%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GRA007+2 : 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 : n026.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 32.90s 9.61s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRA007+2 : TPTP v9.3.1. Bugfixed v3.2.0.
% 0.00/0.06 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/5.42 % Computer : n026.cluster.edu
% 0.15/5.42 % Model : x86_64 x86_64
% 0.15/5.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/5.42 % Memory : 8046.5625MB
% 0.15/5.42 % OS : Linux 6.8.0-71-generic
% 0.15/5.42 % CPULimit : 300
% 0.15/5.42 % WCLimit : 300
% 0.15/5.42 % DateTime : Sun Sep 20 18:23:11 UTC 2026
% 0.15/5.43 % CPUTime :
% 0.15/5.44 % Drodi V4.1.1
% 32.90/9.61 % Refutation found
% 32.90/9.61 % SZS status Theorem for theBenchmark: Theorem is valid
% 32.90/9.61 % SZS output start CNFRefutation for theBenchmark
% 32.90/9.61 fof(f1,axiom,(
% 32.90/9.61 (! [E] :( edge(E)=> head_of(E) != tail_of(E) ) )),
% 32.90/9.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 32.90/9.61 fof(f3,axiom,(
% 32.90/9.61 ( 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) ) ) ) )) )) ),
% 32.90/9.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 32.90/9.61 fof(f6,axiom,(
% 32.90/9.61 (! [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) ) ) )),
% 32.90/9.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 32.90/9.61 fof(f7,axiom,(
% 32.90/9.61 (! [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) ) ) )) ) )),
% 32.90/9.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 32.90/9.61 fof(f8,axiom,(
% 32.90/9.61 (! [E1,E2] :( sequential(E1,E2)<=> ( edge(E1)& edge(E2)& E1 != E2& head_of(E1) = tail_of(E2) ) ) )),
% 32.90/9.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 32.90/9.61 fof(f9,axiom,(
% 32.90/9.61 (! [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) ) )) ) ) )) )),
% 32.90/9.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 32.90/9.61 fof(f10,axiom,(
% 32.90/9.61 (! [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) ) )) ) ) )) )),
% 32.90/9.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 32.90/9.61 fof(f11,axiom,(
% 32.90/9.61 (! [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)) ) )) ) )),
% 32.90/9.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 32.90/9.61 fof(f12,axiom,(
% 32.90/9.61 (! [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) ) ) )),
% 32.90/9.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 32.90/9.61 fof(f19,conjecture,(
% 32.90/9.61 ( 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) ) )) )) ),
% 32.90/9.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 32.90/9.61 fof(f20,negated_conjecture,(
% 32.90/9.61 ~(( 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) ) )) )) )),
% 32.90/9.61 inference(negated_conjecture,[status(cth)],[f19])).
% 32.90/9.61 fof(f21,plain,(
% 32.90/9.61 ![E]: (~edge(E)|~head_of(E)=tail_of(E))),
% 32.90/9.61 inference(pre_NNF_transformation,[status(thm)],[f1])).
% 32.90/9.61 fof(f22,plain,(
% 32.90/9.61 ![X0]: (~edge(X0)|~head_of(X0)=tail_of(X0))),
% 32.90/9.61 inference(cnf_transformation,[status(thm)],[f21])).
% 32.90/9.61 fof(f26,plain,(
% 32.90/9.61 ~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)))))))),
% 32.90/9.61 inference(pre_NNF_transformation,[status(thm)],[f3])).
% 32.90/9.61 fof(f27,definition,(
% 32.90/9.61 ![V1,V2,E]: (sP0_prd(E,V2,V1)<=>(V1=head_of(E)&V2=tail_of(E)))),
% 32.90/9.61 introduced(definition,[new_symbols(definition,[sP0_prd])],[])).
% 32.90/9.61 fof(f28,plain,(
% 32.90/9.61 ~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)))))))),
% 32.90/9.61 inference(formula_renaming,[status(thm)],[f26,f27])).
% 32.90/9.61 fof(f29,plain,(
% 32.90/9.61 ~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))))))))),
% 32.90/9.61 inference(NNF_transformation,[status(thm)],[f28])).
% 32.90/9.61 fof(f30,plain,(
% 32.90/9.61 ~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))))))))),
% 32.90/9.61 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(E,sK0_skl(V2,V1))],[f29])).
