TSTP Solution File: LAT319+1 by Drodi---3.6.0

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%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : LAT319+1 : TPTP v8.1.2. Released v3.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n009.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue Apr 30 20:25:47 EDT 2024

% Result   : Theorem 0.09s 0.34s
% Output   : CNFRefutation 0.09s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   28
% Syntax   : Number of formulae    :  142 (  10 unt;   0 def)
%            Number of atoms       :  701 (   5 equ)
%            Maximal formula atoms :   23 (   4 avg)
%            Number of connectives :  882 ( 323   ~; 351   |; 169   &)
%                                         (  24 <=>;  13  =>;   0  <=;   2 <~>)
%            Maximal formula depth :   15 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   37 (  35 usr;  18 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   2 con; 0-3 aty)
%            Number of variables   :   50 (  46   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,conjecture,
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ( ( ~ v3_struct_0(A)
          & v10_lattices(A)
          & v17_lattices(A)
          & l3_lattices(A) )
      <=> ( ~ v3_struct_0(k1_lattice2(A))
          & v10_lattices(k1_lattice2(A))
          & v17_lattices(k1_lattice2(A))
          & l3_lattices(k1_lattice2(A)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f2,negated_conjecture,
    ~ ! [A] :
        ( ( ~ v3_struct_0(A)
          & v10_lattices(A)
          & l3_lattices(A) )
       => ( ( ~ v3_struct_0(A)
            & v10_lattices(A)
            & v17_lattices(A)
            & l3_lattices(A) )
        <=> ( ~ v3_struct_0(k1_lattice2(A))
            & v10_lattices(k1_lattice2(A))
            & v17_lattices(k1_lattice2(A))
            & l3_lattices(k1_lattice2(A)) ) ) ),
    inference(negated_conjecture,[status(cth)],[f1]) ).

fof(f3,axiom,
    ! [A] :
      ( l3_lattices(A)
     => ( v3_lattices(A)
       => A = g3_lattices(u1_struct_0(A),u2_lattices(A),u1_lattices(A)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f12,axiom,
    ! [A] :
      ( l3_lattices(A)
     => ( ( ~ v3_struct_0(A)
          & v17_lattices(A) )
       => ( ~ v3_struct_0(A)
          & v11_lattices(A)
          & v13_lattices(A)
          & v14_lattices(A)
          & v15_lattices(A)
          & v16_lattices(A) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f13,axiom,
    ! [A] :
      ( l3_lattices(A)
     => ( ( ~ v3_struct_0(A)
          & v11_lattices(A)
          & v15_lattices(A)
          & v16_lattices(A) )
       => ( ~ v3_struct_0(A)
          & v17_lattices(A) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f18,axiom,
    ! [A] :
      ( l3_lattices(A)
     => ( v3_lattices(k1_lattice2(A))
        & l3_lattices(k1_lattice2(A)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f39,axiom,
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l3_lattices(A) )
     => ( ~ v3_struct_0(k1_lattice2(A))
        & v3_lattices(k1_lattice2(A)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f49,axiom,
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ( ~ v3_struct_0(k1_lattice2(A))
        & v3_lattices(k1_lattice2(A))
        & v4_lattices(k1_lattice2(A))
        & v5_lattices(k1_lattice2(A))
        & v6_lattices(k1_lattice2(A))
        & v7_lattices(k1_lattice2(A))
        & v8_lattices(k1_lattice2(A))
        & v9_lattices(k1_lattice2(A))
        & v10_lattices(k1_lattice2(A)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f51,axiom,
    ? [A] :
      ( l3_lattices(A)
      & ~ v3_struct_0(A)
      & v3_lattices(A)
      & v4_lattices(A)
      & v5_lattices(A)
      & v6_lattices(A)
      & v7_lattices(A)
      & v8_lattices(A)
      & v9_lattices(A)
      & v10_lattices(A)
      & v11_lattices(A)
      & v12_lattices(A)
      & v13_lattices(A)
      & v14_lattices(A) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f73,axiom,
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ( ( ~ v3_struct_0(A)
          & v10_lattices(A)
          & v15_lattices(A)
          & v16_lattices(A)
          & l3_lattices(A) )
      <=> ( ~ v3_struct_0(k1_lattice2(A))
          & v10_lattices(k1_lattice2(A))
          & v15_lattices(k1_lattice2(A))
          & v16_lattices(k1_lattice2(A))
          & l3_lattices(k1_lattice2(A)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f75,axiom,
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ( ( ~ v3_struct_0(A)
          & v10_lattices(A)
          & v11_lattices(A)
          & l3_lattices(A) )
      <=> ( ~ v3_struct_0(k1_lattice2(A))
          & v10_lattices(k1_lattice2(A))
          & v11_lattices(k1_lattice2(A))
          & l3_lattices(k1_lattice2(A)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f79,plain,
    ? [A] :
      ( ~ v3_struct_0(A)
      & v10_lattices(A)
      & l3_lattices(A)
      & ( ( ~ v3_struct_0(A)
          & v10_lattices(A)
          & v17_lattices(A)
          & l3_lattices(A) )
      <~> ( ~ v3_struct_0(k1_lattice2(A))
          & v10_lattices(k1_lattice2(A))
          & v17_lattices(k1_lattice2(A))
          & l3_lattices(k1_lattice2(A)) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f2]) ).

fof(f80,plain,
    ! [A] :
      ( pd0_0(A)
    <=> ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_lattices(A)
        & l3_lattices(A) ) ),
    introduced(predicate_definition,[f79]) ).

