TSTP Solution File: NUM401+1 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : NUM401+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n013.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 12:29:01 EDT 2023
% Result : Theorem 0.19s 0.51s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUM401+1 : TPTP v8.1.2. Released v3.2.0.
% 0.06/0.12 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.33 % Computer : n013.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 09:53:50 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.12/0.34 % Drodi V3.5.1
% 0.19/0.51 % Refutation found
% 0.19/0.51 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.19/0.51 % SZS output start CNFRefutation for theBenchmark
% 0.19/0.51 fof(f1,axiom,(
% 0.19/0.51 (! [A,B] :( in(A,B)=> ~ in(B,A) ) )),
% 0.19/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.51 fof(f2,axiom,(
% 0.19/0.51 (! [A] :( empty(A)=> function(A) ) )),
% 0.19/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.51 fof(f3,axiom,(
% 0.19/0.51 (! [A] :( ordinal(A)=> ( epsilon_transitive(A)& epsilon_connected(A) ) ) )),
% 0.19/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.51 fof(f4,axiom,(
% 0.19/0.51 (! [A] :( empty(A)=> relation(A) ) )),
% 0.19/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.51 fof(f5,axiom,(
% 0.19/0.51 (! [A] :( ( relation(A)& empty(A)& function(A) )=> ( relation(A)& function(A)& one_to_one(A) ) ) )),
% 0.19/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.51 fof(f6,axiom,(
% 0.19/0.51 (! [A] :( ( epsilon_transitive(A)& epsilon_connected(A) )=> ordinal(A) ) )),
% 0.19/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.51 fof(f7,axiom,(
% 0.19/0.51 (! [A] :( empty(A)=> ( epsilon_transitive(A)& epsilon_connected(A)& ordinal(A) ) ) )),
% 0.19/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.51 fof(f8,axiom,(
% 0.19/0.51 (! [A,B] : set_union2(A,B) = set_union2(B,A) )),
% 0.19/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.51 fof(f9,axiom,(
% 0.19/0.51 (! [A,B] :( ( ordinal(A)& ordinal(B) )=> ( ordinal_subset(A,B)| ordinal_subset(B,A) ) ) )),
% 0.19/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.51 fof(f10,axiom,(
% 0.19/0.51 (! [A,B] :( A = B<=> ( subset(A,B)& subset(B,A) ) ) )),
% 0.19/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.51 fof(f11,axiom,(
% 0.19/0.51 (! [A] : succ(A) = set_union2(A,singleton(A)) )),
% 0.19/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.51 fof(f12,axiom,(
% 0.19/0.51 (! [A,B] :( B = singleton(A)<=> (! [C] :( in(C,B)<=> C = A ) )) )),
% 0.19/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.51 fof(f13,axiom,(
% 0.19/0.51 (! [A] :( epsilon_transitive(A)<=> (! [B] :( in(B,A)=> subset(B,A) ) )) )),
% 0.19/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.51 fof(f14,axiom,(
% 0.19/0.51 (! [A,B,C] :( C = set_union2(A,B)<=> (! [D] :( in(D,C)<=> ( in(D,A)| in(D,B) ) ) )) )),
% 0.19/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.51 fof(f15,axiom,(
% 0.19/0.51 (! [A] :(? [B] : element(B,A) ))),
% 0.19/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.51 fof(f16,axiom,(
% 0.19/0.51 ( empty(empty_set)& relation(empty_set)& relation_empty_yielding(empty_set) ) ),
% 0.19/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.51 fof(f17,axiom,(
% 0.19/0.51 (! [A] : ~ empty(succ(A)) )),
% 0.19/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.51 fof(f19,axiom,(
% 0.19/0.51 ( relation(empty_set)& relation_empty_yielding(empty_set)& function(empty_set)& one_to_one(empty_set)& empty(empty_set)& epsilon_transitive(empty_set)& epsilon_connected(empty_set)& ordinal(empty_set) ) ),
% 0.19/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.51 fof(f20,axiom,(
% 0.19/0.51 (! [A,B] :( ( relation(A)& relation(B) )=> relation(set_union2(A,B)) ) )),
% 0.19/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.51 fof(f22,axiom,(
% 0.19/0.51 (! [A] :( ordinal(A)=> ( ~ empty(succ(A))& epsilon_transitive(succ(A))& epsilon_connected(succ(A))& ordinal(succ(A)) ) ) )),
% 0.19/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.51 fof(f27,axiom,(
% 0.19/0.51 (? [A] :( epsilon_transitive(A)& epsilon_connected(A)& ordinal(A) ) )),
% 0.19/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.51 fof(f28,axiom,(
% 0.19/0.51 (? [A] :( empty(A)& relation(A) ) )),
% 0.19/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.51 fof(f29,axiom,(
% 0.19/0.51 (? [A] : empty(A) )),
% 0.19/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.51 fof(f30,axiom,(
% 0.19/0.51 (? [A] :( relation(A)& empty(A)& function(A) ) )),
% 0.19/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.51 fof(f31,axiom,(
% 0.19/0.51 (? [A] :( relation(A)& function(A)& one_to_one(A)& empty(A)& epsilon_transitive(A)& epsilon_connected(A)& ordinal(A) ) )),
% 0.19/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.51 fof(f35,axiom,(
% 0.19/0.51 (? [A] :( ~ empty(A)& epsilon_transitive(A)& epsilon_connected(A)& ordinal(A) ) )),
% 0.19/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.51 fof(f39,axiom,(
% 0.19/0.51 (! [A,B] :( ( ordinal(A)& ordinal(B) )=> ( ordinal_subset(A,B)<=> subset(A,B) ) ) )),
% 0.19/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.51 fof(f40,axiom,(
% 0.19/0.51 (! [A,B] :( ( ordinal(A)& ordinal(B) )=> ordinal_subset(A,A) ) )),
% 0.19/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.51 fof(f42,axiom,(
% 0.19/0.51 (! [A] : in(A,succ(A)) )),
% 0.19/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.51 fof(f43,axiom,(
% 0.19/0.51 (! [A] : A != succ(A) )),
% 0.19/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.51 fof(f44,axiom,(
% 0.19/0.51 (! [A] : set_union2(A,empty_set) = A )),
% 0.19/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.51 fof(f46,axiom,(
% 0.19/0.51 (! [A] :( ordinal(A)=> (! [B] :( ordinal(B)=> ~ ( ~ in(A,B)& A != B& ~ in(B,A) ) ) )) )),
% 0.19/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.51 fof(f47,axiom,(
% 0.19/0.51 (! [A,B] :( element(A,B)=> ( empty(B)| in(A,B) ) ) )),
% 0.19/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.51 fof(f48,conjecture,(
% 0.19/0.51 (! [A] :( ordinal(A)=> (! [B] :( ordinal(B)=> ( in(A,succ(B))<=> ordinal_subset(A,B) ) ) )) )),
% 0.19/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.51 fof(f49,negated_conjecture,(
% 0.19/0.51 ~((! [A] :( ordinal(A)=> (! [B] :( ordinal(B)=> ( in(A,succ(B))<=> ordinal_subset(A,B) ) ) )) ))),
% 0.19/0.51 inference(negated_conjecture,[status(cth)],[f48])).
% 0.19/0.51 fof(f54,axiom,(
% 0.19/0.51 (! [A,B] :~ ( in(A,B)& empty(B) ) )),
% 0.19/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.51 fof(f56,plain,(
% 0.19/0.51 ![A,B]: (~in(A,B)|~in(B,A))),
% 0.19/0.51 inference(pre_NNF_transformation,[status(esa)],[f1])).
% 0.19/0.51 fof(f57,plain,(
% 0.19/0.51 ![X0,X1]: (~in(X0,X1)|~in(X1,X0))),
% 0.19/0.51 inference(cnf_transformation,[status(esa)],[f56])).
% 0.19/0.51 fof(f58,plain,(
% 0.19/0.51 ![A]: (~empty(A)|function(A))),
% 0.19/0.51 inference(pre_NNF_transformation,[status(esa)],[f2])).
% 0.19/0.51 fof(f59,plain,(
% 0.19/0.51 ![X0]: (~empty(X0)|function(X0))),
% 0.19/0.51 inference(cnf_transformation,[status(esa)],[f58])).
% 0.19/0.51 fof(f60,plain,(
% 0.19/0.51 ![A]: (~ordinal(A)|(epsilon_transitive(A)&epsilon_connected(A)))),
% 0.19/0.51 inference(pre_NNF_transformation,[status(esa)],[f3])).
% 0.19/0.51 fof(f61,plain,(
% 0.19/0.51 ![X0]: (~ordinal(X0)|epsilon_transitive(X0))),
% 0.19/0.51 inference(cnf_transformation,[status(esa)],[f60])).
% 0.19/0.51 fof(f62,plain,(
% 0.19/0.51 ![X0]: (~ordinal(X0)|epsilon_connected(X0))),
% 0.19/0.51 inference(cnf_transformation,[status(esa)],[f60])).
% 0.19/0.51 fof(f63,plain,(
% 0.19/0.51 ![A]: (~empty(A)|relation(A))),
% 0.19/0.51 inference(pre_NNF_transformation,[status(esa)],[f4])).
% 0.19/0.51 fof(f64,plain,(
% 0.19/0.51 ![X0]: (~empty(X0)|relation(X0))),
% 0.19/0.51 inference(cnf_transformation,[status(esa)],[f63])).
% 0.19/0.51 fof(f65,plain,(
% 0.19/0.51 ![A]: (((~relation(A)|~empty(A))|~function(A))|((relation(A)&function(A))&one_to_one(A)))),
% 0.19/0.51 inference(pre_NNF_transformation,[status(esa)],[f5])).
% 0.19/0.51 fof(f68,plain,(
% 0.19/0.51 ![X0]: (~relation(X0)|~empty(X0)|~function(X0)|one_to_one(X0))),
% 0.19/0.51 inference(cnf_transformation,[status(esa)],[f65])).
% 0.19/0.51 fof(f69,plain,(
% 0.19/0.51 ![A]: ((~epsilon_transitive(A)|~epsilon_connected(A))|ordinal(A))),
% 0.19/0.51 inference(pre_NNF_transformation,[status(esa)],[f6])).
% 0.19/0.51 fof(f70,plain,(
% 0.19/0.51 ![X0]: (~epsilon_transitive(X0)|~epsilon_connected(X0)|ordinal(X0))),
% 0.19/0.51 inference(cnf_transformation,[status(esa)],[f69])).
% 0.19/0.51 fof(f71,plain,(
% 0.19/0.51 ![A]: (~empty(A)|((epsilon_transitive(A)&epsilon_connected(A))&ordinal(A)))),
% 0.19/0.51 inference(pre_NNF_transformation,[status(esa)],[f7])).
% 0.19/0.51 fof(f74,plain,(
% 0.19/0.51 ![X0]: (~empty(X0)|ordinal(X0))),
% 0.19/0.51 inference(cnf_transformation,[status(esa)],[f71])).
% 0.19/0.51 fof(f75,plain,(
% 0.19/0.51 ![X0,X1]: (set_union2(X0,X1)=set_union2(X1,X0))),
% 0.19/0.51 inference(cnf_transformation,[status(esa)],[f8])).
% 0.19/0.51 fof(f76,plain,(
% 0.19/0.51 ![A,B]: ((~ordinal(A)|~ordinal(B))|(ordinal_subset(A,B)|ordinal_subset(B,A)))),
% 0.19/0.51 inference(pre_NNF_transformation,[status(esa)],[f9])).
% 0.19/0.51 fof(f77,plain,(
% 0.19/0.51 ![X0,X1]: (~ordinal(X0)|~ordinal(X1)|ordinal_subset(X0,X1)|ordinal_subset(X1,X0))),
% 0.19/0.51 inference(cnf_transformation,[status(esa)],[f76])).
% 0.19/0.51 fof(f78,plain,(
% 0.19/0.51 ![A,B]: ((~A=B|(subset(A,B)&subset(B,A)))&(A=B|(~subset(A,B)|~subset(B,A))))),
% 0.19/0.51 inference(NNF_transformation,[status(esa)],[f10])).
% 0.19/0.51 fof(f79,plain,(
% 0.19/0.51 (![A,B]: (~A=B|(subset(A,B)&subset(B,A))))&(![A,B]: (A=B|(~subset(A,B)|~subset(B,A))))),
% 0.19/0.51 inference(miniscoping,[status(esa)],[f78])).
% 0.19/0.51 fof(f80,plain,(
% 0.19/0.51 ![X0,X1]: (~X0=X1|subset(X0,X1))),
% 0.19/0.51 inference(cnf_transformation,[status(esa)],[f79])).
% 0.19/0.51 fof(f82,plain,(
% 0.19/0.51 ![X0,X1]: (X0=X1|~subset(X0,X1)|~subset(X1,X0))),
% 0.19/0.51 inference(cnf_transformation,[status(esa)],[f79])).
% 0.19/0.51 fof(f83,plain,(
% 0.19/0.51 ![X0]: (succ(X0)=set_union2(X0,singleton(X0)))),
% 0.19/0.51 inference(cnf_transformation,[status(esa)],[f11])).
% 0.19/0.51 fof(f84,plain,(
% 0.19/0.51 ![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)))))),
% 0.19/0.51 inference(NNF_transformation,[status(esa)],[f12])).
% 0.19/0.51 fof(f85,plain,(
% 0.19/0.51 (![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)))))),
% 0.19/0.51 inference(miniscoping,[status(esa)],[f84])).
% 0.19/0.51 fof(f86,plain,(
% 0.19/0.51 (![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))))),
% 0.19/0.51 inference(skolemization,[status(esa)],[f85])).
% 0.19/0.51 fof(f87,plain,(
% 0.19/0.51 ![X0,X1,X2]: (~X0=singleton(X1)|~in(X2,X0)|X2=X1)),
% 0.19/0.51 inference(cnf_transformation,[status(esa)],[f86])).
% 0.19/0.51 fof(f88,plain,(
% 0.19/0.51 ![X0,X1,X2]: (~X0=singleton(X1)|in(X2,X0)|~X2=X1)),
% 0.19/0.51 inference(cnf_transformation,[status(esa)],[f86])).
% 0.19/0.51 fof(f89,plain,(
% 0.19/0.51 ![X0,X1]: (X0=singleton(X1)|~in(sk0_0(X0,X1),X0)|~sk0_0(X0,X1)=X1)),
% 0.19/0.51 inference(cnf_transformation,[status(esa)],[f86])).
% 0.19/0.51 fof(f90,plain,(
% 0.19/0.51 ![X0,X1]: (X0=singleton(X1)|in(sk0_0(X0,X1),X0)|sk0_0(X0,X1)=X1)),
% 0.19/0.51 inference(cnf_transformation,[status(esa)],[f86])).
% 0.19/0.51 fof(f91,plain,(
% 0.19/0.51 ![A]: (epsilon_transitive(A)<=>(![B]: (~in(B,A)|subset(B,A))))),
% 0.19/0.51 inference(pre_NNF_transformation,[status(esa)],[f13])).
% 0.19/0.51 fof(f92,plain,(
% 0.19/0.51 ![A]: ((~epsilon_transitive(A)|(![B]: (~in(B,A)|subset(B,A))))&(epsilon_transitive(A)|(?[B]: (in(B,A)&~subset(B,A)))))),
% 0.19/0.51 inference(NNF_transformation,[status(esa)],[f91])).
% 0.19/0.51 fof(f93,plain,(
% 0.19/0.51 (![A]: (~epsilon_transitive(A)|(![B]: (~in(B,A)|subset(B,A)))))&(![A]: (epsilon_transitive(A)|(?[B]: (in(B,A)&~subset(B,A)))))),
% 0.19/0.51 inference(miniscoping,[status(esa)],[f92])).
% 0.19/0.51 fof(f94,plain,(
% 0.19/0.51 (![A]: (~epsilon_transitive(A)|(![B]: (~in(B,A)|subset(B,A)))))&(![A]: (epsilon_transitive(A)|(in(sk0_1(A),A)&~subset(sk0_1(A),A))))),
% 0.19/0.51 inference(skolemization,[status(esa)],[f93])).
% 0.19/0.51 fof(f95,plain,(
% 0.19/0.51 ![X0,X1]: (~epsilon_transitive(X0)|~in(X1,X0)|subset(X1,X0))),
% 0.19/0.51 inference(cnf_transformation,[status(esa)],[f94])).
% 0.19/0.51 fof(f96,plain,(
% 0.19/0.51 ![X0]: (epsilon_transitive(X0)|in(sk0_1(X0),X0))),
% 0.19/0.51 inference(cnf_transformation,[status(esa)],[f94])).
% 0.19/0.51 fof(f97,plain,(
% 0.19/0.51 ![X0]: (epsilon_transitive(X0)|~subset(sk0_1(X0),X0))),
% 0.19/0.51 inference(cnf_transformation,[status(esa)],[f94])).
% 0.19/0.51 fof(f98,plain,(
% 0.19/0.51 ![A,B,C]: ((~C=set_union2(A,B)|(![D]: ((~in(D,C)|(in(D,A)|in(D,B)))&(in(D,C)|(~in(D,A)&~in(D,B))))))&(C=set_union2(A,B)|(?[D]: ((~in(D,C)|(~in(D,A)&~in(D,B)))&(in(D,C)|(in(D,A)|in(D,B)))))))),
% 0.19/0.51 inference(NNF_transformation,[status(esa)],[f14])).
% 0.19/0.51 fof(f99,plain,(
% 0.19/0.51 (![A,B,C]: (~C=set_union2(A,B)|((![D]: (~in(D,C)|(in(D,A)|in(D,B))))&(![D]: (in(D,C)|(~in(D,A)&~in(D,B)))))))&(![A,B,C]: (C=set_union2(A,B)|(?[D]: ((~in(D,C)|(~in(D,A)&~in(D,B)))&(in(D,C)|(in(D,A)|in(D,B)))))))),
% 0.19/0.51 inference(miniscoping,[status(esa)],[f98])).
% 0.19/0.51 fof(f100,plain,(
% 0.19/0.51 (![A,B,C]: (~C=set_union2(A,B)|((![D]: (~in(D,C)|(in(D,A)|in(D,B))))&(![D]: (in(D,C)|(~in(D,A)&~in(D,B)))))))&(![A,B,C]: (C=set_union2(A,B)|((~in(sk0_2(C,B,A),C)|(~in(sk0_2(C,B,A),A)&~in(sk0_2(C,B,A),B)))&(in(sk0_2(C,B,A),C)|(in(sk0_2(C,B,A),A)|in(sk0_2(C,B,A),B))))))),
% 0.19/0.51 inference(skolemization,[status(esa)],[f99])).
% 0.19/0.51 fof(f101,plain,(
% 0.19/0.51 ![X0,X1,X2,X3]: (~X0=set_union2(X1,X2)|~in(X3,X0)|in(X3,X1)|in(X3,X2))),
% 0.19/0.51 inference(cnf_transformation,[status(esa)],[f100])).
% 0.19/0.51 fof(f102,plain,(
% 0.19/0.51 ![X0,X1,X2,X3]: (~X0=set_union2(X1,X2)|in(X3,X0)|~in(X3,X1))),
% 0.19/0.51 inference(cnf_transformation,[status(esa)],[f100])).
% 0.19/0.51 fof(f103,plain,(
% 0.19/0.51 ![X0,X1,X2,X3]: (~X0=set_union2(X1,X2)|in(X3,X0)|~in(X3,X2))),
% 0.19/0.51 inference(cnf_transformation,[status(esa)],[f100])).
