TSTP Solution File: SEU028+1 by Drodi---3.5.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SEU028+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n017.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 12:35:43 EDT 2023
% Result : Theorem 18.34s 2.84s
% Output : CNFRefutation 18.86s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.11 % Problem : SEU028+1 : TPTP v8.1.2. Released v3.2.0.
% 0.05/0.12 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.32 % Computer : n017.cluster.edu
% 0.09/0.32 % Model : x86_64 x86_64
% 0.09/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.32 % Memory : 8042.1875MB
% 0.09/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.32 % CPULimit : 300
% 0.09/0.32 % WCLimit : 300
% 0.09/0.32 % DateTime : Tue May 30 08:44:10 EDT 2023
% 0.09/0.32 % CPUTime :
% 0.09/0.33 % Drodi V3.5.1
% 18.34/2.84 % Refutation found
% 18.34/2.84 % SZS status Theorem for theBenchmark: Theorem is valid
% 18.34/2.84 % SZS output start CNFRefutation for theBenchmark
% 18.34/2.84 fof(f1,axiom,(
% 18.34/2.84 (! [A,B] :( in(A,B)=> ~ in(B,A) ) )),
% 18.34/2.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 18.34/2.84 fof(f2,axiom,(
% 18.34/2.84 (! [A] :( empty(A)=> function(A) ) )),
% 18.34/2.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 18.34/2.84 fof(f3,axiom,(
% 18.34/2.84 (! [A] :( empty(A)=> relation(A) ) )),
% 18.34/2.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 18.34/2.84 fof(f4,axiom,(
% 18.34/2.84 (! [A] :( ( relation(A)& empty(A)& function(A) )=> ( relation(A)& function(A)& one_to_one(A) ) ) )),
% 18.34/2.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 18.34/2.84 fof(f5,axiom,(
% 18.34/2.84 (! [A] :( ( relation(A)& function(A) )=> ( relation(function_inverse(A))& function(function_inverse(A)) ) ) )),
% 18.34/2.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 18.34/2.84 fof(f6,axiom,(
% 18.34/2.84 (! [A,B] :( ( relation(A)& relation(B) )=> relation(relation_composition(A,B)) ) )),
% 18.34/2.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 18.34/2.84 fof(f7,axiom,(
% 18.34/2.84 (! [A] : relation(identity_relation(A)) )),
% 18.34/2.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 18.34/2.84 fof(f8,axiom,(
% 18.34/2.84 (! [A] :(? [B] : element(B,A) ))),
% 18.34/2.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 18.34/2.84 fof(f9,axiom,(
% 18.34/2.84 (! [A,B] :( ( empty(A)& relation(B) )=> ( empty(relation_composition(B,A))& relation(relation_composition(B,A)) ) ) )),
% 18.34/2.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 18.34/2.84 fof(f10,axiom,(
% 18.34/2.84 ( empty(empty_set)& relation(empty_set)& relation_empty_yielding(empty_set) ) ),
% 18.34/2.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 18.34/2.84 fof(f11,axiom,(
% 18.34/2.84 (! [A,B] :( ( relation(A)& function(A)& relation(B)& function(B) )=> ( relation(relation_composition(A,B))& function(relation_composition(A,B)) ) ) )),
% 18.34/2.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 18.34/2.84 fof(f12,axiom,(
% 18.34/2.84 (! [A] : ~ empty(powerset(A)) )),
% 18.34/2.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 18.34/2.84 fof(f14,axiom,(
% 18.34/2.84 (! [A] :( relation(identity_relation(A))& function(identity_relation(A)) ) )),
% 18.34/2.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 18.34/2.84 fof(f16,axiom,(
% 18.34/2.84 (! [A] :( ( ~ empty(A)& relation(A) )=> ~ empty(relation_dom(A)) ) )),
% 18.34/2.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 18.34/2.84 fof(f17,axiom,(
% 18.34/2.84 (! [A] :( ( ~ empty(A)& relation(A) )=> ~ empty(relation_rng(A)) ) )),
% 18.34/2.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 18.34/2.84 fof(f18,axiom,(
% 18.34/2.84 (! [A] :( empty(A)=> ( empty(relation_dom(A))& relation(relation_dom(A)) ) ) )),
% 18.34/2.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 18.34/2.84 fof(f19,axiom,(
% 18.34/2.84 (! [A] :( empty(A)=> ( empty(relation_rng(A))& relation(relation_rng(A)) ) ) )),
% 18.34/2.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 18.34/2.84 fof(f20,axiom,(
% 18.34/2.84 (! [A,B] :( ( empty(A)& relation(B) )=> ( empty(relation_composition(A,B))& relation(relation_composition(A,B)) ) ) )),
% 18.34/2.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 18.34/2.84 fof(f21,axiom,(
% 18.34/2.84 (? [A] :( relation(A)& function(A) ) )),
% 18.34/2.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 18.34/2.84 fof(f22,axiom,(
% 18.34/2.84 (? [A] :( empty(A)& relation(A) ) )),
% 18.34/2.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 18.34/2.84 fof(f23,axiom,(
% 18.34/2.84 (! [A] :( ~ empty(A)=> (? [B] :( element(B,powerset(A))& ~ empty(B) ) )) )),
% 18.34/2.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 18.34/2.84 fof(f24,axiom,(
% 18.34/2.84 (? [A] : empty(A) )),
% 18.34/2.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 18.34/2.84 fof(f25,axiom,(
% 18.34/2.84 (? [A] :( relation(A)& empty(A)& function(A) ) )),
% 18.34/2.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 18.34/2.84 fof(f26,axiom,(
% 18.34/2.84 (? [A] :( ~ empty(A)& relation(A) ) )),
% 18.34/2.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 18.34/2.84 fof(f27,axiom,(
% 18.34/2.84 (! [A] :(? [B] :( element(B,powerset(A))& empty(B) ) ))),
% 18.34/2.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 18.34/2.84 fof(f29,axiom,(
% 18.34/2.84 (? [A] :( relation(A)& function(A)& one_to_one(A) ) )),
% 18.34/2.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 18.34/2.84 fof(f30,axiom,(
% 18.34/2.84 (? [A] :( relation(A)& relation_empty_yielding(A) ) )),
% 18.34/2.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 18.34/2.84 fof(f32,axiom,(
% 18.34/2.84 (! [A,B] :( in(A,B)=> element(A,B) ) )),
% 18.34/2.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 18.34/2.84 fof(f33,axiom,(
% 18.34/2.84 (! [A,B] :( element(A,B)=> ( empty(B)| in(A,B) ) ) )),
% 18.34/2.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 18.34/2.84 fof(f34,axiom,(
% 18.34/2.84 (! [A,B] :( ( relation(B)& function(B) )=> ( B = identity_relation(A)<=> ( relation_dom(B) = A& (! [C] :( in(C,A)=> apply(B,C) = C ) )) ) ) )),
% 18.34/2.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 18.34/2.84 fof(f35,axiom,(
% 18.34/2.84 (! [A,B] :( element(A,powerset(B))<=> subset(A,B) ) )),
% 18.34/2.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 18.34/2.84 fof(f36,axiom,(
% 18.34/2.84 (! [A,B,C] :( ( in(A,B)& element(B,powerset(C)) )=> element(A,C) ) )),
% 18.34/2.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 18.34/2.84 fof(f37,axiom,(
% 18.34/2.84 (! [A,B] :( ( relation(B)& function(B) )=> ( ( one_to_one(B)& in(A,relation_dom(B)) )=> ( A = apply(function_inverse(B),apply(B,A))& A = apply(relation_composition(B,function_inverse(B)),A) ) ) ) )),
% 18.34/2.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 18.34/2.84 fof(f38,axiom,(
% 18.34/2.84 (! [A,B] :( ( relation(B)& function(B) )=> ( ( one_to_one(B)& in(A,relation_rng(B)) )=> ( A = apply(B,apply(function_inverse(B),A))& A = apply(relation_composition(function_inverse(B),B),A) ) ) ) )),
% 18.34/2.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 18.34/2.84 fof(f39,axiom,(
% 18.34/2.84 (! [A] :( ( relation(A)& function(A) )=> ( one_to_one(A)=> ( relation_dom(relation_composition(A,function_inverse(A))) = relation_dom(A)& relation_rng(relation_composition(A,function_inverse(A))) = relation_dom(A) ) ) ) )),
% 18.34/2.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 18.34/2.84 fof(f40,axiom,(
% 18.34/2.84 (! [A] :( ( relation(A)& function(A) )=> ( one_to_one(A)=> ( relation_dom(relation_composition(function_inverse(A),A)) = relation_rng(A)& relation_rng(relation_composition(function_inverse(A),A)) = relation_rng(A) ) ) ) )),
% 18.34/2.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 18.34/2.84 fof(f41,axiom,(
% 18.34/2.84 (! [A,B,C] :~ ( in(A,B)& element(B,powerset(C))& empty(C) ) )),
% 18.34/2.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 18.34/2.84 fof(f42,conjecture,(
% 18.34/2.84 (! [A] :( ( relation(A)& function(A) )=> ( one_to_one(A)=> ( relation_composition(A,function_inverse(A)) = identity_relation(relation_dom(A))& relation_composition(function_inverse(A),A) = identity_relation(relation_rng(A)) ) ) ) )),
% 18.34/2.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 18.34/2.84 fof(f43,negated_conjecture,(
% 18.34/2.84 ~((! [A] :( ( relation(A)& function(A) )=> ( one_to_one(A)=> ( relation_composition(A,function_inverse(A)) = identity_relation(relation_dom(A))& relation_composition(function_inverse(A),A) = identity_relation(relation_rng(A)) ) ) ) ))),
% 18.34/2.84 inference(negated_conjecture,[status(cth)],[f42])).
% 18.34/2.84 fof(f44,axiom,(
% 18.34/2.84 (! [A] :( empty(A)=> A = empty_set ) )),
% 18.34/2.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 18.34/2.84 fof(f45,axiom,(
% 18.34/2.84 (! [A,B] :~ ( in(A,B)& empty(B) ) )),
% 18.34/2.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 18.34/2.84 fof(f47,plain,(
% 18.34/2.84 ![A,B]: (~in(A,B)|~in(B,A))),
% 18.34/2.84 inference(pre_NNF_transformation,[status(esa)],[f1])).
% 18.34/2.84 fof(f48,plain,(
% 18.34/2.84 ![X0,X1]: (~in(X0,X1)|~in(X1,X0))),
% 18.34/2.84 inference(cnf_transformation,[status(esa)],[f47])).
% 18.34/2.84 fof(f49,plain,(
% 18.34/2.84 ![A]: (~empty(A)|function(A))),
% 18.34/2.84 inference(pre_NNF_transformation,[status(esa)],[f2])).
% 18.34/2.84 fof(f50,plain,(
% 18.34/2.84 ![X0]: (~empty(X0)|function(X0))),
% 18.34/2.84 inference(cnf_transformation,[status(esa)],[f49])).
% 18.34/2.84 fof(f51,plain,(
% 18.34/2.84 ![A]: (~empty(A)|relation(A))),
% 18.34/2.84 inference(pre_NNF_transformation,[status(esa)],[f3])).
% 18.34/2.84 fof(f52,plain,(
% 18.34/2.84 ![X0]: (~empty(X0)|relation(X0))),
% 18.34/2.84 inference(cnf_transformation,[status(esa)],[f51])).
% 18.34/2.84 fof(f53,plain,(
% 18.34/2.84 ![A]: (((~relation(A)|~empty(A))|~function(A))|((relation(A)&function(A))&one_to_one(A)))),
% 18.34/2.84 inference(pre_NNF_transformation,[status(esa)],[f4])).
% 18.34/2.84 fof(f56,plain,(
% 18.34/2.84 ![X0]: (~relation(X0)|~empty(X0)|~function(X0)|one_to_one(X0))),
% 18.34/2.84 inference(cnf_transformation,[status(esa)],[f53])).
% 18.34/2.84 fof(f57,plain,(
% 18.34/2.84 ![A]: ((~relation(A)|~function(A))|(relation(function_inverse(A))&function(function_inverse(A))))),
% 18.34/2.84 inference(pre_NNF_transformation,[status(esa)],[f5])).
% 18.34/2.84 fof(f58,plain,(
% 18.34/2.84 ![X0]: (~relation(X0)|~function(X0)|relation(function_inverse(X0)))),
% 18.34/2.84 inference(cnf_transformation,[status(esa)],[f57])).
% 18.34/2.84 fof(f59,plain,(
% 18.34/2.84 ![X0]: (~relation(X0)|~function(X0)|function(function_inverse(X0)))),
% 18.34/2.84 inference(cnf_transformation,[status(esa)],[f57])).
% 18.34/2.84 fof(f60,plain,(
% 18.34/2.84 ![A,B]: ((~relation(A)|~relation(B))|relation(relation_composition(A,B)))),
% 18.34/2.84 inference(pre_NNF_transformation,[status(esa)],[f6])).
% 18.34/2.84 fof(f61,plain,(
% 18.34/2.84 ![X0,X1]: (~relation(X0)|~relation(X1)|relation(relation_composition(X0,X1)))),
% 18.34/2.84 inference(cnf_transformation,[status(esa)],[f60])).
% 18.34/2.84 fof(f62,plain,(
% 18.34/2.84 ![X0]: (relation(identity_relation(X0)))),
% 18.34/2.84 inference(cnf_transformation,[status(esa)],[f7])).
% 18.34/2.84 fof(f63,plain,(
% 18.34/2.84 ![A]: element(sk0_0(A),A)),
% 18.34/2.84 inference(skolemization,[status(esa)],[f8])).
% 18.34/2.84 fof(f64,plain,(
% 18.34/2.84 ![X0]: (element(sk0_0(X0),X0))),
% 18.34/2.84 inference(cnf_transformation,[status(esa)],[f63])).
% 18.34/2.84 fof(f65,plain,(
% 18.34/2.84 ![A,B]: ((~empty(A)|~relation(B))|(empty(relation_composition(B,A))&relation(relation_composition(B,A))))),
% 18.34/2.84 inference(pre_NNF_transformation,[status(esa)],[f9])).
% 18.34/2.84 fof(f66,plain,(
% 18.34/2.84 ![X0,X1]: (~empty(X0)|~relation(X1)|empty(relation_composition(X1,X0)))),
% 18.34/2.84 inference(cnf_transformation,[status(esa)],[f65])).
% 18.34/2.84 fof(f68,plain,(
% 18.34/2.84 empty(empty_set)),
% 18.34/2.84 inference(cnf_transformation,[status(esa)],[f10])).
% 18.34/2.84 fof(f69,plain,(
% 18.34/2.84 relation(empty_set)),
% 18.34/2.84 inference(cnf_transformation,[status(esa)],[f10])).
% 18.34/2.84 fof(f71,plain,(
% 18.34/2.84 ![A,B]: ((((~relation(A)|~function(A))|~relation(B))|~function(B))|(relation(relation_composition(A,B))&function(relation_composition(A,B))))),
% 18.34/2.84 inference(pre_NNF_transformation,[status(esa)],[f11])).
% 18.34/2.84 fof(f73,plain,(
% 18.34/2.84 ![X0,X1]: (~relation(X0)|~function(X0)|~relation(X1)|~function(X1)|function(relation_composition(X0,X1)))),
% 18.34/2.84 inference(cnf_transformation,[status(esa)],[f71])).
% 18.34/2.84 fof(f74,plain,(
% 18.34/2.84 ![X0]: (~empty(powerset(X0)))),
% 18.34/2.84 inference(cnf_transformation,[status(esa)],[f12])).
% 18.34/2.84 fof(f76,plain,(
% 18.34/2.84 (![A]: relation(identity_relation(A)))&(![A]: function(identity_relation(A)))),
% 18.34/2.84 inference(miniscoping,[status(esa)],[f14])).
% 18.34/2.84 fof(f78,plain,(
% 18.34/2.84 ![X0]: (function(identity_relation(X0)))),
% 18.34/2.84 inference(cnf_transformation,[status(esa)],[f76])).
% 18.34/2.84 fof(f81,plain,(
% 18.34/2.84 ![A]: ((empty(A)|~relation(A))|~empty(relation_dom(A)))),
% 18.34/2.84 inference(pre_NNF_transformation,[status(esa)],[f16])).
% 18.34/2.84 fof(f82,plain,(
% 18.34/2.84 ![X0]: (empty(X0)|~relation(X0)|~empty(relation_dom(X0)))),
% 18.34/2.84 inference(cnf_transformation,[status(esa)],[f81])).
% 18.34/2.84 fof(f83,plain,(
% 18.34/2.84 ![A]: ((empty(A)|~relation(A))|~empty(relation_rng(A)))),
% 18.34/2.84 inference(pre_NNF_transformation,[status(esa)],[f17])).
% 18.34/2.84 fof(f84,plain,(
% 18.34/2.84 ![X0]: (empty(X0)|~relation(X0)|~empty(relation_rng(X0)))),
% 18.34/2.84 inference(cnf_transformation,[status(esa)],[f83])).
% 18.34/2.84 fof(f85,plain,(
% 18.34/2.84 ![A]: (~empty(A)|(empty(relation_dom(A))&relation(relation_dom(A))))),
% 18.34/2.84 inference(pre_NNF_transformation,[status(esa)],[f18])).
% 18.34/2.84 fof(f86,plain,(
% 18.34/2.84 ![X0]: (~empty(X0)|empty(relation_dom(X0)))),
% 18.34/2.84 inference(cnf_transformation,[status(esa)],[f85])).
% 18.34/2.84 fof(f87,plain,(
% 18.34/2.84 ![X0]: (~empty(X0)|relation(relation_dom(X0)))),
% 18.34/2.84 inference(cnf_transformation,[status(esa)],[f85])).
% 18.34/2.84 fof(f88,plain,(
% 18.34/2.84 ![A]: (~empty(A)|(empty(relation_rng(A))&relation(relation_rng(A))))),
% 18.34/2.84 inference(pre_NNF_transformation,[status(esa)],[f19])).
% 18.34/2.84 fof(f89,plain,(
% 18.34/2.84 ![X0]: (~empty(X0)|empty(relation_rng(X0)))),
% 18.34/2.84 inference(cnf_transformation,[status(esa)],[f88])).
% 18.34/2.84 fof(f91,plain,(
% 18.34/2.84 ![A,B]: ((~empty(A)|~relation(B))|(empty(relation_composition(A,B))&relation(relation_composition(A,B))))),
% 18.34/2.84 inference(pre_NNF_transformation,[status(esa)],[f20])).
% 18.34/2.84 fof(f92,plain,(
% 18.34/2.84 ![X0,X1]: (~empty(X0)|~relation(X1)|empty(relation_composition(X0,X1)))),
% 18.34/2.84 inference(cnf_transformation,[status(esa)],[f91])).
% 18.34/2.84 fof(f93,plain,(
% 18.34/2.84 ![X0,X1]: (~empty(X0)|~relation(X1)|relation(relation_composition(X0,X1)))),
% 18.34/2.84 inference(cnf_transformation,[status(esa)],[f91])).
% 18.34/2.84 fof(f94,plain,(
% 18.34/2.84 (relation(sk0_1)&function(sk0_1))),
% 18.34/2.84 inference(skolemization,[status(esa)],[f21])).
% 18.34/2.84 fof(f95,plain,(
% 18.34/2.84 relation(sk0_1)),
% 18.34/2.84 inference(cnf_transformation,[status(esa)],[f94])).
% 18.34/2.84 fof(f96,plain,(
% 18.34/2.84 function(sk0_1)),
% 18.34/2.84 inference(cnf_transformation,[status(esa)],[f94])).
% 18.34/2.84 fof(f97,plain,(
% 18.34/2.84 (empty(sk0_2)&relation(sk0_2))),
% 18.34/2.84 inference(skolemization,[status(esa)],[f22])).
% 18.34/2.84 fof(f98,plain,(
% 18.34/2.84 empty(sk0_2)),
% 18.34/2.84 inference(cnf_transformation,[status(esa)],[f97])).
% 18.34/2.84 fof(f100,plain,(
% 18.34/2.84 ![A]: (empty(A)|(?[B]: (element(B,powerset(A))&~empty(B))))),
% 18.34/2.84 inference(pre_NNF_transformation,[status(esa)],[f23])).
% 18.34/2.84 fof(f101,plain,(
% 18.34/2.84 ![A]: (empty(A)|(element(sk0_3(A),powerset(A))&~empty(sk0_3(A))))),
% 18.34/2.84 inference(skolemization,[status(esa)],[f100])).
% 18.34/2.84 fof(f102,plain,(
% 18.34/2.84 ![X0]: (empty(X0)|element(sk0_3(X0),powerset(X0)))),
% 18.34/2.84 inference(cnf_transformation,[status(esa)],[f101])).
% 18.34/2.84 fof(f103,plain,(
% 18.34/2.84 ![X0]: (empty(X0)|~empty(sk0_3(X0)))),
% 18.34/2.84 inference(cnf_transformation,[status(esa)],[f101])).
% 18.34/2.84 fof(f104,plain,(
% 18.34/2.84 empty(sk0_4)),
% 18.34/2.84 inference(skolemization,[status(esa)],[f24])).
% 18.34/2.84 fof(f105,plain,(
% 18.34/2.84 empty(sk0_4)),
% 18.34/2.84 inference(cnf_transformation,[status(esa)],[f104])).
% 18.34/2.84 fof(f106,plain,(
% 18.34/2.84 ((relation(sk0_5)&empty(sk0_5))&function(sk0_5))),
% 18.34/2.84 inference(skolemization,[status(esa)],[f25])).
% 18.34/2.84 fof(f107,plain,(
% 18.34/2.84 relation(sk0_5)),
% 18.34/2.84 inference(cnf_transformation,[status(esa)],[f106])).
% 18.34/2.84 fof(f108,plain,(
% 18.34/2.84 empty(sk0_5)),
% 18.34/2.84 inference(cnf_transformation,[status(esa)],[f106])).
% 18.34/2.84 fof(f109,plain,(
% 18.34/2.84 function(sk0_5)),
% 18.34/2.84 inference(cnf_transformation,[status(esa)],[f106])).
% 18.34/2.84 fof(f110,plain,(
% 18.34/2.84 (~empty(sk0_6)&relation(sk0_6))),
% 18.34/2.84 inference(skolemization,[status(esa)],[f26])).
% 18.34/2.84 fof(f112,plain,(
% 18.34/2.84 relation(sk0_6)),
% 18.34/2.84 inference(cnf_transformation,[status(esa)],[f110])).
% 18.34/2.84 fof(f113,plain,(
% 18.34/2.84 ![A]: (element(sk0_7(A),powerset(A))&empty(sk0_7(A)))),
% 18.34/2.84 inference(skolemization,[status(esa)],[f27])).
% 18.34/2.84 fof(f114,plain,(
% 18.34/2.84 ![X0]: (element(sk0_7(X0),powerset(X0)))),
% 18.34/2.84 inference(cnf_transformation,[status(esa)],[f113])).
% 18.34/2.84 fof(f115,plain,(
% 18.34/2.84 ![X0]: (empty(sk0_7(X0)))),
% 18.34/2.84 inference(cnf_transformation,[status(esa)],[f113])).
% 18.34/2.84 fof(f118,plain,(
% 18.34/2.84 ((relation(sk0_9)&function(sk0_9))&one_to_one(sk0_9))),
% 18.34/2.84 inference(skolemization,[status(esa)],[f29])).
% 18.34/2.84 fof(f119,plain,(
% 18.34/2.84 relation(sk0_9)),
% 18.34/2.84 inference(cnf_transformation,[status(esa)],[f118])).
% 18.34/2.84 fof(f120,plain,(
% 18.34/2.84 function(sk0_9)),
% 18.34/2.84 inference(cnf_transformation,[status(esa)],[f118])).
% 18.34/2.84 fof(f121,plain,(
% 18.34/2.84 one_to_one(sk0_9)),
% 18.34/2.84 inference(cnf_transformation,[status(esa)],[f118])).
% 18.34/2.84 fof(f122,plain,(
% 18.34/2.84 (relation(sk0_10)&relation_empty_yielding(sk0_10))),
% 18.34/2.84 inference(skolemization,[status(esa)],[f30])).
% 18.34/2.84 fof(f123,plain,(
% 18.34/2.84 relation(sk0_10)),
% 18.34/2.84 inference(cnf_transformation,[status(esa)],[f122])).
% 18.34/2.84 fof(f127,plain,(
% 18.34/2.84 ![A,B]: (~in(A,B)|element(A,B))),
% 18.34/2.84 inference(pre_NNF_transformation,[status(esa)],[f32])).
% 18.34/2.84 fof(f128,plain,(
% 18.34/2.84 ![X0,X1]: (~in(X0,X1)|element(X0,X1))),
% 18.34/2.84 inference(cnf_transformation,[status(esa)],[f127])).
% 18.34/2.84 fof(f129,plain,(
% 18.34/2.84 ![A,B]: (~element(A,B)|(empty(B)|in(A,B)))),
% 18.34/2.84 inference(pre_NNF_transformation,[status(esa)],[f33])).
% 18.34/2.84 fof(f130,plain,(
% 18.34/2.84 ![X0,X1]: (~element(X0,X1)|empty(X1)|in(X0,X1))),
% 18.34/2.84 inference(cnf_transformation,[status(esa)],[f129])).
% 18.34/2.84 fof(f131,plain,(
% 18.34/2.84 ![A,B]: ((~relation(B)|~function(B))|(B=identity_relation(A)<=>(relation_dom(B)=A&(![C]: (~in(C,A)|apply(B,C)=C)))))),
% 18.34/2.84 inference(pre_NNF_transformation,[status(esa)],[f34])).
% 18.34/2.84 fof(f132,plain,(
% 18.34/2.84 ![A,B]: ((~relation(B)|~function(B))|((~B=identity_relation(A)|(relation_dom(B)=A&(![C]: (~in(C,A)|apply(B,C)=C))))&(B=identity_relation(A)|(~relation_dom(B)=A|(?[C]: (in(C,A)&~apply(B,C)=C))))))),
% 18.34/2.84 inference(NNF_transformation,[status(esa)],[f131])).
% 18.34/2.84 fof(f133,plain,(
% 18.34/2.84 ![B]: ((~relation(B)|~function(B))|((![A]: (~B=identity_relation(A)|(relation_dom(B)=A&(![C]: (~in(C,A)|apply(B,C)=C)))))&(![A]: (B=identity_relation(A)|(~relation_dom(B)=A|(?[C]: (in(C,A)&~apply(B,C)=C)))))))),
% 18.34/2.84 inference(miniscoping,[status(esa)],[f132])).
% 18.34/2.84 fof(f134,plain,(
% 18.34/2.84 ![B]: ((~relation(B)|~function(B))|((![A]: (~B=identity_relation(A)|(relation_dom(B)=A&(![C]: (~in(C,A)|apply(B,C)=C)))))&(![A]: (B=identity_relation(A)|(~relation_dom(B)=A|(in(sk0_11(A,B),A)&~apply(B,sk0_11(A,B))=sk0_11(A,B)))))))),
% 18.34/2.84 inference(skolemization,[status(esa)],[f133])).
% 18.34/2.84 fof(f135,plain,(
% 18.34/2.84 ![X0,X1]: (~relation(X0)|~function(X0)|~X0=identity_relation(X1)|relation_dom(X0)=X1)),
% 18.34/2.84 inference(cnf_transformation,[status(esa)],[f134])).
% 18.34/2.84 fof(f136,plain,(
% 18.34/2.84 ![X0,X1,X2]: (~relation(X0)|~function(X0)|~X0=identity_relation(X1)|~in(X2,X1)|apply(X0,X2)=X2)),
% 18.34/2.84 inference(cnf_transformation,[status(esa)],[f134])).
% 18.34/2.84 fof(f137,plain,(
% 18.34/2.84 ![X0,X1]: (~relation(X0)|~function(X0)|X0=identity_relation(X1)|~relation_dom(X0)=X1|in(sk0_11(X1,X0),X1))),
% 18.34/2.84 inference(cnf_transformation,[status(esa)],[f134])).
% 18.34/2.84 fof(f138,plain,(
% 18.34/2.84 ![X0,X1]: (~relation(X0)|~function(X0)|X0=identity_relation(X1)|~relation_dom(X0)=X1|~apply(X0,sk0_11(X1,X0))=sk0_11(X1,X0))),
% 18.34/2.84 inference(cnf_transformation,[status(esa)],[f134])).
% 18.34/2.84 fof(f139,plain,(
% 18.34/2.84 ![A,B]: ((~element(A,powerset(B))|subset(A,B))&(element(A,powerset(B))|~subset(A,B)))),
% 18.34/2.84 inference(NNF_transformation,[status(esa)],[f35])).
% 18.34/2.84 fof(f140,plain,(
% 18.34/2.84 (![A,B]: (~element(A,powerset(B))|subset(A,B)))&(![A,B]: (element(A,powerset(B))|~subset(A,B)))),
% 18.34/2.84 inference(miniscoping,[status(esa)],[f139])).
% 18.34/2.84 fof(f141,plain,(
% 18.34/2.84 ![X0,X1]: (~element(X0,powerset(X1))|subset(X0,X1))),
% 18.34/2.84 inference(cnf_transformation,[status(esa)],[f140])).
% 18.34/2.84 fof(f142,plain,(
% 18.34/2.84 ![X0,X1]: (element(X0,powerset(X1))|~subset(X0,X1))),
% 18.34/2.84 inference(cnf_transformation,[status(esa)],[f140])).
% 18.34/2.84 fof(f143,plain,(
% 18.34/2.84 ![A,B,C]: ((~in(A,B)|~element(B,powerset(C)))|element(A,C))),
% 18.34/2.84 inference(pre_NNF_transformation,[status(esa)],[f36])).
% 18.34/2.84 fof(f144,plain,(
% 18.34/2.84 ![A,C]: ((![B]: (~in(A,B)|~element(B,powerset(C))))|element(A,C))),
% 18.34/2.84 inference(miniscoping,[status(esa)],[f143])).
% 18.34/2.84 fof(f145,plain,(
% 18.34/2.84 ![X0,X1,X2]: (~in(X0,X1)|~element(X1,powerset(X2))|element(X0,X2))),
% 18.34/2.84 inference(cnf_transformation,[status(esa)],[f144])).
% 18.34/2.84 fof(f146,plain,(
% 18.34/2.84 ![A,B]: ((~relation(B)|~function(B))|((~one_to_one(B)|~in(A,relation_dom(B)))|(A=apply(function_inverse(B),apply(B,A))&A=apply(relation_composition(B,function_inverse(B)),A))))),
% 18.34/2.84 inference(pre_NNF_transformation,[status(esa)],[f37])).
% 18.34/2.84 fof(f147,plain,(
% 18.34/2.84 ![B]: ((~relation(B)|~function(B))|(![A]: ((~one_to_one(B)|~in(A,relation_dom(B)))|(A=apply(function_inverse(B),apply(B,A))&A=apply(relation_composition(B,function_inverse(B)),A)))))),
% 18.34/2.84 inference(miniscoping,[status(esa)],[f146])).
% 18.34/2.84 fof(f148,plain,(
% 18.34/2.84 ![X0,X1]: (~relation(X0)|~function(X0)|~one_to_one(X0)|~in(X1,relation_dom(X0))|X1=apply(function_inverse(X0),apply(X0,X1)))),
% 18.34/2.84 inference(cnf_transformation,[status(esa)],[f147])).
% 18.34/2.84 fof(f149,plain,(
% 18.34/2.84 ![X0,X1]: (~relation(X0)|~function(X0)|~one_to_one(X0)|~in(X1,relation_dom(X0))|X1=apply(relation_composition(X0,function_inverse(X0)),X1))),
% 18.34/2.84 inference(cnf_transformation,[status(esa)],[f147])).
% 18.34/2.84 fof(f150,plain,(
% 18.34/2.84 ![A,B]: ((~relation(B)|~function(B))|((~one_to_one(B)|~in(A,relation_rng(B)))|(A=apply(B,apply(function_inverse(B),A))&A=apply(relation_composition(function_inverse(B),B),A))))),
% 18.34/2.84 inference(pre_NNF_transformation,[status(esa)],[f38])).
% 18.34/2.84 fof(f151,plain,(
% 18.34/2.84 ![B]: ((~relation(B)|~function(B))|(![A]: ((~one_to_one(B)|~in(A,relation_rng(B)))|(A=apply(B,apply(function_inverse(B),A))&A=apply(relation_composition(function_inverse(B),B),A)))))),
% 18.34/2.84 inference(miniscoping,[status(esa)],[f150])).
% 18.34/2.84 fof(f152,plain,(
% 18.34/2.84 ![X0,X1]: (~relation(X0)|~function(X0)|~one_to_one(X0)|~in(X1,relation_rng(X0))|X1=apply(X0,apply(function_inverse(X0),X1)))),
% 18.34/2.84 inference(cnf_transformation,[status(esa)],[f151])).
% 18.34/2.84 fof(f153,plain,(
% 18.34/2.84 ![X0,X1]: (~relation(X0)|~function(X0)|~one_to_one(X0)|~in(X1,relation_rng(X0))|X1=apply(relation_composition(function_inverse(X0),X0),X1))),
% 18.34/2.84 inference(cnf_transformation,[status(esa)],[f151])).
% 18.34/2.84 fof(f154,plain,(
% 18.34/2.84 ![A]: ((~relation(A)|~function(A))|(~one_to_one(A)|(relation_dom(relation_composition(A,function_inverse(A)))=relation_dom(A)&relation_rng(relation_composition(A,function_inverse(A)))=relation_dom(A))))),
% 18.34/2.84 inference(pre_NNF_transformation,[status(esa)],[f39])).
% 18.34/2.84 fof(f155,plain,(
% 18.34/2.84 ![X0]: (~relation(X0)|~function(X0)|~one_to_one(X0)|relation_dom(relation_composition(X0,function_inverse(X0)))=relation_dom(X0))),
% 18.34/2.84 inference(cnf_transformation,[status(esa)],[f154])).
% 18.34/2.84 fof(f156,plain,(
% 18.34/2.84 ![X0]: (~relation(X0)|~function(X0)|~one_to_one(X0)|relation_rng(relation_composition(X0,function_inverse(X0)))=relation_dom(X0))),
% 18.34/2.84 inference(cnf_transformation,[status(esa)],[f154])).
% 18.34/2.84 fof(f157,plain,(
% 18.34/2.84 ![A]: ((~relation(A)|~function(A))|(~one_to_one(A)|(relation_dom(relation_composition(function_inverse(A),A))=relation_rng(A)&relation_rng(relation_composition(function_inverse(A),A))=relation_rng(A))))),
% 18.34/2.84 inference(pre_NNF_transformation,[status(esa)],[f40])).
% 18.34/2.84 fof(f158,plain,(
% 18.34/2.84 ![X0]: (~relation(X0)|~function(X0)|~one_to_one(X0)|relation_dom(relation_composition(function_inverse(X0),X0))=relation_rng(X0))),
% 18.34/2.84 inference(cnf_transformation,[status(esa)],[f157])).
% 18.34/2.84 fof(f159,plain,(
% 18.34/2.84 ![X0]: (~relation(X0)|~function(X0)|~one_to_one(X0)|relation_rng(relation_composition(function_inverse(X0),X0))=relation_rng(X0))),
% 18.34/2.84 inference(cnf_transformation,[status(esa)],[f157])).
% 18.34/2.84 fof(f160,plain,(
% 18.34/2.84 ![A,B,C]: ((~in(A,B)|~element(B,powerset(C)))|~empty(C))),
% 18.34/2.84 inference(pre_NNF_transformation,[status(esa)],[f41])).
% 18.34/2.84 fof(f161,plain,(
% 18.34/2.84 ![C]: ((![B]: ((![A]: ~in(A,B))|~element(B,powerset(C))))|~empty(C))),
% 18.34/2.84 inference(miniscoping,[status(esa)],[f160])).
% 18.34/2.84 fof(f162,plain,(
% 18.34/2.84 ![X0,X1,X2]: (~in(X0,X1)|~element(X1,powerset(X2))|~empty(X2))),
% 18.34/2.84 inference(cnf_transformation,[status(esa)],[f161])).
% 18.34/2.84 fof(f163,plain,(
% 18.34/2.84 (?[A]: ((relation(A)&function(A))&(one_to_one(A)&(~relation_composition(A,function_inverse(A))=identity_relation(relation_dom(A))|~relation_composition(function_inverse(A),A)=identity_relation(relation_rng(A))))))),
% 18.34/2.84 inference(pre_NNF_transformation,[status(esa)],[f43])).
% 18.34/2.84 fof(f164,plain,(
% 18.34/2.84 ((relation(sk0_12)&function(sk0_12))&(one_to_one(sk0_12)&(~relation_composition(sk0_12,function_inverse(sk0_12))=identity_relation(relation_dom(sk0_12))|~relation_composition(function_inverse(sk0_12),sk0_12)=identity_relation(relation_rng(sk0_12)))))),
% 18.34/2.84 inference(skolemization,[status(esa)],[f163])).
% 18.34/2.84 fof(f165,plain,(
% 18.34/2.84 relation(sk0_12)),
% 18.34/2.84 inference(cnf_transformation,[status(esa)],[f164])).
% 18.34/2.84 fof(f166,plain,(
% 18.34/2.84 function(sk0_12)),
% 18.34/2.84 inference(cnf_transformation,[status(esa)],[f164])).
% 18.34/2.84 fof(f167,plain,(
% 18.34/2.84 one_to_one(sk0_12)),
% 18.34/2.84 inference(cnf_transformation,[status(esa)],[f164])).
% 18.34/2.84 fof(f168,plain,(
% 18.34/2.84 ~relation_composition(sk0_12,function_inverse(sk0_12))=identity_relation(relation_dom(sk0_12))|~relation_composition(function_inverse(sk0_12),sk0_12)=identity_relation(relation_rng(sk0_12))),
% 18.34/2.84 inference(cnf_transformation,[status(esa)],[f164])).
% 18.34/2.84 fof(f169,plain,(
% 18.34/2.84 ![A]: (~empty(A)|A=empty_set)),
% 18.34/2.84 inference(pre_NNF_transformation,[status(esa)],[f44])).
% 18.34/2.84 fof(f170,plain,(
% 18.34/2.84 ![X0]: (~empty(X0)|X0=empty_set)),
% 18.34/2.84 inference(cnf_transformation,[status(esa)],[f169])).
% 18.34/2.84 fof(f171,plain,(
% 18.34/2.84 ![A,B]: (~in(A,B)|~empty(B))),
% 18.34/2.84 inference(pre_NNF_transformation,[status(esa)],[f45])).
% 18.34/2.84 fof(f172,plain,(
% 18.34/2.84 ![B]: ((![A]: ~in(A,B))|~empty(B))),
% 18.34/2.84 inference(miniscoping,[status(esa)],[f171])).
% 18.34/2.84 fof(f173,plain,(
% 18.34/2.84 ![X0,X1]: (~in(X0,X1)|~empty(X1))),
% 18.34/2.84 inference(cnf_transformation,[status(esa)],[f172])).
% 18.34/2.84 fof(f177,plain,(
% 18.34/2.84 spl0_0 <=> relation_composition(sk0_12,function_inverse(sk0_12))=identity_relation(relation_dom(sk0_12))),
% 18.34/2.84 introduced(split_symbol_definition)).
% 18.34/2.84 fof(f179,plain,(
% 18.34/2.84 ~relation_composition(sk0_12,function_inverse(sk0_12))=identity_relation(relation_dom(sk0_12))|spl0_0),
% 18.34/2.84 inference(component_clause,[status(thm)],[f177])).
% 18.34/2.84 fof(f180,plain,(
% 18.34/2.84 spl0_1 <=> relation_composition(function_inverse(sk0_12),sk0_12)=identity_relation(relation_rng(sk0_12))),
% 18.34/2.84 introduced(split_symbol_definition)).
% 18.34/2.84 fof(f182,plain,(
% 18.34/2.84 ~relation_composition(function_inverse(sk0_12),sk0_12)=identity_relation(relation_rng(sk0_12))|spl0_1),
% 18.34/2.84 inference(component_clause,[status(thm)],[f180])).
% 18.34/2.84 fof(f183,plain,(
% 18.34/2.84 ~spl0_0|~spl0_1),
% 18.34/2.84 inference(split_clause,[status(thm)],[f168,f177,f180])).
% 18.34/2.84 fof(f184,plain,(
% 18.34/2.84 ![X0]: (~relation(identity_relation(X0))|~function(identity_relation(X0))|relation_dom(identity_relation(X0))=X0)),
% 18.34/2.84 inference(destructive_equality_resolution,[status(esa)],[f135])).
% 18.34/2.84 fof(f185,plain,(
% 18.34/2.84 ![X0,X1]: (~relation(identity_relation(X0))|~function(identity_relation(X0))|~in(X1,X0)|apply(identity_relation(X0),X1)=X1)),
% 18.34/2.84 inference(destructive_equality_resolution,[status(esa)],[f136])).
% 18.34/2.84 fof(f186,plain,(
% 18.34/2.84 ![X0]: (~relation(X0)|~function(X0)|X0=identity_relation(relation_dom(X0))|in(sk0_11(relation_dom(X0),X0),relation_dom(X0)))),
% 18.34/2.84 inference(destructive_equality_resolution,[status(esa)],[f137])).
% 18.34/2.84 fof(f187,plain,(
% 18.34/2.84 ![X0]: (~relation(X0)|~function(X0)|X0=identity_relation(relation_dom(X0))|~apply(X0,sk0_11(relation_dom(X0),X0))=sk0_11(relation_dom(X0),X0))),
% 18.34/2.84 inference(destructive_equality_resolution,[status(esa)],[f138])).
% 18.34/2.84 fof(f188,plain,(
% 18.34/2.84 ![X0]: (~relation(X0)|~empty(X0)|one_to_one(X0))),
% 18.34/2.84 inference(forward_subsumption_resolution,[status(thm)],[f56,f50])).
% 18.34/2.84 fof(f189,plain,(
% 18.34/2.84 ![X0]: (~empty(X0)|one_to_one(X0))),
% 18.34/2.84 inference(backward_subsumption_resolution,[status(thm)],[f188,f52])).
% 18.34/2.84 fof(f190,plain,(
% 18.34/2.84 ![X0]: (~function(identity_relation(X0))|relation_dom(identity_relation(X0))=X0)),
% 18.34/2.84 inference(forward_subsumption_resolution,[status(thm)],[f184,f62])).
% 18.34/2.84 fof(f191,plain,(
% 18.34/2.84 ![X0]: (relation_dom(identity_relation(X0))=X0)),
% 18.34/2.84 inference(resolution,[status(thm)],[f190,f78])).
% 18.34/2.84 fof(f193,plain,(
% 18.34/2.84 ![X0]: (empty(identity_relation(X0))|~relation(identity_relation(X0))|~empty(X0))),
% 18.34/2.84 inference(paramodulation,[status(thm)],[f191,f82])).
% 18.34/2.84 fof(f194,plain,(
% 18.34/2.84 ![X0]: (empty(identity_relation(X0))|~empty(X0))),
% 18.34/2.84 inference(forward_subsumption_resolution,[status(thm)],[f193,f62])).
% 18.34/2.84 fof(f195,plain,(
% 18.34/2.84 ![X0]: (~empty(identity_relation(X0))|relation(X0))),
% 18.34/2.84 inference(paramodulation,[status(thm)],[f191,f87])).
% 18.34/2.84 fof(f196,plain,(
% 18.34/2.84 ![X0]: (~empty(identity_relation(X0))|empty(X0))),
% 18.34/2.84 inference(paramodulation,[status(thm)],[f191,f86])).
% 18.34/2.84 fof(f198,plain,(
% 18.34/2.84 spl0_2 <=> relation(sk0_12)),
% 18.34/2.84 introduced(split_symbol_definition)).
% 18.34/2.84 fof(f200,plain,(
% 18.34/2.84 ~relation(sk0_12)|spl0_2),
% 18.34/2.84 inference(component_clause,[status(thm)],[f198])).
% 18.34/2.84 fof(f201,plain,(
% 18.34/2.84 spl0_3 <=> function(sk0_12)),
% 18.34/2.84 introduced(split_symbol_definition)).
% 18.34/2.84 fof(f203,plain,(
% 18.34/2.84 ~function(sk0_12)|spl0_3),
% 18.34/2.84 inference(component_clause,[status(thm)],[f201])).
% 18.34/2.84 fof(f204,plain,(
% 18.34/2.84 spl0_4 <=> relation_dom(relation_composition(sk0_12,function_inverse(sk0_12)))=relation_dom(sk0_12)),
% 18.34/2.84 introduced(split_symbol_definition)).
% 18.34/2.84 fof(f205,plain,(
% 18.34/2.84 relation_dom(relation_composition(sk0_12,function_inverse(sk0_12)))=relation_dom(sk0_12)|~spl0_4),
% 18.34/2.84 inference(component_clause,[status(thm)],[f204])).
% 18.34/2.84 fof(f207,plain,(
% 18.34/2.84 ~relation(sk0_12)|~function(sk0_12)|relation_dom(relation_composition(sk0_12,function_inverse(sk0_12)))=relation_dom(sk0_12)),
% 18.34/2.84 inference(resolution,[status(thm)],[f155,f167])).
% 18.34/2.84 fof(f208,plain,(
% 18.34/2.84 ~spl0_2|~spl0_3|spl0_4),
% 18.34/2.84 inference(split_clause,[status(thm)],[f207,f198,f201,f204])).
% 18.34/2.84 fof(f209,plain,(
% 18.34/2.84 ![X0]: (~relation(X0)|~function(X0)|relation_dom(relation_composition(X0,function_inverse(X0)))=relation_dom(X0)|~empty(X0))),
% 18.34/2.84 inference(resolution,[status(thm)],[f155,f189])).
