TSTP Solution File: SEU028+1 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% 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 : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 20:40:54 EDT 2024
% Result : Theorem 7.99s 1.42s
% Output : CNFRefutation 7.99s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU028+1 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.35 % Computer : n029.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Apr 29 20:10:49 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.36 % Drodi V3.6.0
% 7.99/1.42 % Refutation found
% 7.99/1.42 % SZS status Theorem for theBenchmark: Theorem is valid
% 7.99/1.42 % SZS output start CNFRefutation for theBenchmark
% 7.99/1.42 fof(f2,axiom,(
% 7.99/1.42 (! [A] :( empty(A)=> function(A) ) )),
% 7.99/1.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 7.99/1.42 fof(f3,axiom,(
% 7.99/1.42 (! [A] :( empty(A)=> relation(A) ) )),
% 7.99/1.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 7.99/1.42 fof(f5,axiom,(
% 7.99/1.42 (! [A] :( ( relation(A)& function(A) )=> ( relation(function_inverse(A))& function(function_inverse(A)) ) ) )),
% 7.99/1.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 7.99/1.42 fof(f6,axiom,(
% 7.99/1.42 (! [A,B] :( ( relation(A)& relation(B) )=> relation(relation_composition(A,B)) ) )),
% 7.99/1.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 7.99/1.42 fof(f7,axiom,(
% 7.99/1.42 (! [A] : relation(identity_relation(A)) )),
% 7.99/1.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 7.99/1.42 fof(f10,axiom,(
% 7.99/1.42 ( empty(empty_set)& relation(empty_set)& relation_empty_yielding(empty_set) ) ),
% 7.99/1.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 7.99/1.42 fof(f11,axiom,(
% 7.99/1.42 (! [A,B] :( ( relation(A)& function(A)& relation(B)& function(B) )=> ( relation(relation_composition(A,B))& function(relation_composition(A,B)) ) ) )),
% 7.99/1.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 7.99/1.42 fof(f14,axiom,(
% 7.99/1.42 (! [A] :( relation(identity_relation(A))& function(identity_relation(A)) ) )),
% 7.99/1.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 7.99/1.42 fof(f19,axiom,(
% 7.99/1.42 (! [A] :( empty(A)=> ( empty(relation_rng(A))& relation(relation_rng(A)) ) ) )),
% 7.99/1.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 7.99/1.42 fof(f21,axiom,(
% 7.99/1.42 (? [A] :( relation(A)& function(A) ) )),
% 7.99/1.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 7.99/1.42 fof(f22,axiom,(
% 7.99/1.42 (? [A] :( empty(A)& relation(A) ) )),
% 7.99/1.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 7.99/1.42 fof(f24,axiom,(
% 7.99/1.42 (? [A] : empty(A) )),
% 7.99/1.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 7.99/1.42 fof(f25,axiom,(
% 7.99/1.42 (? [A] :( relation(A)& empty(A)& function(A) ) )),
% 7.99/1.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 7.99/1.42 fof(f29,axiom,(
% 7.99/1.42 (? [A] :( relation(A)& function(A)& one_to_one(A) ) )),
% 7.99/1.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 7.99/1.42 fof(f34,axiom,(
% 7.99/1.42 (! [A,B] :( ( relation(B)& function(B) )=> ( B = identity_relation(A)<=> ( relation_dom(B) = A& (! [C] :( in(C,A)=> apply(B,C) = C ) )) ) ) )),
% 7.99/1.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 7.99/1.42 fof(f37,axiom,(
% 7.99/1.42 (! [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) ) ) ) )),
% 7.99/1.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 7.99/1.42 fof(f38,axiom,(
% 7.99/1.42 (! [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) ) ) ) )),
% 7.99/1.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 7.99/1.42 fof(f39,axiom,(
% 7.99/1.42 (! [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) ) ) ) )),
% 7.99/1.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 7.99/1.42 fof(f40,axiom,(
% 7.99/1.42 (! [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) ) ) ) )),
% 7.99/1.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 7.99/1.42 fof(f42,conjecture,(
% 7.99/1.42 (! [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)) ) ) ) )),
% 7.99/1.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 7.99/1.42 fof(f43,negated_conjecture,(
% 7.99/1.42 ~((! [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)) ) ) ) ))),
% 7.99/1.42 inference(negated_conjecture,[status(cth)],[f42])).
% 7.99/1.42 fof(f44,axiom,(
% 7.99/1.42 (! [A] :( empty(A)=> A = empty_set ) )),
% 7.99/1.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 7.99/1.42 fof(f49,plain,(
% 7.99/1.42 ![A]: (~empty(A)|function(A))),
% 7.99/1.42 inference(pre_NNF_transformation,[status(esa)],[f2])).
% 7.99/1.42 fof(f50,plain,(
% 7.99/1.42 ![X0]: (~empty(X0)|function(X0))),
% 7.99/1.42 inference(cnf_transformation,[status(esa)],[f49])).
% 7.99/1.42 fof(f51,plain,(
% 7.99/1.42 ![A]: (~empty(A)|relation(A))),
% 7.99/1.42 inference(pre_NNF_transformation,[status(esa)],[f3])).
% 7.99/1.42 fof(f52,plain,(
% 7.99/1.42 ![X0]: (~empty(X0)|relation(X0))),
% 7.99/1.42 inference(cnf_transformation,[status(esa)],[f51])).
% 7.99/1.42 fof(f57,plain,(
% 7.99/1.42 ![A]: ((~relation(A)|~function(A))|(relation(function_inverse(A))&function(function_inverse(A))))),
% 7.99/1.42 inference(pre_NNF_transformation,[status(esa)],[f5])).
% 7.99/1.42 fof(f58,plain,(
% 7.99/1.42 ![X0]: (~relation(X0)|~function(X0)|relation(function_inverse(X0)))),
% 7.99/1.42 inference(cnf_transformation,[status(esa)],[f57])).
% 7.99/1.42 fof(f59,plain,(
% 7.99/1.42 ![X0]: (~relation(X0)|~function(X0)|function(function_inverse(X0)))),
% 7.99/1.42 inference(cnf_transformation,[status(esa)],[f57])).
% 7.99/1.42 fof(f60,plain,(
% 7.99/1.42 ![A,B]: ((~relation(A)|~relation(B))|relation(relation_composition(A,B)))),
% 7.99/1.42 inference(pre_NNF_transformation,[status(esa)],[f6])).
% 7.99/1.42 fof(f61,plain,(
% 7.99/1.42 ![X0,X1]: (~relation(X0)|~relation(X1)|relation(relation_composition(X0,X1)))),
% 7.99/1.42 inference(cnf_transformation,[status(esa)],[f60])).
% 7.99/1.42 fof(f62,plain,(
% 7.99/1.42 ![X0]: (relation(identity_relation(X0)))),
% 7.99/1.42 inference(cnf_transformation,[status(esa)],[f7])).
