TSTP Solution File: SEU203+2 by Drodi---3.6.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SEU203+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n031.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 20:41:28 EDT 2024
% Result : Theorem 0.11s 0.36s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : SEU203+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.07 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.07/0.26 % Computer : n031.cluster.edu
% 0.07/0.26 % Model : x86_64 x86_64
% 0.07/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.26 % Memory : 8042.1875MB
% 0.07/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.26 % CPULimit : 300
% 0.07/0.26 % WCLimit : 300
% 0.07/0.26 % DateTime : Mon Apr 29 20:22:13 EDT 2024
% 0.07/0.26 % CPUTime :
% 0.07/0.27 % Drodi V3.6.0
% 0.11/0.36 % Refutation found
% 0.11/0.36 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.36 % SZS output start CNFRefutation for theBenchmark
% 0.11/0.36 fof(f3,axiom,(
% 0.11/0.36 (! [A] :( empty(A)=> relation(A) ) )),
% 0.11/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.36 fof(f5,axiom,(
% 0.11/0.36 (! [A,B] : set_union2(A,B) = set_union2(B,A) )),
% 0.11/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.36 fof(f6,axiom,(
% 0.11/0.36 (! [A,B] : set_intersection2(A,B) = set_intersection2(B,A) )),
% 0.11/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.36 fof(f7,axiom,(
% 0.11/0.36 (! [A,B] :( relation(B)=> ( B = identity_relation(A)<=> (! [C,D] :( in(ordered_pair(C,D),B)<=> ( in(C,A)& C = D ) ) )) ) )),
% 0.11/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.36 fof(f9,axiom,(
% 0.11/0.36 (! [A] :( relation(A)=> (! [B,C] :( relation(C)=> ( C = relation_dom_restriction(A,B)<=> (! [D,E] :( in(ordered_pair(D,E),C)<=> ( in(D,B)& in(ordered_pair(D,E),A) ) ) )) ) )) )),
% 0.11/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.36 fof(f11,axiom,(
% 0.11/0.36 (! [A] :( relation(A)=> (! [B,C] :( C = relation_image(A,B)<=> (! [D] :( in(D,C)<=> (? [E] :( in(ordered_pair(E,D),A)& in(E,B) ) )) )) )) )),
% 0.11/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.36 fof(f14,axiom,(
% 0.11/0.36 (! [A,B] :( B = singleton(A)<=> (! [C] :( in(C,B)<=> C = A ) )) )),
% 0.11/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.36 fof(f15,axiom,(
% 0.11/0.36 (! [A] :( A = empty_set<=> (! [B] : ~ in(B,A) )) )),
% 0.11/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.36 fof(f25,axiom,(
% 0.11/0.36 (! [A] :( relation(A)=> (! [B] :( B = relation_dom(A)<=> (! [C] :( in(C,B)<=> (? [D] : in(ordered_pair(C,D),A) )) )) )) )),
% 0.11/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.36 fof(f52,axiom,(
% 0.11/0.36 (! [A] :( relation(A)=> relation(relation_inverse(A)) ) )),
% 0.11/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.36 fof(f57,axiom,(
% 0.11/0.36 (! [A] : relation(identity_relation(A)) )),
% 0.11/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.36 fof(f69,axiom,(
% 0.11/0.36 empty(empty_set) ),
% 0.11/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.36 fof(f76,axiom,(
% 0.11/0.36 ( empty(empty_set)& relation(empty_set) ) ),
% 0.11/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.36 fof(f78,axiom,(
% 0.11/0.36 (! [A] :( ( ~ empty(A)& relation(A) )=> ~ empty(relation_dom(A)) ) )),
% 0.11/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.36 fof(f80,axiom,(
% 0.11/0.36 (! [A] :( empty(A)=> ( empty(relation_dom(A))& relation(relation_dom(A)) ) ) )),
% 0.11/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.36 fof(f103,axiom,(
% 0.11/0.36 (? [A] : empty(A) )),
% 0.11/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.36 fof(f104,axiom,(
% 0.11/0.36 (? [A] :( ~ empty(A)& relation(A) ) )),
% 0.11/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.36 fof(f105,axiom,(
% 0.11/0.36 (! [A] :(? [B] :( element(B,powerset(A))& empty(B) ) ))),
% 0.11/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.36 fof(f124,conjecture,(
% 0.11/0.36 (! [A,B,C] :( relation(C)=> ( in(A,relation_image(C,B))<=> (? [D] :( in(D,relation_dom(C))& in(ordered_pair(D,A),C)& in(D,B) ) )) ) )),
% 0.11/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.36 fof(f125,negated_conjecture,(
% 0.11/0.36 ~((! [A,B,C] :( relation(C)=> ( in(A,relation_image(C,B))<=> (? [D] :( in(D,relation_dom(C))& in(ordered_pair(D,A),C)& in(D,B) ) )) ) ))),
% 0.11/0.36 inference(negated_conjecture,[status(cth)],[f124])).
% 0.11/0.36 fof(f126,lemma,(
% 0.11/0.36 (! [A,B] : subset(set_intersection2(A,B),A) )),
% 0.11/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.36 fof(f128,axiom,(
% 0.11/0.36 (! [A] : set_union2(A,empty_set) = A )),
% 0.11/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.36 fof(f134,lemma,(
% 0.11/0.36 (! [A] :( relation(A)=> (! [B] :( relation(B)=> ( subset(A,B)=> ( subset(relation_dom(A),relation_dom(B))& subset(relation_rng(A),relation_rng(B)) ) ) ) )) )),
% 0.11/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.36 fof(f137,axiom,(
% 0.11/0.36 (! [A] : set_intersection2(A,empty_set) = empty_set )),
% 0.11/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.36 fof(f140,lemma,(
% 0.11/0.36 (! [A] : subset(empty_set,A) )),
% 0.11/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.36 fof(f144,lemma,(
% 0.11/0.36 (! [A,B] : subset(set_difference(A,B),A) )),
% 0.11/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.36 fof(f167,axiom,(
% 0.11/0.36 (! [A] : set_difference(empty_set,A) = empty_set )),
% 0.11/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.36 fof(f174,lemma,(
% 0.11/0.36 ( relation_dom(empty_set) = empty_set& relation_rng(empty_set) = empty_set ) ),
% 0.11/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.36 fof(f177,lemma,(
% 0.11/0.36 (! [A] :( relation(A)=> ( ( relation_dom(A) = empty_set| relation_rng(A) = empty_set )=> A = empty_set ) ) )),
% 0.11/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.36 fof(f178,lemma,(
% 0.11/0.36 (! [A] :( relation(A)=> ( relation_dom(A) = empty_set<=> relation_rng(A) = empty_set ) ) )),
% 0.11/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.36 fof(f181,axiom,(
% 0.11/0.36 (! [A] :( empty(A)=> A = empty_set ) )),
% 0.11/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.36 fof(f183,lemma,(
% 0.11/0.36 (! [A] :( relation_dom(identity_relation(A)) = A& relation_rng(identity_relation(A)) = A ) )),
% 0.11/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.36 fof(f185,axiom,(
% 0.11/0.36 (! [A,B] :~ ( in(A,B)& empty(B) ) )),
% 0.11/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.36 fof(f186,lemma,(
% 0.11/0.36 (! [A,B] : subset(A,set_union2(A,B)) )),
% 0.11/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.36 fof(f204,plain,(
% 0.11/0.36 ![A]: (~empty(A)|relation(A))),
% 0.11/0.36 inference(pre_NNF_transformation,[status(esa)],[f3])).
% 0.11/0.36 fof(f205,plain,(
% 0.11/0.36 ![X0]: (~empty(X0)|relation(X0))),
% 0.11/0.36 inference(cnf_transformation,[status(esa)],[f204])).
% 0.11/0.36 fof(f207,plain,(
% 0.11/0.36 ![X0,X1]: (set_union2(X0,X1)=set_union2(X1,X0))),
% 0.11/0.36 inference(cnf_transformation,[status(esa)],[f5])).
% 0.11/0.36 fof(f208,plain,(
% 0.11/0.36 ![X0,X1]: (set_intersection2(X0,X1)=set_intersection2(X1,X0))),
% 0.11/0.36 inference(cnf_transformation,[status(esa)],[f6])).
% 0.11/0.36 fof(f209,plain,(
% 0.11/0.36 ![A,B]: (~relation(B)|(B=identity_relation(A)<=>(![C,D]: (in(ordered_pair(C,D),B)<=>(in(C,A)&C=D)))))),
% 0.11/0.36 inference(pre_NNF_transformation,[status(esa)],[f7])).
% 0.11/0.36 fof(f210,plain,(
% 0.11/0.36 ![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)))))))),
% 0.11/0.36 inference(NNF_transformation,[status(esa)],[f209])).
% 0.11/0.36 fof(f211,plain,(
% 0.11/0.36 ![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))))))))),
% 0.11/0.36 inference(miniscoping,[status(esa)],[f210])).
% 0.11/0.36 fof(f212,plain,(
% 0.11/0.36 ![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))))))))),
% 0.11/0.36 inference(skolemization,[status(esa)],[f211])).
% 0.11/0.36 fof(f214,plain,(
% 0.11/0.36 ![X0,X1,X2,X3]: (~relation(X0)|~X0=identity_relation(X1)|~in(ordered_pair(X2,X3),X0)|X2=X3)),
% 0.11/0.36 inference(cnf_transformation,[status(esa)],[f212])).
% 0.11/0.36 fof(f215,plain,(
% 0.11/0.36 ![X0,X1,X2,X3]: (~relation(X0)|~X0=identity_relation(X1)|in(ordered_pair(X2,X3),X0)|~in(X2,X1)|~X2=X3)),
% 0.11/0.36 inference(cnf_transformation,[status(esa)],[f212])).
% 0.11/0.36 fof(f216,plain,(
% 0.11/0.36 ![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))),
% 0.11/0.36 inference(cnf_transformation,[status(esa)],[f212])).
% 0.11/0.36 fof(f217,plain,(
% 0.11/0.36 ![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))),
% 0.11/0.36 inference(cnf_transformation,[status(esa)],[f212])).
% 0.11/0.36 fof(f218,plain,(
% 0.11/0.36 ![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))),
% 0.11/0.36 inference(cnf_transformation,[status(esa)],[f212])).
% 0.11/0.36 fof(f224,plain,(
% 0.11/0.36 ![A]: (~relation(A)|(![B,C]: (~relation(C)|(C=relation_dom_restriction(A,B)<=>(![D,E]: (in(ordered_pair(D,E),C)<=>(in(D,B)&in(ordered_pair(D,E),A))))))))),
% 0.11/0.36 inference(pre_NNF_transformation,[status(esa)],[f9])).
% 0.11/0.36 fof(f225,plain,(
% 0.11/0.36 ![A]: (~relation(A)|(![B,C]: (~relation(C)|((~C=relation_dom_restriction(A,B)|(![D,E]: ((~in(ordered_pair(D,E),C)|(in(D,B)&in(ordered_pair(D,E),A)))&(in(ordered_pair(D,E),C)|(~in(D,B)|~in(ordered_pair(D,E),A))))))&(C=relation_dom_restriction(A,B)|(?[D,E]: ((~in(ordered_pair(D,E),C)|(~in(D,B)|~in(ordered_pair(D,E),A)))&(in(ordered_pair(D,E),C)|(in(D,B)&in(ordered_pair(D,E),A))))))))))),
% 0.11/0.36 inference(NNF_transformation,[status(esa)],[f224])).
% 0.11/0.36 fof(f226,plain,(
% 0.11/0.36 ![A]: (~relation(A)|(![C]: (~relation(C)|((![B]: (~C=relation_dom_restriction(A,B)|((![D,E]: (~in(ordered_pair(D,E),C)|(in(D,B)&in(ordered_pair(D,E),A))))&(![D,E]: (in(ordered_pair(D,E),C)|(~in(D,B)|~in(ordered_pair(D,E),A)))))))&(![B]: (C=relation_dom_restriction(A,B)|(?[D,E]: ((~in(ordered_pair(D,E),C)|(~in(D,B)|~in(ordered_pair(D,E),A)))&(in(ordered_pair(D,E),C)|(in(D,B)&in(ordered_pair(D,E),A)))))))))))),
% 0.11/0.36 inference(miniscoping,[status(esa)],[f225])).
% 0.11/0.36 fof(f227,plain,(
% 0.11/0.36 ![A]: (~relation(A)|(![C]: (~relation(C)|((![B]: (~C=relation_dom_restriction(A,B)|((![D,E]: (~in(ordered_pair(D,E),C)|(in(D,B)&in(ordered_pair(D,E),A))))&(![D,E]: (in(ordered_pair(D,E),C)|(~in(D,B)|~in(ordered_pair(D,E),A)))))))&(![B]: (C=relation_dom_restriction(A,B)|((~in(ordered_pair(sk0_2(B,C,A),sk0_3(B,C,A)),C)|(~in(sk0_2(B,C,A),B)|~in(ordered_pair(sk0_2(B,C,A),sk0_3(B,C,A)),A)))&(in(ordered_pair(sk0_2(B,C,A),sk0_3(B,C,A)),C)|(in(sk0_2(B,C,A),B)&in(ordered_pair(sk0_2(B,C,A),sk0_3(B,C,A)),A))))))))))),
% 0.11/0.36 inference(skolemization,[status(esa)],[f226])).
% 0.11/0.36 fof(f228,plain,(
% 0.11/0.36 ![X0,X1,X2,X3,X4]: (~relation(X0)|~relation(X1)|~X1=relation_dom_restriction(X0,X2)|~in(ordered_pair(X3,X4),X1)|in(X3,X2))),
% 0.11/0.36 inference(cnf_transformation,[status(esa)],[f227])).
% 0.11/0.36 fof(f229,plain,(
% 0.11/0.36 ![X0,X1,X2,X3,X4]: (~relation(X0)|~relation(X1)|~X1=relation_dom_restriction(X0,X2)|~in(ordered_pair(X3,X4),X1)|in(ordered_pair(X3,X4),X0))),
% 0.11/0.36 inference(cnf_transformation,[status(esa)],[f227])).
% 0.11/0.36 fof(f230,plain,(
% 0.11/0.36 ![X0,X1,X2,X3,X4]: (~relation(X0)|~relation(X1)|~X1=relation_dom_restriction(X0,X2)|in(ordered_pair(X3,X4),X1)|~in(X3,X2)|~in(ordered_pair(X3,X4),X0))),
% 0.11/0.36 inference(cnf_transformation,[status(esa)],[f227])).
% 0.11/0.36 fof(f232,plain,(
% 0.11/0.36 ![X0,X1,X2]: (~relation(X0)|~relation(X1)|X1=relation_dom_restriction(X0,X2)|in(ordered_pair(sk0_2(X2,X1,X0),sk0_3(X2,X1,X0)),X1)|in(sk0_2(X2,X1,X0),X2))),
% 0.11/0.36 inference(cnf_transformation,[status(esa)],[f227])).
% 0.11/0.36 fof(f244,plain,(
% 0.11/0.36 ![A]: (~relation(A)|(![B,C]: (C=relation_image(A,B)<=>(![D]: (in(D,C)<=>(?[E]: (in(ordered_pair(E,D),A)&in(E,B))))))))),
% 0.11/0.36 inference(pre_NNF_transformation,[status(esa)],[f11])).
% 0.11/0.36 fof(f245,plain,(
% 0.11/0.36 ![A]: (~relation(A)|(![B,C]: ((~C=relation_image(A,B)|(![D]: ((~in(D,C)|(?[E]: (in(ordered_pair(E,D),A)&in(E,B))))&(in(D,C)|(![E]: (~in(ordered_pair(E,D),A)|~in(E,B)))))))&(C=relation_image(A,B)|(?[D]: ((~in(D,C)|(![E]: (~in(ordered_pair(E,D),A)|~in(E,B))))&(in(D,C)|(?[E]: (in(ordered_pair(E,D),A)&in(E,B))))))))))),
% 0.11/0.36 inference(NNF_transformation,[status(esa)],[f244])).
% 0.11/0.36 fof(f246,plain,(
% 0.11/0.36 ![A]: (~relation(A)|((![B,C]: (~C=relation_image(A,B)|((![D]: (~in(D,C)|(?[E]: (in(ordered_pair(E,D),A)&in(E,B)))))&(![D]: (in(D,C)|(![E]: (~in(ordered_pair(E,D),A)|~in(E,B))))))))&(![B,C]: (C=relation_image(A,B)|(?[D]: ((~in(D,C)|(![E]: (~in(ordered_pair(E,D),A)|~in(E,B))))&(in(D,C)|(?[E]: (in(ordered_pair(E,D),A)&in(E,B))))))))))),
% 0.11/0.36 inference(miniscoping,[status(esa)],[f245])).
% 0.11/0.36 fof(f247,plain,(
% 0.11/0.36 ![A]: (~relation(A)|((![B,C]: (~C=relation_image(A,B)|((![D]: (~in(D,C)|(in(ordered_pair(sk0_6(D,C,B,A),D),A)&in(sk0_6(D,C,B,A),B))))&(![D]: (in(D,C)|(![E]: (~in(ordered_pair(E,D),A)|~in(E,B))))))))&(![B,C]: (C=relation_image(A,B)|((~in(sk0_7(C,B,A),C)|(![E]: (~in(ordered_pair(E,sk0_7(C,B,A)),A)|~in(E,B))))&(in(sk0_7(C,B,A),C)|(in(ordered_pair(sk0_8(C,B,A),sk0_7(C,B,A)),A)&in(sk0_8(C,B,A),B))))))))),
% 0.11/0.36 inference(skolemization,[status(esa)],[f246])).
% 0.11/0.36 fof(f248,plain,(
% 0.11/0.36 ![X0,X1,X2,X3]: (~relation(X0)|~X1=relation_image(X0,X2)|~in(X3,X1)|in(ordered_pair(sk0_6(X3,X1,X2,X0),X3),X0))),
% 0.11/0.36 inference(cnf_transformation,[status(esa)],[f247])).
% 0.11/0.36 fof(f249,plain,(
% 0.11/0.36 ![X0,X1,X2,X3]: (~relation(X0)|~X1=relation_image(X0,X2)|~in(X3,X1)|in(sk0_6(X3,X1,X2,X0),X2))),
% 0.11/0.36 inference(cnf_transformation,[status(esa)],[f247])).
% 0.11/0.36 fof(f250,plain,(
% 0.11/0.36 ![X0,X1,X2,X3,X4]: (~relation(X0)|~X1=relation_image(X0,X2)|in(X3,X1)|~in(ordered_pair(X4,X3),X0)|~in(X4,X2))),
% 0.11/0.36 inference(cnf_transformation,[status(esa)],[f247])).
% 0.11/0.36 fof(f273,plain,(
% 0.11/0.36 ![A,B]: ((~B=singleton(A)|(![C]: ((~in(C,B)|C=A)&(in(C,B)|~C=A))))&(B=singleton(A)|(?[C]: ((~in(C,B)|~C=A)&(in(C,B)|C=A)))))),
% 0.11/0.36 inference(NNF_transformation,[status(esa)],[f14])).
% 0.11/0.36 fof(f274,plain,(
% 0.11/0.36 (![A,B]: (~B=singleton(A)|((![C]: (~in(C,B)|C=A))&(![C]: (in(C,B)|~C=A)))))&(![A,B]: (B=singleton(A)|(?[C]: ((~in(C,B)|~C=A)&(in(C,B)|C=A)))))),
% 0.11/0.36 inference(miniscoping,[status(esa)],[f273])).
