TSTP Solution File: SEU012+1 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SEU012+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n021.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 20:40:53 EDT 2024
% Result : Theorem 3.38s 0.86s
% Output : CNFRefutation 3.38s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU012+1 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.14 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.35 % Computer : n021.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 19:51:10 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.36 % Drodi V3.6.0
% 3.38/0.86 % Refutation found
% 3.38/0.86 % SZS status Theorem for theBenchmark: Theorem is valid
% 3.38/0.86 % SZS output start CNFRefutation for theBenchmark
% 3.38/0.86 fof(f2,axiom,(
% 3.38/0.86 (! [A] :( empty(A)=> function(A) ) )),
% 3.38/0.86 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.38/0.86 fof(f3,axiom,(
% 3.38/0.86 (! [A] :( empty(A)=> relation(A) ) )),
% 3.38/0.86 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.38/0.86 fof(f4,axiom,(
% 3.38/0.86 (! [A] :( ( relation(A)& function(A) )=> (! [B] :( B = relation_rng(A)<=> (! [C] :( in(C,B)<=> (? [D] :( in(D,relation_dom(A))& C = apply(A,D) ) )) )) )) )),
% 3.38/0.86 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.38/0.86 fof(f6,axiom,(
% 3.38/0.86 (! [A] : relation(identity_relation(A)) )),
% 3.38/0.86 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.38/0.86 fof(f8,axiom,(
% 3.38/0.86 (! [A,B] :( ( empty(A)& relation(B) )=> ( empty(relation_composition(B,A))& relation(relation_composition(B,A)) ) ) )),
% 3.38/0.86 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.38/0.86 fof(f9,axiom,(
% 3.38/0.86 ( empty(empty_set)& relation(empty_set)& relation_empty_yielding(empty_set) ) ),
% 3.38/0.86 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.38/0.86 fof(f13,axiom,(
% 3.38/0.86 (! [A] :( relation(identity_relation(A))& function(identity_relation(A)) ) )),
% 3.38/0.86 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.38/0.86 fof(f17,axiom,(
% 3.38/0.86 (! [A] :( empty(A)=> ( empty(relation_dom(A))& relation(relation_dom(A)) ) ) )),
% 3.38/0.86 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.38/0.86 fof(f20,axiom,(
% 3.38/0.86 (? [A] :( relation(A)& function(A) ) )),
% 3.38/0.86 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.38/0.86 fof(f21,axiom,(
% 3.38/0.86 (? [A] :( empty(A)& relation(A) ) )),
% 3.38/0.86 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.38/0.86 fof(f23,axiom,(
% 3.38/0.86 (? [A] : empty(A) )),
% 3.38/0.86 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.38/0.86 fof(f24,axiom,(
% 3.38/0.86 (? [A] :( ~ empty(A)& relation(A) ) )),
% 3.38/0.86 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.38/0.86 fof(f25,axiom,(
% 3.38/0.86 (! [A] :(? [B] :( element(B,powerset(A))& empty(B) ) ))),
% 3.38/0.86 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.38/0.86 fof(f27,axiom,(
% 3.38/0.86 (? [A] :( relation(A)& relation_empty_yielding(A) ) )),
% 3.38/0.86 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.38/0.86 fof(f30,axiom,(
% 3.38/0.86 (! [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)) ) ) )) )),
% 3.38/0.86 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.38/0.86 fof(f32,axiom,(
% 3.38/0.86 (! [A,B] :( ( relation(B)& function(B) )=> ( B = identity_relation(A)<=> ( relation_dom(B) = A& (! [C] :( in(C,A)=> apply(B,C) = C ) )) ) ) )),
% 3.38/0.86 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.38/0.86 fof(f34,conjecture,(
% 3.38/0.86 (! [A] :( ( relation(A)& function(A) )=> (! [B] :( ( relation(B)& function(B) )=> ( ( relation_rng(A) = relation_dom(B)& relation_composition(A,B) = A )=> B = identity_relation(relation_dom(B)) ) ) )) )),
% 3.38/0.86 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.38/0.86 fof(f35,negated_conjecture,(
% 3.38/0.86 ~((! [A] :( ( relation(A)& function(A) )=> (! [B] :( ( relation(B)& function(B) )=> ( ( relation_rng(A) = relation_dom(B)& relation_composition(A,B) = A )=> B = identity_relation(relation_dom(B)) ) ) )) ))),
% 3.38/0.86 inference(negated_conjecture,[status(cth)],[f34])).
% 3.38/0.86 fof(f38,axiom,(
% 3.38/0.86 (! [A] :( empty(A)=> A = empty_set ) )),
% 3.38/0.86 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.38/0.86 fof(f39,axiom,(
% 3.38/0.86 (! [A,B] :~ ( in(A,B)& empty(B) ) )),
% 3.38/0.86 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.38/0.86 fof(f43,plain,(
% 3.38/0.86 ![A]: (~empty(A)|function(A))),
% 3.38/0.86 inference(pre_NNF_transformation,[status(esa)],[f2])).
% 3.38/0.86 fof(f44,plain,(
% 3.38/0.86 ![X0]: (~empty(X0)|function(X0))),
% 3.38/0.86 inference(cnf_transformation,[status(esa)],[f43])).
% 3.38/0.86 fof(f45,plain,(
% 3.38/0.86 ![A]: (~empty(A)|relation(A))),
% 3.38/0.86 inference(pre_NNF_transformation,[status(esa)],[f3])).
% 3.38/0.86 fof(f46,plain,(
% 3.38/0.86 ![X0]: (~empty(X0)|relation(X0))),
% 3.38/0.86 inference(cnf_transformation,[status(esa)],[f45])).
