%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GRA007+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 : n011.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 34.73s 4.91s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRA007+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
% 0.11/0.37 % Computer : n011.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 20 18:28:55 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.38 % Drodi V4.1.1
% 34.73/4.91 % Refutation found
% 34.73/4.91 % SZS status Theorem for theBenchmark: Theorem is valid
% 34.73/4.91 % SZS output start CNFRefutation for theBenchmark
% 34.73/4.91 fof(f3,axiom,(
% 34.73/4.91 ( 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) ) ) ) )) )) ),
% 34.73/4.91 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 34.73/4.91 fof(f6,axiom,(
% 34.73/4.91 (! [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) ) ) )),
% 34.73/4.91 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 34.73/4.91 fof(f7,axiom,(
% 34.73/4.91 (! [V1,V2,P,V] :( ( path(V1,V2,P)& in_path(V,P) )=> ( vertex(V)& (? [E] :( on_path(E,P)& ( V = head_of(E)| V = tail_of(E) ) ) )) ) )),
% 34.73/4.91 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 34.73/4.91 fof(f8,axiom,(
% 34.73/4.91 (! [E1,E2] :( sequential(E1,E2)<=> ( edge(E1)& edge(E2)& E1 != E2& head_of(E1) = tail_of(E2) ) ) )),
% 34.73/4.91 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 34.73/4.91 fof(f9,axiom,(
% 34.73/4.91 (! [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) ) )) ) ) )) )),
% 34.73/4.91 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 34.73/4.91 fof(f10,axiom,(
% 34.73/4.91 (! [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) ) )) ) ) )) )),
% 34.73/4.91 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 34.73/4.91 fof(f11,axiom,(
% 34.73/4.91 (! [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)) ) )) ) )),
% 34.73/4.91 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 34.73/4.91 fof(f12,axiom,(
% 34.73/4.91 (! [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) ) ) )),
% 34.73/4.91 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 34.73/4.91 fof(f18,conjecture,(
% 34.73/4.91 ( complete=> (! [V1,V2,E1,E2,P] :( ( shortest_path(V1,V2,P)& precedes(E1,E2,P) )=> (? [E3] :( edge(E3)& tail_of(E3) = head_of(E2)& head_of(E3) = tail_of(E1) ) )) )) ),
% 34.73/4.91 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 34.73/4.91 fof(f19,negated_conjecture,(
% 34.73/4.91 ~(( complete=> (! [V1,V2,E1,E2,P] :( ( shortest_path(V1,V2,P)& precedes(E1,E2,P) )=> (? [E3] :( edge(E3)& tail_of(E3) = head_of(E2)& head_of(E3) = tail_of(E1) ) )) )) )),
% 34.73/4.91 inference(negated_conjecture,[status(cth)],[f18])).
% 34.73/4.91 fof(f25,plain,(
% 34.73/4.91 ~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)))))))),
% 34.73/4.91 inference(pre_NNF_transformation,[status(thm)],[f3])).
% 34.73/4.91 fof(f26,definition,(
% 34.73/4.91 ![V1,V2,E]: (sP0_prd(E,V2,V1)<=>(V1=head_of(E)&V2=tail_of(E)))),
% 34.73/4.91 introduced(definition,[new_symbols(definition,[sP0_prd])],[])).
% 34.73/4.91 fof(f27,plain,(
% 34.73/4.91 ~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)))))))),
% 34.73/4.91 inference(formula_renaming,[status(thm)],[f25,f26])).
% 34.73/4.91 fof(f28,plain,(
% 34.73/4.91 ~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))))))))),
% 34.73/4.91 inference(NNF_transformation,[status(thm)],[f27])).
% 34.73/4.91 fof(f29,plain,(
% 34.73/4.91 ~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))))))))),
% 34.73/4.91 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(E,sK0_skl(V2,V1))],[f28])).
% 34.73/4.91 fof(f30,plain,(
% 34.73/4.91 ![X0,X1]: (~complete|~vertex(X0)|~vertex(X1)|X0=X1|edge(sK0_skl(X1,X0)))),
% 34.73/4.91 inference(cnf_transformation,[status(thm)],[f29])).