% 18.34/2.84 fof(f210,plain,(
% 18.34/2.84 ![X0]: (~function(X0)|relation_dom(relation_composition(X0,function_inverse(X0)))=relation_dom(X0)|~empty(X0))),
% 18.34/2.84 inference(forward_subsumption_resolution,[status(thm)],[f209,f52])).
% 18.34/2.84 fof(f211,plain,(
% 18.34/2.84 $false|spl0_3),
% 18.34/2.84 inference(forward_subsumption_resolution,[status(thm)],[f203,f166])).
% 18.34/2.84 fof(f212,plain,(
% 18.34/2.84 spl0_3),
% 18.34/2.84 inference(contradiction_clause,[status(thm)],[f211])).
% 18.34/2.84 fof(f213,plain,(
% 18.34/2.84 $false|spl0_2),
% 18.34/2.84 inference(forward_subsumption_resolution,[status(thm)],[f200,f165])).
% 18.34/2.84 fof(f214,plain,(
% 18.34/2.84 spl0_2),
% 18.34/2.84 inference(contradiction_clause,[status(thm)],[f213])).
% 18.34/2.84 fof(f215,plain,(
% 18.34/2.84 spl0_5 <=> empty(relation_composition(sk0_12,function_inverse(sk0_12)))),
% 18.34/2.84 introduced(split_symbol_definition)).
% 18.34/2.84 fof(f217,plain,(
% 18.34/2.84 ~empty(relation_composition(sk0_12,function_inverse(sk0_12)))|spl0_5),
% 18.34/2.84 inference(component_clause,[status(thm)],[f215])).
% 18.34/2.84 fof(f218,plain,(
% 18.34/2.84 spl0_6 <=> relation(relation_composition(sk0_12,function_inverse(sk0_12)))),
% 18.34/2.84 introduced(split_symbol_definition)).
% 18.34/2.84 fof(f220,plain,(
% 18.34/2.84 ~relation(relation_composition(sk0_12,function_inverse(sk0_12)))|spl0_6),
% 18.34/2.84 inference(component_clause,[status(thm)],[f218])).
% 18.34/2.84 fof(f221,plain,(
% 18.34/2.84 spl0_7 <=> empty(relation_dom(sk0_12))),
% 18.34/2.84 introduced(split_symbol_definition)).
% 18.34/2.84 fof(f222,plain,(
% 18.34/2.84 empty(relation_dom(sk0_12))|~spl0_7),
% 18.34/2.84 inference(component_clause,[status(thm)],[f221])).
% 18.34/2.84 fof(f231,plain,(
% 18.34/2.84 ~empty(relation_composition(sk0_12,function_inverse(sk0_12)))|empty(relation_dom(sk0_12))|~spl0_4),
% 18.34/2.84 inference(paramodulation,[status(thm)],[f205,f86])).
% 18.34/2.84 fof(f232,plain,(
% 18.34/2.84 ~spl0_5|spl0_7|~spl0_4),
% 18.34/2.84 inference(split_clause,[status(thm)],[f231,f215,f221,f204])).
% 18.34/2.84 fof(f233,plain,(
% 18.34/2.84 spl0_9 <=> empty(sk0_12)),
% 18.34/2.84 introduced(split_symbol_definition)).
% 18.34/2.84 fof(f234,plain,(
% 18.34/2.84 empty(sk0_12)|~spl0_9),
% 18.34/2.84 inference(component_clause,[status(thm)],[f233])).
% 18.34/2.84 fof(f236,plain,(
% 18.34/2.84 spl0_10 <=> relation(function_inverse(sk0_12))),
% 18.34/2.84 introduced(split_symbol_definition)).
% 18.34/2.84 fof(f237,plain,(
% 18.34/2.84 relation(function_inverse(sk0_12))|~spl0_10),
% 18.34/2.84 inference(component_clause,[status(thm)],[f236])).
% 18.34/2.84 fof(f238,plain,(
% 18.34/2.84 ~relation(function_inverse(sk0_12))|spl0_10),
% 18.34/2.84 inference(component_clause,[status(thm)],[f236])).
% 18.34/2.84 fof(f241,plain,(
% 18.34/2.84 spl0_11 <=> empty(function_inverse(sk0_12))),
% 18.34/2.84 introduced(split_symbol_definition)).
% 18.34/2.84 fof(f246,plain,(
% 18.34/2.84 ~relation(sk0_12)|~relation(function_inverse(sk0_12))|spl0_6),
% 18.34/2.84 inference(resolution,[status(thm)],[f220,f61])).
% 18.34/2.84 fof(f247,plain,(
% 18.34/2.84 ~spl0_2|~spl0_10|spl0_6),
% 18.34/2.84 inference(split_clause,[status(thm)],[f246,f198,f236,f218])).
% 18.34/2.84 fof(f251,plain,(
% 18.34/2.84 ~empty(function_inverse(sk0_12))|~relation(sk0_12)|spl0_5),
% 18.34/2.84 inference(resolution,[status(thm)],[f217,f66])).
% 18.34/2.84 fof(f252,plain,(
% 18.34/2.84 ~spl0_11|~spl0_2|spl0_5),
% 18.34/2.84 inference(split_clause,[status(thm)],[f251,f241,f198,f215])).
% 18.34/2.84 fof(f253,plain,(
% 18.34/2.84 ~relation(sk0_12)|~function(sk0_12)|spl0_10),
% 18.34/2.84 inference(resolution,[status(thm)],[f238,f58])).
% 18.34/2.84 fof(f254,plain,(
% 18.34/2.84 ~spl0_2|~spl0_3|spl0_10),
% 18.34/2.84 inference(split_clause,[status(thm)],[f253,f198,f201,f236])).
% 18.34/2.84 fof(f255,plain,(
% 18.34/2.84 empty(sk0_12)|~relation(sk0_12)|~spl0_7),
% 18.34/2.84 inference(resolution,[status(thm)],[f222,f82])).
% 18.34/2.84 fof(f256,plain,(
% 18.34/2.84 spl0_9|~spl0_2|~spl0_7),
% 18.34/2.84 inference(split_clause,[status(thm)],[f255,f233,f198,f221])).
% 18.34/2.84 fof(f261,plain,(
% 18.34/2.84 ![X0]: (relation_dom(relation_composition(X0,function_inverse(X0)))=relation_dom(X0)|~empty(X0))),
% 18.34/2.84 inference(forward_subsumption_resolution,[status(thm)],[f210,f50])).
% 18.34/2.84 fof(f262,plain,(
% 18.34/2.84 ![X0]: (relation_dom(relation_composition(identity_relation(X0),function_inverse(identity_relation(X0))))=relation_dom(identity_relation(X0))|~empty(X0))),
% 18.34/2.84 inference(resolution,[status(thm)],[f261,f194])).
% 18.34/2.84 fof(f263,plain,(
% 18.34/2.84 ![X0]: (relation_dom(relation_composition(identity_relation(X0),function_inverse(identity_relation(X0))))=X0|~empty(X0))),
% 18.34/2.84 inference(forward_demodulation,[status(thm)],[f191,f262])).
% 18.34/2.84 fof(f264,plain,(
% 18.34/2.84 relation_dom(relation_composition(sk0_5,function_inverse(sk0_5)))=relation_dom(sk0_5)),
% 18.34/2.84 inference(resolution,[status(thm)],[f261,f108])).
% 18.34/2.84 fof(f265,plain,(
% 18.34/2.84 relation_dom(relation_composition(sk0_4,function_inverse(sk0_4)))=relation_dom(sk0_4)),
% 18.34/2.84 inference(resolution,[status(thm)],[f261,f105])).
% 18.34/2.84 fof(f267,plain,(
% 18.34/2.84 relation_dom(relation_composition(empty_set,function_inverse(empty_set)))=relation_dom(empty_set)),
% 18.34/2.84 inference(resolution,[status(thm)],[f261,f68])).
% 18.34/2.84 fof(f272,plain,(
% 18.34/2.84 spl0_12 <=> empty(relation_composition(sk0_5,function_inverse(sk0_5)))),
% 18.34/2.84 introduced(split_symbol_definition)).
% 18.34/2.84 fof(f273,plain,(
% 18.34/2.84 empty(relation_composition(sk0_5,function_inverse(sk0_5)))|~spl0_12),
% 18.34/2.84 inference(component_clause,[status(thm)],[f272])).
% 18.34/2.84 fof(f275,plain,(
% 18.34/2.84 spl0_13 <=> relation(relation_composition(sk0_5,function_inverse(sk0_5)))),
% 18.34/2.84 introduced(split_symbol_definition)).
% 18.34/2.84 fof(f277,plain,(
% 18.34/2.84 ~relation(relation_composition(sk0_5,function_inverse(sk0_5)))|spl0_13),
% 18.34/2.84 inference(component_clause,[status(thm)],[f275])).
% 18.34/2.84 fof(f278,plain,(
% 18.34/2.84 spl0_14 <=> empty(relation_dom(sk0_5))),
% 18.34/2.84 introduced(split_symbol_definition)).
% 18.34/2.84 fof(f280,plain,(
% 18.34/2.84 ~empty(relation_dom(sk0_5))|spl0_14),
% 18.34/2.84 inference(component_clause,[status(thm)],[f278])).
% 18.34/2.84 fof(f281,plain,(
% 18.34/2.84 empty(relation_composition(sk0_5,function_inverse(sk0_5)))|~relation(relation_composition(sk0_5,function_inverse(sk0_5)))|~empty(relation_dom(sk0_5))),
% 18.34/2.84 inference(paramodulation,[status(thm)],[f264,f82])).
% 18.34/2.84 fof(f282,plain,(
% 18.34/2.84 spl0_12|~spl0_13|~spl0_14),
% 18.34/2.84 inference(split_clause,[status(thm)],[f281,f272,f275,f278])).
% 18.34/2.84 fof(f283,plain,(
% 18.34/2.84 spl0_15 <=> relation(relation_dom(sk0_5))),
% 18.34/2.84 introduced(split_symbol_definition)).
% 18.34/2.84 fof(f286,plain,(
% 18.34/2.84 ~empty(relation_composition(sk0_5,function_inverse(sk0_5)))|relation(relation_dom(sk0_5))),
% 18.34/2.84 inference(paramodulation,[status(thm)],[f264,f87])).
% 18.34/2.84 fof(f287,plain,(
% 18.34/2.84 ~spl0_12|spl0_15),
% 18.34/2.84 inference(split_clause,[status(thm)],[f286,f272,f283])).
% 18.34/2.84 fof(f290,plain,(
% 18.34/2.84 spl0_16 <=> empty(sk0_5)),
% 18.34/2.84 introduced(split_symbol_definition)).
% 18.34/2.84 fof(f292,plain,(
% 18.34/2.84 ~empty(sk0_5)|spl0_16),
% 18.34/2.84 inference(component_clause,[status(thm)],[f290])).
% 18.34/2.84 fof(f293,plain,(
% 18.34/2.84 spl0_17 <=> relation(function_inverse(sk0_5))),
% 18.34/2.84 introduced(split_symbol_definition)).
% 18.34/2.84 fof(f294,plain,(
% 18.34/2.84 relation(function_inverse(sk0_5))|~spl0_17),
% 18.34/2.84 inference(component_clause,[status(thm)],[f293])).
% 18.34/2.84 fof(f295,plain,(
% 18.34/2.84 ~relation(function_inverse(sk0_5))|spl0_17),
% 18.34/2.84 inference(component_clause,[status(thm)],[f293])).
% 18.34/2.84 fof(f296,plain,(
% 18.34/2.84 ~empty(sk0_5)|~relation(function_inverse(sk0_5))|spl0_13),
% 18.34/2.84 inference(resolution,[status(thm)],[f277,f93])).
% 18.34/2.84 fof(f297,plain,(
% 18.34/2.84 ~spl0_16|~spl0_17|spl0_13),
% 18.34/2.84 inference(split_clause,[status(thm)],[f296,f290,f293,f275])).
% 18.34/2.84 fof(f301,plain,(
% 18.34/2.84 spl0_19 <=> relation(sk0_5)),
% 18.34/2.84 introduced(split_symbol_definition)).
% 18.34/2.84 fof(f303,plain,(
% 18.34/2.84 ~relation(sk0_5)|spl0_19),
% 18.34/2.84 inference(component_clause,[status(thm)],[f301])).
% 18.34/2.84 fof(f309,plain,(
% 18.34/2.84 $false|spl0_16),
% 18.34/2.84 inference(forward_subsumption_resolution,[status(thm)],[f292,f108])).
% 18.34/2.84 fof(f310,plain,(
% 18.34/2.84 spl0_16),
% 18.34/2.84 inference(contradiction_clause,[status(thm)],[f309])).
% 18.34/2.84 fof(f311,plain,(
% 18.34/2.84 spl0_20 <=> function(sk0_5)),
% 18.34/2.84 introduced(split_symbol_definition)).
% 18.34/2.84 fof(f313,plain,(
% 18.34/2.84 ~function(sk0_5)|spl0_20),
% 18.34/2.84 inference(component_clause,[status(thm)],[f311])).
% 18.34/2.84 fof(f314,plain,(
% 18.34/2.84 ~relation(sk0_5)|~function(sk0_5)|spl0_17),
% 18.34/2.84 inference(resolution,[status(thm)],[f295,f58])).
% 18.34/2.84 fof(f315,plain,(
% 18.34/2.84 ~spl0_19|~spl0_20|spl0_17),
% 18.34/2.84 inference(split_clause,[status(thm)],[f314,f301,f311,f293])).
% 18.34/2.84 fof(f316,plain,(
% 18.34/2.84 $false|spl0_20),
% 18.34/2.84 inference(forward_subsumption_resolution,[status(thm)],[f313,f109])).
% 18.34/2.84 fof(f317,plain,(
% 18.34/2.84 spl0_20),
% 18.34/2.84 inference(contradiction_clause,[status(thm)],[f316])).
% 18.34/2.84 fof(f319,plain,(
% 18.34/2.84 $false|spl0_19),
% 18.34/2.84 inference(forward_subsumption_resolution,[status(thm)],[f303,f107])).
% 18.34/2.84 fof(f320,plain,(
% 18.34/2.84 spl0_19),
% 18.34/2.84 inference(contradiction_clause,[status(thm)],[f319])).
% 18.34/2.84 fof(f323,plain,(
% 18.34/2.84 spl0_21 <=> empty(relation_composition(sk0_4,function_inverse(sk0_4)))),
% 18.34/2.84 introduced(split_symbol_definition)).
% 18.34/2.84 fof(f326,plain,(
% 18.34/2.84 spl0_22 <=> relation(relation_composition(sk0_4,function_inverse(sk0_4)))),
% 18.34/2.84 introduced(split_symbol_definition)).
% 18.34/2.84 fof(f328,plain,(
% 18.34/2.84 ~relation(relation_composition(sk0_4,function_inverse(sk0_4)))|spl0_22),
% 18.34/2.84 inference(component_clause,[status(thm)],[f326])).
% 18.34/2.84 fof(f329,plain,(
% 18.34/2.84 spl0_23 <=> empty(relation_dom(sk0_4))),
% 18.34/2.84 introduced(split_symbol_definition)).
% 18.34/2.84 fof(f331,plain,(
% 18.34/2.84 ~empty(relation_dom(sk0_4))|spl0_23),
% 18.34/2.84 inference(component_clause,[status(thm)],[f329])).
% 18.34/2.84 fof(f332,plain,(
% 18.34/2.84 empty(relation_composition(sk0_4,function_inverse(sk0_4)))|~relation(relation_composition(sk0_4,function_inverse(sk0_4)))|~empty(relation_dom(sk0_4))),
% 18.34/2.84 inference(paramodulation,[status(thm)],[f265,f82])).
% 18.34/2.84 fof(f333,plain,(
% 18.34/2.84 spl0_21|~spl0_22|~spl0_23),
% 18.34/2.84 inference(split_clause,[status(thm)],[f332,f323,f326,f329])).
% 18.34/2.84 fof(f334,plain,(
% 18.34/2.84 spl0_24 <=> relation(relation_dom(sk0_4))),
% 18.34/2.84 introduced(split_symbol_definition)).
% 18.34/2.84 fof(f337,plain,(
% 18.34/2.84 ~empty(relation_composition(sk0_4,function_inverse(sk0_4)))|relation(relation_dom(sk0_4))),
% 18.34/2.84 inference(paramodulation,[status(thm)],[f265,f87])).
% 18.34/2.84 fof(f338,plain,(
% 18.34/2.84 ~spl0_21|spl0_24),
% 18.34/2.84 inference(split_clause,[status(thm)],[f337,f323,f334])).
% 18.34/2.84 fof(f344,plain,(
% 18.34/2.84 spl0_26 <=> relation(relation_composition(sk0_2,function_inverse(sk0_2)))),
% 18.34/2.84 introduced(split_symbol_definition)).
% 18.34/2.84 fof(f346,plain,(
% 18.34/2.84 ~relation(relation_composition(sk0_2,function_inverse(sk0_2)))|spl0_26),
% 18.34/2.84 inference(component_clause,[status(thm)],[f344])).
% 18.34/2.84 fof(f359,plain,(
% 18.34/2.84 spl0_29 <=> empty(relation_composition(empty_set,function_inverse(empty_set)))),
% 18.34/2.84 introduced(split_symbol_definition)).
% 18.34/2.84 fof(f362,plain,(
% 18.34/2.84 spl0_30 <=> relation(relation_composition(empty_set,function_inverse(empty_set)))),
% 18.34/2.84 introduced(split_symbol_definition)).
% 18.34/2.84 fof(f364,plain,(
% 18.34/2.84 ~relation(relation_composition(empty_set,function_inverse(empty_set)))|spl0_30),
% 18.34/2.84 inference(component_clause,[status(thm)],[f362])).
% 18.34/2.84 fof(f365,plain,(
% 18.34/2.84 spl0_31 <=> empty(relation_dom(empty_set))),
% 18.34/2.84 introduced(split_symbol_definition)).
% 18.34/2.84 fof(f366,plain,(
% 18.34/2.84 empty(relation_dom(empty_set))|~spl0_31),
% 18.34/2.84 inference(component_clause,[status(thm)],[f365])).
% 18.34/2.84 fof(f370,plain,(
% 18.34/2.84 spl0_32 <=> relation(relation_dom(empty_set))),
% 18.34/2.84 introduced(split_symbol_definition)).
% 18.34/2.84 fof(f373,plain,(
% 18.34/2.84 ~empty(relation_composition(empty_set,function_inverse(empty_set)))|relation(relation_dom(empty_set))),
% 18.34/2.84 inference(paramodulation,[status(thm)],[f267,f87])).
% 18.34/2.84 fof(f374,plain,(
% 18.34/2.84 ~spl0_29|spl0_32),
% 18.34/2.84 inference(split_clause,[status(thm)],[f373,f359,f370])).
% 18.34/2.84 fof(f375,plain,(
% 18.34/2.84 ~empty(relation_composition(empty_set,function_inverse(empty_set)))|empty(relation_dom(empty_set))),
% 18.34/2.84 inference(paramodulation,[status(thm)],[f267,f86])).
% 18.34/2.84 fof(f376,plain,(
% 18.34/2.84 ~spl0_29|spl0_31),
% 18.34/2.84 inference(split_clause,[status(thm)],[f375,f359,f365])).
% 18.34/2.84 fof(f378,plain,(
% 18.34/2.84 relation_dom(relation_composition(identity_relation(sk0_5),function_inverse(identity_relation(sk0_5))))=sk0_5),
% 18.34/2.84 inference(resolution,[status(thm)],[f263,f108])).
% 18.34/2.84 fof(f379,plain,(
% 18.34/2.84 relation_dom(relation_composition(identity_relation(sk0_4),function_inverse(identity_relation(sk0_4))))=sk0_4),
% 18.34/2.84 inference(resolution,[status(thm)],[f263,f105])).
% 18.34/2.84 fof(f380,plain,(
% 18.34/2.84 relation_dom(relation_composition(identity_relation(sk0_2),function_inverse(identity_relation(sk0_2))))=sk0_2),
% 18.34/2.84 inference(resolution,[status(thm)],[f263,f98])).
% 18.34/2.84 fof(f381,plain,(
% 18.34/2.84 relation_dom(relation_composition(identity_relation(empty_set),function_inverse(identity_relation(empty_set))))=empty_set),
% 18.34/2.84 inference(resolution,[status(thm)],[f263,f68])).
% 18.34/2.84 fof(f387,plain,(
% 18.34/2.84 spl0_33 <=> empty(relation_composition(identity_relation(sk0_5),function_inverse(identity_relation(sk0_5))))),
% 18.34/2.84 introduced(split_symbol_definition)).
% 18.34/2.84 fof(f388,plain,(
% 18.34/2.84 empty(relation_composition(identity_relation(sk0_5),function_inverse(identity_relation(sk0_5))))|~spl0_33),
% 18.34/2.84 inference(component_clause,[status(thm)],[f387])).
% 18.34/2.84 fof(f390,plain,(
% 18.34/2.84 spl0_34 <=> relation(relation_composition(identity_relation(sk0_5),function_inverse(identity_relation(sk0_5))))),
% 18.34/2.84 introduced(split_symbol_definition)).
% 18.34/2.84 fof(f392,plain,(
% 18.34/2.84 ~relation(relation_composition(identity_relation(sk0_5),function_inverse(identity_relation(sk0_5))))|spl0_34),
% 18.34/2.84 inference(component_clause,[status(thm)],[f390])).
% 18.34/2.84 fof(f393,plain,(
% 18.34/2.84 empty(relation_composition(identity_relation(sk0_5),function_inverse(identity_relation(sk0_5))))|~relation(relation_composition(identity_relation(sk0_5),function_inverse(identity_relation(sk0_5))))|~empty(sk0_5)),
% 18.34/2.84 inference(paramodulation,[status(thm)],[f378,f82])).
% 18.34/2.84 fof(f394,plain,(
% 18.34/2.84 spl0_33|~spl0_34|~spl0_16),
% 18.34/2.84 inference(split_clause,[status(thm)],[f393,f387,f390,f290])).
% 18.34/2.84 fof(f399,plain,(
% 18.34/2.84 spl0_35 <=> relation_rng(relation_composition(sk0_12,function_inverse(sk0_12)))=relation_dom(sk0_12)),
% 18.34/2.84 introduced(split_symbol_definition)).
% 18.34/2.84 fof(f402,plain,(
% 18.34/2.84 ~relation(sk0_12)|~function(sk0_12)|relation_rng(relation_composition(sk0_12,function_inverse(sk0_12)))=relation_dom(sk0_12)),
% 18.34/2.84 inference(resolution,[status(thm)],[f156,f167])).
% 18.34/2.84 fof(f403,plain,(
% 18.34/2.84 ~spl0_2|~spl0_3|spl0_35),
% 18.34/2.84 inference(split_clause,[status(thm)],[f402,f198,f201,f399])).
% 18.34/2.84 fof(f406,plain,(
% 18.34/2.84 spl0_36 <=> empty(relation_composition(identity_relation(sk0_4),function_inverse(identity_relation(sk0_4))))),
% 18.34/2.84 introduced(split_symbol_definition)).
% 18.34/2.84 fof(f408,plain,(
% 18.34/2.84 ~empty(relation_composition(identity_relation(sk0_4),function_inverse(identity_relation(sk0_4))))|spl0_36),
% 18.34/2.84 inference(component_clause,[status(thm)],[f406])).
% 18.34/2.84 fof(f409,plain,(
% 18.34/2.84 spl0_37 <=> relation(relation_composition(identity_relation(sk0_4),function_inverse(identity_relation(sk0_4))))),
% 18.34/2.84 introduced(split_symbol_definition)).
% 18.34/2.84 fof(f411,plain,(
% 18.34/2.84 ~relation(relation_composition(identity_relation(sk0_4),function_inverse(identity_relation(sk0_4))))|spl0_37),
% 18.34/2.84 inference(component_clause,[status(thm)],[f409])).
% 18.34/2.84 fof(f412,plain,(
% 18.34/2.84 spl0_38 <=> empty(sk0_4)),
% 18.34/2.84 introduced(split_symbol_definition)).
% 18.34/2.84 fof(f417,plain,(
% 18.34/2.84 spl0_39 <=> relation(sk0_4)),
% 18.34/2.84 introduced(split_symbol_definition)).
% 18.34/2.84 fof(f420,plain,(
% 18.34/2.84 ~empty(relation_composition(identity_relation(sk0_4),function_inverse(identity_relation(sk0_4))))|relation(sk0_4)),
% 18.34/2.84 inference(paramodulation,[status(thm)],[f379,f87])).
% 18.34/2.84 fof(f421,plain,(
% 18.34/2.84 ~spl0_36|spl0_39),
% 18.34/2.84 inference(split_clause,[status(thm)],[f420,f406,f417])).
% 18.34/2.84 fof(f422,plain,(
% 18.34/2.84 ~empty(relation_composition(identity_relation(sk0_4),function_inverse(identity_relation(sk0_4))))|empty(sk0_4)),
% 18.34/2.84 inference(paramodulation,[status(thm)],[f379,f86])).
% 18.34/2.84 fof(f423,plain,(
% 18.34/2.84 ~spl0_36|spl0_38),
% 18.34/2.84 inference(split_clause,[status(thm)],[f422,f406,f412])).
% 18.34/2.84 fof(f424,plain,(
% 18.34/2.84 spl0_40 <=> empty(relation_composition(identity_relation(sk0_2),function_inverse(identity_relation(sk0_2))))),
% 18.34/2.84 introduced(split_symbol_definition)).
% 18.34/2.84 fof(f426,plain,(
% 18.34/2.84 ~empty(relation_composition(identity_relation(sk0_2),function_inverse(identity_relation(sk0_2))))|spl0_40),
% 18.34/2.84 inference(component_clause,[status(thm)],[f424])).
% 18.34/2.84 fof(f427,plain,(
% 18.34/2.84 spl0_41 <=> relation(relation_composition(identity_relation(sk0_2),function_inverse(identity_relation(sk0_2))))),
% 18.34/2.84 introduced(split_symbol_definition)).
% 18.34/2.84 fof(f429,plain,(
% 18.34/2.84 ~relation(relation_composition(identity_relation(sk0_2),function_inverse(identity_relation(sk0_2))))|spl0_41),
% 18.34/2.84 inference(component_clause,[status(thm)],[f427])).
% 18.34/2.84 fof(f430,plain,(
% 18.34/2.84 spl0_42 <=> empty(sk0_2)),
% 18.34/2.84 introduced(split_symbol_definition)).
% 18.34/2.84 fof(f435,plain,(
% 18.34/2.84 spl0_43 <=> relation(sk0_2)),
% 18.34/2.84 introduced(split_symbol_definition)).
% 18.34/2.84 fof(f438,plain,(
% 18.34/2.84 ~empty(relation_composition(identity_relation(sk0_2),function_inverse(identity_relation(sk0_2))))|relation(sk0_2)),
% 18.34/2.84 inference(paramodulation,[status(thm)],[f380,f87])).
% 18.34/2.84 fof(f439,plain,(
% 18.34/2.84 ~spl0_40|spl0_43),
% 18.34/2.84 inference(split_clause,[status(thm)],[f438,f424,f435])).
% 18.34/2.84 fof(f440,plain,(
% 18.34/2.84 ~empty(relation_composition(identity_relation(sk0_2),function_inverse(identity_relation(sk0_2))))|empty(sk0_2)),
% 18.34/2.84 inference(paramodulation,[status(thm)],[f380,f86])).
% 18.34/2.84 fof(f441,plain,(
% 18.34/2.84 ~spl0_40|spl0_42),
% 18.34/2.84 inference(split_clause,[status(thm)],[f440,f424,f430])).
% 18.34/2.84 fof(f442,plain,(
% 18.34/2.84 spl0_44 <=> empty(relation_composition(identity_relation(empty_set),function_inverse(identity_relation(empty_set))))),
% 18.34/2.84 introduced(split_symbol_definition)).
% 18.34/2.84 fof(f445,plain,(
% 18.34/2.84 spl0_45 <=> relation(relation_composition(identity_relation(empty_set),function_inverse(identity_relation(empty_set))))),
% 18.34/2.84 introduced(split_symbol_definition)).
% 18.34/2.84 fof(f447,plain,(
% 18.34/2.84 ~relation(relation_composition(identity_relation(empty_set),function_inverse(identity_relation(empty_set))))|spl0_45),
% 18.34/2.84 inference(component_clause,[status(thm)],[f445])).
% 18.34/2.84 fof(f448,plain,(
% 18.34/2.84 spl0_46 <=> empty(empty_set)),
% 18.34/2.84 introduced(split_symbol_definition)).
% 18.34/2.84 fof(f451,plain,(
% 18.34/2.84 empty(relation_composition(identity_relation(empty_set),function_inverse(identity_relation(empty_set))))|~relation(relation_composition(identity_relation(empty_set),function_inverse(identity_relation(empty_set))))|~empty(empty_set)),
% 18.34/2.84 inference(paramodulation,[status(thm)],[f381,f82])).
% 18.34/2.84 fof(f452,plain,(
% 18.34/2.84 spl0_44|~spl0_45|~spl0_46),
% 18.34/2.84 inference(split_clause,[status(thm)],[f451,f442,f445,f448])).
% 18.34/2.84 fof(f453,plain,(
% 18.34/2.84 spl0_47 <=> relation(empty_set)),
% 18.34/2.84 introduced(split_symbol_definition)).
% 18.34/2.84 fof(f455,plain,(
% 18.34/2.84 ~relation(empty_set)|spl0_47),
% 18.34/2.84 inference(component_clause,[status(thm)],[f453])).
% 18.34/2.84 fof(f513,plain,(
% 18.34/2.84 spl0_48 <=> relation_dom(relation_composition(function_inverse(sk0_12),sk0_12))=relation_rng(sk0_12)),
% 18.34/2.84 introduced(split_symbol_definition)).
% 18.34/2.84 fof(f514,plain,(
% 18.34/2.84 relation_dom(relation_composition(function_inverse(sk0_12),sk0_12))=relation_rng(sk0_12)|~spl0_48),
% 18.34/2.84 inference(component_clause,[status(thm)],[f513])).
% 18.34/2.84 fof(f516,plain,(
% 18.34/2.84 ~relation(sk0_12)|~function(sk0_12)|relation_dom(relation_composition(function_inverse(sk0_12),sk0_12))=relation_rng(sk0_12)),
% 18.34/2.84 inference(resolution,[status(thm)],[f158,f167])).
% 18.34/2.84 fof(f517,plain,(
% 18.34/2.84 ~spl0_2|~spl0_3|spl0_48),
% 18.34/2.84 inference(split_clause,[status(thm)],[f516,f198,f201,f513])).
% 18.34/2.84 fof(f518,plain,(
% 18.34/2.84 ![X0]: (~relation(X0)|~function(X0)|relation_dom(relation_composition(function_inverse(X0),X0))=relation_rng(X0)|~empty(X0))),
% 18.34/2.84 inference(resolution,[status(thm)],[f158,f189])).
% 18.34/2.84 fof(f519,plain,(
% 18.34/2.84 ![X0]: (~function(X0)|relation_dom(relation_composition(function_inverse(X0),X0))=relation_rng(X0)|~empty(X0))),
% 18.34/2.84 inference(forward_subsumption_resolution,[status(thm)],[f518,f52])).
% 18.34/2.84 fof(f520,plain,(
% 18.34/2.84 spl0_49 <=> relation_rng(relation_composition(function_inverse(sk0_12),sk0_12))=relation_rng(sk0_12)),
% 18.34/2.84 introduced(split_symbol_definition)).
% 18.34/2.84 fof(f523,plain,(
% 18.34/2.84 ~relation(sk0_12)|~function(sk0_12)|relation_rng(relation_composition(function_inverse(sk0_12),sk0_12))=relation_rng(sk0_12)),
% 18.34/2.84 inference(resolution,[status(thm)],[f159,f167])).
% 18.34/2.84 fof(f524,plain,(
% 18.34/2.84 ~spl0_2|~spl0_3|spl0_49),
% 18.34/2.84 inference(split_clause,[status(thm)],[f523,f198,f201,f520])).
% 18.34/2.84 fof(f527,plain,(
% 18.34/2.84 spl0_50 <=> relation(sk0_9)),
% 18.34/2.84 introduced(split_symbol_definition)).
% 18.34/2.84 fof(f529,plain,(
% 18.34/2.84 ~relation(sk0_9)|spl0_50),
% 18.34/2.84 inference(component_clause,[status(thm)],[f527])).
% 18.34/2.84 fof(f530,plain,(
% 18.34/2.84 spl0_51 <=> function(sk0_9)),
% 18.34/2.84 introduced(split_symbol_definition)).
% 18.34/2.84 fof(f532,plain,(
% 18.34/2.84 ~function(sk0_9)|spl0_51),
% 18.34/2.84 inference(component_clause,[status(thm)],[f530])).
% 18.34/2.84 fof(f533,plain,(
% 18.34/2.84 spl0_52 <=> relation_rng(relation_composition(function_inverse(sk0_9),sk0_9))=relation_rng(sk0_9)),
% 18.34/2.84 introduced(split_symbol_definition)).
% 18.34/2.84 fof(f536,plain,(
% 18.34/2.84 ~relation(sk0_9)|~function(sk0_9)|relation_rng(relation_composition(function_inverse(sk0_9),sk0_9))=relation_rng(sk0_9)),
% 18.34/2.84 inference(resolution,[status(thm)],[f121,f159])).
% 18.34/2.84 fof(f537,plain,(
% 18.34/2.84 ~spl0_50|~spl0_51|spl0_52),
% 18.34/2.84 inference(split_clause,[status(thm)],[f536,f527,f530,f533])).
% 18.34/2.84 fof(f538,plain,(
% 18.34/2.84 spl0_53 <=> relation_dom(relation_composition(function_inverse(sk0_9),sk0_9))=relation_rng(sk0_9)),
% 18.34/2.84 introduced(split_symbol_definition)).
% 18.34/2.84 fof(f541,plain,(
% 18.34/2.84 ~relation(sk0_9)|~function(sk0_9)|relation_dom(relation_composition(function_inverse(sk0_9),sk0_9))=relation_rng(sk0_9)),
% 18.34/2.84 inference(resolution,[status(thm)],[f121,f158])).
% 18.34/2.84 fof(f542,plain,(
% 18.34/2.84 ~spl0_50|~spl0_51|spl0_53),
% 18.34/2.84 inference(split_clause,[status(thm)],[f541,f527,f530,f538])).
% 18.34/2.84 fof(f543,plain,(
% 18.34/2.84 spl0_54 <=> relation_rng(relation_composition(sk0_9,function_inverse(sk0_9)))=relation_dom(sk0_9)),
% 18.34/2.84 introduced(split_symbol_definition)).
% 18.34/2.84 fof(f546,plain,(
% 18.34/2.84 ~relation(sk0_9)|~function(sk0_9)|relation_rng(relation_composition(sk0_9,function_inverse(sk0_9)))=relation_dom(sk0_9)),
% 18.34/2.84 inference(resolution,[status(thm)],[f121,f156])).
% 18.34/2.84 fof(f547,plain,(
% 18.34/2.84 ~spl0_50|~spl0_51|spl0_54),
% 18.34/2.84 inference(split_clause,[status(thm)],[f546,f527,f530,f543])).
% 18.34/2.84 fof(f548,plain,(
% 18.34/2.84 spl0_55 <=> relation_dom(relation_composition(sk0_9,function_inverse(sk0_9)))=relation_dom(sk0_9)),
% 18.34/2.84 introduced(split_symbol_definition)).
% 18.34/2.84 fof(f551,plain,(
% 18.34/2.84 ~relation(sk0_9)|~function(sk0_9)|relation_dom(relation_composition(sk0_9,function_inverse(sk0_9)))=relation_dom(sk0_9)),
% 18.34/2.84 inference(resolution,[status(thm)],[f121,f155])).
% 18.34/2.84 fof(f552,plain,(
% 18.34/2.84 ~spl0_50|~spl0_51|spl0_55),
% 18.34/2.84 inference(split_clause,[status(thm)],[f551,f527,f530,f548])).
% 18.34/2.84 fof(f553,plain,(
% 18.34/2.84 $false|spl0_51),
% 18.34/2.84 inference(forward_subsumption_resolution,[status(thm)],[f532,f120])).
% 18.34/2.84 fof(f554,plain,(
% 18.34/2.84 spl0_51),
% 18.34/2.84 inference(contradiction_clause,[status(thm)],[f553])).
% 18.34/2.84 fof(f555,plain,(
% 18.34/2.84 $false|spl0_50),
% 18.34/2.84 inference(forward_subsumption_resolution,[status(thm)],[f529,f119])).
% 18.34/2.84 fof(f556,plain,(
% 18.34/2.84 spl0_50),
% 18.34/2.84 inference(contradiction_clause,[status(thm)],[f555])).
% 18.34/2.84 fof(f561,plain,(
% 18.34/2.84 ![X0]: (sk0_7(X0)=empty_set)),
% 18.34/2.84 inference(resolution,[status(thm)],[f170,f115])).
% 18.34/2.84 fof(f562,plain,(
% 18.34/2.84 ![X0]: (identity_relation(X0)=empty_set|~empty(X0))),
% 18.34/2.84 inference(resolution,[status(thm)],[f170,f194])).
% 18.34/2.84 fof(f563,plain,(
% 18.34/2.84 sk0_5=empty_set),
% 18.34/2.84 inference(resolution,[status(thm)],[f170,f108])).
% 18.34/2.84 fof(f564,plain,(
% 18.34/2.84 sk0_4=empty_set),
% 18.34/2.84 inference(resolution,[status(thm)],[f170,f105])).
% 18.34/2.84 fof(f565,plain,(
% 18.34/2.84 sk0_2=empty_set),
% 18.34/2.84 inference(resolution,[status(thm)],[f170,f98])).
% 18.34/2.84 fof(f566,plain,(
% 18.34/2.84 relation_composition(sk0_5,function_inverse(sk0_5))=empty_set|~spl0_12),
% 18.34/2.84 inference(resolution,[status(thm)],[f170,f273])).
% 18.34/2.84 fof(f567,plain,(
% 18.34/2.84 ![X0,X1]: (relation_composition(X0,X1)=empty_set|~empty(X0)|~relation(X1))),
% 18.34/2.84 inference(resolution,[status(thm)],[f170,f92])).
% 18.34/2.84 fof(f568,plain,(
% 18.34/2.84 ![X0,X1]: (relation_composition(X0,X1)=empty_set|~empty(X1)|~relation(X0))),
% 18.34/2.84 inference(resolution,[status(thm)],[f170,f66])).
% 18.34/2.84 fof(f569,plain,(
% 18.34/2.84 ![X0]: (relation_rng(X0)=empty_set|~empty(X0))),
% 18.34/2.84 inference(resolution,[status(thm)],[f170,f89])).
% 18.34/2.84 fof(f570,plain,(
% 18.34/2.84 ![X0]: (relation_dom(X0)=empty_set|~empty(X0))),
% 18.34/2.84 inference(resolution,[status(thm)],[f170,f86])).
% 18.34/2.84 fof(f588,plain,(
% 18.34/2.84 function(empty_set)),
% 18.34/2.84 inference(backward_demodulation,[status(thm)],[f563,f109])).
% 18.34/2.84 fof(f618,plain,(
% 18.34/2.84 spl0_56 <=> empty(relation_composition(function_inverse(sk0_12),sk0_12))),
% 18.34/2.84 introduced(split_symbol_definition)).
% 18.34/2.84 fof(f620,plain,(
% 18.34/2.84 ~empty(relation_composition(function_inverse(sk0_12),sk0_12))|spl0_56),
% 18.34/2.84 inference(component_clause,[status(thm)],[f618])).
% 18.34/2.84 fof(f621,plain,(
% 18.34/2.84 spl0_57 <=> relation(relation_composition(function_inverse(sk0_12),sk0_12))),
% 18.34/2.84 introduced(split_symbol_definition)).
% 18.34/2.84 fof(f623,plain,(
% 18.34/2.84 ~relation(relation_composition(function_inverse(sk0_12),sk0_12))|spl0_57),
% 18.34/2.84 inference(component_clause,[status(thm)],[f621])).
% 18.34/2.84 fof(f624,plain,(
% 18.34/2.84 spl0_58 <=> empty(relation_rng(sk0_12))),
% 18.34/2.84 introduced(split_symbol_definition)).
% 18.34/2.84 fof(f625,plain,(
% 18.34/2.84 empty(relation_rng(sk0_12))|~spl0_58),
% 18.34/2.84 inference(component_clause,[status(thm)],[f624])).
% 18.34/2.84 fof(f626,plain,(
% 18.34/2.84 ~empty(relation_rng(sk0_12))|spl0_58),
% 18.34/2.84 inference(component_clause,[status(thm)],[f624])).
% 18.34/2.84 fof(f634,plain,(
% 18.34/2.84 ~empty(relation_composition(function_inverse(sk0_12),sk0_12))|empty(relation_rng(sk0_12))|~spl0_48),
% 18.34/2.84 inference(paramodulation,[status(thm)],[f514,f86])).
% 18.34/2.84 fof(f635,plain,(
% 18.34/2.84 ~spl0_56|spl0_58|~spl0_48),
% 18.34/2.84 inference(split_clause,[status(thm)],[f634,f618,f624,f513])).
% 18.34/2.84 fof(f640,plain,(
% 18.34/2.84 ~relation(function_inverse(sk0_12))|~relation(sk0_12)|spl0_57),
% 18.34/2.84 inference(resolution,[status(thm)],[f623,f61])).
% 18.34/2.84 fof(f641,plain,(
% 18.34/2.84 ~spl0_10|~spl0_2|spl0_57),
% 18.34/2.84 inference(split_clause,[status(thm)],[f640,f236,f198,f621])).
% 18.34/2.84 fof(f643,plain,(
% 18.34/2.84 empty(sk0_12)|~relation(sk0_12)|~spl0_58),
% 18.34/2.84 inference(resolution,[status(thm)],[f625,f84])).
% 18.34/2.84 fof(f644,plain,(
% 18.34/2.84 spl0_9|~spl0_2|~spl0_58),
% 18.34/2.84 inference(split_clause,[status(thm)],[f643,f233,f198,f624])).
% 18.34/2.84 fof(f657,plain,(
% 18.34/2.84 relation(function_inverse(empty_set))|~spl0_17),
% 18.34/2.84 inference(forward_demodulation,[status(thm)],[f563,f294])).
% 18.34/2.84 fof(f677,plain,(
% 18.34/2.84 $false|spl0_47),
% 18.34/2.84 inference(forward_subsumption_resolution,[status(thm)],[f455,f69])).
% 18.34/2.84 fof(f678,plain,(
% 18.34/2.84 spl0_47),
% 18.34/2.84 inference(contradiction_clause,[status(thm)],[f677])).
% 18.34/2.84 fof(f679,plain,(
% 18.34/2.84 ~relation(relation_composition(empty_set,function_inverse(sk0_4)))|spl0_22),
% 18.34/2.84 inference(forward_demodulation,[status(thm)],[f564,f328])).
% 18.34/2.84 fof(f680,plain,(
% 18.34/2.84 ~relation(relation_composition(empty_set,function_inverse(empty_set)))|spl0_22),
% 18.34/2.84 inference(forward_demodulation,[status(thm)],[f564,f679])).
% 18.34/2.84 fof(f681,plain,(
% 18.34/2.84 spl0_60 <=> relation(function_inverse(empty_set))),
% 18.34/2.84 introduced(split_symbol_definition)).
% 18.34/2.84 fof(f683,plain,(
% 18.34/2.84 ~relation(function_inverse(empty_set))|spl0_60),
% 18.34/2.84 inference(component_clause,[status(thm)],[f681])).
% 18.34/2.84 fof(f684,plain,(
% 18.34/2.84 ~empty(empty_set)|~relation(function_inverse(empty_set))|spl0_22),
% 18.34/2.84 inference(resolution,[status(thm)],[f680,f93])).
% 18.34/2.84 fof(f685,plain,(
% 18.34/2.84 ~spl0_46|~spl0_60|spl0_22),
% 18.34/2.84 inference(split_clause,[status(thm)],[f684,f448,f681,f326])).
% 18.34/2.84 fof(f694,plain,(
% 18.34/2.84 $false|~spl0_17|spl0_60),
% 18.34/2.84 inference(forward_subsumption_resolution,[status(thm)],[f683,f657])).
% 18.34/2.84 fof(f695,plain,(
% 18.34/2.84 ~spl0_17|spl0_60),
% 18.34/2.84 inference(contradiction_clause,[status(thm)],[f694])).
% 18.34/2.84 fof(f707,plain,(
% 18.34/2.84 spl0_63 <=> relation(relation_composition(function_inverse(sk0_9),sk0_9))),
% 18.34/2.84 introduced(split_symbol_definition)).
% 18.34/2.84 fof(f709,plain,(
% 18.34/2.84 ~relation(relation_composition(function_inverse(sk0_9),sk0_9))|spl0_63),
% 18.34/2.84 inference(component_clause,[status(thm)],[f707])).
% 18.34/2.84 fof(f728,plain,(
% 18.34/2.84 ~relation(relation_composition(empty_set,function_inverse(sk0_2)))|spl0_26),
% 18.34/2.84 inference(forward_demodulation,[status(thm)],[f565,f346])).
% 18.34/2.84 fof(f729,plain,(
% 18.34/2.84 ~relation(relation_composition(empty_set,function_inverse(empty_set)))|spl0_26),
% 18.34/2.84 inference(forward_demodulation,[status(thm)],[f565,f728])).
