TSTP Solution File: GRA004+1 by Drodi---3.6.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : GRA004+1 : TPTP v8.1.2. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 20:18:34 EDT 2024
% Result : Theorem 0.07s 0.29s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : GRA004+1 : TPTP v8.1.2. Bugfixed v3.2.0.
% 0.00/0.07 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.07/0.26 % Computer : n016.cluster.edu
% 0.07/0.26 % Model : x86_64 x86_64
% 0.07/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.26 % Memory : 8042.1875MB
% 0.07/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.26 % CPULimit : 300
% 0.07/0.26 % WCLimit : 300
% 0.07/0.26 % DateTime : Mon Apr 29 23:00:10 EDT 2024
% 0.07/0.26 % CPUTime :
% 0.07/0.27 % Drodi V3.6.0
% 0.07/0.29 % Refutation found
% 0.07/0.29 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.07/0.29 % SZS output start CNFRefutation for theBenchmark
% 0.07/0.29 fof(f6,axiom,(
% 0.07/0.29 (! [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) ) ) )),
% 0.07/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.07/0.29 fof(f8,axiom,(
% 0.07/0.29 (! [E1,E2] :( sequential(E1,E2)<=> ( edge(E1)& edge(E2)& E1 != E2& head_of(E1) = tail_of(E2) ) ) )),
% 0.07/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.07/0.29 fof(f9,axiom,(
% 0.07/0.29 (! [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) ) )) ) ) )) )),
% 0.07/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.07/0.29 fof(f10,axiom,(
% 0.07/0.29 (! [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) ) )) ) ) )) )),
% 0.07/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.07/0.29 fof(f11,axiom,(
% 0.07/0.29 (! [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)) ) )) ) )),
% 0.07/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.07/0.29 fof(f12,axiom,(
% 0.07/0.29 (! [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) ) ) )),
% 0.07/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.07/0.29 fof(f18,conjecture,(
% 0.07/0.29 (! [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) ))& head_of(E2) != tail_of(E1)& head_of(E2) != head_of(E1) ) ) )),
% 0.07/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.07/0.29 fof(f19,negated_conjecture,(
% 0.07/0.29 ~((! [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) ))& head_of(E2) != tail_of(E1)& head_of(E2) != head_of(E1) ) ) ))),
% 0.07/0.29 inference(negated_conjecture,[status(cth)],[f18])).
% 0.07/0.29 fof(f49,plain,(
% 0.07/0.29 ![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)))),
% 0.07/0.29 inference(pre_NNF_transformation,[status(esa)],[f6])).
% 0.07/0.29 fof(f50,plain,(
% 0.07/0.29 ![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)))),
% 0.07/0.29 inference(miniscoping,[status(esa)],[f49])).
% 0.07/0.29 fof(f51,plain,(
% 0.07/0.29 ![X0,X1,X2,X3]: (~path(X0,X1,X2)|~on_path(X3,X2)|edge(X3))),
% 0.07/0.29 inference(cnf_transformation,[status(esa)],[f50])).
% 0.07/0.29 fof(f60,plain,(
% 0.07/0.29 ![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))))),
% 0.07/0.29 inference(NNF_transformation,[status(esa)],[f8])).
% 0.07/0.29 fof(f61,plain,(
% 0.07/0.29 (![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))))),
% 0.07/0.29 inference(miniscoping,[status(esa)],[f60])).
% 0.07/0.29 fof(f66,plain,(
% 0.07/0.29 ![X0,X1]: (sequential(X0,X1)|~edge(X0)|~edge(X1)|X0=X1|~head_of(X0)=tail_of(X1))),
% 0.07/0.29 inference(cnf_transformation,[status(esa)],[f61])).
% 0.07/0.29 fof(f67,plain,(
% 0.07/0.29 ![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))))))))),
% 0.07/0.29 inference(pre_NNF_transformation,[status(esa)],[f9])).
% 0.07/0.29 fof(f68,plain,(
% 0.07/0.29 ![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))))))))),
% 0.07/0.29 inference(miniscoping,[status(esa)],[f67])).
% 0.07/0.29 fof(f69,plain,(
% 0.07/0.29 ![X0,X1,X2,X3,X4]: (~path(X0,X1,X2)|precedes(X3,X4,X2)|~on_path(X3,X2)|~on_path(X4,X2)|~sequential(X3,X4))),
% 0.07/0.29 inference(cnf_transformation,[status(esa)],[f68])).
