%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SEU174+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/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 02:21:54 PM UTC 2026
% Result : Theorem 0.13s 0.42s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU174+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n016.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Sep 21 05:59:37 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.13/0.38 % Drodi V4.1.1
% 0.13/0.42 % Refutation found
% 0.13/0.42 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.42 % SZS output start CNFRefutation for theBenchmark
% 0.13/0.42 fof(f3,axiom,(
% 0.13/0.42 (! [A,B] :( element(B,powerset(powerset(A)))=> (! [C] :( element(C,powerset(powerset(A)))=> ( C = complements_of_subsets(A,B)<=> (! [D] :( element(D,powerset(A))=> ( in(D,C)<=> in(subset_complement(A,D),B) ) ) )) ) )) )),
% 0.13/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.42 fof(f13,axiom,(
% 0.13/0.42 (! [A,B] :( element(B,powerset(powerset(A)))=> complements_of_subsets(A,complements_of_subsets(A,B)) = B ) )),
% 0.13/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.42 fof(f15,axiom,(
% 0.13/0.42 (? [A] : empty(A) )),
% 0.13/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.42 fof(f16,axiom,(
% 0.13/0.42 (! [A] :(? [B] :( element(B,powerset(A))& empty(B) ) ))),
% 0.13/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.42 fof(f22,conjecture,(
% 0.13/0.42 (! [A,B] :( element(B,powerset(powerset(A)))=> ~ ( B != empty_set& complements_of_subsets(A,B) = empty_set ) ) )),
% 0.13/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.42 fof(f23,negated_conjecture,(
% 0.13/0.42 ~((! [A,B] :( element(B,powerset(powerset(A)))=> ~ ( B != empty_set& complements_of_subsets(A,B) = empty_set ) ) ))),
% 0.13/0.42 inference(negated_conjecture,[status(cth)],[f22])).
% 0.13/0.42 fof(f26,axiom,(
% 0.13/0.42 (! [A] :( empty(A)=> A = empty_set ) )),
% 0.13/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.42 fof(f27,axiom,(
% 0.13/0.42 (! [A,B] :~ ( in(A,B)& empty(B) ) )),
% 0.13/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.42 fof(f38,plain,(
% 0.13/0.42 ![A,B]: (~element(B,powerset(powerset(A)))|(![C]: (~element(C,powerset(powerset(A)))|(C=complements_of_subsets(A,B)<=>(![D]: (~element(D,powerset(A))|(in(D,C)<=>in(subset_complement(A,D),B))))))))),
% 0.13/0.42 inference(pre_NNF_transformation,[status(thm)],[f3])).
% 0.13/0.42 fof(f39,plain,(
% 0.13/0.42 ![A,B]: (~element(B,powerset(powerset(A)))|(![C]: (~element(C,powerset(powerset(A)))|((~C=complements_of_subsets(A,B)|(![D]: (~element(D,powerset(A))|((~in(D,C)|in(subset_complement(A,D),B))&(in(D,C)|~in(subset_complement(A,D),B))))))&(C=complements_of_subsets(A,B)|(?[D]: (element(D,powerset(A))&((~in(D,C)|~in(subset_complement(A,D),B))&(in(D,C)|in(subset_complement(A,D),B))))))))))),
% 0.13/0.42 inference(NNF_transformation,[status(thm)],[f38])).
% 0.13/0.42 fof(f40,plain,(
% 0.13/0.42 ![A,B]: (~element(B,powerset(powerset(A)))|(![C]: (~element(C,powerset(powerset(A)))|((~C=complements_of_subsets(A,B)|(![D]: (~element(D,powerset(A))|((~in(D,C)|in(subset_complement(A,D),B))&(in(D,C)|~in(subset_complement(A,D),B))))))&(C=complements_of_subsets(A,B)|(element(sK1_skl(C,B,A),powerset(A))&((~in(sK1_skl(C,B,A),C)|~in(subset_complement(A,sK1_skl(C,B,A)),B))&(in(sK1_skl(C,B,A),C)|in(subset_complement(A,sK1_skl(C,B,A)),B)))))))))),
% 0.13/0.42 inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(D,sK1_skl(C,B,A))],[f39])).
% 0.13/0.42 fof(f45,plain,(
% 0.13/0.42 ![X0,X1,X2]: (~element(X0,powerset(powerset(X1)))|~element(X2,powerset(powerset(X1)))|X2=complements_of_subsets(X1,X0)|in(sK1_skl(X2,X0,X1),X2)|in(subset_complement(X1,sK1_skl(X2,X0,X1)),X0))),
% 0.13/0.42 inference(cnf_transformation,[status(thm)],[f40])).
