TSTP Solution File: SEU208+2 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SEU208+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 20:41:29 EDT 2024
% Result : Theorem 0.20s 0.54s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU208+2 : TPTP v8.1.2. Released v3.3.0.
% 0.11/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34 % Computer : n027.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Apr 29 20:11:02 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.13/0.36 % Drodi V3.6.0
% 0.20/0.54 % Refutation found
% 0.20/0.54 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.20/0.54 % SZS output start CNFRefutation for theBenchmark
% 0.20/0.54 fof(f3,axiom,(
% 0.20/0.54 (! [A] :( empty(A)=> relation(A) ) )),
% 0.20/0.54 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.20/0.54 fof(f5,axiom,(
% 0.20/0.54 (! [A,B] : set_union2(A,B) = set_union2(B,A) )),
% 0.20/0.54 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.20/0.54 fof(f6,axiom,(
% 0.20/0.54 (! [A,B] : set_intersection2(A,B) = set_intersection2(B,A) )),
% 0.20/0.54 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.20/0.54 fof(f7,axiom,(
% 0.20/0.54 (! [A,B] :( relation(B)=> ( B = identity_relation(A)<=> (! [C,D] :( in(ordered_pair(C,D),B)<=> ( in(C,A)& C = D ) ) )) ) )),
% 0.20/0.54 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.20/0.54 fof(f12,axiom,(
% 0.20/0.54 (! [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) ) )) )) )) )),
% 0.20/0.54 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.20/0.54 fof(f16,axiom,(
% 0.20/0.54 (! [A] :( A = empty_set<=> (! [B] : ~ in(B,A) )) )),
% 0.20/0.54 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.20/0.54 fof(f30,axiom,(
% 0.20/0.54 (! [A] :( relation(A)=> (! [B] :( B = relation_rng(A)<=> (! [C] :( in(C,B)<=> (? [D] : in(ordered_pair(D,C),A) )) )) )) )),
% 0.20/0.54 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.20/0.54 fof(f54,axiom,(
% 0.20/0.54 (! [A] :( relation(A)=> relation(relation_inverse(A)) ) )),
% 0.20/0.54 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.20/0.54 fof(f59,axiom,(
% 0.20/0.54 (! [A] : relation(identity_relation(A)) )),
% 0.20/0.54 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.20/0.54 fof(f71,axiom,(
% 0.20/0.54 empty(empty_set) ),
% 0.20/0.54 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.20/0.54 fof(f78,axiom,(
% 0.20/0.54 ( empty(empty_set)& relation(empty_set) ) ),
% 0.20/0.54 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.20/0.54 fof(f81,axiom,(
% 0.20/0.54 (! [A] :( ( ~ empty(A)& relation(A) )=> ~ empty(relation_rng(A)) ) )),
% 0.20/0.54 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.20/0.54 fof(f83,axiom,(
% 0.20/0.54 (! [A] :( empty(A)=> ( empty(relation_rng(A))& relation(relation_rng(A)) ) ) )),
% 0.20/0.54 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.20/0.54 fof(f88,axiom,(
% 0.20/0.54 (! [A] :( relation(A)=> relation_inverse(relation_inverse(A)) = A ) )),
% 0.20/0.54 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.20/0.54 fof(f91,lemma,(
% 0.20/0.54 (! [A] : singleton(A) != empty_set )),
% 0.20/0.54 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.20/0.54 fof(f103,axiom,(
% 0.20/0.54 (? [A] :( empty(A)& relation(A) ) )),
% 0.20/0.54 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.20/0.54 fof(f105,axiom,(
% 0.20/0.54 (? [A] : empty(A) )),
% 0.20/0.54 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.20/0.54 fof(f107,axiom,(
% 0.20/0.54 (! [A] :(? [B] :( element(B,powerset(A))& empty(B) ) ))),
% 0.20/0.54 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.20/0.54 fof(f123,lemma,(
% 0.20/0.54 (! [A,B] :( subset(A,B)=> set_union2(A,B) = B ) )),
% 0.20/0.54 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.20/0.54 fof(f131,conjecture,(
% 0.20/0.54 (! [A,B,C] :( relation(C)=> ( in(A,relation_inverse_image(C,B))<=> (? [D] :( in(D,relation_rng(C))& in(ordered_pair(A,D),C)& in(D,B) ) )) ) )),
% 0.20/0.54 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.20/0.54 fof(f132,negated_conjecture,(
% 0.20/0.54 ~((! [A,B,C] :( relation(C)=> ( in(A,relation_inverse_image(C,B))<=> (? [D] :( in(D,relation_rng(C))& in(ordered_pair(A,D),C)& in(D,B) ) )) ) ))),
% 0.20/0.54 inference(negated_conjecture,[status(cth)],[f131])).
% 0.20/0.54 fof(f133,lemma,(
% 0.20/0.54 (! [A,B] : subset(set_intersection2(A,B),A) )),
% 0.20/0.54 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.20/0.54 fof(f135,axiom,(
% 0.20/0.54 (! [A] : set_union2(A,empty_set) = A )),
% 0.20/0.54 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.20/0.54 fof(f141,lemma,(
% 0.20/0.54 (! [A] :( relation(A)=> (! [B] :( relation(B)=> ( subset(A,B)=> ( subset(relation_dom(A),relation_dom(B))& subset(relation_rng(A),relation_rng(B)) ) ) ) )) )),
% 0.20/0.54 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.20/0.54 fof(f144,axiom,(
% 0.20/0.54 (! [A] : set_intersection2(A,empty_set) = empty_set )),
% 0.20/0.54 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.20/0.54 fof(f147,lemma,(
% 0.20/0.54 (! [A] : subset(empty_set,A) )),
% 0.20/0.54 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.20/0.54 fof(f151,lemma,(
% 0.20/0.54 (! [A,B] : subset(set_difference(A,B),A) )),
% 0.20/0.54 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.20/0.54 fof(f174,axiom,(
% 0.20/0.54 (! [A] : set_difference(empty_set,A) = empty_set )),
% 0.20/0.54 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.20/0.54 fof(f181,lemma,(
% 0.20/0.54 ( relation_dom(empty_set) = empty_set& relation_rng(empty_set) = empty_set ) ),
% 0.20/0.54 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.20/0.54 fof(f184,lemma,(
% 0.20/0.54 (! [A] :( relation(A)=> ( ( relation_dom(A) = empty_set| relation_rng(A) = empty_set )=> A = empty_set ) ) )),
% 0.20/0.54 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.20/0.54 fof(f188,axiom,(
% 0.20/0.54 (! [A] :( empty(A)=> A = empty_set ) )),
% 0.20/0.54 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.20/0.54 fof(f190,lemma,(
% 0.20/0.54 (! [A] :( relation_dom(identity_relation(A)) = A& relation_rng(identity_relation(A)) = A ) )),
% 0.20/0.54 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.20/0.54 fof(f193,lemma,(
% 0.20/0.54 (! [A,B] : subset(A,set_union2(A,B)) )),
% 0.20/0.54 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.20/0.54 fof(f211,plain,(
% 0.20/0.54 ![A]: (~empty(A)|relation(A))),
% 0.20/0.54 inference(pre_NNF_transformation,[status(esa)],[f3])).
% 0.20/0.54 fof(f212,plain,(
% 0.20/0.54 ![X0]: (~empty(X0)|relation(X0))),
% 0.20/0.54 inference(cnf_transformation,[status(esa)],[f211])).
% 0.20/0.54 fof(f214,plain,(
% 0.20/0.54 ![X0,X1]: (set_union2(X0,X1)=set_union2(X1,X0))),
% 0.20/0.54 inference(cnf_transformation,[status(esa)],[f5])).
% 0.20/0.54 fof(f215,plain,(
% 0.20/0.54 ![X0,X1]: (set_intersection2(X0,X1)=set_intersection2(X1,X0))),
% 0.20/0.54 inference(cnf_transformation,[status(esa)],[f6])).
% 0.20/0.54 fof(f216,plain,(
% 0.20/0.54 ![A,B]: (~relation(B)|(B=identity_relation(A)<=>(![C,D]: (in(ordered_pair(C,D),B)<=>(in(C,A)&C=D)))))),
% 0.20/0.54 inference(pre_NNF_transformation,[status(esa)],[f7])).
% 0.20/0.54 fof(f217,plain,(
% 0.20/0.54 ![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)))))))),
% 0.20/0.54 inference(NNF_transformation,[status(esa)],[f216])).
% 0.20/0.54 fof(f218,plain,(
% 0.20/0.54 ![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))))))))),
% 0.20/0.54 inference(miniscoping,[status(esa)],[f217])).
% 0.20/0.54 fof(f219,plain,(
% 0.20/0.54 ![B]: (~relation(B)|((![A]: (~B=identity_relation(A)|((![C,D]: (~in(ordered_pair(C,D),B)|(in(C,A)&C=D)))&(![C,D]: (in(ordered_pair(C,D),B)|(~in(C,A)|~C=D))))))&(![A]: (B=identity_relation(A)|((~in(ordered_pair(sk0_0(A,B),sk0_1(A,B)),B)|(~in(sk0_0(A,B),A)|~sk0_0(A,B)=sk0_1(A,B)))&(in(ordered_pair(sk0_0(A,B),sk0_1(A,B)),B)|(in(sk0_0(A,B),A)&sk0_0(A,B)=sk0_1(A,B))))))))),
% 0.20/0.54 inference(skolemization,[status(esa)],[f218])).
% 0.20/0.54 fof(f222,plain,(
% 0.20/0.54 ![X0,X1,X2,X3]: (~relation(X0)|~X0=identity_relation(X1)|in(ordered_pair(X2,X3),X0)|~in(X2,X1)|~X2=X3)),
% 0.20/0.54 inference(cnf_transformation,[status(esa)],[f219])).
% 0.20/0.54 fof(f223,plain,(
% 0.20/0.54 ![X0,X1]: (~relation(X0)|X0=identity_relation(X1)|~in(ordered_pair(sk0_0(X1,X0),sk0_1(X1,X0)),X0)|~in(sk0_0(X1,X0),X1)|~sk0_0(X1,X0)=sk0_1(X1,X0))),
% 0.20/0.54 inference(cnf_transformation,[status(esa)],[f219])).
% 0.20/0.54 fof(f224,plain,(
% 0.20/0.54 ![X0,X1]: (~relation(X0)|X0=identity_relation(X1)|in(ordered_pair(sk0_0(X1,X0),sk0_1(X1,X0)),X0)|in(sk0_0(X1,X0),X1))),
% 0.20/0.54 inference(cnf_transformation,[status(esa)],[f219])).
% 0.20/0.54 fof(f225,plain,(
% 0.20/0.54 ![X0,X1]: (~relation(X0)|X0=identity_relation(X1)|in(ordered_pair(sk0_0(X1,X0),sk0_1(X1,X0)),X0)|sk0_0(X1,X0)=sk0_1(X1,X0))),
% 0.20/0.54 inference(cnf_transformation,[status(esa)],[f219])).
% 0.20/0.54 fof(f261,plain,(
% 0.20/0.54 ![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))))))))),
% 0.20/0.54 inference(pre_NNF_transformation,[status(esa)],[f12])).
% 0.20/0.54 fof(f262,plain,(
% 0.20/0.54 ![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))))))))))),
% 0.20/0.54 inference(NNF_transformation,[status(esa)],[f261])).
% 0.20/0.54 fof(f263,plain,(
% 0.20/0.54 ![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))))))))))),
% 0.20/0.54 inference(miniscoping,[status(esa)],[f262])).
% 0.20/0.54 fof(f264,plain,(
% 0.20/0.54 ![A]: (~relation(A)|((![B,C]: (~C=relation_inverse_image(A,B)|((![D]: (~in(D,C)|(in(ordered_pair(D,sk0_9(D,C,B,A)),A)&in(sk0_9(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(sk0_10(C,B,A),C)|(![E]: (~in(ordered_pair(sk0_10(C,B,A),E),A)|~in(E,B))))&(in(sk0_10(C,B,A),C)|(in(ordered_pair(sk0_10(C,B,A),sk0_11(C,B,A)),A)&in(sk0_11(C,B,A),B))))))))),
% 0.20/0.54 inference(skolemization,[status(esa)],[f263])).
% 0.20/0.54 fof(f265,plain,(
% 0.20/0.54 ![X0,X1,X2,X3]: (~relation(X0)|~X1=relation_inverse_image(X0,X2)|~in(X3,X1)|in(ordered_pair(X3,sk0_9(X3,X1,X2,X0)),X0))),
% 0.20/0.54 inference(cnf_transformation,[status(esa)],[f264])).
% 0.20/0.54 fof(f266,plain,(
% 0.20/0.54 ![X0,X1,X2,X3]: (~relation(X0)|~X1=relation_inverse_image(X0,X2)|~in(X3,X1)|in(sk0_9(X3,X1,X2,X0),X2))),
% 0.20/0.54 inference(cnf_transformation,[status(esa)],[f264])).
% 0.20/0.54 fof(f267,plain,(
% 0.20/0.54 ![X0,X1,X2,X3,X4]: (~relation(X0)|~X1=relation_inverse_image(X0,X2)|in(X3,X1)|~in(ordered_pair(X3,X4),X0)|~in(X4,X2))),
% 0.20/0.54 inference(cnf_transformation,[status(esa)],[f264])).
% 0.20/0.54 fof(f297,plain,(
% 0.20/0.54 ![A]: ((~A=empty_set|(![B]: ~in(B,A)))&(A=empty_set|(?[B]: in(B,A))))),
% 0.20/0.54 inference(NNF_transformation,[status(esa)],[f16])).
% 0.20/0.54 fof(f298,plain,(
% 0.20/0.54 (![A]: (~A=empty_set|(![B]: ~in(B,A))))&(![A]: (A=empty_set|(?[B]: in(B,A))))),
% 0.20/0.54 inference(miniscoping,[status(esa)],[f297])).
% 0.20/0.54 fof(f299,plain,(
% 0.20/0.54 (![A]: (~A=empty_set|(![B]: ~in(B,A))))&(![A]: (A=empty_set|in(sk0_19(A),A)))),
% 0.20/0.54 inference(skolemization,[status(esa)],[f298])).
% 0.20/0.54 fof(f300,plain,(
% 0.20/0.54 ![X0,X1]: (~X0=empty_set|~in(X1,X0))),
% 0.20/0.54 inference(cnf_transformation,[status(esa)],[f299])).
% 0.20/0.54 fof(f400,plain,(
% 0.20/0.54 ![A]: (~relation(A)|(![B]: (B=relation_rng(A)<=>(![C]: (in(C,B)<=>(?[D]: in(ordered_pair(D,C),A)))))))),
% 0.20/0.54 inference(pre_NNF_transformation,[status(esa)],[f30])).
% 0.20/0.54 fof(f401,plain,(
% 0.20/0.54 ![A]: (~relation(A)|(![B]: ((~B=relation_rng(A)|(![C]: ((~in(C,B)|(?[D]: in(ordered_pair(D,C),A)))&(in(C,B)|(![D]: ~in(ordered_pair(D,C),A))))))&(B=relation_rng(A)|(?[C]: ((~in(C,B)|(![D]: ~in(ordered_pair(D,C),A)))&(in(C,B)|(?[D]: in(ordered_pair(D,C),A)))))))))),
% 0.20/0.54 inference(NNF_transformation,[status(esa)],[f400])).
% 0.20/0.54 fof(f402,plain,(
% 0.20/0.54 ![A]: (~relation(A)|((![B]: (~B=relation_rng(A)|((![C]: (~in(C,B)|(?[D]: in(ordered_pair(D,C),A))))&(![C]: (in(C,B)|(![D]: ~in(ordered_pair(D,C),A)))))))&(![B]: (B=relation_rng(A)|(?[C]: ((~in(C,B)|(![D]: ~in(ordered_pair(D,C),A)))&(in(C,B)|(?[D]: in(ordered_pair(D,C),A)))))))))),
% 0.20/0.54 inference(miniscoping,[status(esa)],[f401])).
% 0.20/0.54 fof(f403,plain,(
% 0.20/0.54 ![A]: (~relation(A)|((![B]: (~B=relation_rng(A)|((![C]: (~in(C,B)|in(ordered_pair(sk0_41(C,B,A),C),A)))&(![C]: (in(C,B)|(![D]: ~in(ordered_pair(D,C),A)))))))&(![B]: (B=relation_rng(A)|((~in(sk0_42(B,A),B)|(![D]: ~in(ordered_pair(D,sk0_42(B,A)),A)))&(in(sk0_42(B,A),B)|in(ordered_pair(sk0_43(B,A),sk0_42(B,A)),A)))))))),
% 0.20/0.54 inference(skolemization,[status(esa)],[f402])).
% 0.20/0.54 fof(f405,plain,(
% 0.20/0.54 ![X0,X1,X2,X3]: (~relation(X0)|~X1=relation_rng(X0)|in(X2,X1)|~in(ordered_pair(X3,X2),X0))),
% 0.20/0.54 inference(cnf_transformation,[status(esa)],[f403])).
% 0.20/0.54 fof(f451,plain,(
% 0.20/0.54 ![A]: (~relation(A)|relation(relation_inverse(A)))),
% 0.20/0.54 inference(pre_NNF_transformation,[status(esa)],[f54])).
% 0.20/0.54 fof(f452,plain,(
% 0.20/0.54 ![X0]: (~relation(X0)|relation(relation_inverse(X0)))),
% 0.20/0.54 inference(cnf_transformation,[status(esa)],[f451])).
% 0.20/0.54 fof(f457,plain,(
% 0.20/0.54 ![X0]: (relation(identity_relation(X0)))),
% 0.20/0.54 inference(cnf_transformation,[status(esa)],[f59])).
% 0.20/0.54 fof(f478,plain,(
% 0.20/0.54 empty(empty_set)),
% 0.20/0.54 inference(cnf_transformation,[status(esa)],[f71])).
% 0.20/0.54 fof(f491,plain,(
% 0.20/0.54 relation(empty_set)),
% 0.20/0.54 inference(cnf_transformation,[status(esa)],[f78])).
% 0.20/0.54 fof(f496,plain,(
% 0.20/0.54 ![A]: ((empty(A)|~relation(A))|~empty(relation_rng(A)))),
% 0.20/0.54 inference(pre_NNF_transformation,[status(esa)],[f81])).
% 0.20/0.54 fof(f497,plain,(
% 0.20/0.54 ![X0]: (empty(X0)|~relation(X0)|~empty(relation_rng(X0)))),
% 0.20/0.54 inference(cnf_transformation,[status(esa)],[f496])).
% 0.20/0.54 fof(f501,plain,(
% 0.20/0.54 ![A]: (~empty(A)|(empty(relation_rng(A))&relation(relation_rng(A))))),
% 0.20/0.54 inference(pre_NNF_transformation,[status(esa)],[f83])).
% 0.20/0.54 fof(f502,plain,(
% 0.20/0.54 ![X0]: (~empty(X0)|empty(relation_rng(X0)))),
% 0.20/0.54 inference(cnf_transformation,[status(esa)],[f501])).
% 0.20/0.54 fof(f503,plain,(
% 0.20/0.54 ![X0]: (~empty(X0)|relation(relation_rng(X0)))),
% 0.20/0.54 inference(cnf_transformation,[status(esa)],[f501])).
% 0.20/0.54 fof(f513,plain,(
% 0.20/0.54 ![A]: (~relation(A)|relation_inverse(relation_inverse(A))=A)),
% 0.20/0.54 inference(pre_NNF_transformation,[status(esa)],[f88])).
% 0.20/0.54 fof(f514,plain,(
% 0.20/0.54 ![X0]: (~relation(X0)|relation_inverse(relation_inverse(X0))=X0)),
% 0.20/0.54 inference(cnf_transformation,[status(esa)],[f513])).
% 0.20/0.54 fof(f519,plain,(
% 0.20/0.54 ![X0]: (~singleton(X0)=empty_set)),
% 0.20/0.54 inference(cnf_transformation,[status(esa)],[f91])).
% 0.20/0.54 fof(f555,plain,(
% 0.20/0.54 (empty(sk0_53)&relation(sk0_53))),
% 0.20/0.54 inference(skolemization,[status(esa)],[f103])).
% 0.20/0.54 fof(f556,plain,(
% 0.20/0.54 empty(sk0_53)),
% 0.20/0.54 inference(cnf_transformation,[status(esa)],[f555])).