% 0.07/0.29 fof(f71,plain,(
% 0.07/0.29 ![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))))))))),
% 0.07/0.29 inference(pre_NNF_transformation,[status(esa)],[f10])).
% 0.07/0.30 fof(f72,plain,(
% 0.07/0.30 ![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)))))))))),
% 0.07/0.30 inference(NNF_transformation,[status(esa)],[f71])).
% 0.07/0.30 fof(f73,plain,(
% 0.07/0.30 ![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)))))))))),
% 0.07/0.30 inference(miniscoping,[status(esa)],[f72])).
% 0.07/0.30 fof(f74,plain,(
% 0.07/0.30 ![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,sk0_4(E2,E1,P))&precedes(sk0_4(E2,E1,P),E2,P)))&(~sequential(E1,E2)|(![E3]: (~sequential(E1,E3)|~precedes(E3,E2,P)))))))))),
% 0.07/0.30 inference(skolemization,[status(esa)],[f73])).
% 0.07/0.30 fof(f75,plain,(
% 0.07/0.30 ![X0,X1,X2,X3,X4]: (~path(X0,X1,X2)|~precedes(X3,X4,X2)|on_path(X3,X2))),
% 0.07/0.30 inference(cnf_transformation,[status(esa)],[f74])).
% 0.07/0.30 fof(f76,plain,(
% 0.07/0.30 ![X0,X1,X2,X3,X4]: (~path(X0,X1,X2)|~precedes(X3,X4,X2)|on_path(X4,X2))),
% 0.07/0.30 inference(cnf_transformation,[status(esa)],[f74])).
% 0.07/0.30 fof(f80,plain,(
% 0.07/0.30 ![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))))))),
% 0.07/0.30 inference(pre_NNF_transformation,[status(esa)],[f11])).
% 0.07/0.30 fof(f81,plain,(
% 0.07/0.30 ![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)))))))),
% 0.07/0.30 inference(NNF_transformation,[status(esa)],[f80])).
% 0.07/0.30 fof(f82,plain,(
% 0.07/0.30 (![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)))))))),
% 0.07/0.30 inference(miniscoping,[status(esa)],[f81])).
% 0.07/0.30 fof(f83,plain,(
% 0.07/0.30 (![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,sk0_5(SP,V2,V1))&~less_or_equal(length_of(SP),length_of(sk0_5(SP,V2,V1)))))))),
% 0.07/0.30 inference(skolemization,[status(esa)],[f82])).
% 0.07/0.30 fof(f84,plain,(
% 0.07/0.30 ![X0,X1,X2]: (~shortest_path(X0,X1,X2)|path(X0,X1,X2))),
% 0.07/0.30 inference(cnf_transformation,[status(esa)],[f83])).
% 0.07/0.30 fof(f89,plain,(
% 0.07/0.30 ![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)))),
% 0.07/0.30 inference(pre_NNF_transformation,[status(esa)],[f12])).
% 0.07/0.30 fof(f90,plain,(
% 0.07/0.30 ![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)))),
% 0.07/0.30 inference(miniscoping,[status(esa)],[f89])).
% 0.07/0.30 fof(f91,plain,(
% 0.07/0.30 ![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))),
% 0.07/0.30 inference(cnf_transformation,[status(esa)],[f90])).
% 0.07/0.30 fof(f92,plain,(
% 0.07/0.30 ![X0,X1,X2,X3,X4]: (~shortest_path(X0,X1,X2)|~precedes(X3,X4,X2)|~precedes(X4,X3,X2))),
% 0.07/0.30 inference(cnf_transformation,[status(esa)],[f90])).
% 0.07/0.30 fof(f116,plain,(
% 0.07/0.30 (?[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)))|head_of(E2)=tail_of(E1))|head_of(E2)=head_of(E1))))),
% 0.07/0.30 inference(pre_NNF_transformation,[status(esa)],[f19])).
% 0.07/0.30 fof(f117,plain,(
% 0.07/0.30 ?[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)))|head_of(E2)=tail_of(E1))|head_of(E2)=head_of(E1)))),
% 0.07/0.30 inference(miniscoping,[status(esa)],[f116])).
% 0.07/0.30 fof(f118,plain,(
% 0.07/0.30 ((shortest_path(sk0_11,sk0_12,sk0_10)&precedes(sk0_8,sk0_9,sk0_10))&(((tail_of(sk0_13)=tail_of(sk0_8)&head_of(sk0_13)=head_of(sk0_9))|head_of(sk0_9)=tail_of(sk0_8))|head_of(sk0_9)=head_of(sk0_8)))),
% 0.07/0.30 inference(skolemization,[status(esa)],[f117])).