% 0.11/0.36 fof(f275,plain,(
% 0.11/0.36 (![A,B]: (~B=singleton(A)|((![C]: (~in(C,B)|C=A))&(![C]: (in(C,B)|~C=A)))))&(![A,B]: (B=singleton(A)|((~in(sk0_15(B,A),B)|~sk0_15(B,A)=A)&(in(sk0_15(B,A),B)|sk0_15(B,A)=A))))),
% 0.11/0.36 inference(skolemization,[status(esa)],[f274])).
% 0.11/0.36 fof(f276,plain,(
% 0.11/0.36 ![X0,X1,X2]: (~X0=singleton(X1)|~in(X2,X0)|X2=X1)),
% 0.11/0.36 inference(cnf_transformation,[status(esa)],[f275])).
% 0.11/0.36 fof(f280,plain,(
% 0.11/0.36 ![A]: ((~A=empty_set|(![B]: ~in(B,A)))&(A=empty_set|(?[B]: in(B,A))))),
% 0.11/0.36 inference(NNF_transformation,[status(esa)],[f15])).
% 0.11/0.36 fof(f281,plain,(
% 0.11/0.36 (![A]: (~A=empty_set|(![B]: ~in(B,A))))&(![A]: (A=empty_set|(?[B]: in(B,A))))),
% 0.11/0.36 inference(miniscoping,[status(esa)],[f280])).
% 0.11/0.36 fof(f282,plain,(
% 0.11/0.36 (![A]: (~A=empty_set|(![B]: ~in(B,A))))&(![A]: (A=empty_set|in(sk0_16(A),A)))),
% 0.11/0.36 inference(skolemization,[status(esa)],[f281])).
% 0.11/0.36 fof(f283,plain,(
% 0.11/0.36 ![X0,X1]: (~X0=empty_set|~in(X1,X0))),
% 0.11/0.36 inference(cnf_transformation,[status(esa)],[f282])).
% 0.11/0.36 fof(f356,plain,(
% 0.11/0.36 ![A]: (~relation(A)|(![B]: (B=relation_dom(A)<=>(![C]: (in(C,B)<=>(?[D]: in(ordered_pair(C,D),A)))))))),
% 0.11/0.36 inference(pre_NNF_transformation,[status(esa)],[f25])).
% 0.11/0.36 fof(f357,plain,(
% 0.11/0.36 ![A]: (~relation(A)|(![B]: ((~B=relation_dom(A)|(![C]: ((~in(C,B)|(?[D]: in(ordered_pair(C,D),A)))&(in(C,B)|(![D]: ~in(ordered_pair(C,D),A))))))&(B=relation_dom(A)|(?[C]: ((~in(C,B)|(![D]: ~in(ordered_pair(C,D),A)))&(in(C,B)|(?[D]: in(ordered_pair(C,D),A)))))))))),
% 0.11/0.36 inference(NNF_transformation,[status(esa)],[f356])).
% 0.11/0.36 fof(f358,plain,(
% 0.11/0.36 ![A]: (~relation(A)|((![B]: (~B=relation_dom(A)|((![C]: (~in(C,B)|(?[D]: in(ordered_pair(C,D),A))))&(![C]: (in(C,B)|(![D]: ~in(ordered_pair(C,D),A)))))))&(![B]: (B=relation_dom(A)|(?[C]: ((~in(C,B)|(![D]: ~in(ordered_pair(C,D),A)))&(in(C,B)|(?[D]: in(ordered_pair(C,D),A)))))))))),
% 0.11/0.36 inference(miniscoping,[status(esa)],[f357])).
% 0.11/0.36 fof(f359,plain,(
% 0.11/0.36 ![A]: (~relation(A)|((![B]: (~B=relation_dom(A)|((![C]: (~in(C,B)|in(ordered_pair(C,sk0_31(C,B,A)),A)))&(![C]: (in(C,B)|(![D]: ~in(ordered_pair(C,D),A)))))))&(![B]: (B=relation_dom(A)|((~in(sk0_32(B,A),B)|(![D]: ~in(ordered_pair(sk0_32(B,A),D),A)))&(in(sk0_32(B,A),B)|in(ordered_pair(sk0_32(B,A),sk0_33(B,A)),A)))))))),
% 0.11/0.36 inference(skolemization,[status(esa)],[f358])).
% 0.11/0.36 fof(f361,plain,(
% 0.11/0.36 ![X0,X1,X2,X3]: (~relation(X0)|~X1=relation_dom(X0)|in(X2,X1)|~in(ordered_pair(X2,X3),X0))),
% 0.11/0.36 inference(cnf_transformation,[status(esa)],[f359])).
% 0.11/0.36 fof(f434,plain,(
% 0.11/0.36 ![A]: (~relation(A)|relation(relation_inverse(A)))),
% 0.11/0.36 inference(pre_NNF_transformation,[status(esa)],[f52])).
% 0.11/0.36 fof(f435,plain,(
% 0.11/0.36 ![X0]: (~relation(X0)|relation(relation_inverse(X0)))),
% 0.11/0.36 inference(cnf_transformation,[status(esa)],[f434])).
% 0.11/0.36 fof(f440,plain,(
% 0.11/0.36 ![X0]: (relation(identity_relation(X0)))),
% 0.11/0.36 inference(cnf_transformation,[status(esa)],[f57])).
% 0.11/0.36 fof(f461,plain,(
% 0.11/0.36 empty(empty_set)),
% 0.11/0.36 inference(cnf_transformation,[status(esa)],[f69])).
% 0.11/0.36 fof(f474,plain,(
% 0.11/0.36 relation(empty_set)),
% 0.11/0.36 inference(cnf_transformation,[status(esa)],[f76])).
% 0.11/0.36 fof(f477,plain,(
% 0.11/0.36 ![A]: ((empty(A)|~relation(A))|~empty(relation_dom(A)))),
% 0.11/0.36 inference(pre_NNF_transformation,[status(esa)],[f78])).
% 0.11/0.36 fof(f478,plain,(
% 0.11/0.36 ![X0]: (empty(X0)|~relation(X0)|~empty(relation_dom(X0)))),
% 0.11/0.36 inference(cnf_transformation,[status(esa)],[f477])).
% 0.11/0.36 fof(f481,plain,(
% 0.11/0.36 ![A]: (~empty(A)|(empty(relation_dom(A))&relation(relation_dom(A))))),
% 0.11/0.36 inference(pre_NNF_transformation,[status(esa)],[f80])).
% 0.11/0.36 fof(f482,plain,(
% 0.11/0.36 ![X0]: (~empty(X0)|empty(relation_dom(X0)))),
% 0.11/0.36 inference(cnf_transformation,[status(esa)],[f481])).
% 0.11/0.36 fof(f483,plain,(
% 0.11/0.36 ![X0]: (~empty(X0)|relation(relation_dom(X0)))),
% 0.11/0.36 inference(cnf_transformation,[status(esa)],[f481])).
% 0.11/0.36 fof(f545,plain,(
% 0.11/0.36 empty(sk0_52)),
% 0.11/0.36 inference(skolemization,[status(esa)],[f103])).
% 0.11/0.36 fof(f546,plain,(
% 0.11/0.36 empty(sk0_52)),
% 0.11/0.36 inference(cnf_transformation,[status(esa)],[f545])).
% 0.11/0.36 fof(f547,plain,(
% 0.11/0.36 (~empty(sk0_53)&relation(sk0_53))),
% 0.11/0.36 inference(skolemization,[status(esa)],[f104])).
% 0.11/0.36 fof(f548,plain,(
% 0.11/0.36 ~empty(sk0_53)),
% 0.11/0.36 inference(cnf_transformation,[status(esa)],[f547])).
% 0.11/0.36 fof(f549,plain,(
% 0.11/0.36 relation(sk0_53)),
% 0.11/0.36 inference(cnf_transformation,[status(esa)],[f547])).
% 0.11/0.36 fof(f550,plain,(
% 0.11/0.36 ![A]: (element(sk0_54(A),powerset(A))&empty(sk0_54(A)))),
% 0.11/0.36 inference(skolemization,[status(esa)],[f105])).
% 0.11/0.36 fof(f552,plain,(
% 0.11/0.36 ![X0]: (empty(sk0_54(X0)))),
% 0.11/0.36 inference(cnf_transformation,[status(esa)],[f550])).
% 0.11/0.36 fof(f609,plain,(
% 0.11/0.36 (?[A,B,C]: (relation(C)&(in(A,relation_image(C,B))<~>(?[D]: ((in(D,relation_dom(C))&in(ordered_pair(D,A),C))&in(D,B))))))),
% 0.11/0.36 inference(pre_NNF_transformation,[status(esa)],[f125])).
% 0.11/0.36 fof(f610,plain,(
% 0.11/0.36 ?[A,B,C]: (relation(C)&((in(A,relation_image(C,B))|(?[D]: ((in(D,relation_dom(C))&in(ordered_pair(D,A),C))&in(D,B))))&(~in(A,relation_image(C,B))|(![D]: ((~in(D,relation_dom(C))|~in(ordered_pair(D,A),C))|~in(D,B))))))),
% 0.11/0.36 inference(NNF_transformation,[status(esa)],[f609])).
% 0.11/0.36 fof(f611,plain,(
% 0.11/0.36 ?[C]: (relation(C)&(?[A,B]: ((in(A,relation_image(C,B))|(?[D]: ((in(D,relation_dom(C))&in(ordered_pair(D,A),C))&in(D,B))))&(~in(A,relation_image(C,B))|(![D]: ((~in(D,relation_dom(C))|~in(ordered_pair(D,A),C))|~in(D,B)))))))),
% 0.11/0.36 inference(miniscoping,[status(esa)],[f610])).
% 0.11/0.36 fof(f612,plain,(
% 0.11/0.36 (relation(sk0_57)&((in(sk0_58,relation_image(sk0_57,sk0_59))|((in(sk0_60,relation_dom(sk0_57))&in(ordered_pair(sk0_60,sk0_58),sk0_57))&in(sk0_60,sk0_59)))&(~in(sk0_58,relation_image(sk0_57,sk0_59))|(![D]: ((~in(D,relation_dom(sk0_57))|~in(ordered_pair(D,sk0_58),sk0_57))|~in(D,sk0_59))))))),
% 0.11/0.36 inference(skolemization,[status(esa)],[f611])).
% 0.11/0.36 fof(f613,plain,(
% 0.11/0.36 relation(sk0_57)),
% 0.11/0.36 inference(cnf_transformation,[status(esa)],[f612])).
% 0.11/0.36 fof(f615,plain,(
% 0.11/0.36 in(sk0_58,relation_image(sk0_57,sk0_59))|in(ordered_pair(sk0_60,sk0_58),sk0_57)),
% 0.11/0.36 inference(cnf_transformation,[status(esa)],[f612])).
% 0.11/0.36 fof(f616,plain,(
% 0.11/0.36 in(sk0_58,relation_image(sk0_57,sk0_59))|in(sk0_60,sk0_59)),
% 0.11/0.36 inference(cnf_transformation,[status(esa)],[f612])).
% 0.11/0.36 fof(f617,plain,(
% 0.11/0.36 ![X0]: (~in(sk0_58,relation_image(sk0_57,sk0_59))|~in(X0,relation_dom(sk0_57))|~in(ordered_pair(X0,sk0_58),sk0_57)|~in(X0,sk0_59))),
% 0.11/0.36 inference(cnf_transformation,[status(esa)],[f612])).
% 0.11/0.36 fof(f618,plain,(
% 0.11/0.36 ![X0,X1]: (subset(set_intersection2(X0,X1),X0))),
% 0.11/0.36 inference(cnf_transformation,[status(esa)],[f126])).
% 0.11/0.36 fof(f621,plain,(
% 0.11/0.36 ![X0]: (set_union2(X0,empty_set)=X0)),
% 0.11/0.36 inference(cnf_transformation,[status(esa)],[f128])).
% 0.11/0.36 fof(f634,plain,(
% 0.11/0.36 ![A]: (~relation(A)|(![B]: (~relation(B)|(~subset(A,B)|(subset(relation_dom(A),relation_dom(B))&subset(relation_rng(A),relation_rng(B)))))))),
% 0.11/0.36 inference(pre_NNF_transformation,[status(esa)],[f134])).
% 0.11/0.36 fof(f635,plain,(
% 0.11/0.36 ![X0,X1]: (~relation(X0)|~relation(X1)|~subset(X0,X1)|subset(relation_dom(X0),relation_dom(X1)))),
% 0.11/0.36 inference(cnf_transformation,[status(esa)],[f634])).
% 0.11/0.36 fof(f642,plain,(
% 0.11/0.36 ![X0]: (set_intersection2(X0,empty_set)=empty_set)),
% 0.11/0.36 inference(cnf_transformation,[status(esa)],[f137])).
% 0.11/0.36 fof(f650,plain,(
% 0.11/0.36 ![X0]: (subset(empty_set,X0))),
% 0.11/0.36 inference(cnf_transformation,[status(esa)],[f140])).
% 0.11/0.36 fof(f661,plain,(
% 0.11/0.36 ![X0,X1]: (subset(set_difference(X0,X1),X0))),
% 0.11/0.36 inference(cnf_transformation,[status(esa)],[f144])).
% 0.11/0.36 fof(f721,plain,(
% 0.11/0.36 ![X0]: (set_difference(empty_set,X0)=empty_set)),
% 0.11/0.36 inference(cnf_transformation,[status(esa)],[f167])).
% 0.11/0.36 fof(f741,plain,(
% 0.11/0.36 relation_dom(empty_set)=empty_set),
% 0.11/0.36 inference(cnf_transformation,[status(esa)],[f174])).
% 0.11/0.36 fof(f748,plain,(
% 0.11/0.36 ![A]: (~relation(A)|((~relation_dom(A)=empty_set&~relation_rng(A)=empty_set)|A=empty_set))),
% 0.11/0.36 inference(pre_NNF_transformation,[status(esa)],[f177])).
% 0.11/0.36 fof(f749,plain,(
% 0.11/0.36 ![X0]: (~relation(X0)|~relation_dom(X0)=empty_set|X0=empty_set)),
% 0.11/0.36 inference(cnf_transformation,[status(esa)],[f748])).
% 0.11/0.36 fof(f751,plain,(
% 0.11/0.36 ![A]: (~relation(A)|(relation_dom(A)=empty_set<=>relation_rng(A)=empty_set))),
% 0.11/0.36 inference(pre_NNF_transformation,[status(esa)],[f178])).
% 0.11/0.36 fof(f752,plain,(
% 0.11/0.36 ![A]: (~relation(A)|((~relation_dom(A)=empty_set|relation_rng(A)=empty_set)&(relation_dom(A)=empty_set|~relation_rng(A)=empty_set)))),
% 0.11/0.36 inference(NNF_transformation,[status(esa)],[f751])).
% 0.11/0.36 fof(f753,plain,(
% 0.11/0.36 ![X0]: (~relation(X0)|~relation_dom(X0)=empty_set|relation_rng(X0)=empty_set)),
% 0.11/0.36 inference(cnf_transformation,[status(esa)],[f752])).
% 0.11/0.36 fof(f754,plain,(
% 0.11/0.36 ![X0]: (~relation(X0)|relation_dom(X0)=empty_set|~relation_rng(X0)=empty_set)),
% 0.11/0.36 inference(cnf_transformation,[status(esa)],[f752])).
% 0.11/0.36 fof(f760,plain,(
% 0.11/0.36 ![A]: (~empty(A)|A=empty_set)),
% 0.11/0.36 inference(pre_NNF_transformation,[status(esa)],[f181])).
% 0.11/0.36 fof(f761,plain,(
% 0.11/0.36 ![X0]: (~empty(X0)|X0=empty_set)),
% 0.11/0.36 inference(cnf_transformation,[status(esa)],[f760])).
% 0.11/0.36 fof(f764,plain,(
% 0.11/0.36 (![A]: relation_dom(identity_relation(A))=A)&(![A]: relation_rng(identity_relation(A))=A)),
% 0.11/0.36 inference(miniscoping,[status(esa)],[f183])).
% 0.11/0.36 fof(f765,plain,(
% 0.11/0.36 ![X0]: (relation_dom(identity_relation(X0))=X0)),
% 0.11/0.36 inference(cnf_transformation,[status(esa)],[f764])).
% 0.11/0.36 fof(f773,plain,(
% 0.11/0.36 ![A,B]: (~in(A,B)|~empty(B))),
% 0.11/0.36 inference(pre_NNF_transformation,[status(esa)],[f185])).
% 0.11/0.36 fof(f774,plain,(
% 0.11/0.36 ![B]: ((![A]: ~in(A,B))|~empty(B))),
% 0.11/0.36 inference(miniscoping,[status(esa)],[f773])).
% 0.11/0.36 fof(f775,plain,(
% 0.11/0.36 ![X0,X1]: (~in(X0,X1)|~empty(X1))),
% 0.11/0.36 inference(cnf_transformation,[status(esa)],[f774])).
% 0.11/0.36 fof(f776,plain,(
% 0.11/0.36 ![X0,X1]: (subset(X0,set_union2(X0,X1)))),
% 0.11/0.36 inference(cnf_transformation,[status(esa)],[f186])).
% 0.11/0.36 fof(f827,plain,(
% 0.11/0.36 spl0_0 <=> in(sk0_58,relation_image(sk0_57,sk0_59))),
% 0.11/0.36 introduced(split_symbol_definition)).
% 0.11/0.36 fof(f828,plain,(
% 0.11/0.36 in(sk0_58,relation_image(sk0_57,sk0_59))|~spl0_0),
% 0.11/0.36 inference(component_clause,[status(thm)],[f827])).
% 0.11/0.36 fof(f834,plain,(
% 0.11/0.36 spl0_2 <=> in(ordered_pair(sk0_60,sk0_58),sk0_57)),
% 0.11/0.36 introduced(split_symbol_definition)).
% 0.11/0.36 fof(f835,plain,(
% 0.11/0.36 in(ordered_pair(sk0_60,sk0_58),sk0_57)|~spl0_2),
% 0.11/0.36 inference(component_clause,[status(thm)],[f834])).
% 0.11/0.36 fof(f837,plain,(
% 0.11/0.36 spl0_0|spl0_2),
% 0.11/0.36 inference(split_clause,[status(thm)],[f615,f827,f834])).
% 0.11/0.36 fof(f838,plain,(
% 0.11/0.36 spl0_3 <=> in(sk0_60,sk0_59)),
% 0.11/0.36 introduced(split_symbol_definition)).
% 0.11/0.36 fof(f839,plain,(
% 0.11/0.36 in(sk0_60,sk0_59)|~spl0_3),
% 0.11/0.36 inference(component_clause,[status(thm)],[f838])).
% 0.11/0.36 fof(f841,plain,(
% 0.11/0.36 spl0_0|spl0_3),
% 0.11/0.36 inference(split_clause,[status(thm)],[f616,f827,f838])).
% 0.11/0.36 fof(f842,plain,(
% 0.11/0.36 spl0_4 <=> ~in(X0,relation_dom(sk0_57))|~in(ordered_pair(X0,sk0_58),sk0_57)|~in(X0,sk0_59)),
% 0.11/0.36 introduced(split_symbol_definition)).
% 0.11/0.36 fof(f843,plain,(
% 0.11/0.36 ![X0]: (~in(X0,relation_dom(sk0_57))|~in(ordered_pair(X0,sk0_58),sk0_57)|~in(X0,sk0_59)|~spl0_4)),
% 0.11/0.36 inference(component_clause,[status(thm)],[f842])).
% 0.11/0.36 fof(f845,plain,(
% 0.11/0.36 ~spl0_0|spl0_4),
% 0.11/0.36 inference(split_clause,[status(thm)],[f617,f827,f842])).
