%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SET872+1 : 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 : n017.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 02:12:47 PM UTC 2026
% Result : Theorem 0.14s 0.46s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET872+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.42 % Computer : n017.cluster.edu
% 0.14/0.42 % Model : x86_64 x86_64
% 0.14/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.42 % Memory : 8046.5625MB
% 0.14/0.42 % OS : Linux 6.8.0-71-generic
% 0.14/0.42 % CPULimit : 300
% 0.14/0.42 % WCLimit : 300
% 0.14/0.42 % DateTime : Mon Sep 21 05:37:57 UTC 2026
% 0.14/0.43 % CPUTime :
% 0.14/0.44 % Drodi V4.1.1
% 0.14/0.46 % Refutation found
% 0.14/0.46 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.46 % SZS output start CNFRefutation for theBenchmark
% 0.14/0.46 fof(f2,axiom,(
% 0.14/0.46 (! [A,B] : unordered_pair(A,B) = unordered_pair(B,A) )),
% 0.14/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.46 fof(f3,axiom,(
% 0.14/0.46 (! [A,B] :( B = singleton(A)<=> (! [C] :( in(C,B)<=> C = A ) )) )),
% 0.14/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.46 fof(f4,axiom,(
% 0.14/0.46 (! [A,B,C] :( C = unordered_pair(A,B)<=> (! [D] :( in(D,C)<=> ( D = A| D = B ) ) )) )),
% 0.14/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.46 fof(f5,axiom,(
% 0.14/0.46 (! [A,B] :( subset(A,B)<=> (! [C] :( in(C,A)=> in(C,B) ) )) )),
% 0.14/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.46 fof(f9,conjecture,(
% 0.14/0.46 (! [A,B] : subset(singleton(A),unordered_pair(A,B)) )),
% 0.14/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.46 fof(f10,negated_conjecture,(
% 0.14/0.46 ~((! [A,B] : subset(singleton(A),unordered_pair(A,B)) ))),
% 0.14/0.46 inference(negated_conjecture,[status(cth)],[f9])).
% 0.14/0.46 fof(f13,plain,(
% 0.14/0.46 ![X0,X1]: (unordered_pair(X0,X1)=unordered_pair(X1,X0))),
% 0.14/0.46 inference(cnf_transformation,[status(thm)],[f2])).
% 0.14/0.46 fof(f14,plain,(
% 0.14/0.46 ![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)))))),
% 0.14/0.46 inference(NNF_transformation,[status(thm)],[f3])).
% 0.14/0.46 fof(f15,plain,(
% 0.14/0.46 (![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)))))),
% 0.14/0.46 inference(miniscoping,[status(thm)],[f14])).
% 0.14/0.46 fof(f16,plain,(
% 0.14/0.46 (![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))))),
% 0.14/0.46 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(C,sK0_skl(B,A))],[f15])).
% 0.14/0.46 fof(f17,plain,(
% 0.14/0.46 ![X0,X1,X2]: (~X0=singleton(X1)|~in(X2,X0)|X2=X1)),
% 0.14/0.46 inference(cnf_transformation,[status(thm)],[f16])).
% 0.14/0.46 fof(f21,plain,(
% 0.14/0.46 ![A,B,C]: ((~C=unordered_pair(A,B)|(![D]: ((~in(D,C)|(D=A|D=B))&(in(D,C)|(~D=A&~D=B)))))&(C=unordered_pair(A,B)|(?[D]: ((~in(D,C)|(~D=A&~D=B))&(in(D,C)|(D=A|D=B))))))),
% 0.14/0.46 inference(NNF_transformation,[status(thm)],[f4])).
% 0.14/0.46 fof(f22,plain,(
% 0.14/0.46 (![A,B,C]: (~C=unordered_pair(A,B)|((![D]: (~in(D,C)|(D=A|D=B)))&(![D]: (in(D,C)|(~D=A&~D=B))))))&(![A,B,C]: (C=unordered_pair(A,B)|(?[D]: ((~in(D,C)|(~D=A&~D=B))&(in(D,C)|(D=A|D=B))))))),
% 0.14/0.46 inference(miniscoping,[status(thm)],[f21])).
