TSTP Solution File: SEU197+2 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SEU197+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n032.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed May 31 12:36:13 EDT 2023
% Result : Theorem 106.73s 13.75s
% Output : CNFRefutation 107.32s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : SEU197+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.09 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.07/0.27 % Computer : n032.cluster.edu
% 0.07/0.27 % Model : x86_64 x86_64
% 0.07/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.27 % Memory : 8042.1875MB
% 0.07/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.27 % CPULimit : 300
% 0.07/0.27 % WCLimit : 300
% 0.07/0.27 % DateTime : Tue May 30 09:16:31 EDT 2023
% 0.07/0.27 % CPUTime :
% 0.12/0.29 % Drodi V3.5.1
% 106.73/13.75 % Refutation found
% 106.73/13.75 % SZS status Theorem for theBenchmark: Theorem is valid
% 106.73/13.75 % SZS output start CNFRefutation for theBenchmark
% 106.73/13.75 fof(f1,axiom,(
% 106.73/13.75 (! [A,B] :( in(A,B)=> ~ in(B,A) ) )),
% 106.73/13.75 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 106.73/13.75 fof(f3,axiom,(
% 106.73/13.75 (! [A] :( empty(A)=> relation(A) ) )),
% 106.73/13.75 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 106.73/13.75 fof(f5,axiom,(
% 106.73/13.75 (! [A,B] : set_union2(A,B) = set_union2(B,A) )),
% 106.73/13.75 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 106.73/13.75 fof(f6,axiom,(
% 106.73/13.75 (! [A,B] : set_intersection2(A,B) = set_intersection2(B,A) )),
% 106.73/13.75 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 106.73/13.75 fof(f7,axiom,(
% 106.73/13.75 (! [A,B] :( relation(B)=> ( B = identity_relation(A)<=> (! [C,D] :( in(ordered_pair(C,D),B)<=> ( in(C,A)& C = D ) ) )) ) )),
% 106.73/13.75 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 106.73/13.75 fof(f8,axiom,(
% 106.73/13.75 (! [A,B] :( A = B<=> ( subset(A,B)& subset(B,A) ) ) )),
% 106.73/13.75 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 106.73/13.75 fof(f9,axiom,(
% 106.73/13.75 (! [A] :( relation(A)=> (! [B,C] :( relation(C)=> ( C = relation_dom_restriction(A,B)<=> (! [D,E] :( in(ordered_pair(D,E),C)<=> ( in(D,B)& in(ordered_pair(D,E),A) ) ) )) ) )) )),
% 106.73/13.75 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 106.73/13.75 fof(f10,axiom,(
% 106.73/13.75 (! [A,B] :( relation(B)=> (! [C] :( relation(C)=> ( C = relation_rng_restriction(A,B)<=> (! [D,E] :( in(ordered_pair(D,E),C)<=> ( in(E,A)& in(ordered_pair(D,E),B) ) ) )) ) )) )),
% 106.73/13.75 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 106.73/13.75 fof(f13,axiom,(
% 106.73/13.75 (! [A,B] :( B = singleton(A)<=> (! [C] :( in(C,B)<=> C = A ) )) )),
% 106.73/13.75 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 106.73/13.75 fof(f14,axiom,(
% 106.73/13.75 (! [A] :( A = empty_set<=> (! [B] : ~ in(B,A) )) )),
% 106.73/13.75 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 106.73/13.75 fof(f15,axiom,(
% 106.73/13.75 (! [A,B] :( B = powerset(A)<=> (! [C] :( in(C,B)<=> subset(C,A) ) )) )),
% 106.73/13.75 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 106.73/13.75 fof(f16,axiom,(
% 106.73/13.75 (! [A] :( relation(A)=> (! [B] :( relation(B)=> ( A = B<=> (! [C,D] :( in(ordered_pair(C,D),A)<=> in(ordered_pair(C,D),B) ) )) ) )) )),
% 106.73/13.75 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 106.73/13.75 fof(f18,axiom,(
% 106.73/13.75 (! [A,B,C] :( C = unordered_pair(A,B)<=> (! [D] :( in(D,C)<=> ( D = A| D = B ) ) )) )),
% 106.73/13.75 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 106.73/13.75 fof(f21,axiom,(
% 106.73/13.75 (! [A] :( relation(A)=> (! [B] :( relation(B)=> ( subset(A,B)<=> (! [C,D] :( in(ordered_pair(C,D),A)=> in(ordered_pair(C,D),B) ) )) ) )) )),
% 106.73/13.75 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 106.73/13.75 fof(f22,axiom,(
% 106.73/13.75 (! [A,B] :( subset(A,B)<=> (! [C] :( in(C,A)=> in(C,B) ) )) )),
% 106.73/13.75 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 106.73/13.75 fof(f24,axiom,(
% 106.73/13.75 (! [A] :( relation(A)=> (! [B] :( B = relation_dom(A)<=> (! [C] :( in(C,B)<=> (? [D] : in(ordered_pair(C,D),A) )) )) )) )),
% 106.73/13.75 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 106.73/13.75 fof(f28,axiom,(
% 106.73/13.75 (! [A] :( relation(A)=> (! [B] :( B = relation_rng(A)<=> (! [C] :( in(C,B)<=> (? [D] : in(ordered_pair(D,C),A) )) )) )) )),
% 106.73/13.75 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 106.73/13.75 fof(f31,axiom,(
% 106.73/13.75 (! [A] :( relation(A)=> relation_field(A) = set_union2(relation_dom(A),relation_rng(A)) ) )),
% 106.73/13.75 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 106.73/13.75 fof(f32,axiom,(
% 106.73/13.75 (! [A] :( relation(A)=> (! [B] :( relation(B)=> ( B = relation_inverse(A)<=> (! [C,D] :( in(ordered_pair(C,D),B)<=> in(ordered_pair(D,C),A) ) )) ) )) )),
% 106.73/13.75 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 106.73/13.75 fof(f33,axiom,(
% 106.73/13.75 (! [A,B] :( disjoint(A,B)<=> set_intersection2(A,B) = empty_set ) )),
% 106.73/13.75 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 106.73/13.75 fof(f34,axiom,(
% 106.73/13.75 (! [A] :( relation(A)=> (! [B] :( relation(B)=> (! [C] :( relation(C)=> ( C = relation_composition(A,B)<=> (! [D,E] :( in(ordered_pair(D,E),C)<=> (? [F] :( in(ordered_pair(D,F),A)& in(ordered_pair(F,E),B) ) )) )) ) )) )) )),
% 106.73/13.75 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 106.73/13.75 fof(f36,axiom,(
% 106.73/13.75 (! [A,B] :( proper_subset(A,B)<=> ( subset(A,B)& A != B ) ) )),
% 106.73/13.75 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 106.73/13.76 fof(f54,axiom,(
% 106.73/13.76 (! [A,B] :( ( relation(A)& relation(B) )=> relation(relation_composition(A,B)) ) )),
% 106.73/13.76 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 106.73/13.76 fof(f56,axiom,(
% 106.73/13.76 (! [A] : relation(identity_relation(A)) )),
% 106.73/13.76 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 106.73/13.76 fof(f59,axiom,(
% 106.73/13.76 (! [A,B] :( relation(A)=> relation(relation_dom_restriction(A,B)) ) )),
% 106.73/13.76 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 106.73/13.76 fof(f61,axiom,(
% 106.73/13.76 (! [A,B] :( relation(B)=> relation(relation_rng_restriction(A,B)) ) )),
% 106.73/13.76 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 106.73/13.76 fof(f67,axiom,(
% 106.73/13.76 empty(empty_set) ),
% 106.73/13.76 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 106.73/13.76 fof(f69,axiom,(
% 106.73/13.76 (! [A,B] :( ( relation(A)& relation(B) )=> relation(set_union2(A,B)) ) )),
% 106.73/13.76 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 106.73/13.76 fof(f71,axiom,(
% 106.73/13.76 (! [A,B] :( ~ empty(A)=> ~ empty(set_union2(A,B)) ) )),
% 106.73/13.76 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 106.73/13.76 fof(f79,axiom,(
% 106.73/13.76 (! [A] :( empty(A)=> ( empty(relation_rng(A))& relation(relation_rng(A)) ) ) )),
% 106.73/13.76 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 106.73/13.76 fof(f81,axiom,(
% 106.73/13.76 (! [A,B] : set_union2(A,A) = A )),
% 106.73/13.76 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 106.73/13.76 fof(f82,axiom,(
% 106.73/13.76 (! [A,B] : set_intersection2(A,A) = A )),
% 106.73/13.76 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 106.73/13.76 fof(f91,lemma,(
% 106.73/13.76 (! [A,B] :( subset(singleton(A),B)<=> in(A,B) ) )),
% 106.73/13.76 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 106.73/13.76 fof(f101,axiom,(
% 106.73/13.76 (? [A] : empty(A) )),
% 106.73/13.76 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 106.73/13.76 fof(f112,conjecture,(
% 106.73/13.76 (! [A,B,C] :( relation(C)=> ( in(A,relation_rng(relation_rng_restriction(B,C)))<=> ( in(A,B)& in(A,relation_rng(C)) ) ) ) )),
% 106.73/13.76 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 106.73/13.76 fof(f113,negated_conjecture,(
% 106.73/13.76 ~((! [A,B,C] :( relation(C)=> ( in(A,relation_rng(relation_rng_restriction(B,C)))<=> ( in(A,B)& in(A,relation_rng(C)) ) ) ) ))),
% 106.73/13.76 inference(negated_conjecture,[status(cth)],[f112])).
% 106.73/13.76 fof(f117,lemma,(
% 106.73/13.76 (! [A] :(? [B] :( in(A,B)& (! [C,D] :( ( in(C,B)& subset(D,C) )=> in(D,B) ))& (! [C] :( in(C,B)=> in(powerset(C),B) ))& (! [C] :~ ( subset(C,B)& ~ are_equipotent(C,B)& ~ in(C,B) ) )) ))),
% 106.73/13.76 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 106.73/13.76 fof(f118,lemma,(
% 106.73/13.76 (! [A,B] : subset(set_intersection2(A,B),A) )),
% 106.73/13.76 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 106.73/13.76 fof(f120,axiom,(
% 106.73/13.76 (! [A] : set_union2(A,empty_set) = A )),
% 106.73/13.76 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 106.73/13.76 fof(f122,lemma,(
% 106.73/13.76 (! [A,B,C] :( ( subset(A,B)& subset(B,C) )=> subset(A,C) ) )),
% 106.73/13.76 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 106.73/13.76 fof(f126,lemma,(
% 106.73/13.76 (! [A] :( relation(A)=> (! [B] :( relation(B)=> ( subset(A,B)=> ( subset(relation_dom(A),relation_dom(B))& subset(relation_rng(A),relation_rng(B)) ) ) ) )) )),
% 106.73/13.76 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 106.73/13.76 fof(f129,axiom,(
% 106.73/13.76 (! [A] : set_intersection2(A,empty_set) = empty_set )),
% 106.73/13.76 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 106.73/13.76 fof(f136,lemma,(
% 106.73/13.76 (! [A,B] : subset(set_difference(A,B),A) )),
% 106.73/13.76 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 106.73/13.76 fof(f143,axiom,(
% 106.73/13.76 (! [A] : set_difference(A,empty_set) = A )),
% 106.73/13.76 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 106.73/13.76 fof(f159,axiom,(
% 106.73/13.76 (! [A] : set_difference(empty_set,A) = empty_set )),
% 106.73/13.76 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 106.73/13.76 fof(f161,lemma,(
% 106.73/13.76 (! [A,B] :( ~ ( ~ disjoint(A,B)& (! [C] : ~ in(C,set_intersection2(A,B)) ))& ~ ( (? [C] : in(C,set_intersection2(A,B)))& disjoint(A,B) ) ) )),
% 106.73/13.76 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 106.73/13.76 fof(f166,lemma,(
% 106.73/13.76 ( relation_dom(empty_set) = empty_set& relation_rng(empty_set) = empty_set ) ),
% 106.73/13.76 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 106.73/13.76 fof(f167,lemma,(
% 106.73/13.76 (! [A,B] :~ ( subset(A,B)& proper_subset(B,A) ) )),
% 106.73/13.76 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 106.73/13.76 fof(f168,lemma,(
% 106.73/13.76 (! [A,B,C] :( ( subset(A,B)& disjoint(B,C) )=> disjoint(A,C) ) )),
% 106.73/13.76 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 106.73/13.76 fof(f169,lemma,(
% 106.73/13.76 (! [A] :( relation(A)=> ( ( relation_dom(A) = empty_set| relation_rng(A) = empty_set )=> A = empty_set ) ) )),
% 106.73/13.76 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 106.73/13.76 fof(f170,lemma,(
% 106.73/13.76 (! [A] :( relation(A)=> ( relation_dom(A) = empty_set<=> relation_rng(A) = empty_set ) ) )),
% 106.73/13.76 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 106.73/13.76 fof(f171,lemma,(
% 106.73/13.76 (! [A,B] :( set_difference(A,singleton(B)) = A<=> ~ in(B,A) ) )),
% 106.73/13.76 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 106.73/13.76 fof(f173,axiom,(
% 106.73/13.76 (! [A] :( empty(A)=> A = empty_set ) )),
% 106.73/13.76 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 106.73/13.76 fof(f175,lemma,(
% 106.73/13.76 (! [A] :( relation_dom(identity_relation(A)) = A& relation_rng(identity_relation(A)) = A ) )),
% 106.73/13.76 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 106.73/13.76 fof(f177,axiom,(
% 106.73/13.76 (! [A,B] :~ ( in(A,B)& empty(B) ) )),
% 106.73/13.76 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 106.73/13.76 fof(f178,lemma,(
% 106.73/13.76 (! [A,B] : subset(A,set_union2(A,B)) )),
% 106.73/13.76 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 106.73/13.76 fof(f179,lemma,(
% 106.73/13.76 (! [A,B] :( disjoint(A,B)<=> set_difference(A,B) = A ) )),
% 106.73/13.76 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 106.73/13.76 fof(f181,lemma,(
% 106.73/13.76 (! [A,B] :( relation(B)=> subset(relation_dom_restriction(B,A),B) ) )),
% 106.73/13.76 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 106.73/13.76 fof(f182,axiom,(
% 106.73/13.76 (! [A,B] :~ ( empty(A)& A != B& empty(B) ) )),
% 106.73/13.76 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 106.73/13.76 fof(f190,axiom,(
% 106.73/13.76 (! [A] :(? [B] :( in(A,B)& (! [C,D] :( ( in(C,B)& subset(D,C) )=> in(D,B) ))& (! [C] :~ ( in(C,B)& (! [D] :~ ( in(D,B)& (! [E] :( subset(E,C)=> in(E,D) ) )) )))& (! [C] :~ ( subset(C,B)& ~ are_equipotent(C,B)& ~ in(C,B) ) )) ))),
% 106.73/13.76 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 106.73/13.76 fof(f192,plain,(
% 106.73/13.76 ![A,B]: (~in(A,B)|~in(B,A))),
% 106.73/13.76 inference(pre_NNF_transformation,[status(esa)],[f1])).
% 106.73/13.76 fof(f193,plain,(
% 106.73/13.76 ![X0,X1]: (~in(X0,X1)|~in(X1,X0))),
% 106.73/13.76 inference(cnf_transformation,[status(esa)],[f192])).
% 106.73/13.76 fof(f196,plain,(
% 106.73/13.76 ![A]: (~empty(A)|relation(A))),
% 106.73/13.76 inference(pre_NNF_transformation,[status(esa)],[f3])).
% 106.73/13.76 fof(f197,plain,(
% 106.73/13.76 ![X0]: (~empty(X0)|relation(X0))),
% 106.73/13.76 inference(cnf_transformation,[status(esa)],[f196])).
% 106.73/13.76 fof(f199,plain,(
% 106.73/13.76 ![X0,X1]: (set_union2(X0,X1)=set_union2(X1,X0))),
% 106.73/13.76 inference(cnf_transformation,[status(esa)],[f5])).
% 106.73/13.76 fof(f200,plain,(
% 106.73/13.76 ![X0,X1]: (set_intersection2(X0,X1)=set_intersection2(X1,X0))),
% 106.73/13.76 inference(cnf_transformation,[status(esa)],[f6])).
% 106.73/13.76 fof(f201,plain,(
% 106.73/13.76 ![A,B]: (~relation(B)|(B=identity_relation(A)<=>(![C,D]: (in(ordered_pair(C,D),B)<=>(in(C,A)&C=D)))))),
% 106.73/13.76 inference(pre_NNF_transformation,[status(esa)],[f7])).
% 106.73/13.76 fof(f202,plain,(
% 106.73/13.76 ![A,B]: (~relation(B)|((~B=identity_relation(A)|(![C,D]: ((~in(ordered_pair(C,D),B)|(in(C,A)&C=D))&(in(ordered_pair(C,D),B)|(~in(C,A)|~C=D)))))&(B=identity_relation(A)|(?[C,D]: ((~in(ordered_pair(C,D),B)|(~in(C,A)|~C=D))&(in(ordered_pair(C,D),B)|(in(C,A)&C=D)))))))),
% 106.73/13.76 inference(NNF_transformation,[status(esa)],[f201])).
% 106.73/13.76 fof(f203,plain,(
% 106.73/13.76 ![B]: (~relation(B)|((![A]: (~B=identity_relation(A)|((![C,D]: (~in(ordered_pair(C,D),B)|(in(C,A)&C=D)))&(![C,D]: (in(ordered_pair(C,D),B)|(~in(C,A)|~C=D))))))&(![A]: (B=identity_relation(A)|(?[C,D]: ((~in(ordered_pair(C,D),B)|(~in(C,A)|~C=D))&(in(ordered_pair(C,D),B)|(in(C,A)&C=D))))))))),
% 106.73/13.76 inference(miniscoping,[status(esa)],[f202])).
% 106.73/13.76 fof(f204,plain,(
% 106.73/13.76 ![B]: (~relation(B)|((![A]: (~B=identity_relation(A)|((![C,D]: (~in(ordered_pair(C,D),B)|(in(C,A)&C=D)))&(![C,D]: (in(ordered_pair(C,D),B)|(~in(C,A)|~C=D))))))&(![A]: (B=identity_relation(A)|((~in(ordered_pair(sk0_0(A,B),sk0_1(A,B)),B)|(~in(sk0_0(A,B),A)|~sk0_0(A,B)=sk0_1(A,B)))&(in(ordered_pair(sk0_0(A,B),sk0_1(A,B)),B)|(in(sk0_0(A,B),A)&sk0_0(A,B)=sk0_1(A,B))))))))),
% 106.73/13.76 inference(skolemization,[status(esa)],[f203])).
% 106.73/13.76 fof(f209,plain,(
% 106.73/13.76 ![X0,X1]: (~relation(X0)|X0=identity_relation(X1)|in(ordered_pair(sk0_0(X1,X0),sk0_1(X1,X0)),X0)|in(sk0_0(X1,X0),X1))),
% 106.73/13.76 inference(cnf_transformation,[status(esa)],[f204])).
% 106.73/13.76 fof(f210,plain,(
% 106.73/13.76 ![X0,X1]: (~relation(X0)|X0=identity_relation(X1)|in(ordered_pair(sk0_0(X1,X0),sk0_1(X1,X0)),X0)|sk0_0(X1,X0)=sk0_1(X1,X0))),
% 106.73/13.76 inference(cnf_transformation,[status(esa)],[f204])).
% 106.73/13.76 fof(f211,plain,(
% 106.73/13.76 ![A,B]: ((~A=B|(subset(A,B)&subset(B,A)))&(A=B|(~subset(A,B)|~subset(B,A))))),
% 106.73/13.76 inference(NNF_transformation,[status(esa)],[f8])).
% 106.73/13.76 fof(f212,plain,(
% 106.73/13.76 (![A,B]: (~A=B|(subset(A,B)&subset(B,A))))&(![A,B]: (A=B|(~subset(A,B)|~subset(B,A))))),
% 106.73/13.76 inference(miniscoping,[status(esa)],[f211])).
% 106.73/13.76 fof(f213,plain,(
% 106.73/13.76 ![X0,X1]: (~X0=X1|subset(X0,X1))),
% 106.73/13.76 inference(cnf_transformation,[status(esa)],[f212])).
% 106.73/13.76 fof(f215,plain,(
% 106.73/13.76 ![X0,X1]: (X0=X1|~subset(X0,X1)|~subset(X1,X0))),
% 106.73/13.76 inference(cnf_transformation,[status(esa)],[f212])).
% 106.73/13.76 fof(f216,plain,(
% 106.73/13.76 ![A]: (~relation(A)|(![B,C]: (~relation(C)|(C=relation_dom_restriction(A,B)<=>(![D,E]: (in(ordered_pair(D,E),C)<=>(in(D,B)&in(ordered_pair(D,E),A))))))))),
% 106.73/13.76 inference(pre_NNF_transformation,[status(esa)],[f9])).
% 106.73/13.76 fof(f217,plain,(
% 106.73/13.76 ![A]: (~relation(A)|(![B,C]: (~relation(C)|((~C=relation_dom_restriction(A,B)|(![D,E]: ((~in(ordered_pair(D,E),C)|(in(D,B)&in(ordered_pair(D,E),A)))&(in(ordered_pair(D,E),C)|(~in(D,B)|~in(ordered_pair(D,E),A))))))&(C=relation_dom_restriction(A,B)|(?[D,E]: ((~in(ordered_pair(D,E),C)|(~in(D,B)|~in(ordered_pair(D,E),A)))&(in(ordered_pair(D,E),C)|(in(D,B)&in(ordered_pair(D,E),A))))))))))),
% 106.73/13.76 inference(NNF_transformation,[status(esa)],[f216])).
% 106.73/13.76 fof(f218,plain,(
% 106.73/13.76 ![A]: (~relation(A)|(![C]: (~relation(C)|((![B]: (~C=relation_dom_restriction(A,B)|((![D,E]: (~in(ordered_pair(D,E),C)|(in(D,B)&in(ordered_pair(D,E),A))))&(![D,E]: (in(ordered_pair(D,E),C)|(~in(D,B)|~in(ordered_pair(D,E),A)))))))&(![B]: (C=relation_dom_restriction(A,B)|(?[D,E]: ((~in(ordered_pair(D,E),C)|(~in(D,B)|~in(ordered_pair(D,E),A)))&(in(ordered_pair(D,E),C)|(in(D,B)&in(ordered_pair(D,E),A)))))))))))),
% 106.73/13.76 inference(miniscoping,[status(esa)],[f217])).
% 106.73/13.76 fof(f219,plain,(
% 106.73/13.76 ![A]: (~relation(A)|(![C]: (~relation(C)|((![B]: (~C=relation_dom_restriction(A,B)|((![D,E]: (~in(ordered_pair(D,E),C)|(in(D,B)&in(ordered_pair(D,E),A))))&(![D,E]: (in(ordered_pair(D,E),C)|(~in(D,B)|~in(ordered_pair(D,E),A)))))))&(![B]: (C=relation_dom_restriction(A,B)|((~in(ordered_pair(sk0_2(B,C,A),sk0_3(B,C,A)),C)|(~in(sk0_2(B,C,A),B)|~in(ordered_pair(sk0_2(B,C,A),sk0_3(B,C,A)),A)))&(in(ordered_pair(sk0_2(B,C,A),sk0_3(B,C,A)),C)|(in(sk0_2(B,C,A),B)&in(ordered_pair(sk0_2(B,C,A),sk0_3(B,C,A)),A))))))))))),
% 106.73/13.76 inference(skolemization,[status(esa)],[f218])).
% 106.73/13.76 fof(f222,plain,(
% 106.73/13.76 ![X0,X1,X2,X3,X4]: (~relation(X0)|~relation(X1)|~X1=relation_dom_restriction(X0,X2)|in(ordered_pair(X3,X4),X1)|~in(X3,X2)|~in(ordered_pair(X3,X4),X0))),
% 106.73/13.76 inference(cnf_transformation,[status(esa)],[f219])).
% 106.73/13.76 fof(f224,plain,(
% 106.73/13.76 ![X0,X1,X2]: (~relation(X0)|~relation(X1)|X1=relation_dom_restriction(X0,X2)|in(ordered_pair(sk0_2(X2,X1,X0),sk0_3(X2,X1,X0)),X1)|in(sk0_2(X2,X1,X0),X2))),
% 106.73/13.76 inference(cnf_transformation,[status(esa)],[f219])).
% 106.73/13.76 fof(f225,plain,(
% 106.73/13.76 ![X0,X1,X2]: (~relation(X0)|~relation(X1)|X1=relation_dom_restriction(X0,X2)|in(ordered_pair(sk0_2(X2,X1,X0),sk0_3(X2,X1,X0)),X1)|in(ordered_pair(sk0_2(X2,X1,X0),sk0_3(X2,X1,X0)),X0))),
% 106.73/13.76 inference(cnf_transformation,[status(esa)],[f219])).
% 106.73/13.76 fof(f226,plain,(
% 106.73/13.76 ![A,B]: (~relation(B)|(![C]: (~relation(C)|(C=relation_rng_restriction(A,B)<=>(![D,E]: (in(ordered_pair(D,E),C)<=>(in(E,A)&in(ordered_pair(D,E),B))))))))),
% 106.73/13.76 inference(pre_NNF_transformation,[status(esa)],[f10])).
% 106.73/13.76 fof(f227,plain,(
% 106.73/13.76 ![A,B]: (~relation(B)|(![C]: (~relation(C)|((~C=relation_rng_restriction(A,B)|(![D,E]: ((~in(ordered_pair(D,E),C)|(in(E,A)&in(ordered_pair(D,E),B)))&(in(ordered_pair(D,E),C)|(~in(E,A)|~in(ordered_pair(D,E),B))))))&(C=relation_rng_restriction(A,B)|(?[D,E]: ((~in(ordered_pair(D,E),C)|(~in(E,A)|~in(ordered_pair(D,E),B)))&(in(ordered_pair(D,E),C)|(in(E,A)&in(ordered_pair(D,E),B))))))))))),
% 106.73/13.76 inference(NNF_transformation,[status(esa)],[f226])).
% 106.73/13.76 fof(f228,plain,(
% 106.73/13.76 ![B]: (~relation(B)|(![C]: (~relation(C)|((![A]: (~C=relation_rng_restriction(A,B)|((![D,E]: (~in(ordered_pair(D,E),C)|(in(E,A)&in(ordered_pair(D,E),B))))&(![D,E]: (in(ordered_pair(D,E),C)|(~in(E,A)|~in(ordered_pair(D,E),B)))))))&(![A]: (C=relation_rng_restriction(A,B)|(?[D,E]: ((~in(ordered_pair(D,E),C)|(~in(E,A)|~in(ordered_pair(D,E),B)))&(in(ordered_pair(D,E),C)|(in(E,A)&in(ordered_pair(D,E),B)))))))))))),
% 106.73/13.76 inference(miniscoping,[status(esa)],[f227])).
% 106.73/13.76 fof(f229,plain,(
% 106.73/13.76 ![B]: (~relation(B)|(![C]: (~relation(C)|((![A]: (~C=relation_rng_restriction(A,B)|((![D,E]: (~in(ordered_pair(D,E),C)|(in(E,A)&in(ordered_pair(D,E),B))))&(![D,E]: (in(ordered_pair(D,E),C)|(~in(E,A)|~in(ordered_pair(D,E),B)))))))&(![A]: (C=relation_rng_restriction(A,B)|((~in(ordered_pair(sk0_4(A,C,B),sk0_5(A,C,B)),C)|(~in(sk0_5(A,C,B),A)|~in(ordered_pair(sk0_4(A,C,B),sk0_5(A,C,B)),B)))&(in(ordered_pair(sk0_4(A,C,B),sk0_5(A,C,B)),C)|(in(sk0_5(A,C,B),A)&in(ordered_pair(sk0_4(A,C,B),sk0_5(A,C,B)),B))))))))))),
% 106.73/13.76 inference(skolemization,[status(esa)],[f228])).
% 106.73/13.76 fof(f230,plain,(
% 106.73/13.76 ![X0,X1,X2,X3,X4]: (~relation(X0)|~relation(X1)|~X1=relation_rng_restriction(X2,X0)|~in(ordered_pair(X3,X4),X1)|in(X4,X2))),
% 106.73/13.76 inference(cnf_transformation,[status(esa)],[f229])).
% 106.73/13.76 fof(f231,plain,(
% 106.73/13.76 ![X0,X1,X2,X3,X4]: (~relation(X0)|~relation(X1)|~X1=relation_rng_restriction(X2,X0)|~in(ordered_pair(X3,X4),X1)|in(ordered_pair(X3,X4),X0))),
% 106.73/13.76 inference(cnf_transformation,[status(esa)],[f229])).
% 106.73/13.76 fof(f232,plain,(
% 106.73/13.76 ![X0,X1,X2,X3,X4]: (~relation(X0)|~relation(X1)|~X1=relation_rng_restriction(X2,X0)|in(ordered_pair(X3,X4),X1)|~in(X4,X2)|~in(ordered_pair(X3,X4),X0))),
% 106.73/13.76 inference(cnf_transformation,[status(esa)],[f229])).
% 106.73/13.76 fof(f234,plain,(
% 106.73/13.76 ![X0,X1,X2]: (~relation(X0)|~relation(X1)|X1=relation_rng_restriction(X2,X0)|in(ordered_pair(sk0_4(X2,X1,X0),sk0_5(X2,X1,X0)),X1)|in(sk0_5(X2,X1,X0),X2))),
% 106.73/13.76 inference(cnf_transformation,[status(esa)],[f229])).
% 106.73/13.76 fof(f235,plain,(
% 106.73/13.76 ![X0,X1,X2]: (~relation(X0)|~relation(X1)|X1=relation_rng_restriction(X2,X0)|in(ordered_pair(sk0_4(X2,X1,X0),sk0_5(X2,X1,X0)),X1)|in(ordered_pair(sk0_4(X2,X1,X0),sk0_5(X2,X1,X0)),X0))),
% 106.73/13.76 inference(cnf_transformation,[status(esa)],[f229])).
% 106.73/13.76 fof(f255,plain,(
% 106.73/13.76 ![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)))))),
% 106.73/13.76 inference(NNF_transformation,[status(esa)],[f13])).
% 106.73/13.76 fof(f256,plain,(
% 106.73/13.76 (![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)))))),
% 106.73/13.76 inference(miniscoping,[status(esa)],[f255])).
% 106.73/13.76 fof(f257,plain,(
% 106.73/13.76 (![A,B]: (~B=singleton(A)|((![C]: (~in(C,B)|C=A))&(![C]: (in(C,B)|~C=A)))))&(![A,B]: (B=singleton(A)|((~in(sk0_12(B,A),B)|~sk0_12(B,A)=A)&(in(sk0_12(B,A),B)|sk0_12(B,A)=A))))),
% 106.73/13.76 inference(skolemization,[status(esa)],[f256])).
