TSTP Solution File: SEU293+1 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SEU293+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n024.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 20:41:50 EDT 2024
% Result : Theorem 0.19s 0.47s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEU293+1 : TPTP v8.1.2. Released v3.3.0.
% 0.06/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.34 % Computer : n024.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Apr 29 19:50:06 EDT 2024
% 0.12/0.34 % CPUTime :
% 0.12/0.35 % Drodi V3.6.0
% 0.19/0.47 % Refutation found
% 0.19/0.47 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.19/0.47 % SZS output start CNFRefutation for theBenchmark
% 0.19/0.47 fof(f2,axiom,(
% 0.19/0.47 (! [A] :( empty(A)=> function(A) ) )),
% 0.19/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.47 fof(f3,axiom,(
% 0.19/0.47 (! [A] :( empty(A)=> relation(A) ) )),
% 0.19/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.47 fof(f4,axiom,(
% 0.19/0.47 (! [A,B,C] :( element(C,powerset(cartesian_product2(A,B)))=> relation(C) ) )),
% 0.19/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.47 fof(f5,axiom,(
% 0.19/0.47 (! [A] :( ( relation(A)& empty(A)& function(A) )=> ( relation(A)& function(A)& one_to_one(A) ) ) )),
% 0.19/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.47 fof(f6,axiom,(
% 0.19/0.47 (! [A] :( ( relation(A)& function(A) )=> (! [B,C] :( C = relation_inverse_image(A,B)<=> (! [D] :( in(D,C)<=> ( in(D,relation_dom(A))& in(apply(A,D),B) ) ) )) )) )),
% 0.19/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.47 fof(f7,axiom,(
% 0.19/0.47 (! [A,B,C] :( relation_of2_as_subset(C,A,B)=> ( ( ( B = empty_set=> A = empty_set )=> ( quasi_total(C,A,B)<=> A = relation_dom_as_subset(A,B,C) ) )& ( B = empty_set=> ( A = empty_set| ( quasi_total(C,A,B)<=> C = empty_set ) ) ) ) ) )),
% 0.19/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.47 fof(f17,axiom,(
% 0.19/0.47 (! [A,B,C] :( relation_of2_as_subset(C,A,B)=> element(C,powerset(cartesian_product2(A,B))) ) )),
% 0.19/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.47 fof(f21,axiom,(
% 0.19/0.47 ( empty(empty_set)& relation(empty_set)& relation_empty_yielding(empty_set) ) ),
% 0.19/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.47 fof(f26,axiom,(
% 0.19/0.47 (! [A] :( ( ~ empty(A)& relation(A) )=> ~ empty(relation_dom(A)) ) )),
% 0.19/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.47 fof(f27,axiom,(
% 0.19/0.47 (! [A] :( empty(A)=> ( empty(relation_dom(A))& relation(relation_dom(A)) ) ) )),
% 0.19/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.47 fof(f28,axiom,(
% 0.19/0.47 (? [A] :( relation(A)& function(A) ) )),
% 0.19/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.47 fof(f30,axiom,(
% 0.19/0.47 (? [A] :( relation(A)& function(A)& one_to_one(A)& empty(A) ) )),
% 0.19/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.47 fof(f31,axiom,(
% 0.19/0.47 (? [A] :( empty(A)& relation(A) ) )),
% 0.19/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.47 fof(f33,axiom,(
% 0.19/0.47 (? [A] : empty(A) )),
% 0.19/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.47 fof(f34,axiom,(
% 0.19/0.47 (? [A] :( relation(A)& empty(A)& function(A) ) )),
% 0.19/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.47 fof(f39,axiom,(
% 0.19/0.47 (? [A] :( relation(A)& function(A)& one_to_one(A) ) )),
% 0.19/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.47 fof(f41,axiom,(
% 0.19/0.47 (? [A] :( relation(A)& relation_empty_yielding(A)& function(A) ) )),
% 0.19/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.47 fof(f42,axiom,(
% 0.19/0.47 (! [A,B,C] :( relation_of2(C,A,B)=> relation_dom_as_subset(A,B,C) = relation_dom(C) ) )),
% 0.19/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.47 fof(f43,axiom,(
% 0.19/0.47 (! [A,B,C] :( relation_of2_as_subset(C,A,B)<=> relation_of2(C,A,B) ) )),
% 0.19/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.47 fof(f48,conjecture,(
% 0.19/0.47 (! [A,B,C,D] :( ( function(D)& quasi_total(D,A,B)& relation_of2_as_subset(D,A,B) )=> ( B != empty_set=> (! [E] :( in(E,relation_inverse_image(D,C))<=> ( in(E,A)& in(apply(D,E),C) ) ) )) ) )),
% 0.19/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.47 fof(f49,negated_conjecture,(
% 0.19/0.47 ~((! [A,B,C,D] :( ( function(D)& quasi_total(D,A,B)& relation_of2_as_subset(D,A,B) )=> ( B != empty_set=> (! [E] :( in(E,relation_inverse_image(D,C))<=> ( in(E,A)& in(apply(D,E),C) ) ) )) ) ))),
% 0.19/0.47 inference(negated_conjecture,[status(cth)],[f48])).
% 0.19/0.47 fof(f52,axiom,(
% 0.19/0.47 (! [A] :( empty(A)=> A = empty_set ) )),
% 0.19/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.47 fof(f53,axiom,(
% 0.19/0.47 (! [A,B] :~ ( in(A,B)& empty(B) ) )),
% 0.19/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.47 fof(f57,plain,(
% 0.19/0.47 ![A]: (~empty(A)|function(A))),
% 0.19/0.47 inference(pre_NNF_transformation,[status(esa)],[f2])).
% 0.19/0.47 fof(f58,plain,(
% 0.19/0.47 ![X0]: (~empty(X0)|function(X0))),
% 0.19/0.48 inference(cnf_transformation,[status(esa)],[f57])).
% 0.19/0.48 fof(f59,plain,(
% 0.19/0.48 ![A]: (~empty(A)|relation(A))),
% 0.19/0.48 inference(pre_NNF_transformation,[status(esa)],[f3])).
% 0.19/0.48 fof(f60,plain,(
% 0.19/0.48 ![X0]: (~empty(X0)|relation(X0))),
% 0.19/0.48 inference(cnf_transformation,[status(esa)],[f59])).
% 0.19/0.48 fof(f61,plain,(
% 0.19/0.48 ![A,B,C]: (~element(C,powerset(cartesian_product2(A,B)))|relation(C))),
% 0.19/0.48 inference(pre_NNF_transformation,[status(esa)],[f4])).
% 0.19/0.48 fof(f62,plain,(
% 0.19/0.48 ![C]: ((![A,B]: ~element(C,powerset(cartesian_product2(A,B))))|relation(C))),
% 0.19/0.48 inference(miniscoping,[status(esa)],[f61])).
% 0.19/0.48 fof(f63,plain,(
% 0.19/0.48 ![X0,X1,X2]: (~element(X0,powerset(cartesian_product2(X1,X2)))|relation(X0))),
% 0.19/0.48 inference(cnf_transformation,[status(esa)],[f62])).
% 0.19/0.48 fof(f64,plain,(
% 0.19/0.48 ![A]: (((~relation(A)|~empty(A))|~function(A))|((relation(A)&function(A))&one_to_one(A)))),
% 0.19/0.48 inference(pre_NNF_transformation,[status(esa)],[f5])).
% 0.19/0.48 fof(f67,plain,(
% 0.19/0.48 ![X0]: (~relation(X0)|~empty(X0)|~function(X0)|one_to_one(X0))),
% 0.19/0.48 inference(cnf_transformation,[status(esa)],[f64])).
% 0.19/0.48 fof(f68,plain,(
% 0.19/0.48 ![A]: ((~relation(A)|~function(A))|(![B,C]: (C=relation_inverse_image(A,B)<=>(![D]: (in(D,C)<=>(in(D,relation_dom(A))&in(apply(A,D),B)))))))),
% 0.19/0.48 inference(pre_NNF_transformation,[status(esa)],[f6])).
% 0.19/0.48 fof(f69,plain,(
% 0.19/0.48 ![A]: ((~relation(A)|~function(A))|(![B,C]: ((~C=relation_inverse_image(A,B)|(![D]: ((~in(D,C)|(in(D,relation_dom(A))&in(apply(A,D),B)))&(in(D,C)|(~in(D,relation_dom(A))|~in(apply(A,D),B))))))&(C=relation_inverse_image(A,B)|(?[D]: ((~in(D,C)|(~in(D,relation_dom(A))|~in(apply(A,D),B)))&(in(D,C)|(in(D,relation_dom(A))&in(apply(A,D),B)))))))))),
% 0.19/0.48 inference(NNF_transformation,[status(esa)],[f68])).
% 0.19/0.48 fof(f70,plain,(
% 0.19/0.48 ![A]: ((~relation(A)|~function(A))|((![B,C]: (~C=relation_inverse_image(A,B)|((![D]: (~in(D,C)|(in(D,relation_dom(A))&in(apply(A,D),B))))&(![D]: (in(D,C)|(~in(D,relation_dom(A))|~in(apply(A,D),B)))))))&(![B,C]: (C=relation_inverse_image(A,B)|(?[D]: ((~in(D,C)|(~in(D,relation_dom(A))|~in(apply(A,D),B)))&(in(D,C)|(in(D,relation_dom(A))&in(apply(A,D),B)))))))))),
% 0.19/0.48 inference(miniscoping,[status(esa)],[f69])).
% 0.19/0.48 fof(f71,plain,(
% 0.19/0.48 ![A]: ((~relation(A)|~function(A))|((![B,C]: (~C=relation_inverse_image(A,B)|((![D]: (~in(D,C)|(in(D,relation_dom(A))&in(apply(A,D),B))))&(![D]: (in(D,C)|(~in(D,relation_dom(A))|~in(apply(A,D),B)))))))&(![B,C]: (C=relation_inverse_image(A,B)|((~in(sk0_0(C,B,A),C)|(~in(sk0_0(C,B,A),relation_dom(A))|~in(apply(A,sk0_0(C,B,A)),B)))&(in(sk0_0(C,B,A),C)|(in(sk0_0(C,B,A),relation_dom(A))&in(apply(A,sk0_0(C,B,A)),B))))))))),
% 0.19/0.48 inference(skolemization,[status(esa)],[f70])).
% 0.19/0.48 fof(f72,plain,(
% 0.19/0.48 ![X0,X1,X2,X3]: (~relation(X0)|~function(X0)|~X1=relation_inverse_image(X0,X2)|~in(X3,X1)|in(X3,relation_dom(X0)))),
% 0.19/0.48 inference(cnf_transformation,[status(esa)],[f71])).
% 0.19/0.48 fof(f73,plain,(
% 0.19/0.48 ![X0,X1,X2,X3]: (~relation(X0)|~function(X0)|~X1=relation_inverse_image(X0,X2)|~in(X3,X1)|in(apply(X0,X3),X2))),
% 0.19/0.48 inference(cnf_transformation,[status(esa)],[f71])).
% 0.19/0.48 fof(f74,plain,(
% 0.19/0.48 ![X0,X1,X2,X3]: (~relation(X0)|~function(X0)|~X1=relation_inverse_image(X0,X2)|in(X3,X1)|~in(X3,relation_dom(X0))|~in(apply(X0,X3),X2))),
% 0.19/0.48 inference(cnf_transformation,[status(esa)],[f71])).
% 0.19/0.48 fof(f75,plain,(
% 0.19/0.48 ![X0,X1,X2]: (~relation(X0)|~function(X0)|X1=relation_inverse_image(X0,X2)|~in(sk0_0(X1,X2,X0),X1)|~in(sk0_0(X1,X2,X0),relation_dom(X0))|~in(apply(X0,sk0_0(X1,X2,X0)),X2))),
% 0.19/0.48 inference(cnf_transformation,[status(esa)],[f71])).
% 0.19/0.48 fof(f76,plain,(
% 0.19/0.48 ![X0,X1,X2]: (~relation(X0)|~function(X0)|X1=relation_inverse_image(X0,X2)|in(sk0_0(X1,X2,X0),X1)|in(sk0_0(X1,X2,X0),relation_dom(X0)))),
% 0.19/0.48 inference(cnf_transformation,[status(esa)],[f71])).
% 0.19/0.48 fof(f77,plain,(
% 0.19/0.48 ![X0,X1,X2]: (~relation(X0)|~function(X0)|X1=relation_inverse_image(X0,X2)|in(sk0_0(X1,X2,X0),X1)|in(apply(X0,sk0_0(X1,X2,X0)),X2))),
% 0.19/0.48 inference(cnf_transformation,[status(esa)],[f71])).
% 0.19/0.48 fof(f78,plain,(
% 0.19/0.48 ![A,B,C]: (~relation_of2_as_subset(C,A,B)|(((B=empty_set&~A=empty_set)|(quasi_total(C,A,B)<=>A=relation_dom_as_subset(A,B,C)))&(~B=empty_set|(A=empty_set|(quasi_total(C,A,B)<=>C=empty_set)))))),
% 0.19/0.48 inference(pre_NNF_transformation,[status(esa)],[f7])).
% 0.19/0.48 fof(f79,plain,(
% 0.19/0.48 ![A,B]: (pd0_0(B,A)=>(B=empty_set&~A=empty_set))),
% 0.19/0.48 introduced(predicate_definition,[f78])).
% 0.19/0.48 fof(f80,plain,(
% 0.19/0.48 ![A,B,C]: (~relation_of2_as_subset(C,A,B)|((pd0_0(B,A)|(quasi_total(C,A,B)<=>A=relation_dom_as_subset(A,B,C)))&(~B=empty_set|(A=empty_set|(quasi_total(C,A,B)<=>C=empty_set)))))),
% 0.19/0.48 inference(formula_renaming,[status(thm)],[f78,f79])).
% 0.19/0.48 fof(f81,plain,(
% 0.19/0.48 ![A,B,C]: (~relation_of2_as_subset(C,A,B)|((pd0_0(B,A)|((~quasi_total(C,A,B)|A=relation_dom_as_subset(A,B,C))&(quasi_total(C,A,B)|~A=relation_dom_as_subset(A,B,C))))&(~B=empty_set|(A=empty_set|((~quasi_total(C,A,B)|C=empty_set)&(quasi_total(C,A,B)|~C=empty_set))))))),
% 0.19/0.48 inference(NNF_transformation,[status(esa)],[f80])).
