TSTP Solution File: SEU061+1 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SEU061+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed May 31 12:35:46 EDT 2023
% Result : Theorem 0.12s 0.34s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.07 % Problem : SEU061+1 : TPTP v8.1.2. Released v3.2.0.
% 0.06/0.08 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.07/0.26 % Computer : n020.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 : Tue May 30 09:13:58 EDT 2023
% 0.07/0.27 % CPUTime :
% 0.07/0.27 % Drodi V3.5.1
% 0.12/0.34 % Refutation found
% 0.12/0.34 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.34 % SZS output start CNFRefutation for theBenchmark
% 0.12/0.34 fof(f1,axiom,(
% 0.12/0.34 (! [A,B] :( in(A,B)=> ~ in(B,A) ) )),
% 0.12/0.34 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.34 fof(f2,axiom,(
% 0.12/0.34 (! [A] :( empty(A)=> function(A) ) )),
% 0.12/0.34 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.34 fof(f3,axiom,(
% 0.12/0.34 (! [A] :( empty(A)=> relation(A) ) )),
% 0.12/0.34 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.34 fof(f4,axiom,(
% 0.12/0.34 (! [A] :( ( relation(A)& empty(A)& function(A) )=> ( relation(A)& function(A)& one_to_one(A) ) ) )),
% 0.12/0.34 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.34 fof(f6,axiom,(
% 0.12/0.34 (! [A] :( relation(A)=> (! [B,C] :( C = relation_inverse_image(A,B)<=> (! [D] :( in(D,C)<=> (? [E] :( in(ordered_pair(D,E),A)& in(E,B) ) )) )) )) )),
% 0.12/0.34 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.34 fof(f7,axiom,(
% 0.12/0.34 (! [A,B] :( B = singleton(A)<=> (! [C] :( in(C,B)<=> C = A ) )) )),
% 0.12/0.34 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.34 fof(f8,axiom,(
% 0.12/0.34 (! [A] :( A = empty_set<=> (! [B] : ~ in(B,A) )) )),
% 0.12/0.34 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.34 fof(f9,axiom,(
% 0.12/0.34 (! [A] :( relation(A)=> (! [B] :( B = relation_rng(A)<=> (! [C] :( in(C,B)<=> (? [D] : in(ordered_pair(D,C),A) )) )) )) )),
% 0.12/0.34 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.34 fof(f12,axiom,(
% 0.12/0.34 ( empty(empty_set)& relation(empty_set)& relation_empty_yielding(empty_set) ) ),
% 0.12/0.34 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.34 fof(f20,axiom,(
% 0.12/0.34 (! [A] :( empty(A)=> ( empty(relation_rng(A))& relation(relation_rng(A)) ) ) )),
% 0.12/0.34 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.34 fof(f21,axiom,(
% 0.12/0.34 (? [A] :( relation(A)& function(A) ) )),
% 0.12/0.34 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.34 fof(f26,axiom,(
% 0.12/0.34 (? [A] :( ~ empty(A)& relation(A) ) )),
% 0.12/0.34 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.34 fof(f29,axiom,(
% 0.12/0.34 (? [A] :( relation(A)& function(A)& one_to_one(A) ) )),
% 0.12/0.34 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.34 fof(f30,axiom,(
% 0.12/0.34 (? [A] :( relation(A)& relation_empty_yielding(A) ) )),
% 0.12/0.34 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.34 fof(f32,conjecture,(
% 0.12/0.34 (! [A,B] :( relation(B)=> ( in(A,relation_rng(B))<=> relation_inverse_image(B,singleton(A)) != empty_set ) ) )),
% 0.12/0.34 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.34 fof(f33,negated_conjecture,(
% 0.12/0.34 ~((! [A,B] :( relation(B)=> ( in(A,relation_rng(B))<=> relation_inverse_image(B,singleton(A)) != empty_set ) ) ))),
% 0.12/0.34 inference(negated_conjecture,[status(cth)],[f32])).
% 0.12/0.34 fof(f34,axiom,(
% 0.12/0.34 (! [A,B] :( in(A,B)=> element(A,B) ) )),
% 0.12/0.34 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.34 fof(f39,axiom,(
% 0.12/0.34 (! [A] :( empty(A)=> A = empty_set ) )),
% 0.12/0.34 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.34 fof(f40,axiom,(
% 0.12/0.34 (! [A,B] :~ ( in(A,B)& empty(B) ) )),
% 0.12/0.34 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.34 fof(f42,plain,(
% 0.12/0.34 ![A,B]: (~in(A,B)|~in(B,A))),
% 0.12/0.34 inference(pre_NNF_transformation,[status(esa)],[f1])).
% 0.12/0.34 fof(f43,plain,(
% 0.12/0.34 ![X0,X1]: (~in(X0,X1)|~in(X1,X0))),
% 0.12/0.34 inference(cnf_transformation,[status(esa)],[f42])).
% 0.12/0.34 fof(f44,plain,(
% 0.12/0.34 ![A]: (~empty(A)|function(A))),
% 0.12/0.34 inference(pre_NNF_transformation,[status(esa)],[f2])).
% 0.12/0.34 fof(f45,plain,(
% 0.12/0.34 ![X0]: (~empty(X0)|function(X0))),
% 0.12/0.34 inference(cnf_transformation,[status(esa)],[f44])).
% 0.12/0.34 fof(f46,plain,(
% 0.12/0.34 ![A]: (~empty(A)|relation(A))),
% 0.12/0.34 inference(pre_NNF_transformation,[status(esa)],[f3])).
% 0.12/0.34 fof(f47,plain,(
% 0.12/0.34 ![X0]: (~empty(X0)|relation(X0))),
% 0.12/0.34 inference(cnf_transformation,[status(esa)],[f46])).
% 0.12/0.34 fof(f48,plain,(
% 0.12/0.34 ![A]: (((~relation(A)|~empty(A))|~function(A))|((relation(A)&function(A))&one_to_one(A)))),
% 0.12/0.34 inference(pre_NNF_transformation,[status(esa)],[f4])).
% 0.12/0.34 fof(f51,plain,(
% 0.12/0.34 ![X0]: (~relation(X0)|~empty(X0)|~function(X0)|one_to_one(X0))),
% 0.12/0.34 inference(cnf_transformation,[status(esa)],[f48])).
% 0.12/0.34 fof(f53,plain,(
% 0.12/0.34 ![A]: (~relation(A)|(![B,C]: (C=relation_inverse_image(A,B)<=>(![D]: (in(D,C)<=>(?[E]: (in(ordered_pair(D,E),A)&in(E,B))))))))),
% 0.12/0.34 inference(pre_NNF_transformation,[status(esa)],[f6])).
% 0.12/0.34 fof(f54,plain,(
% 0.12/0.34 ![A]: (~relation(A)|(![B,C]: ((~C=relation_inverse_image(A,B)|(![D]: ((~in(D,C)|(?[E]: (in(ordered_pair(D,E),A)&in(E,B))))&(in(D,C)|(![E]: (~in(ordered_pair(D,E),A)|~in(E,B)))))))&(C=relation_inverse_image(A,B)|(?[D]: ((~in(D,C)|(![E]: (~in(ordered_pair(D,E),A)|~in(E,B))))&(in(D,C)|(?[E]: (in(ordered_pair(D,E),A)&in(E,B))))))))))),
% 0.12/0.34 inference(NNF_transformation,[status(esa)],[f53])).
% 0.12/0.34 fof(f55,plain,(
% 0.12/0.34 ![A]: (~relation(A)|((![B,C]: (~C=relation_inverse_image(A,B)|((![D]: (~in(D,C)|(?[E]: (in(ordered_pair(D,E),A)&in(E,B)))))&(![D]: (in(D,C)|(![E]: (~in(ordered_pair(D,E),A)|~in(E,B))))))))&(![B,C]: (C=relation_inverse_image(A,B)|(?[D]: ((~in(D,C)|(![E]: (~in(ordered_pair(D,E),A)|~in(E,B))))&(in(D,C)|(?[E]: (in(ordered_pair(D,E),A)&in(E,B))))))))))),
% 0.12/0.34 inference(miniscoping,[status(esa)],[f54])).
% 0.12/0.34 fof(f56,plain,(
% 0.12/0.34 ![A]: (~relation(A)|((![B,C]: (~C=relation_inverse_image(A,B)|((![D]: (~in(D,C)|(in(ordered_pair(D,sk0_0(D,C,B,A)),A)&in(sk0_0(D,C,B,A),B))))&(![D]: (in(D,C)|(![E]: (~in(ordered_pair(D,E),A)|~in(E,B))))))))&(![B,C]: (C=relation_inverse_image(A,B)|((~in(sk0_1(C,B,A),C)|(![E]: (~in(ordered_pair(sk0_1(C,B,A),E),A)|~in(E,B))))&(in(sk0_1(C,B,A),C)|(in(ordered_pair(sk0_1(C,B,A),sk0_2(C,B,A)),A)&in(sk0_2(C,B,A),B))))))))),
% 0.12/0.34 inference(skolemization,[status(esa)],[f55])).
% 0.12/0.34 fof(f57,plain,(
% 0.12/0.34 ![X0,X1,X2,X3]: (~relation(X0)|~X1=relation_inverse_image(X0,X2)|~in(X3,X1)|in(ordered_pair(X3,sk0_0(X3,X1,X2,X0)),X0))),
% 0.12/0.34 inference(cnf_transformation,[status(esa)],[f56])).
% 0.12/0.34 fof(f58,plain,(
% 0.12/0.34 ![X0,X1,X2,X3]: (~relation(X0)|~X1=relation_inverse_image(X0,X2)|~in(X3,X1)|in(sk0_0(X3,X1,X2,X0),X2))),
% 0.12/0.34 inference(cnf_transformation,[status(esa)],[f56])).
% 0.12/0.34 fof(f59,plain,(
% 0.12/0.34 ![X0,X1,X2,X3,X4]: (~relation(X0)|~X1=relation_inverse_image(X0,X2)|in(X3,X1)|~in(ordered_pair(X3,X4),X0)|~in(X4,X2))),
% 0.12/0.34 inference(cnf_transformation,[status(esa)],[f56])).
% 0.12/0.34 fof(f60,plain,(
% 0.12/0.34 ![X0,X1,X2,X3]: (~relation(X0)|X1=relation_inverse_image(X0,X2)|~in(sk0_1(X1,X2,X0),X1)|~in(ordered_pair(sk0_1(X1,X2,X0),X3),X0)|~in(X3,X2))),
% 0.12/0.34 inference(cnf_transformation,[status(esa)],[f56])).
% 0.12/0.34 fof(f61,plain,(
% 0.12/0.34 ![X0,X1,X2]: (~relation(X0)|X1=relation_inverse_image(X0,X2)|in(sk0_1(X1,X2,X0),X1)|in(ordered_pair(sk0_1(X1,X2,X0),sk0_2(X1,X2,X0)),X0))),
% 0.12/0.34 inference(cnf_transformation,[status(esa)],[f56])).
% 0.12/0.34 fof(f62,plain,(
% 0.12/0.34 ![X0,X1,X2]: (~relation(X0)|X1=relation_inverse_image(X0,X2)|in(sk0_1(X1,X2,X0),X1)|in(sk0_2(X1,X2,X0),X2))),
% 0.12/0.34 inference(cnf_transformation,[status(esa)],[f56])).
% 0.12/0.34 fof(f63,plain,(
% 0.12/0.34 ![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)))))),
% 0.12/0.34 inference(NNF_transformation,[status(esa)],[f7])).
% 0.12/0.34 fof(f64,plain,(
% 0.12/0.34 (![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)))))),
% 0.12/0.34 inference(miniscoping,[status(esa)],[f63])).
% 0.12/0.34 fof(f65,plain,(
% 0.12/0.34 (![A,B]: (~B=singleton(A)|((![C]: (~in(C,B)|C=A))&(![C]: (in(C,B)|~C=A)))))&(![A,B]: (B=singleton(A)|((~in(sk0_3(B,A),B)|~sk0_3(B,A)=A)&(in(sk0_3(B,A),B)|sk0_3(B,A)=A))))),
% 0.12/0.34 inference(skolemization,[status(esa)],[f64])).
% 0.12/0.34 fof(f66,plain,(
% 0.12/0.34 ![X0,X1,X2]: (~X0=singleton(X1)|~in(X2,X0)|X2=X1)),
% 0.12/0.34 inference(cnf_transformation,[status(esa)],[f65])).
% 0.12/0.34 fof(f67,plain,(
% 0.12/0.34 ![X0,X1,X2]: (~X0=singleton(X1)|in(X2,X0)|~X2=X1)),
% 0.12/0.34 inference(cnf_transformation,[status(esa)],[f65])).
% 0.12/0.34 fof(f70,plain,(
% 0.12/0.34 ![A]: ((~A=empty_set|(![B]: ~in(B,A)))&(A=empty_set|(?[B]: in(B,A))))),
% 0.12/0.34 inference(NNF_transformation,[status(esa)],[f8])).
% 0.12/0.34 fof(f71,plain,(
% 0.12/0.34 (![A]: (~A=empty_set|(![B]: ~in(B,A))))&(![A]: (A=empty_set|(?[B]: in(B,A))))),
% 0.12/0.34 inference(miniscoping,[status(esa)],[f70])).
% 0.12/0.34 fof(f72,plain,(
% 0.12/0.34 (![A]: (~A=empty_set|(![B]: ~in(B,A))))&(![A]: (A=empty_set|in(sk0_4(A),A)))),
% 0.12/0.34 inference(skolemization,[status(esa)],[f71])).
% 0.12/0.34 fof(f73,plain,(
% 0.12/0.34 ![X0,X1]: (~X0=empty_set|~in(X1,X0))),
% 0.12/0.34 inference(cnf_transformation,[status(esa)],[f72])).
% 0.12/0.34 fof(f75,plain,(
% 0.12/0.34 ![A]: (~relation(A)|(![B]: (B=relation_rng(A)<=>(![C]: (in(C,B)<=>(?[D]: in(ordered_pair(D,C),A)))))))),
% 0.12/0.34 inference(pre_NNF_transformation,[status(esa)],[f9])).
% 0.12/0.34 fof(f76,plain,(
% 0.12/0.34 ![A]: (~relation(A)|(![B]: ((~B=relation_rng(A)|(![C]: ((~in(C,B)|(?[D]: in(ordered_pair(D,C),A)))&(in(C,B)|(![D]: ~in(ordered_pair(D,C),A))))))&(B=relation_rng(A)|(?[C]: ((~in(C,B)|(![D]: ~in(ordered_pair(D,C),A)))&(in(C,B)|(?[D]: in(ordered_pair(D,C),A)))))))))),
% 0.12/0.34 inference(NNF_transformation,[status(esa)],[f75])).