% 0.13/0.42 fof(f56,plain,(
% 0.13/0.42 ![A,B]: (~element(B,powerset(powerset(A)))|complements_of_subsets(A,complements_of_subsets(A,B))=B)),
% 0.13/0.42 inference(pre_NNF_transformation,[status(thm)],[f13])).
% 0.13/0.42 fof(f57,plain,(
% 0.13/0.42 ![X0,X1]: (~element(X0,powerset(powerset(X1)))|complements_of_subsets(X1,complements_of_subsets(X1,X0))=X0)),
% 0.13/0.42 inference(cnf_transformation,[status(thm)],[f56])).
% 0.13/0.42 fof(f62,plain,(
% 0.13/0.42 empty(sK4_skl)),
% 0.13/0.42 inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl]),skolemize(A,sK4_skl)],[f15])).
% 0.13/0.42 fof(f63,plain,(
% 0.13/0.42 empty(sK4_skl)),
% 0.13/0.42 inference(cnf_transformation,[status(thm)],[f62])).
% 0.13/0.42 fof(f64,plain,(
% 0.13/0.42 ![A]: (element(sK5_skl(A),powerset(A))&empty(sK5_skl(A)))),
% 0.13/0.42 inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl]),skolemize(B,sK5_skl(A))],[f16])).
% 0.13/0.42 fof(f65,plain,(
% 0.13/0.42 ![X0]: (element(sK5_skl(X0),powerset(X0)))),
% 0.13/0.42 inference(cnf_transformation,[status(thm)],[f64])).
% 0.13/0.42 fof(f66,plain,(
% 0.13/0.42 ![X0]: (empty(sK5_skl(X0)))),
% 0.13/0.42 inference(cnf_transformation,[status(thm)],[f64])).
% 0.13/0.42 fof(f79,plain,(
% 0.13/0.42 (?[A,B]: (element(B,powerset(powerset(A)))&(~B=empty_set&complements_of_subsets(A,B)=empty_set)))),
% 0.13/0.42 inference(pre_NNF_transformation,[status(thm)],[f23])).
% 0.13/0.42 fof(f80,plain,(
% 0.13/0.42 (element(sK8_skl,powerset(powerset(sK7_skl)))&(~sK8_skl=empty_set&complements_of_subsets(sK7_skl,sK8_skl)=empty_set))),
% 0.13/0.42 inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl,sK8_skl]),skolemize(A,sK7_skl),skolemize(B,sK8_skl)],[f79])).
% 0.13/0.42 fof(f81,plain,(
% 0.13/0.42 element(sK8_skl,powerset(powerset(sK7_skl)))),
% 0.13/0.42 inference(cnf_transformation,[status(thm)],[f80])).
% 0.13/0.42 fof(f82,plain,(
% 0.13/0.42 ~sK8_skl=empty_set),
% 0.13/0.42 inference(cnf_transformation,[status(thm)],[f80])).
% 0.13/0.42 fof(f83,plain,(
% 0.13/0.42 complements_of_subsets(sK7_skl,sK8_skl)=empty_set),
% 0.13/0.42 inference(cnf_transformation,[status(thm)],[f80])).
% 0.13/0.42 fof(f90,plain,(
% 0.13/0.42 ![A]: (~empty(A)|A=empty_set)),
% 0.13/0.42 inference(pre_NNF_transformation,[status(thm)],[f26])).
% 0.13/0.42 fof(f91,plain,(
% 0.13/0.42 ![X0]: (~empty(X0)|X0=empty_set)),
% 0.13/0.42 inference(cnf_transformation,[status(thm)],[f90])).
% 0.13/0.42 fof(f92,plain,(
% 0.13/0.42 ![A,B]: (~in(A,B)|~empty(B))),
% 0.13/0.42 inference(pre_NNF_transformation,[status(thm)],[f27])).
% 0.13/0.42 fof(f93,plain,(
% 0.13/0.42 ![B]: ((![A]: ~in(A,B))|~empty(B))),
% 0.13/0.42 inference(miniscoping,[status(thm)],[f92])).
% 0.13/0.42 fof(f94,plain,(
% 0.13/0.42 ![X0,X1]: (~in(X0,X1)|~empty(X1))),
% 0.13/0.42 inference(cnf_transformation,[status(thm)],[f93])).
