%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SET798+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 : n018.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 0.40s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET798+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
% 0.08/0.35 % Computer : n018.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 05:40:43 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 0.13/0.40 % Refutation found
% 0.13/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.40 % SZS output start CNFRefutation for theBenchmark
% 0.13/0.40 fof(f1,axiom,(
% 0.13/0.40 (! [A,B] :( subset(A,B)<=> (! [X] :( member(X,A)=> member(X,B) ) )) )),
% 0.13/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.40 fof(f15,axiom,(
% 0.13/0.40 (! [R,E,M] :( lower_bound(M,R,E)<=> (! [X] :( member(X,E)=> apply(R,M,X) ) )) )),
% 0.13/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.40 fof(f22,conjecture,(
% 0.13/0.40 (! [R,E] :( order(R,E)=> (! [X,Y] :( ( subset(X,E)& subset(Y,E)& subset(X,Y) )=> (! [M] :( lower_bound(M,R,Y)=> lower_bound(M,R,X) ) )) )) )),
% 0.13/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.40 fof(f23,negated_conjecture,(
% 0.13/0.40 ~((! [R,E] :( order(R,E)=> (! [X,Y] :( ( subset(X,E)& subset(Y,E)& subset(X,Y) )=> (! [M] :( lower_bound(M,R,Y)=> lower_bound(M,R,X) ) )) )) ))),
% 0.13/0.40 inference(negated_conjecture,[status(cth)],[f22])).
% 0.13/0.40 fof(f24,plain,(
% 0.13/0.40 ![A,B]: (subset(A,B)<=>(![X]: (~member(X,A)|member(X,B))))),
% 0.13/0.40 inference(pre_NNF_transformation,[status(thm)],[f1])).
% 0.13/0.40 fof(f25,plain,(
% 0.13/0.40 ![A,B]: ((~subset(A,B)|(![X]: (~member(X,A)|member(X,B))))&(subset(A,B)|(?[X]: (member(X,A)&~member(X,B)))))),
% 0.13/0.40 inference(NNF_transformation,[status(thm)],[f24])).
% 0.13/0.40 fof(f26,plain,(
% 0.13/0.40 (![A,B]: (~subset(A,B)|(![X]: (~member(X,A)|member(X,B)))))&(![A,B]: (subset(A,B)|(?[X]: (member(X,A)&~member(X,B)))))),
% 0.13/0.40 inference(miniscoping,[status(thm)],[f25])).
% 0.13/0.40 fof(f27,plain,(
% 0.13/0.40 (![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))))),
% 0.13/0.40 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(X,sK0_skl(B,A))],[f26])).
% 0.13/0.40 fof(f28,plain,(
% 0.13/0.40 ![X0,X1,X2]: (~subset(X0,X1)|~member(X2,X0)|member(X2,X1))),
% 0.13/0.40 inference(cnf_transformation,[status(thm)],[f27])).
% 0.13/0.40 fof(f109,plain,(
% 0.13/0.40 ![R,E,M]: (lower_bound(M,R,E)<=>(![X]: (~member(X,E)|apply(R,M,X))))),
% 0.13/0.40 inference(pre_NNF_transformation,[status(thm)],[f15])).
% 0.13/0.40 fof(f110,plain,(
% 0.13/0.40 ![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)))))),
% 0.13/0.40 inference(NNF_transformation,[status(thm)],[f109])).
% 0.13/0.40 fof(f111,plain,(
% 0.13/0.40 (![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)))))),
% 0.13/0.40 inference(miniscoping,[status(thm)],[f110])).
% 0.13/0.40 fof(f112,plain,(
% 0.13/0.40 (![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)))))),
% 0.13/0.40 inference(skolemize,[status(esa),new_symbols(skolem,[sK9_skl]),skolemize(X,sK9_skl(M,E,R))],[f111])).
% 0.13/0.40 fof(f113,plain,(
% 0.13/0.40 ![X0,X1,X2,X3]: (~lower_bound(X0,X1,X2)|~member(X3,X2)|apply(X1,X0,X3))),
% 0.13/0.40 inference(cnf_transformation,[status(thm)],[f112])).
% 0.13/0.40 fof(f114,plain,(
% 0.13/0.40 ![X0,X1,X2]: (lower_bound(X0,X1,X2)|member(sK9_skl(X0,X2,X1),X2))),
% 0.13/0.40 inference(cnf_transformation,[status(thm)],[f112])).
