%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SEU145+2 : 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 : n009.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 02:21:47 PM UTC 2026
% Result : Theorem 5.54s 1.27s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU145+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n009.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 05:52:57 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.14/0.38 % Drodi V4.1.1
% 5.54/1.27 % Refutation found
% 5.54/1.27 % SZS status Theorem for theBenchmark: Theorem is valid
% 5.54/1.27 % SZS output start CNFRefutation for theBenchmark
% 5.54/1.27 fof(f6,axiom,(
% 5.54/1.27 (! [A,B] :( A = B<=> ( subset(A,B)& subset(B,A) ) ) )),
% 5.54/1.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 5.54/1.27 fof(f7,axiom,(
% 5.54/1.27 (! [A,B] :( B = singleton(A)<=> (! [C] :( in(C,B)<=> C = A ) )) )),
% 5.54/1.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 5.54/1.27 fof(f13,axiom,(
% 5.54/1.27 (! [A,B,C] :( C = set_difference(A,B)<=> (! [D] :( in(D,C)<=> ( in(D,A)& ~ in(D,B) ) ) )) )),
% 5.54/1.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 5.54/1.27 fof(f29,lemma,(
% 5.54/1.27 (! [A,B] :( subset(singleton(A),B)<=> in(A,B) ) )),
% 5.54/1.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 5.54/1.27 fof(f31,conjecture,(
% 5.54/1.27 (! [A,B,C] :( subset(A,B)=> ( in(C,A)| subset(A,set_difference(B,singleton(C))) ) ) )),
% 5.54/1.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 5.54/1.27 fof(f32,negated_conjecture,(
% 5.54/1.27 ~((! [A,B,C] :( subset(A,B)=> ( in(C,A)| subset(A,set_difference(B,singleton(C))) ) ) ))),
% 5.54/1.27 inference(negated_conjecture,[status(cth)],[f31])).
% 5.54/1.27 fof(f36,axiom,(
% 5.54/1.27 (! [A,B] :( disjoint(A,B)=> disjoint(B,A) ) )),
% 5.54/1.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 5.54/1.27 fof(f47,lemma,(
% 5.54/1.27 (! [A,B,C] :( subset(A,B)=> subset(set_difference(A,C),set_difference(B,C)) ) )),
% 5.54/1.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 5.54/1.27 fof(f48,lemma,(
% 5.54/1.27 (! [A,B] : subset(set_difference(A,B),A) )),
% 5.54/1.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 5.54/1.27 fof(f65,lemma,(
% 5.54/1.27 (! [A,B] :( disjoint(A,B)<=> set_difference(A,B) = A ) )),
% 5.54/1.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 5.54/1.27 fof(f75,plain,(
% 5.54/1.27 ![A,B]: ((~A=B|(subset(A,B)&subset(B,A)))&(A=B|(~subset(A,B)|~subset(B,A))))),
% 5.54/1.27 inference(NNF_transformation,[status(thm)],[f6])).
% 5.54/1.27 fof(f76,plain,(
% 5.54/1.27 (![A,B]: (~A=B|(subset(A,B)&subset(B,A))))&(![A,B]: (A=B|(~subset(A,B)|~subset(B,A))))),
% 5.54/1.27 inference(miniscoping,[status(thm)],[f75])).
% 5.54/1.27 fof(f79,plain,(
% 5.54/1.27 ![X0,X1]: (X0=X1|~subset(X0,X1)|~subset(X1,X0))),
% 5.54/1.27 inference(cnf_transformation,[status(thm)],[f76])).
% 5.54/1.27 fof(f80,plain,(
% 5.54/1.28 ![A,B]: ((~B=singleton(A)|(![C]: ((~in(C,B)|C=A)&(in(C,B)|~C=A))))&(B=singleton(A)|(?[C]: ((~in(C,B)|~C=A)&(in(C,B)|C=A)))))),
% 5.54/1.28 inference(NNF_transformation,[status(thm)],[f7])).
% 5.54/1.28 fof(f81,plain,(
% 5.54/1.28 (![A,B]: (~B=singleton(A)|((![C]: (~in(C,B)|C=A))&(![C]: (in(C,B)|~C=A)))))&(![A,B]: (B=singleton(A)|(?[C]: ((~in(C,B)|~C=A)&(in(C,B)|C=A)))))),
% 5.54/1.28 inference(miniscoping,[status(thm)],[f80])).
