%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SET584+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 : 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 02:12:13 PM UTC 2026
% Result : Theorem 8.77s 1.58s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET584+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n016.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 05:32:07 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 8.77/1.58 % Refutation found
% 8.77/1.58 % SZS status Theorem for theBenchmark: Theorem is valid
% 8.77/1.58 % SZS output start CNFRefutation for theBenchmark
% 8.77/1.58 fof(f1,axiom,(
% 8.77/1.58 (! [B,C,D] :( member(D,union(B,C))<=> ( member(D,B)| member(D,C) ) ) )),
% 8.77/1.58 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 8.77/1.58 fof(f2,axiom,(
% 8.77/1.58 (! [B,C] :( subset(B,C)<=> (! [D] :( member(D,B)=> member(D,C) ) )) )),
% 8.77/1.58 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 8.77/1.58 fof(f3,axiom,(
% 8.77/1.58 (! [B,C] : union(B,C) = union(C,B) )),
% 8.77/1.58 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 8.77/1.58 fof(f5,axiom,(
% 8.77/1.58 (! [B,C] :( B = C<=> (! [D] :( member(D,B)<=> member(D,C) ) )) )),
% 8.77/1.58 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 8.77/1.58 fof(f6,conjecture,(
% 8.77/1.58 (! [B,C,D] :( subset(B,C)=> subset(union(B,D),union(C,D)) ) )),
% 8.77/1.58 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 8.77/1.58 fof(f7,negated_conjecture,(
% 8.77/1.58 ~((! [B,C,D] :( subset(B,C)=> subset(union(B,D),union(C,D)) ) ))),
% 8.77/1.58 inference(negated_conjecture,[status(cth)],[f6])).
% 8.77/1.58 fof(f8,plain,(
% 8.77/1.58 ![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))))),
% 8.77/1.58 inference(NNF_transformation,[status(thm)],[f1])).
% 8.77/1.58 fof(f9,plain,(
% 8.77/1.58 (![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))))),
% 8.77/1.58 inference(miniscoping,[status(thm)],[f8])).
% 8.77/1.58 fof(f10,plain,(
% 8.77/1.58 ![X0,X1,X2]: (~member(X0,union(X1,X2))|member(X0,X1)|member(X0,X2))),
% 8.77/1.58 inference(cnf_transformation,[status(thm)],[f9])).
% 8.77/1.58 fof(f12,plain,(
% 8.77/1.58 ![X0,X1,X2]: (member(X0,union(X1,X2))|~member(X0,X2))),
% 8.77/1.58 inference(cnf_transformation,[status(thm)],[f9])).
% 8.77/1.58 fof(f13,plain,(
% 8.77/1.58 ![B,C]: (subset(B,C)<=>(![D]: (~member(D,B)|member(D,C))))),
% 8.77/1.58 inference(pre_NNF_transformation,[status(thm)],[f2])).
% 8.77/1.58 fof(f14,plain,(
% 8.77/1.58 ![B,C]: ((~subset(B,C)|(![D]: (~member(D,B)|member(D,C))))&(subset(B,C)|(?[D]: (member(D,B)&~member(D,C)))))),
% 8.77/1.58 inference(NNF_transformation,[status(thm)],[f13])).
% 8.77/1.58 fof(f15,plain,(
% 8.77/1.58 (![B,C]: (~subset(B,C)|(![D]: (~member(D,B)|member(D,C)))))&(![B,C]: (subset(B,C)|(?[D]: (member(D,B)&~member(D,C)))))),
% 8.77/1.58 inference(miniscoping,[status(thm)],[f14])).
% 8.77/1.58 fof(f16,plain,(
% 8.77/1.58 (![B,C]: (~subset(B,C)|(![D]: (~member(D,B)|member(D,C)))))&(![B,C]: (subset(B,C)|(member(sK0_skl(C,B),B)&~member(sK0_skl(C,B),C))))),
% 8.77/1.58 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(D,sK0_skl(C,B))],[f15])).