% 106.73/13.76 fof(f259,plain,(
% 106.73/13.76 ![X0,X1,X2]: (~X0=singleton(X1)|in(X2,X0)|~X2=X1)),
% 106.73/13.76 inference(cnf_transformation,[status(esa)],[f257])).
% 106.73/13.76 fof(f262,plain,(
% 106.73/13.76 ![A]: ((~A=empty_set|(![B]: ~in(B,A)))&(A=empty_set|(?[B]: in(B,A))))),
% 106.73/13.76 inference(NNF_transformation,[status(esa)],[f14])).
% 106.73/13.76 fof(f263,plain,(
% 106.73/13.76 (![A]: (~A=empty_set|(![B]: ~in(B,A))))&(![A]: (A=empty_set|(?[B]: in(B,A))))),
% 106.73/13.76 inference(miniscoping,[status(esa)],[f262])).
% 106.73/13.76 fof(f264,plain,(
% 106.73/13.76 (![A]: (~A=empty_set|(![B]: ~in(B,A))))&(![A]: (A=empty_set|in(sk0_13(A),A)))),
% 106.73/13.76 inference(skolemization,[status(esa)],[f263])).
% 106.73/13.76 fof(f265,plain,(
% 106.73/13.76 ![X0,X1]: (~X0=empty_set|~in(X1,X0))),
% 106.73/13.76 inference(cnf_transformation,[status(esa)],[f264])).
% 106.73/13.76 fof(f267,plain,(
% 106.73/13.76 ![A,B]: ((~B=powerset(A)|(![C]: ((~in(C,B)|subset(C,A))&(in(C,B)|~subset(C,A)))))&(B=powerset(A)|(?[C]: ((~in(C,B)|~subset(C,A))&(in(C,B)|subset(C,A))))))),
% 106.73/13.76 inference(NNF_transformation,[status(esa)],[f15])).
% 106.73/13.76 fof(f268,plain,(
% 106.73/13.76 (![A,B]: (~B=powerset(A)|((![C]: (~in(C,B)|subset(C,A)))&(![C]: (in(C,B)|~subset(C,A))))))&(![A,B]: (B=powerset(A)|(?[C]: ((~in(C,B)|~subset(C,A))&(in(C,B)|subset(C,A))))))),
% 106.73/13.76 inference(miniscoping,[status(esa)],[f267])).
% 106.73/13.76 fof(f269,plain,(
% 106.73/13.76 (![A,B]: (~B=powerset(A)|((![C]: (~in(C,B)|subset(C,A)))&(![C]: (in(C,B)|~subset(C,A))))))&(![A,B]: (B=powerset(A)|((~in(sk0_14(B,A),B)|~subset(sk0_14(B,A),A))&(in(sk0_14(B,A),B)|subset(sk0_14(B,A),A)))))),
% 106.73/13.76 inference(skolemization,[status(esa)],[f268])).
% 106.73/13.76 fof(f271,plain,(
% 106.73/13.76 ![X0,X1,X2]: (~X0=powerset(X1)|in(X2,X0)|~subset(X2,X1))),
% 106.73/13.76 inference(cnf_transformation,[status(esa)],[f269])).
% 106.73/13.76 fof(f274,plain,(
% 106.73/13.76 ![A]: (~relation(A)|(![B]: (~relation(B)|(A=B<=>(![C,D]: (in(ordered_pair(C,D),A)<=>in(ordered_pair(C,D),B)))))))),
% 106.73/13.76 inference(pre_NNF_transformation,[status(esa)],[f16])).
% 106.73/13.76 fof(f275,plain,(
% 106.73/13.76 ![A]: (~relation(A)|(![B]: (~relation(B)|((~A=B|(![C,D]: ((~in(ordered_pair(C,D),A)|in(ordered_pair(C,D),B))&(in(ordered_pair(C,D),A)|~in(ordered_pair(C,D),B)))))&(A=B|(?[C,D]: ((~in(ordered_pair(C,D),A)|~in(ordered_pair(C,D),B))&(in(ordered_pair(C,D),A)|in(ordered_pair(C,D),B)))))))))),
% 106.73/13.76 inference(NNF_transformation,[status(esa)],[f274])).
% 106.73/13.76 fof(f276,plain,(
% 106.73/13.76 ![A]: (~relation(A)|(![B]: (~relation(B)|((~A=B|((![C,D]: (~in(ordered_pair(C,D),A)|in(ordered_pair(C,D),B)))&(![C,D]: (in(ordered_pair(C,D),A)|~in(ordered_pair(C,D),B)))))&(A=B|(?[C,D]: ((~in(ordered_pair(C,D),A)|~in(ordered_pair(C,D),B))&(in(ordered_pair(C,D),A)|in(ordered_pair(C,D),B)))))))))),
% 106.73/13.76 inference(miniscoping,[status(esa)],[f275])).
% 106.73/13.76 fof(f277,plain,(
% 106.73/13.76 ![A]: (~relation(A)|(![B]: (~relation(B)|((~A=B|((![C,D]: (~in(ordered_pair(C,D),A)|in(ordered_pair(C,D),B)))&(![C,D]: (in(ordered_pair(C,D),A)|~in(ordered_pair(C,D),B)))))&(A=B|((~in(ordered_pair(sk0_15(B,A),sk0_16(B,A)),A)|~in(ordered_pair(sk0_15(B,A),sk0_16(B,A)),B))&(in(ordered_pair(sk0_15(B,A),sk0_16(B,A)),A)|in(ordered_pair(sk0_15(B,A),sk0_16(B,A)),B))))))))),
% 106.73/13.76 inference(skolemization,[status(esa)],[f276])).
% 106.73/13.76 fof(f281,plain,(
% 106.73/13.76 ![X0,X1]: (~relation(X0)|~relation(X1)|X0=X1|in(ordered_pair(sk0_15(X1,X0),sk0_16(X1,X0)),X0)|in(ordered_pair(sk0_15(X1,X0),sk0_16(X1,X0)),X1))),
% 106.73/13.76 inference(cnf_transformation,[status(esa)],[f277])).
% 106.73/13.76 fof(f289,plain,(
% 106.73/13.76 ![A,B,C]: ((~C=unordered_pair(A,B)|(![D]: ((~in(D,C)|(D=A|D=B))&(in(D,C)|(~D=A&~D=B)))))&(C=unordered_pair(A,B)|(?[D]: ((~in(D,C)|(~D=A&~D=B))&(in(D,C)|(D=A|D=B))))))),
% 106.73/13.76 inference(NNF_transformation,[status(esa)],[f18])).
% 106.73/13.76 fof(f290,plain,(
% 106.73/13.76 (![A,B,C]: (~C=unordered_pair(A,B)|((![D]: (~in(D,C)|(D=A|D=B)))&(![D]: (in(D,C)|(~D=A&~D=B))))))&(![A,B,C]: (C=unordered_pair(A,B)|(?[D]: ((~in(D,C)|(~D=A&~D=B))&(in(D,C)|(D=A|D=B))))))),
% 106.73/13.76 inference(miniscoping,[status(esa)],[f289])).
% 106.73/13.76 fof(f291,plain,(
% 106.73/13.76 (![A,B,C]: (~C=unordered_pair(A,B)|((![D]: (~in(D,C)|(D=A|D=B)))&(![D]: (in(D,C)|(~D=A&~D=B))))))&(![A,B,C]: (C=unordered_pair(A,B)|((~in(sk0_17(C,B,A),C)|(~sk0_17(C,B,A)=A&~sk0_17(C,B,A)=B))&(in(sk0_17(C,B,A),C)|(sk0_17(C,B,A)=A|sk0_17(C,B,A)=B)))))),
% 106.73/13.76 inference(skolemization,[status(esa)],[f290])).
% 106.73/13.76 fof(f293,plain,(
% 106.73/13.76 ![X0,X1,X2,X3]: (~X0=unordered_pair(X1,X2)|in(X3,X0)|~X3=X1)),
% 106.73/13.76 inference(cnf_transformation,[status(esa)],[f291])).
% 106.73/13.76 fof(f294,plain,(
% 106.73/13.76 ![X0,X1,X2,X3]: (~X0=unordered_pair(X1,X2)|in(X3,X0)|~X3=X2)),
% 106.73/13.76 inference(cnf_transformation,[status(esa)],[f291])).
% 106.73/13.76 fof(f316,plain,(
% 106.73/13.76 ![A]: (~relation(A)|(![B]: (~relation(B)|(subset(A,B)<=>(![C,D]: (~in(ordered_pair(C,D),A)|in(ordered_pair(C,D),B)))))))),
% 106.73/13.76 inference(pre_NNF_transformation,[status(esa)],[f21])).
% 106.73/13.76 fof(f317,plain,(
% 106.73/13.76 ![A]: (~relation(A)|(![B]: (~relation(B)|((~subset(A,B)|(![C,D]: (~in(ordered_pair(C,D),A)|in(ordered_pair(C,D),B))))&(subset(A,B)|(?[C,D]: (in(ordered_pair(C,D),A)&~in(ordered_pair(C,D),B))))))))),
% 106.73/13.76 inference(NNF_transformation,[status(esa)],[f316])).
% 106.73/13.76 fof(f318,plain,(
% 106.73/13.76 ![A]: (~relation(A)|(![B]: (~relation(B)|((~subset(A,B)|(![C,D]: (~in(ordered_pair(C,D),A)|in(ordered_pair(C,D),B))))&(subset(A,B)|(in(ordered_pair(sk0_24(B,A),sk0_25(B,A)),A)&~in(ordered_pair(sk0_24(B,A),sk0_25(B,A)),B)))))))),
% 106.73/13.76 inference(skolemization,[status(esa)],[f317])).
% 106.73/13.76 fof(f320,plain,(
% 106.73/13.76 ![X0,X1]: (~relation(X0)|~relation(X1)|subset(X0,X1)|in(ordered_pair(sk0_24(X1,X0),sk0_25(X1,X0)),X0))),
% 106.73/13.76 inference(cnf_transformation,[status(esa)],[f318])).
% 106.73/13.76 fof(f321,plain,(
% 106.73/13.76 ![X0,X1]: (~relation(X0)|~relation(X1)|subset(X0,X1)|~in(ordered_pair(sk0_24(X1,X0),sk0_25(X1,X0)),X1))),
% 106.73/13.76 inference(cnf_transformation,[status(esa)],[f318])).
% 106.73/13.76 fof(f322,plain,(
% 106.73/13.76 ![A,B]: (subset(A,B)<=>(![C]: (~in(C,A)|in(C,B))))),
% 106.73/13.76 inference(pre_NNF_transformation,[status(esa)],[f22])).
% 106.73/13.76 fof(f323,plain,(
% 106.73/13.76 ![A,B]: ((~subset(A,B)|(![C]: (~in(C,A)|in(C,B))))&(subset(A,B)|(?[C]: (in(C,A)&~in(C,B)))))),
% 106.73/13.76 inference(NNF_transformation,[status(esa)],[f322])).
% 106.73/13.76 fof(f324,plain,(
% 106.73/13.76 (![A,B]: (~subset(A,B)|(![C]: (~in(C,A)|in(C,B)))))&(![A,B]: (subset(A,B)|(?[C]: (in(C,A)&~in(C,B)))))),
% 106.73/13.76 inference(miniscoping,[status(esa)],[f323])).
% 106.73/13.76 fof(f325,plain,(
% 106.73/13.76 (![A,B]: (~subset(A,B)|(![C]: (~in(C,A)|in(C,B)))))&(![A,B]: (subset(A,B)|(in(sk0_26(B,A),A)&~in(sk0_26(B,A),B))))),
% 106.73/13.76 inference(skolemization,[status(esa)],[f324])).
% 106.73/13.76 fof(f326,plain,(
% 106.73/13.76 ![X0,X1,X2]: (~subset(X0,X1)|~in(X2,X0)|in(X2,X1))),
% 106.73/13.76 inference(cnf_transformation,[status(esa)],[f325])).
% 106.73/13.76 fof(f327,plain,(
% 106.73/13.76 ![X0,X1]: (subset(X0,X1)|in(sk0_26(X1,X0),X0))),
% 106.73/13.76 inference(cnf_transformation,[status(esa)],[f325])).
% 106.73/13.76 fof(f338,plain,(
% 106.73/13.76 ![A]: (~relation(A)|(![B]: (B=relation_dom(A)<=>(![C]: (in(C,B)<=>(?[D]: in(ordered_pair(C,D),A)))))))),
% 106.73/13.76 inference(pre_NNF_transformation,[status(esa)],[f24])).
% 106.73/13.76 fof(f339,plain,(
% 106.73/13.76 ![A]: (~relation(A)|(![B]: ((~B=relation_dom(A)|(![C]: ((~in(C,B)|(?[D]: in(ordered_pair(C,D),A)))&(in(C,B)|(![D]: ~in(ordered_pair(C,D),A))))))&(B=relation_dom(A)|(?[C]: ((~in(C,B)|(![D]: ~in(ordered_pair(C,D),A)))&(in(C,B)|(?[D]: in(ordered_pair(C,D),A)))))))))),
% 106.73/13.76 inference(NNF_transformation,[status(esa)],[f338])).
% 106.73/13.76 fof(f340,plain,(
% 106.73/13.76 ![A]: (~relation(A)|((![B]: (~B=relation_dom(A)|((![C]: (~in(C,B)|(?[D]: in(ordered_pair(C,D),A))))&(![C]: (in(C,B)|(![D]: ~in(ordered_pair(C,D),A)))))))&(![B]: (B=relation_dom(A)|(?[C]: ((~in(C,B)|(![D]: ~in(ordered_pair(C,D),A)))&(in(C,B)|(?[D]: in(ordered_pair(C,D),A)))))))))),
% 106.73/13.76 inference(miniscoping,[status(esa)],[f339])).
% 106.73/13.76 fof(f341,plain,(
% 106.73/13.76 ![A]: (~relation(A)|((![B]: (~B=relation_dom(A)|((![C]: (~in(C,B)|in(ordered_pair(C,sk0_28(C,B,A)),A)))&(![C]: (in(C,B)|(![D]: ~in(ordered_pair(C,D),A)))))))&(![B]: (B=relation_dom(A)|((~in(sk0_29(B,A),B)|(![D]: ~in(ordered_pair(sk0_29(B,A),D),A)))&(in(sk0_29(B,A),B)|in(ordered_pair(sk0_29(B,A),sk0_30(B,A)),A)))))))),
% 106.73/13.76 inference(skolemization,[status(esa)],[f340])).
% 106.73/13.76 fof(f342,plain,(
% 106.73/13.76 ![X0,X1,X2]: (~relation(X0)|~X1=relation_dom(X0)|~in(X2,X1)|in(ordered_pair(X2,sk0_28(X2,X1,X0)),X0))),
% 106.73/13.76 inference(cnf_transformation,[status(esa)],[f341])).
% 106.73/13.76 fof(f345,plain,(
% 106.73/13.76 ![X0,X1]: (~relation(X0)|X1=relation_dom(X0)|in(sk0_29(X1,X0),X1)|in(ordered_pair(sk0_29(X1,X0),sk0_30(X1,X0)),X0))),
% 106.73/13.76 inference(cnf_transformation,[status(esa)],[f341])).
% 106.73/13.76 fof(f365,plain,(
% 106.73/13.76 ![A]: (~relation(A)|(![B]: (B=relation_rng(A)<=>(![C]: (in(C,B)<=>(?[D]: in(ordered_pair(D,C),A)))))))),
% 106.73/13.76 inference(pre_NNF_transformation,[status(esa)],[f28])).
% 106.73/13.76 fof(f366,plain,(
% 106.73/13.76 ![A]: (~relation(A)|(![B]: ((~B=relation_rng(A)|(![C]: ((~in(C,B)|(?[D]: in(ordered_pair(D,C),A)))&(in(C,B)|(![D]: ~in(ordered_pair(D,C),A))))))&(B=relation_rng(A)|(?[C]: ((~in(C,B)|(![D]: ~in(ordered_pair(D,C),A)))&(in(C,B)|(?[D]: in(ordered_pair(D,C),A)))))))))),
% 106.73/13.76 inference(NNF_transformation,[status(esa)],[f365])).
% 106.73/13.76 fof(f367,plain,(
% 106.73/13.76 ![A]: (~relation(A)|((![B]: (~B=relation_rng(A)|((![C]: (~in(C,B)|(?[D]: in(ordered_pair(D,C),A))))&(![C]: (in(C,B)|(![D]: ~in(ordered_pair(D,C),A)))))))&(![B]: (B=relation_rng(A)|(?[C]: ((~in(C,B)|(![D]: ~in(ordered_pair(D,C),A)))&(in(C,B)|(?[D]: in(ordered_pair(D,C),A)))))))))),
% 106.73/13.76 inference(miniscoping,[status(esa)],[f366])).
% 106.73/13.76 fof(f368,plain,(
% 106.73/13.76 ![A]: (~relation(A)|((![B]: (~B=relation_rng(A)|((![C]: (~in(C,B)|in(ordered_pair(sk0_35(C,B,A),C),A)))&(![C]: (in(C,B)|(![D]: ~in(ordered_pair(D,C),A)))))))&(![B]: (B=relation_rng(A)|((~in(sk0_36(B,A),B)|(![D]: ~in(ordered_pair(D,sk0_36(B,A)),A)))&(in(sk0_36(B,A),B)|in(ordered_pair(sk0_37(B,A),sk0_36(B,A)),A)))))))),
% 106.73/13.76 inference(skolemization,[status(esa)],[f367])).
% 106.73/13.76 fof(f369,plain,(
% 106.73/13.76 ![X0,X1,X2]: (~relation(X0)|~X1=relation_rng(X0)|~in(X2,X1)|in(ordered_pair(sk0_35(X2,X1,X0),X2),X0))),
% 106.73/13.76 inference(cnf_transformation,[status(esa)],[f368])).
% 106.73/13.76 fof(f370,plain,(
% 106.73/13.76 ![X0,X1,X2,X3]: (~relation(X0)|~X1=relation_rng(X0)|in(X2,X1)|~in(ordered_pair(X3,X2),X0))),
% 106.73/13.76 inference(cnf_transformation,[status(esa)],[f368])).
% 106.73/13.76 fof(f372,plain,(
% 106.73/13.76 ![X0,X1]: (~relation(X0)|X1=relation_rng(X0)|in(sk0_36(X1,X0),X1)|in(ordered_pair(sk0_37(X1,X0),sk0_36(X1,X0)),X0))),
% 106.73/13.76 inference(cnf_transformation,[status(esa)],[f368])).
% 106.73/13.76 fof(f376,plain,(
% 106.73/13.76 ![A]: (~relation(A)|relation_field(A)=set_union2(relation_dom(A),relation_rng(A)))),
% 106.73/13.76 inference(pre_NNF_transformation,[status(esa)],[f31])).
% 106.73/13.76 fof(f377,plain,(
% 106.73/13.76 ![X0]: (~relation(X0)|relation_field(X0)=set_union2(relation_dom(X0),relation_rng(X0)))),
% 106.73/13.76 inference(cnf_transformation,[status(esa)],[f376])).
% 106.73/13.76 fof(f378,plain,(
% 106.73/13.76 ![A]: (~relation(A)|(![B]: (~relation(B)|(B=relation_inverse(A)<=>(![C,D]: (in(ordered_pair(C,D),B)<=>in(ordered_pair(D,C),A)))))))),
% 106.73/13.76 inference(pre_NNF_transformation,[status(esa)],[f32])).
% 106.73/13.76 fof(f379,plain,(
% 106.73/13.76 ![A]: (~relation(A)|(![B]: (~relation(B)|((~B=relation_inverse(A)|(![C,D]: ((~in(ordered_pair(C,D),B)|in(ordered_pair(D,C),A))&(in(ordered_pair(C,D),B)|~in(ordered_pair(D,C),A)))))&(B=relation_inverse(A)|(?[C,D]: ((~in(ordered_pair(C,D),B)|~in(ordered_pair(D,C),A))&(in(ordered_pair(C,D),B)|in(ordered_pair(D,C),A)))))))))),
% 106.73/13.76 inference(NNF_transformation,[status(esa)],[f378])).
% 106.73/13.76 fof(f380,plain,(
% 106.73/13.76 ![A]: (~relation(A)|(![B]: (~relation(B)|((~B=relation_inverse(A)|((![C,D]: (~in(ordered_pair(C,D),B)|in(ordered_pair(D,C),A)))&(![C,D]: (in(ordered_pair(C,D),B)|~in(ordered_pair(D,C),A)))))&(B=relation_inverse(A)|(?[C,D]: ((~in(ordered_pair(C,D),B)|~in(ordered_pair(D,C),A))&(in(ordered_pair(C,D),B)|in(ordered_pair(D,C),A)))))))))),
% 106.73/13.76 inference(miniscoping,[status(esa)],[f379])).
% 106.73/13.76 fof(f381,plain,(
% 106.73/13.76 ![A]: (~relation(A)|(![B]: (~relation(B)|((~B=relation_inverse(A)|((![C,D]: (~in(ordered_pair(C,D),B)|in(ordered_pair(D,C),A)))&(![C,D]: (in(ordered_pair(C,D),B)|~in(ordered_pair(D,C),A)))))&(B=relation_inverse(A)|((~in(ordered_pair(sk0_38(B,A),sk0_39(B,A)),B)|~in(ordered_pair(sk0_39(B,A),sk0_38(B,A)),A))&(in(ordered_pair(sk0_38(B,A),sk0_39(B,A)),B)|in(ordered_pair(sk0_39(B,A),sk0_38(B,A)),A))))))))),
% 106.73/13.76 inference(skolemization,[status(esa)],[f380])).
% 106.73/13.76 fof(f385,plain,(
% 106.73/13.76 ![X0,X1]: (~relation(X0)|~relation(X1)|X1=relation_inverse(X0)|in(ordered_pair(sk0_38(X1,X0),sk0_39(X1,X0)),X1)|in(ordered_pair(sk0_39(X1,X0),sk0_38(X1,X0)),X0))),
% 106.73/13.76 inference(cnf_transformation,[status(esa)],[f381])).
% 106.73/13.76 fof(f386,plain,(
% 106.73/13.76 ![A,B]: ((~disjoint(A,B)|set_intersection2(A,B)=empty_set)&(disjoint(A,B)|~set_intersection2(A,B)=empty_set))),
% 106.73/13.76 inference(NNF_transformation,[status(esa)],[f33])).
% 106.73/13.76 fof(f387,plain,(
% 106.73/13.76 (![A,B]: (~disjoint(A,B)|set_intersection2(A,B)=empty_set))&(![A,B]: (disjoint(A,B)|~set_intersection2(A,B)=empty_set))),
% 106.73/13.76 inference(miniscoping,[status(esa)],[f386])).
% 106.73/13.76 fof(f389,plain,(
% 106.73/13.76 ![X0,X1]: (disjoint(X0,X1)|~set_intersection2(X0,X1)=empty_set)),
% 106.73/13.76 inference(cnf_transformation,[status(esa)],[f387])).
% 106.73/13.76 fof(f390,plain,(
% 106.73/13.76 ![A]: (~relation(A)|(![B]: (~relation(B)|(![C]: (~relation(C)|(C=relation_composition(A,B)<=>(![D,E]: (in(ordered_pair(D,E),C)<=>(?[F]: (in(ordered_pair(D,F),A)&in(ordered_pair(F,E),B)))))))))))),
% 106.73/13.76 inference(pre_NNF_transformation,[status(esa)],[f34])).
% 106.73/13.76 fof(f391,plain,(
% 106.73/13.76 ![A]: (~relation(A)|(![B]: (~relation(B)|(![C]: (~relation(C)|((~C=relation_composition(A,B)|(![D,E]: ((~in(ordered_pair(D,E),C)|(?[F]: (in(ordered_pair(D,F),A)&in(ordered_pair(F,E),B))))&(in(ordered_pair(D,E),C)|(![F]: (~in(ordered_pair(D,F),A)|~in(ordered_pair(F,E),B)))))))&(C=relation_composition(A,B)|(?[D,E]: ((~in(ordered_pair(D,E),C)|(![F]: (~in(ordered_pair(D,F),A)|~in(ordered_pair(F,E),B))))&(in(ordered_pair(D,E),C)|(?[F]: (in(ordered_pair(D,F),A)&in(ordered_pair(F,E),B)))))))))))))),
% 106.73/13.76 inference(NNF_transformation,[status(esa)],[f390])).
% 106.73/13.76 fof(f392,plain,(
% 106.73/13.76 ![A]: (~relation(A)|(![B]: (~relation(B)|(![C]: (~relation(C)|((~C=relation_composition(A,B)|((![D,E]: (~in(ordered_pair(D,E),C)|(?[F]: (in(ordered_pair(D,F),A)&in(ordered_pair(F,E),B)))))&(![D,E]: (in(ordered_pair(D,E),C)|(![F]: (~in(ordered_pair(D,F),A)|~in(ordered_pair(F,E),B)))))))&(C=relation_composition(A,B)|(?[D,E]: ((~in(ordered_pair(D,E),C)|(![F]: (~in(ordered_pair(D,F),A)|~in(ordered_pair(F,E),B))))&(in(ordered_pair(D,E),C)|(?[F]: (in(ordered_pair(D,F),A)&in(ordered_pair(F,E),B)))))))))))))),
% 106.73/13.76 inference(miniscoping,[status(esa)],[f391])).
% 106.73/13.76 fof(f393,plain,(
% 106.73/13.76 ![A]: (~relation(A)|(![B]: (~relation(B)|(![C]: (~relation(C)|((~C=relation_composition(A,B)|((![D,E]: (~in(ordered_pair(D,E),C)|(in(ordered_pair(D,sk0_40(E,D,C,B,A)),A)&in(ordered_pair(sk0_40(E,D,C,B,A),E),B))))&(![D,E]: (in(ordered_pair(D,E),C)|(![F]: (~in(ordered_pair(D,F),A)|~in(ordered_pair(F,E),B)))))))&(C=relation_composition(A,B)|((~in(ordered_pair(sk0_41(C,B,A),sk0_42(C,B,A)),C)|(![F]: (~in(ordered_pair(sk0_41(C,B,A),F),A)|~in(ordered_pair(F,sk0_42(C,B,A)),B))))&(in(ordered_pair(sk0_41(C,B,A),sk0_42(C,B,A)),C)|(in(ordered_pair(sk0_41(C,B,A),sk0_43(C,B,A)),A)&in(ordered_pair(sk0_43(C,B,A),sk0_42(C,B,A)),B)))))))))))),
% 106.73/13.76 inference(skolemization,[status(esa)],[f392])).
% 106.73/13.76 fof(f394,plain,(
% 106.73/13.76 ![X0,X1,X2,X3,X4]: (~relation(X0)|~relation(X1)|~relation(X2)|~X2=relation_composition(X0,X1)|~in(ordered_pair(X3,X4),X2)|in(ordered_pair(X3,sk0_40(X4,X3,X2,X1,X0)),X0))),
% 106.73/13.76 inference(cnf_transformation,[status(esa)],[f393])).
% 106.73/13.76 fof(f395,plain,(
% 106.73/13.76 ![X0,X1,X2,X3,X4]: (~relation(X0)|~relation(X1)|~relation(X2)|~X2=relation_composition(X0,X1)|~in(ordered_pair(X3,X4),X2)|in(ordered_pair(sk0_40(X4,X3,X2,X1,X0),X4),X1))),
% 106.73/13.76 inference(cnf_transformation,[status(esa)],[f393])).
% 106.73/13.76 fof(f398,plain,(
% 106.73/13.76 ![X0,X1,X2]: (~relation(X0)|~relation(X1)|~relation(X2)|X2=relation_composition(X0,X1)|in(ordered_pair(sk0_41(X2,X1,X0),sk0_42(X2,X1,X0)),X2)|in(ordered_pair(sk0_41(X2,X1,X0),sk0_43(X2,X1,X0)),X0))),
% 106.73/13.76 inference(cnf_transformation,[status(esa)],[f393])).
% 106.73/13.76 fof(f399,plain,(
% 106.73/13.76 ![X0,X1,X2]: (~relation(X0)|~relation(X1)|~relation(X2)|X2=relation_composition(X0,X1)|in(ordered_pair(sk0_41(X2,X1,X0),sk0_42(X2,X1,X0)),X2)|in(ordered_pair(sk0_43(X2,X1,X0),sk0_42(X2,X1,X0)),X1))),
% 106.73/13.76 inference(cnf_transformation,[status(esa)],[f393])).
% 106.73/13.76 fof(f408,plain,(
% 106.73/13.76 ![A,B]: ((~proper_subset(A,B)|(subset(A,B)&~A=B))&(proper_subset(A,B)|(~subset(A,B)|A=B)))),
% 106.73/13.76 inference(NNF_transformation,[status(esa)],[f36])).
% 106.73/13.76 fof(f409,plain,(
% 106.73/13.76 (![A,B]: (~proper_subset(A,B)|(subset(A,B)&~A=B)))&(![A,B]: (proper_subset(A,B)|(~subset(A,B)|A=B)))),
% 106.73/13.76 inference(miniscoping,[status(esa)],[f408])).
% 106.73/13.76 fof(f412,plain,(
% 106.73/13.76 ![X0,X1]: (proper_subset(X0,X1)|~subset(X0,X1)|X0=X1)),
% 106.73/13.76 inference(cnf_transformation,[status(esa)],[f409])).
% 106.73/13.76 fof(f418,plain,(
% 106.73/13.76 ![A,B]: ((~relation(A)|~relation(B))|relation(relation_composition(A,B)))),
% 106.73/13.76 inference(pre_NNF_transformation,[status(esa)],[f54])).
% 106.73/13.76 fof(f419,plain,(
% 106.73/13.76 ![X0,X1]: (~relation(X0)|~relation(X1)|relation(relation_composition(X0,X1)))),
% 106.73/13.76 inference(cnf_transformation,[status(esa)],[f418])).
% 106.73/13.76 fof(f422,plain,(
% 106.73/13.76 ![X0]: (relation(identity_relation(X0)))),
% 106.73/13.76 inference(cnf_transformation,[status(esa)],[f56])).
% 106.73/13.76 fof(f427,plain,(
% 106.73/13.76 ![A,B]: (~relation(A)|relation(relation_dom_restriction(A,B)))),
% 106.73/13.76 inference(pre_NNF_transformation,[status(esa)],[f59])).
% 106.73/13.76 fof(f428,plain,(
% 106.73/13.76 ![A]: (~relation(A)|(![B]: relation(relation_dom_restriction(A,B))))),
% 106.73/13.76 inference(miniscoping,[status(esa)],[f427])).
% 106.73/13.76 fof(f429,plain,(
% 106.73/13.76 ![X0,X1]: (~relation(X0)|relation(relation_dom_restriction(X0,X1)))),
% 106.73/13.76 inference(cnf_transformation,[status(esa)],[f428])).
