TSTP Solution File: SEU156+2 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SEU156+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n012.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 12:36:02 EDT 2023
% Result : Theorem 0.19s 0.61s
% Output : CNFRefutation 1.53s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU156+2 : TPTP v8.1.2. Released v3.3.0.
% 0.11/0.11 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.33 % Computer : n012.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue May 30 09:07:55 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.12/0.34 % Drodi V3.5.1
% 0.19/0.61 % Refutation found
% 0.19/0.61 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.19/0.61 % SZS output start CNFRefutation for theBenchmark
% 0.19/0.61 fof(f1,axiom,(
% 0.19/0.61 (! [A,B] :( in(A,B)=> ~ in(B,A) ) )),
% 0.19/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.61 fof(f3,axiom,(
% 0.19/0.61 (! [A,B] : unordered_pair(A,B) = unordered_pair(B,A) )),
% 0.19/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.61 fof(f4,axiom,(
% 0.19/0.61 (! [A,B] : set_union2(A,B) = set_union2(B,A) )),
% 0.19/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.61 fof(f5,axiom,(
% 0.19/0.61 (! [A,B] : set_intersection2(A,B) = set_intersection2(B,A) )),
% 0.19/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.61 fof(f7,axiom,(
% 0.19/0.61 (! [A,B] :( B = singleton(A)<=> (! [C] :( in(C,B)<=> C = A ) )) )),
% 0.19/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.61 fof(f8,axiom,(
% 0.19/0.61 (! [A] :( A = empty_set<=> (! [B] : ~ in(B,A) )) )),
% 0.19/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.61 fof(f9,axiom,(
% 0.19/0.61 (! [A,B] :( B = powerset(A)<=> (! [C] :( in(C,B)<=> subset(C,A) ) )) )),
% 0.19/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.61 fof(f10,axiom,(
% 0.19/0.61 (! [A,B,C] :( C = unordered_pair(A,B)<=> (! [D] :( in(D,C)<=> ( D = A| D = B ) ) )) )),
% 0.19/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.61 fof(f16,axiom,(
% 0.19/0.61 (! [A,B] : ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)) )),
% 0.19/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.61 fof(f17,axiom,(
% 0.19/0.61 (! [A,B] :( disjoint(A,B)<=> set_intersection2(A,B) = empty_set ) )),
% 0.19/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.61 fof(f28,axiom,(
% 0.19/0.61 empty(empty_set) ),
% 0.19/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.61 fof(f30,axiom,(
% 0.19/0.61 (! [A,B] :( ~ empty(A)=> ~ empty(set_union2(A,B)) ) )),
% 0.19/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.61 fof(f35,lemma,(
% 0.19/0.61 (! [A] : singleton(A) != empty_set )),
% 0.19/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.61 fof(f52,axiom,(
% 0.19/0.61 (! [A] : set_union2(A,empty_set) = A )),
% 0.19/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.61 fof(f54,lemma,(
% 0.19/0.61 powerset(empty_set) = singleton(empty_set) ),
% 0.19/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.61 fof(f56,lemma,(
% 0.19/0.61 (! [A,B] :( subset(A,B)=> set_intersection2(A,B) = A ) )),
% 0.19/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.61 fof(f57,axiom,(
% 0.19/0.61 (! [A] : set_intersection2(A,empty_set) = empty_set )),
% 0.19/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.61 fof(f59,lemma,(
% 0.19/0.61 (! [A] : subset(empty_set,A) )),
% 0.19/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.61 fof(f61,conjecture,(
% 0.19/0.61 (! [A,B,C,D] :( ordered_pair(A,B) = ordered_pair(C,D)=> ( A = C& B = D ) ) )),
% 0.19/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.61 fof(f62,negated_conjecture,(
% 0.19/0.61 ~((! [A,B,C,D] :( ordered_pair(A,B) = ordered_pair(C,D)=> ( A = C& B = D ) ) ))),
% 0.19/0.61 inference(negated_conjecture,[status(cth)],[f61])).
% 0.19/0.61 fof(f63,lemma,(
% 0.19/0.61 (! [A,B] : subset(set_difference(A,B),A) )),
% 0.19/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.61 fof(f66,axiom,(
% 0.19/0.61 (! [A] : set_difference(A,empty_set) = A )),
% 0.19/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.61 fof(f72,axiom,(
% 0.19/0.61 (! [A] : set_difference(empty_set,A) = empty_set )),
% 0.19/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.61 fof(f76,lemma,(
% 0.19/0.61 (! [A] : unordered_pair(A,A) = singleton(A) )),
% 0.19/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.61 fof(f79,axiom,(
% 0.19/0.61 (! [A,B] :~ ( in(A,B)& empty(B) ) )),
% 0.19/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.61 fof(f81,lemma,(
% 0.19/0.61 (! [A,B] :( disjoint(A,B)<=> set_difference(A,B) = A ) )),
% 0.19/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.61 fof(f84,lemma,(
% 0.19/0.61 (! [A,B,C] :( singleton(A) = unordered_pair(B,C)=> A = B ) )),
% 0.19/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.61 fof(f85,lemma,(
% 0.19/0.61 (! [A,B,C] :( singleton(A) = unordered_pair(B,C)=> B = C ) )),
% 0.19/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.61 fof(f86,plain,(
% 0.19/0.61 ![A,B]: (~in(A,B)|~in(B,A))),
% 0.19/0.61 inference(pre_NNF_transformation,[status(esa)],[f1])).
% 0.19/0.61 fof(f87,plain,(
% 0.19/0.61 ![X0,X1]: (~in(X0,X1)|~in(X1,X0))),
% 0.19/0.61 inference(cnf_transformation,[status(esa)],[f86])).
% 0.19/0.61 fof(f90,plain,(
% 0.19/0.61 ![X0,X1]: (unordered_pair(X0,X1)=unordered_pair(X1,X0))),
% 0.19/0.61 inference(cnf_transformation,[status(esa)],[f3])).
% 0.19/0.61 fof(f91,plain,(
% 0.19/0.61 ![X0,X1]: (set_union2(X0,X1)=set_union2(X1,X0))),
% 0.19/0.61 inference(cnf_transformation,[status(esa)],[f4])).
% 0.19/0.61 fof(f92,plain,(
% 0.19/0.61 ![X0,X1]: (set_intersection2(X0,X1)=set_intersection2(X1,X0))),
% 0.19/0.61 inference(cnf_transformation,[status(esa)],[f5])).
% 0.19/0.61 fof(f98,plain,(
% 0.19/0.61 ![A,B]: ((~B=singleton(A)|(![C]: ((~in(C,B)|C=A)&(in(C,B)|~C=A))))&(B=singleton(A)|(?[C]: ((~in(C,B)|~C=A)&(in(C,B)|C=A)))))),
% 0.19/0.61 inference(NNF_transformation,[status(esa)],[f7])).
% 0.19/0.61 fof(f99,plain,(
% 0.19/0.61 (![A,B]: (~B=singleton(A)|((![C]: (~in(C,B)|C=A))&(![C]: (in(C,B)|~C=A)))))&(![A,B]: (B=singleton(A)|(?[C]: ((~in(C,B)|~C=A)&(in(C,B)|C=A)))))),
% 0.19/0.61 inference(miniscoping,[status(esa)],[f98])).
% 0.19/0.61 fof(f100,plain,(
% 0.19/0.61 (![A,B]: (~B=singleton(A)|((![C]: (~in(C,B)|C=A))&(![C]: (in(C,B)|~C=A)))))&(![A,B]: (B=singleton(A)|((~in(sk0_0(B,A),B)|~sk0_0(B,A)=A)&(in(sk0_0(B,A),B)|sk0_0(B,A)=A))))),
% 0.19/0.61 inference(skolemization,[status(esa)],[f99])).
% 0.19/0.61 fof(f101,plain,(
% 0.19/0.61 ![X0,X1,X2]: (~X0=singleton(X1)|~in(X2,X0)|X2=X1)),
% 0.19/0.61 inference(cnf_transformation,[status(esa)],[f100])).
% 0.19/0.61 fof(f105,plain,(
% 0.19/0.61 ![A]: ((~A=empty_set|(![B]: ~in(B,A)))&(A=empty_set|(?[B]: in(B,A))))),
% 0.19/0.61 inference(NNF_transformation,[status(esa)],[f8])).
% 0.19/0.61 fof(f106,plain,(
% 0.19/0.61 (![A]: (~A=empty_set|(![B]: ~in(B,A))))&(![A]: (A=empty_set|(?[B]: in(B,A))))),
% 0.19/0.61 inference(miniscoping,[status(esa)],[f105])).
% 0.19/0.61 fof(f107,plain,(
% 0.19/0.61 (![A]: (~A=empty_set|(![B]: ~in(B,A))))&(![A]: (A=empty_set|in(sk0_1(A),A)))),
% 0.19/0.61 inference(skolemization,[status(esa)],[f106])).
% 0.19/0.61 fof(f108,plain,(
% 0.19/0.61 ![X0,X1]: (~X0=empty_set|~in(X1,X0))),
% 0.19/0.61 inference(cnf_transformation,[status(esa)],[f107])).
% 0.19/0.61 fof(f109,plain,(
% 0.19/0.61 ![X0]: (X0=empty_set|in(sk0_1(X0),X0))),
% 0.19/0.61 inference(cnf_transformation,[status(esa)],[f107])).
% 0.19/0.61 fof(f110,plain,(
% 0.19/0.61 ![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))))))),
% 0.19/0.61 inference(NNF_transformation,[status(esa)],[f9])).
% 0.19/0.61 fof(f111,plain,(
% 0.19/0.61 (![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))))))),
% 0.19/0.61 inference(miniscoping,[status(esa)],[f110])).
% 0.19/0.61 fof(f112,plain,(
% 0.19/0.61 (![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)))))),
% 0.19/0.61 inference(skolemization,[status(esa)],[f111])).
% 0.19/0.61 fof(f114,plain,(
% 0.19/0.61 ![X0,X1,X2]: (~X0=powerset(X1)|in(X2,X0)|~subset(X2,X1))),
% 0.19/0.61 inference(cnf_transformation,[status(esa)],[f112])).
% 0.19/0.61 fof(f117,plain,(
% 0.19/0.61 ![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))))))),
% 0.19/0.61 inference(NNF_transformation,[status(esa)],[f10])).
% 0.19/0.61 fof(f118,plain,(
% 0.19/0.61 (![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))))))),
% 0.19/0.61 inference(miniscoping,[status(esa)],[f117])).
% 0.19/0.61 fof(f119,plain,(
% 0.19/0.61 (![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)))))),
% 0.19/0.61 inference(skolemization,[status(esa)],[f118])).
% 0.19/0.61 fof(f120,plain,(
% 0.19/0.61 ![X0,X1,X2,X3]: (~X0=unordered_pair(X1,X2)|~in(X3,X0)|X3=X1|X3=X2)),
% 0.19/0.61 inference(cnf_transformation,[status(esa)],[f119])).
% 0.19/0.61 fof(f121,plain,(
% 0.19/0.61 ![X0,X1,X2,X3]: (~X0=unordered_pair(X1,X2)|in(X3,X0)|~X3=X1)),
% 0.19/0.61 inference(cnf_transformation,[status(esa)],[f119])).