% 0.20/0.54 fof(f557,plain,(
% 0.20/0.54 relation(sk0_53)),
% 0.20/0.54 inference(cnf_transformation,[status(esa)],[f555])).
% 0.20/0.54 fof(f562,plain,(
% 0.20/0.54 empty(sk0_55)),
% 0.20/0.54 inference(skolemization,[status(esa)],[f105])).
% 0.20/0.54 fof(f563,plain,(
% 0.20/0.54 empty(sk0_55)),
% 0.20/0.54 inference(cnf_transformation,[status(esa)],[f562])).
% 0.20/0.54 fof(f567,plain,(
% 0.20/0.54 ![A]: (element(sk0_57(A),powerset(A))&empty(sk0_57(A)))),
% 0.20/0.54 inference(skolemization,[status(esa)],[f107])).
% 0.20/0.54 fof(f569,plain,(
% 0.20/0.54 ![X0]: (empty(sk0_57(X0)))),
% 0.20/0.54 inference(cnf_transformation,[status(esa)],[f567])).
% 0.20/0.54 fof(f614,plain,(
% 0.20/0.54 ![A,B]: (~subset(A,B)|set_union2(A,B)=B)),
% 0.20/0.54 inference(pre_NNF_transformation,[status(esa)],[f123])).
% 0.20/0.54 fof(f615,plain,(
% 0.20/0.54 ![X0,X1]: (~subset(X0,X1)|set_union2(X0,X1)=X1)),
% 0.20/0.54 inference(cnf_transformation,[status(esa)],[f614])).
% 0.20/0.54 fof(f644,plain,(
% 0.20/0.54 (?[A,B,C]: (relation(C)&(in(A,relation_inverse_image(C,B))<~>(?[D]: ((in(D,relation_rng(C))&in(ordered_pair(A,D),C))&in(D,B))))))),
% 0.20/0.54 inference(pre_NNF_transformation,[status(esa)],[f132])).
% 0.20/0.54 fof(f645,plain,(
% 0.20/0.54 ?[A,B,C]: (relation(C)&((in(A,relation_inverse_image(C,B))|(?[D]: ((in(D,relation_rng(C))&in(ordered_pair(A,D),C))&in(D,B))))&(~in(A,relation_inverse_image(C,B))|(![D]: ((~in(D,relation_rng(C))|~in(ordered_pair(A,D),C))|~in(D,B))))))),
% 0.20/0.54 inference(NNF_transformation,[status(esa)],[f644])).
% 0.20/0.54 fof(f646,plain,(
% 0.20/0.54 ?[C]: (relation(C)&(?[A,B]: ((in(A,relation_inverse_image(C,B))|(?[D]: ((in(D,relation_rng(C))&in(ordered_pair(A,D),C))&in(D,B))))&(~in(A,relation_inverse_image(C,B))|(![D]: ((~in(D,relation_rng(C))|~in(ordered_pair(A,D),C))|~in(D,B)))))))),
% 0.20/0.54 inference(miniscoping,[status(esa)],[f645])).
% 0.20/0.54 fof(f647,plain,(
% 0.20/0.54 (relation(sk0_61)&((in(sk0_62,relation_inverse_image(sk0_61,sk0_63))|((in(sk0_64,relation_rng(sk0_61))&in(ordered_pair(sk0_62,sk0_64),sk0_61))&in(sk0_64,sk0_63)))&(~in(sk0_62,relation_inverse_image(sk0_61,sk0_63))|(![D]: ((~in(D,relation_rng(sk0_61))|~in(ordered_pair(sk0_62,D),sk0_61))|~in(D,sk0_63))))))),
% 0.20/0.54 inference(skolemization,[status(esa)],[f646])).
% 0.20/0.54 fof(f648,plain,(
% 0.20/0.54 relation(sk0_61)),
% 0.20/0.54 inference(cnf_transformation,[status(esa)],[f647])).
% 0.20/0.54 fof(f650,plain,(
% 0.20/0.54 in(sk0_62,relation_inverse_image(sk0_61,sk0_63))|in(ordered_pair(sk0_62,sk0_64),sk0_61)),
% 0.20/0.54 inference(cnf_transformation,[status(esa)],[f647])).
% 0.20/0.54 fof(f651,plain,(
% 0.20/0.54 in(sk0_62,relation_inverse_image(sk0_61,sk0_63))|in(sk0_64,sk0_63)),
% 0.20/0.54 inference(cnf_transformation,[status(esa)],[f647])).
% 0.20/0.54 fof(f652,plain,(
% 0.20/0.54 ![X0]: (~in(sk0_62,relation_inverse_image(sk0_61,sk0_63))|~in(X0,relation_rng(sk0_61))|~in(ordered_pair(sk0_62,X0),sk0_61)|~in(X0,sk0_63))),
% 0.20/0.54 inference(cnf_transformation,[status(esa)],[f647])).
% 0.20/0.54 fof(f653,plain,(
% 0.20/0.54 ![X0,X1]: (subset(set_intersection2(X0,X1),X0))),
% 0.20/0.54 inference(cnf_transformation,[status(esa)],[f133])).
% 0.20/0.54 fof(f656,plain,(
% 0.20/0.54 ![X0]: (set_union2(X0,empty_set)=X0)),
% 0.20/0.54 inference(cnf_transformation,[status(esa)],[f135])).
% 0.20/0.54 fof(f669,plain,(
% 0.20/0.54 ![A]: (~relation(A)|(![B]: (~relation(B)|(~subset(A,B)|(subset(relation_dom(A),relation_dom(B))&subset(relation_rng(A),relation_rng(B)))))))),
% 0.20/0.54 inference(pre_NNF_transformation,[status(esa)],[f141])).
% 0.20/0.54 fof(f671,plain,(
% 0.20/0.54 ![X0,X1]: (~relation(X0)|~relation(X1)|~subset(X0,X1)|subset(relation_rng(X0),relation_rng(X1)))),
% 0.20/0.54 inference(cnf_transformation,[status(esa)],[f669])).
% 0.20/0.54 fof(f677,plain,(
% 0.20/0.54 ![X0]: (set_intersection2(X0,empty_set)=empty_set)),
% 0.20/0.54 inference(cnf_transformation,[status(esa)],[f144])).
% 0.20/0.54 fof(f685,plain,(
% 0.20/0.54 ![X0]: (subset(empty_set,X0))),
% 0.20/0.54 inference(cnf_transformation,[status(esa)],[f147])).
% 0.20/0.54 fof(f696,plain,(
% 0.20/0.54 ![X0,X1]: (subset(set_difference(X0,X1),X0))),
% 0.20/0.54 inference(cnf_transformation,[status(esa)],[f151])).
% 0.20/0.54 fof(f756,plain,(
% 0.20/0.54 ![X0]: (set_difference(empty_set,X0)=empty_set)),
% 0.20/0.54 inference(cnf_transformation,[status(esa)],[f174])).
% 0.20/0.54 fof(f777,plain,(
% 0.20/0.54 relation_rng(empty_set)=empty_set),
% 0.20/0.54 inference(cnf_transformation,[status(esa)],[f181])).
% 0.20/0.54 fof(f783,plain,(
% 0.20/0.54 ![A]: (~relation(A)|((~relation_dom(A)=empty_set&~relation_rng(A)=empty_set)|A=empty_set))),
% 0.20/0.54 inference(pre_NNF_transformation,[status(esa)],[f184])).
% 0.20/0.54 fof(f785,plain,(
% 0.20/0.54 ![X0]: (~relation(X0)|~relation_rng(X0)=empty_set|X0=empty_set)),
% 0.20/0.54 inference(cnf_transformation,[status(esa)],[f783])).
% 0.20/0.54 fof(f795,plain,(
% 0.20/0.54 ![A]: (~empty(A)|A=empty_set)),
% 0.20/0.54 inference(pre_NNF_transformation,[status(esa)],[f188])).
% 0.20/0.54 fof(f796,plain,(
% 0.20/0.54 ![X0]: (~empty(X0)|X0=empty_set)),
% 0.20/0.54 inference(cnf_transformation,[status(esa)],[f795])).
% 0.20/0.54 fof(f799,plain,(
% 0.20/0.54 (![A]: relation_dom(identity_relation(A))=A)&(![A]: relation_rng(identity_relation(A))=A)),
% 0.20/0.54 inference(miniscoping,[status(esa)],[f190])).
% 0.20/0.54 fof(f801,plain,(
% 0.20/0.54 ![X0]: (relation_rng(identity_relation(X0))=X0)),
% 0.20/0.54 inference(cnf_transformation,[status(esa)],[f799])).
% 0.20/0.54 fof(f811,plain,(
% 0.20/0.54 ![X0,X1]: (subset(X0,set_union2(X0,X1)))),
% 0.20/0.54 inference(cnf_transformation,[status(esa)],[f193])).
% 0.20/0.54 fof(f862,plain,(
% 0.20/0.54 spl0_0 <=> in(sk0_62,relation_inverse_image(sk0_61,sk0_63))),
% 0.20/0.54 introduced(split_symbol_definition)).
% 0.20/0.54 fof(f863,plain,(
% 0.20/0.54 in(sk0_62,relation_inverse_image(sk0_61,sk0_63))|~spl0_0),
% 0.20/0.54 inference(component_clause,[status(thm)],[f862])).
% 0.20/0.54 fof(f869,plain,(
% 0.20/0.54 spl0_2 <=> in(ordered_pair(sk0_62,sk0_64),sk0_61)),
% 0.20/0.54 introduced(split_symbol_definition)).
% 0.20/0.54 fof(f870,plain,(
% 0.20/0.54 in(ordered_pair(sk0_62,sk0_64),sk0_61)|~spl0_2),
% 0.20/0.54 inference(component_clause,[status(thm)],[f869])).
% 0.20/0.54 fof(f872,plain,(
% 0.20/0.54 spl0_0|spl0_2),
% 0.20/0.54 inference(split_clause,[status(thm)],[f650,f862,f869])).
% 0.20/0.54 fof(f873,plain,(
% 0.20/0.54 spl0_3 <=> in(sk0_64,sk0_63)),
% 0.20/0.54 introduced(split_symbol_definition)).
% 0.20/0.54 fof(f874,plain,(
% 0.20/0.54 in(sk0_64,sk0_63)|~spl0_3),
% 0.20/0.54 inference(component_clause,[status(thm)],[f873])).
% 0.20/0.54 fof(f876,plain,(
% 0.20/0.54 spl0_0|spl0_3),
% 0.20/0.54 inference(split_clause,[status(thm)],[f651,f862,f873])).
% 0.20/0.54 fof(f877,plain,(
% 0.20/0.54 spl0_4 <=> ~in(X0,relation_rng(sk0_61))|~in(ordered_pair(sk0_62,X0),sk0_61)|~in(X0,sk0_63)),
% 0.20/0.54 introduced(split_symbol_definition)).
% 0.20/0.54 fof(f878,plain,(
% 0.20/0.54 ![X0]: (~in(X0,relation_rng(sk0_61))|~in(ordered_pair(sk0_62,X0),sk0_61)|~in(X0,sk0_63)|~spl0_4)),
% 0.20/0.54 inference(component_clause,[status(thm)],[f877])).
% 0.20/0.54 fof(f880,plain,(
% 0.20/0.54 ~spl0_0|spl0_4),
% 0.20/0.54 inference(split_clause,[status(thm)],[f652,f862,f877])).
% 0.20/0.54 fof(f883,plain,(
% 0.20/0.54 ![X0,X1]: (~relation(identity_relation(X0))|in(ordered_pair(X1,X1),identity_relation(X0))|~in(X1,X0))),
% 0.20/0.54 inference(destructive_equality_resolution,[status(esa)],[f222])).
% 0.20/0.54 fof(f895,plain,(
% 0.20/0.54 ![X0,X1,X2]: (~relation(X0)|~in(X1,relation_inverse_image(X0,X2))|in(ordered_pair(X1,sk0_9(X1,relation_inverse_image(X0,X2),X2,X0)),X0))),
% 0.20/0.54 inference(destructive_equality_resolution,[status(esa)],[f265])).
% 0.20/0.54 fof(f896,plain,(
% 0.20/0.54 ![X0,X1,X2]: (~relation(X0)|~in(X1,relation_inverse_image(X0,X2))|in(sk0_9(X1,relation_inverse_image(X0,X2),X2,X0),X2))),
% 0.20/0.54 inference(destructive_equality_resolution,[status(esa)],[f266])).
% 0.20/0.54 fof(f897,plain,(
% 0.20/0.54 ![X0,X1,X2,X3]: (~relation(X0)|in(X1,relation_inverse_image(X0,X2))|~in(ordered_pair(X1,X3),X0)|~in(X3,X2))),
% 0.20/0.54 inference(destructive_equality_resolution,[status(esa)],[f267])).
% 0.20/0.54 fof(f905,plain,(
% 0.20/0.54 ![X0]: (~in(X0,empty_set))),
% 0.20/0.54 inference(destructive_equality_resolution,[status(esa)],[f300])).
% 0.20/0.54 fof(f928,plain,(
% 0.20/0.54 ![X0,X1,X2]: (~relation(X0)|in(X1,relation_rng(X0))|~in(ordered_pair(X2,X1),X0))),
% 0.20/0.54 inference(destructive_equality_resolution,[status(esa)],[f405])).
% 0.20/0.54 fof(f942,plain,(
% 0.20/0.54 spl0_5 <=> empty(empty_set)),
% 0.20/0.54 introduced(split_symbol_definition)).
% 0.20/0.54 fof(f944,plain,(
% 0.20/0.54 ~empty(empty_set)|spl0_5),
% 0.20/0.54 inference(component_clause,[status(thm)],[f942])).
% 0.20/0.54 fof(f945,plain,(
% 0.20/0.54 spl0_6 <=> relation(empty_set)),
% 0.20/0.54 introduced(split_symbol_definition)).
% 0.20/0.54 fof(f947,plain,(
% 0.20/0.54 ~relation(empty_set)|spl0_6),
% 0.20/0.54 inference(component_clause,[status(thm)],[f945])).
% 0.20/0.54 fof(f950,plain,(
% 0.20/0.54 spl0_7 <=> relation_rng(sk0_61)=empty_set),
% 0.20/0.54 introduced(split_symbol_definition)).
% 0.20/0.54 fof(f952,plain,(
% 0.20/0.54 ~relation_rng(sk0_61)=empty_set|spl0_7),
% 0.20/0.54 inference(component_clause,[status(thm)],[f950])).
% 0.20/0.54 fof(f953,plain,(
% 0.20/0.54 spl0_8 <=> sk0_61=empty_set),
% 0.20/0.54 introduced(split_symbol_definition)).
% 0.20/0.54 fof(f954,plain,(
% 0.20/0.54 sk0_61=empty_set|~spl0_8),
% 0.20/0.54 inference(component_clause,[status(thm)],[f953])).
% 0.20/0.54 fof(f956,plain,(
% 0.20/0.54 ~relation_rng(sk0_61)=empty_set|sk0_61=empty_set),
% 0.20/0.54 inference(resolution,[status(thm)],[f785,f648])).
% 0.20/0.54 fof(f957,plain,(
% 0.20/0.54 ~spl0_7|spl0_8),
% 0.20/0.54 inference(split_clause,[status(thm)],[f956,f950,f953])).
% 0.20/0.54 fof(f965,plain,(
% 0.20/0.54 spl0_9 <=> relation_rng(empty_set)=empty_set),
% 0.20/0.54 introduced(split_symbol_definition)).
% 0.20/0.54 fof(f967,plain,(
% 0.20/0.54 ~relation_rng(empty_set)=empty_set|spl0_9),
% 0.20/0.54 inference(component_clause,[status(thm)],[f965])).
% 0.20/0.54 fof(f968,plain,(
% 0.20/0.54 spl0_10 <=> empty_set=empty_set),
% 0.20/0.54 introduced(split_symbol_definition)).
% 0.20/0.54 fof(f971,plain,(
% 0.20/0.54 ~relation_rng(empty_set)=empty_set|empty_set=empty_set),
% 0.20/0.54 inference(resolution,[status(thm)],[f491,f785])).
% 0.20/0.54 fof(f972,plain,(
% 0.20/0.54 ~spl0_9|spl0_10),
% 0.20/0.54 inference(split_clause,[status(thm)],[f971,f965,f968])).
% 0.20/0.54 fof(f973,plain,(
% 0.20/0.54 ~empty_set=empty_set|spl0_9),
% 0.20/0.54 inference(forward_demodulation,[status(thm)],[f777,f967])).
% 0.20/0.54 fof(f974,plain,(
% 0.20/0.54 $false|spl0_9),
% 0.20/0.54 inference(trivial_equality_resolution,[status(esa)],[f973])).
% 0.20/0.54 fof(f975,plain,(
% 0.20/0.54 spl0_9),
% 0.20/0.54 inference(contradiction_clause,[status(thm)],[f974])).
% 0.20/0.54 fof(f977,plain,(
% 0.20/0.54 relation(relation_rng(sk0_53))),
% 0.20/0.54 inference(resolution,[status(thm)],[f556,f503])).
% 0.20/0.54 fof(f978,plain,(
% 0.20/0.54 empty(relation_rng(sk0_53))),
% 0.20/0.54 inference(resolution,[status(thm)],[f556,f502])).
% 0.20/0.54 fof(f979,plain,(
% 0.20/0.54 spl0_11 <=> relation_rng(sk0_53)=empty_set),
% 0.20/0.54 introduced(split_symbol_definition)).
% 0.20/0.54 fof(f982,plain,(
% 0.20/0.54 spl0_12 <=> sk0_53=empty_set),
% 0.20/0.54 introduced(split_symbol_definition)).
% 0.20/0.54 fof(f983,plain,(
% 0.20/0.54 sk0_53=empty_set|~spl0_12),
% 0.20/0.54 inference(component_clause,[status(thm)],[f982])).
% 0.20/0.54 fof(f984,plain,(
% 0.20/0.54 ~sk0_53=empty_set|spl0_12),
% 0.20/0.54 inference(component_clause,[status(thm)],[f982])).
% 0.20/0.54 fof(f987,plain,(
% 0.20/0.54 relation(sk0_55)),
% 0.20/0.54 inference(resolution,[status(thm)],[f563,f212])).
% 0.20/0.54 fof(f988,plain,(
% 0.20/0.54 relation(relation_rng(sk0_55))),
% 0.20/0.54 inference(resolution,[status(thm)],[f563,f503])).
% 0.20/0.54 fof(f989,plain,(
% 0.20/0.54 empty(relation_rng(sk0_55))),
% 0.20/0.54 inference(resolution,[status(thm)],[f563,f502])).
% 0.20/0.54 fof(f999,plain,(
% 0.20/0.54 spl0_15 <=> relation_rng(relation_rng(sk0_53))=empty_set),
% 0.20/0.54 introduced(split_symbol_definition)).
% 0.20/0.54 fof(f1001,plain,(
% 0.20/0.54 ~relation_rng(relation_rng(sk0_53))=empty_set|spl0_15),
% 0.20/0.54 inference(component_clause,[status(thm)],[f999])).
% 0.20/0.54 fof(f1002,plain,(
% 0.20/0.54 ~relation_rng(relation_rng(sk0_53))=empty_set|relation_rng(sk0_53)=empty_set),
% 0.20/0.54 inference(resolution,[status(thm)],[f977,f785])).
% 0.20/0.54 fof(f1003,plain,(
% 0.20/0.54 ~spl0_15|spl0_11),
% 0.20/0.54 inference(split_clause,[status(thm)],[f1002,f999,f979])).
% 0.20/0.54 fof(f1008,plain,(
% 0.20/0.54 ~relation_rng(relation_rng(empty_set))=empty_set|~spl0_12|spl0_15),
% 0.20/0.54 inference(forward_demodulation,[status(thm)],[f983,f1001])).
% 0.20/0.54 fof(f1009,plain,(
% 0.20/0.54 ~relation_rng(empty_set)=empty_set|~spl0_12|spl0_15),
% 0.20/0.54 inference(forward_demodulation,[status(thm)],[f777,f1008])).
% 0.20/0.54 fof(f1010,plain,(
% 0.20/0.54 ~empty_set=empty_set|~spl0_12|spl0_15),
% 0.20/0.54 inference(forward_demodulation,[status(thm)],[f777,f1009])).
% 0.20/0.54 fof(f1011,plain,(
% 0.20/0.54 $false|~spl0_12|spl0_15),
% 0.20/0.54 inference(trivial_equality_resolution,[status(esa)],[f1010])).
