%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SEU239+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:22:06 PM UTC 2026
% Result : Theorem 3.39s 0.88s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU239+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n001.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 06:07:58 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.14/0.38 % Drodi V4.1.1
% 3.39/0.88 % Refutation found
% 3.39/0.88 % SZS status Theorem for theBenchmark: Theorem is valid
% 3.39/0.88 % SZS output start CNFRefutation for theBenchmark
% 3.39/0.88 fof(f1,axiom,(
% 3.39/0.88 (! [A,B] :( in(A,B)=> ~ in(B,A) ) )),
% 3.39/0.88 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.39/0.88 fof(f3,axiom,(
% 3.39/0.88 (! [A] :( empty(A)=> function(A) ) )),
% 3.39/0.88 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.39/0.88 fof(f5,axiom,(
% 3.39/0.88 (! [A] :( empty(A)=> relation(A) ) )),
% 3.39/0.88 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.39/0.88 fof(f6,axiom,(
% 3.39/0.88 (! [A] :( ( relation(A)& empty(A)& function(A) )=> ( relation(A)& function(A)& one_to_one(A) ) ) )),
% 3.39/0.88 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.39/0.88 fof(f7,axiom,(
% 3.39/0.88 (! [A] :( ( epsilon_transitive(A)& epsilon_connected(A) )=> ordinal(A) ) )),
% 3.39/0.88 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.39/0.88 fof(f8,axiom,(
% 3.39/0.88 (! [A] :( empty(A)=> ( epsilon_transitive(A)& epsilon_connected(A)& ordinal(A) ) ) )),
% 3.39/0.88 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.39/0.88 fof(f10,axiom,(
% 3.39/0.88 (! [A,B] : set_union2(A,B) = set_union2(B,A) )),
% 3.39/0.88 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.39/0.88 fof(f13,axiom,(
% 3.39/0.88 (! [A,B] :( relation(B)=> ( B = identity_relation(A)<=> (! [C,D] :( in(ordered_pair(C,D),B)<=> ( in(C,A)& C = D ) ) )) ) )),
% 3.39/0.88 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.39/0.88 fof(f18,axiom,(
% 3.39/0.88 (! [A] :( ( relation(A)& function(A) )=> (! [B,C] :( C = relation_inverse_image(A,B)<=> (! [D] :( in(D,C)<=> ( in(D,relation_dom(A))& in(apply(A,D),B) ) ) )) )) )),
% 3.39/0.88 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.39/0.88 fof(f19,axiom,(
% 3.39/0.88 (! [A] :( relation(A)=> (! [B,C] :( C = relation_image(A,B)<=> (! [D] :( in(D,C)<=> (? [E] :( in(ordered_pair(E,D),A)& in(E,B) ) )) )) )) )),
% 3.39/0.88 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.39/0.88 fof(f20,axiom,(
% 3.39/0.88 (! [A] :( relation(A)=> (! [B,C] :( C = relation_inverse_image(A,B)<=> (! [D] :( in(D,C)<=> (? [E] :( in(ordered_pair(D,E),A)& in(E,B) ) )) )) )) )),
% 3.39/0.88 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.39/0.88 fof(f22,axiom,(
% 3.39/0.88 (! [A] : succ(A) = set_union2(A,singleton(A)) )),
% 3.39/0.88 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.39/0.88 fof(f24,axiom,(
% 3.39/0.88 (! [A] :( relation(A)=> (! [B] :( is_reflexive_in(A,B)<=> (! [C] :( in(C,B)=> in(ordered_pair(C,C),A) ) )) )) )),
% 3.39/0.88 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.39/0.88 fof(f25,axiom,(
% 3.39/0.88 (! [A,B] :( ( A != empty_set=> ( B = set_meet(A)<=> (! [C] :( in(C,B)<=> (! [D] :( in(D,A)=> in(C,D) ) )) )) )& ( A = empty_set=> ( B = set_meet(A)<=> B = empty_set ) ) ) )),
% 3.39/0.88 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.39/0.88 fof(f26,axiom,(
% 3.39/0.88 (! [A,B] :( B = singleton(A)<=> (! [C] :( in(C,B)<=> C = A ) )) )),
% 3.39/0.88 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.39/0.88 fof(f27,axiom,(
% 3.39/0.88 (! [A] :( A = empty_set<=> (! [B] : ~ in(B,A) )) )),
% 3.39/0.88 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.39/0.88 fof(f31,axiom,(
% 3.39/0.88 (! [A,B] :( ( ~ empty(A)=> ( element(B,A)<=> in(B,A) ) )& ( empty(A)=> ( element(B,A)<=> empty(B) ) ) ) )),
% 3.39/0.88 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.39/0.88 fof(f50,axiom,(
% 3.39/0.88 (! [A] :( relation(A)=> relation_field(A) = set_union2(relation_dom(A),relation_rng(A)) ) )),
% 3.39/0.88 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.39/0.88 fof(f58,axiom,(
% 3.39/0.88 (! [A] :( relation(A)=> ( reflexive(A)<=> is_reflexive_in(A,relation_field(A)) ) ) )),
% 3.39/0.88 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.39/0.88 fof(f91,axiom,(
% 3.39/0.88 (! [A] :(? [B] : element(B,A) ))),
% 3.39/0.88 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.39/0.88 fof(f93,axiom,(
% 3.39/0.88 (! [A] :( empty(A)=> ( empty(relation_inverse(A))& relation(relation_inverse(A)) ) ) )),
% 3.39/0.88 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.39/0.88 fof(f94,axiom,(
% 3.39/0.88 ( empty(empty_set)& relation(empty_set)& relation_empty_yielding(empty_set) ) ),
% 3.39/0.88 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.39/0.88 fof(f103,axiom,(
% 3.39/0.88 ( relation(empty_set)& relation_empty_yielding(empty_set)& function(empty_set)& one_to_one(empty_set)& empty(empty_set)& epsilon_transitive(empty_set)& epsilon_connected(empty_set)& ordinal(empty_set) ) ),
% 3.39/0.88 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.39/0.88 fof(f108,axiom,(
% 3.39/0.88 (! [A] :( ordinal(A)=> ( ~ empty(succ(A))& epsilon_transitive(succ(A))& epsilon_connected(succ(A))& ordinal(succ(A)) ) ) )),
% 3.39/0.88 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.39/0.88 fof(f113,axiom,(
% 3.39/0.88 (! [A] :( ordinal(A)=> ( epsilon_transitive(union(A))& epsilon_connected(union(A))& ordinal(union(A)) ) ) )),
% 3.39/0.88 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.39/0.88 fof(f127,conjecture,(
% 3.39/0.88 (! [A] :( relation(A)=> ( reflexive(A)<=> (! [B] :( in(B,relation_field(A))=> in(ordered_pair(B,B),A) ) )) ) )),
% 3.39/0.88 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.39/0.88 fof(f128,negated_conjecture,(
% 3.39/0.88 ~((! [A] :( relation(A)=> ( reflexive(A)<=> (! [B] :( in(B,relation_field(A))=> in(ordered_pair(B,B),A) ) )) ) ))),
% 3.39/0.88 inference(negated_conjecture,[status(cth)],[f127])).
% 3.39/0.88 fof(f129,lemma,(
% 3.39/0.88 (! [A] : singleton(A) != empty_set )),
% 3.39/0.88 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.39/0.88 fof(f142,axiom,(
% 3.39/0.88 (? [A] :( relation(A)& function(A) ) )),
% 3.39/0.88 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.39/0.88 fof(f143,axiom,(
% 3.39/0.88 (? [A] :( epsilon_transitive(A)& epsilon_connected(A)& ordinal(A) ) )),
% 3.39/0.88 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.39/0.88 fof(f144,axiom,(
% 3.39/0.88 (? [A] :( empty(A)& relation(A) ) )),
% 3.39/0.88 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.39/0.88 fof(f146,axiom,(
% 3.39/0.88 (? [A] : empty(A) )),
% 3.39/0.88 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.39/0.88 fof(f147,axiom,(
% 3.39/0.88 (? [A] :( relation(A)& empty(A)& function(A) ) )),
% 3.39/0.88 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.39/0.88 fof(f148,axiom,(
% 3.39/0.88 (? [A] :( relation(A)& function(A)& one_to_one(A)& empty(A)& epsilon_transitive(A)& epsilon_connected(A)& ordinal(A) ) )),
% 3.39/0.88 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.39/0.88 fof(f152,axiom,(
% 3.39/0.88 (? [A] :( relation(A)& function(A)& one_to_one(A) ) )),
% 3.39/0.88 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.39/0.88 fof(f153,axiom,(
% 3.39/0.88 (? [A] :( ~ empty(A)& epsilon_transitive(A)& epsilon_connected(A)& ordinal(A) ) )),
% 3.39/0.88 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.39/0.88 fof(f155,axiom,(
% 3.39/0.88 (? [A] :( relation(A)& relation_empty_yielding(A)& function(A) ) )),
% 3.39/0.88 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.39/0.88 fof(f190,axiom,(
% 3.39/0.88 (! [A] : set_union2(A,empty_set) = A )),
% 3.39/0.88 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.39/0.88 fof(f193,lemma,(
% 3.39/0.88 powerset(empty_set) = singleton(empty_set) ),
% 3.39/0.88 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.39/0.88 fof(f209,lemma,(
% 3.39/0.88 (! [A,B,C] :( relation(C)=> ( in(ordered_pair(A,B),C)=> ( in(A,relation_field(C))& in(B,relation_field(C)) ) ) ) )),
% 3.39/0.88 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.39/0.88 fof(f262,axiom,(
% 3.39/0.88 (! [A] :( empty(A)=> A = empty_set ) )),
% 3.39/0.88 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.39/0.88 fof(f265,lemma,(
% 3.39/0.88 (! [A] :( relation_dom(identity_relation(A)) = A& relation_rng(identity_relation(A)) = A ) )),
% 3.39/0.88 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.39/0.88 fof(f282,lemma,(
% 3.39/0.88 (! [A] : union(powerset(A)) = A )),
% 3.39/0.88 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.39/0.88 fof(f285,plain,(
% 3.39/0.88 ![A,B]: (~in(A,B)|~in(B,A))),
% 3.39/0.88 inference(pre_NNF_transformation,[status(thm)],[f1])).
% 3.39/0.88 fof(f286,plain,(
% 3.39/0.88 ![X0,X1]: (~in(X0,X1)|~in(X1,X0))),
% 3.39/0.88 inference(cnf_transformation,[status(thm)],[f285])).
% 3.39/0.88 fof(f289,plain,(
% 3.39/0.88 ![A]: (~empty(A)|function(A))),
% 3.39/0.88 inference(pre_NNF_transformation,[status(thm)],[f3])).
% 3.39/0.88 fof(f290,plain,(
% 3.39/0.88 ![X0]: (~empty(X0)|function(X0))),
% 3.39/0.88 inference(cnf_transformation,[status(thm)],[f289])).
% 3.39/0.88 fof(f294,plain,(
% 3.39/0.88 ![A]: (~empty(A)|relation(A))),
% 3.39/0.88 inference(pre_NNF_transformation,[status(thm)],[f5])).
% 3.39/0.88 fof(f295,plain,(
% 3.39/0.88 ![X0]: (~empty(X0)|relation(X0))),
% 3.39/0.88 inference(cnf_transformation,[status(thm)],[f294])).
% 3.39/0.88 fof(f296,plain,(
% 3.39/0.88 ![A]: (((~relation(A)|~empty(A))|~function(A))|((relation(A)&function(A))&one_to_one(A)))),
% 3.39/0.88 inference(pre_NNF_transformation,[status(thm)],[f6])).
% 3.39/0.88 fof(f299,plain,(
% 3.39/0.88 ![X0]: (~relation(X0)|~empty(X0)|~function(X0)|one_to_one(X0))),
% 3.39/0.88 inference(cnf_transformation,[status(thm)],[f296])).
% 3.39/0.88 fof(f300,plain,(
% 3.39/0.88 ![A]: ((~epsilon_transitive(A)|~epsilon_connected(A))|ordinal(A))),
% 3.39/0.88 inference(pre_NNF_transformation,[status(thm)],[f7])).
% 3.39/0.88 fof(f301,plain,(
% 3.39/0.88 ![X0]: (~epsilon_transitive(X0)|~epsilon_connected(X0)|ordinal(X0))),
% 3.39/0.88 inference(cnf_transformation,[status(thm)],[f300])).
% 3.39/0.88 fof(f302,plain,(
% 3.39/0.88 ![A]: (~empty(A)|((epsilon_transitive(A)&epsilon_connected(A))&ordinal(A)))),
% 3.39/0.88 inference(pre_NNF_transformation,[status(thm)],[f8])).
% 3.39/0.88 fof(f303,plain,(
% 3.39/0.88 ![X0]: (~empty(X0)|epsilon_transitive(X0))),
% 3.39/0.88 inference(cnf_transformation,[status(thm)],[f302])).
% 3.39/0.88 fof(f304,plain,(
% 3.39/0.88 ![X0]: (~empty(X0)|epsilon_connected(X0))),
% 3.39/0.88 inference(cnf_transformation,[status(thm)],[f302])).
% 3.39/0.88 fof(f307,plain,(
% 3.39/0.88 ![X0,X1]: (set_union2(X0,X1)=set_union2(X1,X0))),
% 3.39/0.88 inference(cnf_transformation,[status(thm)],[f10])).
% 3.39/0.88 fof(f311,plain,(
% 3.39/0.88 ![A,B]: (~relation(B)|(B=identity_relation(A)<=>(![C,D]: (in(ordered_pair(C,D),B)<=>(in(C,A)&C=D)))))),
% 3.39/0.88 inference(pre_NNF_transformation,[status(thm)],[f13])).
% 3.39/0.88 fof(f312,plain,(
% 3.39/0.88 ![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)))))))),
% 3.39/0.88 inference(NNF_transformation,[status(thm)],[f311])).
% 3.39/0.88 fof(f313,plain,(
% 3.39/0.88 ![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))))))))),
% 3.39/0.88 inference(miniscoping,[status(thm)],[f312])).
% 3.39/0.88 fof(f314,plain,(
% 3.39/0.88 ![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_skl(A,B),sK1_skl(A,B)),B)|(~in(sK0_skl(A,B),A)|~sK0_skl(A,B)=sK1_skl(A,B)))&(in(ordered_pair(sK0_skl(A,B),sK1_skl(A,B)),B)|(in(sK0_skl(A,B),A)&sK0_skl(A,B)=sK1_skl(A,B))))))))),
% 3.39/0.88 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(C,sK0_skl(A,B)),skolemize(D,sK1_skl(A,B))],[f313])).
% 3.39/0.88 fof(f319,plain,(
% 3.39/0.88 ![X0,X1]: (~relation(X0)|X0=identity_relation(X1)|in(ordered_pair(sK0_skl(X1,X0),sK1_skl(X1,X0)),X0)|in(sK0_skl(X1,X0),X1))),
% 3.39/0.88 inference(cnf_transformation,[status(thm)],[f314])).
% 3.39/0.88 fof(f356,plain,(
% 3.39/0.88 ![A]: ((~relation(A)|~function(A))|(![B,C]: (C=relation_inverse_image(A,B)<=>(![D]: (in(D,C)<=>(in(D,relation_dom(A))&in(apply(A,D),B)))))))),
% 3.39/0.88 inference(pre_NNF_transformation,[status(thm)],[f18])).
% 3.39/0.88 fof(f357,plain,(
% 3.39/0.88 ![A]: ((~relation(A)|~function(A))|(![B,C]: ((~C=relation_inverse_image(A,B)|(![D]: ((~in(D,C)|(in(D,relation_dom(A))&in(apply(A,D),B)))&(in(D,C)|(~in(D,relation_dom(A))|~in(apply(A,D),B))))))&(C=relation_inverse_image(A,B)|(?[D]: ((~in(D,C)|(~in(D,relation_dom(A))|~in(apply(A,D),B)))&(in(D,C)|(in(D,relation_dom(A))&in(apply(A,D),B)))))))))),
% 3.39/0.88 inference(NNF_transformation,[status(thm)],[f356])).
% 3.39/0.88 fof(f358,plain,(
% 3.39/0.88 ![A]: ((~relation(A)|~function(A))|((![B,C]: (~C=relation_inverse_image(A,B)|((![D]: (~in(D,C)|(in(D,relation_dom(A))&in(apply(A,D),B))))&(![D]: (in(D,C)|(~in(D,relation_dom(A))|~in(apply(A,D),B)))))))&(![B,C]: (C=relation_inverse_image(A,B)|(?[D]: ((~in(D,C)|(~in(D,relation_dom(A))|~in(apply(A,D),B)))&(in(D,C)|(in(D,relation_dom(A))&in(apply(A,D),B)))))))))),
% 3.39/0.88 inference(miniscoping,[status(thm)],[f357])).