% 34.73/4.91 fof(f31,plain,(
% 34.73/4.91 ![X0,X1]: (~complete|~vertex(X0)|~vertex(X1)|X0=X1|sP0_prd(sK0_skl(X1,X0),X1,X0)|X1=head_of(sK0_skl(X1,X0)))),
% 34.73/4.91 inference(cnf_transformation,[status(thm)],[f29])).
% 34.73/4.91 fof(f32,plain,(
% 34.73/4.91 ![X0,X1]: (~complete|~vertex(X0)|~vertex(X1)|X0=X1|sP0_prd(sK0_skl(X1,X0),X1,X0)|X0=tail_of(sK0_skl(X1,X0)))),
% 34.73/4.91 inference(cnf_transformation,[status(thm)],[f29])).
% 34.73/4.91 fof(f49,plain,(
% 34.73/4.91 ![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)))),
% 34.73/4.91 inference(pre_NNF_transformation,[status(thm)],[f6])).
% 34.73/4.91 fof(f50,plain,(
% 34.73/4.91 ![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)))),
% 34.73/4.91 inference(miniscoping,[status(thm)],[f49])).
% 34.73/4.91 fof(f51,plain,(
% 34.73/4.91 ![X0,X1,X2,X3]: (~path(X0,X1,X2)|~on_path(X3,X2)|edge(X3))),
% 34.73/4.91 inference(cnf_transformation,[status(thm)],[f50])).
% 34.73/4.91 fof(f52,plain,(
% 34.73/4.91 ![X0,X1,X2,X3]: (~path(X0,X1,X2)|~on_path(X3,X2)|in_path(head_of(X3),X2))),
% 34.73/4.91 inference(cnf_transformation,[status(thm)],[f50])).
% 34.73/4.91 fof(f53,plain,(
% 34.73/4.91 ![X0,X1,X2,X3]: (~path(X0,X1,X2)|~on_path(X3,X2)|in_path(tail_of(X3),X2))),
% 34.73/4.91 inference(cnf_transformation,[status(thm)],[f50])).
% 34.73/4.91 fof(f54,plain,(
% 34.73/4.91 ![V1,V2,P,V]: ((~path(V1,V2,P)|~in_path(V,P))|(vertex(V)&(?[E]: (on_path(E,P)&(V=head_of(E)|V=tail_of(E))))))),
% 34.73/4.91 inference(pre_NNF_transformation,[status(thm)],[f7])).
% 34.73/4.91 fof(f55,plain,(
% 34.73/4.91 ![P,V]: (((![V1,V2]: ~path(V1,V2,P))|~in_path(V,P))|(vertex(V)&(?[E]: (on_path(E,P)&(V=head_of(E)|V=tail_of(E))))))),
% 34.73/4.91 inference(miniscoping,[status(thm)],[f54])).
% 34.73/4.91 fof(f56,plain,(
% 34.73/4.91 ![P,V]: (((![V1,V2]: ~path(V1,V2,P))|~in_path(V,P))|(vertex(V)&(on_path(sK3_skl(V,P),P)&(V=head_of(sK3_skl(V,P))|V=tail_of(sK3_skl(V,P))))))),
% 34.73/4.91 inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl]),skolemize(E,sK3_skl(V,P))],[f55])).
% 34.73/4.91 fof(f57,plain,(
% 34.73/4.91 ![X0,X1,X2,X3]: (~path(X0,X1,X2)|~in_path(X3,X2)|vertex(X3))),
% 34.73/4.91 inference(cnf_transformation,[status(thm)],[f56])).
% 34.73/4.91 fof(f60,plain,(
% 34.73/4.91 ![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))))),
% 34.73/4.91 inference(NNF_transformation,[status(thm)],[f8])).
% 34.73/4.91 fof(f61,plain,(
% 34.73/4.91 (![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))))),
% 34.73/4.91 inference(miniscoping,[status(thm)],[f60])).
% 34.73/4.91 fof(f66,plain,(
% 34.73/4.91 ![X0,X1]: (sequential(X0,X1)|~edge(X0)|~edge(X1)|X0=X1|~head_of(X0)=tail_of(X1))),
% 34.73/4.91 inference(cnf_transformation,[status(thm)],[f61])).
% 34.73/4.91 fof(f67,plain,(
% 34.73/4.91 ![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))))))))),
% 34.73/4.91 inference(pre_NNF_transformation,[status(thm)],[f9])).
