%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SET794+4 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/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 02:12:37 PM UTC 2026
% Result : Theorem 0.13s 0.61s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET794+4 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n020.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 05:39:17 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.36 % Drodi V4.1.1
% 0.13/0.61 % Refutation found
% 0.13/0.61 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.61 % SZS output start CNFRefutation for theBenchmark
% 0.13/0.61 fof(f1,axiom,(
% 0.13/0.61 (! [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) ) ) )) ) )),
% 0.13/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.61 fof(f2,axiom,(
% 0.13/0.61 (! [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) ) ) )) ) )),
% 0.13/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.61 fof(f4,axiom,(
% 0.13/0.61 (! [R,E,M] :( lower_bound(M,R,E)<=> (! [X] :( member(X,E)=> apply(R,M,X) ) )) )),
% 0.13/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.61 fof(f6,axiom,(
% 0.13/0.61 (! [R,E,M] :( least(M,R,E)<=> ( member(M,E)& (! [X] :( member(X,E)=> apply(R,M,X) ) )) ) )),
% 0.13/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.61 fof(f8,axiom,(
% 0.13/0.61 (! [R,E,M] :( min(M,R,E)<=> ( member(M,E)& (! [X] :( ( member(X,E)& apply(R,X,M) )=> M = X ) )) ) )),
% 0.13/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.61 fof(f11,conjecture,(
% 0.13/0.61 (! [R,E,M] :( ( total_order(R,E)& min(M,R,E) )=> least(M,R,E) ) )),
% 0.13/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.61 fof(f12,negated_conjecture,(
% 0.13/0.61 ~((! [R,E,M] :( ( total_order(R,E)& min(M,R,E) )=> least(M,R,E) ) ))),
% 0.13/0.61 inference(negated_conjecture,[status(cth)],[f11])).
% 0.13/0.61 fof(f13,plain,(
% 0.13/0.61 ![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))))))),
% 0.13/0.61 inference(pre_NNF_transformation,[status(thm)],[f1])).
% 0.13/0.61 fof(f14,definition,(
% 0.13/0.61 ![R,E]: (sP0_prd(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)))))),
% 0.13/0.61 introduced(definition,[new_symbols(definition,[sP0_prd])],[])).
% 0.13/0.61 fof(f15,plain,(
% 0.13/0.61 ![R,E]: (order(R,E)<=>(sP0_prd(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))))))),
% 0.13/0.61 inference(formula_renaming,[status(thm)],[f13,f14])).
% 0.13/0.61 fof(f16,plain,(
% 0.13/0.61 ![R,E]: ((~order(R,E)|(sP0_prd(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)|(~sP0_prd(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)))))))),
% 0.13/0.61 inference(NNF_transformation,[status(thm)],[f15])).
% 0.13/0.61 fof(f17,plain,(
% 0.13/0.61 (![R,E]: (~order(R,E)|(sP0_prd(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)|(~sP0_prd(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)))))))),
% 0.13/0.61 inference(miniscoping,[status(thm)],[f16])).
% 0.13/0.61 fof(f18,plain,(
% 0.13/0.61 (![R,E]: (~order(R,E)|(sP0_prd(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)|(~sP0_prd(E,R)|(((member(sK0_skl(E,R),E)&member(sK1_skl(E,R),E))&member(sK2_skl(E,R),E))&((apply(R,sK0_skl(E,R),sK1_skl(E,R))&apply(R,sK1_skl(E,R),sK2_skl(E,R)))&~apply(R,sK0_skl(E,R),sK2_skl(E,R)))))))),
% 0.13/0.61 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl]),skolemize(X,sK0_skl(E,R)),skolemize(Y,sK1_skl(E,R)),skolemize(Z,sK2_skl(E,R))],[f17])).
% 0.13/0.61 fof(f20,plain,(
% 0.13/0.61 ![X0,X1,X2,X3,X4]: (~order(X0,X1)|~member(X2,X1)|~member(X3,X1)|~member(X4,X1)|~apply(X0,X2,X3)|~apply(X0,X3,X4)|apply(X0,X2,X4))),
% 0.13/0.61 inference(cnf_transformation,[status(thm)],[f18])).