% 0.12/0.34 fof(f77,plain,(
% 0.12/0.34 ![A]: (~relation(A)|((![B]: (~B=relation_rng(A)|((![C]: (~in(C,B)|(?[D]: in(ordered_pair(D,C),A))))&(![C]: (in(C,B)|(![D]: ~in(ordered_pair(D,C),A)))))))&(![B]: (B=relation_rng(A)|(?[C]: ((~in(C,B)|(![D]: ~in(ordered_pair(D,C),A)))&(in(C,B)|(?[D]: in(ordered_pair(D,C),A)))))))))),
% 0.12/0.34 inference(miniscoping,[status(esa)],[f76])).
% 0.12/0.34 fof(f78,plain,(
% 0.12/0.34 ![A]: (~relation(A)|((![B]: (~B=relation_rng(A)|((![C]: (~in(C,B)|in(ordered_pair(sk0_5(C,B,A),C),A)))&(![C]: (in(C,B)|(![D]: ~in(ordered_pair(D,C),A)))))))&(![B]: (B=relation_rng(A)|((~in(sk0_6(B,A),B)|(![D]: ~in(ordered_pair(D,sk0_6(B,A)),A)))&(in(sk0_6(B,A),B)|in(ordered_pair(sk0_7(B,A),sk0_6(B,A)),A)))))))),
% 0.12/0.34 inference(skolemization,[status(esa)],[f77])).
% 0.12/0.34 fof(f79,plain,(
% 0.12/0.34 ![X0,X1,X2]: (~relation(X0)|~X1=relation_rng(X0)|~in(X2,X1)|in(ordered_pair(sk0_5(X2,X1,X0),X2),X0))),
% 0.12/0.34 inference(cnf_transformation,[status(esa)],[f78])).
% 0.12/0.34 fof(f80,plain,(
% 0.12/0.34 ![X0,X1,X2,X3]: (~relation(X0)|~X1=relation_rng(X0)|in(X2,X1)|~in(ordered_pair(X3,X2),X0))),
% 0.12/0.34 inference(cnf_transformation,[status(esa)],[f78])).
% 0.12/0.34 fof(f86,plain,(
% 0.12/0.34 empty(empty_set)),
% 0.12/0.34 inference(cnf_transformation,[status(esa)],[f12])).
% 0.12/0.34 fof(f87,plain,(
% 0.12/0.34 relation(empty_set)),
% 0.12/0.34 inference(cnf_transformation,[status(esa)],[f12])).
% 0.12/0.34 fof(f98,plain,(
% 0.12/0.34 ![A]: (~empty(A)|(empty(relation_rng(A))&relation(relation_rng(A))))),
% 0.12/0.34 inference(pre_NNF_transformation,[status(esa)],[f20])).
% 0.12/0.34 fof(f99,plain,(
% 0.12/0.34 ![X0]: (~empty(X0)|empty(relation_rng(X0)))),
% 0.12/0.34 inference(cnf_transformation,[status(esa)],[f98])).
% 0.12/0.34 fof(f101,plain,(
% 0.12/0.34 (relation(sk0_9)&function(sk0_9))),
% 0.12/0.34 inference(skolemization,[status(esa)],[f21])).
% 0.12/0.34 fof(f102,plain,(
% 0.12/0.34 relation(sk0_9)),
% 0.12/0.34 inference(cnf_transformation,[status(esa)],[f101])).
% 0.12/0.34 fof(f117,plain,(
% 0.12/0.34 (~empty(sk0_14)&relation(sk0_14))),
% 0.12/0.34 inference(skolemization,[status(esa)],[f26])).
% 0.12/0.34 fof(f119,plain,(
% 0.12/0.34 relation(sk0_14)),
% 0.12/0.34 inference(cnf_transformation,[status(esa)],[f117])).
% 0.12/0.34 fof(f125,plain,(
% 0.12/0.34 ((relation(sk0_17)&function(sk0_17))&one_to_one(sk0_17))),
% 0.12/0.34 inference(skolemization,[status(esa)],[f29])).
% 0.12/0.34 fof(f126,plain,(
% 0.12/0.34 relation(sk0_17)),
% 0.12/0.34 inference(cnf_transformation,[status(esa)],[f125])).
% 0.12/0.34 fof(f129,plain,(
% 0.12/0.34 (relation(sk0_18)&relation_empty_yielding(sk0_18))),
% 0.12/0.34 inference(skolemization,[status(esa)],[f30])).
% 0.12/0.34 fof(f130,plain,(
% 0.12/0.34 relation(sk0_18)),
% 0.12/0.34 inference(cnf_transformation,[status(esa)],[f129])).
% 0.12/0.34 fof(f134,plain,(
% 0.12/0.34 (?[A,B]: (relation(B)&(in(A,relation_rng(B))<~>~relation_inverse_image(B,singleton(A))=empty_set)))),
% 0.12/0.34 inference(pre_NNF_transformation,[status(esa)],[f33])).
% 0.12/0.34 fof(f135,plain,(
% 0.12/0.34 ?[A,B]: (relation(B)&((in(A,relation_rng(B))|~relation_inverse_image(B,singleton(A))=empty_set)&(~in(A,relation_rng(B))|relation_inverse_image(B,singleton(A))=empty_set)))),
% 0.12/0.34 inference(NNF_transformation,[status(esa)],[f134])).
% 0.12/0.34 fof(f136,plain,(
% 0.12/0.34 ?[B]: (relation(B)&(?[A]: ((in(A,relation_rng(B))|~relation_inverse_image(B,singleton(A))=empty_set)&(~in(A,relation_rng(B))|relation_inverse_image(B,singleton(A))=empty_set))))),
% 0.12/0.34 inference(miniscoping,[status(esa)],[f135])).
% 0.12/0.34 fof(f137,plain,(
% 0.12/0.34 (relation(sk0_19)&((in(sk0_20,relation_rng(sk0_19))|~relation_inverse_image(sk0_19,singleton(sk0_20))=empty_set)&(~in(sk0_20,relation_rng(sk0_19))|relation_inverse_image(sk0_19,singleton(sk0_20))=empty_set)))),
% 0.12/0.34 inference(skolemization,[status(esa)],[f136])).
% 0.12/0.34 fof(f138,plain,(
% 0.12/0.34 relation(sk0_19)),
% 0.12/0.34 inference(cnf_transformation,[status(esa)],[f137])).
% 0.12/0.34 fof(f139,plain,(
% 0.12/0.34 in(sk0_20,relation_rng(sk0_19))|~relation_inverse_image(sk0_19,singleton(sk0_20))=empty_set),
% 0.12/0.34 inference(cnf_transformation,[status(esa)],[f137])).
% 0.12/0.34 fof(f140,plain,(
% 0.12/0.34 ~in(sk0_20,relation_rng(sk0_19))|relation_inverse_image(sk0_19,singleton(sk0_20))=empty_set),
% 0.12/0.34 inference(cnf_transformation,[status(esa)],[f137])).
% 0.12/0.34 fof(f141,plain,(
% 0.12/0.34 ![A,B]: (~in(A,B)|element(A,B))),
% 0.12/0.34 inference(pre_NNF_transformation,[status(esa)],[f34])).
% 0.12/0.34 fof(f142,plain,(
% 0.12/0.34 ![X0,X1]: (~in(X0,X1)|element(X0,X1))),
% 0.12/0.34 inference(cnf_transformation,[status(esa)],[f141])).
% 0.12/0.34 fof(f155,plain,(
% 0.12/0.34 ![A]: (~empty(A)|A=empty_set)),
% 0.12/0.34 inference(pre_NNF_transformation,[status(esa)],[f39])).
% 0.12/0.34 fof(f156,plain,(
% 0.12/0.34 ![X0]: (~empty(X0)|X0=empty_set)),
% 0.12/0.34 inference(cnf_transformation,[status(esa)],[f155])).
% 0.12/0.34 fof(f157,plain,(
% 0.12/0.34 ![A,B]: (~in(A,B)|~empty(B))),
% 0.12/0.34 inference(pre_NNF_transformation,[status(esa)],[f40])).
% 0.12/0.34 fof(f158,plain,(
% 0.12/0.34 ![B]: ((![A]: ~in(A,B))|~empty(B))),
% 0.12/0.34 inference(miniscoping,[status(esa)],[f157])).
% 0.12/0.34 fof(f159,plain,(
% 0.12/0.34 ![X0,X1]: (~in(X0,X1)|~empty(X1))),
% 0.12/0.34 inference(cnf_transformation,[status(esa)],[f158])).
% 0.12/0.34 fof(f163,plain,(
% 0.12/0.34 spl0_0 <=> in(sk0_20,relation_rng(sk0_19))),
% 0.12/0.34 introduced(split_symbol_definition)).
% 0.12/0.34 fof(f164,plain,(
% 0.12/0.34 in(sk0_20,relation_rng(sk0_19))|~spl0_0),
% 0.12/0.34 inference(component_clause,[status(thm)],[f163])).
% 0.12/0.34 fof(f165,plain,(
% 0.12/0.34 ~in(sk0_20,relation_rng(sk0_19))|spl0_0),
% 0.12/0.34 inference(component_clause,[status(thm)],[f163])).
% 0.12/0.34 fof(f166,plain,(
% 0.12/0.34 spl0_1 <=> relation_inverse_image(sk0_19,singleton(sk0_20))=empty_set),
% 0.12/0.34 introduced(split_symbol_definition)).
% 0.12/0.34 fof(f167,plain,(
% 0.12/0.34 relation_inverse_image(sk0_19,singleton(sk0_20))=empty_set|~spl0_1),
% 0.12/0.34 inference(component_clause,[status(thm)],[f166])).
% 0.12/0.34 fof(f168,plain,(
% 0.12/0.34 ~relation_inverse_image(sk0_19,singleton(sk0_20))=empty_set|spl0_1),
% 0.12/0.34 inference(component_clause,[status(thm)],[f166])).
% 0.12/0.34 fof(f169,plain,(
% 0.12/0.34 spl0_0|~spl0_1),
% 0.12/0.34 inference(split_clause,[status(thm)],[f139,f163,f166])).
% 0.12/0.34 fof(f170,plain,(
% 0.12/0.34 ~spl0_0|spl0_1),
% 0.12/0.34 inference(split_clause,[status(thm)],[f140,f163,f166])).
% 0.12/0.34 fof(f171,plain,(
% 0.12/0.34 ![X0]: (~empty(X0)|~function(X0)|one_to_one(X0))),
% 0.12/0.34 inference(forward_subsumption_resolution,[status(thm)],[f51,f47])).
% 0.12/0.34 fof(f172,plain,(
% 0.12/0.34 ![X0,X1,X2]: (~relation(X0)|~in(X1,relation_inverse_image(X0,X2))|in(ordered_pair(X1,sk0_0(X1,relation_inverse_image(X0,X2),X2,X0)),X0))),
% 0.12/0.34 inference(destructive_equality_resolution,[status(esa)],[f57])).
% 0.12/0.34 fof(f173,plain,(
% 0.12/0.34 ![X0,X1,X2]: (~relation(X0)|~in(X1,relation_inverse_image(X0,X2))|in(sk0_0(X1,relation_inverse_image(X0,X2),X2,X0),X2))),
% 0.12/0.34 inference(destructive_equality_resolution,[status(esa)],[f58])).
% 0.12/0.34 fof(f174,plain,(
% 0.12/0.34 ![X0,X1,X2,X3]: (~relation(X0)|in(X1,relation_inverse_image(X0,X2))|~in(ordered_pair(X1,X3),X0)|~in(X3,X2))),
% 0.12/0.34 inference(destructive_equality_resolution,[status(esa)],[f59])).
% 0.12/0.34 fof(f175,plain,(
% 0.12/0.34 ![X0,X1]: (~in(X0,singleton(X1))|X0=X1)),
% 0.12/0.34 inference(destructive_equality_resolution,[status(esa)],[f66])).
% 0.12/0.34 fof(f176,plain,(
% 0.12/0.34 ![X0]: (in(X0,singleton(X0)))),
% 0.12/0.34 inference(destructive_equality_resolution,[status(esa)],[f67])).
% 0.12/0.34 fof(f177,plain,(
% 0.12/0.34 ![X0]: (~in(X0,empty_set))),
% 0.12/0.34 inference(destructive_equality_resolution,[status(esa)],[f73])).
% 0.12/0.34 fof(f178,plain,(
% 0.12/0.34 ![X0,X1]: (~relation(X0)|~in(X1,relation_rng(X0))|in(ordered_pair(sk0_5(X1,relation_rng(X0),X0),X1),X0))),
% 0.12/0.34 inference(destructive_equality_resolution,[status(esa)],[f79])).
% 0.12/0.34 fof(f179,plain,(
% 0.12/0.34 ![X0,X1,X2]: (~relation(X0)|in(X1,relation_rng(X0))|~in(ordered_pair(X2,X1),X0))),
% 0.12/0.34 inference(destructive_equality_resolution,[status(esa)],[f80])).
% 0.12/0.34 fof(f180,plain,(
% 0.12/0.34 ![X0]: (~in(singleton(X0),X0))),
% 0.12/0.34 inference(resolution,[status(thm)],[f43,f176])).
% 0.12/0.34 fof(f181,plain,(
% 0.12/0.34 empty(relation_rng(empty_set))),
% 0.12/0.34 inference(resolution,[status(thm)],[f99,f86])).
% 0.12/0.34 fof(f185,plain,(
% 0.12/0.34 relation_rng(empty_set)=empty_set),
% 0.12/0.34 inference(resolution,[status(thm)],[f181,f156])).
% 0.12/0.34 fof(f192,plain,(
% 0.12/0.34 spl0_2 <=> empty(empty_set)),
% 0.12/0.34 introduced(split_symbol_definition)).
% 0.12/0.34 fof(f194,plain,(
% 0.12/0.34 ~empty(empty_set)|spl0_2),
% 0.12/0.34 inference(component_clause,[status(thm)],[f192])).
% 0.12/0.34 fof(f195,plain,(
% 0.12/0.34 spl0_3 <=> relation(empty_set)),
% 0.12/0.34 introduced(split_symbol_definition)).
% 0.12/0.34 fof(f197,plain,(
% 0.12/0.34 ~relation(empty_set)|spl0_3),
% 0.12/0.34 inference(component_clause,[status(thm)],[f195])).
% 0.12/0.34 fof(f203,plain,(
% 0.12/0.34 spl0_4 <=> ~in(X0,empty_set)|in(ordered_pair(sk0_5(X0,relation_rng(empty_set),empty_set),X0),empty_set)),
% 0.12/0.34 introduced(split_symbol_definition)).