% 0.11/0.36 fof(f847,plain,(
% 0.11/0.36 ![X0,X1,X2]: (~relation(identity_relation(X0))|~in(ordered_pair(X1,X2),identity_relation(X0))|X1=X2)),
% 0.11/0.36 inference(destructive_equality_resolution,[status(esa)],[f214])).
% 0.11/0.36 fof(f848,plain,(
% 0.11/0.36 ![X0,X1]: (~relation(identity_relation(X0))|in(ordered_pair(X1,X1),identity_relation(X0))|~in(X1,X0))),
% 0.11/0.36 inference(destructive_equality_resolution,[status(esa)],[f215])).
% 0.11/0.36 fof(f851,plain,(
% 0.11/0.36 ![X0,X1,X2,X3]: (~relation(X0)|~relation(relation_dom_restriction(X0,X1))|~in(ordered_pair(X2,X3),relation_dom_restriction(X0,X1))|in(X2,X1))),
% 0.11/0.36 inference(destructive_equality_resolution,[status(esa)],[f228])).
% 0.11/0.36 fof(f852,plain,(
% 0.11/0.36 ![X0,X1,X2,X3]: (~relation(X0)|~relation(relation_dom_restriction(X0,X1))|~in(ordered_pair(X2,X3),relation_dom_restriction(X0,X1))|in(ordered_pair(X2,X3),X0))),
% 0.11/0.36 inference(destructive_equality_resolution,[status(esa)],[f229])).
% 0.11/0.36 fof(f853,plain,(
% 0.11/0.36 ![X0,X1,X2,X3]: (~relation(X0)|~relation(relation_dom_restriction(X0,X1))|in(ordered_pair(X2,X3),relation_dom_restriction(X0,X1))|~in(X2,X1)|~in(ordered_pair(X2,X3),X0))),
% 0.11/0.36 inference(destructive_equality_resolution,[status(esa)],[f230])).
% 0.11/0.36 fof(f857,plain,(
% 0.11/0.36 ![X0,X1,X2]: (~relation(X0)|~in(X1,relation_image(X0,X2))|in(ordered_pair(sk0_6(X1,relation_image(X0,X2),X2,X0),X1),X0))),
% 0.11/0.36 inference(destructive_equality_resolution,[status(esa)],[f248])).
% 0.11/0.36 fof(f858,plain,(
% 0.11/0.36 ![X0,X1,X2]: (~relation(X0)|~in(X1,relation_image(X0,X2))|in(sk0_6(X1,relation_image(X0,X2),X2,X0),X2))),
% 0.11/0.36 inference(destructive_equality_resolution,[status(esa)],[f249])).
% 0.11/0.36 fof(f859,plain,(
% 0.11/0.36 ![X0,X1,X2,X3]: (~relation(X0)|in(X1,relation_image(X0,X2))|~in(ordered_pair(X3,X1),X0)|~in(X3,X2))),
% 0.11/0.36 inference(destructive_equality_resolution,[status(esa)],[f250])).
% 0.11/0.36 fof(f865,plain,(
% 0.11/0.36 ![X0,X1]: (~in(X0,singleton(X1))|X0=X1)),
% 0.11/0.36 inference(destructive_equality_resolution,[status(esa)],[f276])).
% 0.11/0.36 fof(f867,plain,(
% 0.11/0.36 ![X0]: (~in(X0,empty_set))),
% 0.11/0.36 inference(destructive_equality_resolution,[status(esa)],[f283])).
% 0.11/0.36 fof(f882,plain,(
% 0.11/0.36 ![X0,X1,X2]: (~relation(X0)|in(X1,relation_dom(X0))|~in(ordered_pair(X1,X2),X0))),
% 0.11/0.36 inference(destructive_equality_resolution,[status(esa)],[f361])).
% 0.11/0.36 fof(f904,plain,(
% 0.11/0.36 spl0_5 <=> empty(empty_set)),
% 0.11/0.36 introduced(split_symbol_definition)).
% 0.11/0.36 fof(f906,plain,(
% 0.11/0.36 ~empty(empty_set)|spl0_5),
% 0.11/0.36 inference(component_clause,[status(thm)],[f904])).
% 0.11/0.36 fof(f907,plain,(
% 0.11/0.36 spl0_6 <=> relation(empty_set)),
% 0.11/0.36 introduced(split_symbol_definition)).
% 0.11/0.36 fof(f909,plain,(
% 0.11/0.36 ~relation(empty_set)|spl0_6),
% 0.11/0.36 inference(component_clause,[status(thm)],[f907])).
% 0.11/0.36 fof(f912,plain,(
% 0.11/0.36 spl0_7 <=> relation_dom(sk0_57)=empty_set),
% 0.11/0.36 introduced(split_symbol_definition)).
% 0.11/0.36 fof(f915,plain,(
% 0.11/0.36 spl0_8 <=> sk0_57=empty_set),
% 0.11/0.36 introduced(split_symbol_definition)).
% 0.11/0.36 fof(f916,plain,(
% 0.11/0.36 sk0_57=empty_set|~spl0_8),
% 0.11/0.36 inference(component_clause,[status(thm)],[f915])).
% 0.11/0.36 fof(f918,plain,(
% 0.11/0.36 ~relation_dom(sk0_57)=empty_set|sk0_57=empty_set),
% 0.11/0.36 inference(resolution,[status(thm)],[f749,f613])).
% 0.11/0.36 fof(f919,plain,(
% 0.11/0.36 ~spl0_7|spl0_8),
% 0.11/0.36 inference(split_clause,[status(thm)],[f918,f912,f915])).
% 0.11/0.36 fof(f920,plain,(
% 0.11/0.36 spl0_9 <=> relation_rng(sk0_57)=empty_set),
% 0.11/0.36 introduced(split_symbol_definition)).
% 0.11/0.36 fof(f925,plain,(
% 0.11/0.36 relation_dom(sk0_57)=empty_set|~relation_rng(sk0_57)=empty_set),
% 0.11/0.36 inference(resolution,[status(thm)],[f754,f613])).
% 0.11/0.36 fof(f926,plain,(
% 0.11/0.36 spl0_7|~spl0_9),
% 0.11/0.36 inference(split_clause,[status(thm)],[f925,f912,f920])).
% 0.11/0.36 fof(f934,plain,(
% 0.11/0.36 spl0_10 <=> relation_dom(empty_set)=empty_set),
% 0.11/0.36 introduced(split_symbol_definition)).
% 0.11/0.36 fof(f936,plain,(
% 0.11/0.36 ~relation_dom(empty_set)=empty_set|spl0_10),
% 0.11/0.36 inference(component_clause,[status(thm)],[f934])).
% 0.11/0.36 fof(f937,plain,(
% 0.11/0.36 spl0_11 <=> relation_rng(empty_set)=empty_set),
% 0.11/0.36 introduced(split_symbol_definition)).
% 0.11/0.36 fof(f942,plain,(
% 0.11/0.36 ~relation_dom(empty_set)=empty_set|relation_rng(empty_set)=empty_set),
% 0.11/0.36 inference(resolution,[status(thm)],[f474,f753])).
% 0.11/0.36 fof(f943,plain,(
% 0.11/0.36 ~spl0_10|spl0_11),
% 0.11/0.36 inference(split_clause,[status(thm)],[f942,f934,f937])).
% 0.11/0.36 fof(f944,plain,(
% 0.11/0.36 spl0_12 <=> empty_set=empty_set),
% 0.11/0.36 introduced(split_symbol_definition)).
% 0.11/0.36 fof(f947,plain,(
% 0.11/0.36 ~relation_dom(empty_set)=empty_set|empty_set=empty_set),
% 0.11/0.36 inference(resolution,[status(thm)],[f474,f749])).
% 0.11/0.36 fof(f948,plain,(
% 0.11/0.36 ~spl0_10|spl0_12),
% 0.11/0.36 inference(split_clause,[status(thm)],[f947,f934,f944])).
% 0.11/0.36 fof(f949,plain,(
% 0.11/0.36 ~empty_set=empty_set|spl0_10),
% 0.11/0.36 inference(forward_demodulation,[status(thm)],[f741,f936])).
% 0.11/0.36 fof(f950,plain,(
% 0.11/0.36 $false|spl0_10),
% 0.11/0.36 inference(trivial_equality_resolution,[status(esa)],[f949])).
% 0.11/0.36 fof(f951,plain,(
% 0.11/0.36 spl0_10),
% 0.11/0.36 inference(contradiction_clause,[status(thm)],[f950])).
% 0.11/0.36 fof(f970,plain,(
% 0.11/0.36 relation(sk0_52)),
% 0.11/0.36 inference(resolution,[status(thm)],[f546,f205])).
% 0.11/0.36 fof(f972,plain,(
% 0.11/0.36 empty(relation_dom(sk0_52))),
% 0.11/0.36 inference(resolution,[status(thm)],[f546,f482])).
% 0.11/0.36 fof(f973,plain,(
% 0.11/0.36 spl0_16 <=> relation_dom(sk0_53)=empty_set),
% 0.11/0.36 introduced(split_symbol_definition)).
% 0.11/0.36 fof(f976,plain,(
% 0.11/0.36 spl0_17 <=> relation_rng(sk0_53)=empty_set),
% 0.11/0.36 introduced(split_symbol_definition)).
% 0.11/0.36 fof(f979,plain,(
% 0.11/0.36 relation_dom(sk0_53)=empty_set|~relation_rng(sk0_53)=empty_set),
% 0.11/0.36 inference(resolution,[status(thm)],[f549,f754])).
% 0.11/0.36 fof(f980,plain,(
% 0.11/0.36 spl0_16|~spl0_17),
% 0.11/0.36 inference(split_clause,[status(thm)],[f979,f973,f976])).
% 0.11/0.36 fof(f983,plain,(
% 0.11/0.36 spl0_18 <=> sk0_53=empty_set),
% 0.11/0.36 introduced(split_symbol_definition)).
% 0.11/0.36 fof(f984,plain,(
% 0.11/0.36 sk0_53=empty_set|~spl0_18),
% 0.11/0.36 inference(component_clause,[status(thm)],[f983])).
% 0.11/0.36 fof(f986,plain,(
% 0.11/0.36 ~relation_dom(sk0_53)=empty_set|sk0_53=empty_set),
% 0.11/0.36 inference(resolution,[status(thm)],[f549,f749])).
% 0.11/0.36 fof(f987,plain,(
% 0.11/0.36 ~spl0_16|spl0_18),
% 0.11/0.36 inference(split_clause,[status(thm)],[f986,f973,f983])).
% 0.11/0.36 fof(f1013,plain,(
% 0.11/0.36 ~empty(empty_set)|~spl0_18),
% 0.11/0.36 inference(backward_demodulation,[status(thm)],[f984,f548])).
% 0.11/0.36 fof(f1014,plain,(
% 0.11/0.36 $false|~spl0_18),
% 0.11/0.36 inference(forward_subsumption_resolution,[status(thm)],[f1013,f461])).
% 0.11/0.36 fof(f1015,plain,(
% 0.11/0.36 ~spl0_18),
% 0.11/0.36 inference(contradiction_clause,[status(thm)],[f1014])).
% 0.11/0.36 fof(f1017,plain,(
% 0.11/0.36 spl0_22 <=> empty(sk0_52)),
% 0.11/0.36 introduced(split_symbol_definition)).
% 0.11/0.36 fof(f1020,plain,(
% 0.11/0.36 spl0_23 <=> relation(sk0_52)),
% 0.11/0.36 introduced(split_symbol_definition)).
% 0.11/0.36 fof(f1022,plain,(
% 0.11/0.36 ~relation(sk0_52)|spl0_23),
% 0.11/0.36 inference(component_clause,[status(thm)],[f1020])).
% 0.11/0.36 fof(f1025,plain,(
% 0.11/0.36 $false|spl0_5),
% 0.11/0.36 inference(forward_subsumption_resolution,[status(thm)],[f906,f461])).
% 0.11/0.36 fof(f1026,plain,(
% 0.11/0.36 spl0_5),
% 0.11/0.36 inference(contradiction_clause,[status(thm)],[f1025])).
% 0.11/0.36 fof(f1031,plain,(
% 0.11/0.36 $false|spl0_23),
% 0.11/0.36 inference(forward_subsumption_resolution,[status(thm)],[f970,f1022])).
% 0.11/0.36 fof(f1032,plain,(
% 0.11/0.36 spl0_23),
% 0.11/0.36 inference(contradiction_clause,[status(thm)],[f1031])).
% 0.11/0.36 fof(f1045,plain,(
% 0.11/0.36 empty(sk0_52)|~relation(sk0_52)),
% 0.11/0.36 inference(resolution,[status(thm)],[f972,f478])).
% 0.11/0.36 fof(f1046,plain,(
% 0.11/0.36 spl0_22|~spl0_23),
% 0.11/0.36 inference(split_clause,[status(thm)],[f1045,f1017,f1020])).
% 0.11/0.36 fof(f1079,plain,(
% 0.11/0.36 ![X0]: (~relation_dom(identity_relation(X0))=empty_set|identity_relation(X0)=empty_set)),
% 0.11/0.36 inference(resolution,[status(thm)],[f440,f749])).
% 0.11/0.36 fof(f1080,plain,(
% 0.11/0.36 ![X0,X1,X2]: (~in(ordered_pair(X0,X1),identity_relation(X2))|X0=X1)),
% 0.11/0.36 inference(forward_subsumption_resolution,[status(thm)],[f847,f440])).
% 0.11/0.36 fof(f1081,plain,(
% 0.11/0.36 ![X0,X1]: (in(ordered_pair(X0,X0),identity_relation(X1))|~in(X0,X1))),
% 0.11/0.36 inference(forward_subsumption_resolution,[status(thm)],[f848,f440])).
% 0.11/0.36 fof(f1085,plain,(
% 0.11/0.36 ![X0]: (empty(relation_dom(sk0_54(X0))))),
% 0.11/0.36 inference(resolution,[status(thm)],[f552,f482])).
% 0.11/0.36 fof(f1086,plain,(
% 0.11/0.36 spl0_26 <=> ~relation(X0)|subset(relation_dom(empty_set),relation_dom(X0))),
% 0.11/0.36 introduced(split_symbol_definition)).
% 0.11/0.36 fof(f1089,plain,(
% 0.11/0.36 ![X0]: (~relation(empty_set)|~relation(X0)|subset(relation_dom(empty_set),relation_dom(X0)))),
% 0.11/0.36 inference(resolution,[status(thm)],[f650,f635])).
% 0.11/0.36 fof(f1090,plain,(
% 0.11/0.36 ~spl0_6|spl0_26),
% 0.11/0.36 inference(split_clause,[status(thm)],[f1089,f907,f1086])).
% 0.11/0.36 fof(f1091,plain,(
% 0.11/0.36 $false|spl0_6),
% 0.11/0.36 inference(forward_subsumption_resolution,[status(thm)],[f909,f474])).
% 0.11/0.36 fof(f1092,plain,(
% 0.11/0.36 spl0_6),
% 0.11/0.36 inference(contradiction_clause,[status(thm)],[f1091])).
% 0.11/0.36 fof(f1107,plain,(
% 0.11/0.36 ![X0]: (set_union2(empty_set,X0)=X0)),
% 0.11/0.36 inference(paramodulation,[status(thm)],[f207,f621])).
% 0.11/0.36 fof(f1116,plain,(
% 0.11/0.36 ![X0]: (sk0_57=identity_relation(X0)|in(ordered_pair(sk0_0(X0,sk0_57),sk0_1(X0,sk0_57)),sk0_57)|in(sk0_0(X0,sk0_57),X0))),
% 0.11/0.36 inference(resolution,[status(thm)],[f217,f613])).
% 0.11/0.36 fof(f1123,plain,(
% 0.11/0.36 ![X0]: (sk0_57=identity_relation(X0)|in(ordered_pair(sk0_0(X0,sk0_57),sk0_1(X0,sk0_57)),sk0_57)|sk0_0(X0,sk0_57)=sk0_1(X0,sk0_57))),
% 0.11/0.36 inference(resolution,[status(thm)],[f218,f613])).
% 0.11/0.36 fof(f1124,plain,(
% 0.11/0.36 spl0_27 <=> relation(identity_relation(relation_image(sk0_57,sk0_59)))),
% 0.11/0.36 introduced(split_symbol_definition)).
% 0.11/0.36 fof(f1126,plain,(
% 0.11/0.36 ~relation(identity_relation(relation_image(sk0_57,sk0_59)))|spl0_27),
% 0.11/0.36 inference(component_clause,[status(thm)],[f1124])).
% 0.11/0.36 fof(f1139,plain,(
% 0.11/0.36 $false|spl0_27),
% 0.11/0.36 inference(forward_subsumption_resolution,[status(thm)],[f1126,f440])).
% 0.11/0.36 fof(f1140,plain,(
% 0.11/0.36 spl0_27),
% 0.11/0.36 inference(contradiction_clause,[status(thm)],[f1139])).
% 0.11/0.36 fof(f1147,plain,(
% 0.11/0.36 spl0_30 <=> relation(sk0_57)),
% 0.11/0.36 introduced(split_symbol_definition)).
% 0.11/0.36 fof(f1149,plain,(
% 0.11/0.36 ~relation(sk0_57)|spl0_30),
% 0.11/0.36 inference(component_clause,[status(thm)],[f1147])).
% 0.11/0.36 fof(f1152,plain,(
% 0.11/0.36 spl0_31 <=> in(sk0_58,relation_image(sk0_57,X0))|~in(sk0_60,X0)),
% 0.11/0.36 introduced(split_symbol_definition)).
% 0.11/0.36 fof(f1153,plain,(
% 0.11/0.36 ![X0]: (in(sk0_58,relation_image(sk0_57,X0))|~in(sk0_60,X0)|~spl0_31)),
% 0.11/0.36 inference(component_clause,[status(thm)],[f1152])).
% 0.11/0.36 fof(f1155,plain,(
% 0.11/0.36 ![X0]: (~relation(sk0_57)|in(sk0_58,relation_image(sk0_57,X0))|~in(sk0_60,X0)|~spl0_2)),
% 0.11/0.36 inference(resolution,[status(thm)],[f835,f859])).
% 0.11/0.36 fof(f1156,plain,(
% 0.11/0.36 ~spl0_30|spl0_31|~spl0_2),
% 0.11/0.36 inference(split_clause,[status(thm)],[f1155,f1147,f1152,f834])).
% 0.11/0.36 fof(f1159,plain,(
% 0.11/0.36 $false|spl0_30),
% 0.11/0.36 inference(forward_subsumption_resolution,[status(thm)],[f1149,f613])).
% 0.11/0.36 fof(f1160,plain,(
% 0.11/0.36 spl0_30),
% 0.11/0.36 inference(contradiction_clause,[status(thm)],[f1159])).
% 0.11/0.36 fof(f1176,plain,(
% 0.11/0.36 spl0_32 <=> relation(identity_relation(identity_relation(relation_image(sk0_57,sk0_59))))),
% 0.11/0.36 introduced(split_symbol_definition)).
% 0.11/0.36 fof(f1178,plain,(
% 0.11/0.36 ~relation(identity_relation(identity_relation(relation_image(sk0_57,sk0_59))))|spl0_32),
% 0.11/0.36 inference(component_clause,[status(thm)],[f1176])).
% 0.11/0.36 fof(f1201,plain,(
% 0.11/0.36 spl0_35 <=> relation(identity_relation(sk0_59))),
% 0.11/0.36 introduced(split_symbol_definition)).
% 0.11/0.36 fof(f1203,plain,(
% 0.11/0.36 ~relation(identity_relation(sk0_59))|spl0_35),
% 0.11/0.36 inference(component_clause,[status(thm)],[f1201])).
