%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SET889+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.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 02:12:49 PM UTC 2026
% Result : Theorem 35.74s 4.97s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET889+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.03 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n005.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 05:42:48 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 % Drodi V4.1.1
% 35.74/4.97 % Refutation found
% 35.74/4.97 % SZS status Theorem for theBenchmark: Theorem is valid
% 35.74/4.97 % SZS output start CNFRefutation for theBenchmark
% 35.74/4.97 fof(f3,axiom,(
% 35.74/4.97 (! [A,B] :( B = powerset(A)<=> (! [C] :( in(C,B)<=> subset(C,A) ) )) )),
% 35.74/4.97 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 35.74/4.97 fof(f4,axiom,(
% 35.74/4.97 (! [A,B,C] :( C = unordered_pair(A,B)<=> (! [D] :( in(D,C)<=> ( D = A| D = B ) ) )) )),
% 35.74/4.97 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 35.74/4.97 fof(f6,axiom,(
% 35.74/4.97 (! [A,B] :( subset(A,singleton(B))<=> ( A = empty_set| A = singleton(B) ) ) )),
% 35.74/4.97 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 35.74/4.97 fof(f9,axiom,(
% 35.74/4.97 (! [A,B] : subset(A,A) )),
% 35.74/4.97 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 35.74/4.97 fof(f11,conjecture,(
% 35.74/4.97 (! [A] : powerset(singleton(A)) = unordered_pair(empty_set,singleton(A)) )),
% 35.74/4.97 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 35.74/4.97 fof(f12,negated_conjecture,(
% 35.74/4.97 ~((! [A] : powerset(singleton(A)) = unordered_pair(empty_set,singleton(A)) ))),
% 35.74/4.97 inference(negated_conjecture,[status(cth)],[f11])).
% 35.74/4.97 fof(f16,plain,(
% 35.74/4.97 ![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))))))),
% 35.74/4.97 inference(NNF_transformation,[status(thm)],[f3])).
% 35.74/4.97 fof(f17,plain,(
% 35.74/4.97 (![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))))))),
% 35.74/4.97 inference(miniscoping,[status(thm)],[f16])).
% 35.74/4.97 fof(f18,plain,(
% 35.74/4.97 (![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(sK0_skl(B,A),B)|~subset(sK0_skl(B,A),A))&(in(sK0_skl(B,A),B)|subset(sK0_skl(B,A),A)))))),
% 35.74/4.97 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(C,sK0_skl(B,A))],[f17])).
% 35.74/4.97 fof(f19,plain,(
% 35.74/4.97 ![X0,X1,X2]: (~X0=powerset(X1)|~in(X2,X0)|subset(X2,X1))),
% 35.74/4.97 inference(cnf_transformation,[status(thm)],[f18])).
% 35.74/4.97 fof(f20,plain,(
% 35.74/4.97 ![X0,X1,X2]: (~X0=powerset(X1)|in(X2,X0)|~subset(X2,X1))),
% 35.74/4.97 inference(cnf_transformation,[status(thm)],[f18])).
% 35.74/4.97 fof(f23,plain,(
% 35.74/4.97 ![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))))))),
% 35.74/4.97 inference(NNF_transformation,[status(thm)],[f4])).
% 35.74/4.97 fof(f24,plain,(
% 35.74/4.97 (![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))))))),
% 35.74/4.97 inference(miniscoping,[status(thm)],[f23])).
% 35.74/4.97 fof(f25,plain,(
% 35.74/4.97 (![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)))))),
% 35.74/4.97 inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(D,sK1_skl(C,B,A))],[f24])).
% 35.74/4.97 fof(f29,plain,(
% 35.74/4.97 ![X0,X1,X2]: (X0=unordered_pair(X1,X2)|~in(sK1_skl(X0,X2,X1),X0)|~sK1_skl(X0,X2,X1)=X1)),
% 35.74/4.97 inference(cnf_transformation,[status(thm)],[f25])).
% 35.74/4.97 fof(f30,plain,(
% 35.74/4.97 ![X0,X1,X2]: (X0=unordered_pair(X1,X2)|~in(sK1_skl(X0,X2,X1),X0)|~sK1_skl(X0,X2,X1)=X2)),
% 35.74/4.97 inference(cnf_transformation,[status(thm)],[f25])).