% 0.07/0.30 fof(f119,plain,(
% 0.07/0.30 shortest_path(sk0_11,sk0_12,sk0_10)),
% 0.07/0.30 inference(cnf_transformation,[status(esa)],[f118])).
% 0.07/0.30 fof(f120,plain,(
% 0.07/0.30 precedes(sk0_8,sk0_9,sk0_10)),
% 0.07/0.30 inference(cnf_transformation,[status(esa)],[f118])).
% 0.07/0.30 fof(f121,plain,(
% 0.07/0.30 tail_of(sk0_13)=tail_of(sk0_8)|head_of(sk0_9)=tail_of(sk0_8)|head_of(sk0_9)=head_of(sk0_8)),
% 0.07/0.30 inference(cnf_transformation,[status(esa)],[f118])).
% 0.07/0.30 fof(f122,plain,(
% 0.07/0.30 head_of(sk0_13)=head_of(sk0_9)|head_of(sk0_9)=tail_of(sk0_8)|head_of(sk0_9)=head_of(sk0_8)),
% 0.07/0.30 inference(cnf_transformation,[status(esa)],[f118])).
% 0.07/0.30 fof(f152,plain,(
% 0.07/0.30 spl0_5 <=> tail_of(sk0_13)=tail_of(sk0_8)),
% 0.07/0.30 introduced(split_symbol_definition)).
% 0.07/0.30 fof(f153,plain,(
% 0.07/0.30 tail_of(sk0_13)=tail_of(sk0_8)|~spl0_5),
% 0.07/0.30 inference(component_clause,[status(thm)],[f152])).
% 0.07/0.30 fof(f155,plain,(
% 0.07/0.30 spl0_6 <=> head_of(sk0_9)=tail_of(sk0_8)),
% 0.07/0.30 introduced(split_symbol_definition)).
% 0.07/0.30 fof(f156,plain,(
% 0.07/0.30 head_of(sk0_9)=tail_of(sk0_8)|~spl0_6),
% 0.07/0.30 inference(component_clause,[status(thm)],[f155])).
% 0.07/0.30 fof(f158,plain,(
% 0.07/0.30 spl0_7 <=> head_of(sk0_9)=head_of(sk0_8)),
% 0.07/0.30 introduced(split_symbol_definition)).
% 0.07/0.30 fof(f159,plain,(
% 0.07/0.30 head_of(sk0_9)=head_of(sk0_8)|~spl0_7),
% 0.07/0.30 inference(component_clause,[status(thm)],[f158])).
% 0.07/0.30 fof(f160,plain,(
% 0.07/0.30 ~head_of(sk0_9)=head_of(sk0_8)|spl0_7),
% 0.07/0.30 inference(component_clause,[status(thm)],[f158])).
% 0.07/0.30 fof(f161,plain,(
% 0.07/0.30 spl0_5|spl0_6|spl0_7),
% 0.07/0.30 inference(split_clause,[status(thm)],[f121,f152,f155,f158])).
% 0.07/0.30 fof(f162,plain,(
% 0.07/0.30 spl0_8 <=> head_of(sk0_13)=head_of(sk0_9)),
% 0.07/0.30 introduced(split_symbol_definition)).
% 0.07/0.30 fof(f165,plain,(
% 0.07/0.30 spl0_8|spl0_6|spl0_7),
% 0.07/0.30 inference(split_clause,[status(thm)],[f122,f162,f155,f158])).
% 0.07/0.30 fof(f172,plain,(
% 0.07/0.30 path(sk0_11,sk0_12,sk0_10)),
% 0.07/0.30 inference(resolution,[status(thm)],[f84,f119])).
% 0.07/0.30 fof(f173,plain,(
% 0.07/0.30 ![X0,X1]: (~precedes(X0,X1,sk0_10)|~precedes(X1,X0,sk0_10))),
% 0.07/0.30 inference(resolution,[status(thm)],[f92,f119])).
% 0.07/0.30 fof(f174,plain,(
% 0.07/0.30 ~precedes(sk0_9,sk0_8,sk0_10)),
% 0.07/0.30 inference(resolution,[status(thm)],[f173,f120])).
% 0.07/0.30 fof(f175,plain,(
% 0.07/0.30 ![X0,X1,X2,X3,X4]: (~shortest_path(X0,X1,X2)|~precedes(X3,X4,X2)|~head_of(X3)=head_of(X4))),
% 0.07/0.30 inference(equality_resolution,[status(esa)],[f91])).