% 3.38/0.86 fof(f47,plain,(
% 3.38/0.86 ![A]: ((~relation(A)|~function(A))|(![B]: (B=relation_rng(A)<=>(![C]: (in(C,B)<=>(?[D]: (in(D,relation_dom(A))&C=apply(A,D))))))))),
% 3.38/0.86 inference(pre_NNF_transformation,[status(esa)],[f4])).
% 3.38/0.86 fof(f48,plain,(
% 3.38/0.86 ![A]: ((~relation(A)|~function(A))|(![B]: ((~B=relation_rng(A)|(![C]: ((~in(C,B)|(?[D]: (in(D,relation_dom(A))&C=apply(A,D))))&(in(C,B)|(![D]: (~in(D,relation_dom(A))|~C=apply(A,D)))))))&(B=relation_rng(A)|(?[C]: ((~in(C,B)|(![D]: (~in(D,relation_dom(A))|~C=apply(A,D))))&(in(C,B)|(?[D]: (in(D,relation_dom(A))&C=apply(A,D))))))))))),
% 3.38/0.86 inference(NNF_transformation,[status(esa)],[f47])).
% 3.38/0.86 fof(f49,plain,(
% 3.38/0.86 ![A]: ((~relation(A)|~function(A))|((![B]: (~B=relation_rng(A)|((![C]: (~in(C,B)|(?[D]: (in(D,relation_dom(A))&C=apply(A,D)))))&(![C]: (in(C,B)|(![D]: (~in(D,relation_dom(A))|~C=apply(A,D))))))))&(![B]: (B=relation_rng(A)|(?[C]: ((~in(C,B)|(![D]: (~in(D,relation_dom(A))|~C=apply(A,D))))&(in(C,B)|(?[D]: (in(D,relation_dom(A))&C=apply(A,D))))))))))),
% 3.38/0.86 inference(miniscoping,[status(esa)],[f48])).
% 3.38/0.86 fof(f50,plain,(
% 3.38/0.86 ![A]: ((~relation(A)|~function(A))|((![B]: (~B=relation_rng(A)|((![C]: (~in(C,B)|(in(sk0_0(C,B,A),relation_dom(A))&C=apply(A,sk0_0(C,B,A)))))&(![C]: (in(C,B)|(![D]: (~in(D,relation_dom(A))|~C=apply(A,D))))))))&(![B]: (B=relation_rng(A)|((~in(sk0_1(B,A),B)|(![D]: (~in(D,relation_dom(A))|~sk0_1(B,A)=apply(A,D))))&(in(sk0_1(B,A),B)|(in(sk0_2(B,A),relation_dom(A))&sk0_1(B,A)=apply(A,sk0_2(B,A)))))))))),
% 3.38/0.86 inference(skolemization,[status(esa)],[f49])).
% 3.38/0.86 fof(f51,plain,(
% 3.38/0.86 ![X0,X1,X2]: (~relation(X0)|~function(X0)|~X1=relation_rng(X0)|~in(X2,X1)|in(sk0_0(X2,X1,X0),relation_dom(X0)))),
% 3.38/0.86 inference(cnf_transformation,[status(esa)],[f50])).
% 3.38/0.86 fof(f52,plain,(
% 3.38/0.86 ![X0,X1,X2]: (~relation(X0)|~function(X0)|~X1=relation_rng(X0)|~in(X2,X1)|X2=apply(X0,sk0_0(X2,X1,X0)))),
% 3.38/0.86 inference(cnf_transformation,[status(esa)],[f50])).
% 3.38/0.86 fof(f59,plain,(
% 3.38/0.86 ![X0]: (relation(identity_relation(X0)))),
% 3.38/0.86 inference(cnf_transformation,[status(esa)],[f6])).
% 3.38/0.86 fof(f62,plain,(
% 3.38/0.86 ![A,B]: ((~empty(A)|~relation(B))|(empty(relation_composition(B,A))&relation(relation_composition(B,A))))),
% 3.38/0.86 inference(pre_NNF_transformation,[status(esa)],[f8])).
% 3.38/0.86 fof(f64,plain,(
% 3.38/0.86 ![X0,X1]: (~empty(X0)|~relation(X1)|relation(relation_composition(X1,X0)))),
% 3.38/0.86 inference(cnf_transformation,[status(esa)],[f62])).
% 3.38/0.86 fof(f65,plain,(
% 3.38/0.86 empty(empty_set)),
% 3.38/0.86 inference(cnf_transformation,[status(esa)],[f9])).
% 3.38/0.86 fof(f73,plain,(
% 3.38/0.86 (![A]: relation(identity_relation(A)))&(![A]: function(identity_relation(A)))),
% 3.38/0.86 inference(miniscoping,[status(esa)],[f13])).
% 3.38/0.86 fof(f75,plain,(
% 3.38/0.86 ![X0]: (function(identity_relation(X0)))),
% 3.38/0.86 inference(cnf_transformation,[status(esa)],[f73])).
% 3.38/0.86 fof(f82,plain,(
% 3.38/0.86 ![A]: (~empty(A)|(empty(relation_dom(A))&relation(relation_dom(A))))),
% 3.38/0.86 inference(pre_NNF_transformation,[status(esa)],[f17])).
% 3.38/0.86 fof(f83,plain,(
% 3.38/0.86 ![X0]: (~empty(X0)|empty(relation_dom(X0)))),
% 3.38/0.86 inference(cnf_transformation,[status(esa)],[f82])).
% 3.38/0.86 fof(f91,plain,(
% 3.38/0.86 (relation(sk0_4)&function(sk0_4))),
% 3.38/0.86 inference(skolemization,[status(esa)],[f20])).
