%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SET885+1 : TPTP v9.3.1. Released v3.2.0.
% 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 02:12:48 PM UTC 2026
% Result : Theorem 0.15s 0.41s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET885+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n009.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 05:42:57 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.15/0.38 % Drodi V4.1.1
% 0.15/0.41 % Refutation found
% 0.15/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.41 % SZS output start CNFRefutation for theBenchmark
% 0.15/0.41 fof(f2,axiom,(
% 0.15/0.41 (! [A,B] : unordered_pair(A,B) = unordered_pair(B,A) )),
% 0.15/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.41 fof(f3,axiom,(
% 0.15/0.41 (! [A,B] :( B = singleton(A)<=> (! [C] :( in(C,B)<=> C = A ) )) )),
% 0.15/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.41 fof(f4,axiom,(
% 0.15/0.41 (! [A,B,C] :( C = unordered_pair(A,B)<=> (! [D] :( in(D,C)<=> ( D = A| D = B ) ) )) )),
% 0.15/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.41 fof(f5,axiom,(
% 0.15/0.41 (! [A,B] :( subset(A,B)<=> (! [C] :( in(C,A)=> in(C,B) ) )) )),
% 0.15/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.41 fof(f9,conjecture,(
% 0.15/0.41 (! [A,B,C] :( subset(unordered_pair(A,B),singleton(C))=> A = C ) )),
% 0.15/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.41 fof(f10,negated_conjecture,(
% 0.15/0.41 ~((! [A,B,C] :( subset(unordered_pair(A,B),singleton(C))=> A = C ) ))),
% 0.15/0.41 inference(negated_conjecture,[status(cth)],[f9])).
% 0.15/0.41 fof(f13,plain,(
% 0.15/0.41 ![X0,X1]: (unordered_pair(X0,X1)=unordered_pair(X1,X0))),
% 0.15/0.41 inference(cnf_transformation,[status(thm)],[f2])).
% 0.15/0.41 fof(f14,plain,(
% 0.15/0.41 ![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)))))),
% 0.15/0.41 inference(NNF_transformation,[status(thm)],[f3])).
% 0.15/0.41 fof(f15,plain,(
% 0.15/0.41 (![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)))))),
% 0.15/0.41 inference(miniscoping,[status(thm)],[f14])).
% 0.15/0.41 fof(f16,plain,(
% 0.15/0.41 (![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))))),
% 0.15/0.41 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(C,sK0_skl(B,A))],[f15])).
% 0.15/0.41 fof(f17,plain,(
% 0.15/0.41 ![X0,X1,X2]: (~X0=singleton(X1)|~in(X2,X0)|X2=X1)),
% 0.15/0.41 inference(cnf_transformation,[status(thm)],[f16])).
% 0.15/0.41 fof(f21,plain,(
% 0.15/0.41 ![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))))))),
% 0.15/0.41 inference(NNF_transformation,[status(thm)],[f4])).
% 0.15/0.41 fof(f22,plain,(
% 0.15/0.41 (![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))))))),
% 0.15/0.41 inference(miniscoping,[status(thm)],[f21])).
% 0.15/0.41 fof(f23,plain,(
% 0.15/0.41 (![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)))))),
% 0.15/0.41 inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(D,sK1_skl(C,B,A))],[f22])).
% 0.15/0.41 fof(f26,plain,(
% 0.15/0.41 ![X0,X1,X2,X3]: (~X0=unordered_pair(X1,X2)|in(X3,X0)|~X3=X2)),
% 0.15/0.41 inference(cnf_transformation,[status(thm)],[f23])).
% 0.15/0.41 fof(f30,plain,(
% 0.15/0.41 ![A,B]: (subset(A,B)<=>(![C]: (~in(C,A)|in(C,B))))),
% 0.15/0.41 inference(pre_NNF_transformation,[status(thm)],[f5])).
% 0.15/0.41 fof(f31,plain,(
% 0.15/0.41 ![A,B]: ((~subset(A,B)|(![C]: (~in(C,A)|in(C,B))))&(subset(A,B)|(?[C]: (in(C,A)&~in(C,B)))))),
% 0.15/0.41 inference(NNF_transformation,[status(thm)],[f30])).
% 0.15/0.41 fof(f32,plain,(
% 0.15/0.41 (![A,B]: (~subset(A,B)|(![C]: (~in(C,A)|in(C,B)))))&(![A,B]: (subset(A,B)|(?[C]: (in(C,A)&~in(C,B)))))),
% 0.15/0.41 inference(miniscoping,[status(thm)],[f31])).
% 0.15/0.41 fof(f33,plain,(
% 0.15/0.41 (![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))))),
% 0.15/0.41 inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(C,sK2_skl(B,A))],[f32])).