fof(f81,plain,
    ? [A] :
      ( ~ v3_struct_0(A)
      & v10_lattices(A)
      & l3_lattices(A)
      & ( pd0_0(A)
      <~> ( ~ v3_struct_0(k1_lattice2(A))
          & v10_lattices(k1_lattice2(A))
          & v17_lattices(k1_lattice2(A))
          & l3_lattices(k1_lattice2(A)) ) ) ),
    inference(formula_renaming,[status(thm)],[f79,f80]) ).

fof(f82,plain,
    ? [A] :
      ( ~ v3_struct_0(A)
      & v10_lattices(A)
      & l3_lattices(A)
      & ( pd0_0(A)
        | ( ~ v3_struct_0(k1_lattice2(A))
          & v10_lattices(k1_lattice2(A))
          & v17_lattices(k1_lattice2(A))
          & l3_lattices(k1_lattice2(A)) ) )
      & ( ~ pd0_0(A)
        | v3_struct_0(k1_lattice2(A))
        | ~ v10_lattices(k1_lattice2(A))
        | ~ v17_lattices(k1_lattice2(A))
        | ~ l3_lattices(k1_lattice2(A)) ) ),
    inference(NNF_transformation,[status(esa)],[f81]) ).

fof(f83,plain,
    ( ~ v3_struct_0(sk0_0)
    & v10_lattices(sk0_0)
    & l3_lattices(sk0_0)
    & ( pd0_0(sk0_0)
      | ( ~ v3_struct_0(k1_lattice2(sk0_0))
        & v10_lattices(k1_lattice2(sk0_0))
        & v17_lattices(k1_lattice2(sk0_0))
        & l3_lattices(k1_lattice2(sk0_0)) ) )
    & ( ~ pd0_0(sk0_0)
      | v3_struct_0(k1_lattice2(sk0_0))
      | ~ v10_lattices(k1_lattice2(sk0_0))
      | ~ v17_lattices(k1_lattice2(sk0_0))
      | ~ l3_lattices(k1_lattice2(sk0_0)) ) ),
    inference(skolemization,[status(esa)],[f82]) ).

fof(f84,plain,
    ~ v3_struct_0(sk0_0),
    inference(cnf_transformation,[status(esa)],[f83]) ).

fof(f85,plain,
    v10_lattices(sk0_0),
    inference(cnf_transformation,[status(esa)],[f83]) ).

fof(f86,plain,
    l3_lattices(sk0_0),
    inference(cnf_transformation,[status(esa)],[f83]) ).

fof(f89,plain,
    ( pd0_0(sk0_0)
    | v17_lattices(k1_lattice2(sk0_0)) ),
    inference(cnf_transformation,[status(esa)],[f83]) ).

fof(f91,plain,
    ( ~ pd0_0(sk0_0)
    | v3_struct_0(k1_lattice2(sk0_0))
    | ~ v10_lattices(k1_lattice2(sk0_0))
    | ~ v17_lattices(k1_lattice2(sk0_0))
    | ~ l3_lattices(k1_lattice2(sk0_0)) ),
    inference(cnf_transformation,[status(esa)],[f83]) ).

fof(f92,plain,
    ! [A] :
      ( ~ l3_lattices(A)
      | ~ v3_lattices(A)
      | A = g3_lattices(u1_struct_0(A),u2_lattices(A),u1_lattices(A)) ),
    inference(pre_NNF_transformation,[status(esa)],[f3]) ).

fof(f93,plain,
    ! [X0] :
      ( ~ l3_lattices(X0)
      | ~ v3_lattices(X0)
      | X0 = g3_lattices(u1_struct_0(X0),u2_lattices(X0),u1_lattices(X0)) ),
    inference(cnf_transformation,[status(esa)],[f92]) ).

fof(f123,plain,
    ! [A] :
      ( ~ l3_lattices(A)
      | v3_struct_0(A)
      | ~ v17_lattices(A)
      | ( ~ v3_struct_0(A)
        & v11_lattices(A)
        & v13_lattices(A)
        & v14_lattices(A)
        & v15_lattices(A)
        & v16_lattices(A) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f12]) ).

fof(f125,plain,
    ! [X0] :
      ( ~ l3_lattices(X0)
      | v3_struct_0(X0)
      | ~ v17_lattices(X0)
      | v11_lattices(X0) ),
    inference(cnf_transformation,[status(esa)],[f123]) ).

fof(f128,plain,
    ! [X0] :
      ( ~ l3_lattices(X0)
      | v3_struct_0(X0)
      | ~ v17_lattices(X0)
      | v15_lattices(X0) ),
    inference(cnf_transformation,[status(esa)],[f123]) ).

fof(f129,plain,
    ! [X0] :
      ( ~ l3_lattices(X0)
      | v3_struct_0(X0)
      | ~ v17_lattices(X0)
      | v16_lattices(X0) ),
    inference(cnf_transformation,[status(esa)],[f123]) ).

fof(f130,plain,
    ! [A] :
      ( ~ l3_lattices(A)
      | v3_struct_0(A)
      | ~ v11_lattices(A)
      | ~ v15_lattices(A)
      | ~ v16_lattices(A)
      | ( ~ v3_struct_0(A)
        & v17_lattices(A) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f13]) ).

fof(f132,plain,
    ! [X0] :
      ( ~ l3_lattices(X0)
      | v3_struct_0(X0)
      | ~ v11_lattices(X0)
      | ~ v15_lattices(X0)
      | ~ v16_lattices(X0)
      | v17_lattices(X0) ),
    inference(cnf_transformation,[status(esa)],[f130]) ).

