%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SET162+3 : TPTP v9.3.1. Released v2.2.0.
% 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 02:11:41 PM UTC 2026
% Result : Theorem 0.14s 0.58s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET162+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.03 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.51 % Computer : n002.cluster.edu
% 0.08/0.51 % Model : x86_64 x86_64
% 0.08/0.51 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.51 % Memory : 8046.5625MB
% 0.08/0.51 % OS : Linux 6.8.0-71-generic
% 0.08/0.51 % CPULimit : 300
% 0.08/0.51 % WCLimit : 300
% 0.08/0.51 % DateTime : Mon Sep 21 05:00:05 UTC 2026
% 0.08/0.51 % CPUTime :
% 0.08/0.52 % Drodi V4.1.1
% 0.14/0.58 % Refutation found
% 0.14/0.58 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.58 % SZS output start CNFRefutation for theBenchmark
% 0.14/0.58 fof(f1,axiom,(
% 0.14/0.58 (! [B,C,D] :( member(D,union(B,C))<=> ( member(D,B)| member(D,C) ) ) )),
% 0.14/0.58 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.58 fof(f2,axiom,(
% 0.14/0.58 (! [B] : ~ member(B,empty_set) )),
% 0.14/0.58 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.58 fof(f4,axiom,(
% 0.14/0.58 (! [B,C] : union(B,C) = union(C,B) )),
% 0.14/0.58 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.58 fof(f8,axiom,(
% 0.14/0.58 (! [B,C] :( B = C<=> (! [D] :( member(D,B)<=> member(D,C) ) )) )),
% 0.14/0.58 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.58 fof(f9,conjecture,(
% 0.14/0.58 (! [B] : union(B,empty_set) = B )),
% 0.14/0.58 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.58 fof(f10,negated_conjecture,(
% 0.14/0.58 ~((! [B] : union(B,empty_set) = B ))),
% 0.14/0.58 inference(negated_conjecture,[status(cth)],[f9])).
% 0.14/0.58 fof(f11,plain,(
% 0.14/0.58 ![B,C,D]: ((~member(D,union(B,C))|(member(D,B)|member(D,C)))&(member(D,union(B,C))|(~member(D,B)&~member(D,C))))),
% 0.14/0.58 inference(NNF_transformation,[status(thm)],[f1])).
% 0.14/0.58 fof(f12,plain,(
% 0.14/0.58 (![B,C,D]: (~member(D,union(B,C))|(member(D,B)|member(D,C))))&(![B,C,D]: (member(D,union(B,C))|(~member(D,B)&~member(D,C))))),
% 0.14/0.58 inference(miniscoping,[status(thm)],[f11])).
% 0.14/0.58 fof(f13,plain,(
% 0.14/0.58 ![X0,X1,X2]: (~member(X0,union(X1,X2))|member(X0,X1)|member(X0,X2))),
% 0.14/0.58 inference(cnf_transformation,[status(thm)],[f12])).
% 0.14/0.58 fof(f15,plain,(
% 0.14/0.58 ![X0,X1,X2]: (member(X0,union(X1,X2))|~member(X0,X2))),
% 0.14/0.58 inference(cnf_transformation,[status(thm)],[f12])).
% 0.14/0.58 fof(f16,plain,(
% 0.14/0.58 ![X0]: (~member(X0,empty_set))),
% 0.14/0.58 inference(cnf_transformation,[status(thm)],[f2])).
% 0.14/0.58 fof(f22,plain,(
% 0.14/0.58 ![X0,X1]: (union(X0,X1)=union(X1,X0))),
% 0.14/0.58 inference(cnf_transformation,[status(thm)],[f4])).
% 0.14/0.58 fof(f36,plain,(
% 0.14/0.58 ![B,C]: ((~B=C|(![D]: ((~member(D,B)|member(D,C))&(member(D,B)|~member(D,C)))))&(B=C|(?[D]: ((~member(D,B)|~member(D,C))&(member(D,B)|member(D,C))))))),
% 0.14/0.58 inference(NNF_transformation,[status(thm)],[f8])).
% 0.14/0.58 fof(f37,plain,(
% 0.14/0.58 (![B,C]: (~B=C|((![D]: (~member(D,B)|member(D,C)))&(![D]: (member(D,B)|~member(D,C))))))&(![B,C]: (B=C|(?[D]: ((~member(D,B)|~member(D,C))&(member(D,B)|member(D,C))))))),
% 0.14/0.58 inference(miniscoping,[status(thm)],[f36])).