% 3.38/0.86 fof(f93,plain,(
% 3.38/0.86 function(sk0_4)),
% 3.38/0.86 inference(cnf_transformation,[status(esa)],[f91])).
% 3.38/0.86 fof(f94,plain,(
% 3.38/0.86 (empty(sk0_5)&relation(sk0_5))),
% 3.38/0.86 inference(skolemization,[status(esa)],[f21])).
% 3.38/0.86 fof(f96,plain,(
% 3.38/0.86 relation(sk0_5)),
% 3.38/0.86 inference(cnf_transformation,[status(esa)],[f94])).
% 3.38/0.86 fof(f101,plain,(
% 3.38/0.86 empty(sk0_7)),
% 3.38/0.86 inference(skolemization,[status(esa)],[f23])).
% 3.38/0.86 fof(f102,plain,(
% 3.38/0.86 empty(sk0_7)),
% 3.38/0.86 inference(cnf_transformation,[status(esa)],[f101])).
% 3.38/0.86 fof(f103,plain,(
% 3.38/0.86 (~empty(sk0_8)&relation(sk0_8))),
% 3.38/0.86 inference(skolemization,[status(esa)],[f24])).
% 3.38/0.86 fof(f105,plain,(
% 3.38/0.86 relation(sk0_8)),
% 3.38/0.86 inference(cnf_transformation,[status(esa)],[f103])).
% 3.38/0.86 fof(f106,plain,(
% 3.38/0.86 ![A]: (element(sk0_9(A),powerset(A))&empty(sk0_9(A)))),
% 3.38/0.86 inference(skolemization,[status(esa)],[f25])).
% 3.38/0.86 fof(f108,plain,(
% 3.38/0.86 ![X0]: (empty(sk0_9(X0)))),
% 3.38/0.86 inference(cnf_transformation,[status(esa)],[f106])).
% 3.38/0.86 fof(f111,plain,(
% 3.38/0.86 (relation(sk0_11)&relation_empty_yielding(sk0_11))),
% 3.38/0.86 inference(skolemization,[status(esa)],[f27])).
% 3.38/0.86 fof(f112,plain,(
% 3.38/0.86 relation(sk0_11)),
% 3.38/0.86 inference(cnf_transformation,[status(esa)],[f111])).
% 3.38/0.86 fof(f118,plain,(
% 3.38/0.86 ![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))))))),
% 3.38/0.86 inference(pre_NNF_transformation,[status(esa)],[f30])).
% 3.38/0.86 fof(f119,plain,(
% 3.38/0.86 ![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)))))))),
% 3.38/0.86 inference(miniscoping,[status(esa)],[f118])).
% 3.38/0.86 fof(f120,plain,(
% 3.38/0.86 ![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)))),
% 3.38/0.86 inference(cnf_transformation,[status(esa)],[f119])).
% 3.38/0.86 fof(f123,plain,(
% 3.38/0.86 ![A,B]: ((~relation(B)|~function(B))|(B=identity_relation(A)<=>(relation_dom(B)=A&(![C]: (~in(C,A)|apply(B,C)=C)))))),
% 3.38/0.86 inference(pre_NNF_transformation,[status(esa)],[f32])).
% 3.38/0.86 fof(f124,plain,(
% 3.38/0.86 ![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))))))),
% 3.38/0.86 inference(NNF_transformation,[status(esa)],[f123])).
% 3.38/0.86 fof(f125,plain,(
% 3.38/0.86 ![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)))))))),
% 3.38/0.86 inference(miniscoping,[status(esa)],[f124])).
% 3.38/0.86 fof(f126,plain,(
% 3.38/0.86 ![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_12(A,B),A)&~apply(B,sk0_12(A,B))=sk0_12(A,B)))))))),
% 3.38/0.86 inference(skolemization,[status(esa)],[f125])).
% 3.38/0.86 fof(f129,plain,(
% 3.38/0.86 ![X0,X1]: (~relation(X0)|~function(X0)|X0=identity_relation(X1)|~relation_dom(X0)=X1|in(sk0_12(X1,X0),X1))),
% 3.38/0.86 inference(cnf_transformation,[status(esa)],[f126])).
% 3.38/0.86 fof(f130,plain,(
% 3.38/0.86 ![X0,X1]: (~relation(X0)|~function(X0)|X0=identity_relation(X1)|~relation_dom(X0)=X1|~apply(X0,sk0_12(X1,X0))=sk0_12(X1,X0))),
% 3.38/0.86 inference(cnf_transformation,[status(esa)],[f126])).
% 3.38/0.86 fof(f135,plain,(
% 3.38/0.86 (?[A]: ((relation(A)&function(A))&(?[B]: ((relation(B)&function(B))&((relation_rng(A)=relation_dom(B)&relation_composition(A,B)=A)&~B=identity_relation(relation_dom(B)))))))),
% 3.38/0.86 inference(pre_NNF_transformation,[status(esa)],[f35])).
% 3.38/0.86 fof(f136,plain,(
% 3.38/0.86 ((relation(sk0_13)&function(sk0_13))&((relation(sk0_14)&function(sk0_14))&((relation_rng(sk0_13)=relation_dom(sk0_14)&relation_composition(sk0_13,sk0_14)=sk0_13)&~sk0_14=identity_relation(relation_dom(sk0_14)))))),
% 3.38/0.86 inference(skolemization,[status(esa)],[f135])).
% 3.38/0.86 fof(f137,plain,(
% 3.38/0.86 relation(sk0_13)),
% 3.38/0.86 inference(cnf_transformation,[status(esa)],[f136])).