% 32.90/9.61 fof(f31,plain,(
% 32.90/9.61 ![X0,X1]: (~complete|~vertex(X0)|~vertex(X1)|X0=X1|edge(sK0_skl(X1,X0)))),
% 32.90/9.62 inference(cnf_transformation,[status(thm)],[f30])).
% 32.90/9.62 fof(f32,plain,(
% 32.90/9.62 ![X0,X1]: (~complete|~vertex(X0)|~vertex(X1)|X0=X1|sP0_prd(sK0_skl(X1,X0),X1,X0)|X1=head_of(sK0_skl(X1,X0)))),
% 32.90/9.62 inference(cnf_transformation,[status(thm)],[f30])).
% 32.90/9.62 fof(f33,plain,(
% 32.90/9.62 ![X0,X1]: (~complete|~vertex(X0)|~vertex(X1)|X0=X1|sP0_prd(sK0_skl(X1,X0),X1,X0)|X0=tail_of(sK0_skl(X1,X0)))),
% 32.90/9.62 inference(cnf_transformation,[status(thm)],[f30])).
% 32.90/9.62 fof(f50,plain,(
% 32.90/9.62 ![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)))),
% 32.90/9.62 inference(pre_NNF_transformation,[status(thm)],[f6])).
% 32.90/9.62 fof(f51,plain,(
% 32.90/9.62 ![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)))),
% 32.90/9.62 inference(miniscoping,[status(thm)],[f50])).
% 32.90/9.62 fof(f52,plain,(
% 32.90/9.62 ![X0,X1,X2,X3]: (~path(X0,X1,X2)|~on_path(X3,X2)|edge(X3))),
% 32.90/9.62 inference(cnf_transformation,[status(thm)],[f51])).
% 32.90/9.62 fof(f53,plain,(
% 32.90/9.62 ![X0,X1,X2,X3]: (~path(X0,X1,X2)|~on_path(X3,X2)|in_path(head_of(X3),X2))),
% 32.90/9.62 inference(cnf_transformation,[status(thm)],[f51])).
% 32.90/9.62 fof(f54,plain,(
% 32.90/9.62 ![X0,X1,X2,X3]: (~path(X0,X1,X2)|~on_path(X3,X2)|in_path(tail_of(X3),X2))),
% 32.90/9.62 inference(cnf_transformation,[status(thm)],[f51])).
% 32.90/9.62 fof(f55,plain,(
% 32.90/9.62 ![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))))))),
% 32.90/9.62 inference(pre_NNF_transformation,[status(thm)],[f7])).
% 32.90/9.62 fof(f56,plain,(
% 32.90/9.62 ![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))))))),
% 32.90/9.62 inference(miniscoping,[status(thm)],[f55])).
% 32.90/9.62 fof(f57,plain,(
% 32.90/9.62 ![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))))))),
% 32.90/9.62 inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl]),skolemize(E,sK3_skl(V,P))],[f56])).
% 32.90/9.62 fof(f58,plain,(
% 32.90/9.62 ![X0,X1,X2,X3]: (~path(X0,X1,X2)|~in_path(X3,X2)|vertex(X3))),
% 32.90/9.62 inference(cnf_transformation,[status(thm)],[f57])).
% 32.90/9.62 fof(f61,plain,(
% 32.90/9.62 ![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))))),
% 32.90/9.62 inference(NNF_transformation,[status(thm)],[f8])).
% 32.90/9.62 fof(f62,plain,(
% 32.90/9.62 (![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))))),
% 32.90/9.62 inference(miniscoping,[status(thm)],[f61])).
% 32.90/9.62 fof(f67,plain,(
% 32.90/9.62 ![X0,X1]: (sequential(X0,X1)|~edge(X0)|~edge(X1)|X0=X1|~head_of(X0)=tail_of(X1))),
% 32.90/9.62 inference(cnf_transformation,[status(thm)],[f62])).
% 32.90/9.62 fof(f68,plain,(
% 32.90/9.62 ![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))))))))),
% 32.90/9.62 inference(pre_NNF_transformation,[status(thm)],[f9])).