% 0.13/0.61 fof(f27,plain,(
% 0.13/0.61 ![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))))))),
% 0.13/0.61 inference(pre_NNF_transformation,[status(thm)],[f2])).
% 0.13/0.61 fof(f28,plain,(
% 0.13/0.61 ![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)))))))),
% 0.13/0.62 inference(NNF_transformation,[status(thm)],[f27])).
% 0.13/0.62 fof(f29,plain,(
% 0.13/0.62 (![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)))))))),
% 0.13/0.62 inference(miniscoping,[status(thm)],[f28])).
% 0.13/0.62 fof(f30,plain,(
% 0.13/0.62 (![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(sK3_skl(E,R),E)&member(sK4_skl(E,R),E))&(~apply(R,sK3_skl(E,R),sK4_skl(E,R))&~apply(R,sK4_skl(E,R),sK3_skl(E,R)))))))),
% 0.13/0.62 inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl,sK4_skl]),skolemize(X,sK3_skl(E,R)),skolemize(Y,sK4_skl(E,R))],[f29])).
% 0.13/0.62 fof(f31,plain,(
% 0.13/0.62 ![X0,X1]: (~total_order(X0,X1)|order(X0,X1))),
% 0.13/0.62 inference(cnf_transformation,[status(thm)],[f30])).
% 0.13/0.62 fof(f32,plain,(
% 0.13/0.62 ![X0,X1,X2,X3]: (~total_order(X0,X1)|~member(X2,X1)|~member(X3,X1)|apply(X0,X2,X3)|apply(X0,X3,X2))),
% 0.13/0.62 inference(cnf_transformation,[status(thm)],[f30])).
% 0.13/0.62 fof(f44,plain,(
% 0.13/0.62 ![R,E,M]: (lower_bound(M,R,E)<=>(![X]: (~member(X,E)|apply(R,M,X))))),
% 0.13/0.62 inference(pre_NNF_transformation,[status(thm)],[f4])).
% 0.13/0.62 fof(f45,plain,(
% 0.13/0.62 ![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)))))),
% 0.13/0.62 inference(NNF_transformation,[status(thm)],[f44])).
% 0.13/0.62 fof(f46,plain,(
% 0.13/0.62 (![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)))))),
% 0.13/0.62 inference(miniscoping,[status(thm)],[f45])).
% 0.13/0.62 fof(f47,plain,(
% 0.13/0.62 (![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(sK6_skl(M,E,R),E)&~apply(R,M,sK6_skl(M,E,R)))))),
% 0.13/0.62 inference(skolemize,[status(esa),new_symbols(skolem,[sK6_skl]),skolemize(X,sK6_skl(M,E,R))],[f46])).
% 0.13/0.62 fof(f48,plain,(
% 0.13/0.62 ![X0,X1,X2,X3]: (~lower_bound(X0,X1,X2)|~member(X3,X2)|apply(X1,X0,X3))),
% 0.13/0.62 inference(cnf_transformation,[status(thm)],[f47])).
% 0.13/0.62 fof(f49,plain,(
% 0.13/0.62 ![X0,X1,X2]: (lower_bound(X0,X1,X2)|member(sK6_skl(X0,X2,X1),X2))),
% 0.13/0.62 inference(cnf_transformation,[status(thm)],[f47])).
% 0.13/0.62 fof(f50,plain,(
% 0.13/0.62 ![X0,X1,X2]: (lower_bound(X0,X1,X2)|~apply(X1,X0,sK6_skl(X0,X2,X1)))),
% 0.13/0.62 inference(cnf_transformation,[status(thm)],[f47])).
% 0.13/0.62 fof(f59,plain,(
% 0.13/0.62 ![R,E,M]: (least(M,R,E)<=>(member(M,E)&(![X]: (~member(X,E)|apply(R,M,X)))))),
% 0.13/0.62 inference(pre_NNF_transformation,[status(thm)],[f6])).
% 0.13/0.62 fof(f60,plain,(
% 0.13/0.62 ![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))))))),
% 0.13/0.62 inference(NNF_transformation,[status(thm)],[f59])).
