TSTP Solution File: SEU220+3 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SEU220+3 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n016.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 12:36:20 EDT 2023
% Result : Theorem 3.76s 0.82s
% Output : CNFRefutation 3.76s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SEU220+3 : TPTP v8.1.2. Released v3.2.0.
% 0.11/0.12 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.33 % Computer : n016.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Tue May 30 09:37:59 EDT 2023
% 0.13/0.33 % CPUTime :
% 0.13/0.34 % Drodi V3.5.1
% 3.76/0.82 % Refutation found
% 3.76/0.82 % SZS status Theorem for theBenchmark: Theorem is valid
% 3.76/0.82 % SZS output start CNFRefutation for theBenchmark
% 3.76/0.82 fof(f2,axiom,(
% 3.76/0.82 (! [A] :( empty(A)=> function(A) ) )),
% 3.76/0.82 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.76/0.82 fof(f5,axiom,(
% 3.76/0.82 (! [A] :( ( relation(A)& function(A) )=> ( relation(function_inverse(A))& function(function_inverse(A)) ) ) )),
% 3.76/0.82 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.76/0.82 fof(f6,axiom,(
% 3.76/0.82 (! [A,B] :( ( relation(A)& relation(B) )=> relation(relation_composition(A,B)) ) )),
% 3.76/0.82 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.76/0.82 fof(f8,axiom,(
% 3.76/0.82 (! [A,B] :( ( empty(A)& relation(B) )=> ( empty(relation_composition(B,A))& relation(relation_composition(B,A)) ) ) )),
% 3.76/0.82 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.76/0.82 fof(f9,axiom,(
% 3.76/0.82 ( empty(empty_set)& relation(empty_set)& relation_empty_yielding(empty_set) ) ),
% 3.76/0.82 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.76/0.82 fof(f17,axiom,(
% 3.76/0.82 (! [A] :( empty(A)=> ( empty(relation_rng(A))& relation(relation_rng(A)) ) ) )),
% 3.76/0.82 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.76/0.82 fof(f18,axiom,(
% 3.76/0.82 (! [A,B] :( ( empty(A)& relation(B) )=> ( empty(relation_composition(A,B))& relation(relation_composition(A,B)) ) ) )),
% 3.76/0.82 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.76/0.82 fof(f19,axiom,(
% 3.76/0.82 (? [A] :( relation(A)& function(A) ) )),
% 3.76/0.82 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.76/0.82 fof(f23,axiom,(
% 3.76/0.82 (? [A] :( relation(A)& empty(A)& function(A) ) )),
% 3.76/0.82 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.76/0.82 fof(f24,axiom,(
% 3.76/0.82 (? [A] :( ~ empty(A)& relation(A) ) )),
% 3.76/0.82 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.76/0.82 fof(f27,axiom,(
% 3.76/0.82 (? [A] :( relation(A)& function(A)& one_to_one(A) ) )),
% 3.76/0.82 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.76/0.82 fof(f28,axiom,(
% 3.76/0.82 (? [A] :( relation(A)& relation_empty_yielding(A) ) )),
% 3.76/0.82 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.76/0.82 fof(f31,axiom,(
% 3.76/0.82 (! [A,B] :( ( relation(B)& function(B) )=> (! [C] :( ( relation(C)& function(C) )=> ( in(A,relation_dom(B))=> apply(relation_composition(B,C),A) = apply(C,apply(B,A)) ) ) )) )),
% 3.76/0.82 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.76/0.82 fof(f35,axiom,(
% 3.76/0.82 (! [A] :( ( relation(A)& function(A) )=> ( one_to_one(A)=> (! [B] :( ( relation(B)& function(B) )=> ( B = function_inverse(A)<=> ( relation_dom(B) = relation_rng(A)& (! [C,D] :( ( ( in(C,relation_rng(A))& D = apply(B,C) )=> ( in(D,relation_dom(A))& C = apply(A,D) ) )& ( ( in(D,relation_dom(A))& C = apply(A,D) )=> ( in(C,relation_rng(A))& D = apply(B,C) ) ) ) )) ) ) )) ) )),
% 3.76/0.82 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.76/0.82 fof(f36,axiom,(
% 3.76/0.82 (! [A] :( ( relation(A)& function(A) )=> ( one_to_one(A)=> ( relation_rng(A) = relation_dom(function_inverse(A))& relation_dom(A) = relation_rng(function_inverse(A)) ) ) ) )),
% 3.76/0.82 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.76/0.82 fof(f37,conjecture,(
% 3.76/0.82 (! [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) ) ) ) )),
% 3.76/0.82 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.76/0.82 fof(f38,negated_conjecture,(
% 3.76/0.82 ~((! [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) ) ) ) ))),
% 3.76/0.82 inference(negated_conjecture,[status(cth)],[f37])).
% 3.76/0.82 fof(f40,axiom,(
% 3.76/0.82 (! [A] :( empty(A)=> A = empty_set ) )),
% 3.76/0.82 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.76/0.82 fof(f41,axiom,(
% 3.76/0.82 (! [A,B] :~ ( in(A,B)& empty(B) ) )),
% 3.76/0.82 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.76/0.82 fof(f45,plain,(
% 3.76/0.82 ![A]: (~empty(A)|function(A))),
% 3.76/0.82 inference(pre_NNF_transformation,[status(esa)],[f2])).
% 3.76/0.82 fof(f46,plain,(
% 3.76/0.82 ![X0]: (~empty(X0)|function(X0))),
% 3.76/0.82 inference(cnf_transformation,[status(esa)],[f45])).
% 3.76/0.82 fof(f53,plain,(
% 3.76/0.82 ![A]: ((~relation(A)|~function(A))|(relation(function_inverse(A))&function(function_inverse(A))))),
% 3.76/0.82 inference(pre_NNF_transformation,[status(esa)],[f5])).
% 3.76/0.82 fof(f54,plain,(
% 3.76/0.82 ![X0]: (~relation(X0)|~function(X0)|relation(function_inverse(X0)))),
% 3.76/0.82 inference(cnf_transformation,[status(esa)],[f53])).
% 3.76/0.82 fof(f55,plain,(
% 3.76/0.82 ![X0]: (~relation(X0)|~function(X0)|function(function_inverse(X0)))),
% 3.76/0.82 inference(cnf_transformation,[status(esa)],[f53])).
% 3.76/0.82 fof(f56,plain,(
% 3.76/0.82 ![A,B]: ((~relation(A)|~relation(B))|relation(relation_composition(A,B)))),
% 3.76/0.82 inference(pre_NNF_transformation,[status(esa)],[f6])).
% 3.76/0.82 fof(f57,plain,(
% 3.76/0.82 ![X0,X1]: (~relation(X0)|~relation(X1)|relation(relation_composition(X0,X1)))),
% 3.76/0.82 inference(cnf_transformation,[status(esa)],[f56])).
