TSTP Solution File: SET776+4 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SET776+4 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n021.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 12:35:10 EDT 2023
% Result : Theorem 0.14s 0.37s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SET776+4 : TPTP v8.1.2. Released v2.2.0.
% 0.12/0.14 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.14/0.35 % Computer : n021.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 : Tue May 30 10:20:22 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.14/0.36 % Drodi V3.5.1
% 0.14/0.37 % Refutation found
% 0.14/0.37 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.37 % SZS output start CNFRefutation for theBenchmark
% 0.14/0.37 fof(f16,axiom,(
% 0.14/0.37 (! [R,E] :( pre_order(R,E)<=> ( (! [X] :( member(X,E)=> apply(R,X,X) ))& (! [X,Y,Z] :( ( member(X,E)& member(Y,E)& member(Z,E) )=> ( ( apply(R,X,Y)& apply(R,Y,Z) )=> apply(R,X,Z) ) ) )) ) )),
% 0.14/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.37 fof(f17,conjecture,(
% 0.14/0.37 (! [E,P,R] :( ( pre_order(P,E)& (! [A,B] :( ( member(A,E)& member(B,E) )=> ( apply(R,A,B)<=> ( apply(P,A,B)& apply(P,B,A) ) ) ) ))=> (! [X1,X2,Y1,Y2] :( ( member(X1,E)& member(X2,E)& member(Y1,E)& member(Y2,E) )=> ( ( apply(R,X1,Y1)& apply(R,X2,Y2)& apply(P,X1,X2) )=> apply(P,Y1,Y2) ) ) )) )),
% 0.14/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.37 fof(f18,negated_conjecture,(
% 0.14/0.37 ~((! [E,P,R] :( ( pre_order(P,E)& (! [A,B] :( ( member(A,E)& member(B,E) )=> ( apply(R,A,B)<=> ( apply(P,A,B)& apply(P,B,A) ) ) ) ))=> (! [X1,X2,Y1,Y2] :( ( member(X1,E)& member(X2,E)& member(Y1,E)& member(Y2,E) )=> ( ( apply(R,X1,Y1)& apply(R,X2,Y2)& apply(P,X1,X2) )=> apply(P,Y1,Y2) ) ) )) ))),
% 0.14/0.37 inference(negated_conjecture,[status(cth)],[f17])).
% 0.14/0.37 fof(f112,plain,(
% 0.14/0.37 ![R,E]: (pre_order(R,E)<=>((![X]: (~member(X,E)|apply(R,X,X)))&(![X,Y,Z]: (((~member(X,E)|~member(Y,E))|~member(Z,E))|((~apply(R,X,Y)|~apply(R,Y,Z))|apply(R,X,Z))))))),
% 0.14/0.37 inference(pre_NNF_transformation,[status(esa)],[f16])).
% 0.14/0.37 fof(f113,plain,(
% 0.14/0.37 ![R,E,X]: (pd0_2(X,E,R)<=>(~member(X,E)|apply(R,X,X)))),
% 0.14/0.37 introduced(predicate_definition,[f112])).
% 0.14/0.37 fof(f114,plain,(
% 0.14/0.37 ![R,E]: (pre_order(R,E)<=>((![X]: pd0_2(X,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))))))),
% 0.14/0.37 inference(formula_renaming,[status(thm)],[f112,f113])).
% 0.14/0.37 fof(f115,plain,(
% 0.14/0.37 ![R,E]: ((~pre_order(R,E)|((![X]: pd0_2(X,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))))))&(pre_order(R,E)|((?[X]: ~pd0_2(X,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)))))))),
% 0.14/0.37 inference(NNF_transformation,[status(esa)],[f114])).
% 0.14/0.37 fof(f116,plain,(
% 0.14/0.37 (![R,E]: (~pre_order(R,E)|((![X]: pd0_2(X,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]: (pre_order(R,E)|((?[X]: ~pd0_2(X,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)))))))),
% 0.14/0.37 inference(miniscoping,[status(esa)],[f115])).
