TSTP Solution File: SET789+4 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SET789+4 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n001.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 12:35:11 EDT 2023
% Result : Theorem 0.13s 0.37s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET789+4 : TPTP v8.1.2. Released v3.2.0.
% 0.06/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34 % Computer : n001.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue May 30 10:50:30 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.13/0.35 % Drodi V3.5.1
% 0.13/0.37 % Refutation found
% 0.13/0.37 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.37 % SZS output start CNFRefutation for theBenchmark
% 0.13/0.37 fof(f1,axiom,(
% 0.13/0.37 (! [R,E] :( order(R,E)<=> ( (! [X] :( member(X,E)=> apply(R,X,X) ))& (! [X,Y] :( ( member(X,E)& member(Y,E) )=> ( ( apply(R,X,Y)& apply(R,Y,X) )=> X = Y ) ))& (! [X,Y,Z] :( ( member(X,E)& member(Y,E)& member(Z,E) )=> ( ( apply(R,X,Y)& apply(R,Y,Z) )=> apply(R,X,Z) ) ) )) ) )),
% 0.13/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.37 fof(f5,axiom,(
% 0.13/0.37 (! [R,E,M] :( greatest(M,R,E)<=> ( member(M,E)& (! [X] :( member(X,E)=> apply(R,X,M) ) )) ) )),
% 0.13/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.37 fof(f11,conjecture,(
% 0.13/0.37 (! [R,E,M] :( ( order(R,E)& greatest(M,R,E) )=> (! [X] :( greatest(X,R,E)=> M = X ) )) )),
% 0.13/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.37 fof(f12,negated_conjecture,(
% 0.13/0.37 ~((! [R,E,M] :( ( order(R,E)& greatest(M,R,E) )=> (! [X] :( greatest(X,R,E)=> M = X ) )) ))),
% 0.13/0.37 inference(negated_conjecture,[status(cth)],[f11])).
% 0.13/0.37 fof(f13,plain,(
% 0.13/0.37 ![R,E]: (order(R,E)<=>(((![X]: (~member(X,E)|apply(R,X,X)))&(![X,Y]: ((~member(X,E)|~member(Y,E))|((~apply(R,X,Y)|~apply(R,Y,X))|X=Y))))&(![X,Y,Z]: (((~member(X,E)|~member(Y,E))|~member(Z,E))|((~apply(R,X,Y)|~apply(R,Y,Z))|apply(R,X,Z))))))),
% 0.13/0.37 inference(pre_NNF_transformation,[status(esa)],[f1])).
% 0.13/0.37 fof(f14,plain,(
% 0.13/0.37 ![R,E]: (pd0_0(E,R)<=>((![X]: (~member(X,E)|apply(R,X,X)))&(![X,Y]: ((~member(X,E)|~member(Y,E))|((~apply(R,X,Y)|~apply(R,Y,X))|X=Y)))))),
% 0.13/0.37 introduced(predicate_definition,[f13])).
% 0.13/0.37 fof(f15,plain,(
% 0.13/0.37 ![R,E]: (order(R,E)<=>(pd0_0(E,R)&(![X,Y,Z]: (((~member(X,E)|~member(Y,E))|~member(Z,E))|((~apply(R,X,Y)|~apply(R,Y,Z))|apply(R,X,Z))))))),
% 0.13/0.37 inference(formula_renaming,[status(thm)],[f13,f14])).
% 0.13/0.37 fof(f16,plain,(
% 0.13/0.37 ![R,E]: ((~order(R,E)|(pd0_0(E,R)&(![X,Y,Z]: (((~member(X,E)|~member(Y,E))|~member(Z,E))|((~apply(R,X,Y)|~apply(R,Y,Z))|apply(R,X,Z))))))&(order(R,E)|(~pd0_0(E,R)|(?[X,Y,Z]: (((member(X,E)&member(Y,E))&member(Z,E))&((apply(R,X,Y)&apply(R,Y,Z))&~apply(R,X,Z)))))))),
% 0.13/0.37 inference(NNF_transformation,[status(esa)],[f15])).
% 0.13/0.37 fof(f17,plain,(
% 0.13/0.37 (![R,E]: (~order(R,E)|(pd0_0(E,R)&(![X,Y,Z]: (((~member(X,E)|~member(Y,E))|~member(Z,E))|((~apply(R,X,Y)|~apply(R,Y,Z))|apply(R,X,Z)))))))&(![R,E]: (order(R,E)|(~pd0_0(E,R)|(?[X,Y,Z]: (((member(X,E)&member(Y,E))&member(Z,E))&((apply(R,X,Y)&apply(R,Y,Z))&~apply(R,X,Z)))))))),
% 0.13/0.37 inference(miniscoping,[status(esa)],[f16])).