% 3.39/0.88 fof(f359,plain,(
% 3.39/0.88 ![A]: ((~relation(A)|~function(A))|((![B,C]: (~C=relation_inverse_image(A,B)|((![D]: (~in(D,C)|(in(D,relation_dom(A))&in(apply(A,D),B))))&(![D]: (in(D,C)|(~in(D,relation_dom(A))|~in(apply(A,D),B)))))))&(![B,C]: (C=relation_inverse_image(A,B)|((~in(sK9_skl(C,B,A),C)|(~in(sK9_skl(C,B,A),relation_dom(A))|~in(apply(A,sK9_skl(C,B,A)),B)))&(in(sK9_skl(C,B,A),C)|(in(sK9_skl(C,B,A),relation_dom(A))&in(apply(A,sK9_skl(C,B,A)),B))))))))),
% 3.39/0.88 inference(skolemize,[status(esa),new_symbols(skolem,[sK9_skl]),skolemize(D,sK9_skl(C,B,A))],[f358])).
% 3.39/0.88 fof(f364,plain,(
% 3.39/0.88 ![X0,X1,X2]: (~relation(X0)|~function(X0)|X1=relation_inverse_image(X0,X2)|in(sK9_skl(X1,X2,X0),X1)|in(sK9_skl(X1,X2,X0),relation_dom(X0)))),
% 3.39/0.88 inference(cnf_transformation,[status(thm)],[f359])).
% 3.39/0.88 fof(f365,plain,(
% 3.39/0.88 ![X0,X1,X2]: (~relation(X0)|~function(X0)|X1=relation_inverse_image(X0,X2)|in(sK9_skl(X1,X2,X0),X1)|in(apply(X0,sK9_skl(X1,X2,X0)),X2))),
% 3.39/0.88 inference(cnf_transformation,[status(thm)],[f359])).
% 3.39/0.88 fof(f366,plain,(
% 3.39/0.88 ![A]: (~relation(A)|(![B,C]: (C=relation_image(A,B)<=>(![D]: (in(D,C)<=>(?[E]: (in(ordered_pair(E,D),A)&in(E,B))))))))),
% 3.39/0.88 inference(pre_NNF_transformation,[status(thm)],[f19])).
% 3.39/0.88 fof(f367,plain,(
% 3.39/0.88 ![A]: (~relation(A)|(![B,C]: ((~C=relation_image(A,B)|(![D]: ((~in(D,C)|(?[E]: (in(ordered_pair(E,D),A)&in(E,B))))&(in(D,C)|(![E]: (~in(ordered_pair(E,D),A)|~in(E,B)))))))&(C=relation_image(A,B)|(?[D]: ((~in(D,C)|(![E]: (~in(ordered_pair(E,D),A)|~in(E,B))))&(in(D,C)|(?[E]: (in(ordered_pair(E,D),A)&in(E,B))))))))))),
% 3.39/0.88 inference(NNF_transformation,[status(thm)],[f366])).
% 3.39/0.88 fof(f368,plain,(
% 3.39/0.88 ![A]: (~relation(A)|((![B,C]: (~C=relation_image(A,B)|((![D]: (~in(D,C)|(?[E]: (in(ordered_pair(E,D),A)&in(E,B)))))&(![D]: (in(D,C)|(![E]: (~in(ordered_pair(E,D),A)|~in(E,B))))))))&(![B,C]: (C=relation_image(A,B)|(?[D]: ((~in(D,C)|(![E]: (~in(ordered_pair(E,D),A)|~in(E,B))))&(in(D,C)|(?[E]: (in(ordered_pair(E,D),A)&in(E,B))))))))))),
% 3.39/0.88 inference(miniscoping,[status(thm)],[f367])).
% 3.39/0.88 fof(f369,plain,(
% 3.39/0.88 ![A]: (~relation(A)|((![B,C]: (~C=relation_image(A,B)|((![D]: (~in(D,C)|(in(ordered_pair(sK10_skl(D,C,B,A),D),A)&in(sK10_skl(D,C,B,A),B))))&(![D]: (in(D,C)|(![E]: (~in(ordered_pair(E,D),A)|~in(E,B))))))))&(![B,C]: (C=relation_image(A,B)|((~in(sK11_skl(C,B,A),C)|(![E]: (~in(ordered_pair(E,sK11_skl(C,B,A)),A)|~in(E,B))))&(in(sK11_skl(C,B,A),C)|(in(ordered_pair(sK12_skl(C,B,A),sK11_skl(C,B,A)),A)&in(sK12_skl(C,B,A),B))))))))),
% 3.39/0.88 inference(skolemize,[status(esa),new_symbols(skolem,[sK10_skl,sK11_skl,sK12_skl]),skolemize(E,sK10_skl(D,C,B,A)),skolemize(D,sK11_skl(C,B,A)),skolemize(E,sK12_skl(C,B,A))],[f368])).
% 3.39/0.88 fof(f373,plain,(
% 3.39/0.88 ![X0,X1,X2,X3]: (~relation(X0)|X1=relation_image(X0,X2)|~in(sK11_skl(X1,X2,X0),X1)|~in(ordered_pair(X3,sK11_skl(X1,X2,X0)),X0)|~in(X3,X2))),
% 3.39/0.88 inference(cnf_transformation,[status(thm)],[f369])).
% 3.39/0.88 fof(f375,plain,(
% 3.39/0.88 ![X0,X1,X2]: (~relation(X0)|X1=relation_image(X0,X2)|in(sK11_skl(X1,X2,X0),X1)|in(sK12_skl(X1,X2,X0),X2))),
% 3.39/0.88 inference(cnf_transformation,[status(thm)],[f369])).
% 3.39/0.88 fof(f376,plain,(
% 3.39/0.88 ![A]: (~relation(A)|(![B,C]: (C=relation_inverse_image(A,B)<=>(![D]: (in(D,C)<=>(?[E]: (in(ordered_pair(D,E),A)&in(E,B))))))))),
% 3.39/0.88 inference(pre_NNF_transformation,[status(thm)],[f20])).
% 3.39/0.88 fof(f377,plain,(
% 3.39/0.88 ![A]: (~relation(A)|(![B,C]: ((~C=relation_inverse_image(A,B)|(![D]: ((~in(D,C)|(?[E]: (in(ordered_pair(D,E),A)&in(E,B))))&(in(D,C)|(![E]: (~in(ordered_pair(D,E),A)|~in(E,B)))))))&(C=relation_inverse_image(A,B)|(?[D]: ((~in(D,C)|(![E]: (~in(ordered_pair(D,E),A)|~in(E,B))))&(in(D,C)|(?[E]: (in(ordered_pair(D,E),A)&in(E,B))))))))))),
% 3.39/0.88 inference(NNF_transformation,[status(thm)],[f376])).
% 3.39/0.88 fof(f378,plain,(
% 3.39/0.88 ![A]: (~relation(A)|((![B,C]: (~C=relation_inverse_image(A,B)|((![D]: (~in(D,C)|(?[E]: (in(ordered_pair(D,E),A)&in(E,B)))))&(![D]: (in(D,C)|(![E]: (~in(ordered_pair(D,E),A)|~in(E,B))))))))&(![B,C]: (C=relation_inverse_image(A,B)|(?[D]: ((~in(D,C)|(![E]: (~in(ordered_pair(D,E),A)|~in(E,B))))&(in(D,C)|(?[E]: (in(ordered_pair(D,E),A)&in(E,B))))))))))),
% 3.39/0.88 inference(miniscoping,[status(thm)],[f377])).
% 3.39/0.88 fof(f379,plain,(
% 3.39/0.88 ![A]: (~relation(A)|((![B,C]: (~C=relation_inverse_image(A,B)|((![D]: (~in(D,C)|(in(ordered_pair(D,sK13_skl(D,C,B,A)),A)&in(sK13_skl(D,C,B,A),B))))&(![D]: (in(D,C)|(![E]: (~in(ordered_pair(D,E),A)|~in(E,B))))))))&(![B,C]: (C=relation_inverse_image(A,B)|((~in(sK14_skl(C,B,A),C)|(![E]: (~in(ordered_pair(sK14_skl(C,B,A),E),A)|~in(E,B))))&(in(sK14_skl(C,B,A),C)|(in(ordered_pair(sK14_skl(C,B,A),sK15_skl(C,B,A)),A)&in(sK15_skl(C,B,A),B))))))))),
% 3.39/0.88 inference(skolemize,[status(esa),new_symbols(skolem,[sK13_skl,sK14_skl,sK15_skl]),skolemize(E,sK13_skl(D,C,B,A)),skolemize(D,sK14_skl(C,B,A)),skolemize(E,sK15_skl(C,B,A))],[f378])).
% 3.39/0.88 fof(f383,plain,(
% 3.39/0.88 ![X0,X1,X2,X3]: (~relation(X0)|X1=relation_inverse_image(X0,X2)|~in(sK14_skl(X1,X2,X0),X1)|~in(ordered_pair(sK14_skl(X1,X2,X0),X3),X0)|~in(X3,X2))),
% 3.39/0.88 inference(cnf_transformation,[status(thm)],[f379])).
% 3.39/0.88 fof(f385,plain,(
% 3.39/0.88 ![X0,X1,X2]: (~relation(X0)|X1=relation_inverse_image(X0,X2)|in(sK14_skl(X1,X2,X0),X1)|in(sK15_skl(X1,X2,X0),X2))),
% 3.39/0.88 inference(cnf_transformation,[status(thm)],[f379])).
% 3.39/0.88 fof(f396,plain,(
% 3.39/0.88 ![X0]: (succ(X0)=set_union2(X0,singleton(X0)))),
% 3.39/0.88 inference(cnf_transformation,[status(thm)],[f22])).
% 3.39/0.88 fof(f404,plain,(
% 3.39/0.88 ![A]: (~relation(A)|(![B]: (is_reflexive_in(A,B)<=>(![C]: (~in(C,B)|in(ordered_pair(C,C),A))))))),
% 3.39/0.88 inference(pre_NNF_transformation,[status(thm)],[f24])).
% 3.39/0.88 fof(f405,plain,(
% 3.39/0.88 ![A]: (~relation(A)|(![B]: ((~is_reflexive_in(A,B)|(![C]: (~in(C,B)|in(ordered_pair(C,C),A))))&(is_reflexive_in(A,B)|(?[C]: (in(C,B)&~in(ordered_pair(C,C),A)))))))),
% 3.39/0.88 inference(NNF_transformation,[status(thm)],[f404])).
% 3.39/0.88 fof(f406,plain,(
% 3.39/0.88 ![A]: (~relation(A)|((![B]: (~is_reflexive_in(A,B)|(![C]: (~in(C,B)|in(ordered_pair(C,C),A)))))&(![B]: (is_reflexive_in(A,B)|(?[C]: (in(C,B)&~in(ordered_pair(C,C),A)))))))),
% 3.39/0.88 inference(miniscoping,[status(thm)],[f405])).
% 3.39/0.88 fof(f407,plain,(
% 3.39/0.88 ![A]: (~relation(A)|((![B]: (~is_reflexive_in(A,B)|(![C]: (~in(C,B)|in(ordered_pair(C,C),A)))))&(![B]: (is_reflexive_in(A,B)|(in(sK20_skl(B,A),B)&~in(ordered_pair(sK20_skl(B,A),sK20_skl(B,A)),A))))))),
% 3.39/0.88 inference(skolemize,[status(esa),new_symbols(skolem,[sK20_skl]),skolemize(C,sK20_skl(B,A))],[f406])).
% 3.39/0.88 fof(f408,plain,(
% 3.39/0.88 ![X0,X1,X2]: (~relation(X0)|~is_reflexive_in(X0,X1)|~in(X2,X1)|in(ordered_pair(X2,X2),X0))),
% 3.39/0.88 inference(cnf_transformation,[status(thm)],[f407])).
% 3.39/0.88 fof(f409,plain,(
% 3.39/0.88 ![X0,X1]: (~relation(X0)|is_reflexive_in(X0,X1)|in(sK20_skl(X1,X0),X1))),
% 3.39/0.88 inference(cnf_transformation,[status(thm)],[f407])).
% 3.39/0.88 fof(f410,plain,(
% 3.39/0.88 ![X0,X1]: (~relation(X0)|is_reflexive_in(X0,X1)|~in(ordered_pair(sK20_skl(X1,X0),sK20_skl(X1,X0)),X0))),
% 3.39/0.88 inference(cnf_transformation,[status(thm)],[f407])).
% 3.39/0.88 fof(f411,plain,(
% 3.39/0.88 ![A,B]: ((A=empty_set|(B=set_meet(A)<=>(![C]: (in(C,B)<=>(![D]: (~in(D,A)|in(C,D)))))))&(~A=empty_set|(B=set_meet(A)<=>B=empty_set)))),
% 3.39/0.88 inference(pre_NNF_transformation,[status(thm)],[f25])).
% 3.39/0.88 fof(f412,plain,(
% 3.39/0.88 ![A,B]: ((A=empty_set|((~B=set_meet(A)|(![C]: ((~in(C,B)|(![D]: (~in(D,A)|in(C,D))))&(in(C,B)|(?[D]: (in(D,A)&~in(C,D)))))))&(B=set_meet(A)|(?[C]: ((~in(C,B)|(?[D]: (in(D,A)&~in(C,D))))&(in(C,B)|(![D]: (~in(D,A)|in(C,D)))))))))&(~A=empty_set|((~B=set_meet(A)|B=empty_set)&(B=set_meet(A)|~B=empty_set))))),
% 3.39/0.88 inference(NNF_transformation,[status(thm)],[f411])).
% 3.39/0.88 fof(f413,plain,(
% 3.39/0.88 (![A]: (A=empty_set|((![B]: (~B=set_meet(A)|((![C]: (~in(C,B)|(![D]: (~in(D,A)|in(C,D)))))&(![C]: (in(C,B)|(?[D]: (in(D,A)&~in(C,D))))))))&(![B]: (B=set_meet(A)|(?[C]: ((~in(C,B)|(?[D]: (in(D,A)&~in(C,D))))&(in(C,B)|(![D]: (~in(D,A)|in(C,D)))))))))))&(![A]: (~A=empty_set|((![B]: (~B=set_meet(A)|B=empty_set))&(![B]: (B=set_meet(A)|~B=empty_set)))))),
% 3.39/0.88 inference(miniscoping,[status(thm)],[f412])).
% 3.39/0.88 fof(f414,plain,(
% 3.39/0.88 (![A]: (A=empty_set|((![B]: (~B=set_meet(A)|((![C]: (~in(C,B)|(![D]: (~in(D,A)|in(C,D)))))&(![C]: (in(C,B)|(in(sK21_skl(C,B,A),A)&~in(C,sK21_skl(C,B,A))))))))&(![B]: (B=set_meet(A)|((~in(sK22_skl(B,A),B)|(in(sK23_skl(B,A),A)&~in(sK22_skl(B,A),sK23_skl(B,A))))&(in(sK22_skl(B,A),B)|(![D]: (~in(D,A)|in(sK22_skl(B,A),D))))))))))&(![A]: (~A=empty_set|((![B]: (~B=set_meet(A)|B=empty_set))&(![B]: (B=set_meet(A)|~B=empty_set)))))),
% 3.39/0.88 inference(skolemize,[status(esa),new_symbols(skolem,[sK21_skl,sK22_skl,sK23_skl]),skolemize(D,sK21_skl(C,B,A)),skolemize(C,sK22_skl(B,A)),skolemize(D,sK23_skl(B,A))],[f413])).
% 3.39/0.88 fof(f420,plain,(
% 3.39/0.88 ![X0,X1,X2]: (X0=empty_set|X1=set_meet(X0)|in(sK22_skl(X1,X0),X1)|~in(X2,X0)|in(sK22_skl(X1,X0),X2))),
% 3.39/0.88 inference(cnf_transformation,[status(thm)],[f414])).
% 3.39/0.88 fof(f423,plain,(
% 3.39/0.88 ![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)))))),
% 3.39/0.88 inference(NNF_transformation,[status(thm)],[f26])).
% 3.39/0.88 fof(f424,plain,(
% 3.39/0.88 (![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)))))),
% 3.39/0.88 inference(miniscoping,[status(thm)],[f423])).
% 3.39/0.88 fof(f425,plain,(
% 3.39/0.88 (![A,B]: (~B=singleton(A)|((![C]: (~in(C,B)|C=A))&(![C]: (in(C,B)|~C=A)))))&(![A,B]: (B=singleton(A)|((~in(sK24_skl(B,A),B)|~sK24_skl(B,A)=A)&(in(sK24_skl(B,A),B)|sK24_skl(B,A)=A))))),
% 3.39/0.88 inference(skolemize,[status(esa),new_symbols(skolem,[sK24_skl]),skolemize(C,sK24_skl(B,A))],[f424])).
% 3.39/0.88 fof(f426,plain,(
% 3.39/0.88 ![X0,X1,X2]: (~X0=singleton(X1)|~in(X2,X0)|X2=X1)),
% 3.39/0.88 inference(cnf_transformation,[status(thm)],[f425])).
% 3.39/0.88 fof(f430,plain,(
% 3.39/0.88 ![A]: ((~A=empty_set|(![B]: ~in(B,A)))&(A=empty_set|(?[B]: in(B,A))))),
% 3.39/0.88 inference(NNF_transformation,[status(thm)],[f27])).