fof(f154,plain,
    ! [A] :
      ( ~ l3_lattices(A)
      | ( v3_lattices(k1_lattice2(A))
        & l3_lattices(k1_lattice2(A)) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f18]) ).

fof(f156,plain,
    ! [X0] :
      ( ~ l3_lattices(X0)
      | l3_lattices(k1_lattice2(X0)) ),
    inference(cnf_transformation,[status(esa)],[f154]) ).

fof(f188,plain,
    ! [A] :
      ( v3_struct_0(A)
      | ~ l3_lattices(A)
      | ( ~ v3_struct_0(k1_lattice2(A))
        & v3_lattices(k1_lattice2(A)) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f39]) ).

fof(f189,plain,
    ! [X0] :
      ( v3_struct_0(X0)
      | ~ l3_lattices(X0)
      | ~ v3_struct_0(k1_lattice2(X0)) ),
    inference(cnf_transformation,[status(esa)],[f188]) ).

fof(f224,plain,
    ! [A] :
      ( v3_struct_0(A)
      | ~ v10_lattices(A)
      | ~ l3_lattices(A)
      | ( ~ v3_struct_0(k1_lattice2(A))
        & v3_lattices(k1_lattice2(A))
        & v4_lattices(k1_lattice2(A))
        & v5_lattices(k1_lattice2(A))
        & v6_lattices(k1_lattice2(A))
        & v7_lattices(k1_lattice2(A))
        & v8_lattices(k1_lattice2(A))
        & v9_lattices(k1_lattice2(A))
        & v10_lattices(k1_lattice2(A)) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f49]) ).

fof(f233,plain,
    ! [X0] :
      ( v3_struct_0(X0)
      | ~ v10_lattices(X0)
      | ~ l3_lattices(X0)
      | v10_lattices(k1_lattice2(X0)) ),
    inference(cnf_transformation,[status(esa)],[f224]) ).

fof(f238,plain,
    ( l3_lattices(sk0_8)
    & ~ v3_struct_0(sk0_8)
    & v3_lattices(sk0_8)
    & v4_lattices(sk0_8)
    & v5_lattices(sk0_8)
    & v6_lattices(sk0_8)
    & v7_lattices(sk0_8)
    & v8_lattices(sk0_8)
    & v9_lattices(sk0_8)
    & v10_lattices(sk0_8)
    & v11_lattices(sk0_8)
    & v12_lattices(sk0_8)
    & v13_lattices(sk0_8)
    & v14_lattices(sk0_8) ),
    inference(skolemization,[status(esa)],[f51]) ).

fof(f239,plain,
    l3_lattices(sk0_8),
    inference(cnf_transformation,[status(esa)],[f238]) ).

fof(f241,plain,
    v3_lattices(sk0_8),
    inference(cnf_transformation,[status(esa)],[f238]) ).

fof(f363,plain,
    ! [A] :
      ( v3_struct_0(A)
      | ~ v10_lattices(A)
      | ~ l3_lattices(A)
      | ( ( ~ v3_struct_0(A)
          & v10_lattices(A)
          & v15_lattices(A)
          & v16_lattices(A)
          & l3_lattices(A) )
      <=> ( ~ v3_struct_0(k1_lattice2(A))
          & v10_lattices(k1_lattice2(A))
          & v15_lattices(k1_lattice2(A))
          & v16_lattices(k1_lattice2(A))
          & l3_lattices(k1_lattice2(A)) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f73]) ).

fof(f364,plain,
    ! [A] :
      ( v3_struct_0(A)
      | ~ v10_lattices(A)
      | ~ l3_lattices(A)
      | ( ( v3_struct_0(A)
          | ~ v10_lattices(A)
          | ~ v15_lattices(A)
          | ~ v16_lattices(A)
          | ~ l3_lattices(A)
          | ( ~ v3_struct_0(k1_lattice2(A))
            & v10_lattices(k1_lattice2(A))
            & v15_lattices(k1_lattice2(A))
            & v16_lattices(k1_lattice2(A))
            & l3_lattices(k1_lattice2(A)) ) )
        & ( ( ~ v3_struct_0(A)
            & v10_lattices(A)
            & v15_lattices(A)
            & v16_lattices(A)
            & l3_lattices(A) )
          | v3_struct_0(k1_lattice2(A))
          | ~ v10_lattices(k1_lattice2(A))
          | ~ v15_lattices(k1_lattice2(A))
          | ~ v16_lattices(k1_lattice2(A))
          | ~ l3_lattices(k1_lattice2(A)) ) ) ),
    inference(NNF_transformation,[status(esa)],[f363]) ).

fof(f367,plain,
    ! [X0] :
      ( v3_struct_0(X0)
      | ~ v10_lattices(X0)
      | ~ l3_lattices(X0)
      | v3_struct_0(X0)
      | ~ v10_lattices(X0)
      | ~ v15_lattices(X0)
      | ~ v16_lattices(X0)
      | ~ l3_lattices(X0)
      | v15_lattices(k1_lattice2(X0)) ),
    inference(cnf_transformation,[status(esa)],[f364]) ).

fof(f368,plain,
    ! [X0] :
      ( v3_struct_0(X0)
      | ~ v10_lattices(X0)
      | ~ l3_lattices(X0)
      | v3_struct_0(X0)
      | ~ v10_lattices(X0)
      | ~ v15_lattices(X0)
      | ~ v16_lattices(X0)
      | ~ l3_lattices(X0)
      | v16_lattices(k1_lattice2(X0)) ),
    inference(cnf_transformation,[status(esa)],[f364]) ).