% 34.73/4.91 fof(f68,plain,(
% 34.73/4.91 ![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))))))))),
% 34.73/4.91 inference(miniscoping,[status(thm)],[f67])).
% 34.73/4.91 fof(f69,plain,(
% 34.73/4.91 ![X0,X1,X2,X3,X4]: (~path(X0,X1,X2)|precedes(X3,X4,X2)|~on_path(X3,X2)|~on_path(X4,X2)|~sequential(X3,X4))),
% 34.73/4.91 inference(cnf_transformation,[status(thm)],[f68])).
% 34.73/4.91 fof(f71,plain,(
% 34.73/4.91 ![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))))))))),
% 34.73/4.91 inference(pre_NNF_transformation,[status(thm)],[f10])).
% 34.73/4.91 fof(f72,plain,(
% 34.73/4.91 ![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)))))))))),
% 34.73/4.91 inference(NNF_transformation,[status(thm)],[f71])).
% 34.73/4.91 fof(f73,plain,(
% 34.73/4.91 ![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)))))))))),
% 34.73/4.91 inference(miniscoping,[status(thm)],[f72])).
% 34.73/4.91 fof(f74,plain,(
% 34.73/4.91 ![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)))))))))),
% 34.73/4.91 inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl]),skolemize(E3,sK4_skl(E2,E1,P))],[f73])).
% 34.73/4.91 fof(f75,plain,(
% 34.73/4.91 ![X0,X1,X2,X3,X4]: (~path(X0,X1,X2)|~precedes(X3,X4,X2)|on_path(X3,X2))),
% 34.73/4.91 inference(cnf_transformation,[status(thm)],[f74])).
% 34.73/4.91 fof(f76,plain,(
% 34.73/4.91 ![X0,X1,X2,X3,X4]: (~path(X0,X1,X2)|~precedes(X3,X4,X2)|on_path(X4,X2))),
% 34.73/4.91 inference(cnf_transformation,[status(thm)],[f74])).
% 34.73/4.91 fof(f80,plain,(
% 34.73/4.91 ![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))))))),
% 34.73/4.91 inference(pre_NNF_transformation,[status(thm)],[f11])).
% 34.73/4.91 fof(f81,plain,(
% 34.73/4.91 ![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)))))))),
% 34.73/4.91 inference(NNF_transformation,[status(thm)],[f80])).
% 34.73/4.91 fof(f82,plain,(
% 34.73/4.91 (![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)))))))),
% 34.73/4.91 inference(miniscoping,[status(thm)],[f81])).
% 34.73/4.91 fof(f83,plain,(
% 34.73/4.91 (![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)))))))),
% 34.73/4.91 inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl]),skolemize(P,sK5_skl(SP,V2,V1))],[f82])).
% 34.73/4.91 fof(f84,plain,(
% 34.73/4.91 ![X0,X1,X2]: (~shortest_path(X0,X1,X2)|path(X0,X1,X2))),
% 34.73/4.91 inference(cnf_transformation,[status(thm)],[f83])).
% 34.73/4.91 fof(f89,plain,(
% 34.73/4.91 ![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)))),
% 34.73/4.91 inference(pre_NNF_transformation,[status(thm)],[f12])).
% 34.73/4.91 fof(f90,plain,(
% 34.73/4.91 ![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)))),
% 34.73/4.91 inference(miniscoping,[status(thm)],[f89])).
% 34.73/4.91 fof(f91,plain,(
% 34.73/4.91 ![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))),
% 34.73/4.91 inference(cnf_transformation,[status(thm)],[f90])).
% 34.73/4.91 fof(f92,plain,(
% 34.73/4.91 ![X0,X1,X2,X3,X4]: (~shortest_path(X0,X1,X2)|~precedes(X3,X4,X2)|~precedes(X4,X3,X2))),
% 34.73/4.91 inference(cnf_transformation,[status(thm)],[f90])).
% 34.73/4.91 fof(f116,plain,(
% 34.73/4.91 (complete&(?[V1,V2,E1,E2,P]: ((shortest_path(V1,V2,P)&precedes(E1,E2,P))&(![E3]: ((~edge(E3)|~tail_of(E3)=head_of(E2))|~head_of(E3)=tail_of(E1))))))),
% 34.73/4.91 inference(pre_NNF_transformation,[status(thm)],[f19])).
