TSTP Solution File: GRA008+2 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : GRA008+2 : TPTP v8.1.2. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n013.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 0.19s 0.44s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRA008+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 : n013.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 22:17:34 EDT 2024
% 0.12/0.34 % CPUTime :
% 0.12/0.34 % Drodi V3.6.0
% 0.19/0.44 % Refutation found
% 0.19/0.44 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.19/0.44 % SZS output start CNFRefutation for theBenchmark
% 0.19/0.44 fof(f1,axiom,(
% 0.19/0.44 (! [E] :( edge(E)=> head_of(E) != tail_of(E) ) )),
% 0.19/0.44 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.44 fof(f8,axiom,(
% 0.19/0.44 (! [E1,E2] :( sequential(E1,E2)<=> ( edge(E1)& edge(E2)& E1 != E2& head_of(E1) = tail_of(E2) ) ) )),
% 0.19/0.44 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.44 fof(f12,axiom,(
% 0.19/0.44 (! [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) ) ) )),
% 0.19/0.44 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.44 fof(f13,axiom,(
% 0.19/0.44 (! [E1,E2,E3] :( triangle(E1,E2,E3)<=> ( edge(E1)& edge(E2)& edge(E3)& sequential(E1,E2)& sequential(E2,E3)& sequential(E3,E1) ) ) )),
% 0.19/0.44 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.44 fof(f18,lemma,(
% 0.19/0.44 ( complete=> (! [V1,V2,E1,E2,P] :( ( shortest_path(V1,V2,P)& precedes(E1,E2,P) )=> (? [E3] :( edge(E3)& tail_of(E3) = head_of(E2)& head_of(E3) = tail_of(E1) ) )) )) ),
% 0.19/0.44 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.44 fof(f19,conjecture,(
% 0.19/0.44 ( complete=> (! [V1,V2,E1,E2,P] :( ( shortest_path(V1,V2,P)& precedes(E1,E2,P)& sequential(E1,E2) )=> (? [E3] : triangle(E1,E2,E3) )) )) ),
% 0.19/0.44 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.44 fof(f20,negated_conjecture,(
% 0.19/0.44 ~(( complete=> (! [V1,V2,E1,E2,P] :( ( shortest_path(V1,V2,P)& precedes(E1,E2,P)& sequential(E1,E2) )=> (? [E3] : triangle(E1,E2,E3) )) )) )),
% 0.19/0.44 inference(negated_conjecture,[status(cth)],[f19])).
% 0.19/0.44 fof(f21,plain,(
% 0.19/0.44 ![E]: (~edge(E)|~head_of(E)=tail_of(E))),
% 0.19/0.44 inference(pre_NNF_transformation,[status(esa)],[f1])).
% 0.19/0.44 fof(f22,plain,(
% 0.19/0.44 ![X0]: (~edge(X0)|~head_of(X0)=tail_of(X0))),
% 0.19/0.44 inference(cnf_transformation,[status(esa)],[f21])).
% 0.19/0.44 fof(f61,plain,(
% 0.19/0.44 ![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))))),
% 0.19/0.44 inference(NNF_transformation,[status(esa)],[f8])).
% 0.19/0.44 fof(f62,plain,(
% 0.19/0.44 (![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))))),
% 0.19/0.44 inference(miniscoping,[status(esa)],[f61])).
% 0.19/0.44 fof(f63,plain,(
% 0.19/0.44 ![X0,X1]: (~sequential(X0,X1)|edge(X0))),
% 0.19/0.44 inference(cnf_transformation,[status(esa)],[f62])).
% 0.19/0.44 fof(f64,plain,(
% 0.19/0.44 ![X0,X1]: (~sequential(X0,X1)|edge(X1))),
% 0.19/0.44 inference(cnf_transformation,[status(esa)],[f62])).
% 0.19/0.44 fof(f66,plain,(
% 0.19/0.44 ![X0,X1]: (~sequential(X0,X1)|head_of(X0)=tail_of(X1))),
% 0.19/0.44 inference(cnf_transformation,[status(esa)],[f62])).
% 0.19/0.44 fof(f67,plain,(
% 0.19/0.44 ![X0,X1]: (sequential(X0,X1)|~edge(X0)|~edge(X1)|X0=X1|~head_of(X0)=tail_of(X1))),
% 0.19/0.44 inference(cnf_transformation,[status(esa)],[f62])).
