%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : LAT300+1 : TPTP v9.3.1. Released v3.4.0.
% 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 01:03:35 PM UTC 2026
% Result : Theorem 0.08s 5.38s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LAT300+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/5.35 % Computer : n014.cluster.edu
% 0.08/5.35 % Model : x86_64 x86_64
% 0.08/5.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.35 % Memory : 8046.5625MB
% 0.08/5.35 % OS : Linux 6.8.0-71-generic
% 0.08/5.35 % CPULimit : 300
% 0.08/5.35 % WCLimit : 300
% 0.08/5.35 % DateTime : Sun Sep 20 23:30:26 UTC 2026
% 0.08/5.36 % CPUTime :
% 0.08/5.36 % Drodi V4.1.1
% 0.08/5.38 % Refutation found
% 0.08/5.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.08/5.38 % SZS output start CNFRefutation for theBenchmark
% 0.08/5.38 fof(f1,conjecture,(
% 0.08/5.38 (! [A] :( ( ~ v3_struct_0(A)& v10_lattices(A)& l3_lattices(A) )=> (! [B] :( m2_filter_2(B,A)=> (? [C] :( m1_subset_1(C,u1_struct_0(A))& r2_hidden(C,B) ) )) )) )),
% 0.08/5.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/5.38 fof(f2,negated_conjecture,(
% 0.08/5.38 ~((! [A] :( ( ~ v3_struct_0(A)& v10_lattices(A)& l3_lattices(A) )=> (! [B] :( m2_filter_2(B,A)=> (? [C] :( m1_subset_1(C,u1_struct_0(A))& r2_hidden(C,B) ) )) )) ))),
% 0.08/5.38 inference(negated_conjecture,[status(cth)],[f1])).
% 0.08/5.38 fof(f9,axiom,(
% 0.08/5.38 (! [A] :( l1_lattices(A)=> l1_struct_0(A) ) )),
% 0.08/5.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/5.38 fof(f12,axiom,(
% 0.08/5.38 (! [A] :( l3_lattices(A)=> ( l1_lattices(A)& l2_lattices(A) ) ) )),
% 0.08/5.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/5.38 fof(f15,axiom,(
% 0.08/5.38 (! [A] :( ( ~ v3_struct_0(A)& v10_lattices(A)& l3_lattices(A) )=> (! [B] :( m2_filter_2(B,A)=> ( ~ v1_xboole_0(B)& m2_lattice4(B,A) ) ) )) )),
% 0.08/5.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/5.38 fof(f16,axiom,(
% 0.08/5.38 (! [A] :( ( ~ v3_struct_0(A)& v10_lattices(A)& l3_lattices(A) )=> (! [B] :( m2_lattice4(B,A)=> m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) )) )),
% 0.08/5.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/5.38 fof(f23,axiom,(
% 0.08/5.38 (! [A] :(? [B] : m1_subset_1(B,A) ))),
% 0.08/5.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/5.38 fof(f27,axiom,(
% 0.08/5.38 (! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)) )),
% 0.08/5.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/5.38 fof(f34,axiom,(
% 0.08/5.38 (? [A] :( l1_struct_0(A)& ~ v3_struct_0(A) ) )),
% 0.08/5.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/5.38 fof(f39,axiom,(
% 0.08/5.38 (! [A,B] :( m1_subset_1(A,B)=> ( v1_xboole_0(B)| r2_hidden(A,B) ) ) )),
% 0.08/5.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/5.38 fof(f41,axiom,(
% 0.08/5.38 (! [A,B,C] :( ( r2_hidden(A,B)& m1_subset_1(B,k1_zfmisc_1(C)) )=> m1_subset_1(A,C) ) )),
% 0.08/5.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/5.38 fof(f46,plain,(
% 0.08/5.38 (?[A]: (((~v3_struct_0(A)&v10_lattices(A))&l3_lattices(A))&(?[B]: (m2_filter_2(B,A)&(![C]: (~m1_subset_1(C,u1_struct_0(A))|~r2_hidden(C,B)))))))),
% 0.08/5.38 inference(pre_NNF_transformation,[status(thm)],[f2])).
% 0.08/5.38 fof(f47,plain,(
% 0.08/5.38 (((~v3_struct_0(sK0_skl)&v10_lattices(sK0_skl))&l3_lattices(sK0_skl))&(m2_filter_2(sK1_skl,sK0_skl)&(![C]: (~m1_subset_1(C,u1_struct_0(sK0_skl))|~r2_hidden(C,sK1_skl)))))),
% 0.08/5.38 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(A,sK0_skl),skolemize(B,sK1_skl)],[f46])).