% 18.34/2.84 fof(f730,plain,(
% 18.34/2.84 ~empty(empty_set)|~relation(function_inverse(empty_set))|spl0_26),
% 18.34/2.84 inference(resolution,[status(thm)],[f729,f93])).
% 18.34/2.84 fof(f731,plain,(
% 18.34/2.84 ~spl0_46|~spl0_60|spl0_26),
% 18.34/2.84 inference(split_clause,[status(thm)],[f730,f448,f681,f344])).
% 18.34/2.84 fof(f745,plain,(
% 18.34/2.84 ~empty(empty_set)|~relation(function_inverse(empty_set))|spl0_30),
% 18.34/2.84 inference(resolution,[status(thm)],[f364,f93])).
% 18.34/2.84 fof(f746,plain,(
% 18.34/2.84 ~spl0_46|~spl0_60|spl0_30),
% 18.34/2.84 inference(split_clause,[status(thm)],[f745,f448,f681,f362])).
% 18.34/2.84 fof(f754,plain,(
% 18.34/2.84 relation_composition(empty_set,function_inverse(sk0_5))=empty_set|~spl0_12),
% 18.34/2.84 inference(forward_demodulation,[status(thm)],[f563,f566])).
% 18.34/2.84 fof(f755,plain,(
% 18.34/2.84 relation_composition(empty_set,function_inverse(empty_set))=empty_set|~spl0_12),
% 18.34/2.84 inference(forward_demodulation,[status(thm)],[f563,f754])).
% 18.34/2.84 fof(f756,plain,(
% 18.34/2.84 spl0_66 <=> function(empty_set)),
% 18.34/2.84 introduced(split_symbol_definition)).
% 18.34/2.84 fof(f758,plain,(
% 18.34/2.84 ~function(empty_set)|spl0_66),
% 18.34/2.84 inference(component_clause,[status(thm)],[f756])).
% 18.34/2.84 fof(f774,plain,(
% 18.34/2.84 ~empty(relation_dom(empty_set))|spl0_14),
% 18.34/2.84 inference(forward_demodulation,[status(thm)],[f563,f280])).
% 18.34/2.84 fof(f777,plain,(
% 18.34/2.84 empty(empty_set)|~relation(empty_set)|~spl0_31),
% 18.34/2.84 inference(resolution,[status(thm)],[f366,f82])).
% 18.34/2.84 fof(f778,plain,(
% 18.34/2.84 spl0_46|~spl0_47|~spl0_31),
% 18.34/2.84 inference(split_clause,[status(thm)],[f777,f448,f453,f365])).
% 18.34/2.84 fof(f779,plain,(
% 18.34/2.84 relation_dom(empty_set)=empty_set|~spl0_31),
% 18.34/2.84 inference(resolution,[status(thm)],[f366,f170])).
% 18.34/2.84 fof(f784,plain,(
% 18.34/2.84 $false|~spl0_31|spl0_14),
% 18.34/2.84 inference(forward_subsumption_resolution,[status(thm)],[f774,f366])).
% 18.34/2.84 fof(f785,plain,(
% 18.34/2.84 ~spl0_31|spl0_14),
% 18.34/2.84 inference(contradiction_clause,[status(thm)],[f784])).
% 18.34/2.84 fof(f818,plain,(
% 18.34/2.84 ~empty(sk0_12)|~relation(function_inverse(sk0_12))|spl0_56),
% 18.34/2.84 inference(resolution,[status(thm)],[f620,f66])).
% 18.34/2.84 fof(f819,plain,(
% 18.34/2.84 ~spl0_9|~spl0_10|spl0_56),
% 18.34/2.84 inference(split_clause,[status(thm)],[f818,f233,f236,f618])).
% 18.34/2.84 fof(f823,plain,(
% 18.34/2.84 spl0_69 <=> relation(relation_composition(sk0_9,function_inverse(sk0_9)))),
% 18.34/2.84 introduced(split_symbol_definition)).
% 18.34/2.84 fof(f825,plain,(
% 18.34/2.84 ~relation(relation_composition(sk0_9,function_inverse(sk0_9)))|spl0_69),
% 18.34/2.84 inference(component_clause,[status(thm)],[f823])).
% 18.34/2.84 fof(f848,plain,(
% 18.34/2.84 ![X0]: (identity_relation(sk0_7(X0))=empty_set)),
% 18.34/2.84 inference(resolution,[status(thm)],[f562,f115])).
% 18.34/2.84 fof(f850,plain,(
% 18.34/2.84 identity_relation(empty_set)=empty_set),
% 18.34/2.84 inference(resolution,[status(thm)],[f562,f68])).
% 18.34/2.84 fof(f854,plain,(
% 18.34/2.84 ![X0]: (identity_relation(relation_dom(X0))=empty_set|~empty(X0))),
% 18.34/2.84 inference(resolution,[status(thm)],[f562,f86])).
% 18.34/2.84 fof(f866,plain,(
% 18.34/2.84 spl0_72 <=> empty(sk0_7(X0))),
% 18.34/2.84 introduced(split_symbol_definition)).
% 18.34/2.84 fof(f869,plain,(
% 18.34/2.84 ![X0]: (~empty(empty_set)|empty(sk0_7(X0)))),
% 18.34/2.84 inference(paramodulation,[status(thm)],[f848,f196])).
% 18.34/2.84 fof(f870,plain,(
% 18.34/2.84 ~spl0_46|spl0_72),
% 18.34/2.84 inference(split_clause,[status(thm)],[f869,f448,f866])).
% 18.34/2.84 fof(f871,plain,(
% 18.34/2.84 spl0_73 <=> relation(sk0_7(X0))),
% 18.34/2.84 introduced(split_symbol_definition)).
% 18.34/2.84 fof(f874,plain,(
% 18.34/2.84 ![X0]: (~empty(empty_set)|relation(sk0_7(X0)))),
% 18.34/2.84 inference(paramodulation,[status(thm)],[f848,f195])).
% 18.34/2.84 fof(f875,plain,(
% 18.34/2.84 ~spl0_46|spl0_73),
% 18.34/2.84 inference(split_clause,[status(thm)],[f874,f448,f871])).
% 18.34/2.84 fof(f876,plain,(
% 18.34/2.84 spl0_74 <=> ~empty(sk0_7(X0))),
% 18.34/2.84 introduced(split_symbol_definition)).
% 18.34/2.84 fof(f877,plain,(
% 18.34/2.84 ![X0]: (~empty(sk0_7(X0))|~spl0_74)),
% 18.34/2.84 inference(component_clause,[status(thm)],[f876])).
% 18.34/2.84 fof(f885,plain,(
% 18.34/2.84 ![X0]: (relation_rng(sk0_7(X0))=empty_set)),
% 18.34/2.84 inference(resolution,[status(thm)],[f569,f115])).
% 18.34/2.84 fof(f887,plain,(
% 18.34/2.84 relation_rng(empty_set)=empty_set),
% 18.34/2.84 inference(resolution,[status(thm)],[f569,f68])).
% 18.34/2.84 fof(f898,plain,(
% 18.34/2.84 ![X0]: (relation_dom(relation_composition(function_inverse(X0),X0))=relation_rng(X0)|~empty(X0))),
% 18.34/2.84 inference(forward_subsumption_resolution,[status(thm)],[f519,f50])).
% 18.34/2.84 fof(f901,plain,(
% 18.34/2.84 relation_dom(relation_composition(function_inverse(empty_set),empty_set))=relation_rng(empty_set)),
% 18.34/2.84 inference(resolution,[status(thm)],[f898,f68])).
% 18.81/2.85 fof(f902,plain,(
% 18.81/2.85 relation_dom(relation_composition(function_inverse(empty_set),empty_set))=empty_set),
% 18.81/2.85 inference(forward_demodulation,[status(thm)],[f887,f901])).
% 18.81/2.85 fof(f907,plain,(
% 18.81/2.85 spl0_75 <=> empty(sk0_7(X0))|~relation(sk0_7(X0))),
% 18.81/2.85 introduced(split_symbol_definition)).
% 18.81/2.85 fof(f910,plain,(
% 18.81/2.85 ![X0]: (empty(sk0_7(X0))|~relation(sk0_7(X0))|~empty(empty_set))),
% 18.81/2.85 inference(paramodulation,[status(thm)],[f885,f84])).
% 18.81/2.85 fof(f911,plain,(
% 18.81/2.85 spl0_75|~spl0_46),
% 18.81/2.85 inference(split_clause,[status(thm)],[f910,f907,f448])).
% 18.81/2.85 fof(f922,plain,(
% 18.81/2.85 ![X0]: (relation_dom(relation_rng(X0))=empty_set|~empty(X0))),
% 18.81/2.85 inference(resolution,[status(thm)],[f570,f89])).
% 18.81/2.85 fof(f1007,plain,(
% 18.81/2.85 ![X0]: (relation_composition(empty_set,X0)=empty_set|~relation(X0))),
% 18.81/2.85 inference(resolution,[status(thm)],[f567,f68])).
% 18.81/2.85 fof(f1015,plain,(
% 18.81/2.85 ![X0]: (element(empty_set,powerset(X0)))),
% 18.81/2.85 inference(backward_demodulation,[status(thm)],[f561,f114])).
% 18.81/2.85 fof(f1026,plain,(
% 18.81/2.85 ![X0,X1]: (subset(X0,X1)|~in(X0,powerset(X1)))),
% 18.81/2.85 inference(resolution,[status(thm)],[f141,f128])).
% 18.81/2.85 fof(f1038,plain,(
% 18.81/2.85 relation_composition(empty_set,sk0_1)=empty_set),
% 18.81/2.85 inference(resolution,[status(thm)],[f1007,f95])).
% 18.81/2.85 fof(f1045,plain,(
% 18.81/2.85 ![X0,X1]: (relation_composition(empty_set,relation_composition(X0,X1))=empty_set|~relation(X0)|~relation(X1))),
% 18.81/2.85 inference(resolution,[status(thm)],[f1007,f61])).
% 18.81/2.85 fof(f1047,plain,(
% 18.81/2.85 relation_composition(empty_set,function_inverse(sk0_12))=empty_set|~spl0_10),
% 18.81/2.85 inference(resolution,[status(thm)],[f1007,f237])).
% 18.81/2.85 fof(f1048,plain,(
% 18.81/2.85 ![X0]: (relation_composition(empty_set,function_inverse(X0))=empty_set|~relation(X0)|~function(X0))),
% 18.81/2.85 inference(resolution,[status(thm)],[f1007,f58])).
% 18.81/2.85 fof(f1052,plain,(
% 18.81/2.85 relation_composition(empty_set,sk0_12)=empty_set),
% 18.81/2.85 inference(resolution,[status(thm)],[f1007,f165])).
% 18.81/2.85 fof(f1054,plain,(
% 18.81/2.85 spl0_76 <=> relation(sk0_10)),
% 18.81/2.85 introduced(split_symbol_definition)).
% 18.81/2.85 fof(f1056,plain,(
% 18.81/2.85 ~relation(sk0_10)|spl0_76),
% 18.81/2.85 inference(component_clause,[status(thm)],[f1054])).
% 18.81/2.85 fof(f1090,plain,(
% 18.81/2.85 spl0_80 <=> relation(sk0_6)),
% 18.81/2.85 introduced(split_symbol_definition)).
% 18.81/2.85 fof(f1092,plain,(
% 18.81/2.85 ~relation(sk0_6)|spl0_80),
% 18.81/2.85 inference(component_clause,[status(thm)],[f1090])).
% 18.81/2.85 fof(f1115,plain,(
% 18.81/2.85 ![X0]: (empty(X0)|in(sk0_0(X0),X0))),
% 18.81/2.85 inference(resolution,[status(thm)],[f130,f64])).
% 18.81/2.85 fof(f1118,plain,(
% 18.81/2.85 ![X0,X1]: (~function(identity_relation(X0))|~in(X1,X0)|apply(identity_relation(X0),X1)=X1)),
% 18.81/2.85 inference(forward_subsumption_resolution,[status(thm)],[f185,f62])).
% 18.81/2.85 fof(f1119,plain,(
% 18.81/2.85 spl0_83 <=> empty_set=identity_relation(relation_dom(empty_set))),
% 18.81/2.85 introduced(split_symbol_definition)).
% 18.81/2.85 fof(f1122,plain,(
% 18.81/2.85 spl0_84 <=> in(sk0_11(relation_dom(empty_set),empty_set),relation_dom(empty_set))),
% 18.81/2.85 introduced(split_symbol_definition)).
% 18.81/2.85 fof(f1123,plain,(
% 18.81/2.85 in(sk0_11(relation_dom(empty_set),empty_set),relation_dom(empty_set))|~spl0_84),
% 18.81/2.85 inference(component_clause,[status(thm)],[f1122])).
% 18.81/2.85 fof(f1135,plain,(
% 18.81/2.85 ![X0,X1]: (~relation(relation_composition(X0,X1))|relation_composition(X0,X1)=identity_relation(relation_dom(relation_composition(X0,X1)))|in(sk0_11(relation_dom(relation_composition(X0,X1)),relation_composition(X0,X1)),relation_dom(relation_composition(X0,X1)))|~relation(X0)|~function(X0)|~relation(X1)|~function(X1))),
% 18.81/2.85 inference(resolution,[status(thm)],[f186,f73])).
% 18.81/2.85 fof(f1136,plain,(
% 18.81/2.85 ![X0,X1]: (relation_composition(X0,X1)=identity_relation(relation_dom(relation_composition(X0,X1)))|in(sk0_11(relation_dom(relation_composition(X0,X1)),relation_composition(X0,X1)),relation_dom(relation_composition(X0,X1)))|~relation(X0)|~function(X0)|~relation(X1)|~function(X1))),
% 18.81/2.85 inference(forward_subsumption_resolution,[status(thm)],[f1135,f61])).
% 18.81/2.85 fof(f1137,plain,(
% 18.81/2.85 spl0_87 <=> relation(sk0_1)),
% 18.81/2.85 introduced(split_symbol_definition)).
% 18.81/2.85 fof(f1139,plain,(
% 18.81/2.85 ~relation(sk0_1)|spl0_87),
% 18.81/2.85 inference(component_clause,[status(thm)],[f1137])).
% 18.81/2.85 fof(f1151,plain,(
% 18.81/2.85 spl0_90 <=> sk0_12=identity_relation(relation_dom(sk0_12))),
% 18.81/2.85 introduced(split_symbol_definition)).
% 18.81/2.85 fof(f1152,plain,(
% 18.81/2.85 sk0_12=identity_relation(relation_dom(sk0_12))|~spl0_90),
% 18.81/2.85 inference(component_clause,[status(thm)],[f1151])).
% 18.81/2.85 fof(f1154,plain,(
% 18.81/2.85 spl0_91 <=> in(sk0_11(relation_dom(sk0_12),sk0_12),relation_dom(sk0_12))),
% 18.81/2.85 introduced(split_symbol_definition)).
% 18.81/2.85 fof(f1155,plain,(
% 18.81/2.85 in(sk0_11(relation_dom(sk0_12),sk0_12),relation_dom(sk0_12))|~spl0_91),
% 18.81/2.85 inference(component_clause,[status(thm)],[f1154])).
% 18.81/2.85 fof(f1157,plain,(
% 18.81/2.85 ~relation(sk0_12)|sk0_12=identity_relation(relation_dom(sk0_12))|in(sk0_11(relation_dom(sk0_12),sk0_12),relation_dom(sk0_12))),
% 18.81/2.85 inference(resolution,[status(thm)],[f186,f166])).
% 18.81/2.85 fof(f1158,plain,(
% 18.81/2.85 ~spl0_2|spl0_90|spl0_91),
% 18.81/2.85 inference(split_clause,[status(thm)],[f1157,f198,f1151,f1154])).
% 18.81/2.85 fof(f1159,plain,(
% 18.81/2.85 ![X0]: (~relation(X0)|X0=identity_relation(relation_dom(X0))|in(sk0_11(relation_dom(X0),X0),relation_dom(X0))|~empty(X0))),
% 18.81/2.85 inference(resolution,[status(thm)],[f186,f50])).
% 18.81/2.85 fof(f1160,plain,(
% 18.81/2.85 ![X0]: (X0=identity_relation(relation_dom(X0))|in(sk0_11(relation_dom(X0),X0),relation_dom(X0))|~empty(X0))),
% 18.81/2.85 inference(forward_subsumption_resolution,[status(thm)],[f1159,f52])).
% 18.81/2.85 fof(f1161,plain,(
% 18.81/2.85 $false|spl0_87),
% 18.81/2.85 inference(forward_subsumption_resolution,[status(thm)],[f1139,f95])).
% 18.81/2.85 fof(f1162,plain,(
% 18.81/2.85 spl0_87),
% 18.81/2.85 inference(contradiction_clause,[status(thm)],[f1161])).
% 18.81/2.85 fof(f1173,plain,(
% 18.81/2.85 spl0_92 <=> function(function_inverse(sk0_12))),
% 18.81/2.85 introduced(split_symbol_definition)).
% 18.81/2.85 fof(f1174,plain,(
% 18.81/2.85 function(function_inverse(sk0_12))|~spl0_92),
% 18.81/2.85 inference(component_clause,[status(thm)],[f1173])).
% 18.81/2.85 fof(f1175,plain,(
% 18.81/2.85 ~function(function_inverse(sk0_12))|spl0_92),
% 18.81/2.85 inference(component_clause,[status(thm)],[f1173])).
% 18.81/2.85 fof(f1188,plain,(
% 18.81/2.85 spl0_93 <=> function(relation_composition(function_inverse(sk0_12),sk0_12))),
% 18.81/2.85 introduced(split_symbol_definition)).
% 18.81/2.85 fof(f1189,plain,(
% 18.81/2.85 function(relation_composition(function_inverse(sk0_12),sk0_12))|~spl0_93),
% 18.81/2.85 inference(component_clause,[status(thm)],[f1188])).
% 18.81/2.85 fof(f1190,plain,(
% 18.81/2.85 ~function(relation_composition(function_inverse(sk0_12),sk0_12))|spl0_93),
% 18.81/2.85 inference(component_clause,[status(thm)],[f1188])).
% 18.81/2.85 fof(f1211,plain,(
% 18.81/2.85 identity_relation(relation_dom(sk0_12))=empty_set|~spl0_9),
% 18.81/2.85 inference(resolution,[status(thm)],[f234,f854])).
% 18.81/2.85 fof(f1212,plain,(
% 18.81/2.85 sk0_12=empty_set|~spl0_90|~spl0_9),
% 18.81/2.85 inference(forward_demodulation,[status(thm)],[f1152,f1211])).
% 18.81/2.85 fof(f1219,plain,(
% 18.81/2.85 sk0_12=empty_set|~spl0_9),
% 18.81/2.85 inference(resolution,[status(thm)],[f234,f170])).
% 18.81/2.85 fof(f1233,plain,(
% 18.81/2.85 relation_composition(empty_set,function_inverse(empty_set))=empty_set|~spl0_90|~spl0_9|~spl0_10),
% 18.81/2.85 inference(backward_demodulation,[status(thm)],[f1212,f1047])).
% 18.81/2.85 fof(f1279,plain,(
% 18.81/2.85 $false|spl0_66),
% 18.81/2.85 inference(forward_subsumption_resolution,[status(thm)],[f758,f588])).
% 18.81/2.85 fof(f1280,plain,(
% 18.81/2.85 spl0_66),
% 18.81/2.85 inference(contradiction_clause,[status(thm)],[f1279])).
% 18.81/2.85 fof(f1288,plain,(
% 18.81/2.85 ~relation_composition(empty_set,function_inverse(sk0_12))=identity_relation(relation_dom(sk0_12))|~spl0_9|spl0_0),
% 18.81/2.85 inference(forward_demodulation,[status(thm)],[f1219,f179])).
% 18.81/2.85 fof(f1289,plain,(
% 18.81/2.85 ~relation_composition(empty_set,function_inverse(empty_set))=identity_relation(relation_dom(sk0_12))|~spl0_9|spl0_0),
% 18.81/2.85 inference(forward_demodulation,[status(thm)],[f1219,f1288])).
% 18.81/2.85 fof(f1290,plain,(
% 18.81/2.85 ~relation_composition(empty_set,function_inverse(empty_set))=identity_relation(relation_dom(empty_set))|~spl0_9|spl0_0),
% 18.81/2.85 inference(forward_demodulation,[status(thm)],[f1219,f1289])).
% 18.81/2.85 fof(f1291,plain,(
% 18.81/2.85 ~relation_composition(empty_set,function_inverse(empty_set))=identity_relation(empty_set)|~spl0_31|~spl0_9|spl0_0),
% 18.81/2.85 inference(forward_demodulation,[status(thm)],[f779,f1290])).
% 18.81/2.85 fof(f1292,plain,(
% 18.81/2.85 ~relation_composition(empty_set,function_inverse(empty_set))=empty_set|~spl0_31|~spl0_9|spl0_0),
% 18.81/2.85 inference(forward_demodulation,[status(thm)],[f850,f1291])).
% 18.81/2.85 fof(f1293,plain,(
% 18.81/2.85 in(sk0_11(relation_dom(empty_set),sk0_12),relation_dom(sk0_12))|~spl0_9|~spl0_91),
% 18.81/2.85 inference(forward_demodulation,[status(thm)],[f1219,f1155])).
% 18.81/2.85 fof(f1294,plain,(
% 18.81/2.85 in(sk0_11(empty_set,sk0_12),relation_dom(sk0_12))|~spl0_31|~spl0_9|~spl0_91),
% 18.81/2.85 inference(forward_demodulation,[status(thm)],[f779,f1293])).
% 18.81/2.85 fof(f1295,plain,(
% 18.81/2.85 in(sk0_11(empty_set,empty_set),relation_dom(sk0_12))|~spl0_31|~spl0_9|~spl0_91),
% 18.81/2.85 inference(forward_demodulation,[status(thm)],[f1219,f1294])).
% 18.81/2.85 fof(f1296,plain,(
% 18.81/2.85 in(sk0_11(empty_set,empty_set),relation_dom(empty_set))|~spl0_31|~spl0_9|~spl0_91),
% 18.81/2.85 inference(forward_demodulation,[status(thm)],[f1219,f1295])).
% 18.81/2.85 fof(f1297,plain,(
% 18.81/2.85 in(sk0_11(empty_set,empty_set),empty_set)|~spl0_31|~spl0_9|~spl0_91),
% 18.81/2.85 inference(forward_demodulation,[status(thm)],[f779,f1296])).
% 18.81/2.85 fof(f1298,plain,(
% 18.81/2.85 spl0_98 <=> function(identity_relation(empty_set))),
% 18.81/2.85 introduced(split_symbol_definition)).
% 18.81/2.85 fof(f1300,plain,(
% 18.81/2.85 ~function(identity_relation(empty_set))|spl0_98),
% 18.81/2.85 inference(component_clause,[status(thm)],[f1298])).
% 18.81/2.85 fof(f1306,plain,(
% 18.81/2.85 ~empty(empty_set)|~spl0_31|~spl0_9|~spl0_91),
% 18.81/2.85 inference(resolution,[status(thm)],[f1297,f173])).
% 18.81/2.85 fof(f1307,plain,(
% 18.81/2.85 ~spl0_46|~spl0_31|~spl0_9|~spl0_91),
% 18.81/2.85 inference(split_clause,[status(thm)],[f1306,f448,f365,f233,f1154])).
% 18.81/2.85 fof(f1318,plain,(
% 18.81/2.85 $false|~spl0_31|spl0_0|~spl0_90|~spl0_9|~spl0_10),
% 18.81/2.85 inference(forward_subsumption_resolution,[status(thm)],[f1233,f1292])).
% 18.81/2.85 fof(f1319,plain,(
% 18.81/2.85 ~spl0_31|spl0_0|~spl0_90|~spl0_9|~spl0_10),
% 18.81/2.85 inference(contradiction_clause,[status(thm)],[f1318])).
% 18.81/2.85 fof(f1390,plain,(
% 18.81/2.85 spl0_103 <=> empty(relation_composition(function_inverse(empty_set),empty_set))),
% 18.81/2.85 introduced(split_symbol_definition)).
% 18.81/2.85 fof(f1393,plain,(
% 18.81/2.85 spl0_104 <=> relation(relation_composition(function_inverse(empty_set),empty_set))),
% 18.81/2.85 introduced(split_symbol_definition)).
% 18.81/2.85 fof(f1395,plain,(
% 18.81/2.85 ~relation(relation_composition(function_inverse(empty_set),empty_set))|spl0_104),
% 18.81/2.85 inference(component_clause,[status(thm)],[f1393])).
% 18.81/2.85 fof(f1417,plain,(
% 18.81/2.85 spl0_105 <=> function(sk0_1)),
% 18.81/2.85 introduced(split_symbol_definition)).
% 18.81/2.85 fof(f1419,plain,(
% 18.81/2.85 ~function(sk0_1)|spl0_105),
% 18.81/2.85 inference(component_clause,[status(thm)],[f1417])).
% 18.81/2.85 fof(f1433,plain,(
% 18.81/2.85 ![X0]: (relation_composition(X0,empty_set)=empty_set|~relation(X0))),
% 18.81/2.85 inference(resolution,[status(thm)],[f568,f68])).
% 18.81/2.85 fof(f1453,plain,(
% 18.81/2.85 spl0_108 <=> ~empty(identity_relation(X0))),
% 18.81/2.85 introduced(split_symbol_definition)).
% 18.81/2.85 fof(f1454,plain,(
% 18.81/2.85 ![X0]: (~empty(identity_relation(X0))|~spl0_108)),
% 18.81/2.85 inference(component_clause,[status(thm)],[f1453])).
% 18.81/2.85 fof(f1497,plain,(
% 18.81/2.85 ![X0,X1]: (relation_composition(relation_composition(X0,X1),empty_set)=empty_set|~relation(X0)|~relation(X1))),
% 18.81/2.85 inference(resolution,[status(thm)],[f1433,f61])).
% 18.81/2.85 fof(f1498,plain,(
% 18.81/2.85 relation_composition(function_inverse(empty_set),empty_set)=empty_set|~spl0_17),
% 18.81/2.85 inference(resolution,[status(thm)],[f1433,f657])).
% 18.81/2.85 fof(f1501,plain,(
% 18.81/2.85 ![X0]: (relation_composition(function_inverse(X0),empty_set)=empty_set|~relation(X0)|~function(X0))),
% 18.81/2.85 inference(resolution,[status(thm)],[f1433,f58])).
% 18.81/2.85 fof(f1619,plain,(
% 18.81/2.85 ![X0]: (empty(X0)|~function(identity_relation(X0))|apply(identity_relation(X0),sk0_0(X0))=sk0_0(X0))),
% 18.81/2.85 inference(resolution,[status(thm)],[f1115,f1118])).
% 18.81/2.85 fof(f1620,plain,(
% 18.81/2.85 ![X0]: (empty(X0)|apply(identity_relation(X0),sk0_0(X0))=sk0_0(X0))),
% 18.81/2.85 inference(forward_subsumption_resolution,[status(thm)],[f1619,f78])).
% 18.81/2.85 fof(f1621,plain,(
% 18.81/2.85 ![X0]: (empty(X0)|~in(X0,sk0_0(X0)))),
% 18.81/2.85 inference(resolution,[status(thm)],[f1115,f48])).
% 18.81/2.85 fof(f1653,plain,(
% 18.81/2.85 spl0_113 <=> function(relation_composition(function_inverse(sk0_9),sk0_9))),
% 18.81/2.85 introduced(split_symbol_definition)).
% 18.81/2.85 fof(f1654,plain,(
% 18.81/2.85 function(relation_composition(function_inverse(sk0_9),sk0_9))|~spl0_113),
% 18.81/2.85 inference(component_clause,[status(thm)],[f1653])).
% 18.81/2.85 fof(f1655,plain,(
% 18.81/2.85 ~function(relation_composition(function_inverse(sk0_9),sk0_9))|spl0_113),
% 18.81/2.85 inference(component_clause,[status(thm)],[f1653])).
% 18.81/2.85 fof(f1667,plain,(
% 18.81/2.85 ![X0,X1,X2]: (~in(X0,X1)|~element(X1,powerset(X2))|empty(X2)|in(X0,X2))),
% 18.81/2.85 inference(resolution,[status(thm)],[f145,f130])).
% 18.81/2.85 fof(f1668,plain,(
% 18.81/2.85 spl0_116 <=> ~in(X0,relation_dom(sk0_12))|X0=apply(function_inverse(sk0_12),apply(sk0_12,X0))),
% 18.81/2.85 introduced(split_symbol_definition)).
% 18.81/2.85 fof(f1669,plain,(
% 18.81/2.85 ![X0]: (~in(X0,relation_dom(sk0_12))|X0=apply(function_inverse(sk0_12),apply(sk0_12,X0))|~spl0_116)),
% 18.81/2.85 inference(component_clause,[status(thm)],[f1668])).
% 18.81/2.85 fof(f1671,plain,(
% 18.81/2.85 ![X0]: (~relation(sk0_12)|~function(sk0_12)|~in(X0,relation_dom(sk0_12))|X0=apply(function_inverse(sk0_12),apply(sk0_12,X0)))),
% 18.81/2.85 inference(resolution,[status(thm)],[f148,f167])).
% 18.81/2.85 fof(f1672,plain,(
% 18.81/2.85 ~spl0_2|~spl0_3|spl0_116),
% 18.81/2.85 inference(split_clause,[status(thm)],[f1671,f198,f201,f1668])).
% 18.81/2.85 fof(f1673,plain,(
% 18.81/2.85 spl0_117 <=> ~in(X0,relation_dom(sk0_9))|X0=apply(function_inverse(sk0_9),apply(sk0_9,X0))),
% 18.81/2.85 introduced(split_symbol_definition)).
% 18.81/2.85 fof(f1676,plain,(
% 18.81/2.85 ![X0]: (~relation(sk0_9)|~function(sk0_9)|~in(X0,relation_dom(sk0_9))|X0=apply(function_inverse(sk0_9),apply(sk0_9,X0)))),
% 18.81/2.85 inference(resolution,[status(thm)],[f148,f121])).
% 18.81/2.85 fof(f1677,plain,(
% 18.81/2.85 ~spl0_50|~spl0_51|spl0_117),
% 18.81/2.85 inference(split_clause,[status(thm)],[f1676,f527,f530,f1673])).
% 18.81/2.85 fof(f1678,plain,(
% 18.81/2.85 ![X0,X1]: (~relation(X0)|~function(X0)|~in(X1,relation_dom(X0))|X1=apply(function_inverse(X0),apply(X0,X1))|~empty(X0))),
% 18.81/2.85 inference(resolution,[status(thm)],[f148,f189])).
% 18.81/2.85 fof(f1679,plain,(
% 18.81/2.85 ![X0,X1]: (~function(X0)|~in(X1,relation_dom(X0))|X1=apply(function_inverse(X0),apply(X0,X1))|~empty(X0))),
% 18.81/2.85 inference(forward_subsumption_resolution,[status(thm)],[f1678,f52])).
% 18.81/2.85 fof(f1728,plain,(
% 18.81/2.85 spl0_119 <=> relation(function_inverse(sk0_9))),
% 18.81/2.85 introduced(split_symbol_definition)).
% 18.81/2.85 fof(f1730,plain,(
% 18.81/2.85 ~relation(function_inverse(sk0_9))|spl0_119),
% 18.81/2.85 inference(component_clause,[status(thm)],[f1728])).
% 18.81/2.85 fof(f1733,plain,(
% 18.81/2.85 ~relation(function_inverse(sk0_9))|~relation(sk0_9)|spl0_63),
% 18.81/2.85 inference(resolution,[status(thm)],[f709,f61])).
% 18.81/2.85 fof(f1734,plain,(
% 18.81/2.85 ~spl0_119|~spl0_50|spl0_63),
% 18.81/2.85 inference(split_clause,[status(thm)],[f1733,f1728,f527,f707])).
% 18.81/2.85 fof(f1736,plain,(
% 18.81/2.85 ~relation(sk0_9)|~function(sk0_9)|spl0_119),
% 18.81/2.85 inference(resolution,[status(thm)],[f1730,f58])).
% 18.81/2.85 fof(f1737,plain,(
% 18.81/2.85 ~spl0_50|~spl0_51|spl0_119),
% 18.81/2.85 inference(split_clause,[status(thm)],[f1736,f527,f530,f1728])).
% 18.81/2.85 fof(f1790,plain,(
% 18.81/2.85 ~relation(sk0_9)|~relation(function_inverse(sk0_9))|spl0_69),
% 18.81/2.85 inference(resolution,[status(thm)],[f825,f61])).
% 18.81/2.85 fof(f1791,plain,(
% 18.81/2.85 ~spl0_50|~spl0_119|spl0_69),
% 18.81/2.85 inference(split_clause,[status(thm)],[f1790,f527,f1728,f823])).
% 18.81/2.85 fof(f1836,plain,(
% 18.81/2.85 spl0_120 <=> relation_composition(function_inverse(sk0_12),sk0_12)=identity_relation(relation_dom(relation_composition(function_inverse(sk0_12),sk0_12)))),
% 18.81/2.85 introduced(split_symbol_definition)).
% 18.81/2.85 fof(f1837,plain,(
% 18.81/2.85 relation_composition(function_inverse(sk0_12),sk0_12)=identity_relation(relation_dom(relation_composition(function_inverse(sk0_12),sk0_12)))|~spl0_120),
% 18.81/2.85 inference(component_clause,[status(thm)],[f1836])).
% 18.81/2.85 fof(f1839,plain,(
% 18.81/2.85 spl0_121 <=> apply(relation_composition(function_inverse(sk0_12),sk0_12),sk0_11(relation_rng(sk0_12),relation_composition(function_inverse(sk0_12),sk0_12)))=sk0_11(relation_dom(relation_composition(function_inverse(sk0_12),sk0_12)),relation_composition(function_inverse(sk0_12),sk0_12))),
% 18.81/2.85 introduced(split_symbol_definition)).
% 18.81/2.85 fof(f1841,plain,(
% 18.81/2.85 ~apply(relation_composition(function_inverse(sk0_12),sk0_12),sk0_11(relation_rng(sk0_12),relation_composition(function_inverse(sk0_12),sk0_12)))=sk0_11(relation_dom(relation_composition(function_inverse(sk0_12),sk0_12)),relation_composition(function_inverse(sk0_12),sk0_12))|spl0_121),
% 18.81/2.85 inference(component_clause,[status(thm)],[f1839])).
% 18.81/2.85 fof(f1842,plain,(
% 18.81/2.85 ~relation(relation_composition(function_inverse(sk0_12),sk0_12))|~function(relation_composition(function_inverse(sk0_12),sk0_12))|relation_composition(function_inverse(sk0_12),sk0_12)=identity_relation(relation_dom(relation_composition(function_inverse(sk0_12),sk0_12)))|~apply(relation_composition(function_inverse(sk0_12),sk0_12),sk0_11(relation_rng(sk0_12),relation_composition(function_inverse(sk0_12),sk0_12)))=sk0_11(relation_dom(relation_composition(function_inverse(sk0_12),sk0_12)),relation_composition(function_inverse(sk0_12),sk0_12))|~spl0_48),
% 18.81/2.85 inference(paramodulation,[status(thm)],[f514,f187])).
% 18.81/2.85 fof(f1843,plain,(
% 18.81/2.85 ~spl0_57|~spl0_93|spl0_120|~spl0_121|~spl0_48),
% 18.81/2.85 inference(split_clause,[status(thm)],[f1842,f621,f1188,f1836,f1839,f513])).
% 18.81/2.85 fof(f1850,plain,(
% 18.81/2.85 ~apply(relation_composition(function_inverse(sk0_12),sk0_12),sk0_11(relation_rng(sk0_12),relation_composition(function_inverse(sk0_12),sk0_12)))=sk0_11(relation_rng(sk0_12),relation_composition(function_inverse(sk0_12),sk0_12))|~spl0_48|spl0_121),
% 18.81/2.85 inference(forward_demodulation,[status(thm)],[f514,f1841])).
% 18.81/2.85 fof(f1857,plain,(
% 18.81/2.85 spl0_122 <=> function(relation_composition(sk0_12,function_inverse(sk0_12)))),
% 18.81/2.85 introduced(split_symbol_definition)).
% 18.81/2.85 fof(f1858,plain,(
% 18.81/2.85 function(relation_composition(sk0_12,function_inverse(sk0_12)))|~spl0_122),
% 18.81/2.85 inference(component_clause,[status(thm)],[f1857])).
% 18.81/2.85 fof(f1859,plain,(
% 18.81/2.85 ~function(relation_composition(sk0_12,function_inverse(sk0_12)))|spl0_122),
% 18.81/2.85 inference(component_clause,[status(thm)],[f1857])).
% 18.81/2.85 fof(f1860,plain,(
% 18.81/2.85 spl0_123 <=> relation_composition(sk0_12,function_inverse(sk0_12))=identity_relation(relation_dom(relation_composition(sk0_12,function_inverse(sk0_12))))),
% 18.81/2.85 introduced(split_symbol_definition)).
% 18.81/2.85 fof(f1861,plain,(
% 18.81/2.85 relation_composition(sk0_12,function_inverse(sk0_12))=identity_relation(relation_dom(relation_composition(sk0_12,function_inverse(sk0_12))))|~spl0_123),
% 18.81/2.85 inference(component_clause,[status(thm)],[f1860])).
% 18.81/2.85 fof(f1863,plain,(
% 18.81/2.85 spl0_124 <=> apply(relation_composition(sk0_12,function_inverse(sk0_12)),sk0_11(relation_dom(sk0_12),relation_composition(sk0_12,function_inverse(sk0_12))))=sk0_11(relation_dom(relation_composition(sk0_12,function_inverse(sk0_12))),relation_composition(sk0_12,function_inverse(sk0_12)))),
% 18.81/2.85 introduced(split_symbol_definition)).
% 18.81/2.85 fof(f1865,plain,(
% 18.81/2.85 ~apply(relation_composition(sk0_12,function_inverse(sk0_12)),sk0_11(relation_dom(sk0_12),relation_composition(sk0_12,function_inverse(sk0_12))))=sk0_11(relation_dom(relation_composition(sk0_12,function_inverse(sk0_12))),relation_composition(sk0_12,function_inverse(sk0_12)))|spl0_124),
% 18.81/2.85 inference(component_clause,[status(thm)],[f1863])).
% 18.81/2.85 fof(f1866,plain,(
% 18.81/2.85 ~relation(relation_composition(sk0_12,function_inverse(sk0_12)))|~function(relation_composition(sk0_12,function_inverse(sk0_12)))|relation_composition(sk0_12,function_inverse(sk0_12))=identity_relation(relation_dom(relation_composition(sk0_12,function_inverse(sk0_12))))|~apply(relation_composition(sk0_12,function_inverse(sk0_12)),sk0_11(relation_dom(sk0_12),relation_composition(sk0_12,function_inverse(sk0_12))))=sk0_11(relation_dom(relation_composition(sk0_12,function_inverse(sk0_12))),relation_composition(sk0_12,function_inverse(sk0_12)))|~spl0_4),
% 18.81/2.85 inference(paramodulation,[status(thm)],[f205,f187])).
% 18.81/2.85 fof(f1867,plain,(
% 18.81/2.85 ~spl0_6|~spl0_122|spl0_123|~spl0_124|~spl0_4),
% 18.81/2.85 inference(split_clause,[status(thm)],[f1866,f218,f1857,f1860,f1863,f204])).
% 18.81/2.85 fof(f1874,plain,(
% 18.81/2.85 ~apply(relation_composition(sk0_12,function_inverse(sk0_12)),sk0_11(relation_dom(sk0_12),relation_composition(sk0_12,function_inverse(sk0_12))))=sk0_11(relation_dom(sk0_12),relation_composition(sk0_12,function_inverse(sk0_12)))|~spl0_4|spl0_124),
% 18.81/2.85 inference(forward_demodulation,[status(thm)],[f205,f1865])).
% 18.81/2.85 fof(f1883,plain,(
% 18.81/2.85 spl0_125 <=> function(relation_composition(function_inverse(empty_set),empty_set))),
% 18.81/2.85 introduced(split_symbol_definition)).
% 18.81/2.85 fof(f1885,plain,(
% 18.81/2.85 ~function(relation_composition(function_inverse(empty_set),empty_set))|spl0_125),
% 18.81/2.85 inference(component_clause,[status(thm)],[f1883])).
% 18.81/2.85 fof(f1894,plain,(
% 18.81/2.85 empty(relation_composition(function_inverse(empty_set),empty_set))|~relation(relation_composition(function_inverse(empty_set),empty_set))|~empty(empty_set)),
% 18.81/2.85 inference(paramodulation,[status(thm)],[f902,f82])).
% 18.81/2.85 fof(f1895,plain,(
% 18.81/2.85 spl0_103|~spl0_104|~spl0_46),
% 18.81/2.85 inference(split_clause,[status(thm)],[f1894,f1390,f1393,f448])).
% 18.81/2.85 fof(f1901,plain,(
% 18.81/2.85 spl0_128 <=> relation_composition(X0,sk0_12)=identity_relation(relation_dom(relation_composition(X0,sk0_12)))|in(sk0_11(relation_dom(relation_composition(X0,sk0_12)),relation_composition(X0,sk0_12)),relation_dom(relation_composition(X0,sk0_12)))|~relation(X0)|~function(X0)),
% 18.81/2.85 introduced(split_symbol_definition)).
% 18.81/2.85 fof(f1902,plain,(
% 18.81/2.85 ![X0]: (relation_composition(X0,sk0_12)=identity_relation(relation_dom(relation_composition(X0,sk0_12)))|in(sk0_11(relation_dom(relation_composition(X0,sk0_12)),relation_composition(X0,sk0_12)),relation_dom(relation_composition(X0,sk0_12)))|~relation(X0)|~function(X0)|~spl0_128)),
% 18.81/2.85 inference(component_clause,[status(thm)],[f1901])).
% 18.81/2.85 fof(f1904,plain,(
% 18.81/2.85 ![X0]: (relation_composition(X0,sk0_12)=identity_relation(relation_dom(relation_composition(X0,sk0_12)))|in(sk0_11(relation_dom(relation_composition(X0,sk0_12)),relation_composition(X0,sk0_12)),relation_dom(relation_composition(X0,sk0_12)))|~relation(X0)|~function(X0)|~relation(sk0_12))),
% 18.81/2.85 inference(resolution,[status(thm)],[f1136,f166])).
% 18.81/2.85 fof(f1905,plain,(
% 18.81/2.85 spl0_128|~spl0_2),
% 18.81/2.85 inference(split_clause,[status(thm)],[f1904,f1901,f198])).
% 18.81/2.85 fof(f1906,plain,(
% 18.81/2.85 spl0_129 <=> relation_composition(X0,empty_set)=identity_relation(relation_dom(relation_composition(X0,empty_set)))|in(sk0_11(relation_dom(relation_composition(X0,empty_set)),relation_composition(X0,empty_set)),relation_dom(relation_composition(X0,empty_set)))|~relation(X0)|~function(X0)),
% 18.81/2.85 introduced(split_symbol_definition)).
% 18.81/2.85 fof(f1909,plain,(
% 18.81/2.85 ![X0]: (relation_composition(X0,empty_set)=identity_relation(relation_dom(relation_composition(X0,empty_set)))|in(sk0_11(relation_dom(relation_composition(X0,empty_set)),relation_composition(X0,empty_set)),relation_dom(relation_composition(X0,empty_set)))|~relation(X0)|~function(X0)|~relation(empty_set))),
% 18.81/2.85 inference(resolution,[status(thm)],[f1136,f588])).
% 18.81/2.85 fof(f1910,plain,(
% 18.81/2.85 spl0_129|~spl0_47),
% 18.81/2.85 inference(split_clause,[status(thm)],[f1909,f1906,f453])).
% 18.81/2.85 fof(f1911,plain,(
% 18.81/2.85 spl0_130 <=> relation_composition(X0,sk0_9)=identity_relation(relation_dom(relation_composition(X0,sk0_9)))|in(sk0_11(relation_dom(relation_composition(X0,sk0_9)),relation_composition(X0,sk0_9)),relation_dom(relation_composition(X0,sk0_9)))|~relation(X0)|~function(X0)),
% 18.81/2.85 introduced(split_symbol_definition)).
% 18.81/2.85 fof(f1914,plain,(
% 18.81/2.85 ![X0]: (relation_composition(X0,sk0_9)=identity_relation(relation_dom(relation_composition(X0,sk0_9)))|in(sk0_11(relation_dom(relation_composition(X0,sk0_9)),relation_composition(X0,sk0_9)),relation_dom(relation_composition(X0,sk0_9)))|~relation(X0)|~function(X0)|~relation(sk0_9))),
% 18.81/2.85 inference(resolution,[status(thm)],[f1136,f120])).
% 18.81/2.85 fof(f1915,plain,(
% 18.81/2.85 spl0_130|~spl0_50),
% 18.81/2.85 inference(split_clause,[status(thm)],[f1914,f1911,f527])).
% 18.81/2.85 fof(f1916,plain,(
% 18.81/2.85 ![X0,X1,X2]: (relation_composition(X0,relation_composition(X1,X2))=identity_relation(relation_dom(relation_composition(X0,relation_composition(X1,X2))))|in(sk0_11(relation_dom(relation_composition(X0,relation_composition(X1,X2))),relation_composition(X0,relation_composition(X1,X2))),relation_dom(relation_composition(X0,relation_composition(X1,X2))))|~relation(X0)|~function(X0)|~relation(relation_composition(X1,X2))|~relation(X1)|~function(X1)|~relation(X2)|~function(X2))),
% 18.81/2.85 inference(resolution,[status(thm)],[f1136,f73])).
