%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SEU165+1 : 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 : n026.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 0.10s 0.39s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU165+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n026.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 05:56:37 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 0.10/0.39 % Refutation found
% 0.10/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.39 % SZS output start CNFRefutation for theBenchmark
% 0.10/0.39 fof(f11,conjecture,(
% 0.10/0.39 (! [A,B,C,D] :( in(ordered_pair(A,B),cartesian_product2(C,D))<=> ( in(A,C)& in(B,D) ) ) )),
% 0.10/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.39 fof(f12,negated_conjecture,(
% 0.10/0.39 ~((! [A,B,C,D] :( in(ordered_pair(A,B),cartesian_product2(C,D))<=> ( in(A,C)& in(B,D) ) ) ))),
% 0.10/0.39 inference(negated_conjecture,[status(cth)],[f11])).
% 0.10/0.39 fof(f13,axiom,(
% 0.10/0.39 (! [A,B,C,D] :( in(ordered_pair(A,B),cartesian_product2(C,D))<=> ( in(A,C)& in(B,D) ) ) )),
% 0.10/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.39 fof(f23,plain,(
% 0.10/0.39 (?[A,B,C,D]: (in(ordered_pair(A,B),cartesian_product2(C,D))<~>(in(A,C)&in(B,D))))),
% 0.10/0.39 inference(pre_NNF_transformation,[status(thm)],[f12])).
% 0.10/0.39 fof(f24,plain,(
% 0.10/0.39 ?[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))))),
% 0.10/0.39 inference(NNF_transformation,[status(thm)],[f23])).
% 0.10/0.39 fof(f25,plain,(
% 0.10/0.39 ((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))))),
% 0.10/0.39 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)],[f24])).
% 0.10/0.39 fof(f26,plain,(
% 0.10/0.39 in(ordered_pair(sK2_skl,sK3_skl),cartesian_product2(sK4_skl,sK5_skl))|in(sK2_skl,sK4_skl)),
% 0.10/0.39 inference(cnf_transformation,[status(thm)],[f25])).
% 0.10/0.39 fof(f27,plain,(
% 0.10/0.39 in(ordered_pair(sK2_skl,sK3_skl),cartesian_product2(sK4_skl,sK5_skl))|in(sK3_skl,sK5_skl)),
% 0.10/0.39 inference(cnf_transformation,[status(thm)],[f25])).
% 0.10/0.39 fof(f28,plain,(
% 0.10/0.39 ~in(ordered_pair(sK2_skl,sK3_skl),cartesian_product2(sK4_skl,sK5_skl))|~in(sK2_skl,sK4_skl)|~in(sK3_skl,sK5_skl)),
% 0.10/0.39 inference(cnf_transformation,[status(thm)],[f25])).
% 0.10/0.39 fof(f29,plain,(
% 0.10/0.39 ![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))))),
% 0.10/0.39 inference(NNF_transformation,[status(thm)],[f13])).
% 0.10/0.39 fof(f30,plain,(
% 0.10/0.39 (![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))))),
% 0.10/0.39 inference(miniscoping,[status(thm)],[f29])).
% 0.10/0.39 fof(f31,plain,(
% 0.10/0.39 ![X0,X1,X2,X3]: (~in(ordered_pair(X0,X1),cartesian_product2(X2,X3))|in(X0,X2))),
% 0.10/0.39 inference(cnf_transformation,[status(thm)],[f30])).
% 0.10/0.39 fof(f32,plain,(
% 0.10/0.39 ![X0,X1,X2,X3]: (~in(ordered_pair(X0,X1),cartesian_product2(X2,X3))|in(X1,X3))),
% 0.10/0.39 inference(cnf_transformation,[status(thm)],[f30])).
% 0.10/0.39 fof(f33,plain,(
% 0.10/0.39 ![X0,X1,X2,X3]: (in(ordered_pair(X0,X1),cartesian_product2(X2,X3))|~in(X0,X2)|~in(X1,X3))),
% 0.10/0.39 inference(cnf_transformation,[status(thm)],[f30])).
% 0.10/0.39 fof(f34,definition,(
% 0.10/0.39 sQ0_spl <=> (in(ordered_pair(sK2_skl,sK3_skl),cartesian_product2(sK4_skl,sK5_skl)))),
% 0.10/0.39 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.10/0.39 fof(f35,plain,(
% 0.10/0.39 in(ordered_pair(sK2_skl,sK3_skl),cartesian_product2(sK4_skl,sK5_skl))|~sQ0_spl),
% 0.10/0.39 inference(component_clause,[status(thm)],[f34])).