% 0.19/0.61 fof(f122,plain,(
% 0.19/0.61 ![X0,X1,X2,X3]: (~X0=unordered_pair(X1,X2)|in(X3,X0)|~X3=X2)),
% 0.19/0.61 inference(cnf_transformation,[status(esa)],[f119])).
% 0.19/0.61 fof(f169,plain,(
% 0.19/0.61 ![X0,X1]: (ordered_pair(X0,X1)=unordered_pair(unordered_pair(X0,X1),singleton(X0)))),
% 0.19/0.61 inference(cnf_transformation,[status(esa)],[f16])).
% 0.19/0.61 fof(f170,plain,(
% 0.19/0.61 ![A,B]: ((~disjoint(A,B)|set_intersection2(A,B)=empty_set)&(disjoint(A,B)|~set_intersection2(A,B)=empty_set))),
% 0.19/0.61 inference(NNF_transformation,[status(esa)],[f17])).
% 0.19/0.61 fof(f171,plain,(
% 0.19/0.61 (![A,B]: (~disjoint(A,B)|set_intersection2(A,B)=empty_set))&(![A,B]: (disjoint(A,B)|~set_intersection2(A,B)=empty_set))),
% 0.19/0.61 inference(miniscoping,[status(esa)],[f170])).
% 0.19/0.61 fof(f173,plain,(
% 0.19/0.61 ![X0,X1]: (disjoint(X0,X1)|~set_intersection2(X0,X1)=empty_set)),
% 0.19/0.61 inference(cnf_transformation,[status(esa)],[f171])).
% 0.19/0.61 fof(f179,plain,(
% 0.19/0.61 empty(empty_set)),
% 0.19/0.61 inference(cnf_transformation,[status(esa)],[f28])).
% 0.19/0.61 fof(f181,plain,(
% 0.19/0.61 ![A,B]: (empty(A)|~empty(set_union2(A,B)))),
% 0.19/0.61 inference(pre_NNF_transformation,[status(esa)],[f30])).
% 0.19/0.61 fof(f182,plain,(
% 0.19/0.61 ![A]: (empty(A)|(![B]: ~empty(set_union2(A,B))))),
% 0.19/0.61 inference(miniscoping,[status(esa)],[f181])).
% 0.19/0.61 fof(f183,plain,(
% 0.19/0.61 ![X0,X1]: (empty(X0)|~empty(set_union2(X0,X1)))),
% 0.19/0.61 inference(cnf_transformation,[status(esa)],[f182])).
% 0.19/0.61 fof(f193,plain,(
% 0.19/0.61 ![X0]: (~singleton(X0)=empty_set)),
% 0.19/0.61 inference(cnf_transformation,[status(esa)],[f35])).
% 0.19/0.61 fof(f234,plain,(
% 0.19/0.61 ![X0]: (set_union2(X0,empty_set)=X0)),
% 0.19/0.61 inference(cnf_transformation,[status(esa)],[f52])).
% 0.19/0.61 fof(f238,plain,(
% 0.19/0.61 powerset(empty_set)=singleton(empty_set)),
% 0.19/0.61 inference(cnf_transformation,[status(esa)],[f54])).
% 0.19/0.61 fof(f242,plain,(
% 0.19/0.61 ![A,B]: (~subset(A,B)|set_intersection2(A,B)=A)),
% 0.19/0.61 inference(pre_NNF_transformation,[status(esa)],[f56])).
% 0.19/0.61 fof(f243,plain,(
% 0.19/0.61 ![X0,X1]: (~subset(X0,X1)|set_intersection2(X0,X1)=X0)),
% 0.19/0.61 inference(cnf_transformation,[status(esa)],[f242])).
% 0.19/0.61 fof(f244,plain,(
% 0.19/0.61 ![X0]: (set_intersection2(X0,empty_set)=empty_set)),
% 0.19/0.61 inference(cnf_transformation,[status(esa)],[f57])).
% 0.19/0.61 fof(f250,plain,(
% 0.19/0.61 ![X0]: (subset(empty_set,X0))),
% 0.19/0.61 inference(cnf_transformation,[status(esa)],[f59])).
% 0.19/0.61 fof(f254,plain,(
% 0.19/0.61 (?[A,B,C,D]: (ordered_pair(A,B)=ordered_pair(C,D)&(~A=C|~B=D)))),
% 0.19/0.61 inference(pre_NNF_transformation,[status(esa)],[f62])).
% 0.19/0.61 fof(f255,plain,(
% 0.19/0.61 (ordered_pair(sk0_14,sk0_15)=ordered_pair(sk0_16,sk0_17)&(~sk0_14=sk0_16|~sk0_15=sk0_17))),
% 0.19/0.61 inference(skolemization,[status(esa)],[f254])).
% 0.19/0.61 fof(f256,plain,(
% 0.19/0.61 ordered_pair(sk0_14,sk0_15)=ordered_pair(sk0_16,sk0_17)),
% 0.19/0.61 inference(cnf_transformation,[status(esa)],[f255])).
% 0.19/0.61 fof(f257,plain,(
% 0.19/0.61 ~sk0_14=sk0_16|~sk0_15=sk0_17),
% 0.19/0.61 inference(cnf_transformation,[status(esa)],[f255])).
% 0.19/0.61 fof(f258,plain,(
% 0.19/0.61 ![X0,X1]: (subset(set_difference(X0,X1),X0))),
% 0.19/0.61 inference(cnf_transformation,[status(esa)],[f63])).
% 0.19/0.61 fof(f264,plain,(
% 0.19/0.61 ![X0]: (set_difference(X0,empty_set)=X0)),
% 0.19/0.61 inference(cnf_transformation,[status(esa)],[f66])).
% 0.19/0.61 fof(f277,plain,(
% 0.19/0.61 ![X0]: (set_difference(empty_set,X0)=empty_set)),
% 0.19/0.61 inference(cnf_transformation,[status(esa)],[f72])).
% 0.19/0.61 fof(f288,plain,(
% 0.19/0.61 ![X0]: (unordered_pair(X0,X0)=singleton(X0))),
% 0.19/0.61 inference(cnf_transformation,[status(esa)],[f76])).
% 0.19/0.61 fof(f293,plain,(
% 0.19/0.61 ![A,B]: (~in(A,B)|~empty(B))),
% 0.19/0.61 inference(pre_NNF_transformation,[status(esa)],[f79])).
% 0.19/0.61 fof(f294,plain,(
% 0.19/0.61 ![B]: ((![A]: ~in(A,B))|~empty(B))),
% 0.19/0.61 inference(miniscoping,[status(esa)],[f293])).
% 0.19/0.61 fof(f295,plain,(
% 0.19/0.61 ![X0,X1]: (~in(X0,X1)|~empty(X1))),
% 0.19/0.61 inference(cnf_transformation,[status(esa)],[f294])).
% 0.19/0.61 fof(f297,plain,(
% 0.19/0.61 ![A,B]: ((~disjoint(A,B)|set_difference(A,B)=A)&(disjoint(A,B)|~set_difference(A,B)=A))),
% 0.19/0.61 inference(NNF_transformation,[status(esa)],[f81])).
% 0.19/0.61 fof(f298,plain,(
% 0.19/0.61 (![A,B]: (~disjoint(A,B)|set_difference(A,B)=A))&(![A,B]: (disjoint(A,B)|~set_difference(A,B)=A))),
% 0.19/0.61 inference(miniscoping,[status(esa)],[f297])).
% 0.19/0.61 fof(f300,plain,(
% 0.19/0.61 ![X0,X1]: (disjoint(X0,X1)|~set_difference(X0,X1)=X0)),
% 0.19/0.61 inference(cnf_transformation,[status(esa)],[f298])).
% 0.19/0.61 fof(f306,plain,(
% 0.19/0.61 ![A,B,C]: (~singleton(A)=unordered_pair(B,C)|A=B)),
% 0.19/0.61 inference(pre_NNF_transformation,[status(esa)],[f84])).
% 0.19/0.61 fof(f307,plain,(
% 0.19/0.61 ![A,B]: ((![C]: ~singleton(A)=unordered_pair(B,C))|A=B)),
% 0.19/0.61 inference(miniscoping,[status(esa)],[f306])).
% 0.19/0.61 fof(f308,plain,(
% 0.19/0.61 ![X0,X1,X2]: (~singleton(X0)=unordered_pair(X1,X2)|X0=X1)),
% 0.19/0.61 inference(cnf_transformation,[status(esa)],[f307])).
% 0.19/0.61 fof(f309,plain,(
% 0.19/0.61 ![A,B,C]: (~singleton(A)=unordered_pair(B,C)|B=C)),
% 0.19/0.61 inference(pre_NNF_transformation,[status(esa)],[f85])).
% 0.19/0.61 fof(f310,plain,(
% 0.19/0.61 ![B,C]: ((![A]: ~singleton(A)=unordered_pair(B,C))|B=C)),
% 0.19/0.61 inference(miniscoping,[status(esa)],[f309])).
% 0.19/0.61 fof(f311,plain,(
% 0.19/0.61 ![X0,X1,X2]: (~singleton(X0)=unordered_pair(X1,X2)|X1=X2)),
% 0.19/0.61 inference(cnf_transformation,[status(esa)],[f310])).
% 0.19/0.61 fof(f312,plain,(
% 0.19/0.61 spl0_0 <=> sk0_14=sk0_16),
% 0.19/0.61 introduced(split_symbol_definition)).
% 0.19/0.61 fof(f313,plain,(
% 0.19/0.61 sk0_14=sk0_16|~spl0_0),
% 0.19/0.61 inference(component_clause,[status(thm)],[f312])).
% 0.19/0.61 fof(f314,plain,(
% 0.19/0.61 ~sk0_14=sk0_16|spl0_0),
% 0.19/0.61 inference(component_clause,[status(thm)],[f312])).
% 0.19/0.61 fof(f315,plain,(
% 0.19/0.61 spl0_1 <=> sk0_15=sk0_17),
% 0.19/0.61 introduced(split_symbol_definition)).
% 0.19/0.61 fof(f317,plain,(
% 0.19/0.61 ~sk0_15=sk0_17|spl0_1),
% 0.19/0.61 inference(component_clause,[status(thm)],[f315])).
% 0.19/0.61 fof(f318,plain,(
% 0.19/0.61 ~spl0_0|~spl0_1),
% 0.19/0.61 inference(split_clause,[status(thm)],[f257,f312,f315])).
% 0.19/0.61 fof(f321,plain,(
% 0.19/0.61 ![X0,X1]: (~in(X0,singleton(X1))|X0=X1)),
% 0.19/0.61 inference(destructive_equality_resolution,[status(esa)],[f101])).
% 0.19/0.61 fof(f323,plain,(
% 0.19/0.61 ![X0]: (~in(X0,empty_set))),
% 0.19/0.61 inference(destructive_equality_resolution,[status(esa)],[f108])).
% 0.19/0.61 fof(f325,plain,(
% 0.19/0.61 ![X0,X1]: (in(X0,powerset(X1))|~subset(X0,X1))),
% 0.19/0.61 inference(destructive_equality_resolution,[status(esa)],[f114])).
% 0.19/0.61 fof(f326,plain,(
% 0.19/0.61 ![X0,X1,X2]: (~in(X0,unordered_pair(X1,X2))|X0=X1|X0=X2)),
% 0.19/0.61 inference(destructive_equality_resolution,[status(esa)],[f120])).