% 0.13/0.37 fof(f18,plain,(
% 0.13/0.37 (![R,E]: (~order(R,E)|(pd0_0(E,R)&(![X,Y,Z]: (((~member(X,E)|~member(Y,E))|~member(Z,E))|((~apply(R,X,Y)|~apply(R,Y,Z))|apply(R,X,Z)))))))&(![R,E]: (order(R,E)|(~pd0_0(E,R)|(((member(sk0_0(E,R),E)&member(sk0_1(E,R),E))&member(sk0_2(E,R),E))&((apply(R,sk0_0(E,R),sk0_1(E,R))&apply(R,sk0_1(E,R),sk0_2(E,R)))&~apply(R,sk0_0(E,R),sk0_2(E,R)))))))),
% 0.13/0.37 inference(skolemization,[status(esa)],[f17])).
% 0.13/0.37 fof(f19,plain,(
% 0.13/0.37 ![X0,X1]: (~order(X0,X1)|pd0_0(X1,X0))),
% 0.13/0.37 inference(cnf_transformation,[status(esa)],[f18])).
% 0.13/0.37 fof(f51,plain,(
% 0.13/0.37 ![R,E,M]: (greatest(M,R,E)<=>(member(M,E)&(![X]: (~member(X,E)|apply(R,X,M)))))),
% 0.13/0.37 inference(pre_NNF_transformation,[status(esa)],[f5])).
% 0.13/0.37 fof(f52,plain,(
% 0.13/0.37 ![R,E,M]: ((~greatest(M,R,E)|(member(M,E)&(![X]: (~member(X,E)|apply(R,X,M)))))&(greatest(M,R,E)|(~member(M,E)|(?[X]: (member(X,E)&~apply(R,X,M))))))),
% 0.13/0.37 inference(NNF_transformation,[status(esa)],[f51])).
% 0.13/0.37 fof(f53,plain,(
% 0.13/0.37 (![R,E,M]: (~greatest(M,R,E)|(member(M,E)&(![X]: (~member(X,E)|apply(R,X,M))))))&(![R,E,M]: (greatest(M,R,E)|(~member(M,E)|(?[X]: (member(X,E)&~apply(R,X,M))))))),
% 0.13/0.37 inference(miniscoping,[status(esa)],[f52])).
% 0.13/0.37 fof(f54,plain,(
% 0.13/0.37 (![R,E,M]: (~greatest(M,R,E)|(member(M,E)&(![X]: (~member(X,E)|apply(R,X,M))))))&(![R,E,M]: (greatest(M,R,E)|(~member(M,E)|(member(sk0_7(M,E,R),E)&~apply(R,sk0_7(M,E,R),M)))))),
% 0.13/0.37 inference(skolemization,[status(esa)],[f53])).
% 0.13/0.37 fof(f55,plain,(
% 0.13/0.37 ![X0,X1,X2]: (~greatest(X0,X1,X2)|member(X0,X2))),
% 0.13/0.37 inference(cnf_transformation,[status(esa)],[f54])).
% 0.13/0.37 fof(f56,plain,(
% 0.13/0.37 ![X0,X1,X2,X3]: (~greatest(X0,X1,X2)|~member(X3,X2)|apply(X1,X3,X0))),
% 0.13/0.37 inference(cnf_transformation,[status(esa)],[f54])).
% 0.13/0.37 fof(f105,plain,(
% 0.13/0.37 (?[R,E,M]: ((order(R,E)&greatest(M,R,E))&(?[X]: (greatest(X,R,E)&~M=X))))),
% 0.13/0.37 inference(pre_NNF_transformation,[status(esa)],[f12])).
% 0.13/0.37 fof(f106,plain,(
% 0.13/0.37 ((order(sk0_13,sk0_14)&greatest(sk0_15,sk0_13,sk0_14))&(greatest(sk0_16,sk0_13,sk0_14)&~sk0_15=sk0_16))),
% 0.13/0.37 inference(skolemization,[status(esa)],[f105])).
% 0.13/0.37 fof(f107,plain,(
% 0.13/0.37 order(sk0_13,sk0_14)),
% 0.13/0.37 inference(cnf_transformation,[status(esa)],[f106])).
% 0.13/0.37 fof(f108,plain,(
% 0.13/0.37 greatest(sk0_15,sk0_13,sk0_14)),
% 0.13/0.37 inference(cnf_transformation,[status(esa)],[f106])).
% 0.13/0.37 fof(f109,plain,(
% 0.13/0.37 greatest(sk0_16,sk0_13,sk0_14)),
% 0.13/0.37 inference(cnf_transformation,[status(esa)],[f106])).
