%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GRA006+1 : TPTP v9.3.1. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:31:01 PM UTC 2026
% Result : Theorem 66.68s 8.97s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRA006+1 : TPTP v9.3.1. Bugfixed v3.2.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.34 % Computer : n007.cluster.edu
% 0.11/0.34 % Model : x86_64 x86_64
% 0.11/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.34 % Memory : 8046.5625MB
% 0.11/0.34 % OS : Linux 6.8.0-71-generic
% 0.11/0.34 % CPULimit : 300
% 0.11/0.35 % WCLimit : 300
% 0.11/0.35 % DateTime : Sun Sep 20 18:17:20 UTC 2026
% 0.11/0.35 % CPUTime :
% 0.13/0.36 % Drodi V4.1.1
% 66.68/8.97 % Refutation found
% 66.68/8.97 % SZS status Theorem for theBenchmark: Theorem is valid
% 66.68/8.97 % SZS output start CNFRefutation for theBenchmark
% 66.68/8.97 fof(f2,axiom,(
% 66.68/8.97 (! [E] :( edge(E)=> ( vertex(head_of(E))& vertex(tail_of(E)) ) ) )),
% 66.68/8.97 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 66.68/8.97 fof(f3,axiom,(
% 66.68/8.97 ( complete=> (! [V1,V2] :( ( vertex(V1)& vertex(V2)& V1 != V2 )=> (? [E] :( edge(E)& ( ( V1 = head_of(E)& V2 = tail_of(E) )<~> ( V2 = head_of(E)& V1 = tail_of(E) ) ) ) )) )) ),
% 66.68/8.97 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 66.68/8.97 fof(f4,axiom,(
% 66.68/8.97 (! [V1,V2,P] :( path(V1,V2,P)<= ( vertex(V1)& vertex(V2)& (? [E] :( edge(E)& V1 = tail_of(E)& ( ( V2 = head_of(E)& P = path_cons(E,empty) )| (? [TP] :( path(head_of(E),V2,TP)& P = path_cons(E,TP) ) )) ) )) ) )),
% 66.68/8.97 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 66.68/8.97 fof(f5,axiom,(
% 66.68/8.97 (! [V1,V2,P] :( path(V1,V2,P)=> ( vertex(V1)& vertex(V2)& (? [E] :( edge(E)& V1 = tail_of(E)& ( ( V2 = head_of(E)& P = path_cons(E,empty) )<~> (? [TP] :( path(head_of(E),V2,TP)& P = path_cons(E,TP) ) )) ) )) ) )),
% 66.68/8.97 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 66.68/8.97 fof(f6,axiom,(
% 66.68/8.97 (! [V1,V2,P,E] :( ( path(V1,V2,P)& on_path(E,P) )=> ( edge(E)& in_path(head_of(E),P)& in_path(tail_of(E),P) ) ) )),
% 66.68/8.97 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 66.68/8.97 fof(f8,axiom,(
% 66.68/8.97 (! [E1,E2] :( sequential(E1,E2)<=> ( edge(E1)& edge(E2)& E1 != E2& head_of(E1) = tail_of(E2) ) ) )),
% 66.68/8.97 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 66.68/8.97 fof(f9,axiom,(
% 66.68/8.97 (! [P,V1,V2] :( path(V1,V2,P)=> (! [E1,E2] :( precedes(E1,E2,P)<= ( on_path(E1,P)& on_path(E2,P)& ( sequential(E1,E2)| (? [E3] :( sequential(E1,E3)& precedes(E3,E2,P) ) )) ) ) )) )),
% 66.68/8.97 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 66.68/8.97 fof(f10,axiom,(
% 66.68/8.97 (! [P,V1,V2] :( path(V1,V2,P)=> (! [E1,E2] :( precedes(E1,E2,P)=> ( on_path(E1,P)& on_path(E2,P)& ( sequential(E1,E2)<~> (? [E3] :( sequential(E1,E3)& precedes(E3,E2,P) ) )) ) ) )) )),
% 66.68/8.97 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 66.68/8.97 fof(f11,axiom,(
% 66.68/8.97 (! [V1,V2,SP] :( shortest_path(V1,V2,SP)<=> ( path(V1,V2,SP)& V1 != V2& (! [P] :( path(V1,V2,P)=> less_or_equal(length_of(SP),length_of(P)) ) )) ) )),
% 66.68/8.97 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 66.68/8.97 fof(f12,axiom,(
% 66.68/8.97 (! [V1,V2,E1,E2,P] :( ( shortest_path(V1,V2,P)& precedes(E1,E2,P) )=> ( ~ (? [E3] :( tail_of(E3) = tail_of(E1)& head_of(E3) = head_of(E2) ))& ~ precedes(E2,E1,P) ) ) )),
% 66.68/8.97 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 66.68/8.97 fof(f18,conjecture,(
% 66.68/8.97 ( complete=> (! [V1,V2,E1,E2,P] :( ( shortest_path(V1,V2,P)& precedes(E1,E2,P) )=> ( (? [E3] :( edge(E3)& tail_of(E3) = tail_of(E1)& head_of(E3) = head_of(E2) ))<~> (? [E3] :( edge(E3)& tail_of(E3) = head_of(E2)& head_of(E3) = tail_of(E1) ) )) ) )) ),
% 66.68/8.97 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 66.68/8.97 fof(f19,negated_conjecture,(
% 66.68/8.97 ~(( complete=> (! [V1,V2,E1,E2,P] :( ( shortest_path(V1,V2,P)& precedes(E1,E2,P) )=> ( (? [E3] :( edge(E3)& tail_of(E3) = tail_of(E1)& head_of(E3) = head_of(E2) ))<~> (? [E3] :( edge(E3)& tail_of(E3) = head_of(E2)& head_of(E3) = tail_of(E1) ) )) ) )) )),
% 66.68/8.97 inference(negated_conjecture,[status(cth)],[f18])).
% 66.68/8.97 fof(f22,plain,(
% 66.68/8.97 ![E]: (~edge(E)|(vertex(head_of(E))&vertex(tail_of(E))))),
% 66.68/8.97 inference(pre_NNF_transformation,[status(thm)],[f2])).
% 66.68/8.97 fof(f23,plain,(
% 66.68/8.97 ![X0]: (~edge(X0)|vertex(head_of(X0)))),
% 66.68/8.97 inference(cnf_transformation,[status(thm)],[f22])).
% 66.68/8.97 fof(f24,plain,(
% 66.68/8.97 ![X0]: (~edge(X0)|vertex(tail_of(X0)))),
% 66.68/8.97 inference(cnf_transformation,[status(thm)],[f22])).
% 66.68/8.97 fof(f25,plain,(
% 66.68/8.97 ~complete|(![V1,V2]: (((~vertex(V1)|~vertex(V2))|V1=V2)|(?[E]: (edge(E)&((V1=head_of(E)&V2=tail_of(E))<~>(V2=head_of(E)&V1=tail_of(E)))))))),
% 66.68/8.97 inference(pre_NNF_transformation,[status(thm)],[f3])).
% 66.68/8.97 fof(f26,definition,(
% 66.68/8.97 ![V1,V2,E]: (sP0_prd(E,V2,V1)<=>(V1=head_of(E)&V2=tail_of(E)))),
% 66.68/8.97 introduced(definition,[new_symbols(definition,[sP0_prd])],[])).
% 66.68/8.97 fof(f27,plain,(
% 66.68/8.97 ~complete|(![V1,V2]: (((~vertex(V1)|~vertex(V2))|V1=V2)|(?[E]: (edge(E)&(sP0_prd(E,V2,V1)<~>(V2=head_of(E)&V1=tail_of(E)))))))),
% 66.68/8.97 inference(formula_renaming,[status(thm)],[f25,f26])).
% 66.68/8.97 fof(f28,plain,(
% 66.68/8.97 ~complete|(![V1,V2]: (((~vertex(V1)|~vertex(V2))|V1=V2)|(?[E]: (edge(E)&((sP0_prd(E,V2,V1)|(V2=head_of(E)&V1=tail_of(E)))&(~sP0_prd(E,V2,V1)|(~V2=head_of(E)|~V1=tail_of(E))))))))),
% 66.68/8.97 inference(NNF_transformation,[status(thm)],[f27])).