% 0.19/0.61 fof(f327,plain,(
% 0.19/0.61 ![X0,X1]: (in(X0,unordered_pair(X0,X1)))),
% 0.19/0.61 inference(destructive_equality_resolution,[status(esa)],[f121])).
% 0.19/0.61 fof(f328,plain,(
% 0.19/0.61 ![X0,X1]: (in(X0,unordered_pair(X1,X0)))),
% 0.19/0.61 inference(destructive_equality_resolution,[status(esa)],[f122])).
% 0.19/0.61 fof(f345,plain,(
% 0.19/0.61 ![X0,X1]: (ordered_pair(unordered_pair(X0,X1),singleton(X0))=unordered_pair(ordered_pair(X0,X1),singleton(unordered_pair(X0,X1))))),
% 0.19/0.61 inference(paramodulation,[status(thm)],[f169,f169])).
% 0.19/0.61 fof(f346,plain,(
% 0.19/0.61 ordered_pair(unordered_pair(sk0_16,sk0_17),singleton(sk0_16))=unordered_pair(ordered_pair(sk0_14,sk0_15),singleton(unordered_pair(sk0_16,sk0_17)))),
% 0.19/0.61 inference(paramodulation,[status(thm)],[f256,f345])).
% 0.19/0.61 fof(f712,plain,(
% 0.19/0.61 ![X0,X1]: (ordered_pair(X0,X1)=unordered_pair(singleton(X0),unordered_pair(X0,X1)))),
% 0.19/0.61 inference(paramodulation,[status(thm)],[f169,f90])).
% 0.19/0.61 fof(f746,plain,(
% 0.19/0.61 ![X0,X1]: (ordered_pair(X0,X1)=unordered_pair(unordered_pair(X1,X0),singleton(X0)))),
% 0.19/0.61 inference(paramodulation,[status(thm)],[f90,f169])).
% 0.19/0.61 fof(f747,plain,(
% 0.19/0.61 ![X0,X1]: (ordered_pair(X0,X1)=unordered_pair(singleton(X0),unordered_pair(X1,X0)))),
% 0.19/0.61 inference(forward_demodulation,[status(thm)],[f90,f746])).
% 0.19/0.61 fof(f1686,plain,(
% 0.19/0.61 ![X0,X1]: (ordered_pair(singleton(X0),unordered_pair(X0,X1))=unordered_pair(singleton(singleton(X0)),ordered_pair(X0,X1)))),
% 0.19/0.61 inference(paramodulation,[status(thm)],[f712,f712])).
% 0.19/0.61 fof(f1780,plain,(
% 0.19/0.61 ![X0,X1]: (ordered_pair(singleton(X0),unordered_pair(X1,X0))=unordered_pair(singleton(singleton(X0)),ordered_pair(X0,X1)))),
% 0.19/0.61 inference(paramodulation,[status(thm)],[f747,f712])).
% 0.19/0.61 fof(f1820,plain,(
% 0.19/0.61 ![X0,X1]: (ordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),singleton(singleton(X0)))=unordered_pair(ordered_pair(singleton(X0),unordered_pair(X1,X0)),singleton(ordered_pair(X0,X1))))),
% 0.19/0.61 inference(paramodulation,[status(thm)],[f747,f345])).
% 0.19/0.61 fof(f1821,plain,(
% 0.19/0.61 ![X0,X1]: (ordered_pair(ordered_pair(X0,X1),singleton(singleton(X0)))=unordered_pair(ordered_pair(singleton(X0),unordered_pair(X1,X0)),singleton(ordered_pair(X0,X1))))),
% 0.19/0.61 inference(forward_demodulation,[status(thm)],[f747,f1820])).
% 0.19/0.61 fof(f1822,plain,(
% 0.19/0.61 ![X0,X1]: (ordered_pair(ordered_pair(X0,X1),singleton(singleton(X0)))=unordered_pair(singleton(ordered_pair(X0,X1)),ordered_pair(singleton(X0),unordered_pair(X1,X0))))),
% 0.19/0.61 inference(forward_demodulation,[status(thm)],[f90,f1821])).
% 0.19/0.61 fof(f1839,plain,(
% 0.19/0.61 ordered_pair(singleton(sk0_16),unordered_pair(sk0_16,sk0_17))=unordered_pair(singleton(singleton(sk0_16)),ordered_pair(sk0_14,sk0_15))),
% 0.19/0.61 inference(paramodulation,[status(thm)],[f256,f1686])).
% 0.19/0.61 fof(f2035,plain,(
% 0.19/0.61 ![X0,X1]: (in(singleton(X0),ordered_pair(X0,X1)))),
% 0.19/0.61 inference(paramodulation,[status(thm)],[f747,f327])).
% 0.19/0.61 fof(f2047,plain,(
% 0.19/0.61 ![X0,X1]: (in(unordered_pair(X0,X1),ordered_pair(X0,X1)))),
% 0.19/0.61 inference(paramodulation,[status(thm)],[f169,f327])).
% 0.19/0.61 fof(f2051,plain,(
% 0.19/0.61 ![X0,X1]: (in(ordered_pair(X0,X1),ordered_pair(singleton(X0),unordered_pair(X0,X1))))),
% 0.19/0.61 inference(paramodulation,[status(thm)],[f1686,f328])).
% 0.19/0.61 fof(f2063,plain,(
% 0.19/0.61 ![X0,X1]: (in(unordered_pair(X0,X1),ordered_pair(X1,X0)))),
% 0.19/0.61 inference(paramodulation,[status(thm)],[f747,f328])).
% 0.19/0.61 fof(f2088,plain,(
% 0.19/0.61 ![X0]: (ordered_pair(X0,X0)=unordered_pair(singleton(X0),singleton(X0)))),
% 0.19/0.61 inference(paramodulation,[status(thm)],[f288,f747])).
% 0.19/0.61 fof(f2089,plain,(
% 0.19/0.61 ![X0]: (ordered_pair(X0,X0)=singleton(singleton(X0)))),
% 0.19/0.61 inference(forward_demodulation,[status(thm)],[f288,f2088])).
% 0.19/0.61 fof(f2168,plain,(
% 0.19/0.61 ![X0]: (X0=set_union2(empty_set,X0))),
% 0.19/0.61 inference(paramodulation,[status(thm)],[f234,f91])).
% 0.19/0.61 fof(f2172,plain,(
% 0.19/0.61 ![X0]: (empty_set=set_intersection2(empty_set,X0))),
% 0.19/0.61 inference(paramodulation,[status(thm)],[f244,f92])).
% 0.19/0.61 fof(f2186,plain,(
% 0.19/0.61 in(ordered_pair(sk0_14,sk0_15),ordered_pair(singleton(sk0_16),unordered_pair(sk0_16,sk0_17)))),
% 0.19/0.61 inference(paramodulation,[status(thm)],[f1839,f328])).
% 0.19/0.61 fof(f2452,plain,(
% 0.19/0.61 in(singleton(sk0_16),ordered_pair(sk0_14,sk0_15))),
% 0.19/0.61 inference(paramodulation,[status(thm)],[f256,f2035])).
% 0.19/0.61 fof(f2575,plain,(
% 0.19/0.61 ![X0,X1]: (in(ordered_pair(X0,X1),ordered_pair(singleton(X0),unordered_pair(X1,X0))))),
% 0.19/0.61 inference(paramodulation,[status(thm)],[f747,f2047])).
% 0.19/0.61 fof(f2592,plain,(
% 0.19/0.61 in(unordered_pair(sk0_16,sk0_17),ordered_pair(sk0_14,sk0_15))),
% 0.19/0.61 inference(paramodulation,[status(thm)],[f256,f2047])).
% 0.19/0.61 fof(f3562,plain,(
% 0.19/0.61 ![X0]: (singleton(X0)=empty_set|sk0_1(singleton(X0))=X0)),
% 0.19/0.61 inference(resolution,[status(thm)],[f109,f321])).
% 0.19/0.61 fof(f3563,plain,(
% 0.19/0.61 ![X0]: (sk0_1(singleton(X0))=X0)),
% 0.19/0.61 inference(forward_subsumption_resolution,[status(thm)],[f3562,f193])).
% 0.19/0.61 fof(f3565,plain,(
% 0.19/0.61 ![X0]: (X0=empty_set|~in(X0,sk0_1(X0)))),
% 0.19/0.61 inference(resolution,[status(thm)],[f109,f87])).
% 0.19/0.61 fof(f3572,plain,(
% 0.19/0.61 ![X0,X1]: (~subset(X0,X1)|~empty(powerset(X1)))),
% 0.19/0.61 inference(resolution,[status(thm)],[f325,f295])).
% 0.19/0.61 fof(f4016,plain,(
% 0.19/0.61 ![X0,X1]: (ordered_pair(singleton(X0),unordered_pair(X1,X0))=ordered_pair(singleton(X0),unordered_pair(X0,X1)))),
% 0.19/0.61 inference(forward_demodulation,[status(thm)],[f1686,f1780])).
% 0.19/0.61 fof(f4205,plain,(
% 0.19/0.61 spl0_2 <=> empty(empty_set)),
% 0.19/0.61 introduced(split_symbol_definition)).
% 0.19/0.61 fof(f4208,plain,(
% 0.19/0.61 spl0_3 <=> ~empty(X0)),
% 0.19/0.61 introduced(split_symbol_definition)).
% 0.19/0.61 fof(f4209,plain,(
% 0.19/0.61 ![X0]: (~empty(X0)|~spl0_3)),
% 0.19/0.61 inference(component_clause,[status(thm)],[f4208])).
% 0.19/0.61 fof(f4211,plain,(
% 0.19/0.61 ![X0]: (empty(empty_set)|~empty(X0))),
% 0.19/0.61 inference(paramodulation,[status(thm)],[f2168,f183])).
% 0.19/0.61 fof(f4212,plain,(
% 0.19/0.61 spl0_2|spl0_3),
% 0.19/0.61 inference(split_clause,[status(thm)],[f4211,f4205,f4208])).
% 0.19/0.61 fof(f4222,plain,(
% 0.19/0.61 spl0_4 <=> ~subset(empty_set,X0)),
% 0.19/0.61 introduced(split_symbol_definition)).
% 0.19/0.61 fof(f4223,plain,(
% 0.19/0.61 ![X0]: (~subset(empty_set,X0)|~spl0_4)),
% 0.19/0.61 inference(component_clause,[status(thm)],[f4222])).
% 0.19/0.61 fof(f4225,plain,(
% 0.19/0.61 spl0_5 <=> empty_set=empty_set),
% 0.19/0.61 introduced(split_symbol_definition)).
% 0.19/0.61 fof(f4228,plain,(
% 0.19/0.61 ![X0]: (~subset(empty_set,X0)|empty_set=empty_set)),
% 0.19/0.61 inference(paramodulation,[status(thm)],[f2172,f243])).
% 0.19/0.61 fof(f4229,plain,(
% 0.19/0.61 spl0_4|spl0_5),
% 0.19/0.61 inference(split_clause,[status(thm)],[f4228,f4222,f4225])).
% 0.19/0.61 fof(f4233,plain,(
% 0.19/0.61 $false|~spl0_4),
% 0.19/0.61 inference(forward_subsumption_resolution,[status(thm)],[f4223,f250])).
% 0.19/0.61 fof(f4234,plain,(
% 0.19/0.61 ~spl0_4),
% 0.19/0.61 inference(contradiction_clause,[status(thm)],[f4233])).
