TSTP Solution File: GRA010+1 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : GRA010+1 : TPTP v8.1.2. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n008.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 0.14s 0.47s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10 % Problem : GRA010+1 : TPTP v8.1.2. Bugfixed v3.2.0.
% 0.02/0.10 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.30 % Computer : n008.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Tue May 30 10:39:53 EDT 2023
% 0.09/0.30 % CPUTime :
% 0.09/0.31 % Drodi V3.5.1
% 0.14/0.47 % Refutation found
% 0.14/0.47 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.47 % SZS output start CNFRefutation for theBenchmark
% 0.14/0.47 fof(f8,axiom,(
% 0.14/0.47 (! [E1,E2] :( sequential(E1,E2)<=> ( edge(E1)& edge(E2)& E1 != E2& head_of(E1) = tail_of(E2) ) ) )),
% 0.14/0.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.47 fof(f13,axiom,(
% 0.14/0.47 (! [E1,E2,E3] :( triangle(E1,E2,E3)<=> ( edge(E1)& edge(E2)& edge(E3)& sequential(E1,E2)& sequential(E2,E3)& sequential(E3,E1) ) ) )),
% 0.14/0.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.47 fof(f16,axiom,(
% 0.14/0.47 (! [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) ) )),
% 0.14/0.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.47 fof(f18,conjecture,(
% 0.14/0.47 ( 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) ) )) ),
% 0.14/0.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.47 fof(f19,negated_conjecture,(
% 0.14/0.47 ~(( 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) ) )) )),
% 0.14/0.47 inference(negated_conjecture,[status(cth)],[f18])).
% 0.14/0.47 fof(f60,plain,(
% 0.14/0.47 ![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))))),
% 0.14/0.47 inference(NNF_transformation,[status(esa)],[f8])).
% 0.14/0.47 fof(f61,plain,(
% 0.14/0.47 (![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))))),
% 0.14/0.47 inference(miniscoping,[status(esa)],[f60])).
% 0.14/0.47 fof(f62,plain,(
% 0.14/0.47 ![X0,X1]: (~sequential(X0,X1)|edge(X0))),
% 0.14/0.47 inference(cnf_transformation,[status(esa)],[f61])).
% 0.14/0.47 fof(f93,plain,(
% 0.14/0.47 ![E1,E2,E3]: ((~triangle(E1,E2,E3)|(((((edge(E1)&edge(E2))&edge(E3))&sequential(E1,E2))&sequential(E2,E3))&sequential(E3,E1)))&(triangle(E1,E2,E3)|(((((~edge(E1)|~edge(E2))|~edge(E3))|~sequential(E1,E2))|~sequential(E2,E3))|~sequential(E3,E1))))),
% 0.14/0.47 inference(NNF_transformation,[status(esa)],[f13])).
% 0.14/0.47 fof(f94,plain,(
% 0.14/0.47 (![E1,E2,E3]: (~triangle(E1,E2,E3)|(((((edge(E1)&edge(E2))&edge(E3))&sequential(E1,E2))&sequential(E2,E3))&sequential(E3,E1))))&(![E1,E2,E3]: (triangle(E1,E2,E3)|(((((~edge(E1)|~edge(E2))|~edge(E3))|~sequential(E1,E2))|~sequential(E2,E3))|~sequential(E3,E1))))),
% 0.14/0.47 inference(miniscoping,[status(esa)],[f93])).
% 0.14/0.47 fof(f99,plain,(
% 0.14/0.47 ![X0,X1,X2]: (~triangle(X0,X1,X2)|sequential(X1,X2))),
% 0.14/0.47 inference(cnf_transformation,[status(esa)],[f94])).
% 0.14/0.47 fof(f100,plain,(
% 0.14/0.47 ![X0,X1,X2]: (~triangle(X0,X1,X2)|sequential(X2,X0))),
% 0.14/0.47 inference(cnf_transformation,[status(esa)],[f94])).
% 0.14/0.47 fof(f101,plain,(
% 0.14/0.47 ![X0,X1,X2]: (triangle(X0,X1,X2)|~edge(X0)|~edge(X1)|~edge(X2)|~sequential(X0,X1)|~sequential(X1,X2)|~sequential(X2,X0))),
% 0.14/0.47 inference(cnf_transformation,[status(esa)],[f94])).