% 0.19/0.44 fof(f90,plain,(
% 0.19/0.44 ![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)))),
% 0.19/0.44 inference(pre_NNF_transformation,[status(esa)],[f12])).
% 0.19/0.44 fof(f91,plain,(
% 0.19/0.44 ![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)))),
% 0.19/0.44 inference(miniscoping,[status(esa)],[f90])).
% 0.19/0.44 fof(f92,plain,(
% 0.19/0.44 ![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))),
% 0.19/0.44 inference(cnf_transformation,[status(esa)],[f91])).
% 0.19/0.44 fof(f94,plain,(
% 0.19/0.44 ![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))))),
% 0.19/0.44 inference(NNF_transformation,[status(esa)],[f13])).
% 0.19/0.44 fof(f95,plain,(
% 0.19/0.44 (![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))))),
% 0.19/0.44 inference(miniscoping,[status(esa)],[f94])).
% 0.19/0.44 fof(f102,plain,(
% 0.19/0.44 ![X0,X1,X2]: (triangle(X0,X1,X2)|~edge(X0)|~edge(X1)|~edge(X2)|~sequential(X0,X1)|~sequential(X1,X2)|~sequential(X2,X0))),
% 0.19/0.44 inference(cnf_transformation,[status(esa)],[f95])).
% 0.19/0.44 fof(f117,plain,(
% 0.19/0.44 ~complete|(![V1,V2,E1,E2,P]: ((~shortest_path(V1,V2,P)|~precedes(E1,E2,P))|(?[E3]: ((edge(E3)&tail_of(E3)=head_of(E2))&head_of(E3)=tail_of(E1)))))),
% 0.19/0.44 inference(pre_NNF_transformation,[status(esa)],[f18])).
% 0.19/0.44 fof(f118,plain,(
% 0.19/0.44 ~complete|(![E1,E2]: ((![P]: ((![V1,V2]: ~shortest_path(V1,V2,P))|~precedes(E1,E2,P)))|(?[E3]: ((edge(E3)&tail_of(E3)=head_of(E2))&head_of(E3)=tail_of(E1)))))),
% 0.19/0.44 inference(miniscoping,[status(esa)],[f117])).
% 0.19/0.44 fof(f119,plain,(
% 0.19/0.44 ~complete|(![E1,E2]: ((![P]: ((![V1,V2]: ~shortest_path(V1,V2,P))|~precedes(E1,E2,P)))|((edge(sk0_8(E2,E1))&tail_of(sk0_8(E2,E1))=head_of(E2))&head_of(sk0_8(E2,E1))=tail_of(E1))))),
% 0.19/0.44 inference(skolemization,[status(esa)],[f118])).
% 0.19/0.44 fof(f120,plain,(
% 0.19/0.44 ![X0,X1,X2,X3,X4]: (~complete|~shortest_path(X0,X1,X2)|~precedes(X3,X4,X2)|edge(sk0_8(X4,X3)))),
% 0.19/0.44 inference(cnf_transformation,[status(esa)],[f119])).
% 0.19/0.44 fof(f121,plain,(
% 0.19/0.44 ![X0,X1,X2,X3,X4]: (~complete|~shortest_path(X0,X1,X2)|~precedes(X3,X4,X2)|tail_of(sk0_8(X4,X3))=head_of(X4))),
% 0.19/0.44 inference(cnf_transformation,[status(esa)],[f119])).
% 0.19/0.44 fof(f122,plain,(
% 0.19/0.44 ![X0,X1,X2,X3,X4]: (~complete|~shortest_path(X0,X1,X2)|~precedes(X3,X4,X2)|head_of(sk0_8(X4,X3))=tail_of(X3))),
% 0.19/0.44 inference(cnf_transformation,[status(esa)],[f119])).
% 0.19/0.44 fof(f123,plain,(
% 0.19/0.44 (complete&(?[V1,V2,E1,E2,P]: (((shortest_path(V1,V2,P)&precedes(E1,E2,P))&sequential(E1,E2))&(![E3]: ~triangle(E1,E2,E3)))))),
% 0.19/0.44 inference(pre_NNF_transformation,[status(esa)],[f20])).
% 0.19/0.44 fof(f124,plain,(
% 0.19/0.44 complete&(?[E1,E2]: (((?[P]: ((?[V1,V2]: shortest_path(V1,V2,P))&precedes(E1,E2,P)))&sequential(E1,E2))&(![E3]: ~triangle(E1,E2,E3))))),
% 0.19/0.44 inference(miniscoping,[status(esa)],[f123])).
