%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SET997+1 : 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 : n012.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 02:12:58 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 : SET997+1 : 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 : n012.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 05:46:08 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.12/0.37 % 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(f4,axiom,(
% 0.12/0.39 (! [A,B] :( subset(A,B)<=> (! [C] :( in(C,A)=> in(C,B) ) )) )),
% 0.12/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.39 fof(f5,axiom,(
% 0.12/0.39 (! [A] :( ( relation(A)& function(A) )=> (! [B] :( B = relation_rng(A)<=> (! [C] :( in(C,B)<=> (? [D] :( in(D,relation_dom(A))& C = apply(A,D) ) )) )) )) )),
% 0.12/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.39 fof(f24,conjecture,(
% 0.12/0.39 (! [A,B] :( ( relation(B)& function(B) )=> ( (! [C] :~ ( in(C,A)& (! [D] :~ ( in(D,relation_dom(B))& C = apply(B,D) ) )))=> subset(A,relation_rng(B)) ) ) )),
% 0.12/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.39 fof(f25,negated_conjecture,(
% 0.12/0.39 ~((! [A,B] :( ( relation(B)& function(B) )=> ( (! [C] :~ ( in(C,A)& (! [D] :~ ( in(D,relation_dom(B))& C = apply(B,D) ) )))=> subset(A,relation_rng(B)) ) ) ))),
% 0.12/0.39 inference(negated_conjecture,[status(cth)],[f24])).
% 0.12/0.39 fof(f40,plain,(
% 0.12/0.39 ![A,B]: (subset(A,B)<=>(![C]: (~in(C,A)|in(C,B))))),
% 0.12/0.40 inference(pre_NNF_transformation,[status(thm)],[f4])).
% 0.12/0.40 fof(f41,plain,(
% 0.12/0.40 ![A,B]: ((~subset(A,B)|(![C]: (~in(C,A)|in(C,B))))&(subset(A,B)|(?[C]: (in(C,A)&~in(C,B)))))),
% 0.12/0.40 inference(NNF_transformation,[status(thm)],[f40])).
% 0.12/0.40 fof(f42,plain,(
% 0.12/0.40 (![A,B]: (~subset(A,B)|(![C]: (~in(C,A)|in(C,B)))))&(![A,B]: (subset(A,B)|(?[C]: (in(C,A)&~in(C,B)))))),
% 0.12/0.40 inference(miniscoping,[status(thm)],[f41])).
% 0.12/0.40 fof(f43,plain,(
% 0.12/0.40 (![A,B]: (~subset(A,B)|(![C]: (~in(C,A)|in(C,B)))))&(![A,B]: (subset(A,B)|(in(sK0_skl(B,A),A)&~in(sK0_skl(B,A),B))))),
% 0.12/0.40 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(C,sK0_skl(B,A))],[f42])).
% 0.12/0.40 fof(f45,plain,(
% 0.12/0.40 ![X0,X1]: (subset(X0,X1)|in(sK0_skl(X1,X0),X0))),
% 0.12/0.40 inference(cnf_transformation,[status(thm)],[f43])).
% 0.12/0.40 fof(f46,plain,(
% 0.12/0.40 ![X0,X1]: (subset(X0,X1)|~in(sK0_skl(X1,X0),X1))),
% 0.12/0.40 inference(cnf_transformation,[status(thm)],[f43])).
% 0.12/0.40 fof(f47,plain,(
% 0.12/0.40 ![A]: ((~relation(A)|~function(A))|(![B]: (B=relation_rng(A)<=>(![C]: (in(C,B)<=>(?[D]: (in(D,relation_dom(A))&C=apply(A,D))))))))),
% 0.12/0.40 inference(pre_NNF_transformation,[status(thm)],[f5])).
% 0.12/0.40 fof(f48,plain,(
% 0.12/0.40 ![A]: ((~relation(A)|~function(A))|(![B]: ((~B=relation_rng(A)|(![C]: ((~in(C,B)|(?[D]: (in(D,relation_dom(A))&C=apply(A,D))))&(in(C,B)|(![D]: (~in(D,relation_dom(A))|~C=apply(A,D)))))))&(B=relation_rng(A)|(?[C]: ((~in(C,B)|(![D]: (~in(D,relation_dom(A))|~C=apply(A,D))))&(in(C,B)|(?[D]: (in(D,relation_dom(A))&C=apply(A,D))))))))))),
% 0.12/0.40 inference(NNF_transformation,[status(thm)],[f47])).
