%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SEU165+3 : 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 : 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 02:21:52 PM UTC 2026
% Result : Theorem 0.12s 0.41s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU165+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.37 % Computer : n007.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Mon Sep 21 05:51:50 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.39 % Drodi V4.1.1
% 0.12/0.41 % Refutation found
% 0.12/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.41 % SZS output start CNFRefutation for theBenchmark
% 0.12/0.41 fof(f7,conjecture,(
% 0.12/0.41 (! [A,B,C,D] :( in(ordered_pair(A,B),cartesian_product2(C,D))<=> ( in(A,C)& in(B,D) ) ) )),
% 0.12/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.41 fof(f8,negated_conjecture,(
% 0.12/0.41 ~((! [A,B,C,D] :( in(ordered_pair(A,B),cartesian_product2(C,D))<=> ( in(A,C)& in(B,D) ) ) ))),
% 0.12/0.41 inference(negated_conjecture,[status(cth)],[f7])).
% 0.12/0.41 fof(f9,axiom,(
% 0.12/0.41 (! [A,B,C,D] :( in(ordered_pair(A,B),cartesian_product2(C,D))<=> ( in(A,C)& in(B,D) ) ) )),
% 0.12/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.41 fof(f19,plain,(
% 0.12/0.41 (?[A,B,C,D]: (in(ordered_pair(A,B),cartesian_product2(C,D))<~>(in(A,C)&in(B,D))))),
% 0.12/0.41 inference(pre_NNF_transformation,[status(thm)],[f8])).
% 0.12/0.41 fof(f20,plain,(
% 0.12/0.41 ?[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))))),
% 0.12/0.41 inference(NNF_transformation,[status(thm)],[f19])).
% 0.12/0.41 fof(f21,plain,(
% 0.12/0.41 ((in(ordered_pair(sK2_skl,sK3_skl),cartesian_product2(sK4_skl,sK5_skl))|(in(sK2_skl,sK4_skl)&in(sK3_skl,sK5_skl)))&(~in(ordered_pair(sK2_skl,sK3_skl),cartesian_product2(sK4_skl,sK5_skl))|(~in(sK2_skl,sK4_skl)|~in(sK3_skl,sK5_skl))))),
% 0.12/0.41 inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl,sK4_skl,sK5_skl]),skolemize(A,sK2_skl),skolemize(B,sK3_skl),skolemize(C,sK4_skl),skolemize(D,sK5_skl)],[f20])).
% 0.12/0.41 fof(f22,plain,(
% 0.12/0.41 in(ordered_pair(sK2_skl,sK3_skl),cartesian_product2(sK4_skl,sK5_skl))|in(sK2_skl,sK4_skl)),
% 0.12/0.41 inference(cnf_transformation,[status(thm)],[f21])).
% 0.12/0.41 fof(f23,plain,(
% 0.12/0.41 in(ordered_pair(sK2_skl,sK3_skl),cartesian_product2(sK4_skl,sK5_skl))|in(sK3_skl,sK5_skl)),
% 0.12/0.41 inference(cnf_transformation,[status(thm)],[f21])).
% 0.12/0.41 fof(f24,plain,(
% 0.12/0.41 ~in(ordered_pair(sK2_skl,sK3_skl),cartesian_product2(sK4_skl,sK5_skl))|~in(sK2_skl,sK4_skl)|~in(sK3_skl,sK5_skl)),
% 0.12/0.41 inference(cnf_transformation,[status(thm)],[f21])).
% 0.12/0.41 fof(f25,plain,(
% 0.12/0.41 ![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))))),
% 0.12/0.41 inference(NNF_transformation,[status(thm)],[f9])).
% 0.12/0.41 fof(f26,plain,(
% 0.12/0.41 (![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))))),
% 0.12/0.41 inference(miniscoping,[status(thm)],[f25])).
% 0.12/0.41 fof(f27,plain,(
% 0.12/0.41 ![X0,X1,X2,X3]: (~in(ordered_pair(X0,X1),cartesian_product2(X2,X3))|in(X0,X2))),
% 0.12/0.41 inference(cnf_transformation,[status(thm)],[f26])).
% 0.12/0.41 fof(f28,plain,(
% 0.12/0.41 ![X0,X1,X2,X3]: (~in(ordered_pair(X0,X1),cartesian_product2(X2,X3))|in(X1,X3))),
% 0.12/0.41 inference(cnf_transformation,[status(thm)],[f26])).
% 0.12/0.41 fof(f29,plain,(
% 0.12/0.41 ![X0,X1,X2,X3]: (in(ordered_pair(X0,X1),cartesian_product2(X2,X3))|~in(X0,X2)|~in(X1,X3))),
% 0.12/0.41 inference(cnf_transformation,[status(thm)],[f26])).
