%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SET918+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 : 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 02:12:51 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 : SET918+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
% 0.09/0.35 % Computer : n015.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 05:46:51 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.13/0.36 % 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,B] :( B = singleton(A)<=> (! [C] :( in(C,B)<=> C = 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_intersection2(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(f10,conjecture,(
% 0.13/0.39 (! [A,B,C] :~ ( set_intersection2(unordered_pair(A,B),C) = singleton(A)& in(B,C)& A != B ) )),
% 0.13/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.39 fof(f11,negated_conjecture,(
% 0.13/0.39 ~((! [A,B,C] :~ ( set_intersection2(unordered_pair(A,B),C) = singleton(A)& in(B,C)& A != B ) ))),
% 0.13/0.39 inference(negated_conjecture,[status(cth)],[f10])).
% 0.13/0.39 fof(f16,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)],[f4])).
% 0.13/0.39 fof(f17,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)],[f16])).
% 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)|((~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))],[f17])).
% 0.13/0.39 fof(f19,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)],[f18])).
% 0.13/0.39 fof(f23,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(f24,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)],[f23])).
% 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)|((~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))],[f24])).
% 0.13/0.39 fof(f28,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)],[f25])).
% 0.13/0.39 fof(f32,plain,(
% 0.13/0.39 ![A,B,C]: ((~C=set_intersection2(A,B)|(![D]: ((~in(D,C)|(in(D,A)&in(D,B)))&(in(D,C)|(~in(D,A)|~in(D,B))))))&(C=set_intersection2(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(f33,plain,(
% 0.13/0.39 (![A,B,C]: (~C=set_intersection2(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_intersection2(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)],[f32])).
% 0.13/0.39 fof(f34,plain,(
% 0.13/0.39 (![A,B,C]: (~C=set_intersection2(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_intersection2(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))],[f33])).
% 0.13/0.39 fof(f37,plain,(
% 0.13/0.39 ![X0,X1,X2,X3]: (~X0=set_intersection2(X1,X2)|in(X3,X0)|~in(X3,X1)|~in(X3,X2))),
% 0.13/0.39 inference(cnf_transformation,[status(thm)],[f34])).
% 0.13/0.39 fof(f47,plain,(
% 0.13/0.39 (?[A,B,C]: ((set_intersection2(unordered_pair(A,B),C)=singleton(A)&in(B,C))&~A=B))),
% 0.13/0.39 inference(pre_NNF_transformation,[status(thm)],[f11])).
% 0.13/0.40 fof(f48,plain,(
% 0.13/0.40 ?[A,B]: ((?[C]: (set_intersection2(unordered_pair(A,B),C)=singleton(A)&in(B,C)))&~A=B)),
% 0.13/0.40 inference(miniscoping,[status(thm)],[f47])).
% 0.13/0.40 fof(f49,plain,(
% 0.13/0.40 ((set_intersection2(unordered_pair(sK5_skl,sK6_skl),sK7_skl)=singleton(sK5_skl)&in(sK6_skl,sK7_skl))&~sK5_skl=sK6_skl)),
% 0.13/0.40 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)],[f48])).
% 0.13/0.40 fof(f50,plain,(
% 0.13/0.40 set_intersection2(unordered_pair(sK5_skl,sK6_skl),sK7_skl)=singleton(sK5_skl)),
% 0.13/0.40 inference(cnf_transformation,[status(thm)],[f49])).
% 0.13/0.40 fof(f51,plain,(
% 0.13/0.40 in(sK6_skl,sK7_skl)),
% 0.13/0.40 inference(cnf_transformation,[status(thm)],[f49])).
% 0.13/0.40 fof(f52,plain,(
% 0.13/0.40 ~sK5_skl=sK6_skl),
% 0.13/0.40 inference(cnf_transformation,[status(thm)],[f49])).
% 0.13/0.40 fof(f53,plain,(
% 0.13/0.40 ![X0,X1]: (~in(X0,singleton(X1))|X0=X1)),
% 0.13/0.40 inference(destructive_equality_resolution,[status(thm)],[f19])).
% 0.13/0.40 fof(f57,plain,(
% 0.13/0.40 ![X0,X1]: (in(X0,unordered_pair(X1,X0)))),
% 0.13/0.40 inference(destructive_equality_resolution,[status(thm)],[f28])).
% 0.13/0.40 fof(f60,plain,(
% 0.13/0.40 ![X0,X1,X2]: (in(X0,set_intersection2(X1,X2))|~in(X0,X1)|~in(X0,X2))),
% 0.13/0.40 inference(destructive_equality_resolution,[status(thm)],[f37])).
% 0.13/0.40 fof(f83,plain,(
% 0.13/0.40 ![X0]: (in(X0,singleton(sK5_skl))|~in(X0,unordered_pair(sK5_skl,sK6_skl))|~in(X0,sK7_skl))),
% 0.13/0.40 inference(paramodulation,[status(thm)],[f50,f60])).
% 0.13/0.40 fof(f129,plain,(
% 0.13/0.40 in(sK6_skl,singleton(sK5_skl))|~in(sK6_skl,unordered_pair(sK5_skl,sK6_skl))),
% 0.13/0.40 inference(resolution,[status(thm)],[f83,f51])).
% 0.13/0.40 fof(f130,plain,(
% 0.13/0.40 in(sK6_skl,singleton(sK5_skl))),
% 0.13/0.40 inference(forward_subsumption_resolution,[status(thm)],[f129,f57])).
% 0.13/0.40 fof(f132,plain,(
% 0.13/0.40 sK6_skl=sK5_skl),
% 0.13/0.40 inference(resolution,[status(thm)],[f130,f53])).
% 0.13/0.40 fof(f135,plain,(
% 0.13/0.40 $false),
% 0.13/0.40 inference(forward_subsumption_resolution,[status(thm)],[f132,f52])).
% 0.13/0.40 % SZS output end CNFRefutation for theBenchmark.p
% 0.13/0.42 % Elapsed time: 0.058731 seconds
% 0.13/0.42 % CPU time: 0.233788 seconds
% 0.13/0.42 % Total memory used: 90.774 MB
% 0.13/0.42 % Net memory used: 90.422 MB
%------------------------------------------------------------------------------