% 0.19/0.51 fof(f107,plain,(
% 0.19/0.51 ![A]: element(sk0_3(A),A)),
% 0.19/0.51 inference(skolemization,[status(esa)],[f15])).
% 0.19/0.51 fof(f108,plain,(
% 0.19/0.51 ![X0]: (element(sk0_3(X0),X0))),
% 0.19/0.51 inference(cnf_transformation,[status(esa)],[f107])).
% 0.19/0.51 fof(f109,plain,(
% 0.19/0.51 empty(empty_set)),
% 0.19/0.51 inference(cnf_transformation,[status(esa)],[f16])).
% 0.19/0.51 fof(f110,plain,(
% 0.19/0.51 relation(empty_set)),
% 0.19/0.51 inference(cnf_transformation,[status(esa)],[f16])).
% 0.19/0.51 fof(f112,plain,(
% 0.19/0.51 ![X0]: (~empty(succ(X0)))),
% 0.19/0.51 inference(cnf_transformation,[status(esa)],[f17])).
% 0.19/0.51 fof(f116,plain,(
% 0.19/0.51 function(empty_set)),
% 0.19/0.51 inference(cnf_transformation,[status(esa)],[f19])).
% 0.19/0.51 fof(f119,plain,(
% 0.19/0.51 epsilon_transitive(empty_set)),
% 0.19/0.51 inference(cnf_transformation,[status(esa)],[f19])).
% 0.19/0.51 fof(f120,plain,(
% 0.19/0.51 epsilon_connected(empty_set)),
% 0.19/0.51 inference(cnf_transformation,[status(esa)],[f19])).
% 0.19/0.51 fof(f122,plain,(
% 0.19/0.51 ![A,B]: ((~relation(A)|~relation(B))|relation(set_union2(A,B)))),
% 0.19/0.51 inference(pre_NNF_transformation,[status(esa)],[f20])).
% 0.19/0.51 fof(f123,plain,(
% 0.19/0.51 ![X0,X1]: (~relation(X0)|~relation(X1)|relation(set_union2(X0,X1)))),
% 0.19/0.51 inference(cnf_transformation,[status(esa)],[f122])).
% 0.19/0.51 fof(f127,plain,(
% 0.19/0.51 ![A]: (~ordinal(A)|(((~empty(succ(A))&epsilon_transitive(succ(A)))&epsilon_connected(succ(A)))&ordinal(succ(A))))),
% 0.19/0.51 inference(pre_NNF_transformation,[status(esa)],[f22])).
% 0.19/0.51 fof(f129,plain,(
% 0.19/0.51 ![X0]: (~ordinal(X0)|epsilon_transitive(succ(X0)))),
% 0.19/0.51 inference(cnf_transformation,[status(esa)],[f127])).
% 0.19/0.51 fof(f131,plain,(
% 0.19/0.51 ![X0]: (~ordinal(X0)|ordinal(succ(X0)))),
% 0.19/0.51 inference(cnf_transformation,[status(esa)],[f127])).
% 0.19/0.51 fof(f142,plain,(
% 0.19/0.51 ((epsilon_transitive(sk0_5)&epsilon_connected(sk0_5))&ordinal(sk0_5))),
% 0.19/0.51 inference(skolemization,[status(esa)],[f27])).
% 0.19/0.51 fof(f143,plain,(
% 0.19/0.51 epsilon_transitive(sk0_5)),
% 0.19/0.51 inference(cnf_transformation,[status(esa)],[f142])).
% 0.19/0.51 fof(f144,plain,(
% 0.19/0.51 epsilon_connected(sk0_5)),
% 0.19/0.51 inference(cnf_transformation,[status(esa)],[f142])).
% 0.19/0.51 fof(f146,plain,(
% 0.19/0.51 (empty(sk0_6)&relation(sk0_6))),
% 0.19/0.51 inference(skolemization,[status(esa)],[f28])).
% 0.19/0.51 fof(f147,plain,(
% 0.19/0.51 empty(sk0_6)),
% 0.19/0.51 inference(cnf_transformation,[status(esa)],[f146])).
% 0.19/0.51 fof(f149,plain,(
% 0.19/0.51 empty(sk0_7)),
% 0.19/0.51 inference(skolemization,[status(esa)],[f29])).
% 0.19/0.51 fof(f150,plain,(
% 0.19/0.51 empty(sk0_7)),
% 0.19/0.51 inference(cnf_transformation,[status(esa)],[f149])).
% 0.19/0.51 fof(f151,plain,(
% 0.19/0.51 ((relation(sk0_8)&empty(sk0_8))&function(sk0_8))),
% 0.19/0.51 inference(skolemization,[status(esa)],[f30])).
% 0.19/0.51 fof(f153,plain,(
% 0.19/0.51 empty(sk0_8)),
% 0.19/0.51 inference(cnf_transformation,[status(esa)],[f151])).
% 0.19/0.51 fof(f154,plain,(
% 0.19/0.51 function(sk0_8)),
% 0.19/0.51 inference(cnf_transformation,[status(esa)],[f151])).
% 0.19/0.51 fof(f155,plain,(
% 0.19/0.51 ((((((relation(sk0_9)&function(sk0_9))&one_to_one(sk0_9))&empty(sk0_9))&epsilon_transitive(sk0_9))&epsilon_connected(sk0_9))&ordinal(sk0_9))),
% 0.19/0.51 inference(skolemization,[status(esa)],[f31])).
% 0.19/0.51 fof(f157,plain,(
% 0.19/0.51 function(sk0_9)),
% 0.19/0.51 inference(cnf_transformation,[status(esa)],[f155])).
% 0.19/0.51 fof(f159,plain,(
% 0.19/0.51 empty(sk0_9)),
% 0.19/0.51 inference(cnf_transformation,[status(esa)],[f155])).
% 0.19/0.51 fof(f160,plain,(
% 0.19/0.51 epsilon_transitive(sk0_9)),
% 0.19/0.51 inference(cnf_transformation,[status(esa)],[f155])).
% 0.19/0.51 fof(f161,plain,(
% 0.19/0.51 epsilon_connected(sk0_9)),
% 0.19/0.51 inference(cnf_transformation,[status(esa)],[f155])).
% 0.19/0.51 fof(f162,plain,(
% 0.19/0.51 ordinal(sk0_9)),
% 0.19/0.51 inference(cnf_transformation,[status(esa)],[f155])).
% 0.19/0.51 fof(f172,plain,(
% 0.19/0.51 (((~empty(sk0_13)&epsilon_transitive(sk0_13))&epsilon_connected(sk0_13))&ordinal(sk0_13))),
% 0.19/0.51 inference(skolemization,[status(esa)],[f35])).
% 0.19/0.51 fof(f174,plain,(
% 0.19/0.51 epsilon_transitive(sk0_13)),
% 0.19/0.51 inference(cnf_transformation,[status(esa)],[f172])).
% 0.19/0.51 fof(f175,plain,(
% 0.19/0.51 epsilon_connected(sk0_13)),
% 0.19/0.51 inference(cnf_transformation,[status(esa)],[f172])).
% 0.19/0.51 fof(f188,plain,(
% 0.19/0.51 ![A,B]: ((~ordinal(A)|~ordinal(B))|(ordinal_subset(A,B)<=>subset(A,B)))),
% 0.19/0.51 inference(pre_NNF_transformation,[status(esa)],[f39])).
% 0.19/0.51 fof(f189,plain,(
% 0.19/0.51 ![A,B]: ((~ordinal(A)|~ordinal(B))|((~ordinal_subset(A,B)|subset(A,B))&(ordinal_subset(A,B)|~subset(A,B))))),
% 0.19/0.51 inference(NNF_transformation,[status(esa)],[f188])).
% 0.19/0.51 fof(f190,plain,(
% 0.19/0.51 ![X0,X1]: (~ordinal(X0)|~ordinal(X1)|~ordinal_subset(X0,X1)|subset(X0,X1))),
% 0.19/0.51 inference(cnf_transformation,[status(esa)],[f189])).
% 0.19/0.51 fof(f191,plain,(
% 0.19/0.51 ![X0,X1]: (~ordinal(X0)|~ordinal(X1)|ordinal_subset(X0,X1)|~subset(X0,X1))),
% 0.19/0.51 inference(cnf_transformation,[status(esa)],[f189])).
% 0.19/0.51 fof(f192,plain,(
% 0.19/0.51 ![A,B]: ((~ordinal(A)|~ordinal(B))|ordinal_subset(A,A))),
% 0.19/0.51 inference(pre_NNF_transformation,[status(esa)],[f40])).
% 0.19/0.51 fof(f193,plain,(
% 0.19/0.51 ![A]: ((~ordinal(A)|(![B]: ~ordinal(B)))|ordinal_subset(A,A))),
% 0.19/0.51 inference(miniscoping,[status(esa)],[f192])).
% 0.19/0.51 fof(f194,plain,(
% 0.19/0.51 ![X0,X1]: (~ordinal(X0)|~ordinal(X1)|ordinal_subset(X0,X0))),
% 0.19/0.51 inference(cnf_transformation,[status(esa)],[f193])).
% 0.19/0.51 fof(f197,plain,(
% 0.19/0.51 ![X0]: (in(X0,succ(X0)))),
% 0.19/0.51 inference(cnf_transformation,[status(esa)],[f42])).
% 0.19/0.51 fof(f198,plain,(
% 0.19/0.51 ![X0]: (~X0=succ(X0))),
% 0.19/0.51 inference(cnf_transformation,[status(esa)],[f43])).
% 0.19/0.51 fof(f199,plain,(
% 0.19/0.51 ![X0]: (set_union2(X0,empty_set)=X0)),
% 0.19/0.51 inference(cnf_transformation,[status(esa)],[f44])).
% 0.19/0.51 fof(f202,plain,(
% 0.19/0.51 ![A]: (~ordinal(A)|(![B]: (~ordinal(B)|((in(A,B)|A=B)|in(B,A)))))),
% 0.19/0.51 inference(pre_NNF_transformation,[status(esa)],[f46])).
% 0.19/0.51 fof(f203,plain,(
% 0.19/0.51 ![X0,X1]: (~ordinal(X0)|~ordinal(X1)|in(X0,X1)|X0=X1|in(X1,X0))),
% 0.19/0.51 inference(cnf_transformation,[status(esa)],[f202])).
% 0.19/0.51 fof(f204,plain,(
% 0.19/0.51 ![A,B]: (~element(A,B)|(empty(B)|in(A,B)))),
% 0.19/0.51 inference(pre_NNF_transformation,[status(esa)],[f47])).
% 0.19/0.51 fof(f205,plain,(
% 0.19/0.51 ![X0,X1]: (~element(X0,X1)|empty(X1)|in(X0,X1))),
% 0.19/0.51 inference(cnf_transformation,[status(esa)],[f204])).
% 0.19/0.51 fof(f206,plain,(
% 0.19/0.51 (?[A]: (ordinal(A)&(?[B]: (ordinal(B)&(in(A,succ(B))<~>ordinal_subset(A,B))))))),
% 0.19/0.51 inference(pre_NNF_transformation,[status(esa)],[f49])).
% 0.19/0.51 fof(f207,plain,(
% 0.19/0.51 ?[A]: (ordinal(A)&(?[B]: (ordinal(B)&((in(A,succ(B))|ordinal_subset(A,B))&(~in(A,succ(B))|~ordinal_subset(A,B))))))),
% 0.19/0.51 inference(NNF_transformation,[status(esa)],[f206])).
% 0.19/0.51 fof(f208,plain,(
% 0.19/0.51 (ordinal(sk0_17)&(ordinal(sk0_18)&((in(sk0_17,succ(sk0_18))|ordinal_subset(sk0_17,sk0_18))&(~in(sk0_17,succ(sk0_18))|~ordinal_subset(sk0_17,sk0_18)))))),
% 0.19/0.51 inference(skolemization,[status(esa)],[f207])).
% 0.19/0.51 fof(f209,plain,(
% 0.19/0.51 ordinal(sk0_17)),
% 0.19/0.51 inference(cnf_transformation,[status(esa)],[f208])).
% 0.19/0.51 fof(f210,plain,(
% 0.19/0.51 ordinal(sk0_18)),
% 0.19/0.51 inference(cnf_transformation,[status(esa)],[f208])).
% 0.19/0.51 fof(f211,plain,(
% 0.19/0.51 in(sk0_17,succ(sk0_18))|ordinal_subset(sk0_17,sk0_18)),
% 0.19/0.51 inference(cnf_transformation,[status(esa)],[f208])).
% 0.19/0.51 fof(f212,plain,(
% 0.19/0.51 ~in(sk0_17,succ(sk0_18))|~ordinal_subset(sk0_17,sk0_18)),
% 0.19/0.51 inference(cnf_transformation,[status(esa)],[f208])).
% 0.19/0.51 fof(f225,plain,(
% 0.19/0.51 ![A,B]: (~in(A,B)|~empty(B))),
% 0.19/0.51 inference(pre_NNF_transformation,[status(esa)],[f54])).
% 0.19/0.51 fof(f226,plain,(
% 0.19/0.51 ![B]: ((![A]: ~in(A,B))|~empty(B))),
% 0.19/0.51 inference(miniscoping,[status(esa)],[f225])).
% 0.19/0.51 fof(f227,plain,(
% 0.19/0.51 ![X0,X1]: (~in(X0,X1)|~empty(X1))),
% 0.19/0.51 inference(cnf_transformation,[status(esa)],[f226])).
% 0.19/0.51 fof(f231,plain,(
% 0.19/0.51 spl0_0 <=> ~ordinal(X0)|ordinal_subset(X0,X0)),
% 0.19/0.51 introduced(split_symbol_definition)).
% 0.19/0.51 fof(f232,plain,(
% 0.19/0.51 ![X0]: (~ordinal(X0)|ordinal_subset(X0,X0)|~spl0_0)),
% 0.19/0.51 inference(component_clause,[status(thm)],[f231])).
% 0.19/0.51 fof(f234,plain,(
% 0.19/0.51 spl0_1 <=> ~ordinal(X1)),
% 0.19/0.51 introduced(split_symbol_definition)).
% 0.19/0.51 fof(f235,plain,(
% 0.19/0.51 ![X0]: (~ordinal(X0)|~spl0_1)),
% 0.19/0.51 inference(component_clause,[status(thm)],[f234])).
% 0.19/0.51 fof(f237,plain,(
% 0.19/0.51 spl0_0|spl0_1),
% 0.19/0.51 inference(split_clause,[status(thm)],[f194,f231,f234])).
% 0.19/0.51 fof(f238,plain,(
% 0.19/0.51 spl0_2 <=> in(sk0_17,succ(sk0_18))),
% 0.19/0.51 introduced(split_symbol_definition)).
% 0.19/0.51 fof(f239,plain,(
% 0.19/0.51 in(sk0_17,succ(sk0_18))|~spl0_2),
% 0.19/0.51 inference(component_clause,[status(thm)],[f238])).
% 0.19/0.51 fof(f240,plain,(
% 0.19/0.51 ~in(sk0_17,succ(sk0_18))|spl0_2),
% 0.19/0.51 inference(component_clause,[status(thm)],[f238])).
% 0.19/0.51 fof(f241,plain,(
% 0.19/0.51 spl0_3 <=> ordinal_subset(sk0_17,sk0_18)),
% 0.19/0.51 introduced(split_symbol_definition)).
% 0.19/0.51 fof(f242,plain,(
% 0.19/0.51 ordinal_subset(sk0_17,sk0_18)|~spl0_3),
% 0.19/0.51 inference(component_clause,[status(thm)],[f241])).
% 0.19/0.51 fof(f243,plain,(
% 0.19/0.51 ~ordinal_subset(sk0_17,sk0_18)|spl0_3),
% 0.19/0.51 inference(component_clause,[status(thm)],[f241])).
% 0.19/0.51 fof(f244,plain,(
% 0.19/0.51 spl0_2|spl0_3),
% 0.19/0.51 inference(split_clause,[status(thm)],[f211,f238,f241])).
% 0.19/0.51 fof(f245,plain,(
% 0.19/0.51 ~spl0_2|~spl0_3),
% 0.19/0.51 inference(split_clause,[status(thm)],[f212,f238,f241])).
% 0.19/0.51 fof(f246,plain,(
% 0.19/0.51 ![X0]: (subset(X0,X0))),
% 0.19/0.51 inference(destructive_equality_resolution,[status(esa)],[f80])).
% 0.19/0.51 fof(f248,plain,(
% 0.19/0.51 ![X0,X1]: (~in(X0,singleton(X1))|X0=X1)),
% 0.19/0.51 inference(destructive_equality_resolution,[status(esa)],[f87])).
% 0.19/0.51 fof(f249,plain,(
% 0.19/0.51 ![X0]: (in(X0,singleton(X0)))),
% 0.19/0.51 inference(destructive_equality_resolution,[status(esa)],[f88])).
% 0.19/0.51 fof(f250,plain,(
% 0.19/0.51 ![X0,X1,X2]: (~in(X0,set_union2(X1,X2))|in(X0,X1)|in(X0,X2))),
% 0.19/0.51 inference(destructive_equality_resolution,[status(esa)],[f101])).
% 0.19/0.51 fof(f251,plain,(
% 0.19/0.51 ![X0,X1,X2]: (in(X0,set_union2(X1,X2))|~in(X0,X1))),
% 0.19/0.51 inference(destructive_equality_resolution,[status(esa)],[f102])).
% 0.19/0.51 fof(f252,plain,(
% 0.19/0.51 ![X0,X1,X2]: (in(X0,set_union2(X1,X2))|~in(X0,X2))),
% 0.19/0.51 inference(destructive_equality_resolution,[status(esa)],[f103])).
% 0.19/0.51 fof(f253,plain,(
% 0.19/0.51 ![X0]: (~in(succ(X0),X0))),
% 0.19/0.51 inference(resolution,[status(thm)],[f197,f57])).
% 0.19/0.51 fof(f254,plain,(
% 0.19/0.51 ![X0,X1]: (~ordinal(X0)|~ordinal(X1)|subset(X0,X1)|~ordinal(X1)|~ordinal(X0)|ordinal_subset(X1,X0))),
% 0.19/0.51 inference(resolution,[status(thm)],[f190,f77])).
% 0.19/0.51 fof(f255,plain,(
% 0.19/0.51 ![X0,X1]: (~ordinal(X0)|~ordinal(X1)|subset(X0,X1)|ordinal_subset(X1,X0))),
% 0.19/0.51 inference(duplicate_literals_removal,[status(esa)],[f254])).
% 0.19/0.51 fof(f260,plain,(
% 0.19/0.51 epsilon_transitive(sk0_18)),
% 0.19/0.51 inference(resolution,[status(thm)],[f61,f210])).
% 0.19/0.51 fof(f261,plain,(
% 0.19/0.51 epsilon_transitive(sk0_17)),
% 0.19/0.51 inference(resolution,[status(thm)],[f61,f209])).
% 0.19/0.51 fof(f272,plain,(
% 0.19/0.51 ![X0]: (~empty(X0)|~function(X0)|one_to_one(X0))),
% 0.19/0.51 inference(forward_subsumption_resolution,[status(thm)],[f68,f64])).
% 0.19/0.51 fof(f273,plain,(
% 0.19/0.51 spl0_4 <=> empty(empty_set)),
% 0.19/0.51 introduced(split_symbol_definition)).
% 0.19/0.51 fof(f275,plain,(
% 0.19/0.51 ~empty(empty_set)|spl0_4),
% 0.19/0.51 inference(component_clause,[status(thm)],[f273])).