% 3.39/0.88 fof(f431,plain,(
% 3.39/0.88 (![A]: (~A=empty_set|(![B]: ~in(B,A))))&(![A]: (A=empty_set|(?[B]: in(B,A))))),
% 3.39/0.88 inference(miniscoping,[status(thm)],[f430])).
% 3.39/0.88 fof(f432,plain,(
% 3.39/0.88 (![A]: (~A=empty_set|(![B]: ~in(B,A))))&(![A]: (A=empty_set|in(sK25_skl(A),A)))),
% 3.39/0.88 inference(skolemize,[status(esa),new_symbols(skolem,[sK25_skl]),skolemize(B,sK25_skl(A))],[f431])).
% 3.39/0.88 fof(f433,plain,(
% 3.39/0.88 ![X0,X1]: (~X0=empty_set|~in(X1,X0))),
% 3.39/0.88 inference(cnf_transformation,[status(thm)],[f432])).
% 3.39/0.88 fof(f434,plain,(
% 3.39/0.88 ![X0]: (X0=empty_set|in(sK25_skl(X0),X0))),
% 3.39/0.88 inference(cnf_transformation,[status(thm)],[f432])).
% 3.39/0.88 fof(f457,plain,(
% 3.39/0.88 ![A,B]: ((empty(A)|(element(B,A)<=>in(B,A)))&(~empty(A)|(element(B,A)<=>empty(B))))),
% 3.39/0.88 inference(pre_NNF_transformation,[status(thm)],[f31])).
% 3.39/0.88 fof(f458,plain,(
% 3.39/0.88 ![A,B]: ((empty(A)|((~element(B,A)|in(B,A))&(element(B,A)|~in(B,A))))&(~empty(A)|((~element(B,A)|empty(B))&(element(B,A)|~empty(B)))))),
% 3.39/0.88 inference(NNF_transformation,[status(thm)],[f457])).
% 3.39/0.88 fof(f459,plain,(
% 3.39/0.88 (![A]: (empty(A)|((![B]: (~element(B,A)|in(B,A)))&(![B]: (element(B,A)|~in(B,A))))))&(![A]: (~empty(A)|((![B]: (~element(B,A)|empty(B)))&(![B]: (element(B,A)|~empty(B))))))),
% 3.39/0.88 inference(miniscoping,[status(thm)],[f458])).
% 3.39/0.88 fof(f462,plain,(
% 3.39/0.88 ![X0,X1]: (~empty(X0)|~element(X1,X0)|empty(X1))),
% 3.39/0.88 inference(cnf_transformation,[status(thm)],[f459])).
% 3.39/0.88 fof(f587,plain,(
% 3.39/0.88 ![A]: (~relation(A)|relation_field(A)=set_union2(relation_dom(A),relation_rng(A)))),
% 3.39/0.88 inference(pre_NNF_transformation,[status(thm)],[f50])).
% 3.39/0.88 fof(f588,plain,(
% 3.39/0.88 ![X0]: (~relation(X0)|relation_field(X0)=set_union2(relation_dom(X0),relation_rng(X0)))),
% 3.39/0.88 inference(cnf_transformation,[status(thm)],[f587])).
% 3.39/0.88 fof(f634,plain,(
% 3.39/0.88 ![A]: (~relation(A)|(reflexive(A)<=>is_reflexive_in(A,relation_field(A))))),
% 3.39/0.88 inference(pre_NNF_transformation,[status(thm)],[f58])).
% 3.39/0.88 fof(f635,plain,(
% 3.39/0.88 ![A]: (~relation(A)|((~reflexive(A)|is_reflexive_in(A,relation_field(A)))&(reflexive(A)|~is_reflexive_in(A,relation_field(A)))))),
% 3.39/0.88 inference(NNF_transformation,[status(thm)],[f634])).
% 3.39/0.88 fof(f636,plain,(
% 3.39/0.88 ![X0]: (~relation(X0)|~reflexive(X0)|is_reflexive_in(X0,relation_field(X0)))),
% 3.39/0.88 inference(cnf_transformation,[status(thm)],[f635])).
% 3.39/0.88 fof(f637,plain,(
% 3.39/0.88 ![X0]: (~relation(X0)|reflexive(X0)|~is_reflexive_in(X0,relation_field(X0)))),
% 3.39/0.88 inference(cnf_transformation,[status(thm)],[f635])).
% 3.39/0.88 fof(f663,plain,(
% 3.39/0.88 ![A]: element(sK65_skl(A),A)),
% 3.39/0.88 inference(skolemize,[status(esa),new_symbols(skolem,[sK65_skl]),skolemize(B,sK65_skl(A))],[f91])).
% 3.39/0.88 fof(f664,plain,(
% 3.39/0.88 ![X0]: (element(sK65_skl(X0),X0))),
% 3.39/0.88 inference(cnf_transformation,[status(thm)],[f663])).
% 3.39/0.88 fof(f668,plain,(
% 3.39/0.88 ![A]: (~empty(A)|(empty(relation_inverse(A))&relation(relation_inverse(A))))),
% 3.39/0.88 inference(pre_NNF_transformation,[status(thm)],[f93])).
% 3.39/0.88 fof(f669,plain,(
% 3.39/0.88 ![X0]: (~empty(X0)|empty(relation_inverse(X0)))),
% 3.39/0.88 inference(cnf_transformation,[status(thm)],[f668])).
% 3.39/0.88 fof(f671,plain,(
% 3.39/0.88 empty(empty_set)),
% 3.39/0.88 inference(cnf_transformation,[status(thm)],[f94])).
% 3.39/0.88 fof(f672,plain,(
% 3.39/0.88 relation(empty_set)),
% 3.39/0.88 inference(cnf_transformation,[status(thm)],[f94])).
% 3.39/0.88 fof(f692,plain,(
% 3.39/0.88 function(empty_set)),
% 3.39/0.88 inference(cnf_transformation,[status(thm)],[f103])).
% 3.39/0.88 fof(f695,plain,(
% 3.39/0.88 epsilon_transitive(empty_set)),
% 3.39/0.88 inference(cnf_transformation,[status(thm)],[f103])).
% 3.39/0.88 fof(f696,plain,(
% 3.39/0.88 epsilon_connected(empty_set)),
% 3.39/0.88 inference(cnf_transformation,[status(thm)],[f103])).
% 3.39/0.88 fof(f697,plain,(
% 3.39/0.88 ordinal(empty_set)),
% 3.39/0.88 inference(cnf_transformation,[status(thm)],[f103])).
% 3.39/0.88 fof(f707,plain,(
% 3.39/0.88 ![A]: (~ordinal(A)|(((~empty(succ(A))&epsilon_transitive(succ(A)))&epsilon_connected(succ(A)))&ordinal(succ(A))))),
% 3.39/0.88 inference(pre_NNF_transformation,[status(thm)],[f108])).
% 3.39/0.88 fof(f711,plain,(
% 3.39/0.88 ![X0]: (~ordinal(X0)|ordinal(succ(X0)))),
% 3.39/0.88 inference(cnf_transformation,[status(thm)],[f707])).
% 3.39/0.88 fof(f722,plain,(
% 3.39/0.88 ![A]: (~ordinal(A)|((epsilon_transitive(union(A))&epsilon_connected(union(A)))&ordinal(union(A))))),
% 3.39/0.88 inference(pre_NNF_transformation,[status(thm)],[f113])).
% 3.39/0.88 fof(f724,plain,(
% 3.39/0.88 ![X0]: (~ordinal(X0)|epsilon_connected(union(X0)))),
% 3.39/0.88 inference(cnf_transformation,[status(thm)],[f722])).
% 3.39/0.88 fof(f755,plain,(
% 3.39/0.88 (?[A]: (relation(A)&(reflexive(A)<~>(![B]: (~in(B,relation_field(A))|in(ordered_pair(B,B),A))))))),
% 3.39/0.88 inference(pre_NNF_transformation,[status(thm)],[f128])).
% 3.39/0.88 fof(f756,plain,(
% 3.39/0.88 ?[A]: (relation(A)&((reflexive(A)|(![B]: (~in(B,relation_field(A))|in(ordered_pair(B,B),A))))&(~reflexive(A)|(?[B]: (in(B,relation_field(A))&~in(ordered_pair(B,B),A))))))),
% 3.39/0.88 inference(NNF_transformation,[status(thm)],[f755])).
% 3.39/0.88 fof(f757,plain,(
% 3.39/0.88 (relation(sK66_skl)&((reflexive(sK66_skl)|(![B]: (~in(B,relation_field(sK66_skl))|in(ordered_pair(B,B),sK66_skl))))&(~reflexive(sK66_skl)|(in(sK67_skl,relation_field(sK66_skl))&~in(ordered_pair(sK67_skl,sK67_skl),sK66_skl)))))),
% 3.39/0.88 inference(skolemize,[status(esa),new_symbols(skolem,[sK66_skl,sK67_skl]),skolemize(A,sK66_skl),skolemize(B,sK67_skl)],[f756])).
% 3.39/0.88 fof(f758,plain,(
% 3.39/0.88 relation(sK66_skl)),
% 3.39/0.88 inference(cnf_transformation,[status(thm)],[f757])).
% 3.39/0.88 fof(f759,plain,(
% 3.39/0.88 ![X0]: (reflexive(sK66_skl)|~in(X0,relation_field(sK66_skl))|in(ordered_pair(X0,X0),sK66_skl))),
% 3.39/0.88 inference(cnf_transformation,[status(thm)],[f757])).
% 3.39/0.88 fof(f760,plain,(
% 3.39/0.88 ~reflexive(sK66_skl)|in(sK67_skl,relation_field(sK66_skl))),
% 3.39/0.88 inference(cnf_transformation,[status(thm)],[f757])).
% 3.39/0.88 fof(f761,plain,(
% 3.39/0.88 ~reflexive(sK66_skl)|~in(ordered_pair(sK67_skl,sK67_skl),sK66_skl)),
% 3.39/0.88 inference(cnf_transformation,[status(thm)],[f757])).
% 3.39/0.88 fof(f762,plain,(
% 3.39/0.88 ![X0]: (~singleton(X0)=empty_set)),
% 3.39/0.88 inference(cnf_transformation,[status(thm)],[f129])).
% 3.39/0.88 fof(f804,plain,(
% 3.39/0.88 (relation(sK69_skl)&function(sK69_skl))),
% 3.39/0.88 inference(skolemize,[status(esa),new_symbols(skolem,[sK69_skl]),skolemize(A,sK69_skl)],[f142])).
% 3.39/0.88 fof(f805,plain,(
% 3.39/0.88 relation(sK69_skl)),
% 3.39/0.88 inference(cnf_transformation,[status(thm)],[f804])).
% 3.39/0.88 fof(f806,plain,(
% 3.39/0.88 function(sK69_skl)),
% 3.39/0.88 inference(cnf_transformation,[status(thm)],[f804])).
% 3.39/0.88 fof(f807,plain,(
% 3.39/0.88 ((epsilon_transitive(sK70_skl)&epsilon_connected(sK70_skl))&ordinal(sK70_skl))),
% 3.39/0.88 inference(skolemize,[status(esa),new_symbols(skolem,[sK70_skl]),skolemize(A,sK70_skl)],[f143])).
% 3.39/0.88 fof(f808,plain,(
% 3.39/0.88 epsilon_transitive(sK70_skl)),
% 3.39/0.88 inference(cnf_transformation,[status(thm)],[f807])).
% 3.39/0.88 fof(f809,plain,(
% 3.39/0.88 epsilon_connected(sK70_skl)),
% 3.39/0.88 inference(cnf_transformation,[status(thm)],[f807])).
% 3.39/0.88 fof(f811,plain,(
% 3.39/0.88 (empty(sK71_skl)&relation(sK71_skl))),
% 3.39/0.88 inference(skolemize,[status(esa),new_symbols(skolem,[sK71_skl]),skolemize(A,sK71_skl)],[f144])).
% 3.39/0.88 fof(f812,plain,(
% 3.39/0.88 empty(sK71_skl)),
% 3.39/0.88 inference(cnf_transformation,[status(thm)],[f811])).
% 3.39/0.88 fof(f813,plain,(
% 3.39/0.88 relation(sK71_skl)),
% 3.39/0.88 inference(cnf_transformation,[status(thm)],[f811])).
% 3.39/0.88 fof(f818,plain,(
% 3.39/0.88 empty(sK73_skl)),
% 3.39/0.88 inference(skolemize,[status(esa),new_symbols(skolem,[sK73_skl]),skolemize(A,sK73_skl)],[f146])).
% 3.39/0.88 fof(f819,plain,(
% 3.39/0.88 empty(sK73_skl)),
% 3.39/0.88 inference(cnf_transformation,[status(thm)],[f818])).
% 3.39/0.88 fof(f820,plain,(
% 3.39/0.88 ((relation(sK74_skl)&empty(sK74_skl))&function(sK74_skl))),
% 3.39/0.88 inference(skolemize,[status(esa),new_symbols(skolem,[sK74_skl]),skolemize(A,sK74_skl)],[f147])).
% 3.39/0.88 fof(f821,plain,(
% 3.39/0.88 relation(sK74_skl)),
% 3.39/0.88 inference(cnf_transformation,[status(thm)],[f820])).
% 3.39/0.88 fof(f822,plain,(
% 3.39/0.88 empty(sK74_skl)),
% 3.39/0.88 inference(cnf_transformation,[status(thm)],[f820])).
% 3.39/0.88 fof(f823,plain,(
% 3.39/0.88 function(sK74_skl)),
% 3.39/0.88 inference(cnf_transformation,[status(thm)],[f820])).
% 3.39/0.88 fof(f824,plain,(
% 3.39/0.88 ((((((relation(sK75_skl)&function(sK75_skl))&one_to_one(sK75_skl))&empty(sK75_skl))&epsilon_transitive(sK75_skl))&epsilon_connected(sK75_skl))&ordinal(sK75_skl))),
% 3.39/0.88 inference(skolemize,[status(esa),new_symbols(skolem,[sK75_skl]),skolemize(A,sK75_skl)],[f148])).
% 3.39/0.88 fof(f825,plain,(
% 3.39/0.88 relation(sK75_skl)),
% 3.39/0.88 inference(cnf_transformation,[status(thm)],[f824])).
% 3.39/0.88 fof(f826,plain,(
% 3.39/0.88 function(sK75_skl)),
% 3.39/0.88 inference(cnf_transformation,[status(thm)],[f824])).
% 3.39/0.88 fof(f828,plain,(
% 3.39/0.88 empty(sK75_skl)),
% 3.39/0.88 inference(cnf_transformation,[status(thm)],[f824])).
% 3.39/0.88 fof(f829,plain,(
% 3.39/0.88 epsilon_transitive(sK75_skl)),
% 3.39/0.88 inference(cnf_transformation,[status(thm)],[f824])).
% 3.39/0.88 fof(f830,plain,(
% 3.39/0.88 epsilon_connected(sK75_skl)),
% 3.39/0.88 inference(cnf_transformation,[status(thm)],[f824])).
% 3.39/0.88 fof(f840,plain,(
% 3.39/0.88 ((relation(sK79_skl)&function(sK79_skl))&one_to_one(sK79_skl))),
% 3.39/0.88 inference(skolemize,[status(esa),new_symbols(skolem,[sK79_skl]),skolemize(A,sK79_skl)],[f152])).
% 3.39/0.88 fof(f841,plain,(
% 3.39/0.88 relation(sK79_skl)),
% 3.39/0.88 inference(cnf_transformation,[status(thm)],[f840])).
% 3.39/0.88 fof(f842,plain,(
% 3.39/0.88 function(sK79_skl)),
% 3.39/0.88 inference(cnf_transformation,[status(thm)],[f840])).
% 3.39/0.88 fof(f844,plain,(
% 3.39/0.88 (((~empty(sK80_skl)&epsilon_transitive(sK80_skl))&epsilon_connected(sK80_skl))&ordinal(sK80_skl))),
% 3.39/0.88 inference(skolemize,[status(esa),new_symbols(skolem,[sK80_skl]),skolemize(A,sK80_skl)],[f153])).
% 3.39/0.88 fof(f846,plain,(
% 3.39/0.88 epsilon_transitive(sK80_skl)),
% 3.39/0.88 inference(cnf_transformation,[status(thm)],[f844])).
% 3.39/0.88 fof(f847,plain,(
% 3.39/0.88 epsilon_connected(sK80_skl)),
% 3.39/0.88 inference(cnf_transformation,[status(thm)],[f844])).
% 3.39/0.88 fof(f852,plain,(
% 3.39/0.88 ((relation(sK82_skl)&relation_empty_yielding(sK82_skl))&function(sK82_skl))),
% 3.39/0.88 inference(skolemize,[status(esa),new_symbols(skolem,[sK82_skl]),skolemize(A,sK82_skl)],[f155])).
% 3.39/0.88 fof(f853,plain,(
% 3.39/0.88 relation(sK82_skl)),
% 3.39/0.88 inference(cnf_transformation,[status(thm)],[f852])).