% 0.14/0.47 fof(f108,plain,(
% 0.14/0.47 ![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))),
% 0.14/0.47 inference(pre_NNF_transformation,[status(esa)],[f16])).
% 0.14/0.47 fof(f109,plain,(
% 0.14/0.47 ![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))),
% 0.14/0.47 inference(miniscoping,[status(esa)],[f108])).
% 0.14/0.47 fof(f110,plain,(
% 0.14/0.47 ![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))),
% 0.14/0.47 inference(skolemization,[status(esa)],[f109])).
% 0.14/0.47 fof(f111,plain,(
% 0.14/0.47 ![X0,X1,X2]: (~path(X0,X1,X2)|on_path(sk0_6(X2),X2)|number_of_in(sequential_pairs,X2)=number_of_in(triangles,X2))),
% 0.14/0.47 inference(cnf_transformation,[status(esa)],[f110])).
% 0.14/0.48 fof(f112,plain,(
% 0.14/0.48 ![X0,X1,X2]: (~path(X0,X1,X2)|on_path(sk0_7(X2),X2)|number_of_in(sequential_pairs,X2)=number_of_in(triangles,X2))),
% 0.14/0.48 inference(cnf_transformation,[status(esa)],[f110])).
% 0.14/0.48 fof(f113,plain,(
% 0.14/0.48 ![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))),
% 0.14/0.48 inference(cnf_transformation,[status(esa)],[f110])).
% 0.14/0.48 fof(f114,plain,(
% 0.14/0.48 ![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))),
% 0.14/0.48 inference(cnf_transformation,[status(esa)],[f110])).
% 0.14/0.48 fof(f116,plain,(
% 0.14/0.48 (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))))),
% 0.14/0.48 inference(pre_NNF_transformation,[status(esa)],[f19])).
% 0.14/0.48 fof(f117,plain,(
% 0.14/0.48 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)))),
% 0.14/0.48 inference(miniscoping,[status(esa)],[f116])).
% 0.14/0.48 fof(f118,plain,(
% 0.14/0.48 complete&((path(sk0_9,sk0_10,sk0_8)&(![E1,E2]: (((~on_path(E1,sk0_8)|~on_path(E2,sk0_8))|~sequential(E1,E2))|triangle(E1,E2,sk0_11(E2,E1)))))&~number_of_in(sequential_pairs,sk0_8)=number_of_in(triangles,sk0_8))),
% 0.14/0.48 inference(skolemization,[status(esa)],[f117])).
% 0.14/0.48 fof(f120,plain,(
% 0.14/0.48 path(sk0_9,sk0_10,sk0_8)),
% 0.14/0.48 inference(cnf_transformation,[status(esa)],[f118])).
% 0.14/0.48 fof(f121,plain,(
% 0.14/0.48 ![X0,X1]: (~on_path(X0,sk0_8)|~on_path(X1,sk0_8)|~sequential(X0,X1)|triangle(X0,X1,sk0_11(X1,X0)))),
% 0.14/0.48 inference(cnf_transformation,[status(esa)],[f118])).
% 0.14/0.48 fof(f122,plain,(
% 0.14/0.48 ~number_of_in(sequential_pairs,sk0_8)=number_of_in(triangles,sk0_8)),
% 0.14/0.48 inference(cnf_transformation,[status(esa)],[f118])).
% 0.14/0.48 fof(f164,plain,(
% 0.14/0.48 ![X0,X1]: (sequential(X0,sk0_11(X0,X1))|~on_path(X1,sk0_8)|~on_path(X0,sk0_8)|~sequential(X1,X0))),
% 0.14/0.48 inference(resolution,[status(thm)],[f99,f121])).
% 0.14/0.48 fof(f165,plain,(
% 0.14/0.48 ![X0,X1]: (sequential(sk0_11(X0,X1),X1)|~on_path(X1,sk0_8)|~on_path(X0,sk0_8)|~sequential(X1,X0))),
% 0.14/0.48 inference(resolution,[status(thm)],[f100,f121])).
% 0.14/0.48 fof(f190,plain,(
% 0.14/0.48 ![X0,X1,X2]: (triangle(X0,X1,X2)|~edge(X1)|~edge(X2)|~sequential(X0,X1)|~sequential(X1,X2)|~sequential(X2,X0))),
% 0.14/0.48 inference(backward_subsumption_resolution,[status(thm)],[f101,f62])).
