%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SEU142+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n007.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 02:21:46 PM UTC 2026
% Result : Theorem 0.21s 0.55s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU142+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.48 % Computer : n007.cluster.edu
% 0.17/0.48 % Model : x86_64 x86_64
% 0.17/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.48 % Memory : 8046.5625MB
% 0.17/0.48 % OS : Linux 6.8.0-71-generic
% 0.17/0.48 % CPULimit : 300
% 0.17/0.48 % WCLimit : 300
% 0.17/0.48 % DateTime : Mon Sep 21 05:50:35 UTC 2026
% 0.17/0.49 % CPUTime :
% 0.17/0.53 % Drodi V4.1.1
% 0.21/0.55 % Refutation found
% 0.21/0.55 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.21/0.55 % SZS output start CNFRefutation for theBenchmark
% 0.21/0.55 fof(f7,axiom,(
% 0.21/0.55 (! [A,B] :( B = singleton(A)<=> (! [C] :( in(C,B)<=> C = A ) )) )),
% 0.21/0.55 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.21/0.55 fof(f9,axiom,(
% 0.21/0.55 (! [A,B,C] :( C = unordered_pair(A,B)<=> (! [D] :( in(D,C)<=> ( D = A| D = B ) ) )) )),
% 0.21/0.55 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.21/0.55 fof(f57,conjecture,(
% 0.21/0.55 (! [A] : unordered_pair(A,A) = singleton(A) )),
% 0.21/0.55 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.21/0.55 fof(f58,negated_conjecture,(
% 0.21/0.55 ~((! [A] : unordered_pair(A,A) = singleton(A) ))),
% 0.21/0.55 inference(negated_conjecture,[status(cth)],[f57])).
% 0.21/0.55 fof(f77,plain,(
% 0.21/0.55 ![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)))))),
% 0.21/0.55 inference(NNF_transformation,[status(thm)],[f7])).
% 0.21/0.55 fof(f78,plain,(
% 0.21/0.55 (![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)))))),
% 0.21/0.55 inference(miniscoping,[status(thm)],[f77])).
% 0.21/0.55 fof(f79,plain,(
% 0.21/0.55 (![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))))),
% 0.21/0.55 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(C,sK0_skl(B,A))],[f78])).
% 0.21/0.55 fof(f82,plain,(
% 0.21/0.55 ![X0,X1]: (X0=singleton(X1)|~in(sK0_skl(X0,X1),X0)|~sK0_skl(X0,X1)=X1)),
% 0.21/0.55 inference(cnf_transformation,[status(thm)],[f79])).
% 0.21/0.55 fof(f83,plain,(
% 0.21/0.55 ![X0,X1]: (X0=singleton(X1)|in(sK0_skl(X0,X1),X0)|sK0_skl(X0,X1)=X1)),
% 0.21/0.55 inference(cnf_transformation,[status(thm)],[f79])).
% 0.21/0.55 fof(f89,plain,(
% 0.21/0.55 ![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))))))),
% 0.21/0.55 inference(NNF_transformation,[status(thm)],[f9])).
% 0.21/0.55 fof(f90,plain,(
% 0.21/0.55 (![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))))))),
% 0.21/0.55 inference(miniscoping,[status(thm)],[f89])).
% 0.21/0.55 fof(f91,plain,(
% 0.21/0.55 (![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(sK2_skl(C,B,A),C)|(~sK2_skl(C,B,A)=A&~sK2_skl(C,B,A)=B))&(in(sK2_skl(C,B,A),C)|(sK2_skl(C,B,A)=A|sK2_skl(C,B,A)=B)))))),
% 0.21/0.55 inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(D,sK2_skl(C,B,A))],[f90])).
% 0.21/0.55 fof(f92,plain,(
% 0.21/0.55 ![X0,X1,X2,X3]: (~X0=unordered_pair(X1,X2)|~in(X3,X0)|X3=X1|X3=X2)),
% 0.21/0.55 inference(cnf_transformation,[status(thm)],[f91])).
% 0.21/0.55 fof(f94,plain,(
% 0.21/0.55 ![X0,X1,X2,X3]: (~X0=unordered_pair(X1,X2)|in(X3,X0)|~X3=X2)),
% 0.21/0.55 inference(cnf_transformation,[status(thm)],[f91])).
