%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SET792+4 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 02:12:36 PM UTC 2026
% Result : Theorem 0.12s 0.39s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET792+4 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.33 % Computer : n009.cluster.edu
% 0.08/0.33 % Model : x86_64 x86_64
% 0.08/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.33 % Memory : 8046.5625MB
% 0.08/0.33 % OS : Linux 6.8.0-71-generic
% 0.08/0.33 % CPULimit : 300
% 0.08/0.33 % WCLimit : 300
% 0.08/0.33 % DateTime : Mon Sep 21 05:38:42 UTC 2026
% 0.08/0.33 % CPUTime :
% 0.08/0.34 % Drodi V4.1.1
% 0.12/0.39 % Refutation found
% 0.12/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.39 % SZS output start CNFRefutation for theBenchmark
% 0.12/0.39 fof(f1,axiom,(
% 0.12/0.39 (! [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) ) ) )) ) )),
% 0.12/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.39 fof(f6,axiom,(
% 0.12/0.39 (! [R,E,M] :( least(M,R,E)<=> ( member(M,E)& (! [X] :( member(X,E)=> apply(R,M,X) ) )) ) )),
% 0.12/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.39 fof(f8,axiom,(
% 0.12/0.39 (! [R,E,M] :( min(M,R,E)<=> ( member(M,E)& (! [X] :( ( member(X,E)& apply(R,X,M) )=> M = X ) )) ) )),
% 0.12/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.39 fof(f11,conjecture,(
% 0.12/0.39 (! [R,E,M] :( ( order(R,E)& least(M,R,E) )=> min(M,R,E) ) )),
% 0.12/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.39 fof(f12,negated_conjecture,(
% 0.12/0.39 ~((! [R,E,M] :( ( order(R,E)& least(M,R,E) )=> min(M,R,E) ) ))),
% 0.12/0.39 inference(negated_conjecture,[status(cth)],[f11])).
% 0.12/0.39 fof(f13,plain,(
% 0.12/0.39 ![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))))))),
% 0.12/0.39 inference(pre_NNF_transformation,[status(thm)],[f1])).
% 0.12/0.39 fof(f14,definition,(
% 0.12/0.39 ![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)))))),
% 0.12/0.39 introduced(definition,[new_symbols(definition,[sP0_prd])],[])).
% 0.12/0.39 fof(f15,plain,(
% 0.12/0.39 ![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))))))),
% 0.12/0.39 inference(formula_renaming,[status(thm)],[f13,f14])).
% 0.12/0.39 fof(f16,plain,(
% 0.12/0.39 ![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)))))))),
% 0.12/0.39 inference(NNF_transformation,[status(thm)],[f15])).
% 0.12/0.39 fof(f17,plain,(
% 0.12/0.39 (![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)))))))),
% 0.12/0.39 inference(miniscoping,[status(thm)],[f16])).
% 0.12/0.39 fof(f18,plain,(
% 0.12/0.39 (![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)))))))),
% 0.12/0.39 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])).
% 0.12/0.39 fof(f19,plain,(
% 0.12/0.39 ![X0,X1]: (~order(X0,X1)|sP0_prd(X1,X0))),
% 0.12/0.39 inference(cnf_transformation,[status(thm)],[f18])).
% 0.12/0.39 fof(f59,plain,(
% 0.12/0.39 ![R,E,M]: (least(M,R,E)<=>(member(M,E)&(![X]: (~member(X,E)|apply(R,M,X)))))),
% 0.12/0.39 inference(pre_NNF_transformation,[status(thm)],[f6])).
% 0.12/0.39 fof(f60,plain,(
% 0.12/0.39 ![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))))))),
% 0.12/0.39 inference(NNF_transformation,[status(thm)],[f59])).
% 0.12/0.39 fof(f61,plain,(
% 0.12/0.39 (![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))))))),
% 0.12/0.39 inference(miniscoping,[status(thm)],[f60])).