% 0.13/0.37 fof(f110,plain,(
% 0.13/0.37 ~sk0_15=sk0_16),
% 0.13/0.37 inference(cnf_transformation,[status(esa)],[f106])).
% 0.13/0.37 fof(f111,plain,(
% 0.13/0.37 ![R,E,X]: (pd0_1(X,E,R)<=>(~member(X,E)|apply(R,X,X)))),
% 0.13/0.37 introduced(predicate_definition,[f14])).
% 0.13/0.37 fof(f112,plain,(
% 0.13/0.37 ![R,E]: (pd0_0(E,R)<=>((![X]: pd0_1(X,E,R))&(![X,Y]: ((~member(X,E)|~member(Y,E))|((~apply(R,X,Y)|~apply(R,Y,X))|X=Y)))))),
% 0.13/0.37 inference(formula_renaming,[status(thm)],[f14,f111])).
% 0.13/0.37 fof(f113,plain,(
% 0.13/0.37 ![R,E]: ((~pd0_0(E,R)|((![X]: pd0_1(X,E,R))&(![X,Y]: ((~member(X,E)|~member(Y,E))|((~apply(R,X,Y)|~apply(R,Y,X))|X=Y)))))&(pd0_0(E,R)|((?[X]: ~pd0_1(X,E,R))|(?[X,Y]: ((member(X,E)&member(Y,E))&((apply(R,X,Y)&apply(R,Y,X))&~X=Y))))))),
% 0.13/0.37 inference(NNF_transformation,[status(esa)],[f112])).
% 0.13/0.37 fof(f114,plain,(
% 0.13/0.37 (![R,E]: (~pd0_0(E,R)|((![X]: pd0_1(X,E,R))&(![X,Y]: ((~member(X,E)|~member(Y,E))|((~apply(R,X,Y)|~apply(R,Y,X))|X=Y))))))&(![R,E]: (pd0_0(E,R)|((?[X]: ~pd0_1(X,E,R))|(?[X,Y]: ((member(X,E)&member(Y,E))&((apply(R,X,Y)&apply(R,Y,X))&~X=Y))))))),
% 0.13/0.37 inference(miniscoping,[status(esa)],[f113])).
% 0.13/0.37 fof(f115,plain,(
% 0.13/0.37 (![R,E]: (~pd0_0(E,R)|((![X]: pd0_1(X,E,R))&(![X,Y]: ((~member(X,E)|~member(Y,E))|((~apply(R,X,Y)|~apply(R,Y,X))|X=Y))))))&(![R,E]: (pd0_0(E,R)|(~pd0_1(sk0_17(E,R),E,R)|((member(sk0_18(E,R),E)&member(sk0_19(E,R),E))&((apply(R,sk0_18(E,R),sk0_19(E,R))&apply(R,sk0_19(E,R),sk0_18(E,R)))&~sk0_18(E,R)=sk0_19(E,R))))))),
% 0.13/0.37 inference(skolemization,[status(esa)],[f114])).
% 0.13/0.37 fof(f117,plain,(
% 0.13/0.37 ![X0,X1,X2,X3]: (~pd0_0(X0,X1)|~member(X2,X0)|~member(X3,X0)|~apply(X1,X2,X3)|~apply(X1,X3,X2)|X2=X3)),
% 0.13/0.37 inference(cnf_transformation,[status(esa)],[f115])).
% 0.13/0.37 fof(f128,plain,(
% 0.13/0.37 pd0_0(sk0_14,sk0_13)),
% 0.13/0.37 inference(resolution,[status(thm)],[f19,f107])).
% 0.13/0.37 fof(f129,plain,(
% 0.13/0.37 member(sk0_16,sk0_14)),
% 0.13/0.37 inference(resolution,[status(thm)],[f55,f109])).
% 0.13/0.37 fof(f130,plain,(
% 0.13/0.37 member(sk0_15,sk0_14)),
% 0.13/0.37 inference(resolution,[status(thm)],[f55,f108])).
% 0.13/0.37 fof(f131,plain,(
% 0.13/0.37 ![X0]: (~member(X0,sk0_14)|apply(sk0_13,X0,sk0_16))),
% 0.13/0.37 inference(resolution,[status(thm)],[f56,f109])).
% 0.13/0.37 fof(f132,plain,(
% 0.13/0.37 ![X0]: (~member(X0,sk0_14)|apply(sk0_13,X0,sk0_15))),
% 0.13/0.37 inference(resolution,[status(thm)],[f56,f108])).
% 0.13/0.37 fof(f138,plain,(
% 0.13/0.37 spl0_1 <=> member(sk0_15,sk0_14)),
% 0.13/0.37 introduced(split_symbol_definition)).
% 0.13/0.37 fof(f140,plain,(
% 0.13/0.37 ~member(sk0_15,sk0_14)|spl0_1),
% 0.13/0.37 inference(component_clause,[status(thm)],[f138])).