% 0.08/5.38 fof(f48,plain,(
% 0.08/5.38 ~v3_struct_0(sK0_skl)),
% 0.08/5.38 inference(cnf_transformation,[status(thm)],[f47])).
% 0.08/5.38 fof(f49,plain,(
% 0.08/5.38 v10_lattices(sK0_skl)),
% 0.08/5.38 inference(cnf_transformation,[status(thm)],[f47])).
% 0.08/5.38 fof(f50,plain,(
% 0.08/5.38 l3_lattices(sK0_skl)),
% 0.08/5.38 inference(cnf_transformation,[status(thm)],[f47])).
% 0.08/5.38 fof(f51,plain,(
% 0.08/5.38 m2_filter_2(sK1_skl,sK0_skl)),
% 0.08/5.38 inference(cnf_transformation,[status(thm)],[f47])).
% 0.08/5.38 fof(f52,plain,(
% 0.08/5.38 ![X0]: (~m1_subset_1(X0,u1_struct_0(sK0_skl))|~r2_hidden(X0,sK1_skl))),
% 0.08/5.38 inference(cnf_transformation,[status(thm)],[f47])).
% 0.08/5.38 fof(f68,plain,(
% 0.08/5.38 ![A]: (~l1_lattices(A)|l1_struct_0(A))),
% 0.08/5.38 inference(pre_NNF_transformation,[status(thm)],[f9])).
% 0.08/5.38 fof(f69,plain,(
% 0.08/5.38 ![X0]: (~l1_lattices(X0)|l1_struct_0(X0))),
% 0.08/5.38 inference(cnf_transformation,[status(thm)],[f68])).
% 0.08/5.38 fof(f72,plain,(
% 0.08/5.38 ![A]: (~l3_lattices(A)|(l1_lattices(A)&l2_lattices(A)))),
% 0.08/5.38 inference(pre_NNF_transformation,[status(thm)],[f12])).
% 0.08/5.38 fof(f73,plain,(
% 0.08/5.38 ![X0]: (~l3_lattices(X0)|l1_lattices(X0))),
% 0.08/5.38 inference(cnf_transformation,[status(thm)],[f72])).
% 0.08/5.38 fof(f77,plain,(
% 0.08/5.38 ![A]: (((v3_struct_0(A)|~v10_lattices(A))|~l3_lattices(A))|(![B]: (~m2_filter_2(B,A)|(~v1_xboole_0(B)&m2_lattice4(B,A)))))),
% 0.08/5.38 inference(pre_NNF_transformation,[status(thm)],[f15])).
% 0.08/5.38 fof(f78,plain,(
% 0.08/5.38 ![X0,X1]: (v3_struct_0(X0)|~v10_lattices(X0)|~l3_lattices(X0)|~m2_filter_2(X1,X0)|~v1_xboole_0(X1))),
% 0.08/5.38 inference(cnf_transformation,[status(thm)],[f77])).
% 0.08/5.38 fof(f79,plain,(
% 0.08/5.38 ![X0,X1]: (v3_struct_0(X0)|~v10_lattices(X0)|~l3_lattices(X0)|~m2_filter_2(X1,X0)|m2_lattice4(X1,X0))),
% 0.08/5.38 inference(cnf_transformation,[status(thm)],[f77])).
% 0.08/5.38 fof(f80,plain,(
% 0.08/5.38 ![A]: (((v3_struct_0(A)|~v10_lattices(A))|~l3_lattices(A))|(![B]: (~m2_lattice4(B,A)|m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))))))),
% 0.08/5.38 inference(pre_NNF_transformation,[status(thm)],[f16])).
% 0.08/5.38 fof(f81,plain,(
% 0.08/5.38 ![X0,X1]: (v3_struct_0(X0)|~v10_lattices(X0)|~l3_lattices(X0)|~m2_lattice4(X1,X0)|m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0))))),
% 0.08/5.38 inference(cnf_transformation,[status(thm)],[f80])).
% 0.08/5.38 fof(f93,plain,(
% 0.08/5.38 ![A]: m1_subset_1(sK7_skl(A),A)),
% 0.08/5.38 inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl]),skolemize(B,sK7_skl(A))],[f23])).