% 18.81/2.85 fof(f1917,plain,(
% 18.81/2.85 ![X0,X1,X2]: (relation_composition(X0,relation_composition(X1,X2))=identity_relation(relation_dom(relation_composition(X0,relation_composition(X1,X2))))|in(sk0_11(relation_dom(relation_composition(X0,relation_composition(X1,X2))),relation_composition(X0,relation_composition(X1,X2))),relation_dom(relation_composition(X0,relation_composition(X1,X2))))|~relation(X0)|~function(X0)|~relation(X1)|~function(X1)|~relation(X2)|~function(X2))),
% 18.81/2.85 inference(forward_subsumption_resolution,[status(thm)],[f1916,f61])).
% 18.81/2.85 fof(f1918,plain,(
% 18.81/2.85 spl0_131 <=> relation_composition(X0,sk0_1)=identity_relation(relation_dom(relation_composition(X0,sk0_1)))|in(sk0_11(relation_dom(relation_composition(X0,sk0_1)),relation_composition(X0,sk0_1)),relation_dom(relation_composition(X0,sk0_1)))|~relation(X0)|~function(X0)),
% 18.81/2.85 introduced(split_symbol_definition)).
% 18.81/2.85 fof(f1919,plain,(
% 18.81/2.85 ![X0]: (relation_composition(X0,sk0_1)=identity_relation(relation_dom(relation_composition(X0,sk0_1)))|in(sk0_11(relation_dom(relation_composition(X0,sk0_1)),relation_composition(X0,sk0_1)),relation_dom(relation_composition(X0,sk0_1)))|~relation(X0)|~function(X0)|~spl0_131)),
% 18.81/2.85 inference(component_clause,[status(thm)],[f1918])).
% 18.81/2.85 fof(f1921,plain,(
% 18.81/2.85 ![X0]: (relation_composition(X0,sk0_1)=identity_relation(relation_dom(relation_composition(X0,sk0_1)))|in(sk0_11(relation_dom(relation_composition(X0,sk0_1)),relation_composition(X0,sk0_1)),relation_dom(relation_composition(X0,sk0_1)))|~relation(X0)|~function(X0)|~relation(sk0_1))),
% 18.81/2.85 inference(resolution,[status(thm)],[f1136,f96])).
% 18.81/2.85 fof(f1922,plain,(
% 18.81/2.85 spl0_131|~spl0_87),
% 18.81/2.85 inference(split_clause,[status(thm)],[f1921,f1918,f1137])).
% 18.81/2.85 fof(f1923,plain,(
% 18.81/2.85 ![X0,X1]: (relation_composition(X0,function_inverse(X1))=identity_relation(relation_dom(relation_composition(X0,function_inverse(X1))))|in(sk0_11(relation_dom(relation_composition(X0,function_inverse(X1))),relation_composition(X0,function_inverse(X1))),relation_dom(relation_composition(X0,function_inverse(X1))))|~relation(X0)|~function(X0)|~relation(function_inverse(X1))|~relation(X1)|~function(X1))),
% 18.81/2.85 inference(resolution,[status(thm)],[f1136,f59])).
% 18.81/2.85 fof(f1924,plain,(
% 18.81/2.85 ![X0,X1]: (relation_composition(X0,function_inverse(X1))=identity_relation(relation_dom(relation_composition(X0,function_inverse(X1))))|in(sk0_11(relation_dom(relation_composition(X0,function_inverse(X1))),relation_composition(X0,function_inverse(X1))),relation_dom(relation_composition(X0,function_inverse(X1))))|~relation(X0)|~function(X0)|~relation(X1)|~function(X1))),
% 18.81/2.85 inference(forward_subsumption_resolution,[status(thm)],[f1923,f58])).
% 18.81/2.85 fof(f1925,plain,(
% 18.81/2.85 ![X0,X1]: (relation_composition(X0,identity_relation(X1))=identity_relation(relation_dom(relation_composition(X0,identity_relation(X1))))|in(sk0_11(relation_dom(relation_composition(X0,identity_relation(X1))),relation_composition(X0,identity_relation(X1))),relation_dom(relation_composition(X0,identity_relation(X1))))|~relation(X0)|~function(X0)|~relation(identity_relation(X1)))),
% 18.81/2.85 inference(resolution,[status(thm)],[f1136,f78])).
% 18.81/2.85 fof(f1926,plain,(
% 18.81/2.85 ![X0,X1]: (relation_composition(X0,identity_relation(X1))=identity_relation(relation_dom(relation_composition(X0,identity_relation(X1))))|in(sk0_11(relation_dom(relation_composition(X0,identity_relation(X1))),relation_composition(X0,identity_relation(X1))),relation_dom(relation_composition(X0,identity_relation(X1))))|~relation(X0)|~function(X0))),
% 18.81/2.85 inference(forward_subsumption_resolution,[status(thm)],[f1925,f62])).
% 18.81/2.85 fof(f2017,plain,(
% 18.81/2.85 empty_set=identity_relation(relation_dom(empty_set))|in(sk0_11(relation_dom(empty_set),empty_set),relation_dom(empty_set))),
% 18.81/2.85 inference(resolution,[status(thm)],[f1160,f68])).
% 18.81/2.85 fof(f2018,plain,(
% 18.81/2.85 spl0_83|spl0_84),
% 18.81/2.85 inference(split_clause,[status(thm)],[f2017,f1119,f1122])).
% 18.81/2.85 fof(f2111,plain,(
% 18.81/2.85 spl0_132 <=> ~in(X0,relation_dom(sk0_12))|X0=apply(relation_composition(sk0_12,function_inverse(sk0_12)),X0)),
% 18.81/2.85 introduced(split_symbol_definition)).
% 18.81/2.85 fof(f2112,plain,(
% 18.81/2.85 ![X0]: (~in(X0,relation_dom(sk0_12))|X0=apply(relation_composition(sk0_12,function_inverse(sk0_12)),X0)|~spl0_132)),
% 18.81/2.85 inference(component_clause,[status(thm)],[f2111])).
% 18.81/2.85 fof(f2114,plain,(
% 18.81/2.85 ![X0]: (~relation(sk0_12)|~function(sk0_12)|~in(X0,relation_dom(sk0_12))|X0=apply(relation_composition(sk0_12,function_inverse(sk0_12)),X0))),
% 18.81/2.85 inference(resolution,[status(thm)],[f149,f167])).
% 18.81/2.85 fof(f2115,plain,(
% 18.81/2.85 ~spl0_2|~spl0_3|spl0_132),
% 18.81/2.85 inference(split_clause,[status(thm)],[f2114,f198,f201,f2111])).
% 18.81/2.85 fof(f2116,plain,(
% 18.81/2.85 spl0_133 <=> ~in(X0,relation_dom(sk0_9))|X0=apply(relation_composition(sk0_9,function_inverse(sk0_9)),X0)),
% 18.81/2.85 introduced(split_symbol_definition)).
% 18.81/2.85 fof(f2119,plain,(
% 18.81/2.85 ![X0]: (~relation(sk0_9)|~function(sk0_9)|~in(X0,relation_dom(sk0_9))|X0=apply(relation_composition(sk0_9,function_inverse(sk0_9)),X0))),
% 18.81/2.85 inference(resolution,[status(thm)],[f149,f121])).
% 18.81/2.85 fof(f2120,plain,(
% 18.81/2.85 ~spl0_50|~spl0_51|spl0_133),
% 18.81/2.85 inference(split_clause,[status(thm)],[f2119,f527,f530,f2116])).
% 18.81/2.85 fof(f2121,plain,(
% 18.81/2.85 ![X0,X1]: (~relation(X0)|~function(X0)|~in(X1,relation_dom(X0))|X1=apply(relation_composition(X0,function_inverse(X0)),X1)|~empty(X0))),
% 18.81/2.85 inference(resolution,[status(thm)],[f149,f189])).
% 18.81/2.85 fof(f2122,plain,(
% 18.81/2.85 ![X0,X1]: (~function(X0)|~in(X1,relation_dom(X0))|X1=apply(relation_composition(X0,function_inverse(X0)),X1)|~empty(X0))),
% 18.81/2.85 inference(forward_subsumption_resolution,[status(thm)],[f2121,f52])).
% 18.81/2.85 fof(f2123,plain,(
% 18.81/2.85 spl0_134 <=> ~in(X0,relation_rng(sk0_12))|X0=apply(sk0_12,apply(function_inverse(sk0_12),X0))),
% 18.81/2.85 introduced(split_symbol_definition)).
% 18.81/2.85 fof(f2124,plain,(
% 18.81/2.85 ![X0]: (~in(X0,relation_rng(sk0_12))|X0=apply(sk0_12,apply(function_inverse(sk0_12),X0))|~spl0_134)),
% 18.81/2.85 inference(component_clause,[status(thm)],[f2123])).
% 18.81/2.85 fof(f2126,plain,(
% 18.81/2.85 ![X0]: (~relation(sk0_12)|~function(sk0_12)|~in(X0,relation_rng(sk0_12))|X0=apply(sk0_12,apply(function_inverse(sk0_12),X0)))),
% 18.81/2.85 inference(resolution,[status(thm)],[f152,f167])).
% 18.81/2.85 fof(f2127,plain,(
% 18.81/2.85 ~spl0_2|~spl0_3|spl0_134),
% 18.81/2.85 inference(split_clause,[status(thm)],[f2126,f198,f201,f2123])).
% 18.81/2.85 fof(f2128,plain,(
% 18.81/2.85 spl0_135 <=> ~in(X0,relation_rng(sk0_9))|X0=apply(sk0_9,apply(function_inverse(sk0_9),X0))),
% 18.81/2.85 introduced(split_symbol_definition)).
% 18.81/2.85 fof(f2131,plain,(
% 18.81/2.85 ![X0]: (~relation(sk0_9)|~function(sk0_9)|~in(X0,relation_rng(sk0_9))|X0=apply(sk0_9,apply(function_inverse(sk0_9),X0)))),
% 18.81/2.85 inference(resolution,[status(thm)],[f152,f121])).
% 18.81/2.85 fof(f2132,plain,(
% 18.81/2.85 ~spl0_50|~spl0_51|spl0_135),
% 18.81/2.85 inference(split_clause,[status(thm)],[f2131,f527,f530,f2128])).
% 18.81/2.85 fof(f2133,plain,(
% 18.81/2.85 ![X0,X1]: (~relation(X0)|~function(X0)|~in(X1,relation_rng(X0))|X1=apply(X0,apply(function_inverse(X0),X1))|~empty(X0))),
% 18.81/2.85 inference(resolution,[status(thm)],[f152,f189])).
% 18.81/2.85 fof(f2134,plain,(
% 18.81/2.85 ![X0,X1]: (~function(X0)|~in(X1,relation_rng(X0))|X1=apply(X0,apply(function_inverse(X0),X1))|~empty(X0))),
% 18.81/2.85 inference(forward_subsumption_resolution,[status(thm)],[f2133,f52])).
% 18.81/2.85 fof(f2135,plain,(
% 18.81/2.85 spl0_136 <=> ~in(X0,relation_rng(sk0_12))|X0=apply(relation_composition(function_inverse(sk0_12),sk0_12),X0)),
% 18.81/2.85 introduced(split_symbol_definition)).
% 18.81/2.85 fof(f2136,plain,(
% 18.81/2.85 ![X0]: (~in(X0,relation_rng(sk0_12))|X0=apply(relation_composition(function_inverse(sk0_12),sk0_12),X0)|~spl0_136)),
% 18.81/2.85 inference(component_clause,[status(thm)],[f2135])).
% 18.81/2.85 fof(f2138,plain,(
% 18.81/2.85 ![X0]: (~relation(sk0_12)|~function(sk0_12)|~in(X0,relation_rng(sk0_12))|X0=apply(relation_composition(function_inverse(sk0_12),sk0_12),X0))),
% 18.81/2.85 inference(resolution,[status(thm)],[f153,f167])).
% 18.81/2.85 fof(f2139,plain,(
% 18.81/2.85 ~spl0_2|~spl0_3|spl0_136),
% 18.81/2.85 inference(split_clause,[status(thm)],[f2138,f198,f201,f2135])).
% 18.81/2.85 fof(f2140,plain,(
% 18.81/2.85 spl0_137 <=> ~in(X0,relation_rng(sk0_9))|X0=apply(relation_composition(function_inverse(sk0_9),sk0_9),X0)),
% 18.81/2.85 introduced(split_symbol_definition)).
% 18.81/2.85 fof(f2143,plain,(
% 18.81/2.85 ![X0]: (~relation(sk0_9)|~function(sk0_9)|~in(X0,relation_rng(sk0_9))|X0=apply(relation_composition(function_inverse(sk0_9),sk0_9),X0))),
% 18.81/2.85 inference(resolution,[status(thm)],[f153,f121])).
% 18.81/2.85 fof(f2144,plain,(
% 18.81/2.85 ~spl0_50|~spl0_51|spl0_137),
% 18.81/2.85 inference(split_clause,[status(thm)],[f2143,f527,f530,f2140])).
% 18.81/2.85 fof(f2145,plain,(
% 18.81/2.85 ![X0,X1]: (~relation(X0)|~function(X0)|~in(X1,relation_rng(X0))|X1=apply(relation_composition(function_inverse(X0),X0),X1)|~empty(X0))),
% 18.81/2.85 inference(resolution,[status(thm)],[f153,f189])).
% 18.81/2.85 fof(f2146,plain,(
% 18.81/2.85 ![X0,X1]: (~function(X0)|~in(X1,relation_rng(X0))|X1=apply(relation_composition(function_inverse(X0),X0),X1)|~empty(X0))),
% 18.81/2.85 inference(forward_subsumption_resolution,[status(thm)],[f2145,f52])).
% 18.81/2.85 fof(f2205,plain,(
% 18.81/2.85 spl0_138 <=> function(function_inverse(sk0_9))),
% 18.81/2.85 introduced(split_symbol_definition)).
% 18.81/2.85 fof(f2206,plain,(
% 18.81/2.85 function(function_inverse(sk0_9))|~spl0_138),
% 18.81/2.85 inference(component_clause,[status(thm)],[f2205])).
% 18.81/2.85 fof(f2207,plain,(
% 18.81/2.85 ~function(function_inverse(sk0_9))|spl0_138),
% 18.81/2.85 inference(component_clause,[status(thm)],[f2205])).
% 18.81/2.85 fof(f2236,plain,(
% 18.81/2.85 spl0_139 <=> sk0_0(relation_dom(sk0_12))=apply(function_inverse(sk0_12),apply(sk0_12,sk0_0(relation_dom(sk0_12))))),
% 18.81/2.85 introduced(split_symbol_definition)).
% 18.81/2.85 fof(f2239,plain,(
% 18.81/2.85 sk0_0(relation_dom(sk0_12))=apply(function_inverse(sk0_12),apply(sk0_12,sk0_0(relation_dom(sk0_12))))|empty(relation_dom(sk0_12))|~spl0_116),
% 18.81/2.85 inference(resolution,[status(thm)],[f1669,f1115])).
% 18.81/2.85 fof(f2240,plain,(
% 18.81/2.85 spl0_139|spl0_7|~spl0_116),
% 18.81/2.85 inference(split_clause,[status(thm)],[f2239,f2236,f221,f1668])).
% 18.81/2.85 fof(f2241,plain,(
% 18.81/2.85 ~relation(function_inverse(sk0_9))|~function(function_inverse(sk0_9))|~relation(sk0_9)|~function(sk0_9)|spl0_113),
% 18.81/2.85 inference(resolution,[status(thm)],[f1655,f73])).
% 18.81/2.85 fof(f2242,plain,(
% 18.81/2.85 ~spl0_119|~spl0_138|~spl0_50|~spl0_51|spl0_113),
% 18.81/2.85 inference(split_clause,[status(thm)],[f2241,f1728,f2205,f527,f530,f1653])).
% 18.81/2.85 fof(f2243,plain,(
% 18.81/2.85 ~relation(sk0_9)|~function(sk0_9)|spl0_138),
% 18.81/2.85 inference(resolution,[status(thm)],[f2207,f59])).
% 18.81/2.85 fof(f2244,plain,(
% 18.81/2.85 ~spl0_50|~spl0_51|spl0_138),
% 18.81/2.85 inference(split_clause,[status(thm)],[f2243,f527,f530,f2205])).
% 18.81/2.85 fof(f2245,plain,(
% 18.81/2.85 spl0_140 <=> relation_composition(X0,function_inverse(sk0_9))=identity_relation(relation_dom(relation_composition(X0,function_inverse(sk0_9))))|in(sk0_11(relation_dom(relation_composition(X0,function_inverse(sk0_9))),relation_composition(X0,function_inverse(sk0_9))),relation_dom(relation_composition(X0,function_inverse(sk0_9))))|~relation(X0)|~function(X0)),
% 18.81/2.85 introduced(split_symbol_definition)).
% 18.81/2.85 fof(f2248,plain,(
% 18.81/2.85 ![X0]: (relation_composition(X0,function_inverse(sk0_9))=identity_relation(relation_dom(relation_composition(X0,function_inverse(sk0_9))))|in(sk0_11(relation_dom(relation_composition(X0,function_inverse(sk0_9))),relation_composition(X0,function_inverse(sk0_9))),relation_dom(relation_composition(X0,function_inverse(sk0_9))))|~relation(X0)|~function(X0)|~relation(function_inverse(sk0_9))|~spl0_138)),
% 18.81/2.85 inference(resolution,[status(thm)],[f2206,f1136])).
% 18.81/2.85 fof(f2249,plain,(
% 18.81/2.85 spl0_140|~spl0_119|~spl0_138),
% 18.81/2.85 inference(split_clause,[status(thm)],[f2248,f2245,f1728,f2205])).
% 18.81/2.85 fof(f2274,plain,(
% 18.81/2.85 ~relation(function_inverse(sk0_12))|~function(function_inverse(sk0_12))|~relation(sk0_12)|~function(sk0_12)|spl0_93),
% 18.81/2.85 inference(resolution,[status(thm)],[f1190,f73])).
% 18.81/2.85 fof(f2275,plain,(
% 18.81/2.85 ~spl0_10|~spl0_92|~spl0_2|~spl0_3|spl0_93),
% 18.81/2.85 inference(split_clause,[status(thm)],[f2274,f236,f1173,f198,f201,f1188])).
% 18.81/2.85 fof(f2276,plain,(
% 18.81/2.85 ~relation(sk0_12)|~function(sk0_12)|spl0_92),
% 18.81/2.85 inference(resolution,[status(thm)],[f1175,f59])).
% 18.81/2.85 fof(f2277,plain,(
% 18.81/2.85 ~spl0_2|~spl0_3|spl0_92),
% 18.81/2.85 inference(split_clause,[status(thm)],[f2276,f198,f201,f1173])).
% 18.81/2.85 fof(f2278,plain,(
% 18.81/2.85 spl0_143 <=> relation_composition(X0,function_inverse(sk0_12))=identity_relation(relation_dom(relation_composition(X0,function_inverse(sk0_12))))|in(sk0_11(relation_dom(relation_composition(X0,function_inverse(sk0_12))),relation_composition(X0,function_inverse(sk0_12))),relation_dom(relation_composition(X0,function_inverse(sk0_12))))|~relation(X0)|~function(X0)),
% 18.81/2.85 introduced(split_symbol_definition)).
% 18.81/2.85 fof(f2281,plain,(
% 18.81/2.85 ![X0]: (relation_composition(X0,function_inverse(sk0_12))=identity_relation(relation_dom(relation_composition(X0,function_inverse(sk0_12))))|in(sk0_11(relation_dom(relation_composition(X0,function_inverse(sk0_12))),relation_composition(X0,function_inverse(sk0_12))),relation_dom(relation_composition(X0,function_inverse(sk0_12))))|~relation(X0)|~function(X0)|~relation(function_inverse(sk0_12))|~spl0_92)),
% 18.81/2.85 inference(resolution,[status(thm)],[f1174,f1136])).
% 18.81/2.85 fof(f2282,plain,(
% 18.81/2.85 spl0_143|~spl0_10|~spl0_92),
% 18.81/2.85 inference(split_clause,[status(thm)],[f2281,f2278,f236,f1173])).
% 18.81/2.85 fof(f2291,plain,(
% 18.81/2.85 ~relation(sk0_12)|~function(sk0_12)|~relation(function_inverse(sk0_12))|~function(function_inverse(sk0_12))|spl0_122),
% 18.81/2.85 inference(resolution,[status(thm)],[f1859,f73])).
% 18.81/2.85 fof(f2292,plain,(
% 18.81/2.85 ~spl0_2|~spl0_3|~spl0_10|~spl0_92|spl0_122),
% 18.81/2.85 inference(split_clause,[status(thm)],[f2291,f198,f201,f236,f1173,f1857])).
% 18.81/2.85 fof(f2293,plain,(
% 18.81/2.85 ~function(empty_set)|~spl0_17|spl0_125),
% 18.81/2.85 inference(forward_demodulation,[status(thm)],[f1498,f1885])).
% 18.81/2.85 fof(f2294,plain,(
% 18.81/2.85 $false|~spl0_17|spl0_125),
% 18.81/2.85 inference(forward_subsumption_resolution,[status(thm)],[f2293,f588])).
% 18.81/2.85 fof(f2295,plain,(
% 18.81/2.85 ~spl0_17|spl0_125),
% 18.81/2.85 inference(contradiction_clause,[status(thm)],[f2294])).
% 18.81/2.85 fof(f2298,plain,(
% 18.81/2.85 spl0_146 <=> relation_composition(X0,relation_composition(function_inverse(sk0_9),sk0_9))=identity_relation(relation_dom(relation_composition(X0,relation_composition(function_inverse(sk0_9),sk0_9))))|in(sk0_11(relation_dom(relation_composition(X0,relation_composition(function_inverse(sk0_9),sk0_9))),relation_composition(X0,relation_composition(function_inverse(sk0_9),sk0_9))),relation_dom(relation_composition(X0,relation_composition(function_inverse(sk0_9),sk0_9))))|~relation(X0)|~function(X0)),
% 18.81/2.85 introduced(split_symbol_definition)).
% 18.81/2.85 fof(f2301,plain,(
% 18.81/2.85 ![X0]: (relation_composition(X0,relation_composition(function_inverse(sk0_9),sk0_9))=identity_relation(relation_dom(relation_composition(X0,relation_composition(function_inverse(sk0_9),sk0_9))))|in(sk0_11(relation_dom(relation_composition(X0,relation_composition(function_inverse(sk0_9),sk0_9))),relation_composition(X0,relation_composition(function_inverse(sk0_9),sk0_9))),relation_dom(relation_composition(X0,relation_composition(function_inverse(sk0_9),sk0_9))))|~relation(X0)|~function(X0)|~relation(relation_composition(function_inverse(sk0_9),sk0_9))|~spl0_113)),
% 18.81/2.85 inference(resolution,[status(thm)],[f1654,f1136])).
% 18.81/2.85 fof(f2302,plain,(
% 18.81/2.85 spl0_146|~spl0_63|~spl0_113),
% 18.81/2.85 inference(split_clause,[status(thm)],[f2301,f2298,f707,f1653])).
% 18.81/2.85 fof(f2309,plain,(
% 18.81/2.85 spl0_148 <=> relation_composition(X0,relation_composition(function_inverse(sk0_12),sk0_12))=identity_relation(relation_dom(relation_composition(X0,relation_composition(function_inverse(sk0_12),sk0_12))))|in(sk0_11(relation_dom(relation_composition(X0,relation_composition(function_inverse(sk0_12),sk0_12))),relation_composition(X0,relation_composition(function_inverse(sk0_12),sk0_12))),relation_dom(relation_composition(X0,relation_composition(function_inverse(sk0_12),sk0_12))))|~relation(X0)|~function(X0)),
% 18.81/2.85 introduced(split_symbol_definition)).
% 18.81/2.85 fof(f2312,plain,(
% 18.81/2.85 ![X0]: (relation_composition(X0,relation_composition(function_inverse(sk0_12),sk0_12))=identity_relation(relation_dom(relation_composition(X0,relation_composition(function_inverse(sk0_12),sk0_12))))|in(sk0_11(relation_dom(relation_composition(X0,relation_composition(function_inverse(sk0_12),sk0_12))),relation_composition(X0,relation_composition(function_inverse(sk0_12),sk0_12))),relation_dom(relation_composition(X0,relation_composition(function_inverse(sk0_12),sk0_12))))|~relation(X0)|~function(X0)|~relation(relation_composition(function_inverse(sk0_12),sk0_12))|~spl0_93)),
% 18.81/2.85 inference(resolution,[status(thm)],[f1189,f1136])).
% 18.81/2.85 fof(f2313,plain,(
% 18.81/2.85 spl0_148|~spl0_57|~spl0_93),
% 18.81/2.85 inference(split_clause,[status(thm)],[f2312,f2309,f621,f1188])).
% 18.81/2.85 fof(f2319,plain,(
% 18.81/2.85 relation_composition(function_inverse(sk0_12),sk0_12)=identity_relation(relation_rng(sk0_12))|~spl0_48|~spl0_120),
% 18.81/2.85 inference(forward_demodulation,[status(thm)],[f514,f1837])).
% 18.81/2.85 fof(f2333,plain,(
% 18.81/2.85 spl0_151 <=> sk0_0(relation_dom(sk0_12))=apply(relation_composition(sk0_12,function_inverse(sk0_12)),sk0_0(relation_dom(sk0_12)))),
% 18.81/2.85 introduced(split_symbol_definition)).
% 18.81/2.85 fof(f2336,plain,(
% 18.81/2.85 sk0_0(relation_dom(sk0_12))=apply(relation_composition(sk0_12,function_inverse(sk0_12)),sk0_0(relation_dom(sk0_12)))|empty(relation_dom(sk0_12))|~spl0_132),
% 18.81/2.85 inference(resolution,[status(thm)],[f2112,f1115])).
% 18.81/2.85 fof(f2337,plain,(
% 18.81/2.85 spl0_151|spl0_7|~spl0_132),
% 18.81/2.85 inference(split_clause,[status(thm)],[f2336,f2333,f221,f2111])).
% 18.81/2.85 fof(f2378,plain,(
% 18.81/2.85 ![X0,X1]: (~in(X0,relation_dom(X1))|X0=apply(function_inverse(X1),apply(X1,X0))|~empty(X1))),
% 18.81/2.85 inference(forward_subsumption_resolution,[status(thm)],[f1679,f50])).
% 18.81/2.85 fof(f2385,plain,(
% 18.81/2.85 ![X0,X1]: (~in(X0,relation_dom(relation_rng(X1)))|X0=apply(function_inverse(relation_rng(X1)),apply(relation_rng(X1),X0))|~empty(X1))),
% 18.81/2.85 inference(resolution,[status(thm)],[f2378,f89])).
% 18.81/2.85 fof(f2386,plain,(
% 18.81/2.85 ![X0,X1]: (~in(X0,relation_dom(relation_dom(X1)))|X0=apply(function_inverse(relation_dom(X1)),apply(relation_dom(X1),X0))|~empty(X1))),
% 18.81/2.85 inference(resolution,[status(thm)],[f2378,f86])).
% 18.81/2.85 fof(f2454,plain,(
% 18.81/2.85 ![X0,X1]: (~in(X0,relation_dom(X1))|X0=apply(relation_composition(X1,function_inverse(X1)),X0)|~empty(X1))),
% 18.81/2.85 inference(forward_subsumption_resolution,[status(thm)],[f2122,f50])).
% 18.81/2.85 fof(f2462,plain,(
% 18.81/2.85 ![X0,X1]: (~in(X0,relation_dom(relation_rng(X1)))|X0=apply(relation_composition(relation_rng(X1),function_inverse(relation_rng(X1))),X0)|~empty(X1))),
% 18.81/2.85 inference(resolution,[status(thm)],[f2454,f89])).
% 18.81/2.85 fof(f2463,plain,(
% 18.81/2.85 ![X0,X1]: (~in(X0,relation_dom(relation_dom(X1)))|X0=apply(relation_composition(relation_dom(X1),function_inverse(relation_dom(X1))),X0)|~empty(X1))),
% 18.81/2.85 inference(resolution,[status(thm)],[f2454,f86])).
% 18.81/2.85 fof(f2464,plain,(
% 18.81/2.85 ![X0,X1]: (~in(X0,relation_rng(X1))|X0=apply(X1,apply(function_inverse(X1),X0))|~empty(X1))),
% 18.81/2.85 inference(forward_subsumption_resolution,[status(thm)],[f2134,f50])).
% 18.81/2.85 fof(f2465,plain,(
% 18.81/2.85 ![X0,X1]: (~in(X0,relation_rng(identity_relation(X1)))|X0=apply(identity_relation(X1),apply(function_inverse(identity_relation(X1)),X0))|~empty(X1))),
% 18.81/2.85 inference(resolution,[status(thm)],[f2464,f194])).
% 18.81/2.85 fof(f2470,plain,(
% 18.81/2.85 ![X0,X1]: (~in(X0,relation_rng(relation_rng(X1)))|X0=apply(relation_rng(X1),apply(function_inverse(relation_rng(X1)),X0))|~empty(X1))),
% 18.81/2.85 inference(resolution,[status(thm)],[f2464,f89])).
% 18.81/2.85 fof(f2471,plain,(
% 18.81/2.85 ![X0,X1]: (~in(X0,relation_rng(relation_dom(X1)))|X0=apply(relation_dom(X1),apply(function_inverse(relation_dom(X1)),X0))|~empty(X1))),
% 18.81/2.85 inference(resolution,[status(thm)],[f2464,f86])).
% 18.81/2.85 fof(f2502,plain,(
% 18.81/2.85 ![X0,X1]: (~element(X0,powerset(X1))|~empty(X1)|empty(X0))),
% 18.81/2.85 inference(resolution,[status(thm)],[f162,f1115])).
% 18.81/2.85 fof(f2511,plain,(
% 18.81/2.85 ![X0]: (~element(X0,powerset(empty_set))|empty(X0))),
% 18.81/2.85 inference(resolution,[status(thm)],[f2502,f68])).
% 18.81/2.85 fof(f2522,plain,(
% 18.81/2.85 empty(sk0_0(powerset(empty_set)))),
% 18.81/2.85 inference(resolution,[status(thm)],[f2511,f64])).
% 18.81/2.85 fof(f2523,plain,(
% 18.81/2.85 ![X0]: (empty(X0)|~subset(X0,empty_set))),
% 18.81/2.85 inference(resolution,[status(thm)],[f2511,f142])).
% 18.81/2.85 fof(f2525,plain,(
% 18.81/2.85 ![X0]: (empty(X0)|~in(X0,powerset(empty_set)))),
% 18.81/2.85 inference(resolution,[status(thm)],[f2511,f128])).
% 18.81/2.85 fof(f2594,plain,(
% 18.81/2.85 relation_rng(sk0_0(powerset(empty_set)))=empty_set),
% 18.81/2.85 inference(resolution,[status(thm)],[f2522,f569])).
% 18.81/2.85 fof(f2595,plain,(
% 18.81/2.85 identity_relation(sk0_0(powerset(empty_set)))=empty_set),
% 18.81/2.85 inference(resolution,[status(thm)],[f2522,f562])).
% 18.81/2.85 fof(f2596,plain,(
% 18.81/2.85 sk0_0(powerset(empty_set))=empty_set),
% 18.81/2.85 inference(resolution,[status(thm)],[f2522,f170])).
% 18.81/2.85 fof(f2604,plain,(
% 18.81/2.85 ![X0,X1,X2]: (~in(X0,X1)|~element(X1,powerset(X2))|in(X0,X2))),
% 18.81/2.85 inference(forward_subsumption_resolution,[status(thm)],[f1667,f162])).
% 18.81/2.85 fof(f2607,plain,(
% 18.81/2.85 ![X0,X1]: (~element(X0,powerset(X1))|in(sk0_0(X0),X1)|empty(X0))),
% 18.81/2.85 inference(resolution,[status(thm)],[f2604,f1115])).
% 18.81/2.85 fof(f2610,plain,(
% 18.81/2.85 ![X0,X1]: (~in(X0,relation_rng(X1))|X0=apply(relation_composition(function_inverse(X1),X1),X0)|~empty(X1))),
% 18.81/2.85 inference(forward_subsumption_resolution,[status(thm)],[f2146,f50])).
% 18.81/2.85 fof(f2612,plain,(
% 18.81/2.85 spl0_156 <=> ~in(X0,empty_set)|X0=apply(relation_composition(function_inverse(empty_set),empty_set),X0)),
% 18.81/2.85 introduced(split_symbol_definition)).
% 18.81/2.85 fof(f2615,plain,(
% 18.81/2.85 ![X0]: (~in(X0,empty_set)|X0=apply(relation_composition(function_inverse(empty_set),empty_set),X0)|~empty(empty_set))),
% 18.81/2.85 inference(paramodulation,[status(thm)],[f887,f2610])).
% 18.81/2.85 fof(f2616,plain,(
% 18.81/2.85 spl0_156|~spl0_46),
% 18.81/2.85 inference(split_clause,[status(thm)],[f2615,f2612,f448])).
% 18.81/2.85 fof(f2638,plain,(
% 18.81/2.85 spl0_161 <=> relation_composition(X0,relation_composition(sk0_12,function_inverse(sk0_12)))=identity_relation(relation_dom(relation_composition(X0,relation_composition(sk0_12,function_inverse(sk0_12)))))|in(sk0_11(relation_dom(relation_composition(X0,relation_composition(sk0_12,function_inverse(sk0_12)))),relation_composition(X0,relation_composition(sk0_12,function_inverse(sk0_12)))),relation_dom(relation_composition(X0,relation_composition(sk0_12,function_inverse(sk0_12)))))|~relation(X0)|~function(X0)),
% 18.81/2.85 introduced(split_symbol_definition)).
% 18.81/2.85 fof(f2641,plain,(
% 18.81/2.85 ![X0]: (relation_composition(X0,relation_composition(sk0_12,function_inverse(sk0_12)))=identity_relation(relation_dom(relation_composition(X0,relation_composition(sk0_12,function_inverse(sk0_12)))))|in(sk0_11(relation_dom(relation_composition(X0,relation_composition(sk0_12,function_inverse(sk0_12)))),relation_composition(X0,relation_composition(sk0_12,function_inverse(sk0_12)))),relation_dom(relation_composition(X0,relation_composition(sk0_12,function_inverse(sk0_12)))))|~relation(X0)|~function(X0)|~relation(relation_composition(sk0_12,function_inverse(sk0_12)))|~spl0_122)),
% 18.81/2.85 inference(resolution,[status(thm)],[f1858,f1136])).
% 18.81/2.85 fof(f2642,plain,(
% 18.81/2.85 spl0_161|~spl0_6|~spl0_122),
% 18.81/2.85 inference(split_clause,[status(thm)],[f2641,f2638,f218,f1857])).
% 18.81/2.85 fof(f2643,plain,(
% 18.81/2.85 spl0_162 <=> in(sk0_11(relation_dom(relation_composition(sk0_12,function_inverse(sk0_12))),relation_composition(sk0_12,function_inverse(sk0_12))),relation_dom(relation_composition(sk0_12,function_inverse(sk0_12))))),
% 18.81/2.85 introduced(split_symbol_definition)).
% 18.81/2.85 fof(f2644,plain,(
% 18.81/2.85 in(sk0_11(relation_dom(relation_composition(sk0_12,function_inverse(sk0_12))),relation_composition(sk0_12,function_inverse(sk0_12))),relation_dom(relation_composition(sk0_12,function_inverse(sk0_12))))|~spl0_162),
% 18.81/2.85 inference(component_clause,[status(thm)],[f2643])).
% 18.81/2.85 fof(f2646,plain,(
% 18.81/2.85 ~relation(relation_composition(sk0_12,function_inverse(sk0_12)))|relation_composition(sk0_12,function_inverse(sk0_12))=identity_relation(relation_dom(relation_composition(sk0_12,function_inverse(sk0_12))))|in(sk0_11(relation_dom(relation_composition(sk0_12,function_inverse(sk0_12))),relation_composition(sk0_12,function_inverse(sk0_12))),relation_dom(relation_composition(sk0_12,function_inverse(sk0_12))))|~spl0_122),
% 18.81/2.85 inference(resolution,[status(thm)],[f1858,f186])).
% 18.81/2.85 fof(f2647,plain,(
% 18.81/2.85 ~spl0_6|spl0_123|spl0_162|~spl0_122),
% 18.81/2.85 inference(split_clause,[status(thm)],[f2646,f218,f1860,f2643,f1857])).
% 18.81/2.85 fof(f2648,plain,(
% 18.81/2.85 relation_composition(sk0_12,function_inverse(sk0_12))=identity_relation(relation_dom(sk0_12))|~spl0_4|~spl0_123),
% 18.81/2.85 inference(forward_demodulation,[status(thm)],[f205,f1861])).
% 18.81/2.85 fof(f2652,plain,(
% 18.81/2.85 in(sk0_11(relation_dom(sk0_12),relation_composition(sk0_12,function_inverse(sk0_12))),relation_dom(relation_composition(sk0_12,function_inverse(sk0_12))))|~spl0_4|~spl0_162),
% 18.81/2.85 inference(forward_demodulation,[status(thm)],[f205,f2644])).
% 18.81/2.85 fof(f2653,plain,(
% 18.81/2.85 in(sk0_11(relation_dom(sk0_12),relation_composition(sk0_12,function_inverse(sk0_12))),relation_dom(sk0_12))|~spl0_4|~spl0_162),
% 18.81/2.85 inference(forward_demodulation,[status(thm)],[f205,f2652])).
% 18.81/2.85 fof(f2693,plain,(
% 18.81/2.85 spl0_165 <=> sk0_0(relation_rng(sk0_12))=apply(sk0_12,apply(function_inverse(sk0_12),sk0_0(relation_rng(sk0_12))))),
% 18.81/2.85 introduced(split_symbol_definition)).
% 18.81/2.85 fof(f2696,plain,(
% 18.81/2.85 sk0_0(relation_rng(sk0_12))=apply(sk0_12,apply(function_inverse(sk0_12),sk0_0(relation_rng(sk0_12))))|empty(relation_rng(sk0_12))|~spl0_134),
% 18.81/2.85 inference(resolution,[status(thm)],[f2124,f1115])).
% 18.81/2.85 fof(f2697,plain,(
% 18.81/2.85 spl0_165|spl0_58|~spl0_134),
% 18.81/2.85 inference(split_clause,[status(thm)],[f2696,f2693,f624,f2123])).
% 18.81/2.85 fof(f2862,plain,(
% 18.81/2.85 spl0_170 <=> sk0_0(relation_rng(sk0_12))=apply(relation_composition(function_inverse(sk0_12),sk0_12),sk0_0(relation_rng(sk0_12)))),
% 18.81/2.85 introduced(split_symbol_definition)).
% 18.81/2.85 fof(f2865,plain,(
% 18.81/2.85 sk0_0(relation_rng(sk0_12))=apply(relation_composition(function_inverse(sk0_12),sk0_12),sk0_0(relation_rng(sk0_12)))|empty(relation_rng(sk0_12))|~spl0_136),
% 18.81/2.85 inference(resolution,[status(thm)],[f2136,f1115])).
% 18.81/2.85 fof(f2866,plain,(
% 18.81/2.85 spl0_170|spl0_58|~spl0_136),
% 18.81/2.85 inference(split_clause,[status(thm)],[f2865,f2862,f624,f2135])).
% 18.81/2.85 fof(f2883,plain,(
% 18.81/2.85 spl0_172 <=> relation_composition(X0,function_inverse(empty_set))=identity_relation(relation_dom(relation_composition(X0,function_inverse(empty_set))))|in(sk0_11(relation_dom(relation_composition(X0,function_inverse(empty_set))),relation_composition(X0,function_inverse(empty_set))),relation_dom(relation_composition(X0,function_inverse(empty_set))))|~relation(X0)|~function(X0)),
% 18.81/2.85 introduced(split_symbol_definition)).
% 18.81/2.85 fof(f2920,plain,(
% 18.81/2.85 spl0_177 <=> relation(sk0_0(powerset(empty_set)))),
% 18.81/2.85 introduced(split_symbol_definition)).
% 18.81/2.85 fof(f2923,plain,(
% 18.81/2.85 spl0_178 <=> function(sk0_0(powerset(empty_set)))),
% 18.81/2.85 introduced(split_symbol_definition)).
% 18.81/2.85 fof(f2925,plain,(
% 18.81/2.85 ~function(sk0_0(powerset(empty_set)))|spl0_178),
% 18.81/2.85 inference(component_clause,[status(thm)],[f2923])).
% 18.81/2.85 fof(f2931,plain,(
% 18.81/2.85 spl0_180 <=> empty(sk0_0(powerset(empty_set)))),
% 18.81/2.85 introduced(split_symbol_definition)).
% 18.81/2.85 fof(f2941,plain,(
% 18.81/2.85 spl0_181 <=> ~in(X0,empty_set)|X0=apply(relation_composition(function_inverse(sk0_0(powerset(empty_set))),sk0_0(powerset(empty_set))),X0)),
% 18.86/2.86 introduced(split_symbol_definition)).
% 18.86/2.86 fof(f2944,plain,(
% 18.86/2.86 ![X0]: (~in(X0,empty_set)|X0=apply(relation_composition(function_inverse(sk0_0(powerset(empty_set))),sk0_0(powerset(empty_set))),X0)|~empty(sk0_0(powerset(empty_set))))),
% 18.86/2.86 inference(paramodulation,[status(thm)],[f2594,f2610])).
% 18.86/2.86 fof(f2945,plain,(
% 18.86/2.86 spl0_181|~spl0_180),
% 18.86/2.86 inference(split_clause,[status(thm)],[f2944,f2941,f2931])).
% 18.86/2.86 fof(f2954,plain,(
% 18.86/2.86 ~empty(empty_set)|empty(sk0_0(powerset(empty_set)))),
% 18.86/2.86 inference(paramodulation,[status(thm)],[f2595,f196])).
% 18.86/2.86 fof(f2955,plain,(
% 18.86/2.86 ~spl0_46|spl0_180),
% 18.86/2.86 inference(split_clause,[status(thm)],[f2954,f448,f2931])).
% 18.86/2.86 fof(f2956,plain,(
% 18.86/2.86 ~empty(empty_set)|relation(sk0_0(powerset(empty_set)))),
% 18.86/2.86 inference(paramodulation,[status(thm)],[f2595,f195])).
% 18.86/2.86 fof(f2957,plain,(
% 18.86/2.86 ~spl0_46|spl0_177),
% 18.86/2.86 inference(split_clause,[status(thm)],[f2956,f448,f2920])).
% 18.86/2.86 fof(f3042,plain,(
% 18.86/2.86 spl0_182 <=> empty(powerset(empty_set))),
% 18.86/2.86 introduced(split_symbol_definition)).
% 18.86/2.86 fof(f3043,plain,(
% 18.86/2.86 empty(powerset(empty_set))|~spl0_182),
% 18.86/2.86 inference(component_clause,[status(thm)],[f3042])).
% 18.86/2.86 fof(f3045,plain,(
% 18.86/2.86 spl0_183 <=> in(powerset(empty_set),empty_set)),
% 18.86/2.86 introduced(split_symbol_definition)).
% 18.86/2.86 fof(f3048,plain,(
% 18.86/2.86 empty(powerset(empty_set))|~in(powerset(empty_set),empty_set)),
% 18.86/2.86 inference(paramodulation,[status(thm)],[f2596,f1621])).
% 18.86/2.86 fof(f3049,plain,(
% 18.86/2.86 spl0_182|~spl0_183),
% 18.86/2.86 inference(split_clause,[status(thm)],[f3048,f3042,f3045])).
% 18.86/2.86 fof(f3050,plain,(
% 18.86/2.86 spl0_184 <=> in(empty_set,powerset(empty_set))),
% 18.86/2.86 introduced(split_symbol_definition)).
% 18.86/2.86 fof(f3053,plain,(
% 18.86/2.86 empty(powerset(empty_set))|in(empty_set,powerset(empty_set))),
% 18.86/2.86 inference(paramodulation,[status(thm)],[f2596,f1115])).
% 18.86/2.86 fof(f3054,plain,(
% 18.86/2.86 spl0_182|spl0_184),
% 18.86/2.86 inference(split_clause,[status(thm)],[f3053,f3042,f3050])).
% 18.86/2.86 fof(f3056,plain,(
% 18.86/2.86 $false|~spl0_182),
% 18.86/2.86 inference(forward_subsumption_resolution,[status(thm)],[f3043,f74])).
% 18.86/2.86 fof(f3057,plain,(
% 18.86/2.86 ~spl0_182),
% 18.86/2.86 inference(contradiction_clause,[status(thm)],[f3056])).
% 18.86/2.86 fof(f3189,plain,(
% 18.86/2.86 spl0_187 <=> empty(identity_relation(relation_rng(sk0_12)))),
% 18.86/2.86 introduced(split_symbol_definition)).
% 18.86/2.86 fof(f3190,plain,(
% 18.86/2.86 empty(identity_relation(relation_rng(sk0_12)))|~spl0_187),
% 18.86/2.86 inference(component_clause,[status(thm)],[f3189])).
% 18.86/2.86 fof(f3233,plain,(
% 18.86/2.86 ~function(empty_set)|spl0_178),
% 18.86/2.86 inference(forward_demodulation,[status(thm)],[f2596,f2925])).
