TSTP Solution File: LAT311+1 by iProver---3.9

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%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : LAT311+1 : TPTP v8.1.2. Released v3.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% 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 : Fri May  3 02:35:13 EDT 2024

% Result   : Theorem 184.50s 25.27s
% Output   : CNFRefutation 184.50s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   25
% Syntax   : Number of formulae    :  169 (  23 unt;   0 def)
%            Number of atoms       :  744 ( 121 equ)
%            Maximal formula atoms :   16 (   4 avg)
%            Number of connectives :  947 ( 372   ~; 394   |; 146   &)
%                                         (   1 <=>;  34  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   6 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   17 (  15 usr;   1 prp; 0-2 aty)
%            Number of functors    :   16 (  16 usr;   3 con; 0-2 aty)
%            Number of variables   :  250 (   2 sgn 140   !;  15   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,conjecture,
    ! [X0] :
      ( ( l3_lattices(X0)
        & v10_lattices(X0)
        & ~ v3_struct_0(X0) )
     => ! [X1] :
          ( m1_subset_1(X1,u1_struct_0(X0))
         => ! [X2] :
              ( ( m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X0)))
                & ~ v1_xboole_0(X2) )
             => ( r2_hidden(X1,X2)
               => r1_tarski(k18_filter_2(X0,X1),k19_filter_2(X0,X2)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_filter_2) ).

fof(f2,negated_conjecture,
    ~ ! [X0] :
        ( ( l3_lattices(X0)
          & v10_lattices(X0)
          & ~ v3_struct_0(X0) )
       => ! [X1] :
            ( m1_subset_1(X1,u1_struct_0(X0))
           => ! [X2] :
                ( ( m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X0)))
                  & ~ v1_xboole_0(X2) )
               => ( r2_hidden(X1,X2)
                 => r1_tarski(k18_filter_2(X0,X1),k19_filter_2(X0,X2)) ) ) ) ),
    inference(negated_conjecture,[],[f1]) ).

fof(f12,axiom,
    ! [X0] :
      ( ( l3_lattices(X0)
        & v10_lattices(X0)
        & ~ v3_struct_0(X0) )
     => ! [X1] :
          ( m1_subset_1(X1,u1_struct_0(X0))
         => k5_filter_2(X0,X1) = X1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_filter_2) ).

fof(f13,axiom,
    ! [X0] :
      ( ( l3_lattices(X0)
        & v10_lattices(X0)
        & ~ v3_struct_0(X0) )
     => ! [X1] :
          ( m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
         => k7_filter_2(X0,X1) = X1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_filter_2) ).

fof(f15,axiom,
    ! [X0] :
      ( ( l3_lattices(X0)
        & v10_lattices(X0)
        & ~ v3_struct_0(X0) )
     => ! [X1] :
          ( m1_subset_1(X1,u1_struct_0(X0))
         => k18_filter_2(X0,X1) = a_2_0_filter_2(X0,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_filter_2) ).

fof(f19,axiom,
    ! [X0] :
      ( l3_lattices(X0)
     => ( l3_lattices(k1_lattice2(X0))
        & v3_lattices(k1_lattice2(X0)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_lattice2) ).

fof(f27,axiom,
    ! [X0,X1] :
      ( ( m1_subset_1(X1,u1_struct_0(X0))
        & l3_lattices(X0)
        & v10_lattices(X0)
        & ~ v3_struct_0(X0) )
     => m1_subset_1(k5_filter_2(X0,X1),u1_struct_0(k1_lattice2(X0))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_filter_2) ).

fof(f28,axiom,
    ! [X0,X1] :
      ( ( m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
        & l3_lattices(X0)
        & v10_lattices(X0)
        & ~ v3_struct_0(X0) )
     => m1_subset_1(k7_filter_2(X0,X1),k1_zfmisc_1(u1_struct_0(k1_lattice2(X0)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_filter_2) ).

fof(f55,axiom,
    ! [X0,X1] :
      ( ( m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
        & ~ v1_xboole_0(X1)
        & l3_lattices(X0)
        & v10_lattices(X0)
        & ~ v3_struct_0(X0) )
     => ~ v1_xboole_0(k7_filter_2(X0,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_filter_2) ).

fof(f67,axiom,
    ! [X0] :
      ( ( l3_lattices(X0)
        & v10_lattices(X0)
        & ~ v3_struct_0(X0) )
     => ( v10_lattices(k1_lattice2(X0))
        & v9_lattices(k1_lattice2(X0))
        & v8_lattices(k1_lattice2(X0))
        & v7_lattices(k1_lattice2(X0))
        & v6_lattices(k1_lattice2(X0))
        & v5_lattices(k1_lattice2(X0))
        & v4_lattices(k1_lattice2(X0))
        & v3_lattices(k1_lattice2(X0))
        & ~ v3_struct_0(k1_lattice2(X0)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_lattice2) ).

fof(f84,axiom,
    ! [X0,X1] :
      ( ( m1_subset_1(X1,u1_struct_0(X0))
        & l3_lattices(X0)
        & v10_lattices(X0)
        & ~ v3_struct_0(X0) )
     => k2_filter_0(X0,X1) = k2_filter_2(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k2_filter_2) ).

fof(f85,axiom,
    ! [X0,X1] :
      ( ( m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
        & ~ v1_xboole_0(X1)
        & l3_lattices(X0)
        & v10_lattices(X0)
        & ~ v3_struct_0(X0) )
     => k3_filter_0(X0,X1) = k3_filter_2(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k3_filter_2) ).