% 5.54/1.28 fof(f82,plain,(
% 5.54/1.28 (![A,B]: (~B=singleton(A)|((![C]: (~in(C,B)|C=A))&(![C]: (in(C,B)|~C=A)))))&(![A,B]: (B=singleton(A)|((~in(sK0_skl(B,A),B)|~sK0_skl(B,A)=A)&(in(sK0_skl(B,A),B)|sK0_skl(B,A)=A))))),
% 5.54/1.28 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(C,sK0_skl(B,A))],[f81])).
% 5.54/1.28 fof(f84,plain,(
% 5.54/1.28 ![X0,X1,X2]: (~X0=singleton(X1)|in(X2,X0)|~X2=X1)),
% 5.54/1.28 inference(cnf_transformation,[status(thm)],[f82])).
% 5.54/1.28 fof(f126,plain,(
% 5.54/1.28 ![A,B,C]: ((~C=set_difference(A,B)|(![D]: ((~in(D,C)|(in(D,A)&~in(D,B)))&(in(D,C)|(~in(D,A)|in(D,B))))))&(C=set_difference(A,B)|(?[D]: ((~in(D,C)|(~in(D,A)|in(D,B)))&(in(D,C)|(in(D,A)&~in(D,B)))))))),
% 5.54/1.28 inference(NNF_transformation,[status(thm)],[f13])).
% 5.54/1.28 fof(f127,plain,(
% 5.54/1.28 (![A,B,C]: (~C=set_difference(A,B)|((![D]: (~in(D,C)|(in(D,A)&~in(D,B))))&(![D]: (in(D,C)|(~in(D,A)|in(D,B)))))))&(![A,B,C]: (C=set_difference(A,B)|(?[D]: ((~in(D,C)|(~in(D,A)|in(D,B)))&(in(D,C)|(in(D,A)&~in(D,B)))))))),
% 5.54/1.28 inference(miniscoping,[status(thm)],[f126])).
% 5.54/1.28 fof(f128,plain,(
% 5.54/1.28 (![A,B,C]: (~C=set_difference(A,B)|((![D]: (~in(D,C)|(in(D,A)&~in(D,B))))&(![D]: (in(D,C)|(~in(D,A)|in(D,B)))))))&(![A,B,C]: (C=set_difference(A,B)|((~in(sK6_skl(C,B,A),C)|(~in(sK6_skl(C,B,A),A)|in(sK6_skl(C,B,A),B)))&(in(sK6_skl(C,B,A),C)|(in(sK6_skl(C,B,A),A)&~in(sK6_skl(C,B,A),B))))))),
% 5.54/1.28 inference(skolemize,[status(esa),new_symbols(skolem,[sK6_skl]),skolemize(D,sK6_skl(C,B,A))],[f127])).
% 5.54/1.28 fof(f131,plain,(
% 5.54/1.28 ![X0,X1,X2,X3]: (~X0=set_difference(X1,X2)|in(X3,X0)|~in(X3,X1)|in(X3,X2))),
% 5.54/1.28 inference(cnf_transformation,[status(thm)],[f128])).
% 5.54/1.28 fof(f158,plain,(
% 5.54/1.28 ![A,B]: ((~subset(singleton(A),B)|in(A,B))&(subset(singleton(A),B)|~in(A,B)))),
% 5.54/1.28 inference(NNF_transformation,[status(thm)],[f29])).
% 5.54/1.28 fof(f159,plain,(
% 5.54/1.28 (![A,B]: (~subset(singleton(A),B)|in(A,B)))&(![A,B]: (subset(singleton(A),B)|~in(A,B)))),
% 5.54/1.28 inference(miniscoping,[status(thm)],[f158])).
% 5.54/1.28 fof(f161,plain,(
% 5.54/1.28 ![X0,X1]: (subset(singleton(X0),X1)|~in(X0,X1))),
% 5.54/1.28 inference(cnf_transformation,[status(thm)],[f159])).
% 5.54/1.28 fof(f166,plain,(
% 5.54/1.28 (?[A,B,C]: (subset(A,B)&(~in(C,A)&~subset(A,set_difference(B,singleton(C))))))),
% 5.54/1.28 inference(pre_NNF_transformation,[status(thm)],[f32])).
% 5.54/1.28 fof(f167,plain,(
% 5.54/1.28 ?[A,B]: (subset(A,B)&(?[C]: (~in(C,A)&~subset(A,set_difference(B,singleton(C))))))),
% 5.54/1.28 inference(miniscoping,[status(thm)],[f166])).
% 5.54/1.28 fof(f168,plain,(
% 5.54/1.28 (subset(sK7_skl,sK8_skl)&(~in(sK9_skl,sK7_skl)&~subset(sK7_skl,set_difference(sK8_skl,singleton(sK9_skl)))))),
% 5.54/1.28 inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl,sK8_skl,sK9_skl]),skolemize(A,sK7_skl),skolemize(B,sK8_skl),skolemize(C,sK9_skl)],[f167])).