% 0.20/0.54 fof(f1012,plain,(
% 0.20/0.54 ~spl0_12|spl0_15),
% 0.20/0.54 inference(contradiction_clause,[status(thm)],[f1011])).
% 0.20/0.54 fof(f1013,plain,(
% 0.20/0.54 spl0_16 <=> empty(sk0_53)),
% 0.20/0.54 introduced(split_symbol_definition)).
% 0.20/0.54 fof(f1016,plain,(
% 0.20/0.54 spl0_17 <=> relation(sk0_53)),
% 0.20/0.54 introduced(split_symbol_definition)).
% 0.20/0.54 fof(f1018,plain,(
% 0.20/0.54 ~relation(sk0_53)|spl0_17),
% 0.20/0.54 inference(component_clause,[status(thm)],[f1016])).
% 0.20/0.54 fof(f1019,plain,(
% 0.20/0.54 empty(sk0_53)|~relation(sk0_53)),
% 0.20/0.54 inference(resolution,[status(thm)],[f978,f497])).
% 0.20/0.54 fof(f1020,plain,(
% 0.20/0.54 spl0_16|~spl0_17),
% 0.20/0.54 inference(split_clause,[status(thm)],[f1019,f1013,f1016])).
% 0.20/0.54 fof(f1022,plain,(
% 0.20/0.54 relation(relation_rng(relation_rng(sk0_53)))),
% 0.20/0.54 inference(resolution,[status(thm)],[f978,f503])).
% 0.20/0.54 fof(f1023,plain,(
% 0.20/0.54 empty(relation_rng(relation_rng(sk0_53)))),
% 0.20/0.54 inference(resolution,[status(thm)],[f978,f502])).
% 0.20/0.54 fof(f1024,plain,(
% 0.20/0.54 spl0_18 <=> relation_rng(relation_rng(sk0_55))=empty_set),
% 0.20/0.54 introduced(split_symbol_definition)).
% 0.20/0.54 fof(f1027,plain,(
% 0.20/0.54 spl0_19 <=> relation_rng(sk0_55)=empty_set),
% 0.20/0.54 introduced(split_symbol_definition)).
% 0.20/0.54 fof(f1030,plain,(
% 0.20/0.54 ~relation_rng(relation_rng(sk0_55))=empty_set|relation_rng(sk0_55)=empty_set),
% 0.20/0.54 inference(resolution,[status(thm)],[f988,f785])).
% 0.20/0.54 fof(f1031,plain,(
% 0.20/0.54 ~spl0_18|spl0_19),
% 0.20/0.54 inference(split_clause,[status(thm)],[f1030,f1024,f1027])).
% 0.20/0.54 fof(f1032,plain,(
% 0.20/0.54 spl0_20 <=> empty(sk0_55)),
% 0.20/0.54 introduced(split_symbol_definition)).
% 0.20/0.54 fof(f1035,plain,(
% 0.20/0.54 spl0_21 <=> relation(sk0_55)),
% 0.20/0.54 introduced(split_symbol_definition)).
% 0.20/0.54 fof(f1037,plain,(
% 0.20/0.54 ~relation(sk0_55)|spl0_21),
% 0.20/0.54 inference(component_clause,[status(thm)],[f1035])).
% 0.20/0.54 fof(f1038,plain,(
% 0.20/0.54 empty(sk0_55)|~relation(sk0_55)),
% 0.20/0.54 inference(resolution,[status(thm)],[f989,f497])).
% 0.20/0.54 fof(f1039,plain,(
% 0.20/0.54 spl0_20|~spl0_21),
% 0.20/0.54 inference(split_clause,[status(thm)],[f1038,f1032,f1035])).
% 0.20/0.54 fof(f1041,plain,(
% 0.20/0.54 relation(relation_rng(relation_rng(sk0_55)))),
% 0.20/0.54 inference(resolution,[status(thm)],[f989,f503])).
% 0.20/0.54 fof(f1042,plain,(
% 0.20/0.54 empty(relation_rng(relation_rng(sk0_55)))),
% 0.20/0.54 inference(resolution,[status(thm)],[f989,f502])).
% 0.20/0.54 fof(f1045,plain,(
% 0.20/0.54 spl0_22 <=> relation_rng(relation_rng(relation_rng(sk0_53)))=empty_set),
% 0.20/0.54 introduced(split_symbol_definition)).
% 0.20/0.54 fof(f1050,plain,(
% 0.20/0.54 spl0_23 <=> empty(relation_rng(sk0_53))),
% 0.20/0.54 introduced(split_symbol_definition)).
% 0.20/0.54 fof(f1053,plain,(
% 0.20/0.54 spl0_24 <=> relation(relation_rng(sk0_53))),
% 0.20/0.54 introduced(split_symbol_definition)).
% 0.20/0.54 fof(f1055,plain,(
% 0.20/0.54 ~relation(relation_rng(sk0_53))|spl0_24),
% 0.20/0.54 inference(component_clause,[status(thm)],[f1053])).
% 0.20/0.54 fof(f1056,plain,(
% 0.20/0.54 empty(relation_rng(sk0_53))|~relation(relation_rng(sk0_53))),
% 0.20/0.54 inference(resolution,[status(thm)],[f1023,f497])).
% 0.20/0.54 fof(f1057,plain,(
% 0.20/0.54 spl0_23|~spl0_24),
% 0.20/0.54 inference(split_clause,[status(thm)],[f1056,f1050,f1053])).
% 0.20/0.54 fof(f1059,plain,(
% 0.20/0.54 relation(relation_rng(relation_rng(relation_rng(sk0_53))))),
% 0.20/0.54 inference(resolution,[status(thm)],[f1023,f503])).
% 0.20/0.54 fof(f1060,plain,(
% 0.20/0.54 empty(relation_rng(relation_rng(relation_rng(sk0_53))))),
% 0.20/0.54 inference(resolution,[status(thm)],[f1023,f502])).
% 0.20/0.54 fof(f1061,plain,(
% 0.20/0.54 $false|spl0_24),
% 0.20/0.54 inference(forward_subsumption_resolution,[status(thm)],[f1055,f977])).
% 0.20/0.54 fof(f1062,plain,(
% 0.20/0.54 spl0_24),
% 0.20/0.54 inference(contradiction_clause,[status(thm)],[f1061])).
% 0.20/0.54 fof(f1063,plain,(
% 0.20/0.54 spl0_25 <=> relation_rng(relation_rng(relation_rng(sk0_55)))=empty_set),
% 0.20/0.54 introduced(split_symbol_definition)).
% 0.20/0.54 fof(f1066,plain,(
% 0.20/0.54 ~relation_rng(relation_rng(relation_rng(sk0_55)))=empty_set|relation_rng(relation_rng(sk0_55))=empty_set),
% 0.20/0.54 inference(resolution,[status(thm)],[f1041,f785])).
% 0.20/0.54 fof(f1067,plain,(
% 0.20/0.54 ~spl0_25|spl0_18),
% 0.20/0.54 inference(split_clause,[status(thm)],[f1066,f1063,f1024])).
% 0.20/0.54 fof(f1086,plain,(
% 0.20/0.54 spl0_26 <=> empty(relation_rng(sk0_55))),
% 0.20/0.54 introduced(split_symbol_definition)).
% 0.20/0.54 fof(f1089,plain,(
% 0.20/0.54 spl0_27 <=> relation(relation_rng(sk0_55))),
% 0.20/0.54 introduced(split_symbol_definition)).
% 0.20/0.54 fof(f1091,plain,(
% 0.20/0.54 ~relation(relation_rng(sk0_55))|spl0_27),
% 0.20/0.54 inference(component_clause,[status(thm)],[f1089])).
% 0.20/0.54 fof(f1092,plain,(
% 0.20/0.54 empty(relation_rng(sk0_55))|~relation(relation_rng(sk0_55))),
% 0.20/0.54 inference(resolution,[status(thm)],[f1042,f497])).
% 0.20/0.54 fof(f1093,plain,(
% 0.20/0.54 spl0_26|~spl0_27),
% 0.20/0.54 inference(split_clause,[status(thm)],[f1092,f1086,f1089])).
% 0.20/0.54 fof(f1095,plain,(
% 0.20/0.54 relation(relation_rng(relation_rng(relation_rng(sk0_55))))),
% 0.20/0.54 inference(resolution,[status(thm)],[f1042,f503])).
% 0.20/0.54 fof(f1096,plain,(
% 0.20/0.54 empty(relation_rng(relation_rng(relation_rng(sk0_55))))),
% 0.20/0.54 inference(resolution,[status(thm)],[f1042,f502])).
% 0.20/0.54 fof(f1097,plain,(
% 0.20/0.54 $false|spl0_27),
% 0.20/0.54 inference(forward_subsumption_resolution,[status(thm)],[f1091,f988])).
% 0.20/0.54 fof(f1098,plain,(
% 0.20/0.54 spl0_27),
% 0.20/0.54 inference(contradiction_clause,[status(thm)],[f1097])).
% 0.20/0.54 fof(f1101,plain,(
% 0.20/0.54 spl0_28 <=> relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))=empty_set),
% 0.20/0.54 introduced(split_symbol_definition)).
% 0.20/0.54 fof(f1104,plain,(
% 0.20/0.54 ~relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))=empty_set|relation_rng(relation_rng(relation_rng(sk0_53)))=empty_set),
% 0.20/0.54 inference(resolution,[status(thm)],[f1059,f785])).
% 0.20/0.54 fof(f1105,plain,(
% 0.20/0.54 ~spl0_28|spl0_22),
% 0.20/0.54 inference(split_clause,[status(thm)],[f1104,f1101,f1045])).
% 0.20/0.54 fof(f1106,plain,(
% 0.20/0.54 spl0_29 <=> empty(relation_rng(relation_rng(sk0_53)))),
% 0.20/0.54 introduced(split_symbol_definition)).
% 0.20/0.54 fof(f1109,plain,(
% 0.20/0.54 spl0_30 <=> relation(relation_rng(relation_rng(sk0_53)))),
% 0.20/0.54 introduced(split_symbol_definition)).
% 0.20/0.54 fof(f1111,plain,(
% 0.20/0.54 ~relation(relation_rng(relation_rng(sk0_53)))|spl0_30),
% 0.20/0.54 inference(component_clause,[status(thm)],[f1109])).
% 0.20/0.54 fof(f1112,plain,(
% 0.20/0.54 empty(relation_rng(relation_rng(sk0_53)))|~relation(relation_rng(relation_rng(sk0_53)))),
% 0.20/0.54 inference(resolution,[status(thm)],[f1060,f497])).
% 0.20/0.54 fof(f1113,plain,(
% 0.20/0.54 spl0_29|~spl0_30),
% 0.20/0.54 inference(split_clause,[status(thm)],[f1112,f1106,f1109])).
% 0.20/0.54 fof(f1115,plain,(
% 0.20/0.54 relation(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53)))))),
% 0.20/0.54 inference(resolution,[status(thm)],[f1060,f503])).
% 0.20/0.54 fof(f1116,plain,(
% 0.20/0.54 empty(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53)))))),
% 0.20/0.54 inference(resolution,[status(thm)],[f1060,f502])).
% 0.20/0.54 fof(f1117,plain,(
% 0.20/0.54 $false|spl0_30),
% 0.20/0.54 inference(forward_subsumption_resolution,[status(thm)],[f1111,f1022])).
% 0.20/0.54 fof(f1118,plain,(
% 0.20/0.54 spl0_30),
% 0.20/0.54 inference(contradiction_clause,[status(thm)],[f1117])).
% 0.20/0.54 fof(f1119,plain,(
% 0.20/0.54 spl0_31 <=> relation_rng(relation_rng(relation_rng(relation_rng(sk0_55))))=empty_set),
% 0.20/0.54 introduced(split_symbol_definition)).
% 0.20/0.54 fof(f1122,plain,(
% 0.20/0.54 ~relation_rng(relation_rng(relation_rng(relation_rng(sk0_55))))=empty_set|relation_rng(relation_rng(relation_rng(sk0_55)))=empty_set),
% 0.20/0.54 inference(resolution,[status(thm)],[f1095,f785])).
% 0.20/0.54 fof(f1123,plain,(
% 0.20/0.54 ~spl0_31|spl0_25),
% 0.20/0.54 inference(split_clause,[status(thm)],[f1122,f1119,f1063])).
% 0.20/0.54 fof(f1124,plain,(
% 0.20/0.54 spl0_32 <=> empty(relation_rng(relation_rng(sk0_55)))),
% 0.20/0.54 introduced(split_symbol_definition)).
% 0.20/0.54 fof(f1127,plain,(
% 0.20/0.54 spl0_33 <=> relation(relation_rng(relation_rng(sk0_55)))),
% 0.20/0.54 introduced(split_symbol_definition)).
% 0.20/0.54 fof(f1129,plain,(
% 0.20/0.54 ~relation(relation_rng(relation_rng(sk0_55)))|spl0_33),
% 0.20/0.54 inference(component_clause,[status(thm)],[f1127])).
% 0.20/0.54 fof(f1130,plain,(
% 0.20/0.54 empty(relation_rng(relation_rng(sk0_55)))|~relation(relation_rng(relation_rng(sk0_55)))),
% 0.20/0.54 inference(resolution,[status(thm)],[f1096,f497])).
% 0.20/0.54 fof(f1131,plain,(
% 0.20/0.54 spl0_32|~spl0_33),
% 0.20/0.54 inference(split_clause,[status(thm)],[f1130,f1124,f1127])).
% 0.20/0.54 fof(f1133,plain,(
% 0.20/0.54 relation(relation_rng(relation_rng(relation_rng(relation_rng(sk0_55)))))),
% 0.20/0.54 inference(resolution,[status(thm)],[f1096,f503])).
% 0.20/0.54 fof(f1134,plain,(
% 0.20/0.54 empty(relation_rng(relation_rng(relation_rng(relation_rng(sk0_55)))))),
% 0.20/0.54 inference(resolution,[status(thm)],[f1096,f502])).
% 0.20/0.54 fof(f1135,plain,(
% 0.20/0.54 $false|spl0_33),
% 0.20/0.54 inference(forward_subsumption_resolution,[status(thm)],[f1129,f1041])).
% 0.20/0.54 fof(f1136,plain,(
% 0.20/0.54 spl0_33),
% 0.20/0.54 inference(contradiction_clause,[status(thm)],[f1135])).
% 0.20/0.54 fof(f1137,plain,(
% 0.20/0.54 spl0_34 <=> relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53)))))=empty_set),
% 0.20/0.54 introduced(split_symbol_definition)).
% 0.20/0.54 fof(f1140,plain,(
% 0.20/0.54 ~relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53)))))=empty_set|relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))=empty_set),
% 0.20/0.54 inference(resolution,[status(thm)],[f1115,f785])).
% 0.20/0.54 fof(f1141,plain,(
% 0.20/0.54 ~spl0_34|spl0_28),
% 0.20/0.54 inference(split_clause,[status(thm)],[f1140,f1137,f1101])).
% 0.20/0.54 fof(f1142,plain,(
% 0.20/0.54 spl0_35 <=> empty(relation_rng(relation_rng(relation_rng(sk0_53))))),
% 0.20/0.54 introduced(split_symbol_definition)).
% 0.20/0.54 fof(f1145,plain,(
% 0.20/0.54 spl0_36 <=> relation(relation_rng(relation_rng(relation_rng(sk0_53))))),
% 0.20/0.54 introduced(split_symbol_definition)).
% 0.20/0.54 fof(f1147,plain,(
% 0.20/0.54 ~relation(relation_rng(relation_rng(relation_rng(sk0_53))))|spl0_36),
% 0.20/0.54 inference(component_clause,[status(thm)],[f1145])).
% 0.20/0.54 fof(f1148,plain,(
% 0.20/0.54 empty(relation_rng(relation_rng(relation_rng(sk0_53))))|~relation(relation_rng(relation_rng(relation_rng(sk0_53))))),
% 0.20/0.54 inference(resolution,[status(thm)],[f1116,f497])).
% 0.20/0.54 fof(f1149,plain,(
% 0.20/0.54 spl0_35|~spl0_36),
% 0.20/0.54 inference(split_clause,[status(thm)],[f1148,f1142,f1145])).
% 0.20/0.54 fof(f1151,plain,(
% 0.20/0.54 relation(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))),
% 0.20/0.54 inference(resolution,[status(thm)],[f1116,f503])).
% 0.20/0.54 fof(f1152,plain,(
% 0.20/0.54 empty(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))),
% 0.20/0.54 inference(resolution,[status(thm)],[f1116,f502])).
% 0.20/0.54 fof(f1153,plain,(
% 0.20/0.54 $false|spl0_36),
% 0.20/0.54 inference(forward_subsumption_resolution,[status(thm)],[f1147,f1059])).
% 0.20/0.54 fof(f1154,plain,(
% 0.20/0.54 spl0_36),
% 0.20/0.54 inference(contradiction_clause,[status(thm)],[f1153])).
% 0.20/0.54 fof(f1155,plain,(
% 0.20/0.54 spl0_37 <=> relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_55)))))=empty_set),
% 0.20/0.54 introduced(split_symbol_definition)).
% 0.20/0.54 fof(f1157,plain,(
% 0.20/0.54 ~relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_55)))))=empty_set|spl0_37),
% 0.20/0.54 inference(component_clause,[status(thm)],[f1155])).
% 0.20/0.54 fof(f1158,plain,(
% 0.20/0.54 ~relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_55)))))=empty_set|relation_rng(relation_rng(relation_rng(relation_rng(sk0_55))))=empty_set),
% 0.20/0.54 inference(resolution,[status(thm)],[f1133,f785])).
% 0.20/0.54 fof(f1159,plain,(
% 0.20/0.54 ~spl0_37|spl0_31),
% 0.20/0.54 inference(split_clause,[status(thm)],[f1158,f1155,f1119])).
% 0.20/0.54 fof(f1160,plain,(
% 0.20/0.54 spl0_38 <=> empty(relation_rng(relation_rng(relation_rng(sk0_55))))),
% 0.20/0.54 introduced(split_symbol_definition)).
% 0.20/0.54 fof(f1163,plain,(
% 0.20/0.54 spl0_39 <=> relation(relation_rng(relation_rng(relation_rng(sk0_55))))),
% 0.20/0.54 introduced(split_symbol_definition)).
% 0.20/0.54 fof(f1165,plain,(
% 0.20/0.54 ~relation(relation_rng(relation_rng(relation_rng(sk0_55))))|spl0_39),
% 0.20/0.54 inference(component_clause,[status(thm)],[f1163])).
% 0.20/0.54 fof(f1166,plain,(
% 0.20/0.54 empty(relation_rng(relation_rng(relation_rng(sk0_55))))|~relation(relation_rng(relation_rng(relation_rng(sk0_55))))),
% 0.20/0.54 inference(resolution,[status(thm)],[f1134,f497])).
% 0.20/0.54 fof(f1167,plain,(
% 0.20/0.54 spl0_38|~spl0_39),
% 0.20/0.54 inference(split_clause,[status(thm)],[f1166,f1160,f1163])).
% 0.20/0.54 fof(f1169,plain,(
% 0.20/0.54 relation(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_55))))))),
% 0.20/0.54 inference(resolution,[status(thm)],[f1134,f503])).
% 0.20/0.54 fof(f1170,plain,(
% 0.20/0.54 empty(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_55))))))),
% 0.20/0.54 inference(resolution,[status(thm)],[f1134,f502])).
% 0.20/0.54 fof(f1171,plain,(
% 0.20/0.54 $false|spl0_39),
% 0.20/0.54 inference(forward_subsumption_resolution,[status(thm)],[f1165,f1095])).
% 0.20/0.54 fof(f1172,plain,(
% 0.20/0.54 spl0_39),
% 0.20/0.54 inference(contradiction_clause,[status(thm)],[f1171])).
% 0.20/0.54 fof(f1173,plain,(
% 0.20/0.54 spl0_40 <=> relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))=empty_set),
% 0.20/0.54 introduced(split_symbol_definition)).
% 0.20/0.54 fof(f1175,plain,(
% 0.20/0.54 ~relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))=empty_set|spl0_40),
% 0.20/0.54 inference(component_clause,[status(thm)],[f1173])).
% 0.20/0.54 fof(f1176,plain,(
% 0.20/0.54 ~relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))=empty_set|relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53)))))=empty_set),
% 0.20/0.54 inference(resolution,[status(thm)],[f1151,f785])).
