%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SEU328+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 : n013.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 02:22:20 PM UTC 2026
% Result : Theorem 1.10s 0.63s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU328+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n013.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 06:11:37 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.13/0.37 % Drodi V4.1.1
% 1.10/0.63 % Refutation found
% 1.10/0.63 % SZS status Theorem for theBenchmark: Theorem is valid
% 1.10/0.63 % SZS output start CNFRefutation for theBenchmark
% 1.10/0.63 fof(f17,axiom,(
% 1.10/0.63 (! [A] : cast_to_subset(A) = A )),
% 1.10/0.63 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.10/0.63 fof(f18,axiom,(
% 1.10/0.63 (! [A,B] :( element(B,powerset(A))=> subset_complement(A,B) = set_difference(A,B) ) )),
% 1.10/0.63 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.10/0.63 fof(f22,axiom,(
% 1.10/0.63 (! [A] : element(cast_to_subset(A),powerset(A)) )),
% 1.10/0.63 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.10/0.63 fof(f27,axiom,(
% 1.10/0.63 (! [A,B] :( element(B,powerset(powerset(A)))=> element(meet_of_subsets(A,B),powerset(A)) ) )),
% 1.10/0.63 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.10/0.63 fof(f45,axiom,(
% 1.10/0.63 (! [A,B] :( element(B,powerset(powerset(A)))=> meet_of_subsets(A,B) = set_meet(B) ) )),
% 1.10/0.63 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.10/0.63 fof(f46,axiom,(
% 1.10/0.63 (! [A,B,C] :( ( element(B,powerset(A))& element(C,powerset(A)) )=> subset_difference(A,B,C) = set_difference(B,C) ) )),
% 1.10/0.63 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.10/0.63 fof(f48,conjecture,(
% 1.10/0.63 (! [A,B] :( element(B,powerset(powerset(A)))=> ( B != empty_set=> union_of_subsets(A,complements_of_subsets(A,B)) = subset_complement(A,meet_of_subsets(A,B)) ) ) )),
% 1.10/0.63 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.10/0.63 fof(f49,negated_conjecture,(
% 1.10/0.63 ~((! [A,B] :( element(B,powerset(powerset(A)))=> ( B != empty_set=> union_of_subsets(A,complements_of_subsets(A,B)) = subset_complement(A,meet_of_subsets(A,B)) ) ) ))),
% 1.10/0.63 inference(negated_conjecture,[status(cth)],[f48])).
% 1.10/0.63 fof(f54,axiom,(
% 1.10/0.63 (! [A,B] :( element(B,powerset(powerset(A)))=> ( B != empty_set=> union_of_subsets(A,complements_of_subsets(A,B)) = subset_difference(A,cast_to_subset(A),meet_of_subsets(A,B)) ) ) )),
% 1.10/0.63 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.10/0.63 fof(f117,plain,(
% 1.10/0.63 ![X0]: (cast_to_subset(X0)=X0)),
% 1.10/0.63 inference(cnf_transformation,[status(thm)],[f17])).
% 1.10/0.63 fof(f118,plain,(
% 1.10/0.63 ![A,B]: (~element(B,powerset(A))|subset_complement(A,B)=set_difference(A,B))),
% 1.10/0.63 inference(pre_NNF_transformation,[status(thm)],[f18])).
% 1.10/0.63 fof(f119,plain,(
% 1.10/0.63 ![X0,X1]: (~element(X0,powerset(X1))|subset_complement(X1,X0)=set_difference(X1,X0))),
% 1.10/0.63 inference(cnf_transformation,[status(thm)],[f118])).
% 1.10/0.63 fof(f120,plain,(
% 1.10/0.63 ![X0]: (element(cast_to_subset(X0),powerset(X0)))),
% 1.10/0.63 inference(cnf_transformation,[status(thm)],[f22])).
% 1.10/0.63 fof(f125,plain,(
% 1.10/0.63 ![A,B]: (~element(B,powerset(powerset(A)))|element(meet_of_subsets(A,B),powerset(A)))),
% 1.10/0.63 inference(pre_NNF_transformation,[status(thm)],[f27])).
% 1.10/0.63 fof(f126,plain,(
% 1.10/0.63 ![X0,X1]: (~element(X0,powerset(powerset(X1)))|element(meet_of_subsets(X1,X0),powerset(X1)))),
% 1.10/0.63 inference(cnf_transformation,[status(thm)],[f125])).
% 1.10/0.63 fof(f185,plain,(
% 1.10/0.63 ![A,B]: (~element(B,powerset(powerset(A)))|meet_of_subsets(A,B)=set_meet(B))),
% 1.10/0.63 inference(pre_NNF_transformation,[status(thm)],[f45])).
