%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SEU165+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.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 02:21:52 PM UTC 2026
% Result : Theorem 0.12s 0.39s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU165+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n014.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 05:53:49 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.12/0.37 % Drodi V4.1.1
% 0.12/0.39 % Refutation found
% 0.12/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.39 % SZS output start CNFRefutation for theBenchmark
% 0.12/0.39 fof(f46,lemma,(
% 0.12/0.39 (! [A,B,C,D] :( in(ordered_pair(A,B),cartesian_product2(C,D))<=> ( in(A,C)& in(B,D) ) ) )),
% 0.12/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.39 fof(f51,conjecture,(
% 0.12/0.39 (! [A,B,C,D] :( in(ordered_pair(A,B),cartesian_product2(C,D))<=> ( in(A,C)& in(B,D) ) ) )),
% 0.12/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.39 fof(f52,negated_conjecture,(
% 0.12/0.39 ~((! [A,B,C,D] :( in(ordered_pair(A,B),cartesian_product2(C,D))<=> ( in(A,C)& in(B,D) ) ) ))),
% 0.12/0.39 inference(negated_conjecture,[status(cth)],[f51])).
% 0.12/0.39 fof(f238,plain,(
% 0.12/0.39 ![A,B,C,D]: ((~in(ordered_pair(A,B),cartesian_product2(C,D))|(in(A,C)&in(B,D)))&(in(ordered_pair(A,B),cartesian_product2(C,D))|(~in(A,C)|~in(B,D))))),
% 0.12/0.39 inference(NNF_transformation,[status(thm)],[f46])).
% 0.12/0.39 fof(f239,plain,(
% 0.12/0.39 (![A,B,C,D]: (~in(ordered_pair(A,B),cartesian_product2(C,D))|(in(A,C)&in(B,D))))&(![A,B,C,D]: (in(ordered_pair(A,B),cartesian_product2(C,D))|(~in(A,C)|~in(B,D))))),
% 0.12/0.39 inference(miniscoping,[status(thm)],[f238])).
% 0.12/0.39 fof(f240,plain,(
% 0.12/0.39 ![X0,X1,X2,X3]: (~in(ordered_pair(X0,X1),cartesian_product2(X2,X3))|in(X0,X2))),
% 0.12/0.39 inference(cnf_transformation,[status(thm)],[f239])).
% 0.12/0.39 fof(f241,plain,(
% 0.12/0.39 ![X0,X1,X2,X3]: (~in(ordered_pair(X0,X1),cartesian_product2(X2,X3))|in(X1,X3))),
% 0.12/0.39 inference(cnf_transformation,[status(thm)],[f239])).
% 0.12/0.39 fof(f242,plain,(
% 0.12/0.39 ![X0,X1,X2,X3]: (in(ordered_pair(X0,X1),cartesian_product2(X2,X3))|~in(X0,X2)|~in(X1,X3))),
% 0.12/0.39 inference(cnf_transformation,[status(thm)],[f239])).
% 0.12/0.39 fof(f251,plain,(
% 0.12/0.39 (?[A,B,C,D]: (in(ordered_pair(A,B),cartesian_product2(C,D))<~>(in(A,C)&in(B,D))))),
% 0.12/0.39 inference(pre_NNF_transformation,[status(thm)],[f52])).
% 0.12/0.39 fof(f252,plain,(
% 0.12/0.39 ?[A,B,C,D]: ((in(ordered_pair(A,B),cartesian_product2(C,D))|(in(A,C)&in(B,D)))&(~in(ordered_pair(A,B),cartesian_product2(C,D))|(~in(A,C)|~in(B,D))))),
% 0.12/0.39 inference(NNF_transformation,[status(thm)],[f251])).
% 0.12/0.39 fof(f253,plain,(
% 0.12/0.39 ((in(ordered_pair(sK18_skl,sK19_skl),cartesian_product2(sK20_skl,sK21_skl))|(in(sK18_skl,sK20_skl)&in(sK19_skl,sK21_skl)))&(~in(ordered_pair(sK18_skl,sK19_skl),cartesian_product2(sK20_skl,sK21_skl))|(~in(sK18_skl,sK20_skl)|~in(sK19_skl,sK21_skl))))),
% 0.12/0.39 inference(skolemize,[status(esa),new_symbols(skolem,[sK18_skl,sK19_skl,sK20_skl,sK21_skl]),skolemize(A,sK18_skl),skolemize(B,sK19_skl),skolemize(C,sK20_skl),skolemize(D,sK21_skl)],[f252])).
% 0.12/0.39 fof(f254,plain,(
% 0.12/0.39 in(ordered_pair(sK18_skl,sK19_skl),cartesian_product2(sK20_skl,sK21_skl))|in(sK18_skl,sK20_skl)),
% 0.12/0.39 inference(cnf_transformation,[status(thm)],[f253])).
% 0.12/0.39 fof(f255,plain,(
% 0.12/0.39 in(ordered_pair(sK18_skl,sK19_skl),cartesian_product2(sK20_skl,sK21_skl))|in(sK19_skl,sK21_skl)),
% 0.12/0.39 inference(cnf_transformation,[status(thm)],[f253])).