% 35.74/4.97 fof(f31,plain,(
% 35.74/4.97 ![X0,X1,X2]: (X0=unordered_pair(X1,X2)|in(sK1_skl(X0,X2,X1),X0)|sK1_skl(X0,X2,X1)=X1|sK1_skl(X0,X2,X1)=X2)),
% 35.74/4.97 inference(cnf_transformation,[status(thm)],[f25])).
% 35.74/4.97 fof(f33,plain,(
% 35.74/4.97 ![A,B]: ((~subset(A,singleton(B))|(A=empty_set|A=singleton(B)))&(subset(A,singleton(B))|(~A=empty_set&~A=singleton(B))))),
% 35.74/4.97 inference(NNF_transformation,[status(thm)],[f6])).
% 35.74/4.97 fof(f34,plain,(
% 35.74/4.97 (![A,B]: (~subset(A,singleton(B))|(A=empty_set|A=singleton(B))))&(![A,B]: (subset(A,singleton(B))|(~A=empty_set&~A=singleton(B))))),
% 35.74/4.97 inference(miniscoping,[status(thm)],[f33])).
% 35.74/4.97 fof(f35,plain,(
% 35.74/4.97 ![X0,X1]: (~subset(X0,singleton(X1))|X0=empty_set|X0=singleton(X1))),
% 35.74/4.97 inference(cnf_transformation,[status(thm)],[f34])).
% 35.74/4.97 fof(f36,plain,(
% 35.74/4.97 ![X0,X1]: (subset(X0,singleton(X1))|~X0=empty_set)),
% 35.74/4.97 inference(cnf_transformation,[status(thm)],[f34])).
% 35.74/4.97 fof(f42,plain,(
% 35.74/4.97 ![A]: subset(A,A)),
% 35.74/4.97 inference(miniscoping,[status(thm)],[f9])).
% 35.74/4.97 fof(f43,plain,(
% 35.74/4.97 ![X0]: (subset(X0,X0))),
% 35.74/4.97 inference(cnf_transformation,[status(thm)],[f42])).
% 35.74/4.97 fof(f49,plain,(
% 35.74/4.97 (?[A]: ~powerset(singleton(A))=unordered_pair(empty_set,singleton(A)))),
% 35.74/4.97 inference(pre_NNF_transformation,[status(thm)],[f12])).
% 35.74/4.97 fof(f50,plain,(
% 35.74/4.97 ~powerset(singleton(sK5_skl))=unordered_pair(empty_set,singleton(sK5_skl))),
% 35.74/4.97 inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl]),skolemize(A,sK5_skl)],[f49])).
% 35.74/4.97 fof(f51,plain,(
% 35.74/4.97 ~powerset(singleton(sK5_skl))=unordered_pair(empty_set,singleton(sK5_skl))),
% 35.74/4.97 inference(cnf_transformation,[status(thm)],[f50])).
% 35.74/4.97 fof(f52,plain,(
% 35.74/4.97 ![X0,X1]: (~in(X0,powerset(X1))|subset(X0,X1))),
% 35.74/4.97 inference(destructive_equality_resolution,[status(thm)],[f19])).
% 35.74/4.97 fof(f53,plain,(
% 35.74/4.97 ![X0,X1]: (in(X0,powerset(X1))|~subset(X0,X1))),
% 35.74/4.97 inference(destructive_equality_resolution,[status(thm)],[f20])).
% 35.74/4.97 fof(f57,plain,(
% 35.74/4.97 ![X0]: (subset(empty_set,singleton(X0)))),
% 35.74/4.97 inference(destructive_equality_resolution,[status(thm)],[f36])).
% 35.74/4.97 fof(f110,plain,(
% 35.74/4.97 ![X0,X1,X2]: (powerset(X0)=unordered_pair(X1,X2)|~sK1_skl(powerset(X0),X2,X1)=X1|~subset(sK1_skl(powerset(X0),X2,X1),X0))),
% 35.74/4.97 inference(resolution,[status(thm)],[f29,f53])).
% 35.74/4.97 fof(f111,plain,(
% 35.74/4.97 ![X0,X1,X2]: (powerset(X0)=unordered_pair(X1,X2)|~sK1_skl(powerset(X0),X2,X1)=X2|~subset(sK1_skl(powerset(X0),X2,X1),X0))),
% 35.74/4.97 inference(resolution,[status(thm)],[f30,f53])).