fof(f372,plain,
    ! [X0] :
      ( v3_struct_0(X0)
      | ~ v10_lattices(X0)
      | ~ l3_lattices(X0)
      | v15_lattices(X0)
      | v3_struct_0(k1_lattice2(X0))
      | ~ v10_lattices(k1_lattice2(X0))
      | ~ v15_lattices(k1_lattice2(X0))
      | ~ v16_lattices(k1_lattice2(X0))
      | ~ l3_lattices(k1_lattice2(X0)) ),
    inference(cnf_transformation,[status(esa)],[f364]) ).

fof(f373,plain,
    ! [X0] :
      ( v3_struct_0(X0)
      | ~ v10_lattices(X0)
      | ~ l3_lattices(X0)
      | v16_lattices(X0)
      | v3_struct_0(k1_lattice2(X0))
      | ~ v10_lattices(k1_lattice2(X0))
      | ~ v15_lattices(k1_lattice2(X0))
      | ~ v16_lattices(k1_lattice2(X0))
      | ~ l3_lattices(k1_lattice2(X0)) ),
    inference(cnf_transformation,[status(esa)],[f364]) ).

fof(f378,plain,
    ! [A] :
      ( v3_struct_0(A)
      | ~ v10_lattices(A)
      | ~ l3_lattices(A)
      | ( ( ~ v3_struct_0(A)
          & v10_lattices(A)
          & v11_lattices(A)
          & l3_lattices(A) )
      <=> ( ~ v3_struct_0(k1_lattice2(A))
          & v10_lattices(k1_lattice2(A))
          & v11_lattices(k1_lattice2(A))
          & l3_lattices(k1_lattice2(A)) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f75]) ).

fof(f379,plain,
    ! [A] :
      ( v3_struct_0(A)
      | ~ v10_lattices(A)
      | ~ l3_lattices(A)
      | ( ( v3_struct_0(A)
          | ~ v10_lattices(A)
          | ~ v11_lattices(A)
          | ~ l3_lattices(A)
          | ( ~ v3_struct_0(k1_lattice2(A))
            & v10_lattices(k1_lattice2(A))
            & v11_lattices(k1_lattice2(A))
            & l3_lattices(k1_lattice2(A)) ) )
        & ( ( ~ v3_struct_0(A)
            & v10_lattices(A)
            & v11_lattices(A)
            & l3_lattices(A) )
          | v3_struct_0(k1_lattice2(A))
          | ~ v10_lattices(k1_lattice2(A))
          | ~ v11_lattices(k1_lattice2(A))
          | ~ l3_lattices(k1_lattice2(A)) ) ) ),
    inference(NNF_transformation,[status(esa)],[f378]) ).

fof(f382,plain,
    ! [X0] :
      ( v3_struct_0(X0)
      | ~ v10_lattices(X0)
      | ~ l3_lattices(X0)
      | v3_struct_0(X0)
      | ~ v10_lattices(X0)
      | ~ v11_lattices(X0)
      | ~ l3_lattices(X0)
      | v11_lattices(k1_lattice2(X0)) ),
    inference(cnf_transformation,[status(esa)],[f379]) ).

fof(f386,plain,
    ! [X0] :
      ( v3_struct_0(X0)
      | ~ v10_lattices(X0)
      | ~ l3_lattices(X0)
      | v11_lattices(X0)
      | v3_struct_0(k1_lattice2(X0))
      | ~ v10_lattices(k1_lattice2(X0))
      | ~ v11_lattices(k1_lattice2(X0))
      | ~ l3_lattices(k1_lattice2(X0)) ),
    inference(cnf_transformation,[status(esa)],[f379]) ).

fof(f396,plain,
    ! [A] :
      ( ( ~ pd0_0(A)
        | ( ~ v3_struct_0(A)
          & v10_lattices(A)
          & v17_lattices(A)
          & l3_lattices(A) ) )
      & ( pd0_0(A)
        | v3_struct_0(A)
        | ~ v10_lattices(A)
        | ~ v17_lattices(A)
        | ~ l3_lattices(A) ) ),
    inference(NNF_transformation,[status(esa)],[f80]) ).

fof(f397,plain,
    ( ! [A] :
        ( ~ pd0_0(A)
        | ( ~ v3_struct_0(A)
          & v10_lattices(A)
          & v17_lattices(A)
          & l3_lattices(A) ) )
    & ! [A] :
        ( pd0_0(A)
        | v3_struct_0(A)
        | ~ v10_lattices(A)
        | ~ v17_lattices(A)
        | ~ l3_lattices(A) ) ),
    inference(miniscoping,[status(esa)],[f396]) ).

fof(f400,plain,
    ! [X0] :
      ( ~ pd0_0(X0)
      | v17_lattices(X0) ),
    inference(cnf_transformation,[status(esa)],[f397]) ).

fof(f402,plain,
    ! [X0] :
      ( pd0_0(X0)
      | v3_struct_0(X0)
      | ~ v10_lattices(X0)
      | ~ v17_lattices(X0)
      | ~ l3_lattices(X0) ),
    inference(cnf_transformation,[status(esa)],[f397]) ).

fof(f403,plain,
    ( spl0_0
  <=> pd0_0(sk0_0) ),
    introduced(split_symbol_definition) ).