% 0.19/0.48 fof(f82,plain,(
% 0.19/0.48 ![X0,X1,X2]: (~relation_of2_as_subset(X0,X1,X2)|pd0_0(X2,X1)|~quasi_total(X0,X1,X2)|X1=relation_dom_as_subset(X1,X2,X0))),
% 0.19/0.48 inference(cnf_transformation,[status(esa)],[f81])).
% 0.19/0.48 fof(f83,plain,(
% 0.19/0.48 ![X0,X1,X2]: (~relation_of2_as_subset(X0,X1,X2)|pd0_0(X2,X1)|quasi_total(X0,X1,X2)|~X1=relation_dom_as_subset(X1,X2,X0))),
% 0.19/0.48 inference(cnf_transformation,[status(esa)],[f81])).
% 0.19/0.48 fof(f88,plain,(
% 0.19/0.48 ![A,B,C]: (~relation_of2_as_subset(C,A,B)|element(C,powerset(cartesian_product2(A,B))))),
% 0.19/0.48 inference(pre_NNF_transformation,[status(esa)],[f17])).
% 0.19/0.48 fof(f89,plain,(
% 0.19/0.48 ![X0,X1,X2]: (~relation_of2_as_subset(X0,X1,X2)|element(X0,powerset(cartesian_product2(X1,X2))))),
% 0.19/0.48 inference(cnf_transformation,[status(esa)],[f88])).
% 0.19/0.48 fof(f96,plain,(
% 0.19/0.48 empty(empty_set)),
% 0.19/0.48 inference(cnf_transformation,[status(esa)],[f21])).
% 0.19/0.48 fof(f97,plain,(
% 0.19/0.48 relation(empty_set)),
% 0.19/0.48 inference(cnf_transformation,[status(esa)],[f21])).
% 0.19/0.48 fof(f105,plain,(
% 0.19/0.48 ![A]: ((empty(A)|~relation(A))|~empty(relation_dom(A)))),
% 0.19/0.48 inference(pre_NNF_transformation,[status(esa)],[f26])).
% 0.19/0.48 fof(f106,plain,(
% 0.19/0.48 ![X0]: (empty(X0)|~relation(X0)|~empty(relation_dom(X0)))),
% 0.19/0.48 inference(cnf_transformation,[status(esa)],[f105])).
% 0.19/0.48 fof(f107,plain,(
% 0.19/0.48 ![A]: (~empty(A)|(empty(relation_dom(A))&relation(relation_dom(A))))),
% 0.19/0.48 inference(pre_NNF_transformation,[status(esa)],[f27])).
% 0.19/0.48 fof(f108,plain,(
% 0.19/0.48 ![X0]: (~empty(X0)|empty(relation_dom(X0)))),
% 0.19/0.48 inference(cnf_transformation,[status(esa)],[f107])).
% 0.19/0.48 fof(f110,plain,(
% 0.19/0.48 (relation(sk0_4)&function(sk0_4))),
% 0.19/0.48 inference(skolemization,[status(esa)],[f28])).
% 0.19/0.48 fof(f111,plain,(
% 0.19/0.48 relation(sk0_4)),
% 0.19/0.48 inference(cnf_transformation,[status(esa)],[f110])).
% 0.19/0.48 fof(f112,plain,(
% 0.19/0.48 function(sk0_4)),
% 0.19/0.48 inference(cnf_transformation,[status(esa)],[f110])).
% 0.19/0.48 fof(f118,plain,(
% 0.19/0.48 (((relation(sk0_6)&function(sk0_6))&one_to_one(sk0_6))&empty(sk0_6))),
% 0.19/0.48 inference(skolemization,[status(esa)],[f30])).
% 0.19/0.48 fof(f119,plain,(
% 0.19/0.48 relation(sk0_6)),
% 0.19/0.48 inference(cnf_transformation,[status(esa)],[f118])).
% 0.19/0.48 fof(f120,plain,(
% 0.19/0.48 function(sk0_6)),
% 0.19/0.48 inference(cnf_transformation,[status(esa)],[f118])).
% 0.19/0.48 fof(f122,plain,(
% 0.19/0.48 empty(sk0_6)),
% 0.19/0.48 inference(cnf_transformation,[status(esa)],[f118])).
% 0.19/0.48 fof(f123,plain,(
% 0.19/0.48 (empty(sk0_7)&relation(sk0_7))),
% 0.19/0.48 inference(skolemization,[status(esa)],[f31])).
% 0.19/0.48 fof(f124,plain,(
% 0.19/0.48 empty(sk0_7)),
% 0.19/0.48 inference(cnf_transformation,[status(esa)],[f123])).
% 0.19/0.48 fof(f125,plain,(
% 0.19/0.48 relation(sk0_7)),
% 0.19/0.48 inference(cnf_transformation,[status(esa)],[f123])).
% 0.19/0.48 fof(f130,plain,(
% 0.19/0.48 empty(sk0_9)),
% 0.19/0.48 inference(skolemization,[status(esa)],[f33])).
% 0.19/0.48 fof(f131,plain,(
% 0.19/0.48 empty(sk0_9)),
% 0.19/0.48 inference(cnf_transformation,[status(esa)],[f130])).
% 0.19/0.48 fof(f132,plain,(
% 0.19/0.48 ((relation(sk0_10)&empty(sk0_10))&function(sk0_10))),
% 0.19/0.48 inference(skolemization,[status(esa)],[f34])).
% 0.19/0.48 fof(f133,plain,(
% 0.19/0.48 relation(sk0_10)),
% 0.19/0.48 inference(cnf_transformation,[status(esa)],[f132])).
% 0.19/0.48 fof(f134,plain,(
% 0.19/0.48 empty(sk0_10)),
% 0.19/0.48 inference(cnf_transformation,[status(esa)],[f132])).
% 0.19/0.48 fof(f135,plain,(
% 0.19/0.48 function(sk0_10)),
% 0.19/0.48 inference(cnf_transformation,[status(esa)],[f132])).
% 0.19/0.48 fof(f148,plain,(
% 0.19/0.48 ((relation(sk0_15)&function(sk0_15))&one_to_one(sk0_15))),
% 0.19/0.48 inference(skolemization,[status(esa)],[f39])).
% 0.19/0.48 fof(f149,plain,(
% 0.19/0.48 relation(sk0_15)),
% 0.19/0.48 inference(cnf_transformation,[status(esa)],[f148])).
% 0.19/0.48 fof(f150,plain,(
% 0.19/0.48 function(sk0_15)),
% 0.19/0.48 inference(cnf_transformation,[status(esa)],[f148])).
% 0.19/0.48 fof(f155,plain,(
% 0.19/0.48 ((relation(sk0_17)&relation_empty_yielding(sk0_17))&function(sk0_17))),
% 0.19/0.48 inference(skolemization,[status(esa)],[f41])).
% 0.19/0.48 fof(f156,plain,(
% 0.19/0.48 relation(sk0_17)),
% 0.19/0.48 inference(cnf_transformation,[status(esa)],[f155])).
% 0.19/0.48 fof(f158,plain,(
% 0.19/0.48 function(sk0_17)),
% 0.19/0.48 inference(cnf_transformation,[status(esa)],[f155])).
% 0.19/0.48 fof(f159,plain,(
% 0.19/0.48 ![A,B,C]: (~relation_of2(C,A,B)|relation_dom_as_subset(A,B,C)=relation_dom(C))),
% 0.19/0.48 inference(pre_NNF_transformation,[status(esa)],[f42])).
% 0.19/0.48 fof(f160,plain,(
% 0.19/0.48 ![X0,X1,X2]: (~relation_of2(X0,X1,X2)|relation_dom_as_subset(X1,X2,X0)=relation_dom(X0))),
% 0.19/0.48 inference(cnf_transformation,[status(esa)],[f159])).
% 0.19/0.48 fof(f161,plain,(
% 0.19/0.48 ![A,B,C]: ((~relation_of2_as_subset(C,A,B)|relation_of2(C,A,B))&(relation_of2_as_subset(C,A,B)|~relation_of2(C,A,B)))),
% 0.19/0.48 inference(NNF_transformation,[status(esa)],[f43])).
% 0.19/0.48 fof(f162,plain,(
% 0.19/0.48 (![A,B,C]: (~relation_of2_as_subset(C,A,B)|relation_of2(C,A,B)))&(![A,B,C]: (relation_of2_as_subset(C,A,B)|~relation_of2(C,A,B)))),
% 0.19/0.48 inference(miniscoping,[status(esa)],[f161])).
% 0.19/0.48 fof(f163,plain,(
% 0.19/0.48 ![X0,X1,X2]: (~relation_of2_as_subset(X0,X1,X2)|relation_of2(X0,X1,X2))),
% 0.19/0.48 inference(cnf_transformation,[status(esa)],[f162])).
% 0.19/0.48 fof(f175,plain,(
% 0.19/0.48 (?[A,B,C,D]: (((function(D)&quasi_total(D,A,B))&relation_of2_as_subset(D,A,B))&(~B=empty_set&(?[E]: (in(E,relation_inverse_image(D,C))<~>(in(E,A)&in(apply(D,E),C)))))))),
% 0.19/0.48 inference(pre_NNF_transformation,[status(esa)],[f49])).
% 0.19/0.48 fof(f176,plain,(
% 0.19/0.48 ?[A,B,C,D]: (((function(D)&quasi_total(D,A,B))&relation_of2_as_subset(D,A,B))&(~B=empty_set&(?[E]: ((in(E,relation_inverse_image(D,C))|(in(E,A)&in(apply(D,E),C)))&(~in(E,relation_inverse_image(D,C))|(~in(E,A)|~in(apply(D,E),C)))))))),
% 0.19/0.48 inference(NNF_transformation,[status(esa)],[f175])).
% 0.19/0.48 fof(f177,plain,(
% 0.19/0.48 ?[A,B,D]: (((function(D)&quasi_total(D,A,B))&relation_of2_as_subset(D,A,B))&(~B=empty_set&(?[C,E]: ((in(E,relation_inverse_image(D,C))|(in(E,A)&in(apply(D,E),C)))&(~in(E,relation_inverse_image(D,C))|(~in(E,A)|~in(apply(D,E),C)))))))),
% 0.19/0.48 inference(miniscoping,[status(esa)],[f176])).
% 0.19/0.48 fof(f178,plain,(
% 0.19/0.48 (((function(sk0_20)&quasi_total(sk0_20,sk0_18,sk0_19))&relation_of2_as_subset(sk0_20,sk0_18,sk0_19))&(~sk0_19=empty_set&((in(sk0_22,relation_inverse_image(sk0_20,sk0_21))|(in(sk0_22,sk0_18)&in(apply(sk0_20,sk0_22),sk0_21)))&(~in(sk0_22,relation_inverse_image(sk0_20,sk0_21))|(~in(sk0_22,sk0_18)|~in(apply(sk0_20,sk0_22),sk0_21))))))),
% 0.19/0.48 inference(skolemization,[status(esa)],[f177])).
% 0.19/0.48 fof(f179,plain,(
% 0.19/0.48 function(sk0_20)),
% 0.19/0.48 inference(cnf_transformation,[status(esa)],[f178])).
% 0.19/0.48 fof(f180,plain,(
% 0.19/0.48 quasi_total(sk0_20,sk0_18,sk0_19)),
% 0.19/0.48 inference(cnf_transformation,[status(esa)],[f178])).
% 0.19/0.48 fof(f181,plain,(
% 0.19/0.48 relation_of2_as_subset(sk0_20,sk0_18,sk0_19)),
% 0.19/0.48 inference(cnf_transformation,[status(esa)],[f178])).
% 0.19/0.48 fof(f182,plain,(
% 0.19/0.48 ~sk0_19=empty_set),
% 0.19/0.48 inference(cnf_transformation,[status(esa)],[f178])).
% 0.19/0.48 fof(f183,plain,(
% 0.19/0.48 in(sk0_22,relation_inverse_image(sk0_20,sk0_21))|in(sk0_22,sk0_18)),
% 0.19/0.48 inference(cnf_transformation,[status(esa)],[f178])).
% 0.19/0.48 fof(f184,plain,(
% 0.19/0.48 in(sk0_22,relation_inverse_image(sk0_20,sk0_21))|in(apply(sk0_20,sk0_22),sk0_21)),
% 0.19/0.48 inference(cnf_transformation,[status(esa)],[f178])).
% 0.19/0.48 fof(f185,plain,(
% 0.19/0.48 ~in(sk0_22,relation_inverse_image(sk0_20,sk0_21))|~in(sk0_22,sk0_18)|~in(apply(sk0_20,sk0_22),sk0_21)),
% 0.19/0.48 inference(cnf_transformation,[status(esa)],[f178])).
% 0.19/0.48 fof(f192,plain,(
% 0.19/0.48 ![A]: (~empty(A)|A=empty_set)),
% 0.19/0.48 inference(pre_NNF_transformation,[status(esa)],[f52])).
% 0.19/0.48 fof(f193,plain,(
% 0.19/0.48 ![X0]: (~empty(X0)|X0=empty_set)),
% 0.19/0.48 inference(cnf_transformation,[status(esa)],[f192])).
% 0.19/0.48 fof(f194,plain,(
% 0.19/0.48 ![A,B]: (~in(A,B)|~empty(B))),
% 0.19/0.48 inference(pre_NNF_transformation,[status(esa)],[f53])).
% 0.19/0.48 fof(f195,plain,(
% 0.19/0.48 ![B]: ((![A]: ~in(A,B))|~empty(B))),
% 0.19/0.48 inference(miniscoping,[status(esa)],[f194])).
% 0.19/0.48 fof(f196,plain,(
% 0.19/0.48 ![X0,X1]: (~in(X0,X1)|~empty(X1))),
% 0.19/0.48 inference(cnf_transformation,[status(esa)],[f195])).