% 7.99/1.42 fof(f68,plain,(
% 7.99/1.42 empty(empty_set)),
% 7.99/1.42 inference(cnf_transformation,[status(esa)],[f10])).
% 7.99/1.42 fof(f69,plain,(
% 7.99/1.42 relation(empty_set)),
% 7.99/1.42 inference(cnf_transformation,[status(esa)],[f10])).
% 7.99/1.42 fof(f71,plain,(
% 7.99/1.42 ![A,B]: ((((~relation(A)|~function(A))|~relation(B))|~function(B))|(relation(relation_composition(A,B))&function(relation_composition(A,B))))),
% 7.99/1.42 inference(pre_NNF_transformation,[status(esa)],[f11])).
% 7.99/1.42 fof(f73,plain,(
% 7.99/1.42 ![X0,X1]: (~relation(X0)|~function(X0)|~relation(X1)|~function(X1)|function(relation_composition(X0,X1)))),
% 7.99/1.42 inference(cnf_transformation,[status(esa)],[f71])).
% 7.99/1.42 fof(f76,plain,(
% 7.99/1.42 (![A]: relation(identity_relation(A)))&(![A]: function(identity_relation(A)))),
% 7.99/1.42 inference(miniscoping,[status(esa)],[f14])).
% 7.99/1.42 fof(f78,plain,(
% 7.99/1.42 ![X0]: (function(identity_relation(X0)))),
% 7.99/1.42 inference(cnf_transformation,[status(esa)],[f76])).
% 7.99/1.42 fof(f88,plain,(
% 7.99/1.42 ![A]: (~empty(A)|(empty(relation_rng(A))&relation(relation_rng(A))))),
% 7.99/1.42 inference(pre_NNF_transformation,[status(esa)],[f19])).
% 7.99/1.42 fof(f90,plain,(
% 7.99/1.42 ![X0]: (~empty(X0)|relation(relation_rng(X0)))),
% 7.99/1.42 inference(cnf_transformation,[status(esa)],[f88])).
% 7.99/1.42 fof(f94,plain,(
% 7.99/1.42 (relation(sk0_1)&function(sk0_1))),
% 7.99/1.42 inference(skolemization,[status(esa)],[f21])).
% 7.99/1.42 fof(f95,plain,(
% 7.99/1.42 relation(sk0_1)),
% 7.99/1.42 inference(cnf_transformation,[status(esa)],[f94])).
% 7.99/1.42 fof(f96,plain,(
% 7.99/1.42 function(sk0_1)),
% 7.99/1.42 inference(cnf_transformation,[status(esa)],[f94])).
% 7.99/1.42 fof(f97,plain,(
% 7.99/1.42 (empty(sk0_2)&relation(sk0_2))),
% 7.99/1.42 inference(skolemization,[status(esa)],[f22])).
% 7.99/1.42 fof(f98,plain,(
% 7.99/1.42 empty(sk0_2)),
% 7.99/1.42 inference(cnf_transformation,[status(esa)],[f97])).
% 7.99/1.42 fof(f99,plain,(
% 7.99/1.42 relation(sk0_2)),
% 7.99/1.42 inference(cnf_transformation,[status(esa)],[f97])).
% 7.99/1.42 fof(f104,plain,(
% 7.99/1.42 empty(sk0_4)),
% 7.99/1.42 inference(skolemization,[status(esa)],[f24])).
% 7.99/1.42 fof(f105,plain,(
% 7.99/1.42 empty(sk0_4)),
% 7.99/1.42 inference(cnf_transformation,[status(esa)],[f104])).
% 7.99/1.42 fof(f106,plain,(
% 7.99/1.42 ((relation(sk0_5)&empty(sk0_5))&function(sk0_5))),
% 7.99/1.42 inference(skolemization,[status(esa)],[f25])).
% 7.99/1.42 fof(f107,plain,(
% 7.99/1.42 relation(sk0_5)),
% 7.99/1.42 inference(cnf_transformation,[status(esa)],[f106])).
% 7.99/1.42 fof(f108,plain,(
% 7.99/1.42 empty(sk0_5)),
% 7.99/1.42 inference(cnf_transformation,[status(esa)],[f106])).
% 7.99/1.42 fof(f109,plain,(
% 7.99/1.42 function(sk0_5)),
% 7.99/1.42 inference(cnf_transformation,[status(esa)],[f106])).
% 7.99/1.42 fof(f118,plain,(
% 7.99/1.42 ((relation(sk0_9)&function(sk0_9))&one_to_one(sk0_9))),
% 7.99/1.42 inference(skolemization,[status(esa)],[f29])).
% 7.99/1.42 fof(f119,plain,(
% 7.99/1.42 relation(sk0_9)),
% 7.99/1.42 inference(cnf_transformation,[status(esa)],[f118])).
% 7.99/1.42 fof(f120,plain,(
% 7.99/1.42 function(sk0_9)),
% 7.99/1.42 inference(cnf_transformation,[status(esa)],[f118])).
% 7.99/1.42 fof(f131,plain,(
% 7.99/1.42 ![A,B]: ((~relation(B)|~function(B))|(B=identity_relation(A)<=>(relation_dom(B)=A&(![C]: (~in(C,A)|apply(B,C)=C)))))),
% 7.99/1.42 inference(pre_NNF_transformation,[status(esa)],[f34])).
% 7.99/1.42 fof(f132,plain,(
% 7.99/1.42 ![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))))))),
% 7.99/1.42 inference(NNF_transformation,[status(esa)],[f131])).
% 7.99/1.42 fof(f133,plain,(
% 7.99/1.42 ![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)))))))),
% 7.99/1.42 inference(miniscoping,[status(esa)],[f132])).
% 7.99/1.42 fof(f134,plain,(
% 7.99/1.42 ![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)))))))),
% 7.99/1.42 inference(skolemization,[status(esa)],[f133])).
% 7.99/1.42 fof(f137,plain,(
% 7.99/1.42 ![X0,X1]: (~relation(X0)|~function(X0)|X0=identity_relation(X1)|~relation_dom(X0)=X1|in(sk0_11(X1,X0),X1))),
% 7.99/1.42 inference(cnf_transformation,[status(esa)],[f134])).
% 7.99/1.42 fof(f138,plain,(
% 7.99/1.42 ![X0,X1]: (~relation(X0)|~function(X0)|X0=identity_relation(X1)|~relation_dom(X0)=X1|~apply(X0,sk0_11(X1,X0))=sk0_11(X1,X0))),
% 7.99/1.42 inference(cnf_transformation,[status(esa)],[f134])).
% 7.99/1.42 fof(f146,plain,(
% 7.99/1.42 ![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))))),
% 7.99/1.42 inference(pre_NNF_transformation,[status(esa)],[f37])).