% 0.08/5.38 fof(f94,plain,(
% 0.08/5.38 ![X0]: (m1_subset_1(sK7_skl(X0),X0))),
% 0.08/5.38 inference(cnf_transformation,[status(thm)],[f93])).
% 0.08/5.38 fof(f103,plain,(
% 0.08/5.38 ![X0]: (~v1_xboole_0(k1_zfmisc_1(X0)))),
% 0.08/5.38 inference(cnf_transformation,[status(thm)],[f27])).
% 0.08/5.38 fof(f120,plain,(
% 0.08/5.38 (l1_struct_0(sK15_skl)&~v3_struct_0(sK15_skl))),
% 0.08/5.38 inference(skolemize,[status(esa),new_symbols(skolem,[sK15_skl]),skolemize(A,sK15_skl)],[f34])).
% 0.08/5.38 fof(f122,plain,(
% 0.08/5.38 ~v3_struct_0(sK15_skl)),
% 0.08/5.38 inference(cnf_transformation,[status(thm)],[f120])).
% 0.08/5.38 fof(f136,plain,(
% 0.08/5.38 ![A,B]: (~m1_subset_1(A,B)|(v1_xboole_0(B)|r2_hidden(A,B)))),
% 0.08/5.38 inference(pre_NNF_transformation,[status(thm)],[f39])).
% 0.08/5.38 fof(f137,plain,(
% 0.08/5.38 ![X0,X1]: (~m1_subset_1(X0,X1)|v1_xboole_0(X1)|r2_hidden(X0,X1))),
% 0.08/5.38 inference(cnf_transformation,[status(thm)],[f136])).
% 0.08/5.38 fof(f142,plain,(
% 0.08/5.38 ![A,B,C]: ((~r2_hidden(A,B)|~m1_subset_1(B,k1_zfmisc_1(C)))|m1_subset_1(A,C))),
% 0.08/5.38 inference(pre_NNF_transformation,[status(thm)],[f41])).
% 0.08/5.38 fof(f143,plain,(
% 0.08/5.38 ![A,C]: ((![B]: (~r2_hidden(A,B)|~m1_subset_1(B,k1_zfmisc_1(C))))|m1_subset_1(A,C))),
% 0.08/5.38 inference(miniscoping,[status(thm)],[f142])).
% 0.08/5.38 fof(f144,plain,(
% 0.08/5.38 ![X0,X1,X2]: (~r2_hidden(X0,X1)|~m1_subset_1(X1,k1_zfmisc_1(X2))|m1_subset_1(X0,X2))),
% 0.08/5.38 inference(cnf_transformation,[status(thm)],[f143])).
% 0.08/5.38 fof(f156,plain,(
% 0.08/5.38 v3_struct_0(sK0_skl)|~v10_lattices(sK0_skl)|~l3_lattices(sK0_skl)|~v1_xboole_0(sK1_skl)),
% 0.08/5.38 inference(resolution,[status(thm)],[f78,f51])).
% 0.08/5.38 fof(f157,definition,(
% 0.08/5.38 sQ0_spl <=> (v3_struct_0(sK0_skl))),
% 0.08/5.38 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.08/5.38 fof(f158,plain,(
% 0.08/5.38 v3_struct_0(sK0_skl)|~sQ0_spl),
% 0.08/5.38 inference(component_clause,[status(thm)],[f157])).
% 0.08/5.38 fof(f160,definition,(
% 0.08/5.38 sQ1_spl <=> (v10_lattices(sK0_skl))),
% 0.08/5.38 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.08/5.38 fof(f162,plain,(
% 0.08/5.38 ~v10_lattices(sK0_skl)|sQ1_spl),
% 0.08/5.38 inference(component_clause,[status(thm)],[f160])).
% 0.08/5.38 fof(f163,definition,(
% 0.08/5.38 sQ2_spl <=> (l3_lattices(sK0_skl))),
% 0.08/5.38 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.08/5.38 fof(f165,plain,(
% 0.08/5.38 ~l3_lattices(sK0_skl)|sQ2_spl),
% 0.08/5.38 inference(component_clause,[status(thm)],[f163])).
% 0.08/5.38 fof(f166,definition,(
% 0.08/5.38 sQ3_spl <=> (v1_xboole_0(sK1_skl))),
% 0.08/5.38 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 0.08/5.38 fof(f168,plain,(
% 0.08/5.38 ~v1_xboole_0(sK1_skl)|sQ3_spl),
% 0.08/5.38 inference(component_clause,[status(thm)],[f166])).
