TSTP Solution File: GRA010+2 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : GRA010+2 : TPTP v8.1.2. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n019.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 : Wed May 31 12:09:30 EDT 2023
% Result : Theorem 6.11s 1.19s
% Output : CNFRefutation 6.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : GRA010+2 : TPTP v8.1.2. Bugfixed v3.2.0.
% 0.10/0.12 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.33 % Computer : n019.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue May 30 10:38:55 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.12/0.35 % Drodi V3.5.1
% 6.11/1.19 % Refutation found
% 6.11/1.19 % SZS status Theorem for theBenchmark: Theorem is valid
% 6.11/1.19 % SZS output start CNFRefutation for theBenchmark
% 6.11/1.19 fof(f5,axiom,(
% 6.11/1.19 (! [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) ) )) ) )) ) )),
% 6.11/1.19 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 6.11/1.19 fof(f16,axiom,(
% 6.11/1.19 (! [P,V1,V2] :( ( path(V1,V2,P)& (! [E1,E2] :( ( on_path(E1,P)& on_path(E2,P)& sequential(E1,E2) )=> (? [E3] : triangle(E1,E2,E3) )) ))=> number_of_in(sequential_pairs,P) = number_of_in(triangles,P) ) )),
% 6.11/1.19 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 6.11/1.19 fof(f19,conjecture,(
% 6.11/1.19 ( complete=> (! [P,V1,V2] :( ( path(V1,V2,P)& (! [E1,E2] :( ( on_path(E1,P)& on_path(E2,P)& sequential(E1,E2) )=> (? [E3] : triangle(E1,E2,E3) )) ))=> number_of_in(sequential_pairs,P) = number_of_in(triangles,P) ) )) ),
% 6.11/1.19 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 6.11/1.19 fof(f20,negated_conjecture,(
% 6.11/1.19 ~(( complete=> (! [P,V1,V2] :( ( path(V1,V2,P)& (! [E1,E2] :( ( on_path(E1,P)& on_path(E2,P)& sequential(E1,E2) )=> (? [E3] : triangle(E1,E2,E3) )) ))=> number_of_in(sequential_pairs,P) = number_of_in(triangles,P) ) )) )),
% 6.11/1.19 inference(negated_conjecture,[status(cth)],[f19])).
% 6.11/1.19 fof(f38,plain,(
% 6.11/1.19 ![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))))))))),
% 6.11/1.19 inference(pre_NNF_transformation,[status(esa)],[f5])).
% 6.11/1.19 fof(f39,plain,(
% 6.11/1.19 ![V2,P,E]: (pd0_1(E,P,V2)<=>(V2=head_of(E)&P=path_cons(E,empty)))),
% 6.11/1.19 introduced(predicate_definition,[f38])).
% 6.11/1.19 fof(f40,plain,(
% 6.11/1.19 ![V1,V2,P]: (~path(V1,V2,P)|((vertex(V1)&vertex(V2))&(?[E]: ((edge(E)&V1=tail_of(E))&(pd0_1(E,P,V2)<~>(?[TP]: (path(head_of(E),V2,TP)&P=path_cons(E,TP))))))))),
% 6.11/1.19 inference(formula_renaming,[status(thm)],[f38,f39])).
% 6.11/1.19 fof(f41,plain,(
% 6.11/1.19 ![V1,V2,P]: (~path(V1,V2,P)|((vertex(V1)&vertex(V2))&(?[E]: ((edge(E)&V1=tail_of(E))&((pd0_1(E,P,V2)|(?[TP]: (path(head_of(E),V2,TP)&P=path_cons(E,TP))))&(~pd0_1(E,P,V2)|(![TP]: (~path(head_of(E),V2,TP)|~P=path_cons(E,TP)))))))))),
% 6.11/1.19 inference(NNF_transformation,[status(esa)],[f40])).
% 6.11/1.19 fof(f42,plain,(
% 6.11/1.19 ![V1,V2,P]: (~path(V1,V2,P)|((vertex(V1)&vertex(V2))&((edge(sk0_1(P,V2,V1))&V1=tail_of(sk0_1(P,V2,V1)))&((pd0_1(sk0_1(P,V2,V1),P,V2)|(path(head_of(sk0_1(P,V2,V1)),V2,sk0_2(P,V2,V1))&P=path_cons(sk0_1(P,V2,V1),sk0_2(P,V2,V1))))&(~pd0_1(sk0_1(P,V2,V1),P,V2)|(![TP]: (~path(head_of(sk0_1(P,V2,V1)),V2,TP)|~P=path_cons(sk0_1(P,V2,V1),TP))))))))),
% 6.11/1.19 inference(skolemization,[status(esa)],[f41])).