% 0.12/0.41 fof(f30,definition,(
% 0.12/0.41 sQ0_spl <=> (in(ordered_pair(sK2_skl,sK3_skl),cartesian_product2(sK4_skl,sK5_skl)))),
% 0.12/0.41 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.12/0.41 fof(f31,plain,(
% 0.12/0.41 in(ordered_pair(sK2_skl,sK3_skl),cartesian_product2(sK4_skl,sK5_skl))|~sQ0_spl),
% 0.12/0.41 inference(component_clause,[status(thm)],[f30])).
% 0.12/0.41 fof(f33,definition,(
% 0.12/0.41 sQ1_spl <=> (in(sK2_skl,sK4_skl))),
% 0.12/0.41 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.12/0.41 fof(f34,plain,(
% 0.12/0.41 in(sK2_skl,sK4_skl)|~sQ1_spl),
% 0.12/0.41 inference(component_clause,[status(thm)],[f33])).
% 0.12/0.41 fof(f35,plain,(
% 0.12/0.41 ~in(sK2_skl,sK4_skl)|sQ1_spl),
% 0.12/0.41 inference(component_clause,[status(thm)],[f33])).
% 0.12/0.41 fof(f36,plain,(
% 0.12/0.41 sQ0_spl|sQ1_spl),
% 0.12/0.41 inference(split_clause,[status(thm)],[f22,f30,f33])).
% 0.12/0.41 fof(f37,definition,(
% 0.12/0.41 sQ2_spl <=> (in(sK3_skl,sK5_skl))),
% 0.12/0.41 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.12/0.41 fof(f38,plain,(
% 0.12/0.41 in(sK3_skl,sK5_skl)|~sQ2_spl),
% 0.12/0.41 inference(component_clause,[status(thm)],[f37])).
% 0.12/0.41 fof(f40,plain,(
% 0.12/0.41 sQ0_spl|sQ2_spl),
% 0.12/0.41 inference(split_clause,[status(thm)],[f23,f30,f37])).
% 0.12/0.41 fof(f41,plain,(
% 0.12/0.41 ~sQ0_spl|~sQ1_spl|~sQ2_spl),
% 0.12/0.41 inference(split_clause,[status(thm)],[f24,f30,f33,f37])).
% 0.15/0.44 fof(f43,plain,(
% 0.15/0.44 in(sK2_skl,sK4_skl)|~sQ0_spl),
% 0.15/0.44 inference(resolution,[status(thm)],[f27,f31])).
% 0.15/0.44 fof(f44,plain,(
% 0.15/0.44 $false|sQ1_spl|~sQ0_spl),
% 0.15/0.44 inference(forward_subsumption_resolution,[status(thm)],[f43,f35])).
% 0.15/0.44 fof(f45,plain,(
% 0.15/0.44 sQ1_spl|~sQ0_spl),
% 0.15/0.44 inference(contradiction_clause,[status(thm)],[f44])).
% 0.15/0.44 fof(f48,plain,(
% 0.15/0.44 ![X0,X1]: (in(ordered_pair(X0,sK3_skl),cartesian_product2(X1,sK5_skl))|~in(X0,X1)|~sQ2_spl)),
% 0.15/0.44 inference(resolution,[status(thm)],[f29,f38])).
% 0.15/0.44 fof(f51,plain,(
% 0.15/0.44 in(ordered_pair(sK2_skl,sK3_skl),cartesian_product2(sK4_skl,sK5_skl))|~sQ2_spl|~sQ1_spl),
% 0.15/0.44 inference(resolution,[status(thm)],[f48,f34])).
% 0.15/0.44 fof(f52,plain,(
% 0.15/0.44 sQ0_spl|~sQ2_spl|~sQ1_spl),
% 0.15/0.44 inference(split_clause,[status(thm)],[f51,f30,f37,f33])).
% 0.15/0.44 fof(f53,plain,(
% 0.15/0.44 in(sK3_skl,sK5_skl)|~sQ0_spl),
% 0.15/0.44 inference(resolution,[status(thm)],[f31,f28])).
% 0.15/0.44 fof(f57,plain,(
% 0.15/0.44 sQ2_spl|~sQ0_spl),
% 0.15/0.44 inference(split_clause,[status(thm)],[f53,f37,f30])).
% 0.15/0.44 fof(f58,plain,(
% 0.15/0.44 $false),
% 0.15/0.44 inference(sat_refutation,[status(thm)],[f36,f40,f41,f45,f52,f57])).
% 0.15/0.44 % SZS output end CNFRefutation for theBenchmark.p
% 0.15/0.47 % Elapsed time: 0.082342 seconds
% 0.15/0.47 % CPU time: 0.101898 seconds
% 0.15/0.47 % Total memory used: 3.187 MB
% 0.15/0.47 % Net memory used: 3.184 MB
%------------------------------------------------------------------------------