% 34.73/4.91 fof(f117,plain,(
% 34.73/4.91 complete&(?[E1,E2]: ((?[P]: ((?[V1,V2]: shortest_path(V1,V2,P))&precedes(E1,E2,P)))&(![E3]: ((~edge(E3)|~tail_of(E3)=head_of(E2))|~head_of(E3)=tail_of(E1)))))),
% 34.73/4.91 inference(miniscoping,[status(thm)],[f116])).
% 34.73/4.91 fof(f118,plain,(
% 34.73/4.91 complete&((shortest_path(sK11_skl,sK12_skl,sK10_skl)&precedes(sK8_skl,sK9_skl,sK10_skl))&(![E3]: ((~edge(E3)|~tail_of(E3)=head_of(sK9_skl))|~head_of(E3)=tail_of(sK8_skl))))),
% 34.73/4.91 inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl,sK9_skl,sK10_skl,sK11_skl,sK12_skl]),skolemize(E1,sK8_skl),skolemize(E2,sK9_skl),skolemize(P,sK10_skl),skolemize(V1,sK11_skl),skolemize(V2,sK12_skl)],[f117])).
% 34.73/4.91 fof(f119,plain,(
% 34.73/4.91 complete),
% 34.73/4.91 inference(cnf_transformation,[status(thm)],[f118])).
% 34.73/4.91 fof(f120,plain,(
% 34.73/4.91 shortest_path(sK11_skl,sK12_skl,sK10_skl)),
% 34.73/4.91 inference(cnf_transformation,[status(thm)],[f118])).
% 34.73/4.91 fof(f121,plain,(
% 34.73/4.91 precedes(sK8_skl,sK9_skl,sK10_skl)),
% 34.73/4.91 inference(cnf_transformation,[status(thm)],[f118])).
% 34.73/4.91 fof(f122,plain,(
% 34.73/4.91 ![X0]: (~edge(X0)|~tail_of(X0)=head_of(sK9_skl)|~head_of(X0)=tail_of(sK8_skl))),
% 34.73/4.91 inference(cnf_transformation,[status(thm)],[f118])).
% 34.73/4.91 fof(f123,plain,(
% 34.73/4.91 ![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))))),
% 34.73/4.91 inference(NNF_transformation,[status(thm)],[f26])).
% 34.73/4.91 fof(f124,plain,(
% 34.73/4.91 (![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))))),
% 34.73/4.91 inference(miniscoping,[status(thm)],[f123])).
% 34.73/4.91 fof(f125,plain,(
% 34.73/4.91 ![X0,X1,X2]: (~sP0_prd(X0,X1,X2)|X2=head_of(X0))),
% 34.73/4.91 inference(cnf_transformation,[status(thm)],[f124])).
% 34.73/4.91 fof(f126,plain,(
% 34.73/4.91 ![X0,X1,X2]: (~sP0_prd(X0,X1,X2)|X1=tail_of(X0))),
% 34.73/4.91 inference(cnf_transformation,[status(thm)],[f124])).
% 34.73/4.91 fof(f139,plain,(
% 34.73/4.91 ![X0,X1]: (~vertex(X0)|~vertex(X1)|X0=X1|sP0_prd(sK0_skl(X1,X0),X1,X0)|X0=tail_of(sK0_skl(X1,X0)))),
% 34.73/4.91 inference(backward_subsumption_resolution,[status(thm)],[f32,f119])).
% 34.73/4.91 fof(f140,plain,(
% 34.73/4.91 ![X0,X1]: (~vertex(X0)|~vertex(X1)|X0=X1|sP0_prd(sK0_skl(X1,X0),X1,X0)|X1=head_of(sK0_skl(X1,X0)))),
% 34.73/4.91 inference(backward_subsumption_resolution,[status(thm)],[f31,f119])).
% 34.73/4.91 fof(f141,plain,(
% 34.73/4.91 ![X0,X1]: (~vertex(X0)|~vertex(X1)|X0=X1|edge(sK0_skl(X1,X0)))),
% 34.73/4.91 inference(backward_subsumption_resolution,[status(thm)],[f30,f119])).
% 34.73/4.91 fof(f144,plain,(
% 34.73/4.91 path(sK11_skl,sK12_skl,sK10_skl)),
% 34.73/4.91 inference(resolution,[status(thm)],[f84,f120])).