% 3.76/0.82 fof(f60,plain,(
% 3.76/0.82 ![A,B]: ((~empty(A)|~relation(B))|(empty(relation_composition(B,A))&relation(relation_composition(B,A))))),
% 3.76/0.82 inference(pre_NNF_transformation,[status(esa)],[f8])).
% 3.76/0.82 fof(f61,plain,(
% 3.76/0.82 ![X0,X1]: (~empty(X0)|~relation(X1)|empty(relation_composition(X1,X0)))),
% 3.76/0.82 inference(cnf_transformation,[status(esa)],[f60])).
% 3.76/0.82 fof(f62,plain,(
% 3.76/0.82 ![X0,X1]: (~empty(X0)|~relation(X1)|relation(relation_composition(X1,X0)))),
% 3.76/0.82 inference(cnf_transformation,[status(esa)],[f60])).
% 3.76/0.82 fof(f63,plain,(
% 3.76/0.82 empty(empty_set)),
% 3.76/0.82 inference(cnf_transformation,[status(esa)],[f9])).
% 3.76/0.82 fof(f64,plain,(
% 3.76/0.82 relation(empty_set)),
% 3.76/0.82 inference(cnf_transformation,[status(esa)],[f9])).
% 3.76/0.82 fof(f80,plain,(
% 3.76/0.82 ![A]: (~empty(A)|(empty(relation_rng(A))&relation(relation_rng(A))))),
% 3.76/0.82 inference(pre_NNF_transformation,[status(esa)],[f17])).
% 3.76/0.82 fof(f81,plain,(
% 3.76/0.82 ![X0]: (~empty(X0)|empty(relation_rng(X0)))),
% 3.76/0.82 inference(cnf_transformation,[status(esa)],[f80])).
% 3.76/0.82 fof(f83,plain,(
% 3.76/0.82 ![A,B]: ((~empty(A)|~relation(B))|(empty(relation_composition(A,B))&relation(relation_composition(A,B))))),
% 3.76/0.82 inference(pre_NNF_transformation,[status(esa)],[f18])).
% 3.76/0.82 fof(f84,plain,(
% 3.76/0.82 ![X0,X1]: (~empty(X0)|~relation(X1)|empty(relation_composition(X0,X1)))),
% 3.76/0.82 inference(cnf_transformation,[status(esa)],[f83])).
% 3.76/0.82 fof(f86,plain,(
% 3.76/0.82 (relation(sk0_1)&function(sk0_1))),
% 3.76/0.82 inference(skolemization,[status(esa)],[f19])).
% 3.76/0.82 fof(f87,plain,(
% 3.76/0.82 relation(sk0_1)),
% 3.76/0.82 inference(cnf_transformation,[status(esa)],[f86])).
% 3.76/0.82 fof(f98,plain,(
% 3.76/0.82 ((relation(sk0_5)&empty(sk0_5))&function(sk0_5))),
% 3.76/0.82 inference(skolemization,[status(esa)],[f23])).
% 3.76/0.82 fof(f100,plain,(
% 3.76/0.82 empty(sk0_5)),
% 3.76/0.82 inference(cnf_transformation,[status(esa)],[f98])).
% 3.76/0.82 fof(f102,plain,(
% 3.76/0.82 (~empty(sk0_6)&relation(sk0_6))),
% 3.76/0.82 inference(skolemization,[status(esa)],[f24])).
% 3.76/0.82 fof(f104,plain,(
% 3.76/0.82 relation(sk0_6)),
% 3.76/0.82 inference(cnf_transformation,[status(esa)],[f102])).
% 3.76/0.82 fof(f110,plain,(
% 3.76/0.82 ((relation(sk0_9)&function(sk0_9))&one_to_one(sk0_9))),
% 3.76/0.82 inference(skolemization,[status(esa)],[f27])).
% 3.76/0.82 fof(f111,plain,(
% 3.76/0.82 relation(sk0_9)),
% 3.76/0.82 inference(cnf_transformation,[status(esa)],[f110])).
% 3.76/0.82 fof(f114,plain,(
% 3.76/0.82 (relation(sk0_10)&relation_empty_yielding(sk0_10))),
% 3.76/0.82 inference(skolemization,[status(esa)],[f28])).
% 3.76/0.82 fof(f115,plain,(
% 3.76/0.82 relation(sk0_10)),
% 3.76/0.82 inference(cnf_transformation,[status(esa)],[f114])).
% 3.76/0.82 fof(f121,plain,(
% 3.76/0.82 ![A,B]: ((~relation(B)|~function(B))|(![C]: ((~relation(C)|~function(C))|(~in(A,relation_dom(B))|apply(relation_composition(B,C),A)=apply(C,apply(B,A))))))),
% 3.76/0.82 inference(pre_NNF_transformation,[status(esa)],[f31])).
% 3.76/0.82 fof(f122,plain,(
% 3.76/0.82 ![B]: ((~relation(B)|~function(B))|(![C]: ((~relation(C)|~function(C))|(![A]: (~in(A,relation_dom(B))|apply(relation_composition(B,C),A)=apply(C,apply(B,A)))))))),
% 3.76/0.82 inference(miniscoping,[status(esa)],[f121])).
% 3.76/0.82 fof(f123,plain,(
% 3.76/0.82 ![X0,X1,X2]: (~relation(X0)|~function(X0)|~relation(X1)|~function(X1)|~in(X2,relation_dom(X0))|apply(relation_composition(X0,X1),X2)=apply(X1,apply(X0,X2)))),
% 3.76/0.82 inference(cnf_transformation,[status(esa)],[f122])).
% 3.76/0.82 fof(f133,plain,(
% 3.76/0.82 ![A]: ((~relation(A)|~function(A))|(~one_to_one(A)|(![B]: ((~relation(B)|~function(B))|(B=function_inverse(A)<=>(relation_dom(B)=relation_rng(A)&(![C,D]: (((~in(C,relation_rng(A))|~D=apply(B,C))|(in(D,relation_dom(A))&C=apply(A,D)))&((~in(D,relation_dom(A))|~C=apply(A,D))|(in(C,relation_rng(A))&D=apply(B,C)))))))))))),
% 3.76/0.82 inference(pre_NNF_transformation,[status(esa)],[f35])).
% 3.76/0.82 fof(f134,plain,(
% 3.76/0.82 ![A,B,C,D]: (pd0_0(D,C,B,A)<=>((~in(C,relation_rng(A))|~D=apply(B,C))|(in(D,relation_dom(A))&C=apply(A,D))))),
% 3.76/0.82 introduced(predicate_definition,[f133])).
% 3.76/0.82 fof(f135,plain,(
% 3.76/0.82 ![A]: ((~relation(A)|~function(A))|(~one_to_one(A)|(![B]: ((~relation(B)|~function(B))|(B=function_inverse(A)<=>(relation_dom(B)=relation_rng(A)&(![C,D]: (pd0_0(D,C,B,A)&((~in(D,relation_dom(A))|~C=apply(A,D))|(in(C,relation_rng(A))&D=apply(B,C)))))))))))),
% 3.76/0.82 inference(formula_renaming,[status(thm)],[f133,f134])).