% 0.19/0.44 fof(f125,plain,(
% 0.19/0.44 complete&(((shortest_path(sk0_12,sk0_13,sk0_11)&precedes(sk0_9,sk0_10,sk0_11))&sequential(sk0_9,sk0_10))&(![E3]: ~triangle(sk0_9,sk0_10,E3)))),
% 0.19/0.44 inference(skolemization,[status(esa)],[f124])).
% 0.19/0.44 fof(f126,plain,(
% 0.19/0.44 complete),
% 0.19/0.44 inference(cnf_transformation,[status(esa)],[f125])).
% 0.19/0.44 fof(f127,plain,(
% 0.19/0.44 shortest_path(sk0_12,sk0_13,sk0_11)),
% 0.19/0.44 inference(cnf_transformation,[status(esa)],[f125])).
% 0.19/0.44 fof(f128,plain,(
% 0.19/0.44 precedes(sk0_9,sk0_10,sk0_11)),
% 0.19/0.44 inference(cnf_transformation,[status(esa)],[f125])).
% 0.19/0.44 fof(f129,plain,(
% 0.19/0.44 sequential(sk0_9,sk0_10)),
% 0.19/0.44 inference(cnf_transformation,[status(esa)],[f125])).
% 0.19/0.44 fof(f130,plain,(
% 0.19/0.44 ![X0]: (~triangle(sk0_9,sk0_10,X0))),
% 0.19/0.44 inference(cnf_transformation,[status(esa)],[f125])).
% 0.19/0.44 fof(f141,plain,(
% 0.19/0.44 spl0_0 <=> complete),
% 0.19/0.44 introduced(split_symbol_definition)).
% 0.19/0.44 fof(f143,plain,(
% 0.19/0.44 ~complete|spl0_0),
% 0.19/0.44 inference(component_clause,[status(thm)],[f141])).
% 0.19/0.44 fof(f160,plain,(
% 0.19/0.44 spl0_5 <=> ~shortest_path(X0,X1,X2)|~precedes(X3,X4,X2)|edge(sk0_8(X4,X3))),
% 0.19/0.44 introduced(split_symbol_definition)).
% 0.19/0.44 fof(f161,plain,(
% 0.19/0.44 ![X0,X1,X2,X3,X4]: (~shortest_path(X0,X1,X2)|~precedes(X3,X4,X2)|edge(sk0_8(X4,X3))|~spl0_5)),
% 0.19/0.44 inference(component_clause,[status(thm)],[f160])).
% 0.19/0.44 fof(f163,plain,(
% 0.19/0.44 ~spl0_0|spl0_5),
% 0.19/0.44 inference(split_clause,[status(thm)],[f120,f141,f160])).
% 0.19/0.44 fof(f164,plain,(
% 0.19/0.44 spl0_6 <=> ~shortest_path(X0,X1,X2)|~precedes(X3,X4,X2)|tail_of(sk0_8(X4,X3))=head_of(X4)),
% 0.19/0.44 introduced(split_symbol_definition)).
% 0.19/0.44 fof(f165,plain,(
% 0.19/0.44 ![X0,X1,X2,X3,X4]: (~shortest_path(X0,X1,X2)|~precedes(X3,X4,X2)|tail_of(sk0_8(X4,X3))=head_of(X4)|~spl0_6)),
% 0.19/0.44 inference(component_clause,[status(thm)],[f164])).
% 0.19/0.44 fof(f167,plain,(
% 0.19/0.44 ~spl0_0|spl0_6),
% 0.19/0.44 inference(split_clause,[status(thm)],[f121,f141,f164])).
% 0.19/0.44 fof(f168,plain,(
% 0.19/0.44 spl0_7 <=> ~shortest_path(X0,X1,X2)|~precedes(X3,X4,X2)|head_of(sk0_8(X4,X3))=tail_of(X3)),
% 0.19/0.44 introduced(split_symbol_definition)).
% 0.19/0.44 fof(f169,plain,(
% 0.19/0.44 ![X0,X1,X2,X3,X4]: (~shortest_path(X0,X1,X2)|~precedes(X3,X4,X2)|head_of(sk0_8(X4,X3))=tail_of(X3)|~spl0_7)),
% 0.19/0.44 inference(component_clause,[status(thm)],[f168])).
