TSTP Solution File: SET794+4 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SET794+4 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n004.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 20:40:22 EDT 2024
% Result : Theorem 0.14s 0.40s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET794+4 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.14 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.14/0.35 % Computer : n004.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Apr 29 21:45:48 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.36 % Drodi V3.6.0
% 0.14/0.40 % Refutation found
% 0.14/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.40 % SZS output start CNFRefutation for theBenchmark
% 0.14/0.40 fof(f2,axiom,(
% 0.14/0.40 (! [R,E] :( total_order(R,E)<=> ( order(R,E)& (! [X,Y] :( ( member(X,E)& member(Y,E) )=> ( apply(R,X,Y)| apply(R,Y,X) ) ) )) ) )),
% 0.14/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.40 fof(f4,axiom,(
% 0.14/0.40 (! [R,E,M] :( lower_bound(M,R,E)<=> (! [X] :( member(X,E)=> apply(R,M,X) ) )) )),
% 0.14/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.40 fof(f6,axiom,(
% 0.14/0.40 (! [R,E,M] :( least(M,R,E)<=> ( member(M,E)& (! [X] :( member(X,E)=> apply(R,M,X) ) )) ) )),
% 0.14/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.40 fof(f8,axiom,(
% 0.14/0.40 (! [R,E,M] :( min(M,R,E)<=> ( member(M,E)& (! [X] :( ( member(X,E)& apply(R,X,M) )=> M = X ) )) ) )),
% 0.14/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.40 fof(f11,conjecture,(
% 0.14/0.40 (! [R,E,M] :( ( total_order(R,E)& min(M,R,E) )=> least(M,R,E) ) )),
% 0.14/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.40 fof(f12,negated_conjecture,(
% 0.14/0.40 ~((! [R,E,M] :( ( total_order(R,E)& min(M,R,E) )=> least(M,R,E) ) ))),
% 0.14/0.40 inference(negated_conjecture,[status(cth)],[f11])).
% 0.14/0.40 fof(f27,plain,(
% 0.14/0.40 ![R,E]: (total_order(R,E)<=>(order(R,E)&(![X,Y]: ((~member(X,E)|~member(Y,E))|(apply(R,X,Y)|apply(R,Y,X))))))),
% 0.14/0.40 inference(pre_NNF_transformation,[status(esa)],[f2])).
% 0.14/0.40 fof(f28,plain,(
% 0.14/0.40 ![R,E]: ((~total_order(R,E)|(order(R,E)&(![X,Y]: ((~member(X,E)|~member(Y,E))|(apply(R,X,Y)|apply(R,Y,X))))))&(total_order(R,E)|(~order(R,E)|(?[X,Y]: ((member(X,E)&member(Y,E))&(~apply(R,X,Y)&~apply(R,Y,X)))))))),
% 0.14/0.40 inference(NNF_transformation,[status(esa)],[f27])).
% 0.14/0.40 fof(f29,plain,(
% 0.14/0.40 (![R,E]: (~total_order(R,E)|(order(R,E)&(![X,Y]: ((~member(X,E)|~member(Y,E))|(apply(R,X,Y)|apply(R,Y,X)))))))&(![R,E]: (total_order(R,E)|(~order(R,E)|(?[X,Y]: ((member(X,E)&member(Y,E))&(~apply(R,X,Y)&~apply(R,Y,X)))))))),
% 0.14/0.40 inference(miniscoping,[status(esa)],[f28])).
% 0.14/0.40 fof(f30,plain,(
% 0.14/0.40 (![R,E]: (~total_order(R,E)|(order(R,E)&(![X,Y]: ((~member(X,E)|~member(Y,E))|(apply(R,X,Y)|apply(R,Y,X)))))))&(![R,E]: (total_order(R,E)|(~order(R,E)|((member(sk0_3(E,R),E)&member(sk0_4(E,R),E))&(~apply(R,sk0_3(E,R),sk0_4(E,R))&~apply(R,sk0_4(E,R),sk0_3(E,R)))))))),
% 0.14/0.40 inference(skolemization,[status(esa)],[f29])).
% 0.14/0.40 fof(f32,plain,(
% 0.14/0.40 ![X0,X1,X2,X3]: (~total_order(X0,X1)|~member(X2,X1)|~member(X3,X1)|apply(X0,X2,X3)|apply(X0,X3,X2))),
% 0.14/0.40 inference(cnf_transformation,[status(esa)],[f30])).
% 0.14/0.40 fof(f44,plain,(
% 0.14/0.40 ![R,E,M]: (lower_bound(M,R,E)<=>(![X]: (~member(X,E)|apply(R,M,X))))),
% 0.14/0.40 inference(pre_NNF_transformation,[status(esa)],[f4])).
