TSTP Solution File: GRA010+2 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% 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 : n021.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 20:18:35 EDT 2024
% Result : Theorem 0.18s 0.41s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRA010+2 : TPTP v8.1.2. Bugfixed v3.2.0.
% 0.03/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.34 % Computer : n021.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Apr 29 22:25:55 EDT 2024
% 0.12/0.34 % CPUTime :
% 0.18/0.35 % Drodi V3.6.0
% 0.18/0.41 % Refutation found
% 0.18/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.18/0.41 % SZS output start CNFRefutation for theBenchmark
% 0.18/0.41 fof(f16,axiom,(
% 0.18/0.41 (! [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) ) )),
% 0.18/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.18/0.41 fof(f19,conjecture,(
% 0.18/0.41 ( 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) ) )) ),
% 0.18/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.18/0.41 fof(f20,negated_conjecture,(
% 0.18/0.41 ~(( 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) ) )) )),
% 0.18/0.41 inference(negated_conjecture,[status(cth)],[f19])).
% 0.18/0.41 fof(f109,plain,(
% 0.18/0.41 ![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))),
% 0.18/0.41 inference(pre_NNF_transformation,[status(esa)],[f16])).
% 0.18/0.41 fof(f110,plain,(
% 0.18/0.41 ![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))),
% 0.18/0.41 inference(miniscoping,[status(esa)],[f109])).
% 0.18/0.41 fof(f111,plain,(
% 0.18/0.41 ![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))),
% 0.18/0.41 inference(skolemization,[status(esa)],[f110])).
% 0.18/0.41 fof(f112,plain,(
% 0.18/0.41 ![X0,X1,X2]: (~path(X0,X1,X2)|on_path(sk0_6(X2),X2)|number_of_in(sequential_pairs,X2)=number_of_in(triangles,X2))),
% 0.18/0.41 inference(cnf_transformation,[status(esa)],[f111])).
% 0.18/0.41 fof(f113,plain,(
% 0.18/0.41 ![X0,X1,X2]: (~path(X0,X1,X2)|on_path(sk0_7(X2),X2)|number_of_in(sequential_pairs,X2)=number_of_in(triangles,X2))),
% 0.18/0.41 inference(cnf_transformation,[status(esa)],[f111])).
% 0.18/0.41 fof(f114,plain,(
% 0.18/0.41 ![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))),
% 0.18/0.41 inference(cnf_transformation,[status(esa)],[f111])).
% 0.18/0.41 fof(f115,plain,(
% 0.18/0.41 ![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))),
% 0.18/0.41 inference(cnf_transformation,[status(esa)],[f111])).
% 0.18/0.41 fof(f121,plain,(
% 0.18/0.41 (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))))),
% 0.18/0.41 inference(pre_NNF_transformation,[status(esa)],[f20])).
% 0.18/0.41 fof(f122,plain,(
% 0.18/0.41 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)))),
% 0.18/0.41 inference(miniscoping,[status(esa)],[f121])).
% 0.18/0.41 fof(f123,plain,(
% 0.18/0.41 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))),
% 0.18/0.41 inference(skolemization,[status(esa)],[f122])).
% 0.18/0.41 fof(f125,plain,(
% 0.18/0.41 path(sk0_10,sk0_11,sk0_9)),
% 0.18/0.41 inference(cnf_transformation,[status(esa)],[f123])).
% 0.18/0.41 fof(f126,plain,(
% 0.18/0.41 ![X0,X1]: (~on_path(X0,sk0_9)|~on_path(X1,sk0_9)|~sequential(X0,X1)|triangle(X0,X1,sk0_12(X1,X0)))),
% 0.18/0.41 inference(cnf_transformation,[status(esa)],[f123])).
% 0.18/0.41 fof(f127,plain,(
% 0.18/0.41 ~number_of_in(sequential_pairs,sk0_9)=number_of_in(triangles,sk0_9)),
% 0.18/0.41 inference(cnf_transformation,[status(esa)],[f123])).
% 0.18/0.41 fof(f166,plain,(
% 0.18/0.41 spl0_6 <=> on_path(sk0_6(sk0_9),sk0_9)),
% 0.18/0.41 introduced(split_symbol_definition)).
% 0.18/0.41 fof(f169,plain,(
% 0.18/0.41 spl0_7 <=> number_of_in(sequential_pairs,sk0_9)=number_of_in(triangles,sk0_9)),
% 0.18/0.41 introduced(split_symbol_definition)).
% 0.18/0.41 fof(f170,plain,(
% 0.18/0.41 number_of_in(sequential_pairs,sk0_9)=number_of_in(triangles,sk0_9)|~spl0_7),
% 0.18/0.41 inference(component_clause,[status(thm)],[f169])).
% 0.18/0.41 fof(f172,plain,(
% 0.18/0.41 on_path(sk0_6(sk0_9),sk0_9)|number_of_in(sequential_pairs,sk0_9)=number_of_in(triangles,sk0_9)),
% 0.18/0.41 inference(resolution,[status(thm)],[f112,f125])).
% 0.18/0.41 fof(f173,plain,(
% 0.18/0.41 spl0_6|spl0_7),
% 0.18/0.41 inference(split_clause,[status(thm)],[f172,f166,f169])).
% 0.18/0.41 fof(f174,plain,(
% 0.18/0.41 spl0_8 <=> on_path(sk0_7(sk0_9),sk0_9)),
% 0.18/0.41 introduced(split_symbol_definition)).
% 0.18/0.41 fof(f175,plain,(
% 0.18/0.41 on_path(sk0_7(sk0_9),sk0_9)|~spl0_8),
% 0.18/0.41 inference(component_clause,[status(thm)],[f174])).