% 0.19/0.48 fof(f200,plain,(
% 0.19/0.48 ![A,B]: (~pd0_0(B,A)|(B=empty_set&~A=empty_set))),
% 0.19/0.48 inference(pre_NNF_transformation,[status(esa)],[f79])).
% 0.19/0.48 fof(f201,plain,(
% 0.19/0.48 ![X0,X1]: (~pd0_0(X0,X1)|X0=empty_set)),
% 0.19/0.48 inference(cnf_transformation,[status(esa)],[f200])).
% 0.19/0.48 fof(f203,plain,(
% 0.19/0.48 spl0_0 <=> in(sk0_22,relation_inverse_image(sk0_20,sk0_21))),
% 0.19/0.48 introduced(split_symbol_definition)).
% 0.19/0.48 fof(f204,plain,(
% 0.19/0.48 in(sk0_22,relation_inverse_image(sk0_20,sk0_21))|~spl0_0),
% 0.19/0.48 inference(component_clause,[status(thm)],[f203])).
% 0.19/0.48 fof(f206,plain,(
% 0.19/0.48 spl0_1 <=> in(sk0_22,sk0_18)),
% 0.19/0.48 introduced(split_symbol_definition)).
% 0.19/0.48 fof(f207,plain,(
% 0.19/0.48 in(sk0_22,sk0_18)|~spl0_1),
% 0.19/0.48 inference(component_clause,[status(thm)],[f206])).
% 0.19/0.48 fof(f208,plain,(
% 0.19/0.48 ~in(sk0_22,sk0_18)|spl0_1),
% 0.19/0.48 inference(component_clause,[status(thm)],[f206])).
% 0.19/0.48 fof(f209,plain,(
% 0.19/0.48 spl0_0|spl0_1),
% 0.19/0.48 inference(split_clause,[status(thm)],[f183,f203,f206])).
% 0.19/0.48 fof(f210,plain,(
% 0.19/0.48 spl0_2 <=> in(apply(sk0_20,sk0_22),sk0_21)),
% 0.19/0.48 introduced(split_symbol_definition)).
% 0.19/0.48 fof(f211,plain,(
% 0.19/0.48 in(apply(sk0_20,sk0_22),sk0_21)|~spl0_2),
% 0.19/0.48 inference(component_clause,[status(thm)],[f210])).
% 0.19/0.48 fof(f213,plain,(
% 0.19/0.48 spl0_0|spl0_2),
% 0.19/0.48 inference(split_clause,[status(thm)],[f184,f203,f210])).
% 0.19/0.48 fof(f214,plain,(
% 0.19/0.48 ~spl0_0|~spl0_1|~spl0_2),
% 0.19/0.48 inference(split_clause,[status(thm)],[f185,f203,f206,f210])).
% 0.19/0.48 fof(f215,plain,(
% 0.19/0.48 ![X0,X1,X2]: (~relation(X0)|~function(X0)|~in(X1,relation_inverse_image(X0,X2))|in(X1,relation_dom(X0)))),
% 0.19/0.48 inference(destructive_equality_resolution,[status(esa)],[f72])).
% 0.19/0.48 fof(f216,plain,(
% 0.19/0.48 ![X0,X1,X2]: (~relation(X0)|~function(X0)|~in(X1,relation_inverse_image(X0,X2))|in(apply(X0,X1),X2))),
% 0.19/0.48 inference(destructive_equality_resolution,[status(esa)],[f73])).
% 0.19/0.48 fof(f217,plain,(
% 0.19/0.48 ![X0,X1,X2]: (~relation(X0)|~function(X0)|in(X1,relation_inverse_image(X0,X2))|~in(X1,relation_dom(X0))|~in(apply(X0,X1),X2))),
% 0.19/0.48 inference(destructive_equality_resolution,[status(esa)],[f74])).
% 0.19/0.48 fof(f222,plain,(
% 0.19/0.48 spl0_3 <=> function(empty_set)),
% 0.19/0.48 introduced(split_symbol_definition)).
% 0.19/0.48 fof(f224,plain,(
% 0.19/0.48 ~function(empty_set)|spl0_3),
% 0.19/0.48 inference(component_clause,[status(thm)],[f222])).
% 0.19/0.48 fof(f225,plain,(
% 0.19/0.48 spl0_4 <=> X0=relation_inverse_image(empty_set,X1)|in(sk0_0(X0,X1,empty_set),X0)|in(apply(empty_set,sk0_0(X0,X1,empty_set)),X1)),
% 0.19/0.48 introduced(split_symbol_definition)).
% 0.19/0.48 fof(f228,plain,(
% 0.19/0.48 ![X0,X1]: (~function(empty_set)|X0=relation_inverse_image(empty_set,X1)|in(sk0_0(X0,X1,empty_set),X0)|in(apply(empty_set,sk0_0(X0,X1,empty_set)),X1))),
% 0.19/0.48 inference(resolution,[status(thm)],[f77,f97])).
% 0.19/0.48 fof(f229,plain,(
% 0.19/0.48 ~spl0_3|spl0_4),
% 0.19/0.48 inference(split_clause,[status(thm)],[f228,f222,f225])).
% 0.19/0.48 fof(f230,plain,(
% 0.19/0.48 spl0_5 <=> function(sk0_4)),
% 0.19/0.48 introduced(split_symbol_definition)).
% 0.19/0.48 fof(f232,plain,(
% 0.19/0.48 ~function(sk0_4)|spl0_5),
% 0.19/0.48 inference(component_clause,[status(thm)],[f230])).
% 0.19/0.48 fof(f233,plain,(
% 0.19/0.48 spl0_6 <=> X0=relation_inverse_image(sk0_4,X1)|in(sk0_0(X0,X1,sk0_4),X0)|in(apply(sk0_4,sk0_0(X0,X1,sk0_4)),X1)),
% 0.19/0.48 introduced(split_symbol_definition)).
% 0.19/0.48 fof(f234,plain,(
% 0.19/0.48 ![X0,X1]: (X0=relation_inverse_image(sk0_4,X1)|in(sk0_0(X0,X1,sk0_4),X0)|in(apply(sk0_4,sk0_0(X0,X1,sk0_4)),X1)|~spl0_6)),
% 0.19/0.48 inference(component_clause,[status(thm)],[f233])).
% 0.19/0.48 fof(f236,plain,(
% 0.19/0.48 ![X0,X1]: (~function(sk0_4)|X0=relation_inverse_image(sk0_4,X1)|in(sk0_0(X0,X1,sk0_4),X0)|in(apply(sk0_4,sk0_0(X0,X1,sk0_4)),X1))),
% 0.19/0.48 inference(resolution,[status(thm)],[f111,f77])).
% 0.19/0.48 fof(f237,plain,(
% 0.19/0.48 ~spl0_5|spl0_6),
% 0.19/0.48 inference(split_clause,[status(thm)],[f236,f230,f233])).
% 0.19/0.48 fof(f238,plain,(
% 0.19/0.48 spl0_7 <=> function(sk0_6)),
% 0.19/0.48 introduced(split_symbol_definition)).
% 0.19/0.48 fof(f240,plain,(
% 0.19/0.48 ~function(sk0_6)|spl0_7),
% 0.19/0.48 inference(component_clause,[status(thm)],[f238])).
% 0.19/0.48 fof(f241,plain,(
% 0.19/0.48 spl0_8 <=> X0=relation_inverse_image(sk0_6,X1)|in(sk0_0(X0,X1,sk0_6),X0)|in(apply(sk0_6,sk0_0(X0,X1,sk0_6)),X1)),
% 0.19/0.48 introduced(split_symbol_definition)).
% 0.19/0.48 fof(f242,plain,(
% 0.19/0.48 ![X0,X1]: (X0=relation_inverse_image(sk0_6,X1)|in(sk0_0(X0,X1,sk0_6),X0)|in(apply(sk0_6,sk0_0(X0,X1,sk0_6)),X1)|~spl0_8)),
% 0.19/0.48 inference(component_clause,[status(thm)],[f241])).
% 0.19/0.48 fof(f244,plain,(
% 0.19/0.48 ![X0,X1]: (~function(sk0_6)|X0=relation_inverse_image(sk0_6,X1)|in(sk0_0(X0,X1,sk0_6),X0)|in(apply(sk0_6,sk0_0(X0,X1,sk0_6)),X1))),
% 0.19/0.48 inference(resolution,[status(thm)],[f119,f77])).
% 0.19/0.48 fof(f245,plain,(
% 0.19/0.48 ~spl0_7|spl0_8),
% 0.19/0.48 inference(split_clause,[status(thm)],[f244,f238,f241])).
% 0.19/0.48 fof(f250,plain,(
% 0.19/0.48 spl0_9 <=> function(sk0_7)),
% 0.19/0.48 introduced(split_symbol_definition)).
% 0.19/0.48 fof(f252,plain,(
% 0.19/0.48 ~function(sk0_7)|spl0_9),
% 0.19/0.48 inference(component_clause,[status(thm)],[f250])).
% 0.19/0.48 fof(f253,plain,(
% 0.19/0.48 spl0_10 <=> X0=relation_inverse_image(sk0_7,X1)|in(sk0_0(X0,X1,sk0_7),X0)|in(apply(sk0_7,sk0_0(X0,X1,sk0_7)),X1)),
% 0.19/0.48 introduced(split_symbol_definition)).
% 0.19/0.48 fof(f256,plain,(
% 0.19/0.48 ![X0,X1]: (~function(sk0_7)|X0=relation_inverse_image(sk0_7,X1)|in(sk0_0(X0,X1,sk0_7),X0)|in(apply(sk0_7,sk0_0(X0,X1,sk0_7)),X1))),
% 0.19/0.48 inference(resolution,[status(thm)],[f125,f77])).
% 0.19/0.48 fof(f257,plain,(
% 0.19/0.48 ~spl0_9|spl0_10),
% 0.19/0.48 inference(split_clause,[status(thm)],[f256,f250,f253])).
% 0.19/0.48 fof(f258,plain,(
% 0.19/0.48 sk0_9=empty_set),
% 0.19/0.48 inference(resolution,[status(thm)],[f131,f193])).
% 0.19/0.48 fof(f260,plain,(
% 0.19/0.48 spl0_11 <=> function(sk0_10)),
% 0.19/0.48 introduced(split_symbol_definition)).
% 0.19/0.48 fof(f262,plain,(
% 0.19/0.48 ~function(sk0_10)|spl0_11),
% 0.19/0.48 inference(component_clause,[status(thm)],[f260])).
% 0.19/0.48 fof(f263,plain,(
% 0.19/0.48 spl0_12 <=> X0=relation_inverse_image(sk0_10,X1)|in(sk0_0(X0,X1,sk0_10),X0)|in(apply(sk0_10,sk0_0(X0,X1,sk0_10)),X1)),
% 0.19/0.48 introduced(split_symbol_definition)).
% 0.19/0.48 fof(f264,plain,(
% 0.19/0.48 ![X0,X1]: (X0=relation_inverse_image(sk0_10,X1)|in(sk0_0(X0,X1,sk0_10),X0)|in(apply(sk0_10,sk0_0(X0,X1,sk0_10)),X1)|~spl0_12)),
% 0.19/0.48 inference(component_clause,[status(thm)],[f263])).
% 0.19/0.48 fof(f266,plain,(
% 0.19/0.48 ![X0,X1]: (~function(sk0_10)|X0=relation_inverse_image(sk0_10,X1)|in(sk0_0(X0,X1,sk0_10),X0)|in(apply(sk0_10,sk0_0(X0,X1,sk0_10)),X1))),
% 0.19/0.48 inference(resolution,[status(thm)],[f133,f77])).
% 0.19/0.48 fof(f267,plain,(
% 0.19/0.48 ~spl0_11|spl0_12),
% 0.19/0.48 inference(split_clause,[status(thm)],[f266,f260,f263])).
% 0.19/0.48 fof(f268,plain,(
% 0.19/0.48 sk0_10=empty_set),
% 0.19/0.48 inference(resolution,[status(thm)],[f134,f193])).
% 0.19/0.48 fof(f278,plain,(
% 0.19/0.48 spl0_15 <=> function(sk0_15)),
% 0.19/0.48 introduced(split_symbol_definition)).
% 0.19/0.48 fof(f280,plain,(
% 0.19/0.48 ~function(sk0_15)|spl0_15),
% 0.19/0.48 inference(component_clause,[status(thm)],[f278])).
% 0.19/0.48 fof(f281,plain,(
% 0.19/0.48 spl0_16 <=> X0=relation_inverse_image(sk0_15,X1)|in(sk0_0(X0,X1,sk0_15),X0)|in(apply(sk0_15,sk0_0(X0,X1,sk0_15)),X1)),
% 0.19/0.48 introduced(split_symbol_definition)).
% 0.19/0.48 fof(f282,plain,(
% 0.19/0.48 ![X0,X1]: (X0=relation_inverse_image(sk0_15,X1)|in(sk0_0(X0,X1,sk0_15),X0)|in(apply(sk0_15,sk0_0(X0,X1,sk0_15)),X1)|~spl0_16)),
% 0.19/0.48 inference(component_clause,[status(thm)],[f281])).
% 0.19/0.48 fof(f284,plain,(
% 0.19/0.48 ![X0,X1]: (~function(sk0_15)|X0=relation_inverse_image(sk0_15,X1)|in(sk0_0(X0,X1,sk0_15),X0)|in(apply(sk0_15,sk0_0(X0,X1,sk0_15)),X1))),
% 0.19/0.48 inference(resolution,[status(thm)],[f149,f77])).
% 0.19/0.48 fof(f285,plain,(
% 0.19/0.48 ~spl0_15|spl0_16),
% 0.19/0.48 inference(split_clause,[status(thm)],[f284,f278,f281])).
% 0.19/0.48 fof(f291,plain,(
% 0.19/0.48 ![X0]: (~empty(X0)|~function(X0)|one_to_one(X0))),
% 0.19/0.48 inference(forward_subsumption_resolution,[status(thm)],[f67,f60])).
% 0.19/0.48 fof(f300,plain,(
% 0.19/0.48 spl0_19 <=> empty(sk0_10)),
% 0.19/0.48 introduced(split_symbol_definition)).
