%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SET813+4 : 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 : n014.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 02:12:38 PM UTC 2026
% Result : Theorem 0.21s 0.69s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET813+4 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.65 % Computer : n014.cluster.edu
% 0.18/0.65 % Model : x86_64 x86_64
% 0.18/0.65 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.65 % Memory : 8046.5625MB
% 0.18/0.65 % OS : Linux 6.8.0-71-generic
% 0.18/0.65 % CPULimit : 300
% 0.18/0.65 % WCLimit : 300
% 0.18/0.65 % DateTime : Mon Sep 21 05:39:05 UTC 2026
% 0.21/0.65 % CPUTime :
% 0.21/0.67 % Drodi V4.1.1
% 0.21/0.69 % Refutation found
% 0.21/0.69 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.21/0.69 % SZS output start CNFRefutation for theBenchmark
% 0.21/0.69 fof(f5,axiom,(
% 0.21/0.69 (! [X,A,B] :( member(X,union(A,B))<=> ( member(X,A)| member(X,B) ) ) )),
% 0.21/0.69 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.21/0.69 fof(f8,axiom,(
% 0.21/0.69 (! [X,A] :( member(X,singleton(A))<=> X = A ) )),
% 0.21/0.69 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.21/0.69 fof(f19,axiom,(
% 0.21/0.69 (! [A,X] :( member(X,suc(A))<=> member(X,union(A,singleton(A))) ) )),
% 0.21/0.69 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.21/0.69 fof(f20,conjecture,(
% 0.21/0.69 (! [A] :( member(A,on)=> member(A,suc(A)) ) )),
% 0.21/0.69 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.21/0.69 fof(f21,negated_conjecture,(
% 0.21/0.69 ~((! [A] :( member(A,on)=> member(A,suc(A)) ) ))),
% 0.21/0.69 inference(negated_conjecture,[status(cth)],[f20])).
% 0.21/0.69 fof(f43,plain,(
% 0.21/0.69 ![X,A,B]: ((~member(X,union(A,B))|(member(X,A)|member(X,B)))&(member(X,union(A,B))|(~member(X,A)&~member(X,B))))),
% 0.21/0.69 inference(NNF_transformation,[status(thm)],[f5])).
% 0.21/0.69 fof(f44,plain,(
% 0.21/0.69 (![X,A,B]: (~member(X,union(A,B))|(member(X,A)|member(X,B))))&(![X,A,B]: (member(X,union(A,B))|(~member(X,A)&~member(X,B))))),
% 0.21/0.69 inference(miniscoping,[status(thm)],[f43])).
% 0.21/0.69 fof(f47,plain,(
% 0.21/0.69 ![X0,X1,X2]: (member(X0,union(X1,X2))|~member(X0,X2))),
% 0.21/0.69 inference(cnf_transformation,[status(thm)],[f44])).
% 0.21/0.69 fof(f54,plain,(
% 0.21/0.69 ![X,A]: ((~member(X,singleton(A))|X=A)&(member(X,singleton(A))|~X=A))),
% 0.21/0.69 inference(NNF_transformation,[status(thm)],[f8])).
% 0.21/0.69 fof(f55,plain,(
% 0.21/0.69 (![X,A]: (~member(X,singleton(A))|X=A))&(![X,A]: (member(X,singleton(A))|~X=A))),
% 0.21/0.69 inference(miniscoping,[status(thm)],[f54])).
% 0.21/0.69 fof(f57,plain,(
% 0.21/0.69 ![X0,X1]: (member(X0,singleton(X1))|~X0=X1)),
% 0.21/0.69 inference(cnf_transformation,[status(thm)],[f55])).
% 0.21/0.69 fof(f128,plain,(
% 0.21/0.69 ![A,X]: ((~member(X,suc(A))|member(X,union(A,singleton(A))))&(member(X,suc(A))|~member(X,union(A,singleton(A)))))),
% 0.21/0.69 inference(NNF_transformation,[status(thm)],[f19])).
% 0.21/0.69 fof(f129,plain,(
% 0.21/0.69 (![A,X]: (~member(X,suc(A))|member(X,union(A,singleton(A)))))&(![A,X]: (member(X,suc(A))|~member(X,union(A,singleton(A)))))),
% 0.21/0.69 inference(miniscoping,[status(thm)],[f128])).
% 0.21/0.69 fof(f131,plain,(
% 0.21/0.69 ![X0,X1]: (member(X0,suc(X1))|~member(X0,union(X1,singleton(X1))))),
% 0.21/0.69 inference(cnf_transformation,[status(thm)],[f129])).
% 0.21/0.69 fof(f132,plain,(
% 0.21/0.69 (?[A]: (member(A,on)&~member(A,suc(A))))),
% 0.21/0.69 inference(pre_NNF_transformation,[status(thm)],[f21])).
% 0.21/0.69 fof(f133,plain,(
% 0.21/0.69 (member(sK13_skl,on)&~member(sK13_skl,suc(sK13_skl)))),
% 0.21/0.69 inference(skolemize,[status(esa),new_symbols(skolem,[sK13_skl]),skolemize(A,sK13_skl)],[f132])).
% 0.21/0.69 fof(f135,plain,(
% 0.21/0.69 ~member(sK13_skl,suc(sK13_skl))),
% 0.21/0.69 inference(cnf_transformation,[status(thm)],[f133])).
% 0.21/0.69 fof(f143,plain,(
% 0.21/0.69 ![X0]: (member(X0,singleton(X0)))),
% 0.21/0.69 inference(destructive_equality_resolution,[status(thm)],[f57])).
% 0.21/0.69 fof(f221,plain,(
% 0.21/0.69 ![X0,X1]: (~member(X0,singleton(X1))|member(X0,suc(X1)))),
% 0.21/0.69 inference(resolution,[status(thm)],[f47,f131])).
% 0.21/0.69 fof(f238,plain,(
% 0.21/0.69 ![X0]: (member(X0,suc(X0)))),
% 0.21/0.69 inference(resolution,[status(thm)],[f221,f143])).
% 0.21/0.69 fof(f240,plain,(
% 0.21/0.69 $false),
% 0.21/0.69 inference(backward_subsumption_resolution,[status(thm)],[f135,f238])).
% 0.21/0.69 % SZS output end CNFRefutation for theBenchmark.p
% 0.22/0.74 % Elapsed time: 0.080498 seconds
% 0.22/0.74 % CPU time: 0.159180 seconds
% 0.22/0.74 % Total memory used: 18.656 MB
% 0.22/0.74 % Net memory used: 18.590 MB
%------------------------------------------------------------------------------