% 0.20/0.54 fof(f1177,plain,(
% 0.20/0.54 ~spl0_40|spl0_34),
% 0.20/0.54 inference(split_clause,[status(thm)],[f1176,f1173,f1137])).
% 0.20/0.54 fof(f1178,plain,(
% 0.20/0.54 spl0_41 <=> empty(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53)))))),
% 0.20/0.54 introduced(split_symbol_definition)).
% 0.20/0.54 fof(f1181,plain,(
% 0.20/0.54 spl0_42 <=> relation(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53)))))),
% 0.20/0.54 introduced(split_symbol_definition)).
% 0.20/0.54 fof(f1183,plain,(
% 0.20/0.54 ~relation(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53)))))|spl0_42),
% 0.20/0.54 inference(component_clause,[status(thm)],[f1181])).
% 0.20/0.54 fof(f1184,plain,(
% 0.20/0.54 empty(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53)))))|~relation(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53)))))),
% 0.20/0.54 inference(resolution,[status(thm)],[f1152,f497])).
% 0.20/0.54 fof(f1185,plain,(
% 0.20/0.54 spl0_41|~spl0_42),
% 0.20/0.54 inference(split_clause,[status(thm)],[f1184,f1178,f1181])).
% 0.20/0.54 fof(f1188,plain,(
% 0.20/0.54 empty(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53)))))))),
% 0.20/0.54 inference(resolution,[status(thm)],[f1152,f502])).
% 0.20/0.54 fof(f1189,plain,(
% 0.20/0.54 $false|spl0_42),
% 0.20/0.54 inference(forward_subsumption_resolution,[status(thm)],[f1183,f1115])).
% 0.20/0.54 fof(f1190,plain,(
% 0.20/0.54 spl0_42),
% 0.20/0.54 inference(contradiction_clause,[status(thm)],[f1189])).
% 0.20/0.54 fof(f1191,plain,(
% 0.20/0.54 spl0_43 <=> relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_55))))))=empty_set),
% 0.20/0.54 introduced(split_symbol_definition)).
% 0.20/0.54 fof(f1196,plain,(
% 0.20/0.54 spl0_44 <=> empty(relation_rng(relation_rng(relation_rng(relation_rng(sk0_55)))))),
% 0.20/0.54 introduced(split_symbol_definition)).
% 0.20/0.54 fof(f1199,plain,(
% 0.20/0.54 spl0_45 <=> relation(relation_rng(relation_rng(relation_rng(relation_rng(sk0_55)))))),
% 0.20/0.54 introduced(split_symbol_definition)).
% 0.20/0.54 fof(f1201,plain,(
% 0.20/0.54 ~relation(relation_rng(relation_rng(relation_rng(relation_rng(sk0_55)))))|spl0_45),
% 0.20/0.54 inference(component_clause,[status(thm)],[f1199])).
% 0.20/0.54 fof(f1202,plain,(
% 0.20/0.54 empty(relation_rng(relation_rng(relation_rng(relation_rng(sk0_55)))))|~relation(relation_rng(relation_rng(relation_rng(relation_rng(sk0_55)))))),
% 0.20/0.54 inference(resolution,[status(thm)],[f1170,f497])).
% 0.20/0.54 fof(f1203,plain,(
% 0.20/0.54 spl0_44|~spl0_45),
% 0.20/0.54 inference(split_clause,[status(thm)],[f1202,f1196,f1199])).
% 0.20/0.54 fof(f1205,plain,(
% 0.20/0.54 relation(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_55)))))))),
% 0.20/0.54 inference(resolution,[status(thm)],[f1170,f503])).
% 0.20/0.54 fof(f1206,plain,(
% 0.20/0.54 empty(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_55)))))))),
% 0.20/0.54 inference(resolution,[status(thm)],[f1170,f502])).
% 0.20/0.54 fof(f1207,plain,(
% 0.20/0.54 $false|spl0_45),
% 0.20/0.54 inference(forward_subsumption_resolution,[status(thm)],[f1201,f1133])).
% 0.20/0.54 fof(f1208,plain,(
% 0.20/0.54 spl0_45),
% 0.20/0.54 inference(contradiction_clause,[status(thm)],[f1207])).
% 0.20/0.54 fof(f1209,plain,(
% 0.20/0.54 spl0_46 <=> relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53)))))))=empty_set),
% 0.20/0.54 introduced(split_symbol_definition)).
% 0.20/0.54 fof(f1214,plain,(
% 0.20/0.54 spl0_47 <=> empty(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))),
% 0.20/0.54 introduced(split_symbol_definition)).
% 0.20/0.54 fof(f1217,plain,(
% 0.20/0.54 spl0_48 <=> relation(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))),
% 0.20/0.54 introduced(split_symbol_definition)).
% 0.20/0.54 fof(f1219,plain,(
% 0.20/0.54 ~relation(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))|spl0_48),
% 0.20/0.54 inference(component_clause,[status(thm)],[f1217])).
% 0.20/0.54 fof(f1220,plain,(
% 0.20/0.54 empty(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))|~relation(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))),
% 0.20/0.54 inference(resolution,[status(thm)],[f1188,f497])).
% 0.20/0.54 fof(f1221,plain,(
% 0.20/0.54 spl0_47|~spl0_48),
% 0.20/0.54 inference(split_clause,[status(thm)],[f1220,f1214,f1217])).
% 0.20/0.54 fof(f1223,plain,(
% 0.20/0.54 relation(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))),
% 0.20/0.54 inference(resolution,[status(thm)],[f1188,f503])).
% 0.20/0.54 fof(f1225,plain,(
% 0.20/0.54 $false|spl0_48),
% 0.20/0.54 inference(forward_subsumption_resolution,[status(thm)],[f1219,f1151])).
% 0.20/0.54 fof(f1226,plain,(
% 0.20/0.54 spl0_48),
% 0.20/0.54 inference(contradiction_clause,[status(thm)],[f1225])).
% 0.20/0.54 fof(f1227,plain,(
% 0.20/0.54 spl0_49 <=> relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_55)))))))=empty_set),
% 0.20/0.54 introduced(split_symbol_definition)).
% 0.20/0.54 fof(f1229,plain,(
% 0.20/0.54 ~relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_55)))))))=empty_set|spl0_49),
% 0.20/0.54 inference(component_clause,[status(thm)],[f1227])).
% 0.20/0.54 fof(f1230,plain,(
% 0.20/0.54 ~relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_55)))))))=empty_set|relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_55))))))=empty_set),
% 0.20/0.54 inference(resolution,[status(thm)],[f1205,f785])).
% 0.20/0.54 fof(f1231,plain,(
% 0.20/0.54 ~spl0_49|spl0_43),
% 0.20/0.54 inference(split_clause,[status(thm)],[f1230,f1227,f1191])).
% 0.20/0.54 fof(f1232,plain,(
% 0.20/0.54 spl0_50 <=> empty(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_55))))))),
% 0.20/0.54 introduced(split_symbol_definition)).
% 0.20/0.54 fof(f1235,plain,(
% 0.20/0.54 spl0_51 <=> relation(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_55))))))),
% 0.20/0.54 introduced(split_symbol_definition)).
% 0.20/0.54 fof(f1237,plain,(
% 0.20/0.54 ~relation(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_55))))))|spl0_51),
% 0.20/0.54 inference(component_clause,[status(thm)],[f1235])).
% 0.20/0.54 fof(f1238,plain,(
% 0.20/0.54 empty(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_55))))))|~relation(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_55))))))),
% 0.20/0.54 inference(resolution,[status(thm)],[f1206,f497])).
% 0.20/0.54 fof(f1239,plain,(
% 0.20/0.54 spl0_50|~spl0_51),
% 0.20/0.54 inference(split_clause,[status(thm)],[f1238,f1232,f1235])).
% 0.20/0.54 fof(f1243,plain,(
% 0.20/0.54 $false|spl0_51),
% 0.20/0.54 inference(forward_subsumption_resolution,[status(thm)],[f1237,f1169])).
% 0.20/0.54 fof(f1244,plain,(
% 0.20/0.54 spl0_51),
% 0.20/0.54 inference(contradiction_clause,[status(thm)],[f1243])).
% 0.20/0.54 fof(f1245,plain,(
% 0.20/0.54 spl0_52 <=> relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))=empty_set),
% 0.20/0.54 introduced(split_symbol_definition)).
% 0.20/0.54 fof(f1247,plain,(
% 0.20/0.54 ~relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))=empty_set|spl0_52),
% 0.20/0.54 inference(component_clause,[status(thm)],[f1245])).
% 0.20/0.54 fof(f1248,plain,(
% 0.20/0.54 ~relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))=empty_set|relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53)))))))=empty_set),
% 0.20/0.54 inference(resolution,[status(thm)],[f1223,f785])).
% 0.20/0.54 fof(f1249,plain,(
% 0.20/0.54 ~spl0_52|spl0_46),
% 0.20/0.54 inference(split_clause,[status(thm)],[f1248,f1245,f1209])).
% 0.20/0.54 fof(f1250,plain,(
% 0.20/0.54 $false|spl0_21),
% 0.20/0.54 inference(forward_subsumption_resolution,[status(thm)],[f987,f1037])).
% 0.20/0.54 fof(f1251,plain,(
% 0.20/0.54 spl0_21),
% 0.20/0.54 inference(contradiction_clause,[status(thm)],[f1250])).
% 0.20/0.54 fof(f1252,plain,(
% 0.20/0.54 $false|spl0_17),
% 0.20/0.54 inference(forward_subsumption_resolution,[status(thm)],[f557,f1018])).
% 0.20/0.54 fof(f1253,plain,(
% 0.20/0.54 spl0_17),
% 0.20/0.54 inference(contradiction_clause,[status(thm)],[f1252])).
% 0.20/0.54 fof(f1257,plain,(
% 0.20/0.54 spl0_53 <=> sk0_55=empty_set),
% 0.20/0.54 introduced(split_symbol_definition)).
% 0.20/0.54 fof(f1258,plain,(
% 0.20/0.54 sk0_55=empty_set|~spl0_53),
% 0.20/0.54 inference(component_clause,[status(thm)],[f1257])).
% 0.20/0.54 fof(f1259,plain,(
% 0.20/0.54 ~sk0_55=empty_set|spl0_53),
% 0.20/0.54 inference(component_clause,[status(thm)],[f1257])).
% 0.20/0.54 fof(f1264,plain,(
% 0.20/0.54 ![X0]: (~relation_rng(identity_relation(X0))=empty_set|identity_relation(X0)=empty_set)),
% 0.20/0.54 inference(resolution,[status(thm)],[f457,f785])).
% 0.20/0.54 fof(f1267,plain,(
% 0.20/0.54 ![X0]: (empty(relation_rng(sk0_57(X0))))),
% 0.20/0.54 inference(resolution,[status(thm)],[f569,f502])).
% 0.20/0.54 fof(f1268,plain,(
% 0.20/0.54 spl0_54 <=> ~relation(X0)|subset(relation_rng(empty_set),relation_rng(X0))),
% 0.20/0.54 introduced(split_symbol_definition)).
% 0.20/0.54 fof(f1271,plain,(
% 0.20/0.54 ![X0]: (~relation(empty_set)|~relation(X0)|subset(relation_rng(empty_set),relation_rng(X0)))),
% 0.20/0.54 inference(resolution,[status(thm)],[f685,f671])).
% 0.20/0.54 fof(f1272,plain,(
% 0.20/0.54 ~spl0_6|spl0_54),
% 0.20/0.54 inference(split_clause,[status(thm)],[f1271,f945,f1268])).
% 0.20/0.54 fof(f1273,plain,(
% 0.20/0.54 $false|spl0_6),
% 0.20/0.54 inference(forward_subsumption_resolution,[status(thm)],[f947,f491])).
% 0.20/0.54 fof(f1274,plain,(
% 0.20/0.54 spl0_6),
% 0.20/0.54 inference(contradiction_clause,[status(thm)],[f1273])).
% 0.20/0.54 fof(f1278,plain,(
% 0.20/0.54 ![X0,X1]: (in(ordered_pair(X0,X0),identity_relation(X1))|~in(X0,X1))),
% 0.20/0.54 inference(forward_subsumption_resolution,[status(thm)],[f883,f457])).
% 0.20/0.54 fof(f1281,plain,(
% 0.20/0.54 spl0_55 <=> relation(identity_relation(relation_inverse_image(sk0_61,sk0_63)))),
% 0.20/0.54 introduced(split_symbol_definition)).
% 0.20/0.54 fof(f1283,plain,(
% 0.20/0.54 ~relation(identity_relation(relation_inverse_image(sk0_61,sk0_63)))|spl0_55),
% 0.20/0.54 inference(component_clause,[status(thm)],[f1281])).
% 0.20/0.54 fof(f1296,plain,(
% 0.20/0.54 $false|spl0_55),
% 0.20/0.54 inference(forward_subsumption_resolution,[status(thm)],[f1283,f457])).
% 0.20/0.54 fof(f1297,plain,(
% 0.20/0.54 spl0_55),
% 0.20/0.54 inference(contradiction_clause,[status(thm)],[f1296])).
% 0.20/0.54 fof(f1304,plain,(
% 0.20/0.54 spl0_58 <=> relation(sk0_61)),
% 0.20/0.54 introduced(split_symbol_definition)).
% 0.20/0.54 fof(f1306,plain,(
% 0.20/0.54 ~relation(sk0_61)|spl0_58),
% 0.20/0.54 inference(component_clause,[status(thm)],[f1304])).
% 0.20/0.54 fof(f1309,plain,(
% 0.20/0.54 spl0_59 <=> in(sk0_62,relation_inverse_image(sk0_61,X0))|~in(sk0_64,X0)),
% 0.20/0.54 introduced(split_symbol_definition)).
% 0.20/0.54 fof(f1310,plain,(
% 0.20/0.54 ![X0]: (in(sk0_62,relation_inverse_image(sk0_61,X0))|~in(sk0_64,X0)|~spl0_59)),
% 0.20/0.54 inference(component_clause,[status(thm)],[f1309])).
% 0.20/0.54 fof(f1312,plain,(
% 0.20/0.54 ![X0]: (~relation(sk0_61)|in(sk0_62,relation_inverse_image(sk0_61,X0))|~in(sk0_64,X0)|~spl0_2)),
% 0.20/0.54 inference(resolution,[status(thm)],[f870,f897])).
% 0.20/0.54 fof(f1313,plain,(
% 0.20/0.54 ~spl0_58|spl0_59|~spl0_2),
% 0.20/0.54 inference(split_clause,[status(thm)],[f1312,f1304,f1309,f869])).
% 0.20/0.54 fof(f1316,plain,(
% 0.20/0.54 $false|spl0_58),
% 0.20/0.54 inference(forward_subsumption_resolution,[status(thm)],[f1306,f648])).
% 0.20/0.54 fof(f1317,plain,(
% 0.20/0.54 spl0_58),
% 0.20/0.54 inference(contradiction_clause,[status(thm)],[f1316])).
% 0.20/0.54 fof(f1382,plain,(
% 0.20/0.54 ~relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(empty_set)))))=empty_set|~spl0_53|spl0_37),
% 0.20/0.54 inference(forward_demodulation,[status(thm)],[f1258,f1157])).
% 0.20/0.54 fof(f1383,plain,(
% 0.20/0.54 ~relation_rng(relation_rng(relation_rng(relation_rng(empty_set))))=empty_set|~spl0_53|spl0_37),
% 0.20/0.54 inference(forward_demodulation,[status(thm)],[f777,f1382])).
% 0.20/0.54 fof(f1384,plain,(
% 0.20/0.54 ~relation_rng(relation_rng(relation_rng(empty_set)))=empty_set|~spl0_53|spl0_37),
% 0.20/0.54 inference(forward_demodulation,[status(thm)],[f777,f1383])).
% 0.20/0.54 fof(f1385,plain,(
% 0.20/0.54 ~relation_rng(relation_rng(empty_set))=empty_set|~spl0_53|spl0_37),
% 0.20/0.54 inference(forward_demodulation,[status(thm)],[f777,f1384])).
% 0.20/0.54 fof(f1386,plain,(
% 0.20/0.54 ~relation_rng(empty_set)=empty_set|~spl0_53|spl0_37),
% 0.20/0.54 inference(forward_demodulation,[status(thm)],[f777,f1385])).
% 0.20/0.54 fof(f1387,plain,(
% 0.20/0.54 ~empty_set=empty_set|~spl0_53|spl0_37),
% 0.20/0.54 inference(forward_demodulation,[status(thm)],[f777,f1386])).
% 0.20/0.54 fof(f1388,plain,(
% 0.20/0.54 $false|~spl0_53|spl0_37),
% 0.20/0.54 inference(trivial_equality_resolution,[status(esa)],[f1387])).
% 0.20/0.54 fof(f1389,plain,(
% 0.20/0.54 ~spl0_53|spl0_37),
% 0.20/0.54 inference(contradiction_clause,[status(thm)],[f1388])).
% 0.20/0.54 fof(f1411,plain,(
% 0.20/0.54 spl0_60 <=> relation(identity_relation(identity_relation(relation_inverse_image(sk0_61,sk0_63))))),
% 0.20/0.54 introduced(split_symbol_definition)).
% 0.20/0.54 fof(f1413,plain,(
% 0.20/0.54 ~relation(identity_relation(identity_relation(relation_inverse_image(sk0_61,sk0_63))))|spl0_60),
% 0.20/0.54 inference(component_clause,[status(thm)],[f1411])).
% 0.20/0.54 fof(f1473,plain,(
% 0.20/0.54 ![X0]: (set_union2(empty_set,X0)=X0)),
% 0.20/0.54 inference(paramodulation,[status(thm)],[f214,f656])).
% 0.20/0.54 fof(f1477,plain,(
% 0.20/0.54 sk0_55=empty_set),
% 0.20/0.54 inference(resolution,[status(thm)],[f796,f563])).
% 0.20/0.54 fof(f1478,plain,(
% 0.20/0.54 $false|spl0_53),
% 0.20/0.54 inference(forward_subsumption_resolution,[status(thm)],[f1477,f1259])).
% 0.20/0.54 fof(f1479,plain,(
% 0.20/0.54 spl0_53),
% 0.20/0.54 inference(contradiction_clause,[status(thm)],[f1478])).
% 0.20/0.54 fof(f1481,plain,(
% 0.20/0.54 sk0_53=empty_set),
% 0.20/0.54 inference(resolution,[status(thm)],[f796,f556])).
% 0.20/0.54 fof(f1482,plain,(
% 0.20/0.54 $false|spl0_12),
% 0.20/0.54 inference(forward_subsumption_resolution,[status(thm)],[f1481,f984])).
% 0.20/0.54 fof(f1483,plain,(
% 0.20/0.54 spl0_12),
% 0.20/0.54 inference(contradiction_clause,[status(thm)],[f1482])).
% 0.20/0.54 fof(f1484,plain,(
% 0.20/0.54 ![X0]: (relation_rng(sk0_57(X0))=empty_set)),
% 0.20/0.54 inference(resolution,[status(thm)],[f796,f1267])).
% 0.20/0.54 fof(f1489,plain,(
% 0.20/0.54 relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))=empty_set),
% 0.20/0.54 inference(resolution,[status(thm)],[f796,f1188])).
% 0.20/0.54 fof(f1490,plain,(
% 0.20/0.54 $false|spl0_40),
% 0.20/0.54 inference(forward_subsumption_resolution,[status(thm)],[f1489,f1175])).
% 0.20/0.54 fof(f1491,plain,(
% 0.20/0.54 spl0_40),
% 0.20/0.54 inference(contradiction_clause,[status(thm)],[f1490])).
% 0.20/0.54 fof(f1532,plain,(
% 0.20/0.54 ![X0]: (sk0_61=identity_relation(X0)|in(ordered_pair(sk0_0(X0,sk0_61),sk0_1(X0,sk0_61)),sk0_61)|in(sk0_0(X0,sk0_61),X0))),
% 0.20/0.54 inference(resolution,[status(thm)],[f224,f648])).
% 0.20/0.54 fof(f1539,plain,(
% 0.20/0.54 ![X0]: (relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53)))))))=identity_relation(X0)|in(ordered_pair(sk0_0(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53)))))))),sk0_1(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))),relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))|sk0_0(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))=sk0_1(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53)))))))))),
% 0.20/0.54 inference(resolution,[status(thm)],[f225,f1223])).