fof(f92,axiom,
    ! [X0] :
      ( ( l3_lattices(X0)
        & v10_lattices(X0)
        & ~ v3_struct_0(X0) )
     => ! [X1] :
          ( m1_subset_1(X1,u1_struct_0(X0))
         => ! [X2] :
              ( ( m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X0)))
                & ~ v1_xboole_0(X2) )
             => ( r2_hidden(X1,X2)
               => r1_tarski(k2_filter_0(X0,X1),k3_filter_0(X0,X2)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_filter_0) ).

fof(f95,axiom,
    ! [X0] :
      ( ( l3_lattices(X0)
        & v10_lattices(X0)
        & ~ v3_struct_0(X0) )
     => ! [X1] :
          ( m1_subset_1(X1,u1_struct_0(X0))
         => ( k2_filter_2(X0,X1) = k18_filter_2(k1_lattice2(X0),k5_filter_2(X0,X1))
            & k18_filter_2(X0,X1) = k2_filter_2(k1_lattice2(X0),k5_filter_2(X0,X1)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_filter_2) ).

fof(f96,axiom,
    ! [X0] :
      ( ( l3_lattices(X0)
        & v10_lattices(X0)
        & ~ v3_struct_0(X0) )
     => ! [X1] :
          ( ( m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
            & ~ v1_xboole_0(X1) )
         => ! [X2] :
              ( ( m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(k1_lattice2(X0))))
                & ~ v1_xboole_0(X2) )
             => ( k3_filter_2(k1_lattice2(X0),X2) = k19_filter_2(X0,k8_filter_2(X0,X2))
                & k3_filter_2(X0,k8_filter_2(X0,X2)) = k19_filter_2(k1_lattice2(X0),X2)
                & k3_filter_2(X0,X1) = k19_filter_2(k1_lattice2(X0),k7_filter_2(X0,X1))
                & k19_filter_2(X0,X1) = k3_filter_2(k1_lattice2(X0),k7_filter_2(X0,X1)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_filter_2) ).

fof(f97,axiom,
    ! [X0,X1] :
      ( m1_subset_1(X0,k1_zfmisc_1(X1))
    <=> r1_tarski(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).

fof(f98,axiom,
    ! [X0,X1,X2] :
      ( ( m1_subset_1(X1,k1_zfmisc_1(X2))
        & r2_hidden(X0,X1) )
     => m1_subset_1(X0,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).

fof(f101,axiom,
    ! [X0,X1] :
      ~ ( v1_xboole_0(X1)
        & r2_hidden(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).

fof(f114,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ~ r1_tarski(k18_filter_2(X0,X1),k19_filter_2(X0,X2))
              & r2_hidden(X1,X2)
              & m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X0)))
              & ~ v1_xboole_0(X2) )
          & m1_subset_1(X1,u1_struct_0(X0)) )
      & l3_lattices(X0)
      & v10_lattices(X0)
      & ~ v3_struct_0(X0) ),
    inference(ennf_transformation,[],[f2]) ).

fof(f115,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ~ r1_tarski(k18_filter_2(X0,X1),k19_filter_2(X0,X2))
              & r2_hidden(X1,X2)
              & m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X0)))
              & ~ v1_xboole_0(X2) )
          & m1_subset_1(X1,u1_struct_0(X0)) )
      & l3_lattices(X0)
      & v10_lattices(X0)
      & ~ v3_struct_0(X0) ),
    inference(flattening,[],[f114]) ).

fof(f130,plain,
    ! [X0] :
      ( ! [X1] :
          ( k5_filter_2(X0,X1) = X1
          | ~ m1_subset_1(X1,u1_struct_0(X0)) )
      | ~ l3_lattices(X0)
      | ~ v10_lattices(X0)
      | v3_struct_0(X0) ),
    inference(ennf_transformation,[],[f12]) ).

fof(f131,plain,
    ! [X0] :
      ( ! [X1] :
          ( k5_filter_2(X0,X1) = X1
          | ~ m1_subset_1(X1,u1_struct_0(X0)) )
      | ~ l3_lattices(X0)
      | ~ v10_lattices(X0)
      | v3_struct_0(X0) ),
    inference(flattening,[],[f130]) ).

fof(f132,plain,
    ! [X0] :
      ( ! [X1] :
          ( k7_filter_2(X0,X1) = X1
          | ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0))) )
      | ~ l3_lattices(X0)
      | ~ v10_lattices(X0)
      | v3_struct_0(X0) ),
    inference(ennf_transformation,[],[f13]) ).

fof(f133,plain,
    ! [X0] :
      ( ! [X1] :
          ( k7_filter_2(X0,X1) = X1
          | ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0))) )
      | ~ l3_lattices(X0)
      | ~ v10_lattices(X0)
      | v3_struct_0(X0) ),
    inference(flattening,[],[f132]) ).

fof(f136,plain,
    ! [X0] :
      ( ! [X1] :
          ( k18_filter_2(X0,X1) = a_2_0_filter_2(X0,X1)
          | ~ m1_subset_1(X1,u1_struct_0(X0)) )
      | ~ l3_lattices(X0)
      | ~ v10_lattices(X0)
      | v3_struct_0(X0) ),
    inference(ennf_transformation,[],[f15]) ).

fof(f137,plain,
    ! [X0] :
      ( ! [X1] :
          ( k18_filter_2(X0,X1) = a_2_0_filter_2(X0,X1)
          | ~ m1_subset_1(X1,u1_struct_0(X0)) )
      | ~ l3_lattices(X0)
      | ~ v10_lattices(X0)
      | v3_struct_0(X0) ),
    inference(flattening,[],[f136]) ).