% 0.11/0.36 fof(f1216,plain,(
% 0.11/0.36 $false|spl0_35),
% 0.11/0.36 inference(forward_subsumption_resolution,[status(thm)],[f1203,f440])).
% 0.11/0.36 fof(f1217,plain,(
% 0.11/0.36 spl0_35),
% 0.11/0.36 inference(contradiction_clause,[status(thm)],[f1216])).
% 0.11/0.36 fof(f1222,plain,(
% 0.11/0.36 in(sk0_58,relation_image(sk0_57,sk0_59))|~spl0_31|~spl0_3),
% 0.11/0.36 inference(resolution,[status(thm)],[f1153,f839])).
% 0.11/0.36 fof(f1223,plain,(
% 0.11/0.36 spl0_0|~spl0_31|~spl0_3),
% 0.11/0.36 inference(split_clause,[status(thm)],[f1222,f827,f1152,f838])).
% 0.11/0.36 fof(f1226,plain,(
% 0.11/0.36 $false|spl0_32),
% 0.11/0.36 inference(forward_subsumption_resolution,[status(thm)],[f1178,f440])).
% 0.11/0.36 fof(f1227,plain,(
% 0.11/0.36 spl0_32),
% 0.11/0.36 inference(contradiction_clause,[status(thm)],[f1226])).
% 0.11/0.36 fof(f1230,plain,(
% 0.11/0.36 spl0_38 <=> sk0_57=identity_relation(X0)|in(sk0_0(X0,sk0_57),X0)|sk0_57=identity_relation(X0)|~in(sk0_0(X0,sk0_57),X0)|~sk0_0(X0,sk0_57)=sk0_1(X0,sk0_57)),
% 0.11/0.36 introduced(split_symbol_definition)).
% 0.11/0.36 fof(f1233,plain,(
% 0.11/0.36 ![X0]: (sk0_57=identity_relation(X0)|in(sk0_0(X0,sk0_57),X0)|~relation(sk0_57)|sk0_57=identity_relation(X0)|~in(sk0_0(X0,sk0_57),X0)|~sk0_0(X0,sk0_57)=sk0_1(X0,sk0_57))),
% 0.11/0.36 inference(resolution,[status(thm)],[f1116,f216])).
% 0.11/0.36 fof(f1234,plain,(
% 0.11/0.36 spl0_38|~spl0_30),
% 0.11/0.36 inference(split_clause,[status(thm)],[f1233,f1230,f1147])).
% 0.11/0.36 fof(f1235,plain,(
% 0.11/0.36 spl0_39 <=> sk0_57=identity_relation(X0)|in(sk0_0(X0,sk0_57),X0)|in(sk0_0(X0,sk0_57),relation_dom(sk0_57))),
% 0.11/0.36 introduced(split_symbol_definition)).
% 0.11/0.36 fof(f1236,plain,(
% 0.11/0.36 ![X0]: (sk0_57=identity_relation(X0)|in(sk0_0(X0,sk0_57),X0)|in(sk0_0(X0,sk0_57),relation_dom(sk0_57))|~spl0_39)),
% 0.11/0.36 inference(component_clause,[status(thm)],[f1235])).
% 0.11/0.36 fof(f1238,plain,(
% 0.11/0.36 ![X0]: (sk0_57=identity_relation(X0)|in(sk0_0(X0,sk0_57),X0)|~relation(sk0_57)|in(sk0_0(X0,sk0_57),relation_dom(sk0_57)))),
% 0.11/0.36 inference(resolution,[status(thm)],[f1116,f882])).
% 0.11/0.36 fof(f1239,plain,(
% 0.11/0.36 spl0_39|~spl0_30),
% 0.11/0.36 inference(split_clause,[status(thm)],[f1238,f1235,f1147])).
% 0.11/0.36 fof(f1240,plain,(
% 0.11/0.36 spl0_40 <=> sk0_57=identity_relation(X0)|in(sk0_0(X0,sk0_57),X0)|in(sk0_1(X0,sk0_57),relation_image(sk0_57,X1))|~in(sk0_0(X0,sk0_57),X1)),
% 0.11/0.36 introduced(split_symbol_definition)).
% 0.11/0.36 fof(f1243,plain,(
% 0.11/0.36 ![X0,X1]: (sk0_57=identity_relation(X0)|in(sk0_0(X0,sk0_57),X0)|~relation(sk0_57)|in(sk0_1(X0,sk0_57),relation_image(sk0_57,X1))|~in(sk0_0(X0,sk0_57),X1))),
% 0.11/0.36 inference(resolution,[status(thm)],[f1116,f859])).
% 0.11/0.36 fof(f1244,plain,(
% 0.11/0.36 spl0_40|~spl0_30),
% 0.11/0.36 inference(split_clause,[status(thm)],[f1243,f1240,f1147])).
% 0.11/0.36 fof(f1245,plain,(
% 0.11/0.36 ![X0]: (sk0_57=identity_relation(X0)|in(sk0_0(X0,sk0_57),X0)|in(ordered_pair(ordered_pair(sk0_0(X0,sk0_57),sk0_1(X0,sk0_57)),ordered_pair(sk0_0(X0,sk0_57),sk0_1(X0,sk0_57))),identity_relation(sk0_57)))),
% 0.11/0.36 inference(resolution,[status(thm)],[f1116,f1081])).
% 0.11/0.36 fof(f1247,plain,(
% 0.11/0.36 spl0_41 <=> sk0_57=identity_relation(X0)|sk0_0(X0,sk0_57)=sk0_1(X0,sk0_57)|sk0_57=identity_relation(X0)|~in(sk0_0(X0,sk0_57),X0)|~sk0_0(X0,sk0_57)=sk0_1(X0,sk0_57)),
% 0.11/0.36 introduced(split_symbol_definition)).
% 0.11/0.36 fof(f1250,plain,(
% 0.11/0.36 ![X0]: (sk0_57=identity_relation(X0)|sk0_0(X0,sk0_57)=sk0_1(X0,sk0_57)|~relation(sk0_57)|sk0_57=identity_relation(X0)|~in(sk0_0(X0,sk0_57),X0)|~sk0_0(X0,sk0_57)=sk0_1(X0,sk0_57))),
% 0.11/0.36 inference(resolution,[status(thm)],[f1123,f216])).
% 0.11/0.36 fof(f1251,plain,(
% 0.11/0.36 spl0_41|~spl0_30),
% 0.11/0.36 inference(split_clause,[status(thm)],[f1250,f1247,f1147])).
% 0.11/0.36 fof(f1252,plain,(
% 0.11/0.36 spl0_42 <=> sk0_57=identity_relation(X0)|sk0_0(X0,sk0_57)=sk0_1(X0,sk0_57)|in(sk0_0(X0,sk0_57),relation_dom(sk0_57))),
% 0.11/0.36 introduced(split_symbol_definition)).
% 0.11/0.36 fof(f1255,plain,(
% 0.11/0.36 ![X0]: (sk0_57=identity_relation(X0)|sk0_0(X0,sk0_57)=sk0_1(X0,sk0_57)|~relation(sk0_57)|in(sk0_0(X0,sk0_57),relation_dom(sk0_57)))),
% 0.11/0.36 inference(resolution,[status(thm)],[f1123,f882])).
% 0.11/0.36 fof(f1256,plain,(
% 0.11/0.36 spl0_42|~spl0_30),
% 0.11/0.36 inference(split_clause,[status(thm)],[f1255,f1252,f1147])).
% 0.11/0.36 fof(f1257,plain,(
% 0.11/0.36 spl0_43 <=> sk0_57=identity_relation(X0)|sk0_0(X0,sk0_57)=sk0_1(X0,sk0_57)|in(sk0_1(X0,sk0_57),relation_image(sk0_57,X1))|~in(sk0_0(X0,sk0_57),X1)),
% 0.11/0.36 introduced(split_symbol_definition)).
% 0.11/0.36 fof(f1260,plain,(
% 0.11/0.36 ![X0,X1]: (sk0_57=identity_relation(X0)|sk0_0(X0,sk0_57)=sk0_1(X0,sk0_57)|~relation(sk0_57)|in(sk0_1(X0,sk0_57),relation_image(sk0_57,X1))|~in(sk0_0(X0,sk0_57),X1))),
% 0.11/0.36 inference(resolution,[status(thm)],[f1123,f859])).
% 0.11/0.36 fof(f1261,plain,(
% 0.11/0.36 spl0_43|~spl0_30),
% 0.11/0.36 inference(split_clause,[status(thm)],[f1260,f1257,f1147])).
% 0.11/0.36 fof(f1262,plain,(
% 0.11/0.36 ![X0]: (sk0_57=identity_relation(X0)|sk0_0(X0,sk0_57)=sk0_1(X0,sk0_57)|in(ordered_pair(ordered_pair(sk0_0(X0,sk0_57),sk0_1(X0,sk0_57)),ordered_pair(sk0_0(X0,sk0_57),sk0_1(X0,sk0_57))),identity_relation(sk0_57)))),
% 0.11/0.36 inference(resolution,[status(thm)],[f1123,f1081])).
% 0.11/0.36 fof(f1264,plain,(
% 0.11/0.36 spl0_44 <=> sk0_57=identity_relation(X0)|in(sk0_0(X0,sk0_57),X0)|in(ordered_pair(sk0_0(X0,sk0_57),sk0_1(X0,sk0_57)),relation_dom(identity_relation(sk0_57)))),
% 0.11/0.36 introduced(split_symbol_definition)).
% 0.11/0.36 fof(f1267,plain,(
% 0.11/0.36 spl0_45 <=> relation(identity_relation(sk0_57))),
% 0.11/0.36 introduced(split_symbol_definition)).
% 0.11/0.36 fof(f1269,plain,(
% 0.11/0.36 ~relation(identity_relation(sk0_57))|spl0_45),
% 0.11/0.36 inference(component_clause,[status(thm)],[f1267])).
% 0.11/0.36 fof(f1270,plain,(
% 0.11/0.36 ![X0]: (sk0_57=identity_relation(X0)|in(sk0_0(X0,sk0_57),X0)|~relation(identity_relation(sk0_57))|in(ordered_pair(sk0_0(X0,sk0_57),sk0_1(X0,sk0_57)),relation_dom(identity_relation(sk0_57))))),
% 0.11/0.36 inference(resolution,[status(thm)],[f1245,f882])).
% 0.11/0.36 fof(f1271,plain,(
% 0.11/0.36 spl0_44|~spl0_45),
% 0.11/0.36 inference(split_clause,[status(thm)],[f1270,f1264,f1267])).
% 0.11/0.36 fof(f1272,plain,(
% 0.11/0.36 spl0_46 <=> sk0_57=identity_relation(X0)|in(sk0_0(X0,sk0_57),X0)|in(ordered_pair(sk0_0(X0,sk0_57),sk0_1(X0,sk0_57)),relation_image(identity_relation(sk0_57),X1))|~in(ordered_pair(sk0_0(X0,sk0_57),sk0_1(X0,sk0_57)),X1)),
% 0.11/0.36 introduced(split_symbol_definition)).
% 0.11/0.36 fof(f1275,plain,(
% 0.11/0.36 ![X0,X1]: (sk0_57=identity_relation(X0)|in(sk0_0(X0,sk0_57),X0)|~relation(identity_relation(sk0_57))|in(ordered_pair(sk0_0(X0,sk0_57),sk0_1(X0,sk0_57)),relation_image(identity_relation(sk0_57),X1))|~in(ordered_pair(sk0_0(X0,sk0_57),sk0_1(X0,sk0_57)),X1))),
% 0.11/0.36 inference(resolution,[status(thm)],[f1245,f859])).
% 0.11/0.36 fof(f1276,plain,(
% 0.11/0.36 spl0_46|~spl0_45),
% 0.11/0.36 inference(split_clause,[status(thm)],[f1275,f1272,f1267])).
% 0.11/0.36 fof(f1277,plain,(
% 0.11/0.36 ![X0]: (sk0_57=identity_relation(X0)|in(sk0_0(X0,sk0_57),X0)|in(ordered_pair(ordered_pair(ordered_pair(sk0_0(X0,sk0_57),sk0_1(X0,sk0_57)),ordered_pair(sk0_0(X0,sk0_57),sk0_1(X0,sk0_57))),ordered_pair(ordered_pair(sk0_0(X0,sk0_57),sk0_1(X0,sk0_57)),ordered_pair(sk0_0(X0,sk0_57),sk0_1(X0,sk0_57)))),identity_relation(identity_relation(sk0_57))))),
% 0.11/0.36 inference(resolution,[status(thm)],[f1245,f1081])).
% 0.11/0.36 fof(f1279,plain,(
% 0.11/0.36 $false|spl0_45),
% 0.11/0.36 inference(forward_subsumption_resolution,[status(thm)],[f1269,f440])).
% 0.11/0.36 fof(f1280,plain,(
% 0.11/0.36 spl0_45),
% 0.11/0.36 inference(contradiction_clause,[status(thm)],[f1279])).
% 0.11/0.36 fof(f1281,plain,(
% 0.11/0.36 spl0_47 <=> sk0_57=identity_relation(X0)|sk0_0(X0,sk0_57)=sk0_1(X0,sk0_57)|in(ordered_pair(sk0_0(X0,sk0_57),sk0_1(X0,sk0_57)),relation_dom(identity_relation(sk0_57)))),
% 0.11/0.36 introduced(split_symbol_definition)).
% 0.11/0.36 fof(f1284,plain,(
% 0.11/0.36 ![X0]: (sk0_57=identity_relation(X0)|sk0_0(X0,sk0_57)=sk0_1(X0,sk0_57)|~relation(identity_relation(sk0_57))|in(ordered_pair(sk0_0(X0,sk0_57),sk0_1(X0,sk0_57)),relation_dom(identity_relation(sk0_57))))),
% 0.11/0.36 inference(resolution,[status(thm)],[f1262,f882])).
% 0.11/0.36 fof(f1285,plain,(
% 0.11/0.36 spl0_47|~spl0_45),
% 0.11/0.36 inference(split_clause,[status(thm)],[f1284,f1281,f1267])).
% 0.11/0.36 fof(f1286,plain,(
% 0.11/0.36 spl0_48 <=> sk0_57=identity_relation(X0)|sk0_0(X0,sk0_57)=sk0_1(X0,sk0_57)|in(ordered_pair(sk0_0(X0,sk0_57),sk0_1(X0,sk0_57)),relation_image(identity_relation(sk0_57),X1))|~in(ordered_pair(sk0_0(X0,sk0_57),sk0_1(X0,sk0_57)),X1)),
% 0.11/0.36 introduced(split_symbol_definition)).
% 0.11/0.36 fof(f1289,plain,(
% 0.11/0.36 ![X0,X1]: (sk0_57=identity_relation(X0)|sk0_0(X0,sk0_57)=sk0_1(X0,sk0_57)|~relation(identity_relation(sk0_57))|in(ordered_pair(sk0_0(X0,sk0_57),sk0_1(X0,sk0_57)),relation_image(identity_relation(sk0_57),X1))|~in(ordered_pair(sk0_0(X0,sk0_57),sk0_1(X0,sk0_57)),X1))),
% 0.11/0.36 inference(resolution,[status(thm)],[f1262,f859])).
% 0.11/0.36 fof(f1290,plain,(
% 0.11/0.36 spl0_48|~spl0_45),
% 0.11/0.36 inference(split_clause,[status(thm)],[f1289,f1286,f1267])).
% 0.11/0.36 fof(f1291,plain,(
% 0.11/0.36 ![X0]: (sk0_57=identity_relation(X0)|sk0_0(X0,sk0_57)=sk0_1(X0,sk0_57)|in(ordered_pair(ordered_pair(ordered_pair(sk0_0(X0,sk0_57),sk0_1(X0,sk0_57)),ordered_pair(sk0_0(X0,sk0_57),sk0_1(X0,sk0_57))),ordered_pair(ordered_pair(sk0_0(X0,sk0_57),sk0_1(X0,sk0_57)),ordered_pair(sk0_0(X0,sk0_57),sk0_1(X0,sk0_57)))),identity_relation(identity_relation(sk0_57))))),
% 0.11/0.36 inference(resolution,[status(thm)],[f1262,f1081])).
% 0.11/0.36 fof(f1300,plain,(
% 0.11/0.36 ![X0]: (relation(relation_dom(relation_dom(sk0_54(X0)))))),
% 0.11/0.36 inference(resolution,[status(thm)],[f1085,f483])).
% 0.11/0.36 fof(f1302,plain,(
% 0.11/0.36 ![X0,X1]: (relation_dom(relation_dom(sk0_54(X0)))=identity_relation(X1)|in(ordered_pair(sk0_0(X1,relation_dom(relation_dom(sk0_54(X0)))),sk0_1(X1,relation_dom(relation_dom(sk0_54(X0))))),relation_dom(relation_dom(sk0_54(X0))))|sk0_0(X1,relation_dom(relation_dom(sk0_54(X0))))=sk0_1(X1,relation_dom(relation_dom(sk0_54(X0)))))),
% 0.11/0.36 inference(resolution,[status(thm)],[f1300,f218])).
% 0.11/0.36 fof(f1303,plain,(
% 0.11/0.36 ![X0,X1]: (relation_dom(relation_dom(sk0_54(X0)))=identity_relation(X1)|in(ordered_pair(sk0_0(X1,relation_dom(relation_dom(sk0_54(X0)))),sk0_1(X1,relation_dom(relation_dom(sk0_54(X0))))),relation_dom(relation_dom(sk0_54(X0))))|in(sk0_0(X1,relation_dom(relation_dom(sk0_54(X0)))),X1))),
% 0.11/0.36 inference(resolution,[status(thm)],[f1300,f217])).
% 0.11/0.36 fof(f1328,plain,(
% 0.11/0.36 ![X0]: (sk0_54(X0)=empty_set)),
% 0.11/0.36 inference(resolution,[status(thm)],[f761,f552])).
% 0.11/0.36 fof(f1362,plain,(
% 0.11/0.36 ![X0]: (~X0=empty_set|identity_relation(X0)=empty_set)),
% 0.11/0.36 inference(backward_demodulation,[status(thm)],[f765,f1079])).
% 0.11/0.36 fof(f1363,plain,(
% 0.11/0.36 identity_relation(empty_set)=empty_set),
% 0.11/0.36 inference(destructive_equality_resolution,[status(esa)],[f1362])).
% 0.11/0.36 fof(f1435,plain,(
% 0.11/0.36 spl0_50 <=> sk0_57=identity_relation(empty_set)),
% 0.11/0.36 introduced(split_symbol_definition)).
% 0.11/0.36 fof(f1436,plain,(
% 0.11/0.36 sk0_57=identity_relation(empty_set)|~spl0_50),
% 0.11/0.36 inference(component_clause,[status(thm)],[f1435])).
% 0.11/0.36 fof(f1437,plain,(
% 0.11/0.36 ~sk0_57=identity_relation(empty_set)|spl0_50),
% 0.11/0.36 inference(component_clause,[status(thm)],[f1435])).
% 0.11/0.36 fof(f1438,plain,(
% 0.11/0.36 spl0_51 <=> in(sk0_0(empty_set,sk0_57),relation_dom(sk0_57))),
% 0.11/0.36 introduced(split_symbol_definition)).
% 0.11/0.36 fof(f1441,plain,(
% 0.11/0.36 sk0_57=identity_relation(empty_set)|in(sk0_0(empty_set,sk0_57),relation_dom(sk0_57))|~spl0_39),
% 0.11/0.36 inference(resolution,[status(thm)],[f1236,f867])).
