%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GRA002+4 : 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 : n020.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 0.14s 0.42s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRA002+4 : TPTP v9.3.1. Bugfixed v3.2.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.40 % Computer : n020.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Sun Sep 20 18:18:02 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.41 % Drodi V4.1.1
% 0.14/0.42 % Refutation found
% 0.14/0.42 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.42 % SZS output start CNFRefutation for theBenchmark
% 0.14/0.42 fof(f11,axiom,(
% 0.14/0.42 (! [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)) ) )) ) )),
% 0.14/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.42 fof(f15,axiom,(
% 0.14/0.42 (! [V1,V2,P] :( path(V1,V2,P)=> number_of_in(sequential_pairs,P) = minus(length_of(P),n1) ) )),
% 0.14/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.42 fof(f17,axiom,(
% 0.14/0.42 (! [Things,InThese] : less_or_equal(number_of_in(Things,InThese),number_of_in(Things,graph)) )),
% 0.14/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.42 fof(f18,lemma,(
% 0.14/0.42 ( complete=> (! [P,V1,V2] :( shortest_path(V1,V2,P)=> number_of_in(sequential_pairs,P) = number_of_in(triangles,P) ) )) ),
% 0.14/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.42 fof(f19,conjecture,(
% 0.14/0.42 ( complete=> (! [P,V1,V2] :( shortest_path(V1,V2,P)=> less_or_equal(minus(length_of(P),n1),number_of_in(triangles,graph)) ) )) ),
% 0.14/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.42 fof(f20,negated_conjecture,(
% 0.14/0.42 ~(( complete=> (! [P,V1,V2] :( shortest_path(V1,V2,P)=> less_or_equal(minus(length_of(P),n1),number_of_in(triangles,graph)) ) )) )),
% 0.14/0.42 inference(negated_conjecture,[status(cth)],[f19])).
% 0.14/0.42 fof(f81,plain,(
% 0.14/0.42 ![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))))))),
% 0.14/0.42 inference(pre_NNF_transformation,[status(thm)],[f11])).
% 0.14/0.42 fof(f82,plain,(
% 0.14/0.42 ![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)))))))),
% 0.14/0.42 inference(NNF_transformation,[status(thm)],[f81])).
% 0.14/0.42 fof(f83,plain,(
% 0.14/0.42 (![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)))))))),
% 0.14/0.42 inference(miniscoping,[status(thm)],[f82])).
% 0.14/0.42 fof(f84,plain,(
% 0.14/0.42 (![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)))))))),
% 0.14/0.42 inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl]),skolemize(P,sK5_skl(SP,V2,V1))],[f83])).
% 0.14/0.42 fof(f85,plain,(
% 0.14/0.42 ![X0,X1,X2]: (~shortest_path(X0,X1,X2)|path(X0,X1,X2))),
% 0.14/0.42 inference(cnf_transformation,[status(thm)],[f84])).
% 0.14/0.42 fof(f106,plain,(
% 0.14/0.42 ![V1,V2,P]: (~path(V1,V2,P)|number_of_in(sequential_pairs,P)=minus(length_of(P),n1))),
% 0.14/0.42 inference(pre_NNF_transformation,[status(thm)],[f15])).
% 0.14/0.42 fof(f107,plain,(
% 0.14/0.42 ![P]: ((![V1,V2]: ~path(V1,V2,P))|number_of_in(sequential_pairs,P)=minus(length_of(P),n1))),
% 0.14/0.42 inference(miniscoping,[status(thm)],[f106])).
% 0.14/0.42 fof(f108,plain,(
% 0.14/0.42 ![X0,X1,X2]: (~path(X0,X1,X2)|number_of_in(sequential_pairs,X2)=minus(length_of(X2),n1))),
% 0.14/0.42 inference(cnf_transformation,[status(thm)],[f107])).
% 0.14/0.42 fof(f116,plain,(
% 0.14/0.42 ![X0,X1]: (less_or_equal(number_of_in(X0,X1),number_of_in(X0,graph)))),
% 0.14/0.42 inference(cnf_transformation,[status(thm)],[f17])).
% 0.14/0.42 fof(f117,plain,(
% 0.14/0.42 ~complete|(![P,V1,V2]: (~shortest_path(V1,V2,P)|number_of_in(sequential_pairs,P)=number_of_in(triangles,P)))),
% 0.14/0.42 inference(pre_NNF_transformation,[status(thm)],[f18])).
