%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SEU113+1 : 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 : n002.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 02:21:42 PM UTC 2026
% Result : Theorem 0.12s 0.41s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU113+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n002.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 05:53:18 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.12/0.41 % Refutation found
% 0.12/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.41 % SZS output start CNFRefutation for theBenchmark
% 0.12/0.41 fof(f7,axiom,(
% 0.12/0.41 (! [A,B] :( subset(A,B)<=> (! [C] :( in(C,A)=> in(C,B) ) )) )),
% 0.12/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.41 fof(f8,axiom,(
% 0.12/0.41 (! [A,B] :( preboolean(B)=> ( B = finite_subsets(A)<=> (! [C] :( in(C,B)<=> ( subset(C,A)& finite(C) ) ) )) ) )),
% 0.12/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.41 fof(f9,axiom,(
% 0.12/0.41 (! [A] : preboolean(finite_subsets(A)) )),
% 0.12/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.41 fof(f11,axiom,(
% 0.12/0.41 (! [A] :( ~ empty(powerset(A))& cup_closed(powerset(A))& diff_closed(powerset(A))& preboolean(powerset(A)) ) )),
% 0.12/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.41 fof(f26,conjecture,(
% 0.12/0.41 (! [A] : subset(finite_subsets(A),powerset(A)) )),
% 0.12/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.41 fof(f27,negated_conjecture,(
% 0.12/0.41 ~((! [A] : subset(finite_subsets(A),powerset(A)) ))),
% 0.12/0.41 inference(negated_conjecture,[status(cth)],[f26])).
% 0.12/0.41 fof(f28,axiom,(
% 0.12/0.41 (! [A,B] :( element(A,B)=> ( empty(B)| in(A,B) ) ) )),
% 0.12/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.41 fof(f29,axiom,(
% 0.12/0.41 (! [A,B] :( element(A,powerset(B))<=> subset(A,B) ) )),
% 0.12/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.41 fof(f49,plain,(
% 0.12/0.41 ![A,B]: (subset(A,B)<=>(![C]: (~in(C,A)|in(C,B))))),
% 0.12/0.41 inference(pre_NNF_transformation,[status(thm)],[f7])).
% 0.12/0.41 fof(f50,plain,(
% 0.12/0.41 ![A,B]: ((~subset(A,B)|(![C]: (~in(C,A)|in(C,B))))&(subset(A,B)|(?[C]: (in(C,A)&~in(C,B)))))),
% 0.12/0.41 inference(NNF_transformation,[status(thm)],[f49])).
% 0.12/0.41 fof(f51,plain,(
% 0.12/0.41 (![A,B]: (~subset(A,B)|(![C]: (~in(C,A)|in(C,B)))))&(![A,B]: (subset(A,B)|(?[C]: (in(C,A)&~in(C,B)))))),
% 0.12/0.41 inference(miniscoping,[status(thm)],[f50])).
% 0.12/0.41 fof(f52,plain,(
% 0.12/0.41 (![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))))),
% 0.12/0.41 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(C,sK0_skl(B,A))],[f51])).
% 0.12/0.41 fof(f54,plain,(
% 0.12/0.41 ![X0,X1]: (subset(X0,X1)|in(sK0_skl(X1,X0),X0))),
% 0.12/0.41 inference(cnf_transformation,[status(thm)],[f52])).
% 0.12/0.41 fof(f55,plain,(
% 0.12/0.41 ![X0,X1]: (subset(X0,X1)|~in(sK0_skl(X1,X0),X1))),
% 0.12/0.41 inference(cnf_transformation,[status(thm)],[f52])).
% 0.12/0.41 fof(f56,plain,(
% 0.12/0.41 ![A,B]: (~preboolean(B)|(B=finite_subsets(A)<=>(![C]: (in(C,B)<=>(subset(C,A)&finite(C))))))),
% 0.12/0.41 inference(pre_NNF_transformation,[status(thm)],[f8])).