% 0.19/0.61 fof(f4241,plain,(
% 0.19/0.61 ![X0]: (~in(X0,ordered_pair(singleton(sk0_16),unordered_pair(sk0_16,sk0_17)))|X0=singleton(singleton(sk0_16))|X0=ordered_pair(sk0_14,sk0_15))),
% 0.19/0.61 inference(paramodulation,[status(thm)],[f1839,f326])).
% 0.19/0.61 fof(f4277,plain,(
% 0.19/0.61 ![X0,X1,X2]: (~in(X0,ordered_pair(X1,X2))|X0=unordered_pair(X1,X2)|X0=singleton(X1))),
% 0.19/0.61 inference(paramodulation,[status(thm)],[f169,f326])).
% 0.19/0.61 fof(f4282,plain,(
% 0.19/0.61 spl0_6 <=> sk0_1(ordered_pair(singleton(sk0_16),unordered_pair(sk0_16,sk0_17)))=singleton(singleton(sk0_16))),
% 0.19/0.61 introduced(split_symbol_definition)).
% 0.19/0.61 fof(f4283,plain,(
% 0.19/0.62 sk0_1(ordered_pair(singleton(sk0_16),unordered_pair(sk0_16,sk0_17)))=singleton(singleton(sk0_16))|~spl0_6),
% 0.19/0.62 inference(component_clause,[status(thm)],[f4282])).
% 0.19/0.62 fof(f4285,plain,(
% 0.19/0.62 spl0_7 <=> sk0_1(ordered_pair(singleton(sk0_16),unordered_pair(sk0_16,sk0_17)))=ordered_pair(sk0_14,sk0_15)),
% 0.19/0.62 introduced(split_symbol_definition)).
% 0.19/0.62 fof(f4286,plain,(
% 0.19/0.62 sk0_1(ordered_pair(singleton(sk0_16),unordered_pair(sk0_16,sk0_17)))=ordered_pair(sk0_14,sk0_15)|~spl0_7),
% 0.19/0.62 inference(component_clause,[status(thm)],[f4285])).
% 0.19/0.62 fof(f4288,plain,(
% 0.19/0.62 spl0_8 <=> ordered_pair(singleton(sk0_16),unordered_pair(sk0_16,sk0_17))=empty_set),
% 0.19/0.62 introduced(split_symbol_definition)).
% 0.19/0.62 fof(f4289,plain,(
% 0.19/0.62 ordered_pair(singleton(sk0_16),unordered_pair(sk0_16,sk0_17))=empty_set|~spl0_8),
% 0.19/0.62 inference(component_clause,[status(thm)],[f4288])).
% 0.19/0.62 fof(f4291,plain,(
% 0.19/0.62 sk0_1(ordered_pair(singleton(sk0_16),unordered_pair(sk0_16,sk0_17)))=singleton(singleton(sk0_16))|sk0_1(ordered_pair(singleton(sk0_16),unordered_pair(sk0_16,sk0_17)))=ordered_pair(sk0_14,sk0_15)|ordered_pair(singleton(sk0_16),unordered_pair(sk0_16,sk0_17))=empty_set),
% 0.19/0.62 inference(resolution,[status(thm)],[f4241,f109])).
% 0.19/0.62 fof(f4292,plain,(
% 0.19/0.62 spl0_6|spl0_7|spl0_8),
% 0.19/0.62 inference(split_clause,[status(thm)],[f4291,f4282,f4285,f4288])).
% 0.19/0.62 fof(f4294,plain,(
% 0.19/0.62 spl0_9 <=> unordered_pair(unordered_pair(sk0_16,sk0_17),singleton(sk0_16))=singleton(singleton(sk0_16))),
% 0.19/0.62 introduced(split_symbol_definition)).
% 0.19/0.62 fof(f4295,plain,(
% 0.19/0.62 unordered_pair(unordered_pair(sk0_16,sk0_17),singleton(sk0_16))=singleton(singleton(sk0_16))|~spl0_9),
% 0.19/0.62 inference(component_clause,[status(thm)],[f4294])).
% 0.19/0.62 fof(f4297,plain,(
% 0.19/0.62 spl0_10 <=> unordered_pair(unordered_pair(sk0_16,sk0_17),singleton(sk0_16))=ordered_pair(sk0_14,sk0_15)),
% 0.19/0.62 introduced(split_symbol_definition)).
% 0.19/0.62 fof(f4300,plain,(
% 0.19/0.62 unordered_pair(unordered_pair(sk0_16,sk0_17),singleton(sk0_16))=singleton(singleton(sk0_16))|unordered_pair(unordered_pair(sk0_16,sk0_17),singleton(sk0_16))=ordered_pair(sk0_14,sk0_15)),
% 0.19/0.62 inference(resolution,[status(thm)],[f4241,f2063])).
% 0.19/0.62 fof(f4301,plain,(
% 0.19/0.62 spl0_9|spl0_10),
% 0.19/0.62 inference(split_clause,[status(thm)],[f4300,f4294,f4297])).
% 0.19/0.62 fof(f4302,plain,(
% 0.19/0.62 spl0_11 <=> unordered_pair(singleton(sk0_16),unordered_pair(sk0_16,sk0_17))=singleton(singleton(sk0_16))),
% 0.19/0.62 introduced(split_symbol_definition)).
% 0.19/0.62 fof(f4303,plain,(
% 0.19/0.62 unordered_pair(singleton(sk0_16),unordered_pair(sk0_16,sk0_17))=singleton(singleton(sk0_16))|~spl0_11),
% 0.19/0.62 inference(component_clause,[status(thm)],[f4302])).
% 0.19/0.62 fof(f4305,plain,(
% 0.19/0.62 spl0_12 <=> unordered_pair(singleton(sk0_16),unordered_pair(sk0_16,sk0_17))=ordered_pair(sk0_14,sk0_15)),
% 0.19/0.62 introduced(split_symbol_definition)).
% 0.19/0.62 fof(f4308,plain,(
% 0.19/0.62 unordered_pair(singleton(sk0_16),unordered_pair(sk0_16,sk0_17))=singleton(singleton(sk0_16))|unordered_pair(singleton(sk0_16),unordered_pair(sk0_16,sk0_17))=ordered_pair(sk0_14,sk0_15)),
% 0.19/0.62 inference(resolution,[status(thm)],[f4241,f2047])).
% 0.19/0.62 fof(f4309,plain,(
% 0.19/0.62 spl0_11|spl0_12),
% 0.19/0.62 inference(split_clause,[status(thm)],[f4308,f4302,f4305])).
% 0.19/0.62 fof(f4310,plain,(
% 0.19/0.62 spl0_13 <=> singleton(singleton(sk0_16))=singleton(singleton(sk0_16))),
% 0.19/0.62 introduced(split_symbol_definition)).
% 0.19/0.62 fof(f4313,plain,(
% 0.19/0.62 spl0_14 <=> singleton(singleton(sk0_16))=ordered_pair(sk0_14,sk0_15)),
% 0.19/0.62 introduced(split_symbol_definition)).
% 0.19/0.62 fof(f4314,plain,(
% 0.19/0.62 singleton(singleton(sk0_16))=ordered_pair(sk0_14,sk0_15)|~spl0_14),
% 0.19/0.62 inference(component_clause,[status(thm)],[f4313])).
% 0.19/0.62 fof(f4316,plain,(
% 0.19/0.62 singleton(singleton(sk0_16))=singleton(singleton(sk0_16))|singleton(singleton(sk0_16))=ordered_pair(sk0_14,sk0_15)),
% 0.19/0.62 inference(resolution,[status(thm)],[f4241,f2035])).
% 0.19/0.62 fof(f4317,plain,(
% 0.19/0.62 spl0_13|spl0_14),
% 0.19/0.62 inference(split_clause,[status(thm)],[f4316,f4310,f4313])).
% 0.19/0.62 fof(f4318,plain,(
% 0.19/0.62 spl0_15 <=> ordered_pair(sk0_14,sk0_15)=ordered_pair(sk0_14,sk0_15)),
% 0.19/0.62 introduced(split_symbol_definition)).
% 0.19/0.62 fof(f4321,plain,(
% 0.19/0.62 ordered_pair(sk0_14,sk0_15)=singleton(singleton(sk0_16))|ordered_pair(sk0_14,sk0_15)=ordered_pair(sk0_14,sk0_15)),
% 0.19/0.62 inference(resolution,[status(thm)],[f4241,f2186])).
% 0.19/0.62 fof(f4322,plain,(
% 0.19/0.62 spl0_14|spl0_15),
% 0.19/0.62 inference(split_clause,[status(thm)],[f4321,f4313,f4318])).
% 0.19/0.62 fof(f4323,plain,(
% 0.19/0.62 spl0_16 <=> ordered_pair(sk0_16,sk0_17)=singleton(singleton(sk0_16))),
% 0.19/0.62 introduced(split_symbol_definition)).
% 0.19/0.62 fof(f4324,plain,(
% 0.19/0.62 ordered_pair(sk0_16,sk0_17)=singleton(singleton(sk0_16))|~spl0_16),
% 0.19/0.62 inference(component_clause,[status(thm)],[f4323])).
% 0.19/0.62 fof(f4326,plain,(
% 0.19/0.62 spl0_17 <=> ordered_pair(sk0_16,sk0_17)=ordered_pair(sk0_14,sk0_15)),
% 0.19/0.62 introduced(split_symbol_definition)).
% 0.19/0.62 fof(f4329,plain,(
% 0.19/0.62 ordered_pair(sk0_16,sk0_17)=singleton(singleton(sk0_16))|ordered_pair(sk0_16,sk0_17)=ordered_pair(sk0_14,sk0_15)),
% 0.19/0.62 inference(resolution,[status(thm)],[f4241,f2051])).
% 0.19/0.62 fof(f4330,plain,(
% 0.19/0.62 spl0_16|spl0_17),
% 0.19/0.62 inference(split_clause,[status(thm)],[f4329,f4323,f4326])).
% 0.19/0.62 fof(f4331,plain,(
% 0.19/0.62 ordered_pair(sk0_14,sk0_15)=singleton(singleton(sk0_16))|~spl0_16),
% 0.19/0.62 inference(forward_demodulation,[status(thm)],[f256,f4324])).
% 0.19/0.62 fof(f4332,plain,(
% 0.19/0.62 ordered_pair(sk0_16,sk0_17)=singleton(singleton(sk0_16))|~spl0_11),
% 0.19/0.62 inference(forward_demodulation,[status(thm)],[f712,f4303])).
% 0.19/0.62 fof(f4333,plain,(
% 0.19/0.62 ordered_pair(sk0_14,sk0_15)=singleton(singleton(sk0_16))|~spl0_11),
% 0.19/0.62 inference(forward_demodulation,[status(thm)],[f256,f4332])).
% 0.19/0.62 fof(f4334,plain,(
% 0.19/0.62 ordered_pair(sk0_16,sk0_17)=singleton(singleton(sk0_16))|~spl0_9),
% 0.19/0.62 inference(forward_demodulation,[status(thm)],[f169,f4295])).
% 0.19/0.62 fof(f4335,plain,(
% 0.19/0.62 ordered_pair(sk0_14,sk0_15)=singleton(singleton(sk0_16))|~spl0_9),
% 0.19/0.62 inference(forward_demodulation,[status(thm)],[f256,f4334])).