% 0.20/0.54 fof(f1549,plain,(
% 0.20/0.54 ![X0]: (sk0_61=identity_relation(X0)|in(ordered_pair(sk0_0(X0,sk0_61),sk0_1(X0,sk0_61)),sk0_61)|sk0_0(X0,sk0_61)=sk0_1(X0,sk0_61))),
% 0.20/0.54 inference(resolution,[status(thm)],[f225,f648])).
% 0.20/0.54 fof(f1634,plain,(
% 0.20/0.54 in(sk0_62,relation_inverse_image(sk0_61,sk0_63))|~spl0_59|~spl0_3),
% 0.20/0.54 inference(resolution,[status(thm)],[f1310,f874])).
% 0.20/0.54 fof(f1635,plain,(
% 0.20/0.54 spl0_0|~spl0_59|~spl0_3),
% 0.20/0.54 inference(split_clause,[status(thm)],[f1634,f862,f1309,f873])).
% 0.20/0.54 fof(f1638,plain,(
% 0.20/0.54 $false|spl0_60),
% 0.20/0.54 inference(forward_subsumption_resolution,[status(thm)],[f1413,f457])).
% 0.20/0.54 fof(f1639,plain,(
% 0.20/0.54 spl0_60),
% 0.20/0.54 inference(contradiction_clause,[status(thm)],[f1638])).
% 0.20/0.54 fof(f1682,plain,(
% 0.20/0.54 spl0_63 <=> sk0_61=identity_relation(X0)|in(sk0_0(X0,sk0_61),X0)|sk0_61=identity_relation(X0)|~in(sk0_0(X0,sk0_61),X0)|~sk0_0(X0,sk0_61)=sk0_1(X0,sk0_61)),
% 0.20/0.54 introduced(split_symbol_definition)).
% 0.20/0.54 fof(f1685,plain,(
% 0.20/0.54 ![X0]: (sk0_61=identity_relation(X0)|in(sk0_0(X0,sk0_61),X0)|~relation(sk0_61)|sk0_61=identity_relation(X0)|~in(sk0_0(X0,sk0_61),X0)|~sk0_0(X0,sk0_61)=sk0_1(X0,sk0_61))),
% 0.20/0.54 inference(resolution,[status(thm)],[f1532,f223])).
% 0.20/0.54 fof(f1686,plain,(
% 0.20/0.54 spl0_63|~spl0_58),
% 0.20/0.54 inference(split_clause,[status(thm)],[f1685,f1682,f1304])).
% 0.20/0.54 fof(f1687,plain,(
% 0.20/0.54 spl0_64 <=> sk0_61=identity_relation(X0)|in(sk0_0(X0,sk0_61),X0)|in(sk0_1(X0,sk0_61),relation_rng(sk0_61))),
% 0.20/0.54 introduced(split_symbol_definition)).
% 0.20/0.54 fof(f1688,plain,(
% 0.20/0.54 ![X0]: (sk0_61=identity_relation(X0)|in(sk0_0(X0,sk0_61),X0)|in(sk0_1(X0,sk0_61),relation_rng(sk0_61))|~spl0_64)),
% 0.20/0.54 inference(component_clause,[status(thm)],[f1687])).
% 0.20/0.54 fof(f1690,plain,(
% 0.20/0.54 ![X0]: (sk0_61=identity_relation(X0)|in(sk0_0(X0,sk0_61),X0)|~relation(sk0_61)|in(sk0_1(X0,sk0_61),relation_rng(sk0_61)))),
% 0.20/0.54 inference(resolution,[status(thm)],[f1532,f928])).
% 0.20/0.54 fof(f1691,plain,(
% 0.20/0.54 spl0_64|~spl0_58),
% 0.20/0.54 inference(split_clause,[status(thm)],[f1690,f1687,f1304])).
% 0.20/0.54 fof(f1692,plain,(
% 0.20/0.54 spl0_65 <=> sk0_61=identity_relation(X0)|in(sk0_0(X0,sk0_61),X0)|in(sk0_0(X0,sk0_61),relation_inverse_image(sk0_61,X1))|~in(sk0_1(X0,sk0_61),X1)),
% 0.20/0.54 introduced(split_symbol_definition)).
% 0.20/0.54 fof(f1695,plain,(
% 0.20/0.54 ![X0,X1]: (sk0_61=identity_relation(X0)|in(sk0_0(X0,sk0_61),X0)|~relation(sk0_61)|in(sk0_0(X0,sk0_61),relation_inverse_image(sk0_61,X1))|~in(sk0_1(X0,sk0_61),X1))),
% 0.20/0.54 inference(resolution,[status(thm)],[f1532,f897])).
% 0.20/0.54 fof(f1696,plain,(
% 0.20/0.54 spl0_65|~spl0_58),
% 0.20/0.54 inference(split_clause,[status(thm)],[f1695,f1692,f1304])).
% 0.20/0.54 fof(f1697,plain,(
% 0.20/0.54 ![X0]: (sk0_61=identity_relation(X0)|in(sk0_0(X0,sk0_61),X0)|in(ordered_pair(ordered_pair(sk0_0(X0,sk0_61),sk0_1(X0,sk0_61)),ordered_pair(sk0_0(X0,sk0_61),sk0_1(X0,sk0_61))),identity_relation(sk0_61)))),
% 0.20/0.54 inference(resolution,[status(thm)],[f1532,f1278])).
% 0.20/0.54 fof(f1699,plain,(
% 0.20/0.54 spl0_66 <=> sk0_61=identity_relation(X0)|sk0_0(X0,sk0_61)=sk0_1(X0,sk0_61)|sk0_61=identity_relation(X0)|~in(sk0_0(X0,sk0_61),X0)|~sk0_0(X0,sk0_61)=sk0_1(X0,sk0_61)),
% 0.20/0.54 introduced(split_symbol_definition)).
% 0.20/0.54 fof(f1702,plain,(
% 0.20/0.54 ![X0]: (sk0_61=identity_relation(X0)|sk0_0(X0,sk0_61)=sk0_1(X0,sk0_61)|~relation(sk0_61)|sk0_61=identity_relation(X0)|~in(sk0_0(X0,sk0_61),X0)|~sk0_0(X0,sk0_61)=sk0_1(X0,sk0_61))),
% 0.20/0.54 inference(resolution,[status(thm)],[f1549,f223])).
% 0.20/0.54 fof(f1703,plain,(
% 0.20/0.54 spl0_66|~spl0_58),
% 0.20/0.54 inference(split_clause,[status(thm)],[f1702,f1699,f1304])).
% 0.20/0.54 fof(f1704,plain,(
% 0.20/0.54 spl0_67 <=> sk0_61=identity_relation(X0)|sk0_0(X0,sk0_61)=sk0_1(X0,sk0_61)|in(sk0_1(X0,sk0_61),relation_rng(sk0_61))),
% 0.20/0.54 introduced(split_symbol_definition)).
% 0.20/0.54 fof(f1707,plain,(
% 0.20/0.54 ![X0]: (sk0_61=identity_relation(X0)|sk0_0(X0,sk0_61)=sk0_1(X0,sk0_61)|~relation(sk0_61)|in(sk0_1(X0,sk0_61),relation_rng(sk0_61)))),
% 0.20/0.54 inference(resolution,[status(thm)],[f1549,f928])).
% 0.20/0.54 fof(f1708,plain,(
% 0.20/0.54 spl0_67|~spl0_58),
% 0.20/0.54 inference(split_clause,[status(thm)],[f1707,f1704,f1304])).
% 0.20/0.54 fof(f1709,plain,(
% 0.20/0.54 spl0_68 <=> sk0_61=identity_relation(X0)|sk0_0(X0,sk0_61)=sk0_1(X0,sk0_61)|in(sk0_0(X0,sk0_61),relation_inverse_image(sk0_61,X1))|~in(sk0_1(X0,sk0_61),X1)),
% 0.20/0.54 introduced(split_symbol_definition)).
% 0.20/0.54 fof(f1712,plain,(
% 0.20/0.54 ![X0,X1]: (sk0_61=identity_relation(X0)|sk0_0(X0,sk0_61)=sk0_1(X0,sk0_61)|~relation(sk0_61)|in(sk0_0(X0,sk0_61),relation_inverse_image(sk0_61,X1))|~in(sk0_1(X0,sk0_61),X1))),
% 0.20/0.54 inference(resolution,[status(thm)],[f1549,f897])).
% 0.20/0.54 fof(f1713,plain,(
% 0.20/0.54 spl0_68|~spl0_58),
% 0.20/0.54 inference(split_clause,[status(thm)],[f1712,f1709,f1304])).
% 0.20/0.54 fof(f1714,plain,(
% 0.20/0.54 ![X0]: (sk0_61=identity_relation(X0)|sk0_0(X0,sk0_61)=sk0_1(X0,sk0_61)|in(ordered_pair(ordered_pair(sk0_0(X0,sk0_61),sk0_1(X0,sk0_61)),ordered_pair(sk0_0(X0,sk0_61),sk0_1(X0,sk0_61))),identity_relation(sk0_61)))),
% 0.20/0.54 inference(resolution,[status(thm)],[f1549,f1278])).
% 0.20/0.54 fof(f1717,plain,(
% 0.20/0.54 spl0_69 <=> sk0_61=identity_relation(X0)|in(sk0_0(X0,sk0_61),X0)|in(ordered_pair(sk0_0(X0,sk0_61),sk0_1(X0,sk0_61)),relation_rng(identity_relation(sk0_61)))),
% 0.20/0.54 introduced(split_symbol_definition)).
% 0.20/0.54 fof(f1720,plain,(
% 0.20/0.54 spl0_70 <=> relation(identity_relation(sk0_61))),
% 0.20/0.54 introduced(split_symbol_definition)).
% 0.20/0.54 fof(f1722,plain,(
% 0.20/0.54 ~relation(identity_relation(sk0_61))|spl0_70),
% 0.20/0.54 inference(component_clause,[status(thm)],[f1720])).
% 0.20/0.54 fof(f1723,plain,(
% 0.20/0.54 ![X0]: (sk0_61=identity_relation(X0)|in(sk0_0(X0,sk0_61),X0)|~relation(identity_relation(sk0_61))|in(ordered_pair(sk0_0(X0,sk0_61),sk0_1(X0,sk0_61)),relation_rng(identity_relation(sk0_61))))),
% 0.20/0.54 inference(resolution,[status(thm)],[f1697,f928])).
% 0.20/0.54 fof(f1724,plain,(
% 0.20/0.54 spl0_69|~spl0_70),
% 0.20/0.54 inference(split_clause,[status(thm)],[f1723,f1717,f1720])).
% 0.20/0.54 fof(f1725,plain,(
% 0.20/0.54 spl0_71 <=> sk0_61=identity_relation(X0)|in(sk0_0(X0,sk0_61),X0)|in(ordered_pair(sk0_0(X0,sk0_61),sk0_1(X0,sk0_61)),relation_inverse_image(identity_relation(sk0_61),X1))|~in(ordered_pair(sk0_0(X0,sk0_61),sk0_1(X0,sk0_61)),X1)),
% 0.20/0.54 introduced(split_symbol_definition)).
% 0.20/0.54 fof(f1728,plain,(
% 0.20/0.54 ![X0,X1]: (sk0_61=identity_relation(X0)|in(sk0_0(X0,sk0_61),X0)|~relation(identity_relation(sk0_61))|in(ordered_pair(sk0_0(X0,sk0_61),sk0_1(X0,sk0_61)),relation_inverse_image(identity_relation(sk0_61),X1))|~in(ordered_pair(sk0_0(X0,sk0_61),sk0_1(X0,sk0_61)),X1))),
% 0.20/0.54 inference(resolution,[status(thm)],[f1697,f897])).
% 0.20/0.54 fof(f1729,plain,(
% 0.20/0.54 spl0_71|~spl0_70),
% 0.20/0.54 inference(split_clause,[status(thm)],[f1728,f1725,f1720])).
% 0.20/0.54 fof(f1732,plain,(
% 0.20/0.54 $false|spl0_70),
% 0.20/0.54 inference(forward_subsumption_resolution,[status(thm)],[f1722,f457])).
% 0.20/0.54 fof(f1733,plain,(
% 0.20/0.54 spl0_70),
% 0.20/0.54 inference(contradiction_clause,[status(thm)],[f1732])).
% 0.20/0.54 fof(f1735,plain,(
% 0.20/0.54 spl0_72 <=> sk0_61=identity_relation(X0)|sk0_0(X0,sk0_61)=sk0_1(X0,sk0_61)|in(ordered_pair(sk0_0(X0,sk0_61),sk0_1(X0,sk0_61)),relation_rng(identity_relation(sk0_61)))),
% 0.20/0.54 introduced(split_symbol_definition)).
% 0.20/0.54 fof(f1738,plain,(
% 0.20/0.54 ![X0]: (sk0_61=identity_relation(X0)|sk0_0(X0,sk0_61)=sk0_1(X0,sk0_61)|~relation(identity_relation(sk0_61))|in(ordered_pair(sk0_0(X0,sk0_61),sk0_1(X0,sk0_61)),relation_rng(identity_relation(sk0_61))))),
% 0.20/0.54 inference(resolution,[status(thm)],[f1714,f928])).
% 0.20/0.54 fof(f1739,plain,(
% 0.20/0.54 spl0_72|~spl0_70),
% 0.20/0.54 inference(split_clause,[status(thm)],[f1738,f1735,f1720])).
% 0.20/0.54 fof(f1740,plain,(
% 0.20/0.54 spl0_73 <=> sk0_61=identity_relation(X0)|sk0_0(X0,sk0_61)=sk0_1(X0,sk0_61)|in(ordered_pair(sk0_0(X0,sk0_61),sk0_1(X0,sk0_61)),relation_inverse_image(identity_relation(sk0_61),X1))|~in(ordered_pair(sk0_0(X0,sk0_61),sk0_1(X0,sk0_61)),X1)),
% 0.20/0.54 introduced(split_symbol_definition)).
% 0.20/0.54 fof(f1743,plain,(
% 0.20/0.54 ![X0,X1]: (sk0_61=identity_relation(X0)|sk0_0(X0,sk0_61)=sk0_1(X0,sk0_61)|~relation(identity_relation(sk0_61))|in(ordered_pair(sk0_0(X0,sk0_61),sk0_1(X0,sk0_61)),relation_inverse_image(identity_relation(sk0_61),X1))|~in(ordered_pair(sk0_0(X0,sk0_61),sk0_1(X0,sk0_61)),X1))),
% 0.20/0.54 inference(resolution,[status(thm)],[f1714,f897])).
% 0.20/0.54 fof(f1744,plain,(
% 0.20/0.54 spl0_73|~spl0_70),
% 0.20/0.54 inference(split_clause,[status(thm)],[f1743,f1740,f1720])).
% 0.20/0.54 fof(f1765,plain,(
% 0.20/0.54 spl0_76 <=> empty(sk0_57(X0))|~relation(sk0_57(X0))),
% 0.20/0.54 introduced(split_symbol_definition)).
% 0.20/0.54 fof(f1768,plain,(
% 0.20/0.54 ![X0]: (empty(sk0_57(X0))|~relation(sk0_57(X0))|~empty(empty_set))),
% 0.20/0.54 inference(paramodulation,[status(thm)],[f1484,f497])).
% 0.20/0.54 fof(f1769,plain,(
% 0.20/0.54 spl0_76|~spl0_5),
% 0.20/0.54 inference(split_clause,[status(thm)],[f1768,f1765,f942])).
% 0.20/0.54 fof(f1770,plain,(
% 0.20/0.54 $false|spl0_5),
% 0.20/0.54 inference(forward_subsumption_resolution,[status(thm)],[f944,f478])).
% 0.20/0.54 fof(f1771,plain,(
% 0.20/0.54 spl0_5),
% 0.20/0.54 inference(contradiction_clause,[status(thm)],[f1770])).
% 0.20/0.54 fof(f1786,plain,(
% 0.20/0.54 ![X0]: (~X0=empty_set|identity_relation(X0)=empty_set)),
% 0.20/0.54 inference(backward_demodulation,[status(thm)],[f801,f1264])).
% 0.20/0.54 fof(f1787,plain,(
% 0.20/0.54 identity_relation(empty_set)=empty_set),
% 0.20/0.54 inference(destructive_equality_resolution,[status(esa)],[f1786])).
% 0.20/0.54 fof(f1835,plain,(
% 0.20/0.54 ~relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(empty_set)))))))=empty_set|spl0_49),
% 0.20/0.54 inference(forward_demodulation,[status(thm)],[f1477,f1229])).
% 0.20/0.54 fof(f1836,plain,(
% 0.20/0.54 ~relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(empty_set))))))=empty_set|spl0_49),
% 0.20/0.54 inference(forward_demodulation,[status(thm)],[f777,f1835])).
% 0.20/0.54 fof(f1837,plain,(
% 0.20/0.54 ~relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(empty_set)))))=empty_set|spl0_49),
% 0.20/0.54 inference(forward_demodulation,[status(thm)],[f777,f1836])).
% 0.20/0.54 fof(f1838,plain,(
% 0.20/0.54 ~relation_rng(relation_rng(relation_rng(relation_rng(empty_set))))=empty_set|spl0_49),
% 0.20/0.54 inference(forward_demodulation,[status(thm)],[f777,f1837])).
% 0.20/0.54 fof(f1839,plain,(
% 0.20/0.54 ~relation_rng(relation_rng(relation_rng(empty_set)))=empty_set|spl0_49),
% 0.20/0.54 inference(forward_demodulation,[status(thm)],[f777,f1838])).
% 0.20/0.54 fof(f1840,plain,(
% 0.20/0.54 ~relation_rng(relation_rng(empty_set))=empty_set|spl0_49),
% 0.20/0.54 inference(forward_demodulation,[status(thm)],[f777,f1839])).
% 0.20/0.54 fof(f1841,plain,(
% 0.20/0.54 ~relation_rng(empty_set)=empty_set|spl0_49),
% 0.20/0.54 inference(forward_demodulation,[status(thm)],[f777,f1840])).
% 0.20/0.54 fof(f1842,plain,(
% 0.20/0.54 ~empty_set=empty_set|spl0_49),
% 0.20/0.54 inference(forward_demodulation,[status(thm)],[f777,f1841])).
% 0.20/0.54 fof(f1843,plain,(
% 0.20/0.54 $false|spl0_49),
% 0.20/0.54 inference(trivial_equality_resolution,[status(esa)],[f1842])).
% 0.20/0.54 fof(f1844,plain,(
% 0.20/0.54 spl0_49),
% 0.20/0.54 inference(contradiction_clause,[status(thm)],[f1843])).
% 0.20/0.54 fof(f1872,plain,(
% 0.20/0.54 ~relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(empty_set))))))))=empty_set|~spl0_12|spl0_52),
% 0.20/0.54 inference(forward_demodulation,[status(thm)],[f983,f1247])).
% 0.20/0.54 fof(f1873,plain,(
% 0.20/0.54 ~relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(empty_set)))))))=empty_set|~spl0_12|spl0_52),
% 0.20/0.54 inference(forward_demodulation,[status(thm)],[f777,f1872])).
% 0.20/0.54 fof(f1874,plain,(
% 0.20/0.54 ~relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(empty_set))))))=empty_set|~spl0_12|spl0_52),
% 0.20/0.54 inference(forward_demodulation,[status(thm)],[f777,f1873])).
% 0.20/0.54 fof(f1875,plain,(
% 0.20/0.54 ~relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(empty_set)))))=empty_set|~spl0_12|spl0_52),
% 0.20/0.54 inference(forward_demodulation,[status(thm)],[f777,f1874])).
% 0.20/0.54 fof(f1876,plain,(
% 0.20/0.54 ~relation_rng(relation_rng(relation_rng(relation_rng(empty_set))))=empty_set|~spl0_12|spl0_52),
% 0.20/0.54 inference(forward_demodulation,[status(thm)],[f777,f1875])).
% 0.20/0.54 fof(f1877,plain,(
% 0.20/0.54 ~relation_rng(relation_rng(relation_rng(empty_set)))=empty_set|~spl0_12|spl0_52),
% 0.20/0.54 inference(forward_demodulation,[status(thm)],[f777,f1876])).