% 66.68/8.97 fof(f29,plain,(
% 66.68/8.97 ~complete|(![V1,V2]: (((~vertex(V1)|~vertex(V2))|V1=V2)|(edge(sK0_skl(V2,V1))&((sP0_prd(sK0_skl(V2,V1),V2,V1)|(V2=head_of(sK0_skl(V2,V1))&V1=tail_of(sK0_skl(V2,V1))))&(~sP0_prd(sK0_skl(V2,V1),V2,V1)|(~V2=head_of(sK0_skl(V2,V1))|~V1=tail_of(sK0_skl(V2,V1))))))))),
% 66.68/8.97 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(E,sK0_skl(V2,V1))],[f28])).
% 66.68/8.97 fof(f30,plain,(
% 66.68/8.97 ![X0,X1]: (~complete|~vertex(X0)|~vertex(X1)|X0=X1|edge(sK0_skl(X1,X0)))),
% 66.68/8.97 inference(cnf_transformation,[status(thm)],[f29])).
% 66.68/8.97 fof(f31,plain,(
% 66.68/8.97 ![X0,X1]: (~complete|~vertex(X0)|~vertex(X1)|X0=X1|sP0_prd(sK0_skl(X1,X0),X1,X0)|X1=head_of(sK0_skl(X1,X0)))),
% 66.68/8.97 inference(cnf_transformation,[status(thm)],[f29])).
% 66.68/8.97 fof(f32,plain,(
% 66.68/8.97 ![X0,X1]: (~complete|~vertex(X0)|~vertex(X1)|X0=X1|sP0_prd(sK0_skl(X1,X0),X1,X0)|X0=tail_of(sK0_skl(X1,X0)))),
% 66.68/8.97 inference(cnf_transformation,[status(thm)],[f29])).
% 66.68/8.97 fof(f34,plain,(
% 66.68/8.97 ![V1,V2,P]: (path(V1,V2,P)|((~vertex(V1)|~vertex(V2))|(![E]: ((~edge(E)|~V1=tail_of(E))|((~V2=head_of(E)|~P=path_cons(E,empty))&(![TP]: (~path(head_of(E),V2,TP)|~P=path_cons(E,TP))))))))),
% 66.68/8.97 inference(pre_NNF_transformation,[status(thm)],[f4])).
% 66.68/8.97 fof(f35,plain,(
% 66.68/8.97 ![X0,X1,X2,X3]: (path(X0,X1,X2)|~vertex(X0)|~vertex(X1)|~edge(X3)|~X0=tail_of(X3)|~X1=head_of(X3)|~X2=path_cons(X3,empty))),
% 66.68/8.97 inference(cnf_transformation,[status(thm)],[f34])).
% 66.68/8.97 fof(f37,plain,(
% 66.68/8.97 ![V1,V2,P]: (~path(V1,V2,P)|((vertex(V1)&vertex(V2))&(?[E]: ((edge(E)&V1=tail_of(E))&((V2=head_of(E)&P=path_cons(E,empty))<~>(?[TP]: (path(head_of(E),V2,TP)&P=path_cons(E,TP))))))))),
% 66.68/8.97 inference(pre_NNF_transformation,[status(thm)],[f5])).
% 66.68/8.97 fof(f38,definition,(
% 66.68/8.97 ![V2,P,E]: (sP1_prd(E,P,V2)<=>(V2=head_of(E)&P=path_cons(E,empty)))),
% 66.68/8.97 introduced(definition,[new_symbols(definition,[sP1_prd])],[])).
% 66.68/8.97 fof(f39,plain,(
% 66.68/8.97 ![V1,V2,P]: (~path(V1,V2,P)|((vertex(V1)&vertex(V2))&(?[E]: ((edge(E)&V1=tail_of(E))&(sP1_prd(E,P,V2)<~>(?[TP]: (path(head_of(E),V2,TP)&P=path_cons(E,TP))))))))),
% 66.68/8.97 inference(formula_renaming,[status(thm)],[f37,f38])).
% 66.68/8.97 fof(f40,plain,(
% 66.68/8.97 ![V1,V2,P]: (~path(V1,V2,P)|((vertex(V1)&vertex(V2))&(?[E]: ((edge(E)&V1=tail_of(E))&((sP1_prd(E,P,V2)|(?[TP]: (path(head_of(E),V2,TP)&P=path_cons(E,TP))))&(~sP1_prd(E,P,V2)|(![TP]: (~path(head_of(E),V2,TP)|~P=path_cons(E,TP)))))))))),
% 66.68/8.97 inference(NNF_transformation,[status(thm)],[f39])).
% 66.68/8.97 fof(f41,plain,(
% 66.68/8.97 ![V1,V2,P]: (~path(V1,V2,P)|((vertex(V1)&vertex(V2))&((edge(sK1_skl(P,V2,V1))&V1=tail_of(sK1_skl(P,V2,V1)))&((sP1_prd(sK1_skl(P,V2,V1),P,V2)|(path(head_of(sK1_skl(P,V2,V1)),V2,sK2_skl(P,V2,V1))&P=path_cons(sK1_skl(P,V2,V1),sK2_skl(P,V2,V1))))&(~sP1_prd(sK1_skl(P,V2,V1),P,V2)|(![TP]: (~path(head_of(sK1_skl(P,V2,V1)),V2,TP)|~P=path_cons(sK1_skl(P,V2,V1),TP))))))))),
% 66.68/8.97 inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl,sK2_skl]),skolemize(E,sK1_skl(P,V2,V1)),skolemize(TP,sK2_skl(P,V2,V1))],[f40])).
% 66.68/8.97 fof(f42,plain,(
% 66.68/8.97 ![X0,X1,X2]: (~path(X0,X1,X2)|vertex(X0))),
% 66.68/8.97 inference(cnf_transformation,[status(thm)],[f41])).
% 66.68/8.97 fof(f43,plain,(
% 66.68/8.97 ![X0,X1,X2]: (~path(X0,X1,X2)|vertex(X1))),
% 66.68/8.97 inference(cnf_transformation,[status(thm)],[f41])).
% 66.68/8.97 fof(f49,plain,(
% 66.68/8.97 ![V1,V2,P,E]: ((~path(V1,V2,P)|~on_path(E,P))|((edge(E)&in_path(head_of(E),P))&in_path(tail_of(E),P)))),
% 66.68/8.97 inference(pre_NNF_transformation,[status(thm)],[f6])).
% 66.68/8.97 fof(f50,plain,(
% 66.68/8.97 ![P,E]: (((![V1,V2]: ~path(V1,V2,P))|~on_path(E,P))|((edge(E)&in_path(head_of(E),P))&in_path(tail_of(E),P)))),
% 66.68/8.97 inference(miniscoping,[status(thm)],[f49])).
% 66.68/8.97 fof(f51,plain,(
% 66.68/8.97 ![X0,X1,X2,X3]: (~path(X0,X1,X2)|~on_path(X3,X2)|edge(X3))),
% 66.68/8.97 inference(cnf_transformation,[status(thm)],[f50])).
% 66.68/8.97 fof(f60,plain,(
% 66.68/8.97 ![E1,E2]: ((~sequential(E1,E2)|(((edge(E1)&edge(E2))&~E1=E2)&head_of(E1)=tail_of(E2)))&(sequential(E1,E2)|(((~edge(E1)|~edge(E2))|E1=E2)|~head_of(E1)=tail_of(E2))))),
% 66.68/8.97 inference(NNF_transformation,[status(thm)],[f8])).
% 66.68/8.97 fof(f61,plain,(
% 66.68/8.97 (![E1,E2]: (~sequential(E1,E2)|(((edge(E1)&edge(E2))&~E1=E2)&head_of(E1)=tail_of(E2))))&(![E1,E2]: (sequential(E1,E2)|(((~edge(E1)|~edge(E2))|E1=E2)|~head_of(E1)=tail_of(E2))))),
% 66.68/8.97 inference(miniscoping,[status(thm)],[f60])).
% 66.68/8.97 fof(f66,plain,(
% 66.68/8.97 ![X0,X1]: (sequential(X0,X1)|~edge(X0)|~edge(X1)|X0=X1|~head_of(X0)=tail_of(X1))),
% 66.68/8.97 inference(cnf_transformation,[status(thm)],[f61])).
% 66.68/8.97 fof(f67,plain,(
% 66.68/8.97 ![P,V1,V2]: (~path(V1,V2,P)|(![E1,E2]: (precedes(E1,E2,P)|((~on_path(E1,P)|~on_path(E2,P))|(~sequential(E1,E2)&(![E3]: (~sequential(E1,E3)|~precedes(E3,E2,P))))))))),
% 66.68/8.97 inference(pre_NNF_transformation,[status(thm)],[f9])).