% 0.15/0.41 fof(f34,plain,(
% 0.15/0.41 ![X0,X1,X2]: (~subset(X0,X1)|~in(X2,X0)|in(X2,X1))),
% 0.15/0.41 inference(cnf_transformation,[status(thm)],[f33])).
% 0.15/0.41 fof(f43,plain,(
% 0.15/0.41 (?[A,B,C]: (subset(unordered_pair(A,B),singleton(C))&~A=C))),
% 0.15/0.41 inference(pre_NNF_transformation,[status(thm)],[f10])).
% 0.15/0.41 fof(f44,plain,(
% 0.15/0.41 ?[A,C]: ((?[B]: subset(unordered_pair(A,B),singleton(C)))&~A=C)),
% 0.15/0.41 inference(miniscoping,[status(thm)],[f43])).
% 0.15/0.41 fof(f45,plain,(
% 0.15/0.41 (subset(unordered_pair(sK5_skl,sK7_skl),singleton(sK6_skl))&~sK5_skl=sK6_skl)),
% 0.15/0.41 inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl,sK6_skl,sK7_skl]),skolemize(A,sK5_skl),skolemize(C,sK6_skl),skolemize(B,sK7_skl)],[f44])).
% 0.15/0.41 fof(f46,plain,(
% 0.15/0.41 subset(unordered_pair(sK5_skl,sK7_skl),singleton(sK6_skl))),
% 0.15/0.41 inference(cnf_transformation,[status(thm)],[f45])).
% 0.15/0.41 fof(f47,plain,(
% 0.15/0.41 ~sK5_skl=sK6_skl),
% 0.15/0.41 inference(cnf_transformation,[status(thm)],[f45])).
% 0.15/0.41 fof(f48,plain,(
% 0.15/0.41 ![X0,X1]: (~in(X0,singleton(X1))|X0=X1)),
% 0.15/0.41 inference(destructive_equality_resolution,[status(thm)],[f17])).
% 0.15/0.41 fof(f52,plain,(
% 0.15/0.41 ![X0,X1]: (in(X0,unordered_pair(X1,X0)))),
% 0.15/0.41 inference(destructive_equality_resolution,[status(thm)],[f26])).
% 0.15/0.41 fof(f57,plain,(
% 0.15/0.41 subset(unordered_pair(sK7_skl,sK5_skl),singleton(sK6_skl))),
% 0.15/0.41 inference(paramodulation,[status(thm)],[f13,f46])).
% 0.15/0.41 fof(f68,plain,(
% 0.15/0.41 ![X0,X1,X2]: (~subset(unordered_pair(X0,X1),X2)|in(X1,X2))),
% 0.15/0.41 inference(resolution,[status(thm)],[f34,f52])).
% 0.15/0.41 fof(f76,plain,(
% 0.15/0.41 in(sK7_skl,singleton(sK6_skl))),
% 0.15/0.41 inference(resolution,[status(thm)],[f68,f46])).
% 0.15/0.41 fof(f80,plain,(
% 0.15/0.41 sK7_skl=sK6_skl),
% 0.15/0.41 inference(resolution,[status(thm)],[f76,f48])).
% 0.15/0.41 fof(f84,plain,(
% 0.15/0.41 ~sK5_skl=sK7_skl),
% 0.15/0.41 inference(backward_demodulation,[status(thm)],[f80,f47])).
% 0.15/0.41 fof(f118,plain,(
% 0.15/0.41 subset(unordered_pair(sK7_skl,sK5_skl),singleton(sK7_skl))),
% 0.15/0.41 inference(forward_demodulation,[status(thm)],[f80,f57])).
% 0.15/0.41 fof(f119,plain,(
% 0.15/0.41 in(sK5_skl,singleton(sK7_skl))),
% 0.15/0.41 inference(resolution,[status(thm)],[f118,f68])).
% 0.15/0.41 fof(f120,plain,(
% 0.15/0.41 sK5_skl=sK7_skl),
% 0.15/0.41 inference(resolution,[status(thm)],[f119,f48])).
% 0.15/0.41 fof(f123,plain,(
% 0.15/0.41 $false),
% 0.15/0.41 inference(forward_subsumption_resolution,[status(thm)],[f120,f84])).
% 0.15/0.41 % SZS output end CNFRefutation for theBenchmark.p
% 0.15/0.44 % Elapsed time: 0.064806 seconds
% 0.15/0.44 % CPU time: 0.154267 seconds
% 0.15/0.44 % Total memory used: 101.702 MB
% 0.15/0.44 % Net memory used: 101.329 MB
%------------------------------------------------------------------------------