% 6.11/1.19 fof(f43,plain,(
% 6.11/1.19 ![X0,X1,X2]: (~path(X0,X1,X2)|vertex(X0))),
% 6.11/1.19 inference(cnf_transformation,[status(esa)],[f42])).
% 6.11/1.19 fof(f44,plain,(
% 6.11/1.19 ![X0,X1,X2]: (~path(X0,X1,X2)|vertex(X1))),
% 6.11/1.19 inference(cnf_transformation,[status(esa)],[f42])).
% 6.11/1.19 fof(f45,plain,(
% 6.11/1.19 ![X0,X1,X2]: (~path(X0,X1,X2)|edge(sk0_1(X2,X1,X0)))),
% 6.11/1.19 inference(cnf_transformation,[status(esa)],[f42])).
% 6.11/1.19 fof(f46,plain,(
% 6.11/1.19 ![X0,X1,X2]: (~path(X0,X1,X2)|X0=tail_of(sk0_1(X2,X1,X0)))),
% 6.11/1.19 inference(cnf_transformation,[status(esa)],[f42])).
% 6.11/1.19 fof(f109,plain,(
% 6.11/1.19 ![P,V1,V2]: ((~path(V1,V2,P)|(?[E1,E2]: (((on_path(E1,P)&on_path(E2,P))&sequential(E1,E2))&(![E3]: ~triangle(E1,E2,E3)))))|number_of_in(sequential_pairs,P)=number_of_in(triangles,P))),
% 6.11/1.19 inference(pre_NNF_transformation,[status(esa)],[f16])).
% 6.11/1.19 fof(f110,plain,(
% 6.11/1.19 ![P]: (((![V1,V2]: ~path(V1,V2,P))|(?[E1,E2]: (((on_path(E1,P)&on_path(E2,P))&sequential(E1,E2))&(![E3]: ~triangle(E1,E2,E3)))))|number_of_in(sequential_pairs,P)=number_of_in(triangles,P))),
% 6.11/1.19 inference(miniscoping,[status(esa)],[f109])).
% 6.11/1.19 fof(f111,plain,(
% 6.11/1.19 ![P]: (((![V1,V2]: ~path(V1,V2,P))|(((on_path(sk0_6(P),P)&on_path(sk0_7(P),P))&sequential(sk0_6(P),sk0_7(P)))&(![E3]: ~triangle(sk0_6(P),sk0_7(P),E3))))|number_of_in(sequential_pairs,P)=number_of_in(triangles,P))),
% 6.11/1.19 inference(skolemization,[status(esa)],[f110])).
% 6.11/1.19 fof(f112,plain,(
% 6.11/1.19 ![X0,X1,X2]: (~path(X0,X1,X2)|on_path(sk0_6(X2),X2)|number_of_in(sequential_pairs,X2)=number_of_in(triangles,X2))),
% 6.11/1.19 inference(cnf_transformation,[status(esa)],[f111])).
% 6.11/1.19 fof(f113,plain,(
% 6.11/1.19 ![X0,X1,X2]: (~path(X0,X1,X2)|on_path(sk0_7(X2),X2)|number_of_in(sequential_pairs,X2)=number_of_in(triangles,X2))),
% 6.11/1.19 inference(cnf_transformation,[status(esa)],[f111])).
% 6.11/1.19 fof(f114,plain,(
% 6.11/1.19 ![X0,X1,X2]: (~path(X0,X1,X2)|sequential(sk0_6(X2),sk0_7(X2))|number_of_in(sequential_pairs,X2)=number_of_in(triangles,X2))),
% 6.11/1.19 inference(cnf_transformation,[status(esa)],[f111])).
% 6.11/1.19 fof(f115,plain,(
% 6.11/1.19 ![X0,X1,X2,X3]: (~path(X0,X1,X2)|~triangle(sk0_6(X2),sk0_7(X2),X3)|number_of_in(sequential_pairs,X2)=number_of_in(triangles,X2))),
% 6.11/1.19 inference(cnf_transformation,[status(esa)],[f111])).
% 6.11/1.19 fof(f121,plain,(
% 6.11/1.19 (complete&(?[P,V1,V2]: ((path(V1,V2,P)&(![E1,E2]: (((~on_path(E1,P)|~on_path(E2,P))|~sequential(E1,E2))|(?[E3]: triangle(E1,E2,E3)))))&~number_of_in(sequential_pairs,P)=number_of_in(triangles,P))))),
% 6.11/1.19 inference(pre_NNF_transformation,[status(esa)],[f20])).