% 3.38/0.86 fof(f138,plain,(
% 3.38/0.86 function(sk0_13)),
% 3.38/0.86 inference(cnf_transformation,[status(esa)],[f136])).
% 3.38/0.86 fof(f139,plain,(
% 3.38/0.86 relation(sk0_14)),
% 3.38/0.86 inference(cnf_transformation,[status(esa)],[f136])).
% 3.38/0.86 fof(f140,plain,(
% 3.38/0.86 function(sk0_14)),
% 3.38/0.86 inference(cnf_transformation,[status(esa)],[f136])).
% 3.38/0.86 fof(f141,plain,(
% 3.38/0.86 relation_rng(sk0_13)=relation_dom(sk0_14)),
% 3.38/0.86 inference(cnf_transformation,[status(esa)],[f136])).
% 3.38/0.86 fof(f142,plain,(
% 3.38/0.86 relation_composition(sk0_13,sk0_14)=sk0_13),
% 3.38/0.86 inference(cnf_transformation,[status(esa)],[f136])).
% 3.38/0.86 fof(f143,plain,(
% 3.38/0.86 ~sk0_14=identity_relation(relation_dom(sk0_14))),
% 3.38/0.86 inference(cnf_transformation,[status(esa)],[f136])).
% 3.38/0.86 fof(f150,plain,(
% 3.38/0.86 ![A]: (~empty(A)|A=empty_set)),
% 3.38/0.86 inference(pre_NNF_transformation,[status(esa)],[f38])).
% 3.38/0.86 fof(f151,plain,(
% 3.38/0.86 ![X0]: (~empty(X0)|X0=empty_set)),
% 3.38/0.86 inference(cnf_transformation,[status(esa)],[f150])).
% 3.38/0.86 fof(f152,plain,(
% 3.38/0.86 ![A,B]: (~in(A,B)|~empty(B))),
% 3.38/0.86 inference(pre_NNF_transformation,[status(esa)],[f39])).
% 3.38/0.86 fof(f153,plain,(
% 3.38/0.86 ![B]: ((![A]: ~in(A,B))|~empty(B))),
% 3.38/0.86 inference(miniscoping,[status(esa)],[f152])).
% 3.38/0.86 fof(f154,plain,(
% 3.38/0.86 ![X0,X1]: (~in(X0,X1)|~empty(X1))),
% 3.38/0.86 inference(cnf_transformation,[status(esa)],[f153])).
% 3.38/0.86 fof(f158,plain,(
% 3.38/0.86 ![X0,X1]: (~relation(X0)|~function(X0)|~in(X1,relation_rng(X0))|in(sk0_0(X1,relation_rng(X0),X0),relation_dom(X0)))),
% 3.38/0.86 inference(destructive_equality_resolution,[status(esa)],[f51])).
% 3.38/0.86 fof(f159,plain,(
% 3.38/0.86 ![X0,X1]: (~relation(X0)|~function(X0)|~in(X1,relation_rng(X0))|X1=apply(X0,sk0_0(X1,relation_rng(X0),X0)))),
% 3.38/0.86 inference(destructive_equality_resolution,[status(esa)],[f52])).
% 3.38/0.86 fof(f165,plain,(
% 3.38/0.86 ![X0]: (~relation(X0)|~function(X0)|X0=identity_relation(relation_dom(X0))|in(sk0_12(relation_dom(X0),X0),relation_dom(X0)))),
% 3.38/0.86 inference(destructive_equality_resolution,[status(esa)],[f129])).
% 3.38/0.86 fof(f166,plain,(
% 3.38/0.86 ![X0]: (~relation(X0)|~function(X0)|X0=identity_relation(relation_dom(X0))|~apply(X0,sk0_12(relation_dom(X0),X0))=sk0_12(relation_dom(X0),X0))),
% 3.38/0.86 inference(destructive_equality_resolution,[status(esa)],[f130])).
% 3.38/0.86 fof(f167,plain,(
% 3.38/0.86 ~sk0_14=identity_relation(relation_rng(sk0_13))),
% 3.38/0.86 inference(forward_demodulation,[status(thm)],[f141,f143])).
% 3.38/0.86 fof(f170,plain,(
% 3.38/0.86 spl0_0 <=> relation(sk0_13)),
% 3.38/0.86 introduced(split_symbol_definition)).
% 3.38/0.86 fof(f172,plain,(
% 3.38/0.86 ~relation(sk0_13)|spl0_0),
% 3.38/0.86 inference(component_clause,[status(thm)],[f170])).
% 3.38/0.86 fof(f173,plain,(
% 3.38/0.86 spl0_1 <=> relation(sk0_14)),
% 3.38/0.86 introduced(split_symbol_definition)).
% 3.38/0.86 fof(f175,plain,(
% 3.38/0.86 ~relation(sk0_14)|spl0_1),
% 3.38/0.86 inference(component_clause,[status(thm)],[f173])).
% 3.38/0.86 fof(f178,plain,(
% 3.38/0.86 spl0_2 <=> function(sk0_13)),
% 3.38/0.86 introduced(split_symbol_definition)).
% 3.38/0.86 fof(f180,plain,(
% 3.38/0.86 ~function(sk0_13)|spl0_2),
% 3.38/0.86 inference(component_clause,[status(thm)],[f178])).
% 3.38/0.86 fof(f181,plain,(
% 3.38/0.86 spl0_3 <=> function(sk0_14)),
% 3.38/0.86 introduced(split_symbol_definition)).
% 3.38/0.86 fof(f183,plain,(
% 3.38/0.86 ~function(sk0_14)|spl0_3),
% 3.38/0.86 inference(component_clause,[status(thm)],[f181])).