% 34.73/4.91 fof(f145,plain,(
% 34.73/4.91 ![X0,X1]: (~precedes(X0,X1,sK10_skl)|~precedes(X1,X0,sK10_skl))),
% 34.73/4.91 inference(resolution,[status(thm)],[f92,f120])).
% 34.73/4.91 fof(f146,plain,(
% 34.73/4.91 ~precedes(sK9_skl,sK8_skl,sK10_skl)),
% 34.73/4.91 inference(resolution,[status(thm)],[f145,f121])).
% 34.73/4.91 fof(f157,plain,(
% 34.73/4.91 ![X0,X1]: (~path(X0,X1,sK10_skl)|on_path(sK8_skl,sK10_skl))),
% 34.73/4.91 inference(resolution,[status(thm)],[f75,f121])).
% 34.73/4.91 fof(f160,plain,(
% 34.73/4.91 on_path(sK8_skl,sK10_skl)),
% 34.73/4.91 inference(resolution,[status(thm)],[f157,f144])).
% 34.73/4.91 fof(f161,plain,(
% 34.73/4.91 ![X0,X1]: (~path(X0,X1,sK10_skl)|edge(sK8_skl))),
% 34.73/4.91 inference(resolution,[status(thm)],[f160,f51])).
% 34.73/4.91 fof(f162,plain,(
% 34.73/4.91 edge(sK8_skl)),
% 34.73/4.91 inference(resolution,[status(thm)],[f161,f144])).
% 34.73/4.91 fof(f164,plain,(
% 34.73/4.91 ![X0]: (sequential(X0,sK8_skl)|~edge(X0)|X0=sK8_skl|~head_of(X0)=tail_of(sK8_skl))),
% 34.73/4.91 inference(resolution,[status(thm)],[f162,f66])).
% 34.73/4.91 fof(f167,plain,(
% 34.73/4.91 ![X0,X1]: (~vertex(X0)|~vertex(X1)|X0=X1|X0=tail_of(sK0_skl(X1,X0))|X0=head_of(sK0_skl(X1,X0)))),
% 34.73/4.91 inference(resolution,[status(thm)],[f139,f125])).
% 34.73/4.91 fof(f170,plain,(
% 34.73/4.91 ![X0,X1,X2]: (~precedes(X0,X1,sK10_skl)|~tail_of(X2)=tail_of(X0)|~head_of(X2)=head_of(X1))),
% 34.73/4.91 inference(resolution,[status(thm)],[f91,f120])).
% 34.73/4.91 fof(f171,plain,(
% 34.73/4.91 ![X0]: (~tail_of(X0)=tail_of(sK8_skl)|~head_of(X0)=head_of(sK9_skl))),
% 34.73/4.91 inference(resolution,[status(thm)],[f170,f121])).
% 34.73/4.91 fof(f172,plain,(
% 34.73/4.91 ~tail_of(sK9_skl)=tail_of(sK8_skl)),
% 34.73/4.91 inference(equality_resolution,[status(thm)],[f171])).
% 34.73/4.91 fof(f181,plain,(
% 34.73/4.91 ![X0,X1]: (~vertex(X0)|~vertex(X1)|X0=X1|X1=head_of(sK0_skl(X1,X0))|X1=tail_of(sK0_skl(X1,X0)))),
% 34.73/4.91 inference(resolution,[status(thm)],[f140,f126])).
% 34.73/4.91 fof(f182,plain,(
% 34.73/4.91 ![X0,X1]: (~vertex(X0)|~vertex(X1)|X0=X1|X1=head_of(sK0_skl(X1,X0))|X0=head_of(sK0_skl(X1,X0)))),
% 34.73/4.91 inference(resolution,[status(thm)],[f140,f125])).
% 34.73/4.91 fof(f189,plain,(
% 34.73/4.91 ![X0,X1]: (~path(X0,X1,sK10_skl)|on_path(sK9_skl,sK10_skl))),
% 34.73/4.91 inference(resolution,[status(thm)],[f76,f121])).
% 34.73/4.91 fof(f190,plain,(
% 34.73/4.91 on_path(sK9_skl,sK10_skl)),
% 34.73/4.91 inference(resolution,[status(thm)],[f189,f144])).