% 0.13/0.62 fof(f61,plain,(
% 0.13/0.62 (![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))))))),
% 0.13/0.62 inference(miniscoping,[status(thm)],[f60])).
% 0.13/0.62 fof(f62,plain,(
% 0.13/0.62 (![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(sK8_skl(M,E,R),E)&~apply(R,M,sK8_skl(M,E,R))))))),
% 0.13/0.62 inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl]),skolemize(X,sK8_skl(M,E,R))],[f61])).
% 0.13/0.62 fof(f65,plain,(
% 0.13/0.62 ![X0,X1,X2]: (least(X0,X1,X2)|~member(X0,X2)|member(sK8_skl(X0,X2,X1),X2))),
% 0.13/0.62 inference(cnf_transformation,[status(thm)],[f62])).
% 0.13/0.62 fof(f66,plain,(
% 0.13/0.62 ![X0,X1,X2]: (least(X0,X1,X2)|~member(X0,X2)|~apply(X1,X0,sK8_skl(X0,X2,X1)))),
% 0.13/0.62 inference(cnf_transformation,[status(thm)],[f62])).
% 0.13/0.62 fof(f76,plain,(
% 0.13/0.62 ![R,E,M]: (min(M,R,E)<=>(member(M,E)&(![X]: ((~member(X,E)|~apply(R,X,M))|M=X))))),
% 0.13/0.62 inference(pre_NNF_transformation,[status(thm)],[f8])).
% 0.13/0.62 fof(f77,plain,(
% 0.13/0.62 ![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)))))),
% 0.13/0.62 inference(NNF_transformation,[status(thm)],[f76])).
% 0.13/0.62 fof(f78,plain,(
% 0.13/0.62 (![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)))))),
% 0.13/0.62 inference(miniscoping,[status(thm)],[f77])).
% 0.13/0.62 fof(f79,plain,(
% 0.13/0.62 (![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(sK10_skl(M,E,R),E)&apply(R,sK10_skl(M,E,R),M))&~M=sK10_skl(M,E,R)))))),
% 0.13/0.62 inference(skolemize,[status(esa),new_symbols(skolem,[sK10_skl]),skolemize(X,sK10_skl(M,E,R))],[f78])).
% 0.13/0.62 fof(f80,plain,(
% 0.13/0.62 ![X0,X1,X2]: (~min(X0,X1,X2)|member(X0,X2))),
% 0.13/0.62 inference(cnf_transformation,[status(thm)],[f79])).
% 0.13/0.62 fof(f81,plain,(
% 0.13/0.62 ![X0,X1,X2,X3]: (~min(X0,X1,X2)|~member(X3,X2)|~apply(X1,X3,X0)|X0=X3)),
% 0.13/0.62 inference(cnf_transformation,[status(thm)],[f79])).
% 0.13/0.62 fof(f105,plain,(
% 0.13/0.62 (?[R,E,M]: ((total_order(R,E)&min(M,R,E))&~least(M,R,E)))),
% 0.13/0.62 inference(pre_NNF_transformation,[status(thm)],[f12])).
% 0.13/0.62 fof(f106,plain,(
% 0.13/0.62 ((total_order(sK13_skl,sK14_skl)&min(sK15_skl,sK13_skl,sK14_skl))&~least(sK15_skl,sK13_skl,sK14_skl))),
% 0.13/0.62 inference(skolemize,[status(esa),new_symbols(skolem,[sK13_skl,sK14_skl,sK15_skl]),skolemize(R,sK13_skl),skolemize(E,sK14_skl),skolemize(M,sK15_skl)],[f105])).
% 0.13/0.62 fof(f107,plain,(
% 0.13/0.62 total_order(sK13_skl,sK14_skl)),
% 0.13/0.62 inference(cnf_transformation,[status(thm)],[f106])).
% 0.13/0.62 fof(f108,plain,(
% 0.13/0.62 min(sK15_skl,sK13_skl,sK14_skl)),
% 0.13/0.62 inference(cnf_transformation,[status(thm)],[f106])).
