%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GRA003+1 : TPTP v9.3.1. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.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 0.13s 0.41s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRA003+1 : TPTP v9.3.1. Bugfixed v3.2.0.
% 0.00/0.03 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n017.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 18:13:56 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 0.13/0.41 % Refutation found
% 0.13/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.41 % SZS output start CNFRefutation for theBenchmark
% 0.13/0.41 fof(f5,axiom,(
% 0.13/0.41 (! [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) ) )) ) )) ) )),
% 0.13/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.41 fof(f6,axiom,(
% 0.13/0.41 (! [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) ) ) )),
% 0.13/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.41 fof(f10,axiom,(
% 0.13/0.41 (! [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) ) )) ) ) )) )),
% 0.13/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.41 fof(f11,axiom,(
% 0.13/0.41 (! [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)) ) )) ) )),
% 0.13/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.41 fof(f12,axiom,(
% 0.13/0.41 (! [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) ) ) )),
% 0.13/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.41 fof(f18,conjecture,(
% 0.13/0.41 (! [V1,V2,E1,E2,P] :( ( shortest_path(V1,V2,P)& precedes(E1,E2,P) )=> ( vertex(V1)& vertex(V2)& V1 != V2& edge(E1)& edge(E2)& E1 != E2& path(V1,V2,P) ) ) )),
% 0.13/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.41 fof(f19,negated_conjecture,(
% 0.13/0.41 ~((! [V1,V2,E1,E2,P] :( ( shortest_path(V1,V2,P)& precedes(E1,E2,P) )=> ( vertex(V1)& vertex(V2)& V1 != V2& edge(E1)& edge(E2)& E1 != E2& path(V1,V2,P) ) ) ))),
% 0.13/0.41 inference(negated_conjecture,[status(cth)],[f18])).
% 0.13/0.41 fof(f37,plain,(
% 0.13/0.41 ![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))))))))),
% 0.13/0.41 inference(pre_NNF_transformation,[status(thm)],[f5])).
% 0.13/0.41 fof(f38,definition,(
% 0.13/0.41 ![V2,P,E]: (sP1_prd(E,P,V2)<=>(V2=head_of(E)&P=path_cons(E,empty)))),
% 0.13/0.41 introduced(definition,[new_symbols(definition,[sP1_prd])],[])).
% 0.13/0.41 fof(f39,plain,(
% 0.13/0.41 ![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))))))))),
% 0.13/0.41 inference(formula_renaming,[status(thm)],[f37,f38])).
% 0.13/0.41 fof(f40,plain,(
% 0.13/0.41 ![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)))))))))),
% 0.13/0.41 inference(NNF_transformation,[status(thm)],[f39])).
% 0.13/0.41 fof(f41,plain,(
% 0.13/0.41 ![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))))))))),
% 0.13/0.41 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])).
% 0.13/0.41 fof(f42,plain,(
% 0.13/0.41 ![X0,X1,X2]: (~path(X0,X1,X2)|vertex(X0))),
% 0.13/0.41 inference(cnf_transformation,[status(thm)],[f41])).
% 0.13/0.41 fof(f43,plain,(
% 0.13/0.41 ![X0,X1,X2]: (~path(X0,X1,X2)|vertex(X1))),
% 0.13/0.41 inference(cnf_transformation,[status(thm)],[f41])).
% 0.13/0.41 fof(f49,plain,(
% 0.13/0.41 ![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)))),
% 0.13/0.41 inference(pre_NNF_transformation,[status(thm)],[f6])).
% 0.13/0.41 fof(f50,plain,(
% 0.13/0.41 ![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)))),
% 0.13/0.41 inference(miniscoping,[status(thm)],[f49])).
% 0.13/0.41 fof(f51,plain,(
% 0.13/0.41 ![X0,X1,X2,X3]: (~path(X0,X1,X2)|~on_path(X3,X2)|edge(X3))),
% 0.13/0.41 inference(cnf_transformation,[status(thm)],[f50])).