% 0.14/0.40 fof(f45,plain,(
% 0.14/0.40 ![R,E,M]: ((~lower_bound(M,R,E)|(![X]: (~member(X,E)|apply(R,M,X))))&(lower_bound(M,R,E)|(?[X]: (member(X,E)&~apply(R,M,X)))))),
% 0.14/0.40 inference(NNF_transformation,[status(esa)],[f44])).
% 0.14/0.40 fof(f46,plain,(
% 0.14/0.40 (![R,E,M]: (~lower_bound(M,R,E)|(![X]: (~member(X,E)|apply(R,M,X)))))&(![R,E,M]: (lower_bound(M,R,E)|(?[X]: (member(X,E)&~apply(R,M,X)))))),
% 0.14/0.40 inference(miniscoping,[status(esa)],[f45])).
% 0.14/0.40 fof(f47,plain,(
% 0.14/0.40 (![R,E,M]: (~lower_bound(M,R,E)|(![X]: (~member(X,E)|apply(R,M,X)))))&(![R,E,M]: (lower_bound(M,R,E)|(member(sk0_6(M,E,R),E)&~apply(R,M,sk0_6(M,E,R)))))),
% 0.14/0.40 inference(skolemization,[status(esa)],[f46])).
% 0.14/0.40 fof(f48,plain,(
% 0.14/0.40 ![X0,X1,X2,X3]: (~lower_bound(X0,X1,X2)|~member(X3,X2)|apply(X1,X0,X3))),
% 0.14/0.40 inference(cnf_transformation,[status(esa)],[f47])).
% 0.14/0.40 fof(f49,plain,(
% 0.14/0.40 ![X0,X1,X2]: (lower_bound(X0,X1,X2)|member(sk0_6(X0,X2,X1),X2))),
% 0.14/0.40 inference(cnf_transformation,[status(esa)],[f47])).
% 0.14/0.40 fof(f50,plain,(
% 0.14/0.40 ![X0,X1,X2]: (lower_bound(X0,X1,X2)|~apply(X1,X0,sk0_6(X0,X2,X1)))),
% 0.14/0.40 inference(cnf_transformation,[status(esa)],[f47])).
% 0.14/0.40 fof(f59,plain,(
% 0.14/0.40 ![R,E,M]: (least(M,R,E)<=>(member(M,E)&(![X]: (~member(X,E)|apply(R,M,X)))))),
% 0.14/0.40 inference(pre_NNF_transformation,[status(esa)],[f6])).
% 0.14/0.40 fof(f60,plain,(
% 0.14/0.40 ![R,E,M]: ((~least(M,R,E)|(member(M,E)&(![X]: (~member(X,E)|apply(R,M,X)))))&(least(M,R,E)|(~member(M,E)|(?[X]: (member(X,E)&~apply(R,M,X))))))),
% 0.14/0.40 inference(NNF_transformation,[status(esa)],[f59])).
% 0.14/0.40 fof(f61,plain,(
% 0.14/0.40 (![R,E,M]: (~least(M,R,E)|(member(M,E)&(![X]: (~member(X,E)|apply(R,M,X))))))&(![R,E,M]: (least(M,R,E)|(~member(M,E)|(?[X]: (member(X,E)&~apply(R,M,X))))))),
% 0.14/0.40 inference(miniscoping,[status(esa)],[f60])).
% 0.14/0.40 fof(f62,plain,(
% 0.14/0.40 (![R,E,M]: (~least(M,R,E)|(member(M,E)&(![X]: (~member(X,E)|apply(R,M,X))))))&(![R,E,M]: (least(M,R,E)|(~member(M,E)|(member(sk0_8(M,E,R),E)&~apply(R,M,sk0_8(M,E,R))))))),
% 0.14/0.40 inference(skolemization,[status(esa)],[f61])).
% 0.14/0.40 fof(f65,plain,(
% 0.14/0.40 ![X0,X1,X2]: (least(X0,X1,X2)|~member(X0,X2)|member(sk0_8(X0,X2,X1),X2))),
% 0.14/0.40 inference(cnf_transformation,[status(esa)],[f62])).
% 0.14/0.40 fof(f66,plain,(
% 0.14/0.40 ![X0,X1,X2]: (least(X0,X1,X2)|~member(X0,X2)|~apply(X1,X0,sk0_8(X0,X2,X1)))),
% 0.14/0.40 inference(cnf_transformation,[status(esa)],[f62])).