% 7.99/1.42 fof(f147,plain,(
% 7.99/1.42 ![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)))))),
% 7.99/1.42 inference(miniscoping,[status(esa)],[f146])).
% 7.99/1.42 fof(f149,plain,(
% 7.99/1.42 ![X0,X1]: (~relation(X0)|~function(X0)|~one_to_one(X0)|~in(X1,relation_dom(X0))|X1=apply(relation_composition(X0,function_inverse(X0)),X1))),
% 7.99/1.42 inference(cnf_transformation,[status(esa)],[f147])).
% 7.99/1.42 fof(f150,plain,(
% 7.99/1.42 ![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))))),
% 7.99/1.42 inference(pre_NNF_transformation,[status(esa)],[f38])).
% 7.99/1.42 fof(f151,plain,(
% 7.99/1.42 ![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)))))),
% 7.99/1.42 inference(miniscoping,[status(esa)],[f150])).
% 7.99/1.42 fof(f153,plain,(
% 7.99/1.42 ![X0,X1]: (~relation(X0)|~function(X0)|~one_to_one(X0)|~in(X1,relation_rng(X0))|X1=apply(relation_composition(function_inverse(X0),X0),X1))),
% 7.99/1.42 inference(cnf_transformation,[status(esa)],[f151])).
% 7.99/1.42 fof(f154,plain,(
% 7.99/1.42 ![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))))),
% 7.99/1.42 inference(pre_NNF_transformation,[status(esa)],[f39])).
% 7.99/1.42 fof(f155,plain,(
% 7.99/1.42 ![X0]: (~relation(X0)|~function(X0)|~one_to_one(X0)|relation_dom(relation_composition(X0,function_inverse(X0)))=relation_dom(X0))),
% 7.99/1.42 inference(cnf_transformation,[status(esa)],[f154])).
% 7.99/1.42 fof(f157,plain,(
% 7.99/1.42 ![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))))),
% 7.99/1.42 inference(pre_NNF_transformation,[status(esa)],[f40])).
% 7.99/1.42 fof(f158,plain,(
% 7.99/1.42 ![X0]: (~relation(X0)|~function(X0)|~one_to_one(X0)|relation_dom(relation_composition(function_inverse(X0),X0))=relation_rng(X0))),
% 7.99/1.42 inference(cnf_transformation,[status(esa)],[f157])).
% 7.99/1.42 fof(f163,plain,(
% 7.99/1.42 (?[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))))))),
% 7.99/1.42 inference(pre_NNF_transformation,[status(esa)],[f43])).
% 7.99/1.42 fof(f164,plain,(
% 7.99/1.42 ((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)))))),
% 7.99/1.42 inference(skolemization,[status(esa)],[f163])).
% 7.99/1.42 fof(f165,plain,(
% 7.99/1.42 relation(sk0_12)),
% 7.99/1.42 inference(cnf_transformation,[status(esa)],[f164])).
% 7.99/1.42 fof(f166,plain,(
% 7.99/1.42 function(sk0_12)),
% 7.99/1.42 inference(cnf_transformation,[status(esa)],[f164])).
% 7.99/1.42 fof(f167,plain,(
% 7.99/1.42 one_to_one(sk0_12)),
% 7.99/1.42 inference(cnf_transformation,[status(esa)],[f164])).
% 7.99/1.42 fof(f168,plain,(
% 7.99/1.42 ~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))),
% 7.99/1.42 inference(cnf_transformation,[status(esa)],[f164])).
% 7.99/1.42 fof(f169,plain,(
% 7.99/1.42 ![A]: (~empty(A)|A=empty_set)),
% 7.99/1.42 inference(pre_NNF_transformation,[status(esa)],[f44])).
% 7.99/1.42 fof(f170,plain,(
% 7.99/1.42 ![X0]: (~empty(X0)|X0=empty_set)),
% 7.99/1.42 inference(cnf_transformation,[status(esa)],[f169])).
% 7.99/1.42 fof(f177,plain,(
% 7.99/1.42 spl0_0 <=> relation_composition(sk0_12,function_inverse(sk0_12))=identity_relation(relation_dom(sk0_12))),
% 7.99/1.42 introduced(split_symbol_definition)).
% 7.99/1.42 fof(f180,plain,(
% 7.99/1.42 spl0_1 <=> relation_composition(function_inverse(sk0_12),sk0_12)=identity_relation(relation_rng(sk0_12))),
% 7.99/1.42 introduced(split_symbol_definition)).
% 7.99/1.42 fof(f183,plain,(
% 7.99/1.42 ~spl0_0|~spl0_1),
% 7.99/1.42 inference(split_clause,[status(thm)],[f168,f177,f180])).
% 7.99/1.42 fof(f185,plain,(
% 7.99/1.42 spl0_2 <=> relation(sk0_12)),
% 7.99/1.42 introduced(split_symbol_definition)).
% 7.99/1.42 fof(f187,plain,(
% 7.99/1.42 ~relation(sk0_12)|spl0_2),
% 7.99/1.42 inference(component_clause,[status(thm)],[f185])).
% 7.99/1.42 fof(f188,plain,(
% 7.99/1.42 spl0_3 <=> function(sk0_12)),
% 7.99/1.42 introduced(split_symbol_definition)).
% 7.99/1.42 fof(f190,plain,(
% 7.99/1.42 ~function(sk0_12)|spl0_3),
% 7.99/1.42 inference(component_clause,[status(thm)],[f188])).
% 7.99/1.42 fof(f191,plain,(
% 7.99/1.42 spl0_4 <=> relation_dom(relation_composition(sk0_12,function_inverse(sk0_12)))=relation_dom(sk0_12)),
% 7.99/1.42 introduced(split_symbol_definition)).
% 7.99/1.42 fof(f194,plain,(
% 7.99/1.42 ~relation(sk0_12)|~function(sk0_12)|relation_dom(relation_composition(sk0_12,function_inverse(sk0_12)))=relation_dom(sk0_12)),
% 7.99/1.42 inference(resolution,[status(thm)],[f155,f167])).
% 7.99/1.42 fof(f195,plain,(
% 7.99/1.42 ~spl0_2|~spl0_3|spl0_4),
% 7.99/1.42 inference(split_clause,[status(thm)],[f194,f185,f188,f191])).
% 7.99/1.42 fof(f199,plain,(
% 7.99/1.42 $false|spl0_3),
% 7.99/1.42 inference(forward_subsumption_resolution,[status(thm)],[f190,f166])).
% 7.99/1.42 fof(f200,plain,(
% 7.99/1.42 spl0_3),
% 7.99/1.42 inference(contradiction_clause,[status(thm)],[f199])).
