.29/1.01 fof(f671,plain,(
% 4.29/1.01 ~spl0_0|spl0_11),
% 4.29/1.01 inference(split_clause,[status(thm)],[f670,f300,f667])).
% 4.29/1.01 fof(f693,plain,(
% 4.29/1.01 spl0_12 <=> subset(set_difference(X0,X1),X0)),
% 4.29/1.01 introduced(split_symbol_definition)).
% 4.29/1.01 fof(f696,plain,(
% 4.29/1.01 ![X0,X1]: (~empty_set=empty_set|subset(set_difference(X0,X1),X0))),
% 4.29/1.01 inference(paramodulation,[status(thm)],[f333,f175])).
% 4.29/1.01 fof(f697,plain,(
% 4.29/1.01 ~spl0_0|spl0_12),
% 4.29/1.01 inference(split_clause,[status(thm)],[f696,f300,f693])).
% 4.29/1.01 fof(f736,plain,(
% 4.29/1.01 spl0_13 <=> subset(singleton(X0),powerset(set_union2(X0,X1)))),
% 4.29/1.01 introduced(split_symbol_definition)).
% 4.29/1.01 fof(f739,plain,(
% 4.29/1.01 ![X0,X1]: (~empty_set=empty_set|subset(singleton(X0),powerset(set_union2(X0,X1))))),
% 4.29/1.01 inference(paramodulation,[status(thm)],[f499,f175])).
% 4.29/1.01 fof(f740,plain,(
% 4.29/1.01 ~spl0_0|spl0_13),
% 4.29/1.01 inference(split_clause,[status(thm)],[f739,f300,f736])).
% 4.29/1.01 fof(f853,plain,(
% 4.29/1.01 ![X0,X1]: (~proper_subset(set_difference(X0,singleton(X1)),X0)|in(X1,X0))),
% 4.29/1.01 inference(resolution,[status(thm)],[f244,f309])).
% 4.29/1.01 fof(f875,plain,(
% 4.29/1.01 ![X0,X1]: (set_union2(singleton(set_intersection2(X0,X1)),powerset(X0))=powerset(X0))),
% 4.29/1.01 inference(resolution,[status(thm)],[f194,f394])).
% 4.29/1.01 fof(f931,plain,(
% 4.29/1.01 ![X0]: (set_intersection2(singleton(empty_set),powerset(X0))=singleton(empty_set))),
% 4.29/1.01 inference(resolution,[status(thm)],[f207,f289])).
% 4.29/1.01 fof(f949,plain,(
% 4.29/1.01 ![X0,X1]: (disjoint(set_difference(X0,X1),X0)|~empty_set=set_difference(X0,X1))),
% 4.29/1.01 inference(paramodulation,[status(thm)],[f333,f258])).
% 4.29/1.01 fof(f956,plain,(
% 4.29/1.01 spl0_16 <=> disjoint(empty_set,X0)),
% 4.29/1.01 introduced(split_symbol_definition)).
% 4.29/1.01 fof(f959,plain,(
% 4.29/1.01 ![X0]: (disjoint(empty_set,X0)|~empty_set=empty_set)),
% 4.29/1.01 inference(paramodulation,[status(thm)],[f237,f258])).
% 4.29/1.01 fof(f960,plain,(
% 4.29/1.01 spl0_16|~spl0_0),
% 4.29/1.01 inference(split_clause,[status(thm)],[f959,f956,f300])).
% 4.29/1.01 fof(f985,plain,(
% 4.29/1.01 ![X0,X1]: (set_difference(singleton(X0),powerset(set_union2(X1,X0)))=empty_set)),
% 4.29/1.01 inference(paramodulation,[status(thm)],[f77,f499])).
% 4.29/1.01 fof(f989,plain,(
% 4.29/1.01 ![X0,X1]: (set_difference(X0,set_union2(X1,X0))=empty_set)),
% 4.29/1.01 inference(paramodulation,[status(thm)],[f77,f344])).
% 4.29/1.01 fof(f990,plain,(
% 4.29/1.01 ![X0,X1]: (subset(X0,set_union2(X1,X0)))),
% 4.29/1.01 inference(paramodulation,[status(thm)],[f77,f254])).
% 4.29/1.01 fof(f1020,plain,(
% 4.29/1.01 ![X0,X1]: (set_difference(singleton(set_intersection2(X0,X1)),powerset(X1))=empty_set)),
% 4.29/1.01 inference(paramodulation,[status(thm)],[f78,f482])).
% 4.29/1.01 fof(f1025,plain,(
% 4.29/1.01 ![X0,X1]: (set_difference(set_intersection2(X0,X1),X1)=empty_set)),
% 4.29/1.01 inference(paramodulation,[status(thm)],[f78,f327])).
% 4.29/1.01 fof(f1103,plain,(
% 4.29/1.01 spl0_17 <=> subset(X0,set_union2(X1,X0))),
% 4.29/1.01 introduced(split_symbol_definition)).
% 4.29/1.01 fof(f1106,plain,(
% 4.29/1.01 ![X0,X1]: (~empty_set=empty_set|subset(X0,set_union2(X1,X0)))),
% 4.29/1.01 inference(paramodulation,[status(thm)],[f989,f175])).
% 4.29/1.01 fof(f1107,plain,(
% 4.29/1.01 ~spl0_0|spl0_17),
% 4.29/1.01 inference(split_clause,[status(thm)],[f1106,f300,f1103])).
% 4.29/1.01 fof(f1163,plain,(
% 4.29/1.01 spl0_18 <=> subset(set_intersection2(X0,X1),X1)),
% 4.29/1.01 introduced(split_symbol_definition)).
% 4.29/1.01 fof(f1166,plain,(
% 4.29/1.01 ![X0,X1]: (~empty_set=empty_set|subset(set_intersection2(X0,X1),X1))),
% 4.29/1.01 inference(paramodulation,[status(thm)],[f1025,f175])).
% 4.29/1.01 fof(f1167,plain,(
% 4.29/1.01 ~spl0_0|spl0_18),
% 4.29/1.01 inference(split_clause,[status(thm)],[f1166,f300,f1163])).
% 4.29/1.01 fof(f1298,plain,(
% 4.29/1.01 spl0_19 <=> subset(singleton(X0),unordered_pair(X0,X1))),
% 4.29/1.01 introduced(split_symbol_definition)).