fof(f144,plain,
    ! [X0] :
      ( ( l3_lattices(k1_lattice2(X0))
        & v3_lattices(k1_lattice2(X0)) )
      | ~ l3_lattices(X0) ),
    inference(ennf_transformation,[],[f19]) ).

fof(f153,plain,
    ! [X0,X1] :
      ( m1_subset_1(k5_filter_2(X0,X1),u1_struct_0(k1_lattice2(X0)))
      | ~ m1_subset_1(X1,u1_struct_0(X0))
      | ~ l3_lattices(X0)
      | ~ v10_lattices(X0)
      | v3_struct_0(X0) ),
    inference(ennf_transformation,[],[f27]) ).

fof(f154,plain,
    ! [X0,X1] :
      ( m1_subset_1(k5_filter_2(X0,X1),u1_struct_0(k1_lattice2(X0)))
      | ~ m1_subset_1(X1,u1_struct_0(X0))
      | ~ l3_lattices(X0)
      | ~ v10_lattices(X0)
      | v3_struct_0(X0) ),
    inference(flattening,[],[f153]) ).

fof(f155,plain,
    ! [X0,X1] :
      ( m1_subset_1(k7_filter_2(X0,X1),k1_zfmisc_1(u1_struct_0(k1_lattice2(X0))))
      | ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
      | ~ l3_lattices(X0)
      | ~ v10_lattices(X0)
      | v3_struct_0(X0) ),
    inference(ennf_transformation,[],[f28]) ).

fof(f156,plain,
    ! [X0,X1] :
      ( m1_subset_1(k7_filter_2(X0,X1),k1_zfmisc_1(u1_struct_0(k1_lattice2(X0))))
      | ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
      | ~ l3_lattices(X0)
      | ~ v10_lattices(X0)
      | v3_struct_0(X0) ),
    inference(flattening,[],[f155]) ).

fof(f181,plain,
    ! [X0,X1] :
      ( ~ v1_xboole_0(k7_filter_2(X0,X1))
      | ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
      | v1_xboole_0(X1)
      | ~ l3_lattices(X0)
      | ~ v10_lattices(X0)
      | v3_struct_0(X0) ),
    inference(ennf_transformation,[],[f55]) ).

fof(f182,plain,
    ! [X0,X1] :
      ( ~ v1_xboole_0(k7_filter_2(X0,X1))
      | ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
      | v1_xboole_0(X1)
      | ~ l3_lattices(X0)
      | ~ v10_lattices(X0)
      | v3_struct_0(X0) ),
    inference(flattening,[],[f181]) ).

fof(f201,plain,
    ! [X0] :
      ( ( v10_lattices(k1_lattice2(X0))
        & v9_lattices(k1_lattice2(X0))
        & v8_lattices(k1_lattice2(X0))
        & v7_lattices(k1_lattice2(X0))
        & v6_lattices(k1_lattice2(X0))
        & v5_lattices(k1_lattice2(X0))
        & v4_lattices(k1_lattice2(X0))
        & v3_lattices(k1_lattice2(X0))
        & ~ v3_struct_0(k1_lattice2(X0)) )
      | ~ l3_lattices(X0)
      | ~ v10_lattices(X0)
      | v3_struct_0(X0) ),
    inference(ennf_transformation,[],[f67]) ).

fof(f202,plain,
    ! [X0] :
      ( ( v10_lattices(k1_lattice2(X0))
        & v9_lattices(k1_lattice2(X0))
        & v8_lattices(k1_lattice2(X0))
        & v7_lattices(k1_lattice2(X0))
        & v6_lattices(k1_lattice2(X0))
        & v5_lattices(k1_lattice2(X0))
        & v4_lattices(k1_lattice2(X0))
        & v3_lattices(k1_lattice2(X0))
        & ~ v3_struct_0(k1_lattice2(X0)) )
      | ~ l3_lattices(X0)
      | ~ v10_lattices(X0)
      | v3_struct_0(X0) ),
    inference(flattening,[],[f201]) ).

fof(f214,plain,
    ! [X0,X1] :
      ( k2_filter_0(X0,X1) = k2_filter_2(X0,X1)
      | ~ m1_subset_1(X1,u1_struct_0(X0))
      | ~ l3_lattices(X0)
      | ~ v10_lattices(X0)
      | v3_struct_0(X0) ),
    inference(ennf_transformation,[],[f84]) ).

fof(f215,plain,
    ! [X0,X1] :
      ( k2_filter_0(X0,X1) = k2_filter_2(X0,X1)
      | ~ m1_subset_1(X1,u1_struct_0(X0))
      | ~ l3_lattices(X0)
      | ~ v10_lattices(X0)
      | v3_struct_0(X0) ),
    inference(flattening,[],[f214]) ).

fof(f216,plain,
    ! [X0,X1] :
      ( k3_filter_0(X0,X1) = k3_filter_2(X0,X1)
      | ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
      | v1_xboole_0(X1)
      | ~ l3_lattices(X0)
      | ~ v10_lattices(X0)
      | v3_struct_0(X0) ),
    inference(ennf_transformation,[],[f85]) ).

fof(f217,plain,
    ! [X0,X1] :
      ( k3_filter_0(X0,X1) = k3_filter_2(X0,X1)
      | ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
      | v1_xboole_0(X1)
      | ~ l3_lattices(X0)
      | ~ v10_lattices(X0)
      | v3_struct_0(X0) ),
    inference(flattening,[],[f216]) ).

fof(f225,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( r1_tarski(k2_filter_0(X0,X1),k3_filter_0(X0,X2))
              | ~ r2_hidden(X1,X2)
              | ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X0)))
              | v1_xboole_0(X2) )
          | ~ m1_subset_1(X1,u1_struct_0(X0)) )
      | ~ l3_lattices(X0)
      | ~ v10_lattices(X0)
      | v3_struct_0(X0) ),
    inference(ennf_transformation,[],[f92]) ).