% 3.39/0.88 fof(f855,plain,(
% 3.39/0.88 function(sK82_skl)),
% 3.39/0.88 inference(cnf_transformation,[status(thm)],[f852])).
% 3.39/0.88 fof(f965,plain,(
% 3.39/0.88 ![X0]: (set_union2(X0,empty_set)=X0)),
% 3.39/0.88 inference(cnf_transformation,[status(thm)],[f190])).
% 3.39/0.88 fof(f971,plain,(
% 3.39/0.88 powerset(empty_set)=singleton(empty_set)),
% 3.39/0.88 inference(cnf_transformation,[status(thm)],[f193])).
% 3.39/0.88 fof(f1014,plain,(
% 3.39/0.88 ![A,B,C]: (~relation(C)|(~in(ordered_pair(A,B),C)|(in(A,relation_field(C))&in(B,relation_field(C)))))),
% 3.39/0.88 inference(pre_NNF_transformation,[status(thm)],[f209])).
% 3.39/0.88 fof(f1015,plain,(
% 3.39/0.88 ![C]: (~relation(C)|(![A,B]: (~in(ordered_pair(A,B),C)|(in(A,relation_field(C))&in(B,relation_field(C))))))),
% 3.39/0.88 inference(miniscoping,[status(thm)],[f1014])).
% 3.39/0.88 fof(f1016,plain,(
% 3.39/0.88 ![X0,X1,X2]: (~relation(X0)|~in(ordered_pair(X1,X2),X0)|in(X1,relation_field(X0)))),
% 3.39/0.88 inference(cnf_transformation,[status(thm)],[f1015])).
% 3.39/0.88 fof(f1017,plain,(
% 3.39/0.88 ![X0,X1,X2]: (~relation(X0)|~in(ordered_pair(X1,X2),X0)|in(X2,relation_field(X0)))),
% 3.39/0.88 inference(cnf_transformation,[status(thm)],[f1015])).
% 3.39/0.88 fof(f1192,plain,(
% 3.39/0.88 ![A]: (~empty(A)|A=empty_set)),
% 3.39/0.88 inference(pre_NNF_transformation,[status(thm)],[f262])).
% 3.39/0.88 fof(f1193,plain,(
% 3.39/0.88 ![X0]: (~empty(X0)|X0=empty_set)),
% 3.39/0.88 inference(cnf_transformation,[status(thm)],[f1192])).
% 3.39/0.88 fof(f1199,plain,(
% 3.39/0.88 (![A]: relation_dom(identity_relation(A))=A)&(![A]: relation_rng(identity_relation(A))=A)),
% 3.39/0.88 inference(miniscoping,[status(thm)],[f265])).
% 3.39/0.88 fof(f1200,plain,(
% 3.39/0.88 ![X0]: (relation_dom(identity_relation(X0))=X0)),
% 3.39/0.88 inference(cnf_transformation,[status(thm)],[f1199])).
% 3.39/0.88 fof(f1201,plain,(
% 3.39/0.88 ![X0]: (relation_rng(identity_relation(X0))=X0)),
% 3.39/0.88 inference(cnf_transformation,[status(thm)],[f1199])).
% 3.39/0.88 fof(f1258,plain,(
% 3.39/0.88 ![X0]: (union(powerset(X0))=X0)),
% 3.39/0.88 inference(cnf_transformation,[status(thm)],[f282])).
% 3.39/0.88 fof(f1295,definition,(
% 3.39/0.88 sQ0_spl <=> (reflexive(sK66_skl))),
% 3.39/0.88 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 3.39/0.88 fof(f1296,plain,(
% 3.39/0.88 reflexive(sK66_skl)|~sQ0_spl),
% 3.39/0.88 inference(component_clause,[status(thm)],[f1295])).
% 3.39/0.88 fof(f1298,definition,(
% 3.39/0.88 ![X0]: (sQ1_spl <=> (~in(X0,relation_field(sK66_skl))|in(ordered_pair(X0,X0),sK66_skl)))),
% 3.39/0.88 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 3.39/0.88 fof(f1299,plain,(
% 3.39/0.88 ![X0]: (~in(X0,relation_field(sK66_skl))|in(ordered_pair(X0,X0),sK66_skl)|~sQ1_spl)),
% 3.39/0.88 inference(component_clause,[status(thm)],[f1298])).
% 3.39/0.88 fof(f1301,plain,(
% 3.39/0.88 sQ0_spl|sQ1_spl),
% 3.39/0.88 inference(split_clause,[status(thm)],[f759,f1295,f1298])).
% 3.39/0.88 fof(f1302,definition,(
% 3.39/0.88 sQ2_spl <=> (in(sK67_skl,relation_field(sK66_skl)))),
% 3.39/0.88 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 3.39/0.88 fof(f1303,plain,(
% 3.39/0.88 in(sK67_skl,relation_field(sK66_skl))|~sQ2_spl),
% 3.39/0.88 inference(component_clause,[status(thm)],[f1302])).
% 3.39/0.88 fof(f1305,plain,(
% 3.39/0.88 ~sQ0_spl|sQ2_spl),
% 3.39/0.88 inference(split_clause,[status(thm)],[f760,f1295,f1302])).
% 3.39/0.88 fof(f1306,definition,(
% 3.39/0.88 sQ3_spl <=> (in(ordered_pair(sK67_skl,sK67_skl),sK66_skl))),
% 3.39/0.88 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 3.39/0.88 fof(f1308,plain,(
% 3.39/0.88 ~in(ordered_pair(sK67_skl,sK67_skl),sK66_skl)|sQ3_spl),
% 3.39/0.88 inference(component_clause,[status(thm)],[f1306])).
% 3.39/0.88 fof(f1309,plain,(
% 3.39/0.88 ~sQ0_spl|~sQ3_spl),
% 3.39/0.88 inference(split_clause,[status(thm)],[f761,f1295,f1306])).
% 3.39/0.88 fof(f1346,plain,(
% 3.39/0.88 ![X0,X1]: (~in(X0,singleton(X1))|X0=X1)),
% 3.39/0.88 inference(destructive_equality_resolution,[status(thm)],[f426])).
% 3.39/0.88 fof(f1348,plain,(
% 3.39/0.88 ![X0]: (~in(X0,empty_set))),
% 3.39/0.88 inference(destructive_equality_resolution,[status(thm)],[f433])).
% 3.39/0.88 fof(f1415,plain,(
% 3.39/0.88 relation_field(sK66_skl)=set_union2(relation_dom(sK66_skl),relation_rng(sK66_skl))),
% 3.39/0.88 inference(resolution,[status(thm)],[f588,f758])).
% 3.39/0.88 fof(f1416,plain,(
% 3.39/0.88 ![X0,X1]: (~in(ordered_pair(X0,X1),sK66_skl)|in(X0,relation_field(sK66_skl)))),
% 3.39/0.88 inference(resolution,[status(thm)],[f1016,f758])).
% 3.39/0.88 fof(f1417,plain,(
% 3.39/0.88 ![X0,X1]: (~in(ordered_pair(X0,X1),sK66_skl)|in(X1,relation_field(sK66_skl)))),
% 3.39/0.88 inference(resolution,[status(thm)],[f1017,f758])).
% 3.39/0.88 fof(f1426,plain,(
% 3.39/0.88 ![X0]: (~empty(X0)|~function(X0)|one_to_one(X0))),
% 3.39/0.88 inference(forward_subsumption_resolution,[status(thm)],[f299,f295])).
% 3.39/0.88 fof(f1427,plain,(
% 3.39/0.88 ~function(empty_set)|one_to_one(empty_set)),
% 3.39/0.88 inference(resolution,[status(thm)],[f1426,f671])).
% 3.39/0.88 fof(f1428,definition,(
% 3.39/0.88 sQ6_spl <=> (function(empty_set))),
% 3.39/0.88 introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition])).
% 3.39/0.88 fof(f1430,plain,(
% 3.39/0.88 ~function(empty_set)|sQ6_spl),
% 3.39/0.88 inference(component_clause,[status(thm)],[f1428])).
% 3.39/0.88 fof(f1431,definition,(
% 3.39/0.88 sQ7_spl <=> (one_to_one(empty_set))),
% 3.39/0.88 introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition])).
% 3.39/0.88 fof(f1434,plain,(
% 3.39/0.88 ~sQ6_spl|sQ7_spl),
% 3.39/0.88 inference(split_clause,[status(thm)],[f1427,f1428,f1431])).
% 3.39/0.88 fof(f1435,plain,(
% 3.39/0.88 $false|sQ6_spl),
% 3.39/0.88 inference(forward_subsumption_resolution,[status(thm)],[f1430,f692])).
% 3.39/0.88 fof(f1436,plain,(
% 3.39/0.88 sQ6_spl),
% 3.39/0.88 inference(contradiction_clause,[status(thm)],[f1435])).
% 3.39/0.88 fof(f1437,plain,(
% 3.39/0.88 ~epsilon_transitive(empty_set)|ordinal(empty_set)),
% 3.39/0.88 inference(resolution,[status(thm)],[f301,f696])).
% 3.39/0.88 fof(f1438,definition,(
% 3.39/0.88 sQ8_spl <=> (epsilon_transitive(empty_set))),
% 3.39/0.88 introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition])).
% 3.39/0.88 fof(f1440,plain,(
% 3.39/0.88 ~epsilon_transitive(empty_set)|sQ8_spl),
% 3.39/0.88 inference(component_clause,[status(thm)],[f1438])).
% 3.39/0.88 fof(f1441,definition,(
% 3.39/0.88 sQ9_spl <=> (ordinal(empty_set))),
% 3.39/0.88 introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition])).
% 3.39/0.88 fof(f1444,plain,(
% 3.39/0.88 ~sQ8_spl|sQ9_spl),
% 3.39/0.88 inference(split_clause,[status(thm)],[f1437,f1438,f1441])).
% 3.39/0.88 fof(f1445,plain,(
% 3.39/0.88 $false|sQ8_spl),
% 3.39/0.88 inference(forward_subsumption_resolution,[status(thm)],[f1440,f695])).
% 3.39/0.88 fof(f1446,plain,(
% 3.39/0.88 sQ8_spl),
% 3.39/0.88 inference(contradiction_clause,[status(thm)],[f1445])).
% 3.39/0.88 fof(f1448,plain,(
% 3.39/0.88 ~relation(sK66_skl)|is_reflexive_in(sK66_skl,relation_field(sK66_skl))|~sQ0_spl),
% 3.39/0.88 inference(resolution,[status(thm)],[f1296,f636])).
% 3.39/0.88 fof(f1449,definition,(
% 3.39/0.88 sQ10_spl <=> (relation(sK66_skl))),
% 3.39/0.88 introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition])).
% 3.39/0.88 fof(f1451,plain,(
% 3.39/0.88 ~relation(sK66_skl)|sQ10_spl),
% 3.39/0.88 inference(component_clause,[status(thm)],[f1449])).
% 3.39/0.88 fof(f1452,definition,(
% 3.39/0.88 sQ11_spl <=> (is_reflexive_in(sK66_skl,relation_field(sK66_skl)))),
% 3.39/0.88 introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition])).
% 3.39/0.88 fof(f1453,plain,(
% 3.39/0.88 is_reflexive_in(sK66_skl,relation_field(sK66_skl))|~sQ11_spl),
% 3.39/0.88 inference(component_clause,[status(thm)],[f1452])).
% 3.39/0.88 fof(f1455,plain,(
% 3.39/0.88 ~sQ10_spl|sQ11_spl|~sQ0_spl),
% 3.39/0.88 inference(split_clause,[status(thm)],[f1448,f1449,f1452,f1295])).
% 3.39/0.88 fof(f1456,plain,(
% 3.39/0.88 $false|sQ10_spl),
% 3.39/0.88 inference(forward_subsumption_resolution,[status(thm)],[f1451,f758])).
% 3.39/0.88 fof(f1457,plain,(
% 3.39/0.88 sQ10_spl),
% 3.39/0.88 inference(contradiction_clause,[status(thm)],[f1456])).
% 3.39/0.88 fof(f1463,plain,(
% 3.39/0.88 ~epsilon_transitive(sK70_skl)|ordinal(sK70_skl)),
% 3.39/0.88 inference(resolution,[status(thm)],[f809,f301])).
% 3.39/0.88 fof(f1464,definition,(
% 3.39/0.88 sQ12_spl <=> (epsilon_transitive(sK70_skl))),
% 3.39/0.88 introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition])).
% 3.39/0.88 fof(f1466,plain,(
% 3.39/0.88 ~epsilon_transitive(sK70_skl)|sQ12_spl),
% 3.39/0.88 inference(component_clause,[status(thm)],[f1464])).
% 3.39/0.88 fof(f1467,definition,(
% 3.39/0.88 sQ13_spl <=> (ordinal(sK70_skl))),
% 3.39/0.88 introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition])).
% 3.39/0.88 fof(f1470,plain,(
% 3.39/0.88 ~sQ12_spl|sQ13_spl),
% 3.39/0.88 inference(split_clause,[status(thm)],[f1463,f1464,f1467])).
% 3.39/0.88 fof(f1471,plain,(
% 3.39/0.88 $false|sQ12_spl),
% 3.39/0.88 inference(forward_subsumption_resolution,[status(thm)],[f1466,f808])).
% 3.39/0.88 fof(f1472,plain,(
% 3.39/0.88 sQ12_spl),
% 3.39/0.88 inference(contradiction_clause,[status(thm)],[f1471])).
% 3.39/0.88 fof(f1476,plain,(
% 3.39/0.88 epsilon_connected(sK71_skl)),
% 3.39/0.88 inference(resolution,[status(thm)],[f812,f304])).
% 3.39/0.88 fof(f1477,plain,(
% 3.39/0.88 epsilon_transitive(sK71_skl)),
% 3.39/0.88 inference(resolution,[status(thm)],[f812,f303])).
% 3.39/0.88 fof(f1478,plain,(
% 3.39/0.88 ~function(sK71_skl)|one_to_one(sK71_skl)),
% 3.39/0.88 inference(resolution,[status(thm)],[f812,f1426])).
% 3.39/0.88 fof(f1480,definition,(
% 3.39/0.88 sQ14_spl <=> (function(sK71_skl))),
% 3.39/0.88 introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition])).
% 3.39/0.88 fof(f1481,plain,(
% 3.39/0.88 function(sK71_skl)|~sQ14_spl),
% 3.39/0.88 inference(component_clause,[status(thm)],[f1480])).
% 3.39/0.88 fof(f1482,plain,(
% 3.39/0.88 ~function(sK71_skl)|sQ14_spl),
% 3.39/0.88 inference(component_clause,[status(thm)],[f1480])).
% 3.39/0.88 fof(f1483,definition,(
% 3.39/0.88 sQ15_spl <=> (one_to_one(sK71_skl))),
% 3.39/0.88 introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition])).
% 3.39/0.88 fof(f1486,plain,(
% 3.39/0.88 ~sQ14_spl|sQ15_spl),
% 3.39/0.88 inference(split_clause,[status(thm)],[f1478,f1480,f1483])).
% 3.39/0.88 fof(f1491,plain,(
% 3.39/0.88 epsilon_connected(sK73_skl)),
% 3.39/0.88 inference(resolution,[status(thm)],[f819,f304])).
% 3.39/0.88 fof(f1492,plain,(
% 3.39/0.88 epsilon_transitive(sK73_skl)),
% 3.39/0.88 inference(resolution,[status(thm)],[f819,f303])).
% 3.39/0.88 fof(f1493,plain,(
% 3.39/0.88 ~function(sK73_skl)|one_to_one(sK73_skl)),
% 3.39/0.88 inference(resolution,[status(thm)],[f819,f1426])).
% 3.39/0.88 fof(f1494,plain,(
% 3.39/0.88 relation(sK73_skl)),
% 3.39/0.88 inference(resolution,[status(thm)],[f819,f295])).
% 3.39/0.88 fof(f1495,definition,(
% 3.39/0.88 sQ16_spl <=> (function(sK73_skl))),
% 3.39/0.88 introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition])).
% 3.39/0.88 fof(f1496,plain,(
% 3.39/0.88 function(sK73_skl)|~sQ16_spl),
% 3.39/0.88 inference(component_clause,[status(thm)],[f1495])).
% 3.39/0.88 fof(f1497,plain,(
% 3.39/0.88 ~function(sK73_skl)|sQ16_spl),
% 3.39/0.88 inference(component_clause,[status(thm)],[f1495])).
% 3.39/0.88 fof(f1498,definition,(
% 3.39/0.88 sQ17_spl <=> (one_to_one(sK73_skl))),
% 3.39/0.88 introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition])).
% 3.39/0.88 fof(f1501,plain,(
% 3.39/0.88 ~sQ16_spl|sQ17_spl),
% 3.39/0.88 inference(split_clause,[status(thm)],[f1493,f1495,f1498])).