% 0.12/0.34 fof(f206,plain,(
% 0.12/0.34 ![X0]: (~relation(empty_set)|~in(X0,empty_set)|in(ordered_pair(sk0_5(X0,relation_rng(empty_set),empty_set),X0),empty_set))),
% 0.12/0.34 inference(paramodulation,[status(thm)],[f185,f178])).
% 0.12/0.34 fof(f207,plain,(
% 0.12/0.34 ~spl0_3|spl0_4),
% 0.12/0.34 inference(split_clause,[status(thm)],[f206,f195,f203])).
% 0.12/0.34 fof(f208,plain,(
% 0.12/0.34 $false|spl0_3),
% 0.12/0.34 inference(forward_subsumption_resolution,[status(thm)],[f197,f87])).
% 0.12/0.34 fof(f209,plain,(
% 0.12/0.34 spl0_3),
% 0.12/0.34 inference(contradiction_clause,[status(thm)],[f208])).
% 0.12/0.34 fof(f217,plain,(
% 0.12/0.34 ![X0,X1]: (X0=relation_inverse_image(empty_set,X1)|in(sk0_1(X0,X1,empty_set),X0)|in(ordered_pair(sk0_1(X0,X1,empty_set),sk0_2(X0,X1,empty_set)),empty_set))),
% 0.12/0.34 inference(resolution,[status(thm)],[f61,f87])).
% 0.12/0.34 fof(f218,plain,(
% 0.12/0.34 ![X0,X1]: (X0=relation_inverse_image(empty_set,X1)|in(sk0_1(X0,X1,empty_set),X0))),
% 0.12/0.34 inference(forward_subsumption_resolution,[status(thm)],[f217,f177])).
% 0.12/0.34 fof(f219,plain,(
% 0.12/0.34 ![X0,X1]: (X0=relation_inverse_image(sk0_19,X1)|in(sk0_1(X0,X1,sk0_19),X0)|in(ordered_pair(sk0_1(X0,X1,sk0_19),sk0_2(X0,X1,sk0_19)),sk0_19))),
% 0.12/0.34 inference(resolution,[status(thm)],[f61,f138])).
% 0.12/0.34 fof(f220,plain,(
% 0.12/0.34 function(empty_set)),
% 0.12/0.34 inference(resolution,[status(thm)],[f45,f86])).
% 0.12/0.34 fof(f231,plain,(
% 0.12/0.34 spl0_5 <=> relation(sk0_19)),
% 0.12/0.34 introduced(split_symbol_definition)).
% 0.12/0.34 fof(f233,plain,(
% 0.12/0.34 ~relation(sk0_19)|spl0_5),
% 0.12/0.34 inference(component_clause,[status(thm)],[f231])).
% 0.12/0.34 fof(f234,plain,(
% 0.12/0.34 spl0_6 <=> in(ordered_pair(sk0_5(sk0_20,relation_rng(sk0_19),sk0_19),sk0_20),sk0_19)),
% 0.12/0.34 introduced(split_symbol_definition)).
% 0.12/0.34 fof(f235,plain,(
% 0.12/0.34 in(ordered_pair(sk0_5(sk0_20,relation_rng(sk0_19),sk0_19),sk0_20),sk0_19)|~spl0_6),
% 0.12/0.34 inference(component_clause,[status(thm)],[f234])).
% 0.12/0.34 fof(f237,plain,(
% 0.12/0.34 ~relation(sk0_19)|in(ordered_pair(sk0_5(sk0_20,relation_rng(sk0_19),sk0_19),sk0_20),sk0_19)|~spl0_0),
% 0.12/0.34 inference(resolution,[status(thm)],[f164,f178])).
% 0.12/0.34 fof(f238,plain,(
% 0.12/0.34 ~spl0_5|spl0_6|~spl0_0),
% 0.12/0.34 inference(split_clause,[status(thm)],[f237,f231,f234,f163])).
% 0.12/0.34 fof(f242,plain,(
% 0.12/0.34 $false|spl0_5),
% 0.12/0.34 inference(forward_subsumption_resolution,[status(thm)],[f233,f138])).
% 0.12/0.34 fof(f243,plain,(
% 0.12/0.34 spl0_5),
% 0.12/0.34 inference(contradiction_clause,[status(thm)],[f242])).
% 0.12/0.34 fof(f244,plain,(
% 0.12/0.34 spl0_7 <=> X0=relation_inverse_image(sk0_19,X1)|in(sk0_1(X0,X1,sk0_19),X0)|in(sk0_1(X0,X1,sk0_19),relation_inverse_image(sk0_19,X2))|~in(sk0_2(X0,X1,sk0_19),X2)),
% 0.12/0.34 introduced(split_symbol_definition)).
% 0.12/0.34 fof(f245,plain,(
% 0.12/0.34 ![X0,X1,X2]: (X0=relation_inverse_image(sk0_19,X1)|in(sk0_1(X0,X1,sk0_19),X0)|in(sk0_1(X0,X1,sk0_19),relation_inverse_image(sk0_19,X2))|~in(sk0_2(X0,X1,sk0_19),X2)|~spl0_7)),
% 0.12/0.34 inference(component_clause,[status(thm)],[f244])).
% 0.12/0.34 fof(f247,plain,(
% 0.12/0.34 ![X0,X1,X2]: (X0=relation_inverse_image(sk0_19,X1)|in(sk0_1(X0,X1,sk0_19),X0)|~relation(sk0_19)|in(sk0_1(X0,X1,sk0_19),relation_inverse_image(sk0_19,X2))|~in(sk0_2(X0,X1,sk0_19),X2))),
% 0.12/0.34 inference(resolution,[status(thm)],[f219,f174])).
% 0.12/0.34 fof(f248,plain,(
% 0.12/0.34 spl0_7|~spl0_5),
% 0.12/0.34 inference(split_clause,[status(thm)],[f247,f244,f231])).
% 0.12/0.34 fof(f249,plain,(
% 0.12/0.34 spl0_8 <=> X0=relation_inverse_image(sk0_19,X1)|in(sk0_1(X0,X1,sk0_19),X0)|in(sk0_2(X0,X1,sk0_19),relation_rng(sk0_19))),
% 0.12/0.34 introduced(split_symbol_definition)).
% 0.12/0.34 fof(f250,plain,(
% 0.12/0.34 ![X0,X1]: (X0=relation_inverse_image(sk0_19,X1)|in(sk0_1(X0,X1,sk0_19),X0)|in(sk0_2(X0,X1,sk0_19),relation_rng(sk0_19))|~spl0_8)),
% 0.12/0.34 inference(component_clause,[status(thm)],[f249])).
% 0.12/0.34 fof(f252,plain,(
% 0.12/0.34 ![X0,X1]: (X0=relation_inverse_image(sk0_19,X1)|in(sk0_1(X0,X1,sk0_19),X0)|~relation(sk0_19)|in(sk0_2(X0,X1,sk0_19),relation_rng(sk0_19)))),
% 0.12/0.34 inference(resolution,[status(thm)],[f219,f179])).
% 0.12/0.34 fof(f253,plain,(
% 0.12/0.34 spl0_8|~spl0_5),
% 0.12/0.34 inference(split_clause,[status(thm)],[f252,f249,f231])).
% 0.12/0.34 fof(f255,plain,(
% 0.12/0.34 spl0_9 <=> X0=relation_inverse_image(sk0_19,X1)|in(sk0_1(X0,X1,sk0_19),X0)),
% 0.12/0.34 introduced(split_symbol_definition)).
% 0.12/0.34 fof(f264,plain,(
% 0.12/0.34 ![X0,X1]: (X0=relation_inverse_image(sk0_19,X1)|in(sk0_1(X0,X1,sk0_19),X0)|in(sk0_1(X0,X1,sk0_19),relation_inverse_image(sk0_19,singleton(sk0_2(X0,X1,sk0_19))))|~spl0_7)),
% 0.12/0.34 inference(resolution,[status(thm)],[f245,f176])).
% 0.12/0.34 fof(f265,plain,(
% 0.12/0.34 spl0_11 <=> X0=relation_inverse_image(sk0_19,X1)|in(sk0_2(X0,X1,sk0_19),relation_rng(sk0_19))|X0=relation_inverse_image(sk0_19,X1)|~in(ordered_pair(sk0_1(X0,X1,sk0_19),X2),sk0_19)|~in(X2,X1)),
% 0.12/0.34 introduced(split_symbol_definition)).
% 0.12/0.34 fof(f268,plain,(
% 0.12/0.34 ![X0,X1,X2]: (X0=relation_inverse_image(sk0_19,X1)|in(sk0_2(X0,X1,sk0_19),relation_rng(sk0_19))|~relation(sk0_19)|X0=relation_inverse_image(sk0_19,X1)|~in(ordered_pair(sk0_1(X0,X1,sk0_19),X2),sk0_19)|~in(X2,X1)|~spl0_8)),
% 0.12/0.34 inference(resolution,[status(thm)],[f250,f60])).
% 0.12/0.34 fof(f269,plain,(
% 0.12/0.34 spl0_11|~spl0_5|~spl0_8),
% 0.12/0.34 inference(split_clause,[status(thm)],[f268,f265,f231,f249])).
% 0.12/0.34 fof(f273,plain,(
% 0.12/0.34 ![X0,X1]: (singleton(X0)=relation_inverse_image(sk0_19,X1)|in(sk0_2(singleton(X0),X1,sk0_19),relation_rng(sk0_19))|sk0_1(singleton(X0),X1,sk0_19)=X0|~spl0_8)),
% 0.12/0.34 inference(resolution,[status(thm)],[f250,f175])).
% 0.12/0.34 fof(f274,plain,(
% 0.12/0.34 ![X0]: (empty_set=relation_inverse_image(sk0_19,X0)|in(sk0_2(empty_set,X0,sk0_19),relation_rng(sk0_19))|~spl0_8)),
% 0.12/0.34 inference(resolution,[status(thm)],[f250,f177])).
% 0.12/0.34 fof(f275,plain,(
% 0.12/0.34 ![X0,X1]: (X0=relation_inverse_image(sk0_19,X1)|in(sk0_2(X0,X1,sk0_19),relation_rng(sk0_19))|element(sk0_1(X0,X1,sk0_19),X0)|~spl0_8)),
% 0.12/0.34 inference(resolution,[status(thm)],[f250,f142])).
% 0.12/0.34 fof(f278,plain,(
% 0.12/0.34 ![X0,X1]: (X0=relation_inverse_image(sk0_19,X1)|in(sk0_1(X0,X1,sk0_19),X0)|X0=relation_inverse_image(sk0_19,X1)|in(sk0_1(X0,X1,sk0_19),X0)|in(sk0_1(X0,X1,sk0_19),relation_inverse_image(sk0_19,relation_rng(sk0_19)))|~spl0_8|~spl0_7)),
% 0.12/0.34 inference(resolution,[status(thm)],[f250,f245])).
% 0.12/0.34 fof(f279,plain,(
% 0.12/0.34 ![X0,X1]: (X0=relation_inverse_image(sk0_19,X1)|in(sk0_1(X0,X1,sk0_19),X0)|in(sk0_1(X0,X1,sk0_19),relation_inverse_image(sk0_19,relation_rng(sk0_19)))|~spl0_8|~spl0_7)),
% 0.12/0.34 inference(duplicate_literals_removal,[status(esa)],[f278])).
% 0.12/0.34 fof(f280,plain,(
% 0.12/0.34 spl0_12 <=> X0=relation_inverse_image(sk0_19,X1)|in(sk0_1(X0,X1,sk0_19),X0)|in(ordered_pair(sk0_5(sk0_2(X0,X1,sk0_19),relation_rng(sk0_19),sk0_19),sk0_2(X0,X1,sk0_19)),sk0_19)),
% 0.12/0.34 introduced(split_symbol_definition)).
% 0.12/0.34 fof(f281,plain,(
% 0.12/0.34 ![X0,X1]: (X0=relation_inverse_image(sk0_19,X1)|in(sk0_1(X0,X1,sk0_19),X0)|in(ordered_pair(sk0_5(sk0_2(X0,X1,sk0_19),relation_rng(sk0_19),sk0_19),sk0_2(X0,X1,sk0_19)),sk0_19)|~spl0_12)),
% 0.12/0.34 inference(component_clause,[status(thm)],[f280])).
% 0.12/0.34 fof(f283,plain,(
% 0.12/0.34 ![X0,X1]: (X0=relation_inverse_image(sk0_19,X1)|in(sk0_1(X0,X1,sk0_19),X0)|~relation(sk0_19)|in(ordered_pair(sk0_5(sk0_2(X0,X1,sk0_19),relation_rng(sk0_19),sk0_19),sk0_2(X0,X1,sk0_19)),sk0_19)|~spl0_8)),
% 0.12/0.34 inference(resolution,[status(thm)],[f250,f178])).
% 0.12/0.34 fof(f284,plain,(
% 0.12/0.34 spl0_12|~spl0_5|~spl0_8),
% 0.12/0.34 inference(split_clause,[status(thm)],[f283,f280,f231,f249])).
% 0.12/0.34 fof(f285,plain,(
% 0.12/0.34 ![X0,X1]: (X0=relation_inverse_image(sk0_19,X1)|in(sk0_1(X0,X1,sk0_19),X0)|element(sk0_2(X0,X1,sk0_19),relation_rng(sk0_19))|~spl0_8)),
% 0.12/0.34 inference(resolution,[status(thm)],[f250,f142])).
% 0.12/0.34 fof(f286,plain,(
% 0.12/0.34 spl0_13 <=> empty(relation_rng(sk0_19))),
% 0.12/0.34 introduced(split_symbol_definition)).
% 0.12/0.34 fof(f288,plain,(
% 0.12/0.34 ~empty(relation_rng(sk0_19))|spl0_13),
% 0.12/0.34 inference(component_clause,[status(thm)],[f286])).
% 0.12/0.34 fof(f289,plain,(
% 0.12/0.34 ![X0,X1]: (X0=relation_inverse_image(sk0_19,X1)|in(sk0_1(X0,X1,sk0_19),X0)|~empty(relation_rng(sk0_19))|~spl0_8)),
% 0.12/0.34 inference(resolution,[status(thm)],[f250,f159])).
% 0.12/0.34 fof(f290,plain,(
% 0.12/0.34 spl0_9|~spl0_13|~spl0_8),
% 0.12/0.34 inference(split_clause,[status(thm)],[f289,f255,f286,f249])).
% 0.12/0.34 fof(f296,plain,(
% 0.12/0.34 spl0_14 <=> empty_set=relation_inverse_image(sk0_19,X0)|in(ordered_pair(sk0_5(sk0_2(empty_set,X0,sk0_19),relation_rng(sk0_19),sk0_19),sk0_2(empty_set,X0,sk0_19)),sk0_19)),
% 0.12/0.34 introduced(split_symbol_definition)).