% 66.68/8.97 fof(f68,plain,(
% 66.68/8.97 ![P]: ((![V1,V2]: ~path(V1,V2,P))|(![E1,E2]: (precedes(E1,E2,P)|((~on_path(E1,P)|~on_path(E2,P))|(~sequential(E1,E2)&(![E3]: (~sequential(E1,E3)|~precedes(E3,E2,P))))))))),
% 66.68/8.97 inference(miniscoping,[status(thm)],[f67])).
% 66.68/8.97 fof(f69,plain,(
% 66.68/8.97 ![X0,X1,X2,X3,X4]: (~path(X0,X1,X2)|precedes(X3,X4,X2)|~on_path(X3,X2)|~on_path(X4,X2)|~sequential(X3,X4))),
% 66.68/8.97 inference(cnf_transformation,[status(thm)],[f68])).
% 66.68/8.97 fof(f71,plain,(
% 66.68/8.97 ![P,V1,V2]: (~path(V1,V2,P)|(![E1,E2]: (~precedes(E1,E2,P)|((on_path(E1,P)&on_path(E2,P))&(sequential(E1,E2)<~>(?[E3]: (sequential(E1,E3)&precedes(E3,E2,P))))))))),
% 66.68/8.97 inference(pre_NNF_transformation,[status(thm)],[f10])).
% 66.68/8.97 fof(f72,plain,(
% 66.68/8.97 ![P,V1,V2]: (~path(V1,V2,P)|(![E1,E2]: (~precedes(E1,E2,P)|((on_path(E1,P)&on_path(E2,P))&((sequential(E1,E2)|(?[E3]: (sequential(E1,E3)&precedes(E3,E2,P))))&(~sequential(E1,E2)|(![E3]: (~sequential(E1,E3)|~precedes(E3,E2,P)))))))))),
% 66.68/8.97 inference(NNF_transformation,[status(thm)],[f71])).
% 66.68/8.97 fof(f73,plain,(
% 66.68/8.97 ![P]: ((![V1,V2]: ~path(V1,V2,P))|(![E1,E2]: (~precedes(E1,E2,P)|((on_path(E1,P)&on_path(E2,P))&((sequential(E1,E2)|(?[E3]: (sequential(E1,E3)&precedes(E3,E2,P))))&(~sequential(E1,E2)|(![E3]: (~sequential(E1,E3)|~precedes(E3,E2,P)))))))))),
% 66.68/8.97 inference(miniscoping,[status(thm)],[f72])).
% 66.68/8.97 fof(f74,plain,(
% 66.68/8.97 ![P]: ((![V1,V2]: ~path(V1,V2,P))|(![E1,E2]: (~precedes(E1,E2,P)|((on_path(E1,P)&on_path(E2,P))&((sequential(E1,E2)|(sequential(E1,sK4_skl(E2,E1,P))&precedes(sK4_skl(E2,E1,P),E2,P)))&(~sequential(E1,E2)|(![E3]: (~sequential(E1,E3)|~precedes(E3,E2,P)))))))))),
% 66.68/8.97 inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl]),skolemize(E3,sK4_skl(E2,E1,P))],[f73])).
% 66.68/8.97 fof(f75,plain,(
% 66.68/8.97 ![X0,X1,X2,X3,X4]: (~path(X0,X1,X2)|~precedes(X3,X4,X2)|on_path(X3,X2))),
% 66.68/8.97 inference(cnf_transformation,[status(thm)],[f74])).
% 66.68/8.97 fof(f76,plain,(
% 66.68/8.97 ![X0,X1,X2,X3,X4]: (~path(X0,X1,X2)|~precedes(X3,X4,X2)|on_path(X4,X2))),
% 66.68/8.97 inference(cnf_transformation,[status(thm)],[f74])).
% 66.68/8.97 fof(f80,plain,(
% 66.68/8.97 ![V1,V2,SP]: (shortest_path(V1,V2,SP)<=>((path(V1,V2,SP)&~V1=V2)&(![P]: (~path(V1,V2,P)|less_or_equal(length_of(SP),length_of(P))))))),
% 66.68/8.97 inference(pre_NNF_transformation,[status(thm)],[f11])).
% 66.68/8.97 fof(f81,plain,(
% 66.68/8.97 ![V1,V2,SP]: ((~shortest_path(V1,V2,SP)|((path(V1,V2,SP)&~V1=V2)&(![P]: (~path(V1,V2,P)|less_or_equal(length_of(SP),length_of(P))))))&(shortest_path(V1,V2,SP)|((~path(V1,V2,SP)|V1=V2)|(?[P]: (path(V1,V2,P)&~less_or_equal(length_of(SP),length_of(P)))))))),
% 66.68/8.97 inference(NNF_transformation,[status(thm)],[f80])).
% 66.68/8.97 fof(f82,plain,(
% 66.68/8.97 (![V1,V2,SP]: (~shortest_path(V1,V2,SP)|((path(V1,V2,SP)&~V1=V2)&(![P]: (~path(V1,V2,P)|less_or_equal(length_of(SP),length_of(P)))))))&(![V1,V2,SP]: (shortest_path(V1,V2,SP)|((~path(V1,V2,SP)|V1=V2)|(?[P]: (path(V1,V2,P)&~less_or_equal(length_of(SP),length_of(P)))))))),
% 66.68/8.97 inference(miniscoping,[status(thm)],[f81])).
% 66.68/8.97 fof(f83,plain,(
% 66.68/8.97 (![V1,V2,SP]: (~shortest_path(V1,V2,SP)|((path(V1,V2,SP)&~V1=V2)&(![P]: (~path(V1,V2,P)|less_or_equal(length_of(SP),length_of(P)))))))&(![V1,V2,SP]: (shortest_path(V1,V2,SP)|((~path(V1,V2,SP)|V1=V2)|(path(V1,V2,sK5_skl(SP,V2,V1))&~less_or_equal(length_of(SP),length_of(sK5_skl(SP,V2,V1)))))))),
% 66.68/8.97 inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl]),skolemize(P,sK5_skl(SP,V2,V1))],[f82])).
% 66.68/8.97 fof(f84,plain,(
% 66.68/8.97 ![X0,X1,X2]: (~shortest_path(X0,X1,X2)|path(X0,X1,X2))),
% 66.68/8.97 inference(cnf_transformation,[status(thm)],[f83])).
% 66.68/8.97 fof(f89,plain,(
% 66.68/8.97 ![V1,V2,E1,E2,P]: ((~shortest_path(V1,V2,P)|~precedes(E1,E2,P))|((![E3]: (~tail_of(E3)=tail_of(E1)|~head_of(E3)=head_of(E2)))&~precedes(E2,E1,P)))),
% 66.68/8.97 inference(pre_NNF_transformation,[status(thm)],[f12])).
% 66.68/8.97 fof(f90,plain,(
% 66.68/8.97 ![E1,E2,P]: (((![V1,V2]: ~shortest_path(V1,V2,P))|~precedes(E1,E2,P))|((![E3]: (~tail_of(E3)=tail_of(E1)|~head_of(E3)=head_of(E2)))&~precedes(E2,E1,P)))),
% 66.68/8.97 inference(miniscoping,[status(thm)],[f89])).
% 66.68/8.97 fof(f91,plain,(
% 66.68/8.97 ![X0,X1,X2,X3,X4,X5]: (~shortest_path(X0,X1,X2)|~precedes(X3,X4,X2)|~tail_of(X5)=tail_of(X3)|~head_of(X5)=head_of(X4))),
% 66.68/8.97 inference(cnf_transformation,[status(thm)],[f90])).
% 66.68/8.97 fof(f92,plain,(
% 66.68/8.97 ![X0,X1,X2,X3,X4]: (~shortest_path(X0,X1,X2)|~precedes(X3,X4,X2)|~precedes(X4,X3,X2))),
% 66.68/8.97 inference(cnf_transformation,[status(thm)],[f90])).
% 66.68/8.97 fof(f116,plain,(
% 66.68/8.97 (complete&(?[V1,V2,E1,E2,P]: ((shortest_path(V1,V2,P)&precedes(E1,E2,P))&((?[E3]: ((edge(E3)&tail_of(E3)=tail_of(E1))&head_of(E3)=head_of(E2)))<=>(?[E3]: ((edge(E3)&tail_of(E3)=head_of(E2))&head_of(E3)=tail_of(E1)))))))),
% 66.68/8.97 inference(pre_NNF_transformation,[status(thm)],[f19])).