% 0.14/0.42 fof(f118,plain,(
% 0.14/0.42 ~complete|(![P]: ((![V1,V2]: ~shortest_path(V1,V2,P))|number_of_in(sequential_pairs,P)=number_of_in(triangles,P)))),
% 0.14/0.42 inference(miniscoping,[status(thm)],[f117])).
% 0.14/0.42 fof(f119,plain,(
% 0.14/0.42 ![X0,X1,X2]: (~complete|~shortest_path(X0,X1,X2)|number_of_in(sequential_pairs,X2)=number_of_in(triangles,X2))),
% 0.14/0.42 inference(cnf_transformation,[status(thm)],[f118])).
% 0.14/0.42 fof(f120,plain,(
% 0.14/0.42 (complete&(?[P,V1,V2]: (shortest_path(V1,V2,P)&~less_or_equal(minus(length_of(P),n1),number_of_in(triangles,graph)))))),
% 0.14/0.43 inference(pre_NNF_transformation,[status(thm)],[f20])).
% 0.14/0.43 fof(f121,plain,(
% 0.14/0.43 complete&(?[P]: ((?[V1,V2]: shortest_path(V1,V2,P))&~less_or_equal(minus(length_of(P),n1),number_of_in(triangles,graph))))),
% 0.14/0.43 inference(miniscoping,[status(thm)],[f120])).
% 0.14/0.43 fof(f122,plain,(
% 0.14/0.43 complete&(shortest_path(sK9_skl,sK10_skl,sK8_skl)&~less_or_equal(minus(length_of(sK8_skl),n1),number_of_in(triangles,graph)))),
% 0.14/0.43 inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl,sK9_skl,sK10_skl]),skolemize(P,sK8_skl),skolemize(V1,sK9_skl),skolemize(V2,sK10_skl)],[f121])).
% 0.14/0.43 fof(f123,plain,(
% 0.14/0.43 complete),
% 0.14/0.43 inference(cnf_transformation,[status(thm)],[f122])).
% 0.14/0.43 fof(f124,plain,(
% 0.14/0.43 shortest_path(sK9_skl,sK10_skl,sK8_skl)),
% 0.14/0.43 inference(cnf_transformation,[status(thm)],[f122])).
% 0.14/0.43 fof(f125,plain,(
% 0.14/0.43 ~less_or_equal(minus(length_of(sK8_skl),n1),number_of_in(triangles,graph))),
% 0.14/0.43 inference(cnf_transformation,[status(thm)],[f122])).
% 0.14/0.43 fof(f142,plain,(
% 0.14/0.43 path(sK9_skl,sK10_skl,sK8_skl)),
% 0.14/0.43 inference(resolution,[status(thm)],[f85,f124])).
% 0.14/0.43 fof(f158,plain,(
% 0.14/0.43 number_of_in(sequential_pairs,sK8_skl)=minus(length_of(sK8_skl),n1)),
% 0.14/0.43 inference(resolution,[status(thm)],[f108,f142])).
% 0.14/0.43 fof(f174,plain,(
% 0.14/0.43 ![X0,X1,X2]: (~shortest_path(X0,X1,X2)|number_of_in(sequential_pairs,X2)=number_of_in(triangles,X2))),
% 0.14/0.43 inference(forward_subsumption_resolution,[status(thm)],[f119,f123])).
% 0.14/0.43 fof(f175,plain,(
% 0.14/0.43 number_of_in(sequential_pairs,sK8_skl)=number_of_in(triangles,sK8_skl)),
% 0.14/0.43 inference(resolution,[status(thm)],[f174,f124])).
% 0.14/0.43 fof(f176,plain,(
% 0.14/0.43 less_or_equal(number_of_in(sequential_pairs,sK8_skl),number_of_in(triangles,graph))),
% 0.14/0.43 inference(paramodulation,[status(thm)],[f175,f116])).
% 0.14/0.43 fof(f177,plain,(
% 0.14/0.43 ~less_or_equal(number_of_in(sequential_pairs,sK8_skl),number_of_in(triangles,graph))),
% 0.14/0.43 inference(backward_demodulation,[status(thm)],[f158,f125])).
% 0.14/0.43 fof(f202,plain,(
% 0.14/0.43 $false),
% 0.14/0.43 inference(forward_subsumption_resolution,[status(thm)],[f176,f177])).
% 0.14/0.43 % SZS output end CNFRefutation for theBenchmark.p
% 0.14/0.45 % Elapsed time: 0.045559 seconds
% 0.14/0.45 % CPU time: 0.118447 seconds
% 0.14/0.45 % Total memory used: 20.838 MB
% 0.14/0.45 % Net memory used: 20.816 MB
%------------------------------------------------------------------------------