% 3.76/0.82 fof(f136,plain,(
% 3.76/0.82 ![A]: ((~relation(A)|~function(A))|(~one_to_one(A)|(![B]: ((~relation(B)|~function(B))|((~B=function_inverse(A)|(relation_dom(B)=relation_rng(A)&(![C,D]: (pd0_0(D,C,B,A)&((~in(D,relation_dom(A))|~C=apply(A,D))|(in(C,relation_rng(A))&D=apply(B,C)))))))&(B=function_inverse(A)|(~relation_dom(B)=relation_rng(A)|(?[C,D]: (~pd0_0(D,C,B,A)|((in(D,relation_dom(A))&C=apply(A,D))&(~in(C,relation_rng(A))|~D=apply(B,C))))))))))))),
% 3.76/0.82 inference(NNF_transformation,[status(esa)],[f135])).
% 3.76/0.82 fof(f137,plain,(
% 3.76/0.82 ![A]: ((~relation(A)|~function(A))|(~one_to_one(A)|(![B]: ((~relation(B)|~function(B))|((~B=function_inverse(A)|(relation_dom(B)=relation_rng(A)&((![C,D]: pd0_0(D,C,B,A))&(![C,D]: ((~in(D,relation_dom(A))|~C=apply(A,D))|(in(C,relation_rng(A))&D=apply(B,C)))))))&(B=function_inverse(A)|(~relation_dom(B)=relation_rng(A)|((?[C,D]: ~pd0_0(D,C,B,A))|(?[C,D]: ((in(D,relation_dom(A))&C=apply(A,D))&(~in(C,relation_rng(A))|~D=apply(B,C))))))))))))),
% 3.76/0.82 inference(miniscoping,[status(esa)],[f136])).
% 3.76/0.82 fof(f138,plain,(
% 3.76/0.82 ![A]: ((~relation(A)|~function(A))|(~one_to_one(A)|(![B]: ((~relation(B)|~function(B))|((~B=function_inverse(A)|(relation_dom(B)=relation_rng(A)&((![C,D]: pd0_0(D,C,B,A))&(![C,D]: ((~in(D,relation_dom(A))|~C=apply(A,D))|(in(C,relation_rng(A))&D=apply(B,C)))))))&(B=function_inverse(A)|(~relation_dom(B)=relation_rng(A)|(~pd0_0(sk0_12(B,A),sk0_11(B,A),B,A)|((in(sk0_14(B,A),relation_dom(A))&sk0_13(B,A)=apply(A,sk0_14(B,A)))&(~in(sk0_13(B,A),relation_rng(A))|~sk0_14(B,A)=apply(B,sk0_13(B,A))))))))))))),
% 3.76/0.82 inference(skolemization,[status(esa)],[f137])).
% 3.76/0.82 fof(f140,plain,(
% 3.76/0.82 ![X0,X1,X2,X3]: (~relation(X0)|~function(X0)|~one_to_one(X0)|~relation(X1)|~function(X1)|~X1=function_inverse(X0)|pd0_0(X2,X3,X1,X0))),
% 3.76/0.82 inference(cnf_transformation,[status(esa)],[f138])).
% 3.76/0.82 fof(f146,plain,(
% 3.76/0.82 ![A]: ((~relation(A)|~function(A))|(~one_to_one(A)|(relation_rng(A)=relation_dom(function_inverse(A))&relation_dom(A)=relation_rng(function_inverse(A)))))),
% 3.76/0.82 inference(pre_NNF_transformation,[status(esa)],[f36])).
% 3.76/0.82 fof(f147,plain,(
% 3.76/0.82 ![X0]: (~relation(X0)|~function(X0)|~one_to_one(X0)|relation_rng(X0)=relation_dom(function_inverse(X0)))),
% 3.76/0.82 inference(cnf_transformation,[status(esa)],[f146])).
% 3.76/0.82 fof(f149,plain,(
% 3.76/0.82 (?[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)))))),
% 3.76/0.82 inference(pre_NNF_transformation,[status(esa)],[f38])).
% 3.76/0.82 fof(f150,plain,(
% 3.76/0.82 ?[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)))))),
% 3.76/0.82 inference(miniscoping,[status(esa)],[f149])).
% 3.76/0.82 fof(f151,plain,(
% 3.76/0.82 ((relation(sk0_15)&function(sk0_15))&((one_to_one(sk0_15)&in(sk0_16,relation_rng(sk0_15)))&(~sk0_16=apply(sk0_15,apply(function_inverse(sk0_15),sk0_16))|~sk0_16=apply(relation_composition(function_inverse(sk0_15),sk0_15),sk0_16))))),
% 3.76/0.82 inference(skolemization,[status(esa)],[f150])).
% 3.76/0.82 fof(f152,plain,(
% 3.76/0.82 relation(sk0_15)),
% 3.76/0.82 inference(cnf_transformation,[status(esa)],[f151])).
% 3.76/0.82 fof(f153,plain,(
% 3.76/0.82 function(sk0_15)),
% 3.76/0.82 inference(cnf_transformation,[status(esa)],[f151])).
% 3.76/0.82 fof(f154,plain,(
% 3.76/0.82 one_to_one(sk0_15)),
% 3.76/0.82 inference(cnf_transformation,[status(esa)],[f151])).
% 3.76/0.82 fof(f155,plain,(
% 3.76/0.82 in(sk0_16,relation_rng(sk0_15))),
% 3.76/0.82 inference(cnf_transformation,[status(esa)],[f151])).
% 3.76/0.82 fof(f156,plain,(
% 3.76/0.82 ~sk0_16=apply(sk0_15,apply(function_inverse(sk0_15),sk0_16))|~sk0_16=apply(relation_composition(function_inverse(sk0_15),sk0_15),sk0_16)),
% 3.76/0.82 inference(cnf_transformation,[status(esa)],[f151])).
% 3.76/0.82 fof(f160,plain,(
% 3.76/0.82 ![A]: (~empty(A)|A=empty_set)),
% 3.76/0.82 inference(pre_NNF_transformation,[status(esa)],[f40])).
% 3.76/0.82 fof(f161,plain,(
% 3.76/0.82 ![X0]: (~empty(X0)|X0=empty_set)),
% 3.76/0.82 inference(cnf_transformation,[status(esa)],[f160])).
% 3.76/0.82 fof(f162,plain,(
% 3.76/0.82 ![A,B]: (~in(A,B)|~empty(B))),
% 3.76/0.82 inference(pre_NNF_transformation,[status(esa)],[f41])).