% 0.19/0.51 fof(f276,plain,(
% 0.19/0.51 spl0_5 <=> one_to_one(empty_set)),
% 0.19/0.51 introduced(split_symbol_definition)).
% 0.19/0.51 fof(f279,plain,(
% 0.19/0.51 ~empty(empty_set)|one_to_one(empty_set)),
% 0.19/0.51 inference(resolution,[status(thm)],[f272,f116])).
% 0.19/0.51 fof(f280,plain,(
% 0.19/0.51 ~spl0_4|spl0_5),
% 0.19/0.51 inference(split_clause,[status(thm)],[f279,f273,f276])).
% 0.19/0.51 fof(f281,plain,(
% 0.19/0.51 $false|spl0_4),
% 0.19/0.51 inference(forward_subsumption_resolution,[status(thm)],[f275,f109])).
% 0.19/0.51 fof(f282,plain,(
% 0.19/0.51 spl0_4),
% 0.19/0.51 inference(contradiction_clause,[status(thm)],[f281])).
% 0.19/0.51 fof(f283,plain,(
% 0.19/0.51 spl0_6 <=> ordinal(sk0_18)),
% 0.19/0.51 introduced(split_symbol_definition)).
% 0.19/0.51 fof(f285,plain,(
% 0.19/0.51 ~ordinal(sk0_18)|spl0_6),
% 0.19/0.51 inference(component_clause,[status(thm)],[f283])).
% 0.19/0.51 fof(f286,plain,(
% 0.19/0.51 spl0_7 <=> ordinal(sk0_17)),
% 0.19/0.51 introduced(split_symbol_definition)).
% 0.19/0.51 fof(f288,plain,(
% 0.19/0.51 ~ordinal(sk0_17)|spl0_7),
% 0.19/0.51 inference(component_clause,[status(thm)],[f286])).
% 0.19/0.51 fof(f289,plain,(
% 0.19/0.51 spl0_8 <=> ordinal_subset(sk0_18,sk0_17)),
% 0.19/0.51 introduced(split_symbol_definition)).
% 0.19/0.51 fof(f290,plain,(
% 0.19/0.51 ordinal_subset(sk0_18,sk0_17)|~spl0_8),
% 0.19/0.51 inference(component_clause,[status(thm)],[f289])).
% 0.19/0.51 fof(f291,plain,(
% 0.19/0.51 ~ordinal_subset(sk0_18,sk0_17)|spl0_8),
% 0.19/0.51 inference(component_clause,[status(thm)],[f289])).
% 0.19/0.51 fof(f292,plain,(
% 0.19/0.51 ~ordinal(sk0_18)|~ordinal(sk0_17)|ordinal_subset(sk0_18,sk0_17)|spl0_3),
% 0.19/0.51 inference(resolution,[status(thm)],[f243,f77])).
% 0.19/0.51 fof(f293,plain,(
% 0.19/0.51 ~spl0_6|~spl0_7|spl0_8|spl0_3),
% 0.19/0.51 inference(split_clause,[status(thm)],[f292,f283,f286,f289,f241])).
% 0.19/0.51 fof(f294,plain,(
% 0.19/0.51 spl0_9 <=> subset(sk0_17,sk0_18)),
% 0.19/0.51 introduced(split_symbol_definition)).
% 0.19/0.51 fof(f295,plain,(
% 0.19/0.51 subset(sk0_17,sk0_18)|~spl0_9),
% 0.19/0.51 inference(component_clause,[status(thm)],[f294])).
% 0.19/0.51 fof(f297,plain,(
% 0.19/0.51 ~ordinal(sk0_17)|~ordinal(sk0_18)|subset(sk0_17,sk0_18)|~spl0_3),
% 0.19/0.51 inference(resolution,[status(thm)],[f242,f190])).
% 0.19/0.51 fof(f298,plain,(
% 0.19/0.51 ~spl0_7|~spl0_6|spl0_9|~spl0_3),
% 0.19/0.51 inference(split_clause,[status(thm)],[f297,f286,f283,f294,f241])).
% 0.19/0.51 fof(f299,plain,(
% 0.19/0.51 $false|spl0_6),
% 0.19/0.51 inference(forward_subsumption_resolution,[status(thm)],[f285,f210])).
% 0.19/0.51 fof(f300,plain,(
% 0.19/0.51 spl0_6),
% 0.19/0.51 inference(contradiction_clause,[status(thm)],[f299])).
% 0.19/0.51 fof(f301,plain,(
% 0.19/0.51 $false|spl0_7),
% 0.19/0.51 inference(forward_subsumption_resolution,[status(thm)],[f288,f209])).
% 0.19/0.51 fof(f302,plain,(
% 0.19/0.51 spl0_7),
% 0.19/0.51 inference(contradiction_clause,[status(thm)],[f301])).
% 0.19/0.51 fof(f305,plain,(
% 0.19/0.51 spl0_10 <=> subset(sk0_18,sk0_17)),
% 0.19/0.51 introduced(split_symbol_definition)).
% 0.19/0.51 fof(f308,plain,(
% 0.19/0.51 ~ordinal(sk0_18)|~ordinal(sk0_17)|subset(sk0_18,sk0_17)|~spl0_8),
% 0.19/0.51 inference(resolution,[status(thm)],[f290,f190])).
% 0.19/0.51 fof(f309,plain,(
% 0.19/0.51 ~spl0_6|~spl0_7|spl0_10|~spl0_8),
% 0.19/0.51 inference(split_clause,[status(thm)],[f308,f283,f286,f305,f289])).
% 0.19/0.51 fof(f328,plain,(
% 0.19/0.51 spl0_11 <=> ordinal(succ(sk0_18))),
% 0.19/0.51 introduced(split_symbol_definition)).
% 0.19/0.51 fof(f329,plain,(
% 0.19/0.51 ordinal(succ(sk0_18))|~spl0_11),
% 0.19/0.51 inference(component_clause,[status(thm)],[f328])).
% 0.19/0.51 fof(f330,plain,(
% 0.19/0.51 ~ordinal(succ(sk0_18))|spl0_11),
% 0.19/0.51 inference(component_clause,[status(thm)],[f328])).
% 0.19/0.51 fof(f331,plain,(
% 0.19/0.51 spl0_12 <=> in(succ(sk0_18),sk0_17)),
% 0.19/0.51 introduced(split_symbol_definition)).
% 0.19/0.51 fof(f332,plain,(
% 0.19/0.51 in(succ(sk0_18),sk0_17)|~spl0_12),
% 0.19/0.51 inference(component_clause,[status(thm)],[f331])).
% 0.19/0.51 fof(f334,plain,(
% 0.19/0.51 spl0_13 <=> succ(sk0_18)=sk0_17),
% 0.19/0.51 introduced(split_symbol_definition)).
% 0.19/0.51 fof(f335,plain,(
% 0.19/0.51 succ(sk0_18)=sk0_17|~spl0_13),
% 0.19/0.51 inference(component_clause,[status(thm)],[f334])).
% 0.19/0.51 fof(f337,plain,(
% 0.19/0.51 ~ordinal(succ(sk0_18))|~ordinal(sk0_17)|in(succ(sk0_18),sk0_17)|succ(sk0_18)=sk0_17|spl0_2),
% 0.19/0.51 inference(resolution,[status(thm)],[f240,f203])).
% 0.19/0.51 fof(f338,plain,(
% 0.19/0.51 ~spl0_11|~spl0_7|spl0_12|spl0_13|spl0_2),
% 0.19/0.51 inference(split_clause,[status(thm)],[f337,f328,f286,f331,f334,f238])).
% 0.19/0.51 fof(f339,plain,(
% 0.19/0.51 ~ordinal(sk0_18)|spl0_11),
% 0.19/0.51 inference(resolution,[status(thm)],[f330,f131])).
% 0.19/0.51 fof(f340,plain,(
% 0.19/0.51 ~spl0_6|spl0_11),
% 0.19/0.51 inference(split_clause,[status(thm)],[f339,f283,f328])).
% 0.19/0.51 fof(f342,plain,(
% 0.19/0.51 epsilon_transitive(succ(sk0_18))|~spl0_11),
% 0.19/0.51 inference(resolution,[status(thm)],[f329,f61])).
% 0.19/0.51 fof(f353,plain,(
% 0.19/0.51 spl0_16 <=> epsilon_transitive(sk0_5)),
% 0.19/0.51 introduced(split_symbol_definition)).
% 0.19/0.51 fof(f355,plain,(
% 0.19/0.51 ~epsilon_transitive(sk0_5)|spl0_16),
% 0.19/0.51 inference(component_clause,[status(thm)],[f353])).
% 0.19/0.51 fof(f356,plain,(
% 0.19/0.51 spl0_17 <=> ordinal(sk0_5)),
% 0.19/0.51 introduced(split_symbol_definition)).
% 0.19/0.51 fof(f359,plain,(
% 0.19/0.51 ~epsilon_transitive(sk0_5)|ordinal(sk0_5)),
% 0.19/0.51 inference(resolution,[status(thm)],[f70,f144])).
% 0.19/0.51 fof(f360,plain,(
% 0.19/0.51 ~spl0_16|spl0_17),
% 0.19/0.51 inference(split_clause,[status(thm)],[f359,f353,f356])).
% 0.19/0.51 fof(f361,plain,(
% 0.19/0.51 spl0_18 <=> epsilon_transitive(sk0_17)),
% 0.19/0.51 introduced(split_symbol_definition)).
% 0.19/0.51 fof(f363,plain,(
% 0.19/0.51 ~epsilon_transitive(sk0_17)|spl0_18),
% 0.19/0.51 inference(component_clause,[status(thm)],[f361])).
% 0.19/0.51 fof(f366,plain,(
% 0.19/0.51 spl0_19 <=> epsilon_transitive(sk0_18)),
% 0.19/0.51 introduced(split_symbol_definition)).
% 0.19/0.51 fof(f368,plain,(
% 0.19/0.51 ~epsilon_transitive(sk0_18)|spl0_19),
% 0.19/0.51 inference(component_clause,[status(thm)],[f366])).
% 0.19/0.51 fof(f371,plain,(
% 0.19/0.51 spl0_20 <=> epsilon_transitive(succ(sk0_18))),
% 0.19/0.51 introduced(split_symbol_definition)).
% 0.19/0.51 fof(f373,plain,(
% 0.19/0.51 ~epsilon_transitive(succ(sk0_18))|spl0_20),
% 0.19/0.51 inference(component_clause,[status(thm)],[f371])).
% 0.19/0.51 fof(f377,plain,(
% 0.19/0.51 spl0_21 <=> epsilon_transitive(empty_set)),
% 0.19/0.51 introduced(split_symbol_definition)).
% 0.19/0.51 fof(f379,plain,(
% 0.19/0.51 ~epsilon_transitive(empty_set)|spl0_21),
% 0.19/0.51 inference(component_clause,[status(thm)],[f377])).
% 0.19/0.51 fof(f380,plain,(
% 0.19/0.51 spl0_22 <=> ordinal(empty_set)),
% 0.19/0.51 introduced(split_symbol_definition)).
% 0.19/0.51 fof(f383,plain,(
% 0.19/0.51 ~epsilon_transitive(empty_set)|ordinal(empty_set)),
% 0.19/0.51 inference(resolution,[status(thm)],[f70,f120])).
% 0.19/0.51 fof(f384,plain,(
% 0.19/0.51 ~spl0_21|spl0_22),
% 0.19/0.51 inference(split_clause,[status(thm)],[f383,f377,f380])).
% 0.19/0.51 fof(f385,plain,(
% 0.19/0.51 $false|spl0_21),
% 0.19/0.51 inference(forward_subsumption_resolution,[status(thm)],[f379,f119])).
% 0.19/0.51 fof(f386,plain,(
% 0.19/0.51 spl0_21),
% 0.19/0.51 inference(contradiction_clause,[status(thm)],[f385])).
% 0.19/0.51 fof(f387,plain,(
% 0.19/0.51 $false|spl0_16),
% 0.19/0.51 inference(forward_subsumption_resolution,[status(thm)],[f355,f143])).
% 0.19/0.51 fof(f388,plain,(
% 0.19/0.51 spl0_16),
% 0.19/0.51 inference(contradiction_clause,[status(thm)],[f387])).
% 0.19/0.51 fof(f394,plain,(
% 0.19/0.51 function(sk0_6)),
% 0.19/0.51 inference(resolution,[status(thm)],[f147,f59])).
% 0.19/0.51 fof(f395,plain,(
% 0.19/0.51 ordinal(sk0_6)),
% 0.19/0.51 inference(resolution,[status(thm)],[f147,f74])).
% 0.19/0.51 fof(f396,plain,(
% 0.19/0.51 epsilon_connected(sk0_6)),
% 0.19/0.51 inference(resolution,[status(thm)],[f395,f62])).
% 0.19/0.51 fof(f397,plain,(
% 0.19/0.51 epsilon_transitive(sk0_6)),
% 0.19/0.51 inference(resolution,[status(thm)],[f395,f61])).
% 0.19/0.51 fof(f398,plain,(
% 0.19/0.51 spl0_23 <=> epsilon_transitive(sk0_6)),
% 0.19/0.51 introduced(split_symbol_definition)).
% 0.19/0.51 fof(f400,plain,(
% 0.19/0.51 ~epsilon_transitive(sk0_6)|spl0_23),
% 0.19/0.51 inference(component_clause,[status(thm)],[f398])).
% 0.19/0.51 fof(f401,plain,(
% 0.19/0.51 spl0_24 <=> ordinal(sk0_6)),
% 0.19/0.51 introduced(split_symbol_definition)).
% 0.19/0.51 fof(f404,plain,(
% 0.19/0.51 ~epsilon_transitive(sk0_6)|ordinal(sk0_6)),
% 0.19/0.51 inference(resolution,[status(thm)],[f396,f70])).
% 0.19/0.51 fof(f405,plain,(
% 0.19/0.51 ~spl0_23|spl0_24),
% 0.19/0.51 inference(split_clause,[status(thm)],[f404,f398,f401])).
% 0.19/0.51 fof(f409,plain,(
% 0.19/0.51 function(sk0_7)),
% 0.19/0.51 inference(resolution,[status(thm)],[f150,f59])).
% 0.19/0.51 fof(f410,plain,(
% 0.19/0.51 ordinal(sk0_7)),
% 0.19/0.51 inference(resolution,[status(thm)],[f150,f74])).
% 0.19/0.51 fof(f411,plain,(
% 0.19/0.51 epsilon_connected(sk0_7)),
% 0.19/0.51 inference(resolution,[status(thm)],[f410,f62])).
% 0.19/0.51 fof(f412,plain,(
% 0.19/0.51 epsilon_transitive(sk0_7)),
% 0.19/0.51 inference(resolution,[status(thm)],[f410,f61])).
% 0.19/0.51 fof(f413,plain,(
% 0.19/0.51 spl0_25 <=> epsilon_transitive(sk0_7)),
% 0.19/0.51 introduced(split_symbol_definition)).
% 0.19/0.51 fof(f415,plain,(
% 0.19/0.51 ~epsilon_transitive(sk0_7)|spl0_25),
% 0.19/0.51 inference(component_clause,[status(thm)],[f413])).
% 0.19/0.51 fof(f416,plain,(
% 0.19/0.51 spl0_26 <=> ordinal(sk0_7)),
% 0.19/0.51 introduced(split_symbol_definition)).
% 0.19/0.51 fof(f419,plain,(
% 0.19/0.51 ~epsilon_transitive(sk0_7)|ordinal(sk0_7)),
% 0.19/0.51 inference(resolution,[status(thm)],[f411,f70])).
% 0.19/0.51 fof(f420,plain,(
% 0.19/0.51 ~spl0_25|spl0_26),
% 0.19/0.51 inference(split_clause,[status(thm)],[f419,f413,f416])).
% 0.19/0.51 fof(f425,plain,(
% 0.19/0.51 ordinal(sk0_8)),
% 0.19/0.51 inference(resolution,[status(thm)],[f153,f74])).
% 0.19/0.51 fof(f426,plain,(
% 0.19/0.51 epsilon_connected(sk0_8)),
% 0.19/0.51 inference(resolution,[status(thm)],[f425,f62])).
% 0.19/0.51 fof(f427,plain,(
% 0.19/0.51 epsilon_transitive(sk0_8)),
% 0.19/0.51 inference(resolution,[status(thm)],[f425,f61])).
% 0.19/0.51 fof(f428,plain,(
% 0.19/0.51 spl0_27 <=> epsilon_transitive(sk0_8)),
% 0.19/0.51 introduced(split_symbol_definition)).
% 0.19/0.51 fof(f430,plain,(
% 0.19/0.51 ~epsilon_transitive(sk0_8)|spl0_27),
% 0.19/0.51 inference(component_clause,[status(thm)],[f428])).
% 0.19/0.51 fof(f431,plain,(
% 0.19/0.51 spl0_28 <=> ordinal(sk0_8)),
% 0.19/0.51 introduced(split_symbol_definition)).
% 0.19/0.51 fof(f434,plain,(
% 0.19/0.51 ~epsilon_transitive(sk0_8)|ordinal(sk0_8)),
% 0.19/0.51 inference(resolution,[status(thm)],[f426,f70])).
% 0.19/0.51 fof(f435,plain,(
% 0.19/0.51 ~spl0_27|spl0_28),
% 0.19/0.51 inference(split_clause,[status(thm)],[f434,f428,f431])).
% 0.19/0.51 fof(f436,plain,(
% 0.19/0.51 spl0_29 <=> empty(sk0_8)),
% 0.19/0.51 introduced(split_symbol_definition)).
% 0.19/0.51 fof(f438,plain,(
% 0.19/0.51 ~empty(sk0_8)|spl0_29),
% 0.19/0.51 inference(component_clause,[status(thm)],[f436])).
% 0.19/0.51 fof(f439,plain,(
% 0.19/0.51 spl0_30 <=> one_to_one(sk0_8)),
% 0.19/0.51 introduced(split_symbol_definition)).
% 0.19/0.51 fof(f442,plain,(
% 0.19/0.51 ~empty(sk0_8)|one_to_one(sk0_8)),
% 0.19/0.51 inference(resolution,[status(thm)],[f154,f272])).
% 0.19/0.51 fof(f443,plain,(
% 0.19/0.51 ~spl0_29|spl0_30),
% 0.19/0.51 inference(split_clause,[status(thm)],[f442,f436,f439])).
% 0.19/0.51 fof(f444,plain,(
% 0.19/0.51 $false|spl0_29),
% 0.19/0.51 inference(forward_subsumption_resolution,[status(thm)],[f438,f153])).
% 0.19/0.51 fof(f445,plain,(
% 0.19/0.51 spl0_29),
% 0.19/0.51 inference(contradiction_clause,[status(thm)],[f444])).
% 0.19/0.51 fof(f446,plain,(
% 0.19/0.51 spl0_31 <=> sk0_18=sk0_17),
% 0.19/0.51 introduced(split_symbol_definition)).
% 0.19/0.51 fof(f447,plain,(
% 0.19/0.51 sk0_18=sk0_17|~spl0_31),
% 0.19/0.51 inference(component_clause,[status(thm)],[f446])).
% 0.19/0.51 fof(f448,plain,(
% 0.19/0.51 ~sk0_18=sk0_17|spl0_31),
% 0.19/0.51 inference(component_clause,[status(thm)],[f446])).