% 3.39/0.88 fof(f1506,plain,(
% 3.39/0.88 epsilon_connected(sK74_skl)),
% 3.39/0.88 inference(resolution,[status(thm)],[f822,f304])).
% 3.39/0.88 fof(f1507,plain,(
% 3.39/0.88 epsilon_transitive(sK74_skl)),
% 3.39/0.88 inference(resolution,[status(thm)],[f822,f303])).
% 3.39/0.88 fof(f1508,plain,(
% 3.39/0.88 ~function(sK74_skl)|one_to_one(sK74_skl)),
% 3.39/0.88 inference(resolution,[status(thm)],[f822,f1426])).
% 3.39/0.88 fof(f1510,definition,(
% 3.39/0.88 sQ18_spl <=> (function(sK74_skl))),
% 3.39/0.88 introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition])).
% 3.39/0.88 fof(f1512,plain,(
% 3.39/0.88 ~function(sK74_skl)|sQ18_spl),
% 3.39/0.88 inference(component_clause,[status(thm)],[f1510])).
% 3.39/0.88 fof(f1513,definition,(
% 3.39/0.88 sQ19_spl <=> (one_to_one(sK74_skl))),
% 3.39/0.88 introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition])).
% 3.39/0.88 fof(f1516,plain,(
% 3.39/0.88 ~sQ18_spl|sQ19_spl),
% 3.39/0.88 inference(split_clause,[status(thm)],[f1508,f1510,f1513])).
% 3.39/0.88 fof(f1523,plain,(
% 3.39/0.88 relation_field(sK66_skl)=set_union2(relation_rng(sK66_skl),relation_dom(sK66_skl))),
% 3.39/0.88 inference(paramodulation,[status(thm)],[f1415,f307])).
% 3.39/0.88 fof(f1555,plain,(
% 3.39/0.88 ~function(sK75_skl)|one_to_one(sK75_skl)),
% 3.39/0.88 inference(resolution,[status(thm)],[f828,f1426])).
% 3.39/0.88 fof(f1557,definition,(
% 3.39/0.88 sQ20_spl <=> (function(sK75_skl))),
% 3.39/0.88 introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition])).
% 3.39/0.88 fof(f1559,plain,(
% 3.39/0.88 ~function(sK75_skl)|sQ20_spl),
% 3.39/0.88 inference(component_clause,[status(thm)],[f1557])).
% 3.39/0.88 fof(f1560,definition,(
% 3.39/0.88 sQ21_spl <=> (one_to_one(sK75_skl))),
% 3.39/0.88 introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition])).
% 3.39/0.88 fof(f1563,plain,(
% 3.39/0.88 ~sQ20_spl|sQ21_spl),
% 3.39/0.88 inference(split_clause,[status(thm)],[f1555,f1557,f1560])).
% 3.39/0.88 fof(f1564,plain,(
% 3.39/0.88 $false|sQ20_spl),
% 3.39/0.88 inference(forward_subsumption_resolution,[status(thm)],[f1559,f826])).
% 3.39/0.88 fof(f1565,plain,(
% 3.39/0.88 sQ20_spl),
% 3.39/0.88 inference(contradiction_clause,[status(thm)],[f1564])).
% 3.39/0.88 fof(f1566,plain,(
% 3.39/0.88 ~epsilon_transitive(sK75_skl)|ordinal(sK75_skl)),
% 3.39/0.88 inference(resolution,[status(thm)],[f830,f301])).
% 3.39/0.88 fof(f1567,definition,(
% 3.39/0.89 sQ22_spl <=> (epsilon_transitive(sK75_skl))),
% 3.39/0.89 introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition])).
% 3.39/0.89 fof(f1569,plain,(
% 3.39/0.89 ~epsilon_transitive(sK75_skl)|sQ22_spl),
% 3.39/0.89 inference(component_clause,[status(thm)],[f1567])).
% 3.39/0.89 fof(f1570,definition,(
% 3.39/0.89 sQ23_spl <=> (ordinal(sK75_skl))),
% 3.39/0.89 introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition])).
% 3.39/0.89 fof(f1573,plain,(
% 3.39/0.89 ~sQ22_spl|sQ23_spl),
% 3.39/0.89 inference(split_clause,[status(thm)],[f1566,f1567,f1570])).
% 3.39/0.89 fof(f1574,plain,(
% 3.39/0.89 $false|sQ22_spl),
% 3.39/0.89 inference(forward_subsumption_resolution,[status(thm)],[f1569,f829])).
% 3.39/0.89 fof(f1575,plain,(
% 3.39/0.89 sQ22_spl),
% 3.39/0.89 inference(contradiction_clause,[status(thm)],[f1574])).
% 3.39/0.89 fof(f1587,plain,(
% 3.39/0.89 ~epsilon_transitive(sK80_skl)|ordinal(sK80_skl)),
% 3.39/0.89 inference(resolution,[status(thm)],[f847,f301])).
% 3.39/0.89 fof(f1588,definition,(
% 3.39/0.89 sQ24_spl <=> (epsilon_transitive(sK80_skl))),
% 3.39/0.89 introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition])).
% 3.39/0.89 fof(f1590,plain,(
% 3.39/0.89 ~epsilon_transitive(sK80_skl)|sQ24_spl),
% 3.39/0.89 inference(component_clause,[status(thm)],[f1588])).
% 3.39/0.89 fof(f1591,definition,(
% 3.39/0.89 sQ25_spl <=> (ordinal(sK80_skl))),
% 3.39/0.89 introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition])).
% 3.39/0.89 fof(f1594,plain,(
% 3.39/0.89 ~sQ24_spl|sQ25_spl),
% 3.39/0.89 inference(split_clause,[status(thm)],[f1587,f1588,f1591])).
% 3.39/0.89 fof(f1595,plain,(
% 3.39/0.89 $false|sQ24_spl),
% 3.39/0.89 inference(forward_subsumption_resolution,[status(thm)],[f1590,f846])).
% 3.39/0.89 fof(f1596,plain,(
% 3.39/0.89 sQ24_spl),
% 3.39/0.89 inference(contradiction_clause,[status(thm)],[f1595])).
% 3.39/0.89 fof(f1611,plain,(
% 3.39/0.89 ![X0]: (sK66_skl=identity_relation(X0)|in(ordered_pair(sK0_skl(X0,sK66_skl),sK1_skl(X0,sK66_skl)),sK66_skl)|in(sK0_skl(X0,sK66_skl),X0))),
% 3.39/0.89 inference(resolution,[status(thm)],[f319,f758])).
% 3.39/0.89 fof(f1612,plain,(
% 3.39/0.89 ![X0]: (sK66_skl=identity_relation(X0)|in(sK0_skl(X0,sK66_skl),X0)|in(sK1_skl(X0,sK66_skl),relation_field(sK66_skl)))),
% 3.39/0.89 inference(resolution,[status(thm)],[f1611,f1417])).
% 3.39/0.89 fof(f1613,plain,(
% 3.39/0.89 ![X0]: (sK66_skl=identity_relation(X0)|in(sK0_skl(X0,sK66_skl),X0)|in(sK0_skl(X0,sK66_skl),relation_field(sK66_skl)))),
% 3.39/0.89 inference(resolution,[status(thm)],[f1611,f1416])).
% 3.39/0.89 fof(f1696,plain,(
% 3.39/0.89 ~epsilon_transitive(sK71_skl)|ordinal(sK71_skl)),
% 3.39/0.89 inference(resolution,[status(thm)],[f1476,f301])).
% 3.39/0.89 fof(f1697,definition,(
% 3.39/0.89 sQ35_spl <=> (epsilon_transitive(sK71_skl))),
% 3.39/0.89 introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition])).
% 3.39/0.89 fof(f1699,plain,(
% 3.39/0.89 ~epsilon_transitive(sK71_skl)|sQ35_spl),
% 3.39/0.89 inference(component_clause,[status(thm)],[f1697])).
% 3.39/0.89 fof(f1700,definition,(
% 3.39/0.89 sQ36_spl <=> (ordinal(sK71_skl))),
% 3.39/0.89 introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition])).
% 3.39/0.89 fof(f1703,plain,(
% 3.39/0.89 ~sQ35_spl|sQ36_spl),
% 3.39/0.89 inference(split_clause,[status(thm)],[f1696,f1697,f1700])).
% 3.39/0.89 fof(f1760,plain,(
% 3.39/0.89 ~empty(sK71_skl)|sQ14_spl),
% 3.39/0.89 inference(resolution,[status(thm)],[f1482,f290])).
% 3.39/0.89 fof(f1761,plain,(
% 3.39/0.89 $false|sQ14_spl),
% 3.39/0.89 inference(forward_subsumption_resolution,[status(thm)],[f1760,f812])).
% 3.39/0.89 fof(f1762,plain,(
% 3.39/0.89 sQ14_spl),
% 3.39/0.89 inference(contradiction_clause,[status(thm)],[f1761])).
% 3.39/0.89 fof(f1766,plain,(
% 3.39/0.89 ~epsilon_transitive(sK73_skl)|ordinal(sK73_skl)),
% 3.39/0.89 inference(resolution,[status(thm)],[f1491,f301])).
% 3.39/0.89 fof(f1767,definition,(
% 3.39/0.89 sQ40_spl <=> (epsilon_transitive(sK73_skl))),
% 3.39/0.89 introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition])).
% 3.39/0.89 fof(f1769,plain,(
% 3.39/0.89 ~epsilon_transitive(sK73_skl)|sQ40_spl),
% 3.39/0.89 inference(component_clause,[status(thm)],[f1767])).
% 3.39/0.89 fof(f1770,definition,(
% 3.39/0.89 sQ41_spl <=> (ordinal(sK73_skl))),
% 3.39/0.89 introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition])).
% 3.39/0.89 fof(f1773,plain,(
% 3.39/0.89 ~sQ40_spl|sQ41_spl),
% 3.39/0.89 inference(split_clause,[status(thm)],[f1766,f1767,f1770])).
% 3.39/0.89 fof(f1779,plain,(
% 3.39/0.89 ~empty(sK73_skl)|sQ16_spl),
% 3.39/0.89 inference(resolution,[status(thm)],[f1497,f290])).
% 3.39/0.89 fof(f1780,plain,(
% 3.39/0.89 $false|sQ16_spl),
% 3.39/0.89 inference(forward_subsumption_resolution,[status(thm)],[f1779,f819])).
% 3.39/0.89 fof(f1781,plain,(
% 3.39/0.89 sQ16_spl),
% 3.39/0.89 inference(contradiction_clause,[status(thm)],[f1780])).
% 3.39/0.89 fof(f1785,plain,(
% 3.39/0.89 ~epsilon_transitive(sK74_skl)|ordinal(sK74_skl)),
% 3.39/0.89 inference(resolution,[status(thm)],[f1506,f301])).
% 3.39/0.89 fof(f1786,definition,(
% 3.39/0.89 sQ42_spl <=> (epsilon_transitive(sK74_skl))),
% 3.39/0.89 introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition])).
% 3.39/0.89 fof(f1788,plain,(
% 3.39/0.89 ~epsilon_transitive(sK74_skl)|sQ42_spl),
% 3.39/0.89 inference(component_clause,[status(thm)],[f1786])).
% 3.39/0.89 fof(f1789,definition,(
% 3.39/0.89 sQ43_spl <=> (ordinal(sK74_skl))),
% 3.39/0.89 introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition])).
% 3.39/0.89 fof(f1792,plain,(
% 3.39/0.89 ~sQ42_spl|sQ43_spl),
% 3.39/0.89 inference(split_clause,[status(thm)],[f1785,f1786,f1789])).
% 3.39/0.89 fof(f1813,plain,(
% 3.39/0.89 $false|sQ18_spl),
% 3.39/0.89 inference(forward_subsumption_resolution,[status(thm)],[f1512,f823])).
% 3.39/0.89 fof(f1814,plain,(
% 3.39/0.89 sQ18_spl),
% 3.39/0.89 inference(contradiction_clause,[status(thm)],[f1813])).
% 3.39/0.89 fof(f1853,plain,(
% 3.39/0.89 $false|sQ35_spl),
% 3.39/0.89 inference(forward_subsumption_resolution,[status(thm)],[f1699,f1477])).
% 3.39/0.89 fof(f1854,plain,(
% 3.39/0.89 sQ35_spl),
% 3.39/0.89 inference(contradiction_clause,[status(thm)],[f1853])).
% 3.39/0.89 fof(f1855,plain,(
% 3.39/0.89 $false|sQ40_spl),
% 3.39/0.89 inference(forward_subsumption_resolution,[status(thm)],[f1769,f1492])).
% 3.39/0.89 fof(f1856,plain,(
% 3.39/0.89 sQ40_spl),
% 3.39/0.89 inference(contradiction_clause,[status(thm)],[f1855])).
% 3.39/0.89 fof(f1878,plain,(
% 3.39/0.89 $false|sQ42_spl),
% 3.39/0.89 inference(forward_subsumption_resolution,[status(thm)],[f1788,f1507])).
% 3.39/0.89 fof(f1879,plain,(
% 3.39/0.89 sQ42_spl),
% 3.39/0.89 inference(contradiction_clause,[status(thm)],[f1878])).
% 3.39/0.89 fof(f1880,plain,(
% 3.39/0.89 sK66_skl=identity_relation(empty_set)|in(sK0_skl(empty_set,sK66_skl),relation_field(sK66_skl))),
% 3.39/0.89 inference(resolution,[status(thm)],[f1348,f1613])).
% 3.39/0.89 fof(f1881,plain,(
% 3.39/0.89 sK66_skl=identity_relation(empty_set)|in(sK1_skl(empty_set,sK66_skl),relation_field(sK66_skl))),
% 3.39/0.89 inference(resolution,[status(thm)],[f1348,f1612])).
% 3.39/0.89 fof(f1882,definition,(
% 3.39/0.89 sQ48_spl <=> (sK66_skl=identity_relation(empty_set))),
% 3.39/0.89 introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition])).
% 3.39/0.89 fof(f1883,plain,(
% 3.39/0.89 sK66_skl=identity_relation(empty_set)|~sQ48_spl),
% 3.39/0.89 inference(component_clause,[status(thm)],[f1882])).
% 3.39/0.89 fof(f1885,definition,(
% 3.39/0.89 sQ49_spl <=> (in(sK0_skl(empty_set,sK66_skl),relation_field(sK66_skl)))),
% 3.39/0.89 introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition])).
% 3.39/0.89 fof(f1886,plain,(
% 3.39/0.89 in(sK0_skl(empty_set,sK66_skl),relation_field(sK66_skl))|~sQ49_spl),
% 3.39/0.89 inference(component_clause,[status(thm)],[f1885])).
% 3.39/0.89 fof(f1888,plain,(
% 3.39/0.89 sQ48_spl|sQ49_spl),
% 3.39/0.89 inference(split_clause,[status(thm)],[f1880,f1882,f1885])).
% 3.39/0.89 fof(f1889,definition,(
% 3.39/0.89 sQ50_spl <=> (in(sK1_skl(empty_set,sK66_skl),relation_field(sK66_skl)))),
% 3.39/0.89 introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition])).
% 3.39/0.89 fof(f1890,plain,(
% 3.39/0.89 in(sK1_skl(empty_set,sK66_skl),relation_field(sK66_skl))|~sQ50_spl),
% 3.39/0.89 inference(component_clause,[status(thm)],[f1889])).
% 3.39/0.89 fof(f1892,plain,(
% 3.39/0.89 sQ48_spl|sQ50_spl),
% 3.39/0.89 inference(split_clause,[status(thm)],[f1881,f1882,f1889])).
% 3.39/0.89 fof(f2117,plain,(
% 3.39/0.89 ![X0]: (set_union2(empty_set,X0)=X0)),
% 3.39/0.89 inference(paramodulation,[status(thm)],[f307,f965])).
% 3.39/0.89 fof(f2133,plain,(
% 3.39/0.89 ![X0,X1]: (~relation(sK73_skl)|X0=relation_inverse_image(sK73_skl,X1)|in(sK9_skl(X0,X1,sK73_skl),X0)|in(sK9_skl(X0,X1,sK73_skl),relation_dom(sK73_skl))|~sQ16_spl)),
% 3.39/0.89 inference(resolution,[status(thm)],[f364,f1496])).
% 3.39/0.89 fof(f2134,plain,(
% 3.39/0.89 ![X0,X1]: (~relation(sK71_skl)|X0=relation_inverse_image(sK71_skl,X1)|in(sK9_skl(X0,X1,sK71_skl),X0)|in(sK9_skl(X0,X1,sK71_skl),relation_dom(sK71_skl))|~sQ14_spl)),
% 3.39/0.89 inference(resolution,[status(thm)],[f364,f1481])).
% 3.39/0.89 fof(f2135,plain,(
% 3.39/0.89 ![X0,X1]: (~relation(sK82_skl)|X0=relation_inverse_image(sK82_skl,X1)|in(sK9_skl(X0,X1,sK82_skl),X0)|in(sK9_skl(X0,X1,sK82_skl),relation_dom(sK82_skl)))),
% 3.39/0.89 inference(resolution,[status(thm)],[f364,f855])).