% 3.76/0.82 fof(f163,plain,(
% 3.76/0.82 ![B]: ((![A]: ~in(A,B))|~empty(B))),
% 3.76/0.82 inference(miniscoping,[status(esa)],[f162])).
% 3.76/0.82 fof(f164,plain,(
% 3.76/0.82 ![X0,X1]: (~in(X0,X1)|~empty(X1))),
% 3.76/0.82 inference(cnf_transformation,[status(esa)],[f163])).
% 3.76/0.82 fof(f168,plain,(
% 3.76/0.82 ![A,B,C,D]: ((~pd0_0(D,C,B,A)|((~in(C,relation_rng(A))|~D=apply(B,C))|(in(D,relation_dom(A))&C=apply(A,D))))&(pd0_0(D,C,B,A)|((in(C,relation_rng(A))&D=apply(B,C))&(~in(D,relation_dom(A))|~C=apply(A,D)))))),
% 3.76/0.82 inference(NNF_transformation,[status(esa)],[f134])).
% 3.76/0.82 fof(f169,plain,(
% 3.76/0.82 (![A,B,C,D]: (~pd0_0(D,C,B,A)|((~in(C,relation_rng(A))|~D=apply(B,C))|(in(D,relation_dom(A))&C=apply(A,D)))))&(![A,B,C,D]: (pd0_0(D,C,B,A)|((in(C,relation_rng(A))&D=apply(B,C))&(~in(D,relation_dom(A))|~C=apply(A,D)))))),
% 3.76/0.82 inference(miniscoping,[status(esa)],[f168])).
% 3.76/0.82 fof(f171,plain,(
% 3.76/0.82 ![X0,X1,X2,X3]: (~pd0_0(X0,X1,X2,X3)|~in(X1,relation_rng(X3))|~X0=apply(X2,X1)|X1=apply(X3,X0))),
% 3.76/0.82 inference(cnf_transformation,[status(esa)],[f169])).
% 3.76/0.82 fof(f175,plain,(
% 3.76/0.82 spl0_0 <=> sk0_16=apply(sk0_15,apply(function_inverse(sk0_15),sk0_16))),
% 3.76/0.82 introduced(split_symbol_definition)).
% 3.76/0.82 fof(f176,plain,(
% 3.76/0.82 sk0_16=apply(sk0_15,apply(function_inverse(sk0_15),sk0_16))|~spl0_0),
% 3.76/0.82 inference(component_clause,[status(thm)],[f175])).
% 3.76/0.82 fof(f177,plain,(
% 3.76/0.82 ~sk0_16=apply(sk0_15,apply(function_inverse(sk0_15),sk0_16))|spl0_0),
% 3.76/0.82 inference(component_clause,[status(thm)],[f175])).
% 3.76/0.82 fof(f178,plain,(
% 3.76/0.82 spl0_1 <=> sk0_16=apply(relation_composition(function_inverse(sk0_15),sk0_15),sk0_16)),
% 3.76/0.82 introduced(split_symbol_definition)).
% 3.76/0.82 fof(f180,plain,(
% 3.76/0.82 ~sk0_16=apply(relation_composition(function_inverse(sk0_15),sk0_15),sk0_16)|spl0_1),
% 3.76/0.82 inference(component_clause,[status(thm)],[f178])).
% 3.76/0.82 fof(f181,plain,(
% 3.76/0.82 ~spl0_0|~spl0_1),
% 3.76/0.82 inference(split_clause,[status(thm)],[f156,f175,f178])).
% 3.76/0.82 fof(f183,plain,(
% 3.76/0.82 ![X0,X1,X2]: (~relation(X0)|~function(X0)|~one_to_one(X0)|~relation(function_inverse(X0))|~function(function_inverse(X0))|pd0_0(X1,X2,function_inverse(X0),X0))),
% 3.76/0.82 inference(destructive_equality_resolution,[status(esa)],[f140])).
% 3.76/0.82 fof(f187,plain,(
% 3.76/0.82 ![X0,X1,X2]: (~pd0_0(apply(X0,X1),X1,X0,X2)|~in(X1,relation_rng(X2))|X1=apply(X2,apply(X0,X1)))),
% 3.76/0.82 inference(destructive_equality_resolution,[status(esa)],[f171])).
% 3.76/0.82 fof(f190,plain,(
% 3.76/0.82 spl0_2 <=> function(sk0_15)),
% 3.76/0.82 introduced(split_symbol_definition)).
% 3.76/0.82 fof(f192,plain,(
% 3.76/0.82 ~function(sk0_15)|spl0_2),
% 3.76/0.82 inference(component_clause,[status(thm)],[f190])).
% 3.76/0.82 fof(f193,plain,(
% 3.76/0.82 spl0_3 <=> relation(function_inverse(sk0_15))),
% 3.76/0.82 introduced(split_symbol_definition)).
% 3.76/0.82 fof(f194,plain,(
% 3.76/0.82 relation(function_inverse(sk0_15))|~spl0_3),
% 3.76/0.82 inference(component_clause,[status(thm)],[f193])).
% 3.76/0.82 fof(f196,plain,(
% 3.76/0.82 ~function(sk0_15)|relation(function_inverse(sk0_15))),
% 3.76/0.82 inference(resolution,[status(thm)],[f54,f152])).
% 3.76/0.82 fof(f197,plain,(
% 3.76/0.82 ~spl0_2|spl0_3),
% 3.76/0.82 inference(split_clause,[status(thm)],[f196,f190,f193])).
% 3.76/0.82 fof(f198,plain,(
% 3.76/0.82 $false|spl0_2),
% 3.76/0.82 inference(forward_subsumption_resolution,[status(thm)],[f192,f153])).
% 3.76/0.82 fof(f199,plain,(
% 3.76/0.82 spl0_2),
% 3.76/0.82 inference(contradiction_clause,[status(thm)],[f198])).
% 3.76/0.82 fof(f200,plain,(
% 3.76/0.82 spl0_4 <=> function(function_inverse(sk0_15))),
% 3.76/0.82 introduced(split_symbol_definition)).
% 3.76/0.82 fof(f201,plain,(
% 3.76/0.82 function(function_inverse(sk0_15))|~spl0_4),
% 3.76/0.82 inference(component_clause,[status(thm)],[f200])).
% 3.76/0.82 fof(f203,plain,(
% 3.76/0.82 ~function(sk0_15)|function(function_inverse(sk0_15))),
% 3.76/0.82 inference(resolution,[status(thm)],[f55,f152])).
% 3.76/0.82 fof(f204,plain,(
% 3.76/0.82 ~spl0_2|spl0_4),
% 3.76/0.82 inference(split_clause,[status(thm)],[f203,f190,f200])).
% 3.76/0.82 fof(f206,plain,(
% 3.76/0.82 spl0_5 <=> empty(sk0_15)),
% 3.76/0.82 introduced(split_symbol_definition)).