% 0.12/0.40 fof(f49,plain,(
% 0.12/0.40 ![A]: ((~relation(A)|~function(A))|((![B]: (~B=relation_rng(A)|((![C]: (~in(C,B)|(?[D]: (in(D,relation_dom(A))&C=apply(A,D)))))&(![C]: (in(C,B)|(![D]: (~in(D,relation_dom(A))|~C=apply(A,D))))))))&(![B]: (B=relation_rng(A)|(?[C]: ((~in(C,B)|(![D]: (~in(D,relation_dom(A))|~C=apply(A,D))))&(in(C,B)|(?[D]: (in(D,relation_dom(A))&C=apply(A,D))))))))))),
% 0.12/0.40 inference(miniscoping,[status(thm)],[f48])).
% 0.12/0.40 fof(f50,plain,(
% 0.12/0.40 ![A]: ((~relation(A)|~function(A))|((![B]: (~B=relation_rng(A)|((![C]: (~in(C,B)|(in(sK1_skl(C,B,A),relation_dom(A))&C=apply(A,sK1_skl(C,B,A)))))&(![C]: (in(C,B)|(![D]: (~in(D,relation_dom(A))|~C=apply(A,D))))))))&(![B]: (B=relation_rng(A)|((~in(sK2_skl(B,A),B)|(![D]: (~in(D,relation_dom(A))|~sK2_skl(B,A)=apply(A,D))))&(in(sK2_skl(B,A),B)|(in(sK3_skl(B,A),relation_dom(A))&sK2_skl(B,A)=apply(A,sK3_skl(B,A)))))))))),
% 0.12/0.40 inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl,sK2_skl,sK3_skl]),skolemize(D,sK1_skl(C,B,A)),skolemize(C,sK2_skl(B,A)),skolemize(D,sK3_skl(B,A))],[f49])).
% 0.12/0.40 fof(f53,plain,(
% 0.12/0.40 ![X0,X1,X2,X3]: (~relation(X0)|~function(X0)|~X1=relation_rng(X0)|in(X2,X1)|~in(X3,relation_dom(X0))|~X2=apply(X0,X3))),
% 0.12/0.40 inference(cnf_transformation,[status(thm)],[f50])).
% 0.12/0.40 fof(f101,plain,(
% 0.12/0.40 (?[A,B]: ((relation(B)&function(B))&((![C]: (~in(C,A)|(?[D]: (in(D,relation_dom(B))&C=apply(B,D)))))&~subset(A,relation_rng(B)))))),
% 0.12/0.40 inference(pre_NNF_transformation,[status(thm)],[f25])).
% 0.12/0.40 fof(f102,plain,(
% 0.12/0.40 ?[B]: ((relation(B)&function(B))&(?[A]: ((![C]: (~in(C,A)|(?[D]: (in(D,relation_dom(B))&C=apply(B,D)))))&~subset(A,relation_rng(B)))))),
% 0.12/0.40 inference(miniscoping,[status(thm)],[f101])).
% 0.12/0.40 fof(f103,plain,(
% 0.12/0.40 ((relation(sK13_skl)&function(sK13_skl))&((![C]: (~in(C,sK14_skl)|(in(sK15_skl(C),relation_dom(sK13_skl))&C=apply(sK13_skl,sK15_skl(C)))))&~subset(sK14_skl,relation_rng(sK13_skl))))),
% 0.12/0.40 inference(skolemize,[status(esa),new_symbols(skolem,[sK13_skl,sK14_skl,sK15_skl]),skolemize(B,sK13_skl),skolemize(A,sK14_skl),skolemize(D,sK15_skl(C))],[f102])).
% 0.12/0.40 fof(f104,plain,(
% 0.12/0.40 relation(sK13_skl)),
% 0.12/0.40 inference(cnf_transformation,[status(thm)],[f103])).
% 0.12/0.40 fof(f105,plain,(
% 0.12/0.40 function(sK13_skl)),
% 0.12/0.40 inference(cnf_transformation,[status(thm)],[f103])).
% 0.12/0.40 fof(f106,plain,(
% 0.12/0.40 ![X0]: (~in(X0,sK14_skl)|in(sK15_skl(X0),relation_dom(sK13_skl)))),
% 0.12/0.40 inference(cnf_transformation,[status(thm)],[f103])).