% 3.39/0.89 fof(f2136,plain,(
% 3.39/0.89 ![X0,X1]: (~relation(sK79_skl)|X0=relation_inverse_image(sK79_skl,X1)|in(sK9_skl(X0,X1,sK79_skl),X0)|in(sK9_skl(X0,X1,sK79_skl),relation_dom(sK79_skl)))),
% 3.39/0.89 inference(resolution,[status(thm)],[f364,f842])).
% 3.39/0.89 fof(f2137,plain,(
% 3.39/0.89 ![X0,X1]: (~relation(sK75_skl)|X0=relation_inverse_image(sK75_skl,X1)|in(sK9_skl(X0,X1,sK75_skl),X0)|in(sK9_skl(X0,X1,sK75_skl),relation_dom(sK75_skl)))),
% 3.39/0.89 inference(resolution,[status(thm)],[f364,f826])).
% 3.39/0.89 fof(f2138,plain,(
% 3.39/0.89 ![X0,X1]: (~relation(sK74_skl)|X0=relation_inverse_image(sK74_skl,X1)|in(sK9_skl(X0,X1,sK74_skl),X0)|in(sK9_skl(X0,X1,sK74_skl),relation_dom(sK74_skl)))),
% 3.39/0.89 inference(resolution,[status(thm)],[f364,f823])).
% 3.39/0.89 fof(f2139,plain,(
% 3.39/0.89 ![X0,X1]: (~relation(sK69_skl)|X0=relation_inverse_image(sK69_skl,X1)|in(sK9_skl(X0,X1,sK69_skl),X0)|in(sK9_skl(X0,X1,sK69_skl),relation_dom(sK69_skl)))),
% 3.39/0.89 inference(resolution,[status(thm)],[f364,f806])).
% 3.39/0.89 fof(f2140,plain,(
% 3.39/0.89 ![X0,X1]: (~relation(empty_set)|X0=relation_inverse_image(empty_set,X1)|in(sK9_skl(X0,X1,empty_set),X0)|in(sK9_skl(X0,X1,empty_set),relation_dom(empty_set)))),
% 3.39/0.89 inference(resolution,[status(thm)],[f364,f692])).
% 3.39/0.89 fof(f2147,definition,(
% 3.39/0.89 sQ55_spl <=> (relation(sK73_skl))),
% 3.39/0.89 introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition])).
% 3.39/0.89 fof(f2149,plain,(
% 3.39/0.89 ~relation(sK73_skl)|sQ55_spl),
% 3.39/0.89 inference(component_clause,[status(thm)],[f2147])).
% 3.39/0.89 fof(f2150,definition,(
% 3.39/0.89 ![X0,X1]: (sQ56_spl <=> (X0=relation_inverse_image(sK73_skl,X1)|in(sK9_skl(X0,X1,sK73_skl),X0)|in(sK9_skl(X0,X1,sK73_skl),relation_dom(sK73_skl))))),
% 3.39/0.89 introduced(definition,[new_symbols(definition,[sQ56_spl])],[split_symbol_definition])).
% 3.39/0.89 fof(f2153,plain,(
% 3.39/0.89 ~sQ55_spl|sQ56_spl|~sQ16_spl),
% 3.39/0.89 inference(split_clause,[status(thm)],[f2133,f2147,f2150,f1495])).
% 3.39/0.89 fof(f2154,definition,(
% 3.39/0.89 sQ57_spl <=> (relation(sK71_skl))),
% 3.39/0.89 introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition])).
% 3.39/0.89 fof(f2156,plain,(
% 3.39/0.89 ~relation(sK71_skl)|sQ57_spl),
% 3.39/0.89 inference(component_clause,[status(thm)],[f2154])).
% 3.39/0.89 fof(f2157,definition,(
% 3.39/0.89 ![X0,X1]: (sQ58_spl <=> (X0=relation_inverse_image(sK71_skl,X1)|in(sK9_skl(X0,X1,sK71_skl),X0)|in(sK9_skl(X0,X1,sK71_skl),relation_dom(sK71_skl))))),
% 3.39/0.89 introduced(definition,[new_symbols(definition,[sQ58_spl])],[split_symbol_definition])).
% 3.39/0.89 fof(f2160,plain,(
% 3.39/0.89 ~sQ57_spl|sQ58_spl|~sQ14_spl),
% 3.39/0.89 inference(split_clause,[status(thm)],[f2134,f2154,f2157,f1480])).
% 3.39/0.89 fof(f2161,definition,(
% 3.39/0.89 sQ59_spl <=> (relation(sK82_skl))),
% 3.39/0.89 introduced(definition,[new_symbols(definition,[sQ59_spl])],[split_symbol_definition])).
% 3.39/0.89 fof(f2163,plain,(
% 3.39/0.89 ~relation(sK82_skl)|sQ59_spl),
% 3.39/0.89 inference(component_clause,[status(thm)],[f2161])).
% 3.39/0.89 fof(f2164,definition,(
% 3.39/0.89 ![X0,X1]: (sQ60_spl <=> (X0=relation_inverse_image(sK82_skl,X1)|in(sK9_skl(X0,X1,sK82_skl),X0)|in(sK9_skl(X0,X1,sK82_skl),relation_dom(sK82_skl))))),
% 3.39/0.89 introduced(definition,[new_symbols(definition,[sQ60_spl])],[split_symbol_definition])).
% 3.39/0.89 fof(f2167,plain,(
% 3.39/0.89 ~sQ59_spl|sQ60_spl),
% 3.39/0.89 inference(split_clause,[status(thm)],[f2135,f2161,f2164])).
% 3.39/0.89 fof(f2168,definition,(
% 3.39/0.89 sQ61_spl <=> (relation(sK79_skl))),
% 3.39/0.89 introduced(definition,[new_symbols(definition,[sQ61_spl])],[split_symbol_definition])).
% 3.39/0.89 fof(f2170,plain,(
% 3.39/0.89 ~relation(sK79_skl)|sQ61_spl),
% 3.39/0.89 inference(component_clause,[status(thm)],[f2168])).
% 3.39/0.89 fof(f2171,definition,(
% 3.39/0.89 ![X0,X1]: (sQ62_spl <=> (X0=relation_inverse_image(sK79_skl,X1)|in(sK9_skl(X0,X1,sK79_skl),X0)|in(sK9_skl(X0,X1,sK79_skl),relation_dom(sK79_skl))))),
% 3.39/0.89 introduced(definition,[new_symbols(definition,[sQ62_spl])],[split_symbol_definition])).
% 3.39/0.89 fof(f2174,plain,(
% 3.39/0.89 ~sQ61_spl|sQ62_spl),
% 3.39/0.89 inference(split_clause,[status(thm)],[f2136,f2168,f2171])).
% 3.39/0.89 fof(f2175,definition,(
% 3.39/0.89 sQ63_spl <=> (relation(sK75_skl))),
% 3.39/0.89 introduced(definition,[new_symbols(definition,[sQ63_spl])],[split_symbol_definition])).
% 3.39/0.89 fof(f2177,plain,(
% 3.39/0.89 ~relation(sK75_skl)|sQ63_spl),
% 3.39/0.89 inference(component_clause,[status(thm)],[f2175])).
% 3.39/0.89 fof(f2178,definition,(
% 3.39/0.89 ![X0,X1]: (sQ64_spl <=> (X0=relation_inverse_image(sK75_skl,X1)|in(sK9_skl(X0,X1,sK75_skl),X0)|in(sK9_skl(X0,X1,sK75_skl),relation_dom(sK75_skl))))),
% 3.39/0.89 introduced(definition,[new_symbols(definition,[sQ64_spl])],[split_symbol_definition])).
% 3.39/0.89 fof(f2181,plain,(
% 3.39/0.89 ~sQ63_spl|sQ64_spl),
% 3.39/0.89 inference(split_clause,[status(thm)],[f2137,f2175,f2178])).
% 3.39/0.89 fof(f2182,definition,(
% 3.39/0.89 sQ65_spl <=> (relation(sK74_skl))),
% 3.39/0.89 introduced(definition,[new_symbols(definition,[sQ65_spl])],[split_symbol_definition])).
% 3.39/0.89 fof(f2184,plain,(
% 3.39/0.89 ~relation(sK74_skl)|sQ65_spl),
% 3.39/0.89 inference(component_clause,[status(thm)],[f2182])).
% 3.39/0.89 fof(f2185,definition,(
% 3.39/0.89 ![X0,X1]: (sQ66_spl <=> (X0=relation_inverse_image(sK74_skl,X1)|in(sK9_skl(X0,X1,sK74_skl),X0)|in(sK9_skl(X0,X1,sK74_skl),relation_dom(sK74_skl))))),
% 3.39/0.89 introduced(definition,[new_symbols(definition,[sQ66_spl])],[split_symbol_definition])).
% 3.39/0.89 fof(f2188,plain,(
% 3.39/0.89 ~sQ65_spl|sQ66_spl),
% 3.39/0.89 inference(split_clause,[status(thm)],[f2138,f2182,f2185])).
% 3.39/0.89 fof(f2189,definition,(
% 3.39/0.89 sQ67_spl <=> (relation(sK69_skl))),
% 3.39/0.89 introduced(definition,[new_symbols(definition,[sQ67_spl])],[split_symbol_definition])).
% 3.39/0.89 fof(f2191,plain,(
% 3.39/0.89 ~relation(sK69_skl)|sQ67_spl),
% 3.39/0.89 inference(component_clause,[status(thm)],[f2189])).
% 3.39/0.89 fof(f2192,definition,(
% 3.39/0.89 ![X0,X1]: (sQ68_spl <=> (X0=relation_inverse_image(sK69_skl,X1)|in(sK9_skl(X0,X1,sK69_skl),X0)|in(sK9_skl(X0,X1,sK69_skl),relation_dom(sK69_skl))))),
% 3.39/0.89 introduced(definition,[new_symbols(definition,[sQ68_spl])],[split_symbol_definition])).
% 3.39/0.89 fof(f2195,plain,(
% 3.39/0.89 ~sQ67_spl|sQ68_spl),
% 3.39/0.89 inference(split_clause,[status(thm)],[f2139,f2189,f2192])).
% 3.39/0.89 fof(f2196,definition,(
% 3.39/0.89 sQ69_spl <=> (relation(empty_set))),
% 3.39/0.89 introduced(definition,[new_symbols(definition,[sQ69_spl])],[split_symbol_definition])).
% 3.39/0.89 fof(f2198,plain,(
% 3.39/0.89 ~relation(empty_set)|sQ69_spl),
% 3.39/0.89 inference(component_clause,[status(thm)],[f2196])).
% 3.39/0.89 fof(f2199,definition,(
% 3.39/0.89 ![X0,X1]: (sQ70_spl <=> (X0=relation_inverse_image(empty_set,X1)|in(sK9_skl(X0,X1,empty_set),X0)|in(sK9_skl(X0,X1,empty_set),relation_dom(empty_set))))),
% 3.39/0.89 introduced(definition,[new_symbols(definition,[sQ70_spl])],[split_symbol_definition])).
% 3.39/0.89 fof(f2202,plain,(
% 3.39/0.89 ~sQ69_spl|sQ70_spl),
% 3.39/0.89 inference(split_clause,[status(thm)],[f2140,f2196,f2199])).
% 3.39/0.89 fof(f2204,plain,(
% 3.39/0.89 $false|sQ57_spl),
% 3.39/0.89 inference(forward_subsumption_resolution,[status(thm)],[f2156,f813])).
% 3.39/0.89 fof(f2205,plain,(
% 3.39/0.89 sQ57_spl),
% 3.39/0.89 inference(contradiction_clause,[status(thm)],[f2204])).
% 3.39/0.89 fof(f2206,plain,(
% 3.39/0.89 $false|sQ55_spl),
% 3.39/0.89 inference(forward_subsumption_resolution,[status(thm)],[f2149,f1494])).
% 3.39/0.89 fof(f2207,plain,(
% 3.39/0.89 sQ55_spl),
% 3.39/0.89 inference(contradiction_clause,[status(thm)],[f2206])).
% 3.39/0.89 fof(f2208,plain,(
% 3.39/0.89 $false|sQ69_spl),
% 3.39/0.89 inference(forward_subsumption_resolution,[status(thm)],[f2198,f672])).
% 3.39/0.89 fof(f2209,plain,(
% 3.39/0.89 sQ69_spl),
% 3.39/0.89 inference(contradiction_clause,[status(thm)],[f2208])).
% 3.39/0.89 fof(f2210,plain,(
% 3.39/0.89 $false|sQ67_spl),
% 3.39/0.89 inference(forward_subsumption_resolution,[status(thm)],[f2191,f805])).
% 3.39/0.89 fof(f2211,plain,(
% 3.39/0.89 sQ67_spl),
% 3.39/0.89 inference(contradiction_clause,[status(thm)],[f2210])).
% 3.39/0.89 fof(f2212,plain,(
% 3.39/0.89 $false|sQ65_spl),
% 3.39/0.89 inference(forward_subsumption_resolution,[status(thm)],[f2184,f821])).
% 3.39/0.89 fof(f2213,plain,(
% 3.39/0.89 sQ65_spl),
% 3.39/0.89 inference(contradiction_clause,[status(thm)],[f2212])).
% 3.39/0.89 fof(f2214,plain,(
% 3.39/0.89 $false|sQ63_spl),
% 3.39/0.89 inference(forward_subsumption_resolution,[status(thm)],[f2177,f825])).
% 3.39/0.89 fof(f2215,plain,(
% 3.39/0.89 sQ63_spl),
% 3.39/0.89 inference(contradiction_clause,[status(thm)],[f2214])).
% 3.39/0.89 fof(f2216,plain,(
% 3.39/0.89 $false|sQ61_spl),
% 3.39/0.89 inference(forward_subsumption_resolution,[status(thm)],[f2170,f841])).
% 3.39/0.89 fof(f2217,plain,(
% 3.39/0.89 sQ61_spl),
% 3.39/0.89 inference(contradiction_clause,[status(thm)],[f2216])).
% 3.39/0.89 fof(f2218,plain,(
% 3.39/0.89 $false|sQ59_spl),
% 3.39/0.89 inference(forward_subsumption_resolution,[status(thm)],[f2163,f853])).
% 3.39/0.89 fof(f2219,plain,(
% 3.39/0.89 sQ59_spl),
% 3.39/0.89 inference(contradiction_clause,[status(thm)],[f2218])).
% 3.39/0.89 fof(f2224,plain,(
% 3.39/0.89 ![X0,X1]: (~relation(sK73_skl)|X0=relation_inverse_image(sK73_skl,X1)|in(sK9_skl(X0,X1,sK73_skl),X0)|in(apply(sK73_skl,sK9_skl(X0,X1,sK73_skl)),X1)|~sQ16_spl)),
% 3.39/0.89 inference(resolution,[status(thm)],[f365,f1496])).
% 3.39/0.89 fof(f2225,plain,(
% 3.39/0.89 ![X0,X1]: (~relation(sK71_skl)|X0=relation_inverse_image(sK71_skl,X1)|in(sK9_skl(X0,X1,sK71_skl),X0)|in(apply(sK71_skl,sK9_skl(X0,X1,sK71_skl)),X1)|~sQ14_spl)),
% 3.39/0.89 inference(resolution,[status(thm)],[f365,f1481])).
% 3.39/0.89 fof(f2226,plain,(
% 3.39/0.89 ![X0,X1]: (~relation(sK82_skl)|X0=relation_inverse_image(sK82_skl,X1)|in(sK9_skl(X0,X1,sK82_skl),X0)|in(apply(sK82_skl,sK9_skl(X0,X1,sK82_skl)),X1))),
% 3.39/0.89 inference(resolution,[status(thm)],[f365,f855])).
% 3.39/0.89 fof(f2227,plain,(
% 3.39/0.89 ![X0,X1]: (~relation(sK79_skl)|X0=relation_inverse_image(sK79_skl,X1)|in(sK9_skl(X0,X1,sK79_skl),X0)|in(apply(sK79_skl,sK9_skl(X0,X1,sK79_skl)),X1))),
% 3.39/0.89 inference(resolution,[status(thm)],[f365,f842])).
% 3.39/0.89 fof(f2228,plain,(
% 3.39/0.89 ![X0,X1]: (~relation(sK75_skl)|X0=relation_inverse_image(sK75_skl,X1)|in(sK9_skl(X0,X1,sK75_skl),X0)|in(apply(sK75_skl,sK9_skl(X0,X1,sK75_skl)),X1))),
% 3.39/0.89 inference(resolution,[status(thm)],[f365,f826])).
% 3.39/0.89 fof(f2229,plain,(
% 3.39/0.89 ![X0,X1]: (~relation(sK74_skl)|X0=relation_inverse_image(sK74_skl,X1)|in(sK9_skl(X0,X1,sK74_skl),X0)|in(apply(sK74_skl,sK9_skl(X0,X1,sK74_skl)),X1))),
% 3.39/0.89 inference(resolution,[status(thm)],[f365,f823])).