% 6.11/1.19 fof(f122,plain,(
% 6.11/1.19 complete&(?[P]: (((?[V1,V2]: path(V1,V2,P))&(![E1,E2]: (((~on_path(E1,P)|~on_path(E2,P))|~sequential(E1,E2))|(?[E3]: triangle(E1,E2,E3)))))&~number_of_in(sequential_pairs,P)=number_of_in(triangles,P)))),
% 6.11/1.19 inference(miniscoping,[status(esa)],[f121])).
% 6.11/1.19 fof(f123,plain,(
% 6.11/1.19 complete&((path(sk0_10,sk0_11,sk0_9)&(![E1,E2]: (((~on_path(E1,sk0_9)|~on_path(E2,sk0_9))|~sequential(E1,E2))|triangle(E1,E2,sk0_12(E2,E1)))))&~number_of_in(sequential_pairs,sk0_9)=number_of_in(triangles,sk0_9))),
% 6.11/1.19 inference(skolemization,[status(esa)],[f122])).
% 6.11/1.19 fof(f125,plain,(
% 6.11/1.19 path(sk0_10,sk0_11,sk0_9)),
% 6.11/1.19 inference(cnf_transformation,[status(esa)],[f123])).
% 6.11/1.19 fof(f126,plain,(
% 6.11/1.19 ![X0,X1]: (~on_path(X0,sk0_9)|~on_path(X1,sk0_9)|~sequential(X0,X1)|triangle(X0,X1,sk0_12(X1,X0)))),
% 6.11/1.19 inference(cnf_transformation,[status(esa)],[f123])).
% 6.11/1.19 fof(f127,plain,(
% 6.11/1.19 ~number_of_in(sequential_pairs,sk0_9)=number_of_in(triangles,sk0_9)),
% 6.11/1.19 inference(cnf_transformation,[status(esa)],[f123])).
% 6.11/1.19 fof(f172,plain,(
% 6.11/1.19 vertex(sk0_10)),
% 6.11/1.19 inference(resolution,[status(thm)],[f43,f125])).
% 6.11/1.19 fof(f197,plain,(
% 6.11/1.19 vertex(sk0_11)),
% 6.11/1.19 inference(resolution,[status(thm)],[f44,f125])).
% 6.11/1.19 fof(f272,plain,(
% 6.11/1.19 spl0_25 <=> on_path(sk0_6(sk0_9),sk0_9)),
% 6.11/1.19 introduced(split_symbol_definition)).
% 6.11/1.19 fof(f275,plain,(
% 6.11/1.19 spl0_26 <=> number_of_in(sequential_pairs,sk0_9)=number_of_in(triangles,sk0_9)),
% 6.11/1.19 introduced(split_symbol_definition)).
% 6.11/1.19 fof(f276,plain,(
% 6.11/1.19 number_of_in(sequential_pairs,sk0_9)=number_of_in(triangles,sk0_9)|~spl0_26),
% 6.11/1.19 inference(component_clause,[status(thm)],[f275])).
% 6.11/1.19 fof(f280,plain,(
% 6.11/1.19 on_path(sk0_6(sk0_9),sk0_9)|number_of_in(sequential_pairs,sk0_9)=number_of_in(triangles,sk0_9)),
% 6.11/1.19 inference(resolution,[status(thm)],[f112,f125])).
% 6.11/1.19 fof(f281,plain,(
% 6.11/1.19 spl0_25|spl0_26),
% 6.11/1.19 inference(split_clause,[status(thm)],[f280,f272,f275])).
% 6.11/1.19 fof(f283,plain,(
% 6.11/1.19 spl0_27 <=> on_path(sk0_7(sk0_9),sk0_9)),
% 6.11/1.19 introduced(split_symbol_definition)).
% 6.11/1.19 fof(f288,plain,(
% 6.11/1.19 on_path(sk0_7(sk0_9),sk0_9)|number_of_in(sequential_pairs,sk0_9)=number_of_in(triangles,sk0_9)),
% 6.11/1.19 inference(resolution,[status(thm)],[f113,f125])).
% 6.11/1.19 fof(f289,plain,(
% 6.11/1.19 spl0_27|spl0_26),
% 6.11/1.19 inference(split_clause,[status(thm)],[f288,f283,f275])).
% 6.11/1.19 fof(f290,plain,(
% 6.11/1.19 $false|~spl0_26),
% 6.11/1.19 inference(forward_subsumption_resolution,[status(thm)],[f276,f127])).
% 6.11/1.19 fof(f291,plain,(
% 6.11/1.19 ~spl0_26),
% 6.11/1.19 inference(contradiction_clause,[status(thm)],[f290])).