% 34.73/4.91 fof(f191,plain,(
% 34.73/4.91 ![X0,X1]: (~path(X0,X1,sK10_skl)|edge(sK9_skl))),
% 34.73/4.91 inference(resolution,[status(thm)],[f190,f51])).
% 34.73/4.91 fof(f192,plain,(
% 34.73/4.91 edge(sK9_skl)),
% 34.73/4.91 inference(resolution,[status(thm)],[f191,f144])).
% 34.73/4.91 fof(f194,plain,(
% 34.73/4.91 sequential(sK9_skl,sK8_skl)|sK9_skl=sK8_skl|~head_of(sK9_skl)=tail_of(sK8_skl)),
% 34.73/4.91 inference(resolution,[status(thm)],[f192,f164])).
% 34.73/4.91 fof(f218,plain,(
% 34.73/4.91 ![X0]: (~on_path(X0,sK10_skl)|in_path(head_of(X0),sK10_skl))),
% 34.73/4.91 inference(resolution,[status(thm)],[f52,f144])).
% 34.73/4.91 fof(f219,plain,(
% 34.73/4.91 ![X0]: (~on_path(X0,sK10_skl)|in_path(tail_of(X0),sK10_skl))),
% 34.73/4.91 inference(resolution,[status(thm)],[f53,f144])).
% 34.73/4.91 fof(f237,plain,(
% 34.73/4.91 ![X0,X1,X2]: (~on_path(X0,sK10_skl)|~path(X1,X2,sK10_skl)|vertex(head_of(X0)))),
% 34.73/4.91 inference(resolution,[status(thm)],[f218,f57])).
% 34.73/4.91 fof(f239,plain,(
% 34.73/4.91 in_path(tail_of(sK8_skl),sK10_skl)),
% 34.73/4.91 inference(resolution,[status(thm)],[f219,f160])).
% 34.73/4.91 fof(f265,plain,(
% 34.73/4.91 ![X0,X1]: (~path(X0,X1,sK10_skl)|vertex(tail_of(sK8_skl)))),
% 34.73/4.91 inference(resolution,[status(thm)],[f239,f57])).
% 34.73/4.91 fof(f266,plain,(
% 34.73/4.91 vertex(tail_of(sK8_skl))),
% 34.73/4.91 inference(resolution,[status(thm)],[f265,f144])).
% 34.73/4.91 fof(f271,plain,(
% 34.73/4.91 ![X0]: (~vertex(X0)|X0=tail_of(sK8_skl)|tail_of(sK8_skl)=head_of(sK0_skl(tail_of(sK8_skl),X0))|X0=head_of(sK0_skl(tail_of(sK8_skl),X0)))),
% 34.73/4.91 inference(resolution,[status(thm)],[f266,f182])).
% 34.73/4.91 fof(f272,plain,(
% 34.73/4.91 ![X0]: (~vertex(X0)|X0=tail_of(sK8_skl)|tail_of(sK8_skl)=head_of(sK0_skl(tail_of(sK8_skl),X0))|tail_of(sK8_skl)=tail_of(sK0_skl(tail_of(sK8_skl),X0)))),
% 34.73/4.91 inference(resolution,[status(thm)],[f266,f181])).
% 34.73/4.91 fof(f273,plain,(
% 34.73/4.91 ![X0]: (~vertex(X0)|X0=tail_of(sK8_skl)|X0=tail_of(sK0_skl(tail_of(sK8_skl),X0))|X0=head_of(sK0_skl(tail_of(sK8_skl),X0)))),
% 34.73/4.91 inference(resolution,[status(thm)],[f266,f167])).
% 34.73/4.91 fof(f400,plain,(
% 34.73/4.91 ![X0]: (~on_path(X0,sK10_skl)|vertex(head_of(X0)))),
% 34.73/4.91 inference(resolution,[status(thm)],[f237,f144])).
% 34.73/4.91 fof(f402,plain,(
% 34.73/4.91 vertex(head_of(sK9_skl))),
% 34.73/4.91 inference(resolution,[status(thm)],[f400,f190])).
% 34.73/4.91 fof(f405,plain,(
% 34.73/4.91 head_of(sK9_skl)=tail_of(sK8_skl)|tail_of(sK8_skl)=head_of(sK0_skl(tail_of(sK8_skl),head_of(sK9_skl)))|head_of(sK9_skl)=head_of(sK0_skl(tail_of(sK8_skl),head_of(sK9_skl)))),
% 34.73/4.91 inference(resolution,[status(thm)],[f402,f271])).