% 3.39/0.89 fof(f2230,plain,(
% 3.39/0.89 ![X0,X1]: (~relation(sK69_skl)|X0=relation_inverse_image(sK69_skl,X1)|in(sK9_skl(X0,X1,sK69_skl),X0)|in(apply(sK69_skl,sK9_skl(X0,X1,sK69_skl)),X1))),
% 3.39/0.89 inference(resolution,[status(thm)],[f365,f806])).
% 3.39/0.89 fof(f2231,plain,(
% 3.39/0.89 ![X0,X1]: (~relation(empty_set)|X0=relation_inverse_image(empty_set,X1)|in(sK9_skl(X0,X1,empty_set),X0)|in(apply(empty_set,sK9_skl(X0,X1,empty_set)),X1))),
% 3.39/0.89 inference(resolution,[status(thm)],[f365,f692])).
% 3.39/0.89 fof(f2238,definition,(
% 3.39/0.89 ![X0,X1]: (sQ72_spl <=> (X0=relation_inverse_image(sK73_skl,X1)|in(sK9_skl(X0,X1,sK73_skl),X0)|in(apply(sK73_skl,sK9_skl(X0,X1,sK73_skl)),X1)))),
% 3.39/0.89 introduced(definition,[new_symbols(definition,[sQ72_spl])],[split_symbol_definition])).
% 3.39/0.89 fof(f2241,plain,(
% 3.39/0.89 ~sQ55_spl|sQ72_spl|~sQ16_spl),
% 3.39/0.89 inference(split_clause,[status(thm)],[f2224,f2147,f2238,f1495])).
% 3.39/0.89 fof(f2242,definition,(
% 3.39/0.89 ![X0,X1]: (sQ73_spl <=> (X0=relation_inverse_image(sK71_skl,X1)|in(sK9_skl(X0,X1,sK71_skl),X0)|in(apply(sK71_skl,sK9_skl(X0,X1,sK71_skl)),X1)))),
% 3.39/0.89 introduced(definition,[new_symbols(definition,[sQ73_spl])],[split_symbol_definition])).
% 3.39/0.89 fof(f2245,plain,(
% 3.39/0.89 ~sQ57_spl|sQ73_spl|~sQ14_spl),
% 3.39/0.89 inference(split_clause,[status(thm)],[f2225,f2154,f2242,f1480])).
% 3.39/0.89 fof(f2246,definition,(
% 3.39/0.89 ![X0,X1]: (sQ74_spl <=> (X0=relation_inverse_image(sK82_skl,X1)|in(sK9_skl(X0,X1,sK82_skl),X0)|in(apply(sK82_skl,sK9_skl(X0,X1,sK82_skl)),X1)))),
% 3.39/0.89 introduced(definition,[new_symbols(definition,[sQ74_spl])],[split_symbol_definition])).
% 3.39/0.89 fof(f2249,plain,(
% 3.39/0.89 ~sQ59_spl|sQ74_spl),
% 3.39/0.89 inference(split_clause,[status(thm)],[f2226,f2161,f2246])).
% 3.39/0.89 fof(f2250,definition,(
% 3.39/0.89 ![X0,X1]: (sQ75_spl <=> (X0=relation_inverse_image(sK79_skl,X1)|in(sK9_skl(X0,X1,sK79_skl),X0)|in(apply(sK79_skl,sK9_skl(X0,X1,sK79_skl)),X1)))),
% 3.39/0.89 introduced(definition,[new_symbols(definition,[sQ75_spl])],[split_symbol_definition])).
% 3.39/0.89 fof(f2253,plain,(
% 3.39/0.89 ~sQ61_spl|sQ75_spl),
% 3.39/0.89 inference(split_clause,[status(thm)],[f2227,f2168,f2250])).
% 3.39/0.89 fof(f2254,definition,(
% 3.39/0.89 ![X0,X1]: (sQ76_spl <=> (X0=relation_inverse_image(sK75_skl,X1)|in(sK9_skl(X0,X1,sK75_skl),X0)|in(apply(sK75_skl,sK9_skl(X0,X1,sK75_skl)),X1)))),
% 3.39/0.89 introduced(definition,[new_symbols(definition,[sQ76_spl])],[split_symbol_definition])).
% 3.39/0.89 fof(f2257,plain,(
% 3.39/0.89 ~sQ63_spl|sQ76_spl),
% 3.39/0.89 inference(split_clause,[status(thm)],[f2228,f2175,f2254])).
% 3.39/0.89 fof(f2258,definition,(
% 3.39/0.89 ![X0,X1]: (sQ77_spl <=> (X0=relation_inverse_image(sK74_skl,X1)|in(sK9_skl(X0,X1,sK74_skl),X0)|in(apply(sK74_skl,sK9_skl(X0,X1,sK74_skl)),X1)))),
% 3.39/0.89 introduced(definition,[new_symbols(definition,[sQ77_spl])],[split_symbol_definition])).
% 3.39/0.89 fof(f2261,plain,(
% 3.39/0.89 ~sQ65_spl|sQ77_spl),
% 3.39/0.89 inference(split_clause,[status(thm)],[f2229,f2182,f2258])).
% 3.39/0.89 fof(f2262,definition,(
% 3.39/0.89 ![X0,X1]: (sQ78_spl <=> (X0=relation_inverse_image(sK69_skl,X1)|in(sK9_skl(X0,X1,sK69_skl),X0)|in(apply(sK69_skl,sK9_skl(X0,X1,sK69_skl)),X1)))),
% 3.39/0.89 introduced(definition,[new_symbols(definition,[sQ78_spl])],[split_symbol_definition])).
% 3.39/0.89 fof(f2265,plain,(
% 3.39/0.89 ~sQ67_spl|sQ78_spl),
% 3.39/0.89 inference(split_clause,[status(thm)],[f2230,f2189,f2262])).
% 3.39/0.89 fof(f2266,definition,(
% 3.39/0.89 ![X0,X1]: (sQ79_spl <=> (X0=relation_inverse_image(empty_set,X1)|in(sK9_skl(X0,X1,empty_set),X0)|in(apply(empty_set,sK9_skl(X0,X1,empty_set)),X1)))),
% 3.39/0.89 introduced(definition,[new_symbols(definition,[sQ79_spl])],[split_symbol_definition])).
% 3.39/0.89 fof(f2269,plain,(
% 3.39/0.89 ~sQ69_spl|sQ79_spl),
% 3.39/0.89 inference(split_clause,[status(thm)],[f2231,f2196,f2266])).
% 3.39/0.89 fof(f2415,plain,(
% 3.39/0.89 relation_dom(sK66_skl)=empty_set|~sQ48_spl),
% 3.39/0.89 inference(paramodulation,[status(thm)],[f1883,f1200])).
% 3.39/0.89 fof(f2417,plain,(
% 3.39/0.89 relation_rng(sK66_skl)=empty_set|~sQ48_spl),
% 3.39/0.89 inference(paramodulation,[status(thm)],[f1883,f1201])).
% 3.39/0.89 fof(f2443,plain,(
% 3.39/0.89 relation_field(sK66_skl)=set_union2(relation_rng(sK66_skl),empty_set)|~sQ48_spl),
% 3.39/0.89 inference(backward_demodulation,[status(thm)],[f2415,f1523])).
% 3.39/0.89 fof(f2445,plain,(
% 3.39/0.89 relation_field(sK66_skl)=relation_rng(sK66_skl)|~sQ48_spl),
% 3.39/0.89 inference(forward_demodulation,[status(thm)],[f965,f2443])).
% 3.39/0.89 fof(f2481,definition,(
% 3.39/0.89 sQ83_spl <=> (is_reflexive_in(sK66_skl,empty_set))),
% 3.39/0.89 introduced(definition,[new_symbols(definition,[sQ83_spl])],[split_symbol_definition])).
% 3.39/0.89 fof(f2482,plain,(
% 3.39/0.89 is_reflexive_in(sK66_skl,empty_set)|~sQ83_spl),
% 3.39/0.89 inference(component_clause,[status(thm)],[f2481])).
% 3.39/0.89 fof(f2483,plain,(
% 3.39/0.89 ~is_reflexive_in(sK66_skl,empty_set)|sQ83_spl),
% 3.39/0.89 inference(component_clause,[status(thm)],[f2481])).
% 3.39/0.89 fof(f2528,plain,(
% 3.39/0.89 ![X0,X1]: (X0=relation_image(sK66_skl,X1)|in(sK11_skl(X0,X1,sK66_skl),X0)|in(sK12_skl(X0,X1,sK66_skl),X1))),
% 3.39/0.89 inference(resolution,[status(thm)],[f375,f758])).
% 3.39/0.89 fof(f2529,plain,(
% 3.39/0.89 in(sK67_skl,empty_set)|~sQ48_spl|~sQ2_spl),
% 3.39/0.89 inference(backward_demodulation,[status(thm)],[f2530,f1303])).
% 3.39/0.89 fof(f2530,plain,(
% 3.39/0.89 relation_field(sK66_skl)=empty_set|~sQ48_spl),
% 3.39/0.89 inference(forward_demodulation,[status(thm)],[f2417,f2445])).
% 3.39/0.89 fof(f2531,plain,(
% 3.39/0.89 ~relation(sK66_skl)|reflexive(sK66_skl)|~is_reflexive_in(sK66_skl,empty_set)|~sQ48_spl),
% 3.39/0.89 inference(paramodulation,[status(thm)],[f2530,f637])).
% 3.39/0.89 fof(f2532,plain,(
% 3.39/0.89 $false|~sQ48_spl|~sQ2_spl),
% 3.39/0.89 inference(forward_subsumption_resolution,[status(thm)],[f2529,f1348])).
% 3.39/0.89 fof(f2533,plain,(
% 3.39/0.89 ~sQ48_spl|~sQ2_spl),
% 3.39/0.89 inference(contradiction_clause,[status(thm)],[f2532])).
% 3.39/0.89 fof(f2534,plain,(
% 3.39/0.89 ~relation(sK66_skl)|reflexive(sK66_skl)|~sQ11_spl),
% 3.39/0.89 inference(resolution,[status(thm)],[f1453,f637])).
% 3.39/0.89 fof(f2535,plain,(
% 3.39/0.89 ~sQ10_spl|sQ0_spl|~sQ11_spl),
% 3.39/0.89 inference(split_clause,[status(thm)],[f2534,f1449,f1295,f1452])).
% 3.39/0.89 fof(f2648,plain,(
% 3.39/0.89 ![X0,X1]: (X0=relation_inverse_image(sK66_skl,X1)|in(sK14_skl(X0,X1,sK66_skl),X0)|in(sK15_skl(X0,X1,sK66_skl),X1))),
% 3.39/0.89 inference(resolution,[status(thm)],[f385,f758])).
% 3.39/0.89 fof(f2722,plain,(
% 3.39/0.89 ![X0,X1,X2]: (X0=relation_image(sK66_skl,X1)|in(sK12_skl(X0,X1,sK66_skl),X1)|~relation(sK66_skl)|X0=relation_image(sK66_skl,X1)|~in(ordered_pair(X2,sK11_skl(X0,X1,sK66_skl)),sK66_skl)|~in(X2,X1))),
% 3.39/0.89 inference(resolution,[status(thm)],[f2528,f373])).
% 3.39/0.89 fof(f2749,definition,(
% 3.39/0.89 ![X0,X1,X2]: (sQ84_spl <=> (X0=relation_image(sK66_skl,X1)|in(sK12_skl(X0,X1,sK66_skl),X1)|X0=relation_image(sK66_skl,X1)|~in(ordered_pair(X2,sK11_skl(X0,X1,sK66_skl)),sK66_skl)|~in(X2,X1)))),
% 3.39/0.89 introduced(definition,[new_symbols(definition,[sQ84_spl])],[split_symbol_definition])).
% 3.39/0.89 fof(f2752,plain,(
% 3.39/0.89 sQ84_spl|~sQ10_spl),
% 3.39/0.89 inference(split_clause,[status(thm)],[f2722,f2749,f1449])).
% 3.39/0.89 fof(f2921,plain,(
% 3.39/0.89 succ(empty_set)=singleton(empty_set)),
% 3.39/0.89 inference(paramodulation,[status(thm)],[f2117,f396])).
% 3.39/0.89 fof(f3001,plain,(
% 3.39/0.89 empty(relation_inverse(empty_set))),
% 3.39/0.89 inference(resolution,[status(thm)],[f669,f671])).
% 3.39/0.89 fof(f3004,plain,(
% 3.39/0.89 relation_inverse(empty_set)=empty_set),
% 3.39/0.89 inference(resolution,[status(thm)],[f3001,f1193])).
% 3.39/0.89 fof(f3008,plain,(
% 3.39/0.89 ~function(relation_inverse(empty_set))|one_to_one(relation_inverse(empty_set))),
% 3.39/0.89 inference(resolution,[status(thm)],[f3001,f1426])).
% 3.39/0.89 fof(f3010,definition,(
% 3.39/0.89 sQ85_spl <=> (function(relation_inverse(empty_set)))),
% 3.39/0.89 introduced(definition,[new_symbols(definition,[sQ85_spl])],[split_symbol_definition])).
% 3.39/0.89 fof(f3012,plain,(
% 3.39/0.89 ~function(relation_inverse(empty_set))|sQ85_spl),
% 3.39/0.89 inference(component_clause,[status(thm)],[f3010])).
% 3.39/0.89 fof(f3013,definition,(
% 3.39/0.89 sQ86_spl <=> (one_to_one(relation_inverse(empty_set)))),
% 3.39/0.89 introduced(definition,[new_symbols(definition,[sQ86_spl])],[split_symbol_definition])).
% 3.39/0.89 fof(f3016,plain,(
% 3.39/0.89 ~sQ85_spl|sQ86_spl),
% 3.39/0.89 inference(split_clause,[status(thm)],[f3008,f3010,f3013])).
% 3.39/0.89 fof(f3022,plain,(
% 3.39/0.89 ~function(empty_set)|sQ85_spl),
% 3.39/0.89 inference(forward_demodulation,[status(thm)],[f3004,f3012])).
% 3.39/0.89 fof(f3023,plain,(
% 3.39/0.89 $false|sQ85_spl),
% 3.39/0.89 inference(forward_subsumption_resolution,[status(thm)],[f3022,f692])).
% 3.39/0.89 fof(f3024,plain,(
% 3.39/0.89 sQ85_spl),
% 3.39/0.89 inference(contradiction_clause,[status(thm)],[f3023])).
% 3.39/0.89 fof(f3073,plain,(
% 3.39/0.89 ![X0]: (~relation(sK66_skl)|~in(X0,relation_field(sK66_skl))|in(ordered_pair(X0,X0),sK66_skl)|~sQ11_spl)),
% 3.39/0.89 inference(resolution,[status(thm)],[f408,f1453])).
% 3.39/0.89 fof(f3075,plain,(
% 3.39/0.89 ~sQ10_spl|sQ1_spl|~sQ11_spl),
% 3.39/0.89 inference(split_clause,[status(thm)],[f3073,f1449,f1298,f1452])).
% 3.39/0.89 fof(f3122,plain,(
% 3.39/0.89 ~in(sK67_skl,relation_field(sK66_skl))|~sQ1_spl|sQ3_spl),
% 3.39/0.89 inference(resolution,[status(thm)],[f1299,f1308])).
% 3.39/0.89 fof(f3129,plain,(
% 3.39/0.89 $false|~sQ2_spl|~sQ1_spl|sQ3_spl),
% 3.39/0.89 inference(forward_subsumption_resolution,[status(thm)],[f3122,f1303])).
% 3.39/0.89 fof(f3130,plain,(
% 3.39/0.89 ~sQ2_spl|~sQ1_spl|sQ3_spl),
% 3.39/0.89 inference(contradiction_clause,[status(thm)],[f3129])).
% 3.39/0.89 fof(f3172,plain,(
% 3.39/0.89 ![X0]: (~relation(X0)|is_reflexive_in(X0,empty_set))),
% 3.39/0.89 inference(resolution,[status(thm)],[f409,f1348])).
% 3.39/0.89 fof(f3176,plain,(
% 3.39/0.89 ![X0]: (~relation(sK66_skl)|is_reflexive_in(sK66_skl,X0)|~in(sK20_skl(X0,sK66_skl),relation_field(sK66_skl))|~sQ1_spl)),
% 3.39/0.89 inference(resolution,[status(thm)],[f410,f1299])).
% 3.39/0.89 fof(f3177,definition,(
% 3.39/0.89 ![X0]: (sQ90_spl <=> (is_reflexive_in(sK66_skl,X0)|~in(sK20_skl(X0,sK66_skl),relation_field(sK66_skl))))),
% 3.39/0.89 introduced(definition,[new_symbols(definition,[sQ90_spl])],[split_symbol_definition])).
% 3.39/0.89 fof(f3178,plain,(
% 3.39/0.89 ![X0]: (is_reflexive_in(sK66_skl,X0)|~in(sK20_skl(X0,sK66_skl),relation_field(sK66_skl))|~sQ90_spl)),
% 3.39/0.89 inference(component_clause,[status(thm)],[f3177])).