% 18.86/2.86 fof(f3234,plain,(
% 18.86/2.86 $false|spl0_178),
% 18.86/2.86 inference(forward_subsumption_resolution,[status(thm)],[f3233,f588])).
% 18.86/2.86 fof(f3235,plain,(
% 18.86/2.86 spl0_178),
% 18.86/2.86 inference(contradiction_clause,[status(thm)],[f3234])).
% 18.86/2.86 fof(f3541,plain,(
% 18.86/2.86 apply(identity_relation(relation_rng(sk0_12)),sk0_0(relation_rng(sk0_12)))=sk0_0(relation_rng(sk0_12))|spl0_58),
% 18.86/2.86 inference(resolution,[status(thm)],[f1620,f626])).
% 18.86/2.86 fof(f3637,plain,(
% 18.86/2.86 ![X0]: (apply(identity_relation(X0),sk0_0(X0))=sk0_0(X0)|X0=empty_set)),
% 18.86/2.86 inference(resolution,[status(thm)],[f1620,f170])).
% 18.86/2.86 fof(f3739,plain,(
% 18.86/2.86 apply(identity_relation(relation_composition(function_inverse(sk0_12),sk0_12)),sk0_0(relation_composition(function_inverse(sk0_12),sk0_12)))=sk0_0(relation_composition(function_inverse(sk0_12),sk0_12))|spl0_56),
% 18.86/2.86 inference(resolution,[status(thm)],[f620,f1620])).
% 18.86/2.86 fof(f4283,plain,(
% 18.86/2.86 ![X0,X1]: (relation_composition(X0,sk0_12)=identity_relation(relation_dom(relation_composition(X0,sk0_12)))|~relation(X0)|~function(X0)|~element(relation_dom(relation_composition(X0,sk0_12)),powerset(X1))|~empty(X1)|~spl0_128)),
% 18.86/2.86 inference(resolution,[status(thm)],[f1902,f162])).
% 18.86/2.86 fof(f4286,plain,(
% 18.86/2.86 ![X0]: (relation_composition(X0,sk0_12)=identity_relation(relation_dom(relation_composition(X0,sk0_12)))|~relation(X0)|~function(X0)|~empty(relation_dom(relation_composition(X0,sk0_12)))|~spl0_128)),
% 18.86/2.86 inference(resolution,[status(thm)],[f1902,f173])).
% 18.86/2.86 fof(f4293,plain,(
% 18.86/2.86 spl0_190 <=> relation_composition(empty_set,sk0_12)=identity_relation(relation_dom(relation_composition(empty_set,sk0_12)))),
% 18.86/2.86 introduced(split_symbol_definition)).
% 18.86/2.86 fof(f4306,plain,(
% 18.86/2.86 spl0_193 <=> in(sk0_11(relation_dom(relation_composition(function_inverse(sk0_12),sk0_12)),relation_composition(function_inverse(sk0_12),sk0_12)),relation_rng(sk0_12))),
% 18.86/2.86 introduced(split_symbol_definition)).
% 18.86/2.86 fof(f4307,plain,(
% 18.86/2.86 in(sk0_11(relation_dom(relation_composition(function_inverse(sk0_12),sk0_12)),relation_composition(function_inverse(sk0_12),sk0_12)),relation_rng(sk0_12))|~spl0_193),
% 18.86/2.86 inference(component_clause,[status(thm)],[f4306])).
% 18.86/2.86 fof(f4309,plain,(
% 18.86/2.86 relation_composition(function_inverse(sk0_12),sk0_12)=identity_relation(relation_dom(relation_composition(function_inverse(sk0_12),sk0_12)))|in(sk0_11(relation_dom(relation_composition(function_inverse(sk0_12),sk0_12)),relation_composition(function_inverse(sk0_12),sk0_12)),relation_rng(sk0_12))|~relation(function_inverse(sk0_12))|~function(function_inverse(sk0_12))|~spl0_128|~spl0_48),
% 18.86/2.86 inference(paramodulation,[status(thm)],[f514,f1902])).
% 18.86/2.86 fof(f4310,plain,(
% 18.86/2.86 spl0_120|spl0_193|~spl0_10|~spl0_92|~spl0_128|~spl0_48),
% 18.86/2.86 inference(split_clause,[status(thm)],[f4309,f1836,f4306,f236,f1173,f1901,f513])).
% 18.86/2.86 fof(f4320,plain,(
% 18.86/2.86 in(sk0_11(relation_rng(sk0_12),relation_composition(function_inverse(sk0_12),sk0_12)),relation_rng(sk0_12))|~spl0_48|~spl0_193),
% 18.86/2.86 inference(forward_demodulation,[status(thm)],[f514,f4307])).
% 18.86/2.86 fof(f4459,plain,(
% 18.86/2.86 ![X0]: (relation_composition(X0,sk0_1)=identity_relation(relation_dom(relation_composition(X0,sk0_1)))|~relation(X0)|~function(X0)|~empty(relation_dom(relation_composition(X0,sk0_1)))|~spl0_131)),
% 18.86/2.86 inference(resolution,[status(thm)],[f1919,f173])).
% 18.86/2.86 fof(f4461,plain,(
% 18.86/2.86 spl0_208 <=> relation_composition(empty_set,sk0_1)=identity_relation(relation_dom(relation_composition(empty_set,sk0_1)))),
% 18.86/2.86 introduced(split_symbol_definition)).
% 18.86/2.86 fof(f4890,plain,(
% 18.86/2.86 empty(relation_composition(identity_relation(empty_set),function_inverse(identity_relation(sk0_5))))|~spl0_33),
% 18.86/2.86 inference(forward_demodulation,[status(thm)],[f563,f388])).
% 18.86/2.86 fof(f4891,plain,(
% 18.86/2.86 empty(relation_composition(empty_set,function_inverse(identity_relation(sk0_5))))|~spl0_33),
% 18.86/2.86 inference(forward_demodulation,[status(thm)],[f850,f4890])).
% 18.86/2.86 fof(f4892,plain,(
% 18.86/2.86 empty(relation_composition(empty_set,function_inverse(identity_relation(empty_set))))|~spl0_33),
% 18.86/2.86 inference(forward_demodulation,[status(thm)],[f563,f4891])).
% 18.86/2.86 fof(f4893,plain,(
% 18.86/2.86 empty(relation_composition(empty_set,function_inverse(empty_set)))|~spl0_33),
% 18.86/2.86 inference(forward_demodulation,[status(thm)],[f850,f4892])).
% 18.86/2.86 fof(f4895,plain,(
% 18.86/2.86 ~relation(relation_composition(identity_relation(empty_set),function_inverse(identity_relation(sk0_4))))|spl0_37),
% 18.86/2.86 inference(forward_demodulation,[status(thm)],[f564,f411])).
% 18.86/2.86 fof(f4896,plain,(
% 18.86/2.86 ~relation(relation_composition(empty_set,function_inverse(identity_relation(sk0_4))))|spl0_37),
% 18.86/2.86 inference(forward_demodulation,[status(thm)],[f850,f4895])).
% 18.86/2.86 fof(f4897,plain,(
% 18.86/2.86 ~relation(relation_composition(empty_set,function_inverse(identity_relation(empty_set))))|spl0_37),
% 18.86/2.86 inference(forward_demodulation,[status(thm)],[f564,f4896])).
% 18.86/2.86 fof(f4898,plain,(
% 18.86/2.86 ~relation(relation_composition(empty_set,function_inverse(empty_set)))|spl0_37),
% 18.86/2.86 inference(forward_demodulation,[status(thm)],[f850,f4897])).
% 18.86/2.86 fof(f4899,plain,(
% 18.86/2.86 ~relation(empty_set)|~spl0_12|spl0_37),
% 18.86/2.86 inference(forward_demodulation,[status(thm)],[f755,f4898])).
% 18.86/2.86 fof(f4900,plain,(
% 18.86/2.86 $false|~spl0_12|spl0_37),
% 18.86/2.86 inference(forward_subsumption_resolution,[status(thm)],[f4899,f69])).
% 18.86/2.86 fof(f4901,plain,(
% 18.86/2.86 ~spl0_12|spl0_37),
% 18.86/2.86 inference(contradiction_clause,[status(thm)],[f4900])).
% 18.86/2.86 fof(f4914,plain,(
% 18.86/2.86 ~relation(relation_composition(identity_relation(empty_set),function_inverse(identity_relation(sk0_2))))|spl0_41),
% 18.86/2.86 inference(forward_demodulation,[status(thm)],[f565,f429])).
% 18.86/2.86 fof(f4915,plain,(
% 18.86/2.86 ~relation(relation_composition(empty_set,function_inverse(identity_relation(sk0_2))))|spl0_41),
% 18.86/2.86 inference(forward_demodulation,[status(thm)],[f850,f4914])).
% 18.86/2.86 fof(f4916,plain,(
% 18.86/2.86 ~relation(relation_composition(empty_set,function_inverse(identity_relation(empty_set))))|spl0_41),
% 18.86/2.86 inference(forward_demodulation,[status(thm)],[f565,f4915])).
% 18.86/2.86 fof(f4917,plain,(
% 18.86/2.86 ~relation(relation_composition(empty_set,function_inverse(empty_set)))|spl0_41),
% 18.86/2.86 inference(forward_demodulation,[status(thm)],[f850,f4916])).
% 18.86/2.86 fof(f4918,plain,(
% 18.86/2.86 ~relation(empty_set)|~spl0_12|spl0_41),
% 18.86/2.86 inference(forward_demodulation,[status(thm)],[f755,f4917])).
% 18.86/2.86 fof(f4919,plain,(
% 18.86/2.86 $false|~spl0_12|spl0_41),
% 18.86/2.86 inference(forward_subsumption_resolution,[status(thm)],[f4918,f69])).
% 18.86/2.86 fof(f4920,plain,(
% 18.86/2.86 ~spl0_12|spl0_41),
% 18.86/2.86 inference(contradiction_clause,[status(thm)],[f4919])).
% 18.86/2.86 fof(f5265,plain,(
% 18.86/2.86 sk0_11(relation_dom(sk0_12),relation_composition(sk0_12,function_inverse(sk0_12)))=apply(relation_composition(sk0_12,function_inverse(sk0_12)),sk0_11(relation_dom(sk0_12),relation_composition(sk0_12,function_inverse(sk0_12))))|~spl0_4|~spl0_162|~spl0_132),
% 18.86/2.86 inference(resolution,[status(thm)],[f2653,f2112])).
% 18.86/2.86 fof(f5266,plain,(
% 18.86/2.86 $false|spl0_124|~spl0_4|~spl0_162|~spl0_132),
% 18.86/2.86 inference(forward_subsumption_resolution,[status(thm)],[f5265,f1874])).
% 18.86/2.86 fof(f5267,plain,(
% 18.86/2.86 spl0_124|~spl0_4|~spl0_162|~spl0_132),
% 18.86/2.86 inference(contradiction_clause,[status(thm)],[f5266])).
% 18.86/2.86 fof(f5534,plain,(
% 18.86/2.86 spl0_222 <=> relation_composition(X0,relation_composition(sk0_12,sk0_12))=identity_relation(relation_dom(relation_composition(X0,relation_composition(sk0_12,sk0_12))))|in(sk0_11(relation_dom(relation_composition(X0,relation_composition(sk0_12,sk0_12))),relation_composition(X0,relation_composition(sk0_12,sk0_12))),relation_dom(relation_composition(X0,relation_composition(sk0_12,sk0_12))))|~relation(X0)|~function(X0)),
% 18.86/2.86 introduced(split_symbol_definition)).
% 18.86/2.86 fof(f5537,plain,(
% 18.86/2.86 ![X0]: (relation_composition(X0,relation_composition(sk0_12,sk0_12))=identity_relation(relation_dom(relation_composition(X0,relation_composition(sk0_12,sk0_12))))|in(sk0_11(relation_dom(relation_composition(X0,relation_composition(sk0_12,sk0_12))),relation_composition(X0,relation_composition(sk0_12,sk0_12))),relation_dom(relation_composition(X0,relation_composition(sk0_12,sk0_12))))|~relation(X0)|~function(X0)|~relation(sk0_12)|~relation(sk0_12))),
% 18.86/2.86 inference(resolution,[status(thm)],[f1917,f166])).
% 18.86/2.86 fof(f5538,plain,(
% 18.86/2.86 spl0_222|~spl0_2),
% 18.86/2.86 inference(split_clause,[status(thm)],[f5537,f5534,f198])).
% 18.86/2.86 fof(f5539,plain,(
% 18.86/2.86 spl0_223 <=> relation_composition(X0,relation_composition(sk0_12,X1))=identity_relation(relation_dom(relation_composition(X0,relation_composition(sk0_12,X1))))|in(sk0_11(relation_dom(relation_composition(X0,relation_composition(sk0_12,X1))),relation_composition(X0,relation_composition(sk0_12,X1))),relation_dom(relation_composition(X0,relation_composition(sk0_12,X1))))|~relation(X0)|~function(X0)|~relation(X1)|~function(X1)),
% 18.86/2.86 introduced(split_symbol_definition)).
% 18.86/2.86 fof(f5540,plain,(
% 18.86/2.86 ![X0,X1]: (relation_composition(X0,relation_composition(sk0_12,X1))=identity_relation(relation_dom(relation_composition(X0,relation_composition(sk0_12,X1))))|in(sk0_11(relation_dom(relation_composition(X0,relation_composition(sk0_12,X1))),relation_composition(X0,relation_composition(sk0_12,X1))),relation_dom(relation_composition(X0,relation_composition(sk0_12,X1))))|~relation(X0)|~function(X0)|~relation(X1)|~function(X1)|~spl0_223)),
% 18.86/2.86 inference(component_clause,[status(thm)],[f5539])).
% 18.86/2.86 fof(f5542,plain,(
% 18.86/2.86 ![X0,X1]: (relation_composition(X0,relation_composition(sk0_12,X1))=identity_relation(relation_dom(relation_composition(X0,relation_composition(sk0_12,X1))))|in(sk0_11(relation_dom(relation_composition(X0,relation_composition(sk0_12,X1))),relation_composition(X0,relation_composition(sk0_12,X1))),relation_dom(relation_composition(X0,relation_composition(sk0_12,X1))))|~relation(X0)|~function(X0)|~relation(sk0_12)|~relation(X1)|~function(X1))),
% 18.86/2.86 inference(resolution,[status(thm)],[f1917,f166])).
% 18.86/2.86 fof(f5543,plain,(
% 18.86/2.86 spl0_223|~spl0_2),
% 18.86/2.86 inference(split_clause,[status(thm)],[f5542,f5539,f198])).
% 18.86/2.86 fof(f5544,plain,(
% 18.86/2.86 spl0_224 <=> relation_composition(X0,relation_composition(empty_set,empty_set))=identity_relation(relation_dom(relation_composition(X0,relation_composition(empty_set,empty_set))))|in(sk0_11(relation_dom(relation_composition(X0,relation_composition(empty_set,empty_set))),relation_composition(X0,relation_composition(empty_set,empty_set))),relation_dom(relation_composition(X0,relation_composition(empty_set,empty_set))))|~relation(X0)|~function(X0)),
% 18.86/2.86 introduced(split_symbol_definition)).
% 18.86/2.86 fof(f5547,plain,(
% 18.86/2.86 ![X0]: (relation_composition(X0,relation_composition(empty_set,empty_set))=identity_relation(relation_dom(relation_composition(X0,relation_composition(empty_set,empty_set))))|in(sk0_11(relation_dom(relation_composition(X0,relation_composition(empty_set,empty_set))),relation_composition(X0,relation_composition(empty_set,empty_set))),relation_dom(relation_composition(X0,relation_composition(empty_set,empty_set))))|~relation(X0)|~function(X0)|~relation(empty_set)|~relation(empty_set))),
% 18.86/2.86 inference(resolution,[status(thm)],[f1917,f588])).
% 18.86/2.86 fof(f5548,plain,(
% 18.86/2.86 spl0_224|~spl0_47),
% 18.86/2.86 inference(split_clause,[status(thm)],[f5547,f5544,f453])).
% 18.86/2.86 fof(f5549,plain,(
% 18.86/2.86 spl0_225 <=> relation_composition(X0,relation_composition(empty_set,X1))=identity_relation(relation_dom(relation_composition(X0,relation_composition(empty_set,X1))))|in(sk0_11(relation_dom(relation_composition(X0,relation_composition(empty_set,X1))),relation_composition(X0,relation_composition(empty_set,X1))),relation_dom(relation_composition(X0,relation_composition(empty_set,X1))))|~relation(X0)|~function(X0)|~relation(X1)|~function(X1)),
% 18.86/2.86 introduced(split_symbol_definition)).
% 18.86/2.86 fof(f5550,plain,(
% 18.86/2.86 ![X0,X1]: (relation_composition(X0,relation_composition(empty_set,X1))=identity_relation(relation_dom(relation_composition(X0,relation_composition(empty_set,X1))))|in(sk0_11(relation_dom(relation_composition(X0,relation_composition(empty_set,X1))),relation_composition(X0,relation_composition(empty_set,X1))),relation_dom(relation_composition(X0,relation_composition(empty_set,X1))))|~relation(X0)|~function(X0)|~relation(X1)|~function(X1)|~spl0_225)),
% 18.86/2.86 inference(component_clause,[status(thm)],[f5549])).
% 18.86/2.86 fof(f5552,plain,(
% 18.86/2.86 ![X0,X1]: (relation_composition(X0,relation_composition(empty_set,X1))=identity_relation(relation_dom(relation_composition(X0,relation_composition(empty_set,X1))))|in(sk0_11(relation_dom(relation_composition(X0,relation_composition(empty_set,X1))),relation_composition(X0,relation_composition(empty_set,X1))),relation_dom(relation_composition(X0,relation_composition(empty_set,X1))))|~relation(X0)|~function(X0)|~relation(empty_set)|~relation(X1)|~function(X1))),
% 18.86/2.86 inference(resolution,[status(thm)],[f1917,f588])).
% 18.86/2.86 fof(f5553,plain,(
% 18.86/2.86 spl0_225|~spl0_47),
% 18.86/2.86 inference(split_clause,[status(thm)],[f5552,f5549,f453])).
% 18.86/2.86 fof(f5554,plain,(
% 18.86/2.86 spl0_226 <=> relation_composition(X0,relation_composition(relation_composition(function_inverse(sk0_12),sk0_12),relation_composition(function_inverse(sk0_12),sk0_12)))=identity_relation(relation_dom(relation_composition(X0,relation_composition(relation_composition(function_inverse(sk0_12),sk0_12),relation_composition(function_inverse(sk0_12),sk0_12)))))|in(sk0_11(relation_dom(relation_composition(X0,relation_composition(relation_composition(function_inverse(sk0_12),sk0_12),relation_composition(function_inverse(sk0_12),sk0_12)))),relation_composition(X0,relation_composition(relation_composition(function_inverse(sk0_12),sk0_12),relation_composition(function_inverse(sk0_12),sk0_12)))),relation_dom(relation_composition(X0,relation_composition(relation_composition(function_inverse(sk0_12),sk0_12),relation_composition(function_inverse(sk0_12),sk0_12)))))|~relation(X0)|~function(X0)),
% 18.86/2.86 introduced(split_symbol_definition)).
% 18.86/2.86 fof(f5557,plain,(
% 18.86/2.86 ![X0]: (relation_composition(X0,relation_composition(relation_composition(function_inverse(sk0_12),sk0_12),relation_composition(function_inverse(sk0_12),sk0_12)))=identity_relation(relation_dom(relation_composition(X0,relation_composition(relation_composition(function_inverse(sk0_12),sk0_12),relation_composition(function_inverse(sk0_12),sk0_12)))))|in(sk0_11(relation_dom(relation_composition(X0,relation_composition(relation_composition(function_inverse(sk0_12),sk0_12),relation_composition(function_inverse(sk0_12),sk0_12)))),relation_composition(X0,relation_composition(relation_composition(function_inverse(sk0_12),sk0_12),relation_composition(function_inverse(sk0_12),sk0_12)))),relation_dom(relation_composition(X0,relation_composition(relation_composition(function_inverse(sk0_12),sk0_12),relation_composition(function_inverse(sk0_12),sk0_12)))))|~relation(X0)|~function(X0)|~relation(relation_composition(function_inverse(sk0_12),sk0_12))|~relation(relation_composition(function_inverse(sk0_12),sk0_12))|~spl0_93)),
% 18.86/2.86 inference(resolution,[status(thm)],[f1917,f1189])).
% 18.86/2.86 fof(f5558,plain,(
% 18.86/2.86 spl0_226|~spl0_57|~spl0_93),
% 18.86/2.86 inference(split_clause,[status(thm)],[f5557,f5554,f621,f1188])).
% 18.86/2.86 fof(f5559,plain,(
% 18.86/2.86 spl0_227 <=> relation_composition(X0,relation_composition(relation_composition(function_inverse(sk0_12),sk0_12),X1))=identity_relation(relation_dom(relation_composition(X0,relation_composition(relation_composition(function_inverse(sk0_12),sk0_12),X1))))|in(sk0_11(relation_dom(relation_composition(X0,relation_composition(relation_composition(function_inverse(sk0_12),sk0_12),X1))),relation_composition(X0,relation_composition(relation_composition(function_inverse(sk0_12),sk0_12),X1))),relation_dom(relation_composition(X0,relation_composition(relation_composition(function_inverse(sk0_12),sk0_12),X1))))|~relation(X0)|~function(X0)|~relation(X1)|~function(X1)),
% 18.86/2.86 introduced(split_symbol_definition)).
% 18.86/2.86 fof(f5562,plain,(
% 18.86/2.86 ![X0,X1]: (relation_composition(X0,relation_composition(relation_composition(function_inverse(sk0_12),sk0_12),X1))=identity_relation(relation_dom(relation_composition(X0,relation_composition(relation_composition(function_inverse(sk0_12),sk0_12),X1))))|in(sk0_11(relation_dom(relation_composition(X0,relation_composition(relation_composition(function_inverse(sk0_12),sk0_12),X1))),relation_composition(X0,relation_composition(relation_composition(function_inverse(sk0_12),sk0_12),X1))),relation_dom(relation_composition(X0,relation_composition(relation_composition(function_inverse(sk0_12),sk0_12),X1))))|~relation(X0)|~function(X0)|~relation(relation_composition(function_inverse(sk0_12),sk0_12))|~relation(X1)|~function(X1)|~spl0_93)),
% 18.86/2.86 inference(resolution,[status(thm)],[f1917,f1189])).
% 18.86/2.86 fof(f5563,plain,(
% 18.86/2.86 spl0_227|~spl0_57|~spl0_93),
% 18.86/2.86 inference(split_clause,[status(thm)],[f5562,f5559,f621,f1188])).
% 18.86/2.86 fof(f5569,plain,(
% 18.86/2.86 spl0_228 <=> relation_composition(X0,relation_composition(sk0_1,sk0_1))=identity_relation(relation_dom(relation_composition(X0,relation_composition(sk0_1,sk0_1))))|in(sk0_11(relation_dom(relation_composition(X0,relation_composition(sk0_1,sk0_1))),relation_composition(X0,relation_composition(sk0_1,sk0_1))),relation_dom(relation_composition(X0,relation_composition(sk0_1,sk0_1))))|~relation(X0)|~function(X0)),
% 18.86/2.86 introduced(split_symbol_definition)).
% 18.86/2.86 fof(f5572,plain,(
% 18.86/2.86 ![X0]: (relation_composition(X0,relation_composition(sk0_1,sk0_1))=identity_relation(relation_dom(relation_composition(X0,relation_composition(sk0_1,sk0_1))))|in(sk0_11(relation_dom(relation_composition(X0,relation_composition(sk0_1,sk0_1))),relation_composition(X0,relation_composition(sk0_1,sk0_1))),relation_dom(relation_composition(X0,relation_composition(sk0_1,sk0_1))))|~relation(X0)|~function(X0)|~relation(sk0_1)|~relation(sk0_1))),
% 18.86/2.86 inference(resolution,[status(thm)],[f1917,f96])).
% 18.86/2.86 fof(f5573,plain,(
% 18.86/2.86 spl0_228|~spl0_87),
% 18.86/2.86 inference(split_clause,[status(thm)],[f5572,f5569,f1137])).
% 18.86/2.86 fof(f5574,plain,(
% 18.86/2.86 spl0_229 <=> relation_composition(X0,relation_composition(sk0_1,X1))=identity_relation(relation_dom(relation_composition(X0,relation_composition(sk0_1,X1))))|in(sk0_11(relation_dom(relation_composition(X0,relation_composition(sk0_1,X1))),relation_composition(X0,relation_composition(sk0_1,X1))),relation_dom(relation_composition(X0,relation_composition(sk0_1,X1))))|~relation(X0)|~function(X0)|~relation(X1)|~function(X1)),
% 18.86/2.86 introduced(split_symbol_definition)).
% 18.86/2.86 fof(f5575,plain,(
% 18.86/2.86 ![X0,X1]: (relation_composition(X0,relation_composition(sk0_1,X1))=identity_relation(relation_dom(relation_composition(X0,relation_composition(sk0_1,X1))))|in(sk0_11(relation_dom(relation_composition(X0,relation_composition(sk0_1,X1))),relation_composition(X0,relation_composition(sk0_1,X1))),relation_dom(relation_composition(X0,relation_composition(sk0_1,X1))))|~relation(X0)|~function(X0)|~relation(X1)|~function(X1)|~spl0_229)),
% 18.86/2.86 inference(component_clause,[status(thm)],[f5574])).
% 18.86/2.86 fof(f5577,plain,(
% 18.86/2.86 ![X0,X1]: (relation_composition(X0,relation_composition(sk0_1,X1))=identity_relation(relation_dom(relation_composition(X0,relation_composition(sk0_1,X1))))|in(sk0_11(relation_dom(relation_composition(X0,relation_composition(sk0_1,X1))),relation_composition(X0,relation_composition(sk0_1,X1))),relation_dom(relation_composition(X0,relation_composition(sk0_1,X1))))|~relation(X0)|~function(X0)|~relation(sk0_1)|~relation(X1)|~function(X1))),
% 18.86/2.86 inference(resolution,[status(thm)],[f1917,f96])).
% 18.86/2.86 fof(f5578,plain,(
% 18.86/2.86 spl0_229|~spl0_87),
% 18.86/2.86 inference(split_clause,[status(thm)],[f5577,f5574,f1137])).
% 18.86/2.86 fof(f5589,plain,(
% 18.86/2.86 spl0_232 <=> relation_composition(X0,relation_composition(function_inverse(sk0_12),function_inverse(sk0_12)))=identity_relation(relation_dom(relation_composition(X0,relation_composition(function_inverse(sk0_12),function_inverse(sk0_12)))))|in(sk0_11(relation_dom(relation_composition(X0,relation_composition(function_inverse(sk0_12),function_inverse(sk0_12)))),relation_composition(X0,relation_composition(function_inverse(sk0_12),function_inverse(sk0_12)))),relation_dom(relation_composition(X0,relation_composition(function_inverse(sk0_12),function_inverse(sk0_12)))))|~relation(X0)|~function(X0)),
% 18.86/2.86 introduced(split_symbol_definition)).
% 18.86/2.86 fof(f5592,plain,(
% 18.86/2.86 ![X0]: (relation_composition(X0,relation_composition(function_inverse(sk0_12),function_inverse(sk0_12)))=identity_relation(relation_dom(relation_composition(X0,relation_composition(function_inverse(sk0_12),function_inverse(sk0_12)))))|in(sk0_11(relation_dom(relation_composition(X0,relation_composition(function_inverse(sk0_12),function_inverse(sk0_12)))),relation_composition(X0,relation_composition(function_inverse(sk0_12),function_inverse(sk0_12)))),relation_dom(relation_composition(X0,relation_composition(function_inverse(sk0_12),function_inverse(sk0_12)))))|~relation(X0)|~function(X0)|~relation(function_inverse(sk0_12))|~relation(function_inverse(sk0_12))|~spl0_92)),
% 18.86/2.86 inference(resolution,[status(thm)],[f1917,f1174])).
% 18.86/2.86 fof(f5593,plain,(
% 18.86/2.86 spl0_232|~spl0_10|~spl0_92),
% 18.86/2.86 inference(split_clause,[status(thm)],[f5592,f5589,f236,f1173])).
% 18.86/2.86 fof(f5594,plain,(
% 18.86/2.86 spl0_233 <=> relation_composition(X0,relation_composition(function_inverse(sk0_12),X1))=identity_relation(relation_dom(relation_composition(X0,relation_composition(function_inverse(sk0_12),X1))))|in(sk0_11(relation_dom(relation_composition(X0,relation_composition(function_inverse(sk0_12),X1))),relation_composition(X0,relation_composition(function_inverse(sk0_12),X1))),relation_dom(relation_composition(X0,relation_composition(function_inverse(sk0_12),X1))))|~relation(X0)|~function(X0)|~relation(X1)|~function(X1)),
% 18.86/2.86 introduced(split_symbol_definition)).
% 18.86/2.86 fof(f5597,plain,(
% 18.86/2.86 ![X0,X1]: (relation_composition(X0,relation_composition(function_inverse(sk0_12),X1))=identity_relation(relation_dom(relation_composition(X0,relation_composition(function_inverse(sk0_12),X1))))|in(sk0_11(relation_dom(relation_composition(X0,relation_composition(function_inverse(sk0_12),X1))),relation_composition(X0,relation_composition(function_inverse(sk0_12),X1))),relation_dom(relation_composition(X0,relation_composition(function_inverse(sk0_12),X1))))|~relation(X0)|~function(X0)|~relation(function_inverse(sk0_12))|~relation(X1)|~function(X1)|~spl0_92)),
% 18.86/2.86 inference(resolution,[status(thm)],[f1917,f1174])).
% 18.86/2.86 fof(f5598,plain,(
% 18.86/2.86 spl0_233|~spl0_10|~spl0_92),
% 18.86/2.86 inference(split_clause,[status(thm)],[f5597,f5594,f236,f1173])).
% 18.86/2.86 fof(f5614,plain,(
% 18.86/2.86 spl0_234 <=> relation_composition(X0,relation_composition(X1,sk0_12))=identity_relation(relation_dom(relation_composition(X0,relation_composition(X1,sk0_12))))|in(sk0_11(relation_dom(relation_composition(X0,relation_composition(X1,sk0_12))),relation_composition(X0,relation_composition(X1,sk0_12))),relation_dom(relation_composition(X0,relation_composition(X1,sk0_12))))|~relation(X0)|~function(X0)|~relation(X1)|~function(X1)),
% 18.86/2.86 introduced(split_symbol_definition)).
% 18.86/2.86 fof(f5615,plain,(
% 18.86/2.86 ![X0,X1]: (relation_composition(X0,relation_composition(X1,sk0_12))=identity_relation(relation_dom(relation_composition(X0,relation_composition(X1,sk0_12))))|in(sk0_11(relation_dom(relation_composition(X0,relation_composition(X1,sk0_12))),relation_composition(X0,relation_composition(X1,sk0_12))),relation_dom(relation_composition(X0,relation_composition(X1,sk0_12))))|~relation(X0)|~function(X0)|~relation(X1)|~function(X1)|~spl0_234)),
% 18.86/2.86 inference(component_clause,[status(thm)],[f5614])).
% 18.86/2.86 fof(f5617,plain,(
% 18.86/2.86 ![X0,X1]: (relation_composition(X0,relation_composition(X1,sk0_12))=identity_relation(relation_dom(relation_composition(X0,relation_composition(X1,sk0_12))))|in(sk0_11(relation_dom(relation_composition(X0,relation_composition(X1,sk0_12))),relation_composition(X0,relation_composition(X1,sk0_12))),relation_dom(relation_composition(X0,relation_composition(X1,sk0_12))))|~relation(X0)|~function(X0)|~relation(X1)|~function(X1)|~relation(sk0_12))),
% 18.86/2.86 inference(resolution,[status(thm)],[f1917,f166])).
% 18.86/2.86 fof(f5618,plain,(
% 18.86/2.86 spl0_234|~spl0_2),
% 18.86/2.86 inference(split_clause,[status(thm)],[f5617,f5614,f198])).
% 18.86/2.86 fof(f5619,plain,(
% 18.86/2.86 spl0_235 <=> relation_composition(X0,relation_composition(X1,empty_set))=identity_relation(relation_dom(relation_composition(X0,relation_composition(X1,empty_set))))|in(sk0_11(relation_dom(relation_composition(X0,relation_composition(X1,empty_set))),relation_composition(X0,relation_composition(X1,empty_set))),relation_dom(relation_composition(X0,relation_composition(X1,empty_set))))|~relation(X0)|~function(X0)|~relation(X1)|~function(X1)),
% 18.86/2.86 introduced(split_symbol_definition)).
% 18.86/2.86 fof(f5620,plain,(
% 18.86/2.86 ![X0,X1]: (relation_composition(X0,relation_composition(X1,empty_set))=identity_relation(relation_dom(relation_composition(X0,relation_composition(X1,empty_set))))|in(sk0_11(relation_dom(relation_composition(X0,relation_composition(X1,empty_set))),relation_composition(X0,relation_composition(X1,empty_set))),relation_dom(relation_composition(X0,relation_composition(X1,empty_set))))|~relation(X0)|~function(X0)|~relation(X1)|~function(X1)|~spl0_235)),
% 18.86/2.86 inference(component_clause,[status(thm)],[f5619])).
% 18.86/2.86 fof(f5622,plain,(
% 18.86/2.86 ![X0,X1]: (relation_composition(X0,relation_composition(X1,empty_set))=identity_relation(relation_dom(relation_composition(X0,relation_composition(X1,empty_set))))|in(sk0_11(relation_dom(relation_composition(X0,relation_composition(X1,empty_set))),relation_composition(X0,relation_composition(X1,empty_set))),relation_dom(relation_composition(X0,relation_composition(X1,empty_set))))|~relation(X0)|~function(X0)|~relation(X1)|~function(X1)|~relation(empty_set))),
% 18.86/2.86 inference(resolution,[status(thm)],[f1917,f588])).
% 18.86/2.86 fof(f5623,plain,(
% 18.86/2.86 spl0_235|~spl0_47),
% 18.86/2.86 inference(split_clause,[status(thm)],[f5622,f5619,f453])).
% 18.86/2.86 fof(f5624,plain,(
% 18.86/2.86 spl0_236 <=> relation_composition(X0,relation_composition(X1,relation_composition(function_inverse(sk0_12),sk0_12)))=identity_relation(relation_dom(relation_composition(X0,relation_composition(X1,relation_composition(function_inverse(sk0_12),sk0_12)))))|in(sk0_11(relation_dom(relation_composition(X0,relation_composition(X1,relation_composition(function_inverse(sk0_12),sk0_12)))),relation_composition(X0,relation_composition(X1,relation_composition(function_inverse(sk0_12),sk0_12)))),relation_dom(relation_composition(X0,relation_composition(X1,relation_composition(function_inverse(sk0_12),sk0_12)))))|~relation(X0)|~function(X0)|~relation(X1)|~function(X1)),
% 18.86/2.86 introduced(split_symbol_definition)).
% 18.86/2.86 fof(f5627,plain,(
% 18.86/2.86 ![X0,X1]: (relation_composition(X0,relation_composition(X1,relation_composition(function_inverse(sk0_12),sk0_12)))=identity_relation(relation_dom(relation_composition(X0,relation_composition(X1,relation_composition(function_inverse(sk0_12),sk0_12)))))|in(sk0_11(relation_dom(relation_composition(X0,relation_composition(X1,relation_composition(function_inverse(sk0_12),sk0_12)))),relation_composition(X0,relation_composition(X1,relation_composition(function_inverse(sk0_12),sk0_12)))),relation_dom(relation_composition(X0,relation_composition(X1,relation_composition(function_inverse(sk0_12),sk0_12)))))|~relation(X0)|~function(X0)|~relation(X1)|~function(X1)|~relation(relation_composition(function_inverse(sk0_12),sk0_12))|~spl0_93)),
% 18.86/2.86 inference(resolution,[status(thm)],[f1917,f1189])).
% 18.86/2.86 fof(f5628,plain,(
% 18.86/2.86 spl0_236|~spl0_57|~spl0_93),
% 18.86/2.86 inference(split_clause,[status(thm)],[f5627,f5624,f621,f1188])).
% 18.86/2.86 fof(f5631,plain,(
% 18.86/2.86 spl0_237 <=> relation_composition(X0,relation_composition(X1,sk0_1))=identity_relation(relation_dom(relation_composition(X0,relation_composition(X1,sk0_1))))|in(sk0_11(relation_dom(relation_composition(X0,relation_composition(X1,sk0_1))),relation_composition(X0,relation_composition(X1,sk0_1))),relation_dom(relation_composition(X0,relation_composition(X1,sk0_1))))|~relation(X0)|~function(X0)|~relation(X1)|~function(X1)),
% 18.86/2.86 introduced(split_symbol_definition)).
% 18.86/2.86 fof(f5632,plain,(
% 18.86/2.86 ![X0,X1]: (relation_composition(X0,relation_composition(X1,sk0_1))=identity_relation(relation_dom(relation_composition(X0,relation_composition(X1,sk0_1))))|in(sk0_11(relation_dom(relation_composition(X0,relation_composition(X1,sk0_1))),relation_composition(X0,relation_composition(X1,sk0_1))),relation_dom(relation_composition(X0,relation_composition(X1,sk0_1))))|~relation(X0)|~function(X0)|~relation(X1)|~function(X1)|~spl0_237)),
% 18.86/2.86 inference(component_clause,[status(thm)],[f5631])).
% 18.86/2.86 fof(f5634,plain,(
% 18.86/2.86 ![X0,X1]: (relation_composition(X0,relation_composition(X1,sk0_1))=identity_relation(relation_dom(relation_composition(X0,relation_composition(X1,sk0_1))))|in(sk0_11(relation_dom(relation_composition(X0,relation_composition(X1,sk0_1))),relation_composition(X0,relation_composition(X1,sk0_1))),relation_dom(relation_composition(X0,relation_composition(X1,sk0_1))))|~relation(X0)|~function(X0)|~relation(X1)|~function(X1)|~relation(sk0_1))),
% 18.86/2.86 inference(resolution,[status(thm)],[f1917,f96])).
% 18.86/2.86 fof(f5635,plain,(
% 18.86/2.86 spl0_237|~spl0_87),
% 18.86/2.86 inference(split_clause,[status(thm)],[f5634,f5631,f1137])).
% 18.86/2.86 fof(f5641,plain,(
% 18.86/2.86 spl0_239 <=> relation_composition(X0,relation_composition(X1,function_inverse(sk0_12)))=identity_relation(relation_dom(relation_composition(X0,relation_composition(X1,function_inverse(sk0_12)))))|in(sk0_11(relation_dom(relation_composition(X0,relation_composition(X1,function_inverse(sk0_12)))),relation_composition(X0,relation_composition(X1,function_inverse(sk0_12)))),relation_dom(relation_composition(X0,relation_composition(X1,function_inverse(sk0_12)))))|~relation(X0)|~function(X0)|~relation(X1)|~function(X1)),
% 18.86/2.86 introduced(split_symbol_definition)).
% 18.86/2.86 fof(f5644,plain,(
% 18.86/2.86 ![X0,X1]: (relation_composition(X0,relation_composition(X1,function_inverse(sk0_12)))=identity_relation(relation_dom(relation_composition(X0,relation_composition(X1,function_inverse(sk0_12)))))|in(sk0_11(relation_dom(relation_composition(X0,relation_composition(X1,function_inverse(sk0_12)))),relation_composition(X0,relation_composition(X1,function_inverse(sk0_12)))),relation_dom(relation_composition(X0,relation_composition(X1,function_inverse(sk0_12)))))|~relation(X0)|~function(X0)|~relation(X1)|~function(X1)|~relation(function_inverse(sk0_12))|~spl0_92)),
% 18.86/2.86 inference(resolution,[status(thm)],[f1917,f1174])).
% 18.86/2.86 fof(f5645,plain,(
% 18.86/2.86 spl0_239|~spl0_10|~spl0_92),
% 18.86/2.86 inference(split_clause,[status(thm)],[f5644,f5641,f236,f1173])).
% 18.86/2.86 fof(f5660,plain,(
% 18.86/2.86 spl0_240 <=> function(identity_relation(relation_dom(function_inverse(sk0_12))))),
% 18.86/2.86 introduced(split_symbol_definition)).
% 18.86/2.86 fof(f5662,plain,(
% 18.86/2.86 ~function(identity_relation(relation_dom(function_inverse(sk0_12))))|spl0_240),
% 18.86/2.86 inference(component_clause,[status(thm)],[f5660])).
% 18.86/2.86 fof(f5670,plain,(
% 18.86/2.86 $false|spl0_240),
% 18.86/2.86 inference(forward_subsumption_resolution,[status(thm)],[f5662,f78])).
% 18.86/2.86 fof(f5671,plain,(
% 18.86/2.86 spl0_240),
% 18.86/2.86 inference(contradiction_clause,[status(thm)],[f5670])).
% 18.86/2.86 fof(f5816,plain,(
% 18.86/2.86 spl0_243 <=> function(identity_relation(relation_dom(sk0_12)))),
% 18.86/2.86 introduced(split_symbol_definition)).
% 18.86/2.86 fof(f5818,plain,(
% 18.86/2.86 ~function(identity_relation(relation_dom(sk0_12)))|spl0_243),
% 18.86/2.86 inference(component_clause,[status(thm)],[f5816])).
% 18.86/2.86 fof(f5825,plain,(
% 18.86/2.86 $false|spl0_243),
% 18.86/2.86 inference(forward_subsumption_resolution,[status(thm)],[f5818,f78])).
% 18.86/2.86 fof(f5826,plain,(
% 18.86/2.86 spl0_243),
% 18.86/2.86 inference(contradiction_clause,[status(thm)],[f5825])).
% 18.86/2.86 fof(f5856,plain,(
% 18.86/2.86 ![X0]: (relation_composition(X0,function_inverse(empty_set))=identity_relation(relation_dom(relation_composition(X0,function_inverse(empty_set))))|in(sk0_11(relation_dom(relation_composition(X0,function_inverse(empty_set))),relation_composition(X0,function_inverse(empty_set))),relation_dom(relation_composition(X0,function_inverse(empty_set))))|~relation(X0)|~function(X0)|~relation(empty_set))),
% 18.86/2.86 inference(resolution,[status(thm)],[f1924,f588])).
% 18.86/2.86 fof(f5857,plain,(
% 18.86/2.86 spl0_172|~spl0_47),
% 18.86/2.86 inference(split_clause,[status(thm)],[f5856,f2883,f453])).
% 18.86/2.86 fof(f5858,plain,(
% 18.86/2.86 spl0_245 <=> relation_composition(X0,function_inverse(relation_composition(function_inverse(sk0_12),sk0_12)))=identity_relation(relation_dom(relation_composition(X0,function_inverse(relation_composition(function_inverse(sk0_12),sk0_12)))))|in(sk0_11(relation_dom(relation_composition(X0,function_inverse(relation_composition(function_inverse(sk0_12),sk0_12)))),relation_composition(X0,function_inverse(relation_composition(function_inverse(sk0_12),sk0_12)))),relation_dom(relation_composition(X0,function_inverse(relation_composition(function_inverse(sk0_12),sk0_12)))))|~relation(X0)|~function(X0)),
% 18.86/2.86 introduced(split_symbol_definition)).
% 18.86/2.86 fof(f5861,plain,(
% 18.86/2.86 ![X0]: (relation_composition(X0,function_inverse(relation_composition(function_inverse(sk0_12),sk0_12)))=identity_relation(relation_dom(relation_composition(X0,function_inverse(relation_composition(function_inverse(sk0_12),sk0_12)))))|in(sk0_11(relation_dom(relation_composition(X0,function_inverse(relation_composition(function_inverse(sk0_12),sk0_12)))),relation_composition(X0,function_inverse(relation_composition(function_inverse(sk0_12),sk0_12)))),relation_dom(relation_composition(X0,function_inverse(relation_composition(function_inverse(sk0_12),sk0_12)))))|~relation(X0)|~function(X0)|~relation(relation_composition(function_inverse(sk0_12),sk0_12))|~spl0_93)),
% 18.86/2.86 inference(resolution,[status(thm)],[f1924,f1189])).
% 18.86/2.86 fof(f5862,plain,(
% 18.86/2.86 spl0_245|~spl0_57|~spl0_93),
% 18.86/2.86 inference(split_clause,[status(thm)],[f5861,f5858,f621,f1188])).
% 18.86/2.86 fof(f5865,plain,(
% 18.86/2.86 spl0_246 <=> relation_composition(X0,function_inverse(sk0_1))=identity_relation(relation_dom(relation_composition(X0,function_inverse(sk0_1))))|in(sk0_11(relation_dom(relation_composition(X0,function_inverse(sk0_1))),relation_composition(X0,function_inverse(sk0_1))),relation_dom(relation_composition(X0,function_inverse(sk0_1))))|~relation(X0)|~function(X0)),
% 18.86/2.86 introduced(split_symbol_definition)).
% 18.86/2.86 fof(f5868,plain,(
% 18.86/2.86 ![X0]: (relation_composition(X0,function_inverse(sk0_1))=identity_relation(relation_dom(relation_composition(X0,function_inverse(sk0_1))))|in(sk0_11(relation_dom(relation_composition(X0,function_inverse(sk0_1))),relation_composition(X0,function_inverse(sk0_1))),relation_dom(relation_composition(X0,function_inverse(sk0_1))))|~relation(X0)|~function(X0)|~relation(sk0_1))),
% 18.86/2.86 inference(resolution,[status(thm)],[f1924,f96])).
