%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SET908+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 : n015.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 02:12:50 PM UTC 2026
% Result : Theorem 0.13s 0.39s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET908+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
% 0.08/0.35 % Computer : n015.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 05:46:20 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 0.13/0.39 % Refutation found
% 0.13/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.39 % SZS output start CNFRefutation for theBenchmark
% 0.13/0.39 fof(f3,axiom,(
% 0.13/0.39 (! [A,B] :( B = singleton(A)<=> (! [C] :( in(C,B)<=> C = A ) )) )),
% 0.13/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.39 fof(f4,axiom,(
% 0.13/0.39 (! [A] :( A = empty_set<=> (! [B] : ~ in(B,A) )) )),
% 0.13/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.39 fof(f5,axiom,(
% 0.13/0.39 (! [A,B,C] :( C = set_union2(A,B)<=> (! [D] :( in(D,C)<=> ( in(D,A)| in(D,B) ) ) )) )),
% 0.13/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.39 fof(f12,conjecture,(
% 0.13/0.39 (! [A,B] : set_union2(singleton(A),B) != empty_set )),
% 0.13/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.39 fof(f13,negated_conjecture,(
% 0.13/0.39 ~((! [A,B] : set_union2(singleton(A),B) != empty_set ))),
% 0.13/0.39 inference(negated_conjecture,[status(cth)],[f12])).
% 0.13/0.39 fof(f17,plain,(
% 0.13/0.39 ![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)))))),
% 0.13/0.39 inference(NNF_transformation,[status(thm)],[f3])).
% 0.13/0.39 fof(f18,plain,(
% 0.13/0.39 (![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)))))),
% 0.13/0.39 inference(miniscoping,[status(thm)],[f17])).
% 0.13/0.39 fof(f19,plain,(
% 0.13/0.39 (![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))))),
% 0.13/0.39 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(C,sK0_skl(B,A))],[f18])).
% 0.13/0.39 fof(f21,plain,(
% 0.13/0.39 ![X0,X1,X2]: (~X0=singleton(X1)|in(X2,X0)|~X2=X1)),
% 0.13/0.39 inference(cnf_transformation,[status(thm)],[f19])).
% 0.13/0.39 fof(f24,plain,(
% 0.13/0.39 ![A]: ((~A=empty_set|(![B]: ~in(B,A)))&(A=empty_set|(?[B]: in(B,A))))),
% 0.13/0.39 inference(NNF_transformation,[status(thm)],[f4])).
% 0.13/0.39 fof(f25,plain,(
% 0.13/0.39 (![A]: (~A=empty_set|(![B]: ~in(B,A))))&(![A]: (A=empty_set|(?[B]: in(B,A))))),
% 0.13/0.39 inference(miniscoping,[status(thm)],[f24])).
% 0.13/0.39 fof(f26,plain,(
% 0.13/0.39 (![A]: (~A=empty_set|(![B]: ~in(B,A))))&(![A]: (A=empty_set|in(sK1_skl(A),A)))),
% 0.13/0.39 inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(B,sK1_skl(A))],[f25])).
% 0.13/0.39 fof(f27,plain,(
% 0.13/0.39 ![X0,X1]: (~X0=empty_set|~in(X1,X0))),
% 0.13/0.39 inference(cnf_transformation,[status(thm)],[f26])).
% 0.13/0.39 fof(f29,plain,(
% 0.13/0.39 ![A,B,C]: ((~C=set_union2(A,B)|(![D]: ((~in(D,C)|(in(D,A)|in(D,B)))&(in(D,C)|(~in(D,A)&~in(D,B))))))&(C=set_union2(A,B)|(?[D]: ((~in(D,C)|(~in(D,A)&~in(D,B)))&(in(D,C)|(in(D,A)|in(D,B)))))))),
% 0.13/0.39 inference(NNF_transformation,[status(thm)],[f5])).