% 106.73/13.76 fof(f432,plain,(
% 106.73/13.76 ![A,B]: (~relation(B)|relation(relation_rng_restriction(A,B)))),
% 106.73/13.76 inference(pre_NNF_transformation,[status(esa)],[f61])).
% 106.73/13.76 fof(f433,plain,(
% 106.73/13.76 ![B]: (~relation(B)|(![A]: relation(relation_rng_restriction(A,B))))),
% 106.73/13.76 inference(miniscoping,[status(esa)],[f432])).
% 106.73/13.76 fof(f434,plain,(
% 106.73/13.76 ![X0,X1]: (~relation(X0)|relation(relation_rng_restriction(X1,X0)))),
% 106.73/13.76 inference(cnf_transformation,[status(esa)],[f433])).
% 106.73/13.76 fof(f443,plain,(
% 106.73/13.76 empty(empty_set)),
% 106.73/13.76 inference(cnf_transformation,[status(esa)],[f67])).
% 106.73/13.76 fof(f445,plain,(
% 106.73/13.76 ![A,B]: ((~relation(A)|~relation(B))|relation(set_union2(A,B)))),
% 106.73/13.76 inference(pre_NNF_transformation,[status(esa)],[f69])).
% 106.73/13.76 fof(f446,plain,(
% 106.73/13.76 ![X0,X1]: (~relation(X0)|~relation(X1)|relation(set_union2(X0,X1)))),
% 106.73/13.76 inference(cnf_transformation,[status(esa)],[f445])).
% 106.73/13.76 fof(f448,plain,(
% 106.73/13.76 ![A,B]: (empty(A)|~empty(set_union2(A,B)))),
% 106.73/13.76 inference(pre_NNF_transformation,[status(esa)],[f71])).
% 106.73/13.76 fof(f449,plain,(
% 106.73/13.76 ![A]: (empty(A)|(![B]: ~empty(set_union2(A,B))))),
% 106.73/13.76 inference(miniscoping,[status(esa)],[f448])).
% 106.73/13.76 fof(f450,plain,(
% 106.73/13.76 ![X0,X1]: (empty(X0)|~empty(set_union2(X0,X1)))),
% 106.73/13.76 inference(cnf_transformation,[status(esa)],[f449])).
% 106.73/13.76 fof(f466,plain,(
% 106.73/13.76 ![A]: (~empty(A)|(empty(relation_rng(A))&relation(relation_rng(A))))),
% 106.73/13.76 inference(pre_NNF_transformation,[status(esa)],[f79])).
% 106.73/13.76 fof(f467,plain,(
% 106.73/13.76 ![X0]: (~empty(X0)|empty(relation_rng(X0)))),
% 106.73/13.76 inference(cnf_transformation,[status(esa)],[f466])).
% 106.73/13.76 fof(f472,plain,(
% 106.73/13.76 ![A]: set_union2(A,A)=A),
% 106.73/13.76 inference(miniscoping,[status(esa)],[f81])).
% 106.73/13.76 fof(f473,plain,(
% 106.73/13.76 ![X0]: (set_union2(X0,X0)=X0)),
% 106.73/13.76 inference(cnf_transformation,[status(esa)],[f472])).
% 106.73/13.76 fof(f474,plain,(
% 106.73/13.76 ![A]: set_intersection2(A,A)=A),
% 106.73/13.76 inference(miniscoping,[status(esa)],[f82])).
% 106.73/13.76 fof(f475,plain,(
% 106.73/13.76 ![X0]: (set_intersection2(X0,X0)=X0)),
% 106.73/13.76 inference(cnf_transformation,[status(esa)],[f474])).
% 106.73/13.76 fof(f491,plain,(
% 106.73/13.76 ![A,B]: ((~subset(singleton(A),B)|in(A,B))&(subset(singleton(A),B)|~in(A,B)))),
% 106.73/13.76 inference(NNF_transformation,[status(esa)],[f91])).
% 106.73/13.76 fof(f492,plain,(
% 106.73/13.76 (![A,B]: (~subset(singleton(A),B)|in(A,B)))&(![A,B]: (subset(singleton(A),B)|~in(A,B)))),
% 106.73/13.76 inference(miniscoping,[status(esa)],[f491])).
% 106.73/13.76 fof(f493,plain,(
% 106.73/13.76 ![X0,X1]: (~subset(singleton(X0),X1)|in(X0,X1))),
% 106.73/13.76 inference(cnf_transformation,[status(esa)],[f492])).
% 106.73/13.76 fof(f494,plain,(
% 106.73/13.76 ![X0,X1]: (subset(singleton(X0),X1)|~in(X0,X1))),
% 106.73/13.76 inference(cnf_transformation,[status(esa)],[f492])).
% 106.73/13.76 fof(f527,plain,(
% 106.73/13.76 empty(sk0_49)),
% 106.73/13.76 inference(skolemization,[status(esa)],[f101])).
% 106.73/13.76 fof(f528,plain,(
% 106.73/13.76 empty(sk0_49)),
% 106.73/13.76 inference(cnf_transformation,[status(esa)],[f527])).
% 106.73/13.76 fof(f555,plain,(
% 106.73/13.76 (?[A,B,C]: (relation(C)&(in(A,relation_rng(relation_rng_restriction(B,C)))<~>(in(A,B)&in(A,relation_rng(C))))))),
% 106.73/13.76 inference(pre_NNF_transformation,[status(esa)],[f113])).
% 106.73/13.76 fof(f556,plain,(
% 106.73/13.76 ?[A,B,C]: (relation(C)&((in(A,relation_rng(relation_rng_restriction(B,C)))|(in(A,B)&in(A,relation_rng(C))))&(~in(A,relation_rng(relation_rng_restriction(B,C)))|(~in(A,B)|~in(A,relation_rng(C))))))),
% 106.73/13.76 inference(NNF_transformation,[status(esa)],[f555])).
% 106.73/13.76 fof(f557,plain,(
% 106.73/13.76 ?[C]: (relation(C)&(?[A,B]: ((in(A,relation_rng(relation_rng_restriction(B,C)))|(in(A,B)&in(A,relation_rng(C))))&(~in(A,relation_rng(relation_rng_restriction(B,C)))|(~in(A,B)|~in(A,relation_rng(C)))))))),
% 106.73/13.76 inference(miniscoping,[status(esa)],[f556])).
% 106.73/13.76 fof(f558,plain,(
% 106.73/13.76 (relation(sk0_53)&((in(sk0_54,relation_rng(relation_rng_restriction(sk0_55,sk0_53)))|(in(sk0_54,sk0_55)&in(sk0_54,relation_rng(sk0_53))))&(~in(sk0_54,relation_rng(relation_rng_restriction(sk0_55,sk0_53)))|(~in(sk0_54,sk0_55)|~in(sk0_54,relation_rng(sk0_53))))))),
% 106.73/13.76 inference(skolemization,[status(esa)],[f557])).
% 106.73/13.76 fof(f559,plain,(
% 106.73/13.76 relation(sk0_53)),
% 106.73/13.76 inference(cnf_transformation,[status(esa)],[f558])).
% 106.73/13.76 fof(f560,plain,(
% 106.73/13.76 in(sk0_54,relation_rng(relation_rng_restriction(sk0_55,sk0_53)))|in(sk0_54,sk0_55)),
% 106.73/13.76 inference(cnf_transformation,[status(esa)],[f558])).
% 106.73/13.76 fof(f561,plain,(
% 106.73/13.76 in(sk0_54,relation_rng(relation_rng_restriction(sk0_55,sk0_53)))|in(sk0_54,relation_rng(sk0_53))),
% 106.73/13.76 inference(cnf_transformation,[status(esa)],[f558])).
% 106.73/13.76 fof(f562,plain,(
% 106.73/13.76 ~in(sk0_54,relation_rng(relation_rng_restriction(sk0_55,sk0_53)))|~in(sk0_54,sk0_55)|~in(sk0_54,relation_rng(sk0_53))),
% 106.73/13.76 inference(cnf_transformation,[status(esa)],[f558])).
% 106.73/13.76 fof(f571,plain,(
% 106.73/13.76 ![A]: (?[B]: (((in(A,B)&(![C,D]: ((~in(C,B)|~subset(D,C))|in(D,B))))&(![C]: (~in(C,B)|in(powerset(C),B))))&(![C]: ((~subset(C,B)|are_equipotent(C,B))|in(C,B)))))),
% 106.73/13.76 inference(pre_NNF_transformation,[status(esa)],[f117])).
% 106.73/13.76 fof(f572,plain,(
% 106.73/13.76 ![A]: ?[B]: (((in(A,B)&(![D]: ((![C]: (~in(C,B)|~subset(D,C)))|in(D,B))))&(![C]: (~in(C,B)|in(powerset(C),B))))&(![C]: ((~subset(C,B)|are_equipotent(C,B))|in(C,B))))),
% 106.73/13.76 inference(miniscoping,[status(esa)],[f571])).
% 106.73/13.76 fof(f573,plain,(
% 106.73/13.76 ![A]: (((in(A,sk0_56(A))&(![D]: ((![C]: (~in(C,sk0_56(A))|~subset(D,C)))|in(D,sk0_56(A)))))&(![C]: (~in(C,sk0_56(A))|in(powerset(C),sk0_56(A)))))&(![C]: ((~subset(C,sk0_56(A))|are_equipotent(C,sk0_56(A)))|in(C,sk0_56(A)))))),
% 106.73/13.76 inference(skolemization,[status(esa)],[f572])).
% 106.73/13.76 fof(f574,plain,(
% 106.73/13.76 ![X0]: (in(X0,sk0_56(X0)))),
% 106.73/13.76 inference(cnf_transformation,[status(esa)],[f573])).
% 106.73/13.76 fof(f578,plain,(
% 106.73/13.76 ![X0,X1]: (subset(set_intersection2(X0,X1),X0))),
% 106.73/13.76 inference(cnf_transformation,[status(esa)],[f118])).
% 106.73/13.76 fof(f581,plain,(
% 106.73/13.76 ![X0]: (set_union2(X0,empty_set)=X0)),
% 106.73/13.76 inference(cnf_transformation,[status(esa)],[f120])).
% 106.73/13.76 fof(f584,plain,(
% 106.73/13.76 ![A,B,C]: ((~subset(A,B)|~subset(B,C))|subset(A,C))),
% 106.73/13.76 inference(pre_NNF_transformation,[status(esa)],[f122])).
% 106.73/13.76 fof(f585,plain,(
% 106.73/13.76 ![A,C]: ((![B]: (~subset(A,B)|~subset(B,C)))|subset(A,C))),
% 106.73/13.76 inference(miniscoping,[status(esa)],[f584])).
% 106.73/13.76 fof(f586,plain,(
% 106.73/13.76 ![X0,X1,X2]: (~subset(X0,X1)|~subset(X1,X2)|subset(X0,X2))),
% 106.73/13.76 inference(cnf_transformation,[status(esa)],[f585])).
% 106.73/13.76 fof(f594,plain,(
% 106.73/13.76 ![A]: (~relation(A)|(![B]: (~relation(B)|(~subset(A,B)|(subset(relation_dom(A),relation_dom(B))&subset(relation_rng(A),relation_rng(B)))))))),
% 106.73/13.76 inference(pre_NNF_transformation,[status(esa)],[f126])).
% 106.73/13.76 fof(f596,plain,(
% 106.73/13.76 ![X0,X1]: (~relation(X0)|~relation(X1)|~subset(X0,X1)|subset(relation_rng(X0),relation_rng(X1)))),
% 106.73/13.76 inference(cnf_transformation,[status(esa)],[f594])).
% 106.73/13.76 fof(f602,plain,(
% 106.73/13.76 ![X0]: (set_intersection2(X0,empty_set)=empty_set)),
% 106.73/13.76 inference(cnf_transformation,[status(esa)],[f129])).
% 106.73/13.76 fof(f621,plain,(
% 106.73/13.76 ![X0,X1]: (subset(set_difference(X0,X1),X0))),
% 106.73/13.76 inference(cnf_transformation,[status(esa)],[f136])).
% 106.73/13.76 fof(f644,plain,(
% 106.73/13.76 ![X0]: (set_difference(X0,empty_set)=X0)),
% 106.73/13.76 inference(cnf_transformation,[status(esa)],[f143])).
% 106.73/13.76 fof(f681,plain,(
% 106.73/13.76 ![X0]: (set_difference(empty_set,X0)=empty_set)),
% 106.73/13.76 inference(cnf_transformation,[status(esa)],[f159])).
% 106.73/13.76 fof(f685,plain,(
% 106.73/13.76 ![A,B]: ((disjoint(A,B)|(?[C]: in(C,set_intersection2(A,B))))&((![C]: ~in(C,set_intersection2(A,B)))|~disjoint(A,B)))),
% 106.73/13.76 inference(pre_NNF_transformation,[status(esa)],[f161])).
% 106.73/13.76 fof(f686,plain,(
% 106.73/13.76 (![A,B]: (disjoint(A,B)|(?[C]: in(C,set_intersection2(A,B)))))&(![A,B]: ((![C]: ~in(C,set_intersection2(A,B)))|~disjoint(A,B)))),
% 106.73/13.76 inference(miniscoping,[status(esa)],[f685])).
% 106.73/13.76 fof(f687,plain,(
% 106.73/13.76 (![A,B]: (disjoint(A,B)|in(sk0_59(B,A),set_intersection2(A,B))))&(![A,B]: ((![C]: ~in(C,set_intersection2(A,B)))|~disjoint(A,B)))),
% 106.73/13.76 inference(skolemization,[status(esa)],[f686])).
% 106.73/13.76 fof(f689,plain,(
% 106.73/13.76 ![X0,X1,X2]: (~in(X0,set_intersection2(X1,X2))|~disjoint(X1,X2))),
% 106.73/13.76 inference(cnf_transformation,[status(esa)],[f687])).
% 106.73/13.76 fof(f702,plain,(
% 106.73/13.76 relation_rng(empty_set)=empty_set),
% 106.73/13.76 inference(cnf_transformation,[status(esa)],[f166])).
% 106.73/13.76 fof(f703,plain,(
% 106.73/13.76 ![A,B]: (~subset(A,B)|~proper_subset(B,A))),
% 106.73/13.76 inference(pre_NNF_transformation,[status(esa)],[f167])).
% 106.73/13.76 fof(f704,plain,(
% 106.73/13.76 ![X0,X1]: (~subset(X0,X1)|~proper_subset(X1,X0))),
% 106.73/13.76 inference(cnf_transformation,[status(esa)],[f703])).
% 106.73/13.76 fof(f705,plain,(
% 106.73/13.76 ![A,B,C]: ((~subset(A,B)|~disjoint(B,C))|disjoint(A,C))),
% 106.73/13.76 inference(pre_NNF_transformation,[status(esa)],[f168])).
% 106.73/13.76 fof(f706,plain,(
% 106.73/13.76 ![A,C]: ((![B]: (~subset(A,B)|~disjoint(B,C)))|disjoint(A,C))),
% 106.73/13.76 inference(miniscoping,[status(esa)],[f705])).
% 106.73/13.76 fof(f707,plain,(
% 106.73/13.76 ![X0,X1,X2]: (~subset(X0,X1)|~disjoint(X1,X2)|disjoint(X0,X2))),
% 106.73/13.76 inference(cnf_transformation,[status(esa)],[f706])).
% 106.73/13.76 fof(f708,plain,(
% 106.73/13.76 ![A]: (~relation(A)|((~relation_dom(A)=empty_set&~relation_rng(A)=empty_set)|A=empty_set))),
% 106.73/13.76 inference(pre_NNF_transformation,[status(esa)],[f169])).
% 106.73/13.76 fof(f710,plain,(
% 106.73/13.76 ![X0]: (~relation(X0)|~relation_rng(X0)=empty_set|X0=empty_set)),
% 106.73/13.76 inference(cnf_transformation,[status(esa)],[f708])).
% 106.73/13.76 fof(f711,plain,(
% 106.73/13.76 ![A]: (~relation(A)|(relation_dom(A)=empty_set<=>relation_rng(A)=empty_set))),
% 106.73/13.76 inference(pre_NNF_transformation,[status(esa)],[f170])).
% 106.73/13.76 fof(f712,plain,(
% 106.73/13.76 ![A]: (~relation(A)|((~relation_dom(A)=empty_set|relation_rng(A)=empty_set)&(relation_dom(A)=empty_set|~relation_rng(A)=empty_set)))),
% 106.73/13.76 inference(NNF_transformation,[status(esa)],[f711])).
% 106.73/13.76 fof(f714,plain,(
% 106.73/13.76 ![X0]: (~relation(X0)|relation_dom(X0)=empty_set|~relation_rng(X0)=empty_set)),
% 106.73/13.76 inference(cnf_transformation,[status(esa)],[f712])).
% 106.73/13.76 fof(f715,plain,(
% 106.73/13.76 ![A,B]: ((~set_difference(A,singleton(B))=A|~in(B,A))&(set_difference(A,singleton(B))=A|in(B,A)))),
% 106.73/13.76 inference(NNF_transformation,[status(esa)],[f171])).
% 106.73/13.76 fof(f716,plain,(
% 106.73/13.76 (![A,B]: (~set_difference(A,singleton(B))=A|~in(B,A)))&(![A,B]: (set_difference(A,singleton(B))=A|in(B,A)))),
% 106.73/13.76 inference(miniscoping,[status(esa)],[f715])).
% 106.73/13.76 fof(f717,plain,(
% 106.73/13.76 ![X0,X1]: (~set_difference(X0,singleton(X1))=X0|~in(X1,X0))),
% 106.73/13.76 inference(cnf_transformation,[status(esa)],[f716])).
% 106.73/13.76 fof(f720,plain,(
% 106.73/13.76 ![A]: (~empty(A)|A=empty_set)),
% 106.73/13.76 inference(pre_NNF_transformation,[status(esa)],[f173])).
% 106.73/13.76 fof(f721,plain,(
% 106.73/13.76 ![X0]: (~empty(X0)|X0=empty_set)),
% 106.73/13.76 inference(cnf_transformation,[status(esa)],[f720])).
% 106.73/13.76 fof(f724,plain,(
% 106.73/13.76 (![A]: relation_dom(identity_relation(A))=A)&(![A]: relation_rng(identity_relation(A))=A)),
% 106.73/13.76 inference(miniscoping,[status(esa)],[f175])).
% 106.73/13.76 fof(f726,plain,(
% 106.73/13.76 ![X0]: (relation_rng(identity_relation(X0))=X0)),
% 106.73/13.76 inference(cnf_transformation,[status(esa)],[f724])).
% 106.73/13.76 fof(f733,plain,(
% 106.73/13.76 ![A,B]: (~in(A,B)|~empty(B))),
% 106.73/13.76 inference(pre_NNF_transformation,[status(esa)],[f177])).
% 106.73/13.76 fof(f734,plain,(
% 106.73/13.76 ![B]: ((![A]: ~in(A,B))|~empty(B))),
% 106.73/13.76 inference(miniscoping,[status(esa)],[f733])).
% 106.73/13.76 fof(f735,plain,(
% 106.73/13.76 ![X0,X1]: (~in(X0,X1)|~empty(X1))),
% 106.73/13.76 inference(cnf_transformation,[status(esa)],[f734])).
% 106.73/13.76 fof(f736,plain,(
% 106.73/13.76 ![X0,X1]: (subset(X0,set_union2(X0,X1)))),
% 106.73/13.76 inference(cnf_transformation,[status(esa)],[f178])).
% 106.73/13.76 fof(f737,plain,(
% 106.73/13.76 ![A,B]: ((~disjoint(A,B)|set_difference(A,B)=A)&(disjoint(A,B)|~set_difference(A,B)=A))),
% 106.73/13.76 inference(NNF_transformation,[status(esa)],[f179])).
% 106.73/13.76 fof(f738,plain,(
% 106.73/13.76 (![A,B]: (~disjoint(A,B)|set_difference(A,B)=A))&(![A,B]: (disjoint(A,B)|~set_difference(A,B)=A))),
% 106.73/13.76 inference(miniscoping,[status(esa)],[f737])).
% 106.73/13.76 fof(f740,plain,(
% 106.73/13.76 ![X0,X1]: (disjoint(X0,X1)|~set_difference(X0,X1)=X0)),
% 106.73/13.76 inference(cnf_transformation,[status(esa)],[f738])).
% 106.73/13.76 fof(f747,plain,(
% 106.73/13.76 ![A,B]: (~relation(B)|subset(relation_dom_restriction(B,A),B))),
% 106.73/13.76 inference(pre_NNF_transformation,[status(esa)],[f181])).
% 106.73/13.76 fof(f748,plain,(
% 106.73/13.76 ![B]: (~relation(B)|(![A]: subset(relation_dom_restriction(B,A),B)))),
% 106.73/13.76 inference(miniscoping,[status(esa)],[f747])).
% 106.73/13.76 fof(f749,plain,(
% 106.73/13.76 ![X0,X1]: (~relation(X0)|subset(relation_dom_restriction(X0,X1),X0))),
% 106.73/13.76 inference(cnf_transformation,[status(esa)],[f748])).
% 106.73/13.76 fof(f750,plain,(
% 106.73/13.76 ![A,B]: ((~empty(A)|A=B)|~empty(B))),
% 106.73/13.76 inference(pre_NNF_transformation,[status(esa)],[f182])).
% 106.73/13.76 fof(f751,plain,(
% 106.73/13.76 ![B]: ((![A]: (~empty(A)|A=B))|~empty(B))),
% 106.73/13.76 inference(miniscoping,[status(esa)],[f750])).
% 106.73/13.76 fof(f752,plain,(
% 106.73/13.76 ![X0,X1]: (~empty(X0)|X0=X1|~empty(X1))),
% 106.73/13.76 inference(cnf_transformation,[status(esa)],[f751])).
% 106.73/13.76 fof(f770,plain,(
% 106.73/13.76 ![A]: (?[B]: (((in(A,B)&(![C,D]: ((~in(C,B)|~subset(D,C))|in(D,B))))&(![C]: (~in(C,B)|(?[D]: (in(D,B)&(![E]: (~subset(E,C)|in(E,D))))))))&(![C]: ((~subset(C,B)|are_equipotent(C,B))|in(C,B)))))),
% 106.73/13.76 inference(pre_NNF_transformation,[status(esa)],[f190])).
% 106.73/13.76 fof(f771,plain,(
% 106.73/13.76 ![A]: ?[B]: (((in(A,B)&(![D]: ((![C]: (~in(C,B)|~subset(D,C)))|in(D,B))))&(![C]: (~in(C,B)|(?[D]: (in(D,B)&(![E]: (~subset(E,C)|in(E,D))))))))&(![C]: ((~subset(C,B)|are_equipotent(C,B))|in(C,B))))),
% 106.73/13.76 inference(miniscoping,[status(esa)],[f770])).
% 106.73/13.76 fof(f772,plain,(
% 106.73/13.76 ![A]: (((in(A,sk0_62(A))&(![D]: ((![C]: (~in(C,sk0_62(A))|~subset(D,C)))|in(D,sk0_62(A)))))&(![C]: (~in(C,sk0_62(A))|(in(sk0_63(C,A),sk0_62(A))&(![E]: (~subset(E,C)|in(E,sk0_63(C,A))))))))&(![C]: ((~subset(C,sk0_62(A))|are_equipotent(C,sk0_62(A)))|in(C,sk0_62(A)))))),
% 106.73/13.76 inference(skolemization,[status(esa)],[f771])).
% 106.73/13.76 fof(f773,plain,(
% 106.73/13.76 ![X0]: (in(X0,sk0_62(X0)))),
% 106.73/13.76 inference(cnf_transformation,[status(esa)],[f772])).
% 106.73/13.76 fof(f787,plain,(
% 106.73/13.76 spl0_0 <=> in(sk0_54,relation_rng(relation_rng_restriction(sk0_55,sk0_53)))),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f788,plain,(
% 106.73/13.76 in(sk0_54,relation_rng(relation_rng_restriction(sk0_55,sk0_53)))|~spl0_0),
% 106.73/13.76 inference(component_clause,[status(thm)],[f787])).
% 106.73/13.76 fof(f789,plain,(
% 106.73/13.76 ~in(sk0_54,relation_rng(relation_rng_restriction(sk0_55,sk0_53)))|spl0_0),
% 106.73/13.76 inference(component_clause,[status(thm)],[f787])).
% 106.73/13.76 fof(f790,plain,(
% 106.73/13.76 spl0_1 <=> in(sk0_54,sk0_55)),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f793,plain,(
% 106.73/13.76 spl0_0|spl0_1),
% 106.73/13.76 inference(split_clause,[status(thm)],[f560,f787,f790])).
% 106.73/13.76 fof(f794,plain,(
% 106.73/13.76 spl0_2 <=> in(sk0_54,relation_rng(sk0_53))),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f797,plain,(
% 106.73/13.76 spl0_0|spl0_2),
% 106.73/13.76 inference(split_clause,[status(thm)],[f561,f787,f794])).
% 106.73/13.76 fof(f798,plain,(
% 106.73/13.76 ~spl0_0|~spl0_1|~spl0_2),
% 106.73/13.76 inference(split_clause,[status(thm)],[f562,f787,f790,f794])).
% 106.73/13.76 fof(f802,plain,(
% 106.73/13.76 ![X0]: (subset(X0,X0))),
% 106.73/13.76 inference(destructive_equality_resolution,[status(esa)],[f213])).
% 106.73/13.76 fof(f806,plain,(
% 106.73/13.76 ![X0,X1,X2,X3]: (~relation(X0)|~relation(relation_dom_restriction(X0,X1))|in(ordered_pair(X2,X3),relation_dom_restriction(X0,X1))|~in(X2,X1)|~in(ordered_pair(X2,X3),X0))),
% 106.73/13.76 inference(destructive_equality_resolution,[status(esa)],[f222])).
% 106.73/13.76 fof(f807,plain,(
% 106.73/13.76 ![X0,X1,X2,X3]: (~relation(X0)|~relation(relation_rng_restriction(X1,X0))|~in(ordered_pair(X2,X3),relation_rng_restriction(X1,X0))|in(X3,X1))),
% 106.73/13.76 inference(destructive_equality_resolution,[status(esa)],[f230])).
% 106.73/13.76 fof(f808,plain,(
% 106.73/13.76 ![X0,X1,X2,X3]: (~relation(X0)|~relation(relation_rng_restriction(X1,X0))|~in(ordered_pair(X2,X3),relation_rng_restriction(X1,X0))|in(ordered_pair(X2,X3),X0))),
% 106.73/13.76 inference(destructive_equality_resolution,[status(esa)],[f231])).
% 106.73/13.76 fof(f809,plain,(
% 106.73/13.76 ![X0,X1,X2,X3]: (~relation(X0)|~relation(relation_rng_restriction(X1,X0))|in(ordered_pair(X2,X3),relation_rng_restriction(X1,X0))|~in(X3,X1)|~in(ordered_pair(X2,X3),X0))),
% 106.73/13.76 inference(destructive_equality_resolution,[status(esa)],[f232])).
% 106.73/13.76 fof(f816,plain,(
% 106.73/13.76 ![X0]: (in(X0,singleton(X0)))),
% 106.73/13.76 inference(destructive_equality_resolution,[status(esa)],[f259])).
% 106.73/13.76 fof(f817,plain,(
% 106.73/13.76 ![X0]: (~in(X0,empty_set))),
% 106.73/13.76 inference(destructive_equality_resolution,[status(esa)],[f265])).
% 106.73/13.76 fof(f819,plain,(
% 106.73/13.76 ![X0,X1]: (in(X0,powerset(X1))|~subset(X0,X1))),
% 106.73/13.76 inference(destructive_equality_resolution,[status(esa)],[f271])).
% 106.73/13.76 fof(f821,plain,(
% 106.73/13.76 ![X0,X1]: (in(X0,unordered_pair(X0,X1)))),
% 106.73/13.76 inference(destructive_equality_resolution,[status(esa)],[f293])).
% 106.73/13.76 fof(f822,plain,(
% 106.73/13.76 ![X0,X1]: (in(X0,unordered_pair(X1,X0)))),
% 106.73/13.76 inference(destructive_equality_resolution,[status(esa)],[f294])).
% 106.73/13.76 fof(f831,plain,(
% 106.73/13.76 ![X0,X1]: (~relation(X0)|~in(X1,relation_dom(X0))|in(ordered_pair(X1,sk0_28(X1,relation_dom(X0),X0)),X0))),
% 106.73/13.76 inference(destructive_equality_resolution,[status(esa)],[f342])).
% 106.73/13.76 fof(f839,plain,(
% 106.73/13.76 ![X0,X1]: (~relation(X0)|~in(X1,relation_rng(X0))|in(ordered_pair(sk0_35(X1,relation_rng(X0),X0),X1),X0))),
% 106.73/13.76 inference(destructive_equality_resolution,[status(esa)],[f369])).
% 106.73/13.76 fof(f840,plain,(
% 106.73/13.76 ![X0,X1,X2]: (~relation(X0)|in(X1,relation_rng(X0))|~in(ordered_pair(X2,X1),X0))),
% 106.73/13.76 inference(destructive_equality_resolution,[status(esa)],[f370])).
% 106.73/13.76 fof(f843,plain,(
% 106.73/13.76 ![X0,X1,X2,X3]: (~relation(X0)|~relation(X1)|~relation(relation_composition(X0,X1))|~in(ordered_pair(X2,X3),relation_composition(X0,X1))|in(ordered_pair(X2,sk0_40(X3,X2,relation_composition(X0,X1),X1,X0)),X0))),
% 106.73/13.76 inference(destructive_equality_resolution,[status(esa)],[f394])).
% 106.73/13.76 fof(f844,plain,(
% 106.73/13.76 ![X0,X1,X2,X3]: (~relation(X0)|~relation(X1)|~relation(relation_composition(X0,X1))|~in(ordered_pair(X2,X3),relation_composition(X0,X1))|in(ordered_pair(sk0_40(X3,X2,relation_composition(X0,X1),X1,X0),X3),X1))),
% 106.73/13.76 inference(destructive_equality_resolution,[status(esa)],[f395])).
% 106.73/13.76 fof(f855,plain,(
% 106.73/13.76 ![X0,X1,X2,X3]: (~relation(X0)|~in(ordered_pair(X1,X2),relation_rng_restriction(X3,X0))|in(X2,X3))),
% 106.73/13.76 inference(backward_subsumption_resolution,[status(thm)],[f807,f434])).
% 106.73/13.76 fof(f856,plain,(
% 106.73/13.76 spl0_3 <=> ~relation(X0)|~subset(X0,empty_set)|subset(relation_rng(X0),empty_set)),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f857,plain,(
% 106.73/13.76 ![X0]: (~relation(X0)|~subset(X0,empty_set)|subset(relation_rng(X0),empty_set)|~spl0_3)),
% 106.73/13.76 inference(component_clause,[status(thm)],[f856])).