% 0.13/0.62 fof(f109,plain,(
% 0.13/0.62 ~least(sK15_skl,sK13_skl,sK14_skl)),
% 0.13/0.62 inference(cnf_transformation,[status(thm)],[f106])).
% 0.13/0.62 fof(f127,plain,(
% 0.13/0.62 order(sK13_skl,sK14_skl)),
% 0.13/0.62 inference(resolution,[status(thm)],[f31,f107])).
% 0.13/0.62 fof(f128,plain,(
% 0.13/0.62 member(sK15_skl,sK14_skl)),
% 0.13/0.62 inference(resolution,[status(thm)],[f80,f108])).
% 0.13/0.62 fof(f129,plain,(
% 0.13/0.62 ![X0,X1]: (~member(X0,sK14_skl)|~member(X1,sK14_skl)|apply(sK13_skl,X0,X1)|apply(sK13_skl,X1,X0))),
% 0.13/0.62 inference(resolution,[status(thm)],[f32,f107])).
% 0.13/0.62 fof(f130,plain,(
% 0.13/0.62 ![X0]: (~member(X0,sK14_skl)|apply(sK13_skl,X0,sK15_skl)|apply(sK13_skl,sK15_skl,X0))),
% 0.13/0.62 inference(resolution,[status(thm)],[f129,f128])).
% 0.13/0.62 fof(f131,plain,(
% 0.13/0.62 apply(sK13_skl,sK15_skl,sK15_skl)|apply(sK13_skl,sK15_skl,sK15_skl)),
% 0.13/0.62 inference(resolution,[status(thm)],[f130,f128])).
% 0.13/0.62 fof(f132,plain,(
% 0.13/0.62 apply(sK13_skl,sK15_skl,sK15_skl)),
% 0.13/0.62 inference(duplicate_literals_removal,[status(thm)],[f131])).
% 0.13/0.62 fof(f136,plain,(
% 0.13/0.62 ![X0,X1]: (lower_bound(X0,X1,sK14_skl)|apply(sK13_skl,sK6_skl(X0,sK14_skl,X1),sK15_skl)|apply(sK13_skl,sK15_skl,sK6_skl(X0,sK14_skl,X1)))),
% 0.13/0.62 inference(resolution,[status(thm)],[f49,f130])).
% 0.13/0.62 fof(f138,plain,(
% 0.13/0.62 ![X0,X1,X2]: (~member(X0,sK14_skl)|~member(X1,sK14_skl)|~member(X2,sK14_skl)|~apply(sK13_skl,X0,X1)|~apply(sK13_skl,X1,X2)|apply(sK13_skl,X0,X2))),
% 0.13/0.62 inference(resolution,[status(thm)],[f20,f127])).
% 0.13/0.62 fof(f149,plain,(
% 0.13/0.62 ![X0,X1,X2,X3]: (~member(X0,sK14_skl)|~member(X1,sK14_skl)|~member(X2,sK14_skl)|~apply(sK13_skl,X0,X1)|~apply(sK13_skl,X1,X2)|~min(X2,sK13_skl,X3)|~member(X0,X3)|X2=X0)),
% 0.13/0.62 inference(resolution,[status(thm)],[f138,f81])).
% 0.13/0.62 fof(f150,plain,(
% 0.13/0.62 ![X0,X1]: (~member(X0,sK14_skl)|~member(X1,sK14_skl)|~member(sK15_skl,sK14_skl)|~apply(sK13_skl,X0,X1)|~apply(sK13_skl,X1,sK15_skl)|~member(X0,sK14_skl)|sK15_skl=X0)),
% 0.13/0.62 inference(resolution,[status(thm)],[f149,f108])).
% 0.13/0.62 fof(f151,plain,(
% 0.13/0.62 ![X0,X1]: (~member(X0,sK14_skl)|~member(X1,sK14_skl)|~member(sK15_skl,sK14_skl)|~apply(sK13_skl,X0,X1)|~apply(sK13_skl,X1,sK15_skl)|sK15_skl=X0)),
% 0.13/0.62 inference(duplicate_literals_removal,[status(thm)],[f150])).