% 0.12/0.40 fof(f107,plain,(
% 0.12/0.40 ![X0]: (~in(X0,sK14_skl)|X0=apply(sK13_skl,sK15_skl(X0)))),
% 0.12/0.40 inference(cnf_transformation,[status(thm)],[f103])).
% 0.12/0.40 fof(f108,plain,(
% 0.12/0.40 ~subset(sK14_skl,relation_rng(sK13_skl))),
% 0.12/0.40 inference(cnf_transformation,[status(thm)],[f103])).
% 0.12/0.40 fof(f133,plain,(
% 0.12/0.40 ![X0,X1]: (~relation(X0)|~function(X0)|in(apply(X0,X1),relation_rng(X0))|~in(X1,relation_dom(X0)))),
% 0.12/0.40 inference(destructive_equality_resolution,[status(thm)],[f53])).
% 0.12/0.40 fof(f138,plain,(
% 0.12/0.40 ![X0]: (subset(sK14_skl,X0)|in(sK15_skl(sK0_skl(X0,sK14_skl)),relation_dom(sK13_skl)))),
% 0.12/0.40 inference(resolution,[status(thm)],[f45,f106])).
% 0.12/0.40 fof(f147,plain,(
% 0.12/0.40 ![X0]: (sK0_skl(X0,sK14_skl)=apply(sK13_skl,sK15_skl(sK0_skl(X0,sK14_skl)))|subset(sK14_skl,X0))),
% 0.12/0.40 inference(resolution,[status(thm)],[f107,f45])).
% 0.12/0.40 fof(f148,plain,(
% 0.12/0.40 ![X0]: (subset(sK14_skl,X0)|~relation(sK13_skl)|~function(sK13_skl)|in(apply(sK13_skl,sK15_skl(sK0_skl(X0,sK14_skl))),relation_rng(sK13_skl)))),
% 0.12/0.40 inference(resolution,[status(thm)],[f138,f133])).
% 0.12/0.40 fof(f150,plain,(
% 0.12/0.40 ![X0]: (subset(sK14_skl,X0)|~function(sK13_skl)|in(apply(sK13_skl,sK15_skl(sK0_skl(X0,sK14_skl))),relation_rng(sK13_skl)))),
% 0.12/0.40 inference(forward_subsumption_resolution,[status(thm)],[f148,f104])).
% 0.12/0.40 fof(f170,plain,(
% 0.12/0.40 sK0_skl(relation_rng(sK13_skl),sK14_skl)=apply(sK13_skl,sK15_skl(sK0_skl(relation_rng(sK13_skl),sK14_skl)))),
% 0.12/0.40 inference(resolution,[status(thm)],[f147,f108])).
% 0.12/0.40 fof(f221,plain,(
% 0.12/0.40 ![X0]: (subset(sK14_skl,X0)|in(apply(sK13_skl,sK15_skl(sK0_skl(X0,sK14_skl))),relation_rng(sK13_skl)))),
% 0.12/0.40 inference(forward_subsumption_resolution,[status(thm)],[f150,f105])).
% 0.12/0.40 fof(f587,plain,(
% 0.12/0.40 subset(sK14_skl,relation_rng(sK13_skl))|in(sK0_skl(relation_rng(sK13_skl),sK14_skl),relation_rng(sK13_skl))),
% 0.12/0.40 inference(paramodulation,[status(thm)],[f170,f221])).
% 0.12/0.40 fof(f589,plain,(
% 0.12/0.40 in(sK0_skl(relation_rng(sK13_skl),sK14_skl),relation_rng(sK13_skl))),
% 0.12/0.40 inference(forward_subsumption_resolution,[status(thm)],[f587,f108])).
% 0.12/0.40 fof(f757,plain,(
% 0.12/0.40 subset(sK14_skl,relation_rng(sK13_skl))),
% 0.12/0.40 inference(resolution,[status(thm)],[f589,f46])).
% 0.12/0.40 fof(f763,plain,(
% 0.12/0.40 $false),
% 0.12/0.40 inference(forward_subsumption_resolution,[status(thm)],[f757,f108])).
% 0.12/0.40 % SZS output end CNFRefutation for theBenchmark.p
% 0.12/0.43 % Elapsed time: 0.058446 seconds
% 0.12/0.43 % CPU time: 0.198755 seconds
% 0.12/0.43 % Total memory used: 84.335 MB
% 0.12/0.43 % Net memory used: 84.057 MB
%------------------------------------------------------------------------------