% 0.12/0.39 fof(f62,plain,(
% 0.12/0.39 (![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))))))),
% 0.12/0.39 inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl]),skolemize(X,sK8_skl(M,E,R))],[f61])).
% 0.12/0.39 fof(f63,plain,(
% 0.12/0.39 ![X0,X1,X2]: (~least(X0,X1,X2)|member(X0,X2))),
% 0.12/0.39 inference(cnf_transformation,[status(thm)],[f62])).
% 0.12/0.39 fof(f64,plain,(
% 0.12/0.39 ![X0,X1,X2,X3]: (~least(X0,X1,X2)|~member(X3,X2)|apply(X1,X0,X3))),
% 0.12/0.39 inference(cnf_transformation,[status(thm)],[f62])).
% 0.12/0.39 fof(f76,plain,(
% 0.12/0.39 ![R,E,M]: (min(M,R,E)<=>(member(M,E)&(![X]: ((~member(X,E)|~apply(R,X,M))|M=X))))),
% 0.12/0.39 inference(pre_NNF_transformation,[status(thm)],[f8])).
% 0.12/0.39 fof(f77,plain,(
% 0.12/0.39 ![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)))))),
% 0.12/0.39 inference(NNF_transformation,[status(thm)],[f76])).
% 0.12/0.39 fof(f78,plain,(
% 0.12/0.39 (![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)))))),
% 0.12/0.39 inference(miniscoping,[status(thm)],[f77])).
% 0.12/0.39 fof(f79,plain,(
% 0.12/0.39 (![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)))))),
% 0.12/0.39 inference(skolemize,[status(esa),new_symbols(skolem,[sK10_skl]),skolemize(X,sK10_skl(M,E,R))],[f78])).
% 0.12/0.39 fof(f82,plain,(
% 0.12/0.39 ![X0,X1,X2]: (min(X0,X1,X2)|~member(X0,X2)|member(sK10_skl(X0,X2,X1),X2))),
% 0.12/0.39 inference(cnf_transformation,[status(thm)],[f79])).
% 0.12/0.39 fof(f83,plain,(
% 0.12/0.39 ![X0,X1,X2]: (min(X0,X1,X2)|~member(X0,X2)|apply(X1,sK10_skl(X0,X2,X1),X0))),
% 0.12/0.39 inference(cnf_transformation,[status(thm)],[f79])).
% 0.12/0.39 fof(f84,plain,(
% 0.12/0.39 ![X0,X1,X2]: (min(X0,X1,X2)|~member(X0,X2)|~X0=sK10_skl(X0,X2,X1))),
% 0.12/0.39 inference(cnf_transformation,[status(thm)],[f79])).
% 0.12/0.39 fof(f105,plain,(
% 0.12/0.39 (?[R,E,M]: ((order(R,E)&least(M,R,E))&~min(M,R,E)))),
% 0.12/0.39 inference(pre_NNF_transformation,[status(thm)],[f12])).
% 0.12/0.39 fof(f106,plain,(
% 0.12/0.39 ((order(sK13_skl,sK14_skl)&least(sK15_skl,sK13_skl,sK14_skl))&~min(sK15_skl,sK13_skl,sK14_skl))),
% 0.12/0.39 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])).
% 0.12/0.39 fof(f107,plain,(
% 0.12/0.39 order(sK13_skl,sK14_skl)),
% 0.12/0.39 inference(cnf_transformation,[status(thm)],[f106])).
% 0.12/0.39 fof(f108,plain,(
% 0.12/0.39 least(sK15_skl,sK13_skl,sK14_skl)),
% 0.12/0.39 inference(cnf_transformation,[status(thm)],[f106])).
% 0.12/0.39 fof(f109,plain,(
% 0.12/0.39 ~min(sK15_skl,sK13_skl,sK14_skl)),
% 0.12/0.39 inference(cnf_transformation,[status(thm)],[f106])).