% 4.29/1.01 fof(f1301,plain,(
% 4.29/1.01 ![X0,X1]: (~empty_set=empty_set|subset(singleton(X0),unordered_pair(X0,X1)))),
% 4.29/1.01 inference(paramodulation,[status(thm)],[f363,f175])).
% 4.29/1.01 fof(f1302,plain,(
% 4.29/1.01 ~spl0_0|spl0_19),
% 4.29/1.01 inference(split_clause,[status(thm)],[f1301,f300,f1298])).
% 4.29/1.01 fof(f1622,plain,(
% 4.29/1.01 spl0_20 <=> subset(singleton(X0),unordered_pair(X1,X0))),
% 4.29/1.01 introduced(split_symbol_definition)).
% 4.29/1.01 fof(f1625,plain,(
% 4.29/1.01 ![X0,X1]: (~empty_set=empty_set|subset(singleton(X0),unordered_pair(X1,X0)))),
% 4.29/1.01 inference(paramodulation,[status(thm)],[f369,f175])).
% 4.29/1.01 fof(f1626,plain,(
% 4.29/1.01 ~spl0_0|spl0_20),
% 4.29/1.01 inference(split_clause,[status(thm)],[f1625,f300,f1622])).
% 4.29/1.01 fof(f1766,plain,(
% 4.29/1.01 spl0_22 <=> in(X1,empty_set)|subset(empty_set,set_difference(empty_set,singleton(X1)))),
% 4.29/1.01 introduced(split_symbol_definition)).
% 4.29/1.01 fof(f1769,plain,(
% 4.29/1.01 ![X0,X1]: (in(X0,empty_set)|in(X1,empty_set)|subset(empty_set,set_difference(empty_set,singleton(X1))))),
% 4.29/1.01 inference(paramodulation,[status(thm)],[f237,f441])).
% 4.29/1.01 fof(f1770,plain,(
% 4.29/1.01 spl0_7|spl0_22),
% 4.29/1.01 inference(split_clause,[status(thm)],[f1769,f446,f1766])).
% 4.29/1.01 fof(f1786,plain,(
% 4.29/1.01 spl0_23 <=> proper_subset(empty_set,empty_set)),
% 4.29/1.01 introduced(split_symbol_definition)).
% 4.29/1.01 fof(f1789,plain,(
% 4.29/1.01 ![X0]: (~proper_subset(empty_set,empty_set)|in(X0,empty_set))),
% 4.29/1.01 inference(paramodulation,[status(thm)],[f237,f853])).
% 4.29/1.01 fof(f1790,plain,(
% 4.29/1.01 ~spl0_23|spl0_7),
% 4.29/1.01 inference(split_clause,[status(thm)],[f1789,f1786,f446])).
% 4.29/1.01 fof(f1868,plain,(
% 4.29/1.01 spl0_26 <=> disjoint(set_difference(set_difference(X0,X1),X0),set_difference(X0,X1))),
% 4.29/1.01 introduced(split_symbol_definition)).
% 4.29/1.01 fof(f1871,plain,(
% 4.29/1.01 ![X0,X1]: (disjoint(set_difference(set_difference(X0,X1),X0),set_difference(X0,X1))|~empty_set=empty_set)),
% 4.29/1.01 inference(paramodulation,[status(thm)],[f333,f949])).
% 4.29/1.01 fof(f1872,plain,(
% 4.29/1.01 spl0_26|~spl0_0),
% 4.29/1.01 inference(split_clause,[status(thm)],[f1871,f1868,f300])).
% 4.29/1.01 fof(f1873,plain,(
% 4.29/1.01 spl0_27 <=> disjoint(set_difference(singleton(set_intersection2(X0,X1)),powerset(X0)),singleton(set_intersection2(X0,X1)))),
% 4.29/1.01 introduced(split_symbol_definition)).
% 4.29/1.01 fof(f1876,plain,(
% 4.29/1.01 ![X0,X1]: (disjoint(set_difference(singleton(set_intersection2(X0,X1)),powerset(X0)),singleton(set_intersection2(X0,X1)))|~empty_set=empty_set)),
% 4.29/1.01 inference(paramodulation,[status(thm)],[f482,f949])).
% 4.29/1.01 fof(f1877,plain,(
% 4.29/1.01 spl0_27|~spl0_0),
% 4.29/1.01 inference(split_clause,[status(thm)],[f1876,f1873,f300])).
% 4.29/1.01 fof(f1878,plain,(
% 4.29/1.01 spl0_28 <=> disjoint(set_difference(singleton(X0),unordered_pair(X1,X0)),singleton(X0))),
% 4.29/1.01 introduced(split_symbol_definition)).
% 4.29/1.01 fof(f1881,plain,(
% 4.29/1.01 ![X0,X1]: (disjoint(set_difference(singleton(X0),unordered_pair(X1,X0)),singleton(X0))|~empty_set=empty_set)),
% 4.29/1.01 inference(paramodulation,[status(thm)],[f369,f949])).
% 4.29/1.01 fof(f1882,plain,(
% 4.29/1.01 spl0_28|~spl0_0),
% 4.29/1.01 inference(split_clause,[status(thm)],[f1881,f1878,f300])).
% 4.29/1.01 fof(f1883,plain,(
% 4.29/1.01 spl0_29 <=> disjoint(set_difference(singleton(X0),unordered_pair(X0,X1)),singleton(X0))),
% 4.29/1.01 introduced(split_symbol_definition)).
% 4.29/1.01 fof(f1886,plain,(
% 4.29/1.01 ![X0,X1]: (disjoint(set_difference(singleton(X0),unordered_pair(X0,X1)),singleton(X0))|~empty_set=empty_set)),
% 4.29/1.01 inference(paramodulation,[status(thm)],[f363,f949])).
% 4.29/1.01 fof(f1887,plain,(
% 4.29/1.01 spl0_29|~spl0_0),
% 4.29/1.01 inference(split_clause,[status(thm)],[f1886,f1883,f300])).
% 4.29/1.01 fof(f1888,plain,(
% 4.29/1.01 spl0_30 <=> disjoint(set_difference(singleton(X0),powerset(set_union2(X0,X1))),singleton(X0))),
% 4.29/1.01 introduced(split_symbol_definition)).
% 4.29/1.01 fof(f1891,plain,(
% 4.29/1.01 ![X0,X1]: (disjoint(set_difference(singleton(X0),powerset(set_union2(X0,X1))),singleton(X0))|~empty_set=empty_set)),
% 4.29/1.01 inference(paramodulation,[status(thm)],[f499,f949])).
