%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SET577+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 : n018.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 02:12:12 PM UTC 2026
% Result : Theorem 7.44s 16.44s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET577+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/15.44 % Computer : n018.cluster.edu
% 0.14/15.44 % Model : x86_64 x86_64
% 0.14/15.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/15.44 % Memory : 8046.5625MB
% 0.14/15.44 % OS : Linux 6.8.0-71-generic
% 0.14/15.44 % CPULimit : 300
% 0.14/15.44 % WCLimit : 300
% 0.14/15.44 % DateTime : Mon Sep 21 05:29:14 UTC 2026
% 0.14/15.44 % CPUTime :
% 0.14/15.45 % Drodi V4.1.1
% 7.44/16.44 % Refutation found
% 7.44/16.44 % SZS status Theorem for theBenchmark: Theorem is valid
% 7.44/16.44 % SZS output start CNFRefutation for theBenchmark
% 7.44/16.44 fof(f1,axiom,(
% 7.44/16.44 (! [B,C,D] :( member(D,union(B,C))<=> ( member(D,B)| member(D,C) ) ) )),
% 7.44/16.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 7.44/16.44 fof(f2,axiom,(
% 7.44/16.44 (! [B,C] :( B = C<=> ( subset(B,C)& subset(C,B) ) ) )),
% 7.44/16.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 7.44/16.44 fof(f3,axiom,(
% 7.44/16.44 (! [B,C] : union(B,C) = union(C,B) )),
% 7.44/16.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 7.44/16.44 fof(f4,axiom,(
% 7.44/16.44 (! [B,C] :( subset(B,C)<=> (! [D] :( member(D,B)=> member(D,C) ) )) )),
% 7.44/16.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 7.44/16.44 fof(f7,conjecture,(
% 7.44/16.44 (! [B,C,D] :( (! [E] :( member(E,B)<=> ( member(E,C)| member(E,D) ) ))=> B = union(C,D) ) )),
% 7.44/16.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 7.44/16.44 fof(f8,negated_conjecture,(
% 7.44/16.44 ~((! [B,C,D] :( (! [E] :( member(E,B)<=> ( member(E,C)| member(E,D) ) ))=> B = union(C,D) ) ))),
% 7.44/16.44 inference(negated_conjecture,[status(cth)],[f7])).
% 7.44/16.44 fof(f9,plain,(
% 7.44/16.44 ![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))))),
% 7.44/16.44 inference(NNF_transformation,[status(thm)],[f1])).
% 7.44/16.44 fof(f10,plain,(
% 7.44/16.44 (![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))))),
% 7.44/16.44 inference(miniscoping,[status(thm)],[f9])).
% 7.44/16.44 fof(f11,plain,(
% 7.44/16.44 ![X0,X1,X2]: (~member(X0,union(X1,X2))|member(X0,X1)|member(X0,X2))),
% 7.44/16.44 inference(cnf_transformation,[status(thm)],[f10])).
% 7.44/16.44 fof(f12,plain,(
% 7.44/16.44 ![X0,X1,X2]: (member(X0,union(X1,X2))|~member(X0,X1))),
% 7.44/16.44 inference(cnf_transformation,[status(thm)],[f10])).
% 7.44/16.44 fof(f13,plain,(
% 7.44/16.44 ![X0,X1,X2]: (member(X0,union(X1,X2))|~member(X0,X2))),
% 7.44/16.44 inference(cnf_transformation,[status(thm)],[f10])).
% 7.44/16.44 fof(f14,plain,(
% 7.44/16.44 ![B,C]: ((~B=C|(subset(B,C)&subset(C,B)))&(B=C|(~subset(B,C)|~subset(C,B))))),
% 7.44/16.44 inference(NNF_transformation,[status(thm)],[f2])).
% 7.44/16.44 fof(f15,plain,(
% 7.44/16.44 (![B,C]: (~B=C|(subset(B,C)&subset(C,B))))&(![B,C]: (B=C|(~subset(B,C)|~subset(C,B))))),
% 7.44/16.44 inference(miniscoping,[status(thm)],[f14])).
