%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SET890+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.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 0.27s 0.46s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET890+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.34 % Computer : n004.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Mon Sep 21 05:42:49 UTC 2026
% 0.09/0.34 % CPUTime :
% 0.09/0.35 % Drodi V4.1.1
% 0.27/0.46 % Refutation found
% 0.27/0.46 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.27/0.46 % SZS output start CNFRefutation for theBenchmark
% 0.27/0.46 fof(f3,axiom,(
% 0.27/0.46 (! [A,B] :( B = singleton(A)<=> (! [C] :( in(C,B)<=> C = A ) )) )),
% 0.27/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.27/0.46 fof(f5,axiom,(
% 0.27/0.46 (! [A,B] :( B = union(A)<=> (! [C] :( in(C,B)<=> (? [D] :( in(C,D)& in(D,A) ) )) )) )),
% 0.27/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.27/0.46 fof(f10,conjecture,(
% 0.27/0.46 (! [A] : union(singleton(A)) = A )),
% 0.27/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.27/0.46 fof(f11,negated_conjecture,(
% 0.27/0.46 ~((! [A] : union(singleton(A)) = A ))),
% 0.27/0.46 inference(negated_conjecture,[status(cth)],[f10])).
% 0.27/0.46 fof(f19,plain,(
% 0.27/0.46 ![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)))))),
% 0.27/0.46 inference(NNF_transformation,[status(thm)],[f3])).
% 0.27/0.46 fof(f20,plain,(
% 0.27/0.46 (![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)))))),
% 0.27/0.46 inference(miniscoping,[status(thm)],[f19])).
% 0.27/0.46 fof(f21,plain,(
% 0.27/0.46 (![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))))),
% 0.27/0.46 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(C,sK0_skl(B,A))],[f20])).
% 0.27/0.46 fof(f22,plain,(
% 0.27/0.46 ![X0,X1,X2]: (~X0=singleton(X1)|~in(X2,X0)|X2=X1)),
% 0.27/0.46 inference(cnf_transformation,[status(thm)],[f21])).
% 0.27/0.46 fof(f23,plain,(
% 0.27/0.46 ![X0,X1,X2]: (~X0=singleton(X1)|in(X2,X0)|~X2=X1)),
% 0.27/0.46 inference(cnf_transformation,[status(thm)],[f21])).
% 0.27/0.46 fof(f33,plain,(
% 0.27/0.46 ![A,B]: ((~B=union(A)|(![C]: ((~in(C,B)|(?[D]: (in(C,D)&in(D,A))))&(in(C,B)|(![D]: (~in(C,D)|~in(D,A)))))))&(B=union(A)|(?[C]: ((~in(C,B)|(![D]: (~in(C,D)|~in(D,A))))&(in(C,B)|(?[D]: (in(C,D)&in(D,A))))))))),
% 0.27/0.46 inference(NNF_transformation,[status(thm)],[f5])).
% 0.27/0.46 fof(f34,plain,(
% 0.27/0.46 (![A,B]: (~B=union(A)|((![C]: (~in(C,B)|(?[D]: (in(C,D)&in(D,A)))))&(![C]: (in(C,B)|(![D]: (~in(C,D)|~in(D,A))))))))&(![A,B]: (B=union(A)|(?[C]: ((~in(C,B)|(![D]: (~in(C,D)|~in(D,A))))&(in(C,B)|(?[D]: (in(C,D)&in(D,A))))))))),
% 0.27/0.46 inference(miniscoping,[status(thm)],[f33])).
% 0.27/0.46 fof(f35,plain,(
% 0.27/0.46 (![A,B]: (~B=union(A)|((![C]: (~in(C,B)|(in(C,sK2_skl(C,B,A))&in(sK2_skl(C,B,A),A))))&(![C]: (in(C,B)|(![D]: (~in(C,D)|~in(D,A))))))))&(![A,B]: (B=union(A)|((~in(sK3_skl(B,A),B)|(![D]: (~in(sK3_skl(B,A),D)|~in(D,A))))&(in(sK3_skl(B,A),B)|(in(sK3_skl(B,A),sK4_skl(B,A))&in(sK4_skl(B,A),A))))))),
% 0.27/0.46 inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl,sK4_skl]),skolemize(D,sK2_skl(C,B,A)),skolemize(C,sK3_skl(B,A)),skolemize(D,sK4_skl(B,A))],[f34])).
% 0.27/0.46 fof(f39,plain,(
% 0.27/0.46 ![X0,X1,X2]: (X0=union(X1)|~in(sK3_skl(X0,X1),X0)|~in(sK3_skl(X0,X1),X2)|~in(X2,X1))),
% 0.27/0.46 inference(cnf_transformation,[status(thm)],[f35])).
% 0.27/0.46 fof(f40,plain,(
% 0.27/0.46 ![X0,X1]: (X0=union(X1)|in(sK3_skl(X0,X1),X0)|in(sK3_skl(X0,X1),sK4_skl(X0,X1)))),
% 0.27/0.46 inference(cnf_transformation,[status(thm)],[f35])).
% 0.27/0.46 fof(f41,plain,(
% 0.27/0.46 ![X0,X1]: (X0=union(X1)|in(sK3_skl(X0,X1),X0)|in(sK4_skl(X0,X1),X1))),
% 0.27/0.46 inference(cnf_transformation,[status(thm)],[f35])).