% 34.73/4.91 fof(f414,plain,(
% 34.73/4.91 head_of(sK9_skl)=tail_of(sK8_skl)|head_of(sK9_skl)=tail_of(sK0_skl(tail_of(sK8_skl),head_of(sK9_skl)))|head_of(sK9_skl)=head_of(sK0_skl(tail_of(sK8_skl),head_of(sK9_skl)))),
% 34.73/4.91 inference(resolution,[status(thm)],[f402,f273])).
% 34.73/4.91 fof(f757,plain,(
% 34.73/4.91 head_of(sK9_skl)=tail_of(sK8_skl)|tail_of(sK8_skl)=head_of(sK0_skl(tail_of(sK8_skl),head_of(sK9_skl)))|tail_of(sK8_skl)=tail_of(sK0_skl(tail_of(sK8_skl),head_of(sK9_skl)))),
% 34.73/4.91 inference(resolution,[status(thm)],[f272,f402])).
% 34.73/4.91 fof(f828,plain,(
% 34.73/4.91 ![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))),
% 34.73/4.91 inference(resolution,[status(thm)],[f194,f69])).
% 34.73/4.91 fof(f837,plain,(
% 34.73/4.91 ![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))),
% 34.73/4.91 inference(resolution,[status(thm)],[f828,f190])).
% 34.73/4.91 fof(f838,plain,(
% 34.73/4.91 ![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))),
% 34.73/4.91 inference(forward_subsumption_resolution,[status(thm)],[f837,f146])).
% 34.73/4.91 fof(f839,plain,(
% 34.73/4.91 ![X0,X1]: (sK9_skl=sK8_skl|~head_of(sK9_skl)=tail_of(sK8_skl)|~path(X0,X1,sK10_skl))),
% 34.73/4.91 inference(resolution,[status(thm)],[f838,f160])).
% 34.73/4.91 fof(f840,plain,(
% 34.73/4.91 sK9_skl=sK8_skl|~head_of(sK9_skl)=tail_of(sK8_skl)),
% 34.73/4.91 inference(resolution,[status(thm)],[f839,f144])).
% 34.73/4.91 fof(f2329,plain,(
% 34.73/4.91 head_of(sK9_skl)=tail_of(sK8_skl)|head_of(sK9_skl)=head_of(sK0_skl(tail_of(sK8_skl),head_of(sK9_skl)))|~edge(sK0_skl(tail_of(sK8_skl),head_of(sK9_skl)))|~tail_of(sK0_skl(tail_of(sK8_skl),head_of(sK9_skl)))=head_of(sK9_skl)),
% 34.73/4.91 inference(resolution,[status(thm)],[f405,f122])).
% 34.73/4.91 fof(f2340,plain,(
% 34.73/4.91 head_of(sK9_skl)=tail_of(sK8_skl)|head_of(sK9_skl)=head_of(sK0_skl(tail_of(sK8_skl),head_of(sK9_skl)))|~edge(sK0_skl(tail_of(sK8_skl),head_of(sK9_skl)))),
% 34.73/4.91 inference(forward_subsumption_resolution,[status(thm)],[f2329,f414])).
% 34.73/4.91 fof(f2342,plain,(
% 34.73/4.91 head_of(sK9_skl)=tail_of(sK8_skl)|head_of(sK9_skl)=head_of(sK0_skl(tail_of(sK8_skl),head_of(sK9_skl)))|~vertex(head_of(sK9_skl))|~vertex(tail_of(sK8_skl))|head_of(sK9_skl)=tail_of(sK8_skl)),
% 34.73/4.91 inference(resolution,[status(thm)],[f2340,f141])).
% 34.73/4.91 fof(f2343,plain,(
% 34.73/4.91 head_of(sK9_skl)=tail_of(sK8_skl)|head_of(sK9_skl)=head_of(sK0_skl(tail_of(sK8_skl),head_of(sK9_skl)))|~vertex(head_of(sK9_skl))|~vertex(tail_of(sK8_skl))),
% 34.73/4.91 inference(duplicate_literals_removal,[status(thm)],[f2342])).