% 106.73/13.76 fof(f859,plain,(
% 106.73/13.76 spl0_4 <=> relation(empty_set)),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f860,plain,(
% 106.73/13.76 relation(empty_set)|~spl0_4),
% 106.73/13.76 inference(component_clause,[status(thm)],[f859])).
% 106.73/13.76 fof(f861,plain,(
% 106.73/13.76 ~relation(empty_set)|spl0_4),
% 106.73/13.76 inference(component_clause,[status(thm)],[f859])).
% 106.73/13.76 fof(f862,plain,(
% 106.73/13.76 ![X0]: (~relation(X0)|~relation(empty_set)|~subset(X0,empty_set)|subset(relation_rng(X0),empty_set))),
% 106.73/13.76 inference(paramodulation,[status(thm)],[f702,f596])).
% 106.73/13.76 fof(f863,plain,(
% 106.73/13.76 spl0_3|~spl0_4),
% 106.73/13.76 inference(split_clause,[status(thm)],[f862,f856,f859])).
% 106.73/13.76 fof(f864,plain,(
% 106.73/13.76 spl0_5 <=> ~relation(X0)|~subset(empty_set,X0)|subset(empty_set,relation_rng(X0))),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f867,plain,(
% 106.73/13.76 ![X0]: (~relation(empty_set)|~relation(X0)|~subset(empty_set,X0)|subset(empty_set,relation_rng(X0)))),
% 106.73/13.76 inference(paramodulation,[status(thm)],[f702,f596])).
% 106.73/13.76 fof(f868,plain,(
% 106.73/13.76 ~spl0_4|spl0_5),
% 106.73/13.76 inference(split_clause,[status(thm)],[f867,f859,f864])).
% 106.73/13.76 fof(f869,plain,(
% 106.73/13.76 spl0_6 <=> relation_dom(empty_set)=empty_set),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f870,plain,(
% 106.73/13.76 relation_dom(empty_set)=empty_set|~spl0_6),
% 106.73/13.76 inference(component_clause,[status(thm)],[f869])).
% 106.73/13.76 fof(f872,plain,(
% 106.73/13.76 spl0_7 <=> empty_set=empty_set),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f877,plain,(
% 106.73/13.76 spl0_8 <=> empty(empty_set)),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f886,plain,(
% 106.73/13.76 ~relation(empty_set)|empty_set=empty_set),
% 106.73/13.76 inference(resolution,[status(thm)],[f710,f702])).
% 106.73/13.76 fof(f887,plain,(
% 106.73/13.76 ~spl0_4|spl0_7),
% 106.73/13.76 inference(split_clause,[status(thm)],[f886,f859,f872])).
% 106.73/13.76 fof(f892,plain,(
% 106.73/13.76 ![X0,X1,X2,X3]: (~relation(X0)|~in(ordered_pair(X1,X2),relation_rng_restriction(X3,X0))|in(ordered_pair(X1,X2),X0))),
% 106.73/13.76 inference(forward_subsumption_resolution,[status(thm)],[f808,f434])).
% 106.73/13.76 fof(f893,plain,(
% 106.73/13.76 ![X0,X1,X2,X3]: (~relation(X0)|in(ordered_pair(X1,X2),relation_rng_restriction(X3,X0))|~in(X2,X3)|~in(ordered_pair(X1,X2),X0))),
% 106.73/13.76 inference(forward_subsumption_resolution,[status(thm)],[f809,f434])).
% 106.73/13.76 fof(f895,plain,(
% 106.73/13.76 ~relation(empty_set)|relation_dom(empty_set)=empty_set),
% 106.73/13.76 inference(resolution,[status(thm)],[f714,f702])).
% 106.73/13.76 fof(f896,plain,(
% 106.73/13.76 ~spl0_4|spl0_6),
% 106.73/13.76 inference(split_clause,[status(thm)],[f895,f859,f869])).
% 106.73/13.76 fof(f899,plain,(
% 106.73/13.76 ![X0,X1,X2,X3]: (~relation(relation_rng_restriction(X0,X1))|in(X2,relation_rng(relation_rng_restriction(X0,X1)))|~relation(X1)|~in(X2,X0)|~in(ordered_pair(X3,X2),X1))),
% 106.73/13.76 inference(resolution,[status(thm)],[f840,f893])).
% 106.73/13.76 fof(f900,plain,(
% 106.73/13.76 ![X0,X1,X2,X3]: (in(X0,relation_rng(relation_rng_restriction(X1,X2)))|~relation(X2)|~in(X0,X1)|~in(ordered_pair(X3,X0),X2))),
% 106.73/13.76 inference(forward_subsumption_resolution,[status(thm)],[f899,f434])).
% 106.73/13.76 fof(f1817,plain,(
% 106.73/13.76 relation(sk0_49)),
% 106.73/13.76 inference(resolution,[status(thm)],[f197,f528])).
% 106.73/13.76 fof(f1882,plain,(
% 106.73/13.76 ![X0]: (~in(singleton(X0),X0))),
% 106.73/13.76 inference(resolution,[status(thm)],[f816,f193])).
% 106.73/13.76 fof(f1945,plain,(
% 106.73/13.76 ![X0]: (~in(sk0_56(X0),X0))),
% 106.73/13.76 inference(resolution,[status(thm)],[f574,f193])).
% 106.73/13.76 fof(f1947,plain,(
% 106.73/13.76 sk0_49=empty_set),
% 106.73/13.76 inference(resolution,[status(thm)],[f721,f528])).
% 106.73/13.76 fof(f1950,plain,(
% 106.73/13.76 relation(empty_set)),
% 106.73/13.76 inference(backward_demodulation,[status(thm)],[f1947,f1817])).
% 106.73/13.76 fof(f1951,plain,(
% 106.73/13.76 $false|spl0_4),
% 106.73/13.76 inference(forward_subsumption_resolution,[status(thm)],[f1950,f861])).
% 106.73/13.76 fof(f1952,plain,(
% 106.73/13.76 spl0_4),
% 106.73/13.76 inference(contradiction_clause,[status(thm)],[f1951])).
% 106.73/13.76 fof(f1958,plain,(
% 106.73/13.76 spl0_9 <=> relation(identity_relation(empty_set))),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f1960,plain,(
% 106.73/13.76 ~relation(identity_relation(empty_set))|spl0_9),
% 106.73/13.76 inference(component_clause,[status(thm)],[f1958])).
% 106.73/13.76 fof(f1961,plain,(
% 106.73/13.76 spl0_10 <=> relation_dom(identity_relation(empty_set))=empty_set),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f1964,plain,(
% 106.73/13.76 ~relation(identity_relation(empty_set))|relation_dom(identity_relation(empty_set))=empty_set),
% 106.73/13.76 inference(resolution,[status(thm)],[f726,f714])).
% 106.73/13.76 fof(f1965,plain,(
% 106.73/13.76 ~spl0_9|spl0_10),
% 106.73/13.76 inference(split_clause,[status(thm)],[f1964,f1958,f1961])).
% 106.73/13.76 fof(f1966,plain,(
% 106.73/13.76 spl0_11 <=> identity_relation(empty_set)=empty_set),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f1969,plain,(
% 106.73/13.76 ~relation(identity_relation(empty_set))|identity_relation(empty_set)=empty_set),
% 106.73/13.76 inference(resolution,[status(thm)],[f726,f710])).
% 106.73/13.76 fof(f1970,plain,(
% 106.73/13.76 ~spl0_9|spl0_11),
% 106.73/13.76 inference(split_clause,[status(thm)],[f1969,f1958,f1966])).
% 106.73/13.76 fof(f1974,plain,(
% 106.73/13.76 ![X0]: (~relation(identity_relation(X0))|~X0=empty_set|identity_relation(X0)=empty_set)),
% 106.73/13.76 inference(paramodulation,[status(thm)],[f726,f710])).
% 106.73/13.76 fof(f1975,plain,(
% 106.73/13.76 ~relation(identity_relation(empty_set))|identity_relation(empty_set)=empty_set),
% 106.73/13.76 inference(destructive_equality_resolution,[status(esa)],[f1974])).
% 106.73/13.76 fof(f1976,plain,(
% 106.73/13.76 identity_relation(empty_set)=empty_set),
% 106.73/13.76 inference(forward_subsumption_resolution,[status(thm)],[f1975,f422])).
% 106.73/13.76 fof(f1977,plain,(
% 106.73/13.76 ![X0,X1]: (~relation(X0)|~relation(identity_relation(X1))|~subset(X0,identity_relation(X1))|subset(relation_rng(X0),X1))),
% 106.73/13.76 inference(paramodulation,[status(thm)],[f726,f596])).
% 106.73/13.76 fof(f1978,plain,(
% 106.73/13.76 ![X0,X1]: (~relation(X0)|~subset(X0,identity_relation(X1))|subset(relation_rng(X0),X1))),
% 106.73/13.76 inference(forward_subsumption_resolution,[status(thm)],[f1977,f422])).
% 106.73/13.76 fof(f1987,plain,(
% 106.73/13.76 $false|spl0_9),
% 106.73/13.76 inference(forward_subsumption_resolution,[status(thm)],[f1960,f422])).
% 106.73/13.76 fof(f1988,plain,(
% 106.73/13.76 spl0_9),
% 106.73/13.76 inference(contradiction_clause,[status(thm)],[f1987])).
% 106.73/13.76 fof(f2051,plain,(
% 106.73/13.76 ![X0]: (~in(sk0_62(X0),X0))),
% 106.73/13.76 inference(resolution,[status(thm)],[f773,f193])).
% 106.73/13.76 fof(f2127,plain,(
% 106.73/13.76 ![X0,X1]: (~in(unordered_pair(X0,X1),X0))),
% 106.73/13.76 inference(resolution,[status(thm)],[f821,f193])).
% 106.73/13.76 fof(f2190,plain,(
% 106.73/13.76 ![X0,X1]: (~in(unordered_pair(X0,X1),X1))),
% 106.73/13.76 inference(resolution,[status(thm)],[f822,f193])).
% 106.73/13.76 fof(f2221,plain,(
% 106.73/13.76 ![X0]: (X0=set_union2(empty_set,X0))),
% 106.73/13.76 inference(paramodulation,[status(thm)],[f581,f199])).
% 106.73/13.76 fof(f2224,plain,(
% 106.73/13.76 ![X0,X1]: (subset(X0,set_union2(X1,X0)))),
% 106.73/13.76 inference(paramodulation,[status(thm)],[f199,f736])).
% 106.73/13.76 fof(f2237,plain,(
% 106.73/13.76 ![X0]: (empty_set=set_intersection2(empty_set,X0))),
% 106.73/13.76 inference(paramodulation,[status(thm)],[f602,f200])).
% 106.73/13.76 fof(f2240,plain,(
% 106.73/13.76 ![X0,X1]: (subset(set_intersection2(X0,X1),X1))),
% 106.73/13.76 inference(paramodulation,[status(thm)],[f200,f578])).
% 106.73/13.76 fof(f2363,plain,(
% 106.73/13.76 ![X0,X1,X2]: (~relation(relation_rng_restriction(X0,X1))|relation_rng_restriction(X0,X1)=identity_relation(X2)|in(sk0_0(X2,relation_rng_restriction(X0,X1)),X2)|~relation(X1)|in(ordered_pair(sk0_0(X2,relation_rng_restriction(X0,X1)),sk0_1(X2,relation_rng_restriction(X0,X1))),X1))),
% 106.73/13.76 inference(resolution,[status(thm)],[f209,f892])).
% 106.73/13.76 fof(f2364,plain,(
% 106.73/13.76 ![X0,X1,X2]: (relation_rng_restriction(X0,X1)=identity_relation(X2)|in(sk0_0(X2,relation_rng_restriction(X0,X1)),X2)|~relation(X1)|in(ordered_pair(sk0_0(X2,relation_rng_restriction(X0,X1)),sk0_1(X2,relation_rng_restriction(X0,X1))),X1))),
% 106.73/13.76 inference(forward_subsumption_resolution,[status(thm)],[f2363,f434])).
% 106.73/13.76 fof(f2365,plain,(
% 106.73/13.76 ![X0,X1]: (~relation(X0)|X0=identity_relation(X1)|in(sk0_0(X1,X0),X1)|~relation(X0)|in(sk0_1(X1,X0),relation_rng(X0)))),
% 106.73/13.76 inference(resolution,[status(thm)],[f209,f840])).
% 106.73/13.76 fof(f2366,plain,(
% 106.73/13.76 ![X0,X1]: (~relation(X0)|X0=identity_relation(X1)|in(sk0_0(X1,X0),X1)|in(sk0_1(X1,X0),relation_rng(X0)))),
% 106.73/13.76 inference(duplicate_literals_removal,[status(esa)],[f2365])).
% 106.73/13.76 fof(f2368,plain,(
% 106.73/13.76 spl0_12 <=> empty_set=identity_relation(X0)|in(sk0_0(X0,empty_set),X0)),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f2371,plain,(
% 106.73/13.76 ![X0]: (~relation(empty_set)|empty_set=identity_relation(X0)|in(sk0_0(X0,empty_set),X0))),
% 106.73/13.76 inference(resolution,[status(thm)],[f209,f817])).
% 106.73/13.76 fof(f2372,plain,(
% 106.73/13.76 ~spl0_4|spl0_12),
% 106.73/13.76 inference(split_clause,[status(thm)],[f2371,f859,f2368])).
% 106.73/13.76 fof(f2383,plain,(
% 106.73/13.76 ![X0,X1,X2]: (~relation(relation_rng_restriction(X0,X1))|relation_rng_restriction(X0,X1)=identity_relation(X2)|sk0_0(X2,relation_rng_restriction(X0,X1))=sk0_1(X2,relation_rng_restriction(X0,X1))|~relation(X1)|in(ordered_pair(sk0_0(X2,relation_rng_restriction(X0,X1)),sk0_1(X2,relation_rng_restriction(X0,X1))),X1))),
% 106.73/13.76 inference(resolution,[status(thm)],[f210,f892])).
% 106.73/13.76 fof(f2384,plain,(
% 106.73/13.76 ![X0,X1,X2]: (relation_rng_restriction(X0,X1)=identity_relation(X2)|sk0_0(X2,relation_rng_restriction(X0,X1))=sk0_1(X2,relation_rng_restriction(X0,X1))|~relation(X1)|in(ordered_pair(sk0_0(X2,relation_rng_restriction(X0,X1)),sk0_1(X2,relation_rng_restriction(X0,X1))),X1))),
% 106.73/13.76 inference(forward_subsumption_resolution,[status(thm)],[f2383,f434])).
% 106.73/13.76 fof(f2388,plain,(
% 106.73/13.76 spl0_13 <=> empty_set=identity_relation(X0)|sk0_0(X0,empty_set)=sk0_1(X0,empty_set)),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f2391,plain,(
% 106.73/13.76 ![X0]: (~relation(empty_set)|empty_set=identity_relation(X0)|sk0_0(X0,empty_set)=sk0_1(X0,empty_set))),
% 106.73/13.76 inference(resolution,[status(thm)],[f210,f817])).
% 106.73/13.76 fof(f2392,plain,(
% 106.73/13.76 ~spl0_4|spl0_13),
% 106.73/13.76 inference(split_clause,[status(thm)],[f2391,f859,f2388])).
% 106.73/13.76 fof(f2396,plain,(
% 106.73/13.76 ![X0,X1]: (X0=set_difference(X0,X1)|~subset(X0,set_difference(X0,X1)))),
% 106.73/13.76 inference(resolution,[status(thm)],[f215,f621])).
% 106.73/13.76 fof(f2397,plain,(
% 106.73/13.76 ![X0,X1]: (X0=set_intersection2(X1,X0)|~subset(X0,set_intersection2(X1,X0)))),
% 106.73/13.76 inference(resolution,[status(thm)],[f215,f2240])).
% 106.73/13.76 fof(f2398,plain,(
% 106.73/13.76 ![X0,X1]: (X0=set_intersection2(X0,X1)|~subset(X0,set_intersection2(X0,X1)))),
% 106.73/13.76 inference(resolution,[status(thm)],[f215,f578])).
% 106.73/13.76 fof(f2400,plain,(
% 106.73/13.76 ![X0,X1]: (relation_rng(X0)=relation_rng(X1)|~subset(relation_rng(X0),relation_rng(X1))|~relation(X1)|~relation(X0)|~subset(X1,X0))),
% 106.73/13.76 inference(resolution,[status(thm)],[f215,f596])).
% 106.73/13.76 fof(f2507,plain,(
% 106.73/13.76 ![X0,X1,X2,X3]: (~relation(X0)|~relation(relation_dom_restriction(X0,X1))|~in(X2,X1)|~in(ordered_pair(X2,X3),X0)|~relation(relation_dom_restriction(X0,X1))|in(X3,relation_rng(relation_dom_restriction(X0,X1))))),
% 106.73/13.76 inference(resolution,[status(thm)],[f806,f840])).
% 106.73/13.76 fof(f2508,plain,(
% 106.73/13.76 ![X0,X1,X2,X3]: (~relation(X0)|~relation(relation_dom_restriction(X0,X1))|~in(X2,X1)|~in(ordered_pair(X2,X3),X0)|in(X3,relation_rng(relation_dom_restriction(X0,X1))))),
% 106.73/13.76 inference(duplicate_literals_removal,[status(esa)],[f2507])).
% 106.73/13.76 fof(f2511,plain,(
% 106.73/13.76 ![X0,X1,X2,X3]: (~relation(X0)|~relation(relation_dom_restriction(X0,X1))|~in(X2,X1)|~in(ordered_pair(X2,X3),X0)|~in(relation_dom_restriction(X0,X1),ordered_pair(X2,X3)))),
% 106.73/13.76 inference(resolution,[status(thm)],[f806,f193])).
% 106.73/13.76 fof(f2539,plain,(
% 106.73/13.76 ![X0,X1]: (~relation(set_intersection2(X0,identity_relation(X1)))|subset(relation_rng(set_intersection2(X0,identity_relation(X1))),X1))),
% 106.73/13.76 inference(resolution,[status(thm)],[f1978,f2240])).
% 106.73/13.76 fof(f2962,plain,(
% 106.73/13.76 ![X0,X1]: (relation_rng(X0)=relation_rng(X1)|~relation(X1)|~relation(X0)|~subset(X1,X0)|~relation(X0)|~relation(X1)|~subset(X0,X1))),
% 106.73/13.76 inference(resolution,[status(thm)],[f2400,f596])).
% 106.73/13.76 fof(f2963,plain,(
% 106.73/13.76 ![X0,X1]: (relation_rng(X0)=relation_rng(X1)|~relation(X1)|~relation(X0)|~subset(X1,X0)|~subset(X0,X1))),
% 106.73/13.76 inference(duplicate_literals_removal,[status(esa)],[f2962])).
% 106.73/13.76 fof(f2964,plain,(
% 106.73/13.76 ![X0,X1]: (relation_rng(identity_relation(X0))=relation_rng(X1)|~subset(X0,relation_rng(X1))|~relation(X1)|~relation(identity_relation(X0))|~subset(X1,identity_relation(X0)))),
% 106.73/13.76 inference(paramodulation,[status(thm)],[f726,f2400])).
% 106.73/13.76 fof(f2965,plain,(
% 106.73/13.76 ![X0,X1]: (X0=relation_rng(X1)|~subset(X0,relation_rng(X1))|~relation(X1)|~relation(identity_relation(X0))|~subset(X1,identity_relation(X0)))),
% 106.73/13.76 inference(forward_demodulation,[status(thm)],[f726,f2964])).
% 106.73/13.76 fof(f2966,plain,(
% 106.73/13.76 ![X0,X1]: (X0=relation_rng(X1)|~subset(X0,relation_rng(X1))|~relation(X1)|~subset(X1,identity_relation(X0)))),
% 106.73/13.76 inference(forward_subsumption_resolution,[status(thm)],[f2965,f422])).
% 106.73/13.76 fof(f2967,plain,(
% 106.73/13.76 spl0_14 <=> relation_rng(empty_set)=relation_rng(X0)|~subset(empty_set,relation_rng(X0))|~relation(X0)|~subset(X0,empty_set)),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f2970,plain,(
% 106.73/13.76 ![X0]: (relation_rng(empty_set)=relation_rng(X0)|~subset(empty_set,relation_rng(X0))|~relation(X0)|~relation(empty_set)|~subset(X0,empty_set))),
% 106.73/13.76 inference(paramodulation,[status(thm)],[f702,f2400])).
% 106.73/13.76 fof(f2971,plain,(
% 106.73/13.76 spl0_14|~spl0_4),
% 106.73/13.76 inference(split_clause,[status(thm)],[f2970,f2967,f859])).
% 106.73/13.76 fof(f2975,plain,(
% 106.73/13.76 spl0_15 <=> relation_rng(X0)=relation_rng(empty_set)|~subset(relation_rng(X0),empty_set)|~relation(X0)|~subset(empty_set,X0)),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f2978,plain,(
% 106.73/13.76 ![X0]: (relation_rng(X0)=relation_rng(empty_set)|~subset(relation_rng(X0),empty_set)|~relation(empty_set)|~relation(X0)|~subset(empty_set,X0))),
% 106.73/13.76 inference(paramodulation,[status(thm)],[f702,f2400])).
% 106.73/13.76 fof(f2979,plain,(
% 106.73/13.76 spl0_15|~spl0_4),
% 106.73/13.76 inference(split_clause,[status(thm)],[f2978,f2975,f859])).
% 106.73/13.76 fof(f2982,plain,(
% 106.73/13.76 ![X0,X1]: (set_difference(relation_rng(X0),X1)=relation_rng(X0)|~relation(X0)|~subset(X0,identity_relation(set_difference(relation_rng(X0),X1))))),
% 106.73/13.76 inference(resolution,[status(thm)],[f2966,f621])).
% 106.73/13.76 fof(f2983,plain,(
% 106.73/13.76 ![X0,X1]: (set_intersection2(X0,relation_rng(X1))=relation_rng(X1)|~relation(X1)|~subset(X1,identity_relation(set_intersection2(X0,relation_rng(X1)))))),
% 106.73/13.76 inference(resolution,[status(thm)],[f2966,f2240])).
% 106.73/13.76 fof(f2984,plain,(
% 106.73/13.76 ![X0,X1]: (set_intersection2(relation_rng(X0),X1)=relation_rng(X0)|~relation(X0)|~subset(X0,identity_relation(set_intersection2(relation_rng(X0),X1))))),
% 106.73/13.76 inference(resolution,[status(thm)],[f2966,f578])).
% 106.73/13.76 fof(f2985,plain,(
% 106.73/13.76 ![X0,X1]: (relation_rng(X0)=relation_rng(X1)|~relation(X1)|~subset(X1,identity_relation(relation_rng(X0)))|~relation(X0)|~relation(X1)|~subset(X0,X1))),
% 106.73/13.76 inference(resolution,[status(thm)],[f2966,f596])).
% 106.73/13.76 fof(f2986,plain,(
% 106.73/13.76 ![X0,X1]: (relation_rng(X0)=relation_rng(X1)|~relation(X1)|~subset(X1,identity_relation(relation_rng(X0)))|~relation(X0)|~subset(X0,X1))),
% 106.73/13.76 inference(duplicate_literals_removal,[status(esa)],[f2985])).
% 106.73/13.76 fof(f2990,plain,(
% 106.73/13.76 spl0_16 <=> X0=relation_rng(empty_set)|~subset(X0,empty_set)|~subset(empty_set,identity_relation(X0))),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f2991,plain,(
% 106.73/13.76 ![X0]: (X0=relation_rng(empty_set)|~subset(X0,empty_set)|~subset(empty_set,identity_relation(X0))|~spl0_16)),
% 106.73/13.76 inference(component_clause,[status(thm)],[f2990])).
% 106.73/13.76 fof(f2993,plain,(
% 106.73/13.76 ![X0]: (X0=relation_rng(empty_set)|~subset(X0,empty_set)|~relation(empty_set)|~subset(empty_set,identity_relation(X0)))),
% 106.73/13.76 inference(paramodulation,[status(thm)],[f702,f2966])).
% 106.73/13.76 fof(f2994,plain,(
% 106.73/13.76 spl0_16|~spl0_4),
% 106.73/13.76 inference(split_clause,[status(thm)],[f2993,f2990,f859])).
% 106.73/13.76 fof(f2995,plain,(
% 106.73/13.76 ![X0]: (X0=empty_set|~subset(X0,empty_set)|~subset(empty_set,identity_relation(X0))|~spl0_16)),
% 106.73/13.76 inference(forward_demodulation,[status(thm)],[f702,f2991])).
% 106.73/13.76 fof(f2998,plain,(
% 106.73/13.76 spl0_17 <=> empty_set=relation_rng(X0)|~relation(X0)|~subset(X0,empty_set)|~subset(empty_set,X0)),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f3001,plain,(
% 106.73/13.76 ![X0]: (empty_set=relation_rng(X0)|~relation(X0)|~relation(empty_set)|~subset(X0,empty_set)|~subset(empty_set,X0))),
% 106.73/13.76 inference(paramodulation,[status(thm)],[f702,f2963])).
% 106.73/13.76 fof(f3002,plain,(
% 106.73/13.76 spl0_17|~spl0_4),
% 106.73/13.76 inference(split_clause,[status(thm)],[f3001,f2998,f859])).
% 106.73/13.76 fof(f3015,plain,(
% 106.73/13.76 spl0_18 <=> set_difference(relation_rng(empty_set),X0)=relation_rng(empty_set)|~subset(empty_set,identity_relation(set_difference(empty_set,X0)))),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f3018,plain,(
% 106.73/13.76 ![X0]: (set_difference(relation_rng(empty_set),X0)=relation_rng(empty_set)|~relation(empty_set)|~subset(empty_set,identity_relation(set_difference(empty_set,X0))))),
% 106.73/13.76 inference(paramodulation,[status(thm)],[f702,f2982])).
% 106.73/13.76 fof(f3019,plain,(
% 106.73/13.76 spl0_18|~spl0_4),
% 106.73/13.76 inference(split_clause,[status(thm)],[f3018,f3015,f859])).
% 106.73/13.76 fof(f3022,plain,(
% 106.73/13.76 spl0_19 <=> set_difference(empty_set,X0)=empty_set),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f3025,plain,(
% 106.73/13.76 spl0_20 <=> subset(identity_relation(empty_set),identity_relation(empty_set))),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f3027,plain,(
% 106.73/13.76 ~subset(identity_relation(empty_set),identity_relation(empty_set))|spl0_20),
% 106.73/13.76 inference(component_clause,[status(thm)],[f3025])).
% 106.73/13.76 fof(f3031,plain,(
% 106.73/13.76 $false|spl0_20),
% 106.73/13.76 inference(forward_subsumption_resolution,[status(thm)],[f3027,f802])).
% 106.73/13.76 fof(f3032,plain,(
% 106.73/13.76 spl0_20),
% 106.73/13.76 inference(contradiction_clause,[status(thm)],[f3031])).
% 106.73/13.76 fof(f3033,plain,(
% 106.73/13.76 ![X0]: (set_intersection2(empty_set,relation_rng(X0))=relation_rng(X0)|~relation(X0)|~subset(X0,identity_relation(empty_set)))),
% 106.73/13.76 inference(paramodulation,[status(thm)],[f2237,f2983])).
% 106.73/13.76 fof(f3034,plain,(
% 106.73/13.76 ![X0]: (empty_set=relation_rng(X0)|~relation(X0)|~subset(X0,identity_relation(empty_set)))),
% 106.73/13.76 inference(forward_demodulation,[status(thm)],[f2237,f3033])).
% 106.73/13.76 fof(f3035,plain,(
% 106.73/13.76 ![X0,X1]: (set_intersection2(X0,relation_rng(X1))=relation_rng(X1)|~relation(X1)|~subset(X1,identity_relation(set_intersection2(relation_rng(X1),X0))))),
% 106.73/13.76 inference(paramodulation,[status(thm)],[f200,f2983])).
% 106.73/13.76 fof(f3042,plain,(
% 106.73/13.76 spl0_21 <=> set_intersection2(X0,relation_rng(empty_set))=relation_rng(empty_set)|~subset(empty_set,identity_relation(set_intersection2(X0,empty_set)))),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f3045,plain,(
% 106.73/13.76 ![X0]: (set_intersection2(X0,relation_rng(empty_set))=relation_rng(empty_set)|~relation(empty_set)|~subset(empty_set,identity_relation(set_intersection2(X0,empty_set))))),
% 106.73/13.76 inference(paramodulation,[status(thm)],[f702,f2983])).
% 106.73/13.76 fof(f3046,plain,(
% 106.73/13.76 spl0_21|~spl0_4),
% 106.73/13.76 inference(split_clause,[status(thm)],[f3045,f3042,f859])).
% 106.73/13.76 fof(f3052,plain,(
% 106.73/13.76 spl0_22 <=> empty_set=relation_rng(identity_relation(empty_set))),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f3055,plain,(
% 106.73/13.76 empty_set=relation_rng(identity_relation(empty_set))|~relation(identity_relation(empty_set))),
% 106.73/13.76 inference(resolution,[status(thm)],[f3034,f802])).
% 106.73/13.76 fof(f3056,plain,(
% 106.73/13.76 spl0_22|~spl0_9),
% 106.73/13.76 inference(split_clause,[status(thm)],[f3055,f3052,f1958])).
% 106.73/13.76 fof(f3059,plain,(
% 106.73/13.76 spl0_23 <=> set_intersection2(X0,empty_set)=empty_set),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f3077,plain,(
% 106.73/13.76 spl0_24 <=> subset(empty_set,empty_set)),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f3091,plain,(
% 106.73/13.76 ![X0,X1]: (set_intersection2(relation_rng(X0),X1)=relation_rng(X0)|~relation(X0)|~subset(X0,identity_relation(set_intersection2(X1,relation_rng(X0)))))),
% 106.73/13.76 inference(paramodulation,[status(thm)],[f200,f2984])).
% 106.73/13.76 fof(f3098,plain,(
% 106.73/13.76 spl0_25 <=> set_intersection2(relation_rng(empty_set),X0)=relation_rng(empty_set)|~subset(empty_set,identity_relation(set_intersection2(empty_set,X0)))),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f3101,plain,(
% 106.73/13.76 ![X0]: (set_intersection2(relation_rng(empty_set),X0)=relation_rng(empty_set)|~relation(empty_set)|~subset(empty_set,identity_relation(set_intersection2(empty_set,X0))))),
% 106.73/13.76 inference(paramodulation,[status(thm)],[f702,f2984])).
% 106.73/13.76 fof(f3102,plain,(
% 106.73/13.76 spl0_25|~spl0_4),
% 106.73/13.76 inference(split_clause,[status(thm)],[f3101,f3098,f859])).
