%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SET016+4 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/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 02:11:12 PM UTC 2026
% Result : Theorem 0.12s 0.40s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET016+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n019.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Sep 21 04:42:49 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.37 % Drodi V4.1.1
% 0.12/0.40 % Refutation found
% 0.12/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.40 % SZS output start CNFRefutation for theBenchmark
% 0.12/0.40 fof(f1,axiom,(
% 0.12/0.40 (! [A,B] :( subset(A,B)<=> (! [X] :( member(X,A)=> member(X,B) ) )) )),
% 0.12/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.40 fof(f2,axiom,(
% 0.12/0.40 (! [A,B] :( equal_set(A,B)<=> ( subset(A,B)& subset(B,A) ) ) )),
% 0.12/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.40 fof(f8,axiom,(
% 0.12/0.40 (! [X,A] :( member(X,singleton(A))<=> X = A ) )),
% 0.12/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.40 fof(f9,axiom,(
% 0.12/0.40 (! [X,A,B] :( member(X,unordered_pair(A,B))<=> ( X = A| X = B ) ) )),
% 0.12/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.40 fof(f12,conjecture,(
% 0.12/0.40 (! [A,B,U,V] :( equal_set(unordered_pair(singleton(A),unordered_pair(A,B)),unordered_pair(singleton(U),unordered_pair(U,V)))=> A = U ) )),
% 0.12/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.40 fof(f13,negated_conjecture,(
% 0.12/0.40 ~((! [A,B,U,V] :( equal_set(unordered_pair(singleton(A),unordered_pair(A,B)),unordered_pair(singleton(U),unordered_pair(U,V)))=> A = U ) ))),
% 0.12/0.40 inference(negated_conjecture,[status(cth)],[f12])).
% 0.12/0.40 fof(f14,plain,(
% 0.12/0.40 ![A,B]: (subset(A,B)<=>(![X]: (~member(X,A)|member(X,B))))),
% 0.12/0.40 inference(pre_NNF_transformation,[status(thm)],[f1])).
% 0.12/0.40 fof(f15,plain,(
% 0.12/0.40 ![A,B]: ((~subset(A,B)|(![X]: (~member(X,A)|member(X,B))))&(subset(A,B)|(?[X]: (member(X,A)&~member(X,B)))))),
% 0.12/0.40 inference(NNF_transformation,[status(thm)],[f14])).
% 0.12/0.40 fof(f16,plain,(
% 0.12/0.40 (![A,B]: (~subset(A,B)|(![X]: (~member(X,A)|member(X,B)))))&(![A,B]: (subset(A,B)|(?[X]: (member(X,A)&~member(X,B)))))),
% 0.12/0.40 inference(miniscoping,[status(thm)],[f15])).
% 0.12/0.40 fof(f17,plain,(
% 0.12/0.40 (![A,B]: (~subset(A,B)|(![X]: (~member(X,A)|member(X,B)))))&(![A,B]: (subset(A,B)|(member(sK0_skl(B,A),A)&~member(sK0_skl(B,A),B))))),
% 0.12/0.40 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(X,sK0_skl(B,A))],[f16])).
% 0.12/0.40 fof(f18,plain,(
% 0.12/0.40 ![X0,X1,X2]: (~subset(X0,X1)|~member(X2,X0)|member(X2,X1))),
% 0.12/0.40 inference(cnf_transformation,[status(thm)],[f17])).
% 0.12/0.40 fof(f21,plain,(
% 0.12/0.40 ![A,B]: ((~equal_set(A,B)|(subset(A,B)&subset(B,A)))&(equal_set(A,B)|(~subset(A,B)|~subset(B,A))))),
% 0.12/0.40 inference(NNF_transformation,[status(thm)],[f2])).
% 0.12/0.40 fof(f22,plain,(
% 0.12/0.40 (![A,B]: (~equal_set(A,B)|(subset(A,B)&subset(B,A))))&(![A,B]: (equal_set(A,B)|(~subset(A,B)|~subset(B,A))))),
% 0.12/0.40 inference(miniscoping,[status(thm)],[f21])).
% 0.12/0.40 fof(f24,plain,(
% 0.12/0.40 ![X0,X1]: (~equal_set(X0,X1)|subset(X1,X0))),
% 0.12/0.40 inference(cnf_transformation,[status(thm)],[f22])).
% 0.12/0.40 fof(f46,plain,(
% 0.12/0.40 ![X,A]: ((~member(X,singleton(A))|X=A)&(member(X,singleton(A))|~X=A))),
% 0.12/0.40 inference(NNF_transformation,[status(thm)],[f8])).
% 0.12/0.40 fof(f47,plain,(
% 0.12/0.40 (![X,A]: (~member(X,singleton(A))|X=A))&(![X,A]: (member(X,singleton(A))|~X=A))),
% 0.12/0.40 inference(miniscoping,[status(thm)],[f46])).