% 0.19/0.62 fof(f4512,plain,(
% 0.19/0.62 in(unordered_pair(sk0_16,sk0_17),singleton(singleton(sk0_16)))|~spl0_14),
% 0.19/0.62 inference(backward_demodulation,[status(thm)],[f4314,f2592])).
% 0.19/0.62 fof(f4624,plain,(
% 0.19/0.62 in(unordered_pair(sk0_15,sk0_14),singleton(singleton(sk0_16)))|~spl0_14),
% 0.19/0.62 inference(paramodulation,[status(thm)],[f4314,f2063])).
% 0.19/0.62 fof(f4625,plain,(
% 0.19/0.62 in(unordered_pair(sk0_14,sk0_15),singleton(singleton(sk0_16)))|~spl0_14),
% 0.19/0.62 inference(forward_demodulation,[status(thm)],[f90,f4624])).
% 0.19/0.62 fof(f4628,plain,(
% 0.19/0.62 in(singleton(sk0_14),singleton(singleton(sk0_16)))|~spl0_14),
% 0.19/0.62 inference(paramodulation,[status(thm)],[f4314,f2035])).
% 0.19/0.62 fof(f4711,plain,(
% 0.19/0.62 singleton(sk0_14)=singleton(sk0_16)|~spl0_14),
% 0.19/0.62 inference(resolution,[status(thm)],[f4628,f321])).
% 0.19/0.62 fof(f4718,plain,(
% 0.19/0.62 sk0_1(singleton(sk0_14))=sk0_16|~spl0_14),
% 0.19/0.62 inference(paramodulation,[status(thm)],[f4711,f3563])).
% 0.19/0.62 fof(f4719,plain,(
% 0.19/0.62 sk0_14=sk0_16|~spl0_14),
% 0.19/0.62 inference(forward_demodulation,[status(thm)],[f3563,f4718])).
% 0.19/0.62 fof(f4720,plain,(
% 0.19/0.62 $false|spl0_0|~spl0_14),
% 0.19/0.62 inference(forward_subsumption_resolution,[status(thm)],[f4719,f314])).
% 0.19/0.62 fof(f4721,plain,(
% 0.19/0.62 spl0_0|~spl0_14),
% 0.19/0.62 inference(contradiction_clause,[status(thm)],[f4720])).
% 0.19/0.62 fof(f4722,plain,(
% 0.19/0.62 spl0_14|~spl0_9),
% 0.19/0.62 inference(split_clause,[status(thm)],[f4335,f4313,f4294])).
% 0.19/0.62 fof(f4723,plain,(
% 0.19/0.62 spl0_14|~spl0_11),
% 0.19/0.62 inference(split_clause,[status(thm)],[f4333,f4313,f4302])).
% 0.19/0.62 fof(f4724,plain,(
% 0.19/0.62 spl0_14|~spl0_16),
% 0.19/0.62 inference(split_clause,[status(thm)],[f4331,f4313,f4323])).
% 0.19/0.62 fof(f4818,plain,(
% 0.19/0.62 in(unordered_pair(sk0_14,sk0_17),singleton(singleton(sk0_16)))|~spl0_14),
% 0.19/0.62 inference(forward_demodulation,[status(thm)],[f4719,f4512])).
% 0.19/0.62 fof(f4819,plain,(
% 0.19/0.62 in(unordered_pair(sk0_14,sk0_17),singleton(singleton(sk0_14)))|~spl0_14),
% 0.19/0.62 inference(forward_demodulation,[status(thm)],[f4719,f4818])).
% 0.19/0.62 fof(f4820,plain,(
% 0.19/0.62 unordered_pair(sk0_14,sk0_17)=singleton(sk0_14)|~spl0_14),
% 0.19/0.62 inference(resolution,[status(thm)],[f4819,f321])).
% 0.19/0.62 fof(f4858,plain,(
% 0.19/0.62 in(sk0_17,singleton(sk0_14))|~spl0_14),
% 0.19/0.62 inference(paramodulation,[status(thm)],[f4820,f328])).
% 0.19/0.62 fof(f4996,plain,(
% 0.19/0.62 sk0_17=sk0_14|~spl0_14),
% 0.19/0.62 inference(resolution,[status(thm)],[f4858,f321])).
% 0.19/0.62 fof(f5003,plain,(
% 0.19/0.62 ~sk0_15=sk0_14|~spl0_14|spl0_1),
% 0.19/0.62 inference(backward_demodulation,[status(thm)],[f4996,f317])).
% 0.19/0.62 fof(f5072,plain,(
% 0.19/0.62 spl0_18 <=> in(ordered_pair(sk0_14,sk0_15),ordered_pair(singleton(sk0_16),unordered_pair(sk0_16,sk0_17)))),
% 0.19/0.62 introduced(split_symbol_definition)).
% 0.19/0.62 fof(f5073,plain,(
% 0.19/0.62 in(ordered_pair(sk0_14,sk0_15),ordered_pair(singleton(sk0_16),unordered_pair(sk0_16,sk0_17)))|~spl0_18),
% 0.19/0.62 inference(component_clause,[status(thm)],[f5072])).
% 0.19/0.62 fof(f5075,plain,(
% 0.19/0.62 ordered_pair(singleton(sk0_16),unordered_pair(sk0_16,sk0_17))=empty_set|in(ordered_pair(sk0_14,sk0_15),ordered_pair(singleton(sk0_16),unordered_pair(sk0_16,sk0_17)))|~spl0_7),
% 0.19/0.62 inference(paramodulation,[status(thm)],[f4286,f109])).
% 0.19/0.62 fof(f5076,plain,(
% 0.19/0.62 spl0_8|spl0_18|~spl0_7),
% 0.19/0.62 inference(split_clause,[status(thm)],[f5075,f4288,f5072,f4285])).
% 0.19/0.62 fof(f5079,plain,(
% 0.19/0.62 ordered_pair(sk0_14,sk0_15)=ordered_pair(sk0_14,sk0_17)|~spl0_0),
% 0.19/0.62 inference(forward_demodulation,[status(thm)],[f313,f256])).
% 0.19/0.62 fof(f5130,plain,(
% 0.19/0.62 in(unordered_pair(sk0_14,sk0_17),ordered_pair(sk0_14,sk0_15))|~spl0_0),
% 0.19/0.62 inference(forward_demodulation,[status(thm)],[f313,f2592])).
% 0.19/0.62 fof(f5133,plain,(
% 0.19/0.62 ordered_pair(unordered_pair(sk0_14,sk0_17),singleton(sk0_16))=unordered_pair(ordered_pair(sk0_14,sk0_15),singleton(unordered_pair(sk0_16,sk0_17)))|~spl0_0),
% 0.19/0.62 inference(forward_demodulation,[status(thm)],[f313,f346])).
% 0.19/0.62 fof(f5134,plain,(
% 0.19/0.62 ordered_pair(unordered_pair(sk0_14,sk0_17),singleton(sk0_14))=unordered_pair(ordered_pair(sk0_14,sk0_15),singleton(unordered_pair(sk0_16,sk0_17)))|~spl0_0),
% 0.19/0.62 inference(forward_demodulation,[status(thm)],[f313,f5133])).
% 0.19/0.62 fof(f5135,plain,(
% 0.19/0.62 ordered_pair(unordered_pair(sk0_14,sk0_17),singleton(sk0_14))=unordered_pair(ordered_pair(sk0_14,sk0_15),singleton(unordered_pair(sk0_14,sk0_17)))|~spl0_0),
% 0.19/0.62 inference(forward_demodulation,[status(thm)],[f313,f5134])).
% 0.19/0.62 fof(f5310,plain,(
% 0.19/0.62 spl0_19 <=> unordered_pair(sk0_14,sk0_17)=unordered_pair(sk0_14,sk0_15)),
% 0.19/0.62 introduced(split_symbol_definition)).
% 0.19/0.62 fof(f5311,plain,(
% 0.19/0.62 unordered_pair(sk0_14,sk0_17)=unordered_pair(sk0_14,sk0_15)|~spl0_19),
% 0.19/0.62 inference(component_clause,[status(thm)],[f5310])).
% 0.19/0.62 fof(f5312,plain,(
% 0.19/0.62 ~unordered_pair(sk0_14,sk0_17)=unordered_pair(sk0_14,sk0_15)|spl0_19),
% 0.19/0.62 inference(component_clause,[status(thm)],[f5310])).
% 0.19/0.62 fof(f5313,plain,(
% 0.19/0.62 spl0_20 <=> unordered_pair(sk0_14,sk0_17)=singleton(sk0_14)),
% 0.19/0.62 introduced(split_symbol_definition)).
% 0.19/0.62 fof(f5314,plain,(
% 0.19/0.62 unordered_pair(sk0_14,sk0_17)=singleton(sk0_14)|~spl0_20),
% 0.19/0.62 inference(component_clause,[status(thm)],[f5313])).
% 0.19/0.62 fof(f5315,plain,(
% 0.19/0.62 ~unordered_pair(sk0_14,sk0_17)=singleton(sk0_14)|spl0_20),
% 0.19/0.62 inference(component_clause,[status(thm)],[f5313])).
% 0.19/0.62 fof(f5316,plain,(
% 0.19/0.62 unordered_pair(sk0_14,sk0_17)=unordered_pair(sk0_14,sk0_15)|unordered_pair(sk0_14,sk0_17)=singleton(sk0_14)|~spl0_0),
% 0.19/0.62 inference(resolution,[status(thm)],[f4277,f5130])).
% 0.19/0.62 fof(f5317,plain,(
% 0.19/0.62 spl0_19|spl0_20|~spl0_0),
% 0.19/0.62 inference(split_clause,[status(thm)],[f5316,f5310,f5313,f312])).
% 0.19/0.62 fof(f5456,plain,(
% 0.19/0.62 spl0_21 <=> ~disjoint(empty_set,X0)),
% 0.19/0.62 introduced(split_symbol_definition)).
% 0.19/0.62 fof(f5457,plain,(
% 0.19/0.62 ![X0]: (~disjoint(empty_set,X0)|~spl0_21)),
% 0.19/0.62 inference(component_clause,[status(thm)],[f5456])).
% 0.19/0.62 fof(f5461,plain,(
% 0.19/0.62 ![X0]: (disjoint(empty_set,X0))),
% 0.19/0.62 inference(resolution,[status(thm)],[f300,f277])).
% 0.19/0.62 fof(f5462,plain,(
% 0.19/0.62 ![X0]: (disjoint(X0,empty_set))),
% 0.19/0.62 inference(resolution,[status(thm)],[f300,f264])).
% 0.19/0.62 fof(f5463,plain,(
% 0.19/0.62 spl0_22 <=> disjoint(empty_set,X0)),
% 0.19/0.62 introduced(split_symbol_definition)).
% 0.19/0.62 fof(f5466,plain,(
% 0.19/0.62 ![X0]: (disjoint(empty_set,X0)|~empty_set=empty_set)),
% 0.19/0.62 inference(paramodulation,[status(thm)],[f277,f300])).
% 0.19/0.62 fof(f5467,plain,(
% 0.19/0.62 spl0_22|~spl0_5),
% 0.19/0.62 inference(split_clause,[status(thm)],[f5466,f5463,f4225])).
% 0.19/0.62 fof(f5486,plain,(
% 0.19/0.62 ![X0,X1]: (~singleton(X0)=singleton(X1)|X0=X1)),
% 0.19/0.62 inference(paramodulation,[status(thm)],[f288,f308])).