% 0.12/0.39 fof(f256,plain,(
% 0.12/0.39 ~in(ordered_pair(sK18_skl,sK19_skl),cartesian_product2(sK20_skl,sK21_skl))|~in(sK18_skl,sK20_skl)|~in(sK19_skl,sK21_skl)),
% 0.12/0.39 inference(cnf_transformation,[status(thm)],[f253])).
% 0.12/0.39 fof(f371,definition,(
% 0.12/0.39 sQ0_spl <=> (in(ordered_pair(sK18_skl,sK19_skl),cartesian_product2(sK20_skl,sK21_skl)))),
% 0.12/0.39 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.12/0.39 fof(f372,plain,(
% 0.12/0.39 in(ordered_pair(sK18_skl,sK19_skl),cartesian_product2(sK20_skl,sK21_skl))|~sQ0_spl),
% 0.12/0.39 inference(component_clause,[status(thm)],[f371])).
% 0.12/0.39 fof(f374,definition,(
% 0.12/0.39 sQ1_spl <=> (in(sK18_skl,sK20_skl))),
% 0.12/0.39 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.12/0.39 fof(f375,plain,(
% 0.12/0.39 in(sK18_skl,sK20_skl)|~sQ1_spl),
% 0.12/0.39 inference(component_clause,[status(thm)],[f374])).
% 0.12/0.39 fof(f376,plain,(
% 0.12/0.39 ~in(sK18_skl,sK20_skl)|sQ1_spl),
% 0.12/0.39 inference(component_clause,[status(thm)],[f374])).
% 0.12/0.39 fof(f377,plain,(
% 0.12/0.39 sQ0_spl|sQ1_spl),
% 0.12/0.39 inference(split_clause,[status(thm)],[f254,f371,f374])).
% 0.12/0.39 fof(f378,definition,(
% 0.12/0.39 sQ2_spl <=> (in(sK19_skl,sK21_skl))),
% 0.12/0.39 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.12/0.39 fof(f379,plain,(
% 0.12/0.39 in(sK19_skl,sK21_skl)|~sQ2_spl),
% 0.12/0.39 inference(component_clause,[status(thm)],[f378])).
% 0.12/0.39 fof(f381,plain,(
% 0.12/0.39 sQ0_spl|sQ2_spl),
% 0.12/0.39 inference(split_clause,[status(thm)],[f255,f371,f378])).
% 0.12/0.39 fof(f382,plain,(
% 0.12/0.39 ~sQ0_spl|~sQ1_spl|~sQ2_spl),
% 0.12/0.39 inference(split_clause,[status(thm)],[f256,f371,f374,f378])).
% 0.12/0.39 fof(f417,plain,(
% 0.12/0.39 in(sK18_skl,sK20_skl)|~sQ0_spl),
% 0.12/0.39 inference(resolution,[status(thm)],[f240,f372])).
% 0.12/0.39 fof(f418,plain,(
% 0.12/0.39 $false|sQ1_spl|~sQ0_spl),
% 0.12/0.39 inference(forward_subsumption_resolution,[status(thm)],[f417,f376])).
% 0.12/0.39 fof(f419,plain,(
% 0.12/0.39 sQ1_spl|~sQ0_spl),
% 0.12/0.39 inference(contradiction_clause,[status(thm)],[f418])).
% 0.12/0.39 fof(f422,plain,(
% 0.12/0.39 ![X0,X1]: (in(ordered_pair(X0,sK19_skl),cartesian_product2(X1,sK21_skl))|~in(X0,X1)|~sQ2_spl)),
% 0.12/0.39 inference(resolution,[status(thm)],[f242,f379])).
% 0.12/0.39 fof(f425,plain,(
% 0.12/0.39 in(ordered_pair(sK18_skl,sK19_skl),cartesian_product2(sK20_skl,sK21_skl))|~sQ2_spl|~sQ1_spl),
% 0.12/0.39 inference(resolution,[status(thm)],[f422,f375])).
% 0.12/0.39 fof(f426,plain,(
% 0.12/0.39 sQ0_spl|~sQ2_spl|~sQ1_spl),
% 0.12/0.39 inference(split_clause,[status(thm)],[f425,f371,f378,f374])).
% 0.12/0.39 fof(f427,plain,(
% 0.12/0.39 in(sK19_skl,sK21_skl)|~sQ0_spl),
% 0.12/0.39 inference(resolution,[status(thm)],[f372,f241])).
% 0.12/0.39 fof(f431,plain,(
% 0.12/0.39 sQ2_spl|~sQ0_spl),
% 0.12/0.39 inference(split_clause,[status(thm)],[f427,f378,f371])).
% 0.12/0.39 fof(f432,plain,(
% 0.12/0.39 $false),
% 0.12/0.39 inference(sat_refutation,[status(thm)],[f377,f381,f382,f419,f426,f431])).
% 0.12/0.39 % SZS output end CNFRefutation for theBenchmark.p
% 0.12/0.42 % Elapsed time: 0.053544 seconds
% 0.12/0.42 % CPU time: 0.157668 seconds
% 0.12/0.42 % Total memory used: 87.030 MB
% 0.12/0.42 % Net memory used: 86.913 MB
%------------------------------------------------------------------------------