% 0.11/0.36 fof(f1442,plain,(
% 0.11/0.36 spl0_50|spl0_51|~spl0_39),
% 0.11/0.36 inference(split_clause,[status(thm)],[f1441,f1435,f1438,f1235])).
% 0.11/0.36 fof(f1443,plain,(
% 0.11/0.36 spl0_52 <=> sk0_57=identity_relation(relation_dom(sk0_57))),
% 0.11/0.36 introduced(split_symbol_definition)).
% 0.11/0.36 fof(f1444,plain,(
% 0.11/0.36 sk0_57=identity_relation(relation_dom(sk0_57))|~spl0_52),
% 0.11/0.36 inference(component_clause,[status(thm)],[f1443])).
% 0.11/0.36 fof(f1465,plain,(
% 0.11/0.36 sk0_57=empty_set|~spl0_50),
% 0.11/0.36 inference(forward_demodulation,[status(thm)],[f1363,f1436])).
% 0.11/0.36 fof(f1482,plain,(
% 0.11/0.36 spl0_57 <=> sk0_57=identity_relation(X0)|in(sk0_0(X0,sk0_57),X0)|in(ordered_pair(ordered_pair(sk0_0(X0,sk0_57),sk0_1(X0,sk0_57)),ordered_pair(sk0_0(X0,sk0_57),sk0_1(X0,sk0_57))),relation_dom(identity_relation(identity_relation(sk0_57))))),
% 0.11/0.36 introduced(split_symbol_definition)).
% 0.11/0.36 fof(f1485,plain,(
% 0.11/0.36 spl0_58 <=> relation(identity_relation(identity_relation(sk0_57)))),
% 0.11/0.36 introduced(split_symbol_definition)).
% 0.11/0.36 fof(f1487,plain,(
% 0.11/0.36 ~relation(identity_relation(identity_relation(sk0_57)))|spl0_58),
% 0.11/0.36 inference(component_clause,[status(thm)],[f1485])).
% 0.11/0.36 fof(f1488,plain,(
% 0.11/0.36 ![X0]: (sk0_57=identity_relation(X0)|in(sk0_0(X0,sk0_57),X0)|~relation(identity_relation(identity_relation(sk0_57)))|in(ordered_pair(ordered_pair(sk0_0(X0,sk0_57),sk0_1(X0,sk0_57)),ordered_pair(sk0_0(X0,sk0_57),sk0_1(X0,sk0_57))),relation_dom(identity_relation(identity_relation(sk0_57)))))),
% 0.11/0.36 inference(resolution,[status(thm)],[f1277,f882])).
% 0.11/0.36 fof(f1489,plain,(
% 0.11/0.36 spl0_57|~spl0_58),
% 0.11/0.36 inference(split_clause,[status(thm)],[f1488,f1482,f1485])).
% 0.11/0.36 fof(f1490,plain,(
% 0.11/0.36 spl0_59 <=> sk0_57=identity_relation(X0)|in(sk0_0(X0,sk0_57),X0)|in(ordered_pair(ordered_pair(sk0_0(X0,sk0_57),sk0_1(X0,sk0_57)),ordered_pair(sk0_0(X0,sk0_57),sk0_1(X0,sk0_57))),relation_image(identity_relation(identity_relation(sk0_57)),X1))|~in(ordered_pair(ordered_pair(sk0_0(X0,sk0_57),sk0_1(X0,sk0_57)),ordered_pair(sk0_0(X0,sk0_57),sk0_1(X0,sk0_57))),X1)),
% 0.11/0.36 introduced(split_symbol_definition)).
% 0.11/0.36 fof(f1493,plain,(
% 0.11/0.36 ![X0,X1]: (sk0_57=identity_relation(X0)|in(sk0_0(X0,sk0_57),X0)|~relation(identity_relation(identity_relation(sk0_57)))|in(ordered_pair(ordered_pair(sk0_0(X0,sk0_57),sk0_1(X0,sk0_57)),ordered_pair(sk0_0(X0,sk0_57),sk0_1(X0,sk0_57))),relation_image(identity_relation(identity_relation(sk0_57)),X1))|~in(ordered_pair(ordered_pair(sk0_0(X0,sk0_57),sk0_1(X0,sk0_57)),ordered_pair(sk0_0(X0,sk0_57),sk0_1(X0,sk0_57))),X1))),
% 0.11/0.36 inference(resolution,[status(thm)],[f1277,f859])).
% 0.11/0.36 fof(f1494,plain,(
% 0.11/0.36 spl0_59|~spl0_58),
% 0.11/0.36 inference(split_clause,[status(thm)],[f1493,f1490,f1485])).
% 0.11/0.36 fof(f1495,plain,(
% 0.11/0.36 ![X0]: (sk0_57=identity_relation(X0)|in(sk0_0(X0,sk0_57),X0)|in(ordered_pair(ordered_pair(ordered_pair(ordered_pair(sk0_0(X0,sk0_57),sk0_1(X0,sk0_57)),ordered_pair(sk0_0(X0,sk0_57),sk0_1(X0,sk0_57))),ordered_pair(ordered_pair(sk0_0(X0,sk0_57),sk0_1(X0,sk0_57)),ordered_pair(sk0_0(X0,sk0_57),sk0_1(X0,sk0_57)))),ordered_pair(ordered_pair(ordered_pair(sk0_0(X0,sk0_57),sk0_1(X0,sk0_57)),ordered_pair(sk0_0(X0,sk0_57),sk0_1(X0,sk0_57))),ordered_pair(ordered_pair(sk0_0(X0,sk0_57),sk0_1(X0,sk0_57)),ordered_pair(sk0_0(X0,sk0_57),sk0_1(X0,sk0_57))))),identity_relation(identity_relation(identity_relation(sk0_57)))))),
% 0.11/0.36 inference(resolution,[status(thm)],[f1277,f1081])).
% 0.11/0.36 fof(f1497,plain,(
% 0.11/0.36 $false|spl0_58),
% 0.11/0.36 inference(forward_subsumption_resolution,[status(thm)],[f1487,f440])).
% 0.11/0.36 fof(f1498,plain,(
% 0.11/0.36 spl0_58),
% 0.11/0.36 inference(contradiction_clause,[status(thm)],[f1497])).
% 0.11/0.36 fof(f1500,plain,(
% 0.11/0.36 spl0_60 <=> sk0_57=identity_relation(X0)|sk0_0(X0,sk0_57)=sk0_1(X0,sk0_57)|in(ordered_pair(ordered_pair(sk0_0(X0,sk0_57),sk0_1(X0,sk0_57)),ordered_pair(sk0_0(X0,sk0_57),sk0_1(X0,sk0_57))),relation_dom(identity_relation(identity_relation(sk0_57))))),
% 0.11/0.36 introduced(split_symbol_definition)).
% 0.11/0.36 fof(f1503,plain,(
% 0.11/0.36 ![X0]: (sk0_57=identity_relation(X0)|sk0_0(X0,sk0_57)=sk0_1(X0,sk0_57)|~relation(identity_relation(identity_relation(sk0_57)))|in(ordered_pair(ordered_pair(sk0_0(X0,sk0_57),sk0_1(X0,sk0_57)),ordered_pair(sk0_0(X0,sk0_57),sk0_1(X0,sk0_57))),relation_dom(identity_relation(identity_relation(sk0_57)))))),
% 0.11/0.36 inference(resolution,[status(thm)],[f1291,f882])).
% 0.11/0.36 fof(f1504,plain,(
% 0.11/0.36 spl0_60|~spl0_58),
% 0.11/0.36 inference(split_clause,[status(thm)],[f1503,f1500,f1485])).
% 0.11/0.36 fof(f1505,plain,(
% 0.11/0.36 spl0_61 <=> sk0_57=identity_relation(X0)|sk0_0(X0,sk0_57)=sk0_1(X0,sk0_57)|in(ordered_pair(ordered_pair(sk0_0(X0,sk0_57),sk0_1(X0,sk0_57)),ordered_pair(sk0_0(X0,sk0_57),sk0_1(X0,sk0_57))),relation_image(identity_relation(identity_relation(sk0_57)),X1))|~in(ordered_pair(ordered_pair(sk0_0(X0,sk0_57),sk0_1(X0,sk0_57)),ordered_pair(sk0_0(X0,sk0_57),sk0_1(X0,sk0_57))),X1)),
% 0.11/0.36 introduced(split_symbol_definition)).
% 0.11/0.36 fof(f1508,plain,(
% 0.11/0.36 ![X0,X1]: (sk0_57=identity_relation(X0)|sk0_0(X0,sk0_57)=sk0_1(X0,sk0_57)|~relation(identity_relation(identity_relation(sk0_57)))|in(ordered_pair(ordered_pair(sk0_0(X0,sk0_57),sk0_1(X0,sk0_57)),ordered_pair(sk0_0(X0,sk0_57),sk0_1(X0,sk0_57))),relation_image(identity_relation(identity_relation(sk0_57)),X1))|~in(ordered_pair(ordered_pair(sk0_0(X0,sk0_57),sk0_1(X0,sk0_57)),ordered_pair(sk0_0(X0,sk0_57),sk0_1(X0,sk0_57))),X1))),
% 0.11/0.36 inference(resolution,[status(thm)],[f1291,f859])).
% 0.11/0.36 fof(f1509,plain,(
% 0.11/0.36 spl0_61|~spl0_58),
% 0.11/0.36 inference(split_clause,[status(thm)],[f1508,f1505,f1485])).
% 0.11/0.36 fof(f1513,plain,(
% 0.11/0.36 spl0_62 <=> sk0_57=identity_relation(X0)|in(sk0_0(X0,sk0_57),X0)|in(ordered_pair(ordered_pair(ordered_pair(sk0_0(X0,sk0_57),sk0_1(X0,sk0_57)),ordered_pair(sk0_0(X0,sk0_57),sk0_1(X0,sk0_57))),ordered_pair(ordered_pair(sk0_0(X0,sk0_57),sk0_1(X0,sk0_57)),ordered_pair(sk0_0(X0,sk0_57),sk0_1(X0,sk0_57)))),relation_dom(identity_relation(identity_relation(identity_relation(sk0_57)))))),
% 0.11/0.36 introduced(split_symbol_definition)).
% 0.11/0.36 fof(f1516,plain,(
% 0.11/0.36 spl0_63 <=> relation(identity_relation(identity_relation(identity_relation(sk0_57))))),
% 0.11/0.36 introduced(split_symbol_definition)).
% 0.11/0.36 fof(f1518,plain,(
% 0.11/0.36 ~relation(identity_relation(identity_relation(identity_relation(sk0_57))))|spl0_63),
% 0.11/0.36 inference(component_clause,[status(thm)],[f1516])).
% 0.11/0.36 fof(f1519,plain,(
% 0.11/0.36 ![X0]: (sk0_57=identity_relation(X0)|in(sk0_0(X0,sk0_57),X0)|~relation(identity_relation(identity_relation(identity_relation(sk0_57))))|in(ordered_pair(ordered_pair(ordered_pair(sk0_0(X0,sk0_57),sk0_1(X0,sk0_57)),ordered_pair(sk0_0(X0,sk0_57),sk0_1(X0,sk0_57))),ordered_pair(ordered_pair(sk0_0(X0,sk0_57),sk0_1(X0,sk0_57)),ordered_pair(sk0_0(X0,sk0_57),sk0_1(X0,sk0_57)))),relation_dom(identity_relation(identity_relation(identity_relation(sk0_57))))))),
% 0.11/0.36 inference(resolution,[status(thm)],[f1495,f882])).
% 0.11/0.36 fof(f1520,plain,(
% 0.11/0.36 spl0_62|~spl0_63),
% 0.11/0.36 inference(split_clause,[status(thm)],[f1519,f1513,f1516])).
% 0.11/0.36 fof(f1521,plain,(
% 0.11/0.36 spl0_64 <=> sk0_57=identity_relation(X0)|in(sk0_0(X0,sk0_57),X0)|in(ordered_pair(ordered_pair(ordered_pair(sk0_0(X0,sk0_57),sk0_1(X0,sk0_57)),ordered_pair(sk0_0(X0,sk0_57),sk0_1(X0,sk0_57))),ordered_pair(ordered_pair(sk0_0(X0,sk0_57),sk0_1(X0,sk0_57)),ordered_pair(sk0_0(X0,sk0_57),sk0_1(X0,sk0_57)))),relation_image(identity_relation(identity_relation(identity_relation(sk0_57))),X1))|~in(ordered_pair(ordered_pair(ordered_pair(sk0_0(X0,sk0_57),sk0_1(X0,sk0_57)),ordered_pair(sk0_0(X0,sk0_57),sk0_1(X0,sk0_57))),ordered_pair(ordered_pair(sk0_0(X0,sk0_57),sk0_1(X0,sk0_57)),ordered_pair(sk0_0(X0,sk0_57),sk0_1(X0,sk0_57)))),X1)),
% 0.11/0.36 introduced(split_symbol_definition)).
% 0.11/0.36 fof(f1524,plain,(
% 0.11/0.36 ![X0,X1]: (sk0_57=identity_relation(X0)|in(sk0_0(X0,sk0_57),X0)|~relation(identity_relation(identity_relation(identity_relation(sk0_57))))|in(ordered_pair(ordered_pair(ordered_pair(sk0_0(X0,sk0_57),sk0_1(X0,sk0_57)),ordered_pair(sk0_0(X0,sk0_57),sk0_1(X0,sk0_57))),ordered_pair(ordered_pair(sk0_0(X0,sk0_57),sk0_1(X0,sk0_57)),ordered_pair(sk0_0(X0,sk0_57),sk0_1(X0,sk0_57)))),relation_image(identity_relation(identity_relation(identity_relation(sk0_57))),X1))|~in(ordered_pair(ordered_pair(ordered_pair(sk0_0(X0,sk0_57),sk0_1(X0,sk0_57)),ordered_pair(sk0_0(X0,sk0_57),sk0_1(X0,sk0_57))),ordered_pair(ordered_pair(sk0_0(X0,sk0_57),sk0_1(X0,sk0_57)),ordered_pair(sk0_0(X0,sk0_57),sk0_1(X0,sk0_57)))),X1))),
% 0.11/0.36 inference(resolution,[status(thm)],[f1495,f859])).
% 0.11/0.36 fof(f1525,plain,(
% 0.11/0.36 spl0_64|~spl0_63),
% 0.11/0.36 inference(split_clause,[status(thm)],[f1524,f1521,f1516])).
% 0.11/0.36 fof(f1528,plain,(
% 0.11/0.36 $false|spl0_63),
% 0.11/0.36 inference(forward_subsumption_resolution,[status(thm)],[f1518,f440])).
% 0.11/0.36 fof(f1529,plain,(
% 0.11/0.36 spl0_63),
% 0.11/0.36 inference(contradiction_clause,[status(thm)],[f1528])).
% 0.11/0.36 fof(f1544,plain,(
% 0.11/0.36 ![X0,X1]: (~relation(set_intersection2(X0,X1))|~relation(X0)|subset(relation_dom(set_intersection2(X0,X1)),relation_dom(X0)))),
% 0.11/0.36 inference(resolution,[status(thm)],[f618,f635])).
% 0.11/0.36 fof(f1546,plain,(
% 0.11/0.36 ![X0,X1]: (subset(set_intersection2(X0,X1),X1))),
% 0.11/0.36 inference(paramodulation,[status(thm)],[f208,f618])).
% 0.11/0.36 fof(f1548,plain,(
% 0.11/0.36 ![X0]: (set_intersection2(empty_set,X0)=empty_set)),
% 0.11/0.36 inference(paramodulation,[status(thm)],[f208,f642])).
% 0.11/0.36 fof(f1554,plain,(
% 0.11/0.36 ![X0,X1]: (~relation(set_difference(X0,X1))|~relation(X0)|subset(relation_dom(set_difference(X0,X1)),relation_dom(X0)))),
% 0.11/0.36 inference(resolution,[status(thm)],[f661,f635])).
% 0.11/0.36 fof(f1566,plain,(
% 0.11/0.36 spl0_65 <=> empty(relation_dom(sk0_57))),
% 0.11/0.36 introduced(split_symbol_definition)).
% 0.11/0.36 fof(f1569,plain,(
% 0.11/0.36 ~empty(relation_dom(sk0_57))|sk0_57=identity_relation(relation_dom(sk0_57))|~spl0_39),
% 0.11/0.36 inference(resolution,[status(thm)],[f775,f1236])).
% 0.11/0.36 fof(f1570,plain,(
% 0.11/0.36 ~spl0_65|spl0_52|~spl0_39),
% 0.11/0.36 inference(split_clause,[status(thm)],[f1569,f1566,f1443,f1235])).
% 0.11/0.36 fof(f1571,plain,(
% 0.11/0.36 spl0_66 <=> sk0_57=identity_relation(X0)|in(sk0_0(X0,sk0_57),X0)),
% 0.11/0.36 introduced(split_symbol_definition)).
% 0.11/0.36 fof(f1574,plain,(
% 0.11/0.36 ![X0]: (~empty(relation_dom(sk0_57))|sk0_57=identity_relation(X0)|in(sk0_0(X0,sk0_57),X0)|~spl0_39)),
% 0.11/0.36 inference(resolution,[status(thm)],[f775,f1236])).
% 0.11/0.36 fof(f1575,plain,(
% 0.11/0.36 ~spl0_65|spl0_66|~spl0_39),
% 0.11/0.36 inference(split_clause,[status(thm)],[f1574,f1566,f1571,f1235])).
% 0.11/0.36 fof(f1580,plain,(
% 0.11/0.36 spl0_67 <=> empty(identity_relation(identity_relation(identity_relation(sk0_57))))),
% 0.11/0.36 introduced(split_symbol_definition)).
% 0.11/0.36 fof(f1583,plain,(
% 0.11/0.36 ![X0]: (~empty(identity_relation(identity_relation(identity_relation(sk0_57))))|sk0_57=identity_relation(X0)|in(sk0_0(X0,sk0_57),X0))),
% 0.11/0.36 inference(resolution,[status(thm)],[f775,f1495])).
% 0.11/0.36 fof(f1584,plain,(
% 0.11/0.36 ~spl0_67|spl0_66),
% 0.11/0.36 inference(split_clause,[status(thm)],[f1583,f1580,f1571])).
% 0.11/0.36 fof(f1585,plain,(
% 0.11/0.36 spl0_68 <=> empty(identity_relation(identity_relation(sk0_57)))),
% 0.11/0.36 introduced(split_symbol_definition)).
% 0.11/0.36 fof(f1588,plain,(
% 0.11/0.36 spl0_69 <=> sk0_57=identity_relation(X0)|sk0_0(X0,sk0_57)=sk0_1(X0,sk0_57)),
% 0.11/0.36 introduced(split_symbol_definition)).
% 0.11/0.36 fof(f1591,plain,(
% 0.11/0.36 ![X0]: (~empty(identity_relation(identity_relation(sk0_57)))|sk0_57=identity_relation(X0)|sk0_0(X0,sk0_57)=sk0_1(X0,sk0_57))),
% 0.11/0.36 inference(resolution,[status(thm)],[f775,f1291])).
% 0.11/0.36 fof(f1592,plain,(
% 0.11/0.36 ~spl0_68|spl0_69),
% 0.11/0.36 inference(split_clause,[status(thm)],[f1591,f1585,f1588])).
% 0.11/0.36 fof(f1593,plain,(
% 0.11/0.36 ![X0]: (~empty(identity_relation(identity_relation(sk0_57)))|sk0_57=identity_relation(X0)|in(sk0_0(X0,sk0_57),X0))),
% 0.11/0.36 inference(resolution,[status(thm)],[f775,f1277])).