% 0.13/0.39 fof(f30,plain,(
% 0.13/0.39 (![A,B,C]: (~C=set_union2(A,B)|((![D]: (~in(D,C)|(in(D,A)|in(D,B))))&(![D]: (in(D,C)|(~in(D,A)&~in(D,B)))))))&(![A,B,C]: (C=set_union2(A,B)|(?[D]: ((~in(D,C)|(~in(D,A)&~in(D,B)))&(in(D,C)|(in(D,A)|in(D,B)))))))),
% 0.13/0.39 inference(miniscoping,[status(thm)],[f29])).
% 0.13/0.39 fof(f31,plain,(
% 0.13/0.39 (![A,B,C]: (~C=set_union2(A,B)|((![D]: (~in(D,C)|(in(D,A)|in(D,B))))&(![D]: (in(D,C)|(~in(D,A)&~in(D,B)))))))&(![A,B,C]: (C=set_union2(A,B)|((~in(sK2_skl(C,B,A),C)|(~in(sK2_skl(C,B,A),A)&~in(sK2_skl(C,B,A),B)))&(in(sK2_skl(C,B,A),C)|(in(sK2_skl(C,B,A),A)|in(sK2_skl(C,B,A),B))))))),
% 0.13/0.39 inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(D,sK2_skl(C,B,A))],[f30])).
% 0.13/0.39 fof(f33,plain,(
% 0.13/0.39 ![X0,X1,X2,X3]: (~X0=set_union2(X1,X2)|in(X3,X0)|~in(X3,X1))),
% 0.13/0.39 inference(cnf_transformation,[status(thm)],[f31])).
% 0.13/0.39 fof(f51,plain,(
% 0.13/0.39 (?[A,B]: set_union2(singleton(A),B)=empty_set)),
% 0.13/0.39 inference(pre_NNF_transformation,[status(thm)],[f13])).
% 0.13/0.39 fof(f52,plain,(
% 0.13/0.39 set_union2(singleton(sK5_skl),sK6_skl)=empty_set),
% 0.13/0.39 inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl,sK6_skl]),skolemize(A,sK5_skl),skolemize(B,sK6_skl)],[f51])).
% 0.13/0.39 fof(f53,plain,(
% 0.13/0.39 set_union2(singleton(sK5_skl),sK6_skl)=empty_set),
% 0.13/0.39 inference(cnf_transformation,[status(thm)],[f52])).
% 0.13/0.39 fof(f55,plain,(
% 0.13/0.39 ![X0]: (in(X0,singleton(X0)))),
% 0.13/0.39 inference(destructive_equality_resolution,[status(thm)],[f21])).
% 0.13/0.39 fof(f56,plain,(
% 0.13/0.39 ![X0]: (~in(X0,empty_set))),
% 0.13/0.39 inference(destructive_equality_resolution,[status(thm)],[f27])).
% 0.13/0.39 fof(f58,plain,(
% 0.13/0.39 ![X0,X1,X2]: (in(X0,set_union2(X1,X2))|~in(X0,X1))),
% 0.13/0.39 inference(destructive_equality_resolution,[status(thm)],[f33])).
% 0.13/0.39 fof(f69,plain,(
% 0.13/0.39 ![X0,X1]: (in(X0,set_union2(singleton(X0),X1)))),
% 0.13/0.39 inference(resolution,[status(thm)],[f58,f55])).
% 0.13/0.39 fof(f71,plain,(
% 0.13/0.39 in(sK5_skl,empty_set)),
% 0.13/0.39 inference(paramodulation,[status(thm)],[f53,f69])).
% 0.13/0.39 fof(f75,plain,(
% 0.13/0.39 $false),
% 0.13/0.39 inference(forward_subsumption_resolution,[status(thm)],[f71,f56])).
% 0.13/0.39 % SZS output end CNFRefutation for theBenchmark.p
% 0.13/0.43 % Elapsed time: 0.059991 seconds
% 0.13/0.43 % CPU time: 0.160094 seconds
% 0.13/0.43 % Total memory used: 101.579 MB
% 0.13/0.43 % Net memory used: 101.218 MB
%------------------------------------------------------------------------------