% 0.19/0.51 fof(f449,plain,(
% 0.19/0.51 sk0_18=sk0_17|~subset(sk0_18,sk0_17)|~spl0_9),
% 0.19/0.51 inference(resolution,[status(thm)],[f82,f295])).
% 0.19/0.51 fof(f450,plain,(
% 0.19/0.51 spl0_31|~spl0_10|~spl0_9),
% 0.19/0.51 inference(split_clause,[status(thm)],[f449,f446,f305,f294])).
% 0.19/0.51 fof(f454,plain,(
% 0.19/0.51 spl0_32 <=> empty(sk0_9)),
% 0.19/0.51 introduced(split_symbol_definition)).
% 0.19/0.51 fof(f456,plain,(
% 0.19/0.51 ~empty(sk0_9)|spl0_32),
% 0.19/0.51 inference(component_clause,[status(thm)],[f454])).
% 0.19/0.51 fof(f457,plain,(
% 0.19/0.51 spl0_33 <=> one_to_one(sk0_9)),
% 0.19/0.51 introduced(split_symbol_definition)).
% 0.19/0.51 fof(f460,plain,(
% 0.19/0.51 ~empty(sk0_9)|one_to_one(sk0_9)),
% 0.19/0.51 inference(resolution,[status(thm)],[f157,f272])).
% 0.19/0.51 fof(f461,plain,(
% 0.19/0.51 ~spl0_32|spl0_33),
% 0.19/0.51 inference(split_clause,[status(thm)],[f460,f454,f457])).
% 0.19/0.51 fof(f467,plain,(
% 0.19/0.51 spl0_34 <=> epsilon_transitive(sk0_9)),
% 0.19/0.51 introduced(split_symbol_definition)).
% 0.19/0.51 fof(f469,plain,(
% 0.19/0.51 ~epsilon_transitive(sk0_9)|spl0_34),
% 0.19/0.51 inference(component_clause,[status(thm)],[f467])).
% 0.19/0.51 fof(f470,plain,(
% 0.19/0.51 spl0_35 <=> ordinal(sk0_9)),
% 0.19/0.51 introduced(split_symbol_definition)).
% 0.19/0.51 fof(f473,plain,(
% 0.19/0.51 ~epsilon_transitive(sk0_9)|ordinal(sk0_9)),
% 0.19/0.51 inference(resolution,[status(thm)],[f161,f70])).
% 0.19/0.51 fof(f474,plain,(
% 0.19/0.51 ~spl0_34|spl0_35),
% 0.19/0.51 inference(split_clause,[status(thm)],[f473,f467,f470])).
% 0.19/0.51 fof(f475,plain,(
% 0.19/0.51 $false|spl0_34),
% 0.19/0.51 inference(forward_subsumption_resolution,[status(thm)],[f469,f160])).
% 0.19/0.51 fof(f476,plain,(
% 0.19/0.51 spl0_34),
% 0.19/0.51 inference(contradiction_clause,[status(thm)],[f475])).
% 0.19/0.51 fof(f487,plain,(
% 0.19/0.51 ![X0,X1]: (X0=X1|~ordinal(singleton(X1))|~ordinal(X0)|in(singleton(X1),X0)|singleton(X1)=X0)),
% 0.19/0.51 inference(resolution,[status(thm)],[f248,f203])).
% 0.19/0.51 fof(f488,plain,(
% 0.19/0.51 ![X0]: (~in(singleton(X0),X0))),
% 0.19/0.51 inference(resolution,[status(thm)],[f249,f57])).
% 0.19/0.51 fof(f497,plain,(
% 0.19/0.51 ~ordinal_subset(sk0_17,sk0_17)|~spl0_31|spl0_3),
% 0.19/0.51 inference(forward_demodulation,[status(thm)],[f447,f243])).
% 0.19/0.51 fof(f498,plain,(
% 0.19/0.51 ~ordinal(sk0_17)|~spl0_31|spl0_3|~spl0_0),
% 0.19/0.51 inference(resolution,[status(thm)],[f497,f232])).
% 0.19/0.51 fof(f499,plain,(
% 0.19/0.51 ~spl0_7|~spl0_31|spl0_3|~spl0_0),
% 0.19/0.51 inference(split_clause,[status(thm)],[f498,f286,f446,f241,f231])).
% 0.19/0.51 fof(f505,plain,(
% 0.19/0.51 in(succ(sk0_17),sk0_17)|~spl0_31|~spl0_12),
% 0.19/0.51 inference(forward_demodulation,[status(thm)],[f447,f332])).
% 0.19/0.51 fof(f506,plain,(
% 0.19/0.51 $false|~spl0_31|~spl0_12),
% 0.19/0.51 inference(forward_subsumption_resolution,[status(thm)],[f505,f253])).
% 0.19/0.51 fof(f507,plain,(
% 0.19/0.51 ~spl0_31|~spl0_12),
% 0.19/0.51 inference(contradiction_clause,[status(thm)],[f506])).
% 0.19/0.51 fof(f518,plain,(
% 0.19/0.51 $false|~spl0_1),
% 0.19/0.51 inference(backward_subsumption_resolution,[status(thm)],[f162,f235])).
% 0.19/0.51 fof(f519,plain,(
% 0.19/0.51 ~spl0_1),
% 0.19/0.51 inference(contradiction_clause,[status(thm)],[f518])).
% 0.19/0.51 fof(f520,plain,(
% 0.19/0.51 $false|spl0_23),
% 0.19/0.51 inference(forward_subsumption_resolution,[status(thm)],[f400,f397])).
% 0.19/0.51 fof(f521,plain,(
% 0.19/0.51 spl0_23),
% 0.19/0.51 inference(contradiction_clause,[status(thm)],[f520])).
% 0.19/0.51 fof(f522,plain,(
% 0.19/0.51 $false|spl0_25),
% 0.19/0.51 inference(forward_subsumption_resolution,[status(thm)],[f415,f412])).
% 0.19/0.51 fof(f523,plain,(
% 0.19/0.51 spl0_25),
% 0.19/0.51 inference(contradiction_clause,[status(thm)],[f522])).
% 0.19/0.51 fof(f524,plain,(
% 0.19/0.51 $false|spl0_27),
% 0.19/0.51 inference(forward_subsumption_resolution,[status(thm)],[f430,f427])).
% 0.19/0.51 fof(f525,plain,(
% 0.19/0.51 spl0_27),
% 0.19/0.51 inference(contradiction_clause,[status(thm)],[f524])).
% 0.19/0.51 fof(f530,plain,(
% 0.19/0.51 $false|spl0_32),
% 0.19/0.51 inference(forward_subsumption_resolution,[status(thm)],[f456,f159])).
% 0.19/0.51 fof(f531,plain,(
% 0.19/0.51 spl0_32),
% 0.19/0.51 inference(contradiction_clause,[status(thm)],[f530])).
% 0.19/0.51 fof(f561,plain,(
% 0.19/0.51 ordinal(empty_set)),
% 0.19/0.51 inference(resolution,[status(thm)],[f74,f109])).
% 0.19/0.51 fof(f580,plain,(
% 0.19/0.51 ![X0,X1]: (singleton(X0)=X1|~ordinal(singleton(X1))|~ordinal(singleton(X0))|singleton(X1)=singleton(X0)|singleton(X1)=X0)),
% 0.19/0.51 inference(resolution,[status(thm)],[f487,f248])).
% 0.19/0.51 fof(f582,plain,(
% 0.19/0.51 ![X0,X1]: (singleton(X0)=X1|~ordinal(singleton(X1))|~ordinal(singleton(X0))|~singleton(X0)=X0|singleton(X1)=X0)),
% 0.19/0.51 inference(equality_factoring,[status(esa)],[f580])).
% 0.19/0.51 fof(f585,plain,(
% 0.19/0.51 ![X0,X1]: (singleton(sk0_0(X0,singleton(X1)))=X1|~ordinal(singleton(X1))|~ordinal(singleton(sk0_0(X0,singleton(X1))))|~singleton(sk0_0(X0,singleton(X1)))=sk0_0(X0,singleton(X1))|X0=singleton(singleton(X1))|~in(sk0_0(X0,singleton(X1)),X0))),
% 0.19/0.51 inference(resolution,[status(thm)],[f582,f89])).
% 0.19/0.51 fof(f603,plain,(
% 0.19/0.51 ![X0,X1]: (X0=singleton(X1)|sk0_0(X0,X1)=X1|~in(X0,sk0_0(X0,X1)))),
% 0.19/0.51 inference(resolution,[status(thm)],[f90,f57])).
% 0.19/0.51 fof(f605,plain,(
% 0.19/0.51 ![X0,X1]: (~epsilon_transitive(X0)|subset(singleton(X1),X0)|X0=X1|~ordinal(singleton(X1))|~ordinal(X0)|singleton(X1)=X0)),
% 0.19/0.51 inference(resolution,[status(thm)],[f95,f487])).
% 0.19/0.51 fof(f608,plain,(
% 0.19/0.51 ![X0]: (~epsilon_transitive(singleton(X0))|subset(X0,singleton(X0)))),
% 0.19/0.51 inference(resolution,[status(thm)],[f95,f249])).
% 0.19/0.51 fof(f609,plain,(
% 0.19/0.51 ![X0]: (~epsilon_transitive(succ(X0))|subset(X0,succ(X0)))),
% 0.19/0.51 inference(resolution,[status(thm)],[f95,f197])).
% 0.19/0.51 fof(f610,plain,(
% 0.19/0.51 ![X0,X1]: (~epsilon_transitive(X0)|subset(X1,X0)|~ordinal(X0)|~ordinal(X1)|in(X0,X1)|X0=X1)),
% 0.19/0.51 inference(resolution,[status(thm)],[f95,f203])).
% 0.19/0.51 fof(f621,plain,(
% 0.19/0.51 $false|spl0_18),
% 0.19/0.51 inference(forward_subsumption_resolution,[status(thm)],[f363,f261])).
% 0.19/0.51 fof(f622,plain,(
% 0.19/0.51 spl0_18),
% 0.19/0.51 inference(contradiction_clause,[status(thm)],[f621])).
% 0.19/0.51 fof(f639,plain,(
% 0.19/0.51 ![X0]: (~epsilon_transitive(succ(X0))|~ordinal(X0)|~ordinal(succ(X0))|ordinal_subset(X0,succ(X0)))),
% 0.19/0.51 inference(resolution,[status(thm)],[f609,f191])).
% 0.19/0.51 fof(f640,plain,(
% 0.19/0.51 ![X0]: (~ordinal(X0)|~ordinal(succ(X0))|ordinal_subset(X0,succ(X0)))),
% 0.19/0.51 inference(forward_subsumption_resolution,[status(thm)],[f639,f129])).
% 0.19/0.51 fof(f645,plain,(
% 0.19/0.51 ![X0,X1]: (singleton(X0)=singleton(X1)|sk0_0(singleton(X0),X1)=X1|sk0_0(singleton(X0),X1)=X0|~ordinal(singleton(X0))|~ordinal(sk0_0(singleton(X0),X1))|singleton(X0)=sk0_0(singleton(X0),X1))),
% 0.19/0.51 inference(resolution,[status(thm)],[f603,f487])).
% 0.19/0.51 fof(f650,plain,(
% 0.19/0.51 spl0_50 <=> in(sk0_17,sk0_18)),
% 0.19/0.51 introduced(split_symbol_definition)).
% 0.19/0.51 fof(f651,plain,(
% 0.19/0.51 in(sk0_17,sk0_18)|~spl0_50),
% 0.19/0.51 inference(component_clause,[status(thm)],[f650])).
% 0.19/0.51 fof(f655,plain,(
% 0.19/0.51 ![X0,X1]: (~epsilon_transitive(X0)|~ordinal(X0)|~ordinal(X1)|in(X0,X1)|X0=X1|~ordinal(X1)|~ordinal(X0)|ordinal_subset(X1,X0))),
% 0.19/0.51 inference(resolution,[status(thm)],[f610,f191])).
% 0.19/0.51 fof(f656,plain,(
% 0.19/0.51 ![X0,X1]: (~epsilon_transitive(X0)|~ordinal(X0)|~ordinal(X1)|in(X0,X1)|X0=X1|ordinal_subset(X1,X0))),
% 0.19/0.51 inference(duplicate_literals_removal,[status(esa)],[f655])).
% 0.19/0.51 fof(f657,plain,(
% 0.19/0.51 ![X0,X1]: (~epsilon_transitive(X0)|~ordinal(X0)|~ordinal(X1)|in(X0,X1)|X0=X1|X0=X1|~subset(X0,X1))),
% 0.19/0.51 inference(resolution,[status(thm)],[f610,f82])).
% 0.19/0.51 fof(f658,plain,(
% 0.19/0.51 ![X0,X1]: (~epsilon_transitive(X0)|~ordinal(X0)|~ordinal(X1)|in(X0,X1)|X0=X1|~subset(X0,X1))),
% 0.19/0.51 inference(duplicate_literals_removal,[status(esa)],[f657])).
% 0.19/0.51 fof(f659,plain,(
% 0.19/0.51 ~epsilon_transitive(sk0_18)|subset(sk0_17,sk0_18)|~spl0_50),
% 0.19/0.51 inference(resolution,[status(thm)],[f651,f95])).
% 0.19/0.51 fof(f660,plain,(
% 0.19/0.51 ~spl0_19|spl0_9|~spl0_50),
% 0.19/0.51 inference(split_clause,[status(thm)],[f659,f366,f294,f650])).
% 0.19/0.51 fof(f664,plain,(
% 0.19/0.51 ![X0]: (~ordinal(X0)|ordinal_subset(X0,succ(X0)))),
% 0.19/0.51 inference(forward_subsumption_resolution,[status(thm)],[f640,f131])).
% 0.19/0.51 fof(f665,plain,(
% 0.19/0.51 ![X0]: (~ordinal(X0)|~ordinal(X0)|~ordinal(succ(X0))|subset(X0,succ(X0)))),
% 0.19/0.51 inference(resolution,[status(thm)],[f664,f190])).
% 0.19/0.51 fof(f666,plain,(
% 0.19/0.51 ![X0]: (~ordinal(X0)|~ordinal(succ(X0))|subset(X0,succ(X0)))),
% 0.19/0.51 inference(duplicate_literals_removal,[status(esa)],[f665])).
% 0.19/0.51 fof(f667,plain,(
% 0.19/0.51 ![X0]: (~ordinal(X0)|subset(X0,succ(X0)))),
% 0.19/0.51 inference(forward_subsumption_resolution,[status(thm)],[f666,f131])).
% 0.19/0.51 fof(f670,plain,(
% 0.19/0.51 ![X0]: (~ordinal(X0)|succ(X0)=X0|~subset(succ(X0),X0))),
% 0.19/0.51 inference(resolution,[status(thm)],[f667,f82])).
% 0.19/0.51 fof(f671,plain,(
% 0.19/0.51 ![X0]: (~ordinal(X0)|~subset(succ(X0),X0))),
% 0.19/0.51 inference(forward_subsumption_resolution,[status(thm)],[f670,f198])).
% 0.19/0.51 fof(f676,plain,(
% 0.19/0.51 ~epsilon_transitive(sk0_17)|~ordinal(sk0_17)|~ordinal(sk0_18)|in(sk0_17,sk0_18)|sk0_17=sk0_18|spl0_8),
% 0.19/0.51 inference(resolution,[status(thm)],[f656,f291])).
% 0.19/0.51 fof(f677,plain,(
% 0.19/0.51 ~spl0_18|~spl0_7|~spl0_6|spl0_50|spl0_31|spl0_8),
% 0.19/0.51 inference(split_clause,[status(thm)],[f676,f361,f286,f283,f650,f446,f289])).
% 0.19/0.51 fof(f720,plain,(
% 0.19/0.51 ![X0,X1]: (~epsilon_transitive(X0)|X0=X1|~ordinal(singleton(X1))|~ordinal(X0)|singleton(X1)=X0|X0=singleton(X1)|~subset(X0,singleton(X1)))),
% 0.19/0.51 inference(resolution,[status(thm)],[f605,f82])).
% 0.19/0.51 fof(f721,plain,(
% 0.19/0.51 ![X0,X1]: (~epsilon_transitive(X0)|X0=X1|~ordinal(singleton(X1))|~ordinal(X0)|singleton(X1)=X0|~subset(X0,singleton(X1)))),
% 0.19/0.51 inference(duplicate_literals_removal,[status(esa)],[f720])).
% 0.19/0.51 fof(f741,plain,(
% 0.19/0.51 spl0_51 <=> empty(sk0_6)),
% 0.19/0.51 introduced(split_symbol_definition)).
% 0.19/0.51 fof(f743,plain,(
% 0.19/0.51 ~empty(sk0_6)|spl0_51),
% 0.19/0.51 inference(component_clause,[status(thm)],[f741])).
% 0.19/0.51 fof(f744,plain,(
% 0.19/0.51 spl0_52 <=> one_to_one(sk0_6)),
% 0.19/0.51 introduced(split_symbol_definition)).
% 0.19/0.51 fof(f747,plain,(
% 0.19/0.51 ~empty(sk0_6)|one_to_one(sk0_6)),
% 0.19/0.51 inference(resolution,[status(thm)],[f394,f272])).
% 0.19/0.51 fof(f748,plain,(
% 0.19/0.51 ~spl0_51|spl0_52),
% 0.19/0.51 inference(split_clause,[status(thm)],[f747,f741,f744])).
% 0.19/0.51 fof(f749,plain,(
% 0.19/0.51 $false|spl0_51),
% 0.19/0.51 inference(forward_subsumption_resolution,[status(thm)],[f743,f147])).
% 0.19/0.51 fof(f750,plain,(
% 0.19/0.51 spl0_51),
% 0.19/0.51 inference(contradiction_clause,[status(thm)],[f749])).
% 0.19/0.51 fof(f751,plain,(
% 0.19/0.51 spl0_53 <=> empty(sk0_7)),
% 0.19/0.51 introduced(split_symbol_definition)).
% 0.19/0.51 fof(f753,plain,(
% 0.19/0.51 ~empty(sk0_7)|spl0_53),
% 0.19/0.51 inference(component_clause,[status(thm)],[f751])).
% 0.19/0.51 fof(f754,plain,(
% 0.19/0.51 spl0_54 <=> one_to_one(sk0_7)),
% 0.19/0.51 introduced(split_symbol_definition)).
% 0.19/0.51 fof(f757,plain,(
% 0.19/0.51 ~empty(sk0_7)|one_to_one(sk0_7)),
% 0.19/0.51 inference(resolution,[status(thm)],[f409,f272])).
% 0.19/0.51 fof(f758,plain,(
% 0.19/0.51 ~spl0_53|spl0_54),
% 0.19/0.51 inference(split_clause,[status(thm)],[f757,f751,f754])).
% 0.19/0.51 fof(f759,plain,(
% 0.19/0.51 $false|spl0_53),
% 0.19/0.51 inference(forward_subsumption_resolution,[status(thm)],[f753,f150])).
% 0.19/0.51 fof(f760,plain,(
% 0.19/0.51 spl0_53),
% 0.19/0.51 inference(contradiction_clause,[status(thm)],[f759])).
% 0.19/0.51 fof(f764,plain,(
% 0.19/0.51 ![X0]: (set_union2(empty_set,X0)=X0)),
% 0.19/0.51 inference(paramodulation,[status(thm)],[f75,f199])).
% 0.19/0.51 fof(f795,plain,(
% 0.19/0.51 ![X0,X1,X2]: (in(X0,X1)|in(X0,X2)|~ordinal(set_union2(X1,X2))|~ordinal(X0)|in(set_union2(X1,X2),X0)|set_union2(X1,X2)=X0)),
% 0.19/0.51 inference(resolution,[status(thm)],[f250,f203])).