% 18.86/2.86 fof(f5869,plain,(
% 18.86/2.86 spl0_246|~spl0_87),
% 18.86/2.86 inference(split_clause,[status(thm)],[f5868,f5865,f1137])).
% 18.86/2.86 fof(f5875,plain,(
% 18.86/2.86 spl0_248 <=> relation_composition(X0,function_inverse(function_inverse(sk0_12)))=identity_relation(relation_dom(relation_composition(X0,function_inverse(function_inverse(sk0_12)))))|in(sk0_11(relation_dom(relation_composition(X0,function_inverse(function_inverse(sk0_12)))),relation_composition(X0,function_inverse(function_inverse(sk0_12)))),relation_dom(relation_composition(X0,function_inverse(function_inverse(sk0_12)))))|~relation(X0)|~function(X0)),
% 18.86/2.86 introduced(split_symbol_definition)).
% 18.86/2.86 fof(f5878,plain,(
% 18.86/2.86 ![X0]: (relation_composition(X0,function_inverse(function_inverse(sk0_12)))=identity_relation(relation_dom(relation_composition(X0,function_inverse(function_inverse(sk0_12)))))|in(sk0_11(relation_dom(relation_composition(X0,function_inverse(function_inverse(sk0_12)))),relation_composition(X0,function_inverse(function_inverse(sk0_12)))),relation_dom(relation_composition(X0,function_inverse(function_inverse(sk0_12)))))|~relation(X0)|~function(X0)|~relation(function_inverse(sk0_12))|~spl0_92)),
% 18.86/2.86 inference(resolution,[status(thm)],[f1924,f1174])).
% 18.86/2.86 fof(f5879,plain,(
% 18.86/2.86 spl0_248|~spl0_10|~spl0_92),
% 18.86/2.86 inference(split_clause,[status(thm)],[f5878,f5875,f236,f1173])).
% 18.86/2.86 fof(f5926,plain,(
% 18.86/2.86 spl0_249 <=> relation_composition(sk0_12,identity_relation(X0))=identity_relation(relation_dom(relation_composition(sk0_12,identity_relation(X0))))|in(sk0_11(relation_dom(relation_composition(sk0_12,identity_relation(X0))),relation_composition(sk0_12,identity_relation(X0))),relation_dom(relation_composition(sk0_12,identity_relation(X0))))),
% 18.86/2.86 introduced(split_symbol_definition)).
% 18.86/2.86 fof(f5929,plain,(
% 18.86/2.86 ![X0]: (relation_composition(sk0_12,identity_relation(X0))=identity_relation(relation_dom(relation_composition(sk0_12,identity_relation(X0))))|in(sk0_11(relation_dom(relation_composition(sk0_12,identity_relation(X0))),relation_composition(sk0_12,identity_relation(X0))),relation_dom(relation_composition(sk0_12,identity_relation(X0))))|~relation(sk0_12))),
% 18.86/2.86 inference(resolution,[status(thm)],[f1926,f166])).
% 18.86/2.86 fof(f5930,plain,(
% 18.86/2.86 spl0_249|~spl0_2),
% 18.86/2.86 inference(split_clause,[status(thm)],[f5929,f5926,f198])).
% 18.86/2.86 fof(f5931,plain,(
% 18.86/2.86 spl0_250 <=> relation_composition(empty_set,identity_relation(X0))=identity_relation(relation_dom(relation_composition(empty_set,identity_relation(X0))))|in(sk0_11(relation_dom(relation_composition(empty_set,identity_relation(X0))),relation_composition(empty_set,identity_relation(X0))),relation_dom(relation_composition(empty_set,identity_relation(X0))))),
% 18.86/2.86 introduced(split_symbol_definition)).
% 18.86/2.86 fof(f5934,plain,(
% 18.86/2.86 ![X0]: (relation_composition(empty_set,identity_relation(X0))=identity_relation(relation_dom(relation_composition(empty_set,identity_relation(X0))))|in(sk0_11(relation_dom(relation_composition(empty_set,identity_relation(X0))),relation_composition(empty_set,identity_relation(X0))),relation_dom(relation_composition(empty_set,identity_relation(X0))))|~relation(empty_set))),
% 18.86/2.86 inference(resolution,[status(thm)],[f1926,f588])).
% 18.86/2.86 fof(f5935,plain,(
% 18.86/2.86 spl0_250|~spl0_47),
% 18.86/2.86 inference(split_clause,[status(thm)],[f5934,f5931,f453])).
% 18.86/2.86 fof(f5936,plain,(
% 18.86/2.86 spl0_251 <=> relation_composition(relation_composition(function_inverse(sk0_12),sk0_12),identity_relation(X0))=identity_relation(relation_dom(relation_composition(relation_composition(function_inverse(sk0_12),sk0_12),identity_relation(X0))))|in(sk0_11(relation_dom(relation_composition(relation_composition(function_inverse(sk0_12),sk0_12),identity_relation(X0))),relation_composition(relation_composition(function_inverse(sk0_12),sk0_12),identity_relation(X0))),relation_dom(relation_composition(relation_composition(function_inverse(sk0_12),sk0_12),identity_relation(X0))))),
% 18.86/2.86 introduced(split_symbol_definition)).
% 18.86/2.86 fof(f5939,plain,(
% 18.86/2.86 ![X0]: (relation_composition(relation_composition(function_inverse(sk0_12),sk0_12),identity_relation(X0))=identity_relation(relation_dom(relation_composition(relation_composition(function_inverse(sk0_12),sk0_12),identity_relation(X0))))|in(sk0_11(relation_dom(relation_composition(relation_composition(function_inverse(sk0_12),sk0_12),identity_relation(X0))),relation_composition(relation_composition(function_inverse(sk0_12),sk0_12),identity_relation(X0))),relation_dom(relation_composition(relation_composition(function_inverse(sk0_12),sk0_12),identity_relation(X0))))|~relation(relation_composition(function_inverse(sk0_12),sk0_12))|~spl0_93)),
% 18.86/2.86 inference(resolution,[status(thm)],[f1926,f1189])).
% 18.86/2.86 fof(f5940,plain,(
% 18.86/2.86 spl0_251|~spl0_57|~spl0_93),
% 18.86/2.86 inference(split_clause,[status(thm)],[f5939,f5936,f621,f1188])).
% 18.86/2.86 fof(f5943,plain,(
% 18.86/2.86 spl0_252 <=> relation_composition(sk0_1,identity_relation(X0))=identity_relation(relation_dom(relation_composition(sk0_1,identity_relation(X0))))|in(sk0_11(relation_dom(relation_composition(sk0_1,identity_relation(X0))),relation_composition(sk0_1,identity_relation(X0))),relation_dom(relation_composition(sk0_1,identity_relation(X0))))),
% 18.86/2.86 introduced(split_symbol_definition)).
% 18.86/2.86 fof(f5946,plain,(
% 18.86/2.86 ![X0]: (relation_composition(sk0_1,identity_relation(X0))=identity_relation(relation_dom(relation_composition(sk0_1,identity_relation(X0))))|in(sk0_11(relation_dom(relation_composition(sk0_1,identity_relation(X0))),relation_composition(sk0_1,identity_relation(X0))),relation_dom(relation_composition(sk0_1,identity_relation(X0))))|~relation(sk0_1))),
% 18.86/2.86 inference(resolution,[status(thm)],[f1926,f96])).
% 18.86/2.86 fof(f5947,plain,(
% 18.86/2.86 spl0_252|~spl0_87),
% 18.86/2.86 inference(split_clause,[status(thm)],[f5946,f5943,f1137])).
% 18.86/2.86 fof(f5953,plain,(
% 18.86/2.86 spl0_254 <=> relation_composition(function_inverse(sk0_12),identity_relation(X0))=identity_relation(relation_dom(relation_composition(function_inverse(sk0_12),identity_relation(X0))))|in(sk0_11(relation_dom(relation_composition(function_inverse(sk0_12),identity_relation(X0))),relation_composition(function_inverse(sk0_12),identity_relation(X0))),relation_dom(relation_composition(function_inverse(sk0_12),identity_relation(X0))))),
% 18.86/2.86 introduced(split_symbol_definition)).
% 18.86/2.86 fof(f5956,plain,(
% 18.86/2.86 ![X0]: (relation_composition(function_inverse(sk0_12),identity_relation(X0))=identity_relation(relation_dom(relation_composition(function_inverse(sk0_12),identity_relation(X0))))|in(sk0_11(relation_dom(relation_composition(function_inverse(sk0_12),identity_relation(X0))),relation_composition(function_inverse(sk0_12),identity_relation(X0))),relation_dom(relation_composition(function_inverse(sk0_12),identity_relation(X0))))|~relation(function_inverse(sk0_12))|~spl0_92)),
% 18.86/2.86 inference(resolution,[status(thm)],[f1926,f1174])).
% 18.86/2.86 fof(f5957,plain,(
% 18.86/2.86 spl0_254|~spl0_10|~spl0_92),
% 18.86/2.86 inference(split_clause,[status(thm)],[f5956,f5953,f236,f1173])).
% 18.86/2.86 fof(f6106,plain,(
% 18.86/2.86 spl0_266 <=> relation_composition(relation_composition(sk0_12,function_inverse(sk0_12)),identity_relation(X0))=identity_relation(relation_dom(relation_composition(relation_composition(sk0_12,function_inverse(sk0_12)),identity_relation(X0))))|in(sk0_11(relation_dom(relation_composition(relation_composition(sk0_12,function_inverse(sk0_12)),identity_relation(X0))),relation_composition(relation_composition(sk0_12,function_inverse(sk0_12)),identity_relation(X0))),relation_dom(relation_composition(relation_composition(sk0_12,function_inverse(sk0_12)),identity_relation(X0))))),
% 18.86/2.86 introduced(split_symbol_definition)).
% 18.86/2.86 fof(f6109,plain,(
% 18.86/2.86 ![X0]: (relation_composition(relation_composition(sk0_12,function_inverse(sk0_12)),identity_relation(X0))=identity_relation(relation_dom(relation_composition(relation_composition(sk0_12,function_inverse(sk0_12)),identity_relation(X0))))|in(sk0_11(relation_dom(relation_composition(relation_composition(sk0_12,function_inverse(sk0_12)),identity_relation(X0))),relation_composition(relation_composition(sk0_12,function_inverse(sk0_12)),identity_relation(X0))),relation_dom(relation_composition(relation_composition(sk0_12,function_inverse(sk0_12)),identity_relation(X0))))|~relation(relation_composition(sk0_12,function_inverse(sk0_12)))|~spl0_122)),
% 18.86/2.86 inference(resolution,[status(thm)],[f1858,f1926])).
% 18.86/2.86 fof(f6110,plain,(
% 18.86/2.86 spl0_266|~spl0_6|~spl0_122),
% 18.86/2.86 inference(split_clause,[status(thm)],[f6109,f6106,f218,f1857])).
% 18.86/2.86 fof(f6111,plain,(
% 18.86/2.86 spl0_267 <=> relation_composition(X0,function_inverse(relation_composition(sk0_12,function_inverse(sk0_12))))=identity_relation(relation_dom(relation_composition(X0,function_inverse(relation_composition(sk0_12,function_inverse(sk0_12))))))|in(sk0_11(relation_dom(relation_composition(X0,function_inverse(relation_composition(sk0_12,function_inverse(sk0_12))))),relation_composition(X0,function_inverse(relation_composition(sk0_12,function_inverse(sk0_12))))),relation_dom(relation_composition(X0,function_inverse(relation_composition(sk0_12,function_inverse(sk0_12))))))|~relation(X0)|~function(X0)),
% 18.86/2.86 introduced(split_symbol_definition)).
% 18.86/2.86 fof(f6114,plain,(
% 18.86/2.86 ![X0]: (relation_composition(X0,function_inverse(relation_composition(sk0_12,function_inverse(sk0_12))))=identity_relation(relation_dom(relation_composition(X0,function_inverse(relation_composition(sk0_12,function_inverse(sk0_12))))))|in(sk0_11(relation_dom(relation_composition(X0,function_inverse(relation_composition(sk0_12,function_inverse(sk0_12))))),relation_composition(X0,function_inverse(relation_composition(sk0_12,function_inverse(sk0_12))))),relation_dom(relation_composition(X0,function_inverse(relation_composition(sk0_12,function_inverse(sk0_12))))))|~relation(X0)|~function(X0)|~relation(relation_composition(sk0_12,function_inverse(sk0_12)))|~spl0_122)),
% 18.86/2.86 inference(resolution,[status(thm)],[f1858,f1924])).
% 18.86/2.86 fof(f6115,plain,(
% 18.86/2.86 spl0_267|~spl0_6|~spl0_122),
% 18.86/2.86 inference(split_clause,[status(thm)],[f6114,f6111,f218,f1857])).
% 18.86/2.86 fof(f6116,plain,(
% 18.86/2.86 spl0_268 <=> relation_composition(X0,relation_composition(relation_composition(sk0_12,function_inverse(sk0_12)),relation_composition(sk0_12,function_inverse(sk0_12))))=identity_relation(relation_dom(relation_composition(X0,relation_composition(relation_composition(sk0_12,function_inverse(sk0_12)),relation_composition(sk0_12,function_inverse(sk0_12))))))|in(sk0_11(relation_dom(relation_composition(X0,relation_composition(relation_composition(sk0_12,function_inverse(sk0_12)),relation_composition(sk0_12,function_inverse(sk0_12))))),relation_composition(X0,relation_composition(relation_composition(sk0_12,function_inverse(sk0_12)),relation_composition(sk0_12,function_inverse(sk0_12))))),relation_dom(relation_composition(X0,relation_composition(relation_composition(sk0_12,function_inverse(sk0_12)),relation_composition(sk0_12,function_inverse(sk0_12))))))|~relation(X0)|~function(X0)),
% 18.86/2.86 introduced(split_symbol_definition)).
% 18.86/2.86 fof(f6119,plain,(
% 18.86/2.86 ![X0]: (relation_composition(X0,relation_composition(relation_composition(sk0_12,function_inverse(sk0_12)),relation_composition(sk0_12,function_inverse(sk0_12))))=identity_relation(relation_dom(relation_composition(X0,relation_composition(relation_composition(sk0_12,function_inverse(sk0_12)),relation_composition(sk0_12,function_inverse(sk0_12))))))|in(sk0_11(relation_dom(relation_composition(X0,relation_composition(relation_composition(sk0_12,function_inverse(sk0_12)),relation_composition(sk0_12,function_inverse(sk0_12))))),relation_composition(X0,relation_composition(relation_composition(sk0_12,function_inverse(sk0_12)),relation_composition(sk0_12,function_inverse(sk0_12))))),relation_dom(relation_composition(X0,relation_composition(relation_composition(sk0_12,function_inverse(sk0_12)),relation_composition(sk0_12,function_inverse(sk0_12))))))|~relation(X0)|~function(X0)|~relation(relation_composition(sk0_12,function_inverse(sk0_12)))|~relation(relation_composition(sk0_12,function_inverse(sk0_12)))|~spl0_122)),
% 18.86/2.86 inference(resolution,[status(thm)],[f1858,f1917])).
% 18.86/2.86 fof(f6120,plain,(
% 18.86/2.86 spl0_268|~spl0_6|~spl0_122),
% 18.86/2.86 inference(split_clause,[status(thm)],[f6119,f6116,f218,f1857])).
% 18.86/2.86 fof(f6121,plain,(
% 18.86/2.86 spl0_269 <=> relation_composition(X0,relation_composition(X1,relation_composition(sk0_12,function_inverse(sk0_12))))=identity_relation(relation_dom(relation_composition(X0,relation_composition(X1,relation_composition(sk0_12,function_inverse(sk0_12))))))|in(sk0_11(relation_dom(relation_composition(X0,relation_composition(X1,relation_composition(sk0_12,function_inverse(sk0_12))))),relation_composition(X0,relation_composition(X1,relation_composition(sk0_12,function_inverse(sk0_12))))),relation_dom(relation_composition(X0,relation_composition(X1,relation_composition(sk0_12,function_inverse(sk0_12))))))|~relation(X0)|~function(X0)|~relation(X1)|~function(X1)),
% 18.86/2.86 introduced(split_symbol_definition)).
% 18.86/2.86 fof(f6124,plain,(
% 18.86/2.86 ![X0,X1]: (relation_composition(X0,relation_composition(X1,relation_composition(sk0_12,function_inverse(sk0_12))))=identity_relation(relation_dom(relation_composition(X0,relation_composition(X1,relation_composition(sk0_12,function_inverse(sk0_12))))))|in(sk0_11(relation_dom(relation_composition(X0,relation_composition(X1,relation_composition(sk0_12,function_inverse(sk0_12))))),relation_composition(X0,relation_composition(X1,relation_composition(sk0_12,function_inverse(sk0_12))))),relation_dom(relation_composition(X0,relation_composition(X1,relation_composition(sk0_12,function_inverse(sk0_12))))))|~relation(X0)|~function(X0)|~relation(X1)|~function(X1)|~relation(relation_composition(sk0_12,function_inverse(sk0_12)))|~spl0_122)),
% 18.86/2.86 inference(resolution,[status(thm)],[f1858,f1917])).
% 18.86/2.86 fof(f6125,plain,(
% 18.86/2.86 spl0_269|~spl0_6|~spl0_122),
% 18.86/2.86 inference(split_clause,[status(thm)],[f6124,f6121,f218,f1857])).
% 18.86/2.86 fof(f6128,plain,(
% 18.86/2.86 spl0_270 <=> relation_composition(X0,relation_composition(relation_composition(sk0_12,function_inverse(sk0_12)),X1))=identity_relation(relation_dom(relation_composition(X0,relation_composition(relation_composition(sk0_12,function_inverse(sk0_12)),X1))))|in(sk0_11(relation_dom(relation_composition(X0,relation_composition(relation_composition(sk0_12,function_inverse(sk0_12)),X1))),relation_composition(X0,relation_composition(relation_composition(sk0_12,function_inverse(sk0_12)),X1))),relation_dom(relation_composition(X0,relation_composition(relation_composition(sk0_12,function_inverse(sk0_12)),X1))))|~relation(X0)|~function(X0)|~relation(X1)|~function(X1)),
% 18.86/2.86 introduced(split_symbol_definition)).
% 18.86/2.86 fof(f6131,plain,(
% 18.86/2.86 ![X0,X1]: (relation_composition(X0,relation_composition(relation_composition(sk0_12,function_inverse(sk0_12)),X1))=identity_relation(relation_dom(relation_composition(X0,relation_composition(relation_composition(sk0_12,function_inverse(sk0_12)),X1))))|in(sk0_11(relation_dom(relation_composition(X0,relation_composition(relation_composition(sk0_12,function_inverse(sk0_12)),X1))),relation_composition(X0,relation_composition(relation_composition(sk0_12,function_inverse(sk0_12)),X1))),relation_dom(relation_composition(X0,relation_composition(relation_composition(sk0_12,function_inverse(sk0_12)),X1))))|~relation(X0)|~function(X0)|~relation(relation_composition(sk0_12,function_inverse(sk0_12)))|~relation(X1)|~function(X1)|~spl0_122)),
% 18.86/2.86 inference(resolution,[status(thm)],[f1858,f1917])).
% 18.86/2.86 fof(f6132,plain,(
% 18.86/2.86 spl0_270|~spl0_6|~spl0_122),
% 18.86/2.86 inference(split_clause,[status(thm)],[f6131,f6128,f218,f1857])).
% 18.86/2.86 fof(f6186,plain,(
% 18.86/2.86 spl0_275 <=> relation(function_inverse(sk0_1))),
% 18.86/2.86 introduced(split_symbol_definition)).
% 18.86/2.86 fof(f6188,plain,(
% 18.86/2.86 ~relation(function_inverse(sk0_1))|spl0_275),
% 18.86/2.86 inference(component_clause,[status(thm)],[f6186])).
% 18.86/2.86 fof(f6194,plain,(
% 18.86/2.86 spl0_277 <=> relation_composition(function_inverse(sk0_1),identity_relation(X0))=identity_relation(relation_dom(relation_composition(function_inverse(sk0_1),identity_relation(X0))))|in(sk0_11(relation_dom(relation_composition(function_inverse(sk0_1),identity_relation(X0))),relation_composition(function_inverse(sk0_1),identity_relation(X0))),relation_dom(relation_composition(function_inverse(sk0_1),identity_relation(X0))))),
% 18.86/2.86 introduced(split_symbol_definition)).
% 18.86/2.86 fof(f6199,plain,(
% 18.86/2.86 spl0_278 <=> relation_composition(X0,function_inverse(function_inverse(sk0_1)))=identity_relation(relation_dom(relation_composition(X0,function_inverse(function_inverse(sk0_1)))))|in(sk0_11(relation_dom(relation_composition(X0,function_inverse(function_inverse(sk0_1)))),relation_composition(X0,function_inverse(function_inverse(sk0_1)))),relation_dom(relation_composition(X0,function_inverse(function_inverse(sk0_1)))))|~relation(X0)|~function(X0)),
% 18.86/2.86 introduced(split_symbol_definition)).
% 18.86/2.86 fof(f6204,plain,(
% 18.86/2.86 spl0_279 <=> relation_composition(X0,relation_composition(function_inverse(sk0_1),function_inverse(sk0_1)))=identity_relation(relation_dom(relation_composition(X0,relation_composition(function_inverse(sk0_1),function_inverse(sk0_1)))))|in(sk0_11(relation_dom(relation_composition(X0,relation_composition(function_inverse(sk0_1),function_inverse(sk0_1)))),relation_composition(X0,relation_composition(function_inverse(sk0_1),function_inverse(sk0_1)))),relation_dom(relation_composition(X0,relation_composition(function_inverse(sk0_1),function_inverse(sk0_1)))))|~relation(X0)|~function(X0)),
% 18.86/2.86 introduced(split_symbol_definition)).
% 18.86/2.86 fof(f6209,plain,(
% 18.86/2.86 spl0_280 <=> relation_composition(X0,relation_composition(X1,function_inverse(sk0_1)))=identity_relation(relation_dom(relation_composition(X0,relation_composition(X1,function_inverse(sk0_1)))))|in(sk0_11(relation_dom(relation_composition(X0,relation_composition(X1,function_inverse(sk0_1)))),relation_composition(X0,relation_composition(X1,function_inverse(sk0_1)))),relation_dom(relation_composition(X0,relation_composition(X1,function_inverse(sk0_1)))))|~relation(X0)|~function(X0)|~relation(X1)|~function(X1)),
% 18.86/2.86 introduced(split_symbol_definition)).
% 18.86/2.86 fof(f6216,plain,(
% 18.86/2.86 spl0_281 <=> relation_composition(X0,relation_composition(function_inverse(sk0_1),X1))=identity_relation(relation_dom(relation_composition(X0,relation_composition(function_inverse(sk0_1),X1))))|in(sk0_11(relation_dom(relation_composition(X0,relation_composition(function_inverse(sk0_1),X1))),relation_composition(X0,relation_composition(function_inverse(sk0_1),X1))),relation_dom(relation_composition(X0,relation_composition(function_inverse(sk0_1),X1))))|~relation(X0)|~function(X0)|~relation(X1)|~function(X1)),
% 18.86/2.86 introduced(split_symbol_definition)).
% 18.86/2.86 fof(f6249,plain,(
% 18.86/2.86 spl0_285 <=> function(function_inverse(sk0_1))),
% 18.86/2.86 introduced(split_symbol_definition)).
% 18.86/2.86 fof(f6250,plain,(
% 18.86/2.86 function(function_inverse(sk0_1))|~spl0_285),
% 18.86/2.86 inference(component_clause,[status(thm)],[f6249])).
% 18.86/2.86 fof(f6251,plain,(
% 18.86/2.86 ~function(function_inverse(sk0_1))|spl0_285),
% 18.86/2.86 inference(component_clause,[status(thm)],[f6249])).
% 18.86/2.86 fof(f6443,plain,(
% 18.86/2.86 spl0_307 <=> apply(identity_relation(powerset(empty_set)),empty_set)=sk0_0(powerset(empty_set))),
% 18.86/2.86 introduced(split_symbol_definition)).
% 18.86/2.86 fof(f6446,plain,(
% 18.86/2.86 spl0_308 <=> powerset(empty_set)=empty_set),
% 18.86/2.86 introduced(split_symbol_definition)).
% 18.86/2.86 fof(f6447,plain,(
% 18.86/2.86 powerset(empty_set)=empty_set|~spl0_308),
% 18.86/2.86 inference(component_clause,[status(thm)],[f6446])).
% 18.86/2.86 fof(f6449,plain,(
% 18.86/2.86 apply(identity_relation(powerset(empty_set)),empty_set)=sk0_0(powerset(empty_set))|powerset(empty_set)=empty_set),
% 18.86/2.86 inference(paramodulation,[status(thm)],[f2596,f3637])).
% 18.86/2.86 fof(f6450,plain,(
% 18.86/2.86 spl0_307|spl0_308),
% 18.86/2.86 inference(split_clause,[status(thm)],[f6449,f6443,f6446])).
% 18.86/2.86 fof(f6497,plain,(
% 18.86/2.86 spl0_309 <=> relation_composition(empty_set,function_inverse(sk0_12))=empty_set),
% 18.86/2.86 introduced(split_symbol_definition)).
% 18.86/2.86 fof(f6500,plain,(
% 18.86/2.86 relation_composition(empty_set,function_inverse(sk0_12))=empty_set|~relation(sk0_12)),
% 18.86/2.86 inference(resolution,[status(thm)],[f1048,f166])).
% 18.86/2.86 fof(f6501,plain,(
% 18.86/2.86 spl0_309|~spl0_2),
% 18.86/2.86 inference(split_clause,[status(thm)],[f6500,f6497,f198])).
% 18.86/2.86 fof(f6502,plain,(
% 18.86/2.86 spl0_310 <=> relation_composition(empty_set,function_inverse(empty_set))=empty_set),
% 18.86/2.86 introduced(split_symbol_definition)).
% 18.86/2.86 fof(f6505,plain,(
% 18.86/2.86 relation_composition(empty_set,function_inverse(empty_set))=empty_set|~relation(empty_set)),
% 18.86/2.86 inference(resolution,[status(thm)],[f1048,f588])).
% 18.86/2.86 fof(f6506,plain,(
% 18.86/2.86 spl0_310|~spl0_47),
% 18.86/2.86 inference(split_clause,[status(thm)],[f6505,f6502,f453])).
% 18.86/2.86 fof(f6507,plain,(
% 18.86/2.86 spl0_311 <=> relation_composition(empty_set,function_inverse(relation_composition(function_inverse(sk0_12),sk0_12)))=empty_set),
% 18.86/2.86 introduced(split_symbol_definition)).
% 18.86/2.86 fof(f6510,plain,(
% 18.86/2.86 relation_composition(empty_set,function_inverse(relation_composition(function_inverse(sk0_12),sk0_12)))=empty_set|~relation(relation_composition(function_inverse(sk0_12),sk0_12))|~spl0_93),
% 18.86/2.86 inference(resolution,[status(thm)],[f1048,f1189])).
% 18.86/2.86 fof(f6511,plain,(
% 18.86/2.86 spl0_311|~spl0_57|~spl0_93),
% 18.86/2.86 inference(split_clause,[status(thm)],[f6510,f6507,f621,f1188])).
% 18.86/2.86 fof(f6514,plain,(
% 18.86/2.86 spl0_312 <=> relation_composition(empty_set,function_inverse(sk0_1))=empty_set),
% 18.86/2.86 introduced(split_symbol_definition)).
% 18.86/2.86 fof(f6517,plain,(
% 18.86/2.86 relation_composition(empty_set,function_inverse(sk0_1))=empty_set|~relation(sk0_1)),
% 18.86/2.86 inference(resolution,[status(thm)],[f1048,f96])).
% 18.86/2.86 fof(f6518,plain,(
% 18.86/2.86 spl0_312|~spl0_87),
% 18.86/2.86 inference(split_clause,[status(thm)],[f6517,f6514,f1137])).
% 18.86/2.86 fof(f6519,plain,(
% 18.86/2.86 spl0_313 <=> relation_composition(empty_set,function_inverse(function_inverse(sk0_1)))=empty_set),
% 18.86/2.86 introduced(split_symbol_definition)).
% 18.86/2.86 fof(f6529,plain,(
% 18.86/2.86 spl0_315 <=> relation_composition(empty_set,function_inverse(function_inverse(sk0_12)))=empty_set),
% 18.86/2.86 introduced(split_symbol_definition)).
% 18.86/2.86 fof(f6532,plain,(
% 18.86/2.86 relation_composition(empty_set,function_inverse(function_inverse(sk0_12)))=empty_set|~relation(function_inverse(sk0_12))|~spl0_92),
% 18.86/2.86 inference(resolution,[status(thm)],[f1048,f1174])).
% 18.86/2.86 fof(f6533,plain,(
% 18.86/2.86 spl0_315|~spl0_10|~spl0_92),
% 18.86/2.86 inference(split_clause,[status(thm)],[f6532,f6529,f236,f1173])).
% 18.86/2.86 fof(f6536,plain,(
% 18.86/2.86 ![X0]: (relation_composition(empty_set,function_inverse(identity_relation(X0)))=empty_set|~relation(identity_relation(X0)))),
% 18.86/2.86 inference(resolution,[status(thm)],[f1048,f78])).
% 18.86/2.86 fof(f6537,plain,(
% 18.86/2.86 ![X0]: (relation_composition(empty_set,function_inverse(identity_relation(X0)))=empty_set)),
% 18.86/2.86 inference(forward_subsumption_resolution,[status(thm)],[f6536,f62])).
% 18.86/2.86 fof(f6538,plain,(
% 18.86/2.86 ![X0]: (relation_composition(empty_set,function_inverse(X0))=empty_set|~relation(X0)|~empty(X0))),
% 18.86/2.86 inference(resolution,[status(thm)],[f1048,f50])).
% 18.86/2.86 fof(f6539,plain,(
% 18.86/2.86 ![X0]: (relation_composition(empty_set,function_inverse(X0))=empty_set|~empty(X0))),
% 18.86/2.86 inference(forward_subsumption_resolution,[status(thm)],[f6538,f52])).
% 18.86/2.86 fof(f6569,plain,(
% 18.86/2.86 ![X0]: (relation_composition(empty_set,function_inverse(relation_rng(X0)))=empty_set|~empty(X0))),
% 18.86/2.86 inference(resolution,[status(thm)],[f6539,f89])).
% 18.86/2.86 fof(f6573,plain,(
% 18.86/2.86 relation_composition(empty_set,function_inverse(relation_rng(empty_set)))=empty_set),
% 18.86/2.86 inference(resolution,[status(thm)],[f6569,f68])).
% 18.86/2.86 fof(f6574,plain,(
% 18.86/2.86 relation_composition(empty_set,function_inverse(empty_set))=empty_set),
% 18.86/2.86 inference(forward_demodulation,[status(thm)],[f887,f6573])).
% 18.86/2.86 fof(f6589,plain,(
% 18.86/2.86 spl0_319 <=> relation_composition(function_inverse(sk0_12),empty_set)=empty_set),
% 18.86/2.86 introduced(split_symbol_definition)).
% 18.86/2.86 fof(f6592,plain,(
% 18.86/2.86 relation_composition(function_inverse(sk0_12),empty_set)=empty_set|~relation(sk0_12)),
% 18.86/2.86 inference(resolution,[status(thm)],[f1501,f166])).
% 18.86/2.86 fof(f6593,plain,(
% 18.86/2.86 spl0_319|~spl0_2),
% 18.86/2.86 inference(split_clause,[status(thm)],[f6592,f6589,f198])).
% 18.86/2.86 fof(f6594,plain,(
% 18.86/2.86 spl0_320 <=> relation_composition(function_inverse(empty_set),empty_set)=empty_set),
% 18.86/2.86 introduced(split_symbol_definition)).
% 18.86/2.86 fof(f6597,plain,(
% 18.86/2.86 relation_composition(function_inverse(empty_set),empty_set)=empty_set|~relation(empty_set)),
% 18.86/2.86 inference(resolution,[status(thm)],[f1501,f588])).
% 18.86/2.86 fof(f6598,plain,(
% 18.86/2.86 spl0_320|~spl0_47),
% 18.86/2.86 inference(split_clause,[status(thm)],[f6597,f6594,f453])).
% 18.86/2.86 fof(f6599,plain,(
% 18.86/2.86 spl0_321 <=> relation_composition(function_inverse(relation_composition(function_inverse(sk0_12),sk0_12)),empty_set)=empty_set),
% 18.86/2.86 introduced(split_symbol_definition)).
% 18.86/2.86 fof(f6602,plain,(
% 18.86/2.86 relation_composition(function_inverse(relation_composition(function_inverse(sk0_12),sk0_12)),empty_set)=empty_set|~relation(relation_composition(function_inverse(sk0_12),sk0_12))|~spl0_93),
% 18.86/2.86 inference(resolution,[status(thm)],[f1501,f1189])).
% 18.86/2.86 fof(f6603,plain,(
% 18.86/2.86 spl0_321|~spl0_57|~spl0_93),
% 18.86/2.86 inference(split_clause,[status(thm)],[f6602,f6599,f621,f1188])).
% 18.86/2.86 fof(f6606,plain,(
% 18.86/2.86 spl0_322 <=> relation_composition(function_inverse(sk0_1),empty_set)=empty_set),
% 18.86/2.86 introduced(split_symbol_definition)).
% 18.86/2.86 fof(f6609,plain,(
% 18.86/2.86 relation_composition(function_inverse(sk0_1),empty_set)=empty_set|~relation(sk0_1)),
% 18.86/2.86 inference(resolution,[status(thm)],[f1501,f96])).
% 18.86/2.86 fof(f6610,plain,(
% 18.86/2.86 spl0_322|~spl0_87),
% 18.86/2.86 inference(split_clause,[status(thm)],[f6609,f6606,f1137])).
% 18.86/2.86 fof(f6611,plain,(
% 18.86/2.86 spl0_323 <=> relation_composition(function_inverse(function_inverse(sk0_1)),empty_set)=empty_set),
% 18.86/2.86 introduced(split_symbol_definition)).
% 18.86/2.86 fof(f6621,plain,(
% 18.86/2.86 spl0_325 <=> relation_composition(function_inverse(function_inverse(sk0_12)),empty_set)=empty_set),
% 18.86/2.86 introduced(split_symbol_definition)).
% 18.86/2.86 fof(f6624,plain,(
% 18.86/2.86 relation_composition(function_inverse(function_inverse(sk0_12)),empty_set)=empty_set|~relation(function_inverse(sk0_12))|~spl0_92),
% 18.86/2.86 inference(resolution,[status(thm)],[f1501,f1174])).
% 18.86/2.86 fof(f6625,plain,(
% 18.86/2.86 spl0_325|~spl0_10|~spl0_92),
% 18.86/2.86 inference(split_clause,[status(thm)],[f6624,f6621,f236,f1173])).
% 18.86/2.86 fof(f6701,plain,(
% 18.86/2.86 ![X0]: (in(sk0_0(sk0_3(X0)),X0)|empty(sk0_3(X0))|empty(X0))),
% 18.86/2.86 inference(resolution,[status(thm)],[f2607,f102])).
% 18.86/2.87 fof(f6702,plain,(
% 18.86/2.87 ![X0]: (in(sk0_0(sk0_3(X0)),X0)|empty(X0))),
% 18.86/2.87 inference(forward_subsumption_resolution,[status(thm)],[f6701,f103])).
% 18.86/2.87 fof(f6722,plain,(
% 18.86/2.87 spl0_332 <=> sk0_0(sk0_3(relation_rng(sk0_12)))=apply(sk0_12,apply(function_inverse(sk0_12),sk0_0(sk0_3(relation_rng(sk0_12)))))),
% 18.86/2.87 introduced(split_symbol_definition)).
% 18.86/2.87 fof(f6725,plain,(
% 18.86/2.87 empty(relation_rng(sk0_12))|sk0_0(sk0_3(relation_rng(sk0_12)))=apply(sk0_12,apply(function_inverse(sk0_12),sk0_0(sk0_3(relation_rng(sk0_12)))))|~spl0_134),
% 18.86/2.87 inference(resolution,[status(thm)],[f6702,f2124])).
% 18.86/2.87 fof(f6726,plain,(
% 18.86/2.87 spl0_58|spl0_332|~spl0_134),
% 18.86/2.87 inference(split_clause,[status(thm)],[f6725,f624,f6722,f2123])).
% 18.86/2.87 fof(f6727,plain,(
% 18.86/2.87 spl0_333 <=> sk0_0(sk0_3(relation_rng(sk0_12)))=apply(relation_composition(function_inverse(sk0_12),sk0_12),sk0_0(sk0_3(relation_rng(sk0_12))))),
% 18.86/2.87 introduced(split_symbol_definition)).
% 18.86/2.87 fof(f6730,plain,(
% 18.86/2.87 empty(relation_rng(sk0_12))|sk0_0(sk0_3(relation_rng(sk0_12)))=apply(relation_composition(function_inverse(sk0_12),sk0_12),sk0_0(sk0_3(relation_rng(sk0_12))))|~spl0_136),
% 18.86/2.87 inference(resolution,[status(thm)],[f6702,f2136])).
% 18.86/2.87 fof(f6731,plain,(
% 18.86/2.87 spl0_58|spl0_333|~spl0_136),
% 18.86/2.87 inference(split_clause,[status(thm)],[f6730,f624,f6727,f2135])).
% 18.86/2.87 fof(f6738,plain,(
% 18.86/2.87 spl0_335 <=> sk0_0(sk0_3(relation_dom(sk0_12)))=apply(function_inverse(sk0_12),apply(sk0_12,sk0_0(sk0_3(relation_dom(sk0_12)))))),
% 18.86/2.87 introduced(split_symbol_definition)).
% 18.86/2.87 fof(f6741,plain,(
% 18.86/2.87 empty(relation_dom(sk0_12))|sk0_0(sk0_3(relation_dom(sk0_12)))=apply(function_inverse(sk0_12),apply(sk0_12,sk0_0(sk0_3(relation_dom(sk0_12)))))|~spl0_116),
% 18.86/2.87 inference(resolution,[status(thm)],[f6702,f1669])).
% 18.86/2.87 fof(f6742,plain,(
% 18.86/2.87 spl0_7|spl0_335|~spl0_116),
% 18.86/2.87 inference(split_clause,[status(thm)],[f6741,f221,f6738,f1668])).
% 18.86/2.87 fof(f6743,plain,(
% 18.86/2.87 spl0_336 <=> empty(sk0_0(sk0_3(powerset(empty_set))))),
% 18.86/2.87 introduced(split_symbol_definition)).
% 18.86/2.87 fof(f6746,plain,(
% 18.86/2.87 empty(powerset(empty_set))|empty(sk0_0(sk0_3(powerset(empty_set))))),
% 18.86/2.87 inference(resolution,[status(thm)],[f6702,f2525])).
% 18.86/2.87 fof(f6747,plain,(
% 18.86/2.87 spl0_182|spl0_336),
% 18.86/2.87 inference(split_clause,[status(thm)],[f6746,f3042,f6743])).
% 18.86/2.87 fof(f6748,plain,(
% 18.86/2.87 ![X0]: (empty(powerset(X0))|subset(sk0_0(sk0_3(powerset(X0))),X0))),
% 18.86/2.87 inference(resolution,[status(thm)],[f6702,f1026])).
% 18.86/2.87 fof(f6749,plain,(
% 18.86/2.87 ![X0]: (subset(sk0_0(sk0_3(powerset(X0))),X0))),
% 18.86/2.87 inference(forward_subsumption_resolution,[status(thm)],[f6748,f74])).
% 18.86/2.87 fof(f6755,plain,(
% 18.86/2.87 empty(sk0_0(sk0_3(powerset(empty_set))))),
% 18.86/2.87 inference(resolution,[status(thm)],[f6749,f2523])).
% 18.86/2.87 fof(f6993,plain,(
% 18.86/2.87 relation_dom(relation_rng(sk0_0(sk0_3(powerset(empty_set)))))=empty_set),
% 18.86/2.87 inference(resolution,[status(thm)],[f6755,f922])).
% 18.86/2.87 fof(f7004,plain,(
% 18.86/2.87 sk0_0(sk0_3(powerset(empty_set)))=empty_set),
% 18.86/2.87 inference(resolution,[status(thm)],[f6755,f170])).
% 18.86/2.87 fof(f7013,plain,(
% 18.86/2.87 spl0_341 <=> apply(identity_relation(sk0_3(powerset(empty_set))),empty_set)=sk0_0(sk0_3(powerset(empty_set)))),
% 18.86/2.87 introduced(split_symbol_definition)).
% 18.86/2.87 fof(f7016,plain,(
% 18.86/2.87 spl0_342 <=> sk0_3(powerset(empty_set))=empty_set),
% 18.86/2.87 introduced(split_symbol_definition)).
% 18.86/2.87 fof(f7017,plain,(
% 18.86/2.87 sk0_3(powerset(empty_set))=empty_set|~spl0_342),
% 18.86/2.87 inference(component_clause,[status(thm)],[f7016])).
% 18.86/2.87 fof(f7019,plain,(
% 18.86/2.87 apply(identity_relation(sk0_3(powerset(empty_set))),empty_set)=sk0_0(sk0_3(powerset(empty_set)))|sk0_3(powerset(empty_set))=empty_set),
% 18.86/2.87 inference(paramodulation,[status(thm)],[f7004,f3637])).
% 18.86/2.87 fof(f7020,plain,(
% 18.86/2.87 spl0_341|spl0_342),
% 18.86/2.87 inference(split_clause,[status(thm)],[f7019,f7013,f7016])).
% 18.86/2.87 fof(f7021,plain,(
% 18.86/2.87 spl0_343 <=> empty(sk0_3(powerset(empty_set)))),
% 18.86/2.87 introduced(split_symbol_definition)).
% 18.86/2.87 fof(f7022,plain,(
% 18.86/2.87 empty(sk0_3(powerset(empty_set)))|~spl0_343),
% 18.86/2.87 inference(component_clause,[status(thm)],[f7021])).
% 18.86/2.87 fof(f7024,plain,(
% 18.86/2.87 spl0_344 <=> in(sk0_3(powerset(empty_set)),empty_set)),
% 18.86/2.87 introduced(split_symbol_definition)).
% 18.86/2.87 fof(f7027,plain,(
% 18.86/2.87 empty(sk0_3(powerset(empty_set)))|~in(sk0_3(powerset(empty_set)),empty_set)),
% 18.86/2.87 inference(paramodulation,[status(thm)],[f7004,f1621])).
% 18.86/2.87 fof(f7028,plain,(
% 18.86/2.87 spl0_343|~spl0_344),
% 18.86/2.87 inference(split_clause,[status(thm)],[f7027,f7021,f7024])).
% 18.86/2.87 fof(f7029,plain,(
% 18.86/2.87 spl0_345 <=> in(empty_set,sk0_3(powerset(empty_set)))),
% 18.86/2.87 introduced(split_symbol_definition)).
% 18.86/2.87 fof(f7030,plain,(
% 18.86/2.87 in(empty_set,sk0_3(powerset(empty_set)))|~spl0_345),
% 18.86/2.87 inference(component_clause,[status(thm)],[f7029])).
% 18.86/2.87 fof(f7032,plain,(
% 18.86/2.87 empty(sk0_3(powerset(empty_set)))|in(empty_set,sk0_3(powerset(empty_set)))),
% 18.86/2.87 inference(paramodulation,[status(thm)],[f7004,f1115])).
% 18.86/2.87 fof(f7033,plain,(
% 18.86/2.87 spl0_343|spl0_345),
% 18.86/2.87 inference(split_clause,[status(thm)],[f7032,f7021,f7029])).
% 18.86/2.87 fof(f7443,plain,(
% 18.86/2.87 empty(powerset(empty_set))|~spl0_343),
% 18.86/2.87 inference(resolution,[status(thm)],[f7022,f103])).
% 18.86/2.87 fof(f7444,plain,(
% 18.86/2.87 spl0_182|~spl0_343),
% 18.86/2.87 inference(split_clause,[status(thm)],[f7443,f3042,f7021])).
% 18.86/2.87 fof(f7713,plain,(
% 18.86/2.87 spl0_363 <=> function(identity_relation(sk0_3(powerset(empty_set))))),
% 18.86/2.87 introduced(split_symbol_definition)).
% 18.86/2.87 fof(f7715,plain,(
% 18.86/2.87 ~function(identity_relation(sk0_3(powerset(empty_set))))|spl0_363),
% 18.86/2.87 inference(component_clause,[status(thm)],[f7713])).
% 18.86/2.87 fof(f7716,plain,(
% 18.86/2.87 spl0_364 <=> apply(identity_relation(sk0_3(powerset(empty_set))),empty_set)=empty_set),
% 18.86/2.87 introduced(split_symbol_definition)).
% 18.86/2.87 fof(f7719,plain,(
% 18.86/2.87 ~function(identity_relation(sk0_3(powerset(empty_set))))|apply(identity_relation(sk0_3(powerset(empty_set))),empty_set)=empty_set|~spl0_345),
% 18.86/2.87 inference(resolution,[status(thm)],[f7030,f1118])).
% 18.86/2.87 fof(f7720,plain,(
% 18.86/2.87 ~spl0_363|spl0_364|~spl0_345),
% 18.86/2.87 inference(split_clause,[status(thm)],[f7719,f7713,f7716,f7029])).
% 18.86/2.87 fof(f7721,plain,(
% 18.86/2.87 $false|spl0_363),
% 18.86/2.87 inference(forward_subsumption_resolution,[status(thm)],[f7715,f78])).