% 32.90/9.62 fof(f69,plain,(
% 32.90/9.62 ![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))))))))),
% 32.90/9.62 inference(miniscoping,[status(thm)],[f68])).
% 32.90/9.62 fof(f71,plain,(
% 32.90/9.62 ![X0,X1,X2,X3,X4,X5]: (~path(X0,X1,X2)|precedes(X3,X4,X2)|~on_path(X3,X2)|~on_path(X4,X2)|~sequential(X3,X5)|~precedes(X5,X4,X2))),
% 32.90/9.62 inference(cnf_transformation,[status(thm)],[f69])).
% 32.90/9.62 fof(f72,plain,(
% 32.90/9.62 ![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))))))))),
% 32.90/9.62 inference(pre_NNF_transformation,[status(thm)],[f10])).
% 32.90/9.62 fof(f73,plain,(
% 32.90/9.62 ![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)))))))))),
% 32.90/9.62 inference(NNF_transformation,[status(thm)],[f72])).
% 32.90/9.62 fof(f74,plain,(
% 32.90/9.62 ![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)))))))))),
% 32.90/9.62 inference(miniscoping,[status(thm)],[f73])).
% 32.90/9.62 fof(f75,plain,(
% 32.90/9.62 ![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)))))))))),
% 32.90/9.62 inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl]),skolemize(E3,sK4_skl(E2,E1,P))],[f74])).
% 32.90/9.62 fof(f76,plain,(
% 32.90/9.62 ![X0,X1,X2,X3,X4]: (~path(X0,X1,X2)|~precedes(X3,X4,X2)|on_path(X3,X2))),
% 32.90/9.62 inference(cnf_transformation,[status(thm)],[f75])).
% 32.90/9.62 fof(f77,plain,(
% 32.90/9.62 ![X0,X1,X2,X3,X4]: (~path(X0,X1,X2)|~precedes(X3,X4,X2)|on_path(X4,X2))),
% 32.90/9.62 inference(cnf_transformation,[status(thm)],[f75])).
% 32.90/9.62 fof(f81,plain,(
% 32.90/9.62 ![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))))))),
% 32.90/9.62 inference(pre_NNF_transformation,[status(thm)],[f11])).
% 32.90/9.62 fof(f82,plain,(
% 32.90/9.62 ![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)))))))),
% 32.90/9.62 inference(NNF_transformation,[status(thm)],[f81])).
% 32.90/9.62 fof(f83,plain,(
% 32.90/9.62 (![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)))))))),
% 32.90/9.62 inference(miniscoping,[status(thm)],[f82])).
% 32.90/9.62 fof(f84,plain,(
% 32.90/9.62 (![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)))))))),
% 32.90/9.62 inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl]),skolemize(P,sK5_skl(SP,V2,V1))],[f83])).
% 32.90/9.62 fof(f85,plain,(
% 32.90/9.62 ![X0,X1,X2]: (~shortest_path(X0,X1,X2)|path(X0,X1,X2))),
% 32.90/9.62 inference(cnf_transformation,[status(thm)],[f84])).
% 32.90/9.62 fof(f90,plain,(
% 32.90/9.62 ![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)))),
% 32.90/9.62 inference(pre_NNF_transformation,[status(thm)],[f12])).
% 32.90/9.62 fof(f91,plain,(
% 32.90/9.62 ![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)))),
% 32.90/9.62 inference(miniscoping,[status(thm)],[f90])).
% 32.90/9.62 fof(f92,plain,(
% 32.90/9.62 ![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))),
% 32.90/9.62 inference(cnf_transformation,[status(thm)],[f91])).
% 32.90/9.62 fof(f93,plain,(
% 32.90/9.62 ![X0,X1,X2,X3,X4]: (~shortest_path(X0,X1,X2)|~precedes(X3,X4,X2)|~precedes(X4,X3,X2))),
% 32.90/9.62 inference(cnf_transformation,[status(thm)],[f91])).
% 32.90/9.62 fof(f120,plain,(
% 32.90/9.62 (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))))))),
% 32.90/9.62 inference(pre_NNF_transformation,[status(thm)],[f20])).
% 32.90/9.62 fof(f121,plain,(
% 32.90/9.62 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)))))),
% 32.90/9.62 inference(miniscoping,[status(thm)],[f120])).
