%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SET880+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 : n010.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 0.16s 0.47s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET880+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.43 % Computer : n010.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Mon Sep 21 05:42:40 UTC 2026
% 0.16/0.44 % CPUTime :
% 0.16/0.46 % Drodi V4.1.1
% 0.16/0.47 % Refutation found
% 0.16/0.47 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.16/0.47 % SZS output start CNFRefutation for theBenchmark
% 0.16/0.47 fof(f2,axiom,(
% 0.16/0.47 (! [A,B] :( B = singleton(A)<=> (! [C] :( in(C,B)<=> C = A ) )) )),
% 0.16/0.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.16/0.47 fof(f4,axiom,(
% 0.16/0.47 (! [A,B] :( set_difference(singleton(A),B) = empty_set<=> in(A,B) ) )),
% 0.16/0.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.16/0.47 fof(f7,conjecture,(
% 0.16/0.47 (! [A,B] :( set_difference(singleton(A),singleton(B)) = empty_set=> A = B ) )),
% 0.16/0.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.16/0.47 fof(f8,negated_conjecture,(
% 0.16/0.47 ~((! [A,B] :( set_difference(singleton(A),singleton(B)) = empty_set=> A = B ) ))),
% 0.16/0.47 inference(negated_conjecture,[status(cth)],[f7])).
% 0.16/0.47 fof(f11,plain,(
% 0.16/0.47 ![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)))))),
% 0.16/0.47 inference(NNF_transformation,[status(thm)],[f2])).
% 0.16/0.47 fof(f12,plain,(
% 0.16/0.47 (![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)))))),
% 0.16/0.47 inference(miniscoping,[status(thm)],[f11])).
% 0.16/0.47 fof(f13,plain,(
% 0.16/0.47 (![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))))),
% 0.16/0.47 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(C,sK0_skl(B,A))],[f12])).
% 0.16/0.47 fof(f14,plain,(
% 0.16/0.47 ![X0,X1,X2]: (~X0=singleton(X1)|~in(X2,X0)|X2=X1)),
% 0.16/0.47 inference(cnf_transformation,[status(thm)],[f13])).
% 0.16/0.47 fof(f19,plain,(
% 0.16/0.47 ![A,B]: ((~set_difference(singleton(A),B)=empty_set|in(A,B))&(set_difference(singleton(A),B)=empty_set|~in(A,B)))),
% 0.16/0.47 inference(NNF_transformation,[status(thm)],[f4])).
% 0.16/0.47 fof(f20,plain,(
% 0.16/0.47 (![A,B]: (~set_difference(singleton(A),B)=empty_set|in(A,B)))&(![A,B]: (set_difference(singleton(A),B)=empty_set|~in(A,B)))),
% 0.16/0.47 inference(miniscoping,[status(thm)],[f19])).
% 0.16/0.47 fof(f21,plain,(
% 0.16/0.47 ![X0,X1]: (~set_difference(singleton(X0),X1)=empty_set|in(X0,X1))),
% 0.16/0.47 inference(cnf_transformation,[status(thm)],[f20])).
% 0.16/0.47 fof(f27,plain,(
% 0.16/0.47 (?[A,B]: (set_difference(singleton(A),singleton(B))=empty_set&~A=B))),
% 0.16/0.47 inference(pre_NNF_transformation,[status(thm)],[f8])).
% 0.16/0.47 fof(f28,plain,(
% 0.16/0.47 (set_difference(singleton(sK3_skl),singleton(sK4_skl))=empty_set&~sK3_skl=sK4_skl)),
% 0.16/0.47 inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl,sK4_skl]),skolemize(A,sK3_skl),skolemize(B,sK4_skl)],[f27])).
% 0.16/0.47 fof(f29,plain,(
% 0.16/0.47 set_difference(singleton(sK3_skl),singleton(sK4_skl))=empty_set),
% 0.16/0.47 inference(cnf_transformation,[status(thm)],[f28])).
% 0.16/0.47 fof(f30,plain,(
% 0.16/0.47 ~sK3_skl=sK4_skl),
% 0.16/0.47 inference(cnf_transformation,[status(thm)],[f28])).
% 0.16/0.47 fof(f31,plain,(
% 0.16/0.47 ![X0,X1]: (~in(X0,singleton(X1))|X0=X1)),
% 0.16/0.47 inference(destructive_equality_resolution,[status(thm)],[f14])).
% 0.16/0.47 fof(f34,plain,(
% 0.16/0.47 ![X0,X1]: (~set_difference(singleton(X0),singleton(X1))=empty_set|X0=X1)),
% 0.16/0.47 inference(resolution,[status(thm)],[f21,f31])).
% 0.16/0.47 fof(f37,plain,(
% 0.16/0.47 sK3_skl=sK4_skl),
% 0.16/0.47 inference(resolution,[status(thm)],[f34,f29])).
% 0.16/0.47 fof(f41,plain,(
% 0.16/0.47 $false),
% 0.16/0.47 inference(forward_subsumption_resolution,[status(thm)],[f37,f30])).
% 0.16/0.47 % SZS output end CNFRefutation for theBenchmark.p
% 0.16/0.50 % Elapsed time: 0.055914 seconds
% 0.16/0.50 % CPU time: 0.148032 seconds
% 0.16/0.50 % Total memory used: 47.476 MB
% 0.16/0.50 % Net memory used: 47.291 MB
%------------------------------------------------------------------------------