% 0.19/0.48 fof(f302,plain,(
% 0.19/0.48 ~empty(sk0_10)|spl0_19),
% 0.19/0.48 inference(component_clause,[status(thm)],[f300])).
% 0.19/0.48 fof(f303,plain,(
% 0.19/0.48 spl0_20 <=> one_to_one(sk0_10)),
% 0.19/0.48 introduced(split_symbol_definition)).
% 0.19/0.48 fof(f306,plain,(
% 0.19/0.48 ~empty(sk0_10)|one_to_one(sk0_10)),
% 0.19/0.48 inference(resolution,[status(thm)],[f291,f135])).
% 0.19/0.48 fof(f307,plain,(
% 0.19/0.48 ~spl0_19|spl0_20),
% 0.19/0.48 inference(split_clause,[status(thm)],[f306,f300,f303])).
% 0.19/0.48 fof(f308,plain,(
% 0.19/0.48 spl0_21 <=> empty(sk0_6)),
% 0.19/0.48 introduced(split_symbol_definition)).
% 0.19/0.48 fof(f310,plain,(
% 0.19/0.48 ~empty(sk0_6)|spl0_21),
% 0.19/0.48 inference(component_clause,[status(thm)],[f308])).
% 0.19/0.48 fof(f311,plain,(
% 0.19/0.48 spl0_22 <=> one_to_one(sk0_6)),
% 0.19/0.48 introduced(split_symbol_definition)).
% 0.19/0.48 fof(f314,plain,(
% 0.19/0.48 ~empty(sk0_6)|one_to_one(sk0_6)),
% 0.19/0.48 inference(resolution,[status(thm)],[f291,f120])).
% 0.19/0.48 fof(f315,plain,(
% 0.19/0.48 ~spl0_21|spl0_22),
% 0.19/0.48 inference(split_clause,[status(thm)],[f314,f308,f311])).
% 0.19/0.48 fof(f324,plain,(
% 0.19/0.48 spl0_25 <=> empty(sk0_20)),
% 0.19/0.48 introduced(split_symbol_definition)).
% 0.19/0.48 fof(f327,plain,(
% 0.19/0.48 spl0_26 <=> one_to_one(sk0_20)),
% 0.19/0.48 introduced(split_symbol_definition)).
% 0.19/0.48 fof(f330,plain,(
% 0.19/0.48 ~empty(sk0_20)|one_to_one(sk0_20)),
% 0.19/0.48 inference(resolution,[status(thm)],[f291,f179])).
% 0.19/0.48 fof(f331,plain,(
% 0.19/0.48 ~spl0_25|spl0_26),
% 0.19/0.48 inference(split_clause,[status(thm)],[f330,f324,f327])).
% 0.19/0.48 fof(f332,plain,(
% 0.19/0.48 $false|spl0_21),
% 0.19/0.48 inference(forward_subsumption_resolution,[status(thm)],[f310,f122])).
% 0.19/0.48 fof(f333,plain,(
% 0.19/0.48 spl0_21),
% 0.19/0.48 inference(contradiction_clause,[status(thm)],[f332])).
% 0.19/0.48 fof(f334,plain,(
% 0.19/0.48 $false|spl0_19),
% 0.19/0.48 inference(forward_subsumption_resolution,[status(thm)],[f302,f134])).
% 0.19/0.48 fof(f335,plain,(
% 0.19/0.48 spl0_19),
% 0.19/0.48 inference(contradiction_clause,[status(thm)],[f334])).
% 0.19/0.48 fof(f336,plain,(
% 0.19/0.48 spl0_27 <=> relation(sk0_20)),
% 0.19/0.48 introduced(split_symbol_definition)).
% 0.19/0.48 fof(f338,plain,(
% 0.19/0.48 ~relation(sk0_20)|spl0_27),
% 0.19/0.48 inference(component_clause,[status(thm)],[f336])).
% 0.19/0.48 fof(f339,plain,(
% 0.19/0.48 spl0_28 <=> function(sk0_20)),
% 0.19/0.48 introduced(split_symbol_definition)).
% 0.19/0.48 fof(f341,plain,(
% 0.19/0.48 ~function(sk0_20)|spl0_28),
% 0.19/0.48 inference(component_clause,[status(thm)],[f339])).
% 0.19/0.48 fof(f342,plain,(
% 0.19/0.48 ~relation(sk0_20)|~function(sk0_20)|in(apply(sk0_20,sk0_22),sk0_21)|~spl0_0),
% 0.19/0.48 inference(resolution,[status(thm)],[f204,f216])).
% 0.19/0.48 fof(f343,plain,(
% 0.19/0.48 ~spl0_27|~spl0_28|spl0_2|~spl0_0),
% 0.19/0.48 inference(split_clause,[status(thm)],[f342,f336,f339,f210,f203])).
% 0.19/0.48 fof(f346,plain,(
% 0.19/0.48 $false|spl0_5),
% 0.19/0.48 inference(forward_subsumption_resolution,[status(thm)],[f232,f112])).
% 0.19/0.48 fof(f347,plain,(
% 0.19/0.48 spl0_5),
% 0.19/0.48 inference(contradiction_clause,[status(thm)],[f346])).
% 0.19/0.48 fof(f348,plain,(
% 0.19/0.48 $false|spl0_7),
% 0.19/0.48 inference(forward_subsumption_resolution,[status(thm)],[f240,f120])).
% 0.19/0.48 fof(f349,plain,(
% 0.19/0.48 spl0_7),
% 0.19/0.48 inference(contradiction_clause,[status(thm)],[f348])).
% 0.19/0.48 fof(f350,plain,(
% 0.19/0.48 $false|spl0_11),
% 0.19/0.48 inference(forward_subsumption_resolution,[status(thm)],[f262,f135])).
% 0.19/0.48 fof(f351,plain,(
% 0.19/0.48 spl0_11),
% 0.19/0.48 inference(contradiction_clause,[status(thm)],[f350])).
% 0.19/0.48 fof(f352,plain,(
% 0.19/0.48 $false|spl0_15),
% 0.19/0.48 inference(forward_subsumption_resolution,[status(thm)],[f280,f150])).
% 0.19/0.48 fof(f353,plain,(
% 0.19/0.48 spl0_15),
% 0.19/0.48 inference(contradiction_clause,[status(thm)],[f352])).
% 0.19/0.48 fof(f354,plain,(
% 0.19/0.48 spl0_29 <=> X0=relation_inverse_image(sk0_4,X1)|in(apply(sk0_4,sk0_0(X0,X1,sk0_4)),X1)|X0=relation_inverse_image(sk0_4,X1)|~in(sk0_0(X0,X1,sk0_4),relation_dom(sk0_4))|~in(apply(sk0_4,sk0_0(X0,X1,sk0_4)),X1)),
% 0.19/0.48 introduced(split_symbol_definition)).
% 0.19/0.48 fof(f357,plain,(
% 0.19/0.48 spl0_30 <=> relation(sk0_4)),
% 0.19/0.48 introduced(split_symbol_definition)).
% 0.19/0.48 fof(f359,plain,(
% 0.19/0.48 ~relation(sk0_4)|spl0_30),
% 0.19/0.48 inference(component_clause,[status(thm)],[f357])).
% 0.19/0.48 fof(f360,plain,(
% 0.19/0.48 ![X0,X1]: (X0=relation_inverse_image(sk0_4,X1)|in(apply(sk0_4,sk0_0(X0,X1,sk0_4)),X1)|~relation(sk0_4)|~function(sk0_4)|X0=relation_inverse_image(sk0_4,X1)|~in(sk0_0(X0,X1,sk0_4),relation_dom(sk0_4))|~in(apply(sk0_4,sk0_0(X0,X1,sk0_4)),X1)|~spl0_6)),
% 0.19/0.48 inference(resolution,[status(thm)],[f234,f75])).
% 0.19/0.48 fof(f361,plain,(
% 0.19/0.48 spl0_29|~spl0_30|~spl0_5|~spl0_6),
% 0.19/0.48 inference(split_clause,[status(thm)],[f360,f354,f357,f230,f233])).
% 0.19/0.48 fof(f365,plain,(
% 0.19/0.48 spl0_31 <=> X0=relation_inverse_image(sk0_4,X1)|in(sk0_0(X0,X1,sk0_4),X0)|in(sk0_0(X0,X1,sk0_4),relation_inverse_image(sk0_4,X1))|~in(sk0_0(X0,X1,sk0_4),relation_dom(sk0_4))),
% 0.19/0.48 introduced(split_symbol_definition)).
% 0.19/0.48 fof(f368,plain,(
% 0.19/0.48 ![X0,X1]: (X0=relation_inverse_image(sk0_4,X1)|in(sk0_0(X0,X1,sk0_4),X0)|~relation(sk0_4)|~function(sk0_4)|in(sk0_0(X0,X1,sk0_4),relation_inverse_image(sk0_4,X1))|~in(sk0_0(X0,X1,sk0_4),relation_dom(sk0_4))|~spl0_6)),
% 0.19/0.48 inference(resolution,[status(thm)],[f234,f217])).
% 0.19/0.48 fof(f369,plain,(
% 0.19/0.48 spl0_31|~spl0_30|~spl0_5|~spl0_6),
% 0.19/0.48 inference(split_clause,[status(thm)],[f368,f365,f357,f230,f233])).
% 0.19/0.48 fof(f371,plain,(
% 0.19/0.48 ![X0,X1]: (X0=relation_inverse_image(sk0_4,X1)|in(sk0_0(X0,X1,sk0_4),X0)|~empty(X1)|~spl0_6)),
% 0.19/0.48 inference(resolution,[status(thm)],[f234,f196])).
% 0.19/0.48 fof(f373,plain,(
% 0.19/0.48 $false|spl0_30),
% 0.19/0.48 inference(forward_subsumption_resolution,[status(thm)],[f359,f111])).
% 0.19/0.48 fof(f374,plain,(
% 0.19/0.48 spl0_30),
% 0.19/0.48 inference(contradiction_clause,[status(thm)],[f373])).
% 0.19/0.48 fof(f375,plain,(
% 0.19/0.48 ![X0]: (X0=relation_inverse_image(sk0_4,sk0_10)|in(sk0_0(X0,sk0_10,sk0_4),X0)|~spl0_6)),
% 0.19/0.48 inference(resolution,[status(thm)],[f371,f134])).
% 0.19/0.48 fof(f380,plain,(
% 0.19/0.48 spl0_32 <=> X0=relation_inverse_image(sk0_4,sk0_10)|X0=relation_inverse_image(sk0_4,sk0_10)|~in(sk0_0(X0,sk0_10,sk0_4),relation_dom(sk0_4))|~in(apply(sk0_4,sk0_0(X0,sk0_10,sk0_4)),sk0_10)),
% 0.19/0.48 introduced(split_symbol_definition)).
% 0.19/0.48 fof(f383,plain,(
% 0.19/0.48 ![X0]: (X0=relation_inverse_image(sk0_4,sk0_10)|~relation(sk0_4)|~function(sk0_4)|X0=relation_inverse_image(sk0_4,sk0_10)|~in(sk0_0(X0,sk0_10,sk0_4),relation_dom(sk0_4))|~in(apply(sk0_4,sk0_0(X0,sk0_10,sk0_4)),sk0_10)|~spl0_6)),
% 0.19/0.48 inference(resolution,[status(thm)],[f375,f75])).
% 0.19/0.48 fof(f384,plain,(
% 0.19/0.48 spl0_32|~spl0_30|~spl0_5|~spl0_6),
% 0.19/0.48 inference(split_clause,[status(thm)],[f383,f380,f357,f230,f233])).
% 0.19/0.48 fof(f386,plain,(
% 0.19/0.48 ![X0]: (X0=relation_inverse_image(sk0_4,sk0_10)|~empty(X0)|~spl0_6)),
% 0.19/0.48 inference(resolution,[status(thm)],[f375,f196])).
% 0.19/0.48 fof(f389,plain,(
% 0.19/0.48 spl0_33 <=> X0=relation_inverse_image(sk0_6,X1)|in(apply(sk0_6,sk0_0(X0,X1,sk0_6)),X1)|X0=relation_inverse_image(sk0_6,X1)|~in(sk0_0(X0,X1,sk0_6),relation_dom(sk0_6))|~in(apply(sk0_6,sk0_0(X0,X1,sk0_6)),X1)),
% 0.19/0.48 introduced(split_symbol_definition)).
% 0.19/0.48 fof(f392,plain,(
% 0.19/0.48 spl0_34 <=> relation(sk0_6)),
% 0.19/0.48 introduced(split_symbol_definition)).
% 0.19/0.48 fof(f394,plain,(
% 0.19/0.48 ~relation(sk0_6)|spl0_34),
% 0.19/0.48 inference(component_clause,[status(thm)],[f392])).
% 0.19/0.48 fof(f395,plain,(
% 0.19/0.48 ![X0,X1]: (X0=relation_inverse_image(sk0_6,X1)|in(apply(sk0_6,sk0_0(X0,X1,sk0_6)),X1)|~relation(sk0_6)|~function(sk0_6)|X0=relation_inverse_image(sk0_6,X1)|~in(sk0_0(X0,X1,sk0_6),relation_dom(sk0_6))|~in(apply(sk0_6,sk0_0(X0,X1,sk0_6)),X1)|~spl0_8)),
% 0.19/0.48 inference(resolution,[status(thm)],[f242,f75])).
% 0.19/0.48 fof(f396,plain,(
% 0.19/0.48 spl0_33|~spl0_34|~spl0_7|~spl0_8),
% 0.19/0.48 inference(split_clause,[status(thm)],[f395,f389,f392,f238,f241])).
% 0.19/0.48 fof(f400,plain,(
% 0.19/0.48 spl0_35 <=> X0=relation_inverse_image(sk0_6,X1)|in(sk0_0(X0,X1,sk0_6),X0)|in(sk0_0(X0,X1,sk0_6),relation_inverse_image(sk0_6,X1))|~in(sk0_0(X0,X1,sk0_6),relation_dom(sk0_6))),
% 0.19/0.48 introduced(split_symbol_definition)).