% 3.76/0.82 fof(f207,plain,(
% 3.76/0.82 empty(sk0_15)|~spl0_5),
% 3.76/0.82 inference(component_clause,[status(thm)],[f206])).
% 3.76/0.82 fof(f209,plain,(
% 3.76/0.82 spl0_6 <=> one_to_one(sk0_15)),
% 3.76/0.82 introduced(split_symbol_definition)).
% 3.76/0.82 fof(f211,plain,(
% 3.76/0.82 ~one_to_one(sk0_15)|spl0_6),
% 3.76/0.82 inference(component_clause,[status(thm)],[f209])).
% 3.76/0.82 fof(f214,plain,(
% 3.76/0.82 ![X0]: (~relation(X0)|relation(relation_composition(sk0_15,X0)))),
% 3.76/0.82 inference(resolution,[status(thm)],[f57,f152])).
% 3.76/0.82 fof(f215,plain,(
% 3.76/0.82 relation(relation_composition(sk0_15,sk0_15))),
% 3.76/0.82 inference(resolution,[status(thm)],[f214,f152])).
% 3.76/0.82 fof(f216,plain,(
% 3.76/0.82 ![X0]: (~relation(X0)|relation(relation_composition(X0,empty_set)))),
% 3.76/0.82 inference(resolution,[status(thm)],[f63,f62])).
% 3.76/0.82 fof(f217,plain,(
% 3.76/0.82 ![X0]: (~relation(X0)|empty(relation_composition(X0,empty_set)))),
% 3.76/0.82 inference(resolution,[status(thm)],[f63,f61])).
% 3.76/0.82 fof(f219,plain,(
% 3.76/0.82 empty(relation_rng(empty_set))),
% 3.76/0.82 inference(resolution,[status(thm)],[f63,f81])).
% 3.76/0.82 fof(f220,plain,(
% 3.76/0.82 ![X0]: (~in(X0,empty_set))),
% 3.76/0.82 inference(resolution,[status(thm)],[f63,f164])).
% 3.76/0.82 fof(f222,plain,(
% 3.76/0.82 relation(relation_composition(sk0_15,empty_set))),
% 3.76/0.82 inference(resolution,[status(thm)],[f64,f214])).
% 3.76/0.82 fof(f778,plain,(
% 3.76/0.82 ![X0]: (~relation(X0)|empty(relation_composition(sk0_5,X0)))),
% 3.76/0.82 inference(resolution,[status(thm)],[f84,f100])).
% 3.76/0.82 fof(f816,plain,(
% 3.76/0.82 relation(relation_composition(sk0_15,sk0_9))),
% 3.76/0.82 inference(resolution,[status(thm)],[f111,f214])).
% 3.76/0.82 fof(f893,plain,(
% 3.76/0.82 sk0_5=empty_set),
% 3.76/0.82 inference(resolution,[status(thm)],[f161,f100])).
% 3.76/0.82 fof(f1184,plain,(
% 3.76/0.82 spl0_157 <=> function(relation_composition(empty_set,sk0_10))),
% 3.76/0.82 introduced(split_symbol_definition)).
% 3.76/0.82 fof(f1186,plain,(
% 3.76/0.82 ~function(relation_composition(empty_set,sk0_10))|spl0_157),
% 3.76/0.82 inference(component_clause,[status(thm)],[f1184])).
% 3.76/0.82 fof(f1194,plain,(
% 3.76/0.82 spl0_159 <=> function(relation_composition(empty_set,sk0_6))),
% 3.76/0.82 introduced(split_symbol_definition)).
% 3.76/0.82 fof(f1196,plain,(
% 3.76/0.82 ~function(relation_composition(empty_set,sk0_6))|spl0_159),
% 3.76/0.82 inference(component_clause,[status(thm)],[f1194])).
% 3.76/0.82 fof(f1935,plain,(
% 3.76/0.82 relation_rng(empty_set)=empty_set),
% 3.76/0.82 inference(resolution,[status(thm)],[f219,f161])).
% 3.76/0.82 fof(f2254,plain,(
% 3.76/0.82 spl0_344 <=> ~relation(X0)|~function(X0)|~in(X1,relation_dom(X0))|apply(relation_composition(X0,sk0_15),X1)=apply(sk0_15,apply(X0,X1))),
% 3.76/0.82 introduced(split_symbol_definition)).
% 3.76/0.82 fof(f2255,plain,(
% 3.76/0.82 ![X0,X1]: (~relation(X0)|~function(X0)|~in(X1,relation_dom(X0))|apply(relation_composition(X0,sk0_15),X1)=apply(sk0_15,apply(X0,X1))|~spl0_344)),
% 3.76/0.82 inference(component_clause,[status(thm)],[f2254])).
% 3.76/0.82 fof(f2257,plain,(
% 3.76/0.82 ![X0,X1]: (~relation(X0)|~function(X0)|~function(sk0_15)|~in(X1,relation_dom(X0))|apply(relation_composition(X0,sk0_15),X1)=apply(sk0_15,apply(X0,X1)))),
% 3.76/0.82 inference(resolution,[status(thm)],[f123,f152])).
% 3.76/0.82 fof(f2258,plain,(
% 3.76/0.82 spl0_344|~spl0_2),
% 3.76/0.82 inference(split_clause,[status(thm)],[f2257,f2254,f190])).
% 3.76/0.82 fof(f2459,plain,(
% 3.76/0.82 spl0_375 <=> ~in(X0,relation_dom(function_inverse(sk0_15)))|apply(relation_composition(function_inverse(sk0_15),sk0_15),X0)=apply(sk0_15,apply(function_inverse(sk0_15),X0))),
% 3.76/0.82 introduced(split_symbol_definition)).
% 3.76/0.82 fof(f2460,plain,(
% 3.76/0.82 ![X0]: (~in(X0,relation_dom(function_inverse(sk0_15)))|apply(relation_composition(function_inverse(sk0_15),sk0_15),X0)=apply(sk0_15,apply(function_inverse(sk0_15),X0))|~spl0_375)),
% 3.76/0.82 inference(component_clause,[status(thm)],[f2459])).
% 3.76/0.82 fof(f2462,plain,(
% 3.76/0.82 ![X0]: (~function(function_inverse(sk0_15))|~in(X0,relation_dom(function_inverse(sk0_15)))|apply(relation_composition(function_inverse(sk0_15),sk0_15),X0)=apply(sk0_15,apply(function_inverse(sk0_15),X0))|~spl0_344|~spl0_3)),
% 3.76/0.82 inference(resolution,[status(thm)],[f2255,f194])).
% 3.76/0.82 fof(f2463,plain,(
% 3.76/0.82 ~spl0_4|spl0_375|~spl0_344|~spl0_3),
% 3.76/0.82 inference(split_clause,[status(thm)],[f2462,f200,f2459,f2254,f193])).