% 0.14/0.37 fof(f117,plain,(
% 0.14/0.37 (![R,E]: (~pre_order(R,E)|((![X]: pd0_2(X,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]: (pre_order(R,E)|(~pd0_2(sk0_10(E,R),E,R)|(((member(sk0_11(E,R),E)&member(sk0_12(E,R),E))&member(sk0_13(E,R),E))&((apply(R,sk0_11(E,R),sk0_12(E,R))&apply(R,sk0_12(E,R),sk0_13(E,R)))&~apply(R,sk0_11(E,R),sk0_13(E,R)))))))),
% 0.14/0.37 inference(skolemization,[status(esa)],[f116])).
% 0.14/0.37 fof(f119,plain,(
% 0.14/0.37 ![X0,X1,X2,X3,X4]: (~pre_order(X0,X1)|~member(X2,X1)|~member(X3,X1)|~member(X4,X1)|~apply(X0,X2,X3)|~apply(X0,X3,X4)|apply(X0,X2,X4))),
% 0.14/0.37 inference(cnf_transformation,[status(esa)],[f117])).
% 0.14/0.37 fof(f126,plain,(
% 0.14/0.37 (?[E,P,R]: ((pre_order(P,E)&(![A,B]: ((~member(A,E)|~member(B,E))|(apply(R,A,B)<=>(apply(P,A,B)&apply(P,B,A))))))&(?[X1,X2,Y1,Y2]: ((((member(X1,E)&member(X2,E))&member(Y1,E))&member(Y2,E))&(((apply(R,X1,Y1)&apply(R,X2,Y2))&apply(P,X1,X2))&~apply(P,Y1,Y2))))))),
% 0.14/0.37 inference(pre_NNF_transformation,[status(esa)],[f18])).
% 0.14/0.37 fof(f127,plain,(
% 0.14/0.37 ?[E,P,R]: ((pre_order(P,E)&(![A,B]: ((~member(A,E)|~member(B,E))|((~apply(R,A,B)|(apply(P,A,B)&apply(P,B,A)))&(apply(R,A,B)|(~apply(P,A,B)|~apply(P,B,A)))))))&(?[X1,X2,Y1,Y2]: ((((member(X1,E)&member(X2,E))&member(Y1,E))&member(Y2,E))&(((apply(R,X1,Y1)&apply(R,X2,Y2))&apply(P,X1,X2))&~apply(P,Y1,Y2)))))),
% 0.14/0.37 inference(NNF_transformation,[status(esa)],[f126])).
% 0.14/0.37 fof(f128,plain,(
% 0.14/0.37 ((pre_order(sk0_15,sk0_14)&(![A,B]: ((~member(A,sk0_14)|~member(B,sk0_14))|((~apply(sk0_16,A,B)|(apply(sk0_15,A,B)&apply(sk0_15,B,A)))&(apply(sk0_16,A,B)|(~apply(sk0_15,A,B)|~apply(sk0_15,B,A)))))))&((((member(sk0_17,sk0_14)&member(sk0_18,sk0_14))&member(sk0_19,sk0_14))&member(sk0_20,sk0_14))&(((apply(sk0_16,sk0_17,sk0_19)&apply(sk0_16,sk0_18,sk0_20))&apply(sk0_15,sk0_17,sk0_18))&~apply(sk0_15,sk0_19,sk0_20))))),
% 0.14/0.37 inference(skolemization,[status(esa)],[f127])).
% 0.14/0.37 fof(f129,plain,(
% 0.14/0.37 pre_order(sk0_15,sk0_14)),
% 0.14/0.37 inference(cnf_transformation,[status(esa)],[f128])).
% 0.14/0.37 fof(f130,plain,(
% 0.14/0.37 ![X0,X1]: (~member(X0,sk0_14)|~member(X1,sk0_14)|~apply(sk0_16,X0,X1)|apply(sk0_15,X0,X1))),
% 0.14/0.37 inference(cnf_transformation,[status(esa)],[f128])).
% 0.14/0.37 fof(f131,plain,(
% 0.14/0.37 ![X0,X1]: (~member(X0,sk0_14)|~member(X1,sk0_14)|~apply(sk0_16,X0,X1)|apply(sk0_15,X1,X0))),
% 0.14/0.37 inference(cnf_transformation,[status(esa)],[f128])).
% 0.14/0.37 fof(f133,plain,(
% 0.14/0.37 member(sk0_17,sk0_14)),
% 0.14/0.37 inference(cnf_transformation,[status(esa)],[f128])).