% 106.73/13.76 fof(f3105,plain,(
% 106.73/13.76 spl0_26 <=> set_intersection2(empty_set,X0)=empty_set),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f3130,plain,(
% 106.73/13.76 spl0_27 <=> set_intersection2(X0,relation_rng(empty_set))=relation_rng(empty_set)|~subset(empty_set,identity_relation(set_intersection2(empty_set,X0)))),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f3133,plain,(
% 106.73/13.76 ![X0]: (set_intersection2(X0,relation_rng(empty_set))=relation_rng(empty_set)|~relation(empty_set)|~subset(empty_set,identity_relation(set_intersection2(empty_set,X0))))),
% 106.73/13.76 inference(paramodulation,[status(thm)],[f702,f3035])).
% 106.73/13.76 fof(f3134,plain,(
% 106.73/13.76 spl0_27|~spl0_4),
% 106.73/13.76 inference(split_clause,[status(thm)],[f3133,f3130,f859])).
% 106.73/13.76 fof(f3145,plain,(
% 106.73/13.76 spl0_28 <=> set_intersection2(relation_rng(empty_set),X0)=relation_rng(empty_set)|~subset(empty_set,identity_relation(set_intersection2(X0,empty_set)))),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f3148,plain,(
% 106.73/13.76 ![X0]: (set_intersection2(relation_rng(empty_set),X0)=relation_rng(empty_set)|~relation(empty_set)|~subset(empty_set,identity_relation(set_intersection2(X0,empty_set))))),
% 106.73/13.76 inference(paramodulation,[status(thm)],[f702,f3091])).
% 106.73/13.76 fof(f3149,plain,(
% 106.73/13.76 spl0_28|~spl0_4),
% 106.73/13.76 inference(split_clause,[status(thm)],[f3148,f3145,f859])).
% 106.73/13.76 fof(f3158,plain,(
% 106.73/13.76 spl0_29 <=> relation_rng(empty_set)=relation_rng(X0)|~relation(X0)|~subset(X0,identity_relation(empty_set))|~subset(empty_set,X0)),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f3161,plain,(
% 106.73/13.76 ![X0]: (relation_rng(empty_set)=relation_rng(X0)|~relation(X0)|~subset(X0,identity_relation(empty_set))|~relation(empty_set)|~subset(empty_set,X0))),
% 106.73/13.76 inference(paramodulation,[status(thm)],[f702,f2986])).
% 106.73/13.76 fof(f3162,plain,(
% 106.73/13.76 spl0_29|~spl0_4),
% 106.73/13.76 inference(split_clause,[status(thm)],[f3161,f3158,f859])).
% 106.73/13.76 fof(f3185,plain,(
% 106.73/13.76 ![X0]: (empty_set=relation_rng(X0)|~relation(X0)|~subset(X0,empty_set))),
% 106.73/13.76 inference(backward_demodulation,[status(thm)],[f1976,f3034])).
% 106.73/13.76 fof(f3240,plain,(
% 106.73/13.76 spl0_30 <=> empty_set=relation_rng(empty_set)),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f3243,plain,(
% 106.73/13.76 empty_set=relation_rng(empty_set)|~relation(empty_set)),
% 106.73/13.76 inference(resolution,[status(thm)],[f3185,f802])).
% 106.73/13.76 fof(f3244,plain,(
% 106.73/13.76 spl0_30|~spl0_4),
% 106.73/13.76 inference(split_clause,[status(thm)],[f3243,f3240,f859])).
% 106.73/13.76 fof(f3421,plain,(
% 106.73/13.76 ![X0]: (~relation(set_intersection2(empty_set,identity_relation(X0)))|subset(relation_rng(empty_set),X0))),
% 106.73/13.76 inference(paramodulation,[status(thm)],[f2237,f2539])).
% 106.73/13.76 fof(f3422,plain,(
% 106.73/13.76 ![X0]: (~relation(empty_set)|subset(relation_rng(empty_set),X0))),
% 106.73/13.76 inference(forward_demodulation,[status(thm)],[f2237,f3421])).
% 106.73/13.76 fof(f3423,plain,(
% 106.73/13.76 ![X0]: (~relation(empty_set)|subset(empty_set,X0))),
% 106.73/13.76 inference(forward_demodulation,[status(thm)],[f702,f3422])).
% 106.73/13.76 fof(f3424,plain,(
% 106.73/13.76 ![X0]: (subset(empty_set,X0)|~spl0_4)),
% 106.73/13.76 inference(forward_subsumption_resolution,[status(thm)],[f3423,f860])).
% 106.73/13.76 fof(f3435,plain,(
% 106.73/13.76 ![X0]: (X0=empty_set|~subset(X0,empty_set)|~spl0_4|~spl0_16)),
% 106.73/13.76 inference(backward_subsumption_resolution,[status(thm)],[f2995,f3424])).
% 106.73/13.76 fof(f3440,plain,(
% 106.73/13.76 spl0_31 <=> relation_rng(X0)=relation_rng(empty_set)|~relation(X0)|~subset(X0,empty_set)),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f3443,plain,(
% 106.73/13.76 ![X0]: (relation_rng(X0)=relation_rng(empty_set)|~relation(empty_set)|~relation(X0)|~subset(X0,empty_set)|~spl0_4)),
% 106.73/13.76 inference(resolution,[status(thm)],[f3424,f2986])).
% 106.73/13.76 fof(f3444,plain,(
% 106.73/13.76 spl0_31|~spl0_4),
% 106.73/13.76 inference(split_clause,[status(thm)],[f3443,f3440,f859])).
% 106.73/13.76 fof(f3445,plain,(
% 106.73/13.76 spl0_32 <=> set_intersection2(X0,relation_rng(empty_set))=relation_rng(empty_set)),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f3448,plain,(
% 106.73/13.76 ![X0]: (set_intersection2(X0,relation_rng(empty_set))=relation_rng(empty_set)|~relation(empty_set)|~spl0_4)),
% 106.73/13.76 inference(resolution,[status(thm)],[f3424,f3035])).
% 106.73/13.76 fof(f3449,plain,(
% 106.73/13.76 spl0_32|~spl0_4),
% 106.73/13.76 inference(split_clause,[status(thm)],[f3448,f3445,f859])).
% 106.73/13.76 fof(f3450,plain,(
% 106.73/13.76 spl0_33 <=> set_intersection2(relation_rng(empty_set),X0)=relation_rng(empty_set)),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f3453,plain,(
% 106.73/13.76 ![X0]: (set_intersection2(relation_rng(empty_set),X0)=relation_rng(empty_set)|~relation(empty_set)|~spl0_4)),
% 106.73/13.76 inference(resolution,[status(thm)],[f3424,f2984])).
% 106.73/13.76 fof(f3454,plain,(
% 106.73/13.76 spl0_33|~spl0_4),
% 106.73/13.76 inference(split_clause,[status(thm)],[f3453,f3450,f859])).
% 106.73/13.76 fof(f3459,plain,(
% 106.73/13.76 spl0_34 <=> set_difference(relation_rng(empty_set),X0)=relation_rng(empty_set)),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f3462,plain,(
% 106.73/13.76 ![X0]: (set_difference(relation_rng(empty_set),X0)=relation_rng(empty_set)|~relation(empty_set)|~spl0_4)),
% 106.73/13.76 inference(resolution,[status(thm)],[f3424,f2982])).
% 106.73/13.76 fof(f3463,plain,(
% 106.73/13.76 spl0_34|~spl0_4),
% 106.73/13.76 inference(split_clause,[status(thm)],[f3462,f3459,f859])).
% 106.73/13.76 fof(f3464,plain,(
% 106.73/13.76 spl0_35 <=> subset(relation_rng(empty_set),X0)),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f3467,plain,(
% 106.73/13.76 ![X0]: (~relation(empty_set)|subset(relation_rng(empty_set),X0)|~spl0_4)),
% 106.73/13.76 inference(resolution,[status(thm)],[f3424,f1978])).
% 106.73/13.76 fof(f3468,plain,(
% 106.73/13.76 ~spl0_4|spl0_35),
% 106.73/13.76 inference(split_clause,[status(thm)],[f3467,f859,f3464])).
% 106.73/13.76 fof(f3543,plain,(
% 106.73/13.76 spl0_36 <=> relation_rng_restriction(X0,empty_set)=identity_relation(X1)|in(sk0_0(X1,relation_rng_restriction(X0,empty_set)),X1)),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f3546,plain,(
% 106.73/13.76 ![X0,X1]: (relation_rng_restriction(X0,empty_set)=identity_relation(X1)|in(sk0_0(X1,relation_rng_restriction(X0,empty_set)),X1)|~relation(empty_set))),
% 106.73/13.76 inference(resolution,[status(thm)],[f2364,f817])).
% 106.73/13.76 fof(f3547,plain,(
% 106.73/13.76 spl0_36|~spl0_4),
% 106.73/13.76 inference(split_clause,[status(thm)],[f3546,f3543,f859])).
% 106.73/13.76 fof(f3555,plain,(
% 106.73/13.76 spl0_37 <=> empty_set=identity_relation(X0)|in(sk0_0(X0,empty_set),X0)|in(sk0_1(X0,empty_set),empty_set)),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f3558,plain,(
% 106.73/13.76 ![X0]: (~relation(empty_set)|empty_set=identity_relation(X0)|in(sk0_0(X0,empty_set),X0)|in(sk0_1(X0,empty_set),empty_set))),
% 106.73/13.76 inference(paramodulation,[status(thm)],[f702,f2366])).
% 106.73/13.76 fof(f3559,plain,(
% 106.73/13.76 ~spl0_4|spl0_37),
% 106.73/13.76 inference(split_clause,[status(thm)],[f3558,f859,f3555])).
% 106.73/13.76 fof(f3581,plain,(
% 106.73/13.76 spl0_38 <=> relation_rng_restriction(X0,empty_set)=identity_relation(X1)|sk0_0(X1,relation_rng_restriction(X0,empty_set))=sk0_1(X1,relation_rng_restriction(X0,empty_set))),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f3584,plain,(
% 106.73/13.76 ![X0,X1]: (relation_rng_restriction(X0,empty_set)=identity_relation(X1)|sk0_0(X1,relation_rng_restriction(X0,empty_set))=sk0_1(X1,relation_rng_restriction(X0,empty_set))|~relation(empty_set))),
% 106.73/13.76 inference(resolution,[status(thm)],[f2384,f817])).
% 106.73/13.76 fof(f3585,plain,(
% 106.73/13.76 spl0_38|~spl0_4),
% 106.73/13.76 inference(split_clause,[status(thm)],[f3584,f3581,f859])).
% 106.73/13.76 fof(f3709,plain,(
% 106.73/13.76 ![X0,X1]: (~proper_subset(relation_rng(X0),relation_rng(X1))|~relation(X1)|~relation(X0)|~subset(X1,X0))),
% 106.73/13.76 inference(resolution,[status(thm)],[f704,f596])).
% 106.73/13.76 fof(f3723,plain,(
% 106.73/13.76 ![X0,X1]: (~empty(X0)|X0=relation_rng(X1)|~empty(X1))),
% 106.73/13.76 inference(resolution,[status(thm)],[f752,f467])).
% 106.73/13.76 fof(f3732,plain,(
% 106.73/13.76 ![X0,X1,X2,X3]: (~relation(X0)|~in(X1,X2)|~in(ordered_pair(X1,X3),X0)|in(X3,relation_rng(relation_dom_restriction(X0,X2))))),
% 106.73/13.76 inference(backward_subsumption_resolution,[status(thm)],[f2508,f429])).
% 106.73/13.76 fof(f3745,plain,(
% 106.73/13.76 spl0_40 <=> ~disjoint(empty_set,X0)),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f3746,plain,(
% 106.73/13.76 ![X0]: (~disjoint(empty_set,X0)|~spl0_40)),
% 106.73/13.76 inference(component_clause,[status(thm)],[f3745])).
% 106.73/13.76 fof(f3750,plain,(
% 106.73/13.76 ![X0]: (disjoint(empty_set,X0))),
% 106.73/13.76 inference(resolution,[status(thm)],[f740,f681])).
% 106.73/13.76 fof(f3751,plain,(
% 106.73/13.76 ![X0]: (disjoint(X0,empty_set))),
% 106.73/13.76 inference(resolution,[status(thm)],[f740,f644])).
% 106.73/13.76 fof(f3752,plain,(
% 106.73/13.76 spl0_41 <=> disjoint(empty_set,X0)),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f3755,plain,(
% 106.73/13.76 ![X0]: (disjoint(empty_set,X0)|~empty_set=empty_set)),
% 106.73/13.76 inference(paramodulation,[status(thm)],[f681,f740])).
% 106.73/13.76 fof(f3756,plain,(
% 106.73/13.76 spl0_41|~spl0_7),
% 106.73/13.76 inference(split_clause,[status(thm)],[f3755,f3752,f872])).
% 106.73/13.76 fof(f3778,plain,(
% 106.73/13.76 ![X0]: (~subset(singleton(powerset(X0)),X0))),
% 106.73/13.76 inference(resolution,[status(thm)],[f819,f1882])).
% 106.73/13.76 fof(f3860,plain,(
% 106.73/13.76 ![X0,X1]: (proper_subset(relation_rng(X0),relation_rng(X1))|relation_rng(X0)=relation_rng(X1)|~relation(X0)|~relation(X1)|~subset(X0,X1))),
% 106.73/13.76 inference(resolution,[status(thm)],[f412,f596])).
% 106.73/13.76 fof(f3866,plain,(
% 106.73/13.76 ![X0,X1]: (in(X0,set_union2(X1,singleton(X0))))),
% 106.73/13.76 inference(resolution,[status(thm)],[f493,f2224])).
% 106.73/13.76 fof(f3867,plain,(
% 106.73/13.76 ![X0,X1]: (in(X0,set_union2(singleton(X0),X1)))),
% 106.73/13.76 inference(resolution,[status(thm)],[f493,f736])).
% 106.73/13.76 fof(f3934,plain,(
% 106.73/13.76 ![X0,X1]: (~in(set_union2(X0,singleton(X1)),X1))),
% 106.73/13.76 inference(resolution,[status(thm)],[f3866,f193])).
% 106.73/13.76 fof(f4004,plain,(
% 106.73/13.76 ![X0,X1]: (~in(set_union2(singleton(X0),X1),X0))),
% 106.73/13.76 inference(resolution,[status(thm)],[f3867,f193])).
% 106.73/13.76 fof(f4045,plain,(
% 106.73/13.76 ![X0]: (~in(powerset(X0),X0))),
% 106.73/13.76 inference(resolution,[status(thm)],[f494,f3778])).
% 106.73/13.76 fof(f4079,plain,(
% 106.73/13.76 ![X0,X1,X2,X3]: (~relation(X0)|~relation(relation_rng_restriction(X1,X2))|relation_rng_restriction(X1,X2)=relation_dom_restriction(X0,X3)|in(sk0_2(X3,relation_rng_restriction(X1,X2),X0),X3)|~relation(X2)|in(ordered_pair(sk0_2(X3,relation_rng_restriction(X1,X2),X0),sk0_3(X3,relation_rng_restriction(X1,X2),X0)),X2))),
% 106.73/13.76 inference(resolution,[status(thm)],[f224,f892])).
% 106.73/13.76 fof(f4080,plain,(
% 106.73/13.76 ![X0,X1,X2,X3]: (~relation(X0)|relation_rng_restriction(X1,X2)=relation_dom_restriction(X0,X3)|in(sk0_2(X3,relation_rng_restriction(X1,X2),X0),X3)|~relation(X2)|in(ordered_pair(sk0_2(X3,relation_rng_restriction(X1,X2),X0),sk0_3(X3,relation_rng_restriction(X1,X2),X0)),X2))),
% 106.73/13.76 inference(forward_subsumption_resolution,[status(thm)],[f4079,f434])).
% 106.73/13.76 fof(f4083,plain,(
% 106.73/13.76 ![X0,X1,X2]: (~relation(X0)|~relation(X1)|X1=relation_dom_restriction(X0,X2)|in(sk0_2(X2,X1,X0),X2)|~relation(X1)|in(sk0_3(X2,X1,X0),relation_rng(X1)))),
% 106.73/13.76 inference(resolution,[status(thm)],[f224,f840])).
% 106.73/13.76 fof(f4084,plain,(
% 106.73/13.76 ![X0,X1,X2]: (~relation(X0)|~relation(X1)|X1=relation_dom_restriction(X0,X2)|in(sk0_2(X2,X1,X0),X2)|in(sk0_3(X2,X1,X0),relation_rng(X1)))),
% 106.73/13.76 inference(duplicate_literals_removal,[status(esa)],[f4083])).
% 106.73/13.76 fof(f4087,plain,(
% 106.73/13.76 spl0_42 <=> ~relation(X0)|empty_set=relation_dom_restriction(X0,X1)|in(sk0_2(X1,empty_set,X0),X1)),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f4090,plain,(
% 106.73/13.76 ![X0,X1]: (~relation(X0)|~relation(empty_set)|empty_set=relation_dom_restriction(X0,X1)|in(sk0_2(X1,empty_set,X0),X1))),
% 106.73/13.76 inference(resolution,[status(thm)],[f224,f817])).
% 106.73/13.76 fof(f4091,plain,(
% 106.73/13.76 spl0_42|~spl0_4),
% 106.73/13.76 inference(split_clause,[status(thm)],[f4090,f4087,f859])).
% 106.73/13.76 fof(f4100,plain,(
% 106.73/13.76 ![X0,X1,X2,X3]: (~relation(X0)|~relation(relation_rng_restriction(X1,X2))|relation_rng_restriction(X1,X2)=relation_dom_restriction(X0,X3)|in(ordered_pair(sk0_2(X3,relation_rng_restriction(X1,X2),X0),sk0_3(X3,relation_rng_restriction(X1,X2),X0)),X0)|~relation(X2)|in(sk0_3(X3,relation_rng_restriction(X1,X2),X0),X1))),
% 106.73/13.76 inference(resolution,[status(thm)],[f225,f855])).
% 106.73/13.76 fof(f4101,plain,(
% 106.73/13.76 ![X0,X1,X2,X3]: (~relation(X0)|relation_rng_restriction(X1,X2)=relation_dom_restriction(X0,X3)|in(ordered_pair(sk0_2(X3,relation_rng_restriction(X1,X2),X0),sk0_3(X3,relation_rng_restriction(X1,X2),X0)),X0)|~relation(X2)|in(sk0_3(X3,relation_rng_restriction(X1,X2),X0),X1))),
% 106.73/13.76 inference(forward_subsumption_resolution,[status(thm)],[f4100,f434])).
% 106.73/13.76 fof(f4102,plain,(
% 106.73/13.76 ![X0,X1,X2,X3]: (~relation(X0)|~relation(relation_rng_restriction(X1,X2))|relation_rng_restriction(X1,X2)=relation_dom_restriction(X0,X3)|in(ordered_pair(sk0_2(X3,relation_rng_restriction(X1,X2),X0),sk0_3(X3,relation_rng_restriction(X1,X2),X0)),X0)|~relation(X2)|in(ordered_pair(sk0_2(X3,relation_rng_restriction(X1,X2),X0),sk0_3(X3,relation_rng_restriction(X1,X2),X0)),X2))),
% 106.73/13.76 inference(resolution,[status(thm)],[f225,f892])).
% 106.73/13.76 fof(f4103,plain,(
% 106.73/13.76 ![X0,X1,X2,X3]: (~relation(X0)|relation_rng_restriction(X1,X2)=relation_dom_restriction(X0,X3)|in(ordered_pair(sk0_2(X3,relation_rng_restriction(X1,X2),X0),sk0_3(X3,relation_rng_restriction(X1,X2),X0)),X0)|~relation(X2)|in(ordered_pair(sk0_2(X3,relation_rng_restriction(X1,X2),X0),sk0_3(X3,relation_rng_restriction(X1,X2),X0)),X2))),
% 106.73/13.76 inference(forward_subsumption_resolution,[status(thm)],[f4102,f434])).
% 106.73/13.76 fof(f4106,plain,(
% 106.73/13.76 ![X0,X1,X2]: (~relation(X0)|~relation(X1)|X1=relation_dom_restriction(X0,X2)|in(ordered_pair(sk0_2(X2,X1,X0),sk0_3(X2,X1,X0)),X0)|~relation(X1)|in(sk0_3(X2,X1,X0),relation_rng(X1)))),
% 106.73/13.76 inference(resolution,[status(thm)],[f225,f840])).
% 106.73/13.76 fof(f4107,plain,(
% 106.73/13.76 ![X0,X1,X2]: (~relation(X0)|~relation(X1)|X1=relation_dom_restriction(X0,X2)|in(ordered_pair(sk0_2(X2,X1,X0),sk0_3(X2,X1,X0)),X0)|in(sk0_3(X2,X1,X0),relation_rng(X1)))),
% 106.73/13.76 inference(duplicate_literals_removal,[status(esa)],[f4106])).
% 106.73/13.76 fof(f4110,plain,(
% 106.73/13.76 spl0_43 <=> ~relation(X0)|empty_set=relation_dom_restriction(X0,X1)|in(ordered_pair(sk0_2(X1,empty_set,X0),sk0_3(X1,empty_set,X0)),X0)),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f4113,plain,(
% 106.73/13.76 ![X0,X1]: (~relation(X0)|~relation(empty_set)|empty_set=relation_dom_restriction(X0,X1)|in(ordered_pair(sk0_2(X1,empty_set,X0),sk0_3(X1,empty_set,X0)),X0))),
% 106.73/13.76 inference(resolution,[status(thm)],[f225,f817])).
% 106.73/13.76 fof(f4114,plain,(
% 106.73/13.76 spl0_43|~spl0_4),
% 106.73/13.76 inference(split_clause,[status(thm)],[f4113,f4110,f859])).
% 106.73/13.76 fof(f4141,plain,(
% 106.73/13.76 ![X0,X1,X2,X3]: (~relation(X0)|~relation(relation_rng_restriction(X1,X2))|relation_rng_restriction(X1,X2)=relation_rng_restriction(X3,X0)|in(sk0_5(X3,relation_rng_restriction(X1,X2),X0),X3)|~relation(X2)|in(ordered_pair(sk0_4(X3,relation_rng_restriction(X1,X2),X0),sk0_5(X3,relation_rng_restriction(X1,X2),X0)),X2))),
% 106.73/13.76 inference(resolution,[status(thm)],[f234,f892])).
% 106.73/13.76 fof(f4142,plain,(
% 106.73/13.76 ![X0,X1,X2,X3]: (~relation(X0)|relation_rng_restriction(X1,X2)=relation_rng_restriction(X3,X0)|in(sk0_5(X3,relation_rng_restriction(X1,X2),X0),X3)|~relation(X2)|in(ordered_pair(sk0_4(X3,relation_rng_restriction(X1,X2),X0),sk0_5(X3,relation_rng_restriction(X1,X2),X0)),X2))),
% 106.73/13.76 inference(forward_subsumption_resolution,[status(thm)],[f4141,f434])).
% 106.73/13.76 fof(f4145,plain,(
% 106.73/13.76 ![X0,X1,X2]: (~relation(X0)|~relation(X1)|X1=relation_rng_restriction(X2,X0)|in(sk0_5(X2,X1,X0),X2)|~relation(X1)|in(sk0_5(X2,X1,X0),relation_rng(X1)))),
% 106.73/13.76 inference(resolution,[status(thm)],[f234,f840])).
% 106.73/13.76 fof(f4146,plain,(
% 106.73/13.76 ![X0,X1,X2]: (~relation(X0)|~relation(X1)|X1=relation_rng_restriction(X2,X0)|in(sk0_5(X2,X1,X0),X2)|in(sk0_5(X2,X1,X0),relation_rng(X1)))),
% 106.73/13.76 inference(duplicate_literals_removal,[status(esa)],[f4145])).
% 106.73/13.76 fof(f4149,plain,(
% 106.73/13.76 spl0_44 <=> ~relation(X0)|empty_set=relation_rng_restriction(X1,X0)|in(sk0_5(X1,empty_set,X0),X1)),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f4152,plain,(
% 106.73/13.76 ![X0,X1]: (~relation(X0)|~relation(empty_set)|empty_set=relation_rng_restriction(X1,X0)|in(sk0_5(X1,empty_set,X0),X1))),
% 106.73/13.76 inference(resolution,[status(thm)],[f234,f817])).
% 106.73/13.76 fof(f4153,plain,(
% 106.73/13.76 spl0_44|~spl0_4),
% 106.73/13.76 inference(split_clause,[status(thm)],[f4152,f4149,f859])).
% 106.73/13.76 fof(f4162,plain,(
% 106.73/13.76 ![X0,X1,X2,X3]: (~relation(X0)|~relation(relation_rng_restriction(X1,X2))|relation_rng_restriction(X1,X2)=relation_rng_restriction(X3,X0)|in(ordered_pair(sk0_4(X3,relation_rng_restriction(X1,X2),X0),sk0_5(X3,relation_rng_restriction(X1,X2),X0)),X0)|~relation(X2)|in(sk0_5(X3,relation_rng_restriction(X1,X2),X0),X1))),
% 106.73/13.76 inference(resolution,[status(thm)],[f235,f855])).
% 106.73/13.76 fof(f4163,plain,(
% 106.73/13.76 ![X0,X1,X2,X3]: (~relation(X0)|relation_rng_restriction(X1,X2)=relation_rng_restriction(X3,X0)|in(ordered_pair(sk0_4(X3,relation_rng_restriction(X1,X2),X0),sk0_5(X3,relation_rng_restriction(X1,X2),X0)),X0)|~relation(X2)|in(sk0_5(X3,relation_rng_restriction(X1,X2),X0),X1))),
% 106.73/13.76 inference(forward_subsumption_resolution,[status(thm)],[f4162,f434])).
% 106.73/13.76 fof(f4164,plain,(
% 106.73/13.76 ![X0,X1,X2,X3]: (~relation(X0)|~relation(relation_rng_restriction(X1,X2))|relation_rng_restriction(X1,X2)=relation_rng_restriction(X3,X0)|in(ordered_pair(sk0_4(X3,relation_rng_restriction(X1,X2),X0),sk0_5(X3,relation_rng_restriction(X1,X2),X0)),X0)|~relation(X2)|in(ordered_pair(sk0_4(X3,relation_rng_restriction(X1,X2),X0),sk0_5(X3,relation_rng_restriction(X1,X2),X0)),X2))),
% 106.73/13.76 inference(resolution,[status(thm)],[f235,f892])).
% 106.73/13.76 fof(f4165,plain,(
% 106.73/13.76 ![X0,X1,X2,X3]: (~relation(X0)|relation_rng_restriction(X1,X2)=relation_rng_restriction(X3,X0)|in(ordered_pair(sk0_4(X3,relation_rng_restriction(X1,X2),X0),sk0_5(X3,relation_rng_restriction(X1,X2),X0)),X0)|~relation(X2)|in(ordered_pair(sk0_4(X3,relation_rng_restriction(X1,X2),X0),sk0_5(X3,relation_rng_restriction(X1,X2),X0)),X2))),
% 106.73/13.76 inference(forward_subsumption_resolution,[status(thm)],[f4164,f434])).
% 106.73/13.76 fof(f4168,plain,(
% 106.73/13.76 ![X0,X1,X2]: (~relation(X0)|~relation(X1)|X1=relation_rng_restriction(X2,X0)|in(ordered_pair(sk0_4(X2,X1,X0),sk0_5(X2,X1,X0)),X0)|~relation(X1)|in(sk0_5(X2,X1,X0),relation_rng(X1)))),
% 106.73/13.76 inference(resolution,[status(thm)],[f235,f840])).
% 106.73/13.76 fof(f4169,plain,(
% 106.73/13.76 ![X0,X1,X2]: (~relation(X0)|~relation(X1)|X1=relation_rng_restriction(X2,X0)|in(ordered_pair(sk0_4(X2,X1,X0),sk0_5(X2,X1,X0)),X0)|in(sk0_5(X2,X1,X0),relation_rng(X1)))),
% 106.73/13.76 inference(duplicate_literals_removal,[status(esa)],[f4168])).
% 106.73/13.76 fof(f4172,plain,(
% 106.73/13.76 spl0_45 <=> ~relation(X0)|empty_set=relation_rng_restriction(X1,X0)|in(ordered_pair(sk0_4(X1,empty_set,X0),sk0_5(X1,empty_set,X0)),X0)),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f4175,plain,(
% 106.73/13.76 ![X0,X1]: (~relation(X0)|~relation(empty_set)|empty_set=relation_rng_restriction(X1,X0)|in(ordered_pair(sk0_4(X1,empty_set,X0),sk0_5(X1,empty_set,X0)),X0))),
% 106.73/13.76 inference(resolution,[status(thm)],[f235,f817])).
% 106.73/13.76 fof(f4176,plain,(
% 106.73/13.76 spl0_45|~spl0_4),
% 106.73/13.76 inference(split_clause,[status(thm)],[f4175,f4172,f859])).
% 106.73/13.76 fof(f4227,plain,(
% 106.73/13.76 spl0_49 <=> ~empty(X0)|~relation(X0)|relation_dom(X0)=empty_set),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f4230,plain,(
% 106.73/13.76 ![X0]: (~empty(empty_set)|~empty(X0)|~relation(X0)|relation_dom(X0)=empty_set)),
% 106.73/13.76 inference(resolution,[status(thm)],[f3723,f714])).
% 106.73/13.76 fof(f4231,plain,(
% 106.73/13.76 ~spl0_8|spl0_49),
% 106.73/13.76 inference(split_clause,[status(thm)],[f4230,f877,f4227])).
% 106.73/13.76 fof(f4232,plain,(
% 106.73/13.76 spl0_50 <=> ~empty(X0)|~relation(X0)|X0=empty_set),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f4235,plain,(
% 106.73/13.76 ![X0]: (~empty(empty_set)|~empty(X0)|~relation(X0)|X0=empty_set)),
% 106.73/13.76 inference(resolution,[status(thm)],[f3723,f710])).
% 106.73/13.76 fof(f4236,plain,(
% 106.73/13.76 ~spl0_8|spl0_50),
% 106.73/13.76 inference(split_clause,[status(thm)],[f4235,f877,f4232])).
% 106.73/13.76 fof(f4238,plain,(
% 106.73/13.76 spl0_51 <=> ~empty(X0)|X0=empty_set),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f4241,plain,(
% 106.73/13.76 ![X0]: (~empty(X0)|X0=empty_set|~empty(empty_set))),
% 106.73/13.76 inference(paramodulation,[status(thm)],[f702,f3723])).
% 106.73/13.76 fof(f4242,plain,(
% 106.73/13.76 spl0_51|~spl0_8),
% 106.73/13.76 inference(split_clause,[status(thm)],[f4241,f4238,f877])).
% 106.73/13.76 fof(f4275,plain,(
% 106.73/13.76 ![X0,X1,X2,X3]: (~relation(X0)|~in(X1,X2)|~in(ordered_pair(X1,X3),X0)|~in(relation_dom_restriction(X0,X2),ordered_pair(X1,X3)))),
% 106.73/13.76 inference(forward_subsumption_resolution,[status(thm)],[f2511,f429])).