% 0.13/0.41 fof(f71,plain,(
% 0.13/0.41 ![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))))))))),
% 0.13/0.41 inference(pre_NNF_transformation,[status(thm)],[f10])).
% 0.13/0.41 fof(f72,plain,(
% 0.13/0.41 ![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)))))))))),
% 0.13/0.41 inference(NNF_transformation,[status(thm)],[f71])).
% 0.13/0.41 fof(f73,plain,(
% 0.13/0.41 ![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)))))))))),
% 0.13/0.41 inference(miniscoping,[status(thm)],[f72])).
% 0.13/0.41 fof(f74,plain,(
% 0.13/0.41 ![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)))))))))),
% 0.13/0.41 inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl]),skolemize(E3,sK4_skl(E2,E1,P))],[f73])).
% 0.13/0.41 fof(f75,plain,(
% 0.13/0.41 ![X0,X1,X2,X3,X4]: (~path(X0,X1,X2)|~precedes(X3,X4,X2)|on_path(X3,X2))),
% 0.13/0.41 inference(cnf_transformation,[status(thm)],[f74])).
% 0.13/0.41 fof(f76,plain,(
% 0.13/0.41 ![X0,X1,X2,X3,X4]: (~path(X0,X1,X2)|~precedes(X3,X4,X2)|on_path(X4,X2))),
% 0.13/0.41 inference(cnf_transformation,[status(thm)],[f74])).
% 0.13/0.41 fof(f80,plain,(
% 0.13/0.41 ![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))))))),
% 0.13/0.41 inference(pre_NNF_transformation,[status(thm)],[f11])).
% 0.13/0.41 fof(f81,plain,(
% 0.13/0.41 ![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)))))))),
% 0.13/0.41 inference(NNF_transformation,[status(thm)],[f80])).
% 0.13/0.41 fof(f82,plain,(
% 0.13/0.41 (![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)))))))),
% 0.13/0.41 inference(miniscoping,[status(thm)],[f81])).
% 0.13/0.41 fof(f83,plain,(
% 0.13/0.41 (![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)))))))),
% 0.13/0.41 inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl]),skolemize(P,sK5_skl(SP,V2,V1))],[f82])).
% 0.13/0.41 fof(f84,plain,(
% 0.13/0.41 ![X0,X1,X2]: (~shortest_path(X0,X1,X2)|path(X0,X1,X2))),
% 0.13/0.41 inference(cnf_transformation,[status(thm)],[f83])).
% 0.13/0.41 fof(f85,plain,(
% 0.13/0.41 ![X0,X1,X2]: (~shortest_path(X0,X1,X2)|~X0=X1)),
% 0.13/0.41 inference(cnf_transformation,[status(thm)],[f83])).
% 0.13/0.41 fof(f89,plain,(
% 0.13/0.41 ![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)))),
% 0.13/0.41 inference(pre_NNF_transformation,[status(thm)],[f12])).
% 0.13/0.41 fof(f90,plain,(
% 0.13/0.41 ![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)))),
% 0.13/0.41 inference(miniscoping,[status(thm)],[f89])).
% 0.13/0.41 fof(f91,plain,(
% 0.13/0.41 ![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))),
% 0.13/0.41 inference(cnf_transformation,[status(thm)],[f90])).
% 0.13/0.41 fof(f116,plain,(
% 0.13/0.41 (?[V1,V2,E1,E2,P]: ((shortest_path(V1,V2,P)&precedes(E1,E2,P))&((((((~vertex(V1)|~vertex(V2))|V1=V2)|~edge(E1))|~edge(E2))|E1=E2)|~path(V1,V2,P))))),
% 0.13/0.41 inference(pre_NNF_transformation,[status(thm)],[f19])).
