%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SET921+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 : n001.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 0.17s 0.51s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET921+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.46 % Computer : n001.cluster.edu
% 0.17/0.46 % Model : x86_64 x86_64
% 0.17/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.46 % Memory : 8046.5625MB
% 0.17/0.46 % OS : Linux 6.8.0-71-generic
% 0.17/0.46 % CPULimit : 300
% 0.17/0.46 % WCLimit : 300
% 0.17/0.46 % DateTime : Mon Sep 21 05:49:29 UTC 2026
% 0.17/0.46 % CPUTime :
% 0.17/0.48 % Drodi V4.1.1
% 0.17/0.51 % Refutation found
% 0.17/0.51 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.17/0.51 % SZS output start CNFRefutation for theBenchmark
% 0.17/0.51 fof(f2,axiom,(
% 0.17/0.51 (! [A,B] :( B = singleton(A)<=> (! [C] :( in(C,B)<=> C = A ) )) )),
% 0.17/0.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.51 fof(f3,axiom,(
% 0.17/0.51 (! [A,B,C] :( C = set_difference(A,B)<=> (! [D] :( in(D,C)<=> ( in(D,A)& ~ in(D,B) ) ) )) )),
% 0.17/0.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.51 fof(f6,conjecture,(
% 0.17/0.51 (! [A,B,C] :( in(A,set_difference(B,singleton(C)))<=> ( in(A,B)& A != C ) ) )),
% 0.17/0.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.51 fof(f7,negated_conjecture,(
% 0.17/0.51 ~((! [A,B,C] :( in(A,set_difference(B,singleton(C)))<=> ( in(A,B)& A != C ) ) ))),
% 0.17/0.51 inference(negated_conjecture,[status(cth)],[f6])).
% 0.17/0.51 fof(f10,plain,(
% 0.17/0.51 ![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)))))),
% 0.17/0.51 inference(NNF_transformation,[status(thm)],[f2])).
% 0.17/0.51 fof(f11,plain,(
% 0.17/0.51 (![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)))))),
% 0.17/0.51 inference(miniscoping,[status(thm)],[f10])).
% 0.17/0.51 fof(f12,plain,(
% 0.17/0.51 (![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))))),
% 0.17/0.51 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(C,sK0_skl(B,A))],[f11])).
% 0.17/0.51 fof(f13,plain,(
% 0.17/0.51 ![X0,X1,X2]: (~X0=singleton(X1)|~in(X2,X0)|X2=X1)),
% 0.17/0.51 inference(cnf_transformation,[status(thm)],[f12])).
% 0.17/0.51 fof(f14,plain,(
% 0.17/0.51 ![X0,X1,X2]: (~X0=singleton(X1)|in(X2,X0)|~X2=X1)),
% 0.17/0.51 inference(cnf_transformation,[status(thm)],[f12])).
% 0.17/0.51 fof(f17,plain,(
% 0.17/0.51 ![A,B,C]: ((~C=set_difference(A,B)|(![D]: ((~in(D,C)|(in(D,A)&~in(D,B)))&(in(D,C)|(~in(D,A)|in(D,B))))))&(C=set_difference(A,B)|(?[D]: ((~in(D,C)|(~in(D,A)|in(D,B)))&(in(D,C)|(in(D,A)&~in(D,B)))))))),
% 0.17/0.51 inference(NNF_transformation,[status(thm)],[f3])).
% 0.17/0.51 fof(f18,plain,(
% 0.17/0.51 (![A,B,C]: (~C=set_difference(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_difference(A,B)|(?[D]: ((~in(D,C)|(~in(D,A)|in(D,B)))&(in(D,C)|(in(D,A)&~in(D,B)))))))),
% 0.17/0.51 inference(miniscoping,[status(thm)],[f17])).
% 0.17/0.51 fof(f19,plain,(
% 0.17/0.51 (![A,B,C]: (~C=set_difference(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_difference(A,B)|((~in(sK1_skl(C,B,A),C)|(~in(sK1_skl(C,B,A),A)|in(sK1_skl(C,B,A),B)))&(in(sK1_skl(C,B,A),C)|(in(sK1_skl(C,B,A),A)&~in(sK1_skl(C,B,A),B))))))),
% 0.17/0.51 inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(D,sK1_skl(C,B,A))],[f18])).
% 0.17/0.51 fof(f20,plain,(
% 0.17/0.51 ![X0,X1,X2,X3]: (~X0=set_difference(X1,X2)|~in(X3,X0)|in(X3,X1))),
% 0.17/0.51 inference(cnf_transformation,[status(thm)],[f19])).
% 0.17/0.51 fof(f21,plain,(
% 0.17/0.51 ![X0,X1,X2,X3]: (~X0=set_difference(X1,X2)|~in(X3,X0)|~in(X3,X2))),
% 0.17/0.51 inference(cnf_transformation,[status(thm)],[f19])).
% 0.17/0.51 fof(f22,plain,(
% 0.17/0.51 ![X0,X1,X2,X3]: (~X0=set_difference(X1,X2)|in(X3,X0)|~in(X3,X1)|in(X3,X2))),
% 0.17/0.51 inference(cnf_transformation,[status(thm)],[f19])).
% 0.17/0.51 fof(f30,plain,(
% 0.17/0.51 (?[A,B,C]: (in(A,set_difference(B,singleton(C)))<~>(in(A,B)&~A=C)))),
% 0.17/0.51 inference(pre_NNF_transformation,[status(thm)],[f7])).