% 3.76/0.82 fof(f3368,plain,(
% 3.76/0.82 spl0_536 <=> relation(sk0_15)),
% 3.76/0.82 introduced(split_symbol_definition)).
% 3.76/0.82 fof(f3370,plain,(
% 3.76/0.82 ~relation(sk0_15)|spl0_536),
% 3.76/0.82 inference(component_clause,[status(thm)],[f3368])).
% 3.76/0.82 fof(f3371,plain,(
% 3.76/0.82 spl0_537 <=> relation_dom(function_inverse(sk0_15))=relation_rng(sk0_15)),
% 3.76/0.82 introduced(split_symbol_definition)).
% 3.76/0.82 fof(f3372,plain,(
% 3.76/0.82 relation_dom(function_inverse(sk0_15))=relation_rng(sk0_15)|~spl0_537),
% 3.76/0.82 inference(component_clause,[status(thm)],[f3371])).
% 3.76/0.82 fof(f3378,plain,(
% 3.76/0.82 $false|spl0_536),
% 3.76/0.82 inference(forward_subsumption_resolution,[status(thm)],[f3370,f152])).
% 3.76/0.82 fof(f3379,plain,(
% 3.76/0.82 spl0_536),
% 3.76/0.82 inference(contradiction_clause,[status(thm)],[f3378])).
% 3.76/0.82 fof(f3440,plain,(
% 3.76/0.82 $false|spl0_6),
% 3.76/0.82 inference(forward_subsumption_resolution,[status(thm)],[f211,f154])).
% 3.76/0.82 fof(f3441,plain,(
% 3.76/0.82 spl0_6),
% 3.76/0.82 inference(contradiction_clause,[status(thm)],[f3440])).
% 3.76/0.82 fof(f4082,plain,(
% 3.76/0.82 relation(relation_composition(sk0_10,empty_set))),
% 3.76/0.82 inference(resolution,[status(thm)],[f216,f115])).
% 3.76/0.82 fof(f4083,plain,(
% 3.76/0.82 relation(relation_composition(sk0_9,empty_set))),
% 3.76/0.82 inference(resolution,[status(thm)],[f216,f111])).
% 3.76/0.82 fof(f4084,plain,(
% 3.76/0.82 relation(relation_composition(sk0_6,empty_set))),
% 3.76/0.82 inference(resolution,[status(thm)],[f216,f104])).
% 3.76/0.82 fof(f4108,plain,(
% 3.76/0.82 relation(relation_composition(sk0_1,empty_set))),
% 3.76/0.82 inference(resolution,[status(thm)],[f216,f87])).
% 3.76/0.82 fof(f4109,plain,(
% 3.76/0.82 relation(relation_composition(empty_set,empty_set))),
% 3.76/0.82 inference(resolution,[status(thm)],[f216,f64])).
% 3.76/0.82 fof(f4167,plain,(
% 3.76/0.82 ~relation(sk0_15)|~function(sk0_15)|relation_rng(sk0_15)=relation_dom(function_inverse(sk0_15))),
% 3.76/0.82 inference(resolution,[status(thm)],[f147,f154])).
% 3.76/0.82 fof(f4168,plain,(
% 3.76/0.82 ~spl0_536|~spl0_2|spl0_537),
% 3.76/0.82 inference(split_clause,[status(thm)],[f4167,f3368,f190,f3371])).
% 3.76/0.82 fof(f4185,plain,(
% 3.76/0.82 spl0_657 <=> function(relation_composition(sk0_10,empty_set))),
% 3.76/0.82 introduced(split_symbol_definition)).
% 3.76/0.82 fof(f4187,plain,(
% 3.76/0.82 ~function(relation_composition(sk0_10,empty_set))|spl0_657),
% 3.76/0.82 inference(component_clause,[status(thm)],[f4185])).
% 3.76/0.82 fof(f4356,plain,(
% 3.76/0.82 spl0_688 <=> function(relation_composition(sk0_6,empty_set))),
% 3.76/0.82 introduced(split_symbol_definition)).
% 3.76/0.82 fof(f4358,plain,(
% 3.76/0.82 ~function(relation_composition(sk0_6,empty_set))|spl0_688),
% 3.76/0.82 inference(component_clause,[status(thm)],[f4356])).
% 3.76/0.82 fof(f4616,plain,(
% 3.76/0.82 ![X0,X1,X2]: (~relation(X0)|~function(X0)|~one_to_one(X0)|~function(function_inverse(X0))|pd0_0(X1,X2,function_inverse(X0),X0))),
% 3.76/0.82 inference(forward_subsumption_resolution,[status(thm)],[f183,f54])).
% 3.76/0.82 fof(f4662,plain,(
% 3.76/0.82 spl0_743 <=> pd0_0(X0,X1,function_inverse(sk0_15),sk0_15)),
% 3.76/0.82 introduced(split_symbol_definition)).
% 3.76/0.82 fof(f4663,plain,(
% 3.76/0.82 ![X0,X1]: (pd0_0(X0,X1,function_inverse(sk0_15),sk0_15)|~spl0_743)),
% 3.76/0.82 inference(component_clause,[status(thm)],[f4662])).
% 3.76/0.82 fof(f4665,plain,(
% 3.76/0.82 ![X0,X1]: (~relation(sk0_15)|~function(sk0_15)|~one_to_one(sk0_15)|pd0_0(X0,X1,function_inverse(sk0_15),sk0_15)|~spl0_4)),
% 3.76/0.82 inference(resolution,[status(thm)],[f4616,f201])).
% 3.76/0.82 fof(f4666,plain,(
% 3.76/0.82 ~spl0_536|~spl0_2|~spl0_6|spl0_743|~spl0_4),
% 3.76/0.82 inference(split_clause,[status(thm)],[f4665,f3368,f190,f209,f4662,f200])).
% 3.76/0.82 fof(f4695,plain,(
% 3.76/0.82 sk0_15=empty_set|~spl0_5),
% 3.76/0.82 inference(resolution,[status(thm)],[f207,f161])).
% 3.76/0.82 fof(f4744,plain,(
% 3.76/0.82 in(sk0_16,relation_rng(empty_set))|~spl0_5),
% 3.76/0.82 inference(backward_demodulation,[status(thm)],[f4695,f155])).
% 3.76/0.82 fof(f4745,plain,(
% 3.76/0.82 in(sk0_16,empty_set)|~spl0_5),
% 3.76/0.82 inference(forward_demodulation,[status(thm)],[f1935,f4744])).
% 3.76/0.82 fof(f4746,plain,(
% 3.76/0.82 $false|~spl0_5),
% 3.76/0.82 inference(forward_subsumption_resolution,[status(thm)],[f4745,f220])).
% 3.76/0.82 fof(f4747,plain,(
% 3.76/0.82 ~spl0_5),
% 3.76/0.82 inference(contradiction_clause,[status(thm)],[f4746])).