% 0.12/0.34 fof(f299,plain,(
% 0.12/0.34 ![X0]: (empty_set=relation_inverse_image(sk0_19,X0)|~relation(sk0_19)|in(ordered_pair(sk0_5(sk0_2(empty_set,X0,sk0_19),relation_rng(sk0_19),sk0_19),sk0_2(empty_set,X0,sk0_19)),sk0_19)|~spl0_8)),
% 0.12/0.34 inference(resolution,[status(thm)],[f274,f178])).
% 0.12/0.34 fof(f300,plain,(
% 0.12/0.34 spl0_14|~spl0_5|~spl0_8),
% 0.12/0.34 inference(split_clause,[status(thm)],[f299,f296,f231,f249])).
% 0.12/0.34 fof(f302,plain,(
% 0.12/0.34 spl0_15 <=> empty_set=relation_inverse_image(sk0_19,X0)),
% 0.12/0.34 introduced(split_symbol_definition)).
% 0.12/0.34 fof(f305,plain,(
% 0.12/0.34 ![X0]: (empty_set=relation_inverse_image(sk0_19,X0)|~empty(relation_rng(sk0_19))|~spl0_8)),
% 0.12/0.34 inference(resolution,[status(thm)],[f274,f159])).
% 0.12/0.34 fof(f306,plain,(
% 0.12/0.34 spl0_15|~spl0_13|~spl0_8),
% 0.12/0.34 inference(split_clause,[status(thm)],[f305,f302,f286,f249])).
% 0.12/0.34 fof(f307,plain,(
% 0.12/0.34 ![X0]: (empty_set=relation_inverse_image(sk0_19,X0)|~in(relation_rng(sk0_19),sk0_2(empty_set,X0,sk0_19))|~spl0_8)),
% 0.12/0.34 inference(resolution,[status(thm)],[f274,f43])).
% 0.12/0.34 fof(f311,plain,(
% 0.12/0.34 spl0_16 <=> X0=relation_inverse_image(sk0_19,X1)|element(sk0_1(X0,X1,sk0_19),X0)|in(ordered_pair(sk0_5(sk0_2(X0,X1,sk0_19),relation_rng(sk0_19),sk0_19),sk0_2(X0,X1,sk0_19)),sk0_19)),
% 0.12/0.34 introduced(split_symbol_definition)).
% 0.12/0.34 fof(f314,plain,(
% 0.12/0.34 ![X0,X1]: (X0=relation_inverse_image(sk0_19,X1)|element(sk0_1(X0,X1,sk0_19),X0)|~relation(sk0_19)|in(ordered_pair(sk0_5(sk0_2(X0,X1,sk0_19),relation_rng(sk0_19),sk0_19),sk0_2(X0,X1,sk0_19)),sk0_19)|~spl0_8)),
% 0.12/0.34 inference(resolution,[status(thm)],[f275,f178])).
% 0.12/0.34 fof(f315,plain,(
% 0.12/0.34 spl0_16|~spl0_5|~spl0_8),
% 0.12/0.34 inference(split_clause,[status(thm)],[f314,f311,f231,f249])).
% 0.12/0.34 fof(f317,plain,(
% 0.12/0.34 spl0_17 <=> X0=relation_inverse_image(sk0_19,X1)|element(sk0_1(X0,X1,sk0_19),X0)),
% 0.12/0.34 introduced(split_symbol_definition)).
% 0.12/0.34 fof(f320,plain,(
% 0.12/0.34 ![X0,X1]: (X0=relation_inverse_image(sk0_19,X1)|element(sk0_1(X0,X1,sk0_19),X0)|~empty(relation_rng(sk0_19))|~spl0_8)),
% 0.12/0.34 inference(resolution,[status(thm)],[f275,f159])).
% 0.12/0.34 fof(f321,plain,(
% 0.12/0.34 spl0_17|~spl0_13|~spl0_8),
% 0.12/0.34 inference(split_clause,[status(thm)],[f320,f317,f286,f249])).
% 0.12/0.34 fof(f323,plain,(
% 0.12/0.34 spl0_18 <=> X0=relation_inverse_image(sk0_19,X1)|element(sk0_2(X0,X1,sk0_19),relation_rng(sk0_19))|X0=relation_inverse_image(sk0_19,X1)|~in(ordered_pair(sk0_1(X0,X1,sk0_19),X2),sk0_19)|~in(X2,X1)),
% 0.12/0.34 introduced(split_symbol_definition)).
% 0.12/0.34 fof(f326,plain,(
% 0.12/0.34 ![X0,X1,X2]: (X0=relation_inverse_image(sk0_19,X1)|element(sk0_2(X0,X1,sk0_19),relation_rng(sk0_19))|~relation(sk0_19)|X0=relation_inverse_image(sk0_19,X1)|~in(ordered_pair(sk0_1(X0,X1,sk0_19),X2),sk0_19)|~in(X2,X1)|~spl0_8)),
% 0.12/0.34 inference(resolution,[status(thm)],[f285,f60])).
% 0.12/0.34 fof(f327,plain,(
% 0.12/0.34 spl0_18|~spl0_5|~spl0_8),
% 0.12/0.34 inference(split_clause,[status(thm)],[f326,f323,f231,f249])).
% 0.12/0.34 fof(f337,plain,(
% 0.12/0.34 spl0_19 <=> X0=relation_inverse_image(sk0_19,X1)|in(sk0_1(X0,X1,sk0_19),X0)|in(sk0_0(sk0_1(X0,X1,sk0_19),relation_inverse_image(sk0_19,singleton(sk0_2(X0,X1,sk0_19))),singleton(sk0_2(X0,X1,sk0_19)),sk0_19),singleton(sk0_2(X0,X1,sk0_19)))),
% 0.12/0.34 introduced(split_symbol_definition)).
% 0.12/0.34 fof(f340,plain,(
% 0.12/0.34 ![X0,X1]: (X0=relation_inverse_image(sk0_19,X1)|in(sk0_1(X0,X1,sk0_19),X0)|~relation(sk0_19)|in(sk0_0(sk0_1(X0,X1,sk0_19),relation_inverse_image(sk0_19,singleton(sk0_2(X0,X1,sk0_19))),singleton(sk0_2(X0,X1,sk0_19)),sk0_19),singleton(sk0_2(X0,X1,sk0_19)))|~spl0_7)),
% 0.12/0.34 inference(resolution,[status(thm)],[f264,f173])).
% 0.12/0.34 fof(f341,plain,(
% 0.12/0.34 spl0_19|~spl0_5|~spl0_7),
% 0.12/0.34 inference(split_clause,[status(thm)],[f340,f337,f231,f244])).
% 0.12/0.34 fof(f342,plain,(
% 0.12/0.34 spl0_20 <=> X0=relation_inverse_image(sk0_19,X1)|in(sk0_1(X0,X1,sk0_19),X0)|in(ordered_pair(sk0_1(X0,X1,sk0_19),sk0_0(sk0_1(X0,X1,sk0_19),relation_inverse_image(sk0_19,singleton(sk0_2(X0,X1,sk0_19))),singleton(sk0_2(X0,X1,sk0_19)),sk0_19)),sk0_19)),
% 0.12/0.34 introduced(split_symbol_definition)).
% 0.12/0.34 fof(f345,plain,(
% 0.12/0.34 ![X0,X1]: (X0=relation_inverse_image(sk0_19,X1)|in(sk0_1(X0,X1,sk0_19),X0)|~relation(sk0_19)|in(ordered_pair(sk0_1(X0,X1,sk0_19),sk0_0(sk0_1(X0,X1,sk0_19),relation_inverse_image(sk0_19,singleton(sk0_2(X0,X1,sk0_19))),singleton(sk0_2(X0,X1,sk0_19)),sk0_19)),sk0_19)|~spl0_7)),
% 0.12/0.34 inference(resolution,[status(thm)],[f264,f172])).
% 0.12/0.34 fof(f346,plain,(
% 0.12/0.34 spl0_20|~spl0_5|~spl0_7),
% 0.12/0.34 inference(split_clause,[status(thm)],[f345,f342,f231,f244])).
% 0.12/0.34 fof(f361,plain,(
% 0.12/0.34 spl0_21 <=> singleton(X0)=relation_inverse_image(sk0_19,X1)|sk0_1(singleton(X0),X1,sk0_19)=X0|in(ordered_pair(sk0_5(sk0_2(singleton(X0),X1,sk0_19),relation_rng(sk0_19),sk0_19),sk0_2(singleton(X0),X1,sk0_19)),sk0_19)),
% 0.12/0.34 introduced(split_symbol_definition)).
% 0.12/0.34 fof(f364,plain,(
% 0.12/0.34 ![X0,X1]: (singleton(X0)=relation_inverse_image(sk0_19,X1)|sk0_1(singleton(X0),X1,sk0_19)=X0|~relation(sk0_19)|in(ordered_pair(sk0_5(sk0_2(singleton(X0),X1,sk0_19),relation_rng(sk0_19),sk0_19),sk0_2(singleton(X0),X1,sk0_19)),sk0_19)|~spl0_8)),
% 0.12/0.34 inference(resolution,[status(thm)],[f273,f178])).
% 0.12/0.34 fof(f365,plain,(
% 0.12/0.34 spl0_21|~spl0_5|~spl0_8),
% 0.12/0.34 inference(split_clause,[status(thm)],[f364,f361,f231,f249])).
% 0.12/0.34 fof(f367,plain,(
% 0.12/0.34 spl0_22 <=> singleton(X0)=relation_inverse_image(sk0_19,X1)|sk0_1(singleton(X0),X1,sk0_19)=X0),
% 0.12/0.34 introduced(split_symbol_definition)).
% 0.12/0.34 fof(f370,plain,(
% 0.12/0.34 ![X0,X1]: (singleton(X0)=relation_inverse_image(sk0_19,X1)|sk0_1(singleton(X0),X1,sk0_19)=X0|~empty(relation_rng(sk0_19))|~spl0_8)),
% 0.12/0.34 inference(resolution,[status(thm)],[f273,f159])).
% 0.12/0.34 fof(f371,plain,(
% 0.12/0.34 spl0_22|~spl0_13|~spl0_8),
% 0.12/0.34 inference(split_clause,[status(thm)],[f370,f367,f286,f249])).
% 0.12/0.34 fof(f373,plain,(
% 0.12/0.34 spl0_23 <=> relation_inverse_image(sk0_19,relation_rng(sk0_19))=relation_inverse_image(sk0_19,X0)|relation_inverse_image(sk0_19,relation_rng(sk0_19))=relation_inverse_image(sk0_19,X0)|~in(ordered_pair(sk0_1(relation_inverse_image(sk0_19,relation_rng(sk0_19)),X0,sk0_19),X1),sk0_19)|~in(X1,X0)),
% 0.12/0.34 introduced(split_symbol_definition)).
% 0.12/0.34 fof(f376,plain,(
% 0.12/0.34 ![X0,X1]: (relation_inverse_image(sk0_19,relation_rng(sk0_19))=relation_inverse_image(sk0_19,X0)|~relation(sk0_19)|relation_inverse_image(sk0_19,relation_rng(sk0_19))=relation_inverse_image(sk0_19,X0)|~in(ordered_pair(sk0_1(relation_inverse_image(sk0_19,relation_rng(sk0_19)),X0,sk0_19),X1),sk0_19)|~in(X1,X0)|~spl0_8|~spl0_7)),
% 0.12/0.34 inference(resolution,[status(thm)],[f279,f60])).
% 0.12/0.34 fof(f377,plain,(
% 0.12/0.34 spl0_23|~spl0_5|~spl0_8|~spl0_7),
% 0.12/0.34 inference(split_clause,[status(thm)],[f376,f373,f231,f249,f244])).
% 0.12/0.34 fof(f378,plain,(
% 0.12/0.34 spl0_24 <=> X0=relation_inverse_image(sk0_19,X1)|in(sk0_1(X0,X1,sk0_19),relation_inverse_image(sk0_19,relation_rng(sk0_19)))|X0=relation_inverse_image(sk0_19,X1)|~in(ordered_pair(sk0_1(X0,X1,sk0_19),X2),sk0_19)|~in(X2,X1)),
% 0.12/0.34 introduced(split_symbol_definition)).
% 0.12/0.34 fof(f381,plain,(
% 0.12/0.34 ![X0,X1,X2]: (X0=relation_inverse_image(sk0_19,X1)|in(sk0_1(X0,X1,sk0_19),relation_inverse_image(sk0_19,relation_rng(sk0_19)))|~relation(sk0_19)|X0=relation_inverse_image(sk0_19,X1)|~in(ordered_pair(sk0_1(X0,X1,sk0_19),X2),sk0_19)|~in(X2,X1)|~spl0_8|~spl0_7)),
% 0.12/0.34 inference(resolution,[status(thm)],[f279,f60])).
% 0.12/0.34 fof(f382,plain,(
% 0.12/0.34 spl0_24|~spl0_5|~spl0_8|~spl0_7),
% 0.12/0.34 inference(split_clause,[status(thm)],[f381,f378,f231,f249,f244])).
% 0.12/0.34 fof(f383,plain,(
% 0.12/0.34 spl0_25 <=> relation_inverse_image(sk0_19,relation_rng(sk0_19))=relation_inverse_image(sk0_19,X0)|in(sk0_0(sk0_1(relation_inverse_image(sk0_19,relation_rng(sk0_19)),X0,sk0_19),relation_inverse_image(sk0_19,relation_rng(sk0_19)),relation_rng(sk0_19),sk0_19),relation_rng(sk0_19))),
% 0.12/0.34 introduced(split_symbol_definition)).
% 0.12/0.34 fof(f386,plain,(
% 0.12/0.34 ![X0]: (relation_inverse_image(sk0_19,relation_rng(sk0_19))=relation_inverse_image(sk0_19,X0)|~relation(sk0_19)|in(sk0_0(sk0_1(relation_inverse_image(sk0_19,relation_rng(sk0_19)),X0,sk0_19),relation_inverse_image(sk0_19,relation_rng(sk0_19)),relation_rng(sk0_19),sk0_19),relation_rng(sk0_19))|~spl0_8|~spl0_7)),
% 0.12/0.34 inference(resolution,[status(thm)],[f279,f173])).
% 0.12/0.34 fof(f387,plain,(
% 0.12/0.34 spl0_25|~spl0_5|~spl0_8|~spl0_7),
% 0.12/0.34 inference(split_clause,[status(thm)],[f386,f383,f231,f249,f244])).