% 7.99/1.42 fof(f201,plain,(
% 7.99/1.42 $false|spl0_2),
% 7.99/1.42 inference(forward_subsumption_resolution,[status(thm)],[f187,f165])).
% 7.99/1.42 fof(f202,plain,(
% 7.99/1.42 spl0_2),
% 7.99/1.42 inference(contradiction_clause,[status(thm)],[f201])).
% 7.99/1.42 fof(f239,plain,(
% 7.99/1.42 spl0_10 <=> relation_dom(relation_composition(function_inverse(sk0_12),sk0_12))=relation_rng(sk0_12)),
% 7.99/1.42 introduced(split_symbol_definition)).
% 7.99/1.42 fof(f242,plain,(
% 7.99/1.42 ~relation(sk0_12)|~function(sk0_12)|relation_dom(relation_composition(function_inverse(sk0_12),sk0_12))=relation_rng(sk0_12)),
% 7.99/1.42 inference(resolution,[status(thm)],[f158,f167])).
% 7.99/1.42 fof(f243,plain,(
% 7.99/1.42 ~spl0_2|~spl0_3|spl0_10),
% 7.99/1.42 inference(split_clause,[status(thm)],[f242,f185,f188,f239])).
% 7.99/1.42 fof(f263,plain,(
% 7.99/1.42 spl0_15 <=> relation(function_inverse(sk0_12))),
% 7.99/1.42 introduced(split_symbol_definition)).
% 7.99/1.42 fof(f265,plain,(
% 7.99/1.42 ~relation(function_inverse(sk0_12))|spl0_15),
% 7.99/1.42 inference(component_clause,[status(thm)],[f263])).
% 7.99/1.42 fof(f283,plain,(
% 7.99/1.42 spl0_17 <=> relation(relation_composition(function_inverse(sk0_12),sk0_12))),
% 7.99/1.42 introduced(split_symbol_definition)).
% 7.99/1.42 fof(f285,plain,(
% 7.99/1.42 ~relation(relation_composition(function_inverse(sk0_12),sk0_12))|spl0_17),
% 7.99/1.42 inference(component_clause,[status(thm)],[f283])).
% 7.99/1.42 fof(f288,plain,(
% 7.99/1.42 spl0_18 <=> relation(relation_composition(sk0_12,function_inverse(sk0_12)))),
% 7.99/1.42 introduced(split_symbol_definition)).
% 7.99/1.42 fof(f290,plain,(
% 7.99/1.42 ~relation(relation_composition(sk0_12,function_inverse(sk0_12)))|spl0_18),
% 7.99/1.42 inference(component_clause,[status(thm)],[f288])).
% 7.99/1.42 fof(f297,plain,(
% 7.99/1.42 ~relation(function_inverse(sk0_12))|~relation(sk0_12)|spl0_17),
% 7.99/1.42 inference(resolution,[status(thm)],[f285,f61])).
% 7.99/1.42 fof(f298,plain,(
% 7.99/1.42 ~spl0_15|~spl0_2|spl0_17),
% 7.99/1.42 inference(split_clause,[status(thm)],[f297,f263,f185,f283])).
% 7.99/1.42 fof(f299,plain,(
% 7.99/1.42 ~relation(sk0_12)|~function(sk0_12)|spl0_15),
% 7.99/1.42 inference(resolution,[status(thm)],[f265,f58])).
% 7.99/1.42 fof(f300,plain,(
% 7.99/1.42 ~spl0_2|~spl0_3|spl0_15),
% 7.99/1.42 inference(split_clause,[status(thm)],[f299,f185,f188,f263])).
% 7.99/1.42 fof(f305,plain,(
% 7.99/1.42 ~relation(sk0_12)|~relation(function_inverse(sk0_12))|spl0_18),
% 7.99/1.42 inference(resolution,[status(thm)],[f290,f61])).
% 7.99/1.42 fof(f306,plain,(
% 7.99/1.42 ~spl0_2|~spl0_15|spl0_18),
% 7.99/1.42 inference(split_clause,[status(thm)],[f305,f185,f263,f288])).
% 7.99/1.42 fof(f406,plain,(
% 7.99/1.42 spl0_38 <=> function(relation_composition(function_inverse(sk0_12),sk0_12))),
% 7.99/1.42 introduced(split_symbol_definition)).
% 7.99/1.42 fof(f408,plain,(
% 7.99/1.42 ~function(relation_composition(function_inverse(sk0_12),sk0_12))|spl0_38),
% 7.99/1.42 inference(component_clause,[status(thm)],[f406])).
% 7.99/1.42 fof(f424,plain,(
% 7.99/1.42 spl0_42 <=> function(relation_composition(sk0_12,function_inverse(sk0_12)))),
% 7.99/1.42 introduced(split_symbol_definition)).
% 7.99/1.42 fof(f426,plain,(
% 7.99/1.42 ~function(relation_composition(sk0_12,function_inverse(sk0_12)))|spl0_42),
% 7.99/1.42 inference(component_clause,[status(thm)],[f424])).
% 7.99/1.42 fof(f446,plain,(
% 7.99/1.42 spl0_46 <=> function(function_inverse(sk0_12))),
% 7.99/1.42 introduced(split_symbol_definition)).
% 7.99/1.42 fof(f448,plain,(
% 7.99/1.42 ~function(function_inverse(sk0_12))|spl0_46),
% 7.99/1.42 inference(component_clause,[status(thm)],[f446])).
% 7.99/1.42 fof(f449,plain,(
% 7.99/1.42 ~relation(function_inverse(sk0_12))|~function(function_inverse(sk0_12))|~relation(sk0_12)|~function(sk0_12)|spl0_38),
% 7.99/1.42 inference(resolution,[status(thm)],[f408,f73])).
% 7.99/1.42 fof(f450,plain,(
% 7.99/1.42 ~spl0_15|~spl0_46|~spl0_2|~spl0_3|spl0_38),
% 7.99/1.42 inference(split_clause,[status(thm)],[f449,f263,f446,f185,f188,f406])).
% 7.99/1.42 fof(f451,plain,(
% 7.99/1.42 ~relation(sk0_12)|~function(sk0_12)|spl0_46),
% 7.99/1.42 inference(resolution,[status(thm)],[f448,f59])).
% 7.99/1.42 fof(f452,plain,(
% 7.99/1.42 ~spl0_2|~spl0_3|spl0_46),
% 7.99/1.42 inference(split_clause,[status(thm)],[f451,f185,f188,f446])).
% 7.99/1.42 fof(f455,plain,(
% 7.99/1.42 ~relation(sk0_12)|~function(sk0_12)|~relation(function_inverse(sk0_12))|~function(function_inverse(sk0_12))|spl0_42),
% 7.99/1.42 inference(resolution,[status(thm)],[f426,f73])).