% 66.68/8.97 fof(f117,plain,(
% 66.68/8.97 complete&(?[V1,V2,E1,E2,P]: ((shortest_path(V1,V2,P)&precedes(E1,E2,P))&(((![E3]: ((~edge(E3)|~tail_of(E3)=tail_of(E1))|~head_of(E3)=head_of(E2)))|(?[E3]: ((edge(E3)&tail_of(E3)=head_of(E2))&head_of(E3)=tail_of(E1))))&((?[E3]: ((edge(E3)&tail_of(E3)=tail_of(E1))&head_of(E3)=head_of(E2)))|(![E3]: ((~edge(E3)|~tail_of(E3)=head_of(E2))|~head_of(E3)=tail_of(E1)))))))),
% 66.68/8.97 inference(NNF_transformation,[status(thm)],[f116])).
% 66.68/8.97 fof(f118,plain,(
% 66.68/8.97 complete&(?[E1,E2]: ((?[P]: ((?[V1,V2]: shortest_path(V1,V2,P))&precedes(E1,E2,P)))&(((![E3]: ((~edge(E3)|~tail_of(E3)=tail_of(E1))|~head_of(E3)=head_of(E2)))|(?[E3]: ((edge(E3)&tail_of(E3)=head_of(E2))&head_of(E3)=tail_of(E1))))&((?[E3]: ((edge(E3)&tail_of(E3)=tail_of(E1))&head_of(E3)=head_of(E2)))|(![E3]: ((~edge(E3)|~tail_of(E3)=head_of(E2))|~head_of(E3)=tail_of(E1)))))))),
% 66.68/8.97 inference(miniscoping,[status(thm)],[f117])).
% 66.68/8.97 fof(f119,plain,(
% 66.68/8.97 complete&((shortest_path(sK11_skl,sK12_skl,sK10_skl)&precedes(sK8_skl,sK9_skl,sK10_skl))&(((![E3]: ((~edge(E3)|~tail_of(E3)=tail_of(sK8_skl))|~head_of(E3)=head_of(sK9_skl)))|((edge(sK13_skl)&tail_of(sK13_skl)=head_of(sK9_skl))&head_of(sK13_skl)=tail_of(sK8_skl)))&(((edge(sK14_skl)&tail_of(sK14_skl)=tail_of(sK8_skl))&head_of(sK14_skl)=head_of(sK9_skl))|(![E3]: ((~edge(E3)|~tail_of(E3)=head_of(sK9_skl))|~head_of(E3)=tail_of(sK8_skl))))))),
% 66.68/8.97 inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl,sK9_skl,sK10_skl,sK11_skl,sK12_skl,sK13_skl,sK14_skl]),skolemize(E1,sK8_skl),skolemize(E2,sK9_skl),skolemize(P,sK10_skl),skolemize(V1,sK11_skl),skolemize(V2,sK12_skl),skolemize(E3,sK13_skl),skolemize(E3,sK14_skl)],[f118])).
% 66.68/8.97 fof(f120,plain,(
% 66.68/8.97 complete),
% 66.68/8.97 inference(cnf_transformation,[status(thm)],[f119])).
% 66.68/8.97 fof(f121,plain,(
% 66.68/8.97 shortest_path(sK11_skl,sK12_skl,sK10_skl)),
% 66.68/8.97 inference(cnf_transformation,[status(thm)],[f119])).
% 66.68/8.97 fof(f122,plain,(
% 66.68/8.97 precedes(sK8_skl,sK9_skl,sK10_skl)),
% 66.68/8.97 inference(cnf_transformation,[status(thm)],[f119])).
% 66.68/8.97 fof(f123,plain,(
% 66.68/8.97 ![X0]: (~edge(X0)|~tail_of(X0)=tail_of(sK8_skl)|~head_of(X0)=head_of(sK9_skl)|edge(sK13_skl))),
% 66.68/8.97 inference(cnf_transformation,[status(thm)],[f119])).
% 66.68/8.97 fof(f124,plain,(
% 66.68/8.97 ![X0]: (~edge(X0)|~tail_of(X0)=tail_of(sK8_skl)|~head_of(X0)=head_of(sK9_skl)|tail_of(sK13_skl)=head_of(sK9_skl))),
% 66.68/8.97 inference(cnf_transformation,[status(thm)],[f119])).
% 66.68/8.97 fof(f125,plain,(
% 66.68/8.97 ![X0]: (~edge(X0)|~tail_of(X0)=tail_of(sK8_skl)|~head_of(X0)=head_of(sK9_skl)|head_of(sK13_skl)=tail_of(sK8_skl))),
% 66.68/8.97 inference(cnf_transformation,[status(thm)],[f119])).
% 66.68/8.97 fof(f127,plain,(
% 66.68/8.97 ![X0]: (tail_of(sK14_skl)=tail_of(sK8_skl)|~edge(X0)|~tail_of(X0)=head_of(sK9_skl)|~head_of(X0)=tail_of(sK8_skl))),
% 66.68/8.97 inference(cnf_transformation,[status(thm)],[f119])).
% 66.68/8.97 fof(f128,plain,(
% 66.68/8.97 ![X0]: (head_of(sK14_skl)=head_of(sK9_skl)|~edge(X0)|~tail_of(X0)=head_of(sK9_skl)|~head_of(X0)=tail_of(sK8_skl))),
% 66.68/8.97 inference(cnf_transformation,[status(thm)],[f119])).
% 66.68/8.97 fof(f129,plain,(
% 66.68/8.97 ![V1,V2,E]: ((~sP0_prd(E,V2,V1)|(V1=head_of(E)&V2=tail_of(E)))&(sP0_prd(E,V2,V1)|(~V1=head_of(E)|~V2=tail_of(E))))),
% 66.68/8.97 inference(NNF_transformation,[status(thm)],[f26])).
% 66.68/8.97 fof(f130,plain,(
% 66.68/8.97 (![V1,V2,E]: (~sP0_prd(E,V2,V1)|(V1=head_of(E)&V2=tail_of(E))))&(![V1,V2,E]: (sP0_prd(E,V2,V1)|(~V1=head_of(E)|~V2=tail_of(E))))),
% 66.68/8.97 inference(miniscoping,[status(thm)],[f129])).
% 66.68/8.97 fof(f131,plain,(
% 66.68/8.97 ![X0,X1,X2]: (~sP0_prd(X0,X1,X2)|X2=head_of(X0))),
% 66.68/8.97 inference(cnf_transformation,[status(thm)],[f130])).
% 66.68/8.97 fof(f132,plain,(
% 66.68/8.97 ![X0,X1,X2]: (~sP0_prd(X0,X1,X2)|X1=tail_of(X0))),
% 66.68/8.97 inference(cnf_transformation,[status(thm)],[f130])).
% 66.68/8.97 fof(f139,plain,(
% 66.68/8.97 ![X3]: (path(tail_of(X3),head_of(X3),path_cons(X3,empty))|~vertex(tail_of(X3))|~vertex(head_of(X3))|~edge(X3))),
% 66.68/8.97 inference(destructive_equality_resolution,[status(thm)],[f35])).
% 66.68/8.97 fof(f140,plain,(
% 66.68/8.97 ![X0]: (path(tail_of(X0),head_of(X0),path_cons(X0,empty))|~vertex(head_of(X0))|~edge(X0))),
% 66.68/8.97 inference(forward_subsumption_resolution,[status(thm)],[f139,f24])).
% 66.68/8.97 fof(f149,plain,(
% 66.68/8.97 ![X0,X1]: (~vertex(X0)|~vertex(X1)|X0=X1|sP0_prd(sK0_skl(X1,X0),X1,X0)|X0=tail_of(sK0_skl(X1,X0)))),
% 66.68/8.97 inference(backward_subsumption_resolution,[status(thm)],[f32,f120])).
% 66.68/8.97 fof(f150,plain,(
% 66.68/8.97 ![X0,X1]: (~vertex(X0)|~vertex(X1)|X0=X1|sP0_prd(sK0_skl(X1,X0),X1,X0)|X1=head_of(sK0_skl(X1,X0)))),
% 66.68/8.97 inference(backward_subsumption_resolution,[status(thm)],[f31,f120])).
% 66.68/8.97 fof(f151,plain,(
% 66.68/8.97 ![X0,X1]: (~vertex(X0)|~vertex(X1)|X0=X1|edge(sK0_skl(X1,X0)))),
% 66.68/8.97 inference(backward_subsumption_resolution,[status(thm)],[f30,f120])).
% 66.68/8.97 fof(f154,plain,(
% 66.68/8.97 path(sK11_skl,sK12_skl,sK10_skl)),
% 66.68/8.97 inference(resolution,[status(thm)],[f84,f121])).
% 66.68/8.97 fof(f155,plain,(
% 66.68/8.97 ![X0,X1]: (~precedes(X0,X1,sK10_skl)|~precedes(X1,X0,sK10_skl))),
% 66.68/8.97 inference(resolution,[status(thm)],[f92,f121])).