% 8.77/1.58 fof(f17,plain,(
% 8.77/1.58 ![X0,X1,X2]: (~subset(X0,X1)|~member(X2,X0)|member(X2,X1))),
% 8.77/1.58 inference(cnf_transformation,[status(thm)],[f16])).
% 8.77/1.58 fof(f18,plain,(
% 8.77/1.58 ![X0,X1]: (subset(X0,X1)|member(sK0_skl(X1,X0),X0))),
% 8.77/1.58 inference(cnf_transformation,[status(thm)],[f16])).
% 8.77/1.58 fof(f19,plain,(
% 8.77/1.58 ![X0,X1]: (subset(X0,X1)|~member(sK0_skl(X1,X0),X1))),
% 8.77/1.58 inference(cnf_transformation,[status(thm)],[f16])).
% 8.77/1.58 fof(f20,plain,(
% 8.77/1.58 ![X0,X1]: (union(X0,X1)=union(X1,X0))),
% 8.77/1.58 inference(cnf_transformation,[status(thm)],[f3])).
% 8.77/1.58 fof(f22,plain,(
% 8.77/1.58 ![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))))))),
% 8.77/1.58 inference(NNF_transformation,[status(thm)],[f5])).
% 8.77/1.58 fof(f23,plain,(
% 8.77/1.58 (![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))))))),
% 8.77/1.58 inference(miniscoping,[status(thm)],[f22])).
% 8.77/1.58 fof(f24,plain,(
% 8.77/1.58 (![B,C]: (~B=C|((![D]: (~member(D,B)|member(D,C)))&(![D]: (member(D,B)|~member(D,C))))))&(![B,C]: (B=C|((~member(sK1_skl(C,B),B)|~member(sK1_skl(C,B),C))&(member(sK1_skl(C,B),B)|member(sK1_skl(C,B),C)))))),
% 8.77/1.58 inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(D,sK1_skl(C,B))],[f23])).
% 8.77/1.58 fof(f27,plain,(
% 8.77/1.58 ![X0,X1]: (X0=X1|~member(sK1_skl(X1,X0),X0)|~member(sK1_skl(X1,X0),X1))),
% 8.77/1.58 inference(cnf_transformation,[status(thm)],[f24])).
% 8.77/1.58 fof(f28,plain,(
% 8.77/1.58 ![X0,X1]: (X0=X1|member(sK1_skl(X1,X0),X0)|member(sK1_skl(X1,X0),X1))),
% 8.77/1.58 inference(cnf_transformation,[status(thm)],[f24])).
% 8.77/1.58 fof(f29,plain,(
% 8.77/1.58 (?[B,C,D]: (subset(B,C)&~subset(union(B,D),union(C,D))))),
% 8.77/1.58 inference(pre_NNF_transformation,[status(thm)],[f7])).
% 8.77/1.58 fof(f30,plain,(
% 8.77/1.58 ?[B,C]: (subset(B,C)&(?[D]: ~subset(union(B,D),union(C,D))))),
% 8.77/1.58 inference(miniscoping,[status(thm)],[f29])).
% 8.77/1.58 fof(f31,plain,(
% 8.77/1.58 (subset(sK2_skl,sK3_skl)&~subset(union(sK2_skl,sK4_skl),union(sK3_skl,sK4_skl)))),
% 8.77/1.58 inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl,sK4_skl]),skolemize(B,sK2_skl),skolemize(C,sK3_skl),skolemize(D,sK4_skl)],[f30])).
% 8.77/1.58 fof(f32,plain,(
% 8.77/1.58 subset(sK2_skl,sK3_skl)),
% 8.77/1.58 inference(cnf_transformation,[status(thm)],[f31])).
% 8.77/1.58 fof(f33,plain,(
% 8.77/1.58 ~subset(union(sK2_skl,sK4_skl),union(sK3_skl,sK4_skl))),
% 8.77/1.58 inference(cnf_transformation,[status(thm)],[f31])).