% 7.44/16.44 fof(f18,plain,(
% 7.44/16.44 ![X0,X1]: (X0=X1|~subset(X0,X1)|~subset(X1,X0))),
% 7.44/16.44 inference(cnf_transformation,[status(thm)],[f15])).
% 7.44/16.44 fof(f19,plain,(
% 7.44/16.44 ![X0,X1]: (union(X0,X1)=union(X1,X0))),
% 7.44/16.44 inference(cnf_transformation,[status(thm)],[f3])).
% 7.44/16.44 fof(f20,plain,(
% 7.44/16.44 ![B,C]: (subset(B,C)<=>(![D]: (~member(D,B)|member(D,C))))),
% 7.44/16.44 inference(pre_NNF_transformation,[status(thm)],[f4])).
% 7.44/16.44 fof(f21,plain,(
% 7.44/16.44 ![B,C]: ((~subset(B,C)|(![D]: (~member(D,B)|member(D,C))))&(subset(B,C)|(?[D]: (member(D,B)&~member(D,C)))))),
% 7.44/16.44 inference(NNF_transformation,[status(thm)],[f20])).
% 7.44/16.44 fof(f22,plain,(
% 7.44/16.44 (![B,C]: (~subset(B,C)|(![D]: (~member(D,B)|member(D,C)))))&(![B,C]: (subset(B,C)|(?[D]: (member(D,B)&~member(D,C)))))),
% 7.44/16.44 inference(miniscoping,[status(thm)],[f21])).
% 7.44/16.44 fof(f23,plain,(
% 7.44/16.44 (![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))))),
% 7.44/16.44 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(D,sK0_skl(C,B))],[f22])).
% 7.44/16.44 fof(f25,plain,(
% 7.44/16.44 ![X0,X1]: (subset(X0,X1)|member(sK0_skl(X1,X0),X0))),
% 7.44/16.44 inference(cnf_transformation,[status(thm)],[f23])).
% 7.44/16.44 fof(f26,plain,(
% 7.44/16.44 ![X0,X1]: (subset(X0,X1)|~member(sK0_skl(X1,X0),X1))),
% 7.44/16.44 inference(cnf_transformation,[status(thm)],[f23])).
% 7.44/16.44 fof(f35,plain,(
% 7.44/16.44 (?[B,C,D]: ((![E]: (member(E,B)<=>(member(E,C)|member(E,D))))&~B=union(C,D)))),
% 7.44/16.44 inference(pre_NNF_transformation,[status(thm)],[f8])).
% 7.44/16.44 fof(f36,plain,(
% 7.44/16.44 ?[B,C,D]: ((![E]: ((~member(E,B)|(member(E,C)|member(E,D)))&(member(E,B)|(~member(E,C)&~member(E,D)))))&~B=union(C,D))),
% 7.44/16.44 inference(NNF_transformation,[status(thm)],[f35])).
% 7.44/16.44 fof(f37,plain,(
% 7.44/16.44 ?[B,C,D]: (((![E]: (~member(E,B)|(member(E,C)|member(E,D))))&(![E]: (member(E,B)|(~member(E,C)&~member(E,D)))))&~B=union(C,D))),
% 7.44/16.44 inference(miniscoping,[status(thm)],[f36])).
% 7.44/16.44 fof(f38,plain,(
% 7.44/16.44 (((![E]: (~member(E,sK2_skl)|(member(E,sK3_skl)|member(E,sK4_skl))))&(![E]: (member(E,sK2_skl)|(~member(E,sK3_skl)&~member(E,sK4_skl)))))&~sK2_skl=union(sK3_skl,sK4_skl))),
% 7.44/16.44 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)],[f37])).
% 7.44/16.44 fof(f39,plain,(
% 7.44/16.44 ![X0]: (~member(X0,sK2_skl)|member(X0,sK3_skl)|member(X0,sK4_skl))),
% 7.44/16.44 inference(cnf_transformation,[status(thm)],[f38])).
% 7.44/16.44 fof(f40,plain,(
% 7.44/16.44 ![X0]: (member(X0,sK2_skl)|~member(X0,sK3_skl))),
% 7.44/16.44 inference(cnf_transformation,[status(thm)],[f38])).
