%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SET800+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 : n016.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 0.12s 0.39s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET800+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
% 0.06/0.32 % Computer : n016.cluster.edu
% 0.06/0.32 % Model : x86_64 x86_64
% 0.06/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.32 % Memory : 8046.5625MB
% 0.06/0.32 % OS : Linux 6.8.0-71-generic
% 0.06/0.32 % CPULimit : 300
% 0.06/0.32 % WCLimit : 300
% 0.06/0.32 % DateTime : Mon Sep 21 05:43:52 UTC 2026
% 0.06/0.33 % CPUTime :
% 0.06/0.34 % 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 (! [A,B] :( subset(A,B)<=> (! [X] :( member(X,A)=> member(X,B) ) )) )),
% 0.12/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.39 fof(f15,axiom,(
% 0.12/0.39 (! [R,E,M] :( lower_bound(M,R,E)<=> (! [X] :( member(X,E)=> apply(R,M,X) ) )) )),
% 0.12/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.39 fof(f21,axiom,(
% 0.12/0.39 (! [A,X,R,E] :( greatest_lower_bound(A,X,R,E)<=> ( member(A,X)& lower_bound(A,R,X)& (! [M] :( ( member(M,E)& lower_bound(M,R,X) )=> apply(R,M,A) ) )) ) )),
% 0.12/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.39 fof(f22,conjecture,(
% 0.12/0.39 (! [R,E] :( order(R,E)=> (! [X1,X2] :( ( subset(X1,E)& subset(X2,E)& subset(X1,X2) )=> (! [M1,M2] :( ( greatest_lower_bound(M1,X1,R,E)& greatest_lower_bound(M2,X2,R,E) )=> apply(R,M2,M1) ) )) )) )),
% 0.12/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.39 fof(f23,negated_conjecture,(
% 0.12/0.39 ~((! [R,E] :( order(R,E)=> (! [X1,X2] :( ( subset(X1,E)& subset(X2,E)& subset(X1,X2) )=> (! [M1,M2] :( ( greatest_lower_bound(M1,X1,R,E)& greatest_lower_bound(M2,X2,R,E) )=> apply(R,M2,M1) ) )) )) ))),
% 0.12/0.39 inference(negated_conjecture,[status(cth)],[f22])).
% 0.12/0.39 fof(f24,plain,(
% 0.12/0.39 ![A,B]: (subset(A,B)<=>(![X]: (~member(X,A)|member(X,B))))),
% 0.12/0.39 inference(pre_NNF_transformation,[status(thm)],[f1])).
% 0.12/0.39 fof(f25,plain,(
% 0.12/0.39 ![A,B]: ((~subset(A,B)|(![X]: (~member(X,A)|member(X,B))))&(subset(A,B)|(?[X]: (member(X,A)&~member(X,B)))))),
% 0.12/0.39 inference(NNF_transformation,[status(thm)],[f24])).
% 0.12/0.39 fof(f26,plain,(
% 0.12/0.39 (![A,B]: (~subset(A,B)|(![X]: (~member(X,A)|member(X,B)))))&(![A,B]: (subset(A,B)|(?[X]: (member(X,A)&~member(X,B)))))),
% 0.12/0.39 inference(miniscoping,[status(thm)],[f25])).
% 0.12/0.39 fof(f27,plain,(
% 0.12/0.39 (![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))))),
% 0.12/0.39 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(X,sK0_skl(B,A))],[f26])).
% 0.12/0.39 fof(f28,plain,(
% 0.12/0.39 ![X0,X1,X2]: (~subset(X0,X1)|~member(X2,X0)|member(X2,X1))),
% 0.12/0.39 inference(cnf_transformation,[status(thm)],[f27])).
% 0.12/0.39 fof(f109,plain,(
% 0.12/0.39 ![R,E,M]: (lower_bound(M,R,E)<=>(![X]: (~member(X,E)|apply(R,M,X))))),
% 0.12/0.39 inference(pre_NNF_transformation,[status(thm)],[f15])).