% 0.12/0.41 fof(f57,plain,(
% 0.12/0.41 ![A,B]: (~preboolean(B)|((~B=finite_subsets(A)|(![C]: ((~in(C,B)|(subset(C,A)&finite(C)))&(in(C,B)|(~subset(C,A)|~finite(C))))))&(B=finite_subsets(A)|(?[C]: ((~in(C,B)|(~subset(C,A)|~finite(C)))&(in(C,B)|(subset(C,A)&finite(C))))))))),
% 0.12/0.41 inference(NNF_transformation,[status(thm)],[f56])).
% 0.12/0.41 fof(f58,plain,(
% 0.12/0.41 ![B]: (~preboolean(B)|((![A]: (~B=finite_subsets(A)|((![C]: (~in(C,B)|(subset(C,A)&finite(C))))&(![C]: (in(C,B)|(~subset(C,A)|~finite(C)))))))&(![A]: (B=finite_subsets(A)|(?[C]: ((~in(C,B)|(~subset(C,A)|~finite(C)))&(in(C,B)|(subset(C,A)&finite(C)))))))))),
% 0.12/0.41 inference(miniscoping,[status(thm)],[f57])).
% 0.12/0.41 fof(f59,plain,(
% 0.12/0.41 ![B]: (~preboolean(B)|((![A]: (~B=finite_subsets(A)|((![C]: (~in(C,B)|(subset(C,A)&finite(C))))&(![C]: (in(C,B)|(~subset(C,A)|~finite(C)))))))&(![A]: (B=finite_subsets(A)|((~in(sK1_skl(A,B),B)|(~subset(sK1_skl(A,B),A)|~finite(sK1_skl(A,B))))&(in(sK1_skl(A,B),B)|(subset(sK1_skl(A,B),A)&finite(sK1_skl(A,B)))))))))),
% 0.12/0.41 inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(C,sK1_skl(A,B))],[f58])).
% 0.12/0.41 fof(f60,plain,(
% 0.12/0.41 ![X0,X1,X2]: (~preboolean(X0)|~X0=finite_subsets(X1)|~in(X2,X0)|subset(X2,X1))),
% 0.12/0.41 inference(cnf_transformation,[status(thm)],[f59])).
% 0.12/0.41 fof(f66,plain,(
% 0.12/0.41 ![X0]: (preboolean(finite_subsets(X0)))),
% 0.12/0.41 inference(cnf_transformation,[status(thm)],[f9])).
% 0.12/0.41 fof(f69,plain,(
% 0.12/0.41 (((![A]: ~empty(powerset(A)))&(![A]: cup_closed(powerset(A))))&(![A]: diff_closed(powerset(A))))&(![A]: preboolean(powerset(A)))),
% 0.12/0.41 inference(miniscoping,[status(thm)],[f11])).
% 0.12/0.41 fof(f70,plain,(
% 0.12/0.41 ![X0]: (~empty(powerset(X0)))),
% 0.12/0.41 inference(cnf_transformation,[status(thm)],[f69])).
% 0.12/0.41 fof(f126,plain,(
% 0.12/0.41 (?[A]: ~subset(finite_subsets(A),powerset(A)))),
% 0.12/0.41 inference(pre_NNF_transformation,[status(thm)],[f27])).
% 0.12/0.41 fof(f127,plain,(
% 0.12/0.41 ~subset(finite_subsets(sK12_skl),powerset(sK12_skl))),
% 0.12/0.41 inference(skolemize,[status(esa),new_symbols(skolem,[sK12_skl]),skolemize(A,sK12_skl)],[f126])).
% 0.12/0.41 fof(f128,plain,(
% 0.12/0.41 ~subset(finite_subsets(sK12_skl),powerset(sK12_skl))),
% 0.12/0.41 inference(cnf_transformation,[status(thm)],[f127])).
% 0.12/0.41 fof(f129,plain,(
% 0.12/0.41 ![A,B]: (~element(A,B)|(empty(B)|in(A,B)))),
% 0.12/0.41 inference(pre_NNF_transformation,[status(thm)],[f28])).