% 0.19/0.44 fof(f171,plain,(
% 0.19/0.44 ~spl0_0|spl0_7),
% 0.19/0.44 inference(split_clause,[status(thm)],[f122,f141,f168])).
% 0.19/0.44 fof(f182,plain,(
% 0.19/0.44 head_of(sk0_9)=tail_of(sk0_10)),
% 0.19/0.44 inference(resolution,[status(thm)],[f66,f129])).
% 0.19/0.44 fof(f198,plain,(
% 0.19/0.44 ![X0,X1,X2,X3,X4]: (~shortest_path(X0,X1,X2)|~precedes(X3,X4,X2)|~head_of(sk0_9)=tail_of(X3)|~head_of(sk0_10)=head_of(X4))),
% 0.19/0.44 inference(paramodulation,[status(thm)],[f182,f92])).
% 0.19/0.44 fof(f226,plain,(
% 0.19/0.44 $false|spl0_0),
% 0.19/0.44 inference(forward_subsumption_resolution,[status(thm)],[f143,f126])).
% 0.19/0.44 fof(f227,plain,(
% 0.19/0.44 spl0_0),
% 0.19/0.44 inference(contradiction_clause,[status(thm)],[f226])).
% 0.19/0.44 fof(f228,plain,(
% 0.19/0.44 ![X0,X1]: (~precedes(X0,X1,sk0_11)|tail_of(sk0_8(X1,X0))=head_of(X1)|~spl0_6)),
% 0.19/0.44 inference(resolution,[status(thm)],[f165,f127])).
% 0.19/0.44 fof(f229,plain,(
% 0.19/0.44 tail_of(sk0_8(sk0_10,sk0_9))=head_of(sk0_10)|~spl0_6),
% 0.19/0.44 inference(resolution,[status(thm)],[f228,f128])).
% 0.19/0.44 fof(f233,plain,(
% 0.19/0.44 spl0_15 <=> edge(sk0_8(sk0_10,sk0_9))),
% 0.19/0.44 introduced(split_symbol_definition)).
% 0.19/0.44 fof(f234,plain,(
% 0.19/0.44 edge(sk0_8(sk0_10,sk0_9))|~spl0_15),
% 0.19/0.44 inference(component_clause,[status(thm)],[f233])).
% 0.19/0.44 fof(f235,plain,(
% 0.19/0.44 ~edge(sk0_8(sk0_10,sk0_9))|spl0_15),
% 0.19/0.44 inference(component_clause,[status(thm)],[f233])).
% 0.19/0.44 fof(f247,plain,(
% 0.19/0.44 spl0_18 <=> head_of(sk0_8(sk0_10,sk0_9))=head_of(sk0_10)),
% 0.19/0.44 introduced(split_symbol_definition)).
% 0.19/0.44 fof(f249,plain,(
% 0.19/0.44 ~head_of(sk0_8(sk0_10,sk0_9))=head_of(sk0_10)|spl0_18),
% 0.19/0.44 inference(component_clause,[status(thm)],[f247])).
% 0.19/0.44 fof(f250,plain,(
% 0.19/0.44 ~edge(sk0_8(sk0_10,sk0_9))|~head_of(sk0_8(sk0_10,sk0_9))=head_of(sk0_10)|~spl0_6),
% 0.19/0.44 inference(paramodulation,[status(thm)],[f229,f22])).
% 0.19/0.44 fof(f251,plain,(
% 0.19/0.44 ~spl0_15|~spl0_18|~spl0_6),
% 0.19/0.44 inference(split_clause,[status(thm)],[f250,f233,f247,f164])).
% 0.19/0.44 fof(f256,plain,(
% 0.19/0.44 ![X0,X1,X2]: (~shortest_path(X0,X1,X2)|~precedes(sk0_9,sk0_10,X2)|spl0_15|~spl0_5)),
% 0.19/0.44 inference(resolution,[status(thm)],[f235,f161])).
% 0.19/0.44 fof(f263,plain,(
% 0.19/0.44 ![X0,X1]: (~shortest_path(X0,X1,sk0_11)|spl0_15|~spl0_5)),
% 0.19/0.44 inference(resolution,[status(thm)],[f256,f128])).
% 0.19/0.44 fof(f264,plain,(
% 0.19/0.44 $false|spl0_15|~spl0_5),
% 0.19/0.44 inference(backward_subsumption_resolution,[status(thm)],[f127,f263])).
