%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SEU160+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 : n015.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 02:21:50 PM UTC 2026
% Result : Theorem 0.14s 0.40s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU160+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n015.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 05:56:51 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.14/0.38 % Drodi V4.1.1
% 0.14/0.40 % Refutation found
% 0.14/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.40 % SZS output start CNFRefutation for theBenchmark
% 0.14/0.40 fof(f6,axiom,(
% 0.14/0.40 (! [A,B] :( A = B<=> ( subset(A,B)& subset(B,A) ) ) )),
% 0.14/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.40 fof(f44,lemma,(
% 0.14/0.40 (! [A,B] :( subset(A,singleton(B))<=> ( A = empty_set| A = singleton(B) ) ) )),
% 0.14/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.40 fof(f47,axiom,(
% 0.14/0.40 (? [A] : empty(A) )),
% 0.14/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.40 fof(f62,lemma,(
% 0.14/0.40 (! [A] : subset(empty_set,A) )),
% 0.14/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.40 fof(f70,conjecture,(
% 0.14/0.40 (! [A,B] :( subset(A,singleton(B))<=> ( A = empty_set| A = singleton(B) ) ) )),
% 0.14/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.40 fof(f71,negated_conjecture,(
% 0.14/0.40 ~((! [A,B] :( subset(A,singleton(B))<=> ( A = empty_set| A = singleton(B) ) ) ))),
% 0.14/0.40 inference(negated_conjecture,[status(cth)],[f70])).
% 0.14/0.40 fof(f83,axiom,(
% 0.14/0.40 (! [A] :( empty(A)=> A = empty_set ) )),
% 0.14/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/0.40 fof(f99,plain,(
% 0.14/0.40 ![A,B]: ((~A=B|(subset(A,B)&subset(B,A)))&(A=B|(~subset(A,B)|~subset(B,A))))),
% 0.14/0.40 inference(NNF_transformation,[status(thm)],[f6])).
% 0.14/0.40 fof(f100,plain,(
% 0.14/0.40 (![A,B]: (~A=B|(subset(A,B)&subset(B,A))))&(![A,B]: (A=B|(~subset(A,B)|~subset(B,A))))),
% 0.14/0.40 inference(miniscoping,[status(thm)],[f99])).
% 0.14/0.40 fof(f101,plain,(
% 0.14/0.40 ![X0,X1]: (~X0=X1|subset(X0,X1))),
% 0.14/0.40 inference(cnf_transformation,[status(thm)],[f100])).
% 0.14/0.40 fof(f226,plain,(
% 0.14/0.40 ![A,B]: ((~subset(A,singleton(B))|(A=empty_set|A=singleton(B)))&(subset(A,singleton(B))|(~A=empty_set&~A=singleton(B))))),
% 0.14/0.40 inference(NNF_transformation,[status(thm)],[f44])).
% 0.14/0.40 fof(f227,plain,(
% 0.14/0.40 (![A,B]: (~subset(A,singleton(B))|(A=empty_set|A=singleton(B))))&(![A,B]: (subset(A,singleton(B))|(~A=empty_set&~A=singleton(B))))),
% 0.14/0.40 inference(miniscoping,[status(thm)],[f226])).
% 0.14/0.40 fof(f228,plain,(
% 0.14/0.40 ![X0,X1]: (~subset(X0,singleton(X1))|X0=empty_set|X0=singleton(X1))),
% 0.14/0.40 inference(cnf_transformation,[status(thm)],[f227])).
% 0.14/0.40 fof(f238,plain,(
% 0.14/0.40 empty(sK16_skl)),
% 0.14/0.40 inference(skolemize,[status(esa),new_symbols(skolem,[sK16_skl]),skolemize(A,sK16_skl)],[f47])).
% 0.14/0.40 fof(f239,plain,(
% 0.14/0.40 empty(sK16_skl)),
% 0.14/0.40 inference(cnf_transformation,[status(thm)],[f238])).
% 0.14/0.40 fof(f270,plain,(
% 0.14/0.40 ![X0]: (subset(empty_set,X0))),
% 0.14/0.40 inference(cnf_transformation,[status(thm)],[f62])).
% 0.14/0.40 fof(f292,plain,(
% 0.14/0.40 (?[A,B]: (subset(A,singleton(B))<~>(A=empty_set|A=singleton(B))))),
% 0.14/0.40 inference(pre_NNF_transformation,[status(thm)],[f71])).