% 0.11/0.36 fof(f1594,plain,(
% 0.11/0.36 ~spl0_68|spl0_66),
% 0.11/0.36 inference(split_clause,[status(thm)],[f1593,f1585,f1571])).
% 0.11/0.36 fof(f1596,plain,(
% 0.11/0.36 spl0_70 <=> empty(identity_relation(sk0_57))),
% 0.11/0.36 introduced(split_symbol_definition)).
% 0.11/0.36 fof(f1599,plain,(
% 0.11/0.36 ![X0]: (~empty(identity_relation(sk0_57))|sk0_57=identity_relation(X0)|sk0_0(X0,sk0_57)=sk0_1(X0,sk0_57))),
% 0.11/0.36 inference(resolution,[status(thm)],[f775,f1262])).
% 0.11/0.36 fof(f1600,plain,(
% 0.11/0.36 ~spl0_70|spl0_69),
% 0.11/0.36 inference(split_clause,[status(thm)],[f1599,f1596,f1588])).
% 0.11/0.36 fof(f1601,plain,(
% 0.11/0.36 ![X0]: (~empty(identity_relation(sk0_57))|sk0_57=identity_relation(X0)|in(sk0_0(X0,sk0_57),X0))),
% 0.11/0.36 inference(resolution,[status(thm)],[f775,f1245])).
% 0.11/0.36 fof(f1602,plain,(
% 0.11/0.36 ~spl0_70|spl0_66),
% 0.11/0.36 inference(split_clause,[status(thm)],[f1601,f1596,f1571])).
% 0.11/0.36 fof(f1603,plain,(
% 0.11/0.36 spl0_71 <=> empty(sk0_57)),
% 0.11/0.36 introduced(split_symbol_definition)).
% 0.11/0.36 fof(f1606,plain,(
% 0.11/0.36 ![X0]: (~empty(sk0_57)|sk0_57=identity_relation(X0)|sk0_0(X0,sk0_57)=sk0_1(X0,sk0_57))),
% 0.11/0.36 inference(resolution,[status(thm)],[f775,f1123])).
% 0.11/0.36 fof(f1607,plain,(
% 0.11/0.36 ~spl0_71|spl0_69),
% 0.11/0.36 inference(split_clause,[status(thm)],[f1606,f1603,f1588])).
% 0.11/0.36 fof(f1608,plain,(
% 0.11/0.36 ![X0]: (~empty(sk0_57)|sk0_57=identity_relation(X0)|in(sk0_0(X0,sk0_57),X0))),
% 0.11/0.36 inference(resolution,[status(thm)],[f775,f1116])).
% 0.11/0.36 fof(f1609,plain,(
% 0.11/0.36 ~spl0_71|spl0_66),
% 0.11/0.36 inference(split_clause,[status(thm)],[f1608,f1603,f1571])).
% 0.11/0.36 fof(f1623,plain,(
% 0.11/0.36 ![X0,X1]: (~relation(X0)|~relation(set_union2(X0,X1))|subset(relation_dom(X0),relation_dom(set_union2(X0,X1))))),
% 0.11/0.36 inference(resolution,[status(thm)],[f776,f635])).
% 0.11/0.36 fof(f1627,plain,(
% 0.11/0.36 ![X0,X1]: (subset(X0,set_union2(X1,X0)))),
% 0.11/0.36 inference(paramodulation,[status(thm)],[f207,f776])).
% 0.11/0.36 fof(f1630,plain,(
% 0.11/0.36 ![X0,X1]: (~relation(set_intersection2(X0,X1))|~relation(X1)|subset(relation_dom(set_intersection2(X0,X1)),relation_dom(X1)))),
% 0.11/0.36 inference(resolution,[status(thm)],[f1546,f635])).
% 0.11/0.36 fof(f1644,plain,(
% 0.11/0.36 ![X0,X1]: (~relation(X0)|X0=relation_dom_restriction(sk0_57,X1)|in(ordered_pair(sk0_2(X1,X0,sk0_57),sk0_3(X1,X0,sk0_57)),X0)|in(sk0_2(X1,X0,sk0_57),X1))),
% 0.11/0.36 inference(resolution,[status(thm)],[f232,f613])).
% 0.11/0.36 fof(f1804,plain,(
% 0.11/0.36 in(sk0_58,relation_image(empty_set,sk0_59))|~spl0_50|~spl0_0),
% 0.11/0.36 inference(backward_demodulation,[status(thm)],[f1465,f828])).
% 0.11/0.36 fof(f1835,plain,(
% 0.11/0.36 spl0_72 <=> relation(identity_relation(relation_image(empty_set,sk0_59)))),
% 0.11/0.36 introduced(split_symbol_definition)).
% 0.11/0.36 fof(f1837,plain,(
% 0.11/0.36 ~relation(identity_relation(relation_image(empty_set,sk0_59)))|spl0_72),
% 0.11/0.36 inference(component_clause,[status(thm)],[f1835])).
% 0.11/0.36 fof(f1851,plain,(
% 0.11/0.36 $false|spl0_72),
% 0.11/0.36 inference(forward_subsumption_resolution,[status(thm)],[f1837,f440])).
% 0.11/0.36 fof(f1852,plain,(
% 0.11/0.36 spl0_72),
% 0.11/0.36 inference(contradiction_clause,[status(thm)],[f1851])).
% 0.11/0.36 fof(f1853,plain,(
% 0.11/0.36 spl0_75 <=> 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)),
% 0.11/0.36 introduced(split_symbol_definition)).
% 0.11/0.36 fof(f1885,plain,(
% 0.11/0.36 spl0_76 <=> relation(identity_relation(identity_relation(relation_image(empty_set,sk0_59))))),
% 0.11/0.36 introduced(split_symbol_definition)).
% 0.11/0.36 fof(f1887,plain,(
% 0.11/0.36 ~relation(identity_relation(identity_relation(relation_image(empty_set,sk0_59))))|spl0_76),
% 0.11/0.36 inference(component_clause,[status(thm)],[f1885])).
% 0.11/0.36 fof(f1901,plain,(
% 0.11/0.36 $false|spl0_76),
% 0.11/0.36 inference(forward_subsumption_resolution,[status(thm)],[f1887,f440])).
% 0.11/0.36 fof(f1902,plain,(
% 0.11/0.36 spl0_76),
% 0.11/0.36 inference(contradiction_clause,[status(thm)],[f1901])).
% 0.11/0.36 fof(f2035,plain,(
% 0.11/0.36 spl0_79 <=> subset(relation_dom(set_intersection2(empty_set,X0)),relation_dom(empty_set))),
% 0.11/0.36 introduced(split_symbol_definition)).
% 0.11/0.36 fof(f2038,plain,(
% 0.11/0.36 ![X0]: (~relation(empty_set)|~relation(empty_set)|subset(relation_dom(set_intersection2(empty_set,X0)),relation_dom(empty_set)))),
% 0.11/0.36 inference(paramodulation,[status(thm)],[f1548,f1544])).
% 0.11/0.36 fof(f2039,plain,(
% 0.11/0.36 ~spl0_6|spl0_79),
% 0.11/0.36 inference(split_clause,[status(thm)],[f2038,f907,f2035])).
% 0.11/0.36 fof(f2040,plain,(
% 0.11/0.36 spl0_80 <=> ~relation(X0)|subset(relation_dom(set_intersection2(X0,empty_set)),relation_dom(X0))),
% 0.11/0.36 introduced(split_symbol_definition)).
% 0.11/0.36 fof(f2043,plain,(
% 0.11/0.36 ![X0]: (~relation(empty_set)|~relation(X0)|subset(relation_dom(set_intersection2(X0,empty_set)),relation_dom(X0)))),
% 0.11/0.36 inference(paramodulation,[status(thm)],[f642,f1544])).
% 0.11/0.36 fof(f2044,plain,(
% 0.11/0.36 ~spl0_6|spl0_80),
% 0.11/0.36 inference(split_clause,[status(thm)],[f2043,f907,f2040])).
% 0.11/0.36 fof(f2055,plain,(
% 0.11/0.36 spl0_81 <=> subset(relation_dom(set_difference(empty_set,X0)),relation_dom(empty_set))),
% 0.11/0.36 introduced(split_symbol_definition)).
% 0.11/0.36 fof(f2058,plain,(
% 0.11/0.36 ![X0]: (~relation(empty_set)|~relation(empty_set)|subset(relation_dom(set_difference(empty_set,X0)),relation_dom(empty_set)))),
% 0.11/0.36 inference(paramodulation,[status(thm)],[f721,f1554])).
% 0.11/0.36 fof(f2059,plain,(
% 0.11/0.36 ~spl0_6|spl0_81),
% 0.11/0.36 inference(split_clause,[status(thm)],[f2058,f907,f2055])).
% 0.11/0.36 fof(f2066,plain,(
% 0.11/0.36 spl0_82 <=> ~relation(X0)|subset(relation_dom(empty_set),relation_dom(set_union2(empty_set,X0)))),
% 0.11/0.36 introduced(split_symbol_definition)).
% 0.11/0.36 fof(f2069,plain,(
% 0.11/0.36 ![X0]: (~relation(empty_set)|~relation(X0)|subset(relation_dom(empty_set),relation_dom(set_union2(empty_set,X0))))),
% 0.11/0.36 inference(paramodulation,[status(thm)],[f1107,f1623])).
% 0.11/0.36 fof(f2070,plain,(
% 0.11/0.36 ~spl0_6|spl0_82),
% 0.11/0.36 inference(split_clause,[status(thm)],[f2069,f907,f2066])).
% 0.11/0.36 fof(f2086,plain,(
% 0.11/0.36 ![X0,X1]: (~relation(X0)|~relation(set_union2(X1,X0))|subset(relation_dom(X0),relation_dom(set_union2(X1,X0))))),
% 0.11/0.36 inference(resolution,[status(thm)],[f1627,f635])).
% 0.11/0.36 fof(f2094,plain,(
% 0.11/0.36 ![X0]: (relation(relation_inverse(identity_relation(X0))))),
% 0.11/0.36 inference(resolution,[status(thm)],[f435,f440])).
% 0.11/0.36 fof(f2096,plain,(
% 0.11/0.36 relation(relation_inverse(empty_set))),
% 0.11/0.36 inference(resolution,[status(thm)],[f435,f474])).
% 0.11/0.36 fof(f2142,plain,(
% 0.11/0.36 ![X0]: (relation_dom(relation_inverse(identity_relation(X0)))=empty_set|~relation_rng(relation_inverse(identity_relation(X0)))=empty_set)),
% 0.11/0.36 inference(resolution,[status(thm)],[f2094,f754])).
% 0.11/0.36 fof(f2143,plain,(
% 0.11/0.36 ![X0]: (~relation_dom(relation_inverse(identity_relation(X0)))=empty_set|relation_rng(relation_inverse(identity_relation(X0)))=empty_set)),
% 0.11/0.36 inference(resolution,[status(thm)],[f2094,f753])).
% 0.11/0.36 fof(f2144,plain,(
% 0.11/0.36 ![X0]: (~relation_dom(relation_inverse(identity_relation(X0)))=empty_set|relation_inverse(identity_relation(X0))=empty_set)),
% 0.11/0.36 inference(resolution,[status(thm)],[f2094,f749])).
% 0.11/0.36 fof(f2161,plain,(
% 0.11/0.36 spl0_89 <=> empty_set=identity_relation(singleton(X0))|~in(ordered_pair(X0,sk0_1(singleton(X0),empty_set)),empty_set)|~in(sk0_0(singleton(X0),empty_set),singleton(X0))|~sk0_0(singleton(X0),empty_set)=sk0_1(singleton(X0),empty_set)|empty_set=identity_relation(singleton(X0))),
% 0.11/0.36 introduced(split_symbol_definition)).
% 0.11/0.36 fof(f2185,plain,(
% 0.11/0.36 spl0_93 <=> ~in(ordered_pair(X0,X1),empty_set)|in(X0,empty_set)),
% 0.11/0.36 introduced(split_symbol_definition)).
% 0.11/0.36 fof(f2268,plain,(
% 0.11/0.36 spl0_98 <=> ~relation(X0)|subset(relation_dom(set_intersection2(empty_set,X0)),relation_dom(X0))),
% 0.11/0.36 introduced(split_symbol_definition)).
% 0.11/0.36 fof(f2271,plain,(
% 0.11/0.36 ![X0]: (~relation(empty_set)|~relation(X0)|subset(relation_dom(set_intersection2(empty_set,X0)),relation_dom(X0)))),
% 0.11/0.36 inference(paramodulation,[status(thm)],[f1548,f1630])).
% 0.11/0.36 fof(f2272,plain,(
% 0.11/0.36 ~spl0_6|spl0_98),
% 0.11/0.36 inference(split_clause,[status(thm)],[f2271,f907,f2268])).
% 0.11/0.36 fof(f2273,plain,(
% 0.11/0.36 spl0_99 <=> subset(relation_dom(set_intersection2(X0,empty_set)),relation_dom(empty_set))),
% 0.11/0.36 introduced(split_symbol_definition)).
% 0.11/0.36 fof(f2276,plain,(
% 0.11/0.36 ![X0]: (~relation(empty_set)|~relation(empty_set)|subset(relation_dom(set_intersection2(X0,empty_set)),relation_dom(empty_set)))),
% 0.11/0.36 inference(paramodulation,[status(thm)],[f642,f1630])).
% 0.11/0.36 fof(f2277,plain,(
% 0.11/0.36 ~spl0_6|spl0_99),
% 0.11/0.36 inference(split_clause,[status(thm)],[f2276,f907,f2273])).
% 0.11/0.36 fof(f2314,plain,(
% 0.11/0.36 spl0_100 <=> ~relation(X0)|subset(relation_dom(empty_set),relation_dom(set_union2(X0,empty_set)))),
% 0.11/0.36 introduced(split_symbol_definition)).
% 0.11/0.36 fof(f2317,plain,(
% 0.11/0.36 ![X0]: (~relation(empty_set)|~relation(X0)|subset(relation_dom(empty_set),relation_dom(set_union2(X0,empty_set))))),
% 0.11/0.36 inference(paramodulation,[status(thm)],[f621,f2086])).
% 0.11/0.36 fof(f2318,plain,(
% 0.11/0.36 ~spl0_6|spl0_100),
% 0.11/0.36 inference(split_clause,[status(thm)],[f2317,f907,f2314])).
% 0.11/0.36 fof(f2457,plain,(
% 0.11/0.36 spl0_103 <=> relation(sk0_53)),
% 0.11/0.36 introduced(split_symbol_definition)).
% 0.11/0.36 fof(f2459,plain,(
% 0.11/0.36 ~relation(sk0_53)|spl0_103),
% 0.11/0.36 inference(component_clause,[status(thm)],[f2457])).
% 0.11/0.36 fof(f2483,plain,(
% 0.11/0.36 $false|spl0_103),
% 0.11/0.36 inference(forward_subsumption_resolution,[status(thm)],[f2459,f549])).
% 0.11/0.36 fof(f2484,plain,(
% 0.11/0.36 spl0_103),
% 0.11/0.36 inference(contradiction_clause,[status(thm)],[f2483])).
% 0.11/0.36 fof(f2529,plain,(
% 0.11/0.36 spl0_112 <=> relation(identity_relation(relation_image(identity_relation(relation_image(empty_set,sk0_59)),sk0_56(sk0_58))))),
% 0.11/0.36 introduced(split_symbol_definition)).
% 0.11/0.36 fof(f2531,plain,(
% 0.11/0.36 ~relation(identity_relation(relation_image(identity_relation(relation_image(empty_set,sk0_59)),sk0_56(sk0_58))))|spl0_112),
% 0.11/0.36 inference(component_clause,[status(thm)],[f2529])).
% 0.11/0.36 fof(f2546,plain,(
% 0.11/0.36 $false|spl0_112),
% 0.11/0.36 inference(forward_subsumption_resolution,[status(thm)],[f2531,f440])).
% 0.11/0.36 fof(f2547,plain,(
% 0.11/0.36 spl0_112),
% 0.11/0.36 inference(contradiction_clause,[status(thm)],[f2546])).
% 0.11/0.36 fof(f2549,plain,(
% 0.11/0.36 spl0_115 <=> relation(identity_relation(relation_image(identity_relation(relation_image(empty_set,sk0_59)),singleton(sk0_58))))),
% 0.11/0.36 introduced(split_symbol_definition)).
% 0.11/0.36 fof(f2551,plain,(
% 0.11/0.36 ~relation(identity_relation(relation_image(identity_relation(relation_image(empty_set,sk0_59)),singleton(sk0_58))))|spl0_115),
% 0.11/0.36 inference(component_clause,[status(thm)],[f2549])).
% 0.11/0.36 fof(f2566,plain,(
% 0.11/0.36 $false|spl0_115),
% 0.11/0.36 inference(forward_subsumption_resolution,[status(thm)],[f2551,f440])).
% 0.11/0.36 fof(f2567,plain,(
% 0.11/0.36 spl0_115),
% 0.11/0.36 inference(contradiction_clause,[status(thm)],[f2566])).
% 0.11/0.36 fof(f2569,plain,(
% 0.11/0.36 spl0_118 <=> relation(identity_relation(relation_image(identity_relation(relation_image(empty_set,sk0_59)),sk0_66(sk0_58))))),
% 0.11/0.36 introduced(split_symbol_definition)).
% 0.11/0.36 fof(f2571,plain,(
% 0.11/0.36 ~relation(identity_relation(relation_image(identity_relation(relation_image(empty_set,sk0_59)),sk0_66(sk0_58))))|spl0_118),
% 0.11/0.36 inference(component_clause,[status(thm)],[f2569])).
% 0.11/0.36 fof(f2586,plain,(
% 0.11/0.36 $false|spl0_118),
% 0.11/0.36 inference(forward_subsumption_resolution,[status(thm)],[f2571,f440])).
% 0.11/0.36 fof(f2587,plain,(
% 0.11/0.36 spl0_118),
% 0.11/0.36 inference(contradiction_clause,[status(thm)],[f2586])).
% 0.11/0.36 fof(f2606,plain,(
% 0.11/0.36 spl0_122 <=> relation(relation_inverse(empty_set))),
% 0.11/0.36 introduced(split_symbol_definition)).
% 0.11/0.36 fof(f2608,plain,(
% 0.11/0.36 ~relation(relation_inverse(empty_set))|spl0_122),
% 0.11/0.36 inference(component_clause,[status(thm)],[f2606])).
% 0.11/0.36 fof(f2632,plain,(
% 0.11/0.36 $false|spl0_122),
% 0.11/0.36 inference(forward_subsumption_resolution,[status(thm)],[f2608,f2096])).
% 0.11/0.36 fof(f2633,plain,(
% 0.11/0.36 spl0_122),
% 0.11/0.36 inference(contradiction_clause,[status(thm)],[f2632])).
% 0.11/0.36 fof(f2740,plain,(
% 0.11/0.36 ![X0,X1]: (relation_dom(relation_dom(empty_set))=identity_relation(X0)|in(ordered_pair(sk0_0(X0,relation_dom(relation_dom(sk0_54(X1)))),sk0_1(X0,relation_dom(relation_dom(sk0_54(X1))))),relation_dom(relation_dom(sk0_54(X1))))|sk0_0(X0,relation_dom(relation_dom(sk0_54(X1))))=sk0_1(X0,relation_dom(relation_dom(sk0_54(X1)))))),
% 0.11/0.36 inference(forward_demodulation,[status(thm)],[f1328,f1302])).