% 18.86/2.87 fof(f7722,plain,(
% 18.86/2.87 spl0_363),
% 18.86/2.87 inference(contradiction_clause,[status(thm)],[f7721])).
% 18.86/2.87 fof(f7838,plain,(
% 18.86/2.87 spl0_382 <=> relation_dom(sk0_12)=empty_set),
% 18.86/2.87 introduced(split_symbol_definition)).
% 18.86/2.87 fof(f7839,plain,(
% 18.86/2.87 relation_dom(sk0_12)=empty_set|~spl0_382),
% 18.86/2.87 inference(component_clause,[status(thm)],[f7838])).
% 18.86/2.87 fof(f7840,plain,(
% 18.86/2.87 ~relation_dom(sk0_12)=empty_set|spl0_382),
% 18.86/2.87 inference(component_clause,[status(thm)],[f7838])).
% 18.86/2.87 fof(f7863,plain,(
% 18.86/2.87 relation_dom(relation_rng(empty_set))=empty_set),
% 18.86/2.87 inference(forward_demodulation,[status(thm)],[f7004,f6993])).
% 18.86/2.87 fof(f7864,plain,(
% 18.86/2.87 relation_dom(empty_set)=empty_set),
% 18.86/2.87 inference(forward_demodulation,[status(thm)],[f887,f7863])).
% 18.86/2.87 fof(f7897,plain,(
% 18.86/2.87 spl0_385 <=> ~in(X0,relation_dom(empty_set))|X0=apply(function_inverse(relation_rng(empty_set)),apply(relation_rng(empty_set),X0))),
% 18.86/2.87 introduced(split_symbol_definition)).
% 18.86/2.87 fof(f7900,plain,(
% 18.86/2.87 ![X0]: (~in(X0,relation_dom(empty_set))|X0=apply(function_inverse(relation_rng(empty_set)),apply(relation_rng(empty_set),X0))|~empty(empty_set))),
% 18.86/2.87 inference(paramodulation,[status(thm)],[f887,f2385])).
% 18.86/2.87 fof(f7901,plain,(
% 18.86/2.87 spl0_385|~spl0_46),
% 18.86/2.87 inference(split_clause,[status(thm)],[f7900,f7897,f448])).
% 18.86/2.87 fof(f7911,plain,(
% 18.86/2.87 spl0_387 <=> ~in(X0,relation_dom(empty_set))|X0=apply(function_inverse(relation_dom(empty_set)),apply(relation_dom(empty_set),X0))),
% 18.86/2.87 introduced(split_symbol_definition)).
% 18.86/2.87 fof(f7919,plain,(
% 18.86/2.87 ~empty(relation_composition(identity_relation(empty_set),function_inverse(identity_relation(sk0_2))))|spl0_40),
% 18.86/2.87 inference(forward_demodulation,[status(thm)],[f565,f426])).
% 18.86/2.87 fof(f7920,plain,(
% 18.86/2.87 ~empty(relation_composition(empty_set,function_inverse(identity_relation(sk0_2))))|spl0_40),
% 18.86/2.87 inference(forward_demodulation,[status(thm)],[f850,f7919])).
% 18.86/2.87 fof(f7921,plain,(
% 18.86/2.87 ~empty(empty_set)|spl0_40),
% 18.86/2.87 inference(forward_demodulation,[status(thm)],[f6537,f7920])).
% 18.86/2.87 fof(f7922,plain,(
% 18.86/2.87 $false|spl0_40),
% 18.86/2.87 inference(forward_subsumption_resolution,[status(thm)],[f7921,f68])).
% 18.86/2.87 fof(f7923,plain,(
% 18.86/2.87 spl0_40),
% 18.86/2.87 inference(contradiction_clause,[status(thm)],[f7922])).
% 18.86/2.87 fof(f7924,plain,(
% 18.86/2.87 ~empty(relation_composition(identity_relation(empty_set),function_inverse(identity_relation(sk0_4))))|spl0_36),
% 18.86/2.87 inference(forward_demodulation,[status(thm)],[f564,f408])).
% 18.86/2.87 fof(f7925,plain,(
% 18.86/2.87 ~empty(relation_composition(empty_set,function_inverse(identity_relation(sk0_4))))|spl0_36),
% 18.86/2.87 inference(forward_demodulation,[status(thm)],[f850,f7924])).
% 18.86/2.87 fof(f7926,plain,(
% 18.86/2.87 ~empty(empty_set)|spl0_36),
% 18.86/2.87 inference(forward_demodulation,[status(thm)],[f6537,f7925])).
% 18.86/2.87 fof(f7927,plain,(
% 18.86/2.87 $false|spl0_36),
% 18.86/2.87 inference(forward_subsumption_resolution,[status(thm)],[f7926,f68])).
% 18.86/2.87 fof(f7928,plain,(
% 18.86/2.87 spl0_36),
% 18.86/2.87 inference(contradiction_clause,[status(thm)],[f7927])).
% 18.86/2.87 fof(f7937,plain,(
% 18.86/2.87 spl0_29|~spl0_33),
% 18.86/2.87 inference(split_clause,[status(thm)],[f4893,f359,f387])).
% 18.86/2.87 fof(f8000,plain,(
% 18.86/2.87 ~relation(relation_composition(empty_set,function_inverse(identity_relation(empty_set))))|spl0_45),
% 18.86/2.87 inference(forward_demodulation,[status(thm)],[f850,f447])).
% 18.86/2.87 fof(f8001,plain,(
% 18.86/2.87 ~relation(empty_set)|spl0_45),
% 18.86/2.87 inference(forward_demodulation,[status(thm)],[f6537,f8000])).
% 18.86/2.87 fof(f8002,plain,(
% 18.86/2.87 $false|spl0_45),
% 18.86/2.87 inference(forward_subsumption_resolution,[status(thm)],[f8001,f69])).
% 18.86/2.87 fof(f8003,plain,(
% 18.86/2.87 spl0_45),
% 18.86/2.87 inference(contradiction_clause,[status(thm)],[f8002])).
% 18.86/2.87 fof(f8004,plain,(
% 18.86/2.87 ~relation(relation_composition(identity_relation(empty_set),function_inverse(identity_relation(sk0_5))))|spl0_34),
% 18.86/2.87 inference(forward_demodulation,[status(thm)],[f563,f392])).
% 18.86/2.87 fof(f8005,plain,(
% 18.86/2.87 ~relation(relation_composition(empty_set,function_inverse(identity_relation(sk0_5))))|spl0_34),
% 18.86/2.87 inference(forward_demodulation,[status(thm)],[f850,f8004])).
% 18.86/2.87 fof(f8006,plain,(
% 18.86/2.87 ~relation(empty_set)|spl0_34),
% 18.86/2.87 inference(forward_demodulation,[status(thm)],[f6537,f8005])).
% 18.86/2.87 fof(f8007,plain,(
% 18.86/2.87 $false|spl0_34),
% 18.86/2.87 inference(forward_subsumption_resolution,[status(thm)],[f8006,f69])).
% 18.86/2.87 fof(f8008,plain,(
% 18.86/2.87 spl0_34),
% 18.86/2.87 inference(contradiction_clause,[status(thm)],[f8007])).
% 18.86/2.87 fof(f8009,plain,(
% 18.86/2.87 ~empty(relation_dom(empty_set))|spl0_23),
% 18.86/2.87 inference(forward_demodulation,[status(thm)],[f564,f331])).
% 18.86/2.87 fof(f8029,plain,(
% 18.86/2.87 ![X0]: (~in(X0,relation_dom(empty_set))|X0=apply(function_inverse(relation_dom(empty_set)),apply(relation_dom(empty_set),X0))|~empty(empty_set))),
% 18.86/2.87 inference(paramodulation,[status(thm)],[f7864,f2386])).
% 18.86/2.87 fof(f8030,plain,(
% 18.86/2.87 spl0_387|~spl0_46),
% 18.86/2.87 inference(split_clause,[status(thm)],[f8029,f7911,f448])).
% 18.86/2.87 fof(f8067,plain,(
% 18.86/2.87 spl0_394 <=> ~in(X0,relation_dom(empty_set))|X0=apply(relation_composition(relation_rng(empty_set),function_inverse(relation_rng(empty_set))),X0)),
% 18.86/2.87 introduced(split_symbol_definition)).
% 18.86/2.87 fof(f8070,plain,(
% 18.86/2.87 ![X0]: (~in(X0,relation_dom(empty_set))|X0=apply(relation_composition(relation_rng(empty_set),function_inverse(relation_rng(empty_set))),X0)|~empty(empty_set))),
% 18.86/2.87 inference(paramodulation,[status(thm)],[f887,f2462])).
% 18.86/2.87 fof(f8071,plain,(
% 18.86/2.87 spl0_394|~spl0_46),
% 18.86/2.87 inference(split_clause,[status(thm)],[f8070,f8067,f448])).
% 18.86/2.87 fof(f8117,plain,(
% 18.86/2.87 spl0_399 <=> function(relation_composition(empty_set,function_inverse(empty_set)))),
% 18.86/2.87 introduced(split_symbol_definition)).
% 18.86/2.87 fof(f8119,plain,(
% 18.86/2.87 ~function(relation_composition(empty_set,function_inverse(empty_set)))|spl0_399),
% 18.86/2.87 inference(component_clause,[status(thm)],[f8117])).
% 18.86/2.87 fof(f8145,plain,(
% 18.86/2.87 spl0_402 <=> ~in(X0,relation_dom(empty_set))|X0=apply(relation_composition(relation_dom(empty_set),function_inverse(relation_dom(empty_set))),X0)),
% 18.86/2.87 introduced(split_symbol_definition)).
% 18.86/2.87 fof(f8148,plain,(
% 18.86/2.87 ![X0]: (~in(X0,relation_dom(empty_set))|X0=apply(relation_composition(relation_dom(empty_set),function_inverse(relation_dom(empty_set))),X0)|~empty(empty_set))),
% 18.86/2.87 inference(paramodulation,[status(thm)],[f7864,f2463])).
% 18.86/2.87 fof(f8149,plain,(
% 18.86/2.87 spl0_402|~spl0_46),
% 18.86/2.87 inference(split_clause,[status(thm)],[f8148,f8145,f448])).
% 18.86/2.87 fof(f8211,plain,(
% 18.86/2.87 spl0_408 <=> ~in(X0,relation_rng(empty_set))|X0=apply(relation_rng(empty_set),apply(function_inverse(relation_rng(empty_set)),X0))),
% 18.86/2.87 introduced(split_symbol_definition)).
% 18.86/2.87 fof(f8214,plain,(
% 18.86/2.87 ![X0]: (~in(X0,relation_rng(empty_set))|X0=apply(relation_rng(empty_set),apply(function_inverse(relation_rng(empty_set)),X0))|~empty(empty_set))),
% 18.86/2.87 inference(paramodulation,[status(thm)],[f887,f2470])).
% 18.86/2.87 fof(f8215,plain,(
% 18.86/2.87 spl0_408|~spl0_46),
% 18.86/2.87 inference(split_clause,[status(thm)],[f8214,f8211,f448])).
% 18.86/2.87 fof(f8222,plain,(
% 18.86/2.87 spl0_409 <=> ~in(X0,relation_rng(empty_set))|X0=apply(relation_dom(empty_set),apply(function_inverse(relation_dom(empty_set)),X0))),
% 18.86/2.87 introduced(split_symbol_definition)).
% 18.86/2.87 fof(f8225,plain,(
% 18.86/2.87 ![X0]: (~in(X0,relation_rng(empty_set))|X0=apply(relation_dom(empty_set),apply(function_inverse(relation_dom(empty_set)),X0))|~empty(empty_set))),
% 18.86/2.87 inference(paramodulation,[status(thm)],[f7864,f2471])).
% 18.86/2.87 fof(f8226,plain,(
% 18.86/2.87 spl0_409|~spl0_46),
% 18.86/2.87 inference(split_clause,[status(thm)],[f8225,f8222,f448])).
% 18.86/2.87 fof(f8250,plain,(
% 18.86/2.87 ~empty(empty_set)|spl0_23),
% 18.86/2.87 inference(forward_demodulation,[status(thm)],[f7864,f8009])).
% 18.86/2.87 fof(f8251,plain,(
% 18.86/2.87 $false|spl0_23),
% 18.86/2.87 inference(forward_subsumption_resolution,[status(thm)],[f8250,f68])).
% 18.86/2.87 fof(f8252,plain,(
% 18.86/2.87 spl0_23),
% 18.86/2.87 inference(contradiction_clause,[status(thm)],[f8251])).
% 18.86/2.87 fof(f8652,plain,(
% 18.86/2.87 ~function(empty_set)|spl0_399),
% 18.86/2.87 inference(forward_demodulation,[status(thm)],[f6574,f8119])).
% 18.86/2.87 fof(f8653,plain,(
% 18.86/2.87 $false|spl0_399),
% 18.86/2.87 inference(forward_subsumption_resolution,[status(thm)],[f8652,f588])).
% 18.86/2.87 fof(f8654,plain,(
% 18.86/2.87 spl0_399),
% 18.86/2.87 inference(contradiction_clause,[status(thm)],[f8653])).
% 18.86/2.87 fof(f9332,plain,(
% 18.86/2.87 ![X0]: (relation_composition(empty_set,relation_composition(X0,sk0_12))=empty_set|~relation(X0))),
% 18.86/2.87 inference(resolution,[status(thm)],[f1045,f165])).
% 18.86/2.87 fof(f9404,plain,(
% 18.86/2.87 spl0_440 <=> identity_relation(relation_dom(sk0_12))=empty_set),
% 18.86/2.87 introduced(split_symbol_definition)).
% 18.86/2.87 fof(f9405,plain,(
% 18.86/2.87 identity_relation(relation_dom(sk0_12))=empty_set|~spl0_440),
% 18.86/2.87 inference(component_clause,[status(thm)],[f9404])).
% 18.86/2.87 fof(f9629,plain,(
% 18.86/2.87 spl0_460 <=> sk0_0(relation_composition(function_inverse(sk0_12),sk0_12))=sk0_0(relation_composition(function_inverse(sk0_12),sk0_12))),
% 18.86/2.87 introduced(split_symbol_definition)).
% 18.86/2.87 fof(f9632,plain,(
% 18.86/2.87 spl0_461 <=> relation_composition(function_inverse(sk0_12),sk0_12)=empty_set),
% 18.86/2.87 introduced(split_symbol_definition)).
% 18.86/2.87 fof(f9633,plain,(
% 18.86/2.87 relation_composition(function_inverse(sk0_12),sk0_12)=empty_set|~spl0_461),
% 18.86/2.87 inference(component_clause,[status(thm)],[f9632])).
% 18.86/2.87 fof(f9635,plain,(
% 18.86/2.87 sk0_0(relation_composition(function_inverse(sk0_12),sk0_12))=sk0_0(relation_composition(function_inverse(sk0_12),sk0_12))|relation_composition(function_inverse(sk0_12),sk0_12)=empty_set|spl0_56),
% 18.86/2.87 inference(paramodulation,[status(thm)],[f3637,f3739])).
% 18.86/2.87 fof(f9636,plain,(
% 18.86/2.87 spl0_460|spl0_461|spl0_56),
% 18.86/2.87 inference(split_clause,[status(thm)],[f9635,f9629,f9632,f618])).
% 18.86/2.87 fof(f9652,plain,(
% 18.86/2.87 $false|spl0_1|~spl0_48|~spl0_120),
% 18.86/2.87 inference(forward_subsumption_resolution,[status(thm)],[f2319,f182])).
% 18.86/2.87 fof(f9653,plain,(
% 18.86/2.87 spl0_1|~spl0_48|~spl0_120),
% 18.86/2.87 inference(contradiction_clause,[status(thm)],[f9652])).
% 18.86/2.87 fof(f9673,plain,(
% 18.86/2.87 ![X0]: (relation_composition(empty_set,relation_composition(function_inverse(X0),sk0_12))=empty_set|~relation(X0)|~function(X0))),
% 18.86/2.87 inference(resolution,[status(thm)],[f9332,f58])).
% 18.86/2.87 fof(f9913,plain,(
% 18.86/2.87 ![X0]: (relation_composition(relation_composition(X0,sk0_12),empty_set)=empty_set|~relation(X0))),
% 18.86/2.87 inference(resolution,[status(thm)],[f1497,f165])).
% 18.86/2.87 fof(f10314,plain,(
% 18.86/2.87 $false|spl0_76),
% 18.86/2.87 inference(forward_subsumption_resolution,[status(thm)],[f1056,f123])).
% 18.86/2.87 fof(f10315,plain,(
% 18.86/2.87 spl0_76),
% 18.86/2.87 inference(contradiction_clause,[status(thm)],[f10314])).
% 18.86/2.87 fof(f10322,plain,(
% 18.86/2.87 $false|spl0_80),
% 18.86/2.87 inference(forward_subsumption_resolution,[status(thm)],[f1092,f112])).
% 18.86/2.87 fof(f10323,plain,(
% 18.86/2.87 spl0_80),
% 18.86/2.87 inference(contradiction_clause,[status(thm)],[f10322])).
% 18.86/2.87 fof(f10344,plain,(
% 18.86/2.87 spl0_513 <=> ~element(relation_dom(empty_set),powerset(X0))|~empty(X0)),
% 18.86/2.87 introduced(split_symbol_definition)).
% 18.86/2.87 fof(f10345,plain,(
% 18.86/2.87 ![X0]: (~element(relation_dom(empty_set),powerset(X0))|~empty(X0)|~spl0_513)),
% 18.86/2.87 inference(component_clause,[status(thm)],[f10344])).
% 18.86/2.87 fof(f10347,plain,(
% 18.86/2.87 ![X0]: (relation_composition(empty_set,sk0_12)=identity_relation(relation_dom(relation_composition(empty_set,sk0_12)))|~relation(empty_set)|~function(empty_set)|~element(relation_dom(empty_set),powerset(X0))|~empty(X0)|~spl0_128)),
% 18.86/2.87 inference(paramodulation,[status(thm)],[f1052,f4283])).
% 18.86/2.87 fof(f10348,plain,(
% 18.86/2.87 spl0_190|~spl0_47|~spl0_66|spl0_513|~spl0_128),
% 18.86/2.87 inference(split_clause,[status(thm)],[f10347,f4293,f453,f756,f10344,f1901])).
% 18.86/2.87 fof(f10349,plain,(
% 18.86/2.87 ~identity_relation(relation_dom(sk0_12))=identity_relation(relation_dom(sk0_12))|~spl0_4|~spl0_123|spl0_0),
% 18.86/2.87 inference(forward_demodulation,[status(thm)],[f2648,f179])).
% 18.86/2.87 fof(f10350,plain,(
% 18.86/2.87 $false|~spl0_4|~spl0_123|spl0_0),
% 18.86/2.87 inference(trivial_equality_resolution,[status(esa)],[f10349])).
% 18.86/2.87 fof(f10351,plain,(
% 18.86/2.87 ~spl0_4|~spl0_123|spl0_0),
% 18.86/2.87 inference(contradiction_clause,[status(thm)],[f10350])).
% 18.86/2.87 fof(f10406,plain,(
% 18.86/2.87 spl0_514 <=> sk0_0(relation_rng(sk0_12))=sk0_0(relation_rng(sk0_12))),
% 18.86/2.87 introduced(split_symbol_definition)).
% 18.86/2.87 fof(f10409,plain,(
% 18.86/2.87 spl0_515 <=> relation_rng(sk0_12)=empty_set),
% 18.86/2.87 introduced(split_symbol_definition)).
% 18.86/2.87 fof(f10410,plain,(
% 18.86/2.87 relation_rng(sk0_12)=empty_set|~spl0_515),
% 18.86/2.87 inference(component_clause,[status(thm)],[f10409])).
% 18.86/2.87 fof(f10567,plain,(
% 18.86/2.87 spl0_525 <=> function(identity_relation(relation_dom(sk0_1)))),
% 18.86/2.87 introduced(split_symbol_definition)).
% 18.86/2.87 fof(f10569,plain,(
% 18.86/2.87 ~function(identity_relation(relation_dom(sk0_1)))|spl0_525),
% 18.86/2.87 inference(component_clause,[status(thm)],[f10567])).
% 18.86/2.87 fof(f10577,plain,(
% 18.86/2.87 $false|spl0_525),
% 18.86/2.87 inference(forward_subsumption_resolution,[status(thm)],[f10569,f78])).
% 18.86/2.87 fof(f10578,plain,(
% 18.86/2.87 spl0_525),
% 18.86/2.87 inference(contradiction_clause,[status(thm)],[f10577])).
% 18.86/2.87 fof(f10603,plain,(
% 18.86/2.87 ![X0]: (relation_composition(relation_composition(function_inverse(X0),sk0_12),empty_set)=empty_set|~relation(X0)|~function(X0))),
% 18.86/2.87 inference(resolution,[status(thm)],[f9913,f58])).
% 18.86/2.87 fof(f11229,plain,(
% 18.86/2.87 ~function(empty_set)|spl0_98),
% 18.86/2.87 inference(forward_demodulation,[status(thm)],[f850,f1300])).
% 18.86/2.87 fof(f11230,plain,(
% 18.86/2.87 $false|spl0_98),
% 18.86/2.87 inference(forward_subsumption_resolution,[status(thm)],[f11229,f588])).
% 18.86/2.87 fof(f11231,plain,(
% 18.86/2.87 spl0_98),
% 18.86/2.87 inference(contradiction_clause,[status(thm)],[f11230])).
% 18.86/2.87 fof(f11232,plain,(
% 18.86/2.87 ~relation(empty_set)|~spl0_17|spl0_104),
% 18.86/2.87 inference(forward_demodulation,[status(thm)],[f1498,f1395])).
% 18.86/2.87 fof(f11233,plain,(
% 18.86/2.87 $false|~spl0_17|spl0_104),
% 18.86/2.87 inference(forward_subsumption_resolution,[status(thm)],[f11232,f69])).
% 18.86/2.87 fof(f11234,plain,(
% 18.86/2.87 ~spl0_17|spl0_104),
% 18.86/2.87 inference(contradiction_clause,[status(thm)],[f11233])).
% 18.86/2.87 fof(f11241,plain,(
% 18.86/2.87 in(sk0_11(empty_set,empty_set),relation_dom(empty_set))|~spl0_84),
% 18.86/2.87 inference(forward_demodulation,[status(thm)],[f7864,f1123])).
% 18.86/2.87 fof(f11242,plain,(
% 18.86/2.87 in(sk0_11(empty_set,empty_set),empty_set)|~spl0_84),
% 18.86/2.87 inference(forward_demodulation,[status(thm)],[f7864,f11241])).
% 18.86/2.87 fof(f11243,plain,(
% 18.86/2.87 ~empty(empty_set)|~spl0_74),
% 18.86/2.87 inference(forward_demodulation,[status(thm)],[f561,f877])).
% 18.86/2.87 fof(f11244,plain,(
% 18.86/2.87 $false|~spl0_74),
% 18.86/2.87 inference(forward_subsumption_resolution,[status(thm)],[f11243,f68])).
% 18.86/2.87 fof(f11245,plain,(
% 18.86/2.87 ~spl0_74),
% 18.86/2.87 inference(contradiction_clause,[status(thm)],[f11244])).
% 18.86/2.87 fof(f11364,plain,(
% 18.86/2.87 empty(relation_rng(sk0_12))|~spl0_187),
% 18.86/2.87 inference(resolution,[status(thm)],[f3190,f196])).
% 18.86/2.87 fof(f11365,plain,(
% 18.86/2.87 spl0_58|~spl0_187),
% 18.86/2.87 inference(split_clause,[status(thm)],[f11364,f624,f3189])).
% 18.86/2.87 fof(f11822,plain,(
% 18.86/2.87 ~empty(empty_set)|~spl0_84),
% 18.86/2.87 inference(resolution,[status(thm)],[f11242,f173])).
% 18.86/2.87 fof(f11823,plain,(
% 18.86/2.87 ~spl0_46|~spl0_84),
% 18.86/2.87 inference(split_clause,[status(thm)],[f11822,f448,f1122])).
% 18.86/2.87 fof(f12463,plain,(
% 18.86/2.87 spl0_598 <=> ~in(X0,relation_rng(empty_set))|X0=apply(identity_relation(empty_set),apply(function_inverse(identity_relation(empty_set)),X0))),
% 18.86/2.87 introduced(split_symbol_definition)).
% 18.86/2.87 fof(f12466,plain,(
% 18.86/2.87 ![X0]: (~in(X0,relation_rng(empty_set))|X0=apply(identity_relation(empty_set),apply(function_inverse(identity_relation(empty_set)),X0))|~empty(empty_set))),
% 18.86/2.87 inference(paramodulation,[status(thm)],[f850,f2465])).
% 18.86/2.87 fof(f12467,plain,(
% 18.86/2.87 spl0_598|~spl0_46),
% 18.86/2.87 inference(split_clause,[status(thm)],[f12466,f12463,f448])).
% 18.86/2.87 fof(f13336,plain,(
% 18.86/2.87 ![X0]: (~element(empty_set,powerset(X0))|~empty(X0)|~spl0_513)),
% 18.86/2.87 inference(forward_demodulation,[status(thm)],[f7864,f10345])).
% 18.86/2.87 fof(f13337,plain,(
% 18.86/2.87 ![X0]: (~empty(X0)|~spl0_513)),
% 18.86/2.87 inference(forward_subsumption_resolution,[status(thm)],[f13336,f1015])).
% 18.86/2.87 fof(f13390,plain,(
% 18.86/2.87 $false|~spl0_513),
% 18.86/2.87 inference(backward_subsumption_resolution,[status(thm)],[f68,f13337])).
% 18.86/2.87 fof(f13391,plain,(
% 18.86/2.87 ~spl0_513),
% 18.86/2.87 inference(contradiction_clause,[status(thm)],[f13390])).
% 18.86/2.87 fof(f13415,plain,(
% 18.86/2.87 spl0_621 <=> relation_composition(empty_set,relation_composition(function_inverse(sk0_12),sk0_12))=empty_set),
% 18.86/2.87 introduced(split_symbol_definition)).
% 18.86/2.87 fof(f13418,plain,(
% 18.86/2.87 relation_composition(empty_set,relation_composition(function_inverse(sk0_12),sk0_12))=empty_set|~relation(sk0_12)),
% 18.86/2.87 inference(resolution,[status(thm)],[f9673,f166])).
% 18.86/2.87 fof(f13419,plain,(
% 18.86/2.87 spl0_621|~spl0_2),
% 18.86/2.87 inference(split_clause,[status(thm)],[f13418,f13415,f198])).
% 18.86/2.87 fof(f13420,plain,(
% 18.86/2.87 spl0_622 <=> relation_composition(empty_set,relation_composition(function_inverse(empty_set),sk0_12))=empty_set),
% 18.86/2.87 introduced(split_symbol_definition)).
% 18.86/2.87 fof(f13423,plain,(
% 18.86/2.87 relation_composition(empty_set,relation_composition(function_inverse(empty_set),sk0_12))=empty_set|~relation(empty_set)),
% 18.86/2.87 inference(resolution,[status(thm)],[f9673,f588])).
% 18.86/2.87 fof(f13424,plain,(
% 18.86/2.87 spl0_622|~spl0_47),
% 18.86/2.87 inference(split_clause,[status(thm)],[f13423,f13420,f453])).
% 18.86/2.87 fof(f13425,plain,(
% 18.86/2.87 spl0_623 <=> relation_composition(empty_set,relation_composition(function_inverse(relation_composition(function_inverse(sk0_12),sk0_12)),sk0_12))=empty_set),
% 18.86/2.87 introduced(split_symbol_definition)).
% 18.86/2.87 fof(f13428,plain,(
% 18.86/2.87 relation_composition(empty_set,relation_composition(function_inverse(relation_composition(function_inverse(sk0_12),sk0_12)),sk0_12))=empty_set|~relation(relation_composition(function_inverse(sk0_12),sk0_12))|~spl0_93),
% 18.86/2.87 inference(resolution,[status(thm)],[f9673,f1189])).
% 18.86/2.87 fof(f13429,plain,(
% 18.86/2.87 spl0_623|~spl0_57|~spl0_93),
% 18.86/2.87 inference(split_clause,[status(thm)],[f13428,f13425,f621,f1188])).
% 18.86/2.87 fof(f13432,plain,(
% 18.86/2.87 spl0_624 <=> relation_composition(empty_set,relation_composition(function_inverse(sk0_1),sk0_12))=empty_set),
% 18.86/2.87 introduced(split_symbol_definition)).
% 18.86/2.87 fof(f13435,plain,(
% 18.86/2.87 relation_composition(empty_set,relation_composition(function_inverse(sk0_1),sk0_12))=empty_set|~relation(sk0_1)),
% 18.86/2.87 inference(resolution,[status(thm)],[f9673,f96])).
% 18.86/2.87 fof(f13436,plain,(
% 18.86/2.87 spl0_624|~spl0_87),
% 18.86/2.87 inference(split_clause,[status(thm)],[f13435,f13432,f1137])).
% 18.86/2.87 fof(f13437,plain,(
% 18.86/2.87 spl0_625 <=> relation_composition(empty_set,relation_composition(function_inverse(function_inverse(sk0_12)),sk0_12))=empty_set),
% 18.86/2.87 introduced(split_symbol_definition)).
% 18.86/2.87 fof(f13440,plain,(
% 18.86/2.87 relation_composition(empty_set,relation_composition(function_inverse(function_inverse(sk0_12)),sk0_12))=empty_set|~relation(function_inverse(sk0_12))|~spl0_92),
% 18.86/2.87 inference(resolution,[status(thm)],[f9673,f1174])).
% 18.86/2.87 fof(f13441,plain,(
% 18.86/2.87 spl0_625|~spl0_10|~spl0_92),
% 18.86/2.87 inference(split_clause,[status(thm)],[f13440,f13437,f236,f1173])).
% 18.86/2.87 fof(f13884,plain,(
% 18.86/2.87 ~empty(empty_set)|~spl0_461|spl0_56),
% 18.86/2.87 inference(backward_demodulation,[status(thm)],[f9633,f620])).
% 18.86/2.87 fof(f13885,plain,(
% 18.86/2.87 ~spl0_46|~spl0_461|spl0_56),
% 18.86/2.87 inference(split_clause,[status(thm)],[f13884,f448,f9632,f618])).
% 18.86/2.87 fof(f14336,plain,(
% 18.86/2.87 relation_composition(function_inverse(sk0_12),sk0_12)=identity_relation(relation_dom(relation_composition(function_inverse(sk0_12),sk0_12)))|~relation(function_inverse(sk0_12))|~function(function_inverse(sk0_12))|~empty(relation_rng(sk0_12))|~spl0_128|~spl0_48),
% 18.86/2.87 inference(paramodulation,[status(thm)],[f514,f4286])).
% 18.86/2.87 fof(f14337,plain,(
% 18.86/2.87 spl0_120|~spl0_10|~spl0_92|~spl0_58|~spl0_128|~spl0_48),
% 18.86/2.87 inference(split_clause,[status(thm)],[f14336,f1836,f236,f1173,f624,f1901,f513])).
% 18.86/2.87 fof(f14817,plain,(
% 18.86/2.87 spl0_669 <=> relation_composition(relation_composition(function_inverse(sk0_12),sk0_12),empty_set)=empty_set),
% 18.86/2.87 introduced(split_symbol_definition)).
% 18.86/2.87 fof(f14820,plain,(
% 18.86/2.87 relation_composition(relation_composition(function_inverse(sk0_12),sk0_12),empty_set)=empty_set|~relation(sk0_12)),
% 18.86/2.87 inference(resolution,[status(thm)],[f10603,f166])).
% 18.86/2.87 fof(f14821,plain,(
% 18.86/2.87 spl0_669|~spl0_2),
% 18.86/2.87 inference(split_clause,[status(thm)],[f14820,f14817,f198])).
% 18.86/2.87 fof(f14822,plain,(
% 18.86/2.87 spl0_670 <=> relation_composition(relation_composition(function_inverse(empty_set),sk0_12),empty_set)=empty_set),
% 18.86/2.87 introduced(split_symbol_definition)).
% 18.86/2.87 fof(f14825,plain,(
% 18.86/2.87 relation_composition(relation_composition(function_inverse(empty_set),sk0_12),empty_set)=empty_set|~relation(empty_set)),
% 18.86/2.87 inference(resolution,[status(thm)],[f10603,f588])).
% 18.86/2.87 fof(f14826,plain,(
% 18.86/2.87 spl0_670|~spl0_47),
% 18.86/2.87 inference(split_clause,[status(thm)],[f14825,f14822,f453])).
% 18.86/2.87 fof(f14827,plain,(
% 18.86/2.87 spl0_671 <=> relation_composition(relation_composition(function_inverse(relation_composition(function_inverse(sk0_12),sk0_12)),sk0_12),empty_set)=empty_set),
% 18.86/2.87 introduced(split_symbol_definition)).
% 18.86/2.87 fof(f14830,plain,(
% 18.86/2.87 relation_composition(relation_composition(function_inverse(relation_composition(function_inverse(sk0_12),sk0_12)),sk0_12),empty_set)=empty_set|~relation(relation_composition(function_inverse(sk0_12),sk0_12))|~spl0_93),
% 18.86/2.87 inference(resolution,[status(thm)],[f10603,f1189])).
% 18.86/2.87 fof(f14831,plain,(
% 18.86/2.87 spl0_671|~spl0_57|~spl0_93),
% 18.86/2.87 inference(split_clause,[status(thm)],[f14830,f14827,f621,f1188])).
% 18.86/2.87 fof(f14834,plain,(
% 18.86/2.87 spl0_672 <=> relation_composition(relation_composition(function_inverse(sk0_1),sk0_12),empty_set)=empty_set),
% 18.86/2.87 introduced(split_symbol_definition)).
% 18.86/2.87 fof(f14837,plain,(
% 18.86/2.87 relation_composition(relation_composition(function_inverse(sk0_1),sk0_12),empty_set)=empty_set|~relation(sk0_1)),
% 18.86/2.87 inference(resolution,[status(thm)],[f10603,f96])).
% 18.86/2.87 fof(f14838,plain,(
% 18.86/2.87 spl0_672|~spl0_87),
% 18.86/2.87 inference(split_clause,[status(thm)],[f14837,f14834,f1137])).
% 18.86/2.87 fof(f14839,plain,(
% 18.86/2.87 spl0_673 <=> relation_composition(relation_composition(function_inverse(function_inverse(sk0_12)),sk0_12),empty_set)=empty_set),
% 18.86/2.87 introduced(split_symbol_definition)).
% 18.86/2.87 fof(f14842,plain,(
% 18.86/2.87 relation_composition(relation_composition(function_inverse(function_inverse(sk0_12)),sk0_12),empty_set)=empty_set|~relation(function_inverse(sk0_12))|~spl0_92),
% 18.86/2.87 inference(resolution,[status(thm)],[f10603,f1174])).
% 18.86/2.87 fof(f14843,plain,(
% 18.86/2.87 spl0_673|~spl0_10|~spl0_92),
% 18.86/2.87 inference(split_clause,[status(thm)],[f14842,f14839,f236,f1173])).
% 18.86/2.87 fof(f15139,plain,(
% 18.86/2.87 relation_composition(empty_set,sk0_1)=identity_relation(relation_dom(relation_composition(empty_set,sk0_1)))|~relation(empty_set)|~function(empty_set)|~empty(relation_dom(empty_set))|~spl0_131),
% 18.86/2.87 inference(paramodulation,[status(thm)],[f1038,f4459])).
% 18.86/2.87 fof(f15140,plain,(
% 18.86/2.87 spl0_208|~spl0_47|~spl0_66|~spl0_31|~spl0_131),
% 18.86/2.87 inference(split_clause,[status(thm)],[f15139,f4461,f453,f756,f365,f1918])).
% 18.86/2.87 fof(f16033,plain,(
% 18.86/2.87 empty(sk0_12)|~relation(sk0_12)|~empty(empty_set)|~spl0_515),
% 18.86/2.87 inference(paramodulation,[status(thm)],[f10410,f84])).
% 18.86/2.87 fof(f16034,plain,(
% 18.86/2.87 spl0_9|~spl0_2|~spl0_46|~spl0_515),
% 18.86/2.87 inference(split_clause,[status(thm)],[f16033,f233,f198,f448,f10409])).
% 18.86/2.87 fof(f16035,plain,(
% 18.86/2.87 empty(sk0_12)|~relation(sk0_12)|~empty(empty_set)|~spl0_382),
% 18.86/2.87 inference(paramodulation,[status(thm)],[f7839,f82])).
% 18.86/2.87 fof(f16036,plain,(
% 18.86/2.87 spl0_9|~spl0_2|~spl0_46|~spl0_382),
% 18.86/2.87 inference(split_clause,[status(thm)],[f16035,f233,f198,f448,f7838])).
% 18.86/2.87 fof(f16091,plain,(
% 18.86/2.87 ~empty(empty_set)|~spl0_108),
% 18.86/2.87 inference(paramodulation,[status(thm)],[f850,f1454])).
% 18.86/2.87 fof(f16092,plain,(
% 18.86/2.87 ~spl0_46|~spl0_108),
% 18.86/2.87 inference(split_clause,[status(thm)],[f16091,f448,f1453])).
% 18.86/2.87 fof(f16104,plain,(
% 18.86/2.87 ~empty(empty_set)|~spl0_308),
% 18.86/2.87 inference(paramodulation,[status(thm)],[f6447,f74])).
% 18.86/2.87 fof(f16105,plain,(
% 18.86/2.87 ~spl0_46|~spl0_308),
% 18.86/2.87 inference(split_clause,[status(thm)],[f16104,f448,f6446])).
% 18.86/2.87 fof(f16116,plain,(
% 18.86/2.87 $false|spl0_105),
% 18.86/2.87 inference(forward_subsumption_resolution,[status(thm)],[f1419,f96])).
% 18.86/2.87 fof(f16117,plain,(
% 18.86/2.87 spl0_105),
% 18.86/2.87 inference(contradiction_clause,[status(thm)],[f16116])).
% 18.86/2.87 fof(f16266,plain,(
% 18.86/2.87 relation_dom(empty_set)=relation_dom(sk0_12)|~spl0_440),
% 18.86/2.87 inference(paramodulation,[status(thm)],[f9405,f191])).
% 18.86/2.87 fof(f16267,plain,(
% 18.86/2.87 empty_set=relation_dom(sk0_12)|~spl0_440),
% 18.86/2.87 inference(forward_demodulation,[status(thm)],[f7864,f16266])).
% 18.86/2.87 fof(f16268,plain,(
% 18.86/2.87 $false|spl0_382|~spl0_440),
% 18.86/2.87 inference(forward_subsumption_resolution,[status(thm)],[f16267,f7840])).
% 18.86/2.87 fof(f16269,plain,(
% 18.86/2.87 spl0_382|~spl0_440),
% 18.86/2.87 inference(contradiction_clause,[status(thm)],[f16268])).
% 18.86/2.87 fof(f16402,plain,(
% 18.86/2.87 empty(powerset(empty_set))|~empty(empty_set)|~spl0_342),
% 18.86/2.87 inference(paramodulation,[status(thm)],[f7017,f103])).
% 18.86/2.87 fof(f16403,plain,(
% 18.86/2.87 spl0_182|~spl0_46|~spl0_342),
% 18.86/2.87 inference(split_clause,[status(thm)],[f16402,f3042,f448,f7016])).
% 18.86/2.87 fof(f16439,plain,(
% 18.86/2.87 ~relation(sk0_1)|~function(sk0_1)|spl0_285),
% 18.86/2.87 inference(resolution,[status(thm)],[f6251,f59])).
% 18.86/2.87 fof(f16440,plain,(
% 18.86/2.87 ~spl0_87|~spl0_105|spl0_285),
% 18.86/2.87 inference(split_clause,[status(thm)],[f16439,f1137,f1417,f6249])).
% 18.86/2.87 fof(f16448,plain,(
% 18.86/2.87 relation_composition(function_inverse(function_inverse(sk0_1)),empty_set)=empty_set|~relation(function_inverse(sk0_1))|~spl0_285),
% 18.86/2.87 inference(resolution,[status(thm)],[f6250,f1501])).
% 18.86/2.87 fof(f16449,plain,(
% 18.86/2.87 spl0_323|~spl0_275|~spl0_285),
% 18.86/2.87 inference(split_clause,[status(thm)],[f16448,f6611,f6186,f6249])).
% 18.86/2.87 fof(f16450,plain,(
% 18.86/2.87 relation_composition(empty_set,function_inverse(function_inverse(sk0_1)))=empty_set|~relation(function_inverse(sk0_1))|~spl0_285),
% 18.86/2.87 inference(resolution,[status(thm)],[f6250,f1048])).
% 18.86/2.87 fof(f16451,plain,(
% 18.86/2.87 spl0_313|~spl0_275|~spl0_285),
% 18.86/2.87 inference(split_clause,[status(thm)],[f16450,f6519,f6186,f6249])).
% 18.86/2.87 fof(f16454,plain,(
% 18.86/2.87 ![X0]: (relation_composition(function_inverse(sk0_1),identity_relation(X0))=identity_relation(relation_dom(relation_composition(function_inverse(sk0_1),identity_relation(X0))))|in(sk0_11(relation_dom(relation_composition(function_inverse(sk0_1),identity_relation(X0))),relation_composition(function_inverse(sk0_1),identity_relation(X0))),relation_dom(relation_composition(function_inverse(sk0_1),identity_relation(X0))))|~relation(function_inverse(sk0_1))|~spl0_285)),
% 18.86/2.87 inference(resolution,[status(thm)],[f6250,f1926])).
% 18.86/2.87 fof(f16455,plain,(
% 18.86/2.87 spl0_277|~spl0_275|~spl0_285),
% 18.86/2.87 inference(split_clause,[status(thm)],[f16454,f6194,f6186,f6249])).
% 18.86/2.87 fof(f16456,plain,(
% 18.86/2.87 ![X0]: (relation_composition(X0,function_inverse(function_inverse(sk0_1)))=identity_relation(relation_dom(relation_composition(X0,function_inverse(function_inverse(sk0_1)))))|in(sk0_11(relation_dom(relation_composition(X0,function_inverse(function_inverse(sk0_1)))),relation_composition(X0,function_inverse(function_inverse(sk0_1)))),relation_dom(relation_composition(X0,function_inverse(function_inverse(sk0_1)))))|~relation(X0)|~function(X0)|~relation(function_inverse(sk0_1))|~spl0_285)),
% 18.86/2.87 inference(resolution,[status(thm)],[f6250,f1924])).
% 18.86/2.87 fof(f16457,plain,(
% 18.86/2.87 spl0_278|~spl0_275|~spl0_285),
% 18.86/2.87 inference(split_clause,[status(thm)],[f16456,f6199,f6186,f6249])).
% 18.86/2.87 fof(f16458,plain,(
% 18.86/2.87 ![X0]: (relation_composition(X0,relation_composition(function_inverse(sk0_1),function_inverse(sk0_1)))=identity_relation(relation_dom(relation_composition(X0,relation_composition(function_inverse(sk0_1),function_inverse(sk0_1)))))|in(sk0_11(relation_dom(relation_composition(X0,relation_composition(function_inverse(sk0_1),function_inverse(sk0_1)))),relation_composition(X0,relation_composition(function_inverse(sk0_1),function_inverse(sk0_1)))),relation_dom(relation_composition(X0,relation_composition(function_inverse(sk0_1),function_inverse(sk0_1)))))|~relation(X0)|~function(X0)|~relation(function_inverse(sk0_1))|~relation(function_inverse(sk0_1))|~spl0_285)),
% 18.86/2.87 inference(resolution,[status(thm)],[f6250,f1917])).
% 18.86/2.87 fof(f16459,plain,(
% 18.86/2.87 spl0_279|~spl0_275|~spl0_285),
% 18.86/2.87 inference(split_clause,[status(thm)],[f16458,f6204,f6186,f6249])).
% 18.86/2.87 fof(f16460,plain,(
% 18.86/2.87 ![X0,X1]: (relation_composition(X0,relation_composition(X1,function_inverse(sk0_1)))=identity_relation(relation_dom(relation_composition(X0,relation_composition(X1,function_inverse(sk0_1)))))|in(sk0_11(relation_dom(relation_composition(X0,relation_composition(X1,function_inverse(sk0_1)))),relation_composition(X0,relation_composition(X1,function_inverse(sk0_1)))),relation_dom(relation_composition(X0,relation_composition(X1,function_inverse(sk0_1)))))|~relation(X0)|~function(X0)|~relation(X1)|~function(X1)|~relation(function_inverse(sk0_1))|~spl0_285)),
% 18.86/2.87 inference(resolution,[status(thm)],[f6250,f1917])).
% 18.86/2.87 fof(f16461,plain,(
% 18.86/2.87 spl0_280|~spl0_275|~spl0_285),
% 18.86/2.87 inference(split_clause,[status(thm)],[f16460,f6209,f6186,f6249])).
% 18.86/2.87 fof(f16464,plain,(
% 18.86/2.87 ![X0,X1]: (relation_composition(X0,relation_composition(function_inverse(sk0_1),X1))=identity_relation(relation_dom(relation_composition(X0,relation_composition(function_inverse(sk0_1),X1))))|in(sk0_11(relation_dom(relation_composition(X0,relation_composition(function_inverse(sk0_1),X1))),relation_composition(X0,relation_composition(function_inverse(sk0_1),X1))),relation_dom(relation_composition(X0,relation_composition(function_inverse(sk0_1),X1))))|~relation(X0)|~function(X0)|~relation(function_inverse(sk0_1))|~relation(X1)|~function(X1)|~spl0_285)),
% 18.86/2.87 inference(resolution,[status(thm)],[f6250,f1917])).