% 0.14/0.40 fof(f293,plain,(
% 0.14/0.40 ?[A,B]: ((subset(A,singleton(B))|(A=empty_set|A=singleton(B)))&(~subset(A,singleton(B))|(~A=empty_set&~A=singleton(B))))),
% 0.14/0.40 inference(NNF_transformation,[status(thm)],[f292])).
% 0.14/0.40 fof(f294,plain,(
% 0.14/0.40 ((subset(sK19_skl,singleton(sK20_skl))|(sK19_skl=empty_set|sK19_skl=singleton(sK20_skl)))&(~subset(sK19_skl,singleton(sK20_skl))|(~sK19_skl=empty_set&~sK19_skl=singleton(sK20_skl))))),
% 0.14/0.40 inference(skolemize,[status(esa),new_symbols(skolem,[sK19_skl,sK20_skl]),skolemize(A,sK19_skl),skolemize(B,sK20_skl)],[f293])).
% 0.14/0.40 fof(f295,plain,(
% 0.14/0.40 subset(sK19_skl,singleton(sK20_skl))|sK19_skl=empty_set|sK19_skl=singleton(sK20_skl)),
% 0.14/0.40 inference(cnf_transformation,[status(thm)],[f294])).
% 0.14/0.40 fof(f296,plain,(
% 0.14/0.40 ~subset(sK19_skl,singleton(sK20_skl))|~sK19_skl=empty_set),
% 0.14/0.40 inference(cnf_transformation,[status(thm)],[f294])).
% 0.14/0.40 fof(f297,plain,(
% 0.14/0.40 ~subset(sK19_skl,singleton(sK20_skl))|~sK19_skl=singleton(sK20_skl)),
% 0.14/0.40 inference(cnf_transformation,[status(thm)],[f294])).
% 0.14/0.40 fof(f323,plain,(
% 0.14/0.40 ![A]: (~empty(A)|A=empty_set)),
% 0.14/0.40 inference(pre_NNF_transformation,[status(thm)],[f83])).
% 0.14/0.40 fof(f324,plain,(
% 0.14/0.40 ![X0]: (~empty(X0)|X0=empty_set)),
% 0.14/0.40 inference(cnf_transformation,[status(thm)],[f323])).
% 0.14/0.40 fof(f352,definition,(
% 0.14/0.40 sQ0_spl <=> (subset(sK19_skl,singleton(sK20_skl)))),
% 0.14/0.40 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.14/0.40 fof(f353,plain,(
% 0.14/0.40 subset(sK19_skl,singleton(sK20_skl))|~sQ0_spl),
% 0.14/0.40 inference(component_clause,[status(thm)],[f352])).
% 0.14/0.40 fof(f354,plain,(
% 0.14/0.40 ~subset(sK19_skl,singleton(sK20_skl))|sQ0_spl),
% 0.14/0.40 inference(component_clause,[status(thm)],[f352])).
% 0.14/0.40 fof(f355,definition,(
% 0.14/0.40 sQ1_spl <=> (sK19_skl=empty_set)),
% 0.14/0.40 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.14/0.40 fof(f356,plain,(
% 0.14/0.40 sK19_skl=empty_set|~sQ1_spl),
% 0.14/0.40 inference(component_clause,[status(thm)],[f355])).
% 0.14/0.40 fof(f357,plain,(
% 0.14/0.40 ~sK19_skl=empty_set|sQ1_spl),
% 0.14/0.40 inference(component_clause,[status(thm)],[f355])).
% 0.14/0.40 fof(f358,definition,(
% 0.14/0.40 sQ2_spl <=> (sK19_skl=singleton(sK20_skl))),
% 0.14/0.40 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.14/0.40 fof(f359,plain,(
% 0.14/0.40 sK19_skl=singleton(sK20_skl)|~sQ2_spl),
% 0.14/0.40 inference(component_clause,[status(thm)],[f358])).
% 0.14/0.40 fof(f361,plain,(
% 0.14/0.40 sQ0_spl|sQ1_spl|sQ2_spl),
% 0.14/0.40 inference(split_clause,[status(thm)],[f295,f352,f355,f358])).
% 0.14/0.40 fof(f362,plain,(
% 0.14/0.40 ~sQ0_spl|~sQ1_spl),
% 0.14/0.40 inference(split_clause,[status(thm)],[f296,f352,f355])).