% 0.19/0.48 fof(f403,plain,(
% 0.19/0.48 ![X0,X1]: (X0=relation_inverse_image(sk0_6,X1)|in(sk0_0(X0,X1,sk0_6),X0)|~relation(sk0_6)|~function(sk0_6)|in(sk0_0(X0,X1,sk0_6),relation_inverse_image(sk0_6,X1))|~in(sk0_0(X0,X1,sk0_6),relation_dom(sk0_6))|~spl0_8)),
% 0.19/0.48 inference(resolution,[status(thm)],[f242,f217])).
% 0.19/0.48 fof(f404,plain,(
% 0.19/0.48 spl0_35|~spl0_34|~spl0_7|~spl0_8),
% 0.19/0.48 inference(split_clause,[status(thm)],[f403,f400,f392,f238,f241])).
% 0.19/0.48 fof(f408,plain,(
% 0.19/0.48 $false|spl0_34),
% 0.19/0.48 inference(forward_subsumption_resolution,[status(thm)],[f394,f119])).
% 0.19/0.48 fof(f409,plain,(
% 0.19/0.48 spl0_34),
% 0.19/0.48 inference(contradiction_clause,[status(thm)],[f408])).
% 0.19/0.48 fof(f410,plain,(
% 0.19/0.48 spl0_36 <=> X0=relation_inverse_image(sk0_10,X1)|in(apply(sk0_10,sk0_0(X0,X1,sk0_10)),X1)|X0=relation_inverse_image(sk0_10,X1)|~in(sk0_0(X0,X1,sk0_10),relation_dom(sk0_10))|~in(apply(sk0_10,sk0_0(X0,X1,sk0_10)),X1)),
% 0.19/0.48 introduced(split_symbol_definition)).
% 0.19/0.48 fof(f413,plain,(
% 0.19/0.48 spl0_37 <=> relation(sk0_10)),
% 0.19/0.48 introduced(split_symbol_definition)).
% 0.19/0.48 fof(f415,plain,(
% 0.19/0.48 ~relation(sk0_10)|spl0_37),
% 0.19/0.48 inference(component_clause,[status(thm)],[f413])).
% 0.19/0.48 fof(f416,plain,(
% 0.19/0.48 ![X0,X1]: (X0=relation_inverse_image(sk0_10,X1)|in(apply(sk0_10,sk0_0(X0,X1,sk0_10)),X1)|~relation(sk0_10)|~function(sk0_10)|X0=relation_inverse_image(sk0_10,X1)|~in(sk0_0(X0,X1,sk0_10),relation_dom(sk0_10))|~in(apply(sk0_10,sk0_0(X0,X1,sk0_10)),X1)|~spl0_12)),
% 0.19/0.48 inference(resolution,[status(thm)],[f264,f75])).
% 0.19/0.48 fof(f417,plain,(
% 0.19/0.48 spl0_36|~spl0_37|~spl0_11|~spl0_12),
% 0.19/0.48 inference(split_clause,[status(thm)],[f416,f410,f413,f260,f263])).
% 0.19/0.48 fof(f421,plain,(
% 0.19/0.48 spl0_38 <=> X0=relation_inverse_image(sk0_10,X1)|in(sk0_0(X0,X1,sk0_10),X0)|in(sk0_0(X0,X1,sk0_10),relation_inverse_image(sk0_10,X1))|~in(sk0_0(X0,X1,sk0_10),relation_dom(sk0_10))),
% 0.19/0.48 introduced(split_symbol_definition)).
% 0.19/0.48 fof(f424,plain,(
% 0.19/0.48 ![X0,X1]: (X0=relation_inverse_image(sk0_10,X1)|in(sk0_0(X0,X1,sk0_10),X0)|~relation(sk0_10)|~function(sk0_10)|in(sk0_0(X0,X1,sk0_10),relation_inverse_image(sk0_10,X1))|~in(sk0_0(X0,X1,sk0_10),relation_dom(sk0_10))|~spl0_12)),
% 0.19/0.48 inference(resolution,[status(thm)],[f264,f217])).
% 0.19/0.48 fof(f425,plain,(
% 0.19/0.48 spl0_38|~spl0_37|~spl0_11|~spl0_12),
% 0.19/0.48 inference(split_clause,[status(thm)],[f424,f421,f413,f260,f263])).
% 0.19/0.48 fof(f429,plain,(
% 0.19/0.48 $false|spl0_37),
% 0.19/0.48 inference(forward_subsumption_resolution,[status(thm)],[f415,f133])).
% 0.19/0.48 fof(f430,plain,(
% 0.19/0.48 spl0_37),
% 0.19/0.48 inference(contradiction_clause,[status(thm)],[f429])).
% 0.19/0.48 fof(f431,plain,(
% 0.19/0.48 sk0_10=relation_inverse_image(sk0_4,sk0_10)|~spl0_6),
% 0.19/0.48 inference(resolution,[status(thm)],[f386,f134])).
% 0.19/0.48 fof(f432,plain,(
% 0.19/0.48 sk0_9=relation_inverse_image(sk0_4,sk0_10)|~spl0_6),
% 0.19/0.48 inference(resolution,[status(thm)],[f386,f131])).
% 0.19/0.48 fof(f436,plain,(
% 0.19/0.48 ![X0]: (X0=sk0_10|~empty(X0)|~spl0_6)),
% 0.19/0.48 inference(backward_demodulation,[status(thm)],[f431,f386])).
% 0.19/0.48 fof(f437,plain,(
% 0.19/0.48 ![X0]: (X0=sk0_10|in(sk0_0(X0,sk0_10,sk0_4),X0)|~spl0_6)),
% 0.19/0.48 inference(backward_demodulation,[status(thm)],[f431,f375])).
% 0.19/0.48 fof(f438,plain,(
% 0.19/0.48 spl0_39 <=> ~in(X0,sk0_10)|in(apply(sk0_4,X0),sk0_10)),
% 0.19/0.48 introduced(split_symbol_definition)).
% 0.19/0.48 fof(f441,plain,(
% 0.19/0.48 ![X0]: (~relation(sk0_4)|~function(sk0_4)|~in(X0,sk0_10)|in(apply(sk0_4,X0),sk0_10)|~spl0_6)),
% 0.19/0.48 inference(paramodulation,[status(thm)],[f431,f216])).
% 0.19/0.48 fof(f442,plain,(
% 0.19/0.48 ~spl0_30|~spl0_5|spl0_39|~spl0_6),
% 0.19/0.48 inference(split_clause,[status(thm)],[f441,f357,f230,f438,f233])).
% 0.19/0.48 fof(f443,plain,(
% 0.19/0.48 sk0_9=sk0_10|~spl0_6),
% 0.19/0.48 inference(resolution,[status(thm)],[f436,f131])).
% 0.19/0.48 fof(f444,plain,(
% 0.19/0.48 sk0_7=sk0_10|~spl0_6),
% 0.19/0.48 inference(resolution,[status(thm)],[f436,f124])).
% 0.19/0.48 fof(f445,plain,(
% 0.19/0.48 sk0_6=sk0_10|~spl0_6),
% 0.19/0.48 inference(resolution,[status(thm)],[f436,f122])).
% 0.19/0.48 fof(f446,plain,(
% 0.19/0.48 empty_set=sk0_10|~spl0_6),
% 0.19/0.48 inference(resolution,[status(thm)],[f436,f96])).
% 0.19/0.48 fof(f451,plain,(
% 0.19/0.48 ![X0,X1]: (X0=relation_inverse_image(sk0_10,X1)|in(sk0_0(X0,X1,sk0_10),X0)|in(apply(sk0_10,sk0_0(X0,X1,sk0_9)),X1)|~spl0_6|~spl0_12)),
% 0.19/0.48 inference(backward_demodulation,[status(thm)],[f443,f264])).
% 0.19/0.48 fof(f452,plain,(
% 0.19/0.48 ![X0,X1]: (X0=relation_inverse_image(sk0_9,X1)|in(sk0_0(X0,X1,sk0_10),X0)|in(apply(sk0_10,sk0_0(X0,X1,sk0_9)),X1)|~spl0_6|~spl0_12)),
% 0.19/0.48 inference(forward_demodulation,[status(thm)],[f443,f451])).
% 0.19/0.48 fof(f453,plain,(
% 0.19/0.48 ![X0,X1]: (X0=relation_inverse_image(sk0_9,X1)|in(sk0_0(X0,X1,sk0_9),X0)|in(apply(sk0_10,sk0_0(X0,X1,sk0_9)),X1)|~spl0_6|~spl0_12)),
% 0.19/0.48 inference(forward_demodulation,[status(thm)],[f443,f452])).
% 0.19/0.48 fof(f454,plain,(
% 0.19/0.48 ![X0,X1]: (X0=relation_inverse_image(sk0_9,X1)|in(sk0_0(X0,X1,sk0_9),X0)|in(apply(sk0_9,sk0_0(X0,X1,sk0_9)),X1)|~spl0_6|~spl0_12)),
% 0.19/0.48 inference(forward_demodulation,[status(thm)],[f443,f453])).
% 0.19/0.48 fof(f455,plain,(
% 0.19/0.48 function(sk0_9)|~spl0_6),
% 0.19/0.48 inference(backward_demodulation,[status(thm)],[f443,f135])).
% 0.19/0.48 fof(f458,plain,(
% 0.19/0.48 sk0_7=sk0_9|~spl0_6),
% 0.19/0.48 inference(forward_demodulation,[status(thm)],[f443,f444])).
% 0.19/0.48 fof(f461,plain,(
% 0.19/0.48 empty_set=sk0_6|~spl0_6),
% 0.19/0.48 inference(forward_demodulation,[status(thm)],[f445,f446])).
% 0.19/0.48 fof(f469,plain,(
% 0.19/0.48 function(empty_set)|~spl0_6),
% 0.19/0.48 inference(backward_demodulation,[status(thm)],[f461,f120])).
% 0.19/0.48 fof(f470,plain,(
% 0.19/0.48 $false|spl0_3|~spl0_6),
% 0.19/0.48 inference(forward_subsumption_resolution,[status(thm)],[f469,f224])).
% 0.19/0.48 fof(f471,plain,(
% 0.19/0.48 spl0_3|~spl0_6),
% 0.19/0.48 inference(contradiction_clause,[status(thm)],[f470])).
% 0.19/0.48 fof(f474,plain,(
% 0.19/0.48 function(sk0_7)|~spl0_6),
% 0.19/0.48 inference(forward_demodulation,[status(thm)],[f458,f455])).
% 0.19/0.48 fof(f475,plain,(
% 0.19/0.48 $false|spl0_9|~spl0_6),
% 0.19/0.48 inference(forward_subsumption_resolution,[status(thm)],[f474,f252])).
% 0.19/0.48 fof(f476,plain,(
% 0.19/0.48 spl0_9|~spl0_6),
% 0.19/0.48 inference(contradiction_clause,[status(thm)],[f475])).
% 0.19/0.48 fof(f484,plain,(
% 0.19/0.48 spl0_40 <=> empty(empty_set)),
% 0.19/0.48 introduced(split_symbol_definition)).
% 0.19/0.48 fof(f486,plain,(
% 0.19/0.48 ~empty(empty_set)|spl0_40),
% 0.19/0.48 inference(component_clause,[status(thm)],[f484])).
% 0.19/0.48 fof(f487,plain,(
% 0.19/0.48 spl0_41 <=> one_to_one(empty_set)),
% 0.19/0.48 introduced(split_symbol_definition)).
% 0.19/0.48 fof(f490,plain,(
% 0.19/0.48 ~empty(empty_set)|one_to_one(empty_set)|~spl0_6),
% 0.19/0.48 inference(resolution,[status(thm)],[f469,f291])).
% 0.19/0.48 fof(f491,plain,(
% 0.19/0.48 ~spl0_40|spl0_41|~spl0_6),
% 0.19/0.48 inference(split_clause,[status(thm)],[f490,f484,f487,f233])).
% 0.19/0.48 fof(f492,plain,(
% 0.19/0.48 $false|spl0_40),
% 0.19/0.48 inference(forward_subsumption_resolution,[status(thm)],[f486,f96])).
% 0.19/0.48 fof(f493,plain,(
% 0.19/0.48 spl0_40),
% 0.19/0.48 inference(contradiction_clause,[status(thm)],[f492])).
% 0.19/0.48 fof(f504,plain,(
% 0.19/0.48 spl0_44 <=> function(sk0_17)),
% 0.19/0.48 introduced(split_symbol_definition)).
% 0.19/0.48 fof(f506,plain,(
% 0.19/0.48 ~function(sk0_17)|spl0_44),
% 0.19/0.48 inference(component_clause,[status(thm)],[f504])).
% 0.19/0.48 fof(f507,plain,(
% 0.19/0.48 spl0_45 <=> X0=relation_inverse_image(sk0_17,X1)|in(sk0_0(X0,X1,sk0_17),X0)|in(apply(sk0_17,sk0_0(X0,X1,sk0_17)),X1)),
% 0.19/0.48 introduced(split_symbol_definition)).
% 0.19/0.48 fof(f510,plain,(
% 0.19/0.48 ![X0,X1]: (~function(sk0_17)|X0=relation_inverse_image(sk0_17,X1)|in(sk0_0(X0,X1,sk0_17),X0)|in(apply(sk0_17,sk0_0(X0,X1,sk0_17)),X1))),
% 0.19/0.48 inference(resolution,[status(thm)],[f156,f77])).
% 0.19/0.48 fof(f511,plain,(
% 0.19/0.48 ~spl0_44|spl0_45),
% 0.19/0.48 inference(split_clause,[status(thm)],[f510,f504,f507])).
% 0.19/0.48 fof(f522,plain,(
% 0.19/0.48 spl0_48 <=> in(sk0_22,relation_dom(sk0_20))),
% 0.19/0.48 introduced(split_symbol_definition)).
% 0.19/0.48 fof(f523,plain,(
% 0.19/0.48 in(sk0_22,relation_dom(sk0_20))|~spl0_48),
% 0.19/0.48 inference(component_clause,[status(thm)],[f522])).