% 0.11/0.36 fof(f2741,plain,(
% 0.11/0.36 ![X0,X1]: (relation_dom(empty_set)=identity_relation(X0)|in(ordered_pair(sk0_0(X0,relation_dom(relation_dom(sk0_54(X1)))),sk0_1(X0,relation_dom(relation_dom(sk0_54(X1))))),relation_dom(relation_dom(sk0_54(X1))))|sk0_0(X0,relation_dom(relation_dom(sk0_54(X1))))=sk0_1(X0,relation_dom(relation_dom(sk0_54(X1)))))),
% 0.11/0.36 inference(forward_demodulation,[status(thm)],[f741,f2740])).
% 0.11/0.36 fof(f2742,plain,(
% 0.11/0.36 ![X0,X1]: (empty_set=identity_relation(X0)|in(ordered_pair(sk0_0(X0,relation_dom(relation_dom(sk0_54(X1)))),sk0_1(X0,relation_dom(relation_dom(sk0_54(X1))))),relation_dom(relation_dom(sk0_54(X1))))|sk0_0(X0,relation_dom(relation_dom(sk0_54(X1))))=sk0_1(X0,relation_dom(relation_dom(sk0_54(X1)))))),
% 0.11/0.36 inference(forward_demodulation,[status(thm)],[f741,f2741])).
% 0.11/0.36 fof(f2743,plain,(
% 0.11/0.36 ![X0,X1]: (empty_set=identity_relation(X0)|in(ordered_pair(sk0_0(X0,relation_dom(relation_dom(empty_set))),sk0_1(X0,relation_dom(relation_dom(sk0_54(X1))))),relation_dom(relation_dom(sk0_54(X1))))|sk0_0(X0,relation_dom(relation_dom(sk0_54(X1))))=sk0_1(X0,relation_dom(relation_dom(sk0_54(X1)))))),
% 0.11/0.36 inference(forward_demodulation,[status(thm)],[f1328,f2742])).
% 0.11/0.36 fof(f2744,plain,(
% 0.11/0.36 ![X0,X1]: (empty_set=identity_relation(X0)|in(ordered_pair(sk0_0(X0,relation_dom(empty_set)),sk0_1(X0,relation_dom(relation_dom(sk0_54(X1))))),relation_dom(relation_dom(sk0_54(X1))))|sk0_0(X0,relation_dom(relation_dom(sk0_54(X1))))=sk0_1(X0,relation_dom(relation_dom(sk0_54(X1)))))),
% 0.11/0.36 inference(forward_demodulation,[status(thm)],[f741,f2743])).
% 0.11/0.36 fof(f2745,plain,(
% 0.11/0.36 ![X0,X1]: (empty_set=identity_relation(X0)|in(ordered_pair(sk0_0(X0,empty_set),sk0_1(X0,relation_dom(relation_dom(sk0_54(X1))))),relation_dom(relation_dom(sk0_54(X1))))|sk0_0(X0,relation_dom(relation_dom(sk0_54(X1))))=sk0_1(X0,relation_dom(relation_dom(sk0_54(X1)))))),
% 0.11/0.36 inference(forward_demodulation,[status(thm)],[f741,f2744])).
% 0.11/0.36 fof(f2746,plain,(
% 0.11/0.36 ![X0,X1]: (empty_set=identity_relation(X0)|in(ordered_pair(sk0_0(X0,empty_set),sk0_1(X0,relation_dom(relation_dom(empty_set)))),relation_dom(relation_dom(sk0_54(X1))))|sk0_0(X0,relation_dom(relation_dom(sk0_54(X1))))=sk0_1(X0,relation_dom(relation_dom(sk0_54(X1)))))),
% 0.11/0.36 inference(forward_demodulation,[status(thm)],[f1328,f2745])).
% 0.11/0.36 fof(f2747,plain,(
% 0.11/0.36 ![X0,X1]: (empty_set=identity_relation(X0)|in(ordered_pair(sk0_0(X0,empty_set),sk0_1(X0,relation_dom(empty_set))),relation_dom(relation_dom(sk0_54(X1))))|sk0_0(X0,relation_dom(relation_dom(sk0_54(X1))))=sk0_1(X0,relation_dom(relation_dom(sk0_54(X1)))))),
% 0.11/0.36 inference(forward_demodulation,[status(thm)],[f741,f2746])).
% 0.11/0.36 fof(f2748,plain,(
% 0.11/0.36 ![X0,X1]: (empty_set=identity_relation(X0)|in(ordered_pair(sk0_0(X0,empty_set),sk0_1(X0,empty_set)),relation_dom(relation_dom(sk0_54(X1))))|sk0_0(X0,relation_dom(relation_dom(sk0_54(X1))))=sk0_1(X0,relation_dom(relation_dom(sk0_54(X1)))))),
% 0.11/0.36 inference(forward_demodulation,[status(thm)],[f741,f2747])).
% 0.11/0.36 fof(f2749,plain,(
% 0.11/0.36 ![X0,X1]: (empty_set=identity_relation(X0)|in(ordered_pair(sk0_0(X0,empty_set),sk0_1(X0,empty_set)),relation_dom(relation_dom(empty_set)))|sk0_0(X0,relation_dom(relation_dom(sk0_54(X1))))=sk0_1(X0,relation_dom(relation_dom(sk0_54(X1)))))),
% 0.11/0.36 inference(forward_demodulation,[status(thm)],[f1328,f2748])).
% 0.11/0.36 fof(f2750,plain,(
% 0.11/0.36 ![X0,X1]: (empty_set=identity_relation(X0)|in(ordered_pair(sk0_0(X0,empty_set),sk0_1(X0,empty_set)),relation_dom(empty_set))|sk0_0(X0,relation_dom(relation_dom(sk0_54(X1))))=sk0_1(X0,relation_dom(relation_dom(sk0_54(X1)))))),
% 0.11/0.36 inference(forward_demodulation,[status(thm)],[f741,f2749])).
% 0.11/0.36 fof(f2751,plain,(
% 0.11/0.36 ![X0,X1]: (empty_set=identity_relation(X0)|in(ordered_pair(sk0_0(X0,empty_set),sk0_1(X0,empty_set)),empty_set)|sk0_0(X0,relation_dom(relation_dom(sk0_54(X1))))=sk0_1(X0,relation_dom(relation_dom(sk0_54(X1)))))),
% 0.11/0.36 inference(forward_demodulation,[status(thm)],[f741,f2750])).
% 0.11/0.36 fof(f2752,plain,(
% 0.11/0.36 ![X0,X1]: (empty_set=identity_relation(X0)|in(ordered_pair(sk0_0(X0,empty_set),sk0_1(X0,empty_set)),empty_set)|sk0_0(X0,relation_dom(relation_dom(empty_set)))=sk0_1(X0,relation_dom(relation_dom(sk0_54(X1)))))),
% 0.11/0.36 inference(forward_demodulation,[status(thm)],[f1328,f2751])).
% 0.11/0.36 fof(f2753,plain,(
% 0.11/0.36 ![X0,X1]: (empty_set=identity_relation(X0)|in(ordered_pair(sk0_0(X0,empty_set),sk0_1(X0,empty_set)),empty_set)|sk0_0(X0,relation_dom(empty_set))=sk0_1(X0,relation_dom(relation_dom(sk0_54(X1)))))),
% 0.11/0.36 inference(forward_demodulation,[status(thm)],[f741,f2752])).
% 0.11/0.36 fof(f2754,plain,(
% 0.11/0.36 ![X0,X1]: (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_dom(relation_dom(sk0_54(X1)))))),
% 0.11/0.36 inference(forward_demodulation,[status(thm)],[f741,f2753])).
% 0.11/0.36 fof(f2755,plain,(
% 0.11/0.36 ![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_dom(relation_dom(empty_set))))),
% 0.11/0.36 inference(forward_demodulation,[status(thm)],[f1328,f2754])).
% 0.11/0.36 fof(f2756,plain,(
% 0.11/0.36 ![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_dom(empty_set)))),
% 0.11/0.36 inference(forward_demodulation,[status(thm)],[f741,f2755])).
% 0.11/0.36 fof(f2757,plain,(
% 0.11/0.36 ![X0,X1]: (relation_dom(relation_dom(empty_set))=identity_relation(X0)|in(ordered_pair(sk0_0(X0,relation_dom(relation_dom(sk0_54(X1)))),sk0_1(X0,relation_dom(relation_dom(sk0_54(X1))))),relation_dom(relation_dom(sk0_54(X1))))|in(sk0_0(X0,relation_dom(relation_dom(sk0_54(X1)))),X0))),
% 0.11/0.36 inference(forward_demodulation,[status(thm)],[f1328,f1303])).
% 0.11/0.36 fof(f2758,plain,(
% 0.11/0.36 ![X0,X1]: (relation_dom(empty_set)=identity_relation(X0)|in(ordered_pair(sk0_0(X0,relation_dom(relation_dom(sk0_54(X1)))),sk0_1(X0,relation_dom(relation_dom(sk0_54(X1))))),relation_dom(relation_dom(sk0_54(X1))))|in(sk0_0(X0,relation_dom(relation_dom(sk0_54(X1)))),X0))),
% 0.11/0.36 inference(forward_demodulation,[status(thm)],[f741,f2757])).
% 0.11/0.36 fof(f2759,plain,(
% 0.11/0.36 ![X0,X1]: (empty_set=identity_relation(X0)|in(ordered_pair(sk0_0(X0,relation_dom(relation_dom(sk0_54(X1)))),sk0_1(X0,relation_dom(relation_dom(sk0_54(X1))))),relation_dom(relation_dom(sk0_54(X1))))|in(sk0_0(X0,relation_dom(relation_dom(sk0_54(X1)))),X0))),
% 0.11/0.36 inference(forward_demodulation,[status(thm)],[f741,f2758])).
% 0.11/0.36 fof(f2760,plain,(
% 0.11/0.36 ![X0,X1]: (empty_set=identity_relation(X0)|in(ordered_pair(sk0_0(X0,relation_dom(relation_dom(empty_set))),sk0_1(X0,relation_dom(relation_dom(sk0_54(X1))))),relation_dom(relation_dom(sk0_54(X1))))|in(sk0_0(X0,relation_dom(relation_dom(sk0_54(X1)))),X0))),
% 0.11/0.36 inference(forward_demodulation,[status(thm)],[f1328,f2759])).
% 0.11/0.36 fof(f2761,plain,(
% 0.11/0.36 ![X0,X1]: (empty_set=identity_relation(X0)|in(ordered_pair(sk0_0(X0,relation_dom(empty_set)),sk0_1(X0,relation_dom(relation_dom(sk0_54(X1))))),relation_dom(relation_dom(sk0_54(X1))))|in(sk0_0(X0,relation_dom(relation_dom(sk0_54(X1)))),X0))),
% 0.11/0.36 inference(forward_demodulation,[status(thm)],[f741,f2760])).
% 0.11/0.36 fof(f2762,plain,(
% 0.11/0.36 ![X0,X1]: (empty_set=identity_relation(X0)|in(ordered_pair(sk0_0(X0,empty_set),sk0_1(X0,relation_dom(relation_dom(sk0_54(X1))))),relation_dom(relation_dom(sk0_54(X1))))|in(sk0_0(X0,relation_dom(relation_dom(sk0_54(X1)))),X0))),
% 0.11/0.36 inference(forward_demodulation,[status(thm)],[f741,f2761])).
% 0.11/0.36 fof(f2763,plain,(
% 0.11/0.36 ![X0,X1]: (empty_set=identity_relation(X0)|in(ordered_pair(sk0_0(X0,empty_set),sk0_1(X0,relation_dom(relation_dom(empty_set)))),relation_dom(relation_dom(sk0_54(X1))))|in(sk0_0(X0,relation_dom(relation_dom(sk0_54(X1)))),X0))),
% 0.11/0.36 inference(forward_demodulation,[status(thm)],[f1328,f2762])).
% 0.11/0.36 fof(f2764,plain,(
% 0.11/0.36 ![X0,X1]: (empty_set=identity_relation(X0)|in(ordered_pair(sk0_0(X0,empty_set),sk0_1(X0,relation_dom(empty_set))),relation_dom(relation_dom(sk0_54(X1))))|in(sk0_0(X0,relation_dom(relation_dom(sk0_54(X1)))),X0))),
% 0.11/0.36 inference(forward_demodulation,[status(thm)],[f741,f2763])).
% 0.11/0.36 fof(f2765,plain,(
% 0.11/0.36 ![X0,X1]: (empty_set=identity_relation(X0)|in(ordered_pair(sk0_0(X0,empty_set),sk0_1(X0,empty_set)),relation_dom(relation_dom(sk0_54(X1))))|in(sk0_0(X0,relation_dom(relation_dom(sk0_54(X1)))),X0))),
% 0.11/0.36 inference(forward_demodulation,[status(thm)],[f741,f2764])).
% 0.11/0.36 fof(f2766,plain,(
% 0.11/0.36 ![X0,X1]: (empty_set=identity_relation(X0)|in(ordered_pair(sk0_0(X0,empty_set),sk0_1(X0,empty_set)),relation_dom(relation_dom(empty_set)))|in(sk0_0(X0,relation_dom(relation_dom(sk0_54(X1)))),X0))),
% 0.11/0.36 inference(forward_demodulation,[status(thm)],[f1328,f2765])).
% 0.11/0.36 fof(f2767,plain,(
% 0.11/0.36 ![X0,X1]: (empty_set=identity_relation(X0)|in(ordered_pair(sk0_0(X0,empty_set),sk0_1(X0,empty_set)),relation_dom(empty_set))|in(sk0_0(X0,relation_dom(relation_dom(sk0_54(X1)))),X0))),
% 0.11/0.36 inference(forward_demodulation,[status(thm)],[f741,f2766])).
% 0.11/0.36 fof(f2768,plain,(
% 0.11/0.36 ![X0,X1]: (empty_set=identity_relation(X0)|in(ordered_pair(sk0_0(X0,empty_set),sk0_1(X0,empty_set)),empty_set)|in(sk0_0(X0,relation_dom(relation_dom(sk0_54(X1)))),X0))),
% 0.11/0.36 inference(forward_demodulation,[status(thm)],[f741,f2767])).
% 0.11/0.36 fof(f2769,plain,(
% 0.11/0.36 ![X0]: (empty_set=identity_relation(X0)|in(ordered_pair(sk0_0(X0,empty_set),sk0_1(X0,empty_set)),empty_set)|in(sk0_0(X0,relation_dom(relation_dom(empty_set))),X0))),
% 0.11/0.36 inference(forward_demodulation,[status(thm)],[f1328,f2768])).
% 0.11/0.36 fof(f2770,plain,(
% 0.11/0.36 ![X0]: (empty_set=identity_relation(X0)|in(ordered_pair(sk0_0(X0,empty_set),sk0_1(X0,empty_set)),empty_set)|in(sk0_0(X0,relation_dom(empty_set)),X0))),
% 0.11/0.36 inference(forward_demodulation,[status(thm)],[f741,f2769])).
% 0.11/0.36 fof(f2863,plain,(
% 0.11/0.36 spl0_137 <=> in(ordered_pair(sk0_6(sk0_58,relation_image(empty_set,sk0_59),sk0_59,empty_set),sk0_58),empty_set)),
% 0.11/0.36 introduced(split_symbol_definition)).
% 0.11/0.36 fof(f2864,plain,(
% 0.11/0.36 in(ordered_pair(sk0_6(sk0_58,relation_image(empty_set,sk0_59),sk0_59,empty_set),sk0_58),empty_set)|~spl0_137),
% 0.11/0.36 inference(component_clause,[status(thm)],[f2863])).
% 0.11/0.36 fof(f2866,plain,(
% 0.11/0.36 ~relation(empty_set)|in(ordered_pair(sk0_6(sk0_58,relation_image(empty_set,sk0_59),sk0_59,empty_set),sk0_58),empty_set)|~spl0_50|~spl0_0),
% 0.11/0.36 inference(resolution,[status(thm)],[f857,f1804])).
% 0.11/0.36 fof(f2867,plain,(
% 0.11/0.36 ~spl0_6|spl0_137|~spl0_50|~spl0_0),
% 0.11/0.36 inference(split_clause,[status(thm)],[f2866,f907,f2863,f1435,f827])).
% 0.11/0.36 fof(f2868,plain,(
% 0.11/0.36 $false|~spl0_137),
% 0.11/0.36 inference(forward_subsumption_resolution,[status(thm)],[f2864,f867])).
% 0.11/0.36 fof(f2869,plain,(
% 0.11/0.36 ~spl0_137),
% 0.11/0.36 inference(contradiction_clause,[status(thm)],[f2868])).
% 0.11/0.36 fof(f2870,plain,(
% 0.11/0.36 ![X0]: (empty_set=identity_relation(X0)|in(ordered_pair(sk0_0(X0,empty_set),sk0_1(X0,empty_set)),empty_set)|in(sk0_0(X0,empty_set),X0))),
% 0.11/0.36 inference(forward_demodulation,[status(thm)],[f741,f2770])).
% 0.11/0.36 fof(f2871,plain,(
% 0.11/0.36 ![X0]: (empty_set=identity_relation(X0)|in(sk0_0(X0,empty_set),X0))),
% 0.11/0.36 inference(forward_subsumption_resolution,[status(thm)],[f2870,f867])).
% 0.11/0.36 fof(f2872,plain,(
% 0.11/0.36 ![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))),
% 0.11/0.36 inference(forward_demodulation,[status(thm)],[f741,f2756])).
% 0.11/0.36 fof(f2873,plain,(
% 0.11/0.36 ![X0]: (empty_set=identity_relation(X0)|sk0_0(X0,empty_set)=sk0_1(X0,empty_set))),
% 0.11/0.36 inference(forward_subsumption_resolution,[status(thm)],[f2872,f867])).
% 0.11/0.36 fof(f2878,plain,(
% 0.11/0.36 ~sk0_57=empty_set|spl0_50),
% 0.11/0.36 inference(forward_demodulation,[status(thm)],[f1363,f1437])).
% 0.11/0.36 fof(f2887,plain,(
% 0.11/0.36 ~empty_set=empty_set|~spl0_8|spl0_50),
% 0.11/0.36 inference(forward_demodulation,[status(thm)],[f916,f2878])).
% 0.11/0.36 fof(f2888,plain,(
% 0.11/0.36 $false|~spl0_8|spl0_50),
% 0.11/0.36 inference(trivial_equality_resolution,[status(esa)],[f2887])).
% 0.11/0.36 fof(f2889,plain,(
% 0.11/0.36 ~spl0_8|spl0_50),
% 0.11/0.36 inference(contradiction_clause,[status(thm)],[f2888])).
% 0.11/0.36 fof(f2891,plain,(
% 0.11/0.36 spl0_138 <=> relation_dom(relation_inverse(sk0_57))=empty_set),
% 0.11/0.36 introduced(split_symbol_definition)).
% 0.11/0.36 fof(f2894,plain,(
% 0.11/0.36 spl0_139 <=> relation_rng(relation_inverse(identity_relation(relation_dom(sk0_57))))=empty_set),
% 0.11/0.36 introduced(split_symbol_definition)).
% 0.11/0.36 fof(f2897,plain,(
% 0.11/0.36 ~relation_dom(relation_inverse(sk0_57))=empty_set|relation_rng(relation_inverse(identity_relation(relation_dom(sk0_57))))=empty_set|~spl0_52),
% 0.11/0.36 inference(paramodulation,[status(thm)],[f1444,f2143])).
% 0.11/0.36 fof(f2898,plain,(
% 0.11/0.36 ~spl0_138|spl0_139|~spl0_52),
% 0.11/0.36 inference(split_clause,[status(thm)],[f2897,f2891,f2894,f1443])).