% 0.14/0.58 fof(f38,plain,(
% 0.14/0.58 (![B,C]: (~B=C|((![D]: (~member(D,B)|member(D,C)))&(![D]: (member(D,B)|~member(D,C))))))&(![B,C]: (B=C|((~member(sK2_skl(C,B),B)|~member(sK2_skl(C,B),C))&(member(sK2_skl(C,B),B)|member(sK2_skl(C,B),C)))))),
% 0.14/0.58 inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(D,sK2_skl(C,B))],[f37])).
% 0.14/0.58 fof(f41,plain,(
% 0.14/0.58 ![X0,X1]: (X0=X1|~member(sK2_skl(X1,X0),X0)|~member(sK2_skl(X1,X0),X1))),
% 0.14/0.58 inference(cnf_transformation,[status(thm)],[f38])).
% 0.14/0.58 fof(f42,plain,(
% 0.14/0.58 ![X0,X1]: (X0=X1|member(sK2_skl(X1,X0),X0)|member(sK2_skl(X1,X0),X1))),
% 0.14/0.58 inference(cnf_transformation,[status(thm)],[f38])).
% 0.14/0.58 fof(f43,plain,(
% 0.14/0.58 (?[B]: ~union(B,empty_set)=B)),
% 0.14/0.58 inference(pre_NNF_transformation,[status(thm)],[f10])).
% 0.14/0.58 fof(f44,plain,(
% 0.14/0.58 ~union(sK3_skl,empty_set)=sK3_skl),
% 0.14/0.58 inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl]),skolemize(B,sK3_skl)],[f43])).
% 0.14/0.58 fof(f45,plain,(
% 0.14/0.58 ~union(sK3_skl,empty_set)=sK3_skl),
% 0.14/0.58 inference(cnf_transformation,[status(thm)],[f44])).
% 0.14/0.58 fof(f167,plain,(
% 0.14/0.58 ![X0,X1,X2]: (X0=X1|member(sK2_skl(X1,X0),X1)|member(sK2_skl(X1,X0),union(X2,X0)))),
% 0.14/0.58 inference(resolution,[status(thm)],[f42,f15])).
% 0.14/0.58 fof(f369,plain,(
% 0.14/0.58 ![X0,X1]: (X0=union(X1,X0)|X0=union(X1,X0)|~member(sK2_skl(union(X1,X0),X0),X0))),
% 0.14/0.58 inference(resolution,[status(thm)],[f167,f41])).
% 0.14/0.58 fof(f371,plain,(
% 0.14/0.58 ![X0,X1]: (X0=union(X1,X0)|member(sK2_skl(union(X1,X0),X0),X1)|member(sK2_skl(union(X1,X0),X0),X0))),
% 0.14/0.58 inference(resolution,[status(thm)],[f167,f13])).
% 0.14/0.58 fof(f385,plain,(
% 0.14/0.58 ![X0,X1]: (X0=union(X1,X0)|~member(sK2_skl(union(X1,X0),X0),X0))),
% 0.14/0.58 inference(duplicate_literals_removal,[status(thm)],[f369])).
% 0.14/0.58 fof(f387,plain,(
% 0.14/0.58 ![X0,X1]: (X0=union(X1,X0)|member(sK2_skl(union(X1,X0),X0),X1))),
% 0.14/0.58 inference(forward_subsumption_resolution,[status(thm)],[f371,f385])).
% 0.14/0.58 fof(f420,plain,(
% 0.14/0.58 ![X0]: (X0=union(empty_set,X0))),
% 0.14/0.58 inference(resolution,[status(thm)],[f387,f16])).
% 0.14/0.58 fof(f434,plain,(
% 0.14/0.58 ![X0]: (X0=union(X0,empty_set))),
% 0.14/0.58 inference(paramodulation,[status(thm)],[f22,f420])).
% 0.14/0.58 fof(f470,plain,(
% 0.14/0.58 ~sK3_skl=sK3_skl),
% 0.14/0.58 inference(backward_demodulation,[status(thm)],[f434,f45])).
% 0.14/0.58 fof(f493,plain,(
% 0.14/0.58 $false),
% 0.14/0.58 inference(trivial_equality_resolution,[status(thm)],[f470])).
% 0.14/0.58 % SZS output end CNFRefutation for theBenchmark.p
% 0.14/0.59 % Elapsed time: 0.072464 seconds
% 0.14/0.59 % CPU time: 0.306444 seconds
% 0.14/0.59 % Total memory used: 86.417 MB
% 0.14/0.59 % Net memory used: 85.681 MB
%------------------------------------------------------------------------------