% 0.19/0.62 fof(f5487,plain,(
% 0.19/0.62 ![X0,X1,X2]: (~singleton(X0)=unordered_pair(X1,X2)|X0=X2)),
% 0.19/0.62 inference(paramodulation,[status(thm)],[f90,f308])).
% 0.19/0.62 fof(f5493,plain,(
% 0.19/0.62 ![X0,X1,X2]: (~singleton(X0)=ordered_pair(X1,X2)|singleton(X1)=unordered_pair(X2,X1))),
% 0.19/0.62 inference(paramodulation,[status(thm)],[f747,f311])).
% 0.19/0.62 fof(f5494,plain,(
% 0.19/0.62 ![X0,X1,X2]: (~singleton(X0)=ordered_pair(X1,X2)|singleton(X1)=unordered_pair(X1,X2))),
% 0.19/0.62 inference(paramodulation,[status(thm)],[f712,f311])).
% 0.19/0.62 fof(f5495,plain,(
% 0.19/0.62 spl0_23 <=> ~singleton(X0)=ordered_pair(unordered_pair(sk0_14,sk0_17),singleton(sk0_14))),
% 0.19/0.62 introduced(split_symbol_definition)).
% 0.19/0.62 fof(f5496,plain,(
% 0.19/0.62 ![X0]: (~singleton(X0)=ordered_pair(unordered_pair(sk0_14,sk0_17),singleton(sk0_14))|~spl0_23)),
% 0.19/0.62 inference(component_clause,[status(thm)],[f5495])).
% 0.19/0.62 fof(f5498,plain,(
% 0.19/0.62 spl0_24 <=> ordered_pair(sk0_14,sk0_15)=singleton(unordered_pair(sk0_14,sk0_17))),
% 0.19/0.62 introduced(split_symbol_definition)).
% 0.19/0.62 fof(f5499,plain,(
% 0.19/0.62 ordered_pair(sk0_14,sk0_15)=singleton(unordered_pair(sk0_14,sk0_17))|~spl0_24),
% 0.19/0.62 inference(component_clause,[status(thm)],[f5498])).
% 0.19/0.62 fof(f5501,plain,(
% 0.19/0.62 ![X0]: (~singleton(X0)=ordered_pair(unordered_pair(sk0_14,sk0_17),singleton(sk0_14))|ordered_pair(sk0_14,sk0_15)=singleton(unordered_pair(sk0_14,sk0_17))|~spl0_0)),
% 0.19/0.62 inference(paramodulation,[status(thm)],[f5135,f311])).
% 0.19/0.62 fof(f5502,plain,(
% 0.19/0.62 spl0_23|spl0_24|~spl0_0),
% 0.19/0.62 inference(split_clause,[status(thm)],[f5501,f5495,f5498,f312])).
% 0.19/0.62 fof(f5521,plain,(
% 0.19/0.62 spl0_25 <=> ~subset(X0,empty_set)),
% 0.19/0.62 introduced(split_symbol_definition)).
% 0.19/0.62 fof(f5522,plain,(
% 0.19/0.62 ![X0]: (~subset(X0,empty_set)|~spl0_25)),
% 0.19/0.62 inference(component_clause,[status(thm)],[f5521])).
% 0.19/0.62 fof(f5524,plain,(
% 0.19/0.62 spl0_26 <=> empty(singleton(empty_set))),
% 0.19/0.62 introduced(split_symbol_definition)).
% 0.19/0.62 fof(f5527,plain,(
% 0.19/0.62 ![X0]: (~subset(X0,empty_set)|~empty(singleton(empty_set)))),
% 0.19/0.62 inference(paramodulation,[status(thm)],[f238,f3572])).
% 0.19/0.62 fof(f5528,plain,(
% 0.19/0.62 spl0_25|~spl0_26),
% 0.19/0.62 inference(split_clause,[status(thm)],[f5527,f5521,f5524])).
% 0.19/0.62 fof(f5615,plain,(
% 0.19/0.62 unordered_pair(sk0_14,sk0_14)=unordered_pair(sk0_14,sk0_15)|~spl0_14|~spl0_19),
% 0.19/0.62 inference(forward_demodulation,[status(thm)],[f4996,f5311])).
% 0.19/0.62 fof(f5616,plain,(
% 0.19/0.62 singleton(sk0_14)=unordered_pair(sk0_14,sk0_15)|~spl0_14|~spl0_19),
% 0.19/0.62 inference(forward_demodulation,[status(thm)],[f288,f5615])).
% 0.19/0.62 fof(f5617,plain,(
% 0.19/0.62 sk0_14=sk0_15|~spl0_14|~spl0_19),
% 0.19/0.62 inference(resolution,[status(thm)],[f5616,f311])).
% 0.19/0.62 fof(f5618,plain,(
% 0.19/0.62 $false|spl0_1|~spl0_14|~spl0_19),
% 0.19/0.62 inference(forward_subsumption_resolution,[status(thm)],[f5617,f5003])).
% 0.19/0.62 fof(f5619,plain,(
% 0.19/0.62 spl0_1|~spl0_14|~spl0_19),
% 0.19/0.62 inference(contradiction_clause,[status(thm)],[f5618])).
% 0.19/0.62 fof(f5621,plain,(
% 0.19/0.62 ~unordered_pair(sk0_14,sk0_14)=unordered_pair(sk0_14,sk0_15)|~spl0_14|spl0_19),
% 0.19/0.62 inference(forward_demodulation,[status(thm)],[f4996,f5312])).
% 0.19/0.62 fof(f5622,plain,(
% 0.19/0.62 ~singleton(sk0_14)=unordered_pair(sk0_14,sk0_15)|~spl0_14|spl0_19),
% 0.19/0.62 inference(forward_demodulation,[status(thm)],[f288,f5621])).
% 0.19/0.62 fof(f5629,plain,(
% 0.19/0.62 in(unordered_pair(sk0_14,sk0_15),singleton(singleton(sk0_14)))|~spl0_0|~spl0_14),
% 0.19/0.62 inference(forward_demodulation,[status(thm)],[f313,f4625])).
% 0.19/0.62 fof(f5630,plain,(
% 0.19/0.62 unordered_pair(sk0_14,sk0_15)=singleton(sk0_14)|~spl0_0|~spl0_14),
% 0.19/0.62 inference(resolution,[status(thm)],[f5629,f321])).
% 0.19/0.62 fof(f5631,plain,(
% 0.19/0.62 $false|spl0_19|~spl0_0|~spl0_14),
% 0.19/0.62 inference(forward_subsumption_resolution,[status(thm)],[f5630,f5622])).
% 0.19/0.62 fof(f5632,plain,(
% 0.19/0.62 spl0_19|~spl0_0|~spl0_14),
% 0.19/0.62 inference(contradiction_clause,[status(thm)],[f5631])).
% 0.19/0.62 fof(f5634,plain,(
% 0.19/0.62 spl0_27 <=> ~singleton(X0)=singleton(sk0_14)),
% 0.19/0.62 introduced(split_symbol_definition)).
% 0.19/0.62 fof(f5635,plain,(
% 0.19/0.62 ![X0]: (~singleton(X0)=singleton(sk0_14)|~spl0_27)),
% 0.19/0.62 inference(component_clause,[status(thm)],[f5634])).
% 0.19/0.62 fof(f5637,plain,(
% 0.19/0.62 spl0_28 <=> sk0_14=sk0_17),
% 0.19/0.62 introduced(split_symbol_definition)).
% 0.19/0.62 fof(f5638,plain,(
% 0.19/0.62 sk0_14=sk0_17|~spl0_28),
% 0.19/0.62 inference(component_clause,[status(thm)],[f5637])).
% 0.19/0.62 fof(f5640,plain,(
% 0.19/0.62 ![X0]: (~singleton(X0)=singleton(sk0_14)|sk0_14=sk0_17|~spl0_20)),
% 0.19/0.62 inference(paramodulation,[status(thm)],[f5314,f311])).
% 0.19/0.62 fof(f5641,plain,(
% 0.19/0.62 spl0_27|spl0_28|~spl0_20),
% 0.19/0.62 inference(split_clause,[status(thm)],[f5640,f5634,f5637,f5313])).
% 0.19/0.62 fof(f5747,plain,(
% 0.19/0.62 $false|~spl0_27),
% 0.19/0.62 inference(equality_resolution,[status(esa)],[f5635])).
% 0.19/0.62 fof(f5748,plain,(
% 0.19/0.62 ~spl0_27),
% 0.19/0.62 inference(contradiction_clause,[status(thm)],[f5747])).
% 0.19/0.62 fof(f5750,plain,(
% 0.19/0.62 sk0_1(ordered_pair(singleton(sk0_16),unordered_pair(sk0_16,sk0_14)))=singleton(singleton(sk0_16))|~spl0_28|~spl0_6),
% 0.19/0.62 inference(forward_demodulation,[status(thm)],[f5638,f4283])).
% 0.19/0.62 fof(f5751,plain,(
% 0.19/0.62 sk0_1(ordered_pair(singleton(sk0_16),unordered_pair(sk0_14,sk0_16)))=singleton(singleton(sk0_16))|~spl0_28|~spl0_6),
% 0.19/0.62 inference(forward_demodulation,[status(thm)],[f4016,f5750])).
% 0.19/0.62 fof(f5752,plain,(
% 0.19/0.62 spl0_29 <=> ordered_pair(singleton(sk0_16),unordered_pair(sk0_14,sk0_16))=empty_set),
% 0.19/0.62 introduced(split_symbol_definition)).
% 0.19/0.62 fof(f5753,plain,(
% 0.19/0.62 ordered_pair(singleton(sk0_16),unordered_pair(sk0_14,sk0_16))=empty_set|~spl0_29),
% 0.19/0.62 inference(component_clause,[status(thm)],[f5752])).
% 0.19/0.62 fof(f5755,plain,(
% 0.19/0.62 spl0_30 <=> in(ordered_pair(singleton(sk0_16),unordered_pair(sk0_14,sk0_16)),singleton(singleton(sk0_16)))),
% 0.19/0.62 introduced(split_symbol_definition)).
% 0.19/0.62 fof(f5758,plain,(
% 0.19/0.62 ordered_pair(singleton(sk0_16),unordered_pair(sk0_14,sk0_16))=empty_set|~in(ordered_pair(singleton(sk0_16),unordered_pair(sk0_14,sk0_16)),singleton(singleton(sk0_16)))|~spl0_28|~spl0_6),
% 0.19/0.62 inference(paramodulation,[status(thm)],[f5751,f3565])).
% 0.19/0.62 fof(f5759,plain,(
% 0.19/0.62 spl0_29|~spl0_30|~spl0_28|~spl0_6),
% 0.19/0.62 inference(split_clause,[status(thm)],[f5758,f5752,f5755,f5637,f4282])).
% 0.19/0.62 fof(f5760,plain,(
% 0.19/0.62 spl0_31 <=> in(singleton(singleton(sk0_16)),ordered_pair(singleton(sk0_16),unordered_pair(sk0_14,sk0_16)))),
% 0.19/0.62 introduced(split_symbol_definition)).
% 0.19/0.62 fof(f5763,plain,(
% 0.19/0.62 ordered_pair(singleton(sk0_16),unordered_pair(sk0_14,sk0_16))=empty_set|in(singleton(singleton(sk0_16)),ordered_pair(singleton(sk0_16),unordered_pair(sk0_14,sk0_16)))|~spl0_28|~spl0_6),
% 0.19/0.62 inference(paramodulation,[status(thm)],[f5751,f109])).