% 0.12/0.40 fof(f48,plain,(
% 0.12/0.40 ![X0,X1]: (~member(X0,singleton(X1))|X0=X1)),
% 0.12/0.40 inference(cnf_transformation,[status(thm)],[f47])).
% 0.12/0.40 fof(f49,plain,(
% 0.12/0.40 ![X0,X1]: (member(X0,singleton(X1))|~X0=X1)),
% 0.12/0.40 inference(cnf_transformation,[status(thm)],[f47])).
% 0.12/0.40 fof(f50,plain,(
% 0.12/0.40 ![X,A,B]: ((~member(X,unordered_pair(A,B))|(X=A|X=B))&(member(X,unordered_pair(A,B))|(~X=A&~X=B)))),
% 0.12/0.40 inference(NNF_transformation,[status(thm)],[f9])).
% 0.12/0.40 fof(f51,plain,(
% 0.12/0.40 (![X,A,B]: (~member(X,unordered_pair(A,B))|(X=A|X=B)))&(![X,A,B]: (member(X,unordered_pair(A,B))|(~X=A&~X=B)))),
% 0.12/0.40 inference(miniscoping,[status(thm)],[f50])).
% 0.12/0.40 fof(f52,plain,(
% 0.12/0.40 ![X0,X1,X2]: (~member(X0,unordered_pair(X1,X2))|X0=X1|X0=X2)),
% 0.12/0.40 inference(cnf_transformation,[status(thm)],[f51])).
% 0.12/0.40 fof(f53,plain,(
% 0.12/0.40 ![X0,X1,X2]: (member(X0,unordered_pair(X1,X2))|~X0=X1)),
% 0.12/0.40 inference(cnf_transformation,[status(thm)],[f51])).
% 0.12/0.40 fof(f54,plain,(
% 0.12/0.40 ![X0,X1,X2]: (member(X0,unordered_pair(X1,X2))|~X0=X2)),
% 0.12/0.40 inference(cnf_transformation,[status(thm)],[f51])).
% 0.12/0.40 fof(f68,plain,(
% 0.12/0.40 (?[A,B,U,V]: (equal_set(unordered_pair(singleton(A),unordered_pair(A,B)),unordered_pair(singleton(U),unordered_pair(U,V)))&~A=U))),
% 0.12/0.40 inference(pre_NNF_transformation,[status(thm)],[f13])).
% 0.12/0.40 fof(f69,plain,(
% 0.12/0.40 ?[A,U]: ((?[B,V]: equal_set(unordered_pair(singleton(A),unordered_pair(A,B)),unordered_pair(singleton(U),unordered_pair(U,V))))&~A=U)),
% 0.12/0.40 inference(miniscoping,[status(thm)],[f68])).
% 0.12/0.40 fof(f70,plain,(
% 0.12/0.40 (equal_set(unordered_pair(singleton(sK3_skl),unordered_pair(sK3_skl,sK5_skl)),unordered_pair(singleton(sK4_skl),unordered_pair(sK4_skl,sK6_skl)))&~sK3_skl=sK4_skl)),
% 0.12/0.40 inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl,sK4_skl,sK5_skl,sK6_skl]),skolemize(A,sK3_skl),skolemize(U,sK4_skl),skolemize(B,sK5_skl),skolemize(V,sK6_skl)],[f69])).
% 0.12/0.40 fof(f71,plain,(
% 0.12/0.40 equal_set(unordered_pair(singleton(sK3_skl),unordered_pair(sK3_skl,sK5_skl)),unordered_pair(singleton(sK4_skl),unordered_pair(sK4_skl,sK6_skl)))),
% 0.12/0.40 inference(cnf_transformation,[status(thm)],[f70])).
% 0.12/0.40 fof(f72,plain,(
% 0.12/0.40 ~sK3_skl=sK4_skl),
% 0.12/0.40 inference(cnf_transformation,[status(thm)],[f70])).
% 0.12/0.40 fof(f73,plain,(
% 0.12/0.40 ![X0]: (member(X0,singleton(X0)))),
% 0.12/0.40 inference(destructive_equality_resolution,[status(thm)],[f49])).
% 0.12/0.40 fof(f74,plain,(
% 0.12/0.40 ![X0,X1]: (member(X0,unordered_pair(X0,X1)))),
% 0.12/0.40 inference(destructive_equality_resolution,[status(thm)],[f53])).
% 0.12/0.40 fof(f75,plain,(
% 0.12/0.40 ![X0,X1]: (member(X0,unordered_pair(X1,X0)))),
% 0.12/0.40 inference(destructive_equality_resolution,[status(thm)],[f54])).
% 0.12/0.40 fof(f82,plain,(
% 0.12/0.40 ![X0,X1,X2]: (~member(X0,X1)|member(X0,X2)|~equal_set(X2,X1))),
% 0.12/0.40 inference(resolution,[status(thm)],[f18,f24])).