% 0.14/0.40 fof(f76,plain,(
% 0.14/0.40 ![R,E,M]: (min(M,R,E)<=>(member(M,E)&(![X]: ((~member(X,E)|~apply(R,X,M))|M=X))))),
% 0.14/0.40 inference(pre_NNF_transformation,[status(esa)],[f8])).
% 0.14/0.40 fof(f77,plain,(
% 0.14/0.40 ![R,E,M]: ((~min(M,R,E)|(member(M,E)&(![X]: ((~member(X,E)|~apply(R,X,M))|M=X))))&(min(M,R,E)|(~member(M,E)|(?[X]: ((member(X,E)&apply(R,X,M))&~M=X)))))),
% 0.14/0.40 inference(NNF_transformation,[status(esa)],[f76])).
% 0.14/0.40 fof(f78,plain,(
% 0.14/0.40 (![R,E,M]: (~min(M,R,E)|(member(M,E)&(![X]: ((~member(X,E)|~apply(R,X,M))|M=X)))))&(![R,E,M]: (min(M,R,E)|(~member(M,E)|(?[X]: ((member(X,E)&apply(R,X,M))&~M=X)))))),
% 0.14/0.40 inference(miniscoping,[status(esa)],[f77])).
% 0.14/0.40 fof(f79,plain,(
% 0.14/0.40 (![R,E,M]: (~min(M,R,E)|(member(M,E)&(![X]: ((~member(X,E)|~apply(R,X,M))|M=X)))))&(![R,E,M]: (min(M,R,E)|(~member(M,E)|((member(sk0_10(M,E,R),E)&apply(R,sk0_10(M,E,R),M))&~M=sk0_10(M,E,R)))))),
% 0.14/0.40 inference(skolemization,[status(esa)],[f78])).
% 0.14/0.40 fof(f80,plain,(
% 0.14/0.40 ![X0,X1,X2]: (~min(X0,X1,X2)|member(X0,X2))),
% 0.14/0.40 inference(cnf_transformation,[status(esa)],[f79])).
% 0.14/0.40 fof(f81,plain,(
% 0.14/0.40 ![X0,X1,X2,X3]: (~min(X0,X1,X2)|~member(X3,X2)|~apply(X1,X3,X0)|X0=X3)),
% 0.14/0.40 inference(cnf_transformation,[status(esa)],[f79])).
% 0.14/0.40 fof(f105,plain,(
% 0.14/0.40 (?[R,E,M]: ((total_order(R,E)&min(M,R,E))&~least(M,R,E)))),
% 0.14/0.40 inference(pre_NNF_transformation,[status(esa)],[f12])).
% 0.14/0.40 fof(f106,plain,(
% 0.14/0.40 ((total_order(sk0_13,sk0_14)&min(sk0_15,sk0_13,sk0_14))&~least(sk0_15,sk0_13,sk0_14))),
% 0.14/0.40 inference(skolemization,[status(esa)],[f105])).
% 0.14/0.40 fof(f107,plain,(
% 0.14/0.40 total_order(sk0_13,sk0_14)),
% 0.14/0.40 inference(cnf_transformation,[status(esa)],[f106])).
% 0.14/0.40 fof(f108,plain,(
% 0.14/0.40 min(sk0_15,sk0_13,sk0_14)),
% 0.14/0.40 inference(cnf_transformation,[status(esa)],[f106])).
% 0.14/0.40 fof(f109,plain,(
% 0.14/0.40 ~least(sk0_15,sk0_13,sk0_14)),
% 0.14/0.40 inference(cnf_transformation,[status(esa)],[f106])).
% 0.14/0.40 fof(f128,plain,(
% 0.14/0.40 member(sk0_15,sk0_14)),
% 0.14/0.40 inference(resolution,[status(thm)],[f80,f108])).
% 0.14/0.40 fof(f129,plain,(
% 0.14/0.40 ![X0,X1]: (~total_order(X0,sk0_14)|~member(X1,sk0_14)|apply(X0,X1,sk0_15)|apply(X0,sk0_15,X1))),
% 0.14/0.40 inference(resolution,[status(thm)],[f128,f32])).
% 0.14/0.40 fof(f130,plain,(
% 0.14/0.40 ![X0]: (~member(X0,sk0_14)|apply(sk0_13,X0,sk0_15)|apply(sk0_13,sk0_15,X0))),
% 0.14/0.40 inference(resolution,[status(thm)],[f129,f107])).
% 0.14/0.40 fof(f131,plain,(
% 0.14/0.40 spl0_0 <=> apply(sk0_13,sk0_15,sk0_15)),
% 0.14/0.40 introduced(split_symbol_definition)).
