%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SET879+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 : n013.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 0.09s 0.39s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET879+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
% 0.09/0.36 % Computer : n013.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 05:41:51 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.09/0.39 % Refutation found
% 0.09/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.39 % SZS output start CNFRefutation for theBenchmark
% 0.09/0.39 fof(f2,axiom,(
% 0.09/0.39 (! [A,B] :( B = singleton(A)<=> (! [C] :( in(C,B)<=> C = A ) )) )),
% 0.09/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.39 fof(f3,axiom,(
% 0.09/0.39 (! [A,B] :( set_difference(singleton(A),B) = singleton(A)<=> ~ in(A,B) ) )),
% 0.09/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.39 fof(f6,conjecture,(
% 0.09/0.39 (! [A,B] :( set_difference(singleton(A),singleton(B)) = singleton(A)<=> A != B ) )),
% 0.09/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.39 fof(f7,negated_conjecture,(
% 0.09/0.39 ~((! [A,B] :( set_difference(singleton(A),singleton(B)) = singleton(A)<=> A != B ) ))),
% 0.09/0.39 inference(negated_conjecture,[status(cth)],[f6])).
% 0.09/0.39 fof(f10,plain,(
% 0.09/0.39 ![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)))))),
% 0.09/0.39 inference(NNF_transformation,[status(thm)],[f2])).
% 0.09/0.39 fof(f11,plain,(
% 0.09/0.39 (![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)))))),
% 0.09/0.39 inference(miniscoping,[status(thm)],[f10])).
% 0.09/0.39 fof(f12,plain,(
% 0.09/0.39 (![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))))),
% 0.09/0.39 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(C,sK0_skl(B,A))],[f11])).
% 0.09/0.39 fof(f13,plain,(
% 0.09/0.39 ![X0,X1,X2]: (~X0=singleton(X1)|~in(X2,X0)|X2=X1)),
% 0.09/0.39 inference(cnf_transformation,[status(thm)],[f12])).
% 0.09/0.39 fof(f14,plain,(
% 0.09/0.39 ![X0,X1,X2]: (~X0=singleton(X1)|in(X2,X0)|~X2=X1)),
% 0.09/0.39 inference(cnf_transformation,[status(thm)],[f12])).
% 0.09/0.39 fof(f17,plain,(
% 0.09/0.39 ![A,B]: ((~set_difference(singleton(A),B)=singleton(A)|~in(A,B))&(set_difference(singleton(A),B)=singleton(A)|in(A,B)))),
% 0.09/0.39 inference(NNF_transformation,[status(thm)],[f3])).
% 0.09/0.39 fof(f18,plain,(
% 0.09/0.39 (![A,B]: (~set_difference(singleton(A),B)=singleton(A)|~in(A,B)))&(![A,B]: (set_difference(singleton(A),B)=singleton(A)|in(A,B)))),
% 0.09/0.39 inference(miniscoping,[status(thm)],[f17])).
% 0.09/0.39 fof(f19,plain,(
% 0.09/0.39 ![X0,X1]: (~set_difference(singleton(X0),X1)=singleton(X0)|~in(X0,X1))),
% 0.09/0.39 inference(cnf_transformation,[status(thm)],[f18])).
% 0.09/0.39 fof(f20,plain,(
% 0.09/0.39 ![X0,X1]: (set_difference(singleton(X0),X1)=singleton(X0)|in(X0,X1))),
% 0.09/0.39 inference(cnf_transformation,[status(thm)],[f18])).
% 0.09/0.39 fof(f25,plain,(
% 0.09/0.39 (?[A,B]: (set_difference(singleton(A),singleton(B))=singleton(A)<~>~A=B))),
% 0.09/0.39 inference(pre_NNF_transformation,[status(thm)],[f7])).
% 0.09/0.39 fof(f26,plain,(
% 0.09/0.39 ?[A,B]: ((set_difference(singleton(A),singleton(B))=singleton(A)|~A=B)&(~set_difference(singleton(A),singleton(B))=singleton(A)|A=B))),
% 0.09/0.39 inference(NNF_transformation,[status(thm)],[f25])).