% 0.19/0.62 fof(f5764,plain,(
% 0.19/0.62 spl0_29|spl0_31|~spl0_28|~spl0_6),
% 0.19/0.62 inference(split_clause,[status(thm)],[f5763,f5752,f5760,f5637,f4282])).
% 0.19/0.62 fof(f5765,plain,(
% 0.19/0.62 ![X0]: (~singleton(X0)=ordered_pair(unordered_pair(sk0_14,sk0_14),singleton(sk0_14))|~spl0_28|~spl0_23)),
% 0.19/0.62 inference(forward_demodulation,[status(thm)],[f5638,f5496])).
% 0.19/0.62 fof(f5766,plain,(
% 0.19/0.62 ![X0]: (~singleton(X0)=ordered_pair(singleton(sk0_14),singleton(sk0_14))|~spl0_28|~spl0_23)),
% 0.19/0.62 inference(forward_demodulation,[status(thm)],[f288,f5765])).
% 0.19/0.62 fof(f5767,plain,(
% 0.19/0.62 ![X0]: (~singleton(X0)=singleton(singleton(singleton(sk0_14)))|~spl0_28|~spl0_23)),
% 0.19/0.62 inference(forward_demodulation,[status(thm)],[f2089,f5766])).
% 0.19/0.62 fof(f5768,plain,(
% 0.19/0.62 ordered_pair(sk0_14,sk0_15)=singleton(unordered_pair(sk0_14,sk0_14))|~spl0_28|~spl0_24),
% 0.19/0.62 inference(forward_demodulation,[status(thm)],[f5638,f5499])).
% 0.19/0.62 fof(f5769,plain,(
% 0.19/0.62 ordered_pair(sk0_14,sk0_15)=singleton(singleton(sk0_14))|~spl0_28|~spl0_24),
% 0.19/0.62 inference(forward_demodulation,[status(thm)],[f288,f5768])).
% 0.19/0.62 fof(f5770,plain,(
% 0.19/0.62 $false|~spl0_21),
% 0.19/0.62 inference(forward_subsumption_resolution,[status(thm)],[f5457,f5461])).
% 0.19/0.62 fof(f5771,plain,(
% 0.19/0.62 ~spl0_21),
% 0.19/0.62 inference(contradiction_clause,[status(thm)],[f5770])).
% 0.19/0.62 fof(f5774,plain,(
% 0.19/0.62 ordered_pair(singleton(sk0_16),unordered_pair(sk0_16,sk0_14))=empty_set|~spl0_28|~spl0_8),
% 0.19/0.62 inference(forward_demodulation,[status(thm)],[f5638,f4289])).
% 0.19/0.62 fof(f5775,plain,(
% 0.19/0.62 ordered_pair(singleton(sk0_16),unordered_pair(sk0_14,sk0_16))=empty_set|~spl0_28|~spl0_8),
% 0.19/0.62 inference(forward_demodulation,[status(thm)],[f4016,f5774])).
% 0.19/0.62 fof(f5776,plain,(
% 0.19/0.62 $false|~spl0_28|~spl0_23),
% 0.19/0.62 inference(equality_resolution,[status(esa)],[f5767])).
% 0.19/0.62 fof(f5777,plain,(
% 0.19/0.62 ~spl0_28|~spl0_23),
% 0.19/0.62 inference(contradiction_clause,[status(thm)],[f5776])).
% 0.19/0.62 fof(f5778,plain,(
% 0.19/0.62 $false|~spl0_3),
% 0.19/0.62 inference(backward_subsumption_resolution,[status(thm)],[f179,f4209])).
% 0.19/0.62 fof(f5779,plain,(
% 0.19/0.62 ~spl0_3),
% 0.19/0.62 inference(contradiction_clause,[status(thm)],[f5778])).
% 0.19/0.62 fof(f5782,plain,(
% 0.19/0.62 $false|~spl0_25),
% 0.19/0.62 inference(resolution,[status(thm)],[f5522,f258])).
% 0.19/0.62 fof(f5783,plain,(
% 0.19/0.62 ~spl0_25),
% 0.19/0.62 inference(contradiction_clause,[status(thm)],[f5782])).
% 0.19/0.62 fof(f5852,plain,(
% 0.19/0.62 in(ordered_pair(sk0_16,sk0_14),empty_set)|~spl0_29),
% 0.19/0.62 inference(paramodulation,[status(thm)],[f5753,f2575])).
% 0.19/0.62 fof(f5853,plain,(
% 0.19/0.62 $false|~spl0_29),
% 0.19/0.62 inference(forward_subsumption_resolution,[status(thm)],[f5852,f323])).
% 0.19/0.62 fof(f5854,plain,(
% 0.19/0.62 ~spl0_29),
% 0.19/0.62 inference(contradiction_clause,[status(thm)],[f5853])).
% 0.19/0.62 fof(f5858,plain,(
% 0.19/0.62 in(ordered_pair(sk0_16,sk0_14),empty_set)|~spl0_28|~spl0_8),
% 0.19/0.62 inference(paramodulation,[status(thm)],[f5775,f2575])).
% 0.19/0.62 fof(f5859,plain,(
% 0.19/0.62 $false|~spl0_28|~spl0_8),
% 0.19/0.62 inference(forward_subsumption_resolution,[status(thm)],[f5858,f323])).
% 0.19/0.62 fof(f5860,plain,(
% 0.19/0.62 ~spl0_28|~spl0_8),
% 0.19/0.62 inference(contradiction_clause,[status(thm)],[f5859])).
% 0.19/0.62 fof(f5861,plain,(
% 0.19/0.62 in(ordered_pair(sk0_14,sk0_15),ordered_pair(singleton(sk0_16),unordered_pair(sk0_16,sk0_14)))|~spl0_28|~spl0_18),
% 0.19/0.62 inference(forward_demodulation,[status(thm)],[f5638,f5073])).
% 0.19/0.62 fof(f5862,plain,(
% 0.19/0.62 in(ordered_pair(sk0_14,sk0_15),ordered_pair(singleton(sk0_16),unordered_pair(sk0_14,sk0_16)))|~spl0_28|~spl0_18),
% 0.19/0.62 inference(forward_demodulation,[status(thm)],[f4016,f5861])).
% 0.19/0.62 fof(f5865,plain,(
% 0.19/0.62 spl0_32 <=> ordered_pair(sk0_14,sk0_15)=unordered_pair(singleton(sk0_16),unordered_pair(sk0_14,sk0_16))),
% 0.19/0.62 introduced(split_symbol_definition)).
% 0.19/0.62 fof(f5866,plain,(
% 0.19/0.62 ordered_pair(sk0_14,sk0_15)=unordered_pair(singleton(sk0_16),unordered_pair(sk0_14,sk0_16))|~spl0_32),
% 0.19/0.62 inference(component_clause,[status(thm)],[f5865])).
% 0.19/0.62 fof(f5868,plain,(
% 0.19/0.62 ordered_pair(sk0_14,sk0_15)=unordered_pair(singleton(sk0_16),unordered_pair(sk0_14,sk0_16))|ordered_pair(sk0_14,sk0_15)=singleton(singleton(sk0_16))|~spl0_28|~spl0_18),
% 0.19/0.62 inference(resolution,[status(thm)],[f5862,f4277])).
% 0.19/0.62 fof(f5869,plain,(
% 0.19/0.62 spl0_32|spl0_14|~spl0_28|~spl0_18),
% 0.19/0.62 inference(split_clause,[status(thm)],[f5868,f5865,f4313,f5637,f5072])).
% 0.19/0.62 fof(f5871,plain,(
% 0.19/0.62 ordered_pair(sk0_14,sk0_15)=ordered_pair(sk0_16,sk0_14)|~spl0_32),
% 0.19/0.62 inference(forward_demodulation,[status(thm)],[f747,f5866])).
% 0.19/0.62 fof(f5872,plain,(
% 0.19/0.62 ordered_pair(ordered_pair(sk0_16,sk0_14),singleton(singleton(sk0_16)))=unordered_pair(singleton(ordered_pair(sk0_14,sk0_15)),ordered_pair(singleton(sk0_16),unordered_pair(sk0_14,sk0_16)))|~spl0_32),
% 0.19/0.62 inference(paramodulation,[status(thm)],[f5871,f1822])).
% 0.19/0.62 fof(f5873,plain,(
% 0.19/0.62 ordered_pair(ordered_pair(sk0_14,sk0_15),singleton(singleton(sk0_16)))=unordered_pair(singleton(ordered_pair(sk0_14,sk0_15)),ordered_pair(singleton(sk0_16),unordered_pair(sk0_14,sk0_16)))|~spl0_32),
% 0.19/0.62 inference(forward_demodulation,[status(thm)],[f5871,f5872])).
% 0.19/0.62 fof(f5959,plain,(
% 0.19/0.62 spl0_33 <=> ~singleton(X0)=ordered_pair(ordered_pair(sk0_14,sk0_15),singleton(singleton(sk0_16)))),
% 0.19/0.62 introduced(split_symbol_definition)).
% 0.19/0.62 fof(f5962,plain,(
% 0.19/0.62 spl0_34 <=> singleton(ordered_pair(sk0_14,sk0_15))=ordered_pair(singleton(sk0_16),unordered_pair(sk0_14,sk0_16))),
% 0.19/0.62 introduced(split_symbol_definition)).
% 0.19/0.62 fof(f5965,plain,(
% 0.19/0.62 ![X0]: (~singleton(X0)=ordered_pair(ordered_pair(sk0_14,sk0_15),singleton(singleton(sk0_16)))|singleton(ordered_pair(sk0_14,sk0_15))=ordered_pair(singleton(sk0_16),unordered_pair(sk0_14,sk0_16))|~spl0_32)),
% 0.19/0.62 inference(paramodulation,[status(thm)],[f5873,f311])).
% 0.19/0.62 fof(f5966,plain,(
% 0.19/0.62 spl0_33|spl0_34|~spl0_32),
% 0.19/0.62 inference(split_clause,[status(thm)],[f5965,f5959,f5962,f5865])).
% 0.19/0.62 fof(f6044,plain,(
% 0.19/0.62 spl0_35 <=> singleton(sk0_16)=unordered_pair(sk0_14,sk0_15)),
% 0.19/0.62 introduced(split_symbol_definition)).
% 0.19/0.62 fof(f6045,plain,(
% 0.19/0.62 singleton(sk0_16)=unordered_pair(sk0_14,sk0_15)|~spl0_35),
% 0.19/0.62 inference(component_clause,[status(thm)],[f6044])).
% 0.19/0.62 fof(f6046,plain,(
% 0.19/0.62 ~singleton(sk0_16)=unordered_pair(sk0_14,sk0_15)|spl0_35),
% 0.19/0.62 inference(component_clause,[status(thm)],[f6044])).
% 0.19/0.62 fof(f6047,plain,(
% 0.19/0.62 spl0_36 <=> singleton(sk0_16)=singleton(sk0_14)),
% 0.19/0.62 introduced(split_symbol_definition)).
% 0.19/0.62 fof(f6048,plain,(
% 0.19/0.62 singleton(sk0_16)=singleton(sk0_14)|~spl0_36),
% 0.19/0.62 inference(component_clause,[status(thm)],[f6047])).