% 0.13/0.40 fof(f115,plain,(
% 0.13/0.40 ![X0,X1,X2]: (lower_bound(X0,X1,X2)|~apply(X1,X0,sK9_skl(X0,X2,X1)))),
% 0.13/0.40 inference(cnf_transformation,[status(thm)],[f112])).
% 0.13/0.40 fof(f170,plain,(
% 0.13/0.40 (?[R,E]: (order(R,E)&(?[X,Y]: (((subset(X,E)&subset(Y,E))&subset(X,Y))&(?[M]: (lower_bound(M,R,Y)&~lower_bound(M,R,X)))))))),
% 0.13/0.40 inference(pre_NNF_transformation,[status(thm)],[f23])).
% 0.13/0.40 fof(f171,plain,(
% 0.13/0.40 (order(sK16_skl,sK17_skl)&(((subset(sK18_skl,sK17_skl)&subset(sK19_skl,sK17_skl))&subset(sK18_skl,sK19_skl))&(lower_bound(sK20_skl,sK16_skl,sK19_skl)&~lower_bound(sK20_skl,sK16_skl,sK18_skl))))),
% 0.13/0.40 inference(skolemize,[status(esa),new_symbols(skolem,[sK16_skl,sK17_skl,sK18_skl,sK19_skl,sK20_skl]),skolemize(R,sK16_skl),skolemize(E,sK17_skl),skolemize(X,sK18_skl),skolemize(Y,sK19_skl),skolemize(M,sK20_skl)],[f170])).
% 0.13/0.40 fof(f175,plain,(
% 0.13/0.40 subset(sK18_skl,sK19_skl)),
% 0.13/0.40 inference(cnf_transformation,[status(thm)],[f171])).
% 0.13/0.40 fof(f176,plain,(
% 0.13/0.40 lower_bound(sK20_skl,sK16_skl,sK19_skl)),
% 0.13/0.40 inference(cnf_transformation,[status(thm)],[f171])).
% 0.13/0.40 fof(f177,plain,(
% 0.13/0.40 ~lower_bound(sK20_skl,sK16_skl,sK18_skl)),
% 0.13/0.40 inference(cnf_transformation,[status(thm)],[f171])).
% 0.13/0.40 fof(f351,plain,(
% 0.13/0.40 ![X0,X1,X2,X3]: (lower_bound(X0,X1,X2)|~lower_bound(X0,X1,X3)|~member(sK9_skl(X0,X2,X1),X3))),
% 0.13/0.41 inference(resolution,[status(thm)],[f115,f113])).
% 0.13/0.41 fof(f503,plain,(
% 0.13/0.41 ![X0]: (lower_bound(sK20_skl,sK16_skl,X0)|~member(sK9_skl(sK20_skl,X0,sK16_skl),sK19_skl))),
% 0.13/0.41 inference(resolution,[status(thm)],[f351,f176])).
% 0.13/0.41 fof(f573,plain,(
% 0.13/0.41 ![X0,X1]: (lower_bound(sK20_skl,sK16_skl,X0)|~subset(X1,sK19_skl)|~member(sK9_skl(sK20_skl,X0,sK16_skl),X1))),
% 0.13/0.41 inference(resolution,[status(thm)],[f503,f28])).
% 0.13/0.41 fof(f586,plain,(
% 0.13/0.41 ![X0]: (lower_bound(sK20_skl,sK16_skl,X0)|~member(sK9_skl(sK20_skl,X0,sK16_skl),sK18_skl))),
% 0.13/0.41 inference(resolution,[status(thm)],[f573,f175])).
% 0.13/0.41 fof(f749,plain,(
% 0.13/0.41 lower_bound(sK20_skl,sK16_skl,sK18_skl)|lower_bound(sK20_skl,sK16_skl,sK18_skl)),
% 0.13/0.41 inference(resolution,[status(thm)],[f586,f114])).
% 0.13/0.41 fof(f751,plain,(
% 0.13/0.41 lower_bound(sK20_skl,sK16_skl,sK18_skl)),
% 0.13/0.41 inference(duplicate_literals_removal,[status(thm)],[f749])).
% 0.13/0.41 fof(f752,plain,(
% 0.13/0.41 $false),
% 0.13/0.41 inference(forward_subsumption_resolution,[status(thm)],[f751,f177])).
% 0.13/0.41 % SZS output end CNFRefutation for theBenchmark.p
% 0.13/0.43 % Elapsed time: 0.066046 seconds
% 0.13/0.43 % CPU time: 0.285677 seconds
% 0.13/0.43 % Total memory used: 78.867 MB
% 0.13/0.43 % Net memory used: 78.560 MB
%------------------------------------------------------------------------------