% 0.19/0.44 fof(f265,plain,(
% 0.19/0.44 spl0_15|~spl0_5),
% 0.19/0.44 inference(contradiction_clause,[status(thm)],[f264])).
% 0.19/0.44 fof(f298,plain,(
% 0.19/0.44 ![X0,X1]: (~precedes(X0,X1,sk0_11)|head_of(sk0_8(X1,X0))=tail_of(X0)|~spl0_7)),
% 0.19/0.44 inference(resolution,[status(thm)],[f127,f169])).
% 0.19/0.44 fof(f303,plain,(
% 0.19/0.44 ![X0,X1]: (~precedes(X0,X1,sk0_11)|~head_of(sk0_9)=tail_of(X0)|~head_of(sk0_10)=head_of(X1))),
% 0.19/0.44 inference(resolution,[status(thm)],[f198,f127])).
% 0.19/0.44 fof(f304,plain,(
% 0.19/0.44 spl0_19 <=> head_of(sk0_9)=tail_of(sk0_9)),
% 0.19/0.44 introduced(split_symbol_definition)).
% 0.19/0.44 fof(f306,plain,(
% 0.19/0.44 ~head_of(sk0_9)=tail_of(sk0_9)|spl0_19),
% 0.19/0.44 inference(component_clause,[status(thm)],[f304])).
% 0.19/0.44 fof(f307,plain,(
% 0.19/0.44 spl0_20 <=> head_of(sk0_10)=head_of(sk0_10)),
% 0.19/0.44 introduced(split_symbol_definition)).
% 0.19/0.44 fof(f309,plain,(
% 0.19/0.44 ~head_of(sk0_10)=head_of(sk0_10)|spl0_20),
% 0.19/0.44 inference(component_clause,[status(thm)],[f307])).
% 0.19/0.44 fof(f310,plain,(
% 0.19/0.44 ~head_of(sk0_9)=tail_of(sk0_9)|~head_of(sk0_10)=head_of(sk0_10)),
% 0.19/0.44 inference(resolution,[status(thm)],[f303,f128])).
% 0.19/0.44 fof(f311,plain,(
% 0.19/0.44 ~spl0_19|~spl0_20),
% 0.19/0.44 inference(split_clause,[status(thm)],[f310,f304,f307])).
% 0.19/0.44 fof(f312,plain,(
% 0.19/0.44 ![X0,X1,X2]: (triangle(X0,X1,X2)|~edge(X0)|~edge(X2)|~sequential(X0,X1)|~sequential(X1,X2)|~sequential(X2,X0))),
% 0.19/0.44 inference(forward_subsumption_resolution,[status(thm)],[f102,f64])).
% 0.19/0.44 fof(f370,plain,(
% 0.19/0.44 ![X0,X1,X2]: (~edge(X0)|~edge(X1)|X0=X1|~head_of(X0)=tail_of(X1)|triangle(X1,X2,X0)|~edge(X1)|~edge(X0)|~sequential(X1,X2)|~sequential(X2,X0))),
% 0.19/0.44 inference(resolution,[status(thm)],[f67,f312])).
% 0.19/0.44 fof(f371,plain,(
% 0.19/0.44 ![X0,X1,X2]: (~edge(X0)|~edge(X1)|X0=X1|~head_of(X0)=tail_of(X1)|triangle(X1,X2,X0)|~sequential(X1,X2)|~sequential(X2,X0))),
% 0.19/0.44 inference(duplicate_literals_removal,[status(esa)],[f370])).
% 0.19/0.44 fof(f372,plain,(
% 0.19/0.44 ![X0,X1,X2]: (~edge(X0)|X1=X0|~head_of(X1)=tail_of(X0)|triangle(X0,X2,X1)|~sequential(X0,X2)|~sequential(X2,X1))),
% 0.19/0.44 inference(forward_subsumption_resolution,[status(thm)],[f371,f64])).
% 0.19/0.44 fof(f427,plain,(
% 0.19/0.44 head_of(sk0_8(sk0_10,sk0_9))=tail_of(sk0_9)|~spl0_7),
% 0.19/0.44 inference(resolution,[status(thm)],[f298,f128])).