% 4.29/1.01 fof(f1892,plain,(
% 4.29/1.01 spl0_30|~spl0_0),
% 4.29/1.01 inference(split_clause,[status(thm)],[f1891,f1888,f300])).
% 4.29/1.01 fof(f1893,plain,(
% 4.29/1.01 spl0_31 <=> disjoint(set_difference(singleton(X0),powerset(X0)),singleton(X0))),
% 4.29/1.01 introduced(split_symbol_definition)).
% 4.29/1.01 fof(f1896,plain,(
% 4.29/1.01 ![X0]: (disjoint(set_difference(singleton(X0),powerset(X0)),singleton(X0))|~empty_set=empty_set)),
% 4.29/1.01 inference(paramodulation,[status(thm)],[f359,f949])).
% 4.29/1.01 fof(f1897,plain,(
% 4.29/1.01 spl0_31|~spl0_0),
% 4.29/1.01 inference(split_clause,[status(thm)],[f1896,f1893,f300])).
% 4.29/1.01 fof(f1899,plain,(
% 4.29/1.01 spl0_32 <=> disjoint(set_difference(set_intersection2(X0,X1),X1),set_intersection2(X0,X1))),
% 4.29/1.01 introduced(split_symbol_definition)).
% 4.29/1.01 fof(f1902,plain,(
% 4.29/1.01 ![X0,X1]: (disjoint(set_difference(set_intersection2(X0,X1),X1),set_intersection2(X0,X1))|~empty_set=empty_set)),
% 4.29/1.01 inference(paramodulation,[status(thm)],[f1025,f949])).
% 4.29/1.01 fof(f1903,plain,(
% 4.29/1.01 spl0_32|~spl0_0),
% 4.29/1.01 inference(split_clause,[status(thm)],[f1902,f1899,f300])).
% 4.29/1.01 fof(f1904,plain,(
% 4.29/1.01 spl0_33 <=> disjoint(set_difference(set_intersection2(X0,X1),X0),set_intersection2(X0,X1))),
% 4.29/1.01 introduced(split_symbol_definition)).
% 4.29/1.01 fof(f1907,plain,(
% 4.29/1.01 ![X0,X1]: (disjoint(set_difference(set_intersection2(X0,X1),X0),set_intersection2(X0,X1))|~empty_set=empty_set)),
% 4.29/1.01 inference(paramodulation,[status(thm)],[f327,f949])).
% 4.29/1.01 fof(f1908,plain,(
% 4.29/1.01 spl0_33|~spl0_0),
% 4.29/1.01 inference(split_clause,[status(thm)],[f1907,f1904,f300])).
% 4.29/1.01 fof(f1909,plain,(
% 4.29/1.01 spl0_34 <=> disjoint(set_difference(empty_set,X0),empty_set)),
% 4.29/1.01 introduced(split_symbol_definition)).
% 4.29/1.01 fof(f1912,plain,(
% 4.29/1.01 ![X0]: (disjoint(set_difference(empty_set,X0),empty_set)|~empty_set=empty_set)),
% 4.29/1.01 inference(paramodulation,[status(thm)],[f237,f949])).
% 4.29/1.01 fof(f1913,plain,(
% 4.29/1.01 spl0_34|~spl0_0),
% 4.29/1.01 inference(split_clause,[status(thm)],[f1912,f1909,f300])).
% 4.29/1.01 fof(f1938,plain,(
% 4.29/1.01 spl0_35 <=> disjoint(set_difference(X0,set_union2(X1,X0)),X0)),
% 4.29/1.01 introduced(split_symbol_definition)).
% 4.29/1.01 fof(f1941,plain,(
% 4.29/1.01 ![X0,X1]: (disjoint(set_difference(X0,set_union2(X1,X0)),X0)|~empty_set=empty_set)),
% 4.29/1.01 inference(paramodulation,[status(thm)],[f989,f949])).
% 4.29/1.01 fof(f1942,plain,(
% 4.29/1.01 spl0_35|~spl0_0),
% 4.29/1.01 inference(split_clause,[status(thm)],[f1941,f1938,f300])).
% 4.29/1.01 fof(f1943,plain,(
% 4.29/1.01 spl0_36 <=> disjoint(set_difference(X0,set_union2(X0,X1)),X0)),
% 4.29/1.01 introduced(split_symbol_definition)).
% 4.29/1.01 fof(f1946,plain,(
% 4.29/1.01 ![X0,X1]: (disjoint(set_difference(X0,set_union2(X0,X1)),X0)|~empty_set=empty_set)),
% 4.29/1.01 inference(paramodulation,[status(thm)],[f344,f949])).
% 4.29/1.01 fof(f1947,plain,(
% 4.29/1.01 spl0_36|~spl0_0),
% 4.29/1.01 inference(split_clause,[status(thm)],[f1946,f1943,f300])).
% 4.29/1.01 fof(f1951,plain,(
% 4.29/1.01 spl0_37 <=> disjoint(set_difference(X0,X0),X0)),
% 4.29/1.01 introduced(split_symbol_definition)).
% 4.29/1.01 fof(f1954,plain,(
% 4.29/1.01 ![X0]: (disjoint(set_difference(X0,X0),X0)|~empty_set=empty_set)),
% 4.29/1.01 inference(paramodulation,[status(thm)],[f310,f949])).
% 4.29/1.01 fof(f1955,plain,(
% 4.29/1.01 spl0_37|~spl0_0),
% 4.29/1.01 inference(split_clause,[status(thm)],[f1954,f1951,f300])).
% 4.29/1.01 fof(f2036,plain,(
% 4.29/1.01 spl0_39 <=> disjoint(set_difference(singleton(X0),powerset(set_union2(X1,X0))),singleton(X0))),
% 4.29/1.01 introduced(split_symbol_definition)).
% 4.29/1.01 fof(f2039,plain,(
% 4.29/1.01 ![X0,X1]: (disjoint(set_difference(singleton(X0),powerset(set_union2(X1,X0))),singleton(X0))|~empty_set=empty_set)),
% 4.29/1.01 inference(paramodulation,[status(thm)],[f985,f949])).
% 4.29/1.01 fof(f2040,plain,(
% 4.29/1.01 spl0_39|~spl0_0),
% 4.29/1.01 inference(split_clause,[status(thm)],[f2039,f2036,f300])).