fof(f226,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( r1_tarski(k2_filter_0(X0,X1),k3_filter_0(X0,X2))
              | ~ r2_hidden(X1,X2)
              | ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X0)))
              | v1_xboole_0(X2) )
          | ~ m1_subset_1(X1,u1_struct_0(X0)) )
      | ~ l3_lattices(X0)
      | ~ v10_lattices(X0)
      | v3_struct_0(X0) ),
    inference(flattening,[],[f225]) ).

fof(f230,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( k2_filter_2(X0,X1) = k18_filter_2(k1_lattice2(X0),k5_filter_2(X0,X1))
            & k18_filter_2(X0,X1) = k2_filter_2(k1_lattice2(X0),k5_filter_2(X0,X1)) )
          | ~ m1_subset_1(X1,u1_struct_0(X0)) )
      | ~ l3_lattices(X0)
      | ~ v10_lattices(X0)
      | v3_struct_0(X0) ),
    inference(ennf_transformation,[],[f95]) ).

fof(f231,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( k2_filter_2(X0,X1) = k18_filter_2(k1_lattice2(X0),k5_filter_2(X0,X1))
            & k18_filter_2(X0,X1) = k2_filter_2(k1_lattice2(X0),k5_filter_2(X0,X1)) )
          | ~ m1_subset_1(X1,u1_struct_0(X0)) )
      | ~ l3_lattices(X0)
      | ~ v10_lattices(X0)
      | v3_struct_0(X0) ),
    inference(flattening,[],[f230]) ).

fof(f232,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ( k3_filter_2(k1_lattice2(X0),X2) = k19_filter_2(X0,k8_filter_2(X0,X2))
                & k3_filter_2(X0,k8_filter_2(X0,X2)) = k19_filter_2(k1_lattice2(X0),X2)
                & k3_filter_2(X0,X1) = k19_filter_2(k1_lattice2(X0),k7_filter_2(X0,X1))
                & k19_filter_2(X0,X1) = k3_filter_2(k1_lattice2(X0),k7_filter_2(X0,X1)) )
              | ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(k1_lattice2(X0))))
              | v1_xboole_0(X2) )
          | ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
          | v1_xboole_0(X1) )
      | ~ l3_lattices(X0)
      | ~ v10_lattices(X0)
      | v3_struct_0(X0) ),
    inference(ennf_transformation,[],[f96]) ).

fof(f233,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ( k3_filter_2(k1_lattice2(X0),X2) = k19_filter_2(X0,k8_filter_2(X0,X2))
                & k3_filter_2(X0,k8_filter_2(X0,X2)) = k19_filter_2(k1_lattice2(X0),X2)
                & k3_filter_2(X0,X1) = k19_filter_2(k1_lattice2(X0),k7_filter_2(X0,X1))
                & k19_filter_2(X0,X1) = k3_filter_2(k1_lattice2(X0),k7_filter_2(X0,X1)) )
              | ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(k1_lattice2(X0))))
              | v1_xboole_0(X2) )
          | ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
          | v1_xboole_0(X1) )
      | ~ l3_lattices(X0)
      | ~ v10_lattices(X0)
      | v3_struct_0(X0) ),
    inference(flattening,[],[f232]) ).

fof(f234,plain,
    ! [X0,X1,X2] :
      ( m1_subset_1(X0,X2)
      | ~ m1_subset_1(X1,k1_zfmisc_1(X2))
      | ~ r2_hidden(X0,X1) ),
    inference(ennf_transformation,[],[f98]) ).

fof(f235,plain,
    ! [X0,X1,X2] :
      ( m1_subset_1(X0,X2)
      | ~ m1_subset_1(X1,k1_zfmisc_1(X2))
      | ~ r2_hidden(X0,X1) ),
    inference(flattening,[],[f234]) ).

fof(f238,plain,
    ! [X0,X1] :
      ( ~ v1_xboole_0(X1)
      | ~ r2_hidden(X0,X1) ),
    inference(ennf_transformation,[],[f101]) ).

fof(f240,plain,
    ! [X0] :
      ( ( v10_lattices(k1_lattice2(X0))
        & v9_lattices(k1_lattice2(X0))
        & v8_lattices(k1_lattice2(X0))
        & v7_lattices(k1_lattice2(X0))
        & v6_lattices(k1_lattice2(X0))
        & v5_lattices(k1_lattice2(X0))
        & v4_lattices(k1_lattice2(X0))
        & v3_lattices(k1_lattice2(X0))
        & ~ v3_struct_0(k1_lattice2(X0)) )
      | ~ sP0(X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f241,plain,
    ! [X0] :
      ( sP0(X0)
      | ~ l3_lattices(X0)
      | ~ v10_lattices(X0)
      | v3_struct_0(X0) ),
    inference(definition_folding,[],[f202,f240]) ).

