%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SET901+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 : n013.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 02:12:49 PM UTC 2026
% Result : Theorem 0.14s 0.39s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET901+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
% 0.11/0.36 % Computer : n013.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 05:42:51 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.37 % Drodi V4.1.1
% 0.14/0.39 % Refutation found
% 0.14/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.39 % SZS output start CNFRefutation for theBenchmark
% 0.14/0.39 fof(f2,axiom,(
% 0.14/0.39 (! [A,B] : subset(A,A) )),
% 0.14/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.39 fof(f6,conjecture,(
% 0.14/0.39 (! [A,B,C] :( subset(A,unordered_pair(B,C))<=> ~ ( A != empty_set& A != singleton(B)& A != singleton(C)& A != unordered_pair(B,C) ) ) )),
% 0.14/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.39 fof(f7,negated_conjecture,(
% 0.14/0.39 ~((! [A,B,C] :( subset(A,unordered_pair(B,C))<=> ~ ( A != empty_set& A != singleton(B)& A != singleton(C)& A != unordered_pair(B,C) ) ) ))),
% 0.14/0.39 inference(negated_conjecture,[status(cth)],[f6])).
% 0.14/0.39 fof(f8,axiom,(
% 0.14/0.39 (! [A,B,C] :( subset(A,unordered_pair(B,C))<=> ~ ( A != empty_set& A != singleton(B)& A != singleton(C)& A != unordered_pair(B,C) ) ) )),
% 0.14/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.39 fof(f10,plain,(
% 0.14/0.39 ![A]: subset(A,A)),
% 0.14/0.39 inference(miniscoping,[status(thm)],[f2])).
% 0.14/0.39 fof(f11,plain,(
% 0.14/0.39 ![X0]: (subset(X0,X0))),
% 0.14/0.39 inference(cnf_transformation,[status(thm)],[f10])).
% 0.14/0.39 fof(f17,plain,(
% 0.14/0.39 (?[A,B,C]: (subset(A,unordered_pair(B,C))<~>(((A=empty_set|A=singleton(B))|A=singleton(C))|A=unordered_pair(B,C))))),
% 0.14/0.39 inference(pre_NNF_transformation,[status(thm)],[f7])).
% 0.14/0.39 fof(f18,plain,(
% 0.14/0.39 ?[A,B,C]: ((subset(A,unordered_pair(B,C))|(((A=empty_set|A=singleton(B))|A=singleton(C))|A=unordered_pair(B,C)))&(~subset(A,unordered_pair(B,C))|(((~A=empty_set&~A=singleton(B))&~A=singleton(C))&~A=unordered_pair(B,C))))),
% 0.14/0.39 inference(NNF_transformation,[status(thm)],[f17])).
% 0.14/0.39 fof(f19,plain,(
% 0.14/0.39 ((subset(sK2_skl,unordered_pair(sK3_skl,sK4_skl))|(((sK2_skl=empty_set|sK2_skl=singleton(sK3_skl))|sK2_skl=singleton(sK4_skl))|sK2_skl=unordered_pair(sK3_skl,sK4_skl)))&(~subset(sK2_skl,unordered_pair(sK3_skl,sK4_skl))|(((~sK2_skl=empty_set&~sK2_skl=singleton(sK3_skl))&~sK2_skl=singleton(sK4_skl))&~sK2_skl=unordered_pair(sK3_skl,sK4_skl))))),
% 0.14/0.39 inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl,sK4_skl]),skolemize(A,sK2_skl),skolemize(B,sK3_skl),skolemize(C,sK4_skl)],[f18])).
% 0.14/0.39 fof(f20,plain,(
% 0.14/0.39 subset(sK2_skl,unordered_pair(sK3_skl,sK4_skl))|sK2_skl=empty_set|sK2_skl=singleton(sK3_skl)|sK2_skl=singleton(sK4_skl)|sK2_skl=unordered_pair(sK3_skl,sK4_skl)),
% 0.14/0.39 inference(cnf_transformation,[status(thm)],[f19])).