% 4.29/1.01 fof(f2055,plain,(
% 4.29/1.01 spl0_40 <=> subset(singleton(X0),powerset(set_union2(X1,X0)))),
% 4.29/1.01 introduced(split_symbol_definition)).
% 4.29/1.01 fof(f2058,plain,(
% 4.29/1.01 ![X0,X1]: (~empty_set=empty_set|subset(singleton(X0),powerset(set_union2(X1,X0))))),
% 4.29/1.01 inference(paramodulation,[status(thm)],[f985,f175])).
% 4.29/1.01 fof(f2059,plain,(
% 4.29/1.01 ~spl0_0|spl0_40),
% 4.29/1.01 inference(split_clause,[status(thm)],[f2058,f300,f2055])).
% 4.29/1.01 fof(f2122,plain,(
% 4.29/1.01 spl0_41 <=> disjoint(set_difference(singleton(set_intersection2(X0,X1)),powerset(X1)),singleton(set_intersection2(X0,X1)))),
% 4.29/1.01 introduced(split_symbol_definition)).
% 4.29/1.01 fof(f2125,plain,(
% 4.29/1.01 ![X0,X1]: (disjoint(set_difference(singleton(set_intersection2(X0,X1)),powerset(X1)),singleton(set_intersection2(X0,X1)))|~empty_set=empty_set)),
% 4.29/1.01 inference(paramodulation,[status(thm)],[f1020,f949])).
% 4.29/1.01 fof(f2126,plain,(
% 4.29/1.01 spl0_41|~spl0_0),
% 4.29/1.01 inference(split_clause,[status(thm)],[f2125,f2122,f300])).
% 4.29/1.01 fof(f2141,plain,(
% 4.29/1.01 spl0_42 <=> subset(singleton(set_intersection2(X0,X1)),powerset(X1))),
% 4.29/1.01 introduced(split_symbol_definition)).
% 4.29/1.01 fof(f2144,plain,(
% 4.29/1.01 ![X0,X1]: (~empty_set=empty_set|subset(singleton(set_intersection2(X0,X1)),powerset(X1)))),
% 4.29/1.01 inference(paramodulation,[status(thm)],[f1020,f175])).
% 4.29/1.01 fof(f2145,plain,(
% 4.29/1.01 ~spl0_0|spl0_42),
% 4.29/1.01 inference(split_clause,[status(thm)],[f2144,f300,f2141])).
% 4.29/1.01 fof(f2157,plain,(
% 4.29/1.01 spl0_43 <=> in(empty_set,powerset(empty_set))),
% 4.29/1.01 introduced(split_symbol_definition)).
% 4.29/1.01 fof(f2160,plain,(
% 4.29/1.01 ![X0]: (in(X0,empty_set)|in(empty_set,powerset(empty_set)))),
% 4.29/1.01 inference(paramodulation,[status(thm)],[f237,f444])).
% 4.29/1.01 fof(f2161,plain,(
% 4.29/1.01 spl0_7|spl0_43),
% 4.29/1.01 inference(split_clause,[status(thm)],[f2160,f446,f2157])).
% 4.29/1.01 fof(f2190,plain,(
% 4.29/1.01 spl0_44 <=> in(empty_set,singleton(empty_set))),
% 4.29/1.01 introduced(split_symbol_definition)).
% 4.29/1.01 fof(f2193,plain,(
% 4.29/1.01 spl0_45 <=> subset(set_intersection2(singleton(empty_set),powerset(X0)),empty_set)),
% 4.29/1.01 introduced(split_symbol_definition)).
% 4.29/1.01 fof(f2194,plain,(
% 4.29/1.01 ![X0]: (subset(set_intersection2(singleton(empty_set),powerset(X0)),empty_set)|~spl0_45)),
% 4.29/1.01 inference(component_clause,[status(thm)],[f2193])).
% 4.29/1.01 fof(f2196,plain,(
% 4.29/1.01 ![X0]: (in(empty_set,singleton(empty_set))|subset(set_intersection2(singleton(empty_set),powerset(X0)),empty_set))),
% 4.29/1.01 inference(paramodulation,[status(thm)],[f931,f445])).
% 4.29/1.01 fof(f2197,plain,(
% 4.29/1.01 spl0_44|spl0_45),
% 4.29/1.01 inference(split_clause,[status(thm)],[f2196,f2190,f2193])).
% 4.29/1.01 fof(f2219,plain,(
% 4.29/1.01 spl0_46 <=> in(empty_set,set_intersection2(singleton(empty_set),powerset(X0)))),
% 4.29/1.01 introduced(split_symbol_definition)).
% 4.29/1.01 fof(f2222,plain,(
% 4.29/1.01 spl0_47 <=> subset(singleton(empty_set),empty_set)),
% 4.29/1.01 introduced(split_symbol_definition)).
% 4.29/1.01 fof(f2223,plain,(
% 4.29/1.01 subset(singleton(empty_set),empty_set)|~spl0_47),
% 4.29/1.01 inference(component_clause,[status(thm)],[f2222])).
% 4.29/1.01 fof(f2224,plain,(
% 4.29/1.01 ~subset(singleton(empty_set),empty_set)|spl0_47),
% 4.29/1.01 inference(component_clause,[status(thm)],[f2222])).
% 4.29/1.01 fof(f2225,plain,(
% 4.29/1.01 ![X0]: (in(empty_set,set_intersection2(singleton(empty_set),powerset(X0)))|subset(singleton(empty_set),empty_set))),
% 4.29/1.01 inference(paramodulation,[status(thm)],[f931,f445])).
% 4.29/1.01 fof(f2226,plain,(
% 4.29/1.01 spl0_46|spl0_47),
% 4.29/1.01 inference(split_clause,[status(thm)],[f2225,f2219,f2222])).
% 4.29/1.01 fof(f2575,plain,(
% 4.29/1.01 ![X0]: (powerset(X0)=empty_set|subset(sk0_1(powerset(X0)),X0))),
% 4.29/1.01 inference(resolution,[status(thm)],[f95,f269])).
% 4.29/1.01 fof(f2583,plain,(
% 4.29/1.01 ![X0]: (X0=empty_set|~in(X0,sk0_1(X0)))),
% 4.29/1.01 inference(resolution,[status(thm)],[f95,f73])).
% 4.29/1.01 fof(f2585,plain,(
% 4.29/1.01 ![X0]: (X0=empty_set|subset(singleton(sk0_1(X0)),X0))),
% 4.29/1.01 inference(resolution,[status(thm)],[f95,f172])).