fof(f242,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ? [X2] :
                ( ~ r1_tarski(k18_filter_2(X0,X1),k19_filter_2(X0,X2))
                & r2_hidden(X1,X2)
                & m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X0)))
                & ~ v1_xboole_0(X2) )
            & m1_subset_1(X1,u1_struct_0(X0)) )
        & l3_lattices(X0)
        & v10_lattices(X0)
        & ~ v3_struct_0(X0) )
   => ( ? [X1] :
          ( ? [X2] :
              ( ~ r1_tarski(k18_filter_2(sK1,X1),k19_filter_2(sK1,X2))
              & r2_hidden(X1,X2)
              & m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(sK1)))
              & ~ v1_xboole_0(X2) )
          & m1_subset_1(X1,u1_struct_0(sK1)) )
      & l3_lattices(sK1)
      & v10_lattices(sK1)
      & ~ v3_struct_0(sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f243,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ~ r1_tarski(k18_filter_2(sK1,X1),k19_filter_2(sK1,X2))
            & r2_hidden(X1,X2)
            & m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(sK1)))
            & ~ v1_xboole_0(X2) )
        & m1_subset_1(X1,u1_struct_0(sK1)) )
   => ( ? [X2] :
          ( ~ r1_tarski(k18_filter_2(sK1,sK2),k19_filter_2(sK1,X2))
          & r2_hidden(sK2,X2)
          & m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(sK1)))
          & ~ v1_xboole_0(X2) )
      & m1_subset_1(sK2,u1_struct_0(sK1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f244,plain,
    ( ? [X2] :
        ( ~ r1_tarski(k18_filter_2(sK1,sK2),k19_filter_2(sK1,X2))
        & r2_hidden(sK2,X2)
        & m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(sK1)))
        & ~ v1_xboole_0(X2) )
   => ( ~ r1_tarski(k18_filter_2(sK1,sK2),k19_filter_2(sK1,sK3))
      & r2_hidden(sK2,sK3)
      & m1_subset_1(sK3,k1_zfmisc_1(u1_struct_0(sK1)))
      & ~ v1_xboole_0(sK3) ) ),
    introduced(choice_axiom,[]) ).

fof(f245,plain,
    ( ~ r1_tarski(k18_filter_2(sK1,sK2),k19_filter_2(sK1,sK3))
    & r2_hidden(sK2,sK3)
    & m1_subset_1(sK3,k1_zfmisc_1(u1_struct_0(sK1)))
    & ~ v1_xboole_0(sK3)
    & m1_subset_1(sK2,u1_struct_0(sK1))
    & l3_lattices(sK1)
    & v10_lattices(sK1)
    & ~ v3_struct_0(sK1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f115,f244,f243,f242]) ).

fof(f268,plain,
    ! [X0] :
      ( ( v10_lattices(k1_lattice2(X0))
        & v9_lattices(k1_lattice2(X0))
        & v8_lattices(k1_lattice2(X0))
        & v7_lattices(k1_lattice2(X0))
        & v6_lattices(k1_lattice2(X0))
        & v5_lattices(k1_lattice2(X0))
        & v4_lattices(k1_lattice2(X0))
        & v3_lattices(k1_lattice2(X0))
        & ~ v3_struct_0(k1_lattice2(X0)) )
      | ~ sP0(X0) ),
    inference(nnf_transformation,[],[f240]) ).

fof(f309,plain,
    ! [X0,X1] :
      ( ( m1_subset_1(X0,k1_zfmisc_1(X1))
        | ~ r1_tarski(X0,X1) )
      & ( r1_tarski(X0,X1)
        | ~ m1_subset_1(X0,k1_zfmisc_1(X1)) ) ),
    inference(nnf_transformation,[],[f97]) ).

fof(f310,plain,
    ~ v3_struct_0(sK1),
    inference(cnf_transformation,[],[f245]) ).

fof(f311,plain,
    v10_lattices(sK1),
    inference(cnf_transformation,[],[f245]) ).

fof(f312,plain,
    l3_lattices(sK1),
    inference(cnf_transformation,[],[f245]) ).

fof(f313,plain,
    m1_subset_1(sK2,u1_struct_0(sK1)),
    inference(cnf_transformation,[],[f245]) ).

fof(f314,plain,
    ~ v1_xboole_0(sK3),
    inference(cnf_transformation,[],[f245]) ).

fof(f315,plain,
    m1_subset_1(sK3,k1_zfmisc_1(u1_struct_0(sK1))),
    inference(cnf_transformation,[],[f245]) ).

fof(f316,plain,
    r2_hidden(sK2,sK3),
    inference(cnf_transformation,[],[f245]) ).

fof(f317,plain,
    ~ r1_tarski(k18_filter_2(sK1,sK2),k19_filter_2(sK1,sK3)),
    inference(cnf_transformation,[],[f245]) ).

fof(f335,plain,
    ! [X0,X1] :
      ( k5_filter_2(X0,X1) = X1
      | ~ m1_subset_1(X1,u1_struct_0(X0))
      | ~ l3_lattices(X0)
      | ~ v10_lattices(X0)
      | v3_struct_0(X0) ),
    inference(cnf_transformation,[],[f131]) ).

fof(f336,plain,
    ! [X0,X1] :
      ( k7_filter_2(X0,X1) = X1
      | ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
      | ~ l3_lattices(X0)
      | ~ v10_lattices(X0)
      | v3_struct_0(X0) ),
    inference(cnf_transformation,[],[f133]) ).

fof(f338,plain,
    ! [X0,X1] :
      ( k18_filter_2(X0,X1) = a_2_0_filter_2(X0,X1)
      | ~ m1_subset_1(X1,u1_struct_0(X0))
      | ~ l3_lattices(X0)
      | ~ v10_lattices(X0)
      | v3_struct_0(X0) ),
    inference(cnf_transformation,[],[f137]) ).

fof(f344,plain,
    ! [X0] :
      ( l3_lattices(k1_lattice2(X0))
      | ~ l3_lattices(X0) ),
    inference(cnf_transformation,[],[f144]) ).

fof(f349,plain,
    ! [X0,X1] :
      ( m1_subset_1(k5_filter_2(X0,X1),u1_struct_0(k1_lattice2(X0)))
      | ~ m1_subset_1(X1,u1_struct_0(X0))
      | ~ l3_lattices(X0)
      | ~ v10_lattices(X0)
      | v3_struct_0(X0) ),
    inference(cnf_transformation,[],[f154]) ).