% 0.12/0.39 fof(f110,definition,(
% 0.12/0.39 ![R,E,X]: (sP1_prd(X,E,R)<=>(~member(X,E)|apply(R,X,X)))),
% 0.12/0.39 introduced(definition,[new_symbols(definition,[sP1_prd])],[])).
% 0.12/0.39 fof(f111,plain,(
% 0.12/0.39 ![R,E]: (sP0_prd(E,R)<=>((![X]: sP1_prd(X,E,R))&(![X,Y]: ((~member(X,E)|~member(Y,E))|((~apply(R,X,Y)|~apply(R,Y,X))|X=Y)))))),
% 0.12/0.39 inference(formula_renaming,[status(thm)],[f14,f110])).
% 0.12/0.39 fof(f112,plain,(
% 0.12/0.39 ![R,E]: ((~sP0_prd(E,R)|((![X]: sP1_prd(X,E,R))&(![X,Y]: ((~member(X,E)|~member(Y,E))|((~apply(R,X,Y)|~apply(R,Y,X))|X=Y)))))&(sP0_prd(E,R)|((?[X]: ~sP1_prd(X,E,R))|(?[X,Y]: ((member(X,E)&member(Y,E))&((apply(R,X,Y)&apply(R,Y,X))&~X=Y))))))),
% 0.12/0.39 inference(NNF_transformation,[status(thm)],[f111])).
% 0.12/0.39 fof(f113,plain,(
% 0.12/0.39 (![R,E]: (~sP0_prd(E,R)|((![X]: sP1_prd(X,E,R))&(![X,Y]: ((~member(X,E)|~member(Y,E))|((~apply(R,X,Y)|~apply(R,Y,X))|X=Y))))))&(![R,E]: (sP0_prd(E,R)|((?[X]: ~sP1_prd(X,E,R))|(?[X,Y]: ((member(X,E)&member(Y,E))&((apply(R,X,Y)&apply(R,Y,X))&~X=Y))))))),
% 0.12/0.39 inference(miniscoping,[status(thm)],[f112])).
% 0.12/0.39 fof(f114,plain,(
% 0.12/0.39 (![R,E]: (~sP0_prd(E,R)|((![X]: sP1_prd(X,E,R))&(![X,Y]: ((~member(X,E)|~member(Y,E))|((~apply(R,X,Y)|~apply(R,Y,X))|X=Y))))))&(![R,E]: (sP0_prd(E,R)|(~sP1_prd(sK16_skl(E,R),E,R)|((member(sK17_skl(E,R),E)&member(sK18_skl(E,R),E))&((apply(R,sK17_skl(E,R),sK18_skl(E,R))&apply(R,sK18_skl(E,R),sK17_skl(E,R)))&~sK17_skl(E,R)=sK18_skl(E,R))))))),
% 0.12/0.39 inference(skolemize,[status(esa),new_symbols(skolem,[sK16_skl,sK17_skl,sK18_skl]),skolemize(X,sK16_skl(E,R)),skolemize(X,sK17_skl(E,R)),skolemize(Y,sK18_skl(E,R))],[f113])).
% 0.12/0.39 fof(f116,plain,(
% 0.12/0.39 ![X0,X1,X2,X3]: (~sP0_prd(X0,X1)|~member(X2,X0)|~member(X3,X0)|~apply(X1,X2,X3)|~apply(X1,X3,X2)|X2=X3)),
% 0.12/0.39 inference(cnf_transformation,[status(thm)],[f114])).
% 0.12/0.39 fof(f127,plain,(
% 0.12/0.39 sP0_prd(sK14_skl,sK13_skl)),
% 0.12/0.39 inference(resolution,[status(thm)],[f19,f107])).
% 0.12/0.39 fof(f128,plain,(
% 0.12/0.39 member(sK15_skl,sK14_skl)),
% 0.12/0.39 inference(resolution,[status(thm)],[f63,f108])).