fof(f405,plain,
    ( ~ pd0_0(sk0_0)
    | spl0_0 ),
    inference(component_clause,[status(thm)],[f403]) ).

fof(f406,plain,
    ( spl0_1
  <=> v3_struct_0(k1_lattice2(sk0_0)) ),
    introduced(split_symbol_definition) ).

fof(f407,plain,
    ( v3_struct_0(k1_lattice2(sk0_0))
    | ~ spl0_1 ),
    inference(component_clause,[status(thm)],[f406]) ).

fof(f410,plain,
    ( spl0_2
  <=> v10_lattices(k1_lattice2(sk0_0)) ),
    introduced(split_symbol_definition) ).

fof(f412,plain,
    ( ~ v10_lattices(k1_lattice2(sk0_0))
    | spl0_2 ),
    inference(component_clause,[status(thm)],[f410]) ).

fof(f414,plain,
    ( spl0_3
  <=> v17_lattices(k1_lattice2(sk0_0)) ),
    introduced(split_symbol_definition) ).

fof(f416,plain,
    ( ~ v17_lattices(k1_lattice2(sk0_0))
    | spl0_3 ),
    inference(component_clause,[status(thm)],[f414]) ).

fof(f417,plain,
    ( spl0_0
    | spl0_3 ),
    inference(split_clause,[status(thm)],[f89,f403,f414]) ).

fof(f418,plain,
    ( spl0_4
  <=> l3_lattices(k1_lattice2(sk0_0)) ),
    introduced(split_symbol_definition) ).

fof(f420,plain,
    ( ~ l3_lattices(k1_lattice2(sk0_0))
    | spl0_4 ),
    inference(component_clause,[status(thm)],[f418]) ).

fof(f422,plain,
    ( ~ spl0_0
    | spl0_1
    | ~ spl0_2
    | ~ spl0_3
    | ~ spl0_4 ),
    inference(split_clause,[status(thm)],[f91,f403,f406,f410,f414,f418]) ).

fof(f426,plain,
    ! [X0] :
      ( v3_struct_0(X0)
      | ~ v10_lattices(X0)
      | ~ l3_lattices(X0)
      | ~ v15_lattices(X0)
      | ~ v16_lattices(X0)
      | v15_lattices(k1_lattice2(X0)) ),
    inference(duplicate_literals_removal,[status(esa)],[f367]) ).

fof(f427,plain,
    ! [X0] :
      ( v3_struct_0(X0)
      | ~ v10_lattices(X0)
      | ~ l3_lattices(X0)
      | ~ v15_lattices(X0)
      | ~ v16_lattices(X0)
      | v16_lattices(k1_lattice2(X0)) ),
    inference(duplicate_literals_removal,[status(esa)],[f368]) ).

fof(f429,plain,
    ! [X0] :
      ( v3_struct_0(X0)
      | ~ v10_lattices(X0)
      | ~ l3_lattices(X0)
      | v15_lattices(X0)
      | ~ v10_lattices(k1_lattice2(X0))
      | ~ v15_lattices(k1_lattice2(X0))
      | ~ v16_lattices(k1_lattice2(X0))
      | ~ l3_lattices(k1_lattice2(X0)) ),
    inference(forward_subsumption_resolution,[status(thm)],[f372,f189]) ).

fof(f430,plain,
    ! [X0] :
      ( v3_struct_0(X0)
      | ~ v10_lattices(X0)
      | ~ l3_lattices(X0)
      | v16_lattices(X0)
      | ~ v10_lattices(k1_lattice2(X0))
      | ~ v15_lattices(k1_lattice2(X0))
      | ~ v16_lattices(k1_lattice2(X0))
      | ~ l3_lattices(k1_lattice2(X0)) ),
    inference(forward_subsumption_resolution,[status(thm)],[f373,f189]) ).

fof(f433,plain,
    ! [X0] :
      ( v3_struct_0(X0)
      | ~ v10_lattices(X0)
      | ~ l3_lattices(X0)
      | ~ v11_lattices(X0)
      | v11_lattices(k1_lattice2(X0)) ),
    inference(duplicate_literals_removal,[status(esa)],[f382]) ).

fof(f435,plain,
    ! [X0] :
      ( v3_struct_0(X0)
      | ~ v10_lattices(X0)
      | ~ l3_lattices(X0)
      | v11_lattices(X0)
      | ~ v10_lattices(k1_lattice2(X0))
      | ~ v11_lattices(k1_lattice2(X0))
      | ~ l3_lattices(k1_lattice2(X0)) ),
    inference(forward_subsumption_resolution,[status(thm)],[f386,f189]) ).

fof(f437,plain,
    ( spl0_5
  <=> v3_struct_0(sk0_0) ),
    introduced(split_symbol_definition) ).

fof(f438,plain,
    ( v3_struct_0(sk0_0)
    | ~ spl0_5 ),
    inference(component_clause,[status(thm)],[f437]) ).

fof(f440,plain,
    ( spl0_6
  <=> l3_lattices(sk0_0) ),
    introduced(split_symbol_definition) ).

fof(f442,plain,
    ( ~ l3_lattices(sk0_0)
    | spl0_6 ),
    inference(component_clause,[status(thm)],[f440]) ).

fof(f443,plain,
    ( v3_struct_0(sk0_0)
    | ~ l3_lattices(sk0_0)
    | ~ spl0_1 ),
    inference(resolution,[status(thm)],[f189,f407]) ).