fof(f350,plain,
    ! [X0,X1] :
      ( m1_subset_1(k7_filter_2(X0,X1),k1_zfmisc_1(u1_struct_0(k1_lattice2(X0))))
      | ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
      | ~ l3_lattices(X0)
      | ~ v10_lattices(X0)
      | v3_struct_0(X0) ),
    inference(cnf_transformation,[],[f156]) ).

fof(f381,plain,
    ! [X0,X1] :
      ( ~ v1_xboole_0(k7_filter_2(X0,X1))
      | ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
      | v1_xboole_0(X1)
      | ~ l3_lattices(X0)
      | ~ v10_lattices(X0)
      | v3_struct_0(X0) ),
    inference(cnf_transformation,[],[f182]) ).

fof(f403,plain,
    ! [X0] :
      ( ~ v3_struct_0(k1_lattice2(X0))
      | ~ sP0(X0) ),
    inference(cnf_transformation,[],[f268]) ).

fof(f411,plain,
    ! [X0] :
      ( v10_lattices(k1_lattice2(X0))
      | ~ sP0(X0) ),
    inference(cnf_transformation,[],[f268]) ).

fof(f412,plain,
    ! [X0] :
      ( sP0(X0)
      | ~ l3_lattices(X0)
      | ~ v10_lattices(X0)
      | v3_struct_0(X0) ),
    inference(cnf_transformation,[],[f241]) ).

fof(f458,plain,
    ! [X0,X1] :
      ( k2_filter_0(X0,X1) = k2_filter_2(X0,X1)
      | ~ m1_subset_1(X1,u1_struct_0(X0))
      | ~ l3_lattices(X0)
      | ~ v10_lattices(X0)
      | v3_struct_0(X0) ),
    inference(cnf_transformation,[],[f215]) ).

fof(f459,plain,
    ! [X0,X1] :
      ( k3_filter_0(X0,X1) = k3_filter_2(X0,X1)
      | ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
      | v1_xboole_0(X1)
      | ~ l3_lattices(X0)
      | ~ v10_lattices(X0)
      | v3_struct_0(X0) ),
    inference(cnf_transformation,[],[f217]) ).

fof(f469,plain,
    ! [X2,X0,X1] :
      ( r1_tarski(k2_filter_0(X0,X1),k3_filter_0(X0,X2))
      | ~ r2_hidden(X1,X2)
      | ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X0)))
      | v1_xboole_0(X2)
      | ~ m1_subset_1(X1,u1_struct_0(X0))
      | ~ l3_lattices(X0)
      | ~ v10_lattices(X0)
      | v3_struct_0(X0) ),
    inference(cnf_transformation,[],[f226]) ).

fof(f473,plain,
    ! [X0,X1] :
      ( k18_filter_2(X0,X1) = k2_filter_2(k1_lattice2(X0),k5_filter_2(X0,X1))
      | ~ m1_subset_1(X1,u1_struct_0(X0))
      | ~ l3_lattices(X0)
      | ~ v10_lattices(X0)
      | v3_struct_0(X0) ),
    inference(cnf_transformation,[],[f231]) ).

fof(f475,plain,
    ! [X2,X0,X1] :
      ( k19_filter_2(X0,X1) = k3_filter_2(k1_lattice2(X0),k7_filter_2(X0,X1))
      | ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(k1_lattice2(X0))))
      | v1_xboole_0(X2)
      | ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
      | v1_xboole_0(X1)
      | ~ l3_lattices(X0)
      | ~ v10_lattices(X0)
      | v3_struct_0(X0) ),
    inference(cnf_transformation,[],[f233]) ).

fof(f479,plain,
    ! [X0,X1] :
      ( r1_tarski(X0,X1)
      | ~ m1_subset_1(X0,k1_zfmisc_1(X1)) ),
    inference(cnf_transformation,[],[f309]) ).

fof(f480,plain,
    ! [X0,X1] :
      ( m1_subset_1(X0,k1_zfmisc_1(X1))
      | ~ r1_tarski(X0,X1) ),
    inference(cnf_transformation,[],[f309]) ).

fof(f481,plain,
    ! [X2,X0,X1] :
      ( m1_subset_1(X0,X2)
      | ~ m1_subset_1(X1,k1_zfmisc_1(X2))
      | ~ r2_hidden(X0,X1) ),
    inference(cnf_transformation,[],[f235]) ).

fof(f484,plain,
    ! [X0,X1] :
      ( ~ v1_xboole_0(X1)
      | ~ r2_hidden(X0,X1) ),
    inference(cnf_transformation,[],[f238]) ).

cnf(c_49,negated_conjecture,
    ~ r1_tarski(k18_filter_2(sK1,sK2),k19_filter_2(sK1,sK3)),
    inference(cnf_transformation,[],[f317]) ).

cnf(c_50,negated_conjecture,
    r2_hidden(sK2,sK3),
    inference(cnf_transformation,[],[f316]) ).

cnf(c_51,negated_conjecture,
    m1_subset_1(sK3,k1_zfmisc_1(u1_struct_0(sK1))),
    inference(cnf_transformation,[],[f315]) ).

cnf(c_52,negated_conjecture,
    ~ v1_xboole_0(sK3),
    inference(cnf_transformation,[],[f314]) ).

cnf(c_53,negated_conjecture,
    m1_subset_1(sK2,u1_struct_0(sK1)),
    inference(cnf_transformation,[],[f313]) ).

cnf(c_54,negated_conjecture,
    l3_lattices(sK1),
    inference(cnf_transformation,[],[f312]) ).