% 0.19/0.48 fof(f524,plain,(
% 0.19/0.48 ~in(sk0_22,relation_dom(sk0_20))|spl0_48),
% 0.19/0.48 inference(component_clause,[status(thm)],[f522])).
% 0.19/0.48 fof(f525,plain,(
% 0.19/0.48 ~relation(sk0_20)|~function(sk0_20)|in(sk0_22,relation_dom(sk0_20))|~spl0_0),
% 0.19/0.48 inference(resolution,[status(thm)],[f215,f204])).
% 0.19/0.48 fof(f526,plain,(
% 0.19/0.48 ~spl0_27|~spl0_28|spl0_48|~spl0_0),
% 0.19/0.48 inference(split_clause,[status(thm)],[f525,f336,f339,f522,f203])).
% 0.19/0.48 fof(f527,plain,(
% 0.19/0.48 spl0_49 <=> X0=relation_inverse_image(sk0_17,X1)|in(sk0_0(X0,X1,sk0_17),X0)|in(sk0_0(X0,X1,sk0_17),relation_dom(sk0_17))),
% 0.19/0.48 introduced(split_symbol_definition)).
% 0.19/0.48 fof(f530,plain,(
% 0.19/0.48 ![X0,X1]: (~function(sk0_17)|X0=relation_inverse_image(sk0_17,X1)|in(sk0_0(X0,X1,sk0_17),X0)|in(sk0_0(X0,X1,sk0_17),relation_dom(sk0_17)))),
% 0.19/0.48 inference(resolution,[status(thm)],[f76,f156])).
% 0.19/0.48 fof(f531,plain,(
% 0.19/0.48 ~spl0_44|spl0_49),
% 0.19/0.48 inference(split_clause,[status(thm)],[f530,f504,f527])).
% 0.19/0.48 fof(f537,plain,(
% 0.19/0.48 spl0_51 <=> X0=relation_inverse_image(sk0_15,X1)|in(sk0_0(X0,X1,sk0_15),X0)|in(sk0_0(X0,X1,sk0_15),relation_dom(sk0_15))),
% 0.19/0.48 introduced(split_symbol_definition)).
% 0.19/0.48 fof(f540,plain,(
% 0.19/0.48 ![X0,X1]: (~function(sk0_15)|X0=relation_inverse_image(sk0_15,X1)|in(sk0_0(X0,X1,sk0_15),X0)|in(sk0_0(X0,X1,sk0_15),relation_dom(sk0_15)))),
% 0.19/0.48 inference(resolution,[status(thm)],[f76,f149])).
% 0.19/0.48 fof(f541,plain,(
% 0.19/0.48 ~spl0_15|spl0_51),
% 0.19/0.48 inference(split_clause,[status(thm)],[f540,f278,f537])).
% 0.19/0.48 fof(f547,plain,(
% 0.19/0.48 spl0_53 <=> X0=relation_inverse_image(sk0_4,X1)|in(sk0_0(X0,X1,sk0_4),X0)|in(sk0_0(X0,X1,sk0_4),relation_dom(sk0_4))),
% 0.19/0.48 introduced(split_symbol_definition)).
% 0.19/0.48 fof(f550,plain,(
% 0.19/0.48 ![X0,X1]: (~function(sk0_4)|X0=relation_inverse_image(sk0_4,X1)|in(sk0_0(X0,X1,sk0_4),X0)|in(sk0_0(X0,X1,sk0_4),relation_dom(sk0_4)))),
% 0.19/0.48 inference(resolution,[status(thm)],[f76,f111])).
% 0.19/0.48 fof(f551,plain,(
% 0.19/0.48 ~spl0_5|spl0_53),
% 0.19/0.48 inference(split_clause,[status(thm)],[f550,f230,f547])).
% 0.19/0.48 fof(f552,plain,(
% 0.19/0.48 spl0_54 <=> X0=relation_inverse_image(empty_set,X1)|in(sk0_0(X0,X1,empty_set),X0)|in(sk0_0(X0,X1,empty_set),relation_dom(empty_set))),
% 0.19/0.48 introduced(split_symbol_definition)).
% 0.19/0.48 fof(f553,plain,(
% 0.19/0.48 ![X0,X1]: (X0=relation_inverse_image(empty_set,X1)|in(sk0_0(X0,X1,empty_set),X0)|in(sk0_0(X0,X1,empty_set),relation_dom(empty_set))|~spl0_54)),
% 0.19/0.48 inference(component_clause,[status(thm)],[f552])).
% 0.19/0.48 fof(f555,plain,(
% 0.19/0.48 ![X0,X1]: (~function(empty_set)|X0=relation_inverse_image(empty_set,X1)|in(sk0_0(X0,X1,empty_set),X0)|in(sk0_0(X0,X1,empty_set),relation_dom(empty_set)))),
% 0.19/0.48 inference(resolution,[status(thm)],[f76,f97])).
% 0.19/0.48 fof(f556,plain,(
% 0.19/0.48 ~spl0_3|spl0_54),
% 0.19/0.48 inference(split_clause,[status(thm)],[f555,f222,f552])).
% 0.19/0.48 fof(f567,plain,(
% 0.19/0.48 empty(relation_dom(empty_set))),
% 0.19/0.48 inference(resolution,[status(thm)],[f108,f96])).
% 0.19/0.48 fof(f570,plain,(
% 0.19/0.48 relation(relation_dom(empty_set))),
% 0.19/0.48 inference(resolution,[status(thm)],[f567,f60])).
% 0.19/0.48 fof(f571,plain,(
% 0.19/0.48 relation_dom(empty_set)=empty_set),
% 0.19/0.48 inference(resolution,[status(thm)],[f567,f193])).
% 0.19/0.48 fof(f572,plain,(
% 0.19/0.48 function(relation_dom(empty_set))),
% 0.19/0.48 inference(resolution,[status(thm)],[f567,f58])).
% 0.19/0.48 fof(f573,plain,(
% 0.19/0.48 spl0_55 <=> function(relation_dom(empty_set))),
% 0.19/0.48 introduced(split_symbol_definition)).
% 0.19/0.48 fof(f575,plain,(
% 0.19/0.48 ~function(relation_dom(empty_set))|spl0_55),
% 0.19/0.48 inference(component_clause,[status(thm)],[f573])).
% 0.19/0.48 fof(f576,plain,(
% 0.19/0.48 spl0_56 <=> X0=relation_inverse_image(relation_dom(empty_set),X1)|in(sk0_0(X0,X1,relation_dom(empty_set)),X0)|in(sk0_0(X0,X1,relation_dom(empty_set)),relation_dom(relation_dom(empty_set)))),
% 0.19/0.48 introduced(split_symbol_definition)).
% 0.19/0.48 fof(f579,plain,(
% 0.19/0.48 ![X0,X1]: (~function(relation_dom(empty_set))|X0=relation_inverse_image(relation_dom(empty_set),X1)|in(sk0_0(X0,X1,relation_dom(empty_set)),X0)|in(sk0_0(X0,X1,relation_dom(empty_set)),relation_dom(relation_dom(empty_set))))),
% 0.19/0.48 inference(resolution,[status(thm)],[f570,f76])).
% 0.19/0.48 fof(f580,plain,(
% 0.19/0.48 ~spl0_55|spl0_56),
% 0.19/0.48 inference(split_clause,[status(thm)],[f579,f573,f576])).
% 0.19/0.48 fof(f581,plain,(
% 0.19/0.48 spl0_57 <=> X0=relation_inverse_image(relation_dom(empty_set),X1)|in(sk0_0(X0,X1,relation_dom(empty_set)),X0)|in(apply(relation_dom(empty_set),sk0_0(X0,X1,relation_dom(empty_set))),X1)),
% 0.19/0.48 introduced(split_symbol_definition)).
% 0.19/0.48 fof(f584,plain,(
% 0.19/0.48 ![X0,X1]: (~function(relation_dom(empty_set))|X0=relation_inverse_image(relation_dom(empty_set),X1)|in(sk0_0(X0,X1,relation_dom(empty_set)),X0)|in(apply(relation_dom(empty_set),sk0_0(X0,X1,relation_dom(empty_set))),X1))),
% 0.19/0.48 inference(resolution,[status(thm)],[f570,f77])).
% 0.19/0.48 fof(f585,plain,(
% 0.19/0.48 ~spl0_55|spl0_57),
% 0.19/0.48 inference(split_clause,[status(thm)],[f584,f573,f581])).
% 0.19/0.48 fof(f586,plain,(
% 0.19/0.48 spl0_58 <=> empty(relation_dom(empty_set))),
% 0.19/0.48 introduced(split_symbol_definition)).
% 0.19/0.48 fof(f588,plain,(
% 0.19/0.48 ~empty(relation_dom(empty_set))|spl0_58),
% 0.19/0.48 inference(component_clause,[status(thm)],[f586])).
% 0.19/0.48 fof(f589,plain,(
% 0.19/0.48 spl0_59 <=> one_to_one(relation_dom(empty_set))),
% 0.19/0.48 introduced(split_symbol_definition)).
% 0.19/0.48 fof(f592,plain,(
% 0.19/0.48 ~empty(relation_dom(empty_set))|one_to_one(relation_dom(empty_set))),
% 0.19/0.48 inference(resolution,[status(thm)],[f572,f291])).
% 0.19/0.48 fof(f593,plain,(
% 0.19/0.48 ~spl0_58|spl0_59),
% 0.19/0.48 inference(split_clause,[status(thm)],[f592,f586,f589])).
% 0.19/0.48 fof(f594,plain,(
% 0.19/0.48 $false|spl0_58),
% 0.19/0.48 inference(forward_subsumption_resolution,[status(thm)],[f588,f567])).
% 0.19/0.48 fof(f595,plain,(
% 0.19/0.48 spl0_58),
% 0.19/0.48 inference(contradiction_clause,[status(thm)],[f594])).
% 0.19/0.48 fof(f603,plain,(
% 0.19/0.48 spl0_60 <=> relation_of2_as_subset(sk0_20,sk0_18,sk0_19)),
% 0.19/0.48 introduced(split_symbol_definition)).
% 0.19/0.48 fof(f605,plain,(
% 0.19/0.48 ~relation_of2_as_subset(sk0_20,sk0_18,sk0_19)|spl0_60),
% 0.19/0.48 inference(component_clause,[status(thm)],[f603])).
% 0.19/0.48 fof(f606,plain,(
% 0.19/0.48 spl0_61 <=> pd0_0(sk0_19,sk0_18)),
% 0.19/0.48 introduced(split_symbol_definition)).
% 0.19/0.48 fof(f607,plain,(
% 0.19/0.48 pd0_0(sk0_19,sk0_18)|~spl0_61),
% 0.19/0.48 inference(component_clause,[status(thm)],[f606])).
% 0.19/0.48 fof(f609,plain,(
% 0.19/0.48 spl0_62 <=> sk0_18=relation_dom_as_subset(sk0_18,sk0_19,sk0_20)),
% 0.19/0.48 introduced(split_symbol_definition)).
% 0.19/0.48 fof(f610,plain,(
% 0.19/0.48 sk0_18=relation_dom_as_subset(sk0_18,sk0_19,sk0_20)|~spl0_62),
% 0.19/0.48 inference(component_clause,[status(thm)],[f609])).
% 0.19/0.48 fof(f612,plain,(
% 0.19/0.48 ~relation_of2_as_subset(sk0_20,sk0_18,sk0_19)|pd0_0(sk0_19,sk0_18)|sk0_18=relation_dom_as_subset(sk0_18,sk0_19,sk0_20)),
% 0.19/0.48 inference(resolution,[status(thm)],[f82,f180])).
% 0.19/0.48 fof(f613,plain,(
% 0.19/0.48 ~spl0_60|spl0_61|spl0_62),
% 0.19/0.48 inference(split_clause,[status(thm)],[f612,f603,f606,f609])).
% 0.19/0.48 fof(f614,plain,(
% 0.19/0.48 $false|spl0_60),
% 0.19/0.48 inference(forward_subsumption_resolution,[status(thm)],[f605,f181])).
% 0.19/0.48 fof(f615,plain,(
% 0.19/0.48 spl0_60),
% 0.19/0.48 inference(contradiction_clause,[status(thm)],[f614])).
% 0.19/0.48 fof(f617,plain,(
% 0.19/0.48 spl0_63 <=> quasi_total(sk0_20,sk0_18,sk0_19)),
% 0.19/0.48 introduced(split_symbol_definition)).
% 0.19/0.48 fof(f620,plain,(
% 0.19/0.48 pd0_0(sk0_19,sk0_18)|quasi_total(sk0_20,sk0_18,sk0_19)|~sk0_18=relation_dom_as_subset(sk0_18,sk0_19,sk0_20)),
% 0.19/0.48 inference(resolution,[status(thm)],[f83,f181])).
% 0.19/0.48 fof(f621,plain,(
% 0.19/0.48 spl0_61|spl0_63|~spl0_62),
% 0.19/0.48 inference(split_clause,[status(thm)],[f620,f606,f617,f609])).
% 0.19/0.48 fof(f622,plain,(
% 0.19/0.48 sk0_19=empty_set|~spl0_61),
% 0.19/0.48 inference(resolution,[status(thm)],[f607,f201])).
% 0.19/0.48 fof(f623,plain,(
% 0.19/0.48 $false|~spl0_61),
% 0.19/0.48 inference(forward_subsumption_resolution,[status(thm)],[f622,f182])).
% 0.19/0.48 fof(f624,plain,(
% 0.19/0.48 ~spl0_61),
% 0.19/0.48 inference(contradiction_clause,[status(thm)],[f623])).
% 0.19/0.48 fof(f626,plain,(
% 0.19/0.48 spl0_64 <=> X0=relation_inverse_image(sk0_15,X1)|in(apply(sk0_15,sk0_0(X0,X1,sk0_15)),X1)|X0=relation_inverse_image(sk0_15,X1)|~in(sk0_0(X0,X1,sk0_15),relation_dom(sk0_15))|~in(apply(sk0_15,sk0_0(X0,X1,sk0_15)),X1)),
% 0.19/0.48 introduced(split_symbol_definition)).