% 0.21/0.55 fof(f220,plain,(
% 0.21/0.55 (?[A]: ~unordered_pair(A,A)=singleton(A))),
% 0.21/0.55 inference(pre_NNF_transformation,[status(thm)],[f58])).
% 0.21/0.55 fof(f221,plain,(
% 0.21/0.55 ~unordered_pair(sK12_skl,sK12_skl)=singleton(sK12_skl)),
% 0.21/0.55 inference(skolemize,[status(esa),new_symbols(skolem,[sK12_skl]),skolemize(A,sK12_skl)],[f220])).
% 0.21/0.55 fof(f222,plain,(
% 0.21/0.55 ~unordered_pair(sK12_skl,sK12_skl)=singleton(sK12_skl)),
% 0.21/0.55 inference(cnf_transformation,[status(thm)],[f221])).
% 0.21/0.55 fof(f243,plain,(
% 0.21/0.55 ![X0,X1,X2]: (~in(X0,unordered_pair(X1,X2))|X0=X1|X0=X2)),
% 0.21/0.55 inference(destructive_equality_resolution,[status(thm)],[f92])).
% 0.21/0.55 fof(f245,plain,(
% 0.21/0.55 ![X0,X1]: (in(X0,unordered_pair(X1,X0)))),
% 0.21/0.55 inference(destructive_equality_resolution,[status(thm)],[f94])).
% 0.21/0.55 fof(f295,plain,(
% 0.21/0.55 ![X0,X1,X2]: (unordered_pair(X0,X1)=singleton(X2)|sK0_skl(unordered_pair(X0,X1),X2)=X2|sK0_skl(unordered_pair(X0,X1),X2)=X0|sK0_skl(unordered_pair(X0,X1),X2)=X1)),
% 0.21/0.55 inference(resolution,[status(thm)],[f83,f243])).
% 0.21/0.55 fof(f339,plain,(
% 0.21/0.55 ![X0]: (unordered_pair(X0,X0)=singleton(X0)|sK0_skl(unordered_pair(X0,X0),X0)=X0)),
% 0.21/0.55 inference(factoring,[status(thm)],[f295])).
% 0.21/0.55 fof(f348,plain,(
% 0.21/0.55 ![X0]: (unordered_pair(X0,X0)=singleton(X0)|~in(X0,unordered_pair(X0,X0))|~sK0_skl(unordered_pair(X0,X0),X0)=X0|unordered_pair(X0,X0)=singleton(X0))),
% 0.21/0.56 inference(paramodulation,[status(thm)],[f339,f82])).
% 0.21/0.56 fof(f350,plain,(
% 0.21/0.56 ![X0]: (unordered_pair(X0,X0)=singleton(X0)|~in(X0,unordered_pair(X0,X0))|~sK0_skl(unordered_pair(X0,X0),X0)=X0)),
% 0.21/0.56 inference(duplicate_literals_removal,[status(thm)],[f348])).
% 0.21/0.56 fof(f351,plain,(
% 0.21/0.56 ![X0]: (unordered_pair(X0,X0)=singleton(X0))),
% 0.21/0.56 inference(backward_subsumption_resolution,[status(thm)],[f339,f352])).
% 0.21/0.56 fof(f352,plain,(
% 0.21/0.56 ![X0]: (unordered_pair(X0,X0)=singleton(X0)|~sK0_skl(unordered_pair(X0,X0),X0)=X0)),
% 0.21/0.56 inference(forward_subsumption_resolution,[status(thm)],[f350,f245])).
% 0.21/0.56 fof(f353,plain,(
% 0.21/0.56 ~singleton(sK12_skl)=singleton(sK12_skl)),
% 0.21/0.56 inference(backward_demodulation,[status(thm)],[f351,f222])).
% 0.21/0.56 fof(f355,plain,(
% 0.21/0.56 $false),
% 0.21/0.56 inference(trivial_equality_resolution,[status(thm)],[f353])).
% 0.21/0.56 % SZS output end CNFRefutation for theBenchmark.p
% 0.21/0.59 % Elapsed time: 0.089144 seconds
% 0.21/0.59 % CPU time: 0.182416 seconds
% 0.21/0.59 % Total memory used: 33.503 MB
% 0.21/0.59 % Net memory used: 33.433 MB
%------------------------------------------------------------------------------