%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SEU147+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.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 0.09s 0.40s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU147+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n011.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 :
% 0.09/0.38 % Drodi V4.1.1
% 0.09/0.40 % Refutation found
% 0.09/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.40 % SZS output start CNFRefutation for theBenchmark
% 0.09/0.40 fof(f2,axiom,(
% 0.09/0.40 (! [A,B] :( B = singleton(A)<=> (! [C] :( in(C,B)<=> C = A ) )) )),
% 0.09/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.40 fof(f3,axiom,(
% 0.09/0.40 (! [A,B] :( B = powerset(A)<=> (! [C] :( in(C,B)<=> subset(C,A) ) )) )),
% 0.09/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.40 fof(f10,axiom,(
% 0.09/0.40 (! [A,B] : subset(A,A) )),
% 0.09/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.40 fof(f11,conjecture,(
% 0.09/0.40 powerset(empty_set) = singleton(empty_set) ),
% 0.09/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.40 fof(f12,negated_conjecture,(
% 0.09/0.40 ~(powerset(empty_set) = singleton(empty_set) )),
% 0.09/0.40 inference(negated_conjecture,[status(cth)],[f11])).
% 0.09/0.40 fof(f14,axiom,(
% 0.09/0.40 (! [A] :( subset(A,empty_set)=> A = empty_set ) )),
% 0.09/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.40 fof(f17,plain,(
% 0.09/0.40 ![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)))))),
% 0.09/0.40 inference(NNF_transformation,[status(thm)],[f2])).
% 0.09/0.40 fof(f18,plain,(
% 0.09/0.40 (![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)))))),
% 0.09/0.40 inference(miniscoping,[status(thm)],[f17])).
% 0.09/0.40 fof(f19,plain,(
% 0.09/0.40 (![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))))),
% 0.09/0.40 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(C,sK0_skl(B,A))],[f18])).
% 0.09/0.40 fof(f22,plain,(
% 0.09/0.40 ![X0,X1]: (X0=singleton(X1)|~in(sK0_skl(X0,X1),X0)|~sK0_skl(X0,X1)=X1)),
% 0.09/0.40 inference(cnf_transformation,[status(thm)],[f19])).
% 0.09/0.40 fof(f23,plain,(
% 0.09/0.40 ![X0,X1]: (X0=singleton(X1)|in(sK0_skl(X0,X1),X0)|sK0_skl(X0,X1)=X1)),
% 0.09/0.40 inference(cnf_transformation,[status(thm)],[f19])).
% 0.09/0.40 fof(f24,plain,(
% 0.09/0.40 ![A,B]: ((~B=powerset(A)|(![C]: ((~in(C,B)|subset(C,A))&(in(C,B)|~subset(C,A)))))&(B=powerset(A)|(?[C]: ((~in(C,B)|~subset(C,A))&(in(C,B)|subset(C,A))))))),
% 0.09/0.40 inference(NNF_transformation,[status(thm)],[f3])).
% 0.09/0.40 fof(f25,plain,(
% 0.09/0.40 (![A,B]: (~B=powerset(A)|((![C]: (~in(C,B)|subset(C,A)))&(![C]: (in(C,B)|~subset(C,A))))))&(![A,B]: (B=powerset(A)|(?[C]: ((~in(C,B)|~subset(C,A))&(in(C,B)|subset(C,A))))))),
% 0.09/0.40 inference(miniscoping,[status(thm)],[f24])).
% 0.09/0.40 fof(f26,plain,(
% 0.09/0.40 (![A,B]: (~B=powerset(A)|((![C]: (~in(C,B)|subset(C,A)))&(![C]: (in(C,B)|~subset(C,A))))))&(![A,B]: (B=powerset(A)|((~in(sK1_skl(B,A),B)|~subset(sK1_skl(B,A),A))&(in(sK1_skl(B,A),B)|subset(sK1_skl(B,A),A)))))),
% 0.09/0.40 inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(C,sK1_skl(B,A))],[f25])).
% 0.09/0.40 fof(f27,plain,(
% 0.09/0.40 ![X0,X1,X2]: (~X0=powerset(X1)|~in(X2,X0)|subset(X2,X1))),
% 0.09/0.40 inference(cnf_transformation,[status(thm)],[f26])).
% 0.09/0.40 fof(f28,plain,(
% 0.09/0.40 ![X0,X1,X2]: (~X0=powerset(X1)|in(X2,X0)|~subset(X2,X1))),
% 0.09/0.40 inference(cnf_transformation,[status(thm)],[f26])).
% 0.09/0.40 fof(f36,plain,(
% 0.09/0.40 ![A]: subset(A,A)),
% 0.09/0.40 inference(miniscoping,[status(thm)],[f10])).
% 0.09/0.40 fof(f37,plain,(
% 0.09/0.40 ![X0]: (subset(X0,X0))),
% 0.09/0.40 inference(cnf_transformation,[status(thm)],[f36])).
% 0.09/0.40 fof(f38,plain,(
% 0.09/0.40 ~powerset(empty_set)=singleton(empty_set)),
% 0.09/0.40 inference(cnf_transformation,[status(thm)],[f12])).
% 0.09/0.40 fof(f44,plain,(
% 0.09/0.40 ![A]: (~subset(A,empty_set)|A=empty_set)),
% 0.09/0.40 inference(pre_NNF_transformation,[status(thm)],[f14])).
% 0.09/0.40 fof(f45,plain,(
% 0.09/0.40 ![X0]: (~subset(X0,empty_set)|X0=empty_set)),
% 0.09/0.40 inference(cnf_transformation,[status(thm)],[f44])).