% 0.12/0.39 fof(f315,plain,(
% 0.12/0.39 ![X0,X1]: (~member(X0,sK14_skl)|~member(X1,sK14_skl)|~apply(sK13_skl,X0,X1)|~apply(sK13_skl,X1,X0)|X0=X1)),
% 0.12/0.39 inference(resolution,[status(thm)],[f116,f127])).
% 0.12/0.39 fof(f325,plain,(
% 0.12/0.39 ![X0,X1,X2]: (~member(X0,sK14_skl)|~member(X1,sK14_skl)|~apply(sK13_skl,X0,X1)|X0=X1|~least(X1,sK13_skl,X2)|~member(X0,X2))),
% 0.12/0.39 inference(resolution,[status(thm)],[f315,f64])).
% 0.12/0.39 fof(f350,plain,(
% 0.12/0.39 ![X0]: (~member(X0,sK14_skl)|~member(sK15_skl,sK14_skl)|~apply(sK13_skl,X0,sK15_skl)|X0=sK15_skl|~member(X0,sK14_skl))),
% 0.12/0.39 inference(resolution,[status(thm)],[f325,f108])).
% 0.12/0.39 fof(f351,plain,(
% 0.12/0.39 ![X0]: (~member(X0,sK14_skl)|~member(sK15_skl,sK14_skl)|~apply(sK13_skl,X0,sK15_skl)|X0=sK15_skl)),
% 0.12/0.39 inference(duplicate_literals_removal,[status(thm)],[f350])).
% 0.12/0.39 fof(f352,plain,(
% 0.12/0.39 ![X0]: (~member(X0,sK14_skl)|~apply(sK13_skl,X0,sK15_skl)|X0=sK15_skl)),
% 0.12/0.39 inference(forward_subsumption_resolution,[status(thm)],[f351,f128])).
% 0.12/0.39 fof(f353,plain,(
% 0.12/0.39 ![X0]: (~member(sK10_skl(sK15_skl,X0,sK13_skl),sK14_skl)|sK10_skl(sK15_skl,X0,sK13_skl)=sK15_skl|min(sK15_skl,sK13_skl,X0)|~member(sK15_skl,X0))),
% 0.12/0.39 inference(resolution,[status(thm)],[f352,f83])).
% 0.12/0.39 fof(f358,plain,(
% 0.12/0.39 ![X0]: (~member(sK10_skl(sK15_skl,X0,sK13_skl),sK14_skl)|min(sK15_skl,sK13_skl,X0)|~member(sK15_skl,X0))),
% 0.12/0.39 inference(forward_subsumption_resolution,[status(thm)],[f353,f84])).
% 0.12/0.39 fof(f369,plain,(
% 0.12/0.39 min(sK15_skl,sK13_skl,sK14_skl)|~member(sK15_skl,sK14_skl)|min(sK15_skl,sK13_skl,sK14_skl)|~member(sK15_skl,sK14_skl)),
% 0.12/0.39 inference(resolution,[status(thm)],[f358,f82])).
% 0.12/0.39 fof(f370,plain,(
% 0.12/0.39 min(sK15_skl,sK13_skl,sK14_skl)|~member(sK15_skl,sK14_skl)),
% 0.12/0.39 inference(duplicate_literals_removal,[status(thm)],[f369])).
% 0.12/0.39 fof(f372,plain,(
% 0.12/0.39 ~member(sK15_skl,sK14_skl)),
% 0.12/0.39 inference(forward_subsumption_resolution,[status(thm)],[f370,f109])).
% 0.12/0.39 fof(f373,plain,(
% 0.12/0.39 $false),
% 0.12/0.39 inference(backward_subsumption_resolution,[status(thm)],[f128,f372])).
% 0.12/0.39 % SZS output end CNFRefutation for theBenchmark.p
% 0.12/0.44 % Elapsed time: 0.093578 seconds
% 0.12/0.44 % CPU time: 0.436102 seconds
% 0.12/0.44 % Total memory used: 87.322 MB
% 0.12/0.44 % Net memory used: 86.896 MB
%------------------------------------------------------------------------------