% 6.11/1.19 fof(f298,plain,(
% 6.11/1.19 spl0_28 <=> ~triangle(sk0_6(sk0_9),sk0_7(sk0_9),X0)),
% 6.11/1.19 introduced(split_symbol_definition)).
% 6.11/1.19 fof(f299,plain,(
% 6.11/1.19 ![X0]: (~triangle(sk0_6(sk0_9),sk0_7(sk0_9),X0)|~spl0_28)),
% 6.11/1.19 inference(component_clause,[status(thm)],[f298])).
% 6.11/1.19 fof(f303,plain,(
% 6.11/1.19 ![X0]: (~triangle(sk0_6(sk0_9),sk0_7(sk0_9),X0)|number_of_in(sequential_pairs,sk0_9)=number_of_in(triangles,sk0_9))),
% 6.11/1.19 inference(resolution,[status(thm)],[f115,f125])).
% 6.11/1.19 fof(f304,plain,(
% 6.11/1.19 spl0_28|spl0_26),
% 6.11/1.19 inference(split_clause,[status(thm)],[f303,f298,f275])).
% 6.11/1.19 fof(f826,plain,(
% 6.11/1.19 spl0_138 <=> vertex(sk0_11)),
% 6.11/1.19 introduced(split_symbol_definition)).
% 6.11/1.19 fof(f828,plain,(
% 6.11/1.19 ~vertex(sk0_11)|spl0_138),
% 6.11/1.19 inference(component_clause,[status(thm)],[f826])).
% 6.11/1.19 fof(f829,plain,(
% 6.11/1.19 spl0_139 <=> vertex(sk0_10)),
% 6.11/1.19 introduced(split_symbol_definition)).
% 6.11/1.19 fof(f831,plain,(
% 6.11/1.21 ~vertex(sk0_10)|spl0_139),
% 6.11/1.21 inference(component_clause,[status(thm)],[f829])).
% 6.11/1.21 fof(f838,plain,(
% 6.11/1.21 $false|spl0_139),
% 6.11/1.21 inference(forward_subsumption_resolution,[status(thm)],[f831,f172])).
% 6.11/1.21 fof(f839,plain,(
% 6.11/1.21 spl0_139),
% 6.11/1.21 inference(contradiction_clause,[status(thm)],[f838])).
% 6.11/1.21 fof(f840,plain,(
% 6.11/1.21 $false|spl0_138),
% 6.11/1.21 inference(forward_subsumption_resolution,[status(thm)],[f828,f197])).
% 6.11/1.21 fof(f841,plain,(
% 6.11/1.21 spl0_138),
% 6.11/1.21 inference(contradiction_clause,[status(thm)],[f840])).
% 6.11/1.21 fof(f972,plain,(
% 6.11/1.21 edge(sk0_1(sk0_9,sk0_11,sk0_10))),
% 6.11/1.21 inference(resolution,[status(thm)],[f45,f125])).
% 6.11/1.21 fof(f1359,plain,(
% 6.11/1.21 spl0_244 <=> sk0_10=tail_of(sk0_1(sk0_9,sk0_11,sk0_10))),
% 6.11/1.21 introduced(split_symbol_definition)).
% 6.11/1.21 fof(f1361,plain,(
% 6.11/1.21 ~sk0_10=tail_of(sk0_1(sk0_9,sk0_11,sk0_10))|spl0_244),
% 6.11/1.21 inference(component_clause,[status(thm)],[f1359])).
% 6.11/1.21 fof(f1662,plain,(
% 6.11/1.21 spl0_285 <=> path(sk0_10,sk0_11,sk0_9)),
% 6.11/1.21 introduced(split_symbol_definition)).
% 6.11/1.21 fof(f1664,plain,(
% 6.11/1.21 ~path(sk0_10,sk0_11,sk0_9)|spl0_285),
% 6.11/1.21 inference(component_clause,[status(thm)],[f1662])).
% 6.11/1.21 fof(f1673,plain,(
% 6.11/1.21 $false|spl0_285),
% 6.11/1.21 inference(forward_subsumption_resolution,[status(thm)],[f1664,f125])).
% 6.11/1.21 fof(f1674,plain,(
% 6.11/1.21 spl0_285),
% 6.11/1.21 inference(contradiction_clause,[status(thm)],[f1673])).
% 6.11/1.21 fof(f2289,plain,(
% 6.11/1.21 sk0_10=tail_of(sk0_1(sk0_9,sk0_11,sk0_10))),
% 6.11/1.21 inference(resolution,[status(thm)],[f46,f125])).