% 0.11/0.36 fof(f2899,plain,(
% 0.11/0.36 spl0_140 <=> relation_dom(relation_inverse(identity_relation(relation_dom(sk0_57))))=empty_set),
% 0.11/0.36 introduced(split_symbol_definition)).
% 0.11/0.36 fof(f2902,plain,(
% 0.11/0.36 spl0_141 <=> relation_rng(relation_inverse(sk0_57))=empty_set),
% 0.11/0.36 introduced(split_symbol_definition)).
% 0.11/0.36 fof(f2905,plain,(
% 0.11/0.36 relation_dom(relation_inverse(identity_relation(relation_dom(sk0_57))))=empty_set|~relation_rng(relation_inverse(sk0_57))=empty_set|~spl0_52),
% 0.11/0.36 inference(paramodulation,[status(thm)],[f1444,f2142])).
% 0.11/0.36 fof(f2906,plain,(
% 0.11/0.36 spl0_140|~spl0_141|~spl0_52),
% 0.11/0.36 inference(split_clause,[status(thm)],[f2905,f2899,f2902,f1443])).
% 0.11/0.36 fof(f2907,plain,(
% 0.11/0.36 spl0_142 <=> relation_inverse(identity_relation(relation_dom(sk0_57)))=empty_set),
% 0.11/0.36 introduced(split_symbol_definition)).
% 0.11/0.36 fof(f2910,plain,(
% 0.11/0.36 ~relation_dom(relation_inverse(sk0_57))=empty_set|relation_inverse(identity_relation(relation_dom(sk0_57)))=empty_set|~spl0_52),
% 0.11/0.36 inference(paramodulation,[status(thm)],[f1444,f2144])).
% 0.11/0.36 fof(f2911,plain,(
% 0.11/0.36 ~spl0_138|spl0_142|~spl0_52),
% 0.11/0.36 inference(split_clause,[status(thm)],[f2910,f2891,f2907,f1443])).
% 0.11/0.36 fof(f2912,plain,(
% 0.11/0.36 relation(relation_inverse(sk0_57))|~spl0_52),
% 0.11/0.36 inference(paramodulation,[status(thm)],[f1444,f2094])).
% 0.11/0.36 fof(f2914,plain,(
% 0.11/0.36 ![X0,X1]: (~in(ordered_pair(X0,X1),sk0_57)|X0=X1|~spl0_52)),
% 0.11/0.36 inference(paramodulation,[status(thm)],[f1444,f1080])).
% 0.11/0.36 fof(f2932,plain,(
% 0.11/0.36 relation(relation_inverse(relation_inverse(sk0_57)))|~spl0_52),
% 0.11/0.36 inference(resolution,[status(thm)],[f2912,f435])).
% 0.11/0.36 fof(f2936,plain,(
% 0.11/0.36 relation_dom(relation_inverse(sk0_57))=empty_set|~relation_rng(relation_inverse(sk0_57))=empty_set|~spl0_52),
% 0.11/0.36 inference(resolution,[status(thm)],[f2912,f754])).
% 0.11/0.36 fof(f2937,plain,(
% 0.11/0.36 spl0_138|~spl0_141|~spl0_52),
% 0.11/0.36 inference(split_clause,[status(thm)],[f2936,f2891,f2902,f1443])).
% 0.11/0.36 fof(f2938,plain,(
% 0.11/0.36 ~relation_dom(relation_inverse(sk0_57))=empty_set|relation_rng(relation_inverse(sk0_57))=empty_set|~spl0_52),
% 0.11/0.36 inference(resolution,[status(thm)],[f2912,f753])).
% 0.11/0.36 fof(f2939,plain,(
% 0.11/0.36 ~spl0_138|spl0_141|~spl0_52),
% 0.11/0.36 inference(split_clause,[status(thm)],[f2938,f2891,f2902,f1443])).
% 0.11/0.36 fof(f2940,plain,(
% 0.11/0.36 spl0_143 <=> relation_inverse(sk0_57)=empty_set),
% 0.11/0.36 introduced(split_symbol_definition)).
% 0.11/0.36 fof(f2943,plain,(
% 0.11/0.36 ~relation_dom(relation_inverse(sk0_57))=empty_set|relation_inverse(sk0_57)=empty_set|~spl0_52),
% 0.11/0.36 inference(resolution,[status(thm)],[f2912,f749])).
% 0.11/0.36 fof(f2944,plain,(
% 0.11/0.36 ~spl0_138|spl0_143|~spl0_52),
% 0.11/0.36 inference(split_clause,[status(thm)],[f2943,f2891,f2940,f1443])).
% 0.11/0.36 fof(f2945,plain,(
% 0.11/0.36 spl0_144 <=> in(sk0_6(sk0_58,relation_image(sk0_57,sk0_59),sk0_59,sk0_57),sk0_59)),
% 0.11/0.36 introduced(split_symbol_definition)).
% 0.11/0.36 fof(f2948,plain,(
% 0.11/0.36 ~relation(sk0_57)|in(sk0_6(sk0_58,relation_image(sk0_57,sk0_59),sk0_59,sk0_57),sk0_59)|~spl0_0),
% 0.11/0.36 inference(resolution,[status(thm)],[f828,f858])).
% 0.11/0.36 fof(f2949,plain,(
% 0.11/0.36 ~spl0_30|spl0_144|~spl0_0),
% 0.11/0.36 inference(split_clause,[status(thm)],[f2948,f1147,f2945,f827])).
% 0.11/0.36 fof(f2950,plain,(
% 0.11/0.36 spl0_145 <=> in(ordered_pair(sk0_6(sk0_58,relation_image(sk0_57,sk0_59),sk0_59,sk0_57),sk0_58),sk0_57)),
% 0.11/0.36 introduced(split_symbol_definition)).
% 0.11/0.36 fof(f2951,plain,(
% 0.11/0.36 in(ordered_pair(sk0_6(sk0_58,relation_image(sk0_57,sk0_59),sk0_59,sk0_57),sk0_58),sk0_57)|~spl0_145),
% 0.11/0.36 inference(component_clause,[status(thm)],[f2950])).
% 0.11/0.36 fof(f2953,plain,(
% 0.11/0.36 ~relation(sk0_57)|in(ordered_pair(sk0_6(sk0_58,relation_image(sk0_57,sk0_59),sk0_59,sk0_57),sk0_58),sk0_57)|~spl0_0),
% 0.11/0.36 inference(resolution,[status(thm)],[f828,f857])).
% 0.11/0.36 fof(f2954,plain,(
% 0.11/0.36 ~spl0_30|spl0_145|~spl0_0),
% 0.11/0.36 inference(split_clause,[status(thm)],[f2953,f1147,f2950,f827])).
% 0.11/0.36 fof(f2966,plain,(
% 0.11/0.36 spl0_146 <=> relation_dom(relation_inverse(relation_inverse(sk0_57)))=empty_set),
% 0.11/0.36 introduced(split_symbol_definition)).
% 0.11/0.36 fof(f2969,plain,(
% 0.11/0.36 spl0_147 <=> relation_rng(relation_inverse(relation_inverse(sk0_57)))=empty_set),
% 0.11/0.36 introduced(split_symbol_definition)).
% 0.11/0.36 fof(f2972,plain,(
% 0.11/0.36 relation_dom(relation_inverse(relation_inverse(sk0_57)))=empty_set|~relation_rng(relation_inverse(relation_inverse(sk0_57)))=empty_set|~spl0_52),
% 0.11/0.36 inference(resolution,[status(thm)],[f2932,f754])).
% 0.11/0.36 fof(f2973,plain,(
% 0.11/0.36 spl0_146|~spl0_147|~spl0_52),
% 0.11/0.36 inference(split_clause,[status(thm)],[f2972,f2966,f2969,f1443])).
% 0.11/0.36 fof(f2974,plain,(
% 0.11/0.36 ~relation_dom(relation_inverse(relation_inverse(sk0_57)))=empty_set|relation_rng(relation_inverse(relation_inverse(sk0_57)))=empty_set|~spl0_52),
% 0.11/0.36 inference(resolution,[status(thm)],[f2932,f753])).
% 0.11/0.36 fof(f2975,plain,(
% 0.11/0.36 ~spl0_146|spl0_147|~spl0_52),
% 0.11/0.36 inference(split_clause,[status(thm)],[f2974,f2966,f2969,f1443])).
% 0.11/0.36 fof(f2976,plain,(
% 0.11/0.36 spl0_148 <=> relation_inverse(relation_inverse(sk0_57))=empty_set),
% 0.11/0.36 introduced(split_symbol_definition)).
% 0.11/0.36 fof(f2979,plain,(
% 0.11/0.36 ~relation_dom(relation_inverse(relation_inverse(sk0_57)))=empty_set|relation_inverse(relation_inverse(sk0_57))=empty_set|~spl0_52),
% 0.11/0.36 inference(resolution,[status(thm)],[f2932,f749])).
% 0.11/0.36 fof(f2980,plain,(
% 0.11/0.36 ~spl0_146|spl0_148|~spl0_52),
% 0.11/0.36 inference(split_clause,[status(thm)],[f2979,f2966,f2976,f1443])).
% 0.11/0.36 fof(f3022,plain,(
% 0.11/0.36 ![X0]: (empty_set=relation_dom_restriction(sk0_57,X0)|in(ordered_pair(sk0_2(X0,empty_set,sk0_57),sk0_3(X0,empty_set,sk0_57)),empty_set)|in(sk0_2(X0,empty_set,sk0_57),X0))),
% 0.11/0.36 inference(resolution,[status(thm)],[f1644,f474])).
% 0.11/0.36 fof(f3023,plain,(
% 0.11/0.36 ![X0]: (empty_set=relation_dom_restriction(sk0_57,X0)|in(sk0_2(X0,empty_set,sk0_57),X0))),
% 0.11/0.36 inference(forward_subsumption_resolution,[status(thm)],[f3022,f867])).
% 0.11/0.36 fof(f3026,plain,(
% 0.11/0.36 ![X0]: (empty_set=identity_relation(singleton(X0))|sk0_0(singleton(X0),empty_set)=X0)),
% 0.11/0.36 inference(resolution,[status(thm)],[f2871,f865])).
% 0.11/0.36 fof(f3033,plain,(
% 0.11/0.36 ![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))),
% 0.11/0.36 inference(paramodulation,[status(thm)],[f2873,f216])).
% 0.11/0.36 fof(f3034,plain,(
% 0.11/0.36 ~spl0_6|spl0_75),
% 0.11/0.36 inference(split_clause,[status(thm)],[f3033,f907,f1853])).
% 0.11/0.36 fof(f3041,plain,(
% 0.11/0.36 ![X0]: (~relation(empty_set)|empty_set=identity_relation(singleton(X0))|~in(ordered_pair(X0,sk0_1(singleton(X0),empty_set)),empty_set)|~in(sk0_0(singleton(X0),empty_set),singleton(X0))|~sk0_0(singleton(X0),empty_set)=sk0_1(singleton(X0),empty_set)|empty_set=identity_relation(singleton(X0)))),
% 0.11/0.36 inference(paramodulation,[status(thm)],[f3026,f216])).
% 0.11/0.36 fof(f3042,plain,(
% 0.11/0.36 ~spl0_6|spl0_89),
% 0.11/0.36 inference(split_clause,[status(thm)],[f3041,f907,f2161])).
% 0.11/0.36 fof(f3046,plain,(
% 0.11/0.36 empty_set=relation_dom_restriction(sk0_57,empty_set)),
% 0.11/0.36 inference(resolution,[status(thm)],[f3023,f867])).
% 0.11/0.36 fof(f3051,plain,(
% 0.11/0.36 spl0_149 <=> in(ordered_pair(X0,X1),relation_dom_restriction(sk0_57,empty_set))|~in(X0,empty_set)|~in(ordered_pair(X0,X1),sk0_57)),
% 0.11/0.36 introduced(split_symbol_definition)).
% 0.11/0.36 fof(f3054,plain,(
% 0.11/0.36 ![X0,X1]: (~relation(sk0_57)|~relation(empty_set)|in(ordered_pair(X0,X1),relation_dom_restriction(sk0_57,empty_set))|~in(X0,empty_set)|~in(ordered_pair(X0,X1),sk0_57))),
% 0.11/0.36 inference(paramodulation,[status(thm)],[f3046,f853])).
% 0.11/0.36 fof(f3055,plain,(
% 0.11/0.36 ~spl0_30|~spl0_6|spl0_149),
% 0.11/0.36 inference(split_clause,[status(thm)],[f3054,f1147,f907,f3051])).
% 0.11/0.36 fof(f3056,plain,(
% 0.11/0.36 spl0_150 <=> relation(relation_dom_restriction(sk0_57,empty_set))),
% 0.11/0.36 introduced(split_symbol_definition)).
% 0.11/0.36 fof(f3058,plain,(
% 0.11/0.36 ~relation(relation_dom_restriction(sk0_57,empty_set))|spl0_150),
% 0.11/0.36 inference(component_clause,[status(thm)],[f3056])).
% 0.11/0.36 fof(f3059,plain,(
% 0.11/0.36 spl0_151 <=> ~in(ordered_pair(X0,X1),empty_set)|in(ordered_pair(X0,X1),sk0_57)),
% 0.11/0.36 introduced(split_symbol_definition)).
% 0.11/0.36 fof(f3062,plain,(
% 0.11/0.36 ![X0,X1]: (~relation(sk0_57)|~relation(relation_dom_restriction(sk0_57,empty_set))|~in(ordered_pair(X0,X1),empty_set)|in(ordered_pair(X0,X1),sk0_57))),
% 0.11/0.36 inference(paramodulation,[status(thm)],[f3046,f852])).
% 0.11/0.36 fof(f3063,plain,(
% 0.11/0.36 ~spl0_30|~spl0_150|spl0_151),
% 0.11/0.36 inference(split_clause,[status(thm)],[f3062,f1147,f3056,f3059])).
% 0.11/0.36 fof(f3064,plain,(
% 0.11/0.36 ![X0,X1]: (~relation(sk0_57)|~relation(relation_dom_restriction(sk0_57,empty_set))|~in(ordered_pair(X0,X1),empty_set)|in(X0,empty_set))),
% 0.11/0.36 inference(paramodulation,[status(thm)],[f3046,f851])).
% 0.11/0.36 fof(f3065,plain,(
% 0.11/0.36 ~spl0_30|~spl0_150|spl0_93),
% 0.11/0.36 inference(split_clause,[status(thm)],[f3064,f1147,f3056,f2185])).
% 0.11/0.36 fof(f3066,plain,(
% 0.11/0.36 ~relation(empty_set)|spl0_150),
% 0.11/0.36 inference(forward_demodulation,[status(thm)],[f3046,f3058])).
% 0.11/0.36 fof(f3067,plain,(
% 0.11/0.36 $false|spl0_150),
% 0.11/0.36 inference(forward_subsumption_resolution,[status(thm)],[f3066,f474])).
% 0.11/0.36 fof(f3068,plain,(
% 0.11/0.36 spl0_150),
% 0.11/0.36 inference(contradiction_clause,[status(thm)],[f3067])).
% 0.11/0.36 fof(f3071,plain,(
% 0.11/0.36 ![X0]: (sk0_57=identity_relation(X0)|sk0_0(X0,sk0_57)=sk0_1(X0,sk0_57)|~spl0_52)),
% 0.11/0.36 inference(forward_subsumption_resolution,[status(thm)],[f1123,f2914])).
% 0.11/0.36 fof(f3078,plain,(
% 0.11/0.36 spl0_152 <=> sk0_57=identity_relation(X0)|~in(ordered_pair(sk0_0(X0,sk0_57),sk0_0(X0,sk0_57)),sk0_57)|~in(sk0_0(X0,sk0_57),X0)|~sk0_0(X0,sk0_57)=sk0_1(X0,sk0_57)|sk0_57=identity_relation(X0)),
% 0.11/0.36 introduced(split_symbol_definition)).
% 0.11/0.36 fof(f3081,plain,(
% 0.11/0.36 ![X0]: (~relation(sk0_57)|sk0_57=identity_relation(X0)|~in(ordered_pair(sk0_0(X0,sk0_57),sk0_0(X0,sk0_57)),sk0_57)|~in(sk0_0(X0,sk0_57),X0)|~sk0_0(X0,sk0_57)=sk0_1(X0,sk0_57)|sk0_57=identity_relation(X0)|~spl0_52)),
% 0.11/0.36 inference(paramodulation,[status(thm)],[f3071,f216])).
% 0.11/0.36 fof(f3082,plain,(
% 0.11/0.36 ~spl0_30|spl0_152|~spl0_52),
% 0.11/0.36 inference(split_clause,[status(thm)],[f3081,f1147,f3078,f1443])).
% 0.11/0.36 fof(f3274,plain,(
% 0.11/0.36 spl0_154 <=> in(sk0_6(sk0_58,relation_image(sk0_57,sk0_59),sk0_59,sk0_57),relation_dom(sk0_57))),
% 0.11/0.36 introduced(split_symbol_definition)).
% 0.11/0.36 fof(f3277,plain,(
% 0.11/0.36 ~in(sk0_6(sk0_58,relation_image(sk0_57,sk0_59),sk0_59,sk0_57),relation_dom(sk0_57))|~in(sk0_6(sk0_58,relation_image(sk0_57,sk0_59),sk0_59,sk0_57),sk0_59)|~spl0_145|~spl0_4),
% 0.11/0.36 inference(resolution,[status(thm)],[f2951,f843])).
% 0.11/0.36 fof(f3278,plain,(
% 0.11/0.36 ~spl0_154|~spl0_144|~spl0_145|~spl0_4),
% 0.11/0.36 inference(split_clause,[status(thm)],[f3277,f3274,f2945,f2950,f842])).
% 0.11/0.36 fof(f3280,plain,(
% 0.11/0.36 ~relation(sk0_57)|in(sk0_6(sk0_58,relation_image(sk0_57,sk0_59),sk0_59,sk0_57),relation_dom(sk0_57))|~spl0_145),
% 0.11/0.36 inference(resolution,[status(thm)],[f2951,f882])).
% 0.11/0.36 fof(f3281,plain,(
% 0.11/0.36 ~spl0_30|spl0_154|~spl0_145),
% 0.11/0.36 inference(split_clause,[status(thm)],[f3280,f1147,f3274,f2950])).
% 0.11/0.36 fof(f3291,plain,(
% 0.11/0.36 $false),
% 0.11/0.36 inference(sat_refutation,[status(thm)],[f837,f841,f845,f919,f926,f943,f948,f951,f980,f987,f1015,f1026,f1032,f1046,f1090,f1092,f1140,f1156,f1160,f1217,f1223,f1227,f1234,f1239,f1244,f1251,f1256,f1261,f1271,f1276,f1280,f1285,f1290,f1442,f1489,f1494,f1498,f1504,f1509,f1520,f1525,f1529,f1570,f1575,f1584,f1592,f1594,f1600,f1602,f1607,f1609,f1852,f1902,f2039,f2044,f2059,f2070,f2272,f2277,f2318,f2484,f2547,f2567,f2587,f2633,f2867,f2869,f2889,f2898,f2906,f2911,f2937,f2939,f2944,f2949,f2954,f2973,f2975,f2980,f3034,f3042,f3055,f3063,f3065,f3068,f3082,f3278,f3281])).
% 0.11/0.36 % SZS output end CNFRefutation for theBenchmark.p
% 0.11/0.36 % Elapsed time: 0.095846 seconds
% 0.11/0.36 % CPU time: 0.648452 seconds
% 0.11/0.36 % Total memory used: 82.756 MB
% 0.11/0.36 % Net memory used: 82.383 MB
%------------------------------------------------------------------------------