% 106.73/13.76 fof(f4354,plain,(
% 106.73/13.76 spl0_52 <=> ~proper_subset(empty_set,relation_rng(X0))|~relation(X0)|~subset(X0,empty_set)),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f4357,plain,(
% 106.73/13.76 ![X0]: (~proper_subset(empty_set,relation_rng(X0))|~relation(X0)|~relation(empty_set)|~subset(X0,empty_set))),
% 106.73/13.76 inference(paramodulation,[status(thm)],[f702,f3709])).
% 106.73/13.76 fof(f4358,plain,(
% 106.73/13.76 spl0_52|~spl0_4),
% 106.73/13.76 inference(split_clause,[status(thm)],[f4357,f4354,f859])).
% 106.73/13.76 fof(f4361,plain,(
% 106.73/13.76 spl0_53 <=> ~proper_subset(relation_rng(X0),empty_set)|~relation(X0)|~subset(empty_set,X0)),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f4364,plain,(
% 106.73/13.76 ![X0]: (~proper_subset(relation_rng(X0),empty_set)|~relation(empty_set)|~relation(X0)|~subset(empty_set,X0))),
% 106.73/13.76 inference(paramodulation,[status(thm)],[f702,f3709])).
% 106.73/13.76 fof(f4365,plain,(
% 106.73/13.76 spl0_53|~spl0_4),
% 106.73/13.76 inference(split_clause,[status(thm)],[f4364,f4361,f859])).
% 106.73/13.76 fof(f4368,plain,(
% 106.73/13.76 ![X0,X1,X2]: (~relation(X0)|~in(X1,X2)|~in(ordered_pair(X1,powerset(relation_rng(relation_dom_restriction(X0,X2)))),X0))),
% 106.73/13.76 inference(resolution,[status(thm)],[f3732,f4045])).
% 106.73/13.76 fof(f4369,plain,(
% 106.73/13.76 ![X0,X1,X2,X3]: (~relation(X0)|~in(X1,X2)|~in(ordered_pair(X1,set_union2(singleton(relation_rng(relation_dom_restriction(X0,X2))),X3)),X0))),
% 106.73/13.76 inference(resolution,[status(thm)],[f3732,f4004])).
% 106.73/13.76 fof(f4370,plain,(
% 106.73/13.76 ![X0,X1,X2,X3]: (~relation(X0)|~in(X1,X2)|~in(ordered_pair(X1,set_union2(X3,singleton(relation_rng(relation_dom_restriction(X0,X2))))),X0))),
% 106.73/13.76 inference(resolution,[status(thm)],[f3732,f3934])).
% 106.73/13.76 fof(f4371,plain,(
% 106.73/13.76 ![X0,X1,X2,X3]: (~relation(X0)|~in(X1,X2)|~in(ordered_pair(X1,unordered_pair(X3,relation_rng(relation_dom_restriction(X0,X2)))),X0))),
% 106.73/13.76 inference(resolution,[status(thm)],[f3732,f2190])).
% 106.73/13.76 fof(f4372,plain,(
% 106.73/13.76 ![X0,X1,X2,X3]: (~relation(X0)|~in(X1,X2)|~in(ordered_pair(X1,unordered_pair(relation_rng(relation_dom_restriction(X0,X2)),X3)),X0))),
% 106.73/13.76 inference(resolution,[status(thm)],[f3732,f2127])).
% 106.73/13.76 fof(f4373,plain,(
% 106.73/13.76 ![X0,X1,X2]: (~relation(X0)|~in(X1,X2)|~in(ordered_pair(X1,sk0_62(relation_rng(relation_dom_restriction(X0,X2)))),X0))),
% 106.73/13.76 inference(resolution,[status(thm)],[f3732,f2051])).
% 106.73/13.76 fof(f4374,plain,(
% 106.73/13.76 ![X0,X1,X2]: (~relation(X0)|~in(X1,X2)|~in(ordered_pair(X1,sk0_56(relation_rng(relation_dom_restriction(X0,X2)))),X0))),
% 106.73/13.76 inference(resolution,[status(thm)],[f3732,f1945])).
% 106.73/13.76 fof(f4375,plain,(
% 106.73/13.76 ![X0,X1,X2]: (~relation(X0)|~in(X1,X2)|~in(ordered_pair(X1,singleton(relation_rng(relation_dom_restriction(X0,X2)))),X0))),
% 106.73/13.76 inference(resolution,[status(thm)],[f3732,f1882])).
% 106.73/13.76 fof(f4454,plain,(
% 106.73/13.76 spl0_54 <=> proper_subset(empty_set,relation_rng(X0))|relation_rng(empty_set)=relation_rng(X0)|~relation(X0)|~subset(empty_set,X0)),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f4457,plain,(
% 106.73/13.76 ![X0]: (proper_subset(empty_set,relation_rng(X0))|relation_rng(empty_set)=relation_rng(X0)|~relation(empty_set)|~relation(X0)|~subset(empty_set,X0))),
% 106.73/13.76 inference(paramodulation,[status(thm)],[f702,f3860])).
% 106.73/13.76 fof(f4458,plain,(
% 106.73/13.76 spl0_54|~spl0_4),
% 106.73/13.76 inference(split_clause,[status(thm)],[f4457,f4454,f859])).
% 106.73/13.76 fof(f4459,plain,(
% 106.73/13.76 ![X0,X1]: (proper_subset(relation_rng(X0),X1)|relation_rng(X0)=relation_rng(identity_relation(X1))|~relation(X0)|~relation(identity_relation(X1))|~subset(X0,identity_relation(X1)))),
% 106.73/13.76 inference(paramodulation,[status(thm)],[f726,f3860])).
% 106.73/13.76 fof(f4460,plain,(
% 106.73/13.76 ![X0,X1]: (proper_subset(relation_rng(X0),X1)|relation_rng(X0)=X1|~relation(X0)|~relation(identity_relation(X1))|~subset(X0,identity_relation(X1)))),
% 106.73/13.76 inference(forward_demodulation,[status(thm)],[f726,f4459])).
% 106.73/13.76 fof(f4461,plain,(
% 106.73/13.76 ![X0,X1]: (proper_subset(relation_rng(X0),X1)|relation_rng(X0)=X1|~relation(X0)|~subset(X0,identity_relation(X1)))),
% 106.73/13.76 inference(forward_subsumption_resolution,[status(thm)],[f4460,f422])).
% 106.73/13.76 fof(f4462,plain,(
% 106.73/13.76 spl0_55 <=> proper_subset(relation_rng(X0),empty_set)|relation_rng(X0)=relation_rng(empty_set)|~relation(X0)|~subset(X0,empty_set)),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f4465,plain,(
% 106.73/13.76 ![X0]: (proper_subset(relation_rng(X0),empty_set)|relation_rng(X0)=relation_rng(empty_set)|~relation(X0)|~relation(empty_set)|~subset(X0,empty_set))),
% 106.73/13.76 inference(paramodulation,[status(thm)],[f702,f3860])).
% 106.73/13.76 fof(f4466,plain,(
% 106.73/13.76 spl0_55|~spl0_4),
% 106.73/13.76 inference(split_clause,[status(thm)],[f4465,f4462,f859])).
% 106.73/13.76 fof(f4472,plain,(
% 106.73/13.76 spl0_56 <=> proper_subset(relation_rng(empty_set),X0)|relation_rng(empty_set)=X0),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f4475,plain,(
% 106.73/13.76 ![X0]: (proper_subset(relation_rng(empty_set),X0)|relation_rng(empty_set)=X0|~relation(empty_set)|~spl0_4)),
% 106.73/13.76 inference(resolution,[status(thm)],[f4461,f3424])).
% 106.73/13.76 fof(f4476,plain,(
% 106.73/13.76 spl0_56|~spl0_4),
% 106.73/13.76 inference(split_clause,[status(thm)],[f4475,f4472,f859])).
% 106.73/13.76 fof(f4692,plain,(
% 106.73/13.76 spl0_57 <=> ~relation(X0)|relation_rng_restriction(X1,empty_set)=relation_dom_restriction(X0,X2)|in(sk0_2(X2,relation_rng_restriction(X1,empty_set),X0),X2)),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f4695,plain,(
% 106.73/13.76 ![X0,X1,X2]: (~relation(X0)|relation_rng_restriction(X1,empty_set)=relation_dom_restriction(X0,X2)|in(sk0_2(X2,relation_rng_restriction(X1,empty_set),X0),X2)|~relation(empty_set))),
% 106.73/13.76 inference(resolution,[status(thm)],[f4080,f817])).
% 106.73/13.76 fof(f4696,plain,(
% 106.73/13.76 spl0_57|~spl0_4),
% 106.73/13.76 inference(split_clause,[status(thm)],[f4695,f4692,f859])).
% 106.73/13.76 fof(f4706,plain,(
% 106.73/13.76 spl0_58 <=> ~relation(X0)|empty_set=relation_dom_restriction(X0,X1)|in(sk0_2(X1,empty_set,X0),X1)|in(sk0_3(X1,empty_set,X0),empty_set)),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f4709,plain,(
% 106.73/13.76 ![X0,X1]: (~relation(X0)|~relation(empty_set)|empty_set=relation_dom_restriction(X0,X1)|in(sk0_2(X1,empty_set,X0),X1)|in(sk0_3(X1,empty_set,X0),empty_set))),
% 106.73/13.76 inference(paramodulation,[status(thm)],[f702,f4084])).
% 106.73/13.76 fof(f4710,plain,(
% 106.73/13.76 spl0_58|~spl0_4),
% 106.73/13.76 inference(split_clause,[status(thm)],[f4709,f4706,f859])).
% 106.73/13.76 fof(f5168,plain,(
% 106.73/13.76 spl0_59 <=> relation_rng_restriction(X0,X1)=relation_dom_restriction(empty_set,X2)|~relation(X1)|in(sk0_3(X2,relation_rng_restriction(X0,X1),empty_set),X0)),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f5171,plain,(
% 106.73/13.76 ![X0,X1,X2]: (~relation(empty_set)|relation_rng_restriction(X0,X1)=relation_dom_restriction(empty_set,X2)|~relation(X1)|in(sk0_3(X2,relation_rng_restriction(X0,X1),empty_set),X0))),
% 106.73/13.76 inference(resolution,[status(thm)],[f4101,f817])).
% 106.73/13.76 fof(f5172,plain,(
% 106.73/13.76 ~spl0_4|spl0_59),
% 106.73/13.76 inference(split_clause,[status(thm)],[f5171,f859,f5168])).
% 106.73/13.76 fof(f5192,plain,(
% 106.73/13.76 spl0_60 <=> ~relation(X0)|relation_rng_restriction(X1,empty_set)=relation_dom_restriction(X0,X2)|in(ordered_pair(sk0_2(X2,relation_rng_restriction(X1,empty_set),X0),sk0_3(X2,relation_rng_restriction(X1,empty_set),X0)),X0)),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f5195,plain,(
% 106.73/13.76 ![X0,X1,X2]: (~relation(X0)|relation_rng_restriction(X1,empty_set)=relation_dom_restriction(X0,X2)|in(ordered_pair(sk0_2(X2,relation_rng_restriction(X1,empty_set),X0),sk0_3(X2,relation_rng_restriction(X1,empty_set),X0)),X0)|~relation(empty_set))),
% 106.73/13.76 inference(resolution,[status(thm)],[f4103,f817])).
% 106.73/13.76 fof(f5196,plain,(
% 106.73/13.76 spl0_60|~spl0_4),
% 106.73/13.76 inference(split_clause,[status(thm)],[f5195,f5192,f859])).
% 106.73/13.76 fof(f5220,plain,(
% 106.73/13.76 spl0_61 <=> ~relation(X0)|X0=relation_dom_restriction(empty_set,X1)|in(sk0_3(X1,X0,empty_set),relation_rng(X0))),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f5223,plain,(
% 106.73/13.76 ![X0,X1]: (~relation(empty_set)|~relation(X0)|X0=relation_dom_restriction(empty_set,X1)|in(sk0_3(X1,X0,empty_set),relation_rng(X0)))),
% 106.73/13.76 inference(resolution,[status(thm)],[f4107,f817])).
% 106.73/13.76 fof(f5224,plain,(
% 106.73/13.76 ~spl0_4|spl0_61),
% 106.73/13.76 inference(split_clause,[status(thm)],[f5223,f859,f5220])).
% 106.73/13.76 fof(f5268,plain,(
% 106.73/13.76 spl0_62 <=> ~relation(X0)|relation_rng_restriction(X1,empty_set)=relation_rng_restriction(X2,X0)|in(sk0_5(X2,relation_rng_restriction(X1,empty_set),X0),X2)),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f5271,plain,(
% 106.73/13.76 ![X0,X1,X2]: (~relation(X0)|relation_rng_restriction(X1,empty_set)=relation_rng_restriction(X2,X0)|in(sk0_5(X2,relation_rng_restriction(X1,empty_set),X0),X2)|~relation(empty_set))),
% 106.73/13.76 inference(resolution,[status(thm)],[f4142,f817])).
% 106.73/13.76 fof(f5272,plain,(
% 106.73/13.76 spl0_62|~spl0_4),
% 106.73/13.76 inference(split_clause,[status(thm)],[f5271,f5268,f859])).
% 106.73/13.76 fof(f5282,plain,(
% 106.73/13.76 spl0_63 <=> ~relation(X0)|empty_set=relation_rng_restriction(X1,X0)|in(sk0_5(X1,empty_set,X0),X1)|in(sk0_5(X1,empty_set,X0),empty_set)),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f5285,plain,(
% 106.73/13.76 ![X0,X1]: (~relation(X0)|~relation(empty_set)|empty_set=relation_rng_restriction(X1,X0)|in(sk0_5(X1,empty_set,X0),X1)|in(sk0_5(X1,empty_set,X0),empty_set))),
% 106.73/13.76 inference(paramodulation,[status(thm)],[f702,f4146])).
% 106.73/13.76 fof(f5286,plain,(
% 106.73/13.76 spl0_63|~spl0_4),
% 106.73/13.76 inference(split_clause,[status(thm)],[f5285,f5282,f859])).
% 106.73/13.76 fof(f5326,plain,(
% 106.73/13.76 spl0_64 <=> relation_dom_restriction(empty_set,X0)=empty_set),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f5327,plain,(
% 106.73/13.76 ![X0]: (relation_dom_restriction(empty_set,X0)=empty_set|~spl0_64)),
% 106.73/13.76 inference(component_clause,[status(thm)],[f5326])).
% 106.73/13.76 fof(f5329,plain,(
% 106.73/13.76 ![X0]: (~relation(empty_set)|relation_dom_restriction(empty_set,X0)=empty_set|~spl0_4|~spl0_16)),
% 106.73/13.76 inference(resolution,[status(thm)],[f749,f3435])).
% 106.73/13.76 fof(f5330,plain,(
% 106.73/13.76 ~spl0_4|spl0_64|~spl0_16),
% 106.73/13.76 inference(split_clause,[status(thm)],[f5329,f859,f5326,f2990])).
% 106.73/13.76 fof(f5331,plain,(
% 106.73/13.76 spl0_65 <=> empty_set=relation_rng(relation_dom_restriction(empty_set,X0))|~relation(relation_dom_restriction(empty_set,X0))),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f5334,plain,(
% 106.73/13.76 ![X0]: (~relation(empty_set)|empty_set=relation_rng(relation_dom_restriction(empty_set,X0))|~relation(relation_dom_restriction(empty_set,X0)))),
% 106.73/13.76 inference(resolution,[status(thm)],[f749,f3185])).
% 106.73/13.76 fof(f5335,plain,(
% 106.73/13.76 ~spl0_4|spl0_65),
% 106.73/13.76 inference(split_clause,[status(thm)],[f5334,f859,f5331])).
% 106.73/13.76 fof(f5347,plain,(
% 106.73/13.76 ~relation(empty_set)|subset(empty_set,empty_set)|~spl0_64),
% 106.73/13.76 inference(paramodulation,[status(thm)],[f5327,f749])).
% 106.73/13.76 fof(f5348,plain,(
% 106.73/13.76 ~spl0_4|spl0_24|~spl0_64),
% 106.73/13.76 inference(split_clause,[status(thm)],[f5347,f859,f3077,f5326])).
% 106.73/13.76 fof(f5349,plain,(
% 106.73/13.76 spl0_66 <=> ~in(X0,X1)|~in(ordered_pair(X0,set_union2(X2,singleton(relation_rng(empty_set)))),empty_set)),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f5352,plain,(
% 106.73/13.76 ![X0,X1,X2]: (~relation(empty_set)|~in(X0,X1)|~in(ordered_pair(X0,set_union2(X2,singleton(relation_rng(empty_set)))),empty_set)|~spl0_64)),
% 106.73/13.76 inference(paramodulation,[status(thm)],[f5327,f4370])).
% 106.73/13.76 fof(f5353,plain,(
% 106.73/13.76 ~spl0_4|spl0_66|~spl0_64),
% 106.73/13.76 inference(split_clause,[status(thm)],[f5352,f859,f5349,f5326])).
% 106.73/13.76 fof(f5354,plain,(
% 106.73/13.76 spl0_67 <=> ~in(X0,X1)|~in(ordered_pair(X0,set_union2(singleton(relation_rng(empty_set)),X2)),empty_set)),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f5357,plain,(
% 106.73/13.76 ![X0,X1,X2]: (~relation(empty_set)|~in(X0,X1)|~in(ordered_pair(X0,set_union2(singleton(relation_rng(empty_set)),X2)),empty_set)|~spl0_64)),
% 106.73/13.76 inference(paramodulation,[status(thm)],[f5327,f4369])).
% 106.73/13.76 fof(f5358,plain,(
% 106.73/13.76 ~spl0_4|spl0_67|~spl0_64),
% 106.73/13.76 inference(split_clause,[status(thm)],[f5357,f859,f5354,f5326])).
% 106.73/13.76 fof(f5359,plain,(
% 106.73/13.76 spl0_68 <=> ~in(X0,X1)|~in(ordered_pair(X0,unordered_pair(relation_rng(empty_set),X2)),empty_set)),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f5362,plain,(
% 106.73/13.76 ![X0,X1,X2]: (~relation(empty_set)|~in(X0,X1)|~in(ordered_pair(X0,unordered_pair(relation_rng(empty_set),X2)),empty_set)|~spl0_64)),
% 106.73/13.76 inference(paramodulation,[status(thm)],[f5327,f4372])).
% 106.73/13.76 fof(f5363,plain,(
% 106.73/13.76 ~spl0_4|spl0_68|~spl0_64),
% 106.73/13.76 inference(split_clause,[status(thm)],[f5362,f859,f5359,f5326])).
% 106.73/13.76 fof(f5364,plain,(
% 106.73/13.76 spl0_69 <=> ~in(X0,X1)|~in(ordered_pair(X0,unordered_pair(X2,relation_rng(empty_set))),empty_set)),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f5367,plain,(
% 106.73/13.76 ![X0,X1,X2]: (~relation(empty_set)|~in(X0,X1)|~in(ordered_pair(X0,unordered_pair(X2,relation_rng(empty_set))),empty_set)|~spl0_64)),
% 106.73/13.76 inference(paramodulation,[status(thm)],[f5327,f4371])).
% 106.73/13.76 fof(f5368,plain,(
% 106.73/13.76 ~spl0_4|spl0_69|~spl0_64),
% 106.73/13.76 inference(split_clause,[status(thm)],[f5367,f859,f5364,f5326])).
% 106.73/13.76 fof(f5369,plain,(
% 106.73/13.76 spl0_70 <=> ~in(X0,X1)|~in(ordered_pair(X0,singleton(relation_rng(empty_set))),empty_set)),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f5372,plain,(
% 106.73/13.76 ![X0,X1]: (~relation(empty_set)|~in(X0,X1)|~in(ordered_pair(X0,singleton(relation_rng(empty_set))),empty_set)|~spl0_64)),
% 106.73/13.76 inference(paramodulation,[status(thm)],[f5327,f4375])).
% 106.73/13.76 fof(f5373,plain,(
% 106.73/13.76 ~spl0_4|spl0_70|~spl0_64),
% 106.73/13.76 inference(split_clause,[status(thm)],[f5372,f859,f5369,f5326])).
% 106.73/13.76 fof(f5374,plain,(
% 106.73/13.76 spl0_71 <=> ~in(X0,X1)|~in(ordered_pair(X0,sk0_56(relation_rng(empty_set))),empty_set)),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f5377,plain,(
% 106.73/13.76 ![X0,X1]: (~relation(empty_set)|~in(X0,X1)|~in(ordered_pair(X0,sk0_56(relation_rng(empty_set))),empty_set)|~spl0_64)),
% 106.73/13.76 inference(paramodulation,[status(thm)],[f5327,f4374])).
% 106.73/13.76 fof(f5378,plain,(
% 106.73/13.76 ~spl0_4|spl0_71|~spl0_64),
% 106.73/13.76 inference(split_clause,[status(thm)],[f5377,f859,f5374,f5326])).
% 106.73/13.76 fof(f5379,plain,(
% 106.73/13.76 spl0_72 <=> ~in(X0,X1)|~in(ordered_pair(X0,sk0_62(relation_rng(empty_set))),empty_set)),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f5382,plain,(
% 106.73/13.76 ![X0,X1]: (~relation(empty_set)|~in(X0,X1)|~in(ordered_pair(X0,sk0_62(relation_rng(empty_set))),empty_set)|~spl0_64)),
% 106.73/13.76 inference(paramodulation,[status(thm)],[f5327,f4373])).
% 106.73/13.76 fof(f5383,plain,(
% 106.73/13.76 ~spl0_4|spl0_72|~spl0_64),
% 106.73/13.76 inference(split_clause,[status(thm)],[f5382,f859,f5379,f5326])).
% 106.73/13.76 fof(f5384,plain,(
% 106.73/13.76 spl0_73 <=> ~in(X0,X1)|~in(ordered_pair(X0,powerset(relation_rng(empty_set))),empty_set)),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f5387,plain,(
% 106.73/13.76 ![X0,X1]: (~relation(empty_set)|~in(X0,X1)|~in(ordered_pair(X0,powerset(relation_rng(empty_set))),empty_set)|~spl0_64)),
% 106.73/13.76 inference(paramodulation,[status(thm)],[f5327,f4368])).
% 106.73/13.76 fof(f5388,plain,(
% 106.73/13.76 ~spl0_4|spl0_73|~spl0_64),
% 106.73/13.76 inference(split_clause,[status(thm)],[f5387,f859,f5384,f5326])).
% 106.73/13.76 fof(f5389,plain,(
% 106.73/13.76 spl0_74 <=> ~in(X0,X1)|~in(ordered_pair(X0,X2),empty_set)|in(X2,relation_rng(empty_set))),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f5392,plain,(
% 106.73/13.76 ![X0,X1,X2]: (~relation(empty_set)|~in(X0,X1)|~in(ordered_pair(X0,X2),empty_set)|in(X2,relation_rng(empty_set))|~spl0_64)),
% 106.73/13.76 inference(paramodulation,[status(thm)],[f5327,f3732])).
% 106.73/13.76 fof(f5393,plain,(
% 106.73/13.76 ~spl0_4|spl0_74|~spl0_64),
% 106.73/13.76 inference(split_clause,[status(thm)],[f5392,f859,f5389,f5326])).
% 106.73/13.76 fof(f5394,plain,(
% 106.73/13.76 spl0_75 <=> ~in(X0,X1)|~in(ordered_pair(X0,X2),empty_set)|~in(empty_set,ordered_pair(X0,X2))),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f5397,plain,(
% 106.73/13.76 ![X0,X1,X2]: (~relation(empty_set)|~in(X0,X1)|~in(ordered_pair(X0,X2),empty_set)|~in(empty_set,ordered_pair(X0,X2))|~spl0_64)),
% 106.73/13.76 inference(paramodulation,[status(thm)],[f5327,f4275])).
% 106.73/13.76 fof(f5398,plain,(
% 106.73/13.76 ~spl0_4|spl0_75|~spl0_64),
% 106.73/13.76 inference(split_clause,[status(thm)],[f5397,f859,f5394,f5326])).
% 106.73/13.76 fof(f6311,plain,(
% 106.73/13.76 ![X0,X1,X2]: (~relation(X0)|~relation(relation_rng_restriction(X1,X2))|X0=relation_rng_restriction(X1,X2)|in(ordered_pair(sk0_15(relation_rng_restriction(X1,X2),X0),sk0_16(relation_rng_restriction(X1,X2),X0)),X0)|~relation(X2)|in(sk0_16(relation_rng_restriction(X1,X2),X0),X1))),
% 106.73/13.76 inference(resolution,[status(thm)],[f281,f855])).
% 106.73/13.76 fof(f6312,plain,(
% 106.73/13.76 ![X0,X1,X2]: (~relation(X0)|X0=relation_rng_restriction(X1,X2)|in(ordered_pair(sk0_15(relation_rng_restriction(X1,X2),X0),sk0_16(relation_rng_restriction(X1,X2),X0)),X0)|~relation(X2)|in(sk0_16(relation_rng_restriction(X1,X2),X0),X1))),
% 106.73/13.76 inference(forward_subsumption_resolution,[status(thm)],[f6311,f434])).
% 106.73/13.76 fof(f6313,plain,(
% 106.73/13.76 ![X0,X1,X2]: (~relation(X0)|~relation(relation_rng_restriction(X1,X2))|X0=relation_rng_restriction(X1,X2)|in(ordered_pair(sk0_15(relation_rng_restriction(X1,X2),X0),sk0_16(relation_rng_restriction(X1,X2),X0)),X0)|~relation(X2)|in(ordered_pair(sk0_15(relation_rng_restriction(X1,X2),X0),sk0_16(relation_rng_restriction(X1,X2),X0)),X2))),
% 106.73/13.76 inference(resolution,[status(thm)],[f281,f892])).
% 106.73/13.76 fof(f6314,plain,(
% 106.73/13.76 ![X0,X1,X2]: (~relation(X0)|X0=relation_rng_restriction(X1,X2)|in(ordered_pair(sk0_15(relation_rng_restriction(X1,X2),X0),sk0_16(relation_rng_restriction(X1,X2),X0)),X0)|~relation(X2)|in(ordered_pair(sk0_15(relation_rng_restriction(X1,X2),X0),sk0_16(relation_rng_restriction(X1,X2),X0)),X2))),
% 106.73/13.76 inference(forward_subsumption_resolution,[status(thm)],[f6313,f434])).
% 106.73/13.76 fof(f6317,plain,(
% 106.73/13.76 ![X0,X1]: (~relation(X0)|~relation(X1)|X0=X1|in(ordered_pair(sk0_15(X1,X0),sk0_16(X1,X0)),X0)|~relation(X1)|in(sk0_16(X1,X0),relation_rng(X1)))),
% 106.73/13.76 inference(resolution,[status(thm)],[f281,f840])).
% 106.73/13.76 fof(f6318,plain,(
% 106.73/13.76 ![X0,X1]: (~relation(X0)|~relation(X1)|X0=X1|in(ordered_pair(sk0_15(X1,X0),sk0_16(X1,X0)),X0)|in(sk0_16(X1,X0),relation_rng(X1)))),
% 106.73/13.76 inference(duplicate_literals_removal,[status(esa)],[f6317])).
% 106.73/13.76 fof(f6326,plain,(
% 106.73/13.76 spl0_79 <=> ~relation(X0)|X0=empty_set|in(ordered_pair(sk0_15(empty_set,X0),sk0_16(empty_set,X0)),X0)),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f6329,plain,(
% 106.73/13.76 ![X0]: (~relation(X0)|~relation(empty_set)|X0=empty_set|in(ordered_pair(sk0_15(empty_set,X0),sk0_16(empty_set,X0)),X0))),
% 106.73/13.76 inference(resolution,[status(thm)],[f281,f817])).
% 106.73/13.76 fof(f6330,plain,(
% 106.73/13.76 spl0_79|~spl0_4),
% 106.73/13.76 inference(split_clause,[status(thm)],[f6329,f6326,f859])).
% 106.73/13.76 fof(f6557,plain,(
% 106.73/13.76 spl0_82 <=> relation_rng_restriction(X0,X1)=relation_rng_restriction(X2,empty_set)|~relation(X1)|in(sk0_5(X2,relation_rng_restriction(X0,X1),empty_set),X0)),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f6560,plain,(
% 106.73/13.76 ![X0,X1,X2]: (~relation(empty_set)|relation_rng_restriction(X0,X1)=relation_rng_restriction(X2,empty_set)|~relation(X1)|in(sk0_5(X2,relation_rng_restriction(X0,X1),empty_set),X0))),
% 106.73/13.76 inference(resolution,[status(thm)],[f4163,f817])).
% 106.73/13.76 fof(f6561,plain,(
% 106.73/13.76 ~spl0_4|spl0_82),
% 106.73/13.76 inference(split_clause,[status(thm)],[f6560,f859,f6557])).
% 106.73/13.76 fof(f6586,plain,(
% 106.73/13.76 spl0_83 <=> ~relation(X0)|relation_rng_restriction(X1,empty_set)=relation_rng_restriction(X2,X0)|in(ordered_pair(sk0_4(X2,relation_rng_restriction(X1,empty_set),X0),sk0_5(X2,relation_rng_restriction(X1,empty_set),X0)),X0)),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f6589,plain,(
% 106.73/13.76 ![X0,X1,X2]: (~relation(X0)|relation_rng_restriction(X1,empty_set)=relation_rng_restriction(X2,X0)|in(ordered_pair(sk0_4(X2,relation_rng_restriction(X1,empty_set),X0),sk0_5(X2,relation_rng_restriction(X1,empty_set),X0)),X0)|~relation(empty_set))),
% 106.73/13.76 inference(resolution,[status(thm)],[f4165,f817])).
% 106.73/13.76 fof(f6590,plain,(
% 106.73/13.76 spl0_83|~spl0_4),
% 106.73/13.76 inference(split_clause,[status(thm)],[f6589,f6586,f859])).
% 106.73/13.76 fof(f6719,plain,(
% 106.73/13.76 spl0_84 <=> ~relation(X0)|X0=relation_rng_restriction(X1,empty_set)|in(sk0_5(X1,X0,empty_set),relation_rng(X0))),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f6722,plain,(
% 106.73/13.76 ![X0,X1]: (~relation(empty_set)|~relation(X0)|X0=relation_rng_restriction(X1,empty_set)|in(sk0_5(X1,X0,empty_set),relation_rng(X0)))),
% 106.73/13.76 inference(resolution,[status(thm)],[f4169,f817])).
% 106.73/13.76 fof(f6723,plain,(
% 106.73/13.76 ~spl0_4|spl0_84),
% 106.73/13.76 inference(split_clause,[status(thm)],[f6722,f859,f6719])).