% 6.11/1.21 fof(f2598,plain,(
% 6.11/1.21 spl0_351 <=> edge(sk0_1(sk0_9,sk0_11,sk0_10))),
% 6.11/1.21 introduced(split_symbol_definition)).
% 6.11/1.21 fof(f2600,plain,(
% 6.11/1.21 ~edge(sk0_1(sk0_9,sk0_11,sk0_10))|spl0_351),
% 6.11/1.21 inference(component_clause,[status(thm)],[f2598])).
% 6.11/1.21 fof(f2629,plain,(
% 6.11/1.21 $false|spl0_351),
% 6.11/1.21 inference(forward_subsumption_resolution,[status(thm)],[f2600,f972])).
% 6.11/1.21 fof(f2630,plain,(
% 6.11/1.21 spl0_351),
% 6.11/1.21 inference(contradiction_clause,[status(thm)],[f2629])).
% 6.11/1.21 fof(f2656,plain,(
% 6.11/1.21 $false|spl0_244),
% 6.11/1.21 inference(forward_subsumption_resolution,[status(thm)],[f1361,f2289])).
% 6.11/1.21 fof(f2657,plain,(
% 6.11/1.21 spl0_244),
% 6.11/1.21 inference(contradiction_clause,[status(thm)],[f2656])).
% 6.11/1.21 fof(f3220,plain,(
% 6.11/1.21 spl0_443 <=> sequential(sk0_6(sk0_9),sk0_7(sk0_9))),
% 6.11/1.21 introduced(split_symbol_definition)).
% 6.11/1.21 fof(f3221,plain,(
% 6.11/1.21 sequential(sk0_6(sk0_9),sk0_7(sk0_9))|~spl0_443),
% 6.11/1.21 inference(component_clause,[status(thm)],[f3220])).
% 6.11/1.21 fof(f3223,plain,(
% 6.11/1.21 sequential(sk0_6(sk0_9),sk0_7(sk0_9))|number_of_in(sequential_pairs,sk0_9)=number_of_in(triangles,sk0_9)),
% 6.11/1.21 inference(resolution,[status(thm)],[f114,f125])).
% 6.11/1.21 fof(f3224,plain,(
% 6.11/1.21 spl0_443|spl0_26),
% 6.11/1.21 inference(split_clause,[status(thm)],[f3223,f3220,f275])).
% 6.11/1.21 fof(f3443,plain,(
% 6.11/1.21 spl0_484 <=> triangle(sk0_6(sk0_9),sk0_7(sk0_9),sk0_12(sk0_7(sk0_9),sk0_6(sk0_9)))),
% 6.11/1.21 introduced(split_symbol_definition)).
% 6.11/1.21 fof(f3444,plain,(
% 6.11/1.21 triangle(sk0_6(sk0_9),sk0_7(sk0_9),sk0_12(sk0_7(sk0_9),sk0_6(sk0_9)))|~spl0_484),
% 6.11/1.21 inference(component_clause,[status(thm)],[f3443])).
% 6.11/1.21 fof(f3446,plain,(
% 6.11/1.21 ~on_path(sk0_6(sk0_9),sk0_9)|~on_path(sk0_7(sk0_9),sk0_9)|triangle(sk0_6(sk0_9),sk0_7(sk0_9),sk0_12(sk0_7(sk0_9),sk0_6(sk0_9)))|~spl0_443),
% 6.11/1.21 inference(resolution,[status(thm)],[f3221,f126])).
% 6.11/1.21 fof(f3447,plain,(
% 6.11/1.21 ~spl0_25|~spl0_27|spl0_484|~spl0_443),
% 6.11/1.21 inference(split_clause,[status(thm)],[f3446,f272,f283,f3443,f3220])).
% 6.11/1.21 fof(f3448,plain,(
% 6.11/1.21 $false|~spl0_28|~spl0_484),
% 6.11/1.21 inference(forward_subsumption_resolution,[status(thm)],[f3444,f299])).
% 6.11/1.21 fof(f3449,plain,(
% 6.11/1.21 ~spl0_28|~spl0_484),
% 6.11/1.21 inference(contradiction_clause,[status(thm)],[f3448])).
% 6.11/1.21 fof(f3450,plain,(
% 6.11/1.21 $false),
% 6.11/1.21 inference(sat_refutation,[status(thm)],[f281,f289,f291,f304,f839,f841,f1674,f2630,f2657,f3224,f3447,f3449])).
% 6.11/1.21 % SZS output end CNFRefutation for theBenchmark.p
% 6.11/1.22 % Elapsed time: 0.878007 seconds
% 6.11/1.22 % CPU time: 6.483200 seconds
% 6.11/1.22 % Memory used: 101.573 MB
%------------------------------------------------------------------------------