% 0.14/0.37 fof(f134,plain,(
% 0.14/0.37 member(sk0_18,sk0_14)),
% 0.14/0.37 inference(cnf_transformation,[status(esa)],[f128])).
% 0.14/0.37 fof(f135,plain,(
% 0.14/0.37 member(sk0_19,sk0_14)),
% 0.14/0.37 inference(cnf_transformation,[status(esa)],[f128])).
% 0.14/0.37 fof(f136,plain,(
% 0.14/0.37 member(sk0_20,sk0_14)),
% 0.14/0.37 inference(cnf_transformation,[status(esa)],[f128])).
% 0.14/0.37 fof(f137,plain,(
% 0.14/0.37 apply(sk0_16,sk0_17,sk0_19)),
% 0.14/0.37 inference(cnf_transformation,[status(esa)],[f128])).
% 0.14/0.37 fof(f138,plain,(
% 0.14/0.37 apply(sk0_16,sk0_18,sk0_20)),
% 0.14/0.37 inference(cnf_transformation,[status(esa)],[f128])).
% 0.14/0.37 fof(f139,plain,(
% 0.14/0.37 apply(sk0_15,sk0_17,sk0_18)),
% 0.14/0.37 inference(cnf_transformation,[status(esa)],[f128])).
% 0.14/0.37 fof(f140,plain,(
% 0.14/0.37 ~apply(sk0_15,sk0_19,sk0_20)),
% 0.14/0.37 inference(cnf_transformation,[status(esa)],[f128])).
% 0.14/0.37 fof(f175,plain,(
% 0.14/0.37 spl0_0 <=> member(sk0_17,sk0_14)),
% 0.14/0.37 introduced(split_symbol_definition)).
% 0.14/0.37 fof(f177,plain,(
% 0.14/0.37 ~member(sk0_17,sk0_14)|spl0_0),
% 0.14/0.37 inference(component_clause,[status(thm)],[f175])).
% 0.14/0.37 fof(f178,plain,(
% 0.14/0.37 spl0_1 <=> member(sk0_19,sk0_14)),
% 0.14/0.37 introduced(split_symbol_definition)).
% 0.14/0.37 fof(f180,plain,(
% 0.14/0.37 ~member(sk0_19,sk0_14)|spl0_1),
% 0.14/0.37 inference(component_clause,[status(thm)],[f178])).
% 0.14/0.37 fof(f186,plain,(
% 0.14/0.37 $false|spl0_1),
% 0.14/0.37 inference(forward_subsumption_resolution,[status(thm)],[f180,f135])).
% 0.14/0.37 fof(f187,plain,(
% 0.14/0.37 spl0_1),
% 0.14/0.37 inference(contradiction_clause,[status(thm)],[f186])).
% 0.14/0.37 fof(f188,plain,(
% 0.14/0.37 $false|spl0_0),
% 0.14/0.37 inference(forward_subsumption_resolution,[status(thm)],[f177,f133])).
% 0.14/0.37 fof(f189,plain,(
% 0.14/0.37 spl0_0),
% 0.14/0.37 inference(contradiction_clause,[status(thm)],[f188])).
% 0.14/0.37 fof(f190,plain,(
% 0.14/0.37 spl0_3 <=> member(sk0_18,sk0_14)),
% 0.14/0.37 introduced(split_symbol_definition)).
% 0.14/0.37 fof(f192,plain,(
% 0.14/0.37 ~member(sk0_18,sk0_14)|spl0_3),
% 0.14/0.37 inference(component_clause,[status(thm)],[f190])).
% 0.14/0.37 fof(f193,plain,(
% 0.14/0.37 spl0_4 <=> member(sk0_20,sk0_14)),
% 0.14/0.37 introduced(split_symbol_definition)).
% 0.14/0.37 fof(f195,plain,(
% 0.14/0.37 ~member(sk0_20,sk0_14)|spl0_4),
% 0.14/0.37 inference(component_clause,[status(thm)],[f193])).
% 0.14/0.37 fof(f196,plain,(
% 0.14/0.37 spl0_5 <=> apply(sk0_15,sk0_18,sk0_20)),
% 0.14/0.37 introduced(split_symbol_definition)).