% 8.77/1.58 fof(f40,plain,(
% 8.77/1.58 ![X0,X1,X2]: (subset(union(X0,X1),X2)|member(sK0_skl(X2,union(X0,X1)),X0)|member(sK0_skl(X2,union(X0,X1)),X1))),
% 8.77/1.58 inference(resolution,[status(thm)],[f18,f10])).
% 8.77/1.58 fof(f43,plain,(
% 8.77/1.58 ![X0,X1,X2]: (subset(X0,X1)|~subset(X0,X2)|member(sK0_skl(X1,X0),X2))),
% 8.77/1.58 inference(resolution,[status(thm)],[f18,f17])).
% 8.77/1.58 fof(f66,plain,(
% 8.77/1.58 ![X0]: (subset(sK2_skl,X0)|member(sK0_skl(X0,sK2_skl),sK3_skl))),
% 8.77/1.58 inference(resolution,[status(thm)],[f43,f32])).
% 8.77/1.58 fof(f73,plain,(
% 8.77/1.58 ![X0,X1,X2]: (union(X0,X1)=X2|member(sK1_skl(X2,union(X0,X1)),X2)|member(sK1_skl(X2,union(X0,X1)),X0)|member(sK1_skl(X2,union(X0,X1)),X1))),
% 8.77/1.58 inference(resolution,[status(thm)],[f28,f10])).
% 8.77/1.58 fof(f91,plain,(
% 8.77/1.58 ![X0,X1,X2,X3]: (subset(union(X0,X1),X2)|member(sK0_skl(X2,union(X0,X1)),X1)|member(sK0_skl(X2,union(X0,X1)),union(X3,X0)))),
% 8.77/1.58 inference(resolution,[status(thm)],[f40,f12])).
% 8.77/1.58 fof(f110,plain,(
% 8.77/1.58 ![X0,X1]: (subset(sK2_skl,X0)|member(sK0_skl(X0,sK2_skl),union(X1,sK3_skl)))),
% 8.77/1.58 inference(resolution,[status(thm)],[f66,f12])).
% 8.77/1.58 fof(f116,plain,(
% 8.77/1.58 ![X0,X1,X2]: (subset(sK2_skl,X0)|member(sK0_skl(X0,sK2_skl),union(X1,union(X2,sK3_skl))))),
% 8.77/1.58 inference(resolution,[status(thm)],[f110,f12])).
% 8.77/1.58 fof(f164,plain,(
% 8.77/1.58 ![X0]: (union(X0,X0)=X0|union(X0,X0)=X0|~member(sK1_skl(X0,union(X0,X0)),union(X0,X0)))),
% 8.77/1.58 inference(resolution,[status(thm)],[f73,f27])).
% 8.77/1.58 fof(f168,plain,(
% 8.77/1.58 ![X0,X1]: (union(X0,X0)=X0|member(sK1_skl(X0,union(X0,X0)),union(X1,X0)))),
% 8.77/1.58 inference(resolution,[status(thm)],[f73,f12])).
% 8.77/1.58 fof(f196,plain,(
% 8.77/1.58 ![X0]: (union(X0,X0)=X0|~member(sK1_skl(X0,union(X0,X0)),union(X0,X0)))),
% 8.77/1.58 inference(duplicate_literals_removal,[status(thm)],[f164])).
% 8.77/1.58 fof(f198,plain,(
% 8.77/1.58 ![X0]: (union(X0,X0)=X0)),
% 8.77/1.58 inference(backward_subsumption_resolution,[status(thm)],[f196,f168])).
% 8.77/1.58 fof(f1062,plain,(
% 8.77/1.58 ![X0,X1]: (subset(sK2_skl,union(X0,union(X1,sK3_skl)))|subset(sK2_skl,union(X0,union(X1,sK3_skl))))),
% 8.77/1.58 inference(resolution,[status(thm)],[f116,f19])).
