%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SET799+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 : n005.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 0.15s 0.39s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET799+4 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n005.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 05:38:33 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.15/0.38 % Drodi V4.1.1
% 0.15/0.39 % Refutation found
% 0.15/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.39 % SZS output start CNFRefutation for theBenchmark
% 0.15/0.39 fof(f1,axiom,(
% 0.15/0.39 (! [A,B] :( subset(A,B)<=> (! [X] :( member(X,A)=> member(X,B) ) )) )),
% 0.15/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.39 fof(f14,axiom,(
% 0.15/0.39 (! [R,E,M] :( upper_bound(M,R,E)<=> (! [X] :( member(X,E)=> apply(R,X,M) ) )) )),
% 0.15/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.39 fof(f20,axiom,(
% 0.15/0.39 (! [A,X,R,E] :( least_upper_bound(A,X,R,E)<=> ( member(A,X)& upper_bound(A,R,X)& (! [M] :( ( member(M,E)& upper_bound(M,R,X) )=> apply(R,A,M) ) )) ) )),
% 0.15/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.39 fof(f22,conjecture,(
% 0.15/0.39 (! [R,E] :( order(R,E)=> (! [X1,X2] :( ( subset(X1,E)& subset(X2,E)& subset(X1,X2) )=> (! [M1,M2] :( ( least_upper_bound(M1,X1,R,E)& least_upper_bound(M2,X2,R,E) )=> apply(R,M1,M2) ) )) )) )),
% 0.15/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.39 fof(f23,negated_conjecture,(
% 0.15/0.39 ~((! [R,E] :( order(R,E)=> (! [X1,X2] :( ( subset(X1,E)& subset(X2,E)& subset(X1,X2) )=> (! [M1,M2] :( ( least_upper_bound(M1,X1,R,E)& least_upper_bound(M2,X2,R,E) )=> apply(R,M1,M2) ) )) )) ))),
% 0.15/0.39 inference(negated_conjecture,[status(cth)],[f22])).
% 0.15/0.39 fof(f24,plain,(
% 0.15/0.39 ![A,B]: (subset(A,B)<=>(![X]: (~member(X,A)|member(X,B))))),
% 0.15/0.39 inference(pre_NNF_transformation,[status(thm)],[f1])).
% 0.15/0.39 fof(f25,plain,(
% 0.15/0.39 ![A,B]: ((~subset(A,B)|(![X]: (~member(X,A)|member(X,B))))&(subset(A,B)|(?[X]: (member(X,A)&~member(X,B)))))),
% 0.15/0.39 inference(NNF_transformation,[status(thm)],[f24])).
% 0.15/0.39 fof(f26,plain,(
% 0.15/0.39 (![A,B]: (~subset(A,B)|(![X]: (~member(X,A)|member(X,B)))))&(![A,B]: (subset(A,B)|(?[X]: (member(X,A)&~member(X,B)))))),
% 0.15/0.39 inference(miniscoping,[status(thm)],[f25])).
% 0.15/0.39 fof(f27,plain,(
% 0.15/0.39 (![A,B]: (~subset(A,B)|(![X]: (~member(X,A)|member(X,B)))))&(![A,B]: (subset(A,B)|(member(sK0_skl(B,A),A)&~member(sK0_skl(B,A),B))))),
% 0.15/0.39 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(X,sK0_skl(B,A))],[f26])).
% 0.15/0.39 fof(f28,plain,(
% 0.15/0.39 ![X0,X1,X2]: (~subset(X0,X1)|~member(X2,X0)|member(X2,X1))),
% 0.15/0.39 inference(cnf_transformation,[status(thm)],[f27])).
% 0.15/0.39 fof(f102,plain,(
% 0.15/0.39 ![R,E,M]: (upper_bound(M,R,E)<=>(![X]: (~member(X,E)|apply(R,X,M))))),
% 0.15/0.39 inference(pre_NNF_transformation,[status(thm)],[f14])).
% 0.15/0.39 fof(f103,plain,(
% 0.15/0.39 ![R,E,M]: ((~upper_bound(M,R,E)|(![X]: (~member(X,E)|apply(R,X,M))))&(upper_bound(M,R,E)|(?[X]: (member(X,E)&~apply(R,X,M)))))),
% 0.15/0.39 inference(NNF_transformation,[status(thm)],[f102])).