% 7.44/16.44 fof(f41,plain,(
% 7.44/16.44 ![X0]: (member(X0,sK2_skl)|~member(X0,sK4_skl))),
% 7.44/16.44 inference(cnf_transformation,[status(thm)],[f38])).
% 7.44/16.44 fof(f42,plain,(
% 7.44/16.44 ~sK2_skl=union(sK3_skl,sK4_skl)),
% 7.44/16.44 inference(cnf_transformation,[status(thm)],[f38])).
% 7.44/16.44 fof(f60,plain,(
% 7.44/16.44 ![X0,X1,X2]: (subset(union(X0,X1),X2)|member(sK0_skl(X2,union(X0,X1)),X0)|member(sK0_skl(X2,union(X0,X1)),X1))),
% 7.44/16.44 inference(resolution,[status(thm)],[f25,f11])).
% 7.44/16.44 fof(f63,plain,(
% 7.44/16.44 ![X0,X1,X2]: (subset(X0,union(X1,X2))|~member(sK0_skl(union(X1,X2),X0),X2))),
% 7.44/16.44 inference(resolution,[status(thm)],[f26,f13])).
% 7.44/16.44 fof(f64,plain,(
% 7.44/16.44 ![X0,X1,X2]: (subset(X0,union(X1,X2))|~member(sK0_skl(union(X1,X2),X0),X1))),
% 7.44/16.44 inference(resolution,[status(thm)],[f26,f12])).
% 7.44/16.44 fof(f66,plain,(
% 7.44/16.44 ![X0]: (subset(X0,sK2_skl)|~member(sK0_skl(sK2_skl,X0),sK3_skl))),
% 7.44/16.44 inference(resolution,[status(thm)],[f26,f40])).
% 7.44/16.44 fof(f120,plain,(
% 7.44/16.44 ![X0]: (member(sK0_skl(X0,sK2_skl),sK3_skl)|member(sK0_skl(X0,sK2_skl),sK4_skl)|subset(sK2_skl,X0))),
% 7.44/16.44 inference(resolution,[status(thm)],[f39,f25])).
% 7.44/16.44 fof(f152,plain,(
% 7.44/16.44 ![X0]: (~member(sK0_skl(sK2_skl,X0),sK3_skl)|subset(X0,sK2_skl))),
% 7.44/16.44 inference(resolution,[status(thm)],[f40,f26])).
% 7.44/16.44 fof(f182,plain,(
% 7.44/16.44 ![X0,X1]: (subset(union(X0,X1),X0)|member(sK0_skl(X0,union(X0,X1)),X1)|subset(union(X0,X1),X0))),
% 7.44/16.44 inference(resolution,[status(thm)],[f60,f26])).
% 7.44/16.44 fof(f187,plain,(
% 7.44/16.44 ![X0]: (subset(union(X0,sK3_skl),sK2_skl)|member(sK0_skl(sK2_skl,union(X0,sK3_skl)),X0)|subset(union(X0,sK3_skl),sK2_skl))),
% 7.44/16.44 inference(resolution,[status(thm)],[f60,f66])).
% 7.44/16.44 fof(f201,plain,(
% 7.44/16.44 ![X0,X1]: (subset(union(X0,X1),X0)|member(sK0_skl(X0,union(X0,X1)),X1))),
% 7.44/16.44 inference(duplicate_literals_removal,[status(thm)],[f182])).
% 7.44/16.44 fof(f202,plain,(
% 7.44/16.44 ![X0]: (subset(union(X0,sK3_skl),sK2_skl)|member(sK0_skl(sK2_skl,union(X0,sK3_skl)),X0))),
% 7.44/16.44 inference(duplicate_literals_removal,[status(thm)],[f187])).
% 7.44/16.44 fof(f278,plain,(
% 7.44/16.44 ![X0,X1]: (subset(X0,union(X0,X1))|subset(X0,union(X0,X1)))),
% 7.44/16.44 inference(resolution,[status(thm)],[f64,f25])).
% 7.44/16.44 fof(f287,plain,(
% 7.44/16.44 ![X0,X1]: (subset(X0,union(X0,X1)))),
% 7.44/16.44 inference(duplicate_literals_removal,[status(thm)],[f278])).