% 4.29/1.01 fof(f3311,plain,(
% 4.29/1.01 spl0_66 <=> powerset(empty_set)=empty_set),
% 4.29/1.01 introduced(split_symbol_definition)).
% 4.29/1.01 fof(f3312,plain,(
% 4.29/1.01 powerset(empty_set)=empty_set|~spl0_66),
% 4.29/1.01 inference(component_clause,[status(thm)],[f3311])).
% 4.29/1.01 fof(f3314,plain,(
% 4.29/1.01 spl0_67 <=> sk0_1(powerset(empty_set))=empty_set),
% 4.29/1.01 introduced(split_symbol_definition)).
% 4.29/1.01 fof(f3315,plain,(
% 4.29/1.01 sk0_1(powerset(empty_set))=empty_set|~spl0_67),
% 4.29/1.01 inference(component_clause,[status(thm)],[f3314])).
% 4.29/1.01 fof(f3317,plain,(
% 4.29/1.01 powerset(empty_set)=empty_set|sk0_1(powerset(empty_set))=empty_set),
% 4.29/1.01 inference(resolution,[status(thm)],[f2575,f232])).
% 4.29/1.01 fof(f3318,plain,(
% 4.29/1.01 spl0_66|spl0_67),
% 4.29/1.01 inference(split_clause,[status(thm)],[f3317,f3311,f3314])).
% 4.29/1.01 fof(f3343,plain,(
% 4.29/1.01 ![X0]: (set_union2(singleton(set_intersection2(empty_set,X0)),empty_set)=powerset(empty_set)|~spl0_66)),
% 4.29/1.01 inference(paramodulation,[status(thm)],[f3312,f875])).
% 4.29/1.01 fof(f3344,plain,(
% 4.29/1.01 ![X0]: (singleton(set_intersection2(empty_set,X0))=powerset(empty_set)|~spl0_66)),
% 4.29/1.01 inference(forward_demodulation,[status(thm)],[f198,f3343])).
% 4.29/1.01 fof(f3345,plain,(
% 4.29/1.01 singleton(empty_set)=powerset(empty_set)|~spl0_66),
% 4.29/1.01 inference(forward_demodulation,[status(thm)],[f325,f3344])).
% 4.29/1.01 fof(f3346,plain,(
% 4.29/1.01 singleton(empty_set)=empty_set|~spl0_66),
% 4.29/1.01 inference(forward_demodulation,[status(thm)],[f3312,f3345])).
% 4.29/1.01 fof(f3347,plain,(
% 4.29/1.01 $false|~spl0_66),
% 4.29/1.01 inference(forward_subsumption_resolution,[status(thm)],[f3346,f168])).
% 4.29/1.01 fof(f3348,plain,(
% 4.29/1.01 ~spl0_66),
% 4.29/1.01 inference(contradiction_clause,[status(thm)],[f3347])).
% 4.29/1.01 fof(f4056,plain,(
% 4.29/1.01 spl0_72 <=> ~in(X0,singleton(empty_set))),
% 4.29/1.01 introduced(split_symbol_definition)).
% 4.29/1.01 fof(f4057,plain,(
% 4.29/1.01 ![X0]: (~in(X0,singleton(empty_set))|~spl0_72)),
% 4.29/1.01 inference(component_clause,[status(thm)],[f4056])).
% 4.29/1.01 fof(f4059,plain,(
% 4.29/1.01 spl0_73 <=> ~disjoint(singleton(empty_set),powerset(X1))),
% 4.29/1.01 introduced(split_symbol_definition)).
% 4.29/1.01 fof(f4062,plain,(
% 4.29/1.01 ![X0,X1]: (~in(X0,singleton(empty_set))|~disjoint(singleton(empty_set),powerset(X1)))),
% 4.29/1.01 inference(paramodulation,[status(thm)],[f931,f242])).
% 4.29/1.01 fof(f4063,plain,(
% 4.29/1.01 spl0_72|spl0_73),
% 4.29/1.01 inference(split_clause,[status(thm)],[f4062,f4056,f4059])).
% 4.29/1.01 fof(f4146,plain,(
% 4.29/1.01 ![X0,X1,X2]: (~in(X0,set_intersection2(X1,X2))|~disjoint(X2,X1))),
% 4.29/1.01 inference(paramodulation,[status(thm)],[f78,f242])).
% 4.29/1.01 fof(f4373,plain,(
% 4.29/1.01 spl0_92 <=> ~disjoint(powerset(X1),singleton(empty_set))),
% 4.29/1.01 introduced(split_symbol_definition)).
% 4.29/1.01 fof(f4376,plain,(
% 4.29/1.01 ![X0,X1]: (~in(X0,singleton(empty_set))|~disjoint(powerset(X1),singleton(empty_set)))),
% 4.29/1.01 inference(paramodulation,[status(thm)],[f931,f4146])).
% 4.29/1.01 fof(f4377,plain,(
% 4.29/1.01 spl0_72|spl0_92),
% 4.29/1.01 inference(split_clause,[status(thm)],[f4376,f4056,f4373])).
% 4.29/1.01 fof(f4594,plain,(
% 4.29/1.01 ![X0,X1]: (~subset(powerset(X0),X1)|subset(singleton(X0),X1))),
% 4.29/1.01 inference(resolution,[status(thm)],[f201,f321])).
% 4.29/1.01 fof(f4930,plain,(
% 4.29/1.01 ![X0]: (empty_set=powerset(X0)|subset(sk0_2(empty_set,X0),X0))),
% 4.29/1.01 inference(resolution,[status(thm)],[f102,f268])).
% 4.29/1.01 fof(f4940,plain,(
% 4.29/1.01 ![X0]: (X0=powerset(empty_set)|in(sk0_2(X0,empty_set),X0)|sk0_2(X0,empty_set)=empty_set)),
% 4.29/1.01 inference(resolution,[status(thm)],[f102,f232])).
% 4.29/1.01 fof(f4949,plain,(
% 4.29/1.01 ![X0,X1,X2]: (X0=powerset(X1)|in(sk0_2(X0,X1),X0)|in(X2,sk0_2(X0,X1))|subset(sk0_2(X0,X1),set_difference(X1,singleton(X2))))),
% 4.29/1.01 inference(resolution,[status(thm)],[f102,f179])).
% 4.29/1.01 fof(f4962,plain,(
% 4.29/1.01 singleton(empty_set)=empty_set|~spl0_72),
% 4.29/1.01 inference(resolution,[status(thm)],[f4057,f95])).