% 7.99/1.42 fof(f456,plain,(
% 7.99/1.42 ~spl0_2|~spl0_3|~spl0_15|~spl0_46|spl0_42),
% 7.99/1.42 inference(split_clause,[status(thm)],[f455,f185,f188,f263,f446,f424])).
% 7.99/1.42 fof(f654,plain,(
% 7.99/1.42 spl0_72 <=> function(empty_set)),
% 7.99/1.42 introduced(split_symbol_definition)).
% 7.99/1.42 fof(f656,plain,(
% 7.99/1.42 ~function(empty_set)|spl0_72),
% 7.99/1.42 inference(component_clause,[status(thm)],[f654])).
% 7.99/1.42 fof(f680,plain,(
% 7.99/1.42 spl0_78 <=> relation(sk0_1)),
% 7.99/1.42 introduced(split_symbol_definition)).
% 7.99/1.42 fof(f682,plain,(
% 7.99/1.42 ~relation(sk0_1)|spl0_78),
% 7.99/1.42 inference(component_clause,[status(thm)],[f680])).
% 7.99/1.42 fof(f690,plain,(
% 7.99/1.42 $false|spl0_78),
% 7.99/1.42 inference(forward_subsumption_resolution,[status(thm)],[f682,f95])).
% 7.99/1.42 fof(f691,plain,(
% 7.99/1.42 spl0_78),
% 7.99/1.42 inference(contradiction_clause,[status(thm)],[f690])).
% 7.99/1.42 fof(f711,plain,(
% 7.99/1.42 spl0_83 <=> function(sk0_2)),
% 7.99/1.42 introduced(split_symbol_definition)).
% 7.99/1.42 fof(f713,plain,(
% 7.99/1.42 ~function(sk0_2)|spl0_83),
% 7.99/1.42 inference(component_clause,[status(thm)],[f711])).
% 7.99/1.42 fof(f753,plain,(
% 7.99/1.42 spl0_91 <=> function(sk0_4)),
% 7.99/1.42 introduced(split_symbol_definition)).
% 7.99/1.42 fof(f755,plain,(
% 7.99/1.42 ~function(sk0_4)|spl0_91),
% 7.99/1.42 inference(component_clause,[status(thm)],[f753])).
% 7.99/1.42 fof(f795,plain,(
% 7.99/1.42 spl0_99 <=> function(sk0_5)),
% 7.99/1.42 introduced(split_symbol_definition)).
% 7.99/1.42 fof(f797,plain,(
% 7.99/1.42 ~function(sk0_5)|spl0_99),
% 7.99/1.42 inference(component_clause,[status(thm)],[f795])).
% 7.99/1.42 fof(f818,plain,(
% 7.99/1.42 $false|spl0_99),
% 7.99/1.42 inference(forward_subsumption_resolution,[status(thm)],[f797,f109])).
% 7.99/1.42 fof(f819,plain,(
% 7.99/1.42 spl0_99),
% 7.99/1.42 inference(contradiction_clause,[status(thm)],[f818])).
% 7.99/1.42 fof(f823,plain,(
% 7.99/1.42 spl0_105 <=> relation(sk0_5)),
% 7.99/1.42 introduced(split_symbol_definition)).
% 7.99/1.42 fof(f825,plain,(
% 7.99/1.42 ~relation(sk0_5)|spl0_105),
% 7.99/1.42 inference(component_clause,[status(thm)],[f823])).
% 7.99/1.42 fof(f833,plain,(
% 7.99/1.42 $false|spl0_105),
% 7.99/1.42 inference(forward_subsumption_resolution,[status(thm)],[f825,f107])).
% 7.99/1.42 fof(f834,plain,(
% 7.99/1.42 spl0_105),
% 7.99/1.42 inference(contradiction_clause,[status(thm)],[f833])).
% 7.99/1.42 fof(f838,plain,(
% 7.99/1.42 spl0_108 <=> relation(sk0_9)),
% 7.99/1.42 introduced(split_symbol_definition)).
% 7.99/1.42 fof(f840,plain,(
% 7.99/1.42 ~relation(sk0_9)|spl0_108),
% 7.99/1.42 inference(component_clause,[status(thm)],[f838])).
% 7.99/1.42 fof(f848,plain,(
% 7.99/1.42 $false|spl0_108),
% 7.99/1.42 inference(forward_subsumption_resolution,[status(thm)],[f840,f119])).
% 7.99/1.42 fof(f849,plain,(
% 7.99/1.42 spl0_108),
% 7.99/1.42 inference(contradiction_clause,[status(thm)],[f848])).
% 7.99/1.42 fof(f850,plain,(
% 7.99/1.42 spl0_110 <=> function(sk0_9)),
% 7.99/1.42 introduced(split_symbol_definition)).
% 7.99/1.42 fof(f852,plain,(
% 7.99/1.42 ~function(sk0_9)|spl0_110),
% 7.99/1.42 inference(component_clause,[status(thm)],[f850])).
% 7.99/1.42 fof(f873,plain,(
% 7.99/1.42 $false|spl0_110),
% 7.99/1.42 inference(forward_subsumption_resolution,[status(thm)],[f852,f120])).
% 7.99/1.42 fof(f874,plain,(
% 7.99/1.42 spl0_110),
% 7.99/1.42 inference(contradiction_clause,[status(thm)],[f873])).
% 7.99/1.42 fof(f875,plain,(
% 7.99/1.42 ~empty(empty_set)|spl0_72),
% 7.99/1.42 inference(resolution,[status(thm)],[f656,f50])).
% 7.99/1.42 fof(f876,plain,(
% 7.99/1.42 $false|spl0_72),
% 7.99/1.42 inference(forward_subsumption_resolution,[status(thm)],[f875,f68])).
% 7.99/1.42 fof(f877,plain,(
% 7.99/1.42 spl0_72),
% 7.99/1.42 inference(contradiction_clause,[status(thm)],[f876])).
% 7.99/1.42 fof(f878,plain,(
% 7.99/1.42 ~empty(sk0_2)|spl0_83),
% 7.99/1.42 inference(resolution,[status(thm)],[f713,f50])).
% 7.99/1.42 fof(f879,plain,(
% 7.99/1.42 $false|spl0_83),
% 7.99/1.42 inference(forward_subsumption_resolution,[status(thm)],[f878,f98])).
% 7.99/1.42 fof(f880,plain,(
% 7.99/1.42 spl0_83),
% 7.99/1.42 inference(contradiction_clause,[status(thm)],[f879])).
% 7.99/1.42 fof(f881,plain,(
% 7.99/1.42 ~empty(sk0_4)|spl0_91),
% 7.99/1.42 inference(resolution,[status(thm)],[f755,f50])).
% 7.99/1.42 fof(f882,plain,(
% 7.99/1.42 $false|spl0_91),
% 7.99/1.42 inference(forward_subsumption_resolution,[status(thm)],[f881,f105])).