% 66.68/8.97 fof(f156,plain,(
% 66.68/8.97 ~precedes(sK9_skl,sK8_skl,sK10_skl)),
% 66.68/8.97 inference(resolution,[status(thm)],[f155,f122])).
% 66.68/8.97 fof(f157,plain,(
% 66.68/8.97 ![X0,X1,X2,X3,X4]: (~shortest_path(X0,X1,X2)|~precedes(X3,X4,X2)|~tail_of(X4)=tail_of(X3))),
% 66.68/8.97 inference(equality_resolution,[status(thm)],[f91])).
% 66.68/8.97 fof(f158,plain,(
% 66.68/8.97 ![X0,X1]: (~precedes(X0,X1,sK10_skl)|~tail_of(X1)=tail_of(X0))),
% 66.68/8.97 inference(resolution,[status(thm)],[f157,f121])).
% 66.68/8.97 fof(f159,plain,(
% 66.68/8.97 ~tail_of(sK9_skl)=tail_of(sK8_skl)),
% 66.68/8.97 inference(resolution,[status(thm)],[f158,f122])).
% 66.68/8.97 fof(f163,plain,(
% 66.68/8.97 ![X0,X1]: (~tail_of(sK0_skl(X0,X1))=tail_of(sK8_skl)|~head_of(sK0_skl(X0,X1))=head_of(sK9_skl)|head_of(sK13_skl)=tail_of(sK8_skl)|~vertex(X1)|~vertex(X0)|X1=X0)),
% 66.68/8.97 inference(resolution,[status(thm)],[f125,f151])).
% 66.68/8.97 fof(f178,plain,(
% 66.68/8.97 ![X0,X1]: (~path(X0,X1,sK10_skl)|on_path(sK8_skl,sK10_skl))),
% 66.68/8.97 inference(resolution,[status(thm)],[f75,f122])).
% 66.68/8.97 fof(f179,plain,(
% 66.68/8.97 ![X0]: (path(tail_of(X0),head_of(X0),path_cons(X0,empty))|~edge(X0)|~edge(X0))),
% 66.68/8.97 inference(resolution,[status(thm)],[f140,f23])).
% 66.68/8.97 fof(f180,plain,(
% 66.68/8.97 ![X0]: (path(tail_of(X0),head_of(X0),path_cons(X0,empty))|~edge(X0))),
% 66.68/8.97 inference(duplicate_literals_removal,[status(thm)],[f179])).
% 66.68/8.97 fof(f182,plain,(
% 66.68/8.97 on_path(sK8_skl,sK10_skl)),
% 66.68/8.97 inference(resolution,[status(thm)],[f178,f154])).
% 66.68/8.97 fof(f183,plain,(
% 66.68/8.97 ![X0,X1]: (~path(X0,X1,sK10_skl)|edge(sK8_skl))),
% 66.68/8.97 inference(resolution,[status(thm)],[f182,f51])).
% 66.68/8.97 fof(f184,plain,(
% 66.68/8.97 edge(sK8_skl)),
% 66.68/8.97 inference(resolution,[status(thm)],[f183,f154])).
% 66.68/8.97 fof(f185,plain,(
% 66.68/8.97 ~tail_of(sK8_skl)=tail_of(sK8_skl)|~head_of(sK8_skl)=head_of(sK9_skl)|head_of(sK13_skl)=tail_of(sK8_skl)),
% 66.68/8.97 inference(resolution,[status(thm)],[f184,f125])).
% 66.68/8.97 fof(f187,plain,(
% 66.68/8.97 ~head_of(sK8_skl)=head_of(sK9_skl)|head_of(sK13_skl)=tail_of(sK8_skl)),
% 66.68/8.97 inference(trivial_equality_resolution,[status(thm)],[f185])).
% 66.68/8.97 fof(f195,plain,(
% 66.68/8.97 ![X0]: (tail_of(sK14_skl)=tail_of(sK8_skl)|~tail_of(sK13_skl)=head_of(sK9_skl)|~head_of(sK13_skl)=tail_of(sK8_skl)|~edge(X0)|~tail_of(X0)=tail_of(sK8_skl)|~head_of(X0)=head_of(sK9_skl))),
% 66.68/8.97 inference(resolution,[status(thm)],[f127,f123])).
% 66.68/8.97 fof(f196,plain,(
% 66.68/8.97 ![X0,X1]: (tail_of(sK14_skl)=tail_of(sK8_skl)|~tail_of(sK0_skl(X0,X1))=head_of(sK9_skl)|~head_of(sK0_skl(X0,X1))=tail_of(sK8_skl)|~vertex(X1)|~vertex(X0)|X1=X0)),
% 66.68/8.97 inference(resolution,[status(thm)],[f127,f151])).
% 66.68/8.97 fof(f197,plain,(
% 66.68/8.97 ![X0]: (tail_of(sK14_skl)=tail_of(sK8_skl)|~head_of(sK13_skl)=tail_of(sK8_skl)|~edge(X0)|~tail_of(X0)=tail_of(sK8_skl)|~head_of(X0)=head_of(sK9_skl))),
% 66.68/8.97 inference(forward_subsumption_resolution,[status(thm)],[f195,f124])).
% 66.68/8.97 fof(f200,plain,(
% 66.68/8.97 ![X0]: (head_of(sK14_skl)=head_of(sK9_skl)|~tail_of(sK13_skl)=head_of(sK9_skl)|~head_of(sK13_skl)=tail_of(sK8_skl)|~edge(X0)|~tail_of(X0)=tail_of(sK8_skl)|~head_of(X0)=head_of(sK9_skl))),
% 66.68/8.97 inference(resolution,[status(thm)],[f128,f123])).
% 66.68/8.97 fof(f201,plain,(
% 66.68/8.97 ![X0,X1]: (head_of(sK14_skl)=head_of(sK9_skl)|~tail_of(sK0_skl(X0,X1))=head_of(sK9_skl)|~head_of(sK0_skl(X0,X1))=tail_of(sK8_skl)|~vertex(X1)|~vertex(X0)|X1=X0)),
% 66.68/8.97 inference(resolution,[status(thm)],[f128,f151])).
% 66.68/8.97 fof(f202,plain,(
% 66.68/8.97 ![X0]: (head_of(sK14_skl)=head_of(sK9_skl)|~head_of(sK13_skl)=tail_of(sK8_skl)|~edge(X0)|~tail_of(X0)=tail_of(sK8_skl)|~head_of(X0)=head_of(sK9_skl))),
% 66.68/8.97 inference(forward_subsumption_resolution,[status(thm)],[f200,f124])).
% 66.68/8.97 fof(f218,plain,(
% 66.68/8.97 ![X0,X1]: (tail_of(sK14_skl)=tail_of(sK8_skl)|~head_of(sK13_skl)=tail_of(sK8_skl)|~tail_of(sK0_skl(X0,X1))=tail_of(sK8_skl)|~head_of(sK0_skl(X0,X1))=head_of(sK9_skl)|~vertex(X1)|~vertex(X0)|X1=X0)),
% 66.68/8.97 inference(resolution,[status(thm)],[f197,f151])).
% 66.68/8.97 fof(f221,plain,(
% 66.68/8.97 ![X0,X1]: (tail_of(sK14_skl)=tail_of(sK8_skl)|~tail_of(sK0_skl(X0,X1))=tail_of(sK8_skl)|~head_of(sK0_skl(X0,X1))=head_of(sK9_skl)|~vertex(X1)|~vertex(X0)|X1=X0)),
% 66.68/8.97 inference(forward_subsumption_resolution,[status(thm)],[f218,f163])).
% 66.68/8.97 fof(f225,plain,(
% 66.68/8.97 ![X0,X1]: (head_of(sK14_skl)=head_of(sK9_skl)|~head_of(sK13_skl)=tail_of(sK8_skl)|~tail_of(sK0_skl(X0,X1))=tail_of(sK8_skl)|~head_of(sK0_skl(X0,X1))=head_of(sK9_skl)|~vertex(X1)|~vertex(X0)|X1=X0)),
% 66.68/8.97 inference(resolution,[status(thm)],[f202,f151])).
% 66.68/8.97 fof(f228,plain,(
% 66.68/8.97 ![X0,X1]: (head_of(sK14_skl)=head_of(sK9_skl)|~tail_of(sK0_skl(X0,X1))=tail_of(sK8_skl)|~head_of(sK0_skl(X0,X1))=head_of(sK9_skl)|~vertex(X1)|~vertex(X0)|X1=X0)),
% 66.68/8.97 inference(forward_subsumption_resolution,[status(thm)],[f225,f163])).