% 4.29/1.01 fof(f4963,plain,(
% 4.29/1.01 $false|~spl0_72),
% 4.29/1.01 inference(forward_subsumption_resolution,[status(thm)],[f4962,f168])).
% 4.29/1.01 fof(f4964,plain,(
% 4.29/1.01 ~spl0_72),
% 4.29/1.01 inference(contradiction_clause,[status(thm)],[f4963])).
% 4.29/1.01 fof(f4965,plain,(
% 4.29/1.01 ![X0,X1]: (~in(X0,singleton(empty_set))|in(X0,powerset(X1)))),
% 4.29/1.01 inference(resolution,[status(thm)],[f125,f289])).
% 4.29/1.01 fof(f4972,plain,(
% 4.29/1.01 spl0_101 <=> in(powerset(empty_set),empty_set)),
% 4.29/1.01 introduced(split_symbol_definition)).
% 4.29/1.01 fof(f4975,plain,(
% 4.29/1.01 powerset(empty_set)=empty_set|~in(powerset(empty_set),empty_set)|~spl0_67),
% 4.29/1.01 inference(paramodulation,[status(thm)],[f3315,f2583])).
% 4.29/1.01 fof(f4976,plain,(
% 4.29/1.01 spl0_66|~spl0_101|~spl0_67),
% 4.29/1.01 inference(split_clause,[status(thm)],[f4975,f3311,f4972,f3314])).
% 4.29/1.01 fof(f4977,plain,(
% 4.29/1.01 spl0_102 <=> subset(singleton(empty_set),powerset(empty_set))),
% 4.29/1.01 introduced(split_symbol_definition)).
% 4.29/1.01 fof(f4980,plain,(
% 4.29/1.01 powerset(empty_set)=empty_set|subset(singleton(empty_set),powerset(empty_set))|~spl0_67),
% 4.29/1.01 inference(paramodulation,[status(thm)],[f3315,f2585])).
% 4.29/1.01 fof(f4981,plain,(
% 4.29/1.01 spl0_66|spl0_102|~spl0_67),
% 4.29/1.01 inference(split_clause,[status(thm)],[f4980,f3311,f4977,f3314])).
% 4.29/1.01 fof(f5129,plain,(
% 4.29/1.01 ![X0,X1]: (subset(singleton(X0),set_union2(X1,powerset(X0))))),
% 4.29/1.01 inference(resolution,[status(thm)],[f4594,f990])).
% 4.29/1.01 fof(f5145,plain,(
% 4.29/1.01 ![X0,X1]: (set_difference(singleton(X0),set_union2(X1,powerset(X0)))=empty_set)),
% 4.29/1.01 inference(resolution,[status(thm)],[f5129,f176])).
% 4.29/1.01 fof(f5249,plain,(
% 4.29/1.01 spl0_108 <=> sk0_2(empty_set,empty_set)=empty_set),
% 4.29/1.01 introduced(split_symbol_definition)).
% 4.29/1.01 fof(f5250,plain,(
% 4.29/1.01 sk0_2(empty_set,empty_set)=empty_set|~spl0_108),
% 4.29/1.01 inference(component_clause,[status(thm)],[f5249])).
% 4.29/1.01 fof(f5252,plain,(
% 4.29/1.01 empty_set=powerset(empty_set)|sk0_2(empty_set,empty_set)=empty_set),
% 4.29/1.01 inference(resolution,[status(thm)],[f4930,f232])).
% 4.29/1.01 fof(f5253,plain,(
% 4.29/1.01 spl0_66|spl0_108),
% 4.29/1.01 inference(split_clause,[status(thm)],[f5252,f3311,f5249])).
% 4.29/1.01 fof(f5267,plain,(
% 4.29/1.01 spl0_109 <=> in(sk0_2(empty_set,empty_set),empty_set)),
% 4.29/1.01 introduced(split_symbol_definition)).
% 4.29/1.01 fof(f5268,plain,(
% 4.29/1.01 in(sk0_2(empty_set,empty_set),empty_set)|~spl0_109),
% 4.29/1.01 inference(component_clause,[status(thm)],[f5267])).
% 4.29/1.01 fof(f5272,plain,(
% 4.29/1.01 spl0_110 <=> in(empty_set,empty_set)),
% 4.29/1.01 introduced(split_symbol_definition)).
% 4.29/1.01 fof(f5273,plain,(
% 4.29/1.01 in(empty_set,empty_set)|~spl0_110),
% 4.29/1.01 inference(component_clause,[status(thm)],[f5272])).
% 4.29/1.01 fof(f5275,plain,(
% 4.29/1.01 spl0_111 <=> subset(sk0_2(empty_set,empty_set),empty_set)),
% 4.29/1.01 introduced(split_symbol_definition)).
% 4.29/1.01 fof(f5278,plain,(
% 4.29/1.01 empty_set=powerset(empty_set)|in(empty_set,empty_set)|subset(sk0_2(empty_set,empty_set),empty_set)|~spl0_108),
% 4.29/1.01 inference(paramodulation,[status(thm)],[f5250,f102])).
% 4.29/1.01 fof(f5279,plain,(
% 4.29/1.01 spl0_66|spl0_110|spl0_111|~spl0_108),
% 4.29/1.01 inference(split_clause,[status(thm)],[f5278,f3311,f5272,f5275,f5249])).
% 4.29/1.01 fof(f5282,plain,(
% 4.29/1.01 $false|~spl0_110),
% 4.29/1.01 inference(forward_subsumption_resolution,[status(thm)],[f5273,f268])).
% 4.29/1.01 fof(f5283,plain,(
% 4.29/1.01 ~spl0_110),
% 4.29/1.01 inference(contradiction_clause,[status(thm)],[f5282])).
% 4.29/1.01 fof(f6143,plain,(
% 4.29/1.01 singleton(empty_set)=empty_set|~spl0_47),
% 4.29/1.01 inference(resolution,[status(thm)],[f2223,f232])).
% 4.29/1.01 fof(f6144,plain,(
% 4.29/1.01 $false|~spl0_47),
% 4.29/1.01 inference(forward_subsumption_resolution,[status(thm)],[f6143,f168])).
% 4.29/1.01 fof(f6145,plain,(
% 4.29/1.01 ~spl0_47),
% 4.29/1.01 inference(contradiction_clause,[status(thm)],[f6144])).