% 5.54/1.28 fof(f169,plain,(
% 5.54/1.28 subset(sK7_skl,sK8_skl)),
% 5.54/1.28 inference(cnf_transformation,[status(thm)],[f168])).
% 5.54/1.28 fof(f170,plain,(
% 5.54/1.28 ~in(sK9_skl,sK7_skl)),
% 5.54/1.28 inference(cnf_transformation,[status(thm)],[f168])).
% 5.54/1.28 fof(f171,plain,(
% 5.54/1.28 ~subset(sK7_skl,set_difference(sK8_skl,singleton(sK9_skl)))),
% 5.54/1.28 inference(cnf_transformation,[status(thm)],[f168])).
% 5.54/1.28 fof(f178,plain,(
% 5.54/1.28 ![A,B]: (~disjoint(A,B)|disjoint(B,A))),
% 5.54/1.28 inference(pre_NNF_transformation,[status(thm)],[f36])).
% 5.54/1.28 fof(f179,plain,(
% 5.54/1.28 ![X0,X1]: (~disjoint(X0,X1)|disjoint(X1,X0))),
% 5.54/1.28 inference(cnf_transformation,[status(thm)],[f178])).
% 5.54/1.28 fof(f201,plain,(
% 5.54/1.28 ![A,B,C]: (~subset(A,B)|subset(set_difference(A,C),set_difference(B,C)))),
% 5.54/1.28 inference(pre_NNF_transformation,[status(thm)],[f47])).
% 5.54/1.28 fof(f202,plain,(
% 5.54/1.28 ![A,B]: (~subset(A,B)|(![C]: subset(set_difference(A,C),set_difference(B,C))))),
% 5.54/1.28 inference(miniscoping,[status(thm)],[f201])).
% 5.54/1.28 fof(f203,plain,(
% 5.54/1.28 ![X0,X1,X2]: (~subset(X0,X1)|subset(set_difference(X0,X2),set_difference(X1,X2)))),
% 5.54/1.28 inference(cnf_transformation,[status(thm)],[f202])).
% 5.54/1.28 fof(f204,plain,(
% 5.54/1.28 ![X0,X1]: (subset(set_difference(X0,X1),X0))),
% 5.54/1.28 inference(cnf_transformation,[status(thm)],[f48])).
% 5.54/1.28 fof(f241,plain,(
% 5.54/1.28 ![A,B]: ((~disjoint(A,B)|set_difference(A,B)=A)&(disjoint(A,B)|~set_difference(A,B)=A))),
% 5.54/1.28 inference(NNF_transformation,[status(thm)],[f65])).
% 5.54/1.28 fof(f242,plain,(
% 5.54/1.28 (![A,B]: (~disjoint(A,B)|set_difference(A,B)=A))&(![A,B]: (disjoint(A,B)|~set_difference(A,B)=A))),
% 5.54/1.28 inference(miniscoping,[status(thm)],[f241])).
% 5.54/1.28 fof(f243,plain,(
% 5.54/1.28 ![X0,X1]: (~disjoint(X0,X1)|set_difference(X0,X1)=X0)),
% 5.54/1.28 inference(cnf_transformation,[status(thm)],[f242])).
% 5.54/1.28 fof(f244,plain,(
% 5.54/1.28 ![X0,X1]: (disjoint(X0,X1)|~set_difference(X0,X1)=X0)),
% 5.54/1.28 inference(cnf_transformation,[status(thm)],[f242])).
% 5.54/1.28 fof(f253,plain,(
% 5.54/1.28 ![X0]: (in(X0,singleton(X0)))),
% 5.54/1.28 inference(destructive_equality_resolution,[status(thm)],[f84])).
% 5.54/1.28 fof(f266,plain,(
% 5.54/1.28 ![X0,X1,X2]: (in(X0,set_difference(X1,X2))|~in(X0,X1)|in(X0,X2))),
% 5.54/1.28 inference(destructive_equality_resolution,[status(thm)],[f131])).
% 5.54/1.28 fof(f273,plain,(
% 5.54/1.28 ![X0,X1]: (X0=singleton(X1)|~subset(X0,singleton(X1))|~in(X1,X0))),
% 5.54/1.28 inference(resolution,[status(thm)],[f79,f161])).
% 5.54/1.28 fof(f286,plain,(
% 5.54/1.28 ![X0,X1]: (in(X0,set_difference(singleton(X0),X1))|in(X0,X1))),
% 5.54/1.28 inference(resolution,[status(thm)],[f266,f253])).