fof(f444,plain,
    ( spl0_5
    | ~ spl0_6
    | ~ spl0_1 ),
    inference(split_clause,[status(thm)],[f443,f437,f440,f406]) ).

fof(f445,plain,
    ( $false
    | spl0_6 ),
    inference(forward_subsumption_resolution,[status(thm)],[f442,f86]) ).

fof(f446,plain,
    spl0_6,
    inference(contradiction_clause,[status(thm)],[f445]) ).

fof(f447,plain,
    ( $false
    | ~ spl0_5 ),
    inference(forward_subsumption_resolution,[status(thm)],[f438,f84]) ).

fof(f448,plain,
    ~ spl0_5,
    inference(contradiction_clause,[status(thm)],[f447]) ).

fof(f450,plain,
    ( spl0_7
  <=> l3_lattices(sk0_8) ),
    introduced(split_symbol_definition) ).

fof(f452,plain,
    ( ~ l3_lattices(sk0_8)
    | spl0_7 ),
    inference(component_clause,[status(thm)],[f450]) ).

fof(f453,plain,
    ( spl0_8
  <=> sk0_8 = g3_lattices(u1_struct_0(sk0_8),u2_lattices(sk0_8),u1_lattices(sk0_8)) ),
    introduced(split_symbol_definition) ).

fof(f456,plain,
    ( ~ l3_lattices(sk0_8)
    | sk0_8 = g3_lattices(u1_struct_0(sk0_8),u2_lattices(sk0_8),u1_lattices(sk0_8)) ),
    inference(resolution,[status(thm)],[f93,f241]) ).

fof(f457,plain,
    ( ~ spl0_7
    | spl0_8 ),
    inference(split_clause,[status(thm)],[f456,f450,f453]) ).

fof(f458,plain,
    ( $false
    | spl0_7 ),
    inference(forward_subsumption_resolution,[status(thm)],[f452,f239]) ).

fof(f459,plain,
    spl0_7,
    inference(contradiction_clause,[status(thm)],[f458]) ).

fof(f462,plain,
    ( spl0_9
  <=> v10_lattices(sk0_0) ),
    introduced(split_symbol_definition) ).

fof(f464,plain,
    ( ~ v10_lattices(sk0_0)
    | spl0_9 ),
    inference(component_clause,[status(thm)],[f462]) ).

fof(f465,plain,
    ( v3_struct_0(sk0_0)
    | ~ v10_lattices(sk0_0)
    | ~ l3_lattices(sk0_0)
    | spl0_2 ),
    inference(resolution,[status(thm)],[f233,f412]) ).

fof(f466,plain,
    ( spl0_5
    | ~ spl0_9
    | ~ spl0_6
    | spl0_2 ),
    inference(split_clause,[status(thm)],[f465,f437,f462,f440,f410]) ).

fof(f467,plain,
    ( $false
    | spl0_9 ),
    inference(forward_subsumption_resolution,[status(thm)],[f464,f85]) ).

fof(f468,plain,
    spl0_9,
    inference(contradiction_clause,[status(thm)],[f467]) ).

fof(f469,plain,
    ( spl0_10
  <=> v11_lattices(k1_lattice2(sk0_0)) ),
    introduced(split_symbol_definition) ).

fof(f471,plain,
    ( ~ v11_lattices(k1_lattice2(sk0_0))
    | spl0_10 ),
    inference(component_clause,[status(thm)],[f469]) ).

fof(f472,plain,
    ( spl0_11
  <=> v15_lattices(k1_lattice2(sk0_0)) ),
    introduced(split_symbol_definition) ).

fof(f474,plain,
    ( ~ v15_lattices(k1_lattice2(sk0_0))
    | spl0_11 ),
    inference(component_clause,[status(thm)],[f472]) ).

fof(f475,plain,
    ( spl0_12
  <=> v16_lattices(k1_lattice2(sk0_0)) ),
    introduced(split_symbol_definition) ).

fof(f477,plain,
    ( ~ v16_lattices(k1_lattice2(sk0_0))
    | spl0_12 ),
    inference(component_clause,[status(thm)],[f475]) ).

fof(f478,plain,
    ( ~ l3_lattices(k1_lattice2(sk0_0))
    | v3_struct_0(k1_lattice2(sk0_0))
    | ~ v11_lattices(k1_lattice2(sk0_0))
    | ~ v15_lattices(k1_lattice2(sk0_0))
    | ~ v16_lattices(k1_lattice2(sk0_0))
    | spl0_3 ),
    inference(resolution,[status(thm)],[f416,f132]) ).

fof(f479,plain,
    ( ~ spl0_4
    | spl0_1
    | ~ spl0_10
    | ~ spl0_11
    | ~ spl0_12
    | spl0_3 ),
    inference(split_clause,[status(thm)],[f478,f418,f406,f469,f472,f475,f414]) ).

fof(f481,plain,
    ( ~ l3_lattices(sk0_0)
    | spl0_4 ),
    inference(resolution,[status(thm)],[f420,f156]) ).

fof(f482,plain,
    ( ~ spl0_6
    | spl0_4 ),
    inference(split_clause,[status(thm)],[f481,f440,f418]) ).

fof(f484,plain,
    ( spl0_13
  <=> v17_lattices(sk0_0) ),
    introduced(split_symbol_definition) ).

fof(f486,plain,
    ( ~ v17_lattices(sk0_0)
    | spl0_13 ),
    inference(component_clause,[status(thm)],[f484]) ).