% 0.14/0.40 fof(f134,plain,(
% 0.14/0.40 apply(sk0_13,sk0_15,sk0_15)|apply(sk0_13,sk0_15,sk0_15)),
% 0.14/0.40 inference(resolution,[status(thm)],[f130,f128])).
% 0.14/0.40 fof(f135,plain,(
% 0.14/0.40 spl0_0),
% 0.14/0.40 inference(split_clause,[status(thm)],[f134,f131])).
% 0.14/0.40 fof(f138,plain,(
% 0.14/0.40 ![X0,X1]: (lower_bound(X0,X1,sk0_14)|apply(sk0_13,sk0_6(X0,sk0_14,X1),sk0_15)|apply(sk0_13,sk0_15,sk0_6(X0,sk0_14,X1)))),
% 0.14/0.40 inference(resolution,[status(thm)],[f49,f130])).
% 0.14/0.40 fof(f161,plain,(
% 0.14/0.40 spl0_4 <=> lower_bound(sk0_15,sk0_13,sk0_14)),
% 0.14/0.40 introduced(split_symbol_definition)).
% 0.14/0.40 fof(f162,plain,(
% 0.14/0.40 lower_bound(sk0_15,sk0_13,sk0_14)|~spl0_4),
% 0.14/0.40 inference(component_clause,[status(thm)],[f161])).
% 0.14/0.40 fof(f164,plain,(
% 0.14/0.40 spl0_5 <=> apply(sk0_13,sk0_6(sk0_15,sk0_14,sk0_13),sk0_15)),
% 0.14/0.40 introduced(split_symbol_definition)).
% 0.14/0.40 fof(f165,plain,(
% 0.14/0.40 apply(sk0_13,sk0_6(sk0_15,sk0_14,sk0_13),sk0_15)|~spl0_5),
% 0.14/0.40 inference(component_clause,[status(thm)],[f164])).
% 0.14/0.40 fof(f167,plain,(
% 0.14/0.40 lower_bound(sk0_15,sk0_13,sk0_14)|apply(sk0_13,sk0_6(sk0_15,sk0_14,sk0_13),sk0_15)|lower_bound(sk0_15,sk0_13,sk0_14)),
% 0.14/0.40 inference(resolution,[status(thm)],[f138,f50])).
% 0.14/0.40 fof(f168,plain,(
% 0.14/0.40 spl0_4|spl0_5),
% 0.14/0.40 inference(split_clause,[status(thm)],[f167,f161,f164])).
% 0.14/0.40 fof(f171,plain,(
% 0.14/0.41 ![X0]: (~member(X0,sk0_14)|apply(sk0_13,sk0_15,X0)|~spl0_4)),
% 0.14/0.41 inference(resolution,[status(thm)],[f162,f48])).
% 0.14/0.41 fof(f194,plain,(
% 0.14/0.41 spl0_8 <=> ~min(sk0_15,sk0_13,X0)|~member(sk0_6(sk0_15,sk0_14,sk0_13),X0)),
% 0.14/0.41 introduced(split_symbol_definition)).
% 0.14/0.41 fof(f195,plain,(
% 0.14/0.41 ![X0]: (~min(sk0_15,sk0_13,X0)|~member(sk0_6(sk0_15,sk0_14,sk0_13),X0)|~spl0_8)),
% 0.14/0.41 inference(component_clause,[status(thm)],[f194])).
% 0.14/0.41 fof(f197,plain,(
% 0.14/0.41 spl0_9 <=> sk0_15=sk0_6(sk0_15,sk0_14,sk0_13)),
% 0.14/0.41 introduced(split_symbol_definition)).
% 0.14/0.41 fof(f198,plain,(
% 0.14/0.41 sk0_15=sk0_6(sk0_15,sk0_14,sk0_13)|~spl0_9),
% 0.14/0.41 inference(component_clause,[status(thm)],[f197])).
% 0.14/0.41 fof(f200,plain,(
% 0.14/0.41 ![X0]: (~min(sk0_15,sk0_13,X0)|~member(sk0_6(sk0_15,sk0_14,sk0_13),X0)|sk0_15=sk0_6(sk0_15,sk0_14,sk0_13)|~spl0_5)),
% 0.14/0.41 inference(resolution,[status(thm)],[f165,f81])).
% 0.14/0.41 fof(f201,plain,(
% 0.14/0.41 spl0_8|spl0_9|~spl0_5),
% 0.14/0.41 inference(split_clause,[status(thm)],[f200,f194,f197,f164])).