% 0.19/0.48 fof(f629,plain,(
% 0.19/0.48 spl0_65 <=> relation(sk0_15)),
% 0.19/0.48 introduced(split_symbol_definition)).
% 0.19/0.48 fof(f631,plain,(
% 0.19/0.48 ~relation(sk0_15)|spl0_65),
% 0.19/0.48 inference(component_clause,[status(thm)],[f629])).
% 0.19/0.48 fof(f632,plain,(
% 0.19/0.48 ![X0,X1]: (X0=relation_inverse_image(sk0_15,X1)|in(apply(sk0_15,sk0_0(X0,X1,sk0_15)),X1)|~relation(sk0_15)|~function(sk0_15)|X0=relation_inverse_image(sk0_15,X1)|~in(sk0_0(X0,X1,sk0_15),relation_dom(sk0_15))|~in(apply(sk0_15,sk0_0(X0,X1,sk0_15)),X1)|~spl0_16)),
% 0.19/0.48 inference(resolution,[status(thm)],[f282,f75])).
% 0.19/0.48 fof(f633,plain,(
% 0.19/0.48 spl0_64|~spl0_65|~spl0_15|~spl0_16),
% 0.19/0.48 inference(split_clause,[status(thm)],[f632,f626,f629,f278,f281])).
% 0.19/0.48 fof(f639,plain,(
% 0.19/0.48 spl0_66 <=> X0=relation_inverse_image(sk0_15,X1)|in(sk0_0(X0,X1,sk0_15),X0)|in(sk0_0(X0,X1,sk0_15),relation_inverse_image(sk0_15,X1))|~in(sk0_0(X0,X1,sk0_15),relation_dom(sk0_15))),
% 0.19/0.48 introduced(split_symbol_definition)).
% 0.19/0.48 fof(f642,plain,(
% 0.19/0.48 ![X0,X1]: (X0=relation_inverse_image(sk0_15,X1)|in(sk0_0(X0,X1,sk0_15),X0)|~relation(sk0_15)|~function(sk0_15)|in(sk0_0(X0,X1,sk0_15),relation_inverse_image(sk0_15,X1))|~in(sk0_0(X0,X1,sk0_15),relation_dom(sk0_15))|~spl0_16)),
% 0.19/0.48 inference(resolution,[status(thm)],[f282,f217])).
% 0.19/0.48 fof(f643,plain,(
% 0.19/0.48 spl0_66|~spl0_65|~spl0_15|~spl0_16),
% 0.19/0.48 inference(split_clause,[status(thm)],[f642,f639,f629,f278,f281])).
% 0.19/0.48 fof(f649,plain,(
% 0.19/0.48 $false|spl0_65),
% 0.19/0.48 inference(forward_subsumption_resolution,[status(thm)],[f631,f149])).
% 0.19/0.48 fof(f650,plain,(
% 0.19/0.48 spl0_65),
% 0.19/0.48 inference(contradiction_clause,[status(thm)],[f649])).
% 0.19/0.48 fof(f651,plain,(
% 0.19/0.48 $false|spl0_44),
% 0.19/0.48 inference(forward_subsumption_resolution,[status(thm)],[f506,f158])).
% 0.19/0.48 fof(f652,plain,(
% 0.19/0.48 spl0_44),
% 0.19/0.48 inference(contradiction_clause,[status(thm)],[f651])).
% 0.19/0.48 fof(f654,plain,(
% 0.19/0.48 empty_set=relation_inverse_image(sk0_4,sk0_10)|~spl0_6),
% 0.19/0.48 inference(forward_demodulation,[status(thm)],[f258,f432])).
% 0.19/0.48 fof(f655,plain,(
% 0.19/0.48 empty_set=relation_inverse_image(sk0_4,empty_set)|~spl0_6),
% 0.19/0.48 inference(forward_demodulation,[status(thm)],[f268,f654])).
% 0.19/0.48 fof(f656,plain,(
% 0.19/0.48 spl0_67 <=> ~in(X0,empty_set)|in(X0,relation_dom(sk0_4))),
% 0.19/0.48 introduced(split_symbol_definition)).
% 0.19/0.48 fof(f659,plain,(
% 0.19/0.48 ![X0]: (~relation(sk0_4)|~function(sk0_4)|~in(X0,empty_set)|in(X0,relation_dom(sk0_4))|~spl0_6)),
% 0.19/0.48 inference(paramodulation,[status(thm)],[f655,f215])).
% 0.19/0.48 fof(f660,plain,(
% 0.19/0.48 ~spl0_30|~spl0_5|spl0_67|~spl0_6),
% 0.19/0.48 inference(split_clause,[status(thm)],[f659,f357,f230,f656,f233])).
% 0.19/0.48 fof(f661,plain,(
% 0.19/0.48 spl0_68 <=> ~in(X0,empty_set)|in(apply(sk0_4,X0),empty_set)),
% 0.19/0.48 introduced(split_symbol_definition)).
% 0.19/0.48 fof(f664,plain,(
% 0.19/0.48 ![X0]: (~relation(sk0_4)|~function(sk0_4)|~in(X0,empty_set)|in(apply(sk0_4,X0),empty_set)|~spl0_6)),
% 0.19/0.48 inference(paramodulation,[status(thm)],[f655,f216])).
% 0.19/0.48 fof(f665,plain,(
% 0.19/0.48 ~spl0_30|~spl0_5|spl0_68|~spl0_6),
% 0.19/0.48 inference(split_clause,[status(thm)],[f664,f357,f230,f661,f233])).
% 0.19/0.48 fof(f677,plain,(
% 0.19/0.48 ![X0,X1]: (X0=relation_inverse_image(empty_set,X1)|in(sk0_0(X0,X1,sk0_9),X0)|in(apply(sk0_9,sk0_0(X0,X1,sk0_9)),X1)|~spl0_6|~spl0_12)),
% 0.19/0.48 inference(forward_demodulation,[status(thm)],[f258,f454])).
% 0.19/0.48 fof(f678,plain,(
% 0.19/0.48 ![X0,X1]: (X0=relation_inverse_image(empty_set,X1)|in(sk0_0(X0,X1,empty_set),X0)|in(apply(sk0_9,sk0_0(X0,X1,sk0_9)),X1)|~spl0_6|~spl0_12)),
% 0.19/0.48 inference(forward_demodulation,[status(thm)],[f258,f677])).
% 0.19/0.48 fof(f679,plain,(
% 0.19/0.48 ![X0,X1]: (X0=relation_inverse_image(empty_set,X1)|in(sk0_0(X0,X1,empty_set),X0)|in(apply(empty_set,sk0_0(X0,X1,sk0_9)),X1)|~spl0_6|~spl0_12)),
% 0.19/0.48 inference(forward_demodulation,[status(thm)],[f258,f678])).
% 0.19/0.48 fof(f680,plain,(
% 0.19/0.48 ![X0,X1]: (X0=relation_inverse_image(empty_set,X1)|in(sk0_0(X0,X1,empty_set),X0)|in(apply(empty_set,sk0_0(X0,X1,empty_set)),X1)|~spl0_6|~spl0_12)),
% 0.19/0.48 inference(forward_demodulation,[status(thm)],[f258,f679])).
% 0.19/0.48 fof(f681,plain,(
% 0.19/0.48 spl0_69 <=> X0=relation_inverse_image(empty_set,X1)|in(apply(empty_set,sk0_0(X0,X1,empty_set)),X1)|X0=relation_inverse_image(empty_set,X1)|~in(sk0_0(X0,X1,empty_set),relation_dom(empty_set))|~in(apply(empty_set,sk0_0(X0,X1,empty_set)),X1)),
% 0.19/0.48 introduced(split_symbol_definition)).
% 0.19/0.48 fof(f684,plain,(
% 0.19/0.48 spl0_70 <=> relation(empty_set)),
% 0.19/0.48 introduced(split_symbol_definition)).
% 0.19/0.48 fof(f686,plain,(
% 0.19/0.48 ~relation(empty_set)|spl0_70),
% 0.19/0.48 inference(component_clause,[status(thm)],[f684])).
% 0.19/0.48 fof(f687,plain,(
% 0.19/0.48 ![X0,X1]: (X0=relation_inverse_image(empty_set,X1)|in(apply(empty_set,sk0_0(X0,X1,empty_set)),X1)|~relation(empty_set)|~function(empty_set)|X0=relation_inverse_image(empty_set,X1)|~in(sk0_0(X0,X1,empty_set),relation_dom(empty_set))|~in(apply(empty_set,sk0_0(X0,X1,empty_set)),X1)|~spl0_6|~spl0_12)),
% 0.19/0.48 inference(resolution,[status(thm)],[f680,f75])).
% 0.19/0.48 fof(f688,plain,(
% 0.19/0.48 spl0_69|~spl0_70|~spl0_3|~spl0_6|~spl0_12),
% 0.19/0.48 inference(split_clause,[status(thm)],[f687,f681,f684,f222,f233,f263])).
% 0.19/0.48 fof(f695,plain,(
% 0.19/0.48 spl0_71 <=> X0=relation_inverse_image(empty_set,X1)|in(sk0_0(X0,X1,empty_set),X0)|in(sk0_0(X0,X1,empty_set),relation_inverse_image(empty_set,X1))|~in(sk0_0(X0,X1,empty_set),relation_dom(empty_set))),
% 0.19/0.48 introduced(split_symbol_definition)).
% 0.19/0.48 fof(f698,plain,(
% 0.19/0.48 ![X0,X1]: (X0=relation_inverse_image(empty_set,X1)|in(sk0_0(X0,X1,empty_set),X0)|~relation(empty_set)|~function(empty_set)|in(sk0_0(X0,X1,empty_set),relation_inverse_image(empty_set,X1))|~in(sk0_0(X0,X1,empty_set),relation_dom(empty_set))|~spl0_6|~spl0_12)),
% 0.19/0.48 inference(resolution,[status(thm)],[f680,f217])).
% 0.19/0.48 fof(f699,plain,(
% 0.19/0.48 spl0_71|~spl0_70|~spl0_3|~spl0_6|~spl0_12),
% 0.19/0.48 inference(split_clause,[status(thm)],[f698,f695,f684,f222,f233,f263])).
% 0.19/0.48 fof(f706,plain,(
% 0.19/0.48 $false|spl0_70),
% 0.19/0.48 inference(forward_subsumption_resolution,[status(thm)],[f686,f97])).
% 0.19/0.48 fof(f707,plain,(
% 0.19/0.48 spl0_70),
% 0.19/0.48 inference(contradiction_clause,[status(thm)],[f706])).
% 0.19/0.48 fof(f708,plain,(
% 0.19/0.48 $false|spl0_55),
% 0.19/0.48 inference(forward_subsumption_resolution,[status(thm)],[f575,f572])).
% 0.19/0.48 fof(f709,plain,(
% 0.19/0.48 spl0_55),
% 0.19/0.48 inference(contradiction_clause,[status(thm)],[f708])).
% 0.19/0.48 fof(f718,plain,(
% 0.19/0.48 ![X0]: (X0=empty_set|in(sk0_0(X0,sk0_10,sk0_4),X0)|~spl0_6)),
% 0.19/0.48 inference(forward_demodulation,[status(thm)],[f268,f437])).
% 0.19/0.48 fof(f719,plain,(
% 0.19/0.48 ![X0]: (X0=empty_set|in(sk0_0(X0,empty_set,sk0_4),X0)|~spl0_6)),
% 0.19/0.48 inference(forward_demodulation,[status(thm)],[f268,f718])).
% 0.19/0.48 fof(f720,plain,(
% 0.19/0.48 spl0_72 <=> X0=empty_set|X0=relation_inverse_image(sk0_4,empty_set)|~in(sk0_0(X0,empty_set,sk0_4),relation_dom(sk0_4))|~in(apply(sk0_4,sk0_0(X0,empty_set,sk0_4)),empty_set)),
% 0.19/0.48 introduced(split_symbol_definition)).
% 0.19/0.48 fof(f723,plain,(
% 0.19/0.48 ![X0]: (X0=empty_set|~relation(sk0_4)|~function(sk0_4)|X0=relation_inverse_image(sk0_4,empty_set)|~in(sk0_0(X0,empty_set,sk0_4),relation_dom(sk0_4))|~in(apply(sk0_4,sk0_0(X0,empty_set,sk0_4)),empty_set)|~spl0_6)),
% 0.19/0.48 inference(resolution,[status(thm)],[f719,f75])).
% 0.19/0.48 fof(f724,plain,(
% 0.19/0.48 spl0_72|~spl0_30|~spl0_5|~spl0_6),
% 0.19/0.48 inference(split_clause,[status(thm)],[f723,f720,f357,f230,f233])).
% 0.19/0.48 fof(f760,plain,(
% 0.19/0.48 spl0_76 <=> relation_dom(empty_set)=relation_inverse_image(empty_set,X0)|relation_dom(empty_set)=relation_inverse_image(empty_set,X0)|~in(sk0_0(relation_dom(empty_set),X0,empty_set),relation_dom(empty_set))|~in(apply(empty_set,sk0_0(relation_dom(empty_set),X0,empty_set)),X0)),
% 0.19/0.48 introduced(split_symbol_definition)).
% 0.19/0.48 fof(f763,plain,(
% 0.19/0.48 ![X0]: (relation_dom(empty_set)=relation_inverse_image(empty_set,X0)|~relation(empty_set)|~function(empty_set)|relation_dom(empty_set)=relation_inverse_image(empty_set,X0)|~in(sk0_0(relation_dom(empty_set),X0,empty_set),relation_dom(empty_set))|~in(apply(empty_set,sk0_0(relation_dom(empty_set),X0,empty_set)),X0)|~spl0_54)),
% 0.19/0.48 inference(resolution,[status(thm)],[f553,f75])).
% 0.19/0.48 fof(f764,plain,(
% 0.19/0.48 spl0_76|~spl0_70|~spl0_3|~spl0_54),
% 0.19/0.48 inference(split_clause,[status(thm)],[f763,f760,f684,f222,f552])).