% 3.76/0.82 fof(f5159,plain,(
% 3.76/0.82 empty(relation_composition(sk0_10,empty_set))),
% 3.76/0.82 inference(resolution,[status(thm)],[f217,f115])).
% 3.76/0.82 fof(f5161,plain,(
% 3.76/0.82 empty(relation_composition(sk0_6,empty_set))),
% 3.76/0.82 inference(resolution,[status(thm)],[f217,f104])).
% 3.76/0.82 fof(f5225,plain,(
% 3.76/0.82 function(relation_composition(sk0_10,empty_set))),
% 3.76/0.82 inference(resolution,[status(thm)],[f5159,f46])).
% 3.76/0.82 fof(f5226,plain,(
% 3.76/0.82 $false|spl0_657),
% 3.76/0.82 inference(forward_subsumption_resolution,[status(thm)],[f5225,f4187])).
% 3.76/0.82 fof(f5227,plain,(
% 3.76/0.82 spl0_657),
% 3.76/0.82 inference(contradiction_clause,[status(thm)],[f5226])).
% 3.76/0.82 fof(f5255,plain,(
% 3.76/0.82 function(relation_composition(sk0_6,empty_set))),
% 3.76/0.82 inference(resolution,[status(thm)],[f5161,f46])).
% 3.76/0.82 fof(f5256,plain,(
% 3.76/0.82 $false|spl0_688),
% 3.76/0.82 inference(forward_subsumption_resolution,[status(thm)],[f5255,f4358])).
% 3.76/0.82 fof(f5257,plain,(
% 3.76/0.82 spl0_688),
% 3.76/0.82 inference(contradiction_clause,[status(thm)],[f5256])).
% 3.76/0.82 fof(f5285,plain,(
% 3.76/0.82 spl0_750 <=> relation(relation_composition(sk0_15,empty_set))),
% 3.76/0.82 introduced(split_symbol_definition)).
% 3.76/0.82 fof(f5287,plain,(
% 3.76/0.82 ~relation(relation_composition(sk0_15,empty_set))|spl0_750),
% 3.76/0.82 inference(component_clause,[status(thm)],[f5285])).
% 3.76/0.82 fof(f5298,plain,(
% 3.76/0.82 $false|spl0_750),
% 3.76/0.82 inference(forward_subsumption_resolution,[status(thm)],[f5287,f222])).
% 3.76/0.82 fof(f5299,plain,(
% 3.76/0.82 spl0_750),
% 3.76/0.82 inference(contradiction_clause,[status(thm)],[f5298])).
% 3.76/0.82 fof(f5303,plain,(
% 3.76/0.82 spl0_753 <=> relation(relation_composition(sk0_10,empty_set))),
% 3.76/0.82 introduced(split_symbol_definition)).
% 3.76/0.82 fof(f5305,plain,(
% 3.76/0.82 ~relation(relation_composition(sk0_10,empty_set))|spl0_753),
% 3.76/0.82 inference(component_clause,[status(thm)],[f5303])).
% 3.76/0.82 fof(f5316,plain,(
% 3.76/0.82 $false|spl0_753),
% 3.76/0.82 inference(forward_subsumption_resolution,[status(thm)],[f5305,f4082])).
% 3.76/0.82 fof(f5317,plain,(
% 3.76/0.82 spl0_753),
% 3.76/0.82 inference(contradiction_clause,[status(thm)],[f5316])).
% 3.76/0.82 fof(f5321,plain,(
% 3.76/0.82 spl0_756 <=> relation(relation_composition(sk0_9,empty_set))),
% 3.76/0.82 introduced(split_symbol_definition)).
% 3.76/0.82 fof(f5323,plain,(
% 3.76/0.82 ~relation(relation_composition(sk0_9,empty_set))|spl0_756),
% 3.76/0.82 inference(component_clause,[status(thm)],[f5321])).
% 3.76/0.82 fof(f5334,plain,(
% 3.76/0.82 $false|spl0_756),
% 3.76/0.82 inference(forward_subsumption_resolution,[status(thm)],[f5323,f4083])).
% 3.76/0.82 fof(f5335,plain,(
% 3.76/0.82 spl0_756),
% 3.76/0.82 inference(contradiction_clause,[status(thm)],[f5334])).
% 3.76/0.82 fof(f5339,plain,(
% 3.76/0.82 spl0_759 <=> relation(relation_composition(sk0_6,empty_set))),
% 3.76/0.82 introduced(split_symbol_definition)).
% 3.76/0.82 fof(f5341,plain,(
% 3.76/0.82 ~relation(relation_composition(sk0_6,empty_set))|spl0_759),
% 3.76/0.82 inference(component_clause,[status(thm)],[f5339])).
% 3.76/0.82 fof(f5352,plain,(
% 3.76/0.82 $false|spl0_759),
% 3.76/0.82 inference(forward_subsumption_resolution,[status(thm)],[f5341,f4084])).
% 3.76/0.82 fof(f5353,plain,(
% 3.76/0.82 spl0_759),
% 3.76/0.82 inference(contradiction_clause,[status(thm)],[f5352])).
% 3.76/0.82 fof(f6302,plain,(
% 3.76/0.82 spl0_929 <=> relation(relation_composition(sk0_1,empty_set))),
% 3.76/0.82 introduced(split_symbol_definition)).
% 3.76/0.82 fof(f6304,plain,(
% 3.76/0.82 ~relation(relation_composition(sk0_1,empty_set))|spl0_929),
% 3.76/0.82 inference(component_clause,[status(thm)],[f6302])).
% 3.76/0.82 fof(f6315,plain,(
% 3.76/0.82 $false|spl0_929),
% 3.76/0.82 inference(forward_subsumption_resolution,[status(thm)],[f6304,f4108])).
% 3.76/0.82 fof(f6316,plain,(
% 3.76/0.82 spl0_929),
% 3.76/0.82 inference(contradiction_clause,[status(thm)],[f6315])).
% 3.76/0.82 fof(f6320,plain,(
% 3.76/0.82 spl0_932 <=> relation(relation_composition(empty_set,empty_set))),
% 3.76/0.82 introduced(split_symbol_definition)).
% 3.76/0.82 fof(f6322,plain,(
% 3.76/0.82 ~relation(relation_composition(empty_set,empty_set))|spl0_932),
% 3.76/0.82 inference(component_clause,[status(thm)],[f6320])).
% 3.76/0.82 fof(f6333,plain,(
% 3.76/0.82 $false|spl0_932),
% 3.76/0.82 inference(forward_subsumption_resolution,[status(thm)],[f6322,f4109])).
% 3.76/0.82 fof(f6334,plain,(
% 3.76/0.82 spl0_932),
% 3.76/0.82 inference(contradiction_clause,[status(thm)],[f6333])).
% 3.76/0.82 fof(f6739,plain,(
% 3.76/0.82 ![X0]: (~relation(X0)|empty(relation_composition(empty_set,X0)))),
% 3.76/0.82 inference(forward_demodulation,[status(thm)],[f893,f778])).