% 0.13/0.41 fof(f117,plain,(
% 0.13/0.41 ((shortest_path(sK8_skl,sK9_skl,sK12_skl)&precedes(sK10_skl,sK11_skl,sK12_skl))&((((((~vertex(sK8_skl)|~vertex(sK9_skl))|sK8_skl=sK9_skl)|~edge(sK10_skl))|~edge(sK11_skl))|sK10_skl=sK11_skl)|~path(sK8_skl,sK9_skl,sK12_skl)))),
% 0.13/0.41 inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl,sK9_skl,sK10_skl,sK11_skl,sK12_skl]),skolemize(V1,sK8_skl),skolemize(V2,sK9_skl),skolemize(E1,sK10_skl),skolemize(E2,sK11_skl),skolemize(P,sK12_skl)],[f116])).
% 0.13/0.41 fof(f118,plain,(
% 0.13/0.41 shortest_path(sK8_skl,sK9_skl,sK12_skl)),
% 0.13/0.41 inference(cnf_transformation,[status(thm)],[f117])).
% 0.13/0.41 fof(f119,plain,(
% 0.13/0.41 precedes(sK10_skl,sK11_skl,sK12_skl)),
% 0.13/0.41 inference(cnf_transformation,[status(thm)],[f117])).
% 0.13/0.41 fof(f120,plain,(
% 0.13/0.41 ~vertex(sK8_skl)|~vertex(sK9_skl)|sK8_skl=sK9_skl|~edge(sK10_skl)|~edge(sK11_skl)|sK10_skl=sK11_skl|~path(sK8_skl,sK9_skl,sK12_skl)),
% 0.13/0.41 inference(cnf_transformation,[status(thm)],[f117])).
% 0.13/0.41 fof(f138,plain,(
% 0.13/0.41 ![X0,X1]: (~shortest_path(X0,X0,X1))),
% 0.13/0.41 inference(destructive_equality_resolution,[status(thm)],[f85])).
% 0.13/0.41 fof(f140,plain,(
% 0.13/0.41 ~vertex(sK8_skl)|sK8_skl=sK9_skl|~edge(sK10_skl)|~edge(sK11_skl)|sK10_skl=sK11_skl|~path(sK8_skl,sK9_skl,sK12_skl)),
% 0.13/0.41 inference(forward_subsumption_resolution,[status(thm)],[f120,f43])).
% 0.13/0.41 fof(f143,plain,(
% 0.13/0.41 path(sK8_skl,sK9_skl,sK12_skl)),
% 0.13/0.41 inference(resolution,[status(thm)],[f84,f118])).
% 0.13/0.41 fof(f144,plain,(
% 0.13/0.41 ~vertex(sK8_skl)|sK8_skl=sK9_skl|~edge(sK10_skl)|~edge(sK11_skl)|sK10_skl=sK11_skl),
% 0.13/0.41 inference(backward_subsumption_resolution,[status(thm)],[f140,f143])).
% 0.13/0.41 fof(f146,plain,(
% 0.13/0.41 vertex(sK8_skl)),
% 0.13/0.41 inference(resolution,[status(thm)],[f143,f42])).
% 0.13/0.41 fof(f147,plain,(
% 0.13/0.41 sK8_skl=sK9_skl|~edge(sK10_skl)|~edge(sK11_skl)|sK10_skl=sK11_skl),
% 0.13/0.41 inference(backward_subsumption_resolution,[status(thm)],[f144,f146])).
% 0.13/0.41 fof(f150,plain,(
% 0.13/0.41 ![X0,X1,X2,X3,X4]: (~shortest_path(X0,X1,X2)|~precedes(X3,X4,X2)|~tail_of(X4)=tail_of(X3))),
% 0.13/0.41 inference(equality_resolution,[status(thm)],[f91])).
% 0.13/0.41 fof(f151,plain,(
% 0.13/0.41 ![X0,X1]: (~shortest_path(X0,X1,sK12_skl)|~tail_of(sK11_skl)=tail_of(sK10_skl))),
% 0.13/0.41 inference(resolution,[status(thm)],[f150,f119])).