% 0.14/0.39 fof(f21,plain,(
% 0.14/0.39 ~subset(sK2_skl,unordered_pair(sK3_skl,sK4_skl))|~sK2_skl=empty_set),
% 0.14/0.39 inference(cnf_transformation,[status(thm)],[f19])).
% 0.14/0.39 fof(f22,plain,(
% 0.14/0.39 ~subset(sK2_skl,unordered_pair(sK3_skl,sK4_skl))|~sK2_skl=singleton(sK3_skl)),
% 0.14/0.39 inference(cnf_transformation,[status(thm)],[f19])).
% 0.14/0.39 fof(f23,plain,(
% 0.14/0.39 ~subset(sK2_skl,unordered_pair(sK3_skl,sK4_skl))|~sK2_skl=singleton(sK4_skl)),
% 0.14/0.39 inference(cnf_transformation,[status(thm)],[f19])).
% 0.14/0.39 fof(f24,plain,(
% 0.14/0.39 ~subset(sK2_skl,unordered_pair(sK3_skl,sK4_skl))|~sK2_skl=unordered_pair(sK3_skl,sK4_skl)),
% 0.14/0.39 inference(cnf_transformation,[status(thm)],[f19])).
% 0.14/0.39 fof(f25,plain,(
% 0.14/0.39 ![A,B,C]: (subset(A,unordered_pair(B,C))<=>(((A=empty_set|A=singleton(B))|A=singleton(C))|A=unordered_pair(B,C)))),
% 0.14/0.39 inference(pre_NNF_transformation,[status(thm)],[f8])).
% 0.14/0.39 fof(f26,plain,(
% 0.14/0.39 ![A,B,C]: ((~subset(A,unordered_pair(B,C))|(((A=empty_set|A=singleton(B))|A=singleton(C))|A=unordered_pair(B,C)))&(subset(A,unordered_pair(B,C))|(((~A=empty_set&~A=singleton(B))&~A=singleton(C))&~A=unordered_pair(B,C))))),
% 0.14/0.39 inference(NNF_transformation,[status(thm)],[f25])).
% 0.14/0.39 fof(f27,plain,(
% 0.14/0.39 (![A,B,C]: (~subset(A,unordered_pair(B,C))|(((A=empty_set|A=singleton(B))|A=singleton(C))|A=unordered_pair(B,C))))&(![A,B,C]: (subset(A,unordered_pair(B,C))|(((~A=empty_set&~A=singleton(B))&~A=singleton(C))&~A=unordered_pair(B,C))))),
% 0.14/0.39 inference(miniscoping,[status(thm)],[f26])).
% 0.14/0.39 fof(f28,plain,(
% 0.14/0.39 ![X0,X1,X2]: (~subset(X0,unordered_pair(X1,X2))|X0=empty_set|X0=singleton(X1)|X0=singleton(X2)|X0=unordered_pair(X1,X2))),
% 0.14/0.39 inference(cnf_transformation,[status(thm)],[f27])).
% 0.14/0.39 fof(f29,plain,(
% 0.14/0.39 ![X0,X1,X2]: (subset(X0,unordered_pair(X1,X2))|~X0=empty_set)),
% 0.14/0.39 inference(cnf_transformation,[status(thm)],[f27])).
% 0.14/0.39 fof(f30,plain,(
% 0.14/0.39 ![X0,X1,X2]: (subset(X0,unordered_pair(X1,X2))|~X0=singleton(X1))),
% 0.14/0.39 inference(cnf_transformation,[status(thm)],[f27])).
% 0.14/0.39 fof(f31,plain,(
% 0.14/0.39 ![X0,X1,X2]: (subset(X0,unordered_pair(X1,X2))|~X0=singleton(X2))),
% 0.14/0.39 inference(cnf_transformation,[status(thm)],[f27])).
% 0.14/0.39 fof(f33,definition,(
% 0.14/0.39 sQ0_spl <=> (subset(sK2_skl,unordered_pair(sK3_skl,sK4_skl)))),
% 0.14/0.39 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.14/0.39 fof(f34,plain,(
% 0.14/0.39 subset(sK2_skl,unordered_pair(sK3_skl,sK4_skl))|~sQ0_spl),
% 0.14/0.39 inference(component_clause,[status(thm)],[f33])).