% 3.76/0.82 fof(f6741,plain,(
% 3.76/0.82 empty(relation_composition(empty_set,sk0_10))),
% 3.76/0.82 inference(resolution,[status(thm)],[f6739,f115])).
% 3.76/0.82 fof(f6743,plain,(
% 3.76/0.82 empty(relation_composition(empty_set,sk0_6))),
% 3.76/0.82 inference(resolution,[status(thm)],[f6739,f104])).
% 3.76/0.82 fof(f6801,plain,(
% 3.76/0.82 function(relation_composition(empty_set,sk0_10))),
% 3.76/0.82 inference(resolution,[status(thm)],[f6741,f46])).
% 3.76/0.82 fof(f6802,plain,(
% 3.76/0.82 $false|spl0_157),
% 3.76/0.82 inference(forward_subsumption_resolution,[status(thm)],[f6801,f1186])).
% 3.76/0.82 fof(f6803,plain,(
% 3.76/0.82 spl0_157),
% 3.76/0.82 inference(contradiction_clause,[status(thm)],[f6802])).
% 3.76/0.82 fof(f6804,plain,(
% 3.76/0.82 ![X0]: (~pd0_0(apply(X0,sk0_16),sk0_16,X0,sk0_15)|sk0_16=apply(sk0_15,apply(X0,sk0_16)))),
% 3.76/0.82 inference(resolution,[status(thm)],[f187,f155])).
% 3.76/0.82 fof(f7375,plain,(
% 3.76/0.82 spl0_1096 <=> relation(relation_composition(sk0_15,sk0_15))),
% 3.76/0.82 introduced(split_symbol_definition)).
% 3.76/0.82 fof(f7377,plain,(
% 3.76/0.82 ~relation(relation_composition(sk0_15,sk0_15))|spl0_1096),
% 3.76/0.82 inference(component_clause,[status(thm)],[f7375])).
% 3.76/0.82 fof(f7396,plain,(
% 3.76/0.82 $false|spl0_1096),
% 3.76/0.82 inference(forward_subsumption_resolution,[status(thm)],[f7377,f215])).
% 3.76/0.82 fof(f7397,plain,(
% 3.76/0.82 spl0_1096),
% 3.76/0.82 inference(contradiction_clause,[status(thm)],[f7396])).
% 3.76/0.82 fof(f7528,plain,(
% 3.76/0.82 function(relation_composition(empty_set,sk0_6))),
% 3.76/0.82 inference(resolution,[status(thm)],[f6743,f46])).
% 3.76/0.82 fof(f7529,plain,(
% 3.76/0.82 $false|spl0_159),
% 3.76/0.84 inference(forward_subsumption_resolution,[status(thm)],[f7528,f1196])).
% 3.76/0.84 fof(f7530,plain,(
% 3.76/0.84 spl0_159),
% 3.76/0.84 inference(contradiction_clause,[status(thm)],[f7529])).
% 3.76/0.84 fof(f9384,plain,(
% 3.76/0.84 spl0_1401 <=> relation(relation_composition(sk0_15,sk0_9))),
% 3.76/0.84 introduced(split_symbol_definition)).
% 3.76/0.84 fof(f9386,plain,(
% 3.76/0.84 ~relation(relation_composition(sk0_15,sk0_9))|spl0_1401),
% 3.76/0.84 inference(component_clause,[status(thm)],[f9384])).
% 3.76/0.84 fof(f9405,plain,(
% 3.76/0.84 $false|spl0_1401),
% 3.76/0.84 inference(forward_subsumption_resolution,[status(thm)],[f9386,f816])).
% 3.76/0.84 fof(f9406,plain,(
% 3.76/0.84 spl0_1401),
% 3.76/0.84 inference(contradiction_clause,[status(thm)],[f9405])).
% 3.76/0.84 fof(f10843,plain,(
% 3.76/0.84 sk0_16=apply(sk0_15,apply(function_inverse(sk0_15),sk0_16))|~spl0_743),
% 3.76/0.84 inference(resolution,[status(thm)],[f4663,f6804])).
% 3.76/0.84 fof(f10844,plain,(
% 3.76/0.84 $false|spl0_0|~spl0_743),
% 3.76/0.84 inference(forward_subsumption_resolution,[status(thm)],[f10843,f177])).
% 3.76/0.84 fof(f10845,plain,(
% 3.76/0.84 spl0_0|~spl0_743),
% 3.76/0.84 inference(contradiction_clause,[status(thm)],[f10844])).
% 3.76/0.84 fof(f11103,plain,(
% 3.76/0.84 ![X0]: (~in(X0,relation_rng(sk0_15))|apply(relation_composition(function_inverse(sk0_15),sk0_15),X0)=apply(sk0_15,apply(function_inverse(sk0_15),X0))|~spl0_537|~spl0_375)),
% 3.76/0.84 inference(forward_demodulation,[status(thm)],[f3372,f2460])).
% 3.76/0.84 fof(f11104,plain,(
% 3.76/0.84 apply(relation_composition(function_inverse(sk0_15),sk0_15),sk0_16)=apply(sk0_15,apply(function_inverse(sk0_15),sk0_16))|~spl0_537|~spl0_375),
% 3.76/0.84 inference(resolution,[status(thm)],[f11103,f155])).
% 3.76/0.84 fof(f11105,plain,(
% 3.76/0.84 apply(relation_composition(function_inverse(sk0_15),sk0_15),sk0_16)=sk0_16|~spl0_0|~spl0_537|~spl0_375),
% 3.76/0.84 inference(forward_demodulation,[status(thm)],[f176,f11104])).
% 3.76/0.84 fof(f11106,plain,(
% 3.76/0.84 $false|spl0_1|~spl0_0|~spl0_537|~spl0_375),
% 3.76/0.84 inference(forward_subsumption_resolution,[status(thm)],[f11105,f180])).
% 3.76/0.84 fof(f11107,plain,(
% 3.76/0.84 spl0_1|~spl0_0|~spl0_537|~spl0_375),
% 3.76/0.84 inference(contradiction_clause,[status(thm)],[f11106])).
% 3.76/0.84 fof(f11108,plain,(
% 3.76/0.84 $false),
% 3.76/0.84 inference(sat_refutation,[status(thm)],[f181,f197,f199,f204,f2258,f2463,f3379,f3441,f4168,f4666,f4747,f5227,f5257,f5299,f5317,f5335,f5353,f6316,f6334,f6803,f7397,f7530,f9406,f10845,f11107])).
% 3.76/0.84 % SZS output end CNFRefutation for theBenchmark.p
% 3.76/0.84 % Elapsed time: 0.506112 seconds
% 3.76/0.84 % CPU time: 3.880336 seconds
% 3.76/0.84 % Memory used: 97.591 MB
%------------------------------------------------------------------------------