% 0.14/0.37 fof(f197,plain,(
% 0.14/0.37 apply(sk0_15,sk0_18,sk0_20)|~spl0_5),
% 0.14/0.37 inference(component_clause,[status(thm)],[f196])).
% 0.14/0.37 fof(f199,plain,(
% 0.14/0.37 ~member(sk0_18,sk0_14)|~member(sk0_20,sk0_14)|apply(sk0_15,sk0_18,sk0_20)),
% 0.14/0.37 inference(resolution,[status(thm)],[f138,f130])).
% 0.14/0.37 fof(f200,plain,(
% 0.14/0.37 ~spl0_3|~spl0_4|spl0_5),
% 0.14/0.37 inference(split_clause,[status(thm)],[f199,f190,f193,f196])).
% 0.14/0.37 fof(f201,plain,(
% 0.14/0.37 $false|spl0_4),
% 0.14/0.37 inference(forward_subsumption_resolution,[status(thm)],[f195,f136])).
% 0.14/0.37 fof(f202,plain,(
% 0.14/0.37 spl0_4),
% 0.14/0.37 inference(contradiction_clause,[status(thm)],[f201])).
% 0.14/0.37 fof(f203,plain,(
% 0.14/0.37 $false|spl0_3),
% 0.14/0.37 inference(forward_subsumption_resolution,[status(thm)],[f192,f134])).
% 0.14/0.37 fof(f204,plain,(
% 0.14/0.37 spl0_3),
% 0.14/0.37 inference(contradiction_clause,[status(thm)],[f203])).
% 0.14/0.37 fof(f210,plain,(
% 0.14/0.37 spl0_7 <=> apply(sk0_15,sk0_19,sk0_17)),
% 0.14/0.37 introduced(split_symbol_definition)).
% 0.14/0.37 fof(f211,plain,(
% 0.14/0.37 apply(sk0_15,sk0_19,sk0_17)|~spl0_7),
% 0.14/0.37 inference(component_clause,[status(thm)],[f210])).
% 0.14/0.37 fof(f213,plain,(
% 0.14/0.37 ~member(sk0_17,sk0_14)|~member(sk0_19,sk0_14)|apply(sk0_15,sk0_19,sk0_17)),
% 0.14/0.37 inference(resolution,[status(thm)],[f131,f137])).
% 0.14/0.37 fof(f214,plain,(
% 0.14/0.37 ~spl0_0|~spl0_1|spl0_7),
% 0.14/0.37 inference(split_clause,[status(thm)],[f213,f175,f178,f210])).
% 0.14/0.37 fof(f223,plain,(
% 0.14/0.37 ![X0,X1,X2]: (~member(X0,sk0_14)|~member(X1,sk0_14)|~member(X2,sk0_14)|~apply(sk0_15,X0,X1)|~apply(sk0_15,X1,X2)|apply(sk0_15,X0,X2))),
% 0.14/0.38 inference(resolution,[status(thm)],[f119,f129])).
% 0.14/0.38 fof(f224,plain,(
% 0.14/0.38 spl0_10 <=> ~member(X0,sk0_14)|~apply(sk0_15,X0,sk0_17)|apply(sk0_15,X0,sk0_18)),
% 0.14/0.38 introduced(split_symbol_definition)).
% 0.14/0.38 fof(f225,plain,(
% 0.14/0.38 ![X0]: (~member(X0,sk0_14)|~apply(sk0_15,X0,sk0_17)|apply(sk0_15,X0,sk0_18)|~spl0_10)),
% 0.14/0.38 inference(component_clause,[status(thm)],[f224])).
% 0.14/0.38 fof(f227,plain,(
% 0.14/0.38 ![X0]: (~member(X0,sk0_14)|~member(sk0_17,sk0_14)|~member(sk0_18,sk0_14)|~apply(sk0_15,X0,sk0_17)|apply(sk0_15,X0,sk0_18))),
% 0.14/0.38 inference(resolution,[status(thm)],[f223,f139])).
% 0.14/0.38 fof(f228,plain,(
% 0.14/0.38 spl0_10|~spl0_0|~spl0_3),
% 0.14/0.38 inference(split_clause,[status(thm)],[f227,f224,f175,f190])).