% 3.38/0.86 fof(f196,plain,(
% 3.38/0.86 spl0_6 <=> ~in(X0,relation_dom(sk0_13))|apply(sk0_13,X0)=apply(sk0_14,apply(sk0_13,X0))),
% 3.38/0.86 introduced(split_symbol_definition)).
% 3.38/0.86 fof(f197,plain,(
% 3.38/0.86 ![X0]: (~in(X0,relation_dom(sk0_13))|apply(sk0_13,X0)=apply(sk0_14,apply(sk0_13,X0))|~spl0_6)),
% 3.38/0.86 inference(component_clause,[status(thm)],[f196])).
% 3.38/0.86 fof(f199,plain,(
% 3.38/0.86 ![X0]: (~relation(sk0_13)|~function(sk0_13)|~relation(sk0_14)|~function(sk0_14)|~in(X0,relation_dom(sk0_13))|apply(sk0_13,X0)=apply(sk0_14,apply(sk0_13,X0)))),
% 3.38/0.86 inference(paramodulation,[status(thm)],[f142,f120])).
% 3.38/0.86 fof(f200,plain,(
% 3.38/0.86 ~spl0_0|~spl0_2|~spl0_1|~spl0_3|spl0_6),
% 3.38/0.86 inference(split_clause,[status(thm)],[f199,f170,f178,f173,f181,f196])).
% 3.38/0.86 fof(f201,plain,(
% 3.38/0.86 $false|spl0_3),
% 3.38/0.86 inference(forward_subsumption_resolution,[status(thm)],[f183,f140])).
% 3.38/0.86 fof(f202,plain,(
% 3.38/0.86 spl0_3),
% 3.38/0.86 inference(contradiction_clause,[status(thm)],[f201])).
% 3.38/0.86 fof(f203,plain,(
% 3.38/0.86 $false|spl0_2),
% 3.38/0.86 inference(forward_subsumption_resolution,[status(thm)],[f180,f138])).
% 3.38/0.86 fof(f204,plain,(
% 3.38/0.86 spl0_2),
% 3.38/0.86 inference(contradiction_clause,[status(thm)],[f203])).
% 3.38/0.86 fof(f205,plain,(
% 3.38/0.86 $false|spl0_0),
% 3.38/0.86 inference(forward_subsumption_resolution,[status(thm)],[f172,f137])).
% 3.38/0.86 fof(f206,plain,(
% 3.38/0.86 spl0_0),
% 3.38/0.86 inference(contradiction_clause,[status(thm)],[f205])).
% 3.38/0.86 fof(f207,plain,(
% 3.38/0.86 $false|spl0_1),
% 3.38/0.86 inference(forward_subsumption_resolution,[status(thm)],[f175,f139])).
% 3.38/0.86 fof(f208,plain,(
% 3.38/0.86 spl0_1),
% 3.38/0.86 inference(contradiction_clause,[status(thm)],[f207])).
% 3.38/0.86 fof(f214,plain,(
% 3.38/0.86 ![X0]: (~relation(X0)|relation(relation_composition(X0,empty_set)))),
% 3.38/0.86 inference(resolution,[status(thm)],[f65,f64])).
% 3.38/0.86 fof(f886,plain,(
% 3.38/0.86 spl0_41 <=> sk0_14=identity_relation(relation_dom(sk0_14))),
% 3.38/0.86 introduced(split_symbol_definition)).
% 3.38/0.86 fof(f887,plain,(
% 3.38/0.86 sk0_14=identity_relation(relation_dom(sk0_14))|~spl0_41),
% 3.38/0.86 inference(component_clause,[status(thm)],[f886])).
% 3.38/0.86 fof(f889,plain,(
% 3.38/0.86 spl0_42 <=> in(sk0_12(relation_dom(sk0_14),sk0_14),relation_dom(sk0_14))),
% 3.38/0.86 introduced(split_symbol_definition)).
% 3.38/0.86 fof(f890,plain,(
% 3.38/0.86 in(sk0_12(relation_dom(sk0_14),sk0_14),relation_dom(sk0_14))|~spl0_42),
% 3.38/0.86 inference(component_clause,[status(thm)],[f889])).
% 3.38/0.86 fof(f892,plain,(
% 3.38/0.86 ~relation(sk0_14)|sk0_14=identity_relation(relation_dom(sk0_14))|in(sk0_12(relation_dom(sk0_14),sk0_14),relation_dom(sk0_14))),
% 3.38/0.86 inference(resolution,[status(thm)],[f165,f140])).
% 3.38/0.86 fof(f893,plain,(
% 3.38/0.86 ~spl0_1|spl0_41|spl0_42),
% 3.38/0.86 inference(split_clause,[status(thm)],[f892,f173,f886,f889])).
% 3.38/0.86 fof(f902,plain,(
% 3.38/0.86 ![X0]: (~relation(X0)|X0=identity_relation(relation_dom(X0))|in(sk0_12(relation_dom(X0),X0),relation_dom(X0))|~empty(X0))),
% 3.38/0.86 inference(resolution,[status(thm)],[f165,f44])).
% 3.38/0.86 fof(f903,plain,(
% 3.38/0.86 ![X0]: (X0=identity_relation(relation_dom(X0))|in(sk0_12(relation_dom(X0),X0),relation_dom(X0))|~empty(X0))),
% 3.38/0.86 inference(forward_subsumption_resolution,[status(thm)],[f902,f46])).
% 3.38/0.86 fof(f906,plain,(
% 3.38/0.86 sk0_14=identity_relation(relation_rng(sk0_13))|~spl0_41),
% 3.38/0.86 inference(forward_demodulation,[status(thm)],[f141,f887])).