% 0.12/0.34 fof(f389,plain,(
% 0.12/0.34 spl0_26 <=> relation_inverse_image(sk0_19,relation_rng(sk0_19))=relation_inverse_image(sk0_19,X0)|in(ordered_pair(sk0_1(relation_inverse_image(sk0_19,relation_rng(sk0_19)),X0,sk0_19),sk0_0(sk0_1(relation_inverse_image(sk0_19,relation_rng(sk0_19)),X0,sk0_19),relation_inverse_image(sk0_19,relation_rng(sk0_19)),relation_rng(sk0_19),sk0_19)),sk0_19)),
% 0.12/0.34 introduced(split_symbol_definition)).
% 0.12/0.34 fof(f392,plain,(
% 0.12/0.34 ![X0]: (relation_inverse_image(sk0_19,relation_rng(sk0_19))=relation_inverse_image(sk0_19,X0)|~relation(sk0_19)|in(ordered_pair(sk0_1(relation_inverse_image(sk0_19,relation_rng(sk0_19)),X0,sk0_19),sk0_0(sk0_1(relation_inverse_image(sk0_19,relation_rng(sk0_19)),X0,sk0_19),relation_inverse_image(sk0_19,relation_rng(sk0_19)),relation_rng(sk0_19),sk0_19)),sk0_19)|~spl0_8|~spl0_7)),
% 0.12/0.34 inference(resolution,[status(thm)],[f279,f172])).
% 0.12/0.34 fof(f393,plain,(
% 0.12/0.34 spl0_26|~spl0_5|~spl0_8|~spl0_7),
% 0.12/0.34 inference(split_clause,[status(thm)],[f392,f389,f231,f249,f244])).
% 0.12/0.34 fof(f397,plain,(
% 0.12/0.34 ![X0]: (empty_set=relation_inverse_image(sk0_19,X0)|in(sk0_1(empty_set,X0,sk0_19),relation_inverse_image(sk0_19,relation_rng(sk0_19)))|~spl0_8|~spl0_7)),
% 0.12/0.34 inference(resolution,[status(thm)],[f279,f177])).
% 0.12/0.34 fof(f400,plain,(
% 0.12/0.34 spl0_27 <=> relation_inverse_image(sk0_19,relation_rng(sk0_19))=relation_inverse_image(sk0_19,X0)),
% 0.12/0.34 introduced(split_symbol_definition)).
% 0.12/0.34 fof(f403,plain,(
% 0.12/0.34 spl0_28 <=> empty(relation_inverse_image(sk0_19,relation_rng(sk0_19)))),
% 0.12/0.34 introduced(split_symbol_definition)).
% 0.12/0.34 fof(f406,plain,(
% 0.12/0.34 ![X0]: (relation_inverse_image(sk0_19,relation_rng(sk0_19))=relation_inverse_image(sk0_19,X0)|~empty(relation_inverse_image(sk0_19,relation_rng(sk0_19)))|~spl0_8|~spl0_7)),
% 0.12/0.34 inference(resolution,[status(thm)],[f279,f159])).
% 0.12/0.34 fof(f407,plain,(
% 0.12/0.34 spl0_27|~spl0_28|~spl0_8|~spl0_7),
% 0.12/0.34 inference(split_clause,[status(thm)],[f406,f400,f403,f249,f244])).
% 0.12/0.34 fof(f411,plain,(
% 0.12/0.34 spl0_29 <=> relation_inverse_image(sk0_19,relation_rng(sk0_19))=relation_inverse_image(sk0_19,X0)|in(sk0_1(relation_inverse_image(sk0_19,relation_rng(sk0_19)),X0,sk0_19),relation_inverse_image(sk0_19,relation_rng(sk0_19)))|relation_inverse_image(sk0_19,relation_rng(sk0_19))=relation_inverse_image(sk0_19,X0)|~in(ordered_pair(sk0_1(relation_inverse_image(sk0_19,relation_rng(sk0_19)),X0,sk0_19),X1),sk0_19)|~in(X1,X0)),
% 0.12/0.34 introduced(split_symbol_definition)).
% 0.12/0.34 fof(f414,plain,(
% 0.12/0.34 ![X0,X1]: (relation_inverse_image(sk0_19,relation_rng(sk0_19))=relation_inverse_image(sk0_19,X0)|in(sk0_1(relation_inverse_image(sk0_19,relation_rng(sk0_19)),X0,sk0_19),relation_inverse_image(sk0_19,relation_rng(sk0_19)))|~relation(sk0_19)|relation_inverse_image(sk0_19,relation_rng(sk0_19))=relation_inverse_image(sk0_19,X0)|~in(ordered_pair(sk0_1(relation_inverse_image(sk0_19,relation_rng(sk0_19)),X0,sk0_19),X1),sk0_19)|~in(X1,X0)|~spl0_8|~spl0_7)),
% 0.12/0.34 inference(resolution,[status(thm)],[f279,f60])).
% 0.12/0.34 fof(f415,plain,(
% 0.12/0.34 spl0_29|~spl0_5|~spl0_8|~spl0_7),
% 0.12/0.34 inference(split_clause,[status(thm)],[f414,f411,f231,f249,f244])).
% 0.12/0.34 fof(f416,plain,(
% 0.12/0.34 spl0_30 <=> X0=relation_inverse_image(sk0_19,X1)|in(sk0_1(X0,X1,sk0_19),X0)|in(sk0_0(sk0_1(X0,X1,sk0_19),relation_inverse_image(sk0_19,relation_rng(sk0_19)),relation_rng(sk0_19),sk0_19),relation_rng(sk0_19))),
% 0.12/0.34 introduced(split_symbol_definition)).
% 0.12/0.34 fof(f419,plain,(
% 0.12/0.34 ![X0,X1]: (X0=relation_inverse_image(sk0_19,X1)|in(sk0_1(X0,X1,sk0_19),X0)|~relation(sk0_19)|in(sk0_0(sk0_1(X0,X1,sk0_19),relation_inverse_image(sk0_19,relation_rng(sk0_19)),relation_rng(sk0_19),sk0_19),relation_rng(sk0_19))|~spl0_8|~spl0_7)),
% 0.12/0.34 inference(resolution,[status(thm)],[f279,f173])).
% 0.12/0.34 fof(f420,plain,(
% 0.12/0.34 spl0_30|~spl0_5|~spl0_8|~spl0_7),
% 0.12/0.34 inference(split_clause,[status(thm)],[f419,f416,f231,f249,f244])).
% 0.12/0.34 fof(f421,plain,(
% 0.12/0.34 spl0_31 <=> X0=relation_inverse_image(sk0_19,X1)|in(sk0_1(X0,X1,sk0_19),X0)|in(ordered_pair(sk0_1(X0,X1,sk0_19),sk0_0(sk0_1(X0,X1,sk0_19),relation_inverse_image(sk0_19,relation_rng(sk0_19)),relation_rng(sk0_19),sk0_19)),sk0_19)),
% 0.12/0.34 introduced(split_symbol_definition)).
% 0.12/0.34 fof(f424,plain,(
% 0.12/0.34 ![X0,X1]: (X0=relation_inverse_image(sk0_19,X1)|in(sk0_1(X0,X1,sk0_19),X0)|~relation(sk0_19)|in(ordered_pair(sk0_1(X0,X1,sk0_19),sk0_0(sk0_1(X0,X1,sk0_19),relation_inverse_image(sk0_19,relation_rng(sk0_19)),relation_rng(sk0_19),sk0_19)),sk0_19)|~spl0_8|~spl0_7)),
% 0.12/0.34 inference(resolution,[status(thm)],[f279,f172])).
% 0.12/0.34 fof(f425,plain,(
% 0.12/0.34 spl0_31|~spl0_5|~spl0_8|~spl0_7),
% 0.12/0.34 inference(split_clause,[status(thm)],[f424,f421,f231,f249,f244])).
% 0.12/0.34 fof(f427,plain,(
% 0.12/0.34 ![X0,X1]: (X0=relation_inverse_image(sk0_19,X1)|in(sk0_1(X0,X1,sk0_19),X0)|~empty(relation_inverse_image(sk0_19,relation_rng(sk0_19)))|~spl0_8|~spl0_7)),
% 0.12/0.34 inference(resolution,[status(thm)],[f279,f159])).
% 0.12/0.34 fof(f428,plain,(
% 0.12/0.34 spl0_9|~spl0_28|~spl0_8|~spl0_7),
% 0.12/0.34 inference(split_clause,[status(thm)],[f427,f255,f403,f249,f244])).
% 0.12/0.34 fof(f432,plain,(
% 0.12/0.34 spl0_32 <=> empty_set=relation_inverse_image(sk0_19,X0)|in(sk0_0(sk0_1(empty_set,X0,sk0_19),relation_inverse_image(sk0_19,relation_rng(sk0_19)),relation_rng(sk0_19),sk0_19),relation_rng(sk0_19))),
% 0.12/0.34 introduced(split_symbol_definition)).
% 0.12/0.34 fof(f435,plain,(
% 0.12/0.34 ![X0]: (empty_set=relation_inverse_image(sk0_19,X0)|~relation(sk0_19)|in(sk0_0(sk0_1(empty_set,X0,sk0_19),relation_inverse_image(sk0_19,relation_rng(sk0_19)),relation_rng(sk0_19),sk0_19),relation_rng(sk0_19))|~spl0_8|~spl0_7)),
% 0.12/0.34 inference(resolution,[status(thm)],[f397,f173])).
% 0.12/0.34 fof(f436,plain,(
% 0.12/0.34 spl0_32|~spl0_5|~spl0_8|~spl0_7),
% 0.12/0.34 inference(split_clause,[status(thm)],[f435,f432,f231,f249,f244])).
% 0.12/0.34 fof(f437,plain,(
% 0.12/0.34 spl0_33 <=> empty_set=relation_inverse_image(sk0_19,X0)|in(ordered_pair(sk0_1(empty_set,X0,sk0_19),sk0_0(sk0_1(empty_set,X0,sk0_19),relation_inverse_image(sk0_19,relation_rng(sk0_19)),relation_rng(sk0_19),sk0_19)),sk0_19)),
% 0.12/0.34 introduced(split_symbol_definition)).
% 0.12/0.34 fof(f440,plain,(
% 0.12/0.34 ![X0]: (empty_set=relation_inverse_image(sk0_19,X0)|~relation(sk0_19)|in(ordered_pair(sk0_1(empty_set,X0,sk0_19),sk0_0(sk0_1(empty_set,X0,sk0_19),relation_inverse_image(sk0_19,relation_rng(sk0_19)),relation_rng(sk0_19),sk0_19)),sk0_19)|~spl0_8|~spl0_7)),
% 0.12/0.34 inference(resolution,[status(thm)],[f397,f172])).
% 0.12/0.34 fof(f441,plain,(
% 0.12/0.34 spl0_33|~spl0_5|~spl0_8|~spl0_7),
% 0.12/0.34 inference(split_clause,[status(thm)],[f440,f437,f231,f249,f244])).
% 0.12/0.34 fof(f443,plain,(
% 0.12/0.34 ![X0]: (empty_set=relation_inverse_image(sk0_19,X0)|~empty(relation_inverse_image(sk0_19,relation_rng(sk0_19)))|~spl0_8|~spl0_7)),
% 0.12/0.34 inference(resolution,[status(thm)],[f397,f159])).
% 0.12/0.34 fof(f444,plain,(
% 0.12/0.34 spl0_15|~spl0_28|~spl0_8|~spl0_7),
% 0.12/0.34 inference(split_clause,[status(thm)],[f443,f302,f403,f249,f244])).
% 0.12/0.34 fof(f469,plain,(
% 0.12/0.34 spl0_34 <=> X0=relation_inverse_image(sk0_19,X1)|in(sk0_1(X0,X1,sk0_19),X0)|in(sk0_5(sk0_2(X0,X1,sk0_19),relation_rng(sk0_19),sk0_19),relation_inverse_image(sk0_19,X2))|~in(sk0_2(X0,X1,sk0_19),X2)),
% 0.12/0.34 introduced(split_symbol_definition)).
% 0.12/0.34 fof(f472,plain,(
% 0.12/0.34 ![X0,X1,X2]: (X0=relation_inverse_image(sk0_19,X1)|in(sk0_1(X0,X1,sk0_19),X0)|~relation(sk0_19)|in(sk0_5(sk0_2(X0,X1,sk0_19),relation_rng(sk0_19),sk0_19),relation_inverse_image(sk0_19,X2))|~in(sk0_2(X0,X1,sk0_19),X2)|~spl0_12)),
% 0.12/0.34 inference(resolution,[status(thm)],[f281,f174])).
% 0.12/0.34 fof(f473,plain,(
% 0.12/0.34 spl0_34|~spl0_5|~spl0_12),
% 0.12/0.34 inference(split_clause,[status(thm)],[f472,f469,f231,f280])).
% 0.12/0.34 fof(f480,plain,(
% 0.12/0.34 spl0_35 <=> one_to_one(empty_set)),
% 0.12/0.34 introduced(split_symbol_definition)).
% 0.12/0.34 fof(f483,plain,(
% 0.12/0.34 ~empty(empty_set)|one_to_one(empty_set)),
% 0.12/0.34 inference(resolution,[status(thm)],[f220,f171])).
% 0.12/0.34 fof(f484,plain,(
% 0.12/0.34 ~spl0_2|spl0_35),
% 0.12/0.34 inference(split_clause,[status(thm)],[f483,f192,f480])).
% 0.12/0.34 fof(f485,plain,(
% 0.12/0.34 $false|spl0_2),
% 0.12/0.34 inference(forward_subsumption_resolution,[status(thm)],[f194,f86])).
% 0.12/0.34 fof(f486,plain,(
% 0.12/0.34 spl0_2),
% 0.12/0.34 inference(contradiction_clause,[status(thm)],[f485])).
% 0.12/0.34 fof(f489,plain,(
% 0.12/0.34 spl0_36 <=> X0=relation_inverse_image(empty_set,X1)|X0=relation_inverse_image(empty_set,X1)|~in(ordered_pair(sk0_1(X0,X1,empty_set),X2),empty_set)|~in(X2,X1)),
% 0.12/0.34 introduced(split_symbol_definition)).
% 0.12/0.34 fof(f492,plain,(
% 0.12/0.34 ![X0,X1,X2]: (X0=relation_inverse_image(empty_set,X1)|~relation(empty_set)|X0=relation_inverse_image(empty_set,X1)|~in(ordered_pair(sk0_1(X0,X1,empty_set),X2),empty_set)|~in(X2,X1))),
% 0.12/0.34 inference(resolution,[status(thm)],[f218,f60])).
% 0.12/0.34 fof(f493,plain,(
% 0.12/0.34 spl0_36|~spl0_3),
% 0.12/0.34 inference(split_clause,[status(thm)],[f492,f489,f195])).