% 8.77/1.58 fof(f1073,plain,(
% 8.77/1.58 ![X0,X1]: (subset(sK2_skl,union(X0,union(X1,sK3_skl))))),
% 8.77/1.58 inference(duplicate_literals_removal,[status(thm)],[f1062])).
% 8.77/1.58 fof(f1656,plain,(
% 8.77/1.58 ![X0,X1]: (subset(sK2_skl,union(union(X0,sK3_skl),X1)))),
% 8.77/1.58 inference(paramodulation,[status(thm)],[f20,f1073])).
% 8.77/1.58 fof(f1668,plain,(
% 8.77/1.58 ![X0,X1]: (subset(sK2_skl,union(union(sK3_skl,X0),X1)))),
% 8.77/1.58 inference(paramodulation,[status(thm)],[f20,f1656])).
% 8.77/1.58 fof(f2168,plain,(
% 8.77/1.58 ![X0,X1,X2]: (subset(union(X0,X1),union(X2,X0))|member(sK0_skl(union(X2,X0),union(X0,X1)),X1)|subset(union(X0,X1),union(X2,X0)))),
% 8.77/1.58 inference(resolution,[status(thm)],[f91,f19])).
% 8.77/1.58 fof(f2185,plain,(
% 8.77/1.58 ![X0,X1,X2]: (subset(union(X0,X1),union(X2,X0))|member(sK0_skl(union(X2,X0),union(X0,X1)),X1))),
% 8.77/1.58 inference(duplicate_literals_removal,[status(thm)],[f2168])).
% 8.77/1.58 fof(f2194,plain,(
% 8.77/1.58 ![X0,X1,X2,X3]: (subset(union(X0,X1),union(X2,X0))|~subset(X1,X3)|member(sK0_skl(union(X2,X0),union(X0,X1)),X3))),
% 8.77/1.58 inference(resolution,[status(thm)],[f2185,f17])).
% 8.77/1.58 fof(f2243,plain,(
% 8.77/1.58 ![X0,X1,X2,X3]: (subset(union(X0,sK2_skl),union(X1,X0))|member(sK0_skl(union(X1,X0),union(X0,sK2_skl)),union(union(sK3_skl,X2),X3)))),
% 8.77/1.58 inference(resolution,[status(thm)],[f2194,f1668])).
% 8.77/1.58 fof(f2317,plain,(
% 8.77/1.58 ![X0,X1]: (subset(union(X0,sK2_skl),union(union(sK3_skl,X1),X0))|subset(union(X0,sK2_skl),union(union(sK3_skl,X1),X0)))),
% 8.77/1.58 inference(resolution,[status(thm)],[f2243,f19])).
% 8.77/1.58 fof(f2334,plain,(
% 8.77/1.58 ![X0,X1]: (subset(union(X0,sK2_skl),union(union(sK3_skl,X1),X0)))),
% 8.77/1.58 inference(duplicate_literals_removal,[status(thm)],[f2317])).
% 8.77/1.58 fof(f2349,plain,(
% 8.77/1.58 ![X0]: (subset(union(X0,sK2_skl),union(sK3_skl,X0)))),
% 8.77/1.59 inference(paramodulation,[status(thm)],[f198,f2334])).
% 8.77/1.59 fof(f2420,plain,(
% 8.77/1.59 ![X0]: (subset(union(sK2_skl,X0),union(sK3_skl,X0)))),
% 8.77/1.59 inference(paramodulation,[status(thm)],[f20,f2349])).
% 8.77/1.59 fof(f2426,plain,(
% 8.77/1.59 $false),
% 8.77/1.59 inference(backward_subsumption_resolution,[status(thm)],[f33,f2420])).
% 8.77/1.59 % SZS output end CNFRefutation for theBenchmark.p
% 7.13/1.61 % Elapsed time: 1.238246 seconds
% 7.13/1.61 % CPU time: 9.545266 seconds
% 7.13/1.61 % Total memory used: 189.109 MB
% 7.13/1.61 % Net memory used: 175.031 MB
%------------------------------------------------------------------------------