% 3.38/0.86 fof(f907,plain,(
% 3.38/0.86 $false|~spl0_41),
% 3.38/0.86 inference(forward_subsumption_resolution,[status(thm)],[f906,f167])).
% 3.38/0.86 fof(f908,plain,(
% 3.38/0.86 ~spl0_41),
% 3.38/0.86 inference(contradiction_clause,[status(thm)],[f907])).
% 3.38/0.86 fof(f909,plain,(
% 3.38/0.86 in(sk0_12(relation_rng(sk0_13),sk0_14),relation_dom(sk0_14))|~spl0_42),
% 3.38/0.86 inference(forward_demodulation,[status(thm)],[f141,f890])).
% 3.38/0.86 fof(f910,plain,(
% 3.38/0.86 in(sk0_12(relation_rng(sk0_13),sk0_14),relation_rng(sk0_13))|~spl0_42),
% 3.38/0.86 inference(forward_demodulation,[status(thm)],[f141,f909])).
% 3.38/0.86 fof(f931,plain,(
% 3.38/0.86 ![X0]: (X0=identity_relation(relation_dom(X0))|~empty(X0)|~empty(relation_dom(X0)))),
% 3.38/0.86 inference(resolution,[status(thm)],[f903,f154])).
% 3.38/0.86 fof(f932,plain,(
% 3.38/0.86 ![X0]: (X0=identity_relation(relation_dom(X0))|~empty(X0))),
% 3.38/0.86 inference(forward_subsumption_resolution,[status(thm)],[f931,f83])).
% 3.38/0.86 fof(f1075,plain,(
% 3.38/0.86 spl0_52 <=> relation(sk0_5)),
% 3.38/0.86 introduced(split_symbol_definition)).
% 3.38/0.86 fof(f1077,plain,(
% 3.38/0.86 ~relation(sk0_5)|spl0_52),
% 3.38/0.86 inference(component_clause,[status(thm)],[f1075])).
% 3.38/0.86 fof(f1091,plain,(
% 3.38/0.86 $false|spl0_52),
% 3.38/0.86 inference(forward_subsumption_resolution,[status(thm)],[f1077,f96])).
% 3.38/0.86 fof(f1092,plain,(
% 3.38/0.86 spl0_52),
% 3.38/0.86 inference(contradiction_clause,[status(thm)],[f1091])).
% 3.38/0.86 fof(f1094,plain,(
% 3.38/0.86 sk0_7=identity_relation(relation_dom(sk0_7))),
% 3.38/0.86 inference(resolution,[status(thm)],[f102,f932])).
% 3.38/0.86 fof(f1106,plain,(
% 3.38/0.86 relation(sk0_7)),
% 3.38/0.86 inference(paramodulation,[status(thm)],[f1094,f59])).
% 3.38/0.86 fof(f1107,plain,(
% 3.38/0.86 spl0_56 <=> relation(sk0_7)),
% 3.38/0.86 introduced(split_symbol_definition)).
% 3.38/0.86 fof(f1109,plain,(
% 3.38/0.86 ~relation(sk0_7)|spl0_56),
% 3.38/0.86 inference(component_clause,[status(thm)],[f1107])).
% 3.38/0.86 fof(f1123,plain,(
% 3.38/0.86 $false|spl0_56),
% 3.38/0.86 inference(forward_subsumption_resolution,[status(thm)],[f1109,f1106])).
% 3.38/0.86 fof(f1124,plain,(
% 3.38/0.86 spl0_56),
% 3.38/0.86 inference(contradiction_clause,[status(thm)],[f1123])).
% 3.38/0.86 fof(f1139,plain,(
% 3.38/0.86 ![X0]: (sk0_9(X0)=identity_relation(relation_dom(sk0_9(X0))))),
% 3.38/0.86 inference(resolution,[status(thm)],[f108,f932])).
% 3.38/0.86 fof(f1260,plain,(
% 3.38/0.86 ![X0]: (function(sk0_9(X0)))),
% 3.38/0.86 inference(paramodulation,[status(thm)],[f1139,f75])).
% 3.38/0.86 fof(f1274,plain,(
% 3.38/0.86 spl0_60 <=> apply(sk0_14,sk0_12(relation_rng(sk0_13),sk0_14))=sk0_12(relation_dom(sk0_14),sk0_14)),
% 3.38/0.86 introduced(split_symbol_definition)).
% 3.38/0.86 fof(f1276,plain,(
% 3.38/0.86 ~apply(sk0_14,sk0_12(relation_rng(sk0_13),sk0_14))=sk0_12(relation_dom(sk0_14),sk0_14)|spl0_60),
% 3.38/0.86 inference(component_clause,[status(thm)],[f1274])).
% 3.38/0.86 fof(f1277,plain,(
% 3.38/0.86 ~relation(sk0_14)|~function(sk0_14)|sk0_14=identity_relation(relation_dom(sk0_14))|~apply(sk0_14,sk0_12(relation_rng(sk0_13),sk0_14))=sk0_12(relation_dom(sk0_14),sk0_14)),
% 3.38/0.86 inference(paramodulation,[status(thm)],[f141,f166])).
% 3.38/0.86 fof(f1278,plain,(
% 3.38/0.86 ~spl0_1|~spl0_3|spl0_41|~spl0_60),
% 3.38/0.86 inference(split_clause,[status(thm)],[f1277,f173,f181,f886,f1274])).
% 3.38/0.86 fof(f1279,plain,(
% 3.38/0.86 ~apply(sk0_14,sk0_12(relation_rng(sk0_13),sk0_14))=sk0_12(relation_rng(sk0_13),sk0_14)|spl0_60),
% 3.38/0.86 inference(forward_demodulation,[status(thm)],[f141,f1276])).