% 35.74/4.97 fof(f172,plain,(
% 35.74/4.97 ![X0,X1,X2]: (powerset(X0)=unordered_pair(X1,X2)|sK1_skl(powerset(X0),X2,X1)=X1|sK1_skl(powerset(X0),X2,X1)=X2|subset(sK1_skl(powerset(X0),X2,X1),X0))),
% 35.74/4.97 inference(resolution,[status(thm)],[f31,f52])).
% 35.74/4.97 fof(f201,plain,(
% 35.74/4.97 ![X0,X1,X2]: (powerset(singleton(X0))=unordered_pair(X1,X2)|sK1_skl(powerset(singleton(X0)),X2,X1)=X1|sK1_skl(powerset(singleton(X0)),X2,X1)=X2|sK1_skl(powerset(singleton(X0)),X2,X1)=empty_set|sK1_skl(powerset(singleton(X0)),X2,X1)=singleton(X0))),
% 35.74/4.97 inference(resolution,[status(thm)],[f172,f35])).
% 35.74/4.97 fof(f795,plain,(
% 35.74/4.97 ![X0,X1,X2]: (powerset(singleton(X0))=unordered_pair(X1,X2)|sK1_skl(powerset(singleton(X0)),X2,X1)=X2|sK1_skl(powerset(singleton(X0)),X2,X1)=singleton(X0)|~X1=empty_set|sK1_skl(powerset(singleton(X0)),X2,X1)=empty_set)),
% 35.74/4.97 inference(equality_factoring,[status(thm)],[f201])).
% 35.74/4.97 fof(f805,plain,(
% 35.74/4.97 ![X0,X1]: (powerset(singleton(X0))=unordered_pair(empty_set,X1)|sK1_skl(powerset(singleton(X0)),X1,empty_set)=X1|sK1_skl(powerset(singleton(X0)),X1,empty_set)=singleton(X0)|sK1_skl(powerset(singleton(X0)),X1,empty_set)=empty_set)),
% 35.74/4.97 inference(destructive_equality_resolution,[status(thm)],[f795])).
% 35.74/4.97 fof(f7144,plain,(
% 35.74/4.97 ![X0,X1]: (powerset(singleton(X0))=unordered_pair(empty_set,X1)|~sK1_skl(powerset(singleton(X0)),X1,empty_set)=X1|~subset(X1,singleton(X0))|powerset(singleton(X0))=unordered_pair(empty_set,X1)|sK1_skl(powerset(singleton(X0)),X1,empty_set)=singleton(X0)|sK1_skl(powerset(singleton(X0)),X1,empty_set)=empty_set)),
% 35.74/4.97 inference(paramodulation,[status(thm)],[f805,f111])).
% 35.74/4.97 fof(f7150,plain,(
% 35.74/4.97 ![X0,X1]: (powerset(singleton(X0))=unordered_pair(empty_set,X1)|sK1_skl(powerset(singleton(X0)),X1,empty_set)=empty_set|~X1=singleton(X0)|sK1_skl(powerset(singleton(X0)),X1,empty_set)=singleton(X0))),
% 35.74/4.97 inference(equality_factoring,[status(thm)],[f805])).
% 35.74/4.97 fof(f7157,plain,(
% 35.74/4.97 ![X0,X1]: (powerset(singleton(X0))=unordered_pair(empty_set,X1)|~sK1_skl(powerset(singleton(X0)),X1,empty_set)=X1|~subset(X1,singleton(X0))|sK1_skl(powerset(singleton(X0)),X1,empty_set)=singleton(X0)|sK1_skl(powerset(singleton(X0)),X1,empty_set)=empty_set)),
% 35.74/4.97 inference(duplicate_literals_removal,[status(thm)],[f7144])).
% 35.74/4.97 fof(f7158,plain,(
% 35.74/4.97 ![X0,X1]: (powerset(singleton(X0))=unordered_pair(empty_set,X1)|~subset(X1,singleton(X0))|sK1_skl(powerset(singleton(X0)),X1,empty_set)=singleton(X0)|sK1_skl(powerset(singleton(X0)),X1,empty_set)=empty_set)),
% 35.74/4.97 inference(forward_subsumption_resolution,[status(thm)],[f7157,f805])).
% 35.74/4.97 fof(f7163,plain,(
% 35.74/4.97 ![X0]: (powerset(singleton(X0))=unordered_pair(empty_set,singleton(X0))|sK1_skl(powerset(singleton(X0)),singleton(X0),empty_set)=empty_set|sK1_skl(powerset(singleton(X0)),singleton(X0),empty_set)=singleton(X0))),
% 35.74/4.99 inference(destructive_equality_resolution,[status(thm)],[f7150])).