% 0.08/5.38 fof(f169,plain,(
% 0.08/5.38 sQ0_spl|~sQ1_spl|~sQ2_spl|~sQ3_spl),
% 0.08/5.38 inference(split_clause,[status(thm)],[f156,f157,f160,f163,f166])).
% 0.08/5.38 fof(f170,plain,(
% 0.08/5.38 v3_struct_0(sK0_skl)|~v10_lattices(sK0_skl)|~l3_lattices(sK0_skl)|m2_lattice4(sK1_skl,sK0_skl)),
% 0.08/5.38 inference(resolution,[status(thm)],[f79,f51])).
% 0.08/5.38 fof(f171,definition,(
% 0.08/5.38 sQ4_spl <=> (m2_lattice4(sK1_skl,sK0_skl))),
% 0.08/5.38 introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition])).
% 0.08/5.38 fof(f172,plain,(
% 0.08/5.38 m2_lattice4(sK1_skl,sK0_skl)|~sQ4_spl),
% 0.08/5.38 inference(component_clause,[status(thm)],[f171])).
% 0.08/5.38 fof(f174,plain,(
% 0.08/5.38 sQ0_spl|~sQ1_spl|~sQ2_spl|sQ4_spl),
% 0.08/5.38 inference(split_clause,[status(thm)],[f170,f157,f160,f163,f171])).
% 0.08/5.38 fof(f175,plain,(
% 0.08/5.38 $false|sQ2_spl),
% 0.08/5.38 inference(forward_subsumption_resolution,[status(thm)],[f165,f50])).
% 0.08/5.38 fof(f176,plain,(
% 0.08/5.38 sQ2_spl),
% 0.08/5.38 inference(contradiction_clause,[status(thm)],[f175])).
% 0.08/5.38 fof(f177,plain,(
% 0.08/5.38 $false|sQ1_spl),
% 0.08/5.38 inference(forward_subsumption_resolution,[status(thm)],[f162,f49])).
% 0.08/5.38 fof(f178,plain,(
% 0.08/5.38 sQ1_spl),
% 0.08/5.38 inference(contradiction_clause,[status(thm)],[f177])).
% 0.08/5.39 fof(f179,plain,(
% 0.08/5.39 $false|~sQ0_spl),
% 0.08/5.39 inference(forward_subsumption_resolution,[status(thm)],[f158,f48])).
% 0.08/5.39 fof(f180,plain,(
% 0.08/5.39 ~sQ0_spl),
% 0.08/5.39 inference(contradiction_clause,[status(thm)],[f179])).
% 0.08/5.39 fof(f258,plain,(
% 0.08/5.39 l1_lattices(sK0_skl)),
% 0.08/5.39 inference(resolution,[status(thm)],[f73,f50])).
% 0.08/5.39 fof(f267,plain,(
% 0.08/5.39 l1_struct_0(sK0_skl)),
% 0.08/5.39 inference(resolution,[status(thm)],[f258,f69])).
% 0.08/5.39 fof(f269,plain,(
% 0.08/5.39 v3_struct_0(sK0_skl)|~v10_lattices(sK0_skl)|~l3_lattices(sK0_skl)|m1_subset_1(sK1_skl,k1_zfmisc_1(u1_struct_0(sK0_skl)))|~sQ4_spl),
% 0.08/5.39 inference(resolution,[status(thm)],[f81,f172])).
% 0.08/5.39 fof(f270,definition,(
% 0.08/5.39 sQ19_spl <=> (m1_subset_1(sK1_skl,k1_zfmisc_1(u1_struct_0(sK0_skl))))),
% 0.08/5.39 introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition])).
% 0.08/5.39 fof(f271,plain,(
% 0.08/5.39 m1_subset_1(sK1_skl,k1_zfmisc_1(u1_struct_0(sK0_skl)))|~sQ19_spl),
% 0.08/5.39 inference(component_clause,[status(thm)],[f270])).
% 0.08/5.39 fof(f273,plain,(
% 0.08/5.39 sQ0_spl|~sQ1_spl|~sQ2_spl|sQ19_spl|~sQ4_spl),
% 0.08/5.39 inference(split_clause,[status(thm)],[f269,f157,f160,f163,f270,f171])).
% 0.08/5.39 fof(f279,plain,(
% 0.08/5.39 ![X0]: (v1_xboole_0(X0)|r2_hidden(sK7_skl(X0),X0))),
% 0.08/5.39 inference(resolution,[status(thm)],[f94,f137])).