% 3.38/0.86 fof(f1282,plain,(
% 3.38/0.86 ![X0]: (sk0_9(X0)=empty_set)),
% 3.38/0.86 inference(resolution,[status(thm)],[f151,f108])).
% 3.38/0.86 fof(f1395,plain,(
% 3.38/0.86 function(empty_set)),
% 3.38/0.86 inference(backward_demodulation,[status(thm)],[f1282,f1260])).
% 3.38/0.86 fof(f2539,plain,(
% 3.38/0.86 spl0_61 <=> function(empty_set)),
% 3.38/0.86 introduced(split_symbol_definition)).
% 3.38/0.86 fof(f2541,plain,(
% 3.38/0.86 ~function(empty_set)|spl0_61),
% 3.38/0.86 inference(component_clause,[status(thm)],[f2539])).
% 3.38/0.86 fof(f2551,plain,(
% 3.38/0.86 $false|spl0_61),
% 3.38/0.86 inference(forward_subsumption_resolution,[status(thm)],[f2541,f1395])).
% 3.38/0.86 fof(f2552,plain,(
% 3.38/0.86 spl0_61),
% 3.38/0.86 inference(contradiction_clause,[status(thm)],[f2551])).
% 3.38/0.86 fof(f2635,plain,(
% 3.38/0.86 spl0_71 <=> function(sk0_4)),
% 3.38/0.86 introduced(split_symbol_definition)).
% 3.38/0.86 fof(f2637,plain,(
% 3.38/0.86 ~function(sk0_4)|spl0_71),
% 3.38/0.86 inference(component_clause,[status(thm)],[f2635])).
% 3.38/0.86 fof(f2647,plain,(
% 3.38/0.86 $false|spl0_71),
% 3.38/0.86 inference(forward_subsumption_resolution,[status(thm)],[f2637,f93])).
% 3.38/0.86 fof(f2648,plain,(
% 3.38/0.86 spl0_71),
% 3.38/0.86 inference(contradiction_clause,[status(thm)],[f2647])).
% 3.38/0.86 fof(f2694,plain,(
% 3.38/0.86 spl0_73 <=> sk0_12(relation_rng(sk0_13),sk0_14)=apply(sk0_13,sk0_0(sk0_12(relation_rng(sk0_13),sk0_14),relation_rng(sk0_13),sk0_13))),
% 3.38/0.86 introduced(split_symbol_definition)).
% 3.38/0.86 fof(f2695,plain,(
% 3.38/0.86 sk0_12(relation_rng(sk0_13),sk0_14)=apply(sk0_13,sk0_0(sk0_12(relation_rng(sk0_13),sk0_14),relation_rng(sk0_13),sk0_13))|~spl0_73),
% 3.38/0.86 inference(component_clause,[status(thm)],[f2694])).
% 3.38/0.86 fof(f2697,plain,(
% 3.38/0.86 ~relation(sk0_13)|~function(sk0_13)|sk0_12(relation_rng(sk0_13),sk0_14)=apply(sk0_13,sk0_0(sk0_12(relation_rng(sk0_13),sk0_14),relation_rng(sk0_13),sk0_13))|~spl0_42),
% 3.38/0.86 inference(resolution,[status(thm)],[f910,f159])).
% 3.38/0.86 fof(f2698,plain,(
% 3.38/0.86 ~spl0_0|~spl0_2|spl0_73|~spl0_42),
% 3.38/0.86 inference(split_clause,[status(thm)],[f2697,f170,f178,f2694,f889])).
% 3.38/0.86 fof(f2699,plain,(
% 3.38/0.86 spl0_74 <=> in(sk0_0(sk0_12(relation_rng(sk0_13),sk0_14),relation_rng(sk0_13),sk0_13),relation_dom(sk0_13))),
% 3.38/0.86 introduced(split_symbol_definition)).
% 3.38/0.86 fof(f2700,plain,(
% 3.38/0.86 in(sk0_0(sk0_12(relation_rng(sk0_13),sk0_14),relation_rng(sk0_13),sk0_13),relation_dom(sk0_13))|~spl0_74),
% 3.38/0.86 inference(component_clause,[status(thm)],[f2699])).
% 3.38/0.86 fof(f2702,plain,(
% 3.38/0.86 ~relation(sk0_13)|~function(sk0_13)|in(sk0_0(sk0_12(relation_rng(sk0_13),sk0_14),relation_rng(sk0_13),sk0_13),relation_dom(sk0_13))|~spl0_42),
% 3.38/0.86 inference(resolution,[status(thm)],[f910,f158])).
% 3.38/0.86 fof(f2703,plain,(
% 3.38/0.86 ~spl0_0|~spl0_2|spl0_74|~spl0_42),
% 3.38/0.86 inference(split_clause,[status(thm)],[f2702,f170,f178,f2699,f889])).
% 3.38/0.86 fof(f2705,plain,(
% 3.38/0.86 spl0_75 <=> function(identity_relation(relation_rng(sk0_13)))),
% 3.38/0.86 introduced(split_symbol_definition)).
% 3.38/0.86 fof(f2707,plain,(
% 3.38/0.86 ~function(identity_relation(relation_rng(sk0_13)))|spl0_75),
% 3.38/0.86 inference(component_clause,[status(thm)],[f2705])).
% 3.38/0.86 fof(f2719,plain,(
% 3.38/0.86 $false|spl0_75),
% 3.38/0.86 inference(forward_subsumption_resolution,[status(thm)],[f2707,f75])).
% 3.38/0.86 fof(f2720,plain,(
% 3.38/0.86 spl0_75),
% 3.38/0.86 inference(contradiction_clause,[status(thm)],[f2719])).