% 106.73/13.76 fof(f7818,plain,(
% 106.73/13.76 spl0_86 <=> empty_set=relation_rng_restriction(X0,X1)|~relation(X1)|in(sk0_16(relation_rng_restriction(X0,X1),empty_set),X0)),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f7821,plain,(
% 106.73/13.76 ![X0,X1]: (~relation(empty_set)|empty_set=relation_rng_restriction(X0,X1)|~relation(X1)|in(sk0_16(relation_rng_restriction(X0,X1),empty_set),X0))),
% 106.73/13.76 inference(resolution,[status(thm)],[f6312,f817])).
% 106.73/13.76 fof(f7822,plain,(
% 106.73/13.76 ~spl0_4|spl0_86),
% 106.73/13.76 inference(split_clause,[status(thm)],[f7821,f859,f7818])).
% 106.73/13.76 fof(f7848,plain,(
% 106.73/13.76 spl0_87 <=> ~relation(X0)|X0=relation_rng_restriction(X1,empty_set)|in(ordered_pair(sk0_15(relation_rng_restriction(X1,empty_set),X0),sk0_16(relation_rng_restriction(X1,empty_set),X0)),X0)),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f7851,plain,(
% 106.73/13.76 ![X0,X1]: (~relation(X0)|X0=relation_rng_restriction(X1,empty_set)|in(ordered_pair(sk0_15(relation_rng_restriction(X1,empty_set),X0),sk0_16(relation_rng_restriction(X1,empty_set),X0)),X0)|~relation(empty_set))),
% 106.73/13.76 inference(resolution,[status(thm)],[f6314,f817])).
% 106.73/13.76 fof(f7852,plain,(
% 106.73/13.76 spl0_87|~spl0_4),
% 106.73/13.76 inference(split_clause,[status(thm)],[f7851,f7848,f859])).
% 106.73/13.76 fof(f7880,plain,(
% 106.73/13.76 spl0_88 <=> ~relation(X0)|empty_set=X0|in(sk0_16(X0,empty_set),relation_rng(X0))),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f7883,plain,(
% 106.73/13.76 ![X0]: (~relation(empty_set)|~relation(X0)|empty_set=X0|in(sk0_16(X0,empty_set),relation_rng(X0)))),
% 106.73/13.76 inference(resolution,[status(thm)],[f6318,f817])).
% 106.73/13.76 fof(f7884,plain,(
% 106.73/13.76 ~spl0_4|spl0_88),
% 106.73/13.76 inference(split_clause,[status(thm)],[f7883,f859,f7880])).
% 106.73/13.76 fof(f8159,plain,(
% 106.73/13.76 spl0_89 <=> ~in(X0,empty_set)),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f8164,plain,(
% 106.73/13.76 spl0_90 <=> ~disjoint(X1,empty_set)),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f8165,plain,(
% 106.73/13.76 ![X0]: (~disjoint(X0,empty_set)|~spl0_90)),
% 106.73/13.76 inference(component_clause,[status(thm)],[f8164])).
% 106.73/13.76 fof(f8169,plain,(
% 106.73/13.76 ![X0,X1,X2]: (~in(X0,set_intersection2(X1,X2))|~disjoint(X2,X1))),
% 106.73/13.76 inference(paramodulation,[status(thm)],[f200,f689])).
% 106.73/13.76 fof(f8181,plain,(
% 106.73/13.76 $false|~spl0_40),
% 106.73/13.76 inference(forward_subsumption_resolution,[status(thm)],[f3746,f3750])).
% 106.73/13.76 fof(f8182,plain,(
% 106.73/13.76 ~spl0_40),
% 106.73/13.76 inference(contradiction_clause,[status(thm)],[f8181])).
% 106.73/13.76 fof(f8193,plain,(
% 106.73/13.76 ![X0]: (~empty_set=empty_set|~in(X0,empty_set))),
% 106.73/13.76 inference(paramodulation,[status(thm)],[f681,f717])).
% 106.73/13.76 fof(f8194,plain,(
% 106.73/13.76 ~spl0_7|spl0_89),
% 106.73/13.76 inference(split_clause,[status(thm)],[f8193,f872,f8159])).
% 106.73/13.76 fof(f8368,plain,(
% 106.73/13.76 ![X0,X1,X2]: (~in(X0,relation_rng(X1))|in(X0,relation_rng(X2))|~relation(X1)|~relation(X2)|~subset(X1,X2))),
% 106.73/13.76 inference(resolution,[status(thm)],[f326,f596])).
% 106.73/13.76 fof(f8381,plain,(
% 106.73/13.76 spl0_92 <=> ~relation(X0)|relation(X0)),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f8384,plain,(
% 106.73/13.76 ![X0]: (~relation(empty_set)|~relation(X0)|relation(X0))),
% 106.73/13.76 inference(paramodulation,[status(thm)],[f2221,f446])).
% 106.73/13.76 fof(f8385,plain,(
% 106.73/13.76 ~spl0_4|spl0_92),
% 106.73/13.76 inference(split_clause,[status(thm)],[f8384,f859,f8381])).
% 106.73/13.76 fof(f8592,plain,(
% 106.73/13.76 spl0_93 <=> in(sk0_54,relation_rng(X0))|~relation(X0)|~subset(relation_rng_restriction(sk0_55,sk0_53),X0)),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f8593,plain,(
% 106.73/13.76 ![X0]: (in(sk0_54,relation_rng(X0))|~relation(X0)|~subset(relation_rng_restriction(sk0_55,sk0_53),X0)|~spl0_93)),
% 106.73/13.76 inference(component_clause,[status(thm)],[f8592])).
% 106.73/13.76 fof(f8595,plain,(
% 106.73/13.76 spl0_94 <=> relation(relation_rng_restriction(sk0_55,sk0_53))),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f8596,plain,(
% 106.73/13.76 relation(relation_rng_restriction(sk0_55,sk0_53))|~spl0_94),
% 106.73/13.76 inference(component_clause,[status(thm)],[f8595])).
% 106.73/13.76 fof(f8597,plain,(
% 106.73/13.76 ~relation(relation_rng_restriction(sk0_55,sk0_53))|spl0_94),
% 106.73/13.76 inference(component_clause,[status(thm)],[f8595])).
% 106.73/13.76 fof(f8598,plain,(
% 106.73/13.76 ![X0]: (in(sk0_54,relation_rng(X0))|~relation(relation_rng_restriction(sk0_55,sk0_53))|~relation(X0)|~subset(relation_rng_restriction(sk0_55,sk0_53),X0)|~spl0_0)),
% 106.73/13.76 inference(resolution,[status(thm)],[f8368,f788])).
% 106.73/13.76 fof(f8599,plain,(
% 106.73/13.76 spl0_93|~spl0_94|~spl0_0),
% 106.73/13.76 inference(split_clause,[status(thm)],[f8598,f8592,f8595,f787])).
% 106.73/13.76 fof(f8652,plain,(
% 106.73/13.76 spl0_95 <=> ~in(X0,empty_set)|in(X0,relation_rng(X1))|~relation(X1)|~subset(empty_set,X1)),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f8655,plain,(
% 106.73/13.76 ![X0,X1]: (~in(X0,empty_set)|in(X0,relation_rng(X1))|~relation(empty_set)|~relation(X1)|~subset(empty_set,X1))),
% 106.73/13.76 inference(paramodulation,[status(thm)],[f702,f8368])).
% 106.73/13.76 fof(f8656,plain,(
% 106.73/13.76 spl0_95|~spl0_4),
% 106.73/13.76 inference(split_clause,[status(thm)],[f8655,f8652,f859])).
% 106.73/13.76 fof(f8657,plain,(
% 106.73/13.76 ~relation(sk0_53)|spl0_94),
% 106.73/13.76 inference(resolution,[status(thm)],[f8597,f434])).
% 106.73/13.76 fof(f8658,plain,(
% 106.73/13.76 $false|spl0_94),
% 106.73/13.76 inference(forward_subsumption_resolution,[status(thm)],[f8657,f559])).
% 106.73/13.76 fof(f8659,plain,(
% 106.73/13.76 spl0_94),
% 106.73/13.76 inference(contradiction_clause,[status(thm)],[f8658])).
% 106.73/13.76 fof(f8665,plain,(
% 106.73/13.76 spl0_97 <=> relation(sk0_53)),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f8667,plain,(
% 106.73/13.76 ~relation(sk0_53)|spl0_97),
% 106.73/13.76 inference(component_clause,[status(thm)],[f8665])).
% 106.73/13.76 fof(f8672,plain,(
% 106.73/13.76 $false|spl0_97),
% 106.73/13.76 inference(forward_subsumption_resolution,[status(thm)],[f8667,f559])).
% 106.73/13.76 fof(f8673,plain,(
% 106.73/13.76 spl0_97),
% 106.73/13.76 inference(contradiction_clause,[status(thm)],[f8672])).
% 106.73/13.76 fof(f8680,plain,(
% 106.73/13.76 spl0_98 <=> in(sk0_54,empty_set)),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f8681,plain,(
% 106.73/13.76 in(sk0_54,empty_set)|~spl0_98),
% 106.73/13.76 inference(component_clause,[status(thm)],[f8680])).
% 106.73/13.76 fof(f8712,plain,(
% 106.73/13.76 spl0_103 <=> ~in(ordered_pair(X0,sk0_54),sk0_53)),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f8713,plain,(
% 106.73/13.76 ![X0]: (~in(ordered_pair(X0,sk0_54),sk0_53)|~spl0_103)),
% 106.73/13.76 inference(component_clause,[status(thm)],[f8712])).
% 106.73/13.76 fof(f8715,plain,(
% 106.73/13.76 ![X0]: (~relation(sk0_53)|~in(sk0_54,sk0_55)|~in(ordered_pair(X0,sk0_54),sk0_53)|spl0_0)),
% 106.73/13.76 inference(resolution,[status(thm)],[f789,f900])).
% 106.73/13.76 fof(f8716,plain,(
% 106.73/13.76 ~spl0_97|~spl0_1|spl0_103|spl0_0),
% 106.73/13.76 inference(split_clause,[status(thm)],[f8715,f8665,f790,f8712,f787])).
% 106.73/13.76 fof(f8725,plain,(
% 106.73/13.76 in(sk0_54,relation_rng(relation_rng_restriction(sk0_55,sk0_53)))|~relation(relation_rng_restriction(sk0_55,sk0_53))|~spl0_93),
% 106.73/13.76 inference(resolution,[status(thm)],[f8593,f802])).
% 106.73/13.76 fof(f8726,plain,(
% 106.73/13.76 spl0_0|~spl0_94|~spl0_93),
% 106.73/13.76 inference(split_clause,[status(thm)],[f8725,f787,f8595,f8592])).
% 106.73/13.76 fof(f8774,plain,(
% 106.73/13.76 $false|~spl0_98),
% 106.73/13.76 inference(forward_subsumption_resolution,[status(thm)],[f8681,f817])).
% 106.73/13.76 fof(f8775,plain,(
% 106.73/13.76 ~spl0_98),
% 106.73/13.76 inference(contradiction_clause,[status(thm)],[f8774])).
% 106.73/13.76 fof(f9082,plain,(
% 106.73/13.76 ![X0,X1]: (~subset(X0,empty_set)|subset(X0,X1)|~spl0_4)),
% 106.73/13.76 inference(resolution,[status(thm)],[f586,f3424])).
% 106.73/13.76 fof(f9088,plain,(
% 106.73/13.76 ![X0,X1,X2]: (~subset(X0,relation_rng(X1))|subset(X0,relation_rng(X2))|~relation(X1)|~relation(X2)|~subset(X1,X2))),
% 106.73/13.76 inference(resolution,[status(thm)],[f586,f596])).
% 106.73/13.76 fof(f9093,plain,(
% 106.73/13.76 spl0_114 <=> subset(relation_dom_restriction(empty_set,X0),X1)),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f9096,plain,(
% 106.73/13.76 ![X0,X1]: (subset(relation_dom_restriction(empty_set,X0),X1)|~relation(empty_set)|~spl0_4)),
% 106.73/13.76 inference(resolution,[status(thm)],[f9082,f749])).
% 106.73/13.76 fof(f9097,plain,(
% 106.73/13.76 spl0_114|~spl0_4),
% 106.73/13.76 inference(split_clause,[status(thm)],[f9096,f9093,f859])).
% 106.73/13.76 fof(f9698,plain,(
% 106.73/13.76 ![X0,X1]: (~subset(X0,empty_set)|disjoint(X0,X1))),
% 106.73/13.76 inference(resolution,[status(thm)],[f707,f3750])).
% 106.73/13.76 fof(f9701,plain,(
% 106.73/13.76 spl0_115 <=> disjoint(relation_dom_restriction(empty_set,X0),X1)),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f9704,plain,(
% 106.73/13.76 ![X0,X1]: (disjoint(relation_dom_restriction(empty_set,X0),X1)|~relation(empty_set))),
% 106.73/13.76 inference(resolution,[status(thm)],[f9698,f749])).
% 106.73/13.76 fof(f9705,plain,(
% 106.73/13.76 spl0_115|~spl0_4),
% 106.73/13.76 inference(split_clause,[status(thm)],[f9704,f9701,f859])).
% 106.73/13.76 fof(f9767,plain,(
% 106.73/13.76 ![X0]: (empty_set=set_difference(empty_set,X0)|~subset(empty_set,empty_set))),
% 106.73/13.76 inference(paramodulation,[status(thm)],[f681,f2396])).
% 106.73/13.76 fof(f9768,plain,(
% 106.73/13.76 spl0_19|~spl0_24),
% 106.73/13.76 inference(split_clause,[status(thm)],[f9767,f3022,f3077])).
% 106.73/13.76 fof(f9774,plain,(
% 106.73/13.76 ![X0]: (empty_set=set_intersection2(X0,empty_set)|~subset(empty_set,empty_set))),
% 106.73/13.76 inference(paramodulation,[status(thm)],[f602,f2397])).
% 106.73/13.76 fof(f9775,plain,(
% 106.73/13.76 spl0_23|~spl0_24),
% 106.73/13.76 inference(split_clause,[status(thm)],[f9774,f3059,f3077])).
% 106.73/13.76 fof(f9785,plain,(
% 106.73/13.76 ![X0,X1,X2]: (~relation(relation_rng_restriction(X0,X1))|~relation(X2)|subset(relation_rng_restriction(X0,X1),X2)|~relation(X1)|in(ordered_pair(sk0_24(X2,relation_rng_restriction(X0,X1)),sk0_25(X2,relation_rng_restriction(X0,X1))),X1))),
% 106.73/13.76 inference(resolution,[status(thm)],[f320,f892])).
% 106.73/13.76 fof(f9786,plain,(
% 106.73/13.76 ![X0,X1,X2]: (~relation(X0)|subset(relation_rng_restriction(X1,X2),X0)|~relation(X2)|in(ordered_pair(sk0_24(X0,relation_rng_restriction(X1,X2)),sk0_25(X0,relation_rng_restriction(X1,X2))),X2))),
% 106.73/13.76 inference(forward_subsumption_resolution,[status(thm)],[f9785,f434])).
% 106.73/13.76 fof(f9787,plain,(
% 106.73/13.76 ![X0,X1]: (~relation(X0)|~relation(X1)|subset(X0,X1)|~relation(X0)|in(sk0_25(X1,X0),relation_rng(X0)))),
% 106.73/13.76 inference(resolution,[status(thm)],[f320,f840])).
% 106.73/13.76 fof(f9788,plain,(
% 106.73/13.76 ![X0,X1]: (~relation(X0)|~relation(X1)|subset(X0,X1)|in(sk0_25(X1,X0),relation_rng(X0)))),
% 106.73/13.76 inference(duplicate_literals_removal,[status(esa)],[f9787])).
% 106.73/13.76 fof(f9804,plain,(
% 106.73/13.76 spl0_116 <=> ~relation(X0)|subset(empty_set,X0)),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f9807,plain,(
% 106.73/13.76 ![X0]: (~relation(empty_set)|~relation(X0)|subset(empty_set,X0))),
% 106.73/13.76 inference(resolution,[status(thm)],[f320,f817])).
% 106.73/13.76 fof(f9808,plain,(
% 106.73/13.76 ~spl0_4|spl0_116),
% 106.73/13.76 inference(split_clause,[status(thm)],[f9807,f859,f9804])).
% 106.73/13.76 fof(f9841,plain,(
% 106.73/13.76 ![X0,X1,X2]: (subset(set_intersection2(X0,X1),X2)|~disjoint(X1,X0))),
% 106.73/13.76 inference(resolution,[status(thm)],[f327,f8169])).
% 106.73/13.76 fof(f10149,plain,(
% 106.73/13.76 ![X0,X1,X2]: (~relation(relation_rng_restriction(X0,X1))|~in(X2,relation_dom(relation_rng_restriction(X0,X1)))|~relation(X1)|in(ordered_pair(X2,sk0_28(X2,relation_dom(relation_rng_restriction(X0,X1)),relation_rng_restriction(X0,X1))),X1))),
% 106.73/13.76 inference(resolution,[status(thm)],[f831,f892])).
% 106.73/13.76 fof(f10150,plain,(
% 106.73/13.76 ![X0,X1,X2]: (~in(X0,relation_dom(relation_rng_restriction(X1,X2)))|~relation(X2)|in(ordered_pair(X0,sk0_28(X0,relation_dom(relation_rng_restriction(X1,X2)),relation_rng_restriction(X1,X2))),X2))),
% 106.73/13.76 inference(forward_subsumption_resolution,[status(thm)],[f10149,f434])).
% 106.73/13.76 fof(f10151,plain,(
% 106.73/13.76 ![X0,X1]: (~relation(X0)|~in(X1,relation_dom(X0))|~relation(X0)|in(sk0_28(X1,relation_dom(X0),X0),relation_rng(X0)))),
% 106.73/13.76 inference(resolution,[status(thm)],[f831,f840])).
% 106.73/13.76 fof(f10152,plain,(
% 106.73/13.76 ![X0,X1]: (~relation(X0)|~in(X1,relation_dom(X0))|in(sk0_28(X1,relation_dom(X0),X0),relation_rng(X0)))),
% 106.73/13.76 inference(duplicate_literals_removal,[status(esa)],[f10151])).
% 106.73/13.76 fof(f10168,plain,(
% 106.73/13.76 spl0_117 <=> ~in(X0,relation_dom(empty_set))),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f10171,plain,(
% 106.73/13.76 ![X0]: (~relation(empty_set)|~in(X0,relation_dom(empty_set)))),
% 106.73/13.76 inference(resolution,[status(thm)],[f831,f817])).
% 106.73/13.76 fof(f10172,plain,(
% 106.73/13.76 ~spl0_4|spl0_117),
% 106.73/13.76 inference(split_clause,[status(thm)],[f10171,f859,f10168])).
% 106.73/13.76 fof(f10175,plain,(
% 106.73/13.76 ![X0,X1]: (~relation(X0)|~in(X1,relation_dom(X0))|~in(X0,ordered_pair(X1,sk0_28(X1,relation_dom(X0),X0))))),
% 106.73/13.76 inference(resolution,[status(thm)],[f831,f193])).
% 106.73/13.76 fof(f10176,plain,(
% 106.73/13.76 spl0_118 <=> ~in(X0,relation_dom(empty_set))|in(ordered_pair(X0,sk0_28(X0,empty_set,empty_set)),empty_set)),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f10179,plain,(
% 106.73/13.76 ![X0]: (~relation(empty_set)|~in(X0,relation_dom(empty_set))|in(ordered_pair(X0,sk0_28(X0,empty_set,empty_set)),empty_set)|~spl0_6)),
% 106.73/13.76 inference(paramodulation,[status(thm)],[f870,f831])).
% 106.73/13.76 fof(f10180,plain,(
% 106.73/13.76 ~spl0_4|spl0_118|~spl0_6),
% 106.73/13.76 inference(split_clause,[status(thm)],[f10179,f859,f10176,f869])).
% 106.73/13.76 fof(f10305,plain,(
% 106.73/13.76 ![X0,X1,X2]: (~relation(relation_rng_restriction(X0,X1))|X2=relation_dom(relation_rng_restriction(X0,X1))|in(sk0_29(X2,relation_rng_restriction(X0,X1)),X2)|~relation(X1)|in(ordered_pair(sk0_29(X2,relation_rng_restriction(X0,X1)),sk0_30(X2,relation_rng_restriction(X0,X1))),X1))),
% 106.73/13.76 inference(resolution,[status(thm)],[f345,f892])).
% 106.73/13.76 fof(f10306,plain,(
% 106.73/13.76 ![X0,X1,X2]: (X0=relation_dom(relation_rng_restriction(X1,X2))|in(sk0_29(X0,relation_rng_restriction(X1,X2)),X0)|~relation(X2)|in(ordered_pair(sk0_29(X0,relation_rng_restriction(X1,X2)),sk0_30(X0,relation_rng_restriction(X1,X2))),X2))),
% 106.73/13.76 inference(forward_subsumption_resolution,[status(thm)],[f10305,f434])).
% 106.73/13.76 fof(f10309,plain,(
% 106.73/13.76 ![X0,X1]: (~relation(X0)|X1=relation_dom(X0)|in(sk0_29(X1,X0),X1)|~relation(X0)|in(sk0_30(X1,X0),relation_rng(X0)))),
% 106.73/13.76 inference(resolution,[status(thm)],[f345,f840])).
% 106.73/13.76 fof(f10310,plain,(
% 106.73/13.76 ![X0,X1]: (~relation(X0)|X1=relation_dom(X0)|in(sk0_29(X1,X0),X1)|in(sk0_30(X1,X0),relation_rng(X0)))),
% 106.73/13.76 inference(duplicate_literals_removal,[status(esa)],[f10309])).
% 106.73/13.76 fof(f10326,plain,(
% 106.73/13.76 spl0_119 <=> X0=relation_dom(empty_set)|in(sk0_29(X0,empty_set),X0)),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f10329,plain,(
% 106.73/13.76 ![X0]: (~relation(empty_set)|X0=relation_dom(empty_set)|in(sk0_29(X0,empty_set),X0))),
% 106.73/13.76 inference(resolution,[status(thm)],[f345,f817])).
% 106.73/13.76 fof(f10330,plain,(
% 106.73/13.76 ~spl0_4|spl0_119),
% 106.73/13.76 inference(split_clause,[status(thm)],[f10329,f859,f10326])).
% 106.73/13.76 fof(f10439,plain,(
% 106.73/13.76 spl0_126 <=> relation(set_union2(empty_set,relation_rng_restriction(sk0_55,sk0_53)))),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f10441,plain,(
% 106.73/13.76 ~relation(set_union2(empty_set,relation_rng_restriction(sk0_55,sk0_53)))|spl0_126),
% 106.73/13.76 inference(component_clause,[status(thm)],[f10439])).
% 106.73/13.76 fof(f10446,plain,(
% 106.73/13.76 spl0_127 <=> relation(set_union2(relation_rng_restriction(sk0_55,sk0_53),relation_rng_restriction(sk0_55,sk0_53)))),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f10448,plain,(
% 106.73/13.76 ~relation(set_union2(relation_rng_restriction(sk0_55,sk0_53),relation_rng_restriction(sk0_55,sk0_53)))|spl0_127),
% 106.73/13.76 inference(component_clause,[status(thm)],[f10446])).
% 106.73/13.76 fof(f10535,plain,(
% 106.73/13.76 ~relation(relation_rng_restriction(sk0_55,sk0_53))|spl0_126),
% 106.73/13.76 inference(forward_demodulation,[status(thm)],[f2221,f10441])).
% 106.73/13.76 fof(f10536,plain,(
% 106.73/13.76 $false|~spl0_94|spl0_126),
% 106.73/13.76 inference(forward_subsumption_resolution,[status(thm)],[f10535,f8596])).
% 106.73/13.76 fof(f10537,plain,(
% 106.73/13.76 ~spl0_94|spl0_126),
% 106.73/13.76 inference(contradiction_clause,[status(thm)],[f10536])).
% 106.73/13.76 fof(f10578,plain,(
% 106.73/13.76 spl0_129 <=> relation(set_union2(empty_set,sk0_53))),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f10580,plain,(
% 106.73/13.76 ~relation(set_union2(empty_set,sk0_53))|spl0_129),
% 106.73/13.76 inference(component_clause,[status(thm)],[f10578])).
% 106.73/13.76 fof(f10585,plain,(
% 106.73/13.76 spl0_130 <=> relation(set_union2(sk0_53,sk0_53))),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f10587,plain,(
% 106.73/13.76 ~relation(set_union2(sk0_53,sk0_53))|spl0_130),
% 106.73/13.76 inference(component_clause,[status(thm)],[f10585])).
% 106.73/13.76 fof(f10590,plain,(
% 106.73/13.76 spl0_131 <=> relation(set_union2(sk0_53,empty_set))),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f10592,plain,(
% 106.73/13.76 ~relation(set_union2(sk0_53,empty_set))|spl0_131),
% 106.73/13.76 inference(component_clause,[status(thm)],[f10590])).
% 106.73/13.76 fof(f10654,plain,(
% 106.73/13.76 spl0_133 <=> in(sk0_54,X0)),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f10655,plain,(
% 106.73/13.76 ![X0]: (in(sk0_54,X0)|~spl0_133)),
% 106.73/13.76 inference(component_clause,[status(thm)],[f10654])).
% 106.73/13.76 fof(f11148,plain,(
% 106.73/13.76 spl0_137 <=> ~subset(X0,empty_set)|subset(X0,relation_rng(X1))|~relation(X1)|~subset(empty_set,X1)),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f11151,plain,(
% 106.73/13.76 ![X0,X1]: (~subset(X0,empty_set)|subset(X0,relation_rng(X1))|~relation(empty_set)|~relation(X1)|~subset(empty_set,X1))),
% 106.73/13.76 inference(paramodulation,[status(thm)],[f702,f9088])).
% 106.73/13.76 fof(f11152,plain,(
% 106.73/13.76 spl0_137|~spl0_4),
% 106.73/13.76 inference(split_clause,[status(thm)],[f11151,f11148,f859])).
% 106.73/13.76 fof(f11265,plain,(
% 106.73/13.76 ![X0,X1]: (~relation(X0)|subset(relation_rng_restriction(X1,X0),X0)|~relation(X0)|~relation(relation_rng_restriction(X1,X0))|~relation(X0)|subset(relation_rng_restriction(X1,X0),X0))),
% 106.73/13.76 inference(resolution,[status(thm)],[f9786,f321])).
% 106.73/13.76 fof(f11266,plain,(
% 106.73/13.76 ![X0,X1]: (~relation(X0)|subset(relation_rng_restriction(X1,X0),X0)|~relation(relation_rng_restriction(X1,X0)))),
% 106.73/13.76 inference(duplicate_literals_removal,[status(esa)],[f11265])).
% 106.73/13.76 fof(f11267,plain,(
% 106.73/13.76 ![X0,X1]: (~relation(X0)|subset(relation_rng_restriction(X1,X0),X0))),
% 106.73/13.76 inference(forward_subsumption_resolution,[status(thm)],[f11266,f434])).
% 106.73/13.76 fof(f11297,plain,(
% 106.73/13.76 spl0_138 <=> ~relation(X0)|subset(relation_rng_restriction(X1,empty_set),X0)),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f11300,plain,(
% 106.73/13.76 ![X0,X1]: (~relation(X0)|subset(relation_rng_restriction(X1,empty_set),X0)|~relation(empty_set))),
% 106.73/13.76 inference(resolution,[status(thm)],[f9786,f817])).
% 106.73/13.76 fof(f11301,plain,(
% 106.73/13.76 spl0_138|~spl0_4),
% 106.73/13.76 inference(split_clause,[status(thm)],[f11300,f11297,f859])).
% 106.73/13.76 fof(f11312,plain,(
% 106.73/13.76 spl0_139 <=> ~relation(X0)|subset(empty_set,X0)|in(sk0_25(X0,empty_set),empty_set)),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f11315,plain,(
% 106.73/13.76 ![X0]: (~relation(empty_set)|~relation(X0)|subset(empty_set,X0)|in(sk0_25(X0,empty_set),empty_set))),
% 106.73/13.76 inference(paramodulation,[status(thm)],[f702,f9788])).
% 106.73/13.76 fof(f11316,plain,(
% 106.73/13.76 ~spl0_4|spl0_139),
% 106.73/13.76 inference(split_clause,[status(thm)],[f11315,f859,f11312])).
% 106.73/13.76 fof(f11540,plain,(
% 106.73/13.76 spl0_141 <=> disjoint(relation_rng_restriction(X0,empty_set),X1)),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f11543,plain,(
% 106.73/13.76 ![X0,X1]: (~relation(empty_set)|disjoint(relation_rng_restriction(X0,empty_set),X1))),
% 106.73/13.76 inference(resolution,[status(thm)],[f11267,f9698])).
% 106.73/13.76 fof(f11544,plain,(
% 106.73/13.76 ~spl0_4|spl0_141),
% 106.73/13.76 inference(split_clause,[status(thm)],[f11543,f859,f11540])).
% 106.73/13.76 fof(f11545,plain,(
% 106.73/13.76 spl0_142 <=> subset(relation_rng_restriction(X0,empty_set),X1)),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f11548,plain,(
% 106.73/13.76 ![X0,X1]: (~relation(empty_set)|subset(relation_rng_restriction(X0,empty_set),X1)|~spl0_4)),
% 106.73/13.76 inference(resolution,[status(thm)],[f11267,f9082])).
% 106.73/13.76 fof(f11549,plain,(
% 106.73/13.76 ~spl0_4|spl0_142),
% 106.73/13.76 inference(split_clause,[status(thm)],[f11548,f859,f11545])).
% 106.73/13.76 fof(f11550,plain,(
% 106.73/13.76 spl0_143 <=> relation_rng_restriction(X0,empty_set)=empty_set),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f11553,plain,(
% 106.73/13.76 ![X0]: (~relation(empty_set)|relation_rng_restriction(X0,empty_set)=empty_set|~spl0_4|~spl0_16)),
% 106.73/13.76 inference(resolution,[status(thm)],[f11267,f3435])).
% 106.73/13.76 fof(f11554,plain,(
% 106.73/13.76 ~spl0_4|spl0_143|~spl0_16),
% 106.73/13.76 inference(split_clause,[status(thm)],[f11553,f859,f11550,f2990])).
% 106.73/13.76 fof(f11555,plain,(
% 106.73/13.76 spl0_144 <=> empty_set=relation_rng(relation_rng_restriction(X0,empty_set))|~relation(relation_rng_restriction(X0,empty_set))),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f11558,plain,(
% 106.73/13.76 ![X0]: (~relation(empty_set)|empty_set=relation_rng(relation_rng_restriction(X0,empty_set))|~relation(relation_rng_restriction(X0,empty_set)))),
% 106.73/13.76 inference(resolution,[status(thm)],[f11267,f3185])).
% 106.73/13.76 fof(f11559,plain,(
% 106.73/13.76 ~spl0_4|spl0_144),
% 106.73/13.76 inference(split_clause,[status(thm)],[f11558,f859,f11555])).