% 0.18/0.41 fof(f177,plain,(
% 0.18/0.41 on_path(sk0_7(sk0_9),sk0_9)|number_of_in(sequential_pairs,sk0_9)=number_of_in(triangles,sk0_9)),
% 0.18/0.41 inference(resolution,[status(thm)],[f113,f125])).
% 0.18/0.41 fof(f178,plain,(
% 0.18/0.41 spl0_8|spl0_7),
% 0.18/0.41 inference(split_clause,[status(thm)],[f177,f174,f169])).
% 0.18/0.41 fof(f179,plain,(
% 0.18/0.41 $false|~spl0_7),
% 0.18/0.41 inference(forward_subsumption_resolution,[status(thm)],[f170,f127])).
% 0.18/0.41 fof(f180,plain,(
% 0.18/0.41 ~spl0_7),
% 0.18/0.41 inference(contradiction_clause,[status(thm)],[f179])).
% 0.18/0.41 fof(f181,plain,(
% 0.18/0.41 spl0_9 <=> sequential(sk0_6(sk0_9),sk0_7(sk0_9))),
% 0.18/0.41 introduced(split_symbol_definition)).
% 0.18/0.41 fof(f182,plain,(
% 0.18/0.41 sequential(sk0_6(sk0_9),sk0_7(sk0_9))|~spl0_9),
% 0.18/0.41 inference(component_clause,[status(thm)],[f181])).
% 0.18/0.41 fof(f184,plain,(
% 0.18/0.41 sequential(sk0_6(sk0_9),sk0_7(sk0_9))|number_of_in(sequential_pairs,sk0_9)=number_of_in(triangles,sk0_9)),
% 0.18/0.41 inference(resolution,[status(thm)],[f114,f125])).
% 0.18/0.41 fof(f185,plain,(
% 0.18/0.41 spl0_9|spl0_7),
% 0.18/0.41 inference(split_clause,[status(thm)],[f184,f181,f169])).
% 0.18/0.41 fof(f190,plain,(
% 0.18/0.41 spl0_10 <=> ~path(X0,X1,sk0_9)),
% 0.18/0.41 introduced(split_symbol_definition)).
% 0.18/0.41 fof(f191,plain,(
% 0.18/0.41 ![X0,X1]: (~path(X0,X1,sk0_9)|~spl0_10)),
% 0.18/0.41 inference(component_clause,[status(thm)],[f190])).
% 0.18/0.41 fof(f203,plain,(
% 0.18/0.41 $false|~spl0_10),
% 0.18/0.41 inference(backward_subsumption_resolution,[status(thm)],[f125,f191])).
% 0.18/0.41 fof(f204,plain,(
% 0.18/0.41 ~spl0_10),
% 0.18/0.41 inference(contradiction_clause,[status(thm)],[f203])).
% 0.18/0.41 fof(f208,plain,(
% 0.18/0.41 ![X0]: (~on_path(X0,sk0_9)|~sequential(X0,sk0_7(sk0_9))|triangle(X0,sk0_7(sk0_9),sk0_12(sk0_7(sk0_9),X0))|~spl0_8)),
% 0.18/0.42 inference(resolution,[status(thm)],[f175,f126])).
% 0.18/0.42 fof(f264,plain,(
% 0.18/0.42 spl0_18 <=> triangle(sk0_6(sk0_9),sk0_7(sk0_9),sk0_12(sk0_7(sk0_9),sk0_6(sk0_9)))),
% 0.18/0.42 introduced(split_symbol_definition)).
% 0.18/0.42 fof(f265,plain,(
% 0.18/0.42 triangle(sk0_6(sk0_9),sk0_7(sk0_9),sk0_12(sk0_7(sk0_9),sk0_6(sk0_9)))|~spl0_18),
% 0.18/0.42 inference(component_clause,[status(thm)],[f264])).
% 0.18/0.42 fof(f267,plain,(
% 0.18/0.42 ~on_path(sk0_6(sk0_9),sk0_9)|triangle(sk0_6(sk0_9),sk0_7(sk0_9),sk0_12(sk0_7(sk0_9),sk0_6(sk0_9)))|~spl0_8|~spl0_9),
% 0.18/0.42 inference(resolution,[status(thm)],[f208,f182])).
% 0.18/0.42 fof(f268,plain,(
% 0.18/0.42 ~spl0_6|spl0_18|~spl0_8|~spl0_9),
% 0.18/0.42 inference(split_clause,[status(thm)],[f267,f166,f264,f174,f181])).
% 0.18/0.42 fof(f269,plain,(
% 0.18/0.42 ![X0,X1]: (~path(X0,X1,sk0_9)|number_of_in(sequential_pairs,sk0_9)=number_of_in(triangles,sk0_9)|~spl0_18)),
% 0.18/0.42 inference(resolution,[status(thm)],[f265,f115])).
% 0.18/0.42 fof(f270,plain,(
% 0.18/0.42 spl0_10|spl0_7|~spl0_18),
% 0.18/0.42 inference(split_clause,[status(thm)],[f269,f190,f169,f264])).
% 0.18/0.42 fof(f274,plain,(
% 0.18/0.42 $false),
% 0.18/0.42 inference(sat_refutation,[status(thm)],[f173,f178,f180,f185,f204,f268,f270])).
% 0.18/0.42 % SZS output end CNFRefutation for theBenchmark.p
% 0.18/0.42 % Elapsed time: 0.073554 seconds
% 0.18/0.42 % CPU time: 0.464485 seconds
% 0.18/0.42 % Total memory used: 59.197 MB
% 0.18/0.42 % Net memory used: 58.932 MB
%------------------------------------------------------------------------------