% 0.12/0.41 fof(f130,plain,(
% 0.12/0.41 ![X0,X1]: (~element(X0,X1)|empty(X1)|in(X0,X1))),
% 0.12/0.41 inference(cnf_transformation,[status(thm)],[f129])).
% 0.12/0.41 fof(f131,plain,(
% 0.12/0.41 ![A,B]: ((~element(A,powerset(B))|subset(A,B))&(element(A,powerset(B))|~subset(A,B)))),
% 0.12/0.41 inference(NNF_transformation,[status(thm)],[f29])).
% 0.12/0.41 fof(f132,plain,(
% 0.12/0.41 (![A,B]: (~element(A,powerset(B))|subset(A,B)))&(![A,B]: (element(A,powerset(B))|~subset(A,B)))),
% 0.12/0.41 inference(miniscoping,[status(thm)],[f131])).
% 0.12/0.41 fof(f134,plain,(
% 0.12/0.41 ![X0,X1]: (element(X0,powerset(X1))|~subset(X0,X1))),
% 0.12/0.41 inference(cnf_transformation,[status(thm)],[f132])).
% 0.12/0.41 fof(f149,plain,(
% 0.12/0.41 ![X0,X1]: (~preboolean(finite_subsets(X0))|~in(X1,finite_subsets(X0))|subset(X1,X0))),
% 0.12/0.41 inference(destructive_equality_resolution,[status(thm)],[f60])).
% 0.12/0.41 fof(f153,plain,(
% 0.12/0.41 ![X0,X1]: (~in(X0,finite_subsets(X1))|subset(X0,X1))),
% 0.12/0.41 inference(backward_subsumption_resolution,[status(thm)],[f149,f66])).
% 0.12/0.41 fof(f166,plain,(
% 0.12/0.41 ![X0,X1]: (subset(finite_subsets(X0),X1)|subset(sK0_skl(X1,finite_subsets(X0)),X0))),
% 0.12/0.41 inference(resolution,[status(thm)],[f54,f153])).
% 0.12/0.41 fof(f174,plain,(
% 0.12/0.41 ![X0,X1]: (subset(finite_subsets(X0),X1)|element(sK0_skl(X1,finite_subsets(X0)),powerset(X0)))),
% 0.12/0.41 inference(resolution,[status(thm)],[f166,f134])).
% 0.12/0.41 fof(f365,plain,(
% 0.12/0.41 ![X0,X1]: (empty(powerset(X0))|in(sK0_skl(X1,finite_subsets(X0)),powerset(X0))|subset(finite_subsets(X0),X1))),
% 0.12/0.41 inference(resolution,[status(thm)],[f130,f174])).
% 0.12/0.41 fof(f373,plain,(
% 0.12/0.41 ![X0,X1]: (in(sK0_skl(X0,finite_subsets(X1)),powerset(X1))|subset(finite_subsets(X1),X0))),
% 0.12/0.41 inference(forward_subsumption_resolution,[status(thm)],[f365,f70])).
% 0.12/0.41 fof(f1177,plain,(
% 0.12/0.41 ![X0]: (subset(finite_subsets(X0),powerset(X0))|subset(finite_subsets(X0),powerset(X0)))),
% 0.12/0.41 inference(resolution,[status(thm)],[f373,f55])).
% 0.12/0.41 fof(f1181,plain,(
% 0.12/0.41 ![X0]: (subset(finite_subsets(X0),powerset(X0)))),
% 0.12/0.41 inference(duplicate_literals_removal,[status(thm)],[f1177])).
% 0.12/0.41 fof(f1191,plain,(
% 0.12/0.41 $false),
% 0.12/0.41 inference(backward_subsumption_resolution,[status(thm)],[f128,f1181])).
% 0.12/0.41 % SZS output end CNFRefutation for theBenchmark.p
% 0.12/0.44 % Elapsed time: 0.076005 seconds
% 0.12/0.44 % CPU time: 0.292271 seconds
% 0.12/0.44 % Total memory used: 85.035 MB
% 0.12/0.44 % Net memory used: 84.496 MB
%------------------------------------------------------------------------------