% 0.09/0.39 fof(f27,plain,(
% 0.09/0.39 ((set_difference(singleton(sK3_skl),singleton(sK4_skl))=singleton(sK3_skl)|~sK3_skl=sK4_skl)&(~set_difference(singleton(sK3_skl),singleton(sK4_skl))=singleton(sK3_skl)|sK3_skl=sK4_skl))),
% 0.09/0.39 inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl,sK4_skl]),skolemize(A,sK3_skl),skolemize(B,sK4_skl)],[f26])).
% 0.09/0.39 fof(f28,plain,(
% 0.09/0.39 set_difference(singleton(sK3_skl),singleton(sK4_skl))=singleton(sK3_skl)|~sK3_skl=sK4_skl),
% 0.09/0.39 inference(cnf_transformation,[status(thm)],[f27])).
% 0.09/0.39 fof(f29,plain,(
% 0.09/0.39 ~set_difference(singleton(sK3_skl),singleton(sK4_skl))=singleton(sK3_skl)|sK3_skl=sK4_skl),
% 0.09/0.39 inference(cnf_transformation,[status(thm)],[f27])).
% 0.09/0.39 fof(f30,plain,(
% 0.09/0.39 ![X0,X1]: (~in(X0,singleton(X1))|X0=X1)),
% 0.09/0.39 inference(destructive_equality_resolution,[status(thm)],[f13])).
% 0.09/0.39 fof(f31,plain,(
% 0.09/0.39 ![X0]: (in(X0,singleton(X0)))),
% 0.09/0.39 inference(destructive_equality_resolution,[status(thm)],[f14])).
% 0.09/0.39 fof(f47,plain,(
% 0.09/0.39 ![X0]: (~set_difference(singleton(X0),singleton(X0))=singleton(X0))),
% 0.09/0.39 inference(resolution,[status(thm)],[f31,f19])).
% 0.09/0.39 fof(f54,plain,(
% 0.09/0.39 ![X0,X1]: (X0=X1|set_difference(singleton(X0),singleton(X1))=singleton(X0))),
% 0.09/0.39 inference(resolution,[status(thm)],[f30,f20])).
% 0.09/0.39 fof(f55,plain,(
% 0.09/0.39 set_difference(singleton(sK3_skl),singleton(sK4_skl))=singleton(sK3_skl)),
% 0.09/0.39 inference(backward_subsumption_resolution,[status(thm)],[f28,f54])).
% 0.09/0.40 fof(f56,plain,(
% 0.09/0.40 sK3_skl=sK4_skl),
% 0.09/0.40 inference(backward_subsumption_resolution,[status(thm)],[f29,f54])).
% 0.09/0.40 fof(f58,plain,(
% 0.09/0.40 set_difference(singleton(sK3_skl),singleton(sK4_skl))=singleton(sK4_skl)),
% 0.09/0.40 inference(backward_demodulation,[status(thm)],[f56,f55])).
% 0.09/0.40 fof(f59,plain,(
% 0.09/0.40 set_difference(singleton(sK4_skl),singleton(sK4_skl))=singleton(sK4_skl)),
% 0.09/0.40 inference(forward_demodulation,[status(thm)],[f56,f58])).
% 0.09/0.40 fof(f60,plain,(
% 0.09/0.40 $false),
% 0.09/0.40 inference(forward_subsumption_resolution,[status(thm)],[f59,f47])).
% 0.09/0.40 % SZS output end CNFRefutation for theBenchmark.p
% 0.09/0.41 % Elapsed time: 0.049271 seconds
% 0.09/0.41 % CPU time: 0.149266 seconds
% 0.09/0.41 % Total memory used: 80.038 MB
% 0.09/0.41 % Net memory used: 79.571 MB
%------------------------------------------------------------------------------