% 35.74/4.99 fof(f7860,plain,(
% 35.74/4.99 ![X0]: (powerset(singleton(X0))=unordered_pair(empty_set,singleton(X0))|~sK1_skl(powerset(singleton(X0)),singleton(X0),empty_set)=singleton(X0)|~subset(singleton(X0),singleton(X0))|powerset(singleton(X0))=unordered_pair(empty_set,singleton(X0))|sK1_skl(powerset(singleton(X0)),singleton(X0),empty_set)=empty_set)),
% 35.74/4.99 inference(paramodulation,[status(thm)],[f7163,f111])).
% 35.74/4.99 fof(f7870,plain,(
% 35.74/4.99 ![X0]: (powerset(singleton(X0))=unordered_pair(empty_set,singleton(X0))|~sK1_skl(powerset(singleton(X0)),singleton(X0),empty_set)=singleton(X0)|~subset(singleton(X0),singleton(X0))|sK1_skl(powerset(singleton(X0)),singleton(X0),empty_set)=empty_set)),
% 35.74/4.99 inference(duplicate_literals_removal,[status(thm)],[f7860])).
% 35.74/4.99 fof(f7871,plain,(
% 35.74/4.99 ![X0]: (powerset(singleton(X0))=unordered_pair(empty_set,singleton(X0))|~subset(singleton(X0),singleton(X0))|sK1_skl(powerset(singleton(X0)),singleton(X0),empty_set)=empty_set)),
% 35.74/4.99 inference(forward_subsumption_resolution,[status(thm)],[f7870,f7158])).
% 35.74/4.99 fof(f7977,plain,(
% 35.74/4.99 ![X0]: (powerset(singleton(X0))=unordered_pair(empty_set,singleton(X0))|sK1_skl(powerset(singleton(X0)),singleton(X0),empty_set)=empty_set)),
% 35.74/4.99 inference(resolution,[status(thm)],[f7871,f43])).
% 35.74/4.99 fof(f7984,plain,(
% 35.74/4.99 ![X0]: (powerset(singleton(X0))=unordered_pair(empty_set,singleton(X0))|~sK1_skl(powerset(singleton(X0)),singleton(X0),empty_set)=empty_set|~subset(empty_set,singleton(X0))|powerset(singleton(X0))=unordered_pair(empty_set,singleton(X0)))),
% 35.74/4.99 inference(paramodulation,[status(thm)],[f7977,f110])).
% 35.74/4.99 fof(f7994,plain,(
% 35.74/4.99 ![X0]: (powerset(singleton(X0))=unordered_pair(empty_set,singleton(X0))|~sK1_skl(powerset(singleton(X0)),singleton(X0),empty_set)=empty_set|~subset(empty_set,singleton(X0)))),
% 35.74/4.99 inference(duplicate_literals_removal,[status(thm)],[f7984])).
% 35.74/4.99 fof(f7995,plain,(
% 35.74/4.99 ![X0]: (powerset(singleton(X0))=unordered_pair(empty_set,singleton(X0))|~subset(empty_set,singleton(X0)))),
% 35.74/4.99 inference(forward_subsumption_resolution,[status(thm)],[f7994,f7977])).
% 35.74/4.99 fof(f8001,plain,(
% 35.74/4.99 ![X0]: (powerset(singleton(X0))=unordered_pair(empty_set,singleton(X0)))),
% 35.74/4.99 inference(resolution,[status(thm)],[f7995,f57])).
% 35.74/4.99 fof(f8002,plain,(
% 35.74/4.99 ~powerset(singleton(sK5_skl))=powerset(singleton(sK5_skl))),
% 35.74/4.99 inference(backward_demodulation,[status(thm)],[f8001,f51])).
% 35.74/4.99 fof(f8014,plain,(
% 35.74/4.99 $false),
% 35.74/4.99 inference(trivial_equality_resolution,[status(thm)],[f8002])).
% 35.74/4.99 % SZS output end CNFRefutation for theBenchmark.p
% 35.74/5.01 % Elapsed time: 4.643497 seconds
% 35.74/5.01 % CPU time: 36.305257 seconds
% 35.74/5.01 % Total memory used: 229.505 MB
% 35.74/5.01 % Net memory used: 209.737 MB
%------------------------------------------------------------------------------