% 0.14/0.41 fof(f203,plain,(
% 0.14/0.41 lower_bound(sk0_15,sk0_13,sk0_14)|~apply(sk0_13,sk0_15,sk0_15)|~spl0_9),
% 0.14/0.41 inference(paramodulation,[status(thm)],[f198,f50])).
% 0.14/0.41 fof(f204,plain,(
% 0.14/0.41 spl0_4|~spl0_0|~spl0_9),
% 0.14/0.41 inference(split_clause,[status(thm)],[f203,f161,f131,f197])).
% 0.14/0.41 fof(f205,plain,(
% 0.14/0.41 spl0_10 <=> member(sk0_15,sk0_14)),
% 0.14/0.41 introduced(split_symbol_definition)).
% 0.14/0.41 fof(f207,plain,(
% 0.14/0.41 ~member(sk0_15,sk0_14)|spl0_10),
% 0.14/0.41 inference(component_clause,[status(thm)],[f205])).
% 0.14/0.41 fof(f213,plain,(
% 0.14/0.41 ~member(sk0_6(sk0_15,sk0_14,sk0_13),sk0_14)|~spl0_8),
% 0.14/0.41 inference(resolution,[status(thm)],[f195,f108])).
% 0.14/0.41 fof(f214,plain,(
% 0.14/0.41 lower_bound(sk0_15,sk0_13,sk0_14)|~spl0_8),
% 0.14/0.41 inference(resolution,[status(thm)],[f213,f49])).
% 0.14/0.41 fof(f215,plain,(
% 0.14/0.41 spl0_4|~spl0_8),
% 0.14/0.41 inference(split_clause,[status(thm)],[f214,f161,f194])).
% 0.14/0.41 fof(f327,plain,(
% 0.14/0.41 ![X0]: (least(sk0_15,X0,sk0_14)|member(sk0_8(sk0_15,sk0_14,X0),sk0_14))),
% 0.14/0.41 inference(resolution,[status(thm)],[f65,f128])).
% 0.14/0.41 fof(f365,plain,(
% 0.14/0.41 $false|spl0_10),
% 0.14/0.41 inference(forward_subsumption_resolution,[status(thm)],[f207,f128])).
% 0.14/0.41 fof(f366,plain,(
% 0.14/0.41 spl0_10),
% 0.14/0.41 inference(contradiction_clause,[status(thm)],[f365])).
% 0.14/0.41 fof(f374,plain,(
% 0.14/0.41 ![X0]: (least(sk0_15,X0,sk0_14)|apply(sk0_13,sk0_15,sk0_8(sk0_15,sk0_14,X0))|~spl0_4)),
% 0.14/0.41 inference(resolution,[status(thm)],[f327,f171])).
% 0.14/0.41 fof(f543,plain,(
% 0.14/0.41 spl0_32 <=> least(sk0_15,sk0_13,sk0_14)),
% 0.14/0.41 introduced(split_symbol_definition)).
% 0.14/0.41 fof(f544,plain,(
% 0.14/0.41 least(sk0_15,sk0_13,sk0_14)|~spl0_32),
% 0.14/0.41 inference(component_clause,[status(thm)],[f543])).
% 0.14/0.41 fof(f546,plain,(
% 0.14/0.41 least(sk0_15,sk0_13,sk0_14)|~member(sk0_15,sk0_14)|least(sk0_15,sk0_13,sk0_14)|~spl0_4),
% 0.14/0.41 inference(resolution,[status(thm)],[f66,f374])).
% 0.14/0.41 fof(f547,plain,(
% 0.14/0.41 spl0_32|~spl0_10|~spl0_4),
% 0.14/0.41 inference(split_clause,[status(thm)],[f546,f543,f205,f161])).
% 0.14/0.41 fof(f548,plain,(
% 0.14/0.41 $false|~spl0_32),
% 0.14/0.41 inference(forward_subsumption_resolution,[status(thm)],[f544,f109])).
% 0.14/0.41 fof(f549,plain,(
% 0.14/0.41 ~spl0_32),
% 0.14/0.41 inference(contradiction_clause,[status(thm)],[f548])).
% 0.14/0.41 fof(f550,plain,(
% 0.14/0.41 $false),
% 0.14/0.41 inference(sat_refutation,[status(thm)],[f135,f168,f201,f204,f215,f366,f547,f549])).
% 0.14/0.41 % SZS output end CNFRefutation for theBenchmark.p
% 0.21/0.42 % Elapsed time: 0.060434 seconds
% 0.21/0.42 % CPU time: 0.355307 seconds
% 0.21/0.42 % Total memory used: 55.473 MB
% 0.21/0.42 % Net memory used: 55.378 MB
%------------------------------------------------------------------------------