% 0.14/0.48 fof(f191,plain,(
% 0.14/0.48 ![X0,X1,X2]: (triangle(X0,X1,X2)|~edge(X2)|~sequential(X0,X1)|~sequential(X1,X2)|~sequential(X2,X0))),
% 0.14/0.48 inference(forward_subsumption_resolution,[status(thm)],[f190,f62])).
% 0.14/0.48 fof(f194,plain,(
% 0.14/0.48 ![X0,X1,X2]: (triangle(X0,X1,X2)|~sequential(X0,X1)|~sequential(X1,X2)|~sequential(X2,X0))),
% 0.14/0.48 inference(forward_subsumption_resolution,[status(thm)],[f191,f62])).
% 0.14/0.48 fof(f229,plain,(
% 0.14/0.48 spl0_5 <=> ~path(X0,X1,sk0_8)),
% 0.14/0.48 introduced(split_symbol_definition)).
% 0.14/0.48 fof(f230,plain,(
% 0.14/0.48 ![X0,X1]: (~path(X0,X1,sk0_8)|~spl0_5)),
% 0.14/0.48 inference(component_clause,[status(thm)],[f229])).
% 0.14/0.48 fof(f247,plain,(
% 0.14/0.48 $false|~spl0_5),
% 0.14/0.48 inference(backward_subsumption_resolution,[status(thm)],[f120,f230])).
% 0.14/0.48 fof(f248,plain,(
% 0.14/0.48 ~spl0_5),
% 0.14/0.48 inference(contradiction_clause,[status(thm)],[f247])).
% 0.14/0.48 fof(f293,plain,(
% 0.14/0.48 spl0_9 <=> on_path(sk0_6(sk0_8),sk0_8)),
% 0.14/0.48 introduced(split_symbol_definition)).
% 0.14/0.48 fof(f296,plain,(
% 0.14/0.48 ![X0,X1]: (~path(X0,X1,sk0_8)|on_path(sk0_6(sk0_8),sk0_8))),
% 0.14/0.48 inference(resolution,[status(thm)],[f111,f122])).
% 0.14/0.48 fof(f297,plain,(
% 0.14/0.48 spl0_5|spl0_9),
% 0.14/0.48 inference(split_clause,[status(thm)],[f296,f229,f293])).
% 0.14/0.48 fof(f301,plain,(
% 0.14/0.48 spl0_10 <=> on_path(sk0_7(sk0_8),sk0_8)),
% 0.14/0.48 introduced(split_symbol_definition)).
% 0.14/0.48 fof(f304,plain,(
% 0.14/0.48 ![X0,X1]: (~path(X0,X1,sk0_8)|on_path(sk0_7(sk0_8),sk0_8))),
% 0.14/0.48 inference(resolution,[status(thm)],[f112,f122])).
% 0.14/0.48 fof(f305,plain,(
% 0.14/0.48 spl0_5|spl0_10),
% 0.14/0.48 inference(split_clause,[status(thm)],[f304,f229,f301])).
% 0.14/0.48 fof(f402,plain,(
% 0.14/0.48 spl0_17 <=> sequential(sk0_6(sk0_8),sk0_7(sk0_8))),
% 0.14/0.48 introduced(split_symbol_definition)).
% 0.14/0.48 fof(f405,plain,(
% 0.14/0.48 ![X0,X1]: (~path(X0,X1,sk0_8)|sequential(sk0_6(sk0_8),sk0_7(sk0_8)))),
% 0.14/0.48 inference(resolution,[status(thm)],[f113,f122])).
% 0.14/0.48 fof(f406,plain,(
% 0.14/0.48 spl0_5|spl0_17),
% 0.14/0.48 inference(split_clause,[status(thm)],[f405,f229,f402])).
% 0.14/0.48 fof(f415,plain,(
% 0.14/0.48 ![X0,X1,X2,X3]: (~path(X0,X1,X2)|number_of_in(sequential_pairs,X2)=number_of_in(triangles,X2)|~sequential(sk0_6(X2),sk0_7(X2))|~sequential(sk0_7(X2),X3)|~sequential(X3,sk0_6(X2)))),
% 0.14/0.48 inference(resolution,[status(thm)],[f114,f194])).