% 0.07/0.30 fof(f183,plain,(
% 0.07/0.30 ![X0,X1,X2]: (~shortest_path(X0,X1,X2)|~precedes(sk0_8,sk0_9,X2)|~spl0_7)),
% 0.07/0.30 inference(resolution,[status(thm)],[f159,f175])).
% 0.07/0.30 fof(f185,plain,(
% 0.07/0.30 spl0_9 <=> edge(sk0_9)),
% 0.07/0.30 introduced(split_symbol_definition)).
% 0.07/0.30 fof(f186,plain,(
% 0.07/0.30 edge(sk0_9)|~spl0_9),
% 0.07/0.30 inference(component_clause,[status(thm)],[f185])).
% 0.07/0.30 fof(f196,plain,(
% 0.07/0.30 spl0_11 <=> edge(sk0_8)),
% 0.07/0.30 introduced(split_symbol_definition)).
% 0.07/0.30 fof(f197,plain,(
% 0.07/0.30 edge(sk0_8)|~spl0_11),
% 0.07/0.30 inference(component_clause,[status(thm)],[f196])).
% 0.07/0.30 fof(f232,plain,(
% 0.07/0.30 spl0_15 <=> ~shortest_path(X0,X1,sk0_10)),
% 0.07/0.30 introduced(split_symbol_definition)).
% 0.07/0.30 fof(f233,plain,(
% 0.07/0.30 ![X0,X1]: (~shortest_path(X0,X1,sk0_10)|~spl0_15)),
% 0.07/0.30 inference(component_clause,[status(thm)],[f232])).
% 0.07/0.30 fof(f240,plain,(
% 0.07/0.30 $false|~spl0_15),
% 0.07/0.30 inference(backward_subsumption_resolution,[status(thm)],[f119,f233])).
% 0.07/0.30 fof(f241,plain,(
% 0.07/0.30 ~spl0_15),
% 0.07/0.30 inference(contradiction_clause,[status(thm)],[f240])).
% 0.07/0.30 fof(f314,plain,(
% 0.07/0.30 ~precedes(sk0_8,sk0_9,sk0_10)|~spl0_7),
% 0.07/0.30 inference(resolution,[status(thm)],[f119,f183])).
% 0.07/0.30 fof(f315,plain,(
% 0.07/0.30 $false|~spl0_7),
% 0.07/0.30 inference(forward_subsumption_resolution,[status(thm)],[f314,f120])).
% 0.07/0.30 fof(f316,plain,(
% 0.07/0.30 ~spl0_7),
% 0.07/0.30 inference(contradiction_clause,[status(thm)],[f315])).
% 0.07/0.30 fof(f357,plain,(
% 0.07/0.30 spl0_31 <=> ~path(X0,X1,sk0_10)),
% 0.07/0.30 introduced(split_symbol_definition)).
% 0.07/0.30 fof(f358,plain,(
% 0.07/0.30 ![X0,X1]: (~path(X0,X1,sk0_10)|~spl0_31)),
% 0.07/0.30 inference(component_clause,[status(thm)],[f357])).
% 0.07/0.30 fof(f360,plain,(
% 0.07/0.30 spl0_32 <=> on_path(sk0_8,sk0_10)),
% 0.07/0.30 introduced(split_symbol_definition)).
% 0.07/0.30 fof(f361,plain,(
% 0.07/0.30 on_path(sk0_8,sk0_10)|~spl0_32),
% 0.07/0.30 inference(component_clause,[status(thm)],[f360])).
% 0.07/0.30 fof(f363,plain,(
% 0.07/0.30 ![X0,X1]: (~path(X0,X1,sk0_10)|on_path(sk0_8,sk0_10))),
% 0.07/0.30 inference(resolution,[status(thm)],[f75,f120])).
% 0.07/0.30 fof(f364,plain,(
% 0.07/0.30 spl0_31|spl0_32),
% 0.07/0.30 inference(split_clause,[status(thm)],[f363,f357,f360])).
% 0.07/0.30 fof(f365,plain,(
% 0.07/0.30 spl0_33 <=> on_path(sk0_9,sk0_10)),
% 0.07/0.30 introduced(split_symbol_definition)).
% 0.07/0.30 fof(f366,plain,(
% 0.07/0.30 on_path(sk0_9,sk0_10)|~spl0_33),
% 0.07/0.30 inference(component_clause,[status(thm)],[f365])).