% 3.39/0.89 fof(f3180,plain,(
% 3.39/0.89 ~sQ10_spl|sQ90_spl|~sQ1_spl),
% 3.39/0.89 inference(split_clause,[status(thm)],[f3176,f1449,f3177,f1298])).
% 3.39/0.89 fof(f3314,plain,(
% 3.39/0.89 ![X0,X1,X2]: (X0=relation_inverse_image(sK66_skl,X1)|in(sK15_skl(X0,X1,sK66_skl),X1)|~relation(sK66_skl)|X0=relation_inverse_image(sK66_skl,X1)|~in(ordered_pair(sK14_skl(X0,X1,sK66_skl),X2),sK66_skl)|~in(X2,X1))),
% 3.39/0.89 inference(resolution,[status(thm)],[f2648,f383])).
% 3.39/0.89 fof(f3343,definition,(
% 3.39/0.89 ![X0,X1,X2]: (sQ96_spl <=> (X0=relation_inverse_image(sK66_skl,X1)|in(sK15_skl(X0,X1,sK66_skl),X1)|X0=relation_inverse_image(sK66_skl,X1)|~in(ordered_pair(sK14_skl(X0,X1,sK66_skl),X2),sK66_skl)|~in(X2,X1)))),
% 3.39/0.89 introduced(definition,[new_symbols(definition,[sQ96_spl])],[split_symbol_definition])).
% 3.39/0.89 fof(f3346,plain,(
% 3.39/0.89 sQ96_spl|~sQ10_spl),
% 3.39/0.89 inference(split_clause,[status(thm)],[f3314,f3343,f1449])).
% 3.39/0.89 fof(f3357,plain,(
% 3.39/0.89 union(singleton(empty_set))=empty_set),
% 3.39/0.89 inference(paramodulation,[status(thm)],[f971,f1258])).
% 3.39/0.89 fof(f3367,plain,(
% 3.39/0.89 ![X0]: (relation_field(sK66_skl)=empty_set|X0=set_meet(relation_field(sK66_skl))|in(sK22_skl(X0,relation_field(sK66_skl)),X0)|in(sK22_skl(X0,relation_field(sK66_skl)),sK1_skl(empty_set,sK66_skl))|~sQ50_spl)),
% 3.39/0.89 inference(resolution,[status(thm)],[f420,f1890])).
% 3.39/0.89 fof(f3368,plain,(
% 3.39/0.89 ![X0]: (relation_field(sK66_skl)=empty_set|X0=set_meet(relation_field(sK66_skl))|in(sK22_skl(X0,relation_field(sK66_skl)),X0)|in(sK22_skl(X0,relation_field(sK66_skl)),sK0_skl(empty_set,sK66_skl))|~sQ49_spl)),
% 3.39/0.89 inference(resolution,[status(thm)],[f420,f1886])).
% 3.39/0.89 fof(f3382,definition,(
% 3.39/0.89 sQ97_spl <=> (relation_field(sK66_skl)=empty_set)),
% 3.39/0.89 introduced(definition,[new_symbols(definition,[sQ97_spl])],[split_symbol_definition])).
% 3.39/0.89 fof(f3383,plain,(
% 3.39/0.89 relation_field(sK66_skl)=empty_set|~sQ97_spl),
% 3.39/0.89 inference(component_clause,[status(thm)],[f3382])).
% 3.39/0.89 fof(f3385,definition,(
% 3.39/0.89 ![X0]: (sQ98_spl <=> (X0=set_meet(relation_field(sK66_skl))|in(sK22_skl(X0,relation_field(sK66_skl)),X0)|in(sK22_skl(X0,relation_field(sK66_skl)),sK1_skl(empty_set,sK66_skl))))),
% 3.39/0.89 introduced(definition,[new_symbols(definition,[sQ98_spl])],[split_symbol_definition])).
% 3.39/0.89 fof(f3388,plain,(
% 3.39/0.89 sQ97_spl|sQ98_spl|~sQ50_spl),
% 3.39/0.89 inference(split_clause,[status(thm)],[f3367,f3382,f3385,f1889])).
% 3.39/0.89 fof(f3389,definition,(
% 3.39/0.89 ![X0]: (sQ99_spl <=> (X0=set_meet(relation_field(sK66_skl))|in(sK22_skl(X0,relation_field(sK66_skl)),X0)|in(sK22_skl(X0,relation_field(sK66_skl)),sK0_skl(empty_set,sK66_skl))))),
% 3.39/0.89 introduced(definition,[new_symbols(definition,[sQ99_spl])],[split_symbol_definition])).
% 3.39/0.89 fof(f3392,plain,(
% 3.39/0.89 sQ97_spl|sQ99_spl|~sQ49_spl),
% 3.39/0.89 inference(split_clause,[status(thm)],[f3368,f3382,f3389,f1885])).
% 3.39/0.89 fof(f3532,plain,(
% 3.39/0.89 ~relation(sK66_skl)|reflexive(sK66_skl)|~is_reflexive_in(sK66_skl,empty_set)|~sQ97_spl),
% 3.39/0.89 inference(paramodulation,[status(thm)],[f3383,f637])).
% 3.39/0.89 fof(f3533,plain,(
% 3.39/0.89 ~sQ10_spl|sQ0_spl|~sQ83_spl|~sQ97_spl),
% 3.39/0.89 inference(split_clause,[status(thm)],[f3532,f1449,f1295,f2481,f3382])).
% 3.39/0.89 fof(f3535,plain,(
% 3.39/0.89 ~sQ10_spl|sQ0_spl|~sQ83_spl|~sQ48_spl),
% 3.39/0.89 inference(split_clause,[status(thm)],[f2531,f1449,f1295,f2481,f1882])).
% 3.39/0.89 fof(f3603,plain,(
% 3.39/0.89 ![X0]: (singleton(X0)=empty_set|sK25_skl(singleton(X0))=X0)),
% 3.39/0.89 inference(resolution,[status(thm)],[f434,f1346])).
% 3.39/0.89 fof(f3615,plain,(
% 3.39/0.89 ![X0]: (X0=empty_set|~in(X0,sK25_skl(X0)))),
% 3.39/0.89 inference(resolution,[status(thm)],[f434,f286])).
% 3.39/0.89 fof(f3616,plain,(
% 3.39/0.89 ![X0]: (sK25_skl(singleton(X0))=X0)),
% 3.39/0.89 inference(forward_subsumption_resolution,[status(thm)],[f3603,f762])).
% 3.39/0.89 fof(f3940,plain,(
% 3.39/0.89 sK25_skl(succ(empty_set))=empty_set),
% 3.39/0.89 inference(paramodulation,[status(thm)],[f2921,f3616])).
% 3.39/0.89 fof(f3953,plain,(
% 3.39/0.89 ~succ(empty_set)=empty_set),
% 3.39/0.89 inference(paramodulation,[status(thm)],[f2921,f762])).
% 3.39/0.89 fof(f4020,plain,(
% 3.39/0.89 ~relation(sK66_skl)|sQ83_spl),
% 3.39/0.89 inference(resolution,[status(thm)],[f3172,f2483])).
% 3.39/0.89 fof(f4022,plain,(
% 3.39/0.89 ~sQ10_spl|sQ83_spl),
% 3.39/0.89 inference(split_clause,[status(thm)],[f4020,f1449,f2481])).
% 3.39/0.89 fof(f4024,plain,(
% 3.39/0.89 ![X0]: (~relation(sK66_skl)|~in(X0,empty_set)|in(ordered_pair(X0,X0),sK66_skl)|~sQ83_spl)),
% 3.39/0.89 inference(resolution,[status(thm)],[f2482,f408])).
% 3.39/0.89 fof(f4025,definition,(
% 3.39/0.89 ![X0]: (sQ119_spl <=> (~in(X0,empty_set)|in(ordered_pair(X0,X0),sK66_skl)))),
% 3.39/0.89 introduced(definition,[new_symbols(definition,[sQ119_spl])],[split_symbol_definition])).
% 3.39/0.89 fof(f4028,plain,(
% 3.39/0.89 ~sQ10_spl|sQ119_spl|~sQ83_spl),
% 3.39/0.89 inference(split_clause,[status(thm)],[f4024,f1449,f4025,f2481])).
% 3.39/0.89 fof(f4029,plain,(
% 3.39/0.89 union(succ(empty_set))=empty_set),
% 3.39/0.89 inference(forward_demodulation,[status(thm)],[f2921,f3357])).
% 3.39/0.89 fof(f4031,plain,(
% 3.39/0.89 ~ordinal(succ(empty_set))|epsilon_connected(empty_set)),
% 3.39/0.89 inference(paramodulation,[status(thm)],[f4029,f724])).
% 3.39/0.89 fof(f4033,definition,(
% 3.39/0.89 sQ120_spl <=> (ordinal(succ(empty_set)))),
% 3.39/0.89 introduced(definition,[new_symbols(definition,[sQ120_spl])],[split_symbol_definition])).
% 3.39/0.89 fof(f4035,plain,(
% 3.39/0.89 ~ordinal(succ(empty_set))|sQ120_spl),
% 3.39/0.89 inference(component_clause,[status(thm)],[f4033])).
% 3.39/0.89 fof(f4037,definition,(
% 3.39/0.89 sQ121_spl <=> (epsilon_connected(empty_set))),
% 3.39/0.89 introduced(definition,[new_symbols(definition,[sQ121_spl])],[split_symbol_definition])).
% 3.39/0.89 fof(f4040,plain,(
% 3.39/0.89 ~sQ120_spl|sQ121_spl),
% 3.39/0.89 inference(split_clause,[status(thm)],[f4031,f4033,f4037])).
% 3.39/0.89 fof(f4042,plain,(
% 3.39/0.89 ~ordinal(empty_set)|sQ120_spl),
% 3.39/0.89 inference(resolution,[status(thm)],[f4035,f711])).
% 3.39/0.89 fof(f4043,plain,(
% 3.39/0.89 $false|sQ120_spl),
% 3.39/0.89 inference(forward_subsumption_resolution,[status(thm)],[f4042,f697])).
% 3.39/0.89 fof(f4044,plain,(
% 3.39/0.89 sQ120_spl),
% 3.39/0.89 inference(contradiction_clause,[status(thm)],[f4043])).
% 3.39/0.89 fof(f4053,plain,(
% 3.39/0.89 ![X0]: (~element(X0,empty_set)|empty(X0))),
% 3.39/0.89 inference(resolution,[status(thm)],[f462,f671])).
% 3.39/0.89 fof(f4167,plain,(
% 3.39/0.89 succ(empty_set)=empty_set|~in(succ(empty_set),empty_set)),
% 3.39/0.89 inference(paramodulation,[status(thm)],[f3940,f3615])).
% 3.39/0.89 fof(f4168,plain,(
% 3.39/0.89 succ(empty_set)=empty_set|in(empty_set,succ(empty_set))),
% 3.39/0.89 inference(paramodulation,[status(thm)],[f3940,f434])).
% 3.39/0.89 fof(f4169,definition,(
% 3.39/0.89 sQ130_spl <=> (succ(empty_set)=empty_set)),
% 3.39/0.89 introduced(definition,[new_symbols(definition,[sQ130_spl])],[split_symbol_definition])).
% 3.39/0.89 fof(f4170,plain,(
% 3.39/0.89 succ(empty_set)=empty_set|~sQ130_spl),
% 3.39/0.89 inference(component_clause,[status(thm)],[f4169])).
% 3.39/0.89 fof(f4172,definition,(
% 3.39/0.89 sQ131_spl <=> (in(succ(empty_set),empty_set))),
% 3.39/0.89 introduced(definition,[new_symbols(definition,[sQ131_spl])],[split_symbol_definition])).
% 3.39/0.89 fof(f4175,plain,(
% 3.39/0.89 sQ130_spl|~sQ131_spl),
% 3.39/0.89 inference(split_clause,[status(thm)],[f4167,f4169,f4172])).
% 3.39/0.89 fof(f4176,definition,(
% 3.39/0.89 sQ132_spl <=> (in(empty_set,succ(empty_set)))),
% 3.39/0.89 introduced(definition,[new_symbols(definition,[sQ132_spl])],[split_symbol_definition])).
% 3.39/0.89 fof(f4179,plain,(
% 3.39/0.89 sQ130_spl|sQ132_spl),
% 3.39/0.89 inference(split_clause,[status(thm)],[f4168,f4169,f4176])).
% 3.39/0.89 fof(f4180,plain,(
% 3.39/0.89 $false|~sQ130_spl),
% 3.39/0.89 inference(forward_subsumption_resolution,[status(thm)],[f4170,f3953])).
% 3.39/0.89 fof(f4181,plain,(
% 3.39/0.89 ~sQ130_spl),
% 3.39/0.89 inference(contradiction_clause,[status(thm)],[f4180])).
% 3.39/0.89 fof(f4265,plain,(
% 3.39/0.89 empty(sK65_skl(empty_set))),
% 3.39/0.89 inference(resolution,[status(thm)],[f4053,f664])).
% 3.39/0.89 fof(f4276,plain,(
% 3.39/0.89 sK65_skl(empty_set)=empty_set),
% 3.39/0.89 inference(resolution,[status(thm)],[f4265,f1193])).
% 3.39/0.89 fof(f4280,plain,(
% 3.39/0.89 ~function(sK65_skl(empty_set))|one_to_one(sK65_skl(empty_set))),
% 3.39/0.89 inference(resolution,[status(thm)],[f4265,f1426])).
% 3.39/0.89 fof(f4282,definition,(
% 3.39/0.89 sQ137_spl <=> (function(sK65_skl(empty_set)))),
% 3.39/0.89 introduced(definition,[new_symbols(definition,[sQ137_spl])],[split_symbol_definition])).
% 3.39/0.89 fof(f4284,plain,(
% 3.39/0.89 ~function(sK65_skl(empty_set))|sQ137_spl),
% 3.39/0.89 inference(component_clause,[status(thm)],[f4282])).
% 3.39/0.89 fof(f4285,definition,(
% 3.39/0.89 sQ138_spl <=> (one_to_one(sK65_skl(empty_set)))),
% 3.39/0.89 introduced(definition,[new_symbols(definition,[sQ138_spl])],[split_symbol_definition])).
% 3.39/0.89 fof(f4288,plain,(
% 3.39/0.89 ~sQ137_spl|sQ138_spl),
% 3.39/0.89 inference(split_clause,[status(thm)],[f4280,f4282,f4285])).
% 3.39/0.89 fof(f4295,plain,(
% 3.39/0.89 ~function(empty_set)|sQ137_spl),
% 3.39/0.89 inference(forward_demodulation,[status(thm)],[f4276,f4284])).
% 3.39/0.89 fof(f4296,plain,(
% 3.39/0.89 $false|sQ137_spl),
% 3.39/0.89 inference(forward_subsumption_resolution,[status(thm)],[f4295,f692])).
% 3.39/0.89 fof(f4297,plain,(
% 3.39/0.89 sQ137_spl),
% 3.39/0.89 inference(contradiction_clause,[status(thm)],[f4296])).
% 3.39/0.89 fof(f4398,plain,(
% 3.39/0.89 is_reflexive_in(sK66_skl,relation_field(sK66_skl))|~relation(sK66_skl)|is_reflexive_in(sK66_skl,relation_field(sK66_skl))|~sQ90_spl),
% 3.39/0.89 inference(resolution,[status(thm)],[f3178,f409])).
% 3.39/0.89 fof(f4399,plain,(
% 3.39/0.89 sQ11_spl|~sQ10_spl|~sQ90_spl),
% 3.39/0.89 inference(split_clause,[status(thm)],[f4398,f1452,f1449,f3177])).
% 3.39/0.89 fof(f4400,plain,(
% 3.39/0.89 $false),
% 3.39/0.89 inference(sat_refutation,[status(thm)],[f1301,f1305,f1309,f1434,f1436,f1444,f1446,f1455,f1457,f1470,f1472,f1486,f1501,f1516,f1563,f1565,f1573,f1575,f1594,f1596,f1703,f1762,f1773,f1781,f1792,f1814,f1854,f1856,f1879,f1888,f1892,f2153,f2160,f2167,f2174,f2181,f2188,f2195,f2202,f2205,f2207,f2209,f2211,f2213,f2215,f2217,f2219,f2241,f2245,f2249,f2253,f2257,f2261,f2265,f2269,f2533,f2535,f2752,f3016,f3024,f3075,f3130,f3180,f3346,f3388,f3392,f3533,f3535,f4022,f4028,f4040,f4044,f4175,f4179,f4181,f4288,f4297,f4399])).
% 3.39/0.89 % SZS output end CNFRefutation for theBenchmark.p
% 3.39/0.89 % Elapsed time: 0.535078 seconds
% 3.39/0.89 % CPU time: 3.756809 seconds
% 3.39/0.89 % Total memory used: 170.429 MB
% 3.39/0.89 % Net memory used: 163.820 MB
%------------------------------------------------------------------------------