% 66.68/8.97 fof(f233,plain,(
% 66.68/8.97 ![X0,X1]: (~path(X0,X1,sK10_skl)|on_path(sK9_skl,sK10_skl))),
% 66.68/8.97 inference(resolution,[status(thm)],[f76,f122])).
% 66.68/8.97 fof(f234,plain,(
% 66.68/8.97 on_path(sK9_skl,sK10_skl)),
% 66.68/8.97 inference(resolution,[status(thm)],[f233,f154])).
% 66.68/8.97 fof(f235,plain,(
% 66.68/8.97 ![X0,X1]: (~path(X0,X1,sK10_skl)|edge(sK9_skl))),
% 66.68/8.97 inference(resolution,[status(thm)],[f234,f51])).
% 66.68/8.97 fof(f236,plain,(
% 66.68/8.97 edge(sK9_skl)),
% 66.68/8.97 inference(resolution,[status(thm)],[f235,f154])).
% 66.68/8.97 fof(f251,plain,(
% 66.68/8.97 path(tail_of(sK9_skl),head_of(sK9_skl),path_cons(sK9_skl,empty))),
% 66.68/8.97 inference(resolution,[status(thm)],[f180,f236])).
% 66.68/8.97 fof(f253,plain,(
% 66.68/8.97 path(tail_of(sK8_skl),head_of(sK8_skl),path_cons(sK8_skl,empty))),
% 66.68/8.97 inference(resolution,[status(thm)],[f180,f184])).
% 66.68/8.97 fof(f259,plain,(
% 66.68/8.97 vertex(head_of(sK9_skl))),
% 66.68/8.97 inference(resolution,[status(thm)],[f251,f43])).
% 66.68/8.97 fof(f262,plain,(
% 66.68/8.97 ![X0]: (~vertex(X0)|X0=head_of(sK9_skl)|sP0_prd(sK0_skl(head_of(sK9_skl),X0),head_of(sK9_skl),X0)|head_of(sK9_skl)=head_of(sK0_skl(head_of(sK9_skl),X0)))),
% 66.68/8.97 inference(resolution,[status(thm)],[f259,f150])).
% 66.68/8.97 fof(f263,plain,(
% 66.68/8.97 ![X0]: (~vertex(X0)|X0=head_of(sK9_skl)|sP0_prd(sK0_skl(head_of(sK9_skl),X0),head_of(sK9_skl),X0)|X0=tail_of(sK0_skl(head_of(sK9_skl),X0)))),
% 66.68/8.97 inference(resolution,[status(thm)],[f259,f149])).
% 66.68/8.97 fof(f271,plain,(
% 66.68/8.97 vertex(tail_of(sK8_skl))),
% 66.68/8.97 inference(resolution,[status(thm)],[f253,f42])).
% 66.68/8.97 fof(f280,plain,(
% 66.68/8.97 ![X0]: (sequential(X0,sK8_skl)|~edge(X0)|X0=sK8_skl|~head_of(X0)=tail_of(sK8_skl))),
% 66.68/8.97 inference(resolution,[status(thm)],[f66,f184])).
% 66.68/8.97 fof(f288,plain,(
% 66.68/8.97 sequential(sK9_skl,sK8_skl)|sK9_skl=sK8_skl|~head_of(sK9_skl)=tail_of(sK8_skl)),
% 66.68/8.97 inference(resolution,[status(thm)],[f280,f236])).
% 66.68/8.97 fof(f313,plain,(
% 66.68/8.97 ![X0]: (~vertex(X0)|X0=head_of(sK9_skl)|X0=tail_of(sK0_skl(head_of(sK9_skl),X0))|head_of(sK9_skl)=tail_of(sK0_skl(head_of(sK9_skl),X0)))),
% 66.68/8.97 inference(resolution,[status(thm)],[f263,f132])).
% 66.68/8.97 fof(f314,plain,(
% 66.68/8.97 ![X0]: (~vertex(X0)|X0=head_of(sK9_skl)|X0=tail_of(sK0_skl(head_of(sK9_skl),X0))|X0=head_of(sK0_skl(head_of(sK9_skl),X0)))),
% 66.68/8.97 inference(resolution,[status(thm)],[f263,f131])).
% 66.68/8.97 fof(f317,plain,(
% 66.68/8.97 tail_of(sK8_skl)=head_of(sK9_skl)|tail_of(sK8_skl)=tail_of(sK0_skl(head_of(sK9_skl),tail_of(sK8_skl)))|tail_of(sK8_skl)=head_of(sK0_skl(head_of(sK9_skl),tail_of(sK8_skl)))),
% 66.68/8.97 inference(resolution,[status(thm)],[f314,f271])).
% 66.68/8.97 fof(f325,plain,(
% 66.68/8.97 tail_of(sK8_skl)=head_of(sK9_skl)|tail_of(sK8_skl)=tail_of(sK0_skl(head_of(sK9_skl),tail_of(sK8_skl)))|head_of(sK9_skl)=tail_of(sK0_skl(head_of(sK9_skl),tail_of(sK8_skl)))),
% 66.68/8.97 inference(resolution,[status(thm)],[f313,f271])).
% 66.68/8.97 fof(f446,plain,(
% 66.68/8.97 ![X0]: (~vertex(X0)|X0=head_of(sK9_skl)|head_of(sK9_skl)=head_of(sK0_skl(head_of(sK9_skl),X0))|head_of(sK9_skl)=tail_of(sK0_skl(head_of(sK9_skl),X0)))),
% 66.68/8.97 inference(resolution,[status(thm)],[f262,f132])).
% 66.68/8.97 fof(f447,plain,(
% 66.68/8.97 ![X0]: (~vertex(X0)|X0=head_of(sK9_skl)|head_of(sK9_skl)=head_of(sK0_skl(head_of(sK9_skl),X0))|X0=head_of(sK0_skl(head_of(sK9_skl),X0)))),
% 66.68/8.97 inference(resolution,[status(thm)],[f262,f131])).
% 66.68/8.97 fof(f450,plain,(
% 66.68/8.97 tail_of(sK8_skl)=head_of(sK9_skl)|head_of(sK9_skl)=head_of(sK0_skl(head_of(sK9_skl),tail_of(sK8_skl)))|tail_of(sK8_skl)=head_of(sK0_skl(head_of(sK9_skl),tail_of(sK8_skl)))),
% 66.68/8.97 inference(resolution,[status(thm)],[f447,f271])).
% 66.68/8.97 fof(f458,plain,(
% 66.68/8.97 tail_of(sK8_skl)=head_of(sK9_skl)|head_of(sK9_skl)=head_of(sK0_skl(head_of(sK9_skl),tail_of(sK8_skl)))|head_of(sK9_skl)=tail_of(sK0_skl(head_of(sK9_skl),tail_of(sK8_skl)))),
% 66.68/8.97 inference(resolution,[status(thm)],[f446,f271])).
% 66.68/8.97 fof(f576,plain,(
% 66.68/8.97 ![X0]: (tail_of(sK14_skl)=tail_of(sK8_skl)|~tail_of(sK0_skl(X0,tail_of(sK8_skl)))=head_of(sK9_skl)|~head_of(sK0_skl(X0,tail_of(sK8_skl)))=tail_of(sK8_skl)|~vertex(X0)|tail_of(sK8_skl)=X0)),
% 66.68/8.97 inference(resolution,[status(thm)],[f196,f271])).
% 66.68/8.97 fof(f584,plain,(
% 66.68/8.97 ![X0]: (head_of(sK14_skl)=head_of(sK9_skl)|~tail_of(sK0_skl(X0,tail_of(sK8_skl)))=head_of(sK9_skl)|~head_of(sK0_skl(X0,tail_of(sK8_skl)))=tail_of(sK8_skl)|~vertex(X0)|tail_of(sK8_skl)=X0)),
% 66.68/8.97 inference(resolution,[status(thm)],[f201,f271])).
% 66.68/8.97 fof(f608,plain,(
% 66.68/8.97 ![X0]: (tail_of(sK14_skl)=tail_of(sK8_skl)|~tail_of(sK0_skl(X0,tail_of(sK8_skl)))=tail_of(sK8_skl)|~head_of(sK0_skl(X0,tail_of(sK8_skl)))=head_of(sK9_skl)|~vertex(X0)|tail_of(sK8_skl)=X0)),
% 66.68/8.97 inference(resolution,[status(thm)],[f221,f271])).