% 0.13/0.62 fof(f152,plain,(
% 0.13/0.62 ![X0,X1]: (~member(X0,sK14_skl)|~member(X1,sK14_skl)|~apply(sK13_skl,X0,X1)|~apply(sK13_skl,X1,sK15_skl)|sK15_skl=X0)),
% 0.13/0.62 inference(forward_subsumption_resolution,[status(thm)],[f151,f128])).
% 0.13/0.62 fof(f155,plain,(
% 0.13/0.62 ![X0]: (~member(X0,sK14_skl)|~apply(sK13_skl,X0,sK15_skl)|~apply(sK13_skl,sK15_skl,sK15_skl)|sK15_skl=X0)),
% 0.13/0.62 inference(resolution,[status(thm)],[f152,f128])).
% 0.13/0.62 fof(f156,plain,(
% 0.13/0.62 ![X0]: (~member(X0,sK14_skl)|~apply(sK13_skl,X0,sK15_skl)|sK15_skl=X0)),
% 0.13/0.62 inference(forward_subsumption_resolution,[status(thm)],[f155,f132])).
% 0.13/0.62 fof(f157,plain,(
% 0.13/0.62 ![X0,X1]: (~apply(sK13_skl,sK6_skl(X0,sK14_skl,X1),sK15_skl)|sK15_skl=sK6_skl(X0,sK14_skl,X1)|lower_bound(X0,X1,sK14_skl))),
% 0.13/0.62 inference(resolution,[status(thm)],[f156,f49])).
% 0.13/0.62 fof(f160,plain,(
% 0.13/0.62 ![X0,X1]: (sK15_skl=sK6_skl(X0,sK14_skl,X1)|lower_bound(X0,X1,sK14_skl)|lower_bound(X0,X1,sK14_skl)|apply(sK13_skl,sK15_skl,sK6_skl(X0,sK14_skl,X1)))),
% 0.13/0.62 inference(resolution,[status(thm)],[f157,f136])).
% 0.13/0.62 fof(f162,plain,(
% 0.13/0.62 ![X0,X1]: (sK15_skl=sK6_skl(X0,sK14_skl,X1)|lower_bound(X0,X1,sK14_skl)|apply(sK13_skl,sK15_skl,sK6_skl(X0,sK14_skl,X1)))),
% 0.13/0.62 inference(duplicate_literals_removal,[status(thm)],[f160])).
% 0.13/0.62 fof(f187,plain,(
% 0.13/0.62 lower_bound(sK15_skl,sK13_skl,sK14_skl)|sK15_skl=sK6_skl(sK15_skl,sK14_skl,sK13_skl)|lower_bound(sK15_skl,sK13_skl,sK14_skl)),
% 0.13/0.62 inference(resolution,[status(thm)],[f50,f162])).
% 0.13/0.62 fof(f190,plain,(
% 0.13/0.62 lower_bound(sK15_skl,sK13_skl,sK14_skl)|sK15_skl=sK6_skl(sK15_skl,sK14_skl,sK13_skl)),
% 0.13/0.62 inference(duplicate_literals_removal,[status(thm)],[f187])).
% 0.13/0.62 fof(f206,plain,(
% 0.13/0.62 ![X0]: (sK15_skl=sK6_skl(sK15_skl,sK14_skl,sK13_skl)|~member(X0,sK14_skl)|apply(sK13_skl,sK15_skl,X0))),
% 0.13/0.62 inference(resolution,[status(thm)],[f190,f48])).
% 0.13/0.62 fof(f240,plain,(
% 0.13/0.62 ![X0]: (least(sK15_skl,X0,sK14_skl)|member(sK8_skl(sK15_skl,sK14_skl,X0),sK14_skl))),
% 0.13/0.62 inference(resolution,[status(thm)],[f65,f128])).
% 0.13/0.62 fof(f248,plain,(
% 0.13/0.62 ![X0]: (least(sK15_skl,sK13_skl,X0)|~member(sK15_skl,X0)|sK15_skl=sK6_skl(sK15_skl,sK14_skl,sK13_skl)|~member(sK8_skl(sK15_skl,X0,sK13_skl),sK14_skl))),
% 0.13/0.62 inference(resolution,[status(thm)],[f66,f206])).