% 32.90/9.62 fof(f122,plain,(
% 32.90/9.62 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))))),
% 32.90/9.62 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)],[f121])).
% 32.90/9.62 fof(f123,plain,(
% 32.90/9.62 complete),
% 32.90/9.62 inference(cnf_transformation,[status(thm)],[f122])).
% 32.90/9.62 fof(f124,plain,(
% 32.90/9.62 shortest_path(sK11_skl,sK12_skl,sK10_skl)),
% 32.90/9.62 inference(cnf_transformation,[status(thm)],[f122])).
% 32.90/9.62 fof(f125,plain,(
% 32.90/9.62 precedes(sK8_skl,sK9_skl,sK10_skl)),
% 32.90/9.62 inference(cnf_transformation,[status(thm)],[f122])).
% 32.90/9.62 fof(f126,plain,(
% 32.90/9.62 ![X0]: (~edge(X0)|~tail_of(X0)=head_of(sK9_skl)|~head_of(X0)=tail_of(sK8_skl))),
% 32.90/9.62 inference(cnf_transformation,[status(thm)],[f122])).
% 32.90/9.62 fof(f127,plain,(
% 32.90/9.62 ![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))))),
% 32.90/9.62 inference(NNF_transformation,[status(thm)],[f27])).
% 32.90/9.62 fof(f128,plain,(
% 32.90/9.62 (![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))))),
% 32.90/9.62 inference(miniscoping,[status(thm)],[f127])).
% 32.90/9.62 fof(f129,plain,(
% 32.90/9.62 ![X0,X1,X2]: (~sP0_prd(X0,X1,X2)|X2=head_of(X0))),
% 32.90/9.62 inference(cnf_transformation,[status(thm)],[f128])).
% 32.90/9.62 fof(f130,plain,(
% 32.90/9.62 ![X0,X1,X2]: (~sP0_prd(X0,X1,X2)|X1=tail_of(X0))),
% 32.90/9.62 inference(cnf_transformation,[status(thm)],[f128])).
% 32.90/9.62 fof(f139,plain,(
% 32.90/9.62 ![X0,X1,X2,X3,X4,X5]: (~path(X0,X1,X2)|precedes(X3,X4,X2)|~on_path(X3,X2)|~sequential(X3,X5)|~precedes(X5,X4,X2))),
% 32.90/9.62 inference(backward_subsumption_resolution,[status(thm)],[f71,f77])).
% 32.90/9.62 fof(f143,plain,(
% 32.90/9.62 ![X0,X1]: (~vertex(X0)|~vertex(X1)|X0=X1|sP0_prd(sK0_skl(X1,X0),X1,X0)|X0=tail_of(sK0_skl(X1,X0)))),
% 32.90/9.62 inference(backward_subsumption_resolution,[status(thm)],[f33,f123])).
% 32.90/9.62 fof(f144,plain,(
% 32.90/9.62 ![X0,X1]: (~vertex(X0)|~vertex(X1)|X0=X1|sP0_prd(sK0_skl(X1,X0),X1,X0)|X1=head_of(sK0_skl(X1,X0)))),
% 32.90/9.62 inference(backward_subsumption_resolution,[status(thm)],[f32,f123])).
% 32.90/9.62 fof(f145,plain,(
% 32.90/9.62 ![X0,X1]: (~vertex(X0)|~vertex(X1)|X0=X1|edge(sK0_skl(X1,X0)))),
% 32.90/9.62 inference(backward_subsumption_resolution,[status(thm)],[f31,f123])).
% 32.90/9.62 fof(f146,plain,(
% 32.90/9.62 path(sK11_skl,sK12_skl,sK10_skl)),
% 32.90/9.62 inference(resolution,[status(thm)],[f85,f124])).
% 32.90/9.62 fof(f153,plain,(
% 32.90/9.62 ![X0,X1]: (~precedes(X0,X1,sK10_skl)|~precedes(X1,X0,sK10_skl))),
% 32.90/9.62 inference(resolution,[status(thm)],[f93,f124])).
% 32.90/9.62 fof(f155,plain,(
% 32.90/9.62 ![X0,X1,X2]: (~precedes(X0,X1,sK10_skl)|~tail_of(X2)=tail_of(X0)|~head_of(X2)=head_of(X1))),
% 32.90/9.62 inference(resolution,[status(thm)],[f92,f124])).