% 0.20/0.54 fof(f1878,plain,(
% 0.20/0.54 ~relation_rng(relation_rng(empty_set))=empty_set|~spl0_12|spl0_52),
% 0.20/0.54 inference(forward_demodulation,[status(thm)],[f777,f1877])).
% 0.20/0.54 fof(f1879,plain,(
% 0.20/0.54 ~relation_rng(empty_set)=empty_set|~spl0_12|spl0_52),
% 0.20/0.54 inference(forward_demodulation,[status(thm)],[f777,f1878])).
% 0.20/0.54 fof(f1880,plain,(
% 0.20/0.54 ~empty_set=empty_set|~spl0_12|spl0_52),
% 0.20/0.54 inference(forward_demodulation,[status(thm)],[f777,f1879])).
% 0.20/0.54 fof(f1881,plain,(
% 0.20/0.54 $false|~spl0_12|spl0_52),
% 0.20/0.54 inference(trivial_equality_resolution,[status(esa)],[f1880])).
% 0.20/0.54 fof(f1882,plain,(
% 0.20/0.54 ~spl0_12|spl0_52),
% 0.20/0.54 inference(contradiction_clause,[status(thm)],[f1881])).
% 0.20/0.54 fof(f1901,plain,(
% 0.20/0.54 spl0_77 <=> sk0_61=identity_relation(empty_set)),
% 0.20/0.54 introduced(split_symbol_definition)).
% 0.20/0.54 fof(f1902,plain,(
% 0.20/0.54 sk0_61=identity_relation(empty_set)|~spl0_77),
% 0.20/0.54 inference(component_clause,[status(thm)],[f1901])).
% 0.20/0.54 fof(f1903,plain,(
% 0.20/0.54 ~sk0_61=identity_relation(empty_set)|spl0_77),
% 0.20/0.54 inference(component_clause,[status(thm)],[f1901])).
% 0.20/0.54 fof(f1904,plain,(
% 0.20/0.54 spl0_78 <=> in(sk0_1(empty_set,sk0_61),relation_rng(sk0_61))),
% 0.20/0.54 introduced(split_symbol_definition)).
% 0.20/0.54 fof(f1907,plain,(
% 0.20/0.54 sk0_61=identity_relation(empty_set)|in(sk0_1(empty_set,sk0_61),relation_rng(sk0_61))|~spl0_64),
% 0.20/0.54 inference(resolution,[status(thm)],[f1688,f905])).
% 0.20/0.54 fof(f1908,plain,(
% 0.20/0.54 spl0_77|spl0_78|~spl0_64),
% 0.20/0.54 inference(split_clause,[status(thm)],[f1907,f1901,f1904,f1687])).
% 0.20/0.54 fof(f1913,plain,(
% 0.20/0.54 sk0_61=empty_set|~spl0_77),
% 0.20/0.54 inference(forward_demodulation,[status(thm)],[f1787,f1902])).
% 0.20/0.54 fof(f1987,plain,(
% 0.20/0.54 ~relation_rng(empty_set)=empty_set|~spl0_77|spl0_7),
% 0.20/0.54 inference(backward_demodulation,[status(thm)],[f1913,f952])).
% 0.20/0.54 fof(f1988,plain,(
% 0.20/0.54 ~spl0_9|~spl0_77|spl0_7),
% 0.20/0.54 inference(split_clause,[status(thm)],[f1987,f965,f1901,f950])).
% 0.20/0.54 fof(f1990,plain,(
% 0.20/0.54 ~sk0_61=empty_set|spl0_77),
% 0.20/0.54 inference(forward_demodulation,[status(thm)],[f1787,f1903])).
% 0.20/0.54 fof(f1991,plain,(
% 0.20/0.54 ~empty_set=empty_set|~spl0_8|spl0_77),
% 0.20/0.54 inference(forward_demodulation,[status(thm)],[f954,f1990])).
% 0.20/0.54 fof(f1992,plain,(
% 0.20/0.54 $false|~spl0_8|spl0_77),
% 0.20/0.54 inference(trivial_equality_resolution,[status(esa)],[f1991])).
% 0.20/0.54 fof(f1993,plain,(
% 0.20/0.54 ~spl0_8|spl0_77),
% 0.20/0.54 inference(contradiction_clause,[status(thm)],[f1992])).
% 0.20/0.54 fof(f2000,plain,(
% 0.20/0.54 in(sk0_62,relation_inverse_image(empty_set,sk0_63))|~spl0_8|~spl0_0),
% 0.20/0.54 inference(forward_demodulation,[status(thm)],[f954,f863])).
% 0.20/0.54 fof(f2031,plain,(
% 0.20/0.54 spl0_79 <=> empty_set=identity_relation(X0)|~in(ordered_pair(sk0_0(X0,empty_set),sk0_0(X0,empty_set)),empty_set)|~in(sk0_0(X0,empty_set),X0)|~sk0_0(X0,empty_set)=sk0_1(X0,empty_set)|empty_set=identity_relation(X0)),
% 0.20/0.54 introduced(split_symbol_definition)).
% 0.20/0.54 fof(f2076,plain,(
% 0.20/0.54 ![X0,X1]: (~relation(set_intersection2(X0,X1))|~relation(X0)|subset(relation_rng(set_intersection2(X0,X1)),relation_rng(X0)))),
% 0.20/0.54 inference(resolution,[status(thm)],[f653,f671])).
% 0.20/0.54 fof(f2078,plain,(
% 0.20/0.54 ![X0,X1]: (subset(set_intersection2(X0,X1),X1))),
% 0.20/0.54 inference(paramodulation,[status(thm)],[f215,f653])).
% 0.20/0.54 fof(f2080,plain,(
% 0.20/0.54 ![X0]: (set_intersection2(empty_set,X0)=empty_set)),
% 0.20/0.54 inference(paramodulation,[status(thm)],[f215,f677])).
% 0.20/0.54 fof(f2086,plain,(
% 0.20/0.54 ![X0,X1]: (~relation(set_difference(X0,X1))|~relation(X0)|subset(relation_rng(set_difference(X0,X1)),relation_rng(X0)))),
% 0.20/0.54 inference(resolution,[status(thm)],[f696,f671])).
% 0.20/0.54 fof(f2102,plain,(
% 0.20/0.54 ![X0,X1]: (~relation(X0)|~relation(set_union2(X0,X1))|subset(relation_rng(X0),relation_rng(set_union2(X0,X1))))),
% 0.20/0.54 inference(resolution,[status(thm)],[f811,f671])).
% 0.20/0.54 fof(f2106,plain,(
% 0.20/0.54 ![X0,X1]: (subset(X0,set_union2(X1,X0)))),
% 0.20/0.54 inference(paramodulation,[status(thm)],[f214,f811])).
% 0.20/0.54 fof(f2109,plain,(
% 0.20/0.54 ![X0,X1]: (~relation(set_intersection2(X0,X1))|~relation(X1)|subset(relation_rng(set_intersection2(X0,X1)),relation_rng(X1)))),
% 0.20/0.54 inference(resolution,[status(thm)],[f2078,f671])).
% 0.20/0.54 fof(f2126,plain,(
% 0.20/0.54 spl0_80 <=> relation(identity_relation(relation_inverse_image(empty_set,sk0_63)))),
% 0.20/0.54 introduced(split_symbol_definition)).
% 0.20/0.54 fof(f2128,plain,(
% 0.20/0.54 ~relation(identity_relation(relation_inverse_image(empty_set,sk0_63)))|spl0_80),
% 0.20/0.54 inference(component_clause,[status(thm)],[f2126])).
% 0.20/0.54 fof(f2142,plain,(
% 0.20/0.54 $false|spl0_80),
% 0.20/0.54 inference(forward_subsumption_resolution,[status(thm)],[f2128,f457])).
% 0.20/0.54 fof(f2143,plain,(
% 0.20/0.54 spl0_80),
% 0.20/0.55 inference(contradiction_clause,[status(thm)],[f2142])).
% 0.20/0.55 fof(f2184,plain,(
% 0.20/0.55 spl0_83 <=> relation(identity_relation(identity_relation(relation_inverse_image(empty_set,sk0_63))))),
% 0.20/0.55 introduced(split_symbol_definition)).
% 0.20/0.55 fof(f2186,plain,(
% 0.20/0.55 ~relation(identity_relation(identity_relation(relation_inverse_image(empty_set,sk0_63))))|spl0_83),
% 0.20/0.55 inference(component_clause,[status(thm)],[f2184])).
% 0.20/0.55 fof(f2200,plain,(
% 0.20/0.55 $false|spl0_83),
% 0.20/0.55 inference(forward_subsumption_resolution,[status(thm)],[f2186,f457])).
% 0.20/0.55 fof(f2201,plain,(
% 0.20/0.55 spl0_83),
% 0.20/0.55 inference(contradiction_clause,[status(thm)],[f2200])).
% 0.20/0.55 fof(f2315,plain,(
% 0.20/0.55 ![X0,X1]: (~relation(X0)|~relation(set_union2(X1,X0))|subset(relation_rng(X0),relation_rng(set_union2(X1,X0))))),
% 0.20/0.55 inference(resolution,[status(thm)],[f2106,f671])).
% 0.20/0.55 fof(f2325,plain,(
% 0.20/0.55 relation(relation_inverse(empty_set))),
% 0.20/0.55 inference(resolution,[status(thm)],[f452,f491])).
% 0.20/0.55 fof(f2338,plain,(
% 0.20/0.55 relation(relation_inverse(relation_inverse(empty_set)))),
% 0.20/0.55 inference(resolution,[status(thm)],[f2325,f452])).
% 0.20/0.55 fof(f2456,plain,(
% 0.20/0.55 spl0_94 <=> relation(identity_relation(identity_relation(identity_relation(relation_inverse_image(empty_set,sk0_63)))))),
% 0.20/0.55 introduced(split_symbol_definition)).
% 0.20/0.55 fof(f2458,plain,(
% 0.20/0.55 ~relation(identity_relation(identity_relation(identity_relation(relation_inverse_image(empty_set,sk0_63)))))|spl0_94),
% 0.20/0.55 inference(component_clause,[status(thm)],[f2456])).
% 0.20/0.55 fof(f2472,plain,(
% 0.20/0.55 $false|spl0_94),
% 0.20/0.55 inference(forward_subsumption_resolution,[status(thm)],[f2458,f457])).
% 0.20/0.55 fof(f2473,plain,(
% 0.20/0.55 spl0_94),
% 0.20/0.55 inference(contradiction_clause,[status(thm)],[f2472])).
% 0.20/0.55 fof(f2495,plain,(
% 0.20/0.55 spl0_98 <=> subset(relation_rng(set_intersection2(empty_set,X0)),relation_rng(empty_set))),
% 0.20/0.55 introduced(split_symbol_definition)).
% 0.20/0.55 fof(f2498,plain,(
% 0.20/0.55 ![X0]: (~relation(empty_set)|~relation(empty_set)|subset(relation_rng(set_intersection2(empty_set,X0)),relation_rng(empty_set)))),
% 0.20/0.55 inference(paramodulation,[status(thm)],[f2080,f2076])).
% 0.20/0.55 fof(f2499,plain,(
% 0.20/0.55 ~spl0_6|spl0_98),
% 0.20/0.55 inference(split_clause,[status(thm)],[f2498,f945,f2495])).
% 0.20/0.55 fof(f2500,plain,(
% 0.20/0.55 spl0_99 <=> ~relation(X0)|subset(relation_rng(set_intersection2(X0,empty_set)),relation_rng(X0))),
% 0.20/0.55 introduced(split_symbol_definition)).
% 0.20/0.55 fof(f2503,plain,(
% 0.20/0.55 ![X0]: (~relation(empty_set)|~relation(X0)|subset(relation_rng(set_intersection2(X0,empty_set)),relation_rng(X0)))),
% 0.20/0.55 inference(paramodulation,[status(thm)],[f677,f2076])).
% 0.20/0.55 fof(f2504,plain,(
% 0.20/0.55 ~spl0_6|spl0_99),
% 0.20/0.55 inference(split_clause,[status(thm)],[f2503,f945,f2500])).
% 0.20/0.55 fof(f2515,plain,(
% 0.20/0.55 spl0_100 <=> subset(relation_rng(set_difference(empty_set,X0)),relation_rng(empty_set))),
% 0.20/0.55 introduced(split_symbol_definition)).
% 0.20/0.55 fof(f2518,plain,(
% 0.20/0.55 ![X0]: (~relation(empty_set)|~relation(empty_set)|subset(relation_rng(set_difference(empty_set,X0)),relation_rng(empty_set)))),
% 0.20/0.55 inference(paramodulation,[status(thm)],[f756,f2086])).
% 0.20/0.55 fof(f2519,plain,(
% 0.20/0.55 ~spl0_6|spl0_100),
% 0.20/0.55 inference(split_clause,[status(thm)],[f2518,f945,f2515])).
% 0.20/0.55 fof(f2530,plain,(
% 0.20/0.55 spl0_101 <=> ~relation(X0)|subset(relation_rng(empty_set),relation_rng(set_union2(empty_set,X0)))),
% 0.20/0.55 introduced(split_symbol_definition)).
% 0.20/0.55 fof(f2533,plain,(
% 0.20/0.55 ![X0]: (~relation(empty_set)|~relation(X0)|subset(relation_rng(empty_set),relation_rng(set_union2(empty_set,X0))))),
% 0.20/0.55 inference(paramodulation,[status(thm)],[f1473,f2102])).
% 0.20/0.55 fof(f2534,plain,(
% 0.20/0.55 ~spl0_6|spl0_101),
% 0.20/0.55 inference(split_clause,[status(thm)],[f2533,f945,f2530])).
% 0.20/0.55 fof(f2545,plain,(
% 0.20/0.55 spl0_102 <=> ~relation(X0)|subset(relation_rng(set_intersection2(empty_set,X0)),relation_rng(X0))),
% 0.20/0.55 introduced(split_symbol_definition)).
% 0.20/0.55 fof(f2548,plain,(
% 0.20/0.55 ![X0]: (~relation(empty_set)|~relation(X0)|subset(relation_rng(set_intersection2(empty_set,X0)),relation_rng(X0)))),
% 0.20/0.55 inference(paramodulation,[status(thm)],[f2080,f2109])).
% 0.20/0.55 fof(f2549,plain,(
% 0.20/0.55 ~spl0_6|spl0_102),
% 0.20/0.55 inference(split_clause,[status(thm)],[f2548,f945,f2545])).
% 0.20/0.55 fof(f2550,plain,(
% 0.20/0.55 spl0_103 <=> subset(relation_rng(set_intersection2(X0,empty_set)),relation_rng(empty_set))),
% 0.20/0.55 introduced(split_symbol_definition)).
% 0.20/0.55 fof(f2553,plain,(
% 0.20/0.55 ![X0]: (~relation(empty_set)|~relation(empty_set)|subset(relation_rng(set_intersection2(X0,empty_set)),relation_rng(empty_set)))),
% 0.20/0.55 inference(paramodulation,[status(thm)],[f677,f2109])).
% 0.20/0.55 fof(f2554,plain,(
% 0.20/0.55 ~spl0_6|spl0_103),
% 0.20/0.55 inference(split_clause,[status(thm)],[f2553,f945,f2550])).
% 0.20/0.55 fof(f2568,plain,(
% 0.20/0.55 spl0_104 <=> ~relation(X0)|subset(relation_rng(empty_set),relation_rng(set_union2(X0,empty_set)))),
% 0.20/0.55 introduced(split_symbol_definition)).
% 0.20/0.55 fof(f2571,plain,(
% 0.20/0.55 ![X0]: (~relation(empty_set)|~relation(X0)|subset(relation_rng(empty_set),relation_rng(set_union2(X0,empty_set))))),
% 0.20/0.55 inference(paramodulation,[status(thm)],[f656,f2315])).
% 0.20/0.55 fof(f2572,plain,(
% 0.20/0.55 ~spl0_6|spl0_104),
% 0.20/0.55 inference(split_clause,[status(thm)],[f2571,f945,f2568])).
% 0.20/0.55 fof(f2576,plain,(
% 0.20/0.55 ![X0,X1]: (~relation(X0)|~relation(set_union2(X0,X1))|subset(relation_rng(X0),relation_rng(set_union2(X1,X0))))),
% 0.20/0.55 inference(paramodulation,[status(thm)],[f214,f2315])).
% 0.20/0.55 fof(f2690,plain,(
% 0.20/0.55 spl0_106 <=> relation(identity_relation(relation_inverse_image(identity_relation(relation_inverse_image(empty_set,sk0_63)),sk0_59(sk0_62))))),
% 0.20/0.55 introduced(split_symbol_definition)).
% 0.20/0.55 fof(f2692,plain,(
% 0.20/0.55 ~relation(identity_relation(relation_inverse_image(identity_relation(relation_inverse_image(empty_set,sk0_63)),sk0_59(sk0_62))))|spl0_106),
% 0.20/0.55 inference(component_clause,[status(thm)],[f2690])).
% 0.20/0.55 fof(f2707,plain,(
% 0.20/0.55 $false|spl0_106),
% 0.20/0.55 inference(forward_subsumption_resolution,[status(thm)],[f2692,f457])).
% 0.20/0.55 fof(f2708,plain,(
% 0.20/0.55 spl0_106),
% 0.20/0.55 inference(contradiction_clause,[status(thm)],[f2707])).
% 0.20/0.55 fof(f2726,plain,(
% 0.20/0.55 spl0_109 <=> relation(identity_relation(relation_inverse_image(identity_relation(relation_inverse_image(empty_set,sk0_63)),singleton(sk0_62))))),
% 0.20/0.55 introduced(split_symbol_definition)).
% 0.20/0.55 fof(f2728,plain,(
% 0.20/0.55 ~relation(identity_relation(relation_inverse_image(identity_relation(relation_inverse_image(empty_set,sk0_63)),singleton(sk0_62))))|spl0_109),
% 0.20/0.55 inference(component_clause,[status(thm)],[f2726])).
% 0.20/0.55 fof(f2743,plain,(
% 0.20/0.55 $false|spl0_109),
% 0.20/0.55 inference(forward_subsumption_resolution,[status(thm)],[f2728,f457])).
% 0.20/0.55 fof(f2744,plain,(
% 0.20/0.55 spl0_109),
% 0.20/0.55 inference(contradiction_clause,[status(thm)],[f2743])).
% 0.20/0.55 fof(f2748,plain,(
% 0.20/0.55 spl0_112 <=> relation(identity_relation(relation_inverse_image(identity_relation(relation_inverse_image(empty_set,sk0_63)),sk0_70(sk0_62))))),
% 0.20/0.55 introduced(split_symbol_definition)).
% 0.20/0.55 fof(f2750,plain,(
% 0.20/0.55 ~relation(identity_relation(relation_inverse_image(identity_relation(relation_inverse_image(empty_set,sk0_63)),sk0_70(sk0_62))))|spl0_112),
% 0.20/0.55 inference(component_clause,[status(thm)],[f2748])).
% 0.20/0.55 fof(f2765,plain,(
% 0.20/0.55 $false|spl0_112),
% 0.20/0.55 inference(forward_subsumption_resolution,[status(thm)],[f2750,f457])).
% 0.20/0.55 fof(f2766,plain,(
% 0.20/0.55 spl0_112),
% 0.20/0.55 inference(contradiction_clause,[status(thm)],[f2765])).
% 0.20/0.55 fof(f2789,plain,(
% 0.20/0.55 spl0_115 <=> empty_set=identity_relation(singleton(sk0_62))),
% 0.20/0.55 introduced(split_symbol_definition)).
% 0.20/0.55 fof(f2790,plain,(
% 0.20/0.55 empty_set=identity_relation(singleton(sk0_62))|~spl0_115),
% 0.20/0.55 inference(component_clause,[status(thm)],[f2789])).
% 0.20/0.55 fof(f2837,plain,(
% 0.20/0.55 relation_rng(empty_set)=singleton(sk0_62)|~spl0_115),
% 0.20/0.55 inference(paramodulation,[status(thm)],[f2790,f801])).
% 0.20/0.55 fof(f2838,plain,(
% 0.20/0.55 empty_set=singleton(sk0_62)|~spl0_115),
% 0.20/0.55 inference(forward_demodulation,[status(thm)],[f777,f2837])).
% 0.20/0.55 fof(f2839,plain,(
% 0.20/0.55 $false|~spl0_115),
% 0.20/0.55 inference(forward_subsumption_resolution,[status(thm)],[f2838,f519])).