% 0.14/0.39 fof(f35,plain,(
% 0.14/0.39 ~subset(sK2_skl,unordered_pair(sK3_skl,sK4_skl))|sQ0_spl),
% 0.14/0.39 inference(component_clause,[status(thm)],[f33])).
% 0.14/0.39 fof(f36,definition,(
% 0.14/0.39 sQ1_spl <=> (sK2_skl=empty_set)),
% 0.14/0.39 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.14/0.39 fof(f37,plain,(
% 0.14/0.39 sK2_skl=empty_set|~sQ1_spl),
% 0.14/0.39 inference(component_clause,[status(thm)],[f36])).
% 0.14/0.39 fof(f39,definition,(
% 0.14/0.39 sQ2_spl <=> (sK2_skl=singleton(sK3_skl))),
% 0.14/0.39 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.14/0.39 fof(f40,plain,(
% 0.14/0.39 sK2_skl=singleton(sK3_skl)|~sQ2_spl),
% 0.14/0.39 inference(component_clause,[status(thm)],[f39])).
% 0.14/0.39 fof(f42,definition,(
% 0.14/0.39 sQ3_spl <=> (sK2_skl=singleton(sK4_skl))),
% 0.14/0.39 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 0.14/0.39 fof(f43,plain,(
% 0.14/0.39 sK2_skl=singleton(sK4_skl)|~sQ3_spl),
% 0.14/0.39 inference(component_clause,[status(thm)],[f42])).
% 0.14/0.39 fof(f45,definition,(
% 0.14/0.39 sQ4_spl <=> (sK2_skl=unordered_pair(sK3_skl,sK4_skl))),
% 0.14/0.39 introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition])).
% 0.14/0.39 fof(f46,plain,(
% 0.14/0.39 sK2_skl=unordered_pair(sK3_skl,sK4_skl)|~sQ4_spl),
% 0.14/0.39 inference(component_clause,[status(thm)],[f45])).
% 0.14/0.39 fof(f48,plain,(
% 0.14/0.39 sQ0_spl|sQ1_spl|sQ2_spl|sQ3_spl|sQ4_spl),
% 0.14/0.39 inference(split_clause,[status(thm)],[f20,f33,f36,f39,f42,f45])).
% 0.14/0.39 fof(f49,plain,(
% 0.14/0.39 ~sQ0_spl|~sQ1_spl),
% 0.14/0.39 inference(split_clause,[status(thm)],[f21,f33,f36])).
% 0.14/0.39 fof(f50,plain,(
% 0.14/0.39 ~sQ0_spl|~sQ2_spl),
% 0.14/0.39 inference(split_clause,[status(thm)],[f22,f33,f39])).
% 0.14/0.39 fof(f51,plain,(
% 0.14/0.39 ~sQ0_spl|~sQ3_spl),
% 0.14/0.39 inference(split_clause,[status(thm)],[f23,f33,f42])).
% 0.14/0.39 fof(f52,plain,(
% 0.14/0.39 ~sQ0_spl|~sQ4_spl),
% 0.14/0.39 inference(split_clause,[status(thm)],[f24,f33,f45])).
% 0.14/0.39 fof(f53,plain,(
% 0.14/0.39 ![X0,X1]: (subset(empty_set,unordered_pair(X0,X1)))),
% 0.14/0.39 inference(destructive_equality_resolution,[status(thm)],[f29])).
% 0.14/0.39 fof(f54,plain,(
% 0.14/0.39 ![X0,X1]: (subset(singleton(X0),unordered_pair(X0,X1)))),
% 0.14/0.39 inference(destructive_equality_resolution,[status(thm)],[f30])).
% 0.14/0.39 fof(f55,plain,(
% 0.14/0.39 ![X0,X1]: (subset(singleton(X0),unordered_pair(X1,X0)))),
% 0.14/0.39 inference(destructive_equality_resolution,[status(thm)],[f31])).