% 0.14/0.48 fof(f416,plain,(
% 0.14/0.48 ![X0,X1,X2,X3]: (~path(X0,X1,X2)|number_of_in(sequential_pairs,X2)=number_of_in(triangles,X2)|~sequential(sk0_7(X2),X3)|~sequential(X3,sk0_6(X2)))),
% 0.14/0.48 inference(forward_subsumption_resolution,[status(thm)],[f415,f113])).
% 0.14/0.48 fof(f462,plain,(
% 0.14/0.48 spl0_23 <=> ~sequential(sk0_7(sk0_8),X2)|~sequential(X2,sk0_6(sk0_8))),
% 0.14/0.48 introduced(split_symbol_definition)).
% 0.14/0.48 fof(f463,plain,(
% 0.14/0.48 ![X0]: (~sequential(sk0_7(sk0_8),X0)|~sequential(X0,sk0_6(sk0_8))|~spl0_23)),
% 0.14/0.48 inference(component_clause,[status(thm)],[f462])).
% 0.14/0.48 fof(f465,plain,(
% 0.14/0.48 ![X0,X1,X2]: (~path(X0,X1,sk0_8)|~sequential(sk0_7(sk0_8),X2)|~sequential(X2,sk0_6(sk0_8)))),
% 0.14/0.48 inference(resolution,[status(thm)],[f416,f122])).
% 0.14/0.48 fof(f466,plain,(
% 0.14/0.48 spl0_5|spl0_23),
% 0.14/0.48 inference(split_clause,[status(thm)],[f465,f229,f462])).
% 0.14/0.48 fof(f476,plain,(
% 0.14/0.48 spl0_26 <=> ~sequential(sk0_11(sk0_7(sk0_8),X0),sk0_6(sk0_8))|~on_path(X0,sk0_8)|~sequential(X0,sk0_7(sk0_8))),
% 0.14/0.48 introduced(split_symbol_definition)).
% 0.14/0.48 fof(f477,plain,(
% 0.14/0.48 ![X0]: (~sequential(sk0_11(sk0_7(sk0_8),X0),sk0_6(sk0_8))|~on_path(X0,sk0_8)|~sequential(X0,sk0_7(sk0_8))|~spl0_26)),
% 0.14/0.48 inference(component_clause,[status(thm)],[f476])).
% 0.14/0.48 fof(f479,plain,(
% 0.14/0.48 ![X0]: (~sequential(sk0_11(sk0_7(sk0_8),X0),sk0_6(sk0_8))|~on_path(X0,sk0_8)|~on_path(sk0_7(sk0_8),sk0_8)|~sequential(X0,sk0_7(sk0_8))|~spl0_23)),
% 0.14/0.48 inference(resolution,[status(thm)],[f463,f164])).
% 0.14/0.48 fof(f480,plain,(
% 0.14/0.48 spl0_26|~spl0_10|~spl0_23),
% 0.14/0.48 inference(split_clause,[status(thm)],[f479,f476,f301,f462])).
% 0.14/0.48 fof(f484,plain,(
% 0.14/0.48 ~on_path(sk0_6(sk0_8),sk0_8)|~sequential(sk0_6(sk0_8),sk0_7(sk0_8))|~on_path(sk0_6(sk0_8),sk0_8)|~on_path(sk0_7(sk0_8),sk0_8)|~sequential(sk0_6(sk0_8),sk0_7(sk0_8))|~spl0_26),
% 0.14/0.48 inference(resolution,[status(thm)],[f477,f165])).
% 0.14/0.48 fof(f485,plain,(
% 0.14/0.48 ~spl0_9|~spl0_17|~spl0_10|~spl0_26),
% 0.14/0.48 inference(split_clause,[status(thm)],[f484,f293,f402,f301,f476])).
% 0.14/0.48 fof(f486,plain,(
% 0.14/0.48 $false),
% 0.14/0.48 inference(sat_refutation,[status(thm)],[f248,f297,f305,f406,f466,f480,f485])).
% 0.14/0.48 % SZS output end CNFRefutation for theBenchmark.p
% 0.14/0.49 % Elapsed time: 0.184793 seconds
% 0.14/0.49 % CPU time: 0.723679 seconds
% 0.14/0.49 % Memory used: 56.444 MB
%------------------------------------------------------------------------------