% 1.10/0.63 fof(f186,plain,(
% 1.10/0.63 ![X0,X1]: (~element(X0,powerset(powerset(X1)))|meet_of_subsets(X1,X0)=set_meet(X0))),
% 1.10/0.63 inference(cnf_transformation,[status(thm)],[f185])).
% 1.10/0.63 fof(f187,plain,(
% 1.10/0.63 ![A,B,C]: ((~element(B,powerset(A))|~element(C,powerset(A)))|subset_difference(A,B,C)=set_difference(B,C))),
% 1.10/0.63 inference(pre_NNF_transformation,[status(thm)],[f46])).
% 1.10/0.63 fof(f188,plain,(
% 1.10/0.63 ![X0,X1,X2]: (~element(X0,powerset(X1))|~element(X2,powerset(X1))|subset_difference(X1,X0,X2)=set_difference(X0,X2))),
% 1.10/0.63 inference(cnf_transformation,[status(thm)],[f187])).
% 1.10/0.63 fof(f191,plain,(
% 1.10/0.63 (?[A,B]: (element(B,powerset(powerset(A)))&(~B=empty_set&~union_of_subsets(A,complements_of_subsets(A,B))=subset_complement(A,meet_of_subsets(A,B)))))),
% 1.10/0.63 inference(pre_NNF_transformation,[status(thm)],[f49])).
% 1.10/0.63 fof(f192,plain,(
% 1.10/0.63 (element(sK5_skl,powerset(powerset(sK4_skl)))&(~sK5_skl=empty_set&~union_of_subsets(sK4_skl,complements_of_subsets(sK4_skl,sK5_skl))=subset_complement(sK4_skl,meet_of_subsets(sK4_skl,sK5_skl))))),
% 1.10/0.63 inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl,sK5_skl]),skolemize(A,sK4_skl),skolemize(B,sK5_skl)],[f191])).
% 1.10/0.63 fof(f193,plain,(
% 1.10/0.63 element(sK5_skl,powerset(powerset(sK4_skl)))),
% 1.10/0.63 inference(cnf_transformation,[status(thm)],[f192])).
% 1.10/0.63 fof(f194,plain,(
% 1.10/0.63 ~sK5_skl=empty_set),
% 1.10/0.63 inference(cnf_transformation,[status(thm)],[f192])).
% 1.10/0.63 fof(f195,plain,(
% 1.10/0.63 ~union_of_subsets(sK4_skl,complements_of_subsets(sK4_skl,sK5_skl))=subset_complement(sK4_skl,meet_of_subsets(sK4_skl,sK5_skl))),
% 1.10/0.63 inference(cnf_transformation,[status(thm)],[f192])).
% 1.10/0.63 fof(f205,plain,(
% 1.10/0.63 ![A,B]: (~element(B,powerset(powerset(A)))|(B=empty_set|union_of_subsets(A,complements_of_subsets(A,B))=subset_difference(A,cast_to_subset(A),meet_of_subsets(A,B))))),
% 1.10/0.63 inference(pre_NNF_transformation,[status(thm)],[f54])).
% 1.10/0.63 fof(f206,plain,(
% 1.10/0.63 ![X0,X1]: (~element(X0,powerset(powerset(X1)))|X0=empty_set|union_of_subsets(X1,complements_of_subsets(X1,X0))=subset_difference(X1,cast_to_subset(X1),meet_of_subsets(X1,X0)))),
% 1.10/0.63 inference(cnf_transformation,[status(thm)],[f205])).
% 1.10/0.63 fof(f255,plain,(
% 1.10/0.63 element(meet_of_subsets(sK4_skl,sK5_skl),powerset(sK4_skl))),
% 1.10/0.63 inference(resolution,[status(thm)],[f126,f193])).
% 1.10/0.63 fof(f260,plain,(
% 1.10/0.63 subset_complement(sK4_skl,meet_of_subsets(sK4_skl,sK5_skl))=set_difference(sK4_skl,meet_of_subsets(sK4_skl,sK5_skl))),
% 1.10/0.63 inference(resolution,[status(thm)],[f255,f119])).
% 1.10/0.63 fof(f284,plain,(
% 1.10/0.63 ![X0]: (element(X0,powerset(X0)))),
% 1.10/0.63 inference(forward_demodulation,[status(thm)],[f117,f120])).
% 1.10/0.63 fof(f2033,plain,(
% 1.10/0.63 meet_of_subsets(sK4_skl,sK5_skl)=set_meet(sK5_skl)),
% 1.10/0.63 inference(resolution,[status(thm)],[f186,f193])).