% 0.14/0.39 fof(f57,plain,(
% 0.14/0.39 ~subset(sK2_skl,sK2_skl)|~sQ4_spl|sQ0_spl),
% 0.14/0.39 inference(forward_demodulation,[status(thm)],[f46,f35])).
% 0.14/0.39 fof(f58,plain,(
% 0.14/0.39 $false|~sQ4_spl|sQ0_spl),
% 0.14/0.39 inference(backward_subsumption_resolution,[status(thm)],[f57,f11])).
% 0.14/0.39 fof(f59,plain,(
% 0.14/0.39 ~sQ4_spl|sQ0_spl),
% 0.14/0.39 inference(contradiction_clause,[status(thm)],[f58])).
% 0.14/0.39 fof(f77,plain,(
% 0.14/0.39 sK2_skl=empty_set|sK2_skl=singleton(sK3_skl)|sK2_skl=singleton(sK4_skl)|sK2_skl=unordered_pair(sK3_skl,sK4_skl)|~sQ0_spl),
% 0.14/0.39 inference(resolution,[status(thm)],[f28,f34])).
% 0.14/0.39 fof(f88,plain,(
% 0.14/0.39 sQ1_spl|sQ2_spl|sQ3_spl|sQ4_spl|~sQ0_spl),
% 0.14/0.39 inference(split_clause,[status(thm)],[f77,f36,f39,f42,f45,f33])).
% 0.14/0.39 fof(f89,plain,(
% 0.14/0.39 ![X0]: (subset(sK2_skl,unordered_pair(X0,sK4_skl))|~sQ3_spl)),
% 0.14/0.39 inference(paramodulation,[status(thm)],[f43,f55])).
% 0.14/0.39 fof(f105,plain,(
% 0.14/0.39 $false|~sQ3_spl|sQ0_spl),
% 0.14/0.39 inference(forward_subsumption_resolution,[status(thm)],[f35,f89])).
% 0.14/0.39 fof(f106,plain,(
% 0.14/0.39 ~sQ3_spl|sQ0_spl),
% 0.14/0.39 inference(contradiction_clause,[status(thm)],[f105])).
% 0.14/0.39 fof(f109,plain,(
% 0.14/0.39 ![X0,X1]: (subset(sK2_skl,unordered_pair(X0,X1))|~sQ1_spl)),
% 0.14/0.39 inference(backward_demodulation,[status(thm)],[f37,f53])).
% 0.14/0.39 fof(f112,plain,(
% 0.14/0.39 $false|~sQ1_spl|sQ0_spl),
% 0.14/0.39 inference(forward_subsumption_resolution,[status(thm)],[f35,f109])).
% 0.14/0.39 fof(f113,plain,(
% 0.14/0.39 ~sQ1_spl|sQ0_spl),
% 0.14/0.39 inference(contradiction_clause,[status(thm)],[f112])).
% 0.14/0.39 fof(f115,plain,(
% 0.14/0.39 ![X0]: (subset(sK2_skl,unordered_pair(sK3_skl,X0))|~sQ2_spl)),
% 0.14/0.39 inference(paramodulation,[status(thm)],[f40,f54])).
% 0.14/0.40 fof(f130,plain,(
% 0.14/0.40 $false|~sQ2_spl|sQ0_spl),
% 0.14/0.40 inference(backward_subsumption_resolution,[status(thm)],[f35,f115])).
% 0.14/0.40 fof(f134,plain,(
% 0.14/0.40 ~sQ2_spl|sQ0_spl),
% 0.14/0.40 inference(contradiction_clause,[status(thm)],[f130])).
% 0.14/0.40 fof(f135,plain,(
% 0.14/0.40 $false),
% 0.14/0.40 inference(sat_refutation,[status(thm)],[f48,f49,f50,f51,f52,f59,f88,f106,f113,f134])).
% 0.14/0.40 % SZS output end CNFRefutation for theBenchmark.p
% 0.14/0.42 % Elapsed time: 0.051181 seconds
% 0.14/0.42 % CPU time: 0.153817 seconds
% 0.14/0.42 % Total memory used: 95.339 MB
% 0.14/0.42 % Net memory used: 94.953 MB
%------------------------------------------------------------------------------