% 0.19/0.51 fof(f796,plain,(
% 0.19/0.51 ![X0,X1]: (~in(X0,succ(X1))|in(X0,X1)|in(X0,singleton(X1)))),
% 0.19/0.51 inference(paramodulation,[status(thm)],[f83,f250])).
% 0.19/0.51 fof(f802,plain,(
% 0.19/0.51 ![X0,X1,X2]: (~in(X0,X1)|~in(set_union2(X1,X2),X0))),
% 0.19/0.51 inference(resolution,[status(thm)],[f251,f57])).
% 0.19/0.51 fof(f806,plain,(
% 0.19/0.51 ![X0,X1]: (~in(singleton(set_union2(X0,X1)),X1))),
% 0.19/0.51 inference(resolution,[status(thm)],[f252,f488])).
% 0.19/0.51 fof(f807,plain,(
% 0.19/0.51 ![X0,X1]: (~in(succ(set_union2(X0,X1)),X1))),
% 0.19/0.51 inference(resolution,[status(thm)],[f252,f253])).
% 0.19/0.51 fof(f809,plain,(
% 0.19/0.51 ![X0,X1,X2]: (~in(X0,X1)|~in(set_union2(X2,X1),X0))),
% 0.19/0.51 inference(resolution,[status(thm)],[f252,f57])).
% 0.19/0.51 fof(f810,plain,(
% 0.19/0.51 ![X0,X1]: (in(X0,X1)|~in(X0,empty_set))),
% 0.19/0.51 inference(paramodulation,[status(thm)],[f199,f252])).
% 0.19/0.51 fof(f866,plain,(
% 0.19/0.51 ![X0]: (~in(singleton(X0),empty_set))),
% 0.19/0.51 inference(paramodulation,[status(thm)],[f199,f806])).
% 0.19/0.51 fof(f871,plain,(
% 0.19/0.51 spl0_55 <=> empty_set=X0|~ordinal(singleton(X0))|singleton(X0)=empty_set),
% 0.19/0.51 introduced(split_symbol_definition)).
% 0.19/0.51 fof(f872,plain,(
% 0.19/0.51 ![X0]: (empty_set=X0|~ordinal(singleton(X0))|singleton(X0)=empty_set|~spl0_55)),
% 0.19/0.51 inference(component_clause,[status(thm)],[f871])).
% 0.19/0.51 fof(f874,plain,(
% 0.19/0.51 ![X0]: (empty_set=X0|~ordinal(singleton(X0))|~ordinal(empty_set)|singleton(X0)=empty_set)),
% 0.19/0.51 inference(resolution,[status(thm)],[f866,f487])).
% 0.19/0.51 fof(f875,plain,(
% 0.19/0.51 spl0_55|~spl0_22),
% 0.19/0.51 inference(split_clause,[status(thm)],[f874,f871,f380])).
% 0.19/0.51 fof(f876,plain,(
% 0.19/0.51 spl0_56 <=> ~ordinal(singleton(X0))|in(empty_set,singleton(X0))|empty_set=singleton(X0)),
% 0.19/0.51 introduced(split_symbol_definition)).
% 0.19/0.51 fof(f877,plain,(
% 0.19/0.51 ![X0]: (~ordinal(singleton(X0))|in(empty_set,singleton(X0))|empty_set=singleton(X0)|~spl0_56)),
% 0.19/0.51 inference(component_clause,[status(thm)],[f876])).
% 0.19/0.51 fof(f879,plain,(
% 0.19/0.51 ![X0]: (~ordinal(empty_set)|~ordinal(singleton(X0))|in(empty_set,singleton(X0))|empty_set=singleton(X0))),
% 0.19/0.51 inference(resolution,[status(thm)],[f866,f203])).
% 0.19/0.51 fof(f880,plain,(
% 0.19/0.51 ~spl0_22|spl0_56),
% 0.19/0.51 inference(split_clause,[status(thm)],[f879,f380,f876])).
% 0.19/0.51 fof(f881,plain,(
% 0.19/0.51 ![X0]: (~ordinal(singleton(X0))|empty_set=singleton(X0)|~epsilon_transitive(singleton(X0))|subset(empty_set,singleton(X0))|~spl0_56)),
% 0.19/0.51 inference(resolution,[status(thm)],[f877,f95])).
% 0.19/0.51 fof(f883,plain,(
% 0.19/0.51 spl0_57 <=> ~ordinal(singleton(X0))|empty_set=singleton(X0)|~epsilon_transitive(singleton(X0))|empty_set=X0|~ordinal(singleton(X0))|singleton(X0)=empty_set),
% 0.19/0.51 introduced(split_symbol_definition)).
% 0.19/0.51 fof(f886,plain,(
% 0.19/0.51 ![X0]: (~ordinal(singleton(X0))|empty_set=singleton(X0)|~epsilon_transitive(singleton(X0))|~epsilon_transitive(empty_set)|empty_set=X0|~ordinal(singleton(X0))|~ordinal(empty_set)|singleton(X0)=empty_set|~spl0_56)),
% 0.19/0.51 inference(resolution,[status(thm)],[f881,f721])).
% 0.19/0.51 fof(f887,plain,(
% 0.19/0.51 spl0_57|~spl0_21|~spl0_22|~spl0_56),
% 0.19/0.51 inference(split_clause,[status(thm)],[f886,f883,f377,f380,f876])).
% 0.19/0.51 fof(f888,plain,(
% 0.19/0.51 spl0_58 <=> ~ordinal(singleton(X0))|empty_set=singleton(X0)|~epsilon_transitive(singleton(X0))|~ordinal(singleton(X0))|in(empty_set,singleton(X0))|empty_set=singleton(X0)),
% 0.19/0.51 introduced(split_symbol_definition)).
% 0.19/0.51 fof(f891,plain,(
% 0.19/0.51 ![X0]: (~ordinal(singleton(X0))|empty_set=singleton(X0)|~epsilon_transitive(singleton(X0))|~epsilon_transitive(empty_set)|~ordinal(empty_set)|~ordinal(singleton(X0))|in(empty_set,singleton(X0))|empty_set=singleton(X0)|~spl0_56)),
% 0.19/0.51 inference(resolution,[status(thm)],[f881,f658])).
% 0.19/0.51 fof(f892,plain,(
% 0.19/0.51 spl0_58|~spl0_21|~spl0_22|~spl0_56),
% 0.19/0.51 inference(split_clause,[status(thm)],[f891,f888,f377,f380,f876])).
% 0.19/0.51 fof(f893,plain,(
% 0.19/0.51 spl0_59 <=> ~ordinal(singleton(X0))|empty_set=singleton(X0)|~epsilon_transitive(singleton(X0))|~ordinal(singleton(X0))|ordinal_subset(empty_set,singleton(X0))),
% 0.19/0.51 introduced(split_symbol_definition)).
% 0.19/0.51 fof(f894,plain,(
% 0.19/0.51 ![X0]: (~ordinal(singleton(X0))|empty_set=singleton(X0)|~epsilon_transitive(singleton(X0))|~ordinal(singleton(X0))|ordinal_subset(empty_set,singleton(X0))|~spl0_59)),
% 0.19/0.51 inference(component_clause,[status(thm)],[f893])).
% 0.19/0.51 fof(f896,plain,(
% 0.19/0.51 ![X0]: (~ordinal(singleton(X0))|empty_set=singleton(X0)|~epsilon_transitive(singleton(X0))|~ordinal(empty_set)|~ordinal(singleton(X0))|ordinal_subset(empty_set,singleton(X0))|~spl0_56)),
% 0.19/0.51 inference(resolution,[status(thm)],[f881,f191])).
% 0.19/0.51 fof(f897,plain,(
% 0.19/0.51 spl0_59|~spl0_22|~spl0_56),
% 0.19/0.51 inference(split_clause,[status(thm)],[f896,f893,f380,f876])).
% 0.19/0.51 fof(f900,plain,(
% 0.19/0.51 ![X0]: (~ordinal(singleton(X0))|empty_set=singleton(X0)|~epsilon_transitive(singleton(X0))|ordinal_subset(empty_set,singleton(X0))|~spl0_59)),
% 0.19/0.51 inference(duplicate_literals_removal,[status(esa)],[f894])).
% 0.19/0.51 fof(f907,plain,(
% 0.19/0.51 spl0_60 <=> ~ordinal(singleton(X0))|empty_set=singleton(X0)|~epsilon_transitive(singleton(X0))|~ordinal(singleton(X0))|subset(empty_set,singleton(X0))),
% 0.19/0.51 introduced(split_symbol_definition)).
% 0.19/0.51 fof(f910,plain,(
% 0.19/0.51 ![X0]: (~ordinal(singleton(X0))|empty_set=singleton(X0)|~epsilon_transitive(singleton(X0))|~ordinal(empty_set)|~ordinal(singleton(X0))|subset(empty_set,singleton(X0))|~spl0_59)),
% 0.19/0.51 inference(resolution,[status(thm)],[f900,f190])).
% 0.19/0.51 fof(f911,plain,(
% 0.19/0.51 spl0_60|~spl0_22|~spl0_59),
% 0.19/0.51 inference(split_clause,[status(thm)],[f910,f907,f380,f893])).
% 0.19/0.51 fof(f915,plain,(
% 0.19/0.51 ![X0]: (~in(succ(X0),empty_set))),
% 0.19/0.51 inference(paramodulation,[status(thm)],[f199,f807])).
% 0.19/0.51 fof(f926,plain,(
% 0.19/0.51 ![X0,X1]: (~in(X0,X1)|~in(succ(X1),X0))),
% 0.19/0.51 inference(paramodulation,[status(thm)],[f83,f802])).
% 0.19/0.51 fof(f935,plain,(
% 0.19/0.51 ![X0,X1]: (~in(X0,empty_set)|~in(X1,X0))),
% 0.19/0.51 inference(paramodulation,[status(thm)],[f199,f809])).
% 0.19/0.51 fof(f940,plain,(
% 0.19/0.51 spl0_61 <=> ~ordinal(succ(X0))|in(empty_set,succ(X0))|empty_set=succ(X0)),
% 0.19/0.51 introduced(split_symbol_definition)).
% 0.19/0.51 fof(f941,plain,(
% 0.19/0.51 ![X0]: (~ordinal(succ(X0))|in(empty_set,succ(X0))|empty_set=succ(X0)|~spl0_61)),
% 0.19/0.51 inference(component_clause,[status(thm)],[f940])).
% 0.19/0.51 fof(f943,plain,(
% 0.19/0.51 ![X0]: (~ordinal(empty_set)|~ordinal(succ(X0))|in(empty_set,succ(X0))|empty_set=succ(X0))),
% 0.19/0.51 inference(resolution,[status(thm)],[f915,f203])).
% 0.19/0.51 fof(f944,plain,(
% 0.19/0.51 ~spl0_22|spl0_61),
% 0.19/0.51 inference(split_clause,[status(thm)],[f943,f380,f940])).
% 0.19/0.51 fof(f945,plain,(
% 0.19/0.51 ![X0]: (~ordinal(succ(X0))|empty_set=succ(X0)|~epsilon_transitive(succ(X0))|subset(empty_set,succ(X0))|~spl0_61)),
% 0.19/0.51 inference(resolution,[status(thm)],[f941,f95])).
% 0.19/0.51 fof(f947,plain,(
% 0.19/0.51 spl0_62 <=> ~ordinal(succ(X0))|empty_set=succ(X0)|~epsilon_transitive(succ(X0))|~ordinal(succ(X0))|in(empty_set,succ(X0))|empty_set=succ(X0)),
% 0.19/0.51 introduced(split_symbol_definition)).
% 0.19/0.51 fof(f950,plain,(
% 0.19/0.51 ![X0]: (~ordinal(succ(X0))|empty_set=succ(X0)|~epsilon_transitive(succ(X0))|~epsilon_transitive(empty_set)|~ordinal(empty_set)|~ordinal(succ(X0))|in(empty_set,succ(X0))|empty_set=succ(X0)|~spl0_61)),
% 0.19/0.51 inference(resolution,[status(thm)],[f945,f658])).
% 0.19/0.51 fof(f951,plain,(
% 0.19/0.51 spl0_62|~spl0_21|~spl0_22|~spl0_61),
% 0.19/0.51 inference(split_clause,[status(thm)],[f950,f947,f377,f380,f940])).
% 0.19/0.51 fof(f952,plain,(
% 0.19/0.51 spl0_63 <=> ~ordinal(succ(X0))|empty_set=succ(X0)|~epsilon_transitive(succ(X0))|~ordinal(succ(X0))|ordinal_subset(empty_set,succ(X0))),
% 0.19/0.51 introduced(split_symbol_definition)).
% 0.19/0.51 fof(f953,plain,(
% 0.19/0.51 ![X0]: (~ordinal(succ(X0))|empty_set=succ(X0)|~epsilon_transitive(succ(X0))|~ordinal(succ(X0))|ordinal_subset(empty_set,succ(X0))|~spl0_63)),
% 0.19/0.51 inference(component_clause,[status(thm)],[f952])).
% 0.19/0.51 fof(f955,plain,(
% 0.19/0.51 ![X0]: (~ordinal(succ(X0))|empty_set=succ(X0)|~epsilon_transitive(succ(X0))|~ordinal(empty_set)|~ordinal(succ(X0))|ordinal_subset(empty_set,succ(X0))|~spl0_61)),
% 0.19/0.51 inference(resolution,[status(thm)],[f945,f191])).
% 0.19/0.51 fof(f956,plain,(
% 0.19/0.51 spl0_63|~spl0_22|~spl0_61),
% 0.19/0.51 inference(split_clause,[status(thm)],[f955,f952,f380,f940])).
% 0.19/0.51 fof(f959,plain,(
% 0.19/0.51 ![X0]: (~ordinal(succ(X0))|empty_set=succ(X0)|~epsilon_transitive(succ(X0))|ordinal_subset(empty_set,succ(X0))|~spl0_63)),
% 0.19/0.51 inference(duplicate_literals_removal,[status(esa)],[f953])).
% 0.19/0.51 fof(f964,plain,(
% 0.19/0.51 spl0_64 <=> ~ordinal(succ(X0))|empty_set=succ(X0)|~epsilon_transitive(succ(X0))|~ordinal(succ(X0))|subset(empty_set,succ(X0))),
% 0.19/0.51 introduced(split_symbol_definition)).
% 0.19/0.51 fof(f967,plain,(
% 0.19/0.51 ![X0]: (~ordinal(succ(X0))|empty_set=succ(X0)|~epsilon_transitive(succ(X0))|~ordinal(empty_set)|~ordinal(succ(X0))|subset(empty_set,succ(X0))|~spl0_63)),
% 0.19/0.51 inference(resolution,[status(thm)],[f959,f190])).
% 0.19/0.51 fof(f968,plain,(
% 0.19/0.51 spl0_64|~spl0_22|~spl0_63),
% 0.19/0.51 inference(split_clause,[status(thm)],[f967,f964,f380,f952])).
% 0.19/0.51 fof(f969,plain,(
% 0.19/0.51 spl0_65 <=> ~in(X0,set_union2(X1,X2))|in(empty_set,X1)|in(empty_set,X2)|~ordinal(set_union2(X1,X2))|set_union2(X1,X2)=empty_set),
% 0.19/0.51 introduced(split_symbol_definition)).
% 0.19/0.51 fof(f970,plain,(
% 0.19/0.51 ![X0,X1,X2]: (~in(X0,set_union2(X1,X2))|in(empty_set,X1)|in(empty_set,X2)|~ordinal(set_union2(X1,X2))|set_union2(X1,X2)=empty_set|~spl0_65)),
% 0.19/0.51 inference(component_clause,[status(thm)],[f969])).
% 0.19/0.51 fof(f972,plain,(
% 0.19/0.51 ![X0,X1,X2]: (~in(X0,set_union2(X1,X2))|in(empty_set,X1)|in(empty_set,X2)|~ordinal(set_union2(X1,X2))|~ordinal(empty_set)|set_union2(X1,X2)=empty_set)),
% 0.19/0.51 inference(resolution,[status(thm)],[f935,f795])).
% 0.19/0.51 fof(f973,plain,(
% 0.19/0.51 spl0_65|~spl0_22),
% 0.19/0.51 inference(split_clause,[status(thm)],[f972,f969,f380])).
% 0.19/0.51 fof(f980,plain,(
% 0.19/0.51 spl0_67 <=> ~in(X0,singleton(X1))|empty_set=X1|~ordinal(singleton(X1))|singleton(X1)=empty_set),
% 0.19/0.51 introduced(split_symbol_definition)).
% 0.19/0.51 fof(f983,plain,(
% 0.19/0.51 ![X0,X1]: (~in(X0,singleton(X1))|empty_set=X1|~ordinal(singleton(X1))|~ordinal(empty_set)|singleton(X1)=empty_set)),
% 0.19/0.51 inference(resolution,[status(thm)],[f935,f487])).
% 0.19/0.51 fof(f984,plain,(
% 0.19/0.51 spl0_67|~spl0_22),
% 0.19/0.51 inference(split_clause,[status(thm)],[f983,f980,f380])).
% 0.19/0.51 fof(f985,plain,(
% 0.19/0.51 spl0_68 <=> ~in(X0,X1)|~ordinal(X1)|in(empty_set,X1)|empty_set=X1),
% 0.19/0.51 introduced(split_symbol_definition)).
% 0.19/0.51 fof(f988,plain,(
% 0.19/0.51 ![X0,X1]: (~in(X0,X1)|~ordinal(empty_set)|~ordinal(X1)|in(empty_set,X1)|empty_set=X1)),
% 0.19/0.51 inference(resolution,[status(thm)],[f935,f203])).
% 0.19/0.51 fof(f989,plain,(
% 0.19/0.51 spl0_68|~spl0_22),
% 0.19/0.51 inference(split_clause,[status(thm)],[f988,f985,f380])).
% 0.19/0.51 fof(f999,plain,(
% 0.19/0.51 spl0_70 <=> empty_set=sk0_17),
% 0.19/0.51 introduced(split_symbol_definition)).
% 0.19/0.51 fof(f1000,plain,(
% 0.19/0.51 empty_set=sk0_17|~spl0_70),
% 0.19/0.51 inference(component_clause,[status(thm)],[f999])).
% 0.19/0.51 fof(f1004,plain,(
% 0.19/0.51 spl0_71 <=> in(empty_set,sk0_18)),
% 0.19/0.51 introduced(split_symbol_definition)).
% 0.19/0.51 fof(f1005,plain,(
% 0.19/0.51 in(empty_set,sk0_18)|~spl0_71),
% 0.19/0.51 inference(component_clause,[status(thm)],[f1004])).
% 0.19/0.51 fof(f1007,plain,(
% 0.19/0.51 spl0_72 <=> empty_set=sk0_18),
% 0.19/0.51 introduced(split_symbol_definition)).
% 0.19/0.51 fof(f1008,plain,(
% 0.19/0.51 empty_set=sk0_18|~spl0_72),
% 0.19/0.51 inference(component_clause,[status(thm)],[f1007])).
% 0.19/0.51 fof(f1022,plain,(
% 0.19/0.51 spl0_73 <=> subset(empty_set,sk0_18)),
% 0.19/0.51 introduced(split_symbol_definition)).