fof(f487,plain,
    ( v3_struct_0(sk0_0)
    | ~ v10_lattices(sk0_0)
    | ~ v17_lattices(sk0_0)
    | ~ l3_lattices(sk0_0)
    | spl0_0 ),
    inference(resolution,[status(thm)],[f405,f402]) ).

fof(f488,plain,
    ( spl0_5
    | ~ spl0_9
    | ~ spl0_13
    | ~ spl0_6
    | spl0_0 ),
    inference(split_clause,[status(thm)],[f487,f437,f462,f484,f440,f403]) ).

fof(f489,plain,
    ( spl0_14
  <=> v11_lattices(sk0_0) ),
    introduced(split_symbol_definition) ).

fof(f491,plain,
    ( ~ v11_lattices(sk0_0)
    | spl0_14 ),
    inference(component_clause,[status(thm)],[f489]) ).

fof(f492,plain,
    ( spl0_15
  <=> v15_lattices(sk0_0) ),
    introduced(split_symbol_definition) ).

fof(f494,plain,
    ( ~ v15_lattices(sk0_0)
    | spl0_15 ),
    inference(component_clause,[status(thm)],[f492]) ).

fof(f495,plain,
    ( spl0_16
  <=> v16_lattices(sk0_0) ),
    introduced(split_symbol_definition) ).

fof(f497,plain,
    ( ~ v16_lattices(sk0_0)
    | spl0_16 ),
    inference(component_clause,[status(thm)],[f495]) ).

fof(f498,plain,
    ( ~ l3_lattices(sk0_0)
    | v3_struct_0(sk0_0)
    | ~ v11_lattices(sk0_0)
    | ~ v15_lattices(sk0_0)
    | ~ v16_lattices(sk0_0)
    | spl0_13 ),
    inference(resolution,[status(thm)],[f486,f132]) ).

fof(f499,plain,
    ( ~ spl0_6
    | spl0_5
    | ~ spl0_14
    | ~ spl0_15
    | ~ spl0_16
    | spl0_13 ),
    inference(split_clause,[status(thm)],[f498,f440,f437,f489,f492,f495,f484]) ).

fof(f500,plain,
    ( v3_struct_0(sk0_0)
    | ~ v10_lattices(sk0_0)
    | ~ l3_lattices(sk0_0)
    | ~ v10_lattices(k1_lattice2(sk0_0))
    | ~ v15_lattices(k1_lattice2(sk0_0))
    | ~ v16_lattices(k1_lattice2(sk0_0))
    | ~ l3_lattices(k1_lattice2(sk0_0))
    | spl0_16 ),
    inference(resolution,[status(thm)],[f497,f430]) ).

fof(f501,plain,
    ( spl0_5
    | ~ spl0_9
    | ~ spl0_6
    | ~ spl0_2
    | ~ spl0_11
    | ~ spl0_12
    | ~ spl0_4
    | spl0_16 ),
    inference(split_clause,[status(thm)],[f500,f437,f462,f440,f410,f472,f475,f418,f495]) ).

fof(f502,plain,
    ( ~ l3_lattices(sk0_0)
    | v3_struct_0(sk0_0)
    | ~ v17_lattices(sk0_0)
    | spl0_16 ),
    inference(resolution,[status(thm)],[f497,f129]) ).

fof(f503,plain,
    ( ~ spl0_6
    | spl0_5
    | ~ spl0_13
    | spl0_16 ),
    inference(split_clause,[status(thm)],[f502,f440,f437,f484,f495]) ).

fof(f512,plain,
    ( v3_struct_0(sk0_0)
    | ~ v10_lattices(sk0_0)
    | ~ l3_lattices(sk0_0)
    | ~ v10_lattices(k1_lattice2(sk0_0))
    | ~ v15_lattices(k1_lattice2(sk0_0))
    | ~ v16_lattices(k1_lattice2(sk0_0))
    | ~ l3_lattices(k1_lattice2(sk0_0))
    | spl0_15 ),
    inference(resolution,[status(thm)],[f494,f429]) ).

fof(f513,plain,
    ( spl0_5
    | ~ spl0_9
    | ~ spl0_6
    | ~ spl0_2
    | ~ spl0_11
    | ~ spl0_12
    | ~ spl0_4
    | spl0_15 ),
    inference(split_clause,[status(thm)],[f512,f437,f462,f440,f410,f472,f475,f418,f492]) ).

fof(f514,plain,
    ( ~ l3_lattices(sk0_0)
    | v3_struct_0(sk0_0)
    | ~ v17_lattices(sk0_0)
    | spl0_15 ),
    inference(resolution,[status(thm)],[f494,f128]) ).

fof(f515,plain,
    ( ~ spl0_6
    | spl0_5
    | ~ spl0_13
    | spl0_15 ),
    inference(split_clause,[status(thm)],[f514,f440,f437,f484,f492]) ).

fof(f516,plain,
    ( v3_struct_0(sk0_0)
    | ~ v10_lattices(sk0_0)
    | ~ l3_lattices(sk0_0)
    | ~ v10_lattices(k1_lattice2(sk0_0))
    | ~ v11_lattices(k1_lattice2(sk0_0))
    | ~ l3_lattices(k1_lattice2(sk0_0))
    | spl0_14 ),
    inference(resolution,[status(thm)],[f491,f435]) ).

fof(f517,plain,
    ( spl0_5
    | ~ spl0_9
    | ~ spl0_6
    | ~ spl0_2
    | ~ spl0_10
    | ~ spl0_4
    | spl0_14 ),
    inference(split_clause,[status(thm)],[f516,f437,f462,f440,f410,f469,f418,f489]) ).