% 0.13/0.41 fof(f152,plain,(
% 0.13/0.41 ~tail_of(sK11_skl)=tail_of(sK10_skl)),
% 0.13/0.41 inference(resolution,[status(thm)],[f151,f118])).
% 0.13/0.41 fof(f169,plain,(
% 0.13/0.41 ![X0,X1]: (~precedes(X0,X1,sK12_skl)|on_path(X0,sK12_skl))),
% 0.13/0.41 inference(resolution,[status(thm)],[f75,f143])).
% 0.13/0.41 fof(f170,plain,(
% 0.13/0.41 on_path(sK10_skl,sK12_skl)),
% 0.13/0.41 inference(resolution,[status(thm)],[f169,f119])).
% 0.13/0.41 fof(f171,plain,(
% 0.13/0.41 ![X0,X1]: (~path(X0,X1,sK12_skl)|edge(sK10_skl))),
% 0.13/0.41 inference(resolution,[status(thm)],[f170,f51])).
% 0.13/0.41 fof(f174,plain,(
% 0.13/0.41 edge(sK10_skl)),
% 0.13/0.41 inference(resolution,[status(thm)],[f171,f143])).
% 0.13/0.41 fof(f175,plain,(
% 0.13/0.41 sK8_skl=sK9_skl|~edge(sK11_skl)|sK10_skl=sK11_skl),
% 0.13/0.41 inference(backward_subsumption_resolution,[status(thm)],[f147,f174])).
% 0.13/0.41 fof(f205,plain,(
% 0.13/0.41 ![X0,X1]: (~path(X0,X1,sK12_skl)|on_path(sK11_skl,sK12_skl))),
% 0.13/0.41 inference(resolution,[status(thm)],[f76,f119])).
% 0.13/0.41 fof(f206,plain,(
% 0.13/0.41 on_path(sK11_skl,sK12_skl)),
% 0.13/0.41 inference(resolution,[status(thm)],[f205,f143])).
% 0.13/0.41 fof(f207,plain,(
% 0.13/0.41 ![X0,X1]: (~path(X0,X1,sK12_skl)|edge(sK11_skl))),
% 0.13/0.41 inference(resolution,[status(thm)],[f206,f51])).
% 0.13/0.41 fof(f208,plain,(
% 0.13/0.41 edge(sK11_skl)),
% 0.13/0.41 inference(resolution,[status(thm)],[f207,f143])).
% 0.13/0.41 fof(f209,plain,(
% 0.13/0.41 sK8_skl=sK9_skl|sK10_skl=sK11_skl),
% 0.13/0.41 inference(backward_subsumption_resolution,[status(thm)],[f175,f208])).
% 0.13/0.41 fof(f225,plain,(
% 0.13/0.41 shortest_path(sK9_skl,sK9_skl,sK12_skl)|sK10_skl=sK11_skl),
% 0.13/0.41 inference(paramodulation,[status(thm)],[f209,f118])).
% 0.13/0.41 fof(f236,plain,(
% 0.13/0.41 ~tail_of(sK11_skl)=tail_of(sK11_skl)),
% 0.13/0.41 inference(backward_demodulation,[status(thm)],[f255,f152])).
% 0.13/0.41 fof(f255,plain,(
% 0.13/0.41 sK10_skl=sK11_skl),
% 0.13/0.41 inference(forward_subsumption_resolution,[status(thm)],[f225,f138])).
% 0.13/0.41 fof(f263,plain,(
% 0.13/0.41 $false),
% 0.13/0.41 inference(trivial_equality_resolution,[status(thm)],[f236])).
% 0.13/0.41 % SZS output end CNFRefutation for theBenchmark.p
% 0.13/0.43 % Elapsed time: 0.064673 seconds
% 0.13/0.43 % CPU time: 0.183313 seconds
% 0.13/0.43 % Total memory used: 83.286 MB
% 0.13/0.43 % Net memory used: 83.187 MB
%------------------------------------------------------------------------------