% 0.19/0.51 fof(f1023,plain,(
% 0.19/0.51 subset(empty_set,sk0_18)|~spl0_73),
% 0.19/0.51 inference(component_clause,[status(thm)],[f1022])).
% 0.19/0.51 fof(f1024,plain,(
% 0.19/0.51 ~subset(empty_set,sk0_18)|spl0_73),
% 0.19/0.51 inference(component_clause,[status(thm)],[f1022])).
% 0.19/0.51 fof(f1025,plain,(
% 0.19/0.51 ~epsilon_transitive(sk0_18)|subset(empty_set,sk0_18)|~spl0_71),
% 0.19/0.51 inference(resolution,[status(thm)],[f1005,f95])).
% 0.19/0.51 fof(f1026,plain,(
% 0.19/0.51 ~spl0_19|spl0_73|~spl0_71),
% 0.19/0.51 inference(split_clause,[status(thm)],[f1025,f366,f1022,f1004])).
% 0.19/0.51 fof(f1028,plain,(
% 0.19/0.51 $false|~spl0_11|spl0_20),
% 0.19/0.51 inference(forward_subsumption_resolution,[status(thm)],[f373,f342])).
% 0.19/0.51 fof(f1029,plain,(
% 0.19/0.51 ~spl0_11|spl0_20),
% 0.19/0.51 inference(contradiction_clause,[status(thm)],[f1028])).
% 0.19/0.51 fof(f1030,plain,(
% 0.19/0.51 $false|spl0_19),
% 0.19/0.51 inference(forward_subsumption_resolution,[status(thm)],[f368,f260])).
% 0.19/0.51 fof(f1031,plain,(
% 0.19/0.51 spl0_19),
% 0.19/0.51 inference(contradiction_clause,[status(thm)],[f1030])).
% 0.19/0.51 fof(f1041,plain,(
% 0.19/0.51 ~empty_set=sk0_17|~spl0_72|spl0_31),
% 0.19/0.51 inference(backward_demodulation,[status(thm)],[f1008,f448])).
% 0.19/0.51 fof(f1059,plain,(
% 0.19/0.51 $false|~spl0_72|spl0_31|~spl0_70),
% 0.19/0.51 inference(forward_subsumption_resolution,[status(thm)],[f1000,f1041])).
% 0.19/0.51 fof(f1060,plain,(
% 0.19/0.51 ~spl0_72|spl0_31|~spl0_70),
% 0.19/0.51 inference(contradiction_clause,[status(thm)],[f1059])).
% 0.19/0.51 fof(f1085,plain,(
% 0.19/0.51 ~in(sk0_17,sk0_18)|~spl0_12),
% 0.19/0.51 inference(resolution,[status(thm)],[f926,f332])).
% 0.19/0.51 fof(f1217,plain,(
% 0.19/0.51 ![X0,X1]: (subset(X0,X1)|~ordinal(X1)|~ordinal(X0)|in(X1,X0)|X1=X0)),
% 0.19/0.51 inference(backward_subsumption_resolution,[status(thm)],[f610,f61])).
% 0.19/0.51 fof(f1224,plain,(
% 0.19/0.51 succ(empty_set)=singleton(empty_set)),
% 0.19/0.51 inference(paramodulation,[status(thm)],[f83,f764])).
% 0.19/0.51 fof(f1272,plain,(
% 0.19/0.51 ![X0,X1,X2]: (~empty(set_union2(X0,X1))|~in(X2,X1))),
% 0.19/0.51 inference(resolution,[status(thm)],[f227,f252])).
% 0.19/0.51 fof(f1274,plain,(
% 0.19/0.51 ![X0]: (~empty(singleton(X0)))),
% 0.19/0.51 inference(resolution,[status(thm)],[f227,f249])).
% 0.19/0.51 fof(f1276,plain,(
% 0.19/0.51 ![X0,X1]: (~empty(X0)|~ordinal(X0)|~ordinal(X1)|in(X0,X1)|X0=X1)),
% 0.19/0.51 inference(resolution,[status(thm)],[f227,f203])).
% 0.19/0.51 fof(f1277,plain,(
% 0.19/0.51 ![X0,X1]: (~empty(X0)|~ordinal(X1)|in(X0,X1)|X0=X1)),
% 0.19/0.51 inference(forward_subsumption_resolution,[status(thm)],[f1276,f74])).
% 0.19/0.51 fof(f1295,plain,(
% 0.19/0.51 spl0_75 <=> ordinal(singleton(empty_set))),
% 0.19/0.51 introduced(split_symbol_definition)).
% 0.19/0.51 fof(f1297,plain,(
% 0.19/0.51 ~ordinal(singleton(empty_set))|spl0_75),
% 0.19/0.51 inference(component_clause,[status(thm)],[f1295])).
% 0.19/0.51 fof(f1298,plain,(
% 0.19/0.51 spl0_76 <=> in(empty_set,succ(empty_set))),
% 0.19/0.51 introduced(split_symbol_definition)).
% 0.19/0.51 fof(f1301,plain,(
% 0.19/0.51 spl0_77 <=> empty_set=singleton(empty_set)),
% 0.19/0.51 introduced(split_symbol_definition)).
% 0.19/0.51 fof(f1302,plain,(
% 0.19/0.51 empty_set=singleton(empty_set)|~spl0_77),
% 0.19/0.51 inference(component_clause,[status(thm)],[f1301])).
% 0.19/0.51 fof(f1304,plain,(
% 0.19/0.51 ~ordinal(singleton(empty_set))|in(empty_set,succ(empty_set))|empty_set=singleton(empty_set)|~spl0_56),
% 0.19/0.51 inference(paramodulation,[status(thm)],[f1224,f877])).
% 0.19/0.51 fof(f1305,plain,(
% 0.19/0.51 ~spl0_75|spl0_76|spl0_77|~spl0_56),
% 0.19/0.51 inference(split_clause,[status(thm)],[f1304,f1295,f1298,f1301,f876])).
% 0.19/0.51 fof(f1306,plain,(
% 0.19/0.51 spl0_78 <=> empty_set=empty_set),
% 0.19/0.51 introduced(split_symbol_definition)).
% 0.19/0.51 fof(f1309,plain,(
% 0.19/0.51 spl0_79 <=> ordinal(succ(empty_set))),
% 0.19/0.51 introduced(split_symbol_definition)).
% 0.19/0.51 fof(f1310,plain,(
% 0.19/0.51 ordinal(succ(empty_set))|~spl0_79),
% 0.19/0.51 inference(component_clause,[status(thm)],[f1309])).
% 0.19/0.51 fof(f1311,plain,(
% 0.19/0.51 ~ordinal(succ(empty_set))|spl0_79),
% 0.19/0.51 inference(component_clause,[status(thm)],[f1309])).
% 0.19/0.51 fof(f1312,plain,(
% 0.19/0.51 empty_set=empty_set|~ordinal(succ(empty_set))|singleton(empty_set)=empty_set|~spl0_55),
% 0.19/0.51 inference(paramodulation,[status(thm)],[f1224,f872])).
% 0.19/0.51 fof(f1313,plain,(
% 0.19/0.51 spl0_78|~spl0_79|spl0_77|~spl0_55),
% 0.19/0.51 inference(split_clause,[status(thm)],[f1312,f1306,f1309,f1301,f871])).
% 0.19/0.51 fof(f1315,plain,(
% 0.19/0.51 spl0_80 <=> singleton(sk0_0(X0,singleton(empty_set)))=empty_set|~ordinal(singleton(sk0_0(X0,singleton(empty_set))))|~singleton(sk0_0(X0,succ(empty_set)))=sk0_0(X0,singleton(empty_set))|X0=singleton(singleton(empty_set))|~in(sk0_0(X0,singleton(empty_set)),X0)),
% 0.19/0.51 introduced(split_symbol_definition)).
% 0.19/0.51 fof(f1318,plain,(
% 0.19/0.51 ![X0]: (singleton(sk0_0(X0,singleton(empty_set)))=empty_set|~ordinal(singleton(empty_set))|~ordinal(singleton(sk0_0(X0,singleton(empty_set))))|~singleton(sk0_0(X0,succ(empty_set)))=sk0_0(X0,singleton(empty_set))|X0=singleton(singleton(empty_set))|~in(sk0_0(X0,singleton(empty_set)),X0))),
% 0.19/0.51 inference(paramodulation,[status(thm)],[f1224,f585])).
% 0.19/0.51 fof(f1319,plain,(
% 0.19/0.51 spl0_80|~spl0_75),
% 0.19/0.51 inference(split_clause,[status(thm)],[f1318,f1315,f1295])).
% 0.19/0.51 fof(f1365,plain,(
% 0.19/0.51 spl0_92 <=> singleton(empty_set)=singleton(X0)|sk0_0(singleton(empty_set),X0)=X0|sk0_0(singleton(empty_set),X0)=empty_set|~ordinal(sk0_0(singleton(empty_set),X0))|singleton(empty_set)=sk0_0(succ(empty_set),X0)),
% 0.19/0.51 introduced(split_symbol_definition)).
% 0.19/0.51 fof(f1368,plain,(
% 0.19/0.51 ![X0]: (singleton(empty_set)=singleton(X0)|sk0_0(singleton(empty_set),X0)=X0|sk0_0(singleton(empty_set),X0)=empty_set|~ordinal(singleton(empty_set))|~ordinal(sk0_0(singleton(empty_set),X0))|singleton(empty_set)=sk0_0(succ(empty_set),X0))),
% 0.19/0.51 inference(paramodulation,[status(thm)],[f1224,f645])).
% 0.19/0.51 fof(f1369,plain,(
% 0.19/0.51 spl0_92|~spl0_75),
% 0.19/0.51 inference(split_clause,[status(thm)],[f1368,f1365,f1295])).
% 0.19/0.51 fof(f1370,plain,(
% 0.19/0.51 spl0_93 <=> singleton(X0)=empty_set|~ordinal(singleton(X0))|~singleton(X0)=X0|succ(empty_set)=X0),
% 0.19/0.51 introduced(split_symbol_definition)).
% 0.19/0.51 fof(f1373,plain,(
% 0.19/0.51 ![X0]: (singleton(X0)=empty_set|~ordinal(singleton(empty_set))|~ordinal(singleton(X0))|~singleton(X0)=X0|succ(empty_set)=X0)),
% 0.19/0.51 inference(paramodulation,[status(thm)],[f1224,f582])).
% 0.19/0.51 fof(f1374,plain,(
% 0.19/0.51 spl0_93|~spl0_75),
% 0.19/0.51 inference(split_clause,[status(thm)],[f1373,f1370,f1295])).
% 0.19/0.51 fof(f1375,plain,(
% 0.19/0.51 spl0_94 <=> singleton(empty_set)=X0|~ordinal(singleton(X0))|singleton(X0)=succ(empty_set)|singleton(X0)=empty_set),
% 0.19/0.51 introduced(split_symbol_definition)).
% 0.19/0.51 fof(f1378,plain,(
% 0.19/0.51 ![X0]: (singleton(empty_set)=X0|~ordinal(singleton(X0))|~ordinal(singleton(empty_set))|singleton(X0)=succ(empty_set)|singleton(X0)=empty_set)),
% 0.19/0.51 inference(paramodulation,[status(thm)],[f1224,f580])).
% 0.19/0.51 fof(f1379,plain,(
% 0.19/0.51 spl0_94|~spl0_75),
% 0.19/0.51 inference(split_clause,[status(thm)],[f1378,f1375,f1295])).
% 0.19/0.51 fof(f1382,plain,(
% 0.19/0.51 spl0_95 <=> X0=empty_set|~ordinal(X0)|in(succ(empty_set),X0)|singleton(empty_set)=X0),
% 0.19/0.51 introduced(split_symbol_definition)).
% 0.19/0.51 fof(f1385,plain,(
% 0.19/0.51 ![X0]: (X0=empty_set|~ordinal(singleton(empty_set))|~ordinal(X0)|in(succ(empty_set),X0)|singleton(empty_set)=X0)),
% 0.19/0.51 inference(paramodulation,[status(thm)],[f1224,f487])).
% 0.19/0.51 fof(f1386,plain,(
% 0.19/0.51 spl0_95|~spl0_75),
% 0.19/0.51 inference(split_clause,[status(thm)],[f1385,f1382,f1295])).
% 0.19/0.51 fof(f1389,plain,(
% 0.19/0.51 ![X0]: (~in(X0,succ(empty_set))|X0=empty_set)),
% 0.19/0.51 inference(paramodulation,[status(thm)],[f1224,f248])).
% 0.19/0.51 fof(f1393,plain,(
% 0.19/0.51 ~ordinal(succ(empty_set))|spl0_75),
% 0.19/0.51 inference(forward_demodulation,[status(thm)],[f1224,f1297])).
% 0.19/0.51 fof(f1436,plain,(
% 0.19/0.51 spl0_96 <=> ordinal_subset(empty_set,sk0_18)),
% 0.19/0.51 introduced(split_symbol_definition)).
% 0.19/0.51 fof(f1437,plain,(
% 0.19/0.51 ordinal_subset(empty_set,sk0_18)|~spl0_96),
% 0.19/0.51 inference(component_clause,[status(thm)],[f1436])).
% 0.19/0.51 fof(f1439,plain,(
% 0.19/0.51 ~ordinal(empty_set)|~ordinal(sk0_18)|ordinal_subset(empty_set,sk0_18)|~spl0_73),
% 0.19/0.51 inference(resolution,[status(thm)],[f1023,f191])).
% 0.19/0.51 fof(f1440,plain,(
% 0.19/0.51 ~spl0_22|~spl0_6|spl0_96|~spl0_73),
% 0.19/0.51 inference(split_clause,[status(thm)],[f1439,f380,f283,f1436,f1022])).
% 0.19/0.51 fof(f1441,plain,(
% 0.19/0.51 spl0_97 <=> subset(sk0_18,empty_set)),
% 0.19/0.51 introduced(split_symbol_definition)).
% 0.19/0.51 fof(f1443,plain,(
% 0.19/0.51 ~subset(sk0_18,empty_set)|spl0_97),
% 0.19/0.51 inference(component_clause,[status(thm)],[f1441])).
% 0.19/0.51 fof(f1444,plain,(
% 0.19/0.51 sk0_18=empty_set|~subset(sk0_18,empty_set)|~spl0_73),
% 0.19/0.51 inference(resolution,[status(thm)],[f1023,f82])).
% 0.19/0.51 fof(f1445,plain,(
% 0.19/0.51 spl0_72|~spl0_97|~spl0_73),
% 0.19/0.51 inference(split_clause,[status(thm)],[f1444,f1007,f1441,f1022])).
% 0.19/0.51 fof(f1499,plain,(
% 0.19/0.51 $false|~spl0_50|~spl0_12),
% 0.19/0.51 inference(forward_subsumption_resolution,[status(thm)],[f1085,f651])).
% 0.19/0.51 fof(f1500,plain,(
% 0.19/0.51 ~spl0_50|~spl0_12),
% 0.19/0.51 inference(contradiction_clause,[status(thm)],[f1499])).
% 0.19/0.51 fof(f1501,plain,(
% 0.19/0.51 ~ordinal(empty_set)|spl0_79),
% 0.19/0.51 inference(resolution,[status(thm)],[f1311,f131])).
% 0.19/0.51 fof(f1502,plain,(
% 0.19/0.51 $false|spl0_79),
% 0.19/0.51 inference(forward_subsumption_resolution,[status(thm)],[f1501,f561])).
% 0.19/0.51 fof(f1503,plain,(
% 0.19/0.51 spl0_79),
% 0.19/0.51 inference(contradiction_clause,[status(thm)],[f1502])).
% 0.19/0.51 fof(f1504,plain,(
% 0.19/0.51 empty_set=succ(empty_set)|~spl0_77),
% 0.19/0.51 inference(forward_demodulation,[status(thm)],[f1224,f1302])).
% 0.19/0.51 fof(f1505,plain,(
% 0.19/0.51 $false|~spl0_77),
% 0.19/0.51 inference(forward_subsumption_resolution,[status(thm)],[f1504,f198])).
% 0.19/0.51 fof(f1506,plain,(
% 0.19/0.51 ~spl0_77),
% 0.19/0.51 inference(contradiction_clause,[status(thm)],[f1505])).
% 0.19/0.51 fof(f1508,plain,(
% 0.19/0.51 ~ordinal(empty_set)|spl0_75),
% 0.19/0.51 inference(resolution,[status(thm)],[f1393,f131])).
% 0.19/0.51 fof(f1509,plain,(
% 0.19/0.51 $false|spl0_75),
% 0.19/0.51 inference(forward_subsumption_resolution,[status(thm)],[f1508,f561])).
% 0.19/0.51 fof(f1510,plain,(
% 0.19/0.51 spl0_75),
% 0.19/0.51 inference(contradiction_clause,[status(thm)],[f1509])).
% 0.19/0.51 fof(f1528,plain,(
% 0.19/0.51 spl0_102 <=> ordinal_subset(sk0_18,empty_set)),
% 0.19/0.51 introduced(split_symbol_definition)).
% 0.19/0.51 fof(f1529,plain,(
% 0.19/0.51 ordinal_subset(sk0_18,empty_set)|~spl0_102),
% 0.19/0.51 inference(component_clause,[status(thm)],[f1528])).
% 0.19/0.51 fof(f1531,plain,(
% 0.19/0.51 ~ordinal(empty_set)|~ordinal(sk0_18)|ordinal_subset(sk0_18,empty_set)|spl0_73),
% 0.19/0.51 inference(resolution,[status(thm)],[f1024,f255])).
% 0.19/0.51 fof(f1532,plain,(
% 0.19/0.51 ~spl0_22|~spl0_6|spl0_102|spl0_73),
% 0.19/0.51 inference(split_clause,[status(thm)],[f1531,f380,f283,f1528,f1022])).
% 0.19/0.52 fof(f1631,plain,(
% 0.19/0.52 spl0_106 <=> ~empty(singleton(X0))|singleton(X0)=empty_set),
% 0.19/0.52 introduced(split_symbol_definition)).
% 0.19/0.52 fof(f1634,plain,(
% 0.19/0.52 ![X0]: (~empty(singleton(X0))|~ordinal(empty_set)|singleton(X0)=empty_set)),
% 0.19/0.52 inference(resolution,[status(thm)],[f1277,f866])).
% 0.19/0.52 fof(f1635,plain,(
% 0.19/0.52 spl0_106|~spl0_22),
% 0.19/0.52 inference(split_clause,[status(thm)],[f1634,f1631,f380])).
% 0.19/0.52 fof(f1649,plain,(
% 0.19/0.52 spl0_108 <=> ~empty(succ(X0))|succ(X0)=empty_set),
% 0.19/0.52 introduced(split_symbol_definition)).
% 0.19/0.52 fof(f1652,plain,(
% 0.19/0.52 ![X0]: (~empty(succ(X0))|~ordinal(empty_set)|succ(X0)=empty_set)),
% 0.19/0.52 inference(resolution,[status(thm)],[f1277,f915])).
% 0.19/0.52 fof(f1653,plain,(
% 0.19/0.52 spl0_108|~spl0_22),
% 0.19/0.52 inference(split_clause,[status(thm)],[f1652,f1649,f380])).
% 0.19/0.52 fof(f1656,plain,(
% 0.19/0.52 spl0_109 <=> ~empty(X0)|X0=empty_set|~in(X1,X0)),
% 0.19/0.52 introduced(split_symbol_definition)).