% 0.15/0.39 fof(f104,plain,(
% 0.15/0.39 (![R,E,M]: (~upper_bound(M,R,E)|(![X]: (~member(X,E)|apply(R,X,M)))))&(![R,E,M]: (upper_bound(M,R,E)|(?[X]: (member(X,E)&~apply(R,X,M)))))),
% 0.15/0.39 inference(miniscoping,[status(thm)],[f103])).
% 0.15/0.39 fof(f105,plain,(
% 0.15/0.39 (![R,E,M]: (~upper_bound(M,R,E)|(![X]: (~member(X,E)|apply(R,X,M)))))&(![R,E,M]: (upper_bound(M,R,E)|(member(sK8_skl(M,E,R),E)&~apply(R,sK8_skl(M,E,R),M))))),
% 0.15/0.39 inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl]),skolemize(X,sK8_skl(M,E,R))],[f104])).
% 0.15/0.39 fof(f106,plain,(
% 0.15/0.39 ![X0,X1,X2,X3]: (~upper_bound(X0,X1,X2)|~member(X3,X2)|apply(X1,X3,X0))),
% 0.15/0.39 inference(cnf_transformation,[status(thm)],[f105])).
% 0.15/0.40 fof(f150,plain,(
% 0.15/0.40 ![A,X,R,E]: (least_upper_bound(A,X,R,E)<=>((member(A,X)&upper_bound(A,R,X))&(![M]: ((~member(M,E)|~upper_bound(M,R,X))|apply(R,A,M)))))),
% 0.15/0.40 inference(pre_NNF_transformation,[status(thm)],[f20])).
% 0.15/0.40 fof(f151,plain,(
% 0.15/0.40 ![A,X,R,E]: ((~least_upper_bound(A,X,R,E)|((member(A,X)&upper_bound(A,R,X))&(![M]: ((~member(M,E)|~upper_bound(M,R,X))|apply(R,A,M)))))&(least_upper_bound(A,X,R,E)|((~member(A,X)|~upper_bound(A,R,X))|(?[M]: ((member(M,E)&upper_bound(M,R,X))&~apply(R,A,M))))))),
% 0.15/0.40 inference(NNF_transformation,[status(thm)],[f150])).
% 0.15/0.40 fof(f152,plain,(
% 0.15/0.40 (![A,X,R,E]: (~least_upper_bound(A,X,R,E)|((member(A,X)&upper_bound(A,R,X))&(![M]: ((~member(M,E)|~upper_bound(M,R,X))|apply(R,A,M))))))&(![A,X,R,E]: (least_upper_bound(A,X,R,E)|((~member(A,X)|~upper_bound(A,R,X))|(?[M]: ((member(M,E)&upper_bound(M,R,X))&~apply(R,A,M))))))),
% 0.15/0.40 inference(miniscoping,[status(thm)],[f151])).
% 0.15/0.40 fof(f153,plain,(
% 0.15/0.40 (![A,X,R,E]: (~least_upper_bound(A,X,R,E)|((member(A,X)&upper_bound(A,R,X))&(![M]: ((~member(M,E)|~upper_bound(M,R,X))|apply(R,A,M))))))&(![A,X,R,E]: (least_upper_bound(A,X,R,E)|((~member(A,X)|~upper_bound(A,R,X))|((member(sK14_skl(E,R,X,A),E)&upper_bound(sK14_skl(E,R,X,A),R,X))&~apply(R,A,sK14_skl(E,R,X,A))))))),
% 0.15/0.40 inference(skolemize,[status(esa),new_symbols(skolem,[sK14_skl]),skolemize(M,sK14_skl(E,R,X,A))],[f152])).
% 0.15/0.40 fof(f154,plain,(
% 0.15/0.40 ![X0,X1,X2,X3]: (~least_upper_bound(X0,X1,X2,X3)|member(X0,X1))),
% 0.15/0.40 inference(cnf_transformation,[status(thm)],[f153])).
% 0.15/0.40 fof(f155,plain,(
% 0.15/0.40 ![X0,X1,X2,X3]: (~least_upper_bound(X0,X1,X2,X3)|upper_bound(X0,X2,X1))),
% 0.15/0.40 inference(cnf_transformation,[status(thm)],[f153])).