% 0.19/0.62 fof(f6050,plain,(
% 0.19/0.62 singleton(sk0_16)=unordered_pair(sk0_14,sk0_15)|singleton(sk0_16)=singleton(sk0_14)),
% 0.19/0.62 inference(resolution,[status(thm)],[f2452,f4277])).
% 0.19/0.62 fof(f6051,plain,(
% 0.19/0.62 spl0_35|spl0_36),
% 0.19/0.62 inference(split_clause,[status(thm)],[f6050,f6044,f6047])).
% 0.19/0.62 fof(f6179,plain,(
% 0.19/0.62 spl0_41 <=> ~singleton(X0)=ordered_pair(sk0_14,sk0_15)),
% 0.19/0.62 introduced(split_symbol_definition)).
% 0.19/0.62 fof(f6180,plain,(
% 0.19/0.62 ![X0]: (~singleton(X0)=ordered_pair(sk0_14,sk0_15)|~spl0_41)),
% 0.19/0.62 inference(component_clause,[status(thm)],[f6179])).
% 0.19/0.62 fof(f6182,plain,(
% 0.19/0.62 spl0_42 <=> singleton(sk0_16)=unordered_pair(sk0_14,sk0_16)),
% 0.19/0.62 introduced(split_symbol_definition)).
% 0.19/0.62 fof(f6185,plain,(
% 0.19/0.62 ![X0]: (~singleton(X0)=ordered_pair(sk0_14,sk0_15)|singleton(sk0_16)=unordered_pair(sk0_14,sk0_16)|~spl0_32)),
% 0.19/0.62 inference(paramodulation,[status(thm)],[f5871,f5493])).
% 0.19/0.62 fof(f6186,plain,(
% 0.19/0.62 spl0_41|spl0_42|~spl0_32),
% 0.19/0.62 inference(split_clause,[status(thm)],[f6185,f6179,f6182,f5865])).
% 0.19/0.62 fof(f6198,plain,(
% 0.19/0.62 spl0_43 <=> singleton(sk0_16)=unordered_pair(sk0_16,sk0_14)),
% 0.19/0.62 introduced(split_symbol_definition)).
% 0.19/0.62 fof(f6201,plain,(
% 0.19/0.62 ![X0]: (~singleton(X0)=ordered_pair(sk0_14,sk0_15)|singleton(sk0_16)=unordered_pair(sk0_16,sk0_14)|~spl0_32)),
% 0.19/0.62 inference(paramodulation,[status(thm)],[f5871,f5494])).
% 0.19/0.62 fof(f6202,plain,(
% 0.19/0.62 spl0_41|spl0_43|~spl0_32),
% 0.19/0.62 inference(split_clause,[status(thm)],[f6201,f6179,f6198,f5865])).
% 0.19/0.62 fof(f6302,plain,(
% 0.19/0.62 sk0_16=sk0_15|~spl0_35),
% 0.19/0.62 inference(resolution,[status(thm)],[f6045,f5487])).
% 0.19/0.62 fof(f6304,plain,(
% 0.19/0.62 sk0_16=sk0_14|~spl0_35),
% 0.19/0.62 inference(resolution,[status(thm)],[f6045,f308])).
% 0.19/0.62 fof(f6305,plain,(
% 0.19/0.62 spl0_0|~spl0_35),
% 0.19/0.62 inference(split_clause,[status(thm)],[f6304,f312,f6044])).
% 0.19/0.62 fof(f6397,plain,(
% 0.19/0.62 sk0_16=sk0_14|~spl0_36),
% 0.19/0.62 inference(resolution,[status(thm)],[f6048,f5486])).
% 0.19/0.62 fof(f6398,plain,(
% 0.19/0.62 spl0_0|~spl0_36),
% 0.19/0.62 inference(split_clause,[status(thm)],[f6397,f312,f6047])).
% 0.19/0.62 fof(f6413,plain,(
% 0.19/0.62 $false|~spl0_41|~spl0_28|~spl0_24),
% 0.19/0.62 inference(forward_subsumption_resolution,[status(thm)],[f5769,f6180])).
% 0.19/0.62 fof(f6414,plain,(
% 0.19/0.62 ~spl0_41|~spl0_28|~spl0_24),
% 0.19/0.62 inference(contradiction_clause,[status(thm)],[f6413])).
% 0.19/0.62 fof(f6842,plain,(
% 0.19/0.62 ordered_pair(sk0_14,sk0_15)=ordered_pair(sk0_14,sk0_14)|~spl0_28|~spl0_0),
% 0.19/0.62 inference(forward_demodulation,[status(thm)],[f5638,f5079])).
% 0.19/0.62 fof(f6843,plain,(
% 0.19/0.62 ordered_pair(sk0_14,sk0_15)=singleton(singleton(sk0_14))|~spl0_28|~spl0_0),
% 0.19/0.62 inference(forward_demodulation,[status(thm)],[f2089,f6842])).
% 0.19/0.62 fof(f6846,plain,(
% 0.19/0.62 ~sk0_15=sk0_14|~spl0_28|spl0_1),
% 0.19/0.62 inference(forward_demodulation,[status(thm)],[f5638,f317])).
% 0.19/0.62 fof(f6854,plain,(
% 0.19/0.62 sk0_14=sk0_15|~spl0_0|~spl0_35),
% 0.19/0.62 inference(forward_demodulation,[status(thm)],[f313,f6302])).
% 0.19/0.62 fof(f6856,plain,(
% 0.19/0.62 ~sk0_14=sk0_14|~spl0_0|~spl0_35|~spl0_28|spl0_1),
% 0.19/0.62 inference(forward_demodulation,[status(thm)],[f6854,f6846])).
% 0.19/0.62 fof(f6857,plain,(
% 0.19/0.62 $false|~spl0_0|~spl0_35|~spl0_28|spl0_1),
% 0.19/0.62 inference(trivial_equality_resolution,[status(esa)],[f6856])).
% 0.19/0.62 fof(f6858,plain,(
% 0.19/0.62 ~spl0_0|~spl0_35|~spl0_28|spl0_1),
% 0.19/0.62 inference(contradiction_clause,[status(thm)],[f6857])).
% 0.19/0.62 fof(f6859,plain,(
% 0.19/0.62 ~singleton(sk0_14)=unordered_pair(sk0_14,sk0_15)|~spl0_0|spl0_35),
% 0.19/0.62 inference(forward_demodulation,[status(thm)],[f313,f6046])).
% 0.19/0.62 fof(f7172,plain,(
% 0.19/0.62 singleton(sk0_14)=unordered_pair(sk0_14,sk0_15)|~spl0_28|~spl0_0),
% 0.19/0.62 inference(resolution,[status(thm)],[f6843,f5494])).
% 0.19/0.62 fof(f7173,plain,(
% 0.19/0.62 $false|spl0_35|~spl0_28|~spl0_0),
% 0.19/0.62 inference(forward_subsumption_resolution,[status(thm)],[f7172,f6859])).
% 0.19/0.62 fof(f7174,plain,(
% 0.19/0.62 spl0_35|~spl0_28|~spl0_0),
% 0.19/0.62 inference(contradiction_clause,[status(thm)],[f7173])).
% 0.19/0.62 fof(f7313,plain,(
% 0.19/0.62 spl0_46 <=> singleton(sk0_14)=unordered_pair(sk0_17,sk0_14)),
% 0.19/0.62 introduced(split_symbol_definition)).
% 0.19/0.62 fof(f7314,plain,(
% 0.19/0.62 singleton(sk0_14)=unordered_pair(sk0_17,sk0_14)|~spl0_46),
% 0.19/0.62 inference(component_clause,[status(thm)],[f7313])).
% 0.19/0.62 fof(f7378,plain,(
% 0.19/0.62 singleton(sk0_14)=unordered_pair(sk0_14,sk0_17)|~spl0_46),
% 0.19/0.62 inference(forward_demodulation,[status(thm)],[f90,f7314])).
% 0.19/0.62 fof(f7379,plain,(
% 0.19/0.62 $false|spl0_20|~spl0_46),
% 0.19/0.62 inference(forward_subsumption_resolution,[status(thm)],[f7378,f5315])).
% 0.19/0.62 fof(f7380,plain,(
% 0.19/0.62 spl0_20|~spl0_46),
% 0.19/0.62 inference(contradiction_clause,[status(thm)],[f7379])).
% 0.19/0.62 fof(f7609,plain,(
% 0.19/0.62 spl0_54 <=> ~disjoint(X0,empty_set)),
% 0.19/0.62 introduced(split_symbol_definition)).
% 0.19/0.62 fof(f7610,plain,(
% 0.19/0.62 ![X0]: (~disjoint(X0,empty_set)|~spl0_54)),
% 0.19/0.62 inference(component_clause,[status(thm)],[f7609])).
% 0.19/0.62 fof(f7617,plain,(
% 0.19/0.62 $false|~spl0_54),
% 0.19/0.62 inference(forward_subsumption_resolution,[status(thm)],[f7610,f5462])).
% 0.19/0.62 fof(f7618,plain,(
% 0.19/0.62 ~spl0_54),
% 0.19/0.62 inference(contradiction_clause,[status(thm)],[f7617])).
% 0.19/0.62 fof(f7626,plain,(
% 0.19/0.62 spl0_55 <=> disjoint(X0,empty_set)),
% 0.19/0.62 introduced(split_symbol_definition)).
% 0.19/0.62 fof(f7629,plain,(
% 0.19/0.62 ![X0]: (disjoint(X0,empty_set)|~empty_set=empty_set)),
% 0.19/0.62 inference(paramodulation,[status(thm)],[f244,f173])).
% 0.19/0.62 fof(f7630,plain,(
% 0.19/0.62 spl0_55|~spl0_5),
% 0.19/0.62 inference(split_clause,[status(thm)],[f7629,f7626,f4225])).
% 0.19/0.62 fof(f7742,plain,(
% 0.19/0.62 in(sk0_17,unordered_pair(sk0_14,sk0_15))|~spl0_19),
% 0.19/0.62 inference(paramodulation,[status(thm)],[f5311,f328])).
% 0.19/0.62 fof(f7820,plain,(
% 1.53/0.71 sk0_17=sk0_14|sk0_17=sk0_15|~spl0_19),
% 1.53/0.71 inference(resolution,[status(thm)],[f7742,f326])).
% 1.53/0.71 fof(f7821,plain,(
% 1.53/0.71 spl0_28|spl0_1|~spl0_19),
% 1.53/0.71 inference(split_clause,[status(thm)],[f7820,f5637,f315,f5310])).
% 1.53/0.71 fof(f7824,plain,(
% 1.53/0.71 $false),
% 1.53/0.71 inference(sat_refutation,[status(thm)],[f318,f4212,f4229,f4234,f4292,f4301,f4309,f4317,f4322,f4330,f4721,f4722,f4723,f4724,f5076,f5317,f5467,f5502,f5528,f5619,f5632,f5641,f5748,f5759,f5764,f5771,f5777,f5779,f5783,f5854,f5860,f5869,f5966,f6051,f6186,f6202,f6305,f6398,f6414,f6858,f7174,f7380,f7618,f7630,f7821])).
% 1.53/0.71 % SZS output end CNFRefutation for theBenchmark.p
% 1.53/0.71 % Elapsed time: 0.368050 seconds
% 1.53/0.71 % CPU time: 1.575883 seconds
% 1.53/0.71 % Memory used: 108.652 MB
%------------------------------------------------------------------------------