% 0.08/5.39 fof(f338,plain,(
% 0.08/5.39 ![X0]: (~r2_hidden(X0,sK1_skl)|m1_subset_1(X0,u1_struct_0(sK0_skl))|~sQ19_spl)),
% 0.08/5.39 inference(resolution,[status(thm)],[f271,f144])).
% 0.08/5.39 fof(f340,definition,(
% 0.08/5.39 sQ30_spl <=> (l1_struct_0(sK0_skl))),
% 0.08/5.39 introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition])).
% 0.08/5.39 fof(f342,plain,(
% 0.08/5.39 ~l1_struct_0(sK0_skl)|sQ30_spl),
% 0.08/5.39 inference(component_clause,[status(thm)],[f340])).
% 0.08/5.39 fof(f358,plain,(
% 0.08/5.39 ![X0]: (~r2_hidden(X0,sK1_skl)|~sQ19_spl)),
% 0.08/5.39 inference(forward_subsumption_resolution,[status(thm)],[f338,f52])).
% 0.08/5.39 fof(f359,definition,(
% 0.08/5.39 sQ35_spl <=> (v1_xboole_0(k1_zfmisc_1(u1_struct_0(sK0_skl))))),
% 0.08/5.39 introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition])).
% 0.08/5.39 fof(f360,plain,(
% 0.08/5.39 v1_xboole_0(k1_zfmisc_1(u1_struct_0(sK0_skl)))|~sQ35_spl),
% 0.08/5.39 inference(component_clause,[status(thm)],[f359])).
% 0.08/5.39 fof(f366,plain,(
% 0.08/5.39 $false|sQ30_spl),
% 0.08/5.39 inference(forward_subsumption_resolution,[status(thm)],[f342,f267])).
% 0.08/5.39 fof(f367,plain,(
% 0.08/5.39 sQ30_spl),
% 0.08/5.39 inference(contradiction_clause,[status(thm)],[f366])).
% 0.08/5.39 fof(f368,plain,(
% 0.08/5.39 $false|~sQ35_spl),
% 0.08/5.39 inference(forward_subsumption_resolution,[status(thm)],[f360,f103])).
% 0.08/5.39 fof(f369,plain,(
% 0.08/5.39 ~sQ35_spl),
% 0.08/5.39 inference(contradiction_clause,[status(thm)],[f368])).
% 0.08/5.39 fof(f388,definition,(
% 0.08/5.39 sQ37_spl <=> (v3_struct_0(sK15_skl))),
% 0.08/5.39 introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition])).
% 0.08/5.39 fof(f389,plain,(
% 0.08/5.39 v3_struct_0(sK15_skl)|~sQ37_spl),
% 0.08/5.39 inference(component_clause,[status(thm)],[f388])).
% 0.08/5.39 fof(f406,plain,(
% 0.08/5.39 $false|~sQ37_spl),
% 0.08/5.39 inference(forward_subsumption_resolution,[status(thm)],[f389,f122])).
% 0.08/5.39 fof(f407,plain,(
% 0.08/5.39 ~sQ37_spl),
% 0.08/5.39 inference(contradiction_clause,[status(thm)],[f406])).
% 0.08/5.39 fof(f408,plain,(
% 0.08/5.39 v1_xboole_0(sK1_skl)|~sQ19_spl),
% 0.08/5.39 inference(resolution,[status(thm)],[f358,f279])).
% 0.08/5.39 fof(f409,plain,(
% 0.08/5.39 $false|sQ3_spl|~sQ19_spl),
% 0.08/5.39 inference(forward_subsumption_resolution,[status(thm)],[f408,f168])).
% 0.08/5.39 fof(f410,plain,(
% 0.08/5.39 sQ3_spl|~sQ19_spl),
% 0.08/5.39 inference(contradiction_clause,[status(thm)],[f409])).
% 0.08/5.39 fof(f411,plain,(
% 0.08/5.39 $false),
% 0.08/5.39 inference(sat_refutation,[status(thm)],[f169,f174,f176,f178,f180,f273,f367,f369,f407,f410])).
% 0.08/5.39 % SZS output end CNFRefutation for theBenchmark.p
% 0.14/5.40 % Elapsed time: 0.040197 seconds
% 0.14/5.40 % CPU time: 0.130407 seconds
% 0.14/5.40 % Total memory used: 51.730 MB
% 0.14/5.40 % Net memory used: 51.701 MB
%------------------------------------------------------------------------------