% 0.20/0.55 fof(f2840,plain,(
% 0.20/0.55 ~spl0_115),
% 0.20/0.55 inference(contradiction_clause,[status(thm)],[f2839])).
% 0.20/0.55 fof(f3045,plain,(
% 0.20/0.55 spl0_125 <=> relation_rng(relation_inverse(relation_inverse(empty_set)))=empty_set),
% 0.20/0.55 introduced(split_symbol_definition)).
% 0.20/0.55 fof(f3047,plain,(
% 0.20/0.55 ~relation_rng(relation_inverse(relation_inverse(empty_set)))=empty_set|spl0_125),
% 0.20/0.55 inference(component_clause,[status(thm)],[f3045])).
% 0.20/0.55 fof(f3048,plain,(
% 0.20/0.55 spl0_126 <=> relation_inverse(relation_inverse(empty_set))=empty_set),
% 0.20/0.55 introduced(split_symbol_definition)).
% 0.20/0.55 fof(f3051,plain,(
% 0.20/0.55 ~relation_rng(relation_inverse(relation_inverse(empty_set)))=empty_set|relation_inverse(relation_inverse(empty_set))=empty_set),
% 0.20/0.55 inference(resolution,[status(thm)],[f2338,f785])).
% 0.20/0.55 fof(f3052,plain,(
% 0.20/0.55 ~spl0_125|spl0_126),
% 0.20/0.55 inference(split_clause,[status(thm)],[f3051,f3045,f3048])).
% 0.20/0.55 fof(f3073,plain,(
% 0.20/0.55 spl0_129 <=> empty_set=identity_relation(singleton(ordered_pair(ordered_pair(sk0_62,sk0_62),ordered_pair(sk0_62,sk0_62))))),
% 0.20/0.55 introduced(split_symbol_definition)).
% 0.20/0.55 fof(f3074,plain,(
% 0.20/0.55 empty_set=identity_relation(singleton(ordered_pair(ordered_pair(sk0_62,sk0_62),ordered_pair(sk0_62,sk0_62))))|~spl0_129),
% 0.20/0.55 inference(component_clause,[status(thm)],[f3073])).
% 0.20/0.55 fof(f3081,plain,(
% 0.20/0.55 spl0_131 <=> empty_set=identity_relation(singleton(ordered_pair(sk0_62,sk0_62)))),
% 0.20/0.55 introduced(split_symbol_definition)).
% 0.20/0.55 fof(f3082,plain,(
% 0.20/0.55 empty_set=identity_relation(singleton(ordered_pair(sk0_62,sk0_62)))|~spl0_131),
% 0.20/0.55 inference(component_clause,[status(thm)],[f3081])).
% 0.20/0.55 fof(f3188,plain,(
% 0.20/0.55 relation_rng(empty_set)=singleton(ordered_pair(sk0_62,sk0_62))|~spl0_131),
% 0.20/0.55 inference(paramodulation,[status(thm)],[f3082,f801])).
% 0.20/0.55 fof(f3189,plain,(
% 0.20/0.55 empty_set=singleton(ordered_pair(sk0_62,sk0_62))|~spl0_131),
% 0.20/0.55 inference(forward_demodulation,[status(thm)],[f777,f3188])).
% 0.20/0.55 fof(f3190,plain,(
% 0.20/0.55 $false|~spl0_131),
% 0.20/0.55 inference(forward_subsumption_resolution,[status(thm)],[f3189,f519])).
% 0.20/0.55 fof(f3191,plain,(
% 0.20/0.55 ~spl0_131),
% 0.20/0.55 inference(contradiction_clause,[status(thm)],[f3190])).
% 0.20/0.55 fof(f3377,plain,(
% 0.20/0.55 relation_rng(empty_set)=singleton(ordered_pair(ordered_pair(sk0_62,sk0_62),ordered_pair(sk0_62,sk0_62)))|~spl0_129),
% 0.20/0.55 inference(paramodulation,[status(thm)],[f3074,f801])).
% 0.20/0.55 fof(f3378,plain,(
% 0.20/0.55 empty_set=singleton(ordered_pair(ordered_pair(sk0_62,sk0_62),ordered_pair(sk0_62,sk0_62)))|~spl0_129),
% 0.20/0.55 inference(forward_demodulation,[status(thm)],[f777,f3377])).
% 0.20/0.55 fof(f3379,plain,(
% 0.20/0.55 $false|~spl0_129),
% 0.20/0.55 inference(forward_subsumption_resolution,[status(thm)],[f3378,f519])).
% 0.20/0.55 fof(f3380,plain,(
% 0.20/0.55 ~spl0_129),
% 0.20/0.55 inference(contradiction_clause,[status(thm)],[f3379])).
% 0.20/0.55 fof(f3676,plain,(
% 0.20/0.55 ![X0]: (relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(empty_set)))))))=identity_relation(X0)|in(ordered_pair(sk0_0(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53)))))))),sk0_1(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))),relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))|sk0_0(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))=sk0_1(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))|~spl0_12)),
% 0.20/0.55 inference(forward_demodulation,[status(thm)],[f983,f1539])).
% 0.20/0.55 fof(f3677,plain,(
% 0.20/0.55 ![X0]: (relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(empty_set))))))=identity_relation(X0)|in(ordered_pair(sk0_0(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53)))))))),sk0_1(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))),relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))|sk0_0(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))=sk0_1(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))|~spl0_12)),
% 0.20/0.55 inference(forward_demodulation,[status(thm)],[f777,f3676])).
% 0.20/0.55 fof(f3678,plain,(
% 0.20/0.55 ![X0]: (relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(empty_set)))))=identity_relation(X0)|in(ordered_pair(sk0_0(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53)))))))),sk0_1(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))),relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))|sk0_0(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))=sk0_1(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))|~spl0_12)),
% 0.20/0.55 inference(forward_demodulation,[status(thm)],[f777,f3677])).
% 0.20/0.55 fof(f3679,plain,(
% 0.20/0.55 ![X0]: (relation_rng(relation_rng(relation_rng(relation_rng(empty_set))))=identity_relation(X0)|in(ordered_pair(sk0_0(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53)))))))),sk0_1(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))),relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))|sk0_0(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))=sk0_1(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))|~spl0_12)),
% 0.20/0.55 inference(forward_demodulation,[status(thm)],[f777,f3678])).
% 0.20/0.55 fof(f3680,plain,(
% 0.20/0.55 ![X0]: (relation_rng(relation_rng(relation_rng(empty_set)))=identity_relation(X0)|in(ordered_pair(sk0_0(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53)))))))),sk0_1(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))),relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))|sk0_0(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))=sk0_1(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))|~spl0_12)),
% 0.20/0.55 inference(forward_demodulation,[status(thm)],[f777,f3679])).
% 0.20/0.55 fof(f3681,plain,(
% 0.20/0.55 ![X0]: (relation_rng(relation_rng(empty_set))=identity_relation(X0)|in(ordered_pair(sk0_0(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53)))))))),sk0_1(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))),relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))|sk0_0(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))=sk0_1(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))|~spl0_12)),
% 0.20/0.55 inference(forward_demodulation,[status(thm)],[f777,f3680])).
% 0.20/0.55 fof(f3682,plain,(
% 0.20/0.55 ![X0]: (relation_rng(empty_set)=identity_relation(X0)|in(ordered_pair(sk0_0(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53)))))))),sk0_1(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))),relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))|sk0_0(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))=sk0_1(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))|~spl0_12)),
% 0.20/0.55 inference(forward_demodulation,[status(thm)],[f777,f3681])).
% 0.20/0.55 fof(f3683,plain,(
% 0.20/0.55 ![X0]: (empty_set=identity_relation(X0)|in(ordered_pair(sk0_0(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53)))))))),sk0_1(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))),relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))|sk0_0(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))=sk0_1(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))|~spl0_12)),
% 0.20/0.55 inference(forward_demodulation,[status(thm)],[f777,f3682])).
% 0.20/0.55 fof(f3684,plain,(
% 0.20/0.55 ![X0]: (empty_set=identity_relation(X0)|in(ordered_pair(sk0_0(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(empty_set)))))))),sk0_1(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))),relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))|sk0_0(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))=sk0_1(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))|~spl0_12)),
% 0.20/0.55 inference(forward_demodulation,[status(thm)],[f983,f3683])).
% 0.20/0.55 fof(f3685,plain,(
% 0.20/0.55 ![X0]: (empty_set=identity_relation(X0)|in(ordered_pair(sk0_0(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(empty_set))))))),sk0_1(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))),relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))|sk0_0(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))=sk0_1(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))|~spl0_12)),
% 0.20/0.55 inference(forward_demodulation,[status(thm)],[f777,f3684])).
% 0.20/0.55 fof(f3686,plain,(
% 0.20/0.55 ![X0]: (empty_set=identity_relation(X0)|in(ordered_pair(sk0_0(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(empty_set)))))),sk0_1(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))),relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))|sk0_0(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))=sk0_1(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))|~spl0_12)),
% 0.20/0.55 inference(forward_demodulation,[status(thm)],[f777,f3685])).
% 0.20/0.55 fof(f3687,plain,(
% 0.20/0.55 ![X0]: (empty_set=identity_relation(X0)|in(ordered_pair(sk0_0(X0,relation_rng(relation_rng(relation_rng(relation_rng(empty_set))))),sk0_1(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))),relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))|sk0_0(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))=sk0_1(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))|~spl0_12)),
% 0.20/0.55 inference(forward_demodulation,[status(thm)],[f777,f3686])).
% 0.20/0.55 fof(f3688,plain,(
% 0.20/0.55 ![X0]: (empty_set=identity_relation(X0)|in(ordered_pair(sk0_0(X0,relation_rng(relation_rng(relation_rng(empty_set)))),sk0_1(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))),relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))|sk0_0(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))=sk0_1(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))|~spl0_12)),
% 0.20/0.55 inference(forward_demodulation,[status(thm)],[f777,f3687])).
% 0.20/0.55 fof(f3689,plain,(
% 0.20/0.55 ![X0]: (empty_set=identity_relation(X0)|in(ordered_pair(sk0_0(X0,relation_rng(relation_rng(empty_set))),sk0_1(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))),relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))|sk0_0(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))=sk0_1(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))|~spl0_12)),
% 0.20/0.55 inference(forward_demodulation,[status(thm)],[f777,f3688])).
% 0.20/0.55 fof(f3690,plain,(
% 0.20/0.55 ![X0]: (empty_set=identity_relation(X0)|in(ordered_pair(sk0_0(X0,relation_rng(empty_set)),sk0_1(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))),relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))|sk0_0(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))=sk0_1(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))|~spl0_12)),
% 0.20/0.55 inference(forward_demodulation,[status(thm)],[f777,f3689])).
% 0.20/0.55 fof(f3691,plain,(
% 0.20/0.55 ![X0]: (empty_set=identity_relation(X0)|in(ordered_pair(sk0_0(X0,empty_set),sk0_1(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))),relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))|sk0_0(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))=sk0_1(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))|~spl0_12)),
% 0.20/0.55 inference(forward_demodulation,[status(thm)],[f777,f3690])).
% 0.20/0.55 fof(f3692,plain,(
% 0.20/0.55 ![X0]: (empty_set=identity_relation(X0)|in(ordered_pair(sk0_0(X0,empty_set),sk0_1(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(empty_set))))))))),relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))|sk0_0(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))=sk0_1(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))|~spl0_12)),
% 0.20/0.55 inference(forward_demodulation,[status(thm)],[f983,f3691])).
% 0.20/0.55 fof(f3693,plain,(
% 0.20/0.55 ![X0]: (empty_set=identity_relation(X0)|in(ordered_pair(sk0_0(X0,empty_set),sk0_1(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(empty_set)))))))),relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))|sk0_0(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))=sk0_1(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))|~spl0_12)),
% 0.20/0.55 inference(forward_demodulation,[status(thm)],[f777,f3692])).
% 0.20/0.55 fof(f3694,plain,(
% 0.20/0.55 ![X0]: (empty_set=identity_relation(X0)|in(ordered_pair(sk0_0(X0,empty_set),sk0_1(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(empty_set))))))),relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))|sk0_0(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))=sk0_1(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))|~spl0_12)),
% 0.20/0.55 inference(forward_demodulation,[status(thm)],[f777,f3693])).
% 0.20/0.55 fof(f3695,plain,(
% 0.20/0.55 ![X0]: (empty_set=identity_relation(X0)|in(ordered_pair(sk0_0(X0,empty_set),sk0_1(X0,relation_rng(relation_rng(relation_rng(relation_rng(empty_set)))))),relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))|sk0_0(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))=sk0_1(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))|~spl0_12)),
% 0.20/0.55 inference(forward_demodulation,[status(thm)],[f777,f3694])).
% 0.20/0.55 fof(f3696,plain,(
% 0.20/0.55 ![X0]: (empty_set=identity_relation(X0)|in(ordered_pair(sk0_0(X0,empty_set),sk0_1(X0,relation_rng(relation_rng(relation_rng(empty_set))))),relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))|sk0_0(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))=sk0_1(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))|~spl0_12)),
% 0.20/0.55 inference(forward_demodulation,[status(thm)],[f777,f3695])).
% 0.20/0.55 fof(f3697,plain,(
% 0.20/0.55 ![X0]: (empty_set=identity_relation(X0)|in(ordered_pair(sk0_0(X0,empty_set),sk0_1(X0,relation_rng(relation_rng(empty_set)))),relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))|sk0_0(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))=sk0_1(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))|~spl0_12)),
% 0.20/0.55 inference(forward_demodulation,[status(thm)],[f777,f3696])).
% 0.20/0.55 fof(f3698,plain,(
% 0.20/0.55 ![X0]: (empty_set=identity_relation(X0)|in(ordered_pair(sk0_0(X0,empty_set),sk0_1(X0,relation_rng(empty_set))),relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))|sk0_0(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))=sk0_1(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))|~spl0_12)),
% 0.20/0.55 inference(forward_demodulation,[status(thm)],[f777,f3697])).
% 0.20/0.55 fof(f3699,plain,(
% 0.20/0.55 ![X0]: (empty_set=identity_relation(X0)|in(ordered_pair(sk0_0(X0,empty_set),sk0_1(X0,empty_set)),relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))|sk0_0(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))=sk0_1(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))|~spl0_12)),
% 0.20/0.55 inference(forward_demodulation,[status(thm)],[f777,f3698])).
% 0.20/0.55 fof(f3700,plain,(
% 0.20/0.55 ![X0]: (empty_set=identity_relation(X0)|in(ordered_pair(sk0_0(X0,empty_set),sk0_1(X0,empty_set)),relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(empty_set))))))))|sk0_0(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))=sk0_1(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))|~spl0_12)),
% 0.20/0.55 inference(forward_demodulation,[status(thm)],[f983,f3699])).
% 0.20/0.55 fof(f3701,plain,(
% 0.20/0.55 ![X0]: (empty_set=identity_relation(X0)|in(ordered_pair(sk0_0(X0,empty_set),sk0_1(X0,empty_set)),relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(empty_set)))))))|sk0_0(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))=sk0_1(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))|~spl0_12)),
% 0.20/0.55 inference(forward_demodulation,[status(thm)],[f777,f3700])).
% 0.20/0.55 fof(f3702,plain,(
% 0.20/0.55 ![X0]: (empty_set=identity_relation(X0)|in(ordered_pair(sk0_0(X0,empty_set),sk0_1(X0,empty_set)),relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(empty_set))))))|sk0_0(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))=sk0_1(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))|~spl0_12)),
% 0.20/0.55 inference(forward_demodulation,[status(thm)],[f777,f3701])).
% 0.20/0.55 fof(f3703,plain,(
% 0.20/0.55 ![X0]: (empty_set=identity_relation(X0)|in(ordered_pair(sk0_0(X0,empty_set),sk0_1(X0,empty_set)),relation_rng(relation_rng(relation_rng(relation_rng(empty_set)))))|sk0_0(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))=sk0_1(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))|~spl0_12)),
% 0.20/0.55 inference(forward_demodulation,[status(thm)],[f777,f3702])).
% 0.20/0.55 fof(f3704,plain,(
% 0.20/0.55 ![X0]: (empty_set=identity_relation(X0)|in(ordered_pair(sk0_0(X0,empty_set),sk0_1(X0,empty_set)),relation_rng(relation_rng(relation_rng(empty_set))))|sk0_0(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))=sk0_1(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))|~spl0_12)),
% 0.20/0.55 inference(forward_demodulation,[status(thm)],[f777,f3703])).
% 0.20/0.55 fof(f3705,plain,(
% 0.20/0.55 ![X0]: (empty_set=identity_relation(X0)|in(ordered_pair(sk0_0(X0,empty_set),sk0_1(X0,empty_set)),relation_rng(relation_rng(empty_set)))|sk0_0(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))=sk0_1(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))|~spl0_12)),
% 0.20/0.55 inference(forward_demodulation,[status(thm)],[f777,f3704])).
% 0.20/0.55 fof(f3706,plain,(
% 0.20/0.55 ![X0]: (empty_set=identity_relation(X0)|in(ordered_pair(sk0_0(X0,empty_set),sk0_1(X0,empty_set)),relation_rng(empty_set))|sk0_0(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))=sk0_1(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))|~spl0_12)),
% 0.20/0.55 inference(forward_demodulation,[status(thm)],[f777,f3705])).
% 0.20/0.55 fof(f3707,plain,(
% 0.20/0.55 ![X0]: (empty_set=identity_relation(X0)|in(ordered_pair(sk0_0(X0,empty_set),sk0_1(X0,empty_set)),empty_set)|sk0_0(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))=sk0_1(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))|~spl0_12)),
% 0.20/0.55 inference(forward_demodulation,[status(thm)],[f777,f3706])).
% 0.20/0.55 fof(f3708,plain,(
% 0.20/0.55 ![X0]: (empty_set=identity_relation(X0)|in(ordered_pair(sk0_0(X0,empty_set),sk0_1(X0,empty_set)),empty_set)|sk0_0(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(empty_set))))))))=sk0_1(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))|~spl0_12)),
% 0.20/0.55 inference(forward_demodulation,[status(thm)],[f983,f3707])).
% 0.20/0.55 fof(f3709,plain,(
% 0.20/0.55 ![X0]: (empty_set=identity_relation(X0)|in(ordered_pair(sk0_0(X0,empty_set),sk0_1(X0,empty_set)),empty_set)|sk0_0(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(empty_set)))))))=sk0_1(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))|~spl0_12)),
% 0.20/0.55 inference(forward_demodulation,[status(thm)],[f777,f3708])).
% 0.20/0.55 fof(f3710,plain,(
% 0.20/0.55 ![X0]: (empty_set=identity_relation(X0)|in(ordered_pair(sk0_0(X0,empty_set),sk0_1(X0,empty_set)),empty_set)|sk0_0(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(empty_set))))))=sk0_1(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))|~spl0_12)),
% 0.20/0.55 inference(forward_demodulation,[status(thm)],[f777,f3709])).
% 0.20/0.55 fof(f3711,plain,(
% 0.20/0.55 ![X0]: (empty_set=identity_relation(X0)|in(ordered_pair(sk0_0(X0,empty_set),sk0_1(X0,empty_set)),empty_set)|sk0_0(X0,relation_rng(relation_rng(relation_rng(relation_rng(empty_set)))))=sk0_1(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))|~spl0_12)),
% 0.20/0.55 inference(forward_demodulation,[status(thm)],[f777,f3710])).
% 0.20/0.55 fof(f3712,plain,(
% 0.20/0.55 ![X0]: (empty_set=identity_relation(X0)|in(ordered_pair(sk0_0(X0,empty_set),sk0_1(X0,empty_set)),empty_set)|sk0_0(X0,relation_rng(relation_rng(relation_rng(empty_set))))=sk0_1(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))|~spl0_12)),
% 0.20/0.55 inference(forward_demodulation,[status(thm)],[f777,f3711])).
% 0.20/0.55 fof(f3713,plain,(
% 0.20/0.55 ![X0]: (empty_set=identity_relation(X0)|in(ordered_pair(sk0_0(X0,empty_set),sk0_1(X0,empty_set)),empty_set)|sk0_0(X0,relation_rng(relation_rng(empty_set)))=sk0_1(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))|~spl0_12)),
% 0.20/0.55 inference(forward_demodulation,[status(thm)],[f777,f3712])).