% 7.99/1.42 fof(f883,plain,(
% 7.99/1.42 spl0_91),
% 7.99/1.42 inference(contradiction_clause,[status(thm)],[f882])).
% 7.99/1.42 fof(f887,plain,(
% 7.99/1.42 spl0_116 <=> relation(empty_set)),
% 7.99/1.42 introduced(split_symbol_definition)).
% 7.99/1.42 fof(f889,plain,(
% 7.99/1.42 ~relation(empty_set)|spl0_116),
% 7.99/1.42 inference(component_clause,[status(thm)],[f887])).
% 7.99/1.42 fof(f897,plain,(
% 7.99/1.42 $false|spl0_116),
% 7.99/1.42 inference(forward_subsumption_resolution,[status(thm)],[f889,f69])).
% 7.99/1.42 fof(f898,plain,(
% 7.99/1.42 spl0_116),
% 7.99/1.42 inference(contradiction_clause,[status(thm)],[f897])).
% 7.99/1.42 fof(f902,plain,(
% 7.99/1.42 spl0_119 <=> relation(sk0_2)),
% 7.99/1.42 introduced(split_symbol_definition)).
% 7.99/1.42 fof(f904,plain,(
% 7.99/1.42 ~relation(sk0_2)|spl0_119),
% 7.99/1.42 inference(component_clause,[status(thm)],[f902])).
% 7.99/1.42 fof(f912,plain,(
% 7.99/1.42 $false|spl0_119),
% 7.99/1.42 inference(forward_subsumption_resolution,[status(thm)],[f904,f99])).
% 7.99/1.42 fof(f913,plain,(
% 7.99/1.42 spl0_119),
% 7.99/1.42 inference(contradiction_clause,[status(thm)],[f912])).
% 7.99/1.42 fof(f917,plain,(
% 7.99/1.42 spl0_122 <=> relation(sk0_4)),
% 7.99/1.42 introduced(split_symbol_definition)).
% 7.99/1.42 fof(f919,plain,(
% 7.99/1.42 ~relation(sk0_4)|spl0_122),
% 7.99/1.42 inference(component_clause,[status(thm)],[f917])).
% 7.99/1.42 fof(f927,plain,(
% 7.99/1.42 ~empty(sk0_4)|spl0_122),
% 7.99/1.42 inference(resolution,[status(thm)],[f52,f919])).
% 7.99/1.42 fof(f928,plain,(
% 7.99/1.42 $false|spl0_122),
% 7.99/1.42 inference(forward_subsumption_resolution,[status(thm)],[f927,f105])).
% 7.99/1.42 fof(f929,plain,(
% 7.99/1.42 spl0_122),
% 7.99/1.42 inference(contradiction_clause,[status(thm)],[f928])).
% 7.99/1.42 fof(f930,plain,(
% 7.99/1.42 sk0_5=empty_set),
% 7.99/1.42 inference(resolution,[status(thm)],[f170,f108])).
% 7.99/1.42 fof(f959,plain,(
% 7.99/1.42 spl0_125 <=> empty(empty_set)),
% 7.99/1.42 introduced(split_symbol_definition)).
% 7.99/1.42 fof(f961,plain,(
% 7.99/1.42 ~empty(empty_set)|spl0_125),
% 7.99/1.42 inference(component_clause,[status(thm)],[f959])).
% 7.99/1.42 fof(f1003,plain,(
% 7.99/1.42 spl0_129 <=> relation(relation_rng(sk0_5))),
% 7.99/1.42 introduced(split_symbol_definition)).
% 7.99/1.42 fof(f1005,plain,(
% 7.99/1.42 ~relation(relation_rng(sk0_5))|spl0_129),
% 7.99/1.42 inference(component_clause,[status(thm)],[f1003])).
% 7.99/1.42 fof(f1016,plain,(
% 7.99/1.42 spl0_132 <=> relation(relation_rng(sk0_4))),
% 7.99/1.42 introduced(split_symbol_definition)).
% 7.99/1.42 fof(f1018,plain,(
% 7.99/1.42 ~relation(relation_rng(sk0_4))|spl0_132),
% 7.99/1.42 inference(component_clause,[status(thm)],[f1016])).
% 7.99/1.42 fof(f1029,plain,(
% 7.99/1.42 spl0_135 <=> relation(relation_rng(sk0_2))),
% 7.99/1.42 introduced(split_symbol_definition)).
% 7.99/1.42 fof(f1031,plain,(
% 7.99/1.42 ~relation(relation_rng(sk0_2))|spl0_135),
% 7.99/1.42 inference(component_clause,[status(thm)],[f1029])).
% 7.99/1.42 fof(f1042,plain,(
% 7.99/1.42 spl0_138 <=> relation(relation_rng(empty_set))),
% 7.99/1.42 introduced(split_symbol_definition)).
% 7.99/1.42 fof(f1044,plain,(
% 7.99/1.42 ~relation(relation_rng(empty_set))|spl0_138),
% 7.99/1.42 inference(component_clause,[status(thm)],[f1042])).
% 7.99/1.42 fof(f1052,plain,(
% 7.99/1.42 ~empty(sk0_5)|spl0_129),
% 7.99/1.42 inference(resolution,[status(thm)],[f1005,f90])).
% 7.99/1.42 fof(f1053,plain,(
% 7.99/1.42 $false|spl0_129),
% 7.99/1.42 inference(forward_subsumption_resolution,[status(thm)],[f1052,f108])).
% 7.99/1.42 fof(f1054,plain,(
% 7.99/1.42 spl0_129),
% 7.99/1.42 inference(contradiction_clause,[status(thm)],[f1053])).
% 7.99/1.42 fof(f1055,plain,(
% 7.99/1.42 ~empty(sk0_4)|spl0_132),
% 7.99/1.42 inference(resolution,[status(thm)],[f1018,f90])).
% 7.99/1.42 fof(f1056,plain,(
% 7.99/1.42 $false|spl0_132),
% 7.99/1.42 inference(forward_subsumption_resolution,[status(thm)],[f1055,f105])).
% 7.99/1.42 fof(f1057,plain,(
% 7.99/1.42 spl0_132),
% 7.99/1.42 inference(contradiction_clause,[status(thm)],[f1056])).
% 7.99/1.42 fof(f1058,plain,(
% 7.99/1.42 ~empty(sk0_2)|spl0_135),
% 7.99/1.42 inference(resolution,[status(thm)],[f1031,f90])).
% 7.99/1.42 fof(f1059,plain,(
% 7.99/1.42 $false|spl0_135),
% 7.99/1.42 inference(forward_subsumption_resolution,[status(thm)],[f1058,f98])).
% 7.99/1.42 fof(f1060,plain,(
% 7.99/1.42 spl0_135),
% 7.99/1.42 inference(contradiction_clause,[status(thm)],[f1059])).