% 0.19/0.52 fof(f1659,plain,(
% 0.19/0.52 ![X0,X1]: (~empty(X0)|~ordinal(empty_set)|X0=empty_set|~in(X1,X0))),
% 0.19/0.52 inference(resolution,[status(thm)],[f1277,f935])).
% 0.19/0.52 fof(f1660,plain,(
% 0.19/0.52 spl0_109|~spl0_22),
% 0.19/0.52 inference(split_clause,[status(thm)],[f1659,f1656,f380])).
% 0.19/0.52 fof(f1669,plain,(
% 0.19/0.52 ![X0,X1]: (~empty(X0)|~ordinal(X1)|X0=X1|~epsilon_transitive(X1)|subset(X0,X1))),
% 0.19/0.52 inference(resolution,[status(thm)],[f1277,f95])).
% 0.19/0.52 fof(f1670,plain,(
% 0.19/0.52 ![X0,X1]: (~empty(X0)|~ordinal(X1)|X0=X1|subset(X0,X1))),
% 0.19/0.52 inference(forward_subsumption_resolution,[status(thm)],[f1669,f61])).
% 0.19/0.52 fof(f1672,plain,(
% 0.19/0.52 spl0_110 <=> ~empty(X0)),
% 0.19/0.52 introduced(split_symbol_definition)).
% 0.19/0.52 fof(f1673,plain,(
% 0.19/0.52 ![X0]: (~empty(X0)|~spl0_110)),
% 0.19/0.52 inference(component_clause,[status(thm)],[f1672])).
% 0.19/0.52 fof(f1689,plain,(
% 0.19/0.52 spl0_111 <=> epsilon_transitive(sk0_13)),
% 0.19/0.52 introduced(split_symbol_definition)).
% 0.19/0.52 fof(f1691,plain,(
% 0.19/0.52 ~epsilon_transitive(sk0_13)|spl0_111),
% 0.19/0.52 inference(component_clause,[status(thm)],[f1689])).
% 0.19/0.52 fof(f1692,plain,(
% 0.19/0.52 spl0_112 <=> ordinal(sk0_13)),
% 0.19/0.52 introduced(split_symbol_definition)).
% 0.19/0.52 fof(f1695,plain,(
% 0.19/0.52 ~epsilon_transitive(sk0_13)|ordinal(sk0_13)),
% 0.19/0.52 inference(resolution,[status(thm)],[f70,f175])).
% 0.19/0.52 fof(f1696,plain,(
% 0.19/0.52 ~spl0_111|spl0_112),
% 0.19/0.52 inference(split_clause,[status(thm)],[f1695,f1689,f1692])).
% 0.19/0.52 fof(f1704,plain,(
% 0.19/0.52 $false|spl0_111),
% 0.19/0.52 inference(forward_subsumption_resolution,[status(thm)],[f1691,f174])).
% 0.19/0.52 fof(f1705,plain,(
% 0.19/0.52 spl0_111),
% 0.19/0.52 inference(contradiction_clause,[status(thm)],[f1704])).
% 0.19/0.52 fof(f1714,plain,(
% 0.19/0.52 spl0_113 <=> in(set_union2(X0,X1),X2)|in(empty_set,X0)|in(empty_set,X1)|~ordinal(set_union2(X0,X1))|set_union2(X0,X1)=empty_set),
% 0.19/0.52 introduced(split_symbol_definition)).
% 0.19/0.52 fof(f1715,plain,(
% 0.19/0.52 ![X0,X1,X2]: (in(set_union2(X0,X1),X2)|in(empty_set,X0)|in(empty_set,X1)|~ordinal(set_union2(X0,X1))|set_union2(X0,X1)=empty_set|~spl0_113)),
% 0.19/0.52 inference(component_clause,[status(thm)],[f1714])).
% 0.19/0.52 fof(f1717,plain,(
% 0.19/0.52 ![X0,X1,X2]: (in(set_union2(X0,X1),X2)|in(empty_set,X0)|in(empty_set,X1)|~ordinal(set_union2(X0,X1))|~ordinal(empty_set)|set_union2(X0,X1)=empty_set)),
% 0.19/0.52 inference(resolution,[status(thm)],[f810,f795])).
% 0.19/0.52 fof(f1718,plain,(
% 0.19/0.52 spl0_113|~spl0_22),
% 0.19/0.52 inference(split_clause,[status(thm)],[f1717,f1714,f380])).
% 0.19/0.52 fof(f1725,plain,(
% 0.19/0.52 spl0_115 <=> in(singleton(X0),X1)|empty_set=X0|~ordinal(singleton(X0))|singleton(X0)=empty_set),
% 0.19/0.52 introduced(split_symbol_definition)).
% 0.19/0.52 fof(f1728,plain,(
% 0.19/0.52 ![X0,X1]: (in(singleton(X0),X1)|empty_set=X0|~ordinal(singleton(X0))|~ordinal(empty_set)|singleton(X0)=empty_set)),
% 0.19/0.52 inference(resolution,[status(thm)],[f810,f487])).
% 0.19/0.52 fof(f1729,plain,(
% 0.19/0.52 spl0_115|~spl0_22),
% 0.19/0.52 inference(split_clause,[status(thm)],[f1728,f1725,f380])).
% 0.19/0.52 fof(f1730,plain,(
% 0.19/0.52 spl0_116 <=> in(X0,X1)|~empty(X0)|X0=empty_set),
% 0.19/0.52 introduced(split_symbol_definition)).
% 0.19/0.52 fof(f1733,plain,(
% 0.19/0.52 ![X0,X1]: (in(X0,X1)|~empty(X0)|~ordinal(empty_set)|X0=empty_set)),
% 0.19/0.52 inference(resolution,[status(thm)],[f810,f1277])).
% 0.19/0.52 fof(f1734,plain,(
% 0.19/0.52 spl0_116|~spl0_22),
% 0.19/0.52 inference(split_clause,[status(thm)],[f1733,f1730,f380])).
% 0.19/0.52 fof(f1735,plain,(
% 0.19/0.52 spl0_117 <=> in(X0,X1)|~ordinal(X0)|in(empty_set,X0)|empty_set=X0),
% 0.19/0.52 introduced(split_symbol_definition)).
% 0.19/0.52 fof(f1738,plain,(
% 0.19/0.52 ![X0,X1]: (in(X0,X1)|~ordinal(empty_set)|~ordinal(X0)|in(empty_set,X0)|empty_set=X0)),
% 0.19/0.52 inference(resolution,[status(thm)],[f810,f203])).
% 0.19/0.52 fof(f1739,plain,(
% 0.19/0.52 spl0_117|~spl0_22),
% 0.19/0.52 inference(split_clause,[status(thm)],[f1738,f1735,f380])).
% 0.19/0.52 fof(f1772,plain,(
% 0.19/0.52 spl0_118 <=> ~in(X1,empty_set)),
% 0.19/0.52 introduced(split_symbol_definition)).
% 0.19/0.52 fof(f1773,plain,(
% 0.19/0.52 ![X0]: (~in(X0,empty_set)|~spl0_118)),
% 0.19/0.52 inference(component_clause,[status(thm)],[f1772])).
% 0.19/0.52 fof(f1775,plain,(
% 0.19/0.52 ![X0,X1]: (~empty(X0)|~in(X1,empty_set))),
% 0.19/0.52 inference(paramodulation,[status(thm)],[f199,f1272])).
% 0.19/0.52 fof(f1776,plain,(
% 0.19/0.52 spl0_110|spl0_118),
% 0.19/0.52 inference(split_clause,[status(thm)],[f1775,f1672,f1772])).
% 0.19/0.52 fof(f1788,plain,(
% 0.19/0.52 spl0_119 <=> relation(empty_set)),
% 0.19/0.52 introduced(split_symbol_definition)).
% 0.19/0.52 fof(f1790,plain,(
% 0.19/0.52 ~relation(empty_set)|spl0_119),
% 0.19/0.52 inference(component_clause,[status(thm)],[f1788])).
% 0.19/0.52 fof(f1791,plain,(
% 0.19/0.52 spl0_120 <=> ~relation(X0)|relation(X0)),
% 0.19/0.52 introduced(split_symbol_definition)).
% 0.19/0.52 fof(f1794,plain,(
% 0.19/0.52 ![X0]: (~relation(empty_set)|~relation(X0)|relation(X0))),
% 0.19/0.52 inference(paramodulation,[status(thm)],[f764,f123])).
% 0.19/0.52 fof(f1795,plain,(
% 0.19/0.52 ~spl0_119|spl0_120),
% 0.19/0.52 inference(split_clause,[status(thm)],[f1794,f1788,f1791])).
% 0.19/0.52 fof(f1801,plain,(
% 0.19/0.52 $false|spl0_119),
% 0.19/0.52 inference(forward_subsumption_resolution,[status(thm)],[f1790,f110])).
% 0.19/0.52 fof(f1802,plain,(
% 0.19/0.52 spl0_119),
% 0.19/0.52 inference(contradiction_clause,[status(thm)],[f1801])).
% 0.19/0.52 fof(f1804,plain,(
% 0.19/0.52 ![X0]: (empty(X0)|in(sk0_3(X0),X0))),
% 0.19/0.52 inference(resolution,[status(thm)],[f205,f108])).
% 0.19/0.52 fof(f1846,plain,(
% 0.19/0.52 epsilon_transitive(succ(empty_set))|~spl0_79),
% 0.19/0.52 inference(resolution,[status(thm)],[f1310,f61])).
% 0.19/0.52 fof(f1848,plain,(
% 0.19/0.52 ordinal_subset(empty_set,empty_set)|~spl0_72|~spl0_96),
% 0.19/0.52 inference(forward_demodulation,[status(thm)],[f1008,f1437])).
% 0.19/0.52 fof(f1849,plain,(
% 0.19/0.52 spl0_122 <=> subset(empty_set,empty_set)),
% 0.19/0.52 introduced(split_symbol_definition)).
% 0.19/0.52 fof(f1852,plain,(
% 0.19/0.52 ~ordinal(empty_set)|~ordinal(empty_set)|subset(empty_set,empty_set)|~spl0_72|~spl0_96),
% 0.19/0.52 inference(resolution,[status(thm)],[f1848,f190])).
% 0.19/0.52 fof(f1853,plain,(
% 0.19/0.52 ~spl0_22|spl0_122|~spl0_72|~spl0_96),
% 0.19/0.52 inference(split_clause,[status(thm)],[f1852,f380,f1849,f1007,f1436])).
% 0.19/0.52 fof(f1870,plain,(
% 0.19/0.52 $false|~spl0_110),
% 0.19/0.52 inference(backward_subsumption_resolution,[status(thm)],[f109,f1673])).
% 0.19/0.52 fof(f1871,plain,(
% 0.19/0.52 ~spl0_110),
% 0.19/0.52 inference(contradiction_clause,[status(thm)],[f1870])).
% 0.19/0.52 fof(f1880,plain,(
% 0.19/0.52 spl0_123 <=> in(empty_set,X0)|in(empty_set,X1)|~ordinal(set_union2(X0,X1))|set_union2(X0,X1)=empty_set),
% 0.19/0.52 introduced(split_symbol_definition)).
% 0.19/0.52 fof(f1889,plain,(
% 0.19/0.52 spl0_124 <=> ~ordinal(X0)|in(empty_set,X0)|empty_set=X0),
% 0.19/0.52 introduced(split_symbol_definition)).
% 0.19/0.52 fof(f1892,plain,(
% 0.19/0.52 ![X0]: (~ordinal(empty_set)|~ordinal(X0)|in(empty_set,X0)|empty_set=X0|~spl0_118)),
% 0.19/0.52 inference(resolution,[status(thm)],[f1773,f203])).
% 0.19/0.52 fof(f1893,plain,(
% 0.19/0.52 ~spl0_22|spl0_124|~spl0_118),
% 0.19/0.52 inference(split_clause,[status(thm)],[f1892,f380,f1889,f1772])).
% 0.19/0.52 fof(f1894,plain,(
% 0.19/0.52 ~ordinal(sk0_18)|~ordinal(empty_set)|subset(sk0_18,empty_set)|~spl0_102),
% 0.19/0.52 inference(resolution,[status(thm)],[f1529,f190])).
% 0.19/0.52 fof(f1895,plain,(
% 0.19/0.52 ~spl0_6|~spl0_22|spl0_97|~spl0_102),
% 0.19/0.52 inference(split_clause,[status(thm)],[f1894,f283,f380,f1441,f1528])).
% 0.19/0.52 fof(f1908,plain,(
% 0.19/0.52 spl0_125 <=> epsilon_transitive(succ(empty_set))),
% 0.19/0.52 introduced(split_symbol_definition)).
% 0.19/0.52 fof(f2016,plain,(
% 0.19/0.52 ![X0]: (empty(singleton(X0))|sk0_3(singleton(X0))=X0)),
% 0.19/0.52 inference(resolution,[status(thm)],[f1804,f248])).
% 0.19/0.52 fof(f2017,plain,(
% 0.19/0.52 ![X0]: (sk0_3(singleton(X0))=X0)),
% 0.19/0.52 inference(forward_subsumption_resolution,[status(thm)],[f2016,f1274])).
% 0.19/0.52 fof(f2022,plain,(
% 0.19/0.52 ![X0]: (empty(X0)|~in(X0,sk0_3(X0)))),
% 0.19/0.52 inference(resolution,[status(thm)],[f1804,f57])).
% 0.19/0.52 fof(f2023,plain,(
% 0.19/0.52 sk0_3(succ(empty_set))=empty_set),
% 0.19/0.52 inference(paramodulation,[status(thm)],[f1224,f2017])).
% 0.19/0.52 fof(f2026,plain,(
% 0.19/0.52 spl0_126 <=> empty(succ(empty_set))),
% 0.19/0.52 introduced(split_symbol_definition)).
% 0.19/0.52 fof(f2027,plain,(
% 0.19/0.52 empty(succ(empty_set))|~spl0_126),
% 0.19/0.52 inference(component_clause,[status(thm)],[f2026])).
% 0.19/0.52 fof(f2043,plain,(
% 0.19/0.52 ~ordinal(empty_set)|~ordinal(sk0_18)|subset(empty_set,sk0_18)|~spl0_96),
% 0.19/0.52 inference(resolution,[status(thm)],[f1437,f190])).
% 0.19/0.52 fof(f2044,plain,(
% 0.19/0.52 ~spl0_22|~spl0_6|spl0_73|~spl0_96),
% 0.19/0.52 inference(split_clause,[status(thm)],[f2043,f380,f283,f1022,f1436])).
% 0.19/0.52 fof(f2070,plain,(
% 0.19/0.52 spl0_127 <=> in(sk0_18,empty_set)),
% 0.19/0.52 introduced(split_symbol_definition)).
% 0.19/0.52 fof(f2071,plain,(
% 0.19/0.52 in(sk0_18,empty_set)|~spl0_127),
% 0.19/0.52 inference(component_clause,[status(thm)],[f2070])).
% 0.19/0.52 fof(f2073,plain,(
% 0.19/0.52 ~ordinal(sk0_18)|~ordinal(empty_set)|in(sk0_18,empty_set)|sk0_18=empty_set|spl0_73),
% 0.19/0.52 inference(resolution,[status(thm)],[f1024,f1217])).
% 0.19/0.52 fof(f2074,plain,(
% 0.19/0.52 ~spl0_6|~spl0_22|spl0_127|spl0_72|spl0_73),
% 0.19/0.52 inference(split_clause,[status(thm)],[f2073,f283,f380,f2070,f1007,f1022])).
% 0.19/0.52 fof(f2077,plain,(
% 0.19/0.52 $false|~spl0_118|~spl0_127),
% 0.19/0.52 inference(forward_subsumption_resolution,[status(thm)],[f2071,f1773])).
% 0.19/0.52 fof(f2078,plain,(
% 0.19/0.52 ~spl0_118|~spl0_127),
% 0.19/0.52 inference(contradiction_clause,[status(thm)],[f2077])).
% 0.19/0.52 fof(f2083,plain,(
% 0.19/0.52 ~ordinal(empty_set)|~ordinal(sk0_18)|in(empty_set,sk0_18)|empty_set=sk0_18|spl0_97),
% 0.19/0.52 inference(resolution,[status(thm)],[f1443,f1217])).
% 0.19/0.52 fof(f2084,plain,(
% 0.19/0.52 ~spl0_22|~spl0_6|spl0_71|spl0_72|spl0_97),
% 0.19/0.52 inference(split_clause,[status(thm)],[f2083,f380,f283,f1004,f1007,f1441])).
% 0.19/0.52 fof(f2124,plain,(
% 0.19/0.52 ~ordinal(sk0_18)|~subset(sk0_17,sk0_18)|~spl0_13),
% 0.19/0.52 inference(paramodulation,[status(thm)],[f335,f671])).
% 0.19/0.52 fof(f2125,plain,(
% 0.19/0.52 ~spl0_6|~spl0_9|~spl0_13),
% 0.19/0.52 inference(split_clause,[status(thm)],[f2124,f283,f294,f334])).
% 0.19/0.52 fof(f2132,plain,(
% 0.19/0.52 ~epsilon_transitive(succ(sk0_18))|subset(sk0_18,sk0_17)|~spl0_13),
% 0.19/0.52 inference(paramodulation,[status(thm)],[f335,f609])).
% 0.19/0.52 fof(f2133,plain,(
% 0.19/0.52 ~spl0_20|spl0_10|~spl0_13),
% 0.19/0.52 inference(split_clause,[status(thm)],[f2132,f371,f305,f334])).
% 0.19/0.52 fof(f2159,plain,(
% 0.19/0.52 spl0_129 <=> in(succ(empty_set),empty_set)),
% 0.19/0.52 introduced(split_symbol_definition)).
% 0.19/0.52 fof(f2162,plain,(
% 0.19/0.52 empty(succ(empty_set))|~in(succ(empty_set),empty_set)),
% 0.19/0.52 inference(paramodulation,[status(thm)],[f2023,f2022])).
% 0.19/0.52 fof(f2163,plain,(
% 0.19/0.52 spl0_126|~spl0_129),
% 0.19/0.52 inference(split_clause,[status(thm)],[f2162,f2026,f2159])).
% 0.19/0.52 fof(f2255,plain,(
% 0.19/0.52 spl0_130 <=> sk0_3(succ(empty_set))=empty_set),
% 0.19/0.52 introduced(split_symbol_definition)).
% 0.19/0.52 fof(f2258,plain,(
% 0.19/0.52 sk0_3(succ(empty_set))=empty_set|empty(succ(empty_set))),
% 0.19/0.52 inference(resolution,[status(thm)],[f1389,f1804])).
% 0.19/0.52 fof(f2259,plain,(
% 0.19/0.52 spl0_130|spl0_126),
% 0.19/0.52 inference(split_clause,[status(thm)],[f2258,f2255,f2026])).
% 0.19/0.52 fof(f2266,plain,(
% 0.19/0.52 spl0_131 <=> empty_set=succ(empty_set)),
% 0.19/0.52 introduced(split_symbol_definition)).
% 0.19/0.52 fof(f2267,plain,(
% 0.19/0.52 empty_set=succ(empty_set)|~spl0_131),
% 0.19/0.52 inference(component_clause,[status(thm)],[f2266])).
% 0.19/0.52 fof(f2271,plain,(
% 0.19/0.52 spl0_132 <=> set_union2(X0,X1)=empty_set|in(succ(empty_set),X0)|in(succ(empty_set),X1)|~ordinal(set_union2(X0,X1))|set_union2(X0,X1)=succ(empty_set)),
% 0.19/0.52 introduced(split_symbol_definition)).
