%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SET882+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 02:12:48 PM UTC 2026
% Result : Theorem 0.10s 0.40s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET882+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
% 0.10/0.37 % Computer : n004.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 05:42:04 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 0.10/0.40 % Refutation found
% 0.10/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.40 % SZS output start CNFRefutation for theBenchmark
% 0.10/0.40 fof(f3,axiom,(
% 0.10/0.40 (! [A,B] :( B = singleton(A)<=> (! [C] :( in(C,B)<=> C = A ) )) )),
% 0.10/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.40 fof(f4,axiom,(
% 0.10/0.40 (! [A,B,C] :( set_difference(unordered_pair(A,B),C) = singleton(A)<=> ( ~ in(A,C)& ( in(B,C)| A = B ) ) ) )),
% 0.10/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.40 fof(f7,conjecture,(
% 0.10/0.40 (! [A,B] :( A != B=> set_difference(unordered_pair(A,B),singleton(B)) = singleton(A) ) )),
% 0.10/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.40 fof(f8,negated_conjecture,(
% 0.10/0.40 ~((! [A,B] :( A != B=> set_difference(unordered_pair(A,B),singleton(B)) = singleton(A) ) ))),
% 0.10/0.40 inference(negated_conjecture,[status(cth)],[f7])).
% 0.10/0.40 fof(f12,plain,(
% 0.10/0.40 ![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)))))),
% 0.10/0.40 inference(NNF_transformation,[status(thm)],[f3])).
% 0.10/0.40 fof(f13,plain,(
% 0.10/0.40 (![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)))))),
% 0.10/0.40 inference(miniscoping,[status(thm)],[f12])).
% 0.10/0.40 fof(f14,plain,(
% 0.10/0.40 (![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))))),
% 0.10/0.40 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(C,sK0_skl(B,A))],[f13])).
% 0.10/0.40 fof(f15,plain,(
% 0.10/0.40 ![X0,X1,X2]: (~X0=singleton(X1)|~in(X2,X0)|X2=X1)),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f14])).
% 0.10/0.40 fof(f16,plain,(
% 0.10/0.40 ![X0,X1,X2]: (~X0=singleton(X1)|in(X2,X0)|~X2=X1)),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f14])).
% 0.10/0.40 fof(f19,plain,(
% 0.10/0.40 ![A,B,C]: ((~set_difference(unordered_pair(A,B),C)=singleton(A)|(~in(A,C)&(in(B,C)|A=B)))&(set_difference(unordered_pair(A,B),C)=singleton(A)|(in(A,C)|(~in(B,C)&~A=B))))),
% 0.10/0.40 inference(NNF_transformation,[status(thm)],[f4])).
% 0.10/0.40 fof(f20,plain,(
% 0.10/0.40 (![A,B,C]: (~set_difference(unordered_pair(A,B),C)=singleton(A)|(~in(A,C)&(in(B,C)|A=B))))&(![A,B,C]: (set_difference(unordered_pair(A,B),C)=singleton(A)|(in(A,C)|(~in(B,C)&~A=B))))),
% 0.10/0.40 inference(miniscoping,[status(thm)],[f19])).
% 0.10/0.40 fof(f23,plain,(
% 0.10/0.40 ![X0,X1,X2]: (set_difference(unordered_pair(X0,X1),X2)=singleton(X0)|in(X0,X2)|~in(X1,X2))),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f20])).
% 0.10/0.40 fof(f29,plain,(
% 0.10/0.40 (?[A,B]: (~A=B&~set_difference(unordered_pair(A,B),singleton(B))=singleton(A)))),
% 0.10/0.40 inference(pre_NNF_transformation,[status(thm)],[f8])).
% 0.10/0.40 fof(f30,plain,(
% 0.10/0.40 (~sK3_skl=sK4_skl&~set_difference(unordered_pair(sK3_skl,sK4_skl),singleton(sK4_skl))=singleton(sK3_skl))),
% 0.10/0.40 inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl,sK4_skl]),skolemize(A,sK3_skl),skolemize(B,sK4_skl)],[f29])).
% 0.10/0.40 fof(f31,plain,(
% 0.10/0.40 ~sK3_skl=sK4_skl),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f30])).
% 0.10/0.40 fof(f32,plain,(
% 0.10/0.40 ~set_difference(unordered_pair(sK3_skl,sK4_skl),singleton(sK4_skl))=singleton(sK3_skl)),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f30])).
% 0.10/0.40 fof(f33,plain,(
% 0.10/0.40 ![X0,X1]: (~in(X0,singleton(X1))|X0=X1)),
% 0.10/0.40 inference(destructive_equality_resolution,[status(thm)],[f15])).
% 0.10/0.40 fof(f34,plain,(
% 0.10/0.40 ![X0]: (in(X0,singleton(X0)))),
% 0.10/0.40 inference(destructive_equality_resolution,[status(thm)],[f16])).
% 0.10/0.40 fof(f62,plain,(
% 0.10/0.40 ![X0,X1]: (set_difference(unordered_pair(X0,X1),singleton(X1))=singleton(X0)|in(X0,singleton(X1)))),
% 0.10/0.40 inference(resolution,[status(thm)],[f23,f34])).
% 0.10/0.40 fof(f64,plain,(
% 0.10/0.40 ![X0,X1]: (set_difference(unordered_pair(X0,X1),singleton(X1))=singleton(X0)|X0=X1)),
% 0.10/0.40 inference(resolution,[status(thm)],[f62,f33])).
% 0.10/0.40 fof(f75,plain,(
% 0.10/0.40 sK3_skl=sK4_skl),
% 0.10/0.40 inference(resolution,[status(thm)],[f64,f32])).
% 0.10/0.40 fof(f89,plain,(
% 0.10/0.40 $false),
% 0.10/0.40 inference(forward_subsumption_resolution,[status(thm)],[f75,f31])).
% 0.10/0.40 % SZS output end CNFRefutation for theBenchmark.p
% 0.10/0.42 % Elapsed time: 0.042578 seconds
% 0.10/0.42 % CPU time: 0.115557 seconds
% 0.10/0.42 % Total memory used: 41.436 MB
% 0.10/0.42 % Net memory used: 41.279 MB
%------------------------------------------------------------------------------