% 0.14/0.38 fof(f248,plain,(
% 0.14/0.38 spl0_13 <=> ~member(X0,sk0_14)|~apply(sk0_15,X0,sk0_18)|apply(sk0_15,X0,sk0_20)),
% 0.14/0.38 introduced(split_symbol_definition)).
% 0.14/0.38 fof(f249,plain,(
% 0.14/0.38 ![X0]: (~member(X0,sk0_14)|~apply(sk0_15,X0,sk0_18)|apply(sk0_15,X0,sk0_20)|~spl0_13)),
% 0.14/0.38 inference(component_clause,[status(thm)],[f248])).
% 0.14/0.38 fof(f251,plain,(
% 0.14/0.38 ![X0]: (~member(X0,sk0_14)|~member(sk0_18,sk0_14)|~member(sk0_20,sk0_14)|~apply(sk0_15,X0,sk0_18)|apply(sk0_15,X0,sk0_20)|~spl0_5)),
% 0.14/0.38 inference(resolution,[status(thm)],[f197,f223])).
% 0.14/0.38 fof(f252,plain,(
% 0.14/0.38 spl0_13|~spl0_3|~spl0_4|~spl0_5),
% 0.14/0.38 inference(split_clause,[status(thm)],[f251,f248,f190,f193,f196])).
% 0.14/0.38 fof(f278,plain,(
% 0.14/0.38 spl0_19 <=> apply(sk0_15,sk0_19,sk0_18)),
% 0.14/0.38 introduced(split_symbol_definition)).
% 0.14/0.38 fof(f279,plain,(
% 0.14/0.38 apply(sk0_15,sk0_19,sk0_18)|~spl0_19),
% 0.14/0.38 inference(component_clause,[status(thm)],[f278])).
% 0.14/0.38 fof(f281,plain,(
% 0.14/0.38 ~member(sk0_19,sk0_14)|apply(sk0_15,sk0_19,sk0_18)|~spl0_10|~spl0_7),
% 0.14/0.38 inference(resolution,[status(thm)],[f225,f211])).
% 0.14/0.38 fof(f282,plain,(
% 0.14/0.38 ~spl0_1|spl0_19|~spl0_10|~spl0_7),
% 0.14/0.38 inference(split_clause,[status(thm)],[f281,f178,f278,f224,f210])).
% 0.14/0.38 fof(f330,plain,(
% 0.14/0.38 spl0_27 <=> apply(sk0_15,sk0_19,sk0_20)),
% 0.14/0.38 introduced(split_symbol_definition)).
% 0.14/0.38 fof(f331,plain,(
% 0.14/0.38 apply(sk0_15,sk0_19,sk0_20)|~spl0_27),
% 0.14/0.38 inference(component_clause,[status(thm)],[f330])).
% 0.14/0.38 fof(f333,plain,(
% 0.14/0.38 ~member(sk0_19,sk0_14)|apply(sk0_15,sk0_19,sk0_20)|~spl0_13|~spl0_19),
% 0.14/0.38 inference(resolution,[status(thm)],[f249,f279])).
% 0.14/0.38 fof(f334,plain,(
% 0.14/0.38 ~spl0_1|spl0_27|~spl0_13|~spl0_19),
% 0.14/0.38 inference(split_clause,[status(thm)],[f333,f178,f330,f248,f278])).
% 0.14/0.38 fof(f340,plain,(
% 0.14/0.38 $false|~spl0_27),
% 0.14/0.38 inference(forward_subsumption_resolution,[status(thm)],[f331,f140])).
% 0.14/0.38 fof(f341,plain,(
% 0.14/0.38 ~spl0_27),
% 0.14/0.38 inference(contradiction_clause,[status(thm)],[f340])).
% 0.14/0.38 fof(f342,plain,(
% 0.14/0.38 $false),
% 0.14/0.38 inference(sat_refutation,[status(thm)],[f187,f189,f200,f202,f204,f214,f228,f252,f282,f334,f341])).
% 0.14/0.38 % SZS output end CNFRefutation for theBenchmark.p
% 0.14/0.38 % Elapsed time: 0.026405 seconds
% 0.14/0.38 % CPU time: 0.043188 seconds
% 0.14/0.38 % Memory used: 12.222 MB
%------------------------------------------------------------------------------