% 7.99/1.42 fof(f1360,plain,(
% 7.99/1.42 ~empty(empty_set)|spl0_138),
% 7.99/1.42 inference(resolution,[status(thm)],[f1044,f90])).
% 7.99/1.42 fof(f1361,plain,(
% 7.99/1.42 $false|spl0_138),
% 7.99/1.42 inference(forward_subsumption_resolution,[status(thm)],[f1360,f68])).
% 7.99/1.42 fof(f1362,plain,(
% 7.99/1.42 spl0_138),
% 7.99/1.42 inference(contradiction_clause,[status(thm)],[f1361])).
% 7.99/1.42 fof(f1493,plain,(
% 7.99/1.42 $false|spl0_125),
% 7.99/1.42 inference(forward_subsumption_resolution,[status(thm)],[f961,f68])).
% 7.99/1.42 fof(f1494,plain,(
% 7.99/1.42 spl0_125),
% 7.99/1.42 inference(contradiction_clause,[status(thm)],[f1493])).
% 7.99/1.42 fof(f1967,plain,(
% 7.99/1.42 spl0_234 <=> function(identity_relation(empty_set))),
% 7.99/1.42 introduced(split_symbol_definition)).
% 7.99/1.42 fof(f1969,plain,(
% 7.99/1.42 ~function(identity_relation(empty_set))|spl0_234),
% 7.99/1.42 inference(component_clause,[status(thm)],[f1967])).
% 7.99/1.42 fof(f1990,plain,(
% 7.99/1.42 $false|spl0_234),
% 7.99/1.42 inference(forward_subsumption_resolution,[status(thm)],[f1969,f78])).
% 7.99/1.42 fof(f1991,plain,(
% 7.99/1.42 spl0_234),
% 7.99/1.42 inference(contradiction_clause,[status(thm)],[f1990])).
% 7.99/1.42 fof(f2069,plain,(
% 7.99/1.42 spl0_249 <=> function(sk0_1)),
% 7.99/1.42 introduced(split_symbol_definition)).
% 7.99/1.42 fof(f2071,plain,(
% 7.99/1.42 ~function(sk0_1)|spl0_249),
% 7.99/1.42 inference(component_clause,[status(thm)],[f2069])).
% 7.99/1.42 fof(f2092,plain,(
% 7.99/1.42 $false|spl0_249),
% 7.99/1.42 inference(forward_subsumption_resolution,[status(thm)],[f2071,f96])).
% 7.99/1.42 fof(f2093,plain,(
% 7.99/1.42 spl0_249),
% 7.99/1.42 inference(contradiction_clause,[status(thm)],[f2092])).
% 7.99/1.42 fof(f2147,plain,(
% 7.99/1.42 spl0_257 <=> function(identity_relation(relation_rng(empty_set)))),
% 7.99/1.42 introduced(split_symbol_definition)).
% 7.99/1.42 fof(f2149,plain,(
% 7.99/1.42 ~function(identity_relation(relation_rng(empty_set)))|spl0_257),
% 7.99/1.42 inference(component_clause,[status(thm)],[f2147])).
% 7.99/1.42 fof(f2171,plain,(
% 7.99/1.42 $false|spl0_257),
% 7.99/1.42 inference(forward_subsumption_resolution,[status(thm)],[f2149,f78])).
% 7.99/1.42 fof(f2172,plain,(
% 7.99/1.42 spl0_257),
% 7.99/1.42 inference(contradiction_clause,[status(thm)],[f2171])).
% 7.99/1.42 fof(f2199,plain,(
% 7.99/1.42 spl0_265 <=> function(identity_relation(relation_dom(empty_set)))),
% 7.99/1.42 introduced(split_symbol_definition)).
% 7.99/1.42 fof(f2201,plain,(
% 7.99/1.42 ~function(identity_relation(relation_dom(empty_set)))|spl0_265),
% 7.99/1.42 inference(component_clause,[status(thm)],[f2199])).
% 7.99/1.42 fof(f2223,plain,(
% 7.99/1.42 $false|spl0_265),
% 7.99/1.42 inference(forward_subsumption_resolution,[status(thm)],[f2201,f78])).
% 7.99/1.42 fof(f2224,plain,(
% 7.99/1.42 spl0_265),
% 7.99/1.42 inference(contradiction_clause,[status(thm)],[f2223])).
% 7.99/1.42 fof(f2252,plain,(
% 7.99/1.42 spl0_273 <=> function(identity_relation(identity_relation(empty_set)))),
% 7.99/1.42 introduced(split_symbol_definition)).
% 7.99/1.42 fof(f2254,plain,(
% 7.99/1.42 ~function(identity_relation(identity_relation(empty_set)))|spl0_273),
% 7.99/1.42 inference(component_clause,[status(thm)],[f2252])).
% 7.99/1.42 fof(f2276,plain,(
% 7.99/1.42 $false|spl0_273),
% 7.99/1.42 inference(forward_subsumption_resolution,[status(thm)],[f2254,f78])).
% 7.99/1.42 fof(f2277,plain,(
% 7.99/1.42 spl0_273),
% 7.99/1.42 inference(contradiction_clause,[status(thm)],[f2276])).
% 7.99/1.42 fof(f2282,plain,(
% 7.99/1.42 spl0_279 <=> relation(identity_relation(empty_set))),
% 7.99/1.42 introduced(split_symbol_definition)).
% 7.99/1.42 fof(f2284,plain,(
% 7.99/1.42 ~relation(identity_relation(empty_set))|spl0_279),
% 7.99/1.42 inference(component_clause,[status(thm)],[f2282])).
% 7.99/1.42 fof(f2291,plain,(
% 7.99/1.42 $false|spl0_279),
% 7.99/1.42 inference(forward_subsumption_resolution,[status(thm)],[f2284,f62])).
% 7.99/1.42 fof(f2292,plain,(
% 7.99/1.42 spl0_279),
% 7.99/1.42 inference(contradiction_clause,[status(thm)],[f2291])).
% 7.99/1.42 fof(f2679,plain,(
% 7.99/1.42 spl0_306 <=> ~in(X0,relation_dom(sk0_12))|X0=apply(relation_composition(sk0_12,function_inverse(sk0_12)),X0)),
% 7.99/1.42 introduced(split_symbol_definition)).
% 7.99/1.42 fof(f2680,plain,(
% 7.99/1.42 ![X0]: (~in(X0,relation_dom(sk0_12))|X0=apply(relation_composition(sk0_12,function_inverse(sk0_12)),X0)|~spl0_306)),
% 7.99/1.42 inference(component_clause,[status(thm)],[f2679])).