% 0.19/0.52 fof(f2274,plain,(
% 0.19/0.52 ![X0,X1]: (set_union2(X0,X1)=empty_set|in(succ(empty_set),X0)|in(succ(empty_set),X1)|~ordinal(set_union2(X0,X1))|~ordinal(succ(empty_set))|set_union2(X0,X1)=succ(empty_set))),
% 0.19/0.52 inference(resolution,[status(thm)],[f1389,f795])).
% 0.19/0.52 fof(f2275,plain,(
% 0.19/0.52 spl0_132|~spl0_79),
% 0.19/0.52 inference(split_clause,[status(thm)],[f2274,f2271,f1309])).
% 0.19/0.52 fof(f2276,plain,(
% 0.19/0.52 spl0_133 <=> sk0_1(succ(empty_set))=empty_set),
% 0.19/0.52 introduced(split_symbol_definition)).
% 0.19/0.52 fof(f2277,plain,(
% 0.19/0.52 sk0_1(succ(empty_set))=empty_set|~spl0_133),
% 0.19/0.52 inference(component_clause,[status(thm)],[f2276])).
% 0.19/0.52 fof(f2279,plain,(
% 0.19/0.52 sk0_1(succ(empty_set))=empty_set|epsilon_transitive(succ(empty_set))),
% 0.19/0.52 inference(resolution,[status(thm)],[f1389,f96])).
% 0.19/0.52 fof(f2280,plain,(
% 0.19/0.52 spl0_133|spl0_125),
% 0.19/0.52 inference(split_clause,[status(thm)],[f2279,f2276,f1908])).
% 0.19/0.52 fof(f2282,plain,(
% 0.19/0.52 spl0_134 <=> singleton(X0)=empty_set|succ(empty_set)=X0|~ordinal(singleton(X0))|singleton(X0)=succ(empty_set)),
% 0.19/0.52 introduced(split_symbol_definition)).
% 0.19/0.52 fof(f2285,plain,(
% 0.19/0.52 ![X0]: (singleton(X0)=empty_set|succ(empty_set)=X0|~ordinal(singleton(X0))|~ordinal(succ(empty_set))|singleton(X0)=succ(empty_set))),
% 0.19/0.52 inference(resolution,[status(thm)],[f1389,f487])).
% 0.19/0.52 fof(f2286,plain,(
% 0.19/0.52 spl0_134|~spl0_79),
% 0.19/0.52 inference(split_clause,[status(thm)],[f2285,f2282,f1309])).
% 0.19/0.52 fof(f2287,plain,(
% 0.19/0.52 spl0_135 <=> X0=empty_set|~ordinal(X0)|in(succ(empty_set),X0)|succ(empty_set)=X0),
% 0.19/0.52 introduced(split_symbol_definition)).
% 0.19/0.52 fof(f2290,plain,(
% 0.19/0.52 ![X0]: (X0=empty_set|~ordinal(succ(empty_set))|~ordinal(X0)|in(succ(empty_set),X0)|succ(empty_set)=X0)),
% 0.19/0.52 inference(resolution,[status(thm)],[f1389,f203])).
% 0.19/0.52 fof(f2291,plain,(
% 0.19/0.52 spl0_135|~spl0_79),
% 0.19/0.52 inference(split_clause,[status(thm)],[f2290,f2287,f1309])).
% 0.19/0.52 fof(f2292,plain,(
% 0.19/0.52 $false|~spl0_126),
% 0.19/0.52 inference(forward_subsumption_resolution,[status(thm)],[f2027,f112])).
% 0.19/0.52 fof(f2293,plain,(
% 0.19/0.52 ~spl0_126),
% 0.19/0.52 inference(contradiction_clause,[status(thm)],[f2292])).
% 0.19/0.52 fof(f2311,plain,(
% 0.19/0.52 spl0_136 <=> epsilon_transitive(singleton(empty_set))),
% 0.19/0.52 introduced(split_symbol_definition)).
% 0.19/0.52 fof(f2313,plain,(
% 0.19/0.52 ~epsilon_transitive(singleton(empty_set))|spl0_136),
% 0.19/0.52 inference(component_clause,[status(thm)],[f2311])).
% 0.19/0.52 fof(f2314,plain,(
% 0.19/0.52 spl0_137 <=> subset(empty_set,succ(empty_set))),
% 0.19/0.52 introduced(split_symbol_definition)).
% 0.19/0.52 fof(f2315,plain,(
% 0.19/0.52 subset(empty_set,succ(empty_set))|~spl0_137),
% 0.19/0.52 inference(component_clause,[status(thm)],[f2314])).
% 0.19/0.52 fof(f2317,plain,(
% 0.19/0.52 ~epsilon_transitive(singleton(empty_set))|subset(empty_set,succ(empty_set))),
% 0.19/0.52 inference(paramodulation,[status(thm)],[f1224,f608])).
% 0.19/0.52 fof(f2318,plain,(
% 0.19/0.52 ~spl0_136|spl0_137),
% 0.19/0.52 inference(split_clause,[status(thm)],[f2317,f2311,f2314])).
% 0.19/0.52 fof(f2319,plain,(
% 0.19/0.52 ~epsilon_transitive(succ(empty_set))|spl0_136),
% 0.19/0.52 inference(forward_demodulation,[status(thm)],[f1224,f2313])).
% 0.19/0.52 fof(f2320,plain,(
% 0.19/0.52 $false|~spl0_79|spl0_136),
% 0.19/0.52 inference(forward_subsumption_resolution,[status(thm)],[f2319,f1846])).
% 0.19/0.52 fof(f2321,plain,(
% 0.19/0.52 ~spl0_79|spl0_136),
% 0.19/0.52 inference(contradiction_clause,[status(thm)],[f2320])).
% 0.19/0.52 fof(f2334,plain,(
% 0.19/0.52 spl0_138 <=> empty(sk0_18)),
% 0.19/0.52 introduced(split_symbol_definition)).
% 0.19/0.52 fof(f2336,plain,(
% 0.19/0.52 ~empty(sk0_18)|spl0_138),
% 0.19/0.52 inference(component_clause,[status(thm)],[f2334])).
% 0.19/0.52 fof(f2431,plain,(
% 0.19/0.52 epsilon_transitive(succ(empty_set))|~subset(empty_set,succ(empty_set))|~spl0_133),
% 0.19/0.52 inference(paramodulation,[status(thm)],[f2277,f97])).
% 0.19/0.52 fof(f2432,plain,(
% 0.19/0.52 spl0_125|~spl0_137|~spl0_133),
% 0.19/0.52 inference(split_clause,[status(thm)],[f2431,f1908,f2314,f2276])).
% 0.19/0.52 fof(f2437,plain,(
% 0.19/0.52 spl0_144 <=> ordinal_subset(empty_set,succ(empty_set))),
% 0.19/0.52 introduced(split_symbol_definition)).
% 0.19/0.52 fof(f2440,plain,(
% 0.19/0.52 ~ordinal(empty_set)|~ordinal(succ(empty_set))|ordinal_subset(empty_set,succ(empty_set))|~spl0_137),
% 0.19/0.52 inference(resolution,[status(thm)],[f2315,f191])).
% 0.19/0.52 fof(f2441,plain,(
% 0.19/0.52 ~spl0_22|~spl0_79|spl0_144|~spl0_137),
% 0.19/0.52 inference(split_clause,[status(thm)],[f2440,f380,f1309,f2437,f2314])).
% 0.19/0.52 fof(f2442,plain,(
% 0.19/0.52 spl0_145 <=> subset(succ(empty_set),empty_set)),
% 0.19/0.52 introduced(split_symbol_definition)).
% 0.19/0.52 fof(f2445,plain,(
% 0.19/0.52 succ(empty_set)=empty_set|~subset(succ(empty_set),empty_set)|~spl0_137),
% 0.19/0.52 inference(resolution,[status(thm)],[f2315,f82])).
% 0.19/0.52 fof(f2446,plain,(
% 0.19/0.52 spl0_131|~spl0_145|~spl0_137),
% 0.19/0.52 inference(split_clause,[status(thm)],[f2445,f2266,f2442,f2314])).
% 0.19/0.52 fof(f2477,plain,(
% 0.19/0.52 $false|~spl0_131),
% 0.19/0.52 inference(forward_subsumption_resolution,[status(thm)],[f2267,f198])).
% 0.19/0.52 fof(f2478,plain,(
% 0.19/0.52 ~spl0_131),
% 0.19/0.52 inference(contradiction_clause,[status(thm)],[f2477])).
% 0.19/0.52 fof(f2494,plain,(
% 0.19/0.52 ![X0,X1,X2]: (in(empty_set,X0)|in(empty_set,X1)|~ordinal(set_union2(X0,X1))|set_union2(X0,X1)=empty_set|~empty(X2)|~spl0_113)),
% 0.19/0.52 inference(resolution,[status(thm)],[f1715,f227])).
% 0.19/0.52 fof(f2495,plain,(
% 0.19/0.52 spl0_123|spl0_110|~spl0_113),
% 0.19/0.52 inference(split_clause,[status(thm)],[f2494,f1880,f1672,f1714])).
% 0.19/0.52 fof(f2501,plain,(
% 0.19/0.52 spl0_146 <=> in(X0,X1)|in(empty_set,X0)|~ordinal(set_union2(empty_set,X0))|set_union2(empty_set,X0)=empty_set),
% 0.19/0.52 introduced(split_symbol_definition)).
% 0.19/0.52 fof(f2504,plain,(
% 0.19/0.52 spl0_147 <=> in(empty_set,empty_set)),
% 0.19/0.52 introduced(split_symbol_definition)).
% 0.19/0.52 fof(f2505,plain,(
% 0.19/0.52 in(empty_set,empty_set)|~spl0_147),
% 0.19/0.52 inference(component_clause,[status(thm)],[f2504])).
% 0.19/0.52 fof(f2507,plain,(
% 0.19/0.52 ![X0,X1]: (in(X0,X1)|in(empty_set,empty_set)|in(empty_set,X0)|~ordinal(set_union2(empty_set,X0))|set_union2(empty_set,X0)=empty_set|~spl0_113)),
% 0.19/0.52 inference(paramodulation,[status(thm)],[f764,f1715])).
% 0.19/0.52 fof(f2508,plain,(
% 0.19/0.52 spl0_146|spl0_147|~spl0_113),
% 0.19/0.52 inference(split_clause,[status(thm)],[f2507,f2501,f2504,f1714])).
% 0.19/0.52 fof(f2509,plain,(
% 0.19/0.52 spl0_148 <=> in(X0,X1)|in(empty_set,X0)|~ordinal(set_union2(X0,empty_set))|set_union2(X0,empty_set)=empty_set),
% 0.19/0.52 introduced(split_symbol_definition)).
% 0.19/0.52 fof(f2512,plain,(
% 0.19/0.52 ![X0,X1]: (in(X0,X1)|in(empty_set,X0)|in(empty_set,empty_set)|~ordinal(set_union2(X0,empty_set))|set_union2(X0,empty_set)=empty_set|~spl0_113)),
% 0.19/0.52 inference(paramodulation,[status(thm)],[f199,f1715])).
% 0.19/0.52 fof(f2513,plain,(
% 0.19/0.52 spl0_148|spl0_147|~spl0_113),
% 0.19/0.52 inference(split_clause,[status(thm)],[f2512,f2509,f2504,f1714])).
% 0.19/0.52 fof(f2523,plain,(
% 0.19/0.52 $false|~spl0_118|~spl0_147),
% 0.19/0.52 inference(forward_subsumption_resolution,[status(thm)],[f2505,f1773])).
% 0.19/0.52 fof(f2524,plain,(
% 0.19/0.52 ~spl0_118|~spl0_147),
% 0.19/0.52 inference(contradiction_clause,[status(thm)],[f2523])).
% 0.19/0.52 fof(f2587,plain,(
% 0.19/0.52 spl0_156 <=> ~in(X0,X1)|in(empty_set,X1)|~ordinal(set_union2(empty_set,X1))|set_union2(empty_set,X1)=empty_set),
% 0.19/0.52 introduced(split_symbol_definition)).
% 0.19/0.52 fof(f2590,plain,(
% 0.19/0.52 ![X0,X1]: (~in(X0,X1)|in(empty_set,empty_set)|in(empty_set,X1)|~ordinal(set_union2(empty_set,X1))|set_union2(empty_set,X1)=empty_set|~spl0_65)),
% 0.19/0.52 inference(paramodulation,[status(thm)],[f764,f970])).
% 0.19/0.52 fof(f2591,plain,(
% 0.19/0.52 spl0_156|spl0_147|~spl0_65),
% 0.19/0.52 inference(split_clause,[status(thm)],[f2590,f2587,f2504,f969])).
% 0.19/0.52 fof(f2592,plain,(
% 0.19/0.52 spl0_157 <=> ~in(X0,X1)|in(empty_set,X1)|~ordinal(set_union2(X1,empty_set))|set_union2(X1,empty_set)=empty_set),
% 0.19/0.52 introduced(split_symbol_definition)).
% 0.19/0.52 fof(f2595,plain,(
% 0.19/0.52 ![X0,X1]: (~in(X0,X1)|in(empty_set,X1)|in(empty_set,empty_set)|~ordinal(set_union2(X1,empty_set))|set_union2(X1,empty_set)=empty_set|~spl0_65)),
% 0.19/0.52 inference(paramodulation,[status(thm)],[f199,f970])).
% 0.19/0.52 fof(f2596,plain,(
% 0.19/0.52 spl0_157|spl0_147|~spl0_65),
% 0.19/0.52 inference(split_clause,[status(thm)],[f2595,f2592,f2504,f969])).
% 0.19/0.52 fof(f2607,plain,(
% 0.19/0.52 ~empty(sk0_18)|~ordinal(empty_set)|sk0_18=empty_set|spl0_97),
% 0.19/0.52 inference(resolution,[status(thm)],[f1670,f1443])).
% 0.19/0.52 fof(f2608,plain,(
% 0.19/0.52 ~spl0_138|~spl0_22|spl0_72|spl0_97),
% 0.19/0.52 inference(split_clause,[status(thm)],[f2607,f2334,f380,f1007,f1441])).
% 0.19/0.52 fof(f2699,plain,(
% 0.19/0.52 spl0_158 <=> ~empty(X0)|X0=succ(empty_set)|X0=empty_set),
% 0.19/0.52 introduced(split_symbol_definition)).
% 0.19/0.52 fof(f2702,plain,(
% 0.19/0.52 ![X0]: (~empty(X0)|~ordinal(succ(empty_set))|X0=succ(empty_set)|X0=empty_set)),
% 0.19/0.52 inference(resolution,[status(thm)],[f1277,f1389])).
% 0.19/0.52 fof(f2703,plain,(
% 0.19/0.52 spl0_158|~spl0_79),
% 0.19/0.52 inference(split_clause,[status(thm)],[f2702,f2699,f1309])).
% 0.19/0.52 fof(f2707,plain,(
% 0.19/0.52 spl0_159 <=> ~empty(X0)|X0=empty_set),
% 0.19/0.52 introduced(split_symbol_definition)).
% 0.19/0.52 fof(f2710,plain,(
% 0.19/0.52 ![X0]: (~empty(X0)|~ordinal(empty_set)|X0=empty_set|~spl0_118)),
% 0.19/0.52 inference(resolution,[status(thm)],[f1277,f1773])).
% 0.19/0.52 fof(f2711,plain,(
% 0.19/0.52 spl0_159|~spl0_22|~spl0_118),
% 0.19/0.52 inference(split_clause,[status(thm)],[f2710,f2707,f380,f1772])).
% 0.19/0.52 fof(f2825,plain,(
% 0.19/0.52 spl0_160 <=> in(sk0_17,singleton(sk0_18))),
% 0.19/0.52 introduced(split_symbol_definition)).
% 0.19/0.52 fof(f2826,plain,(
% 0.19/0.52 in(sk0_17,singleton(sk0_18))|~spl0_160),
% 0.19/0.52 inference(component_clause,[status(thm)],[f2825])).
% 0.19/0.52 fof(f2828,plain,(
% 0.19/0.52 in(sk0_17,sk0_18)|in(sk0_17,singleton(sk0_18))|~spl0_2),
% 0.19/0.52 inference(resolution,[status(thm)],[f796,f239])).
% 0.19/0.52 fof(f2829,plain,(
% 0.19/0.52 spl0_50|spl0_160|~spl0_2),
% 0.19/0.52 inference(split_clause,[status(thm)],[f2828,f650,f2825,f238])).
% 0.19/0.52 fof(f2855,plain,(
% 0.19/0.52 ~empty(empty_set)|~spl0_72|spl0_138),
% 0.19/0.52 inference(backward_demodulation,[status(thm)],[f1008,f2336])).
% 0.19/0.52 fof(f2856,plain,(
% 0.19/0.52 ~spl0_4|~spl0_72|spl0_138),
% 0.19/0.52 inference(split_clause,[status(thm)],[f2855,f273,f1007,f2334])).
% 0.19/0.52 fof(f2873,plain,(
% 0.19/0.52 ~subset(empty_set,empty_set)|~spl0_72|spl0_97),
% 0.19/0.52 inference(forward_demodulation,[status(thm)],[f1008,f1443])).
% 0.19/0.52 fof(f2874,plain,(
% 0.19/0.52 $false|~spl0_72|spl0_97),
% 0.19/0.52 inference(forward_subsumption_resolution,[status(thm)],[f2873,f246])).
% 0.19/0.52 fof(f2875,plain,(
% 0.19/0.52 ~spl0_72|spl0_97),
% 0.19/0.52 inference(contradiction_clause,[status(thm)],[f2874])).
% 0.19/0.52 fof(f2946,plain,(
% 0.19/0.52 sk0_17=sk0_18|~spl0_160),
% 0.19/0.52 inference(resolution,[status(thm)],[f2826,f248])).
% 0.19/0.52 fof(f2947,plain,(
% 0.19/0.52 spl0_31|~spl0_160),
% 0.19/0.52 inference(split_clause,[status(thm)],[f2946,f446,f2825])).
% 0.19/0.52 fof(f2967,plain,(
% 0.19/0.52 $false),
% 0.19/0.52 inference(sat_refutation,[status(thm)],[f237,f244,f245,f280,f282,f293,f298,f300,f302,f309,f338,f340,f360,f384,f386,f388,f405,f420,f435,f443,f445,f450,f461,f474,f476,f499,f507,f519,f521,f523,f525,f531,f622,f660,f677,f748,f750,f758,f760,f875,f880,f887,f892,f897,f911,f944,f951,f956,f968,f973,f984,f989,f1026,f1029,f1031,f1060,f1305,f1313,f1319,f1369,f1374,f1379,f1386,f1440,f1445,f1500,f1503,f1506,f1510,f1532,f1635,f1653,f1660,f1696,f1705,f1718,f1729,f1734,f1739,f1776,f1795,f1802,f1853,f1871,f1893,f1895,f2044,f2074,f2078,f2084,f2125,f2133,f2163,f2259,f2275,f2280,f2286,f2291,f2293,f2318,f2321,f2432,f2441,f2446,f2478,f2495,f2508,f2513,f2524,f2591,f2596,f2608,f2703,f2711,f2829,f2856,f2875,f2947])).
% 0.19/0.52 % SZS output end CNFRefutation for theBenchmark.p
% 0.19/0.52 % Elapsed time: 0.181954 seconds
% 0.19/0.52 % CPU time: 1.320461 seconds
% 0.19/0.52 % Memory used: 74.878 MB
%------------------------------------------------------------------------------