% 7.44/16.44 fof(f313,plain,(
% 7.44/16.44 ![X0,X1]: (union(X0,X1)=X0|~subset(union(X0,X1),X0))),
% 7.44/16.44 inference(resolution,[status(thm)],[f287,f18])).
% 7.44/16.44 fof(f586,plain,(
% 7.44/16.44 ![X0,X1]: (subset(union(union(X0,X1),X0),union(X0,X1))|subset(union(union(X0,X1),X0),union(X0,X1)))),
% 7.44/16.44 inference(resolution,[status(thm)],[f201,f64])).
% 7.44/16.44 fof(f597,plain,(
% 7.44/16.44 ![X0,X1]: (subset(union(union(X0,X1),X0),union(X0,X1)))),
% 7.44/16.44 inference(duplicate_literals_removal,[status(thm)],[f586])).
% 7.44/16.44 fof(f737,plain,(
% 7.44/16.44 ![X0]: (~member(sK0_skl(sK2_skl,X0),sK4_skl)|subset(X0,sK2_skl))),
% 7.44/16.44 inference(resolution,[status(thm)],[f41,f26])).
% 7.44/16.44 fof(f1156,plain,(
% 7.44/16.44 subset(union(sK2_skl,sK3_skl),sK2_skl)|subset(union(sK2_skl,sK3_skl),sK2_skl)),
% 7.44/16.44 inference(resolution,[status(thm)],[f152,f201])).
% 7.44/16.44 fof(f1162,definition,(
% 7.44/16.44 sQ52_spl <=> (subset(union(sK2_skl,sK3_skl),sK2_skl))),
% 7.44/16.44 introduced(definition,[new_symbols(definition,[sQ52_spl])],[split_symbol_definition])).
% 7.44/16.44 fof(f1163,plain,(
% 7.44/16.44 subset(union(sK2_skl,sK3_skl),sK2_skl)|~sQ52_spl),
% 7.44/16.44 inference(component_clause,[status(thm)],[f1162])).
% 7.44/16.44 fof(f1165,plain,(
% 7.44/16.44 sQ52_spl),
% 7.44/16.44 inference(split_clause,[status(thm)],[f1156,f1162])).
% 7.44/16.44 fof(f1478,plain,(
% 7.44/16.44 ![X0]: (member(sK0_skl(union(sK4_skl,X0),sK2_skl),sK3_skl)|subset(sK2_skl,union(sK4_skl,X0))|subset(sK2_skl,union(sK4_skl,X0)))),
% 7.44/16.44 inference(resolution,[status(thm)],[f120,f64])).
% 7.44/16.44 fof(f1485,plain,(
% 7.44/16.44 ![X0]: (member(sK0_skl(union(sK4_skl,X0),sK2_skl),sK3_skl)|subset(sK2_skl,union(sK4_skl,X0)))),
% 7.44/16.44 inference(duplicate_literals_removal,[status(thm)],[f1478])).
% 7.44/16.44 fof(f1523,plain,(
% 7.44/16.44 union(sK2_skl,sK3_skl)=sK2_skl|~sQ52_spl),
% 7.44/16.44 inference(resolution,[status(thm)],[f1163,f313])).
% 7.44/16.45 fof(f2578,plain,(
% 7.44/16.45 ![X0,X1]: (union(union(X0,X1),X0)=union(X0,X1))),
% 7.44/16.45 inference(resolution,[status(thm)],[f597,f313])).
% 7.44/16.45 fof(f2695,plain,(
% 7.44/16.45 ![X0,X1]: (union(union(X0,X1),X1)=union(X1,X0))),
% 7.44/16.45 inference(paramodulation,[status(thm)],[f19,f2578])).
% 7.44/16.45 fof(f3341,plain,(
% 7.44/16.45 subset(union(sK4_skl,sK3_skl),sK2_skl)|subset(union(sK4_skl,sK3_skl),sK2_skl)),
% 7.44/16.45 inference(resolution,[status(thm)],[f202,f737])).
% 7.44/16.45 fof(f3352,definition,(
% 7.44/16.45 sQ96_spl <=> (subset(union(sK4_skl,sK3_skl),sK2_skl))),
% 7.44/16.45 introduced(definition,[new_symbols(definition,[sQ96_spl])],[split_symbol_definition])).