% 0.13/0.62 fof(f312,plain,(
% 0.13/0.62 least(sK15_skl,sK13_skl,sK14_skl)|~member(sK15_skl,sK14_skl)|sK15_skl=sK6_skl(sK15_skl,sK14_skl,sK13_skl)|least(sK15_skl,sK13_skl,sK14_skl)),
% 0.13/0.62 inference(resolution,[status(thm)],[f248,f240])).
% 0.13/0.62 fof(f313,plain,(
% 0.13/0.62 least(sK15_skl,sK13_skl,sK14_skl)|~member(sK15_skl,sK14_skl)|sK15_skl=sK6_skl(sK15_skl,sK14_skl,sK13_skl)),
% 0.13/0.62 inference(duplicate_literals_removal,[status(thm)],[f312])).
% 0.13/0.62 fof(f314,plain,(
% 0.13/0.62 ~member(sK15_skl,sK14_skl)|sK15_skl=sK6_skl(sK15_skl,sK14_skl,sK13_skl)),
% 0.13/0.62 inference(forward_subsumption_resolution,[status(thm)],[f313,f109])).
% 0.13/0.62 fof(f315,plain,(
% 0.13/0.62 sK15_skl=sK6_skl(sK15_skl,sK14_skl,sK13_skl)),
% 0.13/0.62 inference(resolution,[status(thm)],[f314,f128])).
% 0.13/0.62 fof(f337,plain,(
% 0.13/0.62 lower_bound(sK15_skl,sK13_skl,sK14_skl)|~apply(sK13_skl,sK15_skl,sK15_skl)),
% 0.13/0.62 inference(paramodulation,[status(thm)],[f315,f50])).
% 0.13/0.62 fof(f353,plain,(
% 0.13/0.62 lower_bound(sK15_skl,sK13_skl,sK14_skl)),
% 0.13/0.62 inference(forward_subsumption_resolution,[status(thm)],[f337,f132])).
% 0.13/0.62 fof(f354,plain,(
% 0.13/0.62 ![X0]: (~member(X0,sK14_skl)|apply(sK13_skl,sK15_skl,X0))),
% 0.13/0.62 inference(resolution,[status(thm)],[f353,f48])).
% 0.13/0.62 fof(f361,plain,(
% 0.13/0.62 ![X0]: (~member(sK8_skl(sK15_skl,X0,sK13_skl),sK14_skl)|least(sK15_skl,sK13_skl,X0)|~member(sK15_skl,X0))),
% 0.13/0.62 inference(resolution,[status(thm)],[f354,f66])).
% 0.13/0.62 fof(f409,plain,(
% 0.13/0.62 least(sK15_skl,sK13_skl,sK14_skl)|~member(sK15_skl,sK14_skl)|least(sK15_skl,sK13_skl,sK14_skl)),
% 0.13/0.62 inference(resolution,[status(thm)],[f361,f240])).
% 0.13/0.62 fof(f410,plain,(
% 0.13/0.62 least(sK15_skl,sK13_skl,sK14_skl)|~member(sK15_skl,sK14_skl)),
% 0.13/0.62 inference(duplicate_literals_removal,[status(thm)],[f409])).
% 0.13/0.62 fof(f412,plain,(
% 0.13/0.62 ~member(sK15_skl,sK14_skl)),
% 0.13/0.62 inference(forward_subsumption_resolution,[status(thm)],[f410,f109])).
% 0.13/0.62 fof(f413,plain,(
% 0.13/0.62 $false),
% 0.13/0.62 inference(backward_subsumption_resolution,[status(thm)],[f128,f412])).
% 0.13/0.62 % SZS output end CNFRefutation for theBenchmark.p
% 1.45/0.64 % Elapsed time: 0.275509 seconds
% 1.45/0.64 % CPU time: 1.954489 seconds
% 1.45/0.64 % Total memory used: 101.650 MB
% 1.45/0.64 % Net memory used: 100.044 MB
%------------------------------------------------------------------------------