% 0.07/0.30 fof(f368,plain,(
% 0.07/0.30 ![X0,X1]: (~path(X0,X1,sk0_10)|on_path(sk0_9,sk0_10))),
% 0.07/0.30 inference(resolution,[status(thm)],[f76,f120])).
% 0.07/0.30 fof(f369,plain,(
% 0.07/0.30 spl0_31|spl0_33),
% 0.07/0.30 inference(split_clause,[status(thm)],[f368,f357,f365])).
% 0.07/0.30 fof(f408,plain,(
% 0.07/0.30 $false|~spl0_31),
% 0.07/0.30 inference(backward_subsumption_resolution,[status(thm)],[f172,f358])).
% 0.07/0.30 fof(f409,plain,(
% 0.07/0.30 ~spl0_31),
% 0.07/0.30 inference(contradiction_clause,[status(thm)],[f408])).
% 0.07/0.30 fof(f420,plain,(
% 0.07/0.30 ![X0,X1]: (~path(X0,X1,sk0_10)|edge(sk0_8)|~spl0_32)),
% 0.07/0.30 inference(resolution,[status(thm)],[f361,f51])).
% 0.07/0.30 fof(f421,plain,(
% 0.07/0.30 spl0_31|spl0_11|~spl0_32),
% 0.07/0.30 inference(split_clause,[status(thm)],[f420,f357,f196,f360])).
% 0.07/0.30 fof(f422,plain,(
% 0.07/0.30 ![X0]: (sequential(X0,sk0_8)|~edge(X0)|X0=sk0_8|~head_of(X0)=tail_of(sk0_8)|~spl0_11)),
% 0.07/0.30 inference(resolution,[status(thm)],[f197,f66])).
% 0.07/0.30 fof(f444,plain,(
% 0.07/0.30 ![X0,X1]: (~path(X0,X1,sk0_10)|edge(sk0_9)|~spl0_33)),
% 0.07/0.30 inference(resolution,[status(thm)],[f366,f51])).
% 0.07/0.30 fof(f445,plain,(
% 0.07/0.30 spl0_31|spl0_9|~spl0_33),
% 0.07/0.30 inference(split_clause,[status(thm)],[f444,f357,f185,f365])).
% 0.07/0.30 fof(f471,plain,(
% 0.07/0.30 ![X0,X1,X2,X3]: (~shortest_path(X0,X1,X2)|~precedes(sk0_8,X3,X2)|~head_of(sk0_13)=head_of(X3)|~spl0_5)),
% 0.07/0.30 inference(resolution,[status(thm)],[f153,f91])).
% 0.07/0.30 fof(f488,plain,(
% 0.07/0.30 spl0_51 <=> head_of(sk0_9)=head_of(sk0_9)),
% 0.07/0.30 introduced(split_symbol_definition)).
% 0.07/0.30 fof(f490,plain,(
% 0.07/0.30 ~head_of(sk0_9)=head_of(sk0_9)|spl0_51),
% 0.07/0.30 inference(component_clause,[status(thm)],[f488])).
% 0.07/0.30 fof(f493,plain,(
% 0.07/0.30 $false|spl0_51),
% 0.07/0.30 inference(trivial_equality_resolution,[status(esa)],[f490])).
% 0.07/0.30 fof(f494,plain,(
% 0.07/0.30 spl0_51),
% 0.07/0.30 inference(contradiction_clause,[status(thm)],[f493])).
% 0.07/0.30 fof(f677,plain,(
% 0.07/0.30 ![X0,X1]: (precedes(X0,X1,sk0_10)|~on_path(X0,sk0_10)|~on_path(X1,sk0_10)|~sequential(X0,X1))),
% 0.07/0.30 inference(resolution,[status(thm)],[f69,f172])).
% 0.07/0.30 fof(f1113,plain,(
% 0.07/0.30 ![X0,X1]: (~shortest_path(X0,X1,sk0_10)|~head_of(sk0_13)=head_of(sk0_9)|~spl0_5)),
% 0.07/0.30 inference(resolution,[status(thm)],[f471,f120])).
% 0.07/0.30 fof(f1114,plain,(
% 0.07/0.30 spl0_15|~spl0_8|~spl0_5),
% 0.07/0.30 inference(split_clause,[status(thm)],[f1113,f232,f162,f152])).
% 0.07/0.30 fof(f1203,plain,(
% 0.07/0.30 ![X0]: (sequential(X0,sk0_8)|~edge(X0)|X0=sk0_8|~head_of(X0)=head_of(sk0_9)|~spl0_6|~spl0_11)),
% 0.07/0.30 inference(forward_demodulation,[status(thm)],[f156,f422])).
