%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SET909+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 : n019.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 : SET909+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
% 0.08/0.35 % Computer : n019.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 05:43:20 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.13/0.37 % 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(f4,axiom,(
% 0.13/0.39 (! [A] :( A = empty_set<=> (! [B] : ~ in(B,A) )) )),
% 0.13/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.39 fof(f5,axiom,(
% 0.13/0.39 (! [A,B,C] :( C = unordered_pair(A,B)<=> (! [D] :( in(D,C)<=> ( D = A| D = B ) ) )) )),
% 0.13/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.39 fof(f6,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/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.39 fof(f13,conjecture,(
% 0.13/0.39 (! [A,B,C] : set_union2(unordered_pair(A,B),C) != empty_set )),
% 0.13/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.39 fof(f14,negated_conjecture,(
% 0.13/0.39 ~((! [A,B,C] : set_union2(unordered_pair(A,B),C) != empty_set ))),
% 0.13/0.39 inference(negated_conjecture,[status(cth)],[f13])).
% 0.13/0.39 fof(f19,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(f20,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)],[f19])).
% 0.13/0.39 fof(f21,plain,(
% 0.13/0.39 (![A]: (~A=empty_set|(![B]: ~in(B,A))))&(![A]: (A=empty_set|in(sK0_skl(A),A)))),
% 0.13/0.39 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(B,sK0_skl(A))],[f20])).
% 0.13/0.39 fof(f22,plain,(
% 0.13/0.39 ![X0,X1]: (~X0=empty_set|~in(X1,X0))),
% 0.13/0.39 inference(cnf_transformation,[status(thm)],[f21])).
% 0.13/0.39 fof(f24,plain,(
% 0.13/0.39 ![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))))))),
% 0.13/0.39 inference(NNF_transformation,[status(thm)],[f5])).
% 0.13/0.39 fof(f25,plain,(
% 0.13/0.39 (![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))))))),
% 0.13/0.39 inference(miniscoping,[status(thm)],[f24])).
% 0.13/0.39 fof(f26,plain,(
% 0.13/0.39 (![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)))))),
% 0.13/0.39 inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(D,sK1_skl(C,B,A))],[f25])).
% 0.13/0.39 fof(f29,plain,(
% 0.13/0.39 ![X0,X1,X2,X3]: (~X0=unordered_pair(X1,X2)|in(X3,X0)|~X3=X2)),
% 0.13/0.39 inference(cnf_transformation,[status(thm)],[f26])).
% 0.13/0.39 fof(f33,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)],[f6])).
% 0.13/0.39 fof(f34,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)],[f33])).
% 0.13/0.39 fof(f35,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))],[f34])).
% 0.13/0.39 fof(f37,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)],[f35])).
% 0.13/0.39 fof(f55,plain,(
% 0.13/0.39 (?[A,B,C]: set_union2(unordered_pair(A,B),C)=empty_set)),
% 0.13/0.39 inference(pre_NNF_transformation,[status(thm)],[f14])).
% 0.13/0.39 fof(f56,plain,(
% 0.13/0.39 set_union2(unordered_pair(sK5_skl,sK6_skl),sK7_skl)=empty_set),
% 0.13/0.39 inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl,sK6_skl,sK7_skl]),skolemize(A,sK5_skl),skolemize(B,sK6_skl),skolemize(C,sK7_skl)],[f55])).
% 0.13/0.39 fof(f57,plain,(
% 0.13/0.39 set_union2(unordered_pair(sK5_skl,sK6_skl),sK7_skl)=empty_set),
% 0.13/0.39 inference(cnf_transformation,[status(thm)],[f56])).
% 0.13/0.39 fof(f58,plain,(
% 0.13/0.40 ![X0]: (~in(X0,empty_set))),
% 0.13/0.40 inference(destructive_equality_resolution,[status(thm)],[f22])).
% 0.13/0.40 fof(f61,plain,(
% 0.13/0.40 ![X0,X1]: (in(X0,unordered_pair(X1,X0)))),
% 0.13/0.40 inference(destructive_equality_resolution,[status(thm)],[f29])).
% 0.13/0.40 fof(f63,plain,(
% 0.13/0.40 ![X0,X1,X2]: (in(X0,set_union2(X1,X2))|~in(X0,X1))),
% 0.13/0.40 inference(destructive_equality_resolution,[status(thm)],[f37])).
% 0.13/0.40 fof(f87,plain,(
% 0.13/0.40 ![X0,X1,X2]: (in(X0,set_union2(unordered_pair(X1,X0),X2)))),
% 0.13/0.40 inference(resolution,[status(thm)],[f63,f61])).
% 0.13/0.40 fof(f90,plain,(
% 0.13/0.40 in(sK6_skl,empty_set)),
% 0.13/0.40 inference(paramodulation,[status(thm)],[f57,f87])).
% 0.13/0.40 fof(f96,plain,(
% 0.13/0.40 $false),
% 0.13/0.40 inference(forward_subsumption_resolution,[status(thm)],[f90,f58])).
% 0.13/0.40 % SZS output end CNFRefutation for theBenchmark.p
% 0.13/0.42 % Elapsed time: 0.062885 seconds
% 0.13/0.42 % CPU time: 0.179106 seconds
% 0.13/0.42 % Total memory used: 101.886 MB
% 0.13/0.42 % Net memory used: 101.557 MB
%------------------------------------------------------------------------------