% 66.68/8.97 fof(f616,plain,(
% 66.68/8.97 ![X0]: (head_of(sK14_skl)=head_of(sK9_skl)|~tail_of(sK0_skl(X0,tail_of(sK8_skl)))=tail_of(sK8_skl)|~head_of(sK0_skl(X0,tail_of(sK8_skl)))=head_of(sK9_skl)|~vertex(X0)|tail_of(sK8_skl)=X0)),
% 66.68/8.97 inference(resolution,[status(thm)],[f228,f271])).
% 66.68/8.97 fof(f1238,plain,(
% 66.68/8.97 tail_of(sK14_skl)=tail_of(sK8_skl)|~tail_of(sK0_skl(head_of(sK9_skl),tail_of(sK8_skl)))=head_of(sK9_skl)|~head_of(sK0_skl(head_of(sK9_skl),tail_of(sK8_skl)))=tail_of(sK8_skl)|tail_of(sK8_skl)=head_of(sK9_skl)),
% 66.68/8.97 inference(resolution,[status(thm)],[f576,f259])).
% 66.68/8.97 fof(f1715,plain,(
% 66.68/8.97 head_of(sK14_skl)=head_of(sK9_skl)|~tail_of(sK0_skl(head_of(sK9_skl),tail_of(sK8_skl)))=head_of(sK9_skl)|~head_of(sK0_skl(head_of(sK9_skl),tail_of(sK8_skl)))=tail_of(sK8_skl)|tail_of(sK8_skl)=head_of(sK9_skl)),
% 66.68/8.97 inference(resolution,[status(thm)],[f584,f259])).
% 66.68/8.97 fof(f2165,plain,(
% 66.68/8.97 tail_of(sK14_skl)=tail_of(sK8_skl)|~tail_of(sK0_skl(head_of(sK9_skl),tail_of(sK8_skl)))=tail_of(sK8_skl)|~head_of(sK0_skl(head_of(sK9_skl),tail_of(sK8_skl)))=head_of(sK9_skl)|tail_of(sK8_skl)=head_of(sK9_skl)),
% 66.68/8.97 inference(resolution,[status(thm)],[f608,f259])).
% 66.68/8.97 fof(f2295,plain,(
% 66.68/8.97 head_of(sK14_skl)=head_of(sK9_skl)|~tail_of(sK0_skl(head_of(sK9_skl),tail_of(sK8_skl)))=tail_of(sK8_skl)|~head_of(sK0_skl(head_of(sK9_skl),tail_of(sK8_skl)))=head_of(sK9_skl)|tail_of(sK8_skl)=head_of(sK9_skl)),
% 66.68/8.97 inference(resolution,[status(thm)],[f616,f259])).
% 66.68/8.97 fof(f2655,plain,(
% 66.68/8.97 ![X0,X1,X2]: (sK9_skl=sK8_skl|~head_of(sK9_skl)=tail_of(sK8_skl)|~path(X0,X1,X2)|precedes(sK9_skl,sK8_skl,X2)|~on_path(sK9_skl,X2)|~on_path(sK8_skl,X2))),
% 66.68/8.97 inference(resolution,[status(thm)],[f288,f69])).
% 66.68/8.97 fof(f2662,plain,(
% 66.68/8.97 ![X0,X1]: (sK9_skl=sK8_skl|~head_of(sK9_skl)=tail_of(sK8_skl)|~path(X0,X1,sK10_skl)|precedes(sK9_skl,sK8_skl,sK10_skl)|~on_path(sK8_skl,sK10_skl))),
% 66.68/8.97 inference(resolution,[status(thm)],[f2655,f234])).
% 66.68/8.97 fof(f2663,plain,(
% 66.68/8.97 ![X0,X1]: (sK9_skl=sK8_skl|~head_of(sK9_skl)=tail_of(sK8_skl)|~path(X0,X1,sK10_skl)|~on_path(sK8_skl,sK10_skl))),
% 66.68/8.97 inference(forward_subsumption_resolution,[status(thm)],[f2662,f156])).
% 66.68/8.97 fof(f2664,plain,(
% 66.68/8.97 ![X0,X1]: (sK9_skl=sK8_skl|~head_of(sK9_skl)=tail_of(sK8_skl)|~path(X0,X1,sK10_skl))),
% 66.68/8.97 inference(resolution,[status(thm)],[f2663,f182])).
% 66.68/8.97 fof(f2665,plain,(
% 66.68/8.97 sK9_skl=sK8_skl|~head_of(sK9_skl)=tail_of(sK8_skl)),
% 66.68/8.97 inference(resolution,[status(thm)],[f2664,f154])).
% 66.68/8.97 fof(f3670,plain,(
% 66.68/8.97 tail_of(sK14_skl)=tail_of(sK8_skl)|~head_of(sK0_skl(head_of(sK9_skl),tail_of(sK8_skl)))=tail_of(sK8_skl)|tail_of(sK8_skl)=head_of(sK9_skl)|tail_of(sK8_skl)=head_of(sK9_skl)|head_of(sK9_skl)=head_of(sK0_skl(head_of(sK9_skl),tail_of(sK8_skl)))),
% 66.68/8.97 inference(resolution,[status(thm)],[f1238,f458])).
% 66.68/8.97 fof(f3674,plain,(
% 66.68/8.97 tail_of(sK14_skl)=tail_of(sK8_skl)|~head_of(sK0_skl(head_of(sK9_skl),tail_of(sK8_skl)))=tail_of(sK8_skl)|tail_of(sK8_skl)=head_of(sK9_skl)|head_of(sK9_skl)=head_of(sK0_skl(head_of(sK9_skl),tail_of(sK8_skl)))),
% 66.68/8.97 inference(duplicate_literals_removal,[status(thm)],[f3670])).
% 66.68/8.97 fof(f3675,plain,(
% 66.68/8.97 tail_of(sK14_skl)=tail_of(sK8_skl)|~tail_of(sK0_skl(head_of(sK9_skl),tail_of(sK8_skl)))=tail_of(sK8_skl)|tail_of(sK8_skl)=head_of(sK9_skl)),
% 66.68/8.97 inference(backward_subsumption_resolution,[status(thm)],[f2165,f3676])).
% 66.68/8.97 fof(f3676,plain,(
% 66.68/8.97 tail_of(sK14_skl)=tail_of(sK8_skl)|tail_of(sK8_skl)=head_of(sK9_skl)|head_of(sK9_skl)=head_of(sK0_skl(head_of(sK9_skl),tail_of(sK8_skl)))),
% 66.68/8.97 inference(forward_subsumption_resolution,[status(thm)],[f3674,f450])).
% 66.68/8.97 fof(f3706,plain,(
% 66.68/8.97 tail_of(sK14_skl)=tail_of(sK8_skl)|tail_of(sK8_skl)=head_of(sK9_skl)|tail_of(sK8_skl)=head_of(sK9_skl)|head_of(sK9_skl)=tail_of(sK0_skl(head_of(sK9_skl),tail_of(sK8_skl)))),
% 66.68/8.97 inference(resolution,[status(thm)],[f3675,f325])).
% 66.68/8.97 fof(f3707,plain,(
% 66.68/8.97 tail_of(sK14_skl)=tail_of(sK8_skl)|tail_of(sK8_skl)=head_of(sK9_skl)|tail_of(sK8_skl)=head_of(sK9_skl)|tail_of(sK8_skl)=head_of(sK0_skl(head_of(sK9_skl),tail_of(sK8_skl)))),
% 66.68/8.97 inference(resolution,[status(thm)],[f3675,f317])).
% 66.68/8.97 fof(f3711,plain,(
% 66.68/8.97 tail_of(sK14_skl)=tail_of(sK8_skl)|~head_of(sK0_skl(head_of(sK9_skl),tail_of(sK8_skl)))=tail_of(sK8_skl)|tail_of(sK8_skl)=head_of(sK9_skl)),
% 66.68/8.97 inference(backward_subsumption_resolution,[status(thm)],[f1238,f3712])).
% 66.68/8.97 fof(f3712,plain,(
% 66.68/8.97 tail_of(sK14_skl)=tail_of(sK8_skl)|tail_of(sK8_skl)=head_of(sK9_skl)|head_of(sK9_skl)=tail_of(sK0_skl(head_of(sK9_skl),tail_of(sK8_skl)))),
% 66.68/8.97 inference(duplicate_literals_removal,[status(thm)],[f3706])).
% 66.68/8.97 fof(f3713,plain,(
% 66.68/8.97 tail_of(sK14_skl)=tail_of(sK8_skl)|tail_of(sK8_skl)=head_of(sK9_skl)|tail_of(sK8_skl)=head_of(sK0_skl(head_of(sK9_skl),tail_of(sK8_skl)))),
% 66.68/8.97 inference(duplicate_literals_removal,[status(thm)],[f3707])).