fof(f518,plain,
    ( ~ l3_lattices(sk0_0)
    | v3_struct_0(sk0_0)
    | ~ v17_lattices(sk0_0)
    | spl0_14 ),
    inference(resolution,[status(thm)],[f491,f125]) ).

fof(f519,plain,
    ( ~ spl0_6
    | spl0_5
    | ~ spl0_13
    | spl0_14 ),
    inference(split_clause,[status(thm)],[f518,f440,f437,f484,f489]) ).

fof(f534,plain,
    ( v3_struct_0(sk0_0)
    | ~ v10_lattices(sk0_0)
    | ~ l3_lattices(sk0_0)
    | ~ v11_lattices(sk0_0)
    | spl0_10 ),
    inference(resolution,[status(thm)],[f471,f433]) ).

fof(f535,plain,
    ( spl0_5
    | ~ spl0_9
    | ~ spl0_6
    | ~ spl0_14
    | spl0_10 ),
    inference(split_clause,[status(thm)],[f534,f437,f462,f440,f489,f469]) ).

fof(f547,plain,
    ( ~ l3_lattices(k1_lattice2(sk0_0))
    | v3_struct_0(k1_lattice2(sk0_0))
    | ~ v17_lattices(k1_lattice2(sk0_0))
    | spl0_10 ),
    inference(resolution,[status(thm)],[f471,f125]) ).

fof(f548,plain,
    ( ~ spl0_4
    | spl0_1
    | ~ spl0_3
    | spl0_10 ),
    inference(split_clause,[status(thm)],[f547,f418,f406,f414,f469]) ).

fof(f553,plain,
    ( v3_struct_0(sk0_0)
    | ~ v10_lattices(sk0_0)
    | ~ l3_lattices(sk0_0)
    | ~ v15_lattices(sk0_0)
    | ~ v16_lattices(sk0_0)
    | spl0_11 ),
    inference(resolution,[status(thm)],[f474,f426]) ).

fof(f554,plain,
    ( spl0_5
    | ~ spl0_9
    | ~ spl0_6
    | ~ spl0_15
    | ~ spl0_16
    | spl0_11 ),
    inference(split_clause,[status(thm)],[f553,f437,f462,f440,f492,f495,f472]) ).

fof(f571,plain,
    ( ~ l3_lattices(k1_lattice2(sk0_0))
    | v3_struct_0(k1_lattice2(sk0_0))
    | ~ v17_lattices(k1_lattice2(sk0_0))
    | spl0_11 ),
    inference(resolution,[status(thm)],[f474,f128]) ).

fof(f572,plain,
    ( ~ spl0_4
    | spl0_1
    | ~ spl0_3
    | spl0_11 ),
    inference(split_clause,[status(thm)],[f571,f418,f406,f414,f472]) ).

fof(f573,plain,
    ( ~ pd0_0(sk0_0)
    | spl0_13 ),
    inference(resolution,[status(thm)],[f486,f400]) ).

fof(f574,plain,
    ( ~ spl0_0
    | spl0_13 ),
    inference(split_clause,[status(thm)],[f573,f403,f484]) ).

fof(f578,plain,
    ( v3_struct_0(sk0_0)
    | ~ v10_lattices(sk0_0)
    | ~ l3_lattices(sk0_0)
    | ~ v15_lattices(sk0_0)
    | ~ v16_lattices(sk0_0)
    | spl0_12 ),
    inference(resolution,[status(thm)],[f477,f427]) ).

fof(f579,plain,
    ( spl0_5
    | ~ spl0_9
    | ~ spl0_6
    | ~ spl0_15
    | ~ spl0_16
    | spl0_12 ),
    inference(split_clause,[status(thm)],[f578,f437,f462,f440,f492,f495,f475]) ).

fof(f582,plain,
    ( ~ l3_lattices(k1_lattice2(sk0_0))
    | v3_struct_0(k1_lattice2(sk0_0))
    | ~ v17_lattices(k1_lattice2(sk0_0))
    | spl0_12 ),
    inference(resolution,[status(thm)],[f477,f129]) ).

fof(f583,plain,
    ( ~ spl0_4
    | spl0_1
    | ~ spl0_3
    | spl0_12 ),
    inference(split_clause,[status(thm)],[f582,f418,f406,f414,f475]) ).

fof(f584,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f417,f422,f444,f446,f448,f457,f459,f466,f468,f479,f482,f488,f499,f501,f503,f513,f515,f517,f519,f535,f548,f554,f572,f574,f579,f583]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.11  % Problem  : LAT319+1 : TPTP v8.1.2. Released v3.4.0.
% 0.08/0.11  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.31  % Computer : n009.cluster.edu
% 0.09/0.31  % Model    : x86_64 x86_64
% 0.09/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.31  % Memory   : 8042.1875MB
% 0.09/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.31  % CPULimit : 300
% 0.09/0.31  % WCLimit  : 300
% 0.09/0.31  % DateTime : Mon Apr 29 19:55:56 EDT 2024
% 0.09/0.32  % CPUTime  : 
% 0.09/0.32  % Drodi V3.6.0
% 0.09/0.34  % Refutation found
% 0.09/0.34  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.34  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.37  % Elapsed time: 0.038007 seconds
% 0.09/0.37  % CPU time: 0.186360 seconds
% 0.09/0.37  % Total memory used: 48.044 MB
% 0.09/0.37  % Net memory used: 47.971 MB
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