% 0.17/0.51 fof(f31,plain,(
% 0.17/0.51 ?[A,B,C]: ((in(A,set_difference(B,singleton(C)))|(in(A,B)&~A=C))&(~in(A,set_difference(B,singleton(C)))|(~in(A,B)|A=C)))),
% 0.17/0.51 inference(NNF_transformation,[status(thm)],[f30])).
% 0.17/0.51 fof(f32,plain,(
% 0.17/0.51 ((in(sK4_skl,set_difference(sK5_skl,singleton(sK6_skl)))|(in(sK4_skl,sK5_skl)&~sK4_skl=sK6_skl))&(~in(sK4_skl,set_difference(sK5_skl,singleton(sK6_skl)))|(~in(sK4_skl,sK5_skl)|sK4_skl=sK6_skl)))),
% 0.17/0.51 inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl,sK5_skl,sK6_skl]),skolemize(A,sK4_skl),skolemize(B,sK5_skl),skolemize(C,sK6_skl)],[f31])).
% 0.17/0.51 fof(f33,plain,(
% 0.17/0.51 in(sK4_skl,set_difference(sK5_skl,singleton(sK6_skl)))|in(sK4_skl,sK5_skl)),
% 0.17/0.51 inference(cnf_transformation,[status(thm)],[f32])).
% 0.17/0.51 fof(f34,plain,(
% 0.17/0.51 in(sK4_skl,set_difference(sK5_skl,singleton(sK6_skl)))|~sK4_skl=sK6_skl),
% 0.17/0.51 inference(cnf_transformation,[status(thm)],[f32])).
% 0.17/0.51 fof(f35,plain,(
% 0.17/0.51 ~in(sK4_skl,set_difference(sK5_skl,singleton(sK6_skl)))|~in(sK4_skl,sK5_skl)|sK4_skl=sK6_skl),
% 0.17/0.51 inference(cnf_transformation,[status(thm)],[f32])).
% 0.17/0.51 fof(f36,plain,(
% 0.17/0.51 ![X0,X1]: (~in(X0,singleton(X1))|X0=X1)),
% 0.17/0.51 inference(destructive_equality_resolution,[status(thm)],[f13])).
% 0.17/0.51 fof(f37,plain,(
% 0.17/0.51 ![X0]: (in(X0,singleton(X0)))),
% 0.17/0.51 inference(destructive_equality_resolution,[status(thm)],[f14])).
% 0.17/0.51 fof(f38,plain,(
% 0.17/0.51 ![X0,X1,X2]: (~in(X0,set_difference(X1,X2))|in(X0,X1))),
% 0.17/0.51 inference(destructive_equality_resolution,[status(thm)],[f20])).
% 0.17/0.51 fof(f39,plain,(
% 0.17/0.51 ![X0,X1,X2]: (~in(X0,set_difference(X1,X2))|~in(X0,X2))),
% 0.17/0.51 inference(destructive_equality_resolution,[status(thm)],[f21])).
% 0.17/0.51 fof(f40,plain,(
% 0.17/0.51 ![X0,X1,X2]: (in(X0,set_difference(X1,X2))|~in(X0,X1)|in(X0,X2))),
% 0.17/0.51 inference(destructive_equality_resolution,[status(thm)],[f22])).
% 0.17/0.51 fof(f41,plain,(
% 0.17/0.51 in(sK4_skl,sK5_skl)),
% 0.17/0.51 inference(forward_subsumption_resolution,[status(thm)],[f33,f38])).
% 0.17/0.51 fof(f42,plain,(
% 0.17/0.51 ~in(sK4_skl,set_difference(sK5_skl,singleton(sK6_skl)))|sK4_skl=sK6_skl),
% 0.17/0.51 inference(forward_subsumption_resolution,[status(thm)],[f35,f38])).
% 0.17/0.51 fof(f49,plain,(
% 0.17/0.51 ~in(sK4_skl,singleton(sK6_skl))|~sK4_skl=sK6_skl),
% 0.17/0.51 inference(resolution,[status(thm)],[f39,f34])).
% 0.17/0.51 fof(f50,plain,(
% 0.17/0.51 ~in(sK4_skl,singleton(sK6_skl))),
% 0.17/0.51 inference(forward_subsumption_resolution,[status(thm)],[f49,f36])).
% 0.17/0.51 fof(f52,plain,(
% 0.17/0.51 ![X0]: (in(sK4_skl,set_difference(sK5_skl,X0))|in(sK4_skl,X0))),
% 0.17/0.51 inference(resolution,[status(thm)],[f40,f41])).
% 0.17/0.51 fof(f62,plain,(
% 0.17/0.51 in(sK4_skl,singleton(sK6_skl))|sK4_skl=sK6_skl),
% 0.17/0.51 inference(resolution,[status(thm)],[f52,f42])).
% 0.17/0.51 fof(f70,plain,(
% 0.17/0.51 ~in(sK6_skl,singleton(sK6_skl))),
% 0.17/0.51 inference(backward_demodulation,[status(thm)],[f77,f50])).
% 0.17/0.51 fof(f77,plain,(
% 0.17/0.51 sK4_skl=sK6_skl),
% 0.17/0.51 inference(forward_subsumption_resolution,[status(thm)],[f62,f50])).
% 0.17/0.51 fof(f91,plain,(
% 0.17/0.51 $false),
% 0.17/0.51 inference(forward_subsumption_resolution,[status(thm)],[f70,f37])).
% 0.17/0.51 % SZS output end CNFRefutation for theBenchmark.p
% 0.21/0.55 % Elapsed time: 0.078685 seconds
% 0.21/0.55 % CPU time: 0.112869 seconds
% 0.21/0.55 % Total memory used: 7.664 MB
% 0.21/0.55 % Net memory used: 7.649 MB
%------------------------------------------------------------------------------