% 0.19/0.44 fof(f451,plain,(
% 0.19/0.44 ~tail_of(sk0_9)=head_of(sk0_10)|~spl0_7|spl0_18),
% 0.19/0.44 inference(backward_demodulation,[status(thm)],[f427,f249])).
% 0.19/0.45 fof(f582,plain,(
% 0.19/0.45 ![X0,X1,X2]: (X0=X1|~head_of(X0)=tail_of(X1)|triangle(X1,X2,X0)|~sequential(X1,X2)|~sequential(X2,X0))),
% 0.19/0.45 inference(forward_subsumption_resolution,[status(thm)],[f372,f63])).
% 0.19/0.45 fof(f584,plain,(
% 0.19/0.45 ![X0,X1,X2]: (X0=X1|~head_of(X0)=tail_of(X1)|triangle(X1,X2,X0)|~sequential(X1,X2)|~edge(X2)|~edge(X0)|X2=X0|~head_of(X2)=tail_of(X0))),
% 0.19/0.45 inference(resolution,[status(thm)],[f582,f67])).
% 0.19/0.45 fof(f585,plain,(
% 0.19/0.45 ![X0,X1,X2]: (X0=X1|~head_of(X0)=tail_of(X1)|triangle(X1,X2,X0)|~sequential(X1,X2)|~edge(X0)|X2=X0|~head_of(X2)=tail_of(X0))),
% 0.19/0.45 inference(forward_subsumption_resolution,[status(thm)],[f584,f64])).
% 0.19/0.45 fof(f621,plain,(
% 0.19/0.45 ![X0]: (X0=sk0_9|~head_of(X0)=tail_of(sk0_9)|triangle(sk0_9,sk0_10,X0)|~edge(X0)|sk0_10=X0|~head_of(sk0_10)=tail_of(X0))),
% 0.19/0.45 inference(resolution,[status(thm)],[f585,f129])).
% 0.19/0.45 fof(f622,plain,(
% 0.19/0.45 ![X0]: (X0=sk0_9|~head_of(X0)=tail_of(sk0_9)|~edge(X0)|sk0_10=X0|~head_of(sk0_10)=tail_of(X0))),
% 0.19/0.45 inference(forward_subsumption_resolution,[status(thm)],[f621,f130])).
% 0.19/0.45 fof(f701,plain,(
% 0.19/0.45 spl0_64 <=> sk0_8(sk0_10,sk0_9)=sk0_9),
% 0.19/0.45 introduced(split_symbol_definition)).
% 0.19/0.45 fof(f702,plain,(
% 0.19/0.45 sk0_8(sk0_10,sk0_9)=sk0_9|~spl0_64),
% 0.19/0.45 inference(component_clause,[status(thm)],[f701])).
% 0.19/0.45 fof(f704,plain,(
% 0.19/0.45 spl0_65 <=> head_of(sk0_8(sk0_10,sk0_9))=tail_of(sk0_9)),
% 0.19/0.45 introduced(split_symbol_definition)).
% 0.19/0.45 fof(f706,plain,(
% 0.19/0.45 ~head_of(sk0_8(sk0_10,sk0_9))=tail_of(sk0_9)|spl0_65),
% 0.19/0.45 inference(component_clause,[status(thm)],[f704])).
% 0.19/0.45 fof(f707,plain,(
% 0.19/0.45 spl0_66 <=> sk0_10=sk0_8(sk0_10,sk0_9)),
% 0.19/0.45 introduced(split_symbol_definition)).
% 0.19/0.45 fof(f708,plain,(
% 0.19/0.45 sk0_10=sk0_8(sk0_10,sk0_9)|~spl0_66),
% 0.19/0.45 inference(component_clause,[status(thm)],[f707])).
% 0.19/0.45 fof(f710,plain,(
% 0.19/0.45 spl0_67 <=> head_of(sk0_10)=tail_of(sk0_8(sk0_10,sk0_9))),
% 0.19/0.45 introduced(split_symbol_definition)).
% 0.19/0.45 fof(f712,plain,(
% 0.19/0.45 ~head_of(sk0_10)=tail_of(sk0_8(sk0_10,sk0_9))|spl0_67),
% 0.19/0.45 inference(component_clause,[status(thm)],[f710])).