% 18.86/2.87 fof(f16465,plain,(
% 18.86/2.87 spl0_281|~spl0_275|~spl0_285),
% 18.86/2.87 inference(split_clause,[status(thm)],[f16464,f6216,f6186,f6249])).
% 18.86/2.87 fof(f16472,plain,(
% 18.86/2.87 ~relation(sk0_1)|~function(sk0_1)|spl0_275),
% 18.86/2.87 inference(resolution,[status(thm)],[f6188,f58])).
% 18.86/2.87 fof(f16473,plain,(
% 18.86/2.87 ~spl0_87|~spl0_105|spl0_275),
% 18.86/2.87 inference(split_clause,[status(thm)],[f16472,f1137,f1417,f6186])).
% 18.86/2.87 fof(f18186,plain,(
% 18.86/2.87 spl0_745 <=> relation_composition(X0,relation_composition(sk0_12,sk0_1))=identity_relation(relation_dom(relation_composition(X0,relation_composition(sk0_12,sk0_1))))|in(sk0_11(relation_dom(relation_composition(X0,relation_composition(sk0_12,sk0_1))),relation_composition(X0,relation_composition(sk0_12,sk0_1))),relation_dom(relation_composition(X0,relation_composition(sk0_12,sk0_1))))|~relation(X0)|~function(X0)),
% 18.86/2.87 introduced(split_symbol_definition)).
% 18.86/2.87 fof(f18189,plain,(
% 18.86/2.87 ![X0]: (relation_composition(X0,relation_composition(sk0_12,sk0_1))=identity_relation(relation_dom(relation_composition(X0,relation_composition(sk0_12,sk0_1))))|in(sk0_11(relation_dom(relation_composition(X0,relation_composition(sk0_12,sk0_1))),relation_composition(X0,relation_composition(sk0_12,sk0_1))),relation_dom(relation_composition(X0,relation_composition(sk0_12,sk0_1))))|~relation(X0)|~function(X0)|~relation(sk0_1)|~spl0_223)),
% 18.86/2.87 inference(resolution,[status(thm)],[f5540,f96])).
% 18.86/2.87 fof(f18190,plain,(
% 18.86/2.87 spl0_745|~spl0_87|~spl0_223),
% 18.86/2.87 inference(split_clause,[status(thm)],[f18189,f18186,f1137,f5539])).
% 18.86/2.87 fof(f18193,plain,(
% 18.86/2.87 spl0_746 <=> relation_composition(X0,relation_composition(sk0_12,empty_set))=identity_relation(relation_dom(relation_composition(X0,relation_composition(sk0_12,empty_set))))|in(sk0_11(relation_dom(relation_composition(X0,relation_composition(sk0_12,empty_set))),relation_composition(X0,relation_composition(sk0_12,empty_set))),relation_dom(relation_composition(X0,relation_composition(sk0_12,empty_set))))|~relation(X0)|~function(X0)),
% 18.86/2.87 introduced(split_symbol_definition)).
% 18.86/2.87 fof(f18196,plain,(
% 18.86/2.87 ![X0]: (relation_composition(X0,relation_composition(sk0_12,empty_set))=identity_relation(relation_dom(relation_composition(X0,relation_composition(sk0_12,empty_set))))|in(sk0_11(relation_dom(relation_composition(X0,relation_composition(sk0_12,empty_set))),relation_composition(X0,relation_composition(sk0_12,empty_set))),relation_dom(relation_composition(X0,relation_composition(sk0_12,empty_set))))|~relation(X0)|~function(X0)|~relation(empty_set)|~spl0_223)),
% 18.86/2.87 inference(resolution,[status(thm)],[f5540,f588])).
% 18.86/2.87 fof(f18197,plain,(
% 18.86/2.87 spl0_746|~spl0_47|~spl0_223),
% 18.86/2.87 inference(split_clause,[status(thm)],[f18196,f18193,f453,f5539])).
% 18.86/2.87 fof(f18198,plain,(
% 18.86/2.87 spl0_747 <=> relation_composition(X0,relation_composition(sk0_12,relation_composition(function_inverse(sk0_12),sk0_12)))=identity_relation(relation_dom(relation_composition(X0,relation_composition(sk0_12,relation_composition(function_inverse(sk0_12),sk0_12)))))|in(sk0_11(relation_dom(relation_composition(X0,relation_composition(sk0_12,relation_composition(function_inverse(sk0_12),sk0_12)))),relation_composition(X0,relation_composition(sk0_12,relation_composition(function_inverse(sk0_12),sk0_12)))),relation_dom(relation_composition(X0,relation_composition(sk0_12,relation_composition(function_inverse(sk0_12),sk0_12)))))|~relation(X0)|~function(X0)),
% 18.86/2.87 introduced(split_symbol_definition)).
% 18.86/2.87 fof(f18201,plain,(
% 18.86/2.87 ![X0]: (relation_composition(X0,relation_composition(sk0_12,relation_composition(function_inverse(sk0_12),sk0_12)))=identity_relation(relation_dom(relation_composition(X0,relation_composition(sk0_12,relation_composition(function_inverse(sk0_12),sk0_12)))))|in(sk0_11(relation_dom(relation_composition(X0,relation_composition(sk0_12,relation_composition(function_inverse(sk0_12),sk0_12)))),relation_composition(X0,relation_composition(sk0_12,relation_composition(function_inverse(sk0_12),sk0_12)))),relation_dom(relation_composition(X0,relation_composition(sk0_12,relation_composition(function_inverse(sk0_12),sk0_12)))))|~relation(X0)|~function(X0)|~relation(relation_composition(function_inverse(sk0_12),sk0_12))|~spl0_223|~spl0_93)),
% 18.86/2.87 inference(resolution,[status(thm)],[f5540,f1189])).
% 18.86/2.87 fof(f18202,plain,(
% 18.86/2.87 spl0_747|~spl0_57|~spl0_223|~spl0_93),
% 18.86/2.87 inference(split_clause,[status(thm)],[f18201,f18198,f621,f5539,f1188])).
% 18.86/2.87 fof(f18210,plain,(
% 18.86/2.87 spl0_749 <=> relation_composition(X0,relation_composition(sk0_12,function_inverse(sk0_1)))=identity_relation(relation_dom(relation_composition(X0,relation_composition(sk0_12,function_inverse(sk0_1)))))|in(sk0_11(relation_dom(relation_composition(X0,relation_composition(sk0_12,function_inverse(sk0_1)))),relation_composition(X0,relation_composition(sk0_12,function_inverse(sk0_1)))),relation_dom(relation_composition(X0,relation_composition(sk0_12,function_inverse(sk0_1)))))|~relation(X0)|~function(X0)),
% 18.86/2.87 introduced(split_symbol_definition)).
% 18.86/2.87 fof(f18213,plain,(
% 18.86/2.87 ![X0]: (relation_composition(X0,relation_composition(sk0_12,function_inverse(sk0_1)))=identity_relation(relation_dom(relation_composition(X0,relation_composition(sk0_12,function_inverse(sk0_1)))))|in(sk0_11(relation_dom(relation_composition(X0,relation_composition(sk0_12,function_inverse(sk0_1)))),relation_composition(X0,relation_composition(sk0_12,function_inverse(sk0_1)))),relation_dom(relation_composition(X0,relation_composition(sk0_12,function_inverse(sk0_1)))))|~relation(X0)|~function(X0)|~relation(function_inverse(sk0_1))|~spl0_223|~spl0_285)),
% 18.86/2.87 inference(resolution,[status(thm)],[f5540,f6250])).
% 18.86/2.87 fof(f18214,plain,(
% 18.86/2.87 spl0_749|~spl0_275|~spl0_223|~spl0_285),
% 18.86/2.87 inference(split_clause,[status(thm)],[f18213,f18210,f6186,f5539,f6249])).
% 18.86/2.87 fof(f18449,plain,(
% 18.86/2.87 spl0_757 <=> relation_composition(X0,relation_composition(sk0_1,sk0_12))=identity_relation(relation_dom(relation_composition(X0,relation_composition(sk0_1,sk0_12))))|in(sk0_11(relation_dom(relation_composition(X0,relation_composition(sk0_1,sk0_12))),relation_composition(X0,relation_composition(sk0_1,sk0_12))),relation_dom(relation_composition(X0,relation_composition(sk0_1,sk0_12))))|~relation(X0)|~function(X0)),
% 18.86/2.87 introduced(split_symbol_definition)).
% 18.86/2.87 fof(f18452,plain,(
% 18.86/2.87 ![X0]: (relation_composition(X0,relation_composition(sk0_1,sk0_12))=identity_relation(relation_dom(relation_composition(X0,relation_composition(sk0_1,sk0_12))))|in(sk0_11(relation_dom(relation_composition(X0,relation_composition(sk0_1,sk0_12))),relation_composition(X0,relation_composition(sk0_1,sk0_12))),relation_dom(relation_composition(X0,relation_composition(sk0_1,sk0_12))))|~relation(X0)|~function(X0)|~relation(sk0_1)|~spl0_234)),
% 18.86/2.87 inference(resolution,[status(thm)],[f5615,f96])).
% 18.86/2.87 fof(f18453,plain,(
% 18.86/2.87 spl0_757|~spl0_87|~spl0_234),
% 18.86/2.87 inference(split_clause,[status(thm)],[f18452,f18449,f1137,f5614])).
% 18.86/2.87 fof(f18456,plain,(
% 18.86/2.87 spl0_758 <=> relation_composition(X0,relation_composition(empty_set,sk0_12))=identity_relation(relation_dom(relation_composition(X0,relation_composition(empty_set,sk0_12))))|in(sk0_11(relation_dom(relation_composition(X0,relation_composition(empty_set,sk0_12))),relation_composition(X0,relation_composition(empty_set,sk0_12))),relation_dom(relation_composition(X0,relation_composition(empty_set,sk0_12))))|~relation(X0)|~function(X0)),
% 18.86/2.87 introduced(split_symbol_definition)).
% 18.86/2.87 fof(f18459,plain,(
% 18.86/2.87 ![X0]: (relation_composition(X0,relation_composition(empty_set,sk0_12))=identity_relation(relation_dom(relation_composition(X0,relation_composition(empty_set,sk0_12))))|in(sk0_11(relation_dom(relation_composition(X0,relation_composition(empty_set,sk0_12))),relation_composition(X0,relation_composition(empty_set,sk0_12))),relation_dom(relation_composition(X0,relation_composition(empty_set,sk0_12))))|~relation(X0)|~function(X0)|~relation(empty_set)|~spl0_234)),
% 18.86/2.87 inference(resolution,[status(thm)],[f5615,f588])).
% 18.86/2.87 fof(f18460,plain,(
% 18.86/2.87 spl0_758|~spl0_47|~spl0_234),
% 18.86/2.87 inference(split_clause,[status(thm)],[f18459,f18456,f453,f5614])).
% 18.86/2.87 fof(f18461,plain,(
% 18.86/2.87 spl0_759 <=> relation_composition(X0,relation_composition(relation_composition(function_inverse(sk0_12),sk0_12),sk0_12))=identity_relation(relation_dom(relation_composition(X0,relation_composition(relation_composition(function_inverse(sk0_12),sk0_12),sk0_12))))|in(sk0_11(relation_dom(relation_composition(X0,relation_composition(relation_composition(function_inverse(sk0_12),sk0_12),sk0_12))),relation_composition(X0,relation_composition(relation_composition(function_inverse(sk0_12),sk0_12),sk0_12))),relation_dom(relation_composition(X0,relation_composition(relation_composition(function_inverse(sk0_12),sk0_12),sk0_12))))|~relation(X0)|~function(X0)),
% 18.86/2.87 introduced(split_symbol_definition)).
% 18.86/2.87 fof(f18464,plain,(
% 18.86/2.87 ![X0]: (relation_composition(X0,relation_composition(relation_composition(function_inverse(sk0_12),sk0_12),sk0_12))=identity_relation(relation_dom(relation_composition(X0,relation_composition(relation_composition(function_inverse(sk0_12),sk0_12),sk0_12))))|in(sk0_11(relation_dom(relation_composition(X0,relation_composition(relation_composition(function_inverse(sk0_12),sk0_12),sk0_12))),relation_composition(X0,relation_composition(relation_composition(function_inverse(sk0_12),sk0_12),sk0_12))),relation_dom(relation_composition(X0,relation_composition(relation_composition(function_inverse(sk0_12),sk0_12),sk0_12))))|~relation(X0)|~function(X0)|~relation(relation_composition(function_inverse(sk0_12),sk0_12))|~spl0_234|~spl0_93)),
% 18.86/2.87 inference(resolution,[status(thm)],[f5615,f1189])).
% 18.86/2.87 fof(f18465,plain,(
% 18.86/2.87 spl0_759|~spl0_57|~spl0_234|~spl0_93),
% 18.86/2.87 inference(split_clause,[status(thm)],[f18464,f18461,f621,f5614,f1188])).
% 18.86/2.87 fof(f18473,plain,(
% 18.86/2.87 spl0_761 <=> relation_composition(X0,relation_composition(function_inverse(sk0_1),sk0_12))=identity_relation(relation_dom(relation_composition(X0,relation_composition(function_inverse(sk0_1),sk0_12))))|in(sk0_11(relation_dom(relation_composition(X0,relation_composition(function_inverse(sk0_1),sk0_12))),relation_composition(X0,relation_composition(function_inverse(sk0_1),sk0_12))),relation_dom(relation_composition(X0,relation_composition(function_inverse(sk0_1),sk0_12))))|~relation(X0)|~function(X0)),
% 18.86/2.87 introduced(split_symbol_definition)).
% 18.86/2.87 fof(f18476,plain,(
% 18.86/2.87 ![X0]: (relation_composition(X0,relation_composition(function_inverse(sk0_1),sk0_12))=identity_relation(relation_dom(relation_composition(X0,relation_composition(function_inverse(sk0_1),sk0_12))))|in(sk0_11(relation_dom(relation_composition(X0,relation_composition(function_inverse(sk0_1),sk0_12))),relation_composition(X0,relation_composition(function_inverse(sk0_1),sk0_12))),relation_dom(relation_composition(X0,relation_composition(function_inverse(sk0_1),sk0_12))))|~relation(X0)|~function(X0)|~relation(function_inverse(sk0_1))|~spl0_234|~spl0_285)),
% 18.86/2.87 inference(resolution,[status(thm)],[f5615,f6250])).
% 18.86/2.87 fof(f18477,plain,(
% 18.86/2.87 spl0_761|~spl0_275|~spl0_234|~spl0_285),
% 18.86/2.87 inference(split_clause,[status(thm)],[f18476,f18473,f6186,f5614,f6249])).
% 18.86/2.87 fof(f18503,plain,(
% 18.86/2.87 spl0_762 <=> relation_composition(X0,relation_composition(empty_set,sk0_1))=identity_relation(relation_dom(relation_composition(X0,relation_composition(empty_set,sk0_1))))|in(sk0_11(relation_dom(relation_composition(X0,relation_composition(empty_set,sk0_1))),relation_composition(X0,relation_composition(empty_set,sk0_1))),relation_dom(relation_composition(X0,relation_composition(empty_set,sk0_1))))|~relation(X0)|~function(X0)),
% 18.86/2.87 introduced(split_symbol_definition)).
% 18.86/2.87 fof(f18506,plain,(
% 18.86/2.87 ![X0]: (relation_composition(X0,relation_composition(empty_set,sk0_1))=identity_relation(relation_dom(relation_composition(X0,relation_composition(empty_set,sk0_1))))|in(sk0_11(relation_dom(relation_composition(X0,relation_composition(empty_set,sk0_1))),relation_composition(X0,relation_composition(empty_set,sk0_1))),relation_dom(relation_composition(X0,relation_composition(empty_set,sk0_1))))|~relation(X0)|~function(X0)|~relation(sk0_1)|~spl0_225)),
% 18.86/2.87 inference(resolution,[status(thm)],[f5550,f96])).
% 18.86/2.87 fof(f18507,plain,(
% 18.86/2.87 spl0_762|~spl0_87|~spl0_225),
% 18.86/2.87 inference(split_clause,[status(thm)],[f18506,f18503,f1137,f5549])).
% 18.86/2.87 fof(f18512,plain,(
% 18.86/2.87 spl0_763 <=> relation_composition(X0,relation_composition(empty_set,relation_composition(function_inverse(sk0_12),sk0_12)))=identity_relation(relation_dom(relation_composition(X0,relation_composition(empty_set,relation_composition(function_inverse(sk0_12),sk0_12)))))|in(sk0_11(relation_dom(relation_composition(X0,relation_composition(empty_set,relation_composition(function_inverse(sk0_12),sk0_12)))),relation_composition(X0,relation_composition(empty_set,relation_composition(function_inverse(sk0_12),sk0_12)))),relation_dom(relation_composition(X0,relation_composition(empty_set,relation_composition(function_inverse(sk0_12),sk0_12)))))|~relation(X0)|~function(X0)),
% 18.86/2.87 introduced(split_symbol_definition)).
% 18.86/2.87 fof(f18515,plain,(
% 18.86/2.87 ![X0]: (relation_composition(X0,relation_composition(empty_set,relation_composition(function_inverse(sk0_12),sk0_12)))=identity_relation(relation_dom(relation_composition(X0,relation_composition(empty_set,relation_composition(function_inverse(sk0_12),sk0_12)))))|in(sk0_11(relation_dom(relation_composition(X0,relation_composition(empty_set,relation_composition(function_inverse(sk0_12),sk0_12)))),relation_composition(X0,relation_composition(empty_set,relation_composition(function_inverse(sk0_12),sk0_12)))),relation_dom(relation_composition(X0,relation_composition(empty_set,relation_composition(function_inverse(sk0_12),sk0_12)))))|~relation(X0)|~function(X0)|~relation(relation_composition(function_inverse(sk0_12),sk0_12))|~spl0_225|~spl0_93)),
% 18.86/2.87 inference(resolution,[status(thm)],[f5550,f1189])).
% 18.86/2.87 fof(f18516,plain,(
% 18.86/2.87 spl0_763|~spl0_57|~spl0_225|~spl0_93),
% 18.86/2.87 inference(split_clause,[status(thm)],[f18515,f18512,f621,f5549,f1188])).
% 18.86/2.87 fof(f18524,plain,(
% 18.86/2.87 spl0_765 <=> relation_composition(X0,relation_composition(empty_set,function_inverse(sk0_1)))=identity_relation(relation_dom(relation_composition(X0,relation_composition(empty_set,function_inverse(sk0_1)))))|in(sk0_11(relation_dom(relation_composition(X0,relation_composition(empty_set,function_inverse(sk0_1)))),relation_composition(X0,relation_composition(empty_set,function_inverse(sk0_1)))),relation_dom(relation_composition(X0,relation_composition(empty_set,function_inverse(sk0_1)))))|~relation(X0)|~function(X0)),
% 18.86/2.87 introduced(split_symbol_definition)).
% 18.86/2.87 fof(f18527,plain,(
% 18.86/2.87 ![X0]: (relation_composition(X0,relation_composition(empty_set,function_inverse(sk0_1)))=identity_relation(relation_dom(relation_composition(X0,relation_composition(empty_set,function_inverse(sk0_1)))))|in(sk0_11(relation_dom(relation_composition(X0,relation_composition(empty_set,function_inverse(sk0_1)))),relation_composition(X0,relation_composition(empty_set,function_inverse(sk0_1)))),relation_dom(relation_composition(X0,relation_composition(empty_set,function_inverse(sk0_1)))))|~relation(X0)|~function(X0)|~relation(function_inverse(sk0_1))|~spl0_225|~spl0_285)),
% 18.86/2.87 inference(resolution,[status(thm)],[f5550,f6250])).
% 18.86/2.87 fof(f18528,plain,(
% 18.86/2.87 spl0_765|~spl0_275|~spl0_225|~spl0_285),
% 18.86/2.87 inference(split_clause,[status(thm)],[f18527,f18524,f6186,f5549,f6249])).
% 18.86/2.87 fof(f18529,plain,(
% 18.86/2.87 spl0_766 <=> relation_composition(X0,relation_composition(empty_set,function_inverse(sk0_12)))=identity_relation(relation_dom(relation_composition(X0,relation_composition(empty_set,function_inverse(sk0_12)))))|in(sk0_11(relation_dom(relation_composition(X0,relation_composition(empty_set,function_inverse(sk0_12)))),relation_composition(X0,relation_composition(empty_set,function_inverse(sk0_12)))),relation_dom(relation_composition(X0,relation_composition(empty_set,function_inverse(sk0_12)))))|~relation(X0)|~function(X0)),
% 18.86/2.87 introduced(split_symbol_definition)).
% 18.86/2.87 fof(f18532,plain,(
% 18.86/2.87 ![X0]: (relation_composition(X0,relation_composition(empty_set,function_inverse(sk0_12)))=identity_relation(relation_dom(relation_composition(X0,relation_composition(empty_set,function_inverse(sk0_12)))))|in(sk0_11(relation_dom(relation_composition(X0,relation_composition(empty_set,function_inverse(sk0_12)))),relation_composition(X0,relation_composition(empty_set,function_inverse(sk0_12)))),relation_dom(relation_composition(X0,relation_composition(empty_set,function_inverse(sk0_12)))))|~relation(X0)|~function(X0)|~relation(function_inverse(sk0_12))|~spl0_225|~spl0_92)),
% 18.86/2.87 inference(resolution,[status(thm)],[f5550,f1174])).
% 18.86/2.87 fof(f18533,plain,(
% 18.86/2.87 spl0_766|~spl0_10|~spl0_225|~spl0_92),
% 18.86/2.87 inference(split_clause,[status(thm)],[f18532,f18529,f236,f5549,f1173])).
% 18.86/2.87 fof(f18557,plain,(
% 18.86/2.87 spl0_767 <=> relation_composition(X0,relation_composition(sk0_1,empty_set))=identity_relation(relation_dom(relation_composition(X0,relation_composition(sk0_1,empty_set))))|in(sk0_11(relation_dom(relation_composition(X0,relation_composition(sk0_1,empty_set))),relation_composition(X0,relation_composition(sk0_1,empty_set))),relation_dom(relation_composition(X0,relation_composition(sk0_1,empty_set))))|~relation(X0)|~function(X0)),
% 18.86/2.87 introduced(split_symbol_definition)).
% 18.86/2.87 fof(f18560,plain,(
% 18.86/2.87 ![X0]: (relation_composition(X0,relation_composition(sk0_1,empty_set))=identity_relation(relation_dom(relation_composition(X0,relation_composition(sk0_1,empty_set))))|in(sk0_11(relation_dom(relation_composition(X0,relation_composition(sk0_1,empty_set))),relation_composition(X0,relation_composition(sk0_1,empty_set))),relation_dom(relation_composition(X0,relation_composition(sk0_1,empty_set))))|~relation(X0)|~function(X0)|~relation(sk0_1)|~spl0_235)),
% 18.86/2.87 inference(resolution,[status(thm)],[f5620,f96])).
% 18.86/2.87 fof(f18561,plain,(
% 18.86/2.87 spl0_767|~spl0_87|~spl0_235),
% 18.86/2.87 inference(split_clause,[status(thm)],[f18560,f18557,f1137,f5619])).
% 18.86/2.87 fof(f18566,plain,(
% 18.86/2.87 spl0_768 <=> relation_composition(X0,relation_composition(relation_composition(function_inverse(sk0_12),sk0_12),empty_set))=identity_relation(relation_dom(relation_composition(X0,relation_composition(relation_composition(function_inverse(sk0_12),sk0_12),empty_set))))|in(sk0_11(relation_dom(relation_composition(X0,relation_composition(relation_composition(function_inverse(sk0_12),sk0_12),empty_set))),relation_composition(X0,relation_composition(relation_composition(function_inverse(sk0_12),sk0_12),empty_set))),relation_dom(relation_composition(X0,relation_composition(relation_composition(function_inverse(sk0_12),sk0_12),empty_set))))|~relation(X0)|~function(X0)),
% 18.86/2.87 introduced(split_symbol_definition)).
% 18.86/2.87 fof(f18569,plain,(
% 18.86/2.87 ![X0]: (relation_composition(X0,relation_composition(relation_composition(function_inverse(sk0_12),sk0_12),empty_set))=identity_relation(relation_dom(relation_composition(X0,relation_composition(relation_composition(function_inverse(sk0_12),sk0_12),empty_set))))|in(sk0_11(relation_dom(relation_composition(X0,relation_composition(relation_composition(function_inverse(sk0_12),sk0_12),empty_set))),relation_composition(X0,relation_composition(relation_composition(function_inverse(sk0_12),sk0_12),empty_set))),relation_dom(relation_composition(X0,relation_composition(relation_composition(function_inverse(sk0_12),sk0_12),empty_set))))|~relation(X0)|~function(X0)|~relation(relation_composition(function_inverse(sk0_12),sk0_12))|~spl0_235|~spl0_93)),
% 18.86/2.87 inference(resolution,[status(thm)],[f5620,f1189])).
% 18.86/2.87 fof(f18570,plain,(
% 18.86/2.87 spl0_768|~spl0_57|~spl0_235|~spl0_93),
% 18.86/2.87 inference(split_clause,[status(thm)],[f18569,f18566,f621,f5619,f1188])).
% 18.86/2.87 fof(f18578,plain,(
% 18.86/2.87 spl0_770 <=> relation_composition(X0,relation_composition(function_inverse(sk0_1),empty_set))=identity_relation(relation_dom(relation_composition(X0,relation_composition(function_inverse(sk0_1),empty_set))))|in(sk0_11(relation_dom(relation_composition(X0,relation_composition(function_inverse(sk0_1),empty_set))),relation_composition(X0,relation_composition(function_inverse(sk0_1),empty_set))),relation_dom(relation_composition(X0,relation_composition(function_inverse(sk0_1),empty_set))))|~relation(X0)|~function(X0)),
% 18.86/2.87 introduced(split_symbol_definition)).
% 18.86/2.87 fof(f18581,plain,(
% 18.86/2.87 ![X0]: (relation_composition(X0,relation_composition(function_inverse(sk0_1),empty_set))=identity_relation(relation_dom(relation_composition(X0,relation_composition(function_inverse(sk0_1),empty_set))))|in(sk0_11(relation_dom(relation_composition(X0,relation_composition(function_inverse(sk0_1),empty_set))),relation_composition(X0,relation_composition(function_inverse(sk0_1),empty_set))),relation_dom(relation_composition(X0,relation_composition(function_inverse(sk0_1),empty_set))))|~relation(X0)|~function(X0)|~relation(function_inverse(sk0_1))|~spl0_235|~spl0_285)),
% 18.86/2.87 inference(resolution,[status(thm)],[f5620,f6250])).
% 18.86/2.87 fof(f18582,plain,(
% 18.86/2.87 spl0_770|~spl0_275|~spl0_235|~spl0_285),
% 18.86/2.87 inference(split_clause,[status(thm)],[f18581,f18578,f6186,f5619,f6249])).
% 18.86/2.87 fof(f18583,plain,(
% 18.86/2.87 spl0_771 <=> relation_composition(X0,relation_composition(function_inverse(sk0_12),empty_set))=identity_relation(relation_dom(relation_composition(X0,relation_composition(function_inverse(sk0_12),empty_set))))|in(sk0_11(relation_dom(relation_composition(X0,relation_composition(function_inverse(sk0_12),empty_set))),relation_composition(X0,relation_composition(function_inverse(sk0_12),empty_set))),relation_dom(relation_composition(X0,relation_composition(function_inverse(sk0_12),empty_set))))|~relation(X0)|~function(X0)),
% 18.86/2.87 introduced(split_symbol_definition)).
% 18.86/2.87 fof(f18586,plain,(
% 18.86/2.87 ![X0]: (relation_composition(X0,relation_composition(function_inverse(sk0_12),empty_set))=identity_relation(relation_dom(relation_composition(X0,relation_composition(function_inverse(sk0_12),empty_set))))|in(sk0_11(relation_dom(relation_composition(X0,relation_composition(function_inverse(sk0_12),empty_set))),relation_composition(X0,relation_composition(function_inverse(sk0_12),empty_set))),relation_dom(relation_composition(X0,relation_composition(function_inverse(sk0_12),empty_set))))|~relation(X0)|~function(X0)|~relation(function_inverse(sk0_12))|~spl0_235|~spl0_92)),
% 18.86/2.87 inference(resolution,[status(thm)],[f5620,f1174])).
% 18.86/2.87 fof(f18587,plain,(
% 18.86/2.87 spl0_771|~spl0_10|~spl0_235|~spl0_92),
% 18.86/2.87 inference(split_clause,[status(thm)],[f18586,f18583,f236,f5619,f1173])).
% 18.86/2.87 fof(f18737,plain,(
% 18.86/2.87 sk0_0(relation_rng(sk0_12))=sk0_0(relation_rng(sk0_12))|relation_rng(sk0_12)=empty_set|spl0_58),
% 18.86/2.87 inference(paramodulation,[status(thm)],[f3637,f3541])).
% 18.86/2.87 fof(f18738,plain,(
% 18.86/2.87 spl0_514|spl0_515|spl0_58),
% 18.86/2.87 inference(split_clause,[status(thm)],[f18737,f10406,f10409,f624])).
% 18.86/2.87 fof(f18759,plain,(
% 18.86/2.87 spl0_776 <=> relation_composition(X0,relation_composition(sk0_1,relation_composition(function_inverse(sk0_12),sk0_12)))=identity_relation(relation_dom(relation_composition(X0,relation_composition(sk0_1,relation_composition(function_inverse(sk0_12),sk0_12)))))|in(sk0_11(relation_dom(relation_composition(X0,relation_composition(sk0_1,relation_composition(function_inverse(sk0_12),sk0_12)))),relation_composition(X0,relation_composition(sk0_1,relation_composition(function_inverse(sk0_12),sk0_12)))),relation_dom(relation_composition(X0,relation_composition(sk0_1,relation_composition(function_inverse(sk0_12),sk0_12)))))|~relation(X0)|~function(X0)),
% 18.86/2.87 introduced(split_symbol_definition)).
% 18.86/2.87 fof(f18762,plain,(
% 18.86/2.87 ![X0]: (relation_composition(X0,relation_composition(sk0_1,relation_composition(function_inverse(sk0_12),sk0_12)))=identity_relation(relation_dom(relation_composition(X0,relation_composition(sk0_1,relation_composition(function_inverse(sk0_12),sk0_12)))))|in(sk0_11(relation_dom(relation_composition(X0,relation_composition(sk0_1,relation_composition(function_inverse(sk0_12),sk0_12)))),relation_composition(X0,relation_composition(sk0_1,relation_composition(function_inverse(sk0_12),sk0_12)))),relation_dom(relation_composition(X0,relation_composition(sk0_1,relation_composition(function_inverse(sk0_12),sk0_12)))))|~relation(X0)|~function(X0)|~relation(relation_composition(function_inverse(sk0_12),sk0_12))|~spl0_229|~spl0_93)),
% 18.86/2.87 inference(resolution,[status(thm)],[f5575,f1189])).
% 18.86/2.87 fof(f18763,plain,(
% 18.86/2.87 spl0_776|~spl0_57|~spl0_229|~spl0_93),
% 18.86/2.87 inference(split_clause,[status(thm)],[f18762,f18759,f621,f5574,f1188])).
% 18.86/2.87 fof(f18771,plain,(
% 18.86/2.87 spl0_778 <=> relation_composition(X0,relation_composition(sk0_1,function_inverse(sk0_1)))=identity_relation(relation_dom(relation_composition(X0,relation_composition(sk0_1,function_inverse(sk0_1)))))|in(sk0_11(relation_dom(relation_composition(X0,relation_composition(sk0_1,function_inverse(sk0_1)))),relation_composition(X0,relation_composition(sk0_1,function_inverse(sk0_1)))),relation_dom(relation_composition(X0,relation_composition(sk0_1,function_inverse(sk0_1)))))|~relation(X0)|~function(X0)),
% 18.86/2.87 introduced(split_symbol_definition)).
% 18.86/2.87 fof(f18774,plain,(
% 18.86/2.87 ![X0]: (relation_composition(X0,relation_composition(sk0_1,function_inverse(sk0_1)))=identity_relation(relation_dom(relation_composition(X0,relation_composition(sk0_1,function_inverse(sk0_1)))))|in(sk0_11(relation_dom(relation_composition(X0,relation_composition(sk0_1,function_inverse(sk0_1)))),relation_composition(X0,relation_composition(sk0_1,function_inverse(sk0_1)))),relation_dom(relation_composition(X0,relation_composition(sk0_1,function_inverse(sk0_1)))))|~relation(X0)|~function(X0)|~relation(function_inverse(sk0_1))|~spl0_229|~spl0_285)),
% 18.86/2.87 inference(resolution,[status(thm)],[f5575,f6250])).
% 18.86/2.87 fof(f18775,plain,(
% 18.86/2.87 spl0_778|~spl0_275|~spl0_229|~spl0_285),
% 18.86/2.87 inference(split_clause,[status(thm)],[f18774,f18771,f6186,f5574,f6249])).
% 18.86/2.87 fof(f18776,plain,(
% 18.86/2.87 spl0_779 <=> relation_composition(X0,relation_composition(sk0_1,function_inverse(sk0_12)))=identity_relation(relation_dom(relation_composition(X0,relation_composition(sk0_1,function_inverse(sk0_12)))))|in(sk0_11(relation_dom(relation_composition(X0,relation_composition(sk0_1,function_inverse(sk0_12)))),relation_composition(X0,relation_composition(sk0_1,function_inverse(sk0_12)))),relation_dom(relation_composition(X0,relation_composition(sk0_1,function_inverse(sk0_12)))))|~relation(X0)|~function(X0)),
% 18.86/2.87 introduced(split_symbol_definition)).
% 18.86/2.87 fof(f18779,plain,(
% 18.86/2.87 ![X0]: (relation_composition(X0,relation_composition(sk0_1,function_inverse(sk0_12)))=identity_relation(relation_dom(relation_composition(X0,relation_composition(sk0_1,function_inverse(sk0_12)))))|in(sk0_11(relation_dom(relation_composition(X0,relation_composition(sk0_1,function_inverse(sk0_12)))),relation_composition(X0,relation_composition(sk0_1,function_inverse(sk0_12)))),relation_dom(relation_composition(X0,relation_composition(sk0_1,function_inverse(sk0_12)))))|~relation(X0)|~function(X0)|~relation(function_inverse(sk0_12))|~spl0_229|~spl0_92)),
% 18.86/2.87 inference(resolution,[status(thm)],[f5575,f1174])).
% 18.86/2.87 fof(f18780,plain,(
% 18.86/2.87 spl0_779|~spl0_10|~spl0_229|~spl0_92),
% 18.86/2.87 inference(split_clause,[status(thm)],[f18779,f18776,f236,f5574,f1173])).
% 18.86/2.87 fof(f18791,plain,(
% 18.86/2.87 spl0_780 <=> relation_composition(X0,relation_composition(relation_composition(function_inverse(sk0_12),sk0_12),sk0_1))=identity_relation(relation_dom(relation_composition(X0,relation_composition(relation_composition(function_inverse(sk0_12),sk0_12),sk0_1))))|in(sk0_11(relation_dom(relation_composition(X0,relation_composition(relation_composition(function_inverse(sk0_12),sk0_12),sk0_1))),relation_composition(X0,relation_composition(relation_composition(function_inverse(sk0_12),sk0_12),sk0_1))),relation_dom(relation_composition(X0,relation_composition(relation_composition(function_inverse(sk0_12),sk0_12),sk0_1))))|~relation(X0)|~function(X0)),
% 18.86/2.87 introduced(split_symbol_definition)).
% 18.86/2.87 fof(f18794,plain,(
% 18.86/2.87 ![X0]: (relation_composition(X0,relation_composition(relation_composition(function_inverse(sk0_12),sk0_12),sk0_1))=identity_relation(relation_dom(relation_composition(X0,relation_composition(relation_composition(function_inverse(sk0_12),sk0_12),sk0_1))))|in(sk0_11(relation_dom(relation_composition(X0,relation_composition(relation_composition(function_inverse(sk0_12),sk0_12),sk0_1))),relation_composition(X0,relation_composition(relation_composition(function_inverse(sk0_12),sk0_12),sk0_1))),relation_dom(relation_composition(X0,relation_composition(relation_composition(function_inverse(sk0_12),sk0_12),sk0_1))))|~relation(X0)|~function(X0)|~relation(relation_composition(function_inverse(sk0_12),sk0_12))|~spl0_237|~spl0_93)),
% 18.86/2.87 inference(resolution,[status(thm)],[f5632,f1189])).
% 18.86/2.87 fof(f18795,plain,(
% 18.86/2.87 spl0_780|~spl0_57|~spl0_237|~spl0_93),
% 18.86/2.87 inference(split_clause,[status(thm)],[f18794,f18791,f621,f5631,f1188])).
% 18.86/2.87 fof(f18803,plain,(
% 18.86/2.87 spl0_782 <=> relation_composition(X0,relation_composition(function_inverse(sk0_1),sk0_1))=identity_relation(relation_dom(relation_composition(X0,relation_composition(function_inverse(sk0_1),sk0_1))))|in(sk0_11(relation_dom(relation_composition(X0,relation_composition(function_inverse(sk0_1),sk0_1))),relation_composition(X0,relation_composition(function_inverse(sk0_1),sk0_1))),relation_dom(relation_composition(X0,relation_composition(function_inverse(sk0_1),sk0_1))))|~relation(X0)|~function(X0)),
% 18.86/2.87 introduced(split_symbol_definition)).
% 18.86/2.87 fof(f18806,plain,(
% 18.86/2.87 ![X0]: (relation_composition(X0,relation_composition(function_inverse(sk0_1),sk0_1))=identity_relation(relation_dom(relation_composition(X0,relation_composition(function_inverse(sk0_1),sk0_1))))|in(sk0_11(relation_dom(relation_composition(X0,relation_composition(function_inverse(sk0_1),sk0_1))),relation_composition(X0,relation_composition(function_inverse(sk0_1),sk0_1))),relation_dom(relation_composition(X0,relation_composition(function_inverse(sk0_1),sk0_1))))|~relation(X0)|~function(X0)|~relation(function_inverse(sk0_1))|~spl0_237|~spl0_285)),
% 18.86/2.87 inference(resolution,[status(thm)],[f5632,f6250])).
% 18.86/2.87 fof(f18807,plain,(
% 18.86/2.87 spl0_782|~spl0_275|~spl0_237|~spl0_285),
% 18.86/2.87 inference(split_clause,[status(thm)],[f18806,f18803,f6186,f5631,f6249])).
% 18.86/2.87 fof(f18808,plain,(
% 18.86/2.87 spl0_783 <=> relation_composition(X0,relation_composition(function_inverse(sk0_12),sk0_1))=identity_relation(relation_dom(relation_composition(X0,relation_composition(function_inverse(sk0_12),sk0_1))))|in(sk0_11(relation_dom(relation_composition(X0,relation_composition(function_inverse(sk0_12),sk0_1))),relation_composition(X0,relation_composition(function_inverse(sk0_12),sk0_1))),relation_dom(relation_composition(X0,relation_composition(function_inverse(sk0_12),sk0_1))))|~relation(X0)|~function(X0)),
% 18.86/2.87 introduced(split_symbol_definition)).
% 18.86/2.87 fof(f18811,plain,(
% 18.86/2.87 ![X0]: (relation_composition(X0,relation_composition(function_inverse(sk0_12),sk0_1))=identity_relation(relation_dom(relation_composition(X0,relation_composition(function_inverse(sk0_12),sk0_1))))|in(sk0_11(relation_dom(relation_composition(X0,relation_composition(function_inverse(sk0_12),sk0_1))),relation_composition(X0,relation_composition(function_inverse(sk0_12),sk0_1))),relation_dom(relation_composition(X0,relation_composition(function_inverse(sk0_12),sk0_1))))|~relation(X0)|~function(X0)|~relation(function_inverse(sk0_12))|~spl0_237|~spl0_92)),
% 18.86/2.87 inference(resolution,[status(thm)],[f5632,f1174])).
% 18.86/2.87 fof(f18812,plain,(
% 18.86/2.87 spl0_783|~spl0_10|~spl0_237|~spl0_92),
% 18.86/2.87 inference(split_clause,[status(thm)],[f18811,f18808,f236,f5631,f1173])).
% 18.86/2.87 fof(f19476,plain,(
% 18.86/2.87 spl0_816 <=> relation_composition(relation_composition(function_inverse(function_inverse(sk0_1)),sk0_12),empty_set)=empty_set),
% 18.86/2.87 introduced(split_symbol_definition)).
% 18.86/2.87 fof(f19479,plain,(
% 18.86/2.87 relation_composition(relation_composition(function_inverse(function_inverse(sk0_1)),sk0_12),empty_set)=empty_set|~relation(function_inverse(sk0_1))|~spl0_285),
% 18.86/2.87 inference(resolution,[status(thm)],[f10603,f6250])).
% 18.86/2.87 fof(f19480,plain,(
% 18.86/2.87 spl0_816|~spl0_275|~spl0_285),
% 18.86/2.87 inference(split_clause,[status(thm)],[f19479,f19476,f6186,f6249])).
% 18.86/2.87 fof(f21238,plain,(
% 18.86/2.87 spl0_898 <=> relation_composition(empty_set,relation_composition(function_inverse(function_inverse(sk0_1)),sk0_12))=empty_set),
% 18.86/2.87 introduced(split_symbol_definition)).
% 18.86/2.87 fof(f21241,plain,(
% 18.86/2.87 relation_composition(empty_set,relation_composition(function_inverse(function_inverse(sk0_1)),sk0_12))=empty_set|~relation(function_inverse(sk0_1))|~spl0_285),
% 18.86/2.87 inference(resolution,[status(thm)],[f9673,f6250])).
% 18.86/2.87 fof(f21242,plain,(
% 18.86/2.87 spl0_898|~spl0_275|~spl0_285),
% 18.86/2.87 inference(split_clause,[status(thm)],[f21241,f21238,f6186,f6249])).
% 18.86/2.87 fof(f22576,plain,(
% 18.86/2.87 sk0_11(relation_rng(sk0_12),relation_composition(function_inverse(sk0_12),sk0_12))=apply(relation_composition(function_inverse(sk0_12),sk0_12),sk0_11(relation_rng(sk0_12),relation_composition(function_inverse(sk0_12),sk0_12)))|~spl0_48|~spl0_193|~spl0_136),
% 18.86/2.89 inference(resolution,[status(thm)],[f4320,f2136])).
% 18.86/2.89 fof(f22577,plain,(
% 18.86/2.89 $false|spl0_121|~spl0_48|~spl0_193|~spl0_136),
% 18.86/2.89 inference(forward_subsumption_resolution,[status(thm)],[f22576,f1850])).
% 18.86/2.89 fof(f22578,plain,(
% 18.86/2.89 spl0_121|~spl0_48|~spl0_193|~spl0_136),
% 18.86/2.89 inference(contradiction_clause,[status(thm)],[f22577])).
% 18.86/2.89 fof(f22579,plain,(
% 18.86/2.89 $false),
% 18.86/2.89 inference(sat_refutation,[status(thm)],[f183,f208,f212,f214,f232,f247,f252,f254,f256,f282,f287,f297,f310,f315,f317,f320,f333,f338,f374,f376,f394,f403,f421,f423,f439,f441,f452,f517,f524,f537,f542,f547,f552,f554,f556,f635,f641,f644,f678,f685,f695,f731,f746,f778,f785,f819,f870,f875,f911,f1158,f1162,f1280,f1307,f1319,f1672,f1677,f1734,f1737,f1791,f1843,f1867,f1895,f1905,f1910,f1915,f1922,f2018,f2115,f2120,f2127,f2132,f2139,f2144,f2240,f2242,f2244,f2249,f2275,f2277,f2282,f2292,f2295,f2302,f2313,f2337,f2616,f2642,f2647,f2697,f2866,f2945,f2955,f2957,f3049,f3054,f3057,f3235,f4310,f4901,f4920,f5267,f5538,f5543,f5548,f5553,f5558,f5563,f5573,f5578,f5593,f5598,f5618,f5623,f5628,f5635,f5645,f5671,f5826,f5857,f5862,f5869,f5879,f5930,f5935,f5940,f5947,f5957,f6110,f6115,f6120,f6125,f6132,f6450,f6501,f6506,f6511,f6518,f6533,f6593,f6598,f6603,f6610,f6625,f6726,f6731,f6742,f6747,f7020,f7028,f7033,f7444,f7720,f7722,f7901,f7923,f7928,f7937,f8003,f8008,f8030,f8071,f8149,f8215,f8226,f8252,f8654,f9636,f9653,f10315,f10323,f10348,f10351,f10578,f11231,f11234,f11245,f11365,f11823,f12467,f13391,f13419,f13424,f13429,f13436,f13441,f13885,f14337,f14821,f14826,f14831,f14838,f14843,f15140,f16034,f16036,f16092,f16105,f16117,f16269,f16403,f16440,f16449,f16451,f16455,f16457,f16459,f16461,f16465,f16473,f18190,f18197,f18202,f18214,f18453,f18460,f18465,f18477,f18507,f18516,f18528,f18533,f18561,f18570,f18582,f18587,f18738,f18763,f18775,f18780,f18795,f18807,f18812,f19480,f21242,f22578])).
% 18.86/2.89 % SZS output end CNFRefutation for theBenchmark.p
% 18.86/2.90 % Elapsed time: 2.564427 seconds
% 18.86/2.90 % CPU time: 19.099803 seconds
% 18.86/2.90 % Memory used: 194.274 MB
%------------------------------------------------------------------------------