% 0.14/0.40 fof(f363,plain,(
% 0.14/0.40 ~sQ0_spl|~sQ2_spl),
% 0.14/0.40 inference(split_clause,[status(thm)],[f297,f352,f358])).
% 0.14/0.40 fof(f364,plain,(
% 0.14/0.40 ![X0]: (subset(X0,X0))),
% 0.14/0.40 inference(destructive_equality_resolution,[status(thm)],[f101])).
% 0.14/0.40 fof(f395,plain,(
% 0.14/0.40 $false|~sQ1_spl|sQ0_spl),
% 0.14/0.40 inference(backward_subsumption_resolution,[status(thm)],[f354,f396])).
% 0.14/0.40 fof(f396,plain,(
% 0.14/0.40 ![X0]: (subset(sK19_skl,X0)|~sQ1_spl)),
% 0.14/0.40 inference(forward_demodulation,[status(thm)],[f356,f270])).
% 0.14/0.40 fof(f398,plain,(
% 0.14/0.40 ~sQ1_spl|sQ0_spl),
% 0.14/0.40 inference(contradiction_clause,[status(thm)],[f395])).
% 0.14/0.40 fof(f408,plain,(
% 0.14/0.40 sK16_skl=empty_set),
% 0.14/0.40 inference(resolution,[status(thm)],[f324,f239])).
% 0.14/0.40 fof(f417,plain,(
% 0.14/0.40 ~sK19_skl=sK16_skl|sQ1_spl),
% 0.14/0.40 inference(backward_demodulation,[status(thm)],[f408,f357])).
% 0.14/0.40 fof(f436,plain,(
% 0.14/0.40 ~subset(sK19_skl,sK19_skl)|~sQ2_spl|sQ0_spl),
% 0.14/0.40 inference(forward_demodulation,[status(thm)],[f359,f354])).
% 0.14/0.40 fof(f437,plain,(
% 0.14/0.40 $false|~sQ2_spl|sQ0_spl),
% 0.14/0.40 inference(forward_subsumption_resolution,[status(thm)],[f436,f364])).
% 0.14/0.40 fof(f438,plain,(
% 0.14/0.40 ~sQ2_spl|sQ0_spl),
% 0.14/0.40 inference(contradiction_clause,[status(thm)],[f437])).
% 0.14/0.40 fof(f532,plain,(
% 0.14/0.40 ![X0,X1]: (~subset(X0,singleton(X1))|X0=sK16_skl|X0=singleton(X1))),
% 0.14/0.40 inference(forward_demodulation,[status(thm)],[f408,f228])).
% 0.14/0.40 fof(f535,plain,(
% 0.14/0.40 sK19_skl=sK16_skl|sK19_skl=singleton(sK20_skl)|~sQ0_spl),
% 0.14/0.40 inference(resolution,[status(thm)],[f532,f353])).
% 0.14/0.40 fof(f538,definition,(
% 0.14/0.40 sQ4_spl <=> (sK19_skl=sK16_skl)),
% 0.14/0.40 introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition])).
% 0.14/0.40 fof(f539,plain,(
% 0.14/0.40 sK19_skl=sK16_skl|~sQ4_spl),
% 0.14/0.40 inference(component_clause,[status(thm)],[f538])).
% 0.14/0.40 fof(f541,plain,(
% 0.14/0.40 sQ4_spl|sQ2_spl|~sQ0_spl),
% 0.14/0.40 inference(split_clause,[status(thm)],[f535,f538,f358,f352])).
% 0.14/0.40 fof(f549,plain,(
% 0.14/0.40 $false|sQ1_spl|~sQ4_spl),
% 0.14/0.40 inference(forward_subsumption_resolution,[status(thm)],[f539,f417])).
% 0.14/0.40 fof(f550,plain,(
% 0.14/0.40 sQ1_spl|~sQ4_spl),
% 0.14/0.40 inference(contradiction_clause,[status(thm)],[f549])).
% 0.14/0.40 fof(f551,plain,(
% 0.14/0.40 $false),
% 0.14/0.40 inference(sat_refutation,[status(thm)],[f361,f362,f363,f398,f438,f541,f550])).
% 0.14/0.40 % SZS output end CNFRefutation for theBenchmark.p
% 0.14/0.43 % Elapsed time: 0.059732 seconds
% 0.14/0.43 % CPU time: 0.171038 seconds
% 0.14/0.43 % Total memory used: 107.061 MB
% 0.14/0.43 % Net memory used: 106.883 MB
%------------------------------------------------------------------------------