% 0.19/0.45 fof(f713,plain,(
% 0.19/0.45 sk0_8(sk0_10,sk0_9)=sk0_9|~head_of(sk0_8(sk0_10,sk0_9))=tail_of(sk0_9)|sk0_10=sk0_8(sk0_10,sk0_9)|~head_of(sk0_10)=tail_of(sk0_8(sk0_10,sk0_9))|~spl0_15),
% 0.19/0.45 inference(resolution,[status(thm)],[f622,f234])).
% 0.19/0.45 fof(f714,plain,(
% 0.19/0.45 spl0_64|~spl0_65|spl0_66|~spl0_67|~spl0_15),
% 0.19/0.45 inference(split_clause,[status(thm)],[f713,f701,f704,f707,f710,f233])).
% 0.19/0.45 fof(f746,plain,(
% 0.19/0.45 $false|spl0_20),
% 0.19/0.45 inference(trivial_equality_resolution,[status(esa)],[f309])).
% 0.19/0.45 fof(f747,plain,(
% 0.19/0.45 spl0_20),
% 0.19/0.45 inference(contradiction_clause,[status(thm)],[f746])).
% 0.19/0.45 fof(f748,plain,(
% 0.19/0.45 ~head_of(sk0_10)=head_of(sk0_10)|~spl0_6|spl0_67),
% 0.19/0.45 inference(forward_demodulation,[status(thm)],[f229,f712])).
% 0.19/0.45 fof(f749,plain,(
% 0.19/0.45 $false|~spl0_6|spl0_67),
% 0.19/0.45 inference(trivial_equality_resolution,[status(esa)],[f748])).
% 0.19/0.45 fof(f750,plain,(
% 0.19/0.45 ~spl0_6|spl0_67),
% 0.19/0.45 inference(contradiction_clause,[status(thm)],[f749])).
% 0.19/0.45 fof(f751,plain,(
% 0.19/0.45 ~tail_of(sk0_9)=tail_of(sk0_9)|~spl0_7|spl0_65),
% 0.19/0.45 inference(forward_demodulation,[status(thm)],[f427,f706])).
% 0.19/0.45 fof(f752,plain,(
% 0.19/0.45 $false|~spl0_7|spl0_65),
% 0.19/0.45 inference(trivial_equality_resolution,[status(esa)],[f751])).
% 0.19/0.45 fof(f753,plain,(
% 0.19/0.45 ~spl0_7|spl0_65),
% 0.19/0.45 inference(contradiction_clause,[status(thm)],[f752])).
% 0.19/0.45 fof(f818,plain,(
% 0.19/0.45 head_of(sk0_9)=tail_of(sk0_9)|~spl0_64|~spl0_7),
% 0.19/0.45 inference(backward_demodulation,[status(thm)],[f702,f427])).
% 0.19/0.45 fof(f819,plain,(
% 0.19/0.45 $false|spl0_19|~spl0_64|~spl0_7),
% 0.19/0.45 inference(forward_subsumption_resolution,[status(thm)],[f818,f306])).
% 0.19/0.45 fof(f820,plain,(
% 0.19/0.45 spl0_19|~spl0_64|~spl0_7),
% 0.19/0.45 inference(contradiction_clause,[status(thm)],[f819])).
% 0.19/0.45 fof(f855,plain,(
% 0.19/0.45 head_of(sk0_10)=tail_of(sk0_9)|~spl0_66|~spl0_7),
% 0.19/0.45 inference(forward_demodulation,[status(thm)],[f708,f427])).
% 0.19/0.45 fof(f856,plain,(
% 0.19/0.45 $false|spl0_18|~spl0_66|~spl0_7),
% 0.19/0.45 inference(forward_subsumption_resolution,[status(thm)],[f855,f451])).
% 0.19/0.45 fof(f857,plain,(
% 0.19/0.45 spl0_18|~spl0_66|~spl0_7),
% 0.19/0.45 inference(contradiction_clause,[status(thm)],[f856])).
% 0.19/0.45 fof(f858,plain,(
% 0.19/0.45 $false),
% 0.19/0.45 inference(sat_refutation,[status(thm)],[f163,f167,f171,f227,f251,f265,f311,f714,f747,f750,f753,f820,f857])).
% 0.19/0.45 % SZS output end CNFRefutation for theBenchmark.p
% 0.19/0.46 % Elapsed time: 0.118452 seconds
% 0.19/0.46 % CPU time: 0.836159 seconds
% 0.19/0.46 % Total memory used: 64.657 MB
% 0.19/0.46 % Net memory used: 64.144 MB
%------------------------------------------------------------------------------