% 0.12/0.39 fof(f110,plain,(
% 0.12/0.39 ![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)))))),
% 0.12/0.39 inference(NNF_transformation,[status(thm)],[f109])).
% 0.12/0.39 fof(f111,plain,(
% 0.12/0.39 (![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)))))),
% 0.12/0.39 inference(miniscoping,[status(thm)],[f110])).
% 0.12/0.39 fof(f112,plain,(
% 0.12/0.39 (![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(sK9_skl(M,E,R),E)&~apply(R,M,sK9_skl(M,E,R)))))),
% 0.12/0.39 inference(skolemize,[status(esa),new_symbols(skolem,[sK9_skl]),skolemize(X,sK9_skl(M,E,R))],[f111])).
% 0.12/0.39 fof(f113,plain,(
% 0.12/0.39 ![X0,X1,X2,X3]: (~lower_bound(X0,X1,X2)|~member(X3,X2)|apply(X1,X0,X3))),
% 0.12/0.39 inference(cnf_transformation,[status(thm)],[f112])).
% 0.12/0.39 fof(f160,plain,(
% 0.12/0.39 ![A,X,R,E]: (greatest_lower_bound(A,X,R,E)<=>((member(A,X)&lower_bound(A,R,X))&(![M]: ((~member(M,E)|~lower_bound(M,R,X))|apply(R,M,A)))))),
% 0.12/0.39 inference(pre_NNF_transformation,[status(thm)],[f21])).
% 0.12/0.39 fof(f161,plain,(
% 0.12/0.39 ![A,X,R,E]: ((~greatest_lower_bound(A,X,R,E)|((member(A,X)&lower_bound(A,R,X))&(![M]: ((~member(M,E)|~lower_bound(M,R,X))|apply(R,M,A)))))&(greatest_lower_bound(A,X,R,E)|((~member(A,X)|~lower_bound(A,R,X))|(?[M]: ((member(M,E)&lower_bound(M,R,X))&~apply(R,M,A))))))),
% 0.12/0.39 inference(NNF_transformation,[status(thm)],[f160])).
% 0.12/0.39 fof(f162,plain,(
% 0.12/0.39 (![A,X,R,E]: (~greatest_lower_bound(A,X,R,E)|((member(A,X)&lower_bound(A,R,X))&(![M]: ((~member(M,E)|~lower_bound(M,R,X))|apply(R,M,A))))))&(![A,X,R,E]: (greatest_lower_bound(A,X,R,E)|((~member(A,X)|~lower_bound(A,R,X))|(?[M]: ((member(M,E)&lower_bound(M,R,X))&~apply(R,M,A))))))),
% 0.12/0.39 inference(miniscoping,[status(thm)],[f161])).
% 0.12/0.39 fof(f163,plain,(
% 0.12/0.39 (![A,X,R,E]: (~greatest_lower_bound(A,X,R,E)|((member(A,X)&lower_bound(A,R,X))&(![M]: ((~member(M,E)|~lower_bound(M,R,X))|apply(R,M,A))))))&(![A,X,R,E]: (greatest_lower_bound(A,X,R,E)|((~member(A,X)|~lower_bound(A,R,X))|((member(sK15_skl(E,R,X,A),E)&lower_bound(sK15_skl(E,R,X,A),R,X))&~apply(R,sK15_skl(E,R,X,A),A)))))),
% 0.12/0.40 inference(skolemize,[status(esa),new_symbols(skolem,[sK15_skl]),skolemize(M,sK15_skl(E,R,X,A))],[f162])).
% 0.12/0.40 fof(f164,plain,(
% 0.12/0.40 ![X0,X1,X2,X3]: (~greatest_lower_bound(X0,X1,X2,X3)|member(X0,X1))),
% 0.12/0.40 inference(cnf_transformation,[status(thm)],[f163])).
% 0.12/0.40 fof(f165,plain,(
% 0.12/0.40 ![X0,X1,X2,X3]: (~greatest_lower_bound(X0,X1,X2,X3)|lower_bound(X0,X2,X1))),
% 0.12/0.40 inference(cnf_transformation,[status(thm)],[f163])).