% 0.12/0.34 fof(f494,plain,(
% 0.12/0.34 ![X0,X1,X2]: (relation_inverse_image(X0,X1)=relation_inverse_image(empty_set,X2)|~relation(X0)|in(sk0_0(sk0_1(relation_inverse_image(X0,X1),X2,empty_set),relation_inverse_image(X0,X1),X1,X0),X1))),
% 0.12/0.34 inference(resolution,[status(thm)],[f218,f173])).
% 0.12/0.34 fof(f496,plain,(
% 0.12/0.34 ![X0,X1]: (relation_rng(X0)=relation_inverse_image(empty_set,X1)|~relation(X0)|in(ordered_pair(sk0_5(sk0_1(relation_rng(X0),X1,empty_set),relation_rng(X0),X0),sk0_1(relation_rng(X0),X1,empty_set)),X0))),
% 0.12/0.34 inference(resolution,[status(thm)],[f218,f178])).
% 0.12/0.34 fof(f497,plain,(
% 0.12/0.34 ![X0,X1]: (singleton(X0)=relation_inverse_image(empty_set,X1)|sk0_1(singleton(X0),X1,empty_set)=X0)),
% 0.12/0.34 inference(resolution,[status(thm)],[f218,f175])).
% 0.12/0.34 fof(f498,plain,(
% 0.12/0.34 ![X0]: (empty_set=relation_inverse_image(empty_set,X0))),
% 0.12/0.34 inference(resolution,[status(thm)],[f218,f177])).
% 0.12/0.34 fof(f505,plain,(
% 0.12/0.34 ![X0,X1]: (X0=empty_set|in(sk0_1(X0,X1,empty_set),X0))),
% 0.12/0.34 inference(backward_demodulation,[status(thm)],[f498,f218])).
% 0.12/0.34 fof(f506,plain,(
% 0.12/0.34 ![X0,X1]: (singleton(X0)=empty_set|sk0_1(singleton(X0),X1,empty_set)=X0)),
% 0.12/0.34 inference(backward_demodulation,[status(thm)],[f498,f497])).
% 0.12/0.34 fof(f507,plain,(
% 0.12/0.34 ![X0,X1]: (relation_rng(X0)=empty_set|~relation(X0)|in(ordered_pair(sk0_5(sk0_1(relation_rng(X0),X1,empty_set),relation_rng(X0),X0),sk0_1(relation_rng(X0),X1,empty_set)),X0))),
% 0.12/0.34 inference(backward_demodulation,[status(thm)],[f498,f496])).
% 0.12/0.34 fof(f509,plain,(
% 0.12/0.34 ![X0,X1,X2]: (relation_inverse_image(X0,X1)=empty_set|~relation(X0)|in(sk0_0(sk0_1(relation_inverse_image(X0,X1),X2,empty_set),relation_inverse_image(X0,X1),X1,X0),X1))),
% 0.12/0.34 inference(backward_demodulation,[status(thm)],[f498,f494])).
% 0.12/0.34 fof(f515,plain,(
% 0.12/0.34 spl0_37 <=> ~in(X0,empty_set)|in(sk0_0(X0,relation_inverse_image(empty_set,X1),X1,empty_set),X1)),
% 0.12/0.34 introduced(split_symbol_definition)).
% 0.12/0.34 fof(f518,plain,(
% 0.12/0.34 ![X0,X1]: (~relation(empty_set)|~in(X0,empty_set)|in(sk0_0(X0,relation_inverse_image(empty_set,X1),X1,empty_set),X1))),
% 0.12/0.34 inference(paramodulation,[status(thm)],[f498,f173])).
% 0.12/0.34 fof(f519,plain,(
% 0.12/0.34 ~spl0_3|spl0_37),
% 0.12/0.34 inference(split_clause,[status(thm)],[f518,f195,f515])).
% 0.12/0.34 fof(f520,plain,(
% 0.12/0.34 spl0_38 <=> ~in(X0,empty_set)|in(ordered_pair(X0,sk0_0(X0,relation_inverse_image(empty_set,X1),X1,empty_set)),empty_set)),
% 0.12/0.34 introduced(split_symbol_definition)).
% 0.12/0.34 fof(f523,plain,(
% 0.12/0.34 ![X0,X1]: (~relation(empty_set)|~in(X0,empty_set)|in(ordered_pair(X0,sk0_0(X0,relation_inverse_image(empty_set,X1),X1,empty_set)),empty_set))),
% 0.12/0.34 inference(paramodulation,[status(thm)],[f498,f172])).
% 0.12/0.34 fof(f524,plain,(
% 0.12/0.34 ~spl0_3|spl0_38),
% 0.12/0.34 inference(split_clause,[status(thm)],[f523,f195,f520])).
% 0.12/0.34 fof(f527,plain,(
% 0.12/0.34 spl0_39 <=> X0=empty_set|X0=relation_inverse_image(empty_set,X1)|~in(ordered_pair(sk0_1(X0,X1,empty_set),X2),empty_set)|~in(X2,X1)),
% 0.12/0.34 introduced(split_symbol_definition)).
% 0.12/0.34 fof(f530,plain,(
% 0.12/0.34 ![X0,X1,X2]: (X0=empty_set|~relation(empty_set)|X0=relation_inverse_image(empty_set,X1)|~in(ordered_pair(sk0_1(X0,X1,empty_set),X2),empty_set)|~in(X2,X1))),
% 0.12/0.34 inference(resolution,[status(thm)],[f505,f60])).
% 0.12/0.34 fof(f531,plain,(
% 0.12/0.34 spl0_39|~spl0_3),
% 0.12/0.34 inference(split_clause,[status(thm)],[f530,f527,f195])).
% 0.12/0.34 fof(f547,plain,(
% 0.12/0.34 spl0_40 <=> singleton(X0)=relation_inverse_image(empty_set,X1)|~in(X0,singleton(X0))|~in(ordered_pair(sk0_1(singleton(X0),X1,empty_set),X2),empty_set)|~in(X2,X1)|singleton(X0)=empty_set),
% 0.12/0.34 introduced(split_symbol_definition)).
% 0.12/0.34 fof(f550,plain,(
% 0.12/0.34 ![X0,X1,X2]: (~relation(empty_set)|singleton(X0)=relation_inverse_image(empty_set,X1)|~in(X0,singleton(X0))|~in(ordered_pair(sk0_1(singleton(X0),X1,empty_set),X2),empty_set)|~in(X2,X1)|singleton(X0)=empty_set)),
% 0.12/0.34 inference(paramodulation,[status(thm)],[f506,f60])).
% 0.12/0.34 fof(f551,plain,(
% 0.12/0.34 ~spl0_3|spl0_40),
% 0.12/0.34 inference(split_clause,[status(thm)],[f550,f195,f547])).
% 0.12/0.34 fof(f554,plain,(
% 0.12/0.34 ![X0,X1]: (relation_inverse_image(sk0_18,X0)=empty_set|in(sk0_0(sk0_1(relation_inverse_image(sk0_18,X0),X1,empty_set),relation_inverse_image(sk0_18,X0),X0,sk0_18),X0))),
% 0.12/0.34 inference(resolution,[status(thm)],[f509,f130])).
% 0.12/0.34 fof(f566,plain,(
% 0.12/0.34 relation_inverse_image(sk0_18,empty_set)=empty_set),
% 0.12/0.34 inference(resolution,[status(thm)],[f554,f177])).
% 0.12/0.34 fof(f583,plain,(
% 0.12/0.34 spl0_44 <=> relation(sk0_18)),
% 0.12/0.34 introduced(split_symbol_definition)).
% 0.12/0.34 fof(f585,plain,(
% 0.12/0.34 ~relation(sk0_18)|spl0_44),
% 0.12/0.34 inference(component_clause,[status(thm)],[f583])).
% 0.12/0.34 fof(f586,plain,(
% 0.12/0.34 spl0_45 <=> ~in(X0,empty_set)|in(sk0_0(X0,relation_inverse_image(sk0_18,empty_set),empty_set,sk0_18),empty_set)),
% 0.12/0.34 introduced(split_symbol_definition)).
% 0.12/0.34 fof(f589,plain,(
% 0.12/0.34 ![X0]: (~relation(sk0_18)|~in(X0,empty_set)|in(sk0_0(X0,relation_inverse_image(sk0_18,empty_set),empty_set,sk0_18),empty_set))),
% 0.12/0.34 inference(paramodulation,[status(thm)],[f566,f173])).
% 0.12/0.34 fof(f590,plain,(
% 0.12/0.34 ~spl0_44|spl0_45),
% 0.12/0.34 inference(split_clause,[status(thm)],[f589,f583,f586])).
% 0.12/0.34 fof(f591,plain,(
% 0.12/0.34 spl0_46 <=> ~in(X0,empty_set)|in(ordered_pair(X0,sk0_0(X0,relation_inverse_image(sk0_18,empty_set),empty_set,sk0_18)),sk0_18)),
% 0.12/0.34 introduced(split_symbol_definition)).
% 0.12/0.34 fof(f594,plain,(
% 0.12/0.34 ![X0]: (~relation(sk0_18)|~in(X0,empty_set)|in(ordered_pair(X0,sk0_0(X0,relation_inverse_image(sk0_18,empty_set),empty_set,sk0_18)),sk0_18))),
% 0.12/0.34 inference(paramodulation,[status(thm)],[f566,f172])).
% 0.12/0.34 fof(f595,plain,(
% 0.12/0.34 ~spl0_44|spl0_46),
% 0.12/0.34 inference(split_clause,[status(thm)],[f594,f583,f591])).
% 0.12/0.34 fof(f596,plain,(
% 0.12/0.34 $false|spl0_44),
% 0.12/0.34 inference(forward_subsumption_resolution,[status(thm)],[f585,f130])).
% 0.12/0.34 fof(f597,plain,(
% 0.12/0.34 spl0_44),
% 0.12/0.34 inference(contradiction_clause,[status(thm)],[f596])).
% 0.12/0.34 fof(f656,plain,(
% 0.12/0.34 spl0_61 <=> relation_rng(sk0_19)=empty_set),
% 0.12/0.34 introduced(split_symbol_definition)).
% 0.12/0.34 fof(f657,plain,(
% 0.12/0.34 relation_rng(sk0_19)=empty_set|~spl0_61),
% 0.12/0.34 inference(component_clause,[status(thm)],[f656])).
% 0.12/0.34 fof(f659,plain,(
% 0.12/0.34 spl0_62 <=> in(ordered_pair(sk0_5(sk0_1(relation_rng(sk0_19),X0,empty_set),relation_rng(sk0_19),sk0_19),sk0_1(relation_rng(sk0_19),X0,empty_set)),sk0_19)),
% 0.12/0.34 introduced(split_symbol_definition)).
% 0.12/0.34 fof(f660,plain,(
% 0.12/0.34 ![X0]: (in(ordered_pair(sk0_5(sk0_1(relation_rng(sk0_19),X0,empty_set),relation_rng(sk0_19),sk0_19),sk0_1(relation_rng(sk0_19),X0,empty_set)),sk0_19)|~spl0_62)),
% 0.12/0.34 inference(component_clause,[status(thm)],[f659])).
% 0.12/0.34 fof(f662,plain,(
% 0.12/0.34 ![X0]: (relation_rng(sk0_19)=empty_set|in(ordered_pair(sk0_5(sk0_1(relation_rng(sk0_19),X0,empty_set),relation_rng(sk0_19),sk0_19),sk0_1(relation_rng(sk0_19),X0,empty_set)),sk0_19))),
% 0.12/0.34 inference(resolution,[status(thm)],[f507,f138])).
% 0.12/0.34 fof(f663,plain,(
% 0.12/0.34 spl0_61|spl0_62),
% 0.12/0.34 inference(split_clause,[status(thm)],[f662,f656,f659])).
% 0.12/0.34 fof(f695,plain,(
% 0.12/0.34 ![X0]: (empty_set=relation_inverse_image(sk0_19,X0)|in(sk0_2(empty_set,X0,sk0_19),empty_set)|~spl0_61|~spl0_8)),
% 0.12/0.34 inference(backward_demodulation,[status(thm)],[f657,f274])).
% 0.12/0.34 fof(f696,plain,(
% 0.12/0.34 ![X0]: (empty_set=relation_inverse_image(sk0_19,X0)|~spl0_61|~spl0_8)),
% 0.12/0.34 inference(forward_subsumption_resolution,[status(thm)],[f695,f177])).
% 0.12/0.34 fof(f700,plain,(
% 0.12/0.34 ~empty(empty_set)|~spl0_61|spl0_13),
% 0.12/0.34 inference(backward_demodulation,[status(thm)],[f657,f288])).
% 0.12/0.34 fof(f701,plain,(
% 0.12/0.34 ~spl0_2|~spl0_61|spl0_13),
% 0.12/0.34 inference(split_clause,[status(thm)],[f700,f192,f656,f286])).
% 0.12/0.34 fof(f829,plain,(
% 0.12/0.34 ~empty_set=empty_set|~spl0_61|~spl0_8|spl0_1),
% 0.12/0.34 inference(backward_demodulation,[status(thm)],[f696,f168])).
% 0.12/0.34 fof(f830,plain,(
% 0.12/0.34 $false|~spl0_61|~spl0_8|spl0_1),
% 0.12/0.34 inference(trivial_equality_resolution,[status(esa)],[f829])).
% 0.12/0.34 fof(f831,plain,(
% 0.12/0.34 ~spl0_61|~spl0_8|spl0_1),
% 0.12/0.34 inference(contradiction_clause,[status(thm)],[f830])).
% 0.12/0.34 fof(f1000,plain,(
% 0.12/0.34 ![X0,X1]: (X0=relation_inverse_image(sk0_19,X1)|in(sk0_1(X0,X1,sk0_19),X0)|in(sk0_2(X0,X1,sk0_19),X1))),
% 0.12/0.34 inference(resolution,[status(thm)],[f62,f138])).
% 0.12/0.34 fof(f1010,plain,(
% 0.12/0.34 spl0_67 <=> relation(sk0_9)),
% 0.12/0.34 introduced(split_symbol_definition)).
% 0.12/0.34 fof(f1012,plain,(
% 0.12/0.34 ~relation(sk0_9)|spl0_67),
% 0.12/0.34 inference(component_clause,[status(thm)],[f1010])).
% 0.12/0.34 fof(f1020,plain,(
% 0.12/0.34 $false|spl0_67),
% 0.12/0.34 inference(forward_subsumption_resolution,[status(thm)],[f1012,f102])).
% 0.12/0.34 fof(f1021,plain,(
% 0.12/0.34 spl0_67),
% 0.12/0.34 inference(contradiction_clause,[status(thm)],[f1020])).