% 0.12/0.40 fof(f84,plain,(
% 0.12/0.40 ![X0]: (~member(X0,unordered_pair(singleton(sK4_skl),unordered_pair(sK4_skl,sK6_skl)))|member(X0,unordered_pair(singleton(sK3_skl),unordered_pair(sK3_skl,sK5_skl))))),
% 0.12/0.40 inference(resolution,[status(thm)],[f82,f71])).
% 0.12/0.40 fof(f117,plain,(
% 0.12/0.40 ![X0]: (~member(X0,unordered_pair(singleton(sK4_skl),unordered_pair(sK4_skl,sK6_skl)))|X0=singleton(sK3_skl)|X0=unordered_pair(sK3_skl,sK5_skl))),
% 0.12/0.40 inference(resolution,[status(thm)],[f84,f52])).
% 0.12/0.40 fof(f120,plain,(
% 0.12/0.40 singleton(sK4_skl)=singleton(sK3_skl)|singleton(sK4_skl)=unordered_pair(sK3_skl,sK5_skl)),
% 0.12/0.40 inference(resolution,[status(thm)],[f117,f74])).
% 0.12/0.40 fof(f124,plain,(
% 0.12/0.40 member(sK5_skl,singleton(sK4_skl))|singleton(sK4_skl)=singleton(sK3_skl)),
% 0.12/0.40 inference(paramodulation,[status(thm)],[f120,f75])).
% 0.12/0.40 fof(f125,plain,(
% 0.12/0.40 member(sK3_skl,singleton(sK4_skl))|singleton(sK4_skl)=singleton(sK3_skl)),
% 0.12/0.40 inference(paramodulation,[status(thm)],[f120,f74])).
% 0.12/0.40 fof(f126,plain,(
% 0.12/0.40 singleton(sK4_skl)=singleton(sK3_skl)|sK5_skl=sK4_skl),
% 0.12/0.40 inference(resolution,[status(thm)],[f124,f48])).
% 0.12/0.40 fof(f137,plain,(
% 0.12/0.40 member(sK3_skl,singleton(sK4_skl))|sK5_skl=sK4_skl),
% 0.12/0.40 inference(paramodulation,[status(thm)],[f126,f73])).
% 0.12/0.40 fof(f138,plain,(
% 0.12/0.40 sK5_skl=sK4_skl|sK3_skl=sK4_skl),
% 0.12/0.40 inference(resolution,[status(thm)],[f137,f48])).
% 0.12/0.40 fof(f147,plain,(
% 0.12/0.40 ~sK3_skl=sK5_skl),
% 0.12/0.40 inference(backward_demodulation,[status(thm)],[f161,f72])).
% 0.12/0.40 fof(f155,plain,(
% 0.12/0.40 member(sK3_skl,singleton(sK4_skl))|singleton(sK5_skl)=singleton(sK3_skl)),
% 0.12/0.40 inference(backward_demodulation,[status(thm)],[f161,f125])).
% 0.12/0.40 fof(f161,plain,(
% 0.12/0.40 sK5_skl=sK4_skl),
% 0.12/0.40 inference(forward_subsumption_resolution,[status(thm)],[f138,f72])).
% 0.12/0.40 fof(f173,plain,(
% 0.12/0.40 member(sK3_skl,singleton(sK5_skl))|singleton(sK5_skl)=singleton(sK3_skl)),
% 0.12/0.40 inference(forward_demodulation,[status(thm)],[f161,f155])).
% 0.12/0.40 fof(f192,plain,(
% 0.12/0.40 singleton(sK5_skl)=singleton(sK3_skl)|sK3_skl=sK5_skl),
% 0.12/0.40 inference(resolution,[status(thm)],[f173,f48])).
% 0.12/0.40 fof(f206,plain,(
% 0.12/0.40 singleton(sK5_skl)=singleton(sK3_skl)),
% 0.12/0.40 inference(forward_subsumption_resolution,[status(thm)],[f192,f147])).
% 0.12/0.40 fof(f216,plain,(
% 0.12/0.40 member(sK3_skl,singleton(sK5_skl))),
% 0.12/0.40 inference(paramodulation,[status(thm)],[f206,f73])).
% 0.12/0.40 fof(f219,plain,(
% 0.12/0.40 sK3_skl=sK5_skl),
% 0.12/0.40 inference(resolution,[status(thm)],[f216,f48])).
% 0.12/0.40 fof(f220,plain,(
% 0.12/0.40 $false),
% 0.12/0.40 inference(forward_subsumption_resolution,[status(thm)],[f219,f147])).
% 0.12/0.40 % SZS output end CNFRefutation for theBenchmark.p
% 0.12/0.43 % Elapsed time: 0.054849 seconds
% 0.12/0.43 % CPU time: 0.192951 seconds
% 0.12/0.43 % Total memory used: 69.089 MB
% 0.12/0.43 % Net memory used: 68.869 MB
%------------------------------------------------------------------------------