% 0.20/0.55 fof(f3714,plain,(
% 0.20/0.55 ![X0]: (empty_set=identity_relation(X0)|in(ordered_pair(sk0_0(X0,empty_set),sk0_1(X0,empty_set)),empty_set)|sk0_0(X0,relation_rng(empty_set))=sk0_1(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))|~spl0_12)),
% 0.20/0.55 inference(forward_demodulation,[status(thm)],[f777,f3713])).
% 0.20/0.55 fof(f3715,plain,(
% 0.20/0.55 ![X0]: (empty_set=identity_relation(X0)|in(ordered_pair(sk0_0(X0,empty_set),sk0_1(X0,empty_set)),empty_set)|sk0_0(X0,empty_set)=sk0_1(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(sk0_53))))))))|~spl0_12)),
% 0.20/0.55 inference(forward_demodulation,[status(thm)],[f777,f3714])).
% 0.20/0.55 fof(f3716,plain,(
% 0.20/0.55 ![X0]: (empty_set=identity_relation(X0)|in(ordered_pair(sk0_0(X0,empty_set),sk0_1(X0,empty_set)),empty_set)|sk0_0(X0,empty_set)=sk0_1(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(empty_set))))))))|~spl0_12)),
% 0.20/0.55 inference(forward_demodulation,[status(thm)],[f983,f3715])).
% 0.20/0.55 fof(f3717,plain,(
% 0.20/0.55 ![X0]: (empty_set=identity_relation(X0)|in(ordered_pair(sk0_0(X0,empty_set),sk0_1(X0,empty_set)),empty_set)|sk0_0(X0,empty_set)=sk0_1(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(empty_set)))))))|~spl0_12)),
% 0.20/0.55 inference(forward_demodulation,[status(thm)],[f777,f3716])).
% 0.20/0.55 fof(f3718,plain,(
% 0.20/0.55 ![X0]: (empty_set=identity_relation(X0)|in(ordered_pair(sk0_0(X0,empty_set),sk0_1(X0,empty_set)),empty_set)|sk0_0(X0,empty_set)=sk0_1(X0,relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(empty_set))))))|~spl0_12)),
% 0.20/0.55 inference(forward_demodulation,[status(thm)],[f777,f3717])).
% 0.20/0.55 fof(f3719,plain,(
% 0.20/0.55 ![X0]: (empty_set=identity_relation(X0)|in(ordered_pair(sk0_0(X0,empty_set),sk0_1(X0,empty_set)),empty_set)|sk0_0(X0,empty_set)=sk0_1(X0,relation_rng(relation_rng(relation_rng(relation_rng(empty_set)))))|~spl0_12)),
% 0.20/0.55 inference(forward_demodulation,[status(thm)],[f777,f3718])).
% 0.20/0.55 fof(f3720,plain,(
% 0.20/0.55 ![X0]: (empty_set=identity_relation(X0)|in(ordered_pair(sk0_0(X0,empty_set),sk0_1(X0,empty_set)),empty_set)|sk0_0(X0,empty_set)=sk0_1(X0,relation_rng(relation_rng(relation_rng(empty_set))))|~spl0_12)),
% 0.20/0.55 inference(forward_demodulation,[status(thm)],[f777,f3719])).
% 0.20/0.55 fof(f3721,plain,(
% 0.20/0.55 ![X0]: (empty_set=identity_relation(X0)|in(ordered_pair(sk0_0(X0,empty_set),sk0_1(X0,empty_set)),empty_set)|sk0_0(X0,empty_set)=sk0_1(X0,relation_rng(relation_rng(empty_set)))|~spl0_12)),
% 0.20/0.55 inference(forward_demodulation,[status(thm)],[f777,f3720])).
% 0.20/0.55 fof(f3722,plain,(
% 0.20/0.55 ![X0]: (empty_set=identity_relation(X0)|in(ordered_pair(sk0_0(X0,empty_set),sk0_1(X0,empty_set)),empty_set)|sk0_0(X0,empty_set)=sk0_1(X0,relation_rng(empty_set))|~spl0_12)),
% 0.20/0.55 inference(forward_demodulation,[status(thm)],[f777,f3721])).
% 0.20/0.55 fof(f3908,plain,(
% 0.20/0.55 relation_inverse(relation_inverse(empty_set))=empty_set),
% 0.20/0.55 inference(resolution,[status(thm)],[f514,f491])).
% 0.20/0.55 fof(f3910,plain,(
% 0.20/0.55 ~relation_rng(empty_set)=empty_set|spl0_125),
% 0.20/0.55 inference(backward_demodulation,[status(thm)],[f3908,f3047])).
% 0.20/0.55 fof(f3911,plain,(
% 0.20/0.55 ~spl0_9|spl0_125),
% 0.20/0.55 inference(split_clause,[status(thm)],[f3910,f965,f3045])).
% 0.20/0.55 fof(f3914,plain,(
% 0.20/0.55 ![X0,X1]: (set_union2(set_difference(X0,X1),X0)=X0)),
% 0.20/0.55 inference(resolution,[status(thm)],[f615,f696])).
% 0.20/0.55 fof(f3915,plain,(
% 0.20/0.55 ![X0,X1]: (set_union2(set_intersection2(X0,X1),X1)=X1)),
% 0.20/0.55 inference(resolution,[status(thm)],[f615,f2078])).
% 0.20/0.55 fof(f3916,plain,(
% 0.20/0.55 ![X0,X1]: (set_union2(set_intersection2(X0,X1),X0)=X0)),
% 0.20/0.55 inference(resolution,[status(thm)],[f615,f653])).
% 0.20/0.55 fof(f3930,plain,(
% 0.20/0.55 ![X0,X1]: (~relation(set_difference(X0,X1))|~relation(X0)|subset(relation_rng(set_difference(X0,X1)),relation_rng(set_union2(X0,set_difference(X0,X1)))))),
% 0.20/0.55 inference(paramodulation,[status(thm)],[f3914,f2576])).
% 0.20/0.55 fof(f3954,plain,(
% 0.20/0.55 ![X0,X1]: (~relation(set_intersection2(X0,X1))|~relation(X1)|subset(relation_rng(set_intersection2(X0,X1)),relation_rng(set_union2(X1,set_intersection2(X0,X1)))))),
% 0.20/0.55 inference(paramodulation,[status(thm)],[f3915,f2576])).
% 0.20/0.55 fof(f3978,plain,(
% 0.20/0.55 ![X0,X1]: (~relation(set_intersection2(X0,X1))|~relation(X0)|subset(relation_rng(set_intersection2(X0,X1)),relation_rng(set_union2(X0,set_intersection2(X0,X1)))))),
% 0.20/0.55 inference(paramodulation,[status(thm)],[f3916,f2576])).
% 0.20/0.55 fof(f4391,plain,(
% 0.20/0.55 spl0_206 <=> subset(relation_rng(set_difference(empty_set,X0)),relation_rng(set_union2(empty_set,set_difference(empty_set,X0))))),
% 0.20/0.55 introduced(split_symbol_definition)).
% 0.20/0.55 fof(f4394,plain,(
% 0.20/0.55 ![X0]: (~relation(empty_set)|~relation(empty_set)|subset(relation_rng(set_difference(empty_set,X0)),relation_rng(set_union2(empty_set,set_difference(empty_set,X0)))))),
% 0.20/0.55 inference(paramodulation,[status(thm)],[f756,f3930])).
% 0.20/0.55 fof(f4395,plain,(
% 0.20/0.55 ~spl0_6|spl0_206),
% 0.20/0.55 inference(split_clause,[status(thm)],[f4394,f945,f4391])).
% 0.20/0.55 fof(f4406,plain,(
% 0.20/0.55 spl0_207 <=> ~relation(X0)|subset(relation_rng(set_intersection2(empty_set,X0)),relation_rng(set_union2(X0,set_intersection2(empty_set,X0))))),
% 0.20/0.55 introduced(split_symbol_definition)).
% 0.20/0.55 fof(f4409,plain,(
% 0.20/0.55 ![X0]: (~relation(empty_set)|~relation(X0)|subset(relation_rng(set_intersection2(empty_set,X0)),relation_rng(set_union2(X0,set_intersection2(empty_set,X0)))))),
% 0.20/0.55 inference(paramodulation,[status(thm)],[f2080,f3954])).
% 0.20/0.55 fof(f4410,plain,(
% 0.20/0.55 ~spl0_6|spl0_207),
% 0.20/0.55 inference(split_clause,[status(thm)],[f4409,f945,f4406])).
% 0.20/0.55 fof(f4411,plain,(
% 0.20/0.55 spl0_208 <=> subset(relation_rng(set_intersection2(X0,empty_set)),relation_rng(set_union2(empty_set,set_intersection2(X0,empty_set))))),
% 0.20/0.55 introduced(split_symbol_definition)).
% 0.20/0.55 fof(f4414,plain,(
% 0.20/0.55 ![X0]: (~relation(empty_set)|~relation(empty_set)|subset(relation_rng(set_intersection2(X0,empty_set)),relation_rng(set_union2(empty_set,set_intersection2(X0,empty_set)))))),
% 0.20/0.55 inference(paramodulation,[status(thm)],[f677,f3954])).
% 0.20/0.55 fof(f4415,plain,(
% 0.20/0.55 ~spl0_6|spl0_208),
% 0.20/0.55 inference(split_clause,[status(thm)],[f4414,f945,f4411])).
% 0.20/0.55 fof(f4432,plain,(
% 0.20/0.55 spl0_209 <=> subset(relation_rng(set_intersection2(empty_set,X0)),relation_rng(set_union2(empty_set,set_intersection2(empty_set,X0))))),
% 0.20/0.55 introduced(split_symbol_definition)).
% 0.20/0.55 fof(f4435,plain,(
% 0.20/0.55 ![X0]: (~relation(empty_set)|~relation(empty_set)|subset(relation_rng(set_intersection2(empty_set,X0)),relation_rng(set_union2(empty_set,set_intersection2(empty_set,X0)))))),
% 0.20/0.55 inference(paramodulation,[status(thm)],[f2080,f3978])).
% 0.20/0.55 fof(f4436,plain,(
% 0.20/0.55 ~spl0_6|spl0_209),
% 0.20/0.55 inference(split_clause,[status(thm)],[f4435,f945,f4432])).
% 0.20/0.55 fof(f4437,plain,(
% 0.20/0.55 spl0_210 <=> ~relation(X0)|subset(relation_rng(set_intersection2(X0,empty_set)),relation_rng(set_union2(X0,set_intersection2(X0,empty_set))))),
% 0.20/0.55 introduced(split_symbol_definition)).
% 0.20/0.55 fof(f4440,plain,(
% 0.20/0.55 ![X0]: (~relation(empty_set)|~relation(X0)|subset(relation_rng(set_intersection2(X0,empty_set)),relation_rng(set_union2(X0,set_intersection2(X0,empty_set)))))),
% 0.20/0.55 inference(paramodulation,[status(thm)],[f677,f3978])).
% 0.20/0.55 fof(f4441,plain,(
% 0.20/0.55 ~spl0_6|spl0_210),
% 0.20/0.55 inference(split_clause,[status(thm)],[f4440,f945,f4437])).
% 0.20/0.55 fof(f4593,plain,(
% 0.20/0.55 spl0_211 <=> relation(identity_relation(singleton(sk0_62)))),
% 0.20/0.55 introduced(split_symbol_definition)).
% 0.20/0.55 fof(f4595,plain,(
% 0.20/0.55 ~relation(identity_relation(singleton(sk0_62)))|spl0_211),
% 0.20/0.55 inference(component_clause,[status(thm)],[f4593])).
% 0.20/0.55 fof(f4631,plain,(
% 0.20/0.55 spl0_219 <=> in(ordered_pair(sk0_62,sk0_9(sk0_62,relation_inverse_image(empty_set,sk0_63),sk0_63,empty_set)),empty_set)),
% 0.20/0.55 introduced(split_symbol_definition)).
% 0.20/0.55 fof(f4632,plain,(
% 0.20/0.55 in(ordered_pair(sk0_62,sk0_9(sk0_62,relation_inverse_image(empty_set,sk0_63),sk0_63,empty_set)),empty_set)|~spl0_219),
% 0.20/0.55 inference(component_clause,[status(thm)],[f4631])).
% 0.20/0.55 fof(f4634,plain,(
% 0.20/0.55 ~relation(empty_set)|in(ordered_pair(sk0_62,sk0_9(sk0_62,relation_inverse_image(empty_set,sk0_63),sk0_63,empty_set)),empty_set)|~spl0_8|~spl0_0),
% 0.20/0.55 inference(resolution,[status(thm)],[f895,f2000])).
% 0.20/0.55 fof(f4635,plain,(
% 0.20/0.55 ~spl0_6|spl0_219|~spl0_8|~spl0_0),
% 0.20/0.55 inference(split_clause,[status(thm)],[f4634,f945,f4631,f953,f862])).
% 0.20/0.55 fof(f4644,plain,(
% 0.20/0.55 $false|spl0_211),
% 0.20/0.55 inference(forward_subsumption_resolution,[status(thm)],[f4595,f457])).
% 0.20/0.55 fof(f4645,plain,(
% 0.20/0.55 spl0_211),
% 0.20/0.55 inference(contradiction_clause,[status(thm)],[f4644])).
% 0.20/0.55 fof(f4646,plain,(
% 0.20/0.55 $false|~spl0_219),
% 0.20/0.55 inference(forward_subsumption_resolution,[status(thm)],[f4632,f905])).
% 0.20/0.55 fof(f4647,plain,(
% 0.20/0.55 ~spl0_219),
% 0.20/0.55 inference(contradiction_clause,[status(thm)],[f4646])).
% 0.20/0.55 fof(f4649,plain,(
% 0.20/0.55 ![X0]: (empty_set=identity_relation(X0)|in(ordered_pair(sk0_0(X0,empty_set),sk0_1(X0,empty_set)),empty_set)|sk0_0(X0,empty_set)=sk0_1(X0,empty_set)|~spl0_12)),
% 0.20/0.55 inference(forward_demodulation,[status(thm)],[f777,f3722])).
% 0.20/0.55 fof(f4650,plain,(
% 0.20/0.55 ![X0]: (empty_set=identity_relation(X0)|sk0_0(X0,empty_set)=sk0_1(X0,empty_set)|~spl0_12)),
% 0.20/0.55 inference(forward_subsumption_resolution,[status(thm)],[f4649,f905])).
% 0.20/0.55 fof(f4689,plain,(
% 0.20/0.55 spl0_220 <=> in(sk0_9(sk0_62,relation_inverse_image(sk0_61,sk0_63),sk0_63,sk0_61),sk0_63)),
% 0.20/0.55 introduced(split_symbol_definition)).
% 0.20/0.55 fof(f4692,plain,(
% 0.20/0.55 ~relation(sk0_61)|in(sk0_9(sk0_62,relation_inverse_image(sk0_61,sk0_63),sk0_63,sk0_61),sk0_63)|~spl0_0),
% 0.20/0.55 inference(resolution,[status(thm)],[f863,f896])).
% 0.20/0.55 fof(f4693,plain,(
% 0.20/0.55 ~spl0_58|spl0_220|~spl0_0),
% 0.20/0.55 inference(split_clause,[status(thm)],[f4692,f1304,f4689,f862])).
% 0.20/0.55 fof(f4694,plain,(
% 0.20/0.55 spl0_221 <=> in(ordered_pair(sk0_62,sk0_9(sk0_62,relation_inverse_image(sk0_61,sk0_63),sk0_63,sk0_61)),sk0_61)),
% 0.20/0.55 introduced(split_symbol_definition)).
% 0.20/0.55 fof(f4695,plain,(
% 0.20/0.55 in(ordered_pair(sk0_62,sk0_9(sk0_62,relation_inverse_image(sk0_61,sk0_63),sk0_63,sk0_61)),sk0_61)|~spl0_221),
% 0.20/0.55 inference(component_clause,[status(thm)],[f4694])).
% 0.20/0.55 fof(f4697,plain,(
% 0.20/0.55 ~relation(sk0_61)|in(ordered_pair(sk0_62,sk0_9(sk0_62,relation_inverse_image(sk0_61,sk0_63),sk0_63,sk0_61)),sk0_61)|~spl0_0),
% 0.20/0.55 inference(resolution,[status(thm)],[f863,f895])).
% 0.20/0.55 fof(f4698,plain,(
% 0.20/0.55 ~spl0_58|spl0_221|~spl0_0),
% 0.20/0.55 inference(split_clause,[status(thm)],[f4697,f1304,f4694,f862])).
% 0.20/0.55 fof(f4732,plain,(
% 0.20/0.55 ![X0]: (~relation(empty_set)|empty_set=identity_relation(X0)|~in(ordered_pair(sk0_0(X0,empty_set),sk0_0(X0,empty_set)),empty_set)|~in(sk0_0(X0,empty_set),X0)|~sk0_0(X0,empty_set)=sk0_1(X0,empty_set)|empty_set=identity_relation(X0)|~spl0_12)),
% 0.20/0.55 inference(paramodulation,[status(thm)],[f4650,f223])).
% 0.20/0.55 fof(f4733,plain,(
% 0.20/0.55 ~spl0_6|spl0_79|~spl0_12),
% 0.20/0.55 inference(split_clause,[status(thm)],[f4732,f945,f2031,f982])).
% 0.20/0.55 fof(f4738,plain,(
% 0.20/0.55 spl0_223 <=> in(sk0_9(sk0_62,relation_inverse_image(sk0_61,sk0_63),sk0_63,sk0_61),relation_rng(sk0_61))),
% 0.20/0.55 introduced(split_symbol_definition)).
% 0.20/0.55 fof(f4741,plain,(
% 0.20/0.55 ~in(sk0_9(sk0_62,relation_inverse_image(sk0_61,sk0_63),sk0_63,sk0_61),relation_rng(sk0_61))|~in(sk0_9(sk0_62,relation_inverse_image(sk0_61,sk0_63),sk0_63,sk0_61),sk0_63)|~spl0_221|~spl0_4),
% 0.20/0.55 inference(resolution,[status(thm)],[f4695,f878])).
% 0.20/0.55 fof(f4742,plain,(
% 0.20/0.55 ~spl0_223|~spl0_220|~spl0_221|~spl0_4),
% 0.20/0.55 inference(split_clause,[status(thm)],[f4741,f4738,f4689,f4694,f877])).
% 0.20/0.55 fof(f4748,plain,(
% 0.20/0.55 ~relation(sk0_61)|in(sk0_9(sk0_62,relation_inverse_image(sk0_61,sk0_63),sk0_63,sk0_61),relation_rng(sk0_61))|~spl0_221),
% 0.20/0.55 inference(resolution,[status(thm)],[f4695,f928])).
% 0.20/0.55 fof(f4749,plain,(
% 0.20/0.55 ~spl0_58|spl0_223|~spl0_221),
% 0.20/0.55 inference(split_clause,[status(thm)],[f4748,f1304,f4738,f4694])).
% 0.20/0.55 fof(f4759,plain,(
% 0.20/0.55 $false),
% 0.20/0.55 inference(sat_refutation,[status(thm)],[f872,f876,f880,f957,f972,f975,f1003,f1012,f1020,f1031,f1039,f1057,f1062,f1067,f1093,f1098,f1105,f1113,f1118,f1123,f1131,f1136,f1141,f1149,f1154,f1159,f1167,f1172,f1177,f1185,f1190,f1203,f1208,f1221,f1226,f1231,f1239,f1244,f1249,f1251,f1253,f1272,f1274,f1297,f1313,f1317,f1389,f1479,f1483,f1491,f1635,f1639,f1686,f1691,f1696,f1703,f1708,f1713,f1724,f1729,f1733,f1739,f1744,f1769,f1771,f1844,f1882,f1908,f1988,f1993,f2143,f2201,f2473,f2499,f2504,f2519,f2534,f2549,f2554,f2572,f2708,f2744,f2766,f2840,f3052,f3191,f3380,f3911,f4395,f4410,f4415,f4436,f4441,f4635,f4645,f4647,f4693,f4698,f4733,f4742,f4749])).
% 0.20/0.55 % SZS output end CNFRefutation for theBenchmark.p
% 0.20/0.56 % Elapsed time: 0.209768 seconds
% 0.20/0.56 % CPU time: 1.479118 seconds
% 0.20/0.56 % Total memory used: 93.238 MB
% 0.20/0.56 % Net memory used: 92.497 MB
%------------------------------------------------------------------------------