% 0.12/0.34 fof(f1022,plain,(
% 0.12/0.34 spl0_69 <=> relation(sk0_14)),
% 0.12/0.34 introduced(split_symbol_definition)).
% 0.12/0.34 fof(f1024,plain,(
% 0.12/0.34 ~relation(sk0_14)|spl0_69),
% 0.12/0.34 inference(component_clause,[status(thm)],[f1022])).
% 0.12/0.34 fof(f1035,plain,(
% 0.12/0.34 $false|spl0_69),
% 0.12/0.34 inference(forward_subsumption_resolution,[status(thm)],[f1024,f119])).
% 0.12/0.34 fof(f1036,plain,(
% 0.12/0.34 spl0_69),
% 0.12/0.34 inference(contradiction_clause,[status(thm)],[f1035])).
% 0.12/0.34 fof(f1037,plain,(
% 0.12/0.34 spl0_72 <=> relation(sk0_17)),
% 0.12/0.34 introduced(split_symbol_definition)).
% 0.12/0.34 fof(f1039,plain,(
% 0.12/0.34 ~relation(sk0_17)|spl0_72),
% 0.12/0.34 inference(component_clause,[status(thm)],[f1037])).
% 0.12/0.34 fof(f1047,plain,(
% 0.12/0.34 $false|spl0_72),
% 0.12/0.34 inference(forward_subsumption_resolution,[status(thm)],[f1039,f126])).
% 0.12/0.34 fof(f1048,plain,(
% 0.12/0.34 spl0_72),
% 0.12/0.34 inference(contradiction_clause,[status(thm)],[f1047])).
% 0.12/0.34 fof(f1097,plain,(
% 0.12/0.34 spl0_76 <=> in(sk0_5(sk0_1(relation_rng(sk0_19),X0,empty_set),relation_rng(sk0_19),sk0_19),relation_inverse_image(sk0_19,X1))|~in(sk0_1(relation_rng(sk0_19),X0,empty_set),X1)),
% 0.12/0.34 introduced(split_symbol_definition)).
% 0.12/0.34 fof(f1100,plain,(
% 0.12/0.34 ![X0,X1]: (~relation(sk0_19)|in(sk0_5(sk0_1(relation_rng(sk0_19),X0,empty_set),relation_rng(sk0_19),sk0_19),relation_inverse_image(sk0_19,X1))|~in(sk0_1(relation_rng(sk0_19),X0,empty_set),X1)|~spl0_62)),
% 0.12/0.34 inference(resolution,[status(thm)],[f660,f174])).
% 0.12/0.34 fof(f1101,plain,(
% 0.12/0.34 ~spl0_5|spl0_76|~spl0_62),
% 0.12/0.34 inference(split_clause,[status(thm)],[f1100,f231,f1097,f659])).
% 0.12/0.34 fof(f1102,plain,(
% 0.12/0.34 spl0_77 <=> in(sk0_1(relation_rng(sk0_19),X0,empty_set),relation_rng(sk0_19))),
% 0.12/0.34 introduced(split_symbol_definition)).
% 0.12/0.34 fof(f1103,plain,(
% 0.12/0.34 ![X0]: (in(sk0_1(relation_rng(sk0_19),X0,empty_set),relation_rng(sk0_19))|~spl0_77)),
% 0.12/0.34 inference(component_clause,[status(thm)],[f1102])).
% 0.12/0.34 fof(f1105,plain,(
% 0.12/0.34 ![X0]: (~relation(sk0_19)|in(sk0_1(relation_rng(sk0_19),X0,empty_set),relation_rng(sk0_19))|~spl0_62)),
% 0.12/0.34 inference(resolution,[status(thm)],[f660,f179])).
% 0.12/0.34 fof(f1106,plain,(
% 0.12/0.34 ~spl0_5|spl0_77|~spl0_62),
% 0.12/0.34 inference(split_clause,[status(thm)],[f1105,f231,f1102,f659])).
% 0.12/0.34 fof(f1128,plain,(
% 0.12/0.34 spl0_78 <=> X0=relation_inverse_image(sk0_19,X1)|in(sk0_2(X0,X1,sk0_19),X1)|X0=relation_inverse_image(sk0_19,X1)|~in(ordered_pair(sk0_1(X0,X1,sk0_19),X2),sk0_19)|~in(X2,X1)),
% 0.12/0.34 introduced(split_symbol_definition)).
% 0.12/0.34 fof(f1131,plain,(
% 0.12/0.34 ![X0,X1,X2]: (X0=relation_inverse_image(sk0_19,X1)|in(sk0_2(X0,X1,sk0_19),X1)|~relation(sk0_19)|X0=relation_inverse_image(sk0_19,X1)|~in(ordered_pair(sk0_1(X0,X1,sk0_19),X2),sk0_19)|~in(X2,X1))),
% 0.12/0.34 inference(resolution,[status(thm)],[f1000,f60])).
% 0.12/0.34 fof(f1132,plain,(
% 0.12/0.34 spl0_78|~spl0_5),
% 0.12/0.34 inference(split_clause,[status(thm)],[f1131,f1128,f231])).
% 0.12/0.34 fof(f1137,plain,(
% 0.12/0.34 ![X0]: (empty_set=relation_inverse_image(sk0_19,X0)|in(sk0_2(empty_set,X0,sk0_19),X0))),
% 0.12/0.34 inference(resolution,[status(thm)],[f1000,f177])).
% 0.12/0.34 fof(f1147,plain,(
% 0.12/0.34 ![X0]: (X0=relation_inverse_image(sk0_19,empty_set)|in(sk0_1(X0,empty_set,sk0_19),X0))),
% 0.12/0.34 inference(resolution,[status(thm)],[f1000,f177])).
% 0.12/0.34 fof(f1157,plain,(
% 0.12/0.34 ![X0]: (empty_set=relation_inverse_image(sk0_19,singleton(X0))|sk0_2(empty_set,singleton(X0),sk0_19)=X0)),
% 0.12/0.34 inference(resolution,[status(thm)],[f1137,f175])).
% 0.12/0.34 fof(f1158,plain,(
% 0.12/0.34 empty_set=relation_inverse_image(sk0_19,empty_set)),
% 0.12/0.34 inference(resolution,[status(thm)],[f1137,f177])).
% 0.12/0.34 fof(f1162,plain,(
% 0.12/0.34 ![X0]: (X0=empty_set|in(sk0_1(X0,empty_set,sk0_19),X0))),
% 0.12/0.34 inference(backward_demodulation,[status(thm)],[f1158,f1147])).
% 0.12/0.34 fof(f1163,plain,(
% 0.12/0.34 spl0_79 <=> ~in(X0,empty_set)|in(sk0_0(X0,relation_inverse_image(sk0_19,empty_set),empty_set,sk0_19),empty_set)),
% 0.12/0.34 introduced(split_symbol_definition)).
% 0.12/0.34 fof(f1166,plain,(
% 0.12/0.34 ![X0]: (~relation(sk0_19)|~in(X0,empty_set)|in(sk0_0(X0,relation_inverse_image(sk0_19,empty_set),empty_set,sk0_19),empty_set))),
% 0.12/0.34 inference(paramodulation,[status(thm)],[f1158,f173])).
% 0.12/0.34 fof(f1167,plain,(
% 0.12/0.34 ~spl0_5|spl0_79),
% 0.12/0.34 inference(split_clause,[status(thm)],[f1166,f231,f1163])).
% 0.12/0.34 fof(f1168,plain,(
% 0.12/0.34 spl0_80 <=> ~in(X0,empty_set)|in(ordered_pair(X0,sk0_0(X0,relation_inverse_image(sk0_19,empty_set),empty_set,sk0_19)),sk0_19)),
% 0.12/0.34 introduced(split_symbol_definition)).
% 0.12/0.34 fof(f1171,plain,(
% 0.12/0.34 ![X0]: (~relation(sk0_19)|~in(X0,empty_set)|in(ordered_pair(X0,sk0_0(X0,relation_inverse_image(sk0_19,empty_set),empty_set,sk0_19)),sk0_19))),
% 0.12/0.34 inference(paramodulation,[status(thm)],[f1158,f172])).
% 0.12/0.34 fof(f1172,plain,(
% 0.12/0.34 ~spl0_5|spl0_80),
% 0.12/0.34 inference(split_clause,[status(thm)],[f1171,f231,f1168])).
% 0.12/0.34 fof(f1179,plain,(
% 0.12/0.34 ![X0]: (empty_set=relation_inverse_image(sk0_19,singleton(X0))|in(X0,relation_rng(sk0_19))|empty_set=relation_inverse_image(sk0_19,singleton(X0))|~spl0_8)),
% 0.12/0.34 inference(paramodulation,[status(thm)],[f1157,f274])).
% 0.12/0.34 fof(f1180,plain,(
% 0.12/0.34 ![X0]: (empty_set=relation_inverse_image(sk0_19,singleton(X0))|in(X0,relation_rng(sk0_19))|~spl0_8)),
% 0.12/0.34 inference(duplicate_literals_removal,[status(esa)],[f1179])).
% 0.12/0.34 fof(f1183,plain,(
% 0.12/0.34 ![X0]: (empty_set=relation_inverse_image(sk0_19,singleton(X0))|~in(relation_rng(sk0_19),X0)|empty_set=relation_inverse_image(sk0_19,singleton(X0))|~spl0_8)),
% 0.12/0.34 inference(paramodulation,[status(thm)],[f1157,f307])).
% 0.12/0.34 fof(f1184,plain,(
% 0.12/0.34 ![X0]: (empty_set=relation_inverse_image(sk0_19,singleton(X0))|~in(relation_rng(sk0_19),X0)|~spl0_8)),
% 0.12/0.34 inference(duplicate_literals_removal,[status(esa)],[f1183])).
% 0.12/0.34 fof(f1204,plain,(
% 0.12/0.34 ![X0]: (empty_set=relation_inverse_image(sk0_19,singleton(X0))|in(sk0_1(empty_set,singleton(X0),sk0_19),empty_set)|in(ordered_pair(sk0_1(empty_set,singleton(X0),sk0_19),X0),sk0_19)|empty_set=relation_inverse_image(sk0_19,singleton(X0)))),
% 0.12/0.34 inference(paramodulation,[status(thm)],[f1157,f219])).
% 0.12/0.34 fof(f1205,plain,(
% 0.12/0.34 ![X0]: (empty_set=relation_inverse_image(sk0_19,singleton(X0))|in(sk0_1(empty_set,singleton(X0),sk0_19),empty_set)|in(ordered_pair(sk0_1(empty_set,singleton(X0),sk0_19),X0),sk0_19))),
% 0.12/0.34 inference(duplicate_literals_removal,[status(esa)],[f1204])).
% 0.12/0.34 fof(f1206,plain,(
% 0.12/0.34 ![X0]: (empty_set=relation_inverse_image(sk0_19,singleton(X0))|in(ordered_pair(sk0_1(empty_set,singleton(X0),sk0_19),X0),sk0_19))),
% 0.12/0.34 inference(forward_subsumption_resolution,[status(thm)],[f1205,f177])).
% 0.12/0.34 fof(f1211,plain,(
% 0.12/0.34 spl0_81 <=> empty_set=relation_inverse_image(sk0_19,singleton(X0))|in(sk0_1(empty_set,singleton(X0),sk0_19),relation_inverse_image(sk0_19,X1))|~in(X0,X1)),
% 0.12/0.34 introduced(split_symbol_definition)).
% 0.12/0.34 fof(f1214,plain,(
% 0.12/0.34 ![X0,X1]: (empty_set=relation_inverse_image(sk0_19,singleton(X0))|~relation(sk0_19)|in(sk0_1(empty_set,singleton(X0),sk0_19),relation_inverse_image(sk0_19,X1))|~in(X0,X1))),
% 0.12/0.34 inference(resolution,[status(thm)],[f1206,f174])).
% 0.12/0.34 fof(f1215,plain,(
% 0.12/0.34 spl0_81|~spl0_5),
% 0.12/0.34 inference(split_clause,[status(thm)],[f1214,f1211,f231])).
% 0.12/0.34 fof(f1216,plain,(
% 0.12/0.34 spl0_82 <=> empty_set=relation_inverse_image(sk0_19,singleton(X0))|in(X0,relation_rng(sk0_19))),
% 0.12/0.34 introduced(split_symbol_definition)).
% 0.12/0.34 fof(f1219,plain,(
% 0.12/0.34 ![X0]: (empty_set=relation_inverse_image(sk0_19,singleton(X0))|~relation(sk0_19)|in(X0,relation_rng(sk0_19)))),
% 0.12/0.34 inference(resolution,[status(thm)],[f1206,f179])).
% 0.12/0.34 fof(f1220,plain,(
% 0.12/0.34 spl0_82|~spl0_5),
% 0.12/0.34 inference(split_clause,[status(thm)],[f1219,f1216,f231])).
% 0.12/0.34 fof(f1222,plain,(
% 0.12/0.34 spl0_83 <=> empty_set=relation_inverse_image(sk0_19,singleton(X0))),
% 0.12/0.34 introduced(split_symbol_definition)).
% 0.12/0.34 fof(f1241,plain,(
% 0.12/0.34 spl0_84 <=> X0=empty_set|X0=relation_inverse_image(sk0_19,empty_set)|~in(ordered_pair(sk0_1(X0,empty_set,sk0_19),X1),sk0_19)|~in(X1,empty_set)),
% 0.12/0.34 introduced(split_symbol_definition)).
% 0.12/0.34 fof(f1244,plain,(
% 0.12/0.34 ![X0,X1]: (X0=empty_set|~relation(sk0_19)|X0=relation_inverse_image(sk0_19,empty_set)|~in(ordered_pair(sk0_1(X0,empty_set,sk0_19),X1),sk0_19)|~in(X1,empty_set))),
% 0.12/0.34 inference(resolution,[status(thm)],[f1162,f60])).
% 0.12/0.34 fof(f1245,plain,(
% 0.12/0.34 spl0_84|~spl0_5),
% 0.12/0.34 inference(split_clause,[status(thm)],[f1244,f1241,f231])).
% 0.12/0.34 fof(f1249,plain,(
% 0.12/0.34 ![X0]: (singleton(X0)=empty_set|sk0_1(singleton(X0),empty_set,sk0_19)=X0)),
% 0.12/0.34 inference(resolution,[status(thm)],[f1162,f175])).
% 0.12/0.34 fof(f1282,plain,(
% 0.12/0.34 spl0_85 <=> singleton(X0)=relation_inverse_image(sk0_19,empty_set)|~in(X0,singleton(X0))|~in(ordered_pair(sk0_1(singleton(X0),empty_set,sk0_19),X1),sk0_19)|~in(X1,empty_set)|singleton(X0)=empty_set),
% 0.12/0.34 introduced(split_symbol_definition)).