% 32.90/9.62 fof(f158,plain,(
% 32.90/9.62 ![X0]: (~tail_of(X0)=tail_of(sK8_skl)|~head_of(X0)=head_of(sK9_skl))),
% 32.90/9.62 inference(resolution,[status(thm)],[f155,f125])).
% 32.90/9.62 fof(f161,plain,(
% 32.90/9.62 ![X0,X1]: (~vertex(X0)|~vertex(X1)|X0=X1|X0=tail_of(sK0_skl(X1,X0))|X1=tail_of(sK0_skl(X1,X0)))),
% 32.90/9.62 inference(resolution,[status(thm)],[f143,f130])).
% 32.90/9.62 fof(f162,plain,(
% 32.90/9.62 ![X0,X1]: (~vertex(X0)|~vertex(X1)|X0=X1|X0=tail_of(sK0_skl(X1,X0))|X0=head_of(sK0_skl(X1,X0)))),
% 32.90/9.62 inference(resolution,[status(thm)],[f143,f129])).
% 32.90/9.62 fof(f173,plain,(
% 32.90/9.62 ![X0,X1]: (~vertex(X0)|~vertex(X1)|X0=X1|X1=head_of(sK0_skl(X1,X0))|X0=head_of(sK0_skl(X1,X0)))),
% 32.90/9.62 inference(resolution,[status(thm)],[f144,f129])).
% 32.90/9.62 fof(f197,plain,(
% 32.90/9.62 ![X0,X1]: (~path(X0,X1,sK10_skl)|on_path(sK8_skl,sK10_skl))),
% 32.90/9.62 inference(resolution,[status(thm)],[f76,f125])).
% 32.90/9.62 fof(f198,plain,(
% 32.90/9.62 on_path(sK8_skl,sK10_skl)),
% 32.90/9.62 inference(resolution,[status(thm)],[f197,f146])).
% 32.90/9.62 fof(f199,plain,(
% 32.90/9.62 ![X0,X1]: (~path(X0,X1,sK10_skl)|edge(sK8_skl))),
% 32.90/9.62 inference(resolution,[status(thm)],[f198,f52])).
% 32.90/9.62 fof(f200,plain,(
% 32.90/9.62 edge(sK8_skl)),
% 32.90/9.62 inference(resolution,[status(thm)],[f199,f146])).
% 32.90/9.62 fof(f203,plain,(
% 32.90/9.62 ![X0]: (sequential(X0,sK8_skl)|~edge(X0)|X0=sK8_skl|~head_of(X0)=tail_of(sK8_skl))),
% 32.90/9.62 inference(resolution,[status(thm)],[f200,f67])).
% 32.90/9.62 fof(f204,plain,(
% 32.90/9.62 ![X0,X1,X2,X3,X4,X5]: (~path(X0,X1,X2)|~on_path(X3,X2)|~path(X4,X5,X2)|vertex(head_of(X3)))),
% 32.90/9.62 inference(resolution,[status(thm)],[f53,f58])).
% 32.90/9.62 fof(f205,plain,(
% 32.90/9.62 ![X0,X1,X2,X3,X4,X5]: (~path(X0,X1,X2)|~on_path(X3,X2)|~path(X4,X5,X2)|vertex(tail_of(X3)))),
% 32.90/9.62 inference(resolution,[status(thm)],[f54,f58])).
% 32.90/9.62 fof(f241,plain,(
% 32.90/9.62 ![X0,X1]: (~path(X0,X1,sK10_skl)|on_path(sK9_skl,sK10_skl))),
% 32.90/9.62 inference(resolution,[status(thm)],[f77,f125])).
% 32.90/9.62 fof(f242,plain,(
% 32.90/9.62 on_path(sK9_skl,sK10_skl)),
% 32.90/9.62 inference(resolution,[status(thm)],[f241,f146])).
% 32.90/9.62 fof(f243,plain,(
% 32.90/9.62 ![X0,X1]: (~path(X0,X1,sK10_skl)|edge(sK9_skl))),
% 32.90/9.62 inference(resolution,[status(thm)],[f242,f52])).