% 106.73/13.76 fof(f11617,plain,(
% 106.73/13.76 spl0_146 <=> subset(empty_set,X0)),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f11622,plain,(
% 106.73/13.76 ![X0,X1]: (subset(empty_set,X0)|~disjoint(empty_set,X1))),
% 106.73/13.76 inference(paramodulation,[status(thm)],[f602,f9841])).
% 106.73/13.76 fof(f11623,plain,(
% 106.73/13.76 spl0_146|spl0_40),
% 106.73/13.76 inference(split_clause,[status(thm)],[f11622,f11617,f3745])).
% 106.73/13.76 fof(f11756,plain,(
% 106.73/13.76 ![X0]: (empty_set=set_intersection2(empty_set,X0)|~subset(empty_set,empty_set))),
% 106.73/13.76 inference(paramodulation,[status(thm)],[f2237,f2398])).
% 106.73/13.76 fof(f11757,plain,(
% 106.73/13.76 spl0_26|~spl0_24),
% 106.73/13.76 inference(split_clause,[status(thm)],[f11756,f3105,f3077])).
% 106.73/13.76 fof(f13366,plain,(
% 106.73/13.76 ![X0,X1,X2]: (~relation(relation_rng_restriction(X0,X1))|~in(X2,relation_rng(relation_rng_restriction(X0,X1)))|~relation(X1)|in(X2,X0))),
% 106.73/13.76 inference(resolution,[status(thm)],[f839,f855])).
% 106.73/13.76 fof(f13367,plain,(
% 106.73/13.76 ![X0,X1,X2]: (~in(X0,relation_rng(relation_rng_restriction(X1,X2)))|~relation(X2)|in(X0,X1))),
% 106.73/13.76 inference(forward_subsumption_resolution,[status(thm)],[f13366,f434])).
% 106.73/13.76 fof(f13390,plain,(
% 106.73/13.76 spl0_150 <=> ~in(X0,relation_rng(empty_set))),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f13393,plain,(
% 106.73/13.76 ![X0]: (~relation(empty_set)|~in(X0,relation_rng(empty_set)))),
% 106.73/13.76 inference(resolution,[status(thm)],[f839,f817])).
% 106.73/13.76 fof(f13394,plain,(
% 106.73/13.76 ~spl0_4|spl0_150),
% 106.73/13.76 inference(split_clause,[status(thm)],[f13393,f859,f13390])).
% 106.73/13.76 fof(f13403,plain,(
% 106.73/13.76 spl0_151 <=> ~in(X0,relation_rng(empty_set))|in(ordered_pair(sk0_35(X0,empty_set,empty_set),X0),empty_set)),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f13406,plain,(
% 106.73/13.76 ![X0]: (~relation(empty_set)|~in(X0,relation_rng(empty_set))|in(ordered_pair(sk0_35(X0,empty_set,empty_set),X0),empty_set))),
% 106.73/13.76 inference(paramodulation,[status(thm)],[f702,f839])).
% 106.73/13.76 fof(f13407,plain,(
% 106.73/13.76 ~spl0_4|spl0_151),
% 106.73/13.76 inference(split_clause,[status(thm)],[f13406,f859,f13403])).
% 106.73/13.76 fof(f13882,plain,(
% 106.73/13.76 spl0_199 <=> relation(set_difference(relation_rng_restriction(sk0_55,sk0_53),empty_set))),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f13884,plain,(
% 106.73/13.76 ~relation(set_difference(relation_rng_restriction(sk0_55,sk0_53),empty_set))|spl0_199),
% 106.73/13.76 inference(component_clause,[status(thm)],[f13882])).
% 106.73/13.76 fof(f13887,plain,(
% 106.73/13.76 spl0_200 <=> relation(set_intersection2(empty_set,relation_rng_restriction(sk0_55,sk0_53)))),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f13889,plain,(
% 106.73/13.76 ~relation(set_intersection2(empty_set,relation_rng_restriction(sk0_55,sk0_53)))|spl0_200),
% 106.73/13.76 inference(component_clause,[status(thm)],[f13887])).
% 106.73/13.76 fof(f13894,plain,(
% 106.73/13.76 spl0_201 <=> relation(set_intersection2(relation_rng_restriction(sk0_55,sk0_53),relation_rng_restriction(sk0_55,sk0_53)))),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f13896,plain,(
% 106.73/13.76 ~relation(set_intersection2(relation_rng_restriction(sk0_55,sk0_53),relation_rng_restriction(sk0_55,sk0_53)))|spl0_201),
% 106.73/13.76 inference(component_clause,[status(thm)],[f13894])).
% 106.73/13.76 fof(f13899,plain,(
% 106.73/13.76 spl0_202 <=> relation(set_intersection2(relation_rng_restriction(sk0_55,sk0_53),empty_set))),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f13901,plain,(
% 106.73/13.76 ~relation(set_intersection2(relation_rng_restriction(sk0_55,sk0_53),empty_set))|spl0_202),
% 106.73/13.76 inference(component_clause,[status(thm)],[f13899])).
% 106.73/13.76 fof(f13920,plain,(
% 106.73/13.76 ~relation(sk0_53)|~in(sk0_54,relation_rng(sk0_53))|~spl0_103),
% 106.73/13.76 inference(resolution,[status(thm)],[f8713,f839])).
% 106.73/13.76 fof(f13921,plain,(
% 106.73/13.76 ~spl0_97|~spl0_2|~spl0_103),
% 106.73/13.76 inference(split_clause,[status(thm)],[f13920,f8665,f794,f8712])).
% 106.73/13.76 fof(f14874,plain,(
% 106.73/13.76 spl0_204 <=> ~in(X0,relation_dom(relation_rng_restriction(X1,empty_set)))),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f14877,plain,(
% 106.73/13.76 ![X0,X1]: (~in(X0,relation_dom(relation_rng_restriction(X1,empty_set)))|~relation(empty_set))),
% 106.73/13.76 inference(resolution,[status(thm)],[f10150,f817])).
% 106.73/13.76 fof(f14878,plain,(
% 106.73/13.76 spl0_204|~spl0_4),
% 106.73/13.76 inference(split_clause,[status(thm)],[f14877,f14874,f859])).
% 106.73/13.76 fof(f14890,plain,(
% 106.73/13.76 spl0_205 <=> ~in(X0,relation_dom(empty_set))|in(sk0_28(X0,empty_set,empty_set),relation_rng(empty_set))),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f14893,plain,(
% 106.73/13.76 ![X0]: (~relation(empty_set)|~in(X0,relation_dom(empty_set))|in(sk0_28(X0,empty_set,empty_set),relation_rng(empty_set))|~spl0_6)),
% 106.73/13.76 inference(paramodulation,[status(thm)],[f870,f10152])).
% 106.73/13.76 fof(f14894,plain,(
% 106.73/13.76 ~spl0_4|spl0_205|~spl0_6),
% 106.73/13.76 inference(split_clause,[status(thm)],[f14893,f859,f14890,f869])).
% 106.73/13.76 fof(f14897,plain,(
% 106.73/13.76 spl0_206 <=> ~in(X0,relation_dom(empty_set))|in(sk0_28(X0,relation_dom(empty_set),empty_set),empty_set)),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f14900,plain,(
% 106.73/13.76 ![X0]: (~relation(empty_set)|~in(X0,relation_dom(empty_set))|in(sk0_28(X0,relation_dom(empty_set),empty_set),empty_set))),
% 106.73/13.76 inference(paramodulation,[status(thm)],[f702,f10152])).
% 106.73/13.76 fof(f14901,plain,(
% 106.73/13.76 ~spl0_4|spl0_206),
% 106.73/13.76 inference(split_clause,[status(thm)],[f14900,f859,f14897])).
% 106.73/13.76 fof(f14907,plain,(
% 106.73/13.76 spl0_207 <=> ~in(X0,relation_dom(empty_set))|~in(empty_set,ordered_pair(X0,sk0_28(X0,empty_set,empty_set)))),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f14910,plain,(
% 106.73/13.76 ![X0]: (~relation(empty_set)|~in(X0,relation_dom(empty_set))|~in(empty_set,ordered_pair(X0,sk0_28(X0,empty_set,empty_set)))|~spl0_6)),
% 106.73/13.76 inference(paramodulation,[status(thm)],[f870,f10175])).
% 106.73/13.76 fof(f14911,plain,(
% 106.73/13.76 ~spl0_4|spl0_207|~spl0_6),
% 106.73/13.76 inference(split_clause,[status(thm)],[f14910,f859,f14907,f869])).
% 106.73/13.76 fof(f17042,plain,(
% 106.73/13.76 spl0_298 <=> X0=relation_rng(empty_set)|in(sk0_36(X0,empty_set),X0)),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f17045,plain,(
% 106.73/13.76 ![X0]: (~relation(empty_set)|X0=relation_rng(empty_set)|in(sk0_36(X0,empty_set),X0))),
% 106.73/13.76 inference(resolution,[status(thm)],[f372,f817])).
% 106.73/13.76 fof(f17046,plain,(
% 106.73/13.76 ~spl0_4|spl0_298),
% 106.73/13.76 inference(split_clause,[status(thm)],[f17045,f859,f17042])).
% 106.73/13.76 fof(f17111,plain,(
% 106.73/13.76 spl0_299 <=> relation_field(empty_set)=set_union2(empty_set,relation_rng(empty_set))),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f17114,plain,(
% 106.73/13.76 ~relation(empty_set)|relation_field(empty_set)=set_union2(empty_set,relation_rng(empty_set))|~spl0_6),
% 106.73/13.76 inference(paramodulation,[status(thm)],[f870,f377])).
% 106.73/13.76 fof(f17115,plain,(
% 106.73/13.76 ~spl0_4|spl0_299|~spl0_6),
% 106.73/13.76 inference(split_clause,[status(thm)],[f17114,f859,f17111,f869])).
% 106.73/13.76 fof(f17118,plain,(
% 106.73/13.76 spl0_300 <=> relation_field(empty_set)=set_union2(relation_dom(empty_set),empty_set)),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f17121,plain,(
% 106.73/13.76 ~relation(empty_set)|relation_field(empty_set)=set_union2(relation_dom(empty_set),empty_set)),
% 106.73/13.76 inference(paramodulation,[status(thm)],[f702,f377])).
% 106.73/13.76 fof(f17122,plain,(
% 106.73/13.76 ~spl0_4|spl0_300),
% 106.73/13.76 inference(split_clause,[status(thm)],[f17121,f859,f17118])).
% 106.73/13.76 fof(f17407,plain,(
% 106.73/13.76 spl0_304 <=> ~relation(X0)|X0=relation_inverse(empty_set)|in(ordered_pair(sk0_38(X0,empty_set),sk0_39(X0,empty_set)),X0)),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f17410,plain,(
% 106.73/13.76 ![X0]: (~relation(empty_set)|~relation(X0)|X0=relation_inverse(empty_set)|in(ordered_pair(sk0_38(X0,empty_set),sk0_39(X0,empty_set)),X0))),
% 106.73/13.76 inference(resolution,[status(thm)],[f385,f817])).
% 106.73/13.76 fof(f17411,plain,(
% 106.73/13.76 ~spl0_4|spl0_304),
% 106.73/13.76 inference(split_clause,[status(thm)],[f17410,f859,f17407])).
% 106.73/13.76 fof(f17431,plain,(
% 106.73/13.76 spl0_305 <=> disjoint(X0,empty_set)),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f17434,plain,(
% 106.73/13.76 ![X0]: (disjoint(X0,empty_set)|~empty_set=empty_set)),
% 106.73/13.76 inference(paramodulation,[status(thm)],[f602,f389])).
% 106.73/13.76 fof(f17435,plain,(
% 106.73/13.76 spl0_305|~spl0_7),
% 106.73/13.76 inference(split_clause,[status(thm)],[f17434,f17431,f872])).
% 106.73/13.76 fof(f17440,plain,(
% 106.73/13.76 ![X0,X1,X2,X3]: (~relation(X0)|~relation(X1)|~in(ordered_pair(X2,X3),relation_composition(X0,X1))|in(ordered_pair(X2,sk0_40(X3,X2,relation_composition(X0,X1),X1,X0)),X0))),
% 106.73/13.76 inference(forward_subsumption_resolution,[status(thm)],[f843,f419])).
% 106.73/13.76 fof(f17492,plain,(
% 106.73/13.76 spl0_309 <=> ~relation(X0)|~in(ordered_pair(X1,X2),relation_composition(empty_set,X0))),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f17495,plain,(
% 106.73/13.76 ![X0,X1,X2]: (~relation(empty_set)|~relation(X0)|~in(ordered_pair(X1,X2),relation_composition(empty_set,X0)))),
% 106.73/13.76 inference(resolution,[status(thm)],[f17440,f817])).
% 106.73/13.76 fof(f17496,plain,(
% 106.73/13.76 ~spl0_4|spl0_309),
% 106.73/13.76 inference(split_clause,[status(thm)],[f17495,f859,f17492])).
% 106.73/13.76 fof(f18010,plain,(
% 106.73/13.76 in(sk0_54,relation_rng(sk0_53))|~relation(sk0_53)|~relation(sk0_53)|~spl0_93),
% 106.73/13.76 inference(resolution,[status(thm)],[f8593,f11267])).
% 106.73/13.76 fof(f18011,plain,(
% 106.73/13.76 spl0_2|~spl0_97|~spl0_93),
% 106.73/13.76 inference(split_clause,[status(thm)],[f18010,f794,f8665,f8592])).
% 106.73/13.76 fof(f18115,plain,(
% 106.73/13.76 $false|~spl0_133),
% 106.73/13.76 inference(resolution,[status(thm)],[f10655,f817])).
% 106.73/13.76 fof(f18116,plain,(
% 106.73/13.76 ~spl0_133),
% 106.73/13.76 inference(contradiction_clause,[status(thm)],[f18115])).
% 106.73/13.76 fof(f18474,plain,(
% 106.73/13.76 spl0_341 <=> X0=relation_dom(relation_rng_restriction(X1,empty_set))|in(sk0_29(X0,relation_rng_restriction(X1,empty_set)),X0)),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f18477,plain,(
% 106.73/13.76 ![X0,X1]: (X0=relation_dom(relation_rng_restriction(X1,empty_set))|in(sk0_29(X0,relation_rng_restriction(X1,empty_set)),X0)|~relation(empty_set))),
% 106.73/13.76 inference(resolution,[status(thm)],[f10306,f817])).
% 106.73/13.76 fof(f18478,plain,(
% 106.73/13.76 spl0_341|~spl0_4),
% 106.73/13.76 inference(split_clause,[status(thm)],[f18477,f18474,f859])).
% 106.73/13.76 fof(f18492,plain,(
% 106.73/13.76 spl0_342 <=> X0=relation_dom(empty_set)|in(sk0_29(X0,empty_set),X0)|in(sk0_30(X0,empty_set),empty_set)),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f18495,plain,(
% 106.73/13.76 ![X0]: (~relation(empty_set)|X0=relation_dom(empty_set)|in(sk0_29(X0,empty_set),X0)|in(sk0_30(X0,empty_set),empty_set))),
% 106.73/13.76 inference(paramodulation,[status(thm)],[f702,f10310])).
% 106.73/13.76 fof(f18496,plain,(
% 106.73/13.76 ~spl0_4|spl0_342),
% 106.73/13.76 inference(split_clause,[status(thm)],[f18495,f859,f18492])).
% 106.73/13.76 fof(f20370,plain,(
% 106.73/13.76 ![X0,X1,X2,X3]: (~relation(X0)|~relation(X1)|~in(ordered_pair(X2,X3),relation_composition(X0,X1))|in(ordered_pair(sk0_40(X3,X2,relation_composition(X0,X1),X1,X0),X3),X1))),
% 106.73/13.76 inference(forward_subsumption_resolution,[status(thm)],[f844,f419])).
% 106.73/13.76 fof(f20541,plain,(
% 106.73/13.76 spl0_346 <=> ~relation(X0)|~in(ordered_pair(X1,X2),relation_composition(X0,empty_set))),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f20544,plain,(
% 106.73/13.76 ![X0,X1,X2]: (~relation(X0)|~relation(empty_set)|~in(ordered_pair(X1,X2),relation_composition(X0,empty_set)))),
% 106.73/13.76 inference(resolution,[status(thm)],[f20370,f817])).
% 106.73/13.76 fof(f20545,plain,(
% 106.73/13.76 spl0_346|~spl0_4),
% 106.73/13.76 inference(split_clause,[status(thm)],[f20544,f20541,f859])).
% 106.73/13.76 fof(f20784,plain,(
% 106.73/13.76 spl0_350 <=> ~relation(X0)|~relation(X1)|X1=relation_composition(empty_set,X0)|in(ordered_pair(sk0_41(X1,X0,empty_set),sk0_42(X1,X0,empty_set)),X1)),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f20787,plain,(
% 106.73/13.76 ![X0,X1]: (~relation(empty_set)|~relation(X0)|~relation(X1)|X1=relation_composition(empty_set,X0)|in(ordered_pair(sk0_41(X1,X0,empty_set),sk0_42(X1,X0,empty_set)),X1))),
% 106.73/13.76 inference(resolution,[status(thm)],[f398,f817])).
% 106.73/13.76 fof(f20788,plain,(
% 106.73/13.76 ~spl0_4|spl0_350),
% 106.73/13.76 inference(split_clause,[status(thm)],[f20787,f859,f20784])).
% 106.73/13.76 fof(f20844,plain,(
% 106.73/13.76 spl0_354 <=> ~relation(X0)|~relation(X1)|X1=relation_composition(X0,empty_set)|in(ordered_pair(sk0_41(X1,empty_set,X0),sk0_42(X1,empty_set,X0)),X1)),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f20847,plain,(
% 106.73/13.76 ![X0,X1]: (~relation(X0)|~relation(empty_set)|~relation(X1)|X1=relation_composition(X0,empty_set)|in(ordered_pair(sk0_41(X1,empty_set,X0),sk0_42(X1,empty_set,X0)),X1))),
% 106.73/13.76 inference(resolution,[status(thm)],[f399,f817])).
% 106.73/13.76 fof(f20848,plain,(
% 106.73/13.76 spl0_354|~spl0_4),
% 106.73/13.76 inference(split_clause,[status(thm)],[f20847,f20844,f859])).
% 106.73/13.76 fof(f21183,plain,(
% 106.73/13.76 spl0_356 <=> relation(set_union2(relation_rng_restriction(sk0_55,sk0_53),empty_set))),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f21185,plain,(
% 106.73/13.76 ~relation(set_union2(relation_rng_restriction(sk0_55,sk0_53),empty_set))|spl0_356),
% 106.73/13.76 inference(component_clause,[status(thm)],[f21183])).
% 106.73/13.76 fof(f22120,plain,(
% 106.73/13.76 ![X0,X1]: (~empty(X0)|subset(X0,X1))),
% 106.73/13.76 inference(resolution,[status(thm)],[f735,f327])).
% 106.73/13.76 fof(f22281,plain,(
% 106.73/13.76 spl0_363 <=> in(sk0_54,relation_rng(X0))|~relation(X0)),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f22282,plain,(
% 106.73/13.76 ![X0]: (in(sk0_54,relation_rng(X0))|~relation(X0)|~spl0_363)),
% 106.73/13.76 inference(component_clause,[status(thm)],[f22281])).
% 106.73/13.76 fof(f22573,plain,(
% 106.73/13.76 ![X0,X1]: (~empty(X0)|X1=X0|~subset(X1,X0))),
% 106.73/13.76 inference(resolution,[status(thm)],[f22120,f215])).
% 106.73/13.76 fof(f22668,plain,(
% 106.73/13.76 spl0_387 <=> ~empty(X0)),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f22669,plain,(
% 106.73/13.76 ![X0]: (~empty(X0)|~spl0_387)),
% 106.73/13.76 inference(component_clause,[status(thm)],[f22668])).
% 106.73/13.76 fof(f22917,plain,(
% 106.73/13.76 spl0_388 <=> relation_rng(X0)=empty_set|~relation(X0)|~subset(X0,empty_set)),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f22920,plain,(
% 106.73/13.76 ![X0]: (~empty(empty_set)|relation_rng(X0)=empty_set|~relation(X0)|~subset(X0,empty_set)|~spl0_3)),
% 106.73/13.76 inference(resolution,[status(thm)],[f22573,f857])).
% 106.73/13.76 fof(f22921,plain,(
% 106.73/13.76 ~spl0_8|spl0_388|~spl0_3),
% 106.73/13.76 inference(split_clause,[status(thm)],[f22920,f877,f22917,f856])).
% 106.73/13.76 fof(f23177,plain,(
% 106.73/13.76 ![X0]: (empty(empty_set)|~empty(X0))),
% 106.73/13.76 inference(paramodulation,[status(thm)],[f2221,f450])).
% 106.73/13.76 fof(f23178,plain,(
% 106.73/13.76 spl0_8|spl0_387),
% 106.73/13.76 inference(split_clause,[status(thm)],[f23177,f877,f22668])).
% 106.73/13.76 fof(f23188,plain,(
% 106.73/13.76 $false|~spl0_387),
% 106.73/13.76 inference(backward_subsumption_resolution,[status(thm)],[f443,f22669])).
% 106.73/13.76 fof(f23189,plain,(
% 106.73/13.76 ~spl0_387),
% 106.73/13.76 inference(contradiction_clause,[status(thm)],[f23188])).
% 106.73/13.76 fof(f23209,plain,(
% 106.73/13.76 spl0_399 <=> in(empty_set,empty_set)),
% 106.73/13.76 introduced(split_symbol_definition)).
% 106.73/13.76 fof(f23210,plain,(
% 106.73/13.76 in(empty_set,empty_set)|~spl0_399),
% 106.73/13.76 inference(component_clause,[status(thm)],[f23209])).
% 106.73/13.76 fof(f23225,plain,(
% 106.73/13.76 ~relation(relation_rng_restriction(sk0_55,sk0_53))|spl0_356),
% 106.73/13.76 inference(forward_demodulation,[status(thm)],[f581,f21185])).
% 106.73/13.76 fof(f23226,plain,(
% 106.73/13.76 $false|~spl0_94|spl0_356),
% 106.73/13.76 inference(forward_subsumption_resolution,[status(thm)],[f23225,f8596])).
% 106.73/13.76 fof(f23227,plain,(
% 106.73/13.76 ~spl0_94|spl0_356),
% 106.73/13.76 inference(contradiction_clause,[status(thm)],[f23226])).
% 106.73/13.76 fof(f23228,plain,(
% 106.73/13.76 ~relation(empty_set)|spl0_202),
% 106.73/13.76 inference(forward_demodulation,[status(thm)],[f602,f13901])).
% 106.73/13.76 fof(f23229,plain,(
% 106.73/13.76 $false|~spl0_4|spl0_202),
% 106.73/13.76 inference(forward_subsumption_resolution,[status(thm)],[f23228,f860])).
% 106.73/13.76 fof(f23230,plain,(
% 106.73/13.76 ~spl0_4|spl0_202),
% 106.73/13.76 inference(contradiction_clause,[status(thm)],[f23229])).
% 106.73/13.76 fof(f23231,plain,(
% 106.73/13.76 ~relation(relation_rng_restriction(sk0_55,sk0_53))|spl0_201),
% 106.73/13.76 inference(forward_demodulation,[status(thm)],[f475,f13896])).
% 106.73/13.76 fof(f23232,plain,(
% 106.73/13.76 $false|~spl0_94|spl0_201),
% 106.73/13.76 inference(forward_subsumption_resolution,[status(thm)],[f23231,f8596])).
% 106.73/13.76 fof(f23233,plain,(
% 106.73/13.76 ~spl0_94|spl0_201),
% 106.73/13.76 inference(contradiction_clause,[status(thm)],[f23232])).
% 106.73/13.76 fof(f23234,plain,(
% 106.73/13.76 ~relation(empty_set)|spl0_200),
% 106.73/13.76 inference(forward_demodulation,[status(thm)],[f2237,f13889])).
% 106.73/13.76 fof(f23235,plain,(
% 106.73/13.76 $false|~spl0_4|spl0_200),
% 106.73/13.76 inference(forward_subsumption_resolution,[status(thm)],[f23234,f860])).
% 106.73/13.76 fof(f23236,plain,(
% 106.73/13.76 ~spl0_4|spl0_200),
% 106.73/13.76 inference(contradiction_clause,[status(thm)],[f23235])).
% 106.73/13.76 fof(f23237,plain,(
% 106.73/13.76 ~relation(relation_rng_restriction(sk0_55,sk0_53))|spl0_199),
% 106.73/13.76 inference(forward_demodulation,[status(thm)],[f644,f13884])).
% 106.73/13.76 fof(f23238,plain,(
% 106.73/13.76 $false|~spl0_94|spl0_199),
% 106.73/13.76 inference(forward_subsumption_resolution,[status(thm)],[f23237,f8596])).
% 106.73/13.76 fof(f23239,plain,(
% 106.73/13.76 ~spl0_94|spl0_199),
% 106.73/13.76 inference(contradiction_clause,[status(thm)],[f23238])).
% 106.73/13.76 fof(f23240,plain,(
% 106.73/13.76 ~relation(sk0_53)|spl0_131),
% 106.73/13.76 inference(forward_demodulation,[status(thm)],[f581,f10592])).
% 106.73/13.76 fof(f23241,plain,(
% 106.73/13.76 $false|spl0_131),
% 106.73/13.76 inference(forward_subsumption_resolution,[status(thm)],[f23240,f559])).
% 106.73/13.76 fof(f23242,plain,(
% 106.73/13.76 spl0_131),
% 106.73/13.76 inference(contradiction_clause,[status(thm)],[f23241])).
% 107.32/13.80 fof(f23243,plain,(
% 107.32/13.80 ~relation(sk0_53)|spl0_130),
% 107.32/13.80 inference(forward_demodulation,[status(thm)],[f473,f10587])).
% 107.32/13.80 fof(f23244,plain,(
% 107.32/13.80 $false|spl0_130),
% 107.32/13.80 inference(forward_subsumption_resolution,[status(thm)],[f23243,f559])).
% 107.32/13.80 fof(f23245,plain,(
% 107.32/13.80 spl0_130),
% 107.32/13.80 inference(contradiction_clause,[status(thm)],[f23244])).
% 107.32/13.80 fof(f23246,plain,(
% 107.32/13.80 ~relation(sk0_53)|spl0_129),
% 107.32/13.80 inference(forward_demodulation,[status(thm)],[f2221,f10580])).
% 107.32/13.80 fof(f23247,plain,(
% 107.32/13.80 $false|spl0_129),
% 107.32/13.80 inference(forward_subsumption_resolution,[status(thm)],[f23246,f559])).
% 107.32/13.80 fof(f23248,plain,(
% 107.32/13.80 spl0_129),
% 107.32/13.80 inference(contradiction_clause,[status(thm)],[f23247])).
% 107.32/13.80 fof(f23249,plain,(
% 107.32/13.80 ~relation(relation_rng_restriction(sk0_55,sk0_53))|spl0_127),
% 107.32/13.80 inference(forward_demodulation,[status(thm)],[f473,f10448])).
% 107.32/13.80 fof(f23250,plain,(
% 107.32/13.80 $false|~spl0_94|spl0_127),
% 107.32/13.80 inference(forward_subsumption_resolution,[status(thm)],[f23249,f8596])).
% 107.32/13.80 fof(f23251,plain,(
% 107.32/13.80 ~spl0_94|spl0_127),
% 107.32/13.80 inference(contradiction_clause,[status(thm)],[f23250])).
% 107.32/13.80 fof(f23252,plain,(
% 107.32/13.80 $false|~spl0_90),
% 107.32/13.80 inference(forward_subsumption_resolution,[status(thm)],[f8165,f3751])).
% 107.32/13.80 fof(f23253,plain,(
% 107.32/13.80 ~spl0_90),
% 107.32/13.80 inference(contradiction_clause,[status(thm)],[f23252])).
% 107.32/13.80 fof(f23254,plain,(
% 107.32/13.80 $false|~spl0_399),
% 107.32/13.80 inference(forward_subsumption_resolution,[status(thm)],[f23210,f817])).
% 107.32/13.80 fof(f23255,plain,(
% 107.32/13.80 ~spl0_399),
% 107.32/13.80 inference(contradiction_clause,[status(thm)],[f23254])).
% 107.32/13.80 fof(f23275,plain,(
% 107.32/13.80 in(sk0_54,empty_set)|~relation(empty_set)|~spl0_363),
% 107.32/13.80 inference(paramodulation,[status(thm)],[f702,f22282])).
% 107.32/13.80 fof(f23276,plain,(
% 107.32/13.80 spl0_98|~spl0_4|~spl0_363),
% 107.32/13.80 inference(split_clause,[status(thm)],[f23275,f8680,f859,f22281])).
% 107.32/13.80 fof(f23760,plain,(
% 107.32/13.80 ~relation(sk0_53)|in(sk0_54,sk0_55)|~spl0_0),
% 107.32/13.80 inference(resolution,[status(thm)],[f13367,f788])).
% 107.32/13.80 fof(f23761,plain,(
% 107.32/13.80 ~spl0_97|spl0_1|~spl0_0),
% 107.32/13.80 inference(split_clause,[status(thm)],[f23760,f8665,f790,f787])).
% 107.32/13.80 fof(f23831,plain,(
% 107.32/13.80 $false),
% 107.32/13.80 inference(sat_refutation,[status(thm)],[f793,f797,f798,f863,f868,f887,f896,f1952,f1965,f1970,f1988,f2372,f2392,f2971,f2979,f2994,f3002,f3019,f3032,f3046,f3056,f3102,f3134,f3149,f3162,f3244,f3444,f3449,f3454,f3463,f3468,f3547,f3559,f3585,f3756,f4091,f4114,f4153,f4176,f4231,f4236,f4242,f4358,f4365,f4458,f4466,f4476,f4696,f4710,f5172,f5196,f5224,f5272,f5286,f5330,f5335,f5348,f5353,f5358,f5363,f5368,f5373,f5378,f5383,f5388,f5393,f5398,f6330,f6561,f6590,f6723,f7822,f7852,f7884,f8182,f8194,f8385,f8599,f8656,f8659,f8673,f8716,f8726,f8775,f9097,f9705,f9768,f9775,f9808,f10172,f10180,f10330,f10537,f11152,f11301,f11316,f11544,f11549,f11554,f11559,f11623,f11757,f13394,f13407,f13921,f14878,f14894,f14901,f14911,f17046,f17115,f17122,f17411,f17435,f17496,f18011,f18116,f18478,f18496,f20545,f20788,f20848,f22921,f23178,f23189,f23227,f23230,f23233,f23236,f23239,f23242,f23245,f23248,f23251,f23253,f23255,f23276,f23761])).
% 107.32/13.80 % SZS output end CNFRefutation for theBenchmark.p
% 108.03/13.88 % Elapsed time: 13.587561 seconds
% 108.03/13.88 % CPU time: 107.839215 seconds
% 108.03/13.88 % Memory used: 691.741 MB
%------------------------------------------------------------------------------