% 0.12/0.34 fof(f1285,plain,(
% 0.12/0.34 ![X0,X1]: (~relation(sk0_19)|singleton(X0)=relation_inverse_image(sk0_19,empty_set)|~in(X0,singleton(X0))|~in(ordered_pair(sk0_1(singleton(X0),empty_set,sk0_19),X1),sk0_19)|~in(X1,empty_set)|singleton(X0)=empty_set)),
% 0.12/0.34 inference(paramodulation,[status(thm)],[f1249,f60])).
% 0.12/0.34 fof(f1286,plain,(
% 0.12/0.34 ~spl0_5|spl0_85),
% 0.12/0.34 inference(split_clause,[status(thm)],[f1285,f231,f1282])).
% 0.12/0.34 fof(f1374,plain,(
% 0.12/0.34 empty_set=relation_inverse_image(sk0_19,singleton(sk0_20))|~spl0_8|spl0_0),
% 0.12/0.34 inference(resolution,[status(thm)],[f1180,f165])).
% 0.12/0.34 fof(f1375,plain,(
% 0.12/0.34 spl0_1|~spl0_8|spl0_0),
% 0.12/0.34 inference(split_clause,[status(thm)],[f1374,f166,f249,f163])).
% 0.12/0.34 fof(f1391,plain,(
% 0.12/0.34 empty_set=relation_inverse_image(sk0_19,singleton(singleton(relation_rng(sk0_19))))|~spl0_8),
% 0.12/0.34 inference(resolution,[status(thm)],[f1180,f180])).
% 0.12/0.34 fof(f1392,plain,(
% 0.12/0.34 spl0_89 <=> empty_set=relation_inverse_image(sk0_19,singleton(X0))|in(ordered_pair(sk0_5(X0,relation_rng(sk0_19),sk0_19),X0),sk0_19)),
% 0.12/0.34 introduced(split_symbol_definition)).
% 0.12/0.34 fof(f1393,plain,(
% 0.12/0.34 ![X0]: (empty_set=relation_inverse_image(sk0_19,singleton(X0))|in(ordered_pair(sk0_5(X0,relation_rng(sk0_19),sk0_19),X0),sk0_19)|~spl0_89)),
% 0.12/0.34 inference(component_clause,[status(thm)],[f1392])).
% 0.12/0.34 fof(f1395,plain,(
% 0.12/0.34 ![X0]: (empty_set=relation_inverse_image(sk0_19,singleton(X0))|~relation(sk0_19)|in(ordered_pair(sk0_5(X0,relation_rng(sk0_19),sk0_19),X0),sk0_19)|~spl0_8)),
% 0.12/0.34 inference(resolution,[status(thm)],[f1180,f178])).
% 0.12/0.34 fof(f1396,plain,(
% 0.12/0.34 spl0_89|~spl0_5|~spl0_8),
% 0.12/0.34 inference(split_clause,[status(thm)],[f1395,f1392,f231,f249])).
% 0.12/0.34 fof(f1398,plain,(
% 0.12/0.34 ![X0]: (empty_set=relation_inverse_image(sk0_19,singleton(X0))|~empty(relation_rng(sk0_19))|~spl0_8)),
% 0.12/0.34 inference(resolution,[status(thm)],[f1180,f159])).
% 0.12/0.34 fof(f1399,plain,(
% 0.12/0.34 spl0_83|~spl0_13|~spl0_8),
% 0.12/0.34 inference(split_clause,[status(thm)],[f1398,f1222,f286,f249])).
% 0.12/0.34 fof(f1417,plain,(
% 0.12/0.34 spl0_92 <=> empty_set=relation_inverse_image(sk0_19,singleton(relation_rng(sk0_19)))),
% 0.12/0.34 introduced(split_symbol_definition)).
% 0.12/0.34 fof(f1418,plain,(
% 0.12/0.34 empty_set=relation_inverse_image(sk0_19,singleton(relation_rng(sk0_19)))|~spl0_92),
% 0.12/0.34 inference(component_clause,[status(thm)],[f1417])).
% 0.12/0.34 fof(f1420,plain,(
% 0.12/0.34 empty_set=relation_inverse_image(sk0_19,singleton(relation_rng(sk0_19)))|empty_set=relation_inverse_image(sk0_19,singleton(relation_rng(sk0_19)))|~spl0_8),
% 0.12/0.34 inference(resolution,[status(thm)],[f1184,f1180])).
% 0.12/0.34 fof(f1421,plain,(
% 0.12/0.34 spl0_92|~spl0_8),
% 0.12/0.34 inference(split_clause,[status(thm)],[f1420,f1417,f249])).
% 0.12/0.34 fof(f1423,plain,(
% 0.12/0.34 spl0_93 <=> in(sk0_5(sk0_20,relation_rng(sk0_19),sk0_19),relation_inverse_image(sk0_19,X0))|~in(sk0_20,X0)),
% 0.12/0.34 introduced(split_symbol_definition)).
% 0.12/0.34 fof(f1424,plain,(
% 0.12/0.34 ![X0]: (in(sk0_5(sk0_20,relation_rng(sk0_19),sk0_19),relation_inverse_image(sk0_19,X0))|~in(sk0_20,X0)|~spl0_93)),
% 0.12/0.34 inference(component_clause,[status(thm)],[f1423])).
% 0.12/0.34 fof(f1426,plain,(
% 0.12/0.34 ![X0]: (~relation(sk0_19)|in(sk0_5(sk0_20,relation_rng(sk0_19),sk0_19),relation_inverse_image(sk0_19,X0))|~in(sk0_20,X0)|~spl0_6)),
% 0.12/0.34 inference(resolution,[status(thm)],[f235,f174])).
% 0.12/0.34 fof(f1427,plain,(
% 0.12/0.34 ~spl0_5|spl0_93|~spl0_6),
% 0.12/0.34 inference(split_clause,[status(thm)],[f1426,f231,f1423,f234])).
% 0.12/0.34 fof(f1432,plain,(
% 0.12/0.34 spl0_94 <=> ~in(X0,empty_set)|in(sk0_0(X0,relation_inverse_image(sk0_19,singleton(relation_rng(sk0_19))),singleton(relation_rng(sk0_19)),sk0_19),singleton(relation_rng(sk0_19)))),
% 0.12/0.34 introduced(split_symbol_definition)).
% 0.12/0.34 fof(f1435,plain,(
% 0.12/0.34 ![X0]: (~relation(sk0_19)|~in(X0,empty_set)|in(sk0_0(X0,relation_inverse_image(sk0_19,singleton(relation_rng(sk0_19))),singleton(relation_rng(sk0_19)),sk0_19),singleton(relation_rng(sk0_19)))|~spl0_92)),
% 0.12/0.34 inference(paramodulation,[status(thm)],[f1418,f173])).
% 0.12/0.34 fof(f1436,plain,(
% 0.12/0.34 ~spl0_5|spl0_94|~spl0_92),
% 0.12/0.34 inference(split_clause,[status(thm)],[f1435,f231,f1432,f1417])).
% 0.12/0.34 fof(f1437,plain,(
% 0.12/0.34 spl0_95 <=> ~in(X0,empty_set)|in(ordered_pair(X0,sk0_0(X0,relation_inverse_image(sk0_19,singleton(relation_rng(sk0_19))),singleton(relation_rng(sk0_19)),sk0_19)),sk0_19)),
% 0.12/0.34 introduced(split_symbol_definition)).
% 0.12/0.34 fof(f1440,plain,(
% 0.12/0.34 ![X0]: (~relation(sk0_19)|~in(X0,empty_set)|in(ordered_pair(X0,sk0_0(X0,relation_inverse_image(sk0_19,singleton(relation_rng(sk0_19))),singleton(relation_rng(sk0_19)),sk0_19)),sk0_19)|~spl0_92)),
% 0.12/0.34 inference(paramodulation,[status(thm)],[f1418,f172])).
% 0.12/0.34 fof(f1441,plain,(
% 0.12/0.34 ~spl0_5|spl0_95|~spl0_92),
% 0.12/0.34 inference(split_clause,[status(thm)],[f1440,f231,f1437,f1417])).
% 0.12/0.34 fof(f1444,plain,(
% 0.12/0.34 spl0_96 <=> empty_set=relation_inverse_image(sk0_19,singleton(X0))|in(sk0_5(X0,relation_rng(sk0_19),sk0_19),relation_inverse_image(sk0_19,X1))|~in(X0,X1)),
% 0.12/0.34 introduced(split_symbol_definition)).
% 0.12/0.34 fof(f1447,plain,(
% 0.12/0.34 ![X0,X1]: (empty_set=relation_inverse_image(sk0_19,singleton(X0))|~relation(sk0_19)|in(sk0_5(X0,relation_rng(sk0_19),sk0_19),relation_inverse_image(sk0_19,X1))|~in(X0,X1)|~spl0_89)),
% 0.12/0.34 inference(resolution,[status(thm)],[f1393,f174])).
% 0.12/0.34 fof(f1448,plain,(
% 0.12/0.34 spl0_96|~spl0_5|~spl0_89),
% 0.12/0.34 inference(split_clause,[status(thm)],[f1447,f1444,f231,f1392])).
% 0.12/0.34 fof(f1455,plain,(
% 0.12/0.34 spl0_97 <=> ~in(X0,empty_set)|in(sk0_0(X0,relation_inverse_image(sk0_19,singleton(singleton(relation_rng(sk0_19)))),singleton(singleton(relation_rng(sk0_19))),sk0_19),singleton(singleton(relation_rng(sk0_19))))),
% 0.12/0.34 introduced(split_symbol_definition)).
% 0.12/0.34 fof(f1458,plain,(
% 0.12/0.34 ![X0]: (~relation(sk0_19)|~in(X0,empty_set)|in(sk0_0(X0,relation_inverse_image(sk0_19,singleton(singleton(relation_rng(sk0_19)))),singleton(singleton(relation_rng(sk0_19))),sk0_19),singleton(singleton(relation_rng(sk0_19))))|~spl0_8)),
% 0.12/0.34 inference(paramodulation,[status(thm)],[f1391,f173])).
% 0.12/0.34 fof(f1459,plain,(
% 0.12/0.34 ~spl0_5|spl0_97|~spl0_8),
% 0.12/0.34 inference(split_clause,[status(thm)],[f1458,f231,f1455,f249])).
% 0.12/0.34 fof(f1460,plain,(
% 0.12/0.34 spl0_98 <=> ~in(X0,empty_set)|in(ordered_pair(X0,sk0_0(X0,relation_inverse_image(sk0_19,singleton(singleton(relation_rng(sk0_19)))),singleton(singleton(relation_rng(sk0_19))),sk0_19)),sk0_19)),
% 0.12/0.34 introduced(split_symbol_definition)).
% 0.12/0.34 fof(f1463,plain,(
% 0.12/0.34 ![X0]: (~relation(sk0_19)|~in(X0,empty_set)|in(ordered_pair(X0,sk0_0(X0,relation_inverse_image(sk0_19,singleton(singleton(relation_rng(sk0_19)))),singleton(singleton(relation_rng(sk0_19))),sk0_19)),sk0_19)|~spl0_8)),
% 0.12/0.34 inference(paramodulation,[status(thm)],[f1391,f172])).
% 0.12/0.34 fof(f1464,plain,(
% 0.12/0.34 ~spl0_5|spl0_98|~spl0_8),
% 0.12/0.34 inference(split_clause,[status(thm)],[f1463,f231,f1460,f249])).
% 0.12/0.34 fof(f1467,plain,(
% 0.12/0.34 spl0_99 <=> relation_rng(sk0_19)=relation_inverse_image(empty_set,X0)|~in(ordered_pair(sk0_1(relation_rng(sk0_19),X0,empty_set),X1),empty_set)|~in(X1,X0)),
% 0.12/0.34 introduced(split_symbol_definition)).
% 0.12/0.34 fof(f1470,plain,(
% 0.12/0.34 ![X0,X1]: (~relation(empty_set)|relation_rng(sk0_19)=relation_inverse_image(empty_set,X0)|~in(ordered_pair(sk0_1(relation_rng(sk0_19),X0,empty_set),X1),empty_set)|~in(X1,X0)|~spl0_77)),
% 0.12/0.34 inference(resolution,[status(thm)],[f1103,f60])).
% 0.12/0.34 fof(f1471,plain,(
% 0.12/0.34 ~spl0_3|spl0_99|~spl0_77),
% 0.12/0.34 inference(split_clause,[status(thm)],[f1470,f195,f1467,f1102])).
% 0.12/0.34 fof(f1488,plain,(
% 0.12/0.34 in(sk0_5(sk0_20,relation_rng(sk0_19),sk0_19),relation_inverse_image(sk0_19,singleton(sk0_20)))|~spl0_93),
% 0.12/0.34 inference(resolution,[status(thm)],[f1424,f176])).
% 0.12/0.34 fof(f1489,plain,(
% 0.12/0.34 in(sk0_5(sk0_20,relation_rng(sk0_19),sk0_19),empty_set)|~spl0_1|~spl0_93),
% 0.12/0.34 inference(forward_demodulation,[status(thm)],[f167,f1488])).
% 0.12/0.34 fof(f1490,plain,(
% 0.12/0.34 $false|~spl0_1|~spl0_93),
% 0.12/0.34 inference(forward_subsumption_resolution,[status(thm)],[f1489,f177])).
% 0.12/0.34 fof(f1491,plain,(
% 0.12/0.34 ~spl0_1|~spl0_93),
% 0.12/0.34 inference(contradiction_clause,[status(thm)],[f1490])).
% 0.12/0.34 fof(f1492,plain,(
% 0.12/0.34 $false),
% 0.12/0.34 inference(sat_refutation,[status(thm)],[f169,f170,f207,f209,f238,f243,f248,f253,f269,f284,f290,f300,f306,f315,f321,f327,f341,f346,f365,f371,f377,f382,f387,f393,f407,f415,f420,f425,f428,f436,f441,f444,f473,f484,f486,f493,f519,f524,f531,f551,f590,f595,f597,f663,f701,f831,f1021,f1036,f1048,f1101,f1106,f1132,f1167,f1172,f1215,f1220,f1245,f1286,f1375,f1396,f1399,f1421,f1427,f1436,f1441,f1448,f1459,f1464,f1471,f1491])).
% 0.12/0.34 % SZS output end CNFRefutation for theBenchmark.p
% 0.12/0.36 % Elapsed time: 0.093366 seconds
% 0.12/0.36 % CPU time: 0.500597 seconds
% 0.12/0.36 % Memory used: 38.324 MB
%------------------------------------------------------------------------------