% 0.12/0.40 fof(f170,plain,(
% 0.12/0.40 (?[R,E]: (order(R,E)&(?[X1,X2]: (((subset(X1,E)&subset(X2,E))&subset(X1,X2))&(?[M1,M2]: ((greatest_lower_bound(M1,X1,R,E)&greatest_lower_bound(M2,X2,R,E))&~apply(R,M2,M1)))))))),
% 0.12/0.40 inference(pre_NNF_transformation,[status(thm)],[f23])).
% 0.12/0.40 fof(f171,plain,(
% 0.12/0.40 (order(sK16_skl,sK17_skl)&(((subset(sK18_skl,sK17_skl)&subset(sK19_skl,sK17_skl))&subset(sK18_skl,sK19_skl))&((greatest_lower_bound(sK20_skl,sK18_skl,sK16_skl,sK17_skl)&greatest_lower_bound(sK21_skl,sK19_skl,sK16_skl,sK17_skl))&~apply(sK16_skl,sK21_skl,sK20_skl))))),
% 0.12/0.40 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])).
% 0.12/0.40 fof(f175,plain,(
% 0.12/0.40 subset(sK18_skl,sK19_skl)),
% 0.12/0.40 inference(cnf_transformation,[status(thm)],[f171])).
% 0.12/0.40 fof(f176,plain,(
% 0.12/0.40 greatest_lower_bound(sK20_skl,sK18_skl,sK16_skl,sK17_skl)),
% 0.12/0.40 inference(cnf_transformation,[status(thm)],[f171])).
% 0.12/0.40 fof(f177,plain,(
% 0.12/0.40 greatest_lower_bound(sK21_skl,sK19_skl,sK16_skl,sK17_skl)),
% 0.12/0.40 inference(cnf_transformation,[status(thm)],[f171])).
% 0.12/0.40 fof(f178,plain,(
% 0.12/0.40 ~apply(sK16_skl,sK21_skl,sK20_skl)),
% 0.12/0.40 inference(cnf_transformation,[status(thm)],[f171])).
% 0.12/0.40 fof(f200,plain,(
% 0.12/0.40 member(sK20_skl,sK18_skl)),
% 0.12/0.40 inference(resolution,[status(thm)],[f164,f176])).
% 0.12/0.40 fof(f202,plain,(
% 0.12/0.40 lower_bound(sK21_skl,sK16_skl,sK19_skl)),
% 0.12/0.40 inference(resolution,[status(thm)],[f165,f177])).
% 0.12/0.40 fof(f405,plain,(
% 0.12/0.40 ![X0]: (~member(X0,sK19_skl)|apply(sK16_skl,sK21_skl,X0))),
% 0.12/0.40 inference(resolution,[status(thm)],[f113,f202])).
% 0.12/0.40 fof(f409,plain,(
% 0.12/0.40 ~member(sK20_skl,sK19_skl)),
% 0.12/0.40 inference(resolution,[status(thm)],[f405,f178])).
% 0.12/0.40 fof(f415,plain,(
% 0.12/0.40 ![X0]: (~subset(X0,sK19_skl)|~member(sK20_skl,X0))),
% 0.12/0.40 inference(resolution,[status(thm)],[f409,f28])).
% 0.12/0.40 fof(f418,plain,(
% 0.12/0.40 ~member(sK20_skl,sK18_skl)),
% 0.12/0.40 inference(resolution,[status(thm)],[f415,f175])).
% 0.12/0.40 fof(f422,plain,(
% 0.12/0.40 $false),
% 0.12/0.40 inference(forward_subsumption_resolution,[status(thm)],[f418,f200])).
% 0.12/0.40 % SZS output end CNFRefutation for theBenchmark.p
% 0.12/0.43 % Elapsed time: 0.092750 seconds
% 0.12/0.43 % CPU time: 0.423005 seconds
% 0.12/0.43 % Total memory used: 87.497 MB
% 0.12/0.43 % Net memory used: 86.964 MB
%------------------------------------------------------------------------------