% 5.54/1.28 fof(f312,plain,(
% 5.54/1.28 ![X0,X1]: (set_difference(X0,X1)=X0|~disjoint(X1,X0))),
% 5.54/1.28 inference(resolution,[status(thm)],[f243,f179])).
% 5.54/1.28 fof(f314,plain,(
% 5.54/1.28 ![X0,X1]: (set_difference(X0,X1)=X0|~set_difference(X1,X0)=X1)),
% 5.54/1.28 inference(resolution,[status(thm)],[f312,f244])).
% 5.54/1.28 fof(f832,plain,(
% 5.54/1.28 ![X0,X1]: (in(X0,X1)|set_difference(singleton(X0),X1)=singleton(X0)|~subset(set_difference(singleton(X0),X1),singleton(X0)))),
% 5.54/1.28 inference(resolution,[status(thm)],[f286,f273])).
% 5.54/1.28 fof(f840,plain,(
% 5.54/1.28 ![X0,X1]: (in(X0,X1)|set_difference(singleton(X0),X1)=singleton(X0))),
% 5.54/1.28 inference(forward_subsumption_resolution,[status(thm)],[f832,f204])).
% 5.54/1.28 fof(f1002,plain,(
% 5.54/1.28 set_difference(singleton(sK9_skl),sK7_skl)=singleton(sK9_skl)),
% 5.54/1.28 inference(resolution,[status(thm)],[f840,f170])).
% 5.54/1.28 fof(f1052,definition,(
% 5.54/1.28 sQ10_spl <=> (set_difference(sK7_skl,singleton(sK9_skl))=sK7_skl)),
% 5.54/1.28 introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition])).
% 5.54/1.29 fof(f1053,plain,(
% 5.54/1.29 set_difference(sK7_skl,singleton(sK9_skl))=sK7_skl|~sQ10_spl),
% 5.54/1.29 inference(component_clause,[status(thm)],[f1052])).
% 5.54/1.29 fof(f1054,plain,(
% 5.54/1.29 ~set_difference(sK7_skl,singleton(sK9_skl))=sK7_skl|sQ10_spl),
% 5.54/1.29 inference(component_clause,[status(thm)],[f1052])).
% 5.54/1.29 fof(f1496,plain,(
% 5.54/1.29 ~set_difference(singleton(sK9_skl),sK7_skl)=singleton(sK9_skl)|sQ10_spl),
% 5.54/1.29 inference(resolution,[status(thm)],[f1054,f314])).
% 5.54/1.29 fof(f1497,plain,(
% 5.54/1.29 ~singleton(sK9_skl)=singleton(sK9_skl)|sQ10_spl),
% 5.54/1.29 inference(forward_demodulation,[status(thm)],[f1002,f1496])).
% 5.54/1.29 fof(f1498,plain,(
% 5.54/1.29 $false|sQ10_spl),
% 5.54/1.29 inference(trivial_equality_resolution,[status(thm)],[f1497])).
% 5.54/1.29 fof(f1499,plain,(
% 5.54/1.29 sQ10_spl),
% 5.54/1.29 inference(contradiction_clause,[status(thm)],[f1498])).
% 5.54/1.29 fof(f1592,plain,(
% 5.54/1.29 ![X0]: (subset(set_difference(sK7_skl,X0),set_difference(sK8_skl,X0)))),
% 5.54/1.29 inference(resolution,[status(thm)],[f169,f203])).
% 5.54/1.29 fof(f1856,plain,(
% 5.54/1.29 subset(sK7_skl,set_difference(sK8_skl,singleton(sK9_skl)))|~sQ10_spl),
% 5.54/1.29 inference(paramodulation,[status(thm)],[f1053,f1592])).
% 5.54/1.29 fof(f1864,plain,(
% 5.54/1.29 $false|~sQ10_spl),
% 5.54/1.29 inference(forward_subsumption_resolution,[status(thm)],[f1856,f171])).
% 5.54/1.29 fof(f1865,plain,(
% 5.54/1.29 ~sQ10_spl),
% 5.54/1.29 inference(contradiction_clause,[status(thm)],[f1864])).
% 5.54/1.29 fof(f1866,plain,(
% 5.54/1.29 $false),
% 5.54/1.29 inference(sat_refutation,[status(thm)],[f1499,f1865])).
% 5.54/1.29 % SZS output end CNFRefutation for theBenchmark.p
% 5.54/1.30 % Elapsed time: 0.921927 seconds
% 5.54/1.30 % CPU time: 6.918687 seconds
% 5.54/1.30 % Total memory used: 152.832 MB
% 5.54/1.30 % Net memory used: 146.587 MB
%------------------------------------------------------------------------------