% 7.99/1.42 fof(f2682,plain,(
% 7.99/1.42 ![X0]: (~relation(sk0_12)|~function(sk0_12)|~in(X0,relation_dom(sk0_12))|X0=apply(relation_composition(sk0_12,function_inverse(sk0_12)),X0))),
% 7.99/1.42 inference(resolution,[status(thm)],[f149,f167])).
% 7.99/1.42 fof(f2683,plain,(
% 7.99/1.42 ~spl0_2|~spl0_3|spl0_306),
% 7.99/1.42 inference(split_clause,[status(thm)],[f2682,f185,f188,f2679])).
% 7.99/1.42 fof(f2705,plain,(
% 7.99/1.42 spl0_310 <=> ~in(X0,relation_rng(sk0_12))|X0=apply(relation_composition(function_inverse(sk0_12),sk0_12),X0)),
% 7.99/1.42 introduced(split_symbol_definition)).
% 7.99/1.42 fof(f2706,plain,(
% 7.99/1.42 ![X0]: (~in(X0,relation_rng(sk0_12))|X0=apply(relation_composition(function_inverse(sk0_12),sk0_12),X0)|~spl0_310)),
% 7.99/1.42 inference(component_clause,[status(thm)],[f2705])).
% 7.99/1.42 fof(f2708,plain,(
% 7.99/1.42 ![X0]: (~relation(sk0_12)|~function(sk0_12)|~in(X0,relation_rng(sk0_12))|X0=apply(relation_composition(function_inverse(sk0_12),sk0_12),X0))),
% 7.99/1.42 inference(resolution,[status(thm)],[f153,f167])).
% 7.99/1.42 fof(f2709,plain,(
% 7.99/1.42 ~spl0_2|~spl0_3|spl0_310),
% 7.99/1.42 inference(split_clause,[status(thm)],[f2708,f185,f188,f2705])).
% 7.99/1.42 fof(f2733,plain,(
% 7.99/1.42 spl0_311 <=> sk0_5=empty_set),
% 7.99/1.42 introduced(split_symbol_definition)).
% 7.99/1.42 fof(f2735,plain,(
% 7.99/1.42 ~sk0_5=empty_set|spl0_311),
% 7.99/1.42 inference(component_clause,[status(thm)],[f2733])).
% 7.99/1.42 fof(f2756,plain,(
% 7.99/1.42 $false|spl0_311),
% 7.99/1.42 inference(forward_subsumption_resolution,[status(thm)],[f2735,f930])).
% 7.99/1.42 fof(f2757,plain,(
% 7.99/1.42 spl0_311),
% 7.99/1.42 inference(contradiction_clause,[status(thm)],[f2756])).
% 7.99/1.42 fof(f2932,plain,(
% 7.99/1.42 ![X0]: (sk0_11(relation_dom(sk0_12),X0)=apply(relation_composition(sk0_12,function_inverse(sk0_12)),sk0_11(relation_dom(sk0_12),X0))|~relation(X0)|~function(X0)|X0=identity_relation(relation_dom(sk0_12))|~relation_dom(X0)=relation_dom(sk0_12)|~spl0_306)),
% 7.99/1.42 inference(resolution,[status(thm)],[f2680,f137])).
% 7.99/1.42 fof(f3170,plain,(
% 7.99/1.42 ![X0]: (sk0_11(relation_rng(sk0_12),X0)=apply(relation_composition(function_inverse(sk0_12),sk0_12),sk0_11(relation_rng(sk0_12),X0))|~relation(X0)|~function(X0)|X0=identity_relation(relation_rng(sk0_12))|~relation_dom(X0)=relation_rng(sk0_12)|~spl0_310)),
% 7.99/1.42 inference(resolution,[status(thm)],[f2706,f137])).
% 7.99/1.42 fof(f3602,plain,(
% 7.99/1.42 ~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(sk0_12))|~relation_dom(relation_composition(sk0_12,function_inverse(sk0_12)))=relation_dom(sk0_12)|~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(sk0_12))|~relation_dom(relation_composition(sk0_12,function_inverse(sk0_12)))=relation_dom(sk0_12)|~spl0_306),
% 7.99/1.42 inference(resolution,[status(thm)],[f2932,f138])).
% 7.99/1.42 fof(f3603,plain,(
% 7.99/1.42 ~spl0_18|~spl0_42|spl0_0|~spl0_4|~spl0_306),
% 7.99/1.42 inference(split_clause,[status(thm)],[f3602,f288,f424,f177,f191,f2679])).
% 7.99/1.42 fof(f3698,plain,(
% 7.99/1.42 spl0_396 <=> sk0_5=sk0_5),
% 7.99/1.42 introduced(split_symbol_definition)).
% 7.99/1.42 fof(f3700,plain,(
% 7.99/1.42 ~sk0_5=sk0_5|spl0_396),
% 7.99/1.42 inference(component_clause,[status(thm)],[f3698])).
% 7.99/1.42 fof(f3727,plain,(
% 7.99/1.42 $false|spl0_396),
% 7.99/1.42 inference(equality_resolution,[status(esa)],[f3700])).
% 7.99/1.42 fof(f3728,plain,(
% 7.99/1.42 spl0_396),
% 7.99/1.42 inference(contradiction_clause,[status(thm)],[f3727])).
% 7.99/1.42 fof(f5716,plain,(
% 7.99/1.42 ~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_rng(sk0_12))|~relation_dom(relation_composition(function_inverse(sk0_12),sk0_12))=relation_rng(sk0_12)|~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_rng(sk0_12))|~relation_dom(relation_composition(function_inverse(sk0_12),sk0_12))=relation_rng(sk0_12)|~spl0_310),
% 7.99/1.43 inference(resolution,[status(thm)],[f3170,f138])).
% 7.99/1.43 fof(f5717,plain,(
% 7.99/1.43 ~spl0_17|~spl0_38|spl0_1|~spl0_10|~spl0_310),
% 7.99/1.43 inference(split_clause,[status(thm)],[f5716,f283,f406,f180,f239,f2705])).
% 7.99/1.43 fof(f5718,plain,(
% 7.99/1.43 $false),
% 7.99/1.43 inference(sat_refutation,[status(thm)],[f183,f195,f200,f202,f243,f298,f300,f306,f450,f452,f456,f691,f819,f834,f849,f874,f877,f880,f883,f898,f913,f929,f1054,f1057,f1060,f1362,f1494,f1991,f2093,f2172,f2224,f2277,f2292,f2683,f2709,f2757,f3603,f3728,f5717])).
% 7.99/1.43 % SZS output end CNFRefutation for theBenchmark.p
% 8.53/1.47 % Elapsed time: 1.103187 seconds
% 8.53/1.47 % CPU time: 8.575105 seconds
% 8.53/1.47 % Total memory used: 182.930 MB
% 8.53/1.47 % Net memory used: 178.928 MB
%------------------------------------------------------------------------------