cnf(c_55,negated_conjecture,
    v10_lattices(sK1),
    inference(cnf_transformation,[],[f311]) ).

cnf(c_56,negated_conjecture,
    ~ v3_struct_0(sK1),
    inference(cnf_transformation,[],[f310]) ).

cnf(c_70,plain,
    ( ~ m1_subset_1(X0,u1_struct_0(X1))
    | ~ l3_lattices(X1)
    | ~ v10_lattices(X1)
    | k5_filter_2(X1,X0) = X0
    | v3_struct_0(X1) ),
    inference(cnf_transformation,[],[f335]) ).

cnf(c_71,plain,
    ( ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(X1)))
    | ~ l3_lattices(X1)
    | ~ v10_lattices(X1)
    | k7_filter_2(X1,X0) = X0
    | v3_struct_0(X1) ),
    inference(cnf_transformation,[],[f336]) ).

cnf(c_73,plain,
    ( ~ m1_subset_1(X0,u1_struct_0(X1))
    | ~ l3_lattices(X1)
    | ~ v10_lattices(X1)
    | k18_filter_2(X1,X0) = a_2_0_filter_2(X1,X0)
    | v3_struct_0(X1) ),
    inference(cnf_transformation,[],[f338]) ).

cnf(c_78,plain,
    ( ~ l3_lattices(X0)
    | l3_lattices(k1_lattice2(X0)) ),
    inference(cnf_transformation,[],[f344]) ).

cnf(c_84,plain,
    ( ~ m1_subset_1(X0,u1_struct_0(X1))
    | ~ l3_lattices(X1)
    | ~ v10_lattices(X1)
    | m1_subset_1(k5_filter_2(X1,X0),u1_struct_0(k1_lattice2(X1)))
    | v3_struct_0(X1) ),
    inference(cnf_transformation,[],[f349]) ).

cnf(c_85,plain,
    ( ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(X1)))
    | ~ l3_lattices(X1)
    | ~ v10_lattices(X1)
    | m1_subset_1(k7_filter_2(X1,X0),k1_zfmisc_1(u1_struct_0(k1_lattice2(X1))))
    | v3_struct_0(X1) ),
    inference(cnf_transformation,[],[f350]) ).

cnf(c_116,plain,
    ( ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(X1)))
    | ~ v1_xboole_0(k7_filter_2(X1,X0))
    | ~ l3_lattices(X1)
    | ~ v10_lattices(X1)
    | v1_xboole_0(X0)
    | v3_struct_0(X1) ),
    inference(cnf_transformation,[],[f381]) ).

cnf(c_138,plain,
    ( ~ sP0(X0)
    | v10_lattices(k1_lattice2(X0)) ),
    inference(cnf_transformation,[],[f411]) ).

cnf(c_146,plain,
    ( ~ v3_struct_0(k1_lattice2(X0))
    | ~ sP0(X0) ),
    inference(cnf_transformation,[],[f403]) ).

cnf(c_147,plain,
    ( ~ l3_lattices(X0)
    | ~ v10_lattices(X0)
    | v3_struct_0(X0)
    | sP0(X0) ),
    inference(cnf_transformation,[],[f412]) ).

cnf(c_193,plain,
    ( ~ m1_subset_1(X0,u1_struct_0(X1))
    | ~ l3_lattices(X1)
    | ~ v10_lattices(X1)
    | k2_filter_0(X1,X0) = k2_filter_2(X1,X0)
    | v3_struct_0(X1) ),
    inference(cnf_transformation,[],[f458]) ).

cnf(c_194,plain,
    ( ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(X1)))
    | ~ l3_lattices(X1)
    | ~ v10_lattices(X1)
    | k3_filter_0(X1,X0) = k3_filter_2(X1,X0)
    | v1_xboole_0(X0)
    | v3_struct_0(X1) ),
    inference(cnf_transformation,[],[f459]) ).

cnf(c_204,plain,
    ( ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(X1)))
    | ~ m1_subset_1(X2,u1_struct_0(X1))
    | ~ r2_hidden(X2,X0)
    | ~ l3_lattices(X1)
    | ~ v10_lattices(X1)
    | r1_tarski(k2_filter_0(X1,X2),k3_filter_0(X1,X0))
    | v1_xboole_0(X0)
    | v3_struct_0(X1) ),
    inference(cnf_transformation,[],[f469]) ).

cnf(c_209,plain,
    ( ~ m1_subset_1(X0,u1_struct_0(X1))
    | ~ l3_lattices(X1)
    | ~ v10_lattices(X1)
    | k2_filter_2(k1_lattice2(X1),k5_filter_2(X1,X0)) = k18_filter_2(X1,X0)
    | v3_struct_0(X1) ),
    inference(cnf_transformation,[],[f473]) ).

cnf(c_213,plain,
    ( ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(k1_lattice2(X1))))
    | ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
    | ~ l3_lattices(X1)
    | ~ v10_lattices(X1)
    | k3_filter_2(k1_lattice2(X1),k7_filter_2(X1,X2)) = k19_filter_2(X1,X2)
    | v1_xboole_0(X0)
    | v1_xboole_0(X2)
    | v3_struct_0(X1) ),
    inference(cnf_transformation,[],[f475]) ).

cnf(c_214,plain,
    ( ~ r1_tarski(X0,X1)
    | m1_subset_1(X0,k1_zfmisc_1(X1)) ),
    inference(cnf_transformation,[],[f480]) ).

cnf(c_215,plain,
    ( ~ m1_subset_1(X0,k1_zfmisc_1(X1))
    | r1_tarski(X0,X1) ),
    inference(cnf_transformation,[],[f479]) ).