% 4.29/1.01 fof(f6149,plain,(
% 4.29/1.01 set_intersection2(singleton(singleton(empty_set)),powerset(empty_set))=empty_set|spl0_47),
% 4.29/1.01 inference(resolution,[status(thm)],[f2224,f521])).
% 4.29/1.01 fof(f6629,plain,(
% 4.29/1.01 spl0_113 <=> disjoint(set_difference(singleton(X0),set_union2(X1,powerset(X0))),singleton(X0))),
% 4.29/1.01 introduced(split_symbol_definition)).
% 4.29/1.01 fof(f6632,plain,(
% 4.29/1.01 ![X0,X1]: (disjoint(set_difference(singleton(X0),set_union2(X1,powerset(X0))),singleton(X0))|~empty_set=empty_set)),
% 4.29/1.01 inference(paramodulation,[status(thm)],[f5145,f949])).
% 4.29/1.01 fof(f6633,plain,(
% 4.29/1.01 spl0_113|~spl0_0),
% 4.29/1.01 inference(split_clause,[status(thm)],[f6632,f6629,f300])).
% 4.29/1.01 fof(f6648,plain,(
% 4.29/1.01 spl0_114 <=> subset(singleton(X0),set_union2(X1,powerset(X0)))),
% 4.29/1.01 introduced(split_symbol_definition)).
% 4.29/1.01 fof(f6651,plain,(
% 4.29/1.01 ![X0,X1]: (~empty_set=empty_set|subset(singleton(X0),set_union2(X1,powerset(X0))))),
% 4.29/1.01 inference(paramodulation,[status(thm)],[f5145,f175])).
% 4.29/1.01 fof(f6652,plain,(
% 4.29/1.01 ~spl0_0|spl0_114),
% 4.29/1.01 inference(split_clause,[status(thm)],[f6651,f300,f6648])).
% 4.29/1.01 fof(f6682,plain,(
% 4.29/1.01 spl0_115 <=> singleton(empty_set)=powerset(empty_set)),
% 4.29/1.01 introduced(split_symbol_definition)).
% 4.29/1.01 fof(f6683,plain,(
% 4.29/1.01 singleton(empty_set)=powerset(empty_set)|~spl0_115),
% 4.29/1.01 inference(component_clause,[status(thm)],[f6682])).
% 4.29/1.01 fof(f6685,plain,(
% 4.29/1.01 spl0_116 <=> sk0_2(singleton(empty_set),empty_set)=empty_set),
% 4.29/1.01 introduced(split_symbol_definition)).
% 4.29/1.01 fof(f6686,plain,(
% 4.29/1.01 sk0_2(singleton(empty_set),empty_set)=empty_set|~spl0_116),
% 4.29/1.01 inference(component_clause,[status(thm)],[f6685])).
% 4.29/1.01 fof(f6688,plain,(
% 4.29/1.01 spl0_117 <=> in(sk0_2(singleton(empty_set),empty_set),powerset(X0))),
% 4.29/1.01 introduced(split_symbol_definition)).
% 4.29/1.01 fof(f6689,plain,(
% 4.29/1.01 ![X0]: (in(sk0_2(singleton(empty_set),empty_set),powerset(X0))|~spl0_117)),
% 4.29/1.01 inference(component_clause,[status(thm)],[f6688])).
% 4.29/1.01 fof(f6691,plain,(
% 4.29/1.01 ![X0]: (singleton(empty_set)=powerset(empty_set)|sk0_2(singleton(empty_set),empty_set)=empty_set|in(sk0_2(singleton(empty_set),empty_set),powerset(X0)))),
% 4.29/1.01 inference(resolution,[status(thm)],[f4940,f4965])).
% 4.29/1.01 fof(f6692,plain,(
% 4.29/1.01 spl0_115|spl0_116|spl0_117),
% 4.29/1.01 inference(split_clause,[status(thm)],[f6691,f6682,f6685,f6688])).
% 4.29/1.01 fof(f6760,plain,(
% 4.29/1.01 spl0_118 <=> in(X0,sk0_2(empty_set,empty_set))|subset(sk0_2(empty_set,empty_set),set_difference(empty_set,singleton(X0)))),
% 4.29/1.01 introduced(split_symbol_definition)).
% 4.29/1.01 fof(f6763,plain,(
% 4.29/1.01 ![X0]: (empty_set=powerset(empty_set)|in(empty_set,empty_set)|in(X0,sk0_2(empty_set,empty_set))|subset(sk0_2(empty_set,empty_set),set_difference(empty_set,singleton(X0)))|~spl0_108)),
% 4.29/1.01 inference(paramodulation,[status(thm)],[f5250,f4949])).
% 4.29/1.01 fof(f6764,plain,(
% 4.29/1.01 spl0_66|spl0_110|spl0_118|~spl0_108),
% 4.29/1.01 inference(split_clause,[status(thm)],[f6763,f3311,f5272,f6760,f5249])).
% 4.29/1.01 fof(f6765,plain,(
% 4.29/1.01 spl0_119 <=> in(X0,sk0_2(empty_set,empty_set))|subset(empty_set,set_difference(empty_set,singleton(X0)))),
% 4.29/1.01 introduced(split_symbol_definition)).
% 4.29/1.01 fof(f6768,plain,(
% 4.29/1.01 ![X0]: (empty_set=powerset(empty_set)|in(sk0_2(empty_set,empty_set),empty_set)|in(X0,sk0_2(empty_set,empty_set))|subset(empty_set,set_difference(empty_set,singleton(X0)))|~spl0_108)),
% 4.29/1.01 inference(paramodulation,[status(thm)],[f5250,f4949])).
% 4.29/1.01 fof(f6769,plain,(
% 4.29/1.01 spl0_66|spl0_109|spl0_119|~spl0_108),
% 4.29/1.01 inference(split_clause,[status(thm)],[f6768,f3311,f5267,f6765,f5249])).
% 4.29/1.01 fof(f6792,plain,(
% 4.29/1.01 in(empty_set,empty_set)|~spl0_108|~spl0_109),
% 4.29/1.01 inference(forward_demodulation,[status(thm)],[f5250,f5268])).
% 4.29/1.01 fof(f6793,plain,(
% 4.29/1.01 $false|~spl0_108|~spl0_109),
% 4.29/1.01 inference(forward_subsumption_resolution,[status(thm)],[f6792,f268])).
% 4.29/1.01 fof(f6794,plain,(
% 4.29/1.01 ~spl0_108|~spl0_109),
% 4.29/1.01 inference(contradiction_clause,[status(thm)],[f6793])).