% 3.38/0.86 fof(f2739,plain,(
% 3.38/0.86 spl0_82 <=> function(identity_relation(relation_dom(sk0_13)))),
% 3.38/0.86 introduced(split_symbol_definition)).
% 3.38/0.86 fof(f2741,plain,(
% 3.38/0.86 ~function(identity_relation(relation_dom(sk0_13)))|spl0_82),
% 3.38/0.86 inference(component_clause,[status(thm)],[f2739])).
% 3.38/0.86 fof(f2758,plain,(
% 3.38/0.86 $false|spl0_82),
% 3.38/0.86 inference(forward_subsumption_resolution,[status(thm)],[f2741,f75])).
% 3.38/0.86 fof(f2759,plain,(
% 3.38/0.86 spl0_82),
% 3.38/0.86 inference(contradiction_clause,[status(thm)],[f2758])).
% 3.38/0.86 fof(f2948,plain,(
% 3.38/0.86 spl0_90 <=> relation(relation_composition(sk0_11,empty_set))),
% 3.38/0.86 introduced(split_symbol_definition)).
% 3.38/0.86 fof(f2950,plain,(
% 3.38/0.86 ~relation(relation_composition(sk0_11,empty_set))|spl0_90),
% 3.38/0.86 inference(component_clause,[status(thm)],[f2948])).
% 3.38/0.86 fof(f2970,plain,(
% 3.38/0.86 ~relation(sk0_11)|spl0_90),
% 3.38/0.86 inference(resolution,[status(thm)],[f2950,f214])).
% 3.38/0.86 fof(f2971,plain,(
% 3.38/0.86 $false|spl0_90),
% 3.38/0.86 inference(forward_subsumption_resolution,[status(thm)],[f2970,f112])).
% 3.38/0.86 fof(f2972,plain,(
% 3.38/0.86 spl0_90),
% 3.38/0.86 inference(contradiction_clause,[status(thm)],[f2971])).
% 3.38/0.86 fof(f2989,plain,(
% 3.38/0.86 spl0_93 <=> relation(relation_composition(sk0_8,empty_set))),
% 3.38/0.86 introduced(split_symbol_definition)).
% 3.38/0.86 fof(f2991,plain,(
% 3.38/0.86 ~relation(relation_composition(sk0_8,empty_set))|spl0_93),
% 3.38/0.86 inference(component_clause,[status(thm)],[f2989])).
% 3.38/0.86 fof(f3011,plain,(
% 3.38/0.86 ~relation(sk0_8)|spl0_93),
% 3.38/0.86 inference(resolution,[status(thm)],[f2991,f214])).
% 3.38/0.86 fof(f3012,plain,(
% 3.38/0.86 $false|spl0_93),
% 3.38/0.86 inference(forward_subsumption_resolution,[status(thm)],[f3011,f105])).
% 3.38/0.86 fof(f3013,plain,(
% 3.38/0.86 spl0_93),
% 3.38/0.86 inference(contradiction_clause,[status(thm)],[f3012])).
% 3.38/0.86 fof(f3074,plain,(
% 3.38/0.86 apply(sk0_13,sk0_0(sk0_12(relation_rng(sk0_13),sk0_14),relation_rng(sk0_13),sk0_13))=apply(sk0_14,apply(sk0_13,sk0_0(sk0_12(relation_rng(sk0_13),sk0_14),relation_rng(sk0_13),sk0_13)))|~spl0_74|~spl0_6),
% 3.38/0.86 inference(resolution,[status(thm)],[f2700,f197])).
% 3.38/0.86 fof(f3075,plain,(
% 3.38/0.86 sk0_12(relation_rng(sk0_13),sk0_14)=apply(sk0_14,apply(sk0_13,sk0_0(sk0_12(relation_rng(sk0_13),sk0_14),relation_rng(sk0_13),sk0_13)))|~spl0_73|~spl0_74|~spl0_6),
% 3.38/0.86 inference(forward_demodulation,[status(thm)],[f2695,f3074])).
% 3.38/0.86 fof(f3076,plain,(
% 3.38/0.86 sk0_12(relation_rng(sk0_13),sk0_14)=apply(sk0_14,sk0_12(relation_rng(sk0_13),sk0_14))|~spl0_73|~spl0_74|~spl0_6),
% 3.38/0.86 inference(forward_demodulation,[status(thm)],[f2695,f3075])).
% 3.38/0.86 fof(f3077,plain,(
% 3.38/0.86 $false|spl0_60|~spl0_73|~spl0_74|~spl0_6),
% 3.38/0.86 inference(forward_subsumption_resolution,[status(thm)],[f3076,f1279])).
% 3.38/0.86 fof(f3078,plain,(
% 3.38/0.86 spl0_60|~spl0_73|~spl0_74|~spl0_6),
% 3.38/0.86 inference(contradiction_clause,[status(thm)],[f3077])).
% 3.38/0.86 fof(f3079,plain,(
% 3.38/0.86 $false),
% 3.38/0.86 inference(sat_refutation,[status(thm)],[f200,f202,f204,f206,f208,f893,f908,f1092,f1124,f1278,f2552,f2648,f2698,f2703,f2720,f2759,f2972,f3013,f3078])).
% 3.38/0.86 % SZS output end CNFRefutation for theBenchmark.p
% 4.18/0.87 % Elapsed time: 0.509132 seconds
% 4.18/0.87 % CPU time: 3.924692 seconds
% 4.18/0.87 % Total memory used: 122.247 MB
% 4.18/0.87 % Net memory used: 119.190 MB
%------------------------------------------------------------------------------