% 34.73/4.91 fof(f2344,plain,(
% 34.73/4.91 head_of(sK9_skl)=tail_of(sK8_skl)|head_of(sK9_skl)=head_of(sK0_skl(tail_of(sK8_skl),head_of(sK9_skl)))|~vertex(tail_of(sK8_skl))),
% 34.73/4.91 inference(forward_subsumption_resolution,[status(thm)],[f2343,f402])).
% 34.73/4.91 fof(f2345,plain,(
% 34.73/4.91 head_of(sK9_skl)=tail_of(sK8_skl)|head_of(sK9_skl)=head_of(sK0_skl(tail_of(sK8_skl),head_of(sK9_skl)))),
% 34.73/4.91 inference(resolution,[status(thm)],[f2344,f266])).
% 31.17/4.97 fof(f2347,plain,(
% 31.17/4.97 head_of(sK9_skl)=tail_of(sK8_skl)|~tail_of(sK0_skl(tail_of(sK8_skl),head_of(sK9_skl)))=tail_of(sK8_skl)),
% 31.17/4.97 inference(resolution,[status(thm)],[f2345,f171])).
% 31.17/4.97 fof(f2358,plain,(
% 31.17/4.97 head_of(sK9_skl)=tail_of(sK8_skl)|tail_of(sK8_skl)=head_of(sK0_skl(tail_of(sK8_skl),head_of(sK9_skl)))),
% 31.17/4.97 inference(backward_subsumption_resolution,[status(thm)],[f757,f2347])).
% 31.17/4.97 fof(f2404,plain,(
% 31.17/4.97 head_of(sK9_skl)=tail_of(sK8_skl)|tail_of(sK8_skl)=head_of(sK9_skl)|head_of(sK9_skl)=tail_of(sK8_skl)),
% 31.17/4.97 inference(paramodulation,[status(thm)],[f2345,f2358])).
% 31.17/4.97 fof(f2429,plain,(
% 31.17/4.97 sK9_skl=sK8_skl|~head_of(sK9_skl)=head_of(sK9_skl)),
% 31.17/4.97 inference(backward_demodulation,[status(thm)],[f2840,f840])).
% 31.17/4.97 fof(f2453,plain,(
% 31.17/4.97 ~tail_of(sK9_skl)=head_of(sK9_skl)),
% 31.17/4.97 inference(backward_demodulation,[status(thm)],[f2840,f172])).
% 31.17/4.97 fof(f2840,plain,(
% 31.17/4.97 head_of(sK9_skl)=tail_of(sK8_skl)),
% 31.17/4.97 inference(duplicate_literals_removal,[status(thm)],[f2404])).
% 31.17/4.97 fof(f3515,plain,(
% 31.17/4.97 sK9_skl=sK8_skl),
% 31.17/4.97 inference(trivial_equality_resolution,[status(thm)],[f2429])).
% 31.17/4.97 fof(f3655,plain,(
% 31.17/4.97 ~tail_of(sK8_skl)=head_of(sK9_skl)),
% 31.17/4.97 inference(forward_demodulation,[status(thm)],[f3515,f2453])).
% 31.17/4.97 fof(f3656,plain,(
% 31.17/4.97 ~head_of(sK9_skl)=head_of(sK9_skl)),
% 31.17/4.97 inference(forward_demodulation,[status(thm)],[f2840,f3655])).
% 31.17/4.97 fof(f3657,plain,(
% 31.17/4.97 ~head_of(sK8_skl)=head_of(sK9_skl)),
% 31.17/4.97 inference(forward_demodulation,[status(thm)],[f3515,f3656])).
% 31.17/4.97 fof(f3658,plain,(
% 31.17/4.97 ~head_of(sK8_skl)=head_of(sK8_skl)),
% 31.17/4.97 inference(forward_demodulation,[status(thm)],[f3515,f3657])).
% 31.17/4.97 fof(f3659,plain,(
% 31.17/4.97 $false),
% 31.17/4.97 inference(trivial_equality_resolution,[status(thm)],[f3658])).
% 31.17/4.97 % SZS output end CNFRefutation for theBenchmark.p
% 3.67/5.04 % Elapsed time: 4.652181 seconds
% 3.67/5.04 % CPU time: 36.155287 seconds
% 3.67/5.04 % Total memory used: 381.710 MB
% 3.67/5.04 % Net memory used: 368.826 MB
%------------------------------------------------------------------------------