% 0.10/0.39 fof(f37,definition,(
% 0.10/0.39 sQ1_spl <=> (in(sK2_skl,sK4_skl))),
% 0.10/0.39 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.10/0.39 fof(f38,plain,(
% 0.10/0.39 in(sK2_skl,sK4_skl)|~sQ1_spl),
% 0.10/0.39 inference(component_clause,[status(thm)],[f37])).
% 0.10/0.39 fof(f39,plain,(
% 0.10/0.39 ~in(sK2_skl,sK4_skl)|sQ1_spl),
% 0.10/0.39 inference(component_clause,[status(thm)],[f37])).
% 0.10/0.39 fof(f40,plain,(
% 0.10/0.39 sQ0_spl|sQ1_spl),
% 0.10/0.39 inference(split_clause,[status(thm)],[f26,f34,f37])).
% 0.10/0.39 fof(f41,definition,(
% 0.10/0.39 sQ2_spl <=> (in(sK3_skl,sK5_skl))),
% 0.10/0.39 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.10/0.39 fof(f42,plain,(
% 0.10/0.39 in(sK3_skl,sK5_skl)|~sQ2_spl),
% 0.10/0.39 inference(component_clause,[status(thm)],[f41])).
% 0.10/0.39 fof(f44,plain,(
% 0.10/0.39 sQ0_spl|sQ2_spl),
% 0.10/0.39 inference(split_clause,[status(thm)],[f27,f34,f41])).
% 0.10/0.39 fof(f45,plain,(
% 0.10/0.39 ~sQ0_spl|~sQ1_spl|~sQ2_spl),
% 0.10/0.39 inference(split_clause,[status(thm)],[f28,f34,f37,f41])).
% 0.10/0.39 fof(f47,plain,(
% 0.10/0.39 in(sK2_skl,sK4_skl)|~sQ0_spl),
% 0.10/0.39 inference(resolution,[status(thm)],[f31,f35])).
% 0.10/0.39 fof(f48,plain,(
% 0.10/0.39 $false|sQ1_spl|~sQ0_spl),
% 0.10/0.39 inference(forward_subsumption_resolution,[status(thm)],[f47,f39])).
% 0.10/0.39 fof(f49,plain,(
% 0.10/0.39 sQ1_spl|~sQ0_spl),
% 0.10/0.39 inference(contradiction_clause,[status(thm)],[f48])).
% 0.10/0.39 fof(f52,plain,(
% 0.10/0.39 ![X0,X1]: (in(ordered_pair(X0,sK3_skl),cartesian_product2(X1,sK5_skl))|~in(X0,X1)|~sQ2_spl)),
% 0.10/0.39 inference(resolution,[status(thm)],[f33,f42])).
% 0.10/0.39 fof(f55,plain,(
% 0.10/0.39 in(ordered_pair(sK2_skl,sK3_skl),cartesian_product2(sK4_skl,sK5_skl))|~sQ2_spl|~sQ1_spl),
% 0.10/0.39 inference(resolution,[status(thm)],[f52,f38])).
% 0.10/0.39 fof(f56,plain,(
% 0.10/0.39 sQ0_spl|~sQ2_spl|~sQ1_spl),
% 0.10/0.39 inference(split_clause,[status(thm)],[f55,f34,f41,f37])).
% 0.10/0.39 fof(f57,plain,(
% 0.10/0.39 in(sK3_skl,sK5_skl)|~sQ0_spl),
% 0.10/0.39 inference(resolution,[status(thm)],[f35,f32])).
% 0.10/0.39 fof(f61,plain,(
% 0.10/0.39 sQ2_spl|~sQ0_spl),
% 0.10/0.39 inference(split_clause,[status(thm)],[f57,f41,f34])).
% 0.10/0.39 fof(f62,plain,(
% 0.10/0.39 $false),
% 0.10/0.39 inference(sat_refutation,[status(thm)],[f40,f44,f45,f49,f56,f61])).
% 0.10/0.39 % SZS output end CNFRefutation for theBenchmark.p
% 0.15/0.42 % Elapsed time: 0.038462 seconds
% 0.15/0.42 % CPU time: 0.086595 seconds
% 0.15/0.42 % Total memory used: 9.528 MB
% 0.15/0.42 % Net memory used: 9.506 MB
%------------------------------------------------------------------------------