% 1.10/0.63 fof(f2085,plain,(
% 1.10/0.63 ![X0,X1]: (~element(X0,powerset(X1))|subset_difference(X1,X1,X0)=set_difference(X1,X0))),
% 1.10/0.63 inference(resolution,[status(thm)],[f188,f284])).
% 1.10/0.63 fof(f2160,plain,(
% 1.10/0.63 element(set_meet(sK5_skl),powerset(sK4_skl))),
% 1.10/0.63 inference(backward_demodulation,[status(thm)],[f2033,f255])).
% 1.10/0.63 fof(f2161,plain,(
% 1.10/0.63 ~union_of_subsets(sK4_skl,complements_of_subsets(sK4_skl,sK5_skl))=subset_complement(sK4_skl,set_meet(sK5_skl))),
% 1.10/0.63 inference(backward_demodulation,[status(thm)],[f2033,f195])).
% 1.10/0.63 fof(f2317,plain,(
% 1.10/0.63 ![X0,X1]: (~element(X0,powerset(powerset(X1)))|X0=empty_set|union_of_subsets(X1,complements_of_subsets(X1,X0))=subset_difference(X1,X1,meet_of_subsets(X1,X0)))),
% 1.10/0.63 inference(forward_demodulation,[status(thm)],[f117,f206])).
% 1.10/0.63 fof(f2335,plain,(
% 1.10/0.63 sK5_skl=empty_set|union_of_subsets(sK4_skl,complements_of_subsets(sK4_skl,sK5_skl))=subset_difference(sK4_skl,sK4_skl,meet_of_subsets(sK4_skl,sK5_skl))),
% 1.10/0.63 inference(resolution,[status(thm)],[f2317,f193])).
% 1.10/0.63 fof(f2345,plain,(
% 1.10/0.63 sK5_skl=empty_set|union_of_subsets(sK4_skl,complements_of_subsets(sK4_skl,sK5_skl))=subset_difference(sK4_skl,sK4_skl,set_meet(sK5_skl))),
% 1.10/0.63 inference(forward_demodulation,[status(thm)],[f2033,f2335])).
% 1.10/0.63 fof(f2346,plain,(
% 1.10/0.63 union_of_subsets(sK4_skl,complements_of_subsets(sK4_skl,sK5_skl))=subset_difference(sK4_skl,sK4_skl,set_meet(sK5_skl))),
% 1.10/0.63 inference(forward_subsumption_resolution,[status(thm)],[f2345,f194])).
% 1.10/0.63 fof(f3250,plain,(
% 1.10/0.63 ~subset_difference(sK4_skl,sK4_skl,set_meet(sK5_skl))=subset_complement(sK4_skl,set_meet(sK5_skl))),
% 1.10/0.63 inference(backward_demodulation,[status(thm)],[f2346,f2161])).
% 1.10/0.63 fof(f3681,plain,(
% 1.10/0.63 subset_complement(sK4_skl,set_meet(sK5_skl))=set_difference(sK4_skl,meet_of_subsets(sK4_skl,sK5_skl))),
% 1.10/0.63 inference(forward_demodulation,[status(thm)],[f2033,f260])).
% 1.10/0.63 fof(f3682,plain,(
% 1.10/0.63 ~subset_difference(sK4_skl,sK4_skl,set_meet(sK5_skl))=set_difference(sK4_skl,set_meet(sK5_skl))),
% 1.10/0.63 inference(backward_demodulation,[status(thm)],[f3683,f3250])).
% 1.10/0.63 fof(f3683,plain,(
% 1.10/0.63 subset_complement(sK4_skl,set_meet(sK5_skl))=set_difference(sK4_skl,set_meet(sK5_skl))),
% 1.10/0.63 inference(forward_demodulation,[status(thm)],[f2033,f3681])).
% 1.10/0.63 fof(f5676,plain,(
% 1.10/0.63 subset_difference(sK4_skl,sK4_skl,set_meet(sK5_skl))=set_difference(sK4_skl,set_meet(sK5_skl))),
% 1.10/0.63 inference(resolution,[status(thm)],[f2085,f2160])).
% 1.10/0.63 fof(f5698,plain,(
% 1.10/0.63 $false),
% 1.10/0.63 inference(forward_subsumption_resolution,[status(thm)],[f5676,f3682])).
% 1.10/0.63 % SZS output end CNFRefutation for theBenchmark.p
% 1.10/0.66 % Elapsed time: 0.283465 seconds
% 1.10/0.66 % CPU time: 1.885145 seconds
% 1.10/0.66 % Total memory used: 154.574 MB
% 1.10/0.66 % Net memory used: 151.511 MB
%------------------------------------------------------------------------------