% 0.14/0.46 fof(f23,plain,(
% 0.14/0.46 (![A,B,C]: (~C=unordered_pair(A,B)|((![D]: (~in(D,C)|(D=A|D=B)))&(![D]: (in(D,C)|(~D=A&~D=B))))))&(![A,B,C]: (C=unordered_pair(A,B)|((~in(sK1_skl(C,B,A),C)|(~sK1_skl(C,B,A)=A&~sK1_skl(C,B,A)=B))&(in(sK1_skl(C,B,A),C)|(sK1_skl(C,B,A)=A|sK1_skl(C,B,A)=B)))))),
% 0.14/0.46 inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(D,sK1_skl(C,B,A))],[f22])).
% 0.14/0.46 fof(f26,plain,(
% 0.14/0.46 ![X0,X1,X2,X3]: (~X0=unordered_pair(X1,X2)|in(X3,X0)|~X3=X2)),
% 0.14/0.46 inference(cnf_transformation,[status(thm)],[f23])).
% 0.14/0.46 fof(f30,plain,(
% 0.14/0.46 ![A,B]: (subset(A,B)<=>(![C]: (~in(C,A)|in(C,B))))),
% 0.14/0.46 inference(pre_NNF_transformation,[status(thm)],[f5])).
% 0.14/0.46 fof(f31,plain,(
% 0.14/0.46 ![A,B]: ((~subset(A,B)|(![C]: (~in(C,A)|in(C,B))))&(subset(A,B)|(?[C]: (in(C,A)&~in(C,B)))))),
% 0.14/0.46 inference(NNF_transformation,[status(thm)],[f30])).
% 0.14/0.46 fof(f32,plain,(
% 0.14/0.46 (![A,B]: (~subset(A,B)|(![C]: (~in(C,A)|in(C,B)))))&(![A,B]: (subset(A,B)|(?[C]: (in(C,A)&~in(C,B)))))),
% 0.14/0.46 inference(miniscoping,[status(thm)],[f31])).
% 0.14/0.46 fof(f33,plain,(
% 0.14/0.46 (![A,B]: (~subset(A,B)|(![C]: (~in(C,A)|in(C,B)))))&(![A,B]: (subset(A,B)|(in(sK2_skl(B,A),A)&~in(sK2_skl(B,A),B))))),
% 0.14/0.46 inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(C,sK2_skl(B,A))],[f32])).
% 0.14/0.46 fof(f35,plain,(
% 0.14/0.46 ![X0,X1]: (subset(X0,X1)|in(sK2_skl(X1,X0),X0))),
% 0.14/0.46 inference(cnf_transformation,[status(thm)],[f33])).
% 0.14/0.46 fof(f36,plain,(
% 0.14/0.46 ![X0,X1]: (subset(X0,X1)|~in(sK2_skl(X1,X0),X1))),
% 0.14/0.46 inference(cnf_transformation,[status(thm)],[f33])).
% 0.14/0.46 fof(f43,plain,(
% 0.14/0.46 (?[A,B]: ~subset(singleton(A),unordered_pair(A,B)))),
% 0.14/0.46 inference(pre_NNF_transformation,[status(thm)],[f10])).
% 0.14/0.46 fof(f44,plain,(
% 0.14/0.46 ~subset(singleton(sK5_skl),unordered_pair(sK5_skl,sK6_skl))),
% 0.14/0.47 inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl,sK6_skl]),skolemize(A,sK5_skl),skolemize(B,sK6_skl)],[f43])).
% 0.14/0.47 fof(f45,plain,(
% 0.14/0.47 ~subset(singleton(sK5_skl),unordered_pair(sK5_skl,sK6_skl))),
% 0.14/0.47 inference(cnf_transformation,[status(thm)],[f44])).
% 0.14/0.47 fof(f46,plain,(
% 0.14/0.47 ![X0,X1]: (~in(X0,singleton(X1))|X0=X1)),
% 0.14/0.47 inference(destructive_equality_resolution,[status(thm)],[f17])).