% 4.29/1.01 fof(f7903,plain,(
% 4.29/1.01 spl0_120 <=> singleton(singleton(empty_set))=empty_set),
% 4.29/1.01 introduced(split_symbol_definition)).
% 4.29/1.01 fof(f7904,plain,(
% 4.29/1.01 singleton(singleton(empty_set))=empty_set|~spl0_120),
% 4.29/1.01 inference(component_clause,[status(thm)],[f7903])).
% 4.29/1.01 fof(f7906,plain,(
% 4.29/1.01 spl0_121 <=> set_intersection2(singleton(singleton(empty_set)),powerset(empty_set))=empty_set),
% 4.29/1.01 introduced(split_symbol_definition)).
% 4.29/1.01 fof(f7909,plain,(
% 4.29/1.01 singleton(singleton(empty_set))=empty_set|set_intersection2(singleton(singleton(empty_set)),powerset(empty_set))=empty_set|spl0_47),
% 4.29/1.01 inference(paramodulation,[status(thm)],[f324,f6149])).
% 4.29/1.01 fof(f7910,plain,(
% 4.29/1.01 spl0_120|spl0_121|spl0_47),
% 4.29/1.01 inference(split_clause,[status(thm)],[f7909,f7903,f7906,f2222])).
% 4.29/1.01 fof(f7988,plain,(
% 4.29/1.01 $false|~spl0_120),
% 4.29/1.01 inference(forward_subsumption_resolution,[status(thm)],[f7904,f168])).
% 4.29/1.01 fof(f7989,plain,(
% 4.29/1.01 ~spl0_120),
% 4.29/1.01 inference(contradiction_clause,[status(thm)],[f7988])).
% 4.29/1.01 fof(f7992,plain,(
% 4.29/1.01 ![X0]: (subset(sk0_2(singleton(empty_set),empty_set),X0)|~spl0_117)),
% 4.29/1.01 inference(resolution,[status(thm)],[f6689,f269])).
% 4.29/1.01 fof(f8007,plain,(
% 4.29/1.01 sk0_2(singleton(empty_set),empty_set)=empty_set|~spl0_117),
% 4.29/1.01 inference(resolution,[status(thm)],[f7992,f232])).
% 4.29/1.01 fof(f8067,plain,(
% 4.29/1.01 spl0_128 <=> subset(sk0_2(singleton(empty_set),empty_set),empty_set)),
% 4.29/1.01 introduced(split_symbol_definition)).
% 4.29/1.01 fof(f8069,plain,(
% 4.29/1.01 ~subset(sk0_2(singleton(empty_set),empty_set),empty_set)|spl0_128),
% 4.29/1.01 inference(component_clause,[status(thm)],[f8067])).
% 4.29/1.01 fof(f8084,plain,(
% 4.29/1.01 singleton(empty_set)=powerset(empty_set)|~in(empty_set,singleton(empty_set))|~subset(sk0_2(singleton(empty_set),empty_set),empty_set)|~spl0_116),
% 4.29/1.01 inference(paramodulation,[status(thm)],[f6686,f101])).
% 4.29/1.01 fof(f8085,plain,(
% 4.29/1.01 spl0_115|~spl0_44|~spl0_128|~spl0_116),
% 4.29/1.01 inference(split_clause,[status(thm)],[f8084,f6682,f2190,f8067,f6685])).
% 4.29/1.01 fof(f8086,plain,(
% 4.29/1.01 $false|~spl0_115),
% 4.29/1.01 inference(forward_subsumption_resolution,[status(thm)],[f6683,f202])).
% 4.29/1.01 fof(f8087,plain,(
% 4.29/1.01 ~spl0_115),
% 4.29/1.01 inference(contradiction_clause,[status(thm)],[f8086])).
% 4.29/1.01 fof(f8088,plain,(
% 4.29/1.01 ~subset(empty_set,empty_set)|~spl0_116|spl0_128),
% 4.29/1.01 inference(forward_demodulation,[status(thm)],[f6686,f8069])).
% 4.29/1.01 fof(f8089,plain,(
% 4.29/1.01 $false|~spl0_116|spl0_128),
% 4.29/1.01 inference(forward_subsumption_resolution,[status(thm)],[f8088,f214])).
% 4.29/1.02 fof(f8090,plain,(
% 4.29/1.02 ~spl0_116|spl0_128),
% 4.29/1.02 inference(contradiction_clause,[status(thm)],[f8089])).
% 4.29/1.02 fof(f8093,plain,(
% 4.29/1.02 subset(singleton(empty_set),empty_set)|~spl0_45),
% 4.29/1.02 inference(forward_demodulation,[status(thm)],[f931,f2194])).
% 4.29/1.02 fof(f8094,plain,(
% 4.29/1.02 $false|spl0_47|~spl0_45),
% 4.29/1.02 inference(forward_subsumption_resolution,[status(thm)],[f8093,f2224])).
% 4.29/1.02 fof(f8095,plain,(
% 4.29/1.02 spl0_47|~spl0_45),
% 4.29/1.02 inference(contradiction_clause,[status(thm)],[f8094])).
% 4.29/1.02 fof(f8096,plain,(
% 4.29/1.02 spl0_116|~spl0_117),
% 4.29/1.02 inference(split_clause,[status(thm)],[f8007,f6685,f6688])).
% 4.29/1.02 fof(f8097,plain,(
% 4.29/1.02 $false),
% 4.29/1.02 inference(sat_refutation,[status(thm)],[f307,f317,f319,f379,f390,f413,f435,f453,f456,f671,f697,f740,f960,f1107,f1167,f1302,f1626,f1770,f1790,f1872,f1877,f1882,f1887,f1892,f1897,f1903,f1908,f1913,f1942,f1947,f1955,f2040,f2059,f2126,f2145,f2161,f2197,f2226,f3318,f3348,f4063,f4377,f4964,f4976,f4981,f5253,f5279,f5283,f6145,f6633,f6652,f6692,f6764,f6769,f6794,f7910,f7989,f8085,f8087,f8090,f8095,f8096])).
% 4.29/1.02 % SZS output end CNFRefutation for theBenchmark.p
% 4.29/1.03 % Elapsed time: 0.687515 seconds
% 4.29/1.03 % CPU time: 4.839157 seconds
% 4.29/1.03 % Memory used: 101.038 MB
%------------------------------------------------------------------------------