% 0.09/0.40 fof(f48,plain,(
% 0.09/0.40 ![X0,X1]: (~in(X0,powerset(X1))|subset(X0,X1))),
% 0.09/0.40 inference(destructive_equality_resolution,[status(thm)],[f27])).
% 0.09/0.40 fof(f49,plain,(
% 0.09/0.40 ![X0,X1]: (in(X0,powerset(X1))|~subset(X0,X1))),
% 0.09/0.40 inference(destructive_equality_resolution,[status(thm)],[f28])).
% 0.09/0.40 fof(f53,plain,(
% 0.09/0.40 ![X0,X1]: (powerset(X0)=singleton(X1)|sK0_skl(powerset(X0),X1)=X1|subset(sK0_skl(powerset(X0),X1),X0))),
% 0.09/0.40 inference(resolution,[status(thm)],[f23,f48])).
% 0.09/0.40 fof(f63,plain,(
% 0.09/0.40 ![X0]: (in(X0,powerset(X0)))),
% 0.09/0.40 inference(resolution,[status(thm)],[f37,f49])).
% 0.09/0.40 fof(f80,plain,(
% 0.09/0.40 ![X0]: (powerset(empty_set)=singleton(X0)|sK0_skl(powerset(empty_set),X0)=X0|sK0_skl(powerset(empty_set),X0)=empty_set)),
% 0.09/0.40 inference(resolution,[status(thm)],[f53,f45])).
% 0.09/0.40 fof(f163,plain,(
% 0.09/0.40 ![X0]: (powerset(empty_set)=singleton(X0)|~X0=empty_set|sK0_skl(powerset(empty_set),X0)=empty_set)),
% 0.09/0.40 inference(equality_factoring,[status(thm)],[f80])).
% 0.09/0.40 fof(f164,plain,(
% 0.09/0.40 powerset(empty_set)=singleton(empty_set)|sK0_skl(powerset(empty_set),empty_set)=empty_set),
% 0.09/0.40 inference(factoring,[status(thm)],[f80])).
% 0.09/0.40 fof(f170,plain,(
% 0.09/0.40 powerset(empty_set)=singleton(empty_set)|sK0_skl(powerset(empty_set),empty_set)=empty_set),
% 0.09/0.40 inference(destructive_equality_resolution,[status(thm)],[f163])).
% 0.09/0.40 fof(f171,plain,(
% 0.09/0.40 sK0_skl(powerset(empty_set),empty_set)=empty_set),
% 0.09/0.40 inference(forward_subsumption_resolution,[status(thm)],[f170,f38])).
% 0.09/0.40 fof(f172,definition,(
% 0.09/0.40 sQ2_spl <=> (powerset(empty_set)=singleton(empty_set))),
% 0.09/0.40 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.09/0.40 fof(f173,plain,(
% 0.09/0.40 powerset(empty_set)=singleton(empty_set)|~sQ2_spl),
% 0.09/0.40 inference(component_clause,[status(thm)],[f172])).
% 0.09/0.40 fof(f175,definition,(
% 0.09/0.40 sQ3_spl <=> (sK0_skl(powerset(empty_set),empty_set)=empty_set)),
% 0.09/0.40 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 0.09/0.40 fof(f178,plain,(
% 0.09/0.40 sQ2_spl|sQ3_spl),
% 0.09/0.40 inference(split_clause,[status(thm)],[f164,f172,f175])).
% 0.09/0.40 fof(f179,plain,(
% 0.09/0.40 $false|~sQ2_spl),
% 0.09/0.40 inference(forward_subsumption_resolution,[status(thm)],[f173,f38])).
% 0.09/0.40 fof(f180,plain,(
% 0.09/0.40 ~sQ2_spl),
% 0.09/0.40 inference(contradiction_clause,[status(thm)],[f179])).
% 0.09/0.40 fof(f186,plain,(
% 0.09/0.40 powerset(empty_set)=singleton(empty_set)|~in(empty_set,powerset(empty_set))|~sK0_skl(powerset(empty_set),empty_set)=empty_set),
% 0.09/0.40 inference(paramodulation,[status(thm)],[f171,f22])).
% 0.09/0.40 fof(f200,definition,(
% 0.09/0.40 sQ7_spl <=> (in(empty_set,powerset(empty_set)))),
% 0.09/0.40 introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition])).
% 0.09/0.40 fof(f202,plain,(
% 0.09/0.40 ~in(empty_set,powerset(empty_set))|sQ7_spl),
% 0.09/0.40 inference(component_clause,[status(thm)],[f200])).
% 0.09/0.40 fof(f204,plain,(
% 0.09/0.40 sQ2_spl|~sQ7_spl|~sQ3_spl),
% 0.09/0.40 inference(split_clause,[status(thm)],[f186,f172,f200,f175])).
% 0.09/0.40 fof(f205,plain,(
% 0.09/0.40 $false|sQ7_spl),
% 0.09/0.40 inference(forward_subsumption_resolution,[status(thm)],[f202,f63])).
% 0.09/0.40 fof(f206,plain,(
% 0.09/0.40 sQ7_spl),
% 0.09/0.40 inference(contradiction_clause,[status(thm)],[f205])).
% 0.09/0.40 fof(f207,plain,(
% 0.09/0.40 $false),
% 0.09/0.40 inference(sat_refutation,[status(thm)],[f178,f180,f204,f206])).
% 0.09/0.40 % SZS output end CNFRefutation for theBenchmark.p
% 0.09/0.42 % Elapsed time: 0.049367 seconds
% 0.09/0.42 % CPU time: 0.174572 seconds
% 0.09/0.42 % Total memory used: 76.242 MB
% 0.09/0.42 % Net memory used: 75.760 MB
%------------------------------------------------------------------------------