% 0.14/0.47 fof(f50,plain,(
% 0.14/0.47 ![X0,X1]: (in(X0,unordered_pair(X1,X0)))),
% 0.14/0.47 inference(destructive_equality_resolution,[status(thm)],[f26])).
% 0.14/0.47 fof(f55,plain,(
% 0.14/0.47 ~subset(singleton(sK5_skl),unordered_pair(sK6_skl,sK5_skl))),
% 0.14/0.47 inference(paramodulation,[status(thm)],[f13,f45])).
% 0.14/0.47 fof(f108,plain,(
% 0.14/0.47 ![X0,X1]: (subset(singleton(X0),X1)|sK2_skl(X1,singleton(X0))=X0)),
% 0.14/0.47 inference(resolution,[status(thm)],[f35,f46])).
% 0.14/0.47 fof(f173,plain,(
% 0.14/0.47 sK2_skl(unordered_pair(sK6_skl,sK5_skl),singleton(sK5_skl))=sK5_skl),
% 0.14/0.47 inference(resolution,[status(thm)],[f108,f55])).
% 0.14/0.47 fof(f245,plain,(
% 0.14/0.47 subset(singleton(sK5_skl),unordered_pair(sK6_skl,sK5_skl))|~in(sK5_skl,unordered_pair(sK6_skl,sK5_skl))),
% 0.14/0.47 inference(paramodulation,[status(thm)],[f173,f36])).
% 0.14/0.47 fof(f247,definition,(
% 0.14/0.47 sQ0_spl <=> (subset(singleton(sK5_skl),unordered_pair(sK6_skl,sK5_skl)))),
% 0.14/0.47 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.14/0.47 fof(f248,plain,(
% 0.14/0.47 subset(singleton(sK5_skl),unordered_pair(sK6_skl,sK5_skl))|~sQ0_spl),
% 0.14/0.47 inference(component_clause,[status(thm)],[f247])).
% 0.14/0.47 fof(f254,definition,(
% 0.14/0.47 sQ2_spl <=> (in(sK5_skl,unordered_pair(sK6_skl,sK5_skl)))),
% 0.14/0.47 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.14/0.47 fof(f256,plain,(
% 0.14/0.47 ~in(sK5_skl,unordered_pair(sK6_skl,sK5_skl))|sQ2_spl),
% 0.14/0.47 inference(component_clause,[status(thm)],[f254])).
% 0.14/0.47 fof(f257,plain,(
% 0.14/0.47 sQ0_spl|~sQ2_spl),
% 0.14/0.47 inference(split_clause,[status(thm)],[f245,f247,f254])).
% 0.14/0.47 fof(f262,plain,(
% 0.14/0.47 $false|~sQ0_spl),
% 0.14/0.47 inference(forward_subsumption_resolution,[status(thm)],[f248,f55])).
% 0.14/0.47 fof(f263,plain,(
% 0.14/0.47 ~sQ0_spl),
% 0.14/0.47 inference(contradiction_clause,[status(thm)],[f262])).
% 0.14/0.47 fof(f264,plain,(
% 0.14/0.47 $false|sQ2_spl),
% 0.14/0.47 inference(forward_subsumption_resolution,[status(thm)],[f256,f50])).
% 0.14/0.47 fof(f265,plain,(
% 0.14/0.47 sQ2_spl),
% 0.14/0.47 inference(contradiction_clause,[status(thm)],[f264])).
% 0.14/0.47 fof(f266,plain,(
% 0.14/0.47 $false),
% 0.14/0.47 inference(sat_refutation,[status(thm)],[f257,f263,f265])).
% 0.14/0.47 % SZS output end CNFRefutation for theBenchmark.p
% 0.14/0.56 % Elapsed time: 0.119993 seconds
% 0.14/0.56 % CPU time: 0.127062 seconds
% 0.14/0.56 % Total memory used: 9.767 MB
% 0.14/0.56 % Net memory used: 9.736 MB
%------------------------------------------------------------------------------