% 32.90/9.62 fof(f244,plain,(
% 32.90/9.62 edge(sK9_skl)),
% 32.90/9.62 inference(resolution,[status(thm)],[f243,f146])).
% 32.90/9.62 fof(f246,plain,(
% 32.90/9.62 sequential(sK9_skl,sK8_skl)|sK9_skl=sK8_skl|~head_of(sK9_skl)=tail_of(sK8_skl)),
% 32.90/9.62 inference(resolution,[status(thm)],[f244,f203])).
% 32.90/9.62 fof(f247,plain,(
% 32.90/9.62 ~tail_of(sK9_skl)=head_of(sK9_skl)|~head_of(sK9_skl)=tail_of(sK8_skl)),
% 32.90/9.62 inference(resolution,[status(thm)],[f244,f126])).
% 32.90/9.62 fof(f288,plain,(
% 32.90/9.62 ![X0,X1,X2]: (~path(X0,X1,sK10_skl)|precedes(X2,sK9_skl,sK10_skl)|~on_path(X2,sK10_skl)|~sequential(X2,sK8_skl))),
% 32.90/9.62 inference(resolution,[status(thm)],[f139,f125])).
% 32.90/9.62 fof(f289,plain,(
% 32.90/9.62 ![X0,X1]: (~path(X0,X1,sK10_skl)|precedes(sK9_skl,sK9_skl,sK10_skl)|~on_path(sK9_skl,sK10_skl)|sK9_skl=sK8_skl|~head_of(sK9_skl)=tail_of(sK8_skl))),
% 32.90/9.62 inference(resolution,[status(thm)],[f288,f246])).
% 32.90/9.62 fof(f290,plain,(
% 32.90/9.62 ![X0,X1]: (~path(X0,X1,sK10_skl)|precedes(sK9_skl,sK9_skl,sK10_skl)|sK9_skl=sK8_skl|~head_of(sK9_skl)=tail_of(sK8_skl))),
% 32.90/9.62 inference(forward_subsumption_resolution,[status(thm)],[f289,f242])).
% 32.90/9.62 fof(f291,plain,(
% 32.90/9.62 precedes(sK9_skl,sK9_skl,sK10_skl)|sK9_skl=sK8_skl|~head_of(sK9_skl)=tail_of(sK8_skl)),
% 32.90/9.62 inference(resolution,[status(thm)],[f290,f146])).
% 32.90/9.62 fof(f293,plain,(
% 32.90/9.62 sK9_skl=sK8_skl|~head_of(sK9_skl)=tail_of(sK8_skl)|~precedes(sK9_skl,sK9_skl,sK10_skl)),
% 32.90/9.62 inference(resolution,[status(thm)],[f291,f153])).
% 32.90/9.62 fof(f298,plain,(
% 32.90/9.62 sK9_skl=sK8_skl|~head_of(sK9_skl)=tail_of(sK8_skl)),
% 32.90/9.62 inference(forward_subsumption_resolution,[status(thm)],[f293,f291])).
% 32.90/9.62 fof(f442,plain,(
% 32.90/9.62 ![X0,X1,X2]: (~path(X0,X1,sK10_skl)|~on_path(X2,sK10_skl)|vertex(head_of(X2)))),
% 32.90/9.62 inference(resolution,[status(thm)],[f204,f146])).
% 32.90/9.62 fof(f443,plain,(
% 32.90/9.62 ![X0]: (~on_path(X0,sK10_skl)|vertex(head_of(X0)))),
% 32.90/9.62 inference(resolution,[status(thm)],[f442,f146])).
% 32.90/9.62 fof(f447,plain,(
% 32.90/9.62 vertex(head_of(sK9_skl))),
% 32.90/9.62 inference(resolution,[status(thm)],[f443,f242])).
% 32.90/9.62 fof(f479,plain,(
% 32.90/9.62 ![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)))),
% 32.90/9.62 inference(resolution,[status(thm)],[f447,f173])).
% 32.90/9.62 fof(f487,plain,(
% 32.90/9.62 ![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)))),
% 32.90/9.62 inference(resolution,[status(thm)],[f447,f162])).
% 32.90/9.62 fof(f488,plain,(
% 32.90/9.62 ![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)))),
% 32.90/9.62 inference(resolution,[status(thm)],[f447,f161])).