% 66.68/8.97 fof(f3722,plain,(
% 66.68/8.97 tail_of(sK14_skl)=tail_of(sK8_skl)|tail_of(sK8_skl)=head_of(sK9_skl)),
% 66.68/8.97 inference(forward_subsumption_resolution,[status(thm)],[f3711,f3713])).
% 66.68/8.97 fof(f4334,plain,(
% 66.68/8.97 head_of(sK14_skl)=head_of(sK9_skl)|~head_of(sK0_skl(head_of(sK9_skl),tail_of(sK8_skl)))=tail_of(sK8_skl)|tail_of(sK8_skl)=head_of(sK9_skl)|tail_of(sK8_skl)=head_of(sK9_skl)|head_of(sK9_skl)=head_of(sK0_skl(head_of(sK9_skl),tail_of(sK8_skl)))),
% 66.68/8.97 inference(resolution,[status(thm)],[f1715,f458])).
% 66.68/8.97 fof(f4338,plain,(
% 66.68/8.97 head_of(sK14_skl)=head_of(sK9_skl)|~head_of(sK0_skl(head_of(sK9_skl),tail_of(sK8_skl)))=tail_of(sK8_skl)|tail_of(sK8_skl)=head_of(sK9_skl)|head_of(sK9_skl)=head_of(sK0_skl(head_of(sK9_skl),tail_of(sK8_skl)))),
% 66.68/8.97 inference(duplicate_literals_removal,[status(thm)],[f4334])).
% 66.68/8.97 fof(f4339,plain,(
% 66.68/8.97 head_of(sK14_skl)=head_of(sK9_skl)|~tail_of(sK0_skl(head_of(sK9_skl),tail_of(sK8_skl)))=tail_of(sK8_skl)|tail_of(sK8_skl)=head_of(sK9_skl)),
% 66.68/8.97 inference(backward_subsumption_resolution,[status(thm)],[f2295,f4340])).
% 66.68/8.97 fof(f4340,plain,(
% 66.68/8.97 head_of(sK14_skl)=head_of(sK9_skl)|tail_of(sK8_skl)=head_of(sK9_skl)|head_of(sK9_skl)=head_of(sK0_skl(head_of(sK9_skl),tail_of(sK8_skl)))),
% 66.68/8.97 inference(forward_subsumption_resolution,[status(thm)],[f4338,f450])).
% 66.68/8.97 fof(f4370,plain,(
% 66.68/8.97 head_of(sK14_skl)=head_of(sK9_skl)|tail_of(sK8_skl)=head_of(sK9_skl)|tail_of(sK8_skl)=head_of(sK9_skl)|head_of(sK9_skl)=tail_of(sK0_skl(head_of(sK9_skl),tail_of(sK8_skl)))),
% 66.68/8.97 inference(resolution,[status(thm)],[f4339,f325])).
% 66.68/8.97 fof(f4371,plain,(
% 66.68/8.97 head_of(sK14_skl)=head_of(sK9_skl)|tail_of(sK8_skl)=head_of(sK9_skl)|tail_of(sK8_skl)=head_of(sK9_skl)|tail_of(sK8_skl)=head_of(sK0_skl(head_of(sK9_skl),tail_of(sK8_skl)))),
% 66.68/9.03 inference(resolution,[status(thm)],[f4339,f317])).
% 66.68/9.03 fof(f4375,plain,(
% 66.68/9.03 head_of(sK14_skl)=head_of(sK9_skl)|~head_of(sK0_skl(head_of(sK9_skl),tail_of(sK8_skl)))=tail_of(sK8_skl)|tail_of(sK8_skl)=head_of(sK9_skl)),
% 66.68/9.03 inference(backward_subsumption_resolution,[status(thm)],[f1715,f4376])).
% 66.68/9.03 fof(f4376,plain,(
% 66.68/9.03 head_of(sK14_skl)=head_of(sK9_skl)|tail_of(sK8_skl)=head_of(sK9_skl)|head_of(sK9_skl)=tail_of(sK0_skl(head_of(sK9_skl),tail_of(sK8_skl)))),
% 66.68/9.03 inference(duplicate_literals_removal,[status(thm)],[f4370])).
% 66.68/9.03 fof(f4377,plain,(
% 66.68/9.03 head_of(sK14_skl)=head_of(sK9_skl)|tail_of(sK8_skl)=head_of(sK9_skl)|tail_of(sK8_skl)=head_of(sK0_skl(head_of(sK9_skl),tail_of(sK8_skl)))),
% 66.68/9.03 inference(duplicate_literals_removal,[status(thm)],[f4371])).
% 66.68/9.03 fof(f4386,plain,(
% 66.68/9.03 head_of(sK14_skl)=head_of(sK9_skl)|tail_of(sK8_skl)=head_of(sK9_skl)),
% 66.68/9.03 inference(forward_subsumption_resolution,[status(thm)],[f4375,f4377])).
% 66.68/9.03 fof(f4396,plain,(
% 66.68/9.03 head_of(sK14_skl)=head_of(sK9_skl)|sK9_skl=sK8_skl),
% 66.68/9.03 inference(resolution,[status(thm)],[f4386,f2665])).
% 66.68/9.03 fof(f4548,plain,(
% 66.68/9.03 ![X0,X1,X2,X3]: (sK9_skl=sK8_skl|~shortest_path(X0,X1,X2)|~precedes(X3,sK9_skl,X2)|~tail_of(sK14_skl)=tail_of(X3))),
% 66.68/9.03 inference(resolution,[status(thm)],[f4396,f91])).
% 66.68/9.03 fof(f4575,plain,(
% 66.68/9.03 ![X0]: (sK9_skl=sK8_skl|~precedes(X0,sK9_skl,sK10_skl)|~tail_of(sK14_skl)=tail_of(X0))),
% 66.68/9.03 inference(resolution,[status(thm)],[f4548,f121])).
% 66.68/9.03 fof(f4577,plain,(
% 66.68/9.03 sK9_skl=sK8_skl|~tail_of(sK14_skl)=tail_of(sK8_skl)),
% 66.68/9.03 inference(resolution,[status(thm)],[f4575,f122])).
% 66.68/9.03 fof(f4580,plain,(
% 66.68/9.03 sK9_skl=sK8_skl|tail_of(sK8_skl)=head_of(sK9_skl)),
% 66.68/9.03 inference(resolution,[status(thm)],[f4577,f3722])).
% 66.68/9.03 fof(f4976,plain,(
% 66.68/9.03 ~head_of(sK8_skl)=head_of(sK8_skl)|head_of(sK13_skl)=tail_of(sK8_skl)),
% 66.68/9.03 inference(backward_demodulation,[status(thm)],[f6408,f187])).
% 66.68/9.03 fof(f4979,plain,(
% 66.68/9.03 ~tail_of(sK8_skl)=tail_of(sK8_skl)),
% 66.68/9.03 inference(backward_demodulation,[status(thm)],[f6408,f159])).
% 66.68/9.03 fof(f6408,plain,(
% 66.68/9.03 sK9_skl=sK8_skl),
% 66.68/9.03 inference(forward_subsumption_resolution,[status(thm)],[f4580,f2665])).
% 66.68/9.03 fof(f7503,plain,(
% 66.68/9.03 head_of(sK13_skl)=tail_of(sK8_skl)),
% 66.68/9.03 inference(trivial_equality_resolution,[status(thm)],[f4976])).
% 66.68/9.03 fof(f7507,plain,(
% 66.68/9.03 ~head_of(sK13_skl)=tail_of(sK8_skl)),
% 66.68/9.03 inference(forward_demodulation,[status(thm)],[f7503,f4979])).
% 66.68/9.03 fof(f7508,plain,(
% 66.68/9.03 ~head_of(sK13_skl)=head_of(sK13_skl)),
% 66.68/9.03 inference(forward_demodulation,[status(thm)],[f7503,f7507])).
% 66.68/9.03 fof(f7509,plain,(
% 66.68/9.03 $false),
% 66.68/9.03 inference(trivial_equality_resolution,[status(thm)],[f7508])).
% 66.68/9.03 % SZS output end CNFRefutation for theBenchmark.p
% 6.22/9.09 % Elapsed time: 8.725419 seconds
% 6.22/9.09 % CPU time: 68.665777 seconds
% 6.22/9.09 % Total memory used: 531.582 MB
% 6.22/9.09 % Net memory used: 505.059 MB
%------------------------------------------------------------------------------