% 0.07/0.30 fof(f1236,plain,(
% 0.07/0.30 spl0_160 <=> sequential(sk0_9,sk0_8)),
% 0.07/0.30 introduced(split_symbol_definition)).
% 0.07/0.30 fof(f1237,plain,(
% 0.07/0.30 sequential(sk0_9,sk0_8)|~spl0_160),
% 0.07/0.30 inference(component_clause,[status(thm)],[f1236])).
% 0.07/0.30 fof(f1239,plain,(
% 0.07/0.30 spl0_161 <=> sk0_9=sk0_8),
% 0.07/0.30 introduced(split_symbol_definition)).
% 0.07/0.30 fof(f1240,plain,(
% 0.07/0.30 sk0_9=sk0_8|~spl0_161),
% 0.07/0.30 inference(component_clause,[status(thm)],[f1239])).
% 0.07/0.30 fof(f1242,plain,(
% 0.07/0.30 sequential(sk0_9,sk0_8)|sk0_9=sk0_8|~head_of(sk0_9)=head_of(sk0_9)|~spl0_6|~spl0_11|~spl0_9),
% 0.07/0.30 inference(resolution,[status(thm)],[f1203,f186])).
% 0.07/0.30 fof(f1243,plain,(
% 0.07/0.30 spl0_160|spl0_161|~spl0_51|~spl0_6|~spl0_11|~spl0_9),
% 0.07/0.30 inference(split_clause,[status(thm)],[f1242,f1236,f1239,f488,f155,f196,f185])).
% 0.07/0.30 fof(f1347,plain,(
% 0.07/0.30 ~head_of(sk0_8)=head_of(sk0_8)|~spl0_161|spl0_7),
% 0.07/0.30 inference(backward_demodulation,[status(thm)],[f1240,f160])).
% 0.07/0.30 fof(f1348,plain,(
% 0.07/0.30 $false|~spl0_161|spl0_7),
% 0.07/0.30 inference(trivial_equality_resolution,[status(esa)],[f1347])).
% 0.07/0.30 fof(f1349,plain,(
% 0.07/0.30 ~spl0_161|spl0_7),
% 0.07/0.30 inference(contradiction_clause,[status(thm)],[f1348])).
% 0.07/0.30 fof(f1374,plain,(
% 0.07/0.30 spl0_184 <=> precedes(sk0_9,sk0_8,sk0_10)),
% 0.07/0.30 introduced(split_symbol_definition)).
% 0.07/0.30 fof(f1375,plain,(
% 0.07/0.30 precedes(sk0_9,sk0_8,sk0_10)|~spl0_184),
% 0.07/0.30 inference(component_clause,[status(thm)],[f1374])).
% 0.07/0.30 fof(f1377,plain,(
% 0.07/0.30 precedes(sk0_9,sk0_8,sk0_10)|~on_path(sk0_9,sk0_10)|~on_path(sk0_8,sk0_10)|~spl0_160),
% 0.07/0.30 inference(resolution,[status(thm)],[f1237,f677])).
% 0.07/0.30 fof(f1378,plain,(
% 0.07/0.30 spl0_184|~spl0_33|~spl0_32|~spl0_160),
% 0.07/0.30 inference(split_clause,[status(thm)],[f1377,f1374,f365,f360,f1236])).
% 0.07/0.30 fof(f1485,plain,(
% 0.07/0.30 $false|~spl0_184),
% 0.07/0.30 inference(forward_subsumption_resolution,[status(thm)],[f174,f1375])).
% 0.07/0.30 fof(f1486,plain,(
% 0.07/0.30 ~spl0_184),
% 0.07/0.30 inference(contradiction_clause,[status(thm)],[f1485])).
% 0.07/0.30 fof(f1487,plain,(
% 0.07/0.30 $false),
% 0.07/0.30 inference(sat_refutation,[status(thm)],[f161,f165,f241,f316,f364,f369,f409,f421,f445,f494,f1114,f1243,f1349,f1378,f1486])).
% 0.07/0.30 % SZS output end CNFRefutation for theBenchmark.p
% 0.07/0.30 % Elapsed time: 0.037871 seconds
% 0.07/0.30 % CPU time: 0.220304 seconds
% 0.07/0.30 % Total memory used: 43.371 MB
% 0.07/0.30 % Net memory used: 43.221 MB
%------------------------------------------------------------------------------