% 32.90/9.62 fof(f531,plain,(
% 32.90/9.62 ![X0,X1,X2]: (~path(X0,X1,sK10_skl)|~on_path(X2,sK10_skl)|vertex(tail_of(X2)))),
% 32.90/9.62 inference(resolution,[status(thm)],[f205,f146])).
% 32.90/9.62 fof(f597,plain,(
% 32.90/9.62 ![X0]: (~on_path(X0,sK10_skl)|vertex(tail_of(X0)))),
% 32.90/9.62 inference(resolution,[status(thm)],[f531,f146])).
% 32.90/9.62 fof(f603,plain,(
% 32.90/9.62 vertex(tail_of(sK8_skl))),
% 32.90/9.62 inference(resolution,[status(thm)],[f597,f198])).
% 32.90/9.62 fof(f655,plain,(
% 32.90/9.62 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)))),
% 32.90/9.62 inference(resolution,[status(thm)],[f603,f488])).
% 32.90/9.62 fof(f656,plain,(
% 32.90/9.62 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)))),
% 32.90/9.62 inference(resolution,[status(thm)],[f603,f479])).
% 32.90/9.62 fof(f658,plain,(
% 32.90/9.62 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)))),
% 32.90/9.62 inference(resolution,[status(thm)],[f603,f487])).
% 32.90/9.62 fof(f1271,plain,(
% 32.90/9.62 ~edge(sK0_skl(head_of(sK9_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)=tail_of(sK0_skl(head_of(sK9_skl),tail_of(sK8_skl)))),
% 32.90/9.62 inference(paramodulation,[status(thm)],[f655,f22])).
% 32.90/9.62 fof(f1275,plain,(
% 32.90/9.62 ~edge(sK0_skl(head_of(sK9_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)),
% 32.90/9.62 inference(forward_subsumption_resolution,[status(thm)],[f1271,f126])).
% 32.90/9.62 fof(f1276,plain,(
% 32.90/9.62 ~head_of(sK0_skl(head_of(sK9_skl),tail_of(sK8_skl)))=tail_of(sK8_skl)|tail_of(sK8_skl)=head_of(sK9_skl)|~vertex(tail_of(sK8_skl))|~vertex(head_of(sK9_skl))|tail_of(sK8_skl)=head_of(sK9_skl)),
% 32.90/9.64 inference(resolution,[status(thm)],[f1275,f145])).
% 32.90/9.64 fof(f1277,plain,(
% 32.90/9.64 ~head_of(sK0_skl(head_of(sK9_skl),tail_of(sK8_skl)))=tail_of(sK8_skl)|tail_of(sK8_skl)=head_of(sK9_skl)|~vertex(tail_of(sK8_skl))|~vertex(head_of(sK9_skl))),
% 32.90/9.64 inference(duplicate_literals_removal,[status(thm)],[f1276])).
% 32.90/9.64 fof(f1278,plain,(
% 32.90/9.64 ~head_of(sK0_skl(head_of(sK9_skl),tail_of(sK8_skl)))=tail_of(sK8_skl)|tail_of(sK8_skl)=head_of(sK9_skl)|~vertex(head_of(sK9_skl))),
% 32.90/9.64 inference(forward_subsumption_resolution,[status(thm)],[f1277,f603])).
% 32.90/9.64 fof(f1327,plain,(
% 32.90/9.64 ~head_of(sK0_skl(head_of(sK9_skl),tail_of(sK8_skl)))=tail_of(sK8_skl)|tail_of(sK8_skl)=head_of(sK9_skl)),
% 32.90/9.64 inference(resolution,[status(thm)],[f1278,f447])).
% 32.90/9.64 fof(f1329,plain,(
% 32.90/9.64 tail_of(sK8_skl)=head_of(sK9_skl)|tail_of(sK8_skl)=tail_of(sK0_skl(head_of(sK9_skl),tail_of(sK8_skl)))),
% 32.90/9.64 inference(backward_subsumption_resolution,[status(thm)],[f658,f1327])).
% 32.90/9.64 fof(f1330,plain,(
% 32.90/9.64 tail_of(sK8_skl)=head_of(sK9_skl)|head_of(sK9_skl)=head_of(sK0_skl(head_of(sK9_skl),tail_of(sK8_skl)))),
% 32.90/9.64 inference(backward_subsumption_resolution,[status(thm)],[f656,f1327])).