% 0.13/0.42 fof(f104,plain,(
% 0.13/0.42 complements_of_subsets(sK7_skl,complements_of_subsets(sK7_skl,sK8_skl))=sK8_skl),
% 0.13/0.42 inference(resolution,[status(thm)],[f57,f81])).
% 0.13/0.42 fof(f105,plain,(
% 0.13/0.42 complements_of_subsets(sK7_skl,empty_set)=sK8_skl),
% 0.13/0.42 inference(forward_demodulation,[status(thm)],[f83,f104])).
% 0.13/0.42 fof(f112,plain,(
% 0.13/0.42 sK4_skl=empty_set),
% 0.13/0.42 inference(resolution,[status(thm)],[f63,f91])).
% 0.13/0.42 fof(f125,plain,(
% 0.13/0.42 complements_of_subsets(sK7_skl,sK4_skl)=sK8_skl),
% 0.13/0.42 inference(backward_demodulation,[status(thm)],[f112,f105])).
% 0.13/0.42 fof(f127,plain,(
% 0.13/0.42 ![X0]: (~empty(X0)|X0=sK4_skl)),
% 0.13/0.42 inference(backward_demodulation,[status(thm)],[f112,f91])).
% 0.13/0.42 fof(f130,plain,(
% 0.13/0.42 ~sK8_skl=sK4_skl),
% 0.13/0.42 inference(backward_demodulation,[status(thm)],[f112,f82])).
% 0.13/0.42 fof(f138,plain,(
% 0.13/0.42 ![X0]: (sK5_skl(X0)=sK4_skl)),
% 0.13/0.42 inference(resolution,[status(thm)],[f66,f127])).
% 0.13/0.42 fof(f205,plain,(
% 0.13/0.42 ![X0]: (~in(X0,sK4_skl))),
% 0.13/0.42 inference(resolution,[status(thm)],[f94,f63])).
% 0.13/0.42 fof(f226,plain,(
% 0.13/0.42 ![X0]: (element(sK4_skl,powerset(X0)))),
% 0.13/0.42 inference(forward_demodulation,[status(thm)],[f138,f65])).
% 0.13/0.42 fof(f229,plain,(
% 0.13/0.42 ![X0,X1]: (~element(X0,powerset(powerset(X1)))|sK4_skl=complements_of_subsets(X1,X0)|in(sK1_skl(sK4_skl,X0,X1),sK4_skl)|in(subset_complement(X1,sK1_skl(sK4_skl,X0,X1)),X0))),
% 0.13/0.42 inference(resolution,[status(thm)],[f226,f45])).
% 0.13/0.42 fof(f236,plain,(
% 0.13/0.42 ![X0,X1]: (~element(X0,powerset(powerset(X1)))|sK4_skl=complements_of_subsets(X1,X0)|in(subset_complement(X1,sK1_skl(sK4_skl,X0,X1)),X0))),
% 0.13/0.42 inference(forward_subsumption_resolution,[status(thm)],[f229,f205])).
% 0.13/0.42 fof(f353,plain,(
% 0.13/0.42 ![X0]: (~element(sK4_skl,powerset(powerset(X0)))|sK4_skl=complements_of_subsets(X0,sK4_skl))),
% 0.13/0.42 inference(resolution,[status(thm)],[f236,f205])).
% 0.13/0.42 fof(f359,plain,(
% 0.13/0.42 ![X0]: (sK4_skl=complements_of_subsets(X0,sK4_skl))),
% 0.13/0.42 inference(forward_subsumption_resolution,[status(thm)],[f353,f226])).
% 0.13/0.42 fof(f474,plain,(
% 0.13/0.42 sK4_skl=sK8_skl),
% 0.13/0.42 inference(backward_demodulation,[status(thm)],[f359,f125])).
% 0.13/0.42 fof(f477,plain,(
% 0.13/0.42 $false),
% 0.13/0.42 inference(forward_subsumption_resolution,[status(thm)],[f474,f130])).
% 0.13/0.42 % SZS output end CNFRefutation for theBenchmark.p
% 0.13/0.44 % Elapsed time: 0.074573 seconds
% 0.13/0.44 % CPU time: 0.244056 seconds
% 0.13/0.44 % Total memory used: 105.203 MB
% 0.13/0.44 % Net memory used: 104.826 MB
%------------------------------------------------------------------------------