% 0.15/0.40 fof(f170,plain,(
% 0.15/0.40 (?[R,E]: (order(R,E)&(?[X1,X2]: (((subset(X1,E)&subset(X2,E))&subset(X1,X2))&(?[M1,M2]: ((least_upper_bound(M1,X1,R,E)&least_upper_bound(M2,X2,R,E))&~apply(R,M1,M2)))))))),
% 0.15/0.40 inference(pre_NNF_transformation,[status(thm)],[f23])).
% 0.15/0.40 fof(f171,plain,(
% 0.15/0.40 (order(sK16_skl,sK17_skl)&(((subset(sK18_skl,sK17_skl)&subset(sK19_skl,sK17_skl))&subset(sK18_skl,sK19_skl))&((least_upper_bound(sK20_skl,sK18_skl,sK16_skl,sK17_skl)&least_upper_bound(sK21_skl,sK19_skl,sK16_skl,sK17_skl))&~apply(sK16_skl,sK20_skl,sK21_skl))))),
% 0.15/0.40 inference(skolemize,[status(esa),new_symbols(skolem,[sK16_skl,sK17_skl,sK18_skl,sK19_skl,sK20_skl,sK21_skl]),skolemize(R,sK16_skl),skolemize(E,sK17_skl),skolemize(X1,sK18_skl),skolemize(X2,sK19_skl),skolemize(M1,sK20_skl),skolemize(M2,sK21_skl)],[f170])).
% 0.15/0.40 fof(f175,plain,(
% 0.15/0.40 subset(sK18_skl,sK19_skl)),
% 0.15/0.40 inference(cnf_transformation,[status(thm)],[f171])).
% 0.15/0.40 fof(f176,plain,(
% 0.15/0.40 least_upper_bound(sK20_skl,sK18_skl,sK16_skl,sK17_skl)),
% 0.15/0.40 inference(cnf_transformation,[status(thm)],[f171])).
% 0.15/0.40 fof(f177,plain,(
% 0.15/0.40 least_upper_bound(sK21_skl,sK19_skl,sK16_skl,sK17_skl)),
% 0.15/0.40 inference(cnf_transformation,[status(thm)],[f171])).
% 0.15/0.40 fof(f178,plain,(
% 0.15/0.40 ~apply(sK16_skl,sK20_skl,sK21_skl)),
% 0.15/0.40 inference(cnf_transformation,[status(thm)],[f171])).
% 0.15/0.40 fof(f199,plain,(
% 0.15/0.40 member(sK20_skl,sK18_skl)),
% 0.15/0.40 inference(resolution,[status(thm)],[f154,f176])).
% 0.15/0.40 fof(f201,plain,(
% 0.15/0.40 upper_bound(sK21_skl,sK16_skl,sK19_skl)),
% 0.15/0.40 inference(resolution,[status(thm)],[f155,f177])).
% 0.15/0.40 fof(f205,plain,(
% 0.15/0.40 ![X0]: (~upper_bound(sK21_skl,sK16_skl,X0)|~member(sK20_skl,X0))),
% 0.15/0.40 inference(resolution,[status(thm)],[f106,f178])).
% 0.15/0.40 fof(f238,plain,(
% 0.15/0.40 ~member(sK20_skl,sK19_skl)),
% 0.15/0.40 inference(resolution,[status(thm)],[f205,f201])).
% 0.15/0.40 fof(f239,plain,(
% 0.15/0.40 ![X0]: (~subset(X0,sK19_skl)|~member(sK20_skl,X0))),
% 0.15/0.40 inference(resolution,[status(thm)],[f238,f28])).
% 0.15/0.40 fof(f245,plain,(
% 0.15/0.40 ~subset(sK18_skl,sK19_skl)),
% 0.15/0.40 inference(resolution,[status(thm)],[f239,f199])).
% 0.15/0.40 fof(f247,plain,(
% 0.15/0.40 $false),
% 0.15/0.40 inference(forward_subsumption_resolution,[status(thm)],[f245,f175])).
% 0.15/0.40 % SZS output end CNFRefutation for theBenchmark.p
% 0.15/0.42 % Elapsed time: 0.052108 seconds
% 0.15/0.42 % CPU time: 0.168652 seconds
% 0.15/0.42 % Total memory used: 27.775 MB
% 0.15/0.42 % Net memory used: 27.605 MB
%------------------------------------------------------------------------------