% 0.13/0.37 fof(f146,plain,(
% 0.13/0.37 spl0_3 <=> member(sk0_16,sk0_14)),
% 0.13/0.37 introduced(split_symbol_definition)).
% 0.13/0.37 fof(f148,plain,(
% 0.13/0.37 ~member(sk0_16,sk0_14)|spl0_3),
% 0.13/0.37 inference(component_clause,[status(thm)],[f146])).
% 0.13/0.37 fof(f151,plain,(
% 0.13/0.37 $false|spl0_3),
% 0.13/0.37 inference(forward_subsumption_resolution,[status(thm)],[f148,f129])).
% 0.13/0.37 fof(f152,plain,(
% 0.13/0.37 spl0_3),
% 0.13/0.37 inference(contradiction_clause,[status(thm)],[f151])).
% 0.13/0.37 fof(f153,plain,(
% 0.13/0.37 $false|spl0_1),
% 0.13/0.37 inference(forward_subsumption_resolution,[status(thm)],[f140,f130])).
% 0.13/0.37 fof(f154,plain,(
% 0.13/0.37 spl0_1),
% 0.13/0.37 inference(contradiction_clause,[status(thm)],[f153])).
% 0.13/0.37 fof(f167,plain,(
% 0.13/0.37 ![X0,X1]: (~pd0_0(X0,sk0_13)|~member(sk0_15,X0)|~member(X1,X0)|~apply(sk0_13,sk0_15,X1)|sk0_15=X1|~member(X1,sk0_14))),
% 0.13/0.37 inference(resolution,[status(thm)],[f117,f132])).
% 0.13/0.37 fof(f177,plain,(
% 0.13/0.37 spl0_8 <=> ~pd0_0(X0,sk0_13)|~member(sk0_15,X0)|~member(sk0_16,X0)),
% 0.13/0.37 introduced(split_symbol_definition)).
% 0.13/0.37 fof(f178,plain,(
% 0.13/0.37 ![X0]: (~pd0_0(X0,sk0_13)|~member(sk0_15,X0)|~member(sk0_16,X0)|~spl0_8)),
% 0.13/0.37 inference(component_clause,[status(thm)],[f177])).
% 0.13/0.37 fof(f180,plain,(
% 0.13/0.37 spl0_9 <=> sk0_15=sk0_16),
% 0.13/0.37 introduced(split_symbol_definition)).
% 0.13/0.37 fof(f181,plain,(
% 0.13/0.37 sk0_15=sk0_16|~spl0_9),
% 0.13/0.38 inference(component_clause,[status(thm)],[f180])).
% 0.13/0.38 fof(f183,plain,(
% 0.13/0.38 ![X0]: (~pd0_0(X0,sk0_13)|~member(sk0_15,X0)|~member(sk0_16,X0)|sk0_15=sk0_16|~member(sk0_16,sk0_14)|~member(sk0_15,sk0_14))),
% 0.13/0.38 inference(resolution,[status(thm)],[f167,f131])).
% 0.13/0.38 fof(f184,plain,(
% 0.13/0.38 spl0_8|spl0_9|~spl0_3|~spl0_1),
% 0.13/0.38 inference(split_clause,[status(thm)],[f183,f177,f180,f146,f138])).
% 0.13/0.38 fof(f188,plain,(
% 0.13/0.38 ~member(sk0_15,sk0_14)|~member(sk0_16,sk0_14)|~spl0_8),
% 0.13/0.38 inference(resolution,[status(thm)],[f178,f128])).
% 0.13/0.38 fof(f189,plain,(
% 0.13/0.38 ~spl0_1|~spl0_3|~spl0_8),
% 0.13/0.38 inference(split_clause,[status(thm)],[f188,f138,f146,f177])).
% 0.13/0.38 fof(f190,plain,(
% 0.13/0.38 $false|~spl0_9),
% 0.13/0.38 inference(forward_subsumption_resolution,[status(thm)],[f181,f110])).
% 0.13/0.38 fof(f191,plain,(
% 0.13/0.38 ~spl0_9),
% 0.13/0.38 inference(contradiction_clause,[status(thm)],[f190])).
% 0.13/0.38 fof(f192,plain,(
% 0.13/0.38 $false),
% 0.13/0.38 inference(sat_refutation,[status(thm)],[f152,f154,f184,f189,f191])).
% 0.13/0.38 % SZS output end CNFRefutation for theBenchmark.p
% 0.13/0.39 % Elapsed time: 0.046476 seconds
% 0.13/0.39 % CPU time: 0.217652 seconds
% 0.13/0.39 % Memory used: 19.302 MB
%------------------------------------------------------------------------------