% 7.44/16.45 fof(f3353,plain,(
% 7.44/16.45 subset(union(sK4_skl,sK3_skl),sK2_skl)|~sQ96_spl),
% 7.44/16.45 inference(component_clause,[status(thm)],[f3352])).
% 7.44/16.45 fof(f3355,plain,(
% 7.44/16.45 sQ96_spl),
% 7.44/16.45 inference(split_clause,[status(thm)],[f3341,f3352])).
% 7.44/16.45 fof(f3425,plain,(
% 7.44/16.45 sK2_skl=union(sK4_skl,sK3_skl)|~subset(sK2_skl,union(sK4_skl,sK3_skl))|~sQ96_spl),
% 7.44/16.45 inference(resolution,[status(thm)],[f3353,f18])).
% 7.44/16.45 fof(f3428,definition,(
% 7.44/16.45 sQ102_spl <=> (sK2_skl=union(sK4_skl,sK3_skl))),
% 7.44/16.45 introduced(definition,[new_symbols(definition,[sQ102_spl])],[split_symbol_definition])).
% 7.44/16.45 fof(f3429,plain,(
% 7.44/16.45 sK2_skl=union(sK4_skl,sK3_skl)|~sQ102_spl),
% 7.44/16.45 inference(component_clause,[status(thm)],[f3428])).
% 7.44/16.45 fof(f3431,definition,(
% 7.44/16.45 sQ103_spl <=> (subset(sK2_skl,union(sK4_skl,sK3_skl)))),
% 7.44/16.45 introduced(definition,[new_symbols(definition,[sQ103_spl])],[split_symbol_definition])).
% 7.44/16.45 fof(f3434,plain,(
% 7.44/16.45 sQ102_spl|~sQ103_spl|~sQ96_spl),
% 7.44/16.45 inference(split_clause,[status(thm)],[f3425,f3428,f3431,f3352])).
% 7.44/16.45 fof(f3445,plain,(
% 7.44/16.45 union(sK2_skl,sK3_skl)=union(sK3_skl,sK4_skl)|~sQ102_spl),
% 7.44/16.45 inference(paramodulation,[status(thm)],[f3429,f2695])).
% 7.44/16.45 fof(f3491,plain,(
% 7.44/16.45 sK2_skl=union(sK3_skl,sK4_skl)|~sQ52_spl|~sQ102_spl),
% 7.44/16.45 inference(forward_demodulation,[status(thm)],[f1523,f3445])).
% 7.44/16.45 fof(f3492,plain,(
% 7.44/16.45 $false|~sQ52_spl|~sQ102_spl),
% 7.44/16.45 inference(forward_subsumption_resolution,[status(thm)],[f3491,f42])).
% 7.44/16.45 fof(f3493,plain,(
% 7.44/16.45 ~sQ52_spl|~sQ102_spl),
% 7.44/16.45 inference(contradiction_clause,[status(thm)],[f3492])).
% 7.44/16.45 fof(f18974,plain,(
% 7.44/16.45 subset(sK2_skl,union(sK4_skl,sK3_skl))|subset(sK2_skl,union(sK4_skl,sK3_skl))),
% 7.44/16.45 inference(resolution,[status(thm)],[f1485,f63])).
% 7.44/16.45 fof(f18988,plain,(
% 7.44/16.45 sQ103_spl),
% 7.44/16.45 inference(split_clause,[status(thm)],[f18974,f3431])).
% 7.44/16.45 fof(f18996,plain,(
% 7.44/16.45 $false),
% 7.44/16.45 inference(sat_refutation,[status(thm)],[f1165,f3355,f3434,f3493,f18988])).
% 7.44/16.45 % SZS output end CNFRefutation for theBenchmark.p
% 7.44/16.47 % Elapsed time: 1.012689 seconds
% 7.44/16.47 % CPU time: 7.844245 seconds
% 7.44/16.47 % Total memory used: 193.508 MB
% 7.44/16.47 % Net memory used: 182.510 MB
%------------------------------------------------------------------------------