% 32.90/9.64 fof(f1334,plain,(
% 32.90/9.64 tail_of(sK8_skl)=head_of(sK9_skl)|~tail_of(sK0_skl(head_of(sK9_skl),tail_of(sK8_skl)))=tail_of(sK8_skl)),
% 32.90/9.64 inference(resolution,[status(thm)],[f1330,f158])).
% 32.90/9.64 fof(f1364,plain,(
% 32.90/9.64 sK9_skl=sK8_skl|~head_of(sK9_skl)=head_of(sK9_skl)),
% 32.90/9.64 inference(backward_demodulation,[status(thm)],[f1501,f298])).
% 32.90/9.64 fof(f1365,plain,(
% 32.90/9.64 ~tail_of(sK9_skl)=head_of(sK9_skl)|~head_of(sK9_skl)=head_of(sK9_skl)),
% 32.90/9.64 inference(backward_demodulation,[status(thm)],[f1501,f247])).
% 32.90/9.64 fof(f1501,plain,(
% 32.90/9.64 tail_of(sK8_skl)=head_of(sK9_skl)),
% 32.90/9.64 inference(forward_subsumption_resolution,[status(thm)],[f1334,f1329])).
% 32.90/9.64 fof(f1826,plain,(
% 32.90/9.64 sK9_skl=sK8_skl),
% 32.90/9.64 inference(trivial_equality_resolution,[status(thm)],[f1364])).
% 32.90/9.64 fof(f1827,plain,(
% 32.90/9.64 ~tail_of(sK8_skl)=head_of(sK9_skl)|~head_of(sK9_skl)=head_of(sK9_skl)),
% 32.90/9.64 inference(forward_demodulation,[status(thm)],[f1826,f1365])).
% 32.90/9.64 fof(f1828,plain,(
% 32.90/9.64 ~head_of(sK9_skl)=head_of(sK9_skl)|~head_of(sK9_skl)=head_of(sK9_skl)),
% 32.90/9.64 inference(forward_demodulation,[status(thm)],[f1501,f1827])).
% 32.90/9.64 fof(f1829,plain,(
% 32.90/9.64 ~head_of(sK8_skl)=head_of(sK9_skl)|~head_of(sK9_skl)=head_of(sK9_skl)),
% 32.90/9.64 inference(forward_demodulation,[status(thm)],[f1826,f1828])).
% 32.90/9.64 fof(f1830,plain,(
% 32.90/9.64 ~head_of(sK8_skl)=head_of(sK8_skl)|~head_of(sK9_skl)=head_of(sK9_skl)),
% 32.90/9.64 inference(forward_demodulation,[status(thm)],[f1826,f1829])).
% 32.90/9.64 fof(f1831,plain,(
% 32.90/9.64 ~head_of(sK8_skl)=head_of(sK8_skl)|~head_of(sK8_skl)=head_of(sK9_skl)),
% 32.90/9.64 inference(forward_demodulation,[status(thm)],[f1826,f1830])).
% 32.90/9.64 fof(f1832,plain,(
% 32.90/9.64 ~head_of(sK8_skl)=head_of(sK8_skl)|~head_of(sK8_skl)=head_of(sK8_skl)),
% 32.90/9.64 inference(forward_demodulation,[status(thm)],[f1826,f1831])).
% 32.90/9.64 fof(f1833,plain,(
% 32.90/9.64 ~head_of(sK8_skl)=head_of(sK8_skl)),
% 32.90/9.64 inference(duplicate_literals_removal,[status(thm)],[f1832])).
% 32.90/9.64 fof(f1834,plain,(
% 32.90/9.64 $false),
% 32.90/9.64 inference(trivial_equality_resolution,[status(thm)],[f1833])).
% 32.90/9.64 % SZS output end CNFRefutation for theBenchmark.p
% 32.90/9.69 % Elapsed time: 4.243454 seconds
% 32.90/9.69 % CPU time: 33.397753 seconds
% 32.90/9.69 % Total memory used: 432.560 MB
% 32.90/9.69 % Net memory used: 414.927 MB
%------------------------------------------------------------------------------