% 0.19/0.48 fof(f765,plain,(
% 0.19/0.48 spl0_77 <=> X0=relation_inverse_image(empty_set,X1)|in(sk0_0(X0,X1,empty_set),relation_dom(empty_set))|X0=relation_inverse_image(empty_set,X1)|~in(sk0_0(X0,X1,empty_set),relation_dom(empty_set))|~in(apply(empty_set,sk0_0(X0,X1,empty_set)),X1)),
% 0.19/0.48 introduced(split_symbol_definition)).
% 0.19/0.48 fof(f768,plain,(
% 0.19/0.48 ![X0,X1]: (X0=relation_inverse_image(empty_set,X1)|in(sk0_0(X0,X1,empty_set),relation_dom(empty_set))|~relation(empty_set)|~function(empty_set)|X0=relation_inverse_image(empty_set,X1)|~in(sk0_0(X0,X1,empty_set),relation_dom(empty_set))|~in(apply(empty_set,sk0_0(X0,X1,empty_set)),X1)|~spl0_54)),
% 0.19/0.48 inference(resolution,[status(thm)],[f553,f75])).
% 0.19/0.48 fof(f769,plain,(
% 0.19/0.48 spl0_77|~spl0_70|~spl0_3|~spl0_54),
% 0.19/0.48 inference(split_clause,[status(thm)],[f768,f765,f684,f222,f552])).
% 0.19/0.48 fof(f776,plain,(
% 0.19/0.48 spl0_78 <=> relation_dom(empty_set)=relation_inverse_image(empty_set,X0)),
% 0.19/0.48 introduced(split_symbol_definition)).
% 0.19/0.48 fof(f777,plain,(
% 0.19/0.48 ![X0]: (relation_dom(empty_set)=relation_inverse_image(empty_set,X0)|~spl0_78)),
% 0.19/0.48 inference(component_clause,[status(thm)],[f776])).
% 0.19/0.48 fof(f779,plain,(
% 0.19/0.48 ![X0]: (relation_dom(empty_set)=relation_inverse_image(empty_set,X0)|~empty(relation_dom(empty_set))|~spl0_54)),
% 0.19/0.48 inference(resolution,[status(thm)],[f553,f196])).
% 0.19/0.48 fof(f780,plain,(
% 0.19/0.48 spl0_78|~spl0_58|~spl0_54),
% 0.19/0.48 inference(split_clause,[status(thm)],[f779,f776,f586,f552])).
% 0.19/0.48 fof(f784,plain,(
% 0.19/0.48 spl0_79 <=> relation_dom(empty_set)=relation_inverse_image(empty_set,X0)|in(sk0_0(relation_dom(empty_set),X0,empty_set),relation_dom(empty_set))|relation_dom(empty_set)=relation_inverse_image(empty_set,X0)|~in(sk0_0(relation_dom(empty_set),X0,empty_set),relation_dom(empty_set))|~in(apply(empty_set,sk0_0(relation_dom(empty_set),X0,empty_set)),X0)),
% 0.19/0.48 introduced(split_symbol_definition)).
% 0.19/0.48 fof(f787,plain,(
% 0.19/0.48 ![X0]: (relation_dom(empty_set)=relation_inverse_image(empty_set,X0)|in(sk0_0(relation_dom(empty_set),X0,empty_set),relation_dom(empty_set))|~relation(empty_set)|~function(empty_set)|relation_dom(empty_set)=relation_inverse_image(empty_set,X0)|~in(sk0_0(relation_dom(empty_set),X0,empty_set),relation_dom(empty_set))|~in(apply(empty_set,sk0_0(relation_dom(empty_set),X0,empty_set)),X0)|~spl0_54)),
% 0.19/0.48 inference(resolution,[status(thm)],[f553,f75])).
% 0.19/0.48 fof(f788,plain,(
% 0.19/0.48 spl0_79|~spl0_70|~spl0_3|~spl0_54),
% 0.19/0.48 inference(split_clause,[status(thm)],[f787,f784,f684,f222,f552])).
% 0.19/0.48 fof(f790,plain,(
% 0.19/0.48 spl0_80 <=> X0=relation_inverse_image(empty_set,X1)|in(sk0_0(X0,X1,empty_set),X0)),
% 0.19/0.48 introduced(split_symbol_definition)).
% 0.19/0.48 fof(f793,plain,(
% 0.19/0.48 ![X0,X1]: (X0=relation_inverse_image(empty_set,X1)|in(sk0_0(X0,X1,empty_set),X0)|~empty(relation_dom(empty_set))|~spl0_54)),
% 0.19/0.48 inference(resolution,[status(thm)],[f553,f196])).
% 0.19/0.48 fof(f794,plain,(
% 0.19/0.48 spl0_80|~spl0_58|~spl0_54),
% 0.19/0.48 inference(split_clause,[status(thm)],[f793,f790,f586,f552])).
% 0.19/0.48 fof(f831,plain,(
% 0.19/0.48 relation_of2(sk0_20,sk0_18,sk0_19)),
% 0.19/0.48 inference(resolution,[status(thm)],[f163,f181])).
% 0.19/0.48 fof(f835,plain,(
% 0.19/0.48 relation_dom_as_subset(sk0_18,sk0_19,sk0_20)=relation_dom(sk0_20)),
% 0.19/0.48 inference(resolution,[status(thm)],[f160,f831])).
% 0.19/0.48 fof(f836,plain,(
% 0.19/0.48 sk0_18=relation_dom(sk0_20)|~spl0_62),
% 0.19/0.48 inference(forward_demodulation,[status(thm)],[f610,f835])).
% 0.19/0.48 fof(f838,plain,(
% 0.19/0.48 element(sk0_20,powerset(cartesian_product2(sk0_18,sk0_19)))),
% 0.19/0.48 inference(resolution,[status(thm)],[f89,f181])).
% 0.19/0.48 fof(f839,plain,(
% 0.19/0.48 relation(sk0_20)),
% 0.19/0.48 inference(resolution,[status(thm)],[f838,f63])).
% 0.19/0.48 fof(f840,plain,(
% 0.19/0.48 $false|spl0_27),
% 0.19/0.48 inference(forward_subsumption_resolution,[status(thm)],[f839,f338])).
% 0.19/0.48 fof(f841,plain,(
% 0.19/0.48 spl0_27),
% 0.19/0.48 inference(contradiction_clause,[status(thm)],[f840])).
% 0.19/0.48 fof(f842,plain,(
% 0.19/0.48 $false|spl0_28),
% 0.19/0.48 inference(forward_subsumption_resolution,[status(thm)],[f341,f179])).
% 0.19/0.48 fof(f843,plain,(
% 0.19/0.48 spl0_28),
% 0.19/0.48 inference(contradiction_clause,[status(thm)],[f842])).
% 0.19/0.48 fof(f844,plain,(
% 0.19/0.48 spl0_84 <=> X0=relation_inverse_image(sk0_20,X1)|in(sk0_0(X0,X1,sk0_20),X0)|in(sk0_0(X0,X1,sk0_20),relation_dom(sk0_20))),
% 0.19/0.48 introduced(split_symbol_definition)).
% 0.19/0.48 fof(f847,plain,(
% 0.19/0.48 ![X0,X1]: (~function(sk0_20)|X0=relation_inverse_image(sk0_20,X1)|in(sk0_0(X0,X1,sk0_20),X0)|in(sk0_0(X0,X1,sk0_20),relation_dom(sk0_20)))),
% 0.19/0.48 inference(resolution,[status(thm)],[f839,f76])).
% 0.19/0.48 fof(f848,plain,(
% 0.19/0.48 ~spl0_28|spl0_84),
% 0.19/0.48 inference(split_clause,[status(thm)],[f847,f339,f844])).
% 0.19/0.48 fof(f849,plain,(
% 0.19/0.48 spl0_85 <=> X0=relation_inverse_image(sk0_20,X1)|in(sk0_0(X0,X1,sk0_20),X0)|in(apply(sk0_20,sk0_0(X0,X1,sk0_20)),X1)),
% 0.19/0.48 introduced(split_symbol_definition)).
% 0.19/0.48 fof(f852,plain,(
% 0.19/0.48 ![X0,X1]: (~function(sk0_20)|X0=relation_inverse_image(sk0_20,X1)|in(sk0_0(X0,X1,sk0_20),X0)|in(apply(sk0_20,sk0_0(X0,X1,sk0_20)),X1))),
% 0.19/0.48 inference(resolution,[status(thm)],[f839,f77])).
% 0.19/0.48 fof(f853,plain,(
% 0.19/0.48 ~spl0_28|spl0_85),
% 0.19/0.48 inference(split_clause,[status(thm)],[f852,f339,f849])).
% 0.19/0.48 fof(f876,plain,(
% 0.19/0.48 spl0_86 <=> empty(sk0_18)),
% 0.19/0.48 introduced(split_symbol_definition)).
% 0.19/0.48 fof(f879,plain,(
% 0.19/0.48 empty(sk0_20)|~relation(sk0_20)|~empty(sk0_18)|~spl0_62),
% 0.19/0.49 inference(paramodulation,[status(thm)],[f836,f106])).
% 0.19/0.49 fof(f880,plain,(
% 0.19/0.49 spl0_25|~spl0_27|~spl0_86|~spl0_62),
% 0.19/0.49 inference(split_clause,[status(thm)],[f879,f324,f336,f876,f609])).
% 0.19/0.49 fof(f884,plain,(
% 0.19/0.49 ![X0]: (empty_set=relation_inverse_image(empty_set,X0)|~spl0_78)),
% 0.19/0.49 inference(forward_demodulation,[status(thm)],[f571,f777])).
% 0.19/0.49 fof(f886,plain,(
% 0.19/0.49 spl0_87 <=> ~in(X0,empty_set)|in(X0,relation_dom(empty_set))),
% 0.19/0.49 introduced(split_symbol_definition)).
% 0.19/0.49 fof(f889,plain,(
% 0.19/0.49 ![X0]: (~relation(empty_set)|~function(empty_set)|~in(X0,empty_set)|in(X0,relation_dom(empty_set))|~spl0_78)),
% 0.19/0.49 inference(paramodulation,[status(thm)],[f884,f215])).
% 0.19/0.49 fof(f890,plain,(
% 0.19/0.49 ~spl0_70|~spl0_3|spl0_87|~spl0_78),
% 0.19/0.49 inference(split_clause,[status(thm)],[f889,f684,f222,f886,f776])).
% 0.19/0.49 fof(f891,plain,(
% 0.19/0.49 spl0_88 <=> ~in(X0,empty_set)|in(apply(empty_set,X0),X1)),
% 0.19/0.49 introduced(split_symbol_definition)).
% 0.19/0.49 fof(f894,plain,(
% 0.19/0.49 ![X0,X1]: (~relation(empty_set)|~function(empty_set)|~in(X0,empty_set)|in(apply(empty_set,X0),X1)|~spl0_78)),
% 0.19/0.49 inference(paramodulation,[status(thm)],[f884,f216])).
% 0.19/0.49 fof(f895,plain,(
% 0.19/0.49 ~spl0_70|~spl0_3|spl0_88|~spl0_78),
% 0.19/0.49 inference(split_clause,[status(thm)],[f894,f684,f222,f891,f776])).
% 0.19/0.49 fof(f896,plain,(
% 0.19/0.49 ~relation(sk0_20)|~function(sk0_20)|in(sk0_22,relation_inverse_image(sk0_20,sk0_21))|~in(sk0_22,relation_dom(sk0_20))|~spl0_2),
% 0.19/0.49 inference(resolution,[status(thm)],[f211,f217])).
% 0.19/0.49 fof(f897,plain,(
% 0.19/0.49 ~spl0_27|~spl0_28|spl0_0|~spl0_48|~spl0_2),
% 0.19/0.49 inference(split_clause,[status(thm)],[f896,f336,f339,f203,f522,f210])).
% 0.19/0.49 fof(f901,plain,(
% 0.19/0.49 ~in(sk0_22,sk0_18)|~spl0_62|spl0_48),
% 0.19/0.49 inference(forward_demodulation,[status(thm)],[f836,f524])).
% 0.19/0.49 fof(f902,plain,(
% 0.19/0.49 $false|~spl0_1|~spl0_62|spl0_48),
% 0.19/0.49 inference(forward_subsumption_resolution,[status(thm)],[f901,f207])).
% 0.19/0.49 fof(f903,plain,(
% 0.19/0.49 ~spl0_1|~spl0_62|spl0_48),
% 0.19/0.49 inference(contradiction_clause,[status(thm)],[f902])).
% 0.19/0.49 fof(f904,plain,(
% 0.19/0.49 in(sk0_22,sk0_18)|~spl0_62|~spl0_48),
% 0.19/0.49 inference(forward_demodulation,[status(thm)],[f836,f523])).
% 0.19/0.49 fof(f925,plain,(
% 0.19/0.49 $false|~spl0_62|~spl0_48|spl0_1),
% 0.19/0.49 inference(forward_subsumption_resolution,[status(thm)],[f208,f904])).
% 0.19/0.49 fof(f926,plain,(
% 0.19/0.49 ~spl0_62|~spl0_48|spl0_1),
% 0.19/0.49 inference(contradiction_clause,[status(thm)],[f925])).
% 0.19/0.49 fof(f927,plain,(
% 0.19/0.49 $false),
% 0.19/0.49 inference(sat_refutation,[status(thm)],[f209,f213,f214,f229,f237,f245,f257,f267,f285,f307,f315,f331,f333,f335,f343,f347,f349,f351,f353,f361,f369,f374,f384,f396,f404,f409,f417,f425,f430,f442,f471,f476,f491,f493,f511,f526,f531,f541,f551,f556,f580,f585,f593,f595,f613,f615,f621,f624,f633,f643,f650,f652,f660,f665,f688,f699,f707,f709,f724,f764,f769,f780,f788,f794,f841,f843,f848,f853,f880,f890,f895,f897,f903,f926])).
% 0.19/0.49 % SZS output end CNFRefutation for theBenchmark.p
% 0.19/0.49 % Elapsed time: 0.142547 seconds
% 0.19/0.49 % CPU time: 1.029588 seconds
% 0.19/0.49 % Total memory used: 68.422 MB
% 0.19/0.49 % Net memory used: 67.854 MB
%------------------------------------------------------------------------------