% 0.27/0.46 fof(f50,plain,(
% 0.27/0.46 (?[A]: ~union(singleton(A))=A)),
% 0.27/0.46 inference(pre_NNF_transformation,[status(thm)],[f11])).
% 0.27/0.46 fof(f51,plain,(
% 0.27/0.46 ~union(singleton(sK7_skl))=sK7_skl),
% 0.27/0.46 inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl]),skolemize(A,sK7_skl)],[f50])).
% 0.27/0.46 fof(f52,plain,(
% 0.27/0.46 ~union(singleton(sK7_skl))=sK7_skl),
% 0.27/0.46 inference(cnf_transformation,[status(thm)],[f51])).
% 0.27/0.46 fof(f55,plain,(
% 0.27/0.46 ![X0,X1]: (~in(X0,singleton(X1))|X0=X1)),
% 0.27/0.46 inference(destructive_equality_resolution,[status(thm)],[f22])).
% 0.27/0.46 fof(f56,plain,(
% 0.27/0.46 ![X0]: (in(X0,singleton(X0)))),
% 0.27/0.46 inference(destructive_equality_resolution,[status(thm)],[f23])).
% 0.27/0.46 fof(f386,plain,(
% 0.27/0.46 ![X0,X1]: (X0=union(X1)|in(sK4_skl(X0,X1),X1)|X0=union(X1)|~in(sK3_skl(X0,X1),X0)|~in(X0,X1))),
% 0.27/0.46 inference(resolution,[status(thm)],[f41,f39])).
% 0.27/0.46 fof(f415,plain,(
% 0.27/0.46 ![X0,X1]: (X0=union(X1)|in(sK4_skl(X0,X1),X1)|~in(sK3_skl(X0,X1),X0)|~in(X0,X1))),
% 0.27/0.46 inference(duplicate_literals_removal,[status(thm)],[f386])).
% 0.27/0.47 fof(f416,plain,(
% 0.27/0.47 ![X0,X1]: (X0=union(X1)|in(sK4_skl(X0,X1),X1)|~in(X0,X1))),
% 0.27/0.47 inference(forward_subsumption_resolution,[status(thm)],[f415,f41])).
% 0.27/0.47 fof(f564,plain,(
% 0.27/0.47 ![X0]: (X0=union(singleton(X0))|in(sK4_skl(X0,singleton(X0)),singleton(X0)))),
% 0.27/0.47 inference(resolution,[status(thm)],[f416,f56])).
% 0.27/0.47 fof(f566,plain,(
% 0.27/0.47 ![X0]: (X0=union(singleton(X0))|sK4_skl(X0,singleton(X0))=X0)),
% 0.27/0.47 inference(resolution,[status(thm)],[f564,f55])).
% 0.27/0.47 fof(f579,plain,(
% 0.27/0.47 ![X0]: (X0=union(singleton(X0))|in(sK3_skl(X0,singleton(X0)),X0)|in(sK3_skl(X0,singleton(X0)),X0)|X0=union(singleton(X0)))),
% 0.27/0.47 inference(paramodulation,[status(thm)],[f566,f40])).
% 0.27/0.47 fof(f582,plain,(
% 0.27/0.47 ![X0]: (X0=union(singleton(X0))|in(sK3_skl(X0,singleton(X0)),X0))),
% 0.27/0.47 inference(duplicate_literals_removal,[status(thm)],[f579])).
% 0.27/0.47 fof(f583,plain,(
% 0.27/0.47 ![X0]: (X0=union(singleton(X0))|X0=union(singleton(X0))|~in(sK3_skl(X0,singleton(X0)),X0)|~in(X0,singleton(X0)))),
% 0.27/0.47 inference(resolution,[status(thm)],[f582,f39])).
% 0.27/0.47 fof(f600,plain,(
% 0.27/0.47 ![X0]: (X0=union(singleton(X0))|~in(sK3_skl(X0,singleton(X0)),X0)|~in(X0,singleton(X0)))),
% 0.27/0.47 inference(duplicate_literals_removal,[status(thm)],[f583])).
% 0.27/0.47 fof(f601,plain,(
% 0.27/0.47 ![X0]: (X0=union(singleton(X0))|~in(X0,singleton(X0)))),
% 0.27/0.47 inference(forward_subsumption_resolution,[status(thm)],[f600,f582])).
% 0.27/0.47 fof(f626,plain,(
% 0.27/0.47 ~sK7_skl=sK7_skl),
% 0.27/0.47 inference(backward_demodulation,[status(thm)],[f639,f52])).
% 0.27/0.47 fof(f639,plain,(
% 0.27/0.47 ![X0]: (X0=union(singleton(X0)))),
% 0.27/0.47 inference(forward_subsumption_resolution,[status(thm)],[f601,f56])).
% 0.27/0.47 fof(f679,plain,(
% 0.27/0.47 $false),
% 0.27/0.47 inference(trivial_equality_resolution,[status(thm)],[f626])).
% 0.27/0.47 % SZS output end CNFRefutation for theBenchmark.p
% 0.27/0.48 % Elapsed time: 0.124177 seconds
% 0.27/0.48 % CPU time: 0.689662 seconds
% 0.27/0.48 % Total memory used: 91.272 MB
% 0.27/0.48 % Net memory used: 89.149 MB
%------------------------------------------------------------------------------