cnf(c_216,plain,
    ( ~ m1_subset_1(X0,k1_zfmisc_1(X1))
    | ~ r2_hidden(X2,X0)
    | m1_subset_1(X2,X1) ),
    inference(cnf_transformation,[],[f481]) ).

cnf(c_219,plain,
    ( ~ r2_hidden(X0,X1)
    | ~ v1_xboole_0(X1) ),
    inference(cnf_transformation,[],[f484]) ).

cnf(c_354,plain,
    ( r1_tarski(X0,X1)
    | ~ m1_subset_1(X0,k1_zfmisc_1(X1)) ),
    inference(prop_impl_just,[status(thm)],[c_215]) ).

cnf(c_355,plain,
    ( ~ m1_subset_1(X0,k1_zfmisc_1(X1))
    | r1_tarski(X0,X1) ),
    inference(renaming,[status(thm)],[c_354]) ).

cnf(c_356,plain,
    ( ~ r1_tarski(X0,X1)
    | m1_subset_1(X0,k1_zfmisc_1(X1)) ),
    inference(prop_impl_just,[status(thm)],[c_214]) ).

cnf(c_372,plain,
    ( ~ r2_hidden(X0,X1)
    | ~ v1_xboole_0(X1) ),
    inference(prop_impl_just,[status(thm)],[c_219]) ).

cnf(c_698,plain,
    ( ~ r1_tarski(X0,X1)
    | ~ r2_hidden(X2,X0)
    | m1_subset_1(X2,X1) ),
    inference(bin_hyper_res,[status(thm)],[c_216,c_356]) ).

cnf(c_868,plain,
    ( ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(X1)))
    | ~ m1_subset_1(X2,u1_struct_0(X1))
    | ~ r2_hidden(X2,X0)
    | ~ l3_lattices(X1)
    | ~ v10_lattices(X1)
    | r1_tarski(k2_filter_0(X1,X2),k3_filter_0(X1,X0))
    | v3_struct_0(X1) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_204,c_372]) ).

cnf(c_3684,plain,
    ( X0 != X1
    | X2 != X3
    | ~ m1_subset_1(X0,k1_zfmisc_1(X2))
    | ~ r2_hidden(X4,X1)
    | m1_subset_1(X4,X3) ),
    inference(resolution_lifted,[status(thm)],[c_355,c_698]) ).

cnf(c_3685,plain,
    ( ~ m1_subset_1(X0,k1_zfmisc_1(X1))
    | ~ r2_hidden(X2,X0)
    | m1_subset_1(X2,X1) ),
    inference(unflattening,[status(thm)],[c_3684]) ).

cnf(c_3816,plain,
    ( ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(X1)))
    | ~ r2_hidden(X2,X0)
    | ~ l3_lattices(X1)
    | ~ v10_lattices(X1)
    | r1_tarski(k2_filter_0(X1,X2),k3_filter_0(X1,X0))
    | v3_struct_0(X1) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_868,c_3685]) ).

cnf(c_4828,plain,
    ( X0 != sK1
    | ~ l3_lattices(X0)
    | v3_struct_0(X0)
    | sP0(X0) ),
    inference(resolution_lifted,[status(thm)],[c_55,c_147]) ).

cnf(c_4829,plain,
    ( ~ l3_lattices(sK1)
    | v3_struct_0(sK1)
    | sP0(sK1) ),
    inference(unflattening,[status(thm)],[c_4828]) ).

cnf(c_13348,plain,
    X0 = X0,
    theory(equality) ).

cnf(c_13350,plain,
    ( X0 != X1
    | X2 != X1
    | X2 = X0 ),
    theory(equality) ).

cnf(c_13353,plain,
    ( X0 != X1
    | X2 != X3
    | ~ r1_tarski(X1,X3)
    | r1_tarski(X0,X2) ),
    theory(equality) ).

cnf(c_13354,plain,
    ( X0 != X1
    | X2 != X3
    | ~ r2_hidden(X1,X3)
    | r2_hidden(X0,X2) ),
    theory(equality) ).

cnf(c_16610,plain,
    ( ~ m1_subset_1(sK2,u1_struct_0(sK1))
    | ~ l3_lattices(sK1)
    | ~ v10_lattices(sK1)
    | k5_filter_2(sK1,sK2) = sK2
    | v3_struct_0(sK1) ),
    inference(instantiation,[status(thm)],[c_70]) ).

cnf(c_16615,plain,
    ( ~ m1_subset_1(sK3,k1_zfmisc_1(u1_struct_0(sK1)))
    | ~ l3_lattices(sK1)
    | ~ v10_lattices(sK1)
    | k7_filter_2(sK1,sK3) = sK3
    | v3_struct_0(sK1) ),
    inference(instantiation,[status(thm)],[c_71]) ).

cnf(c_16662,plain,
    ( ~ m1_subset_1(sK2,u1_struct_0(sK1))
    | ~ l3_lattices(sK1)
    | ~ v10_lattices(sK1)
    | m1_subset_1(k5_filter_2(sK1,sK2),u1_struct_0(k1_lattice2(sK1)))
    | v3_struct_0(sK1) ),
    inference(instantiation,[status(thm)],[c_84]) ).

cnf(c_16670,plain,
    ( ~ m1_subset_1(sK3,k1_zfmisc_1(u1_struct_0(sK1)))
    | ~ l3_lattices(sK1)
    | ~ v10_lattices(sK1)
    | m1_subset_1(k7_filter_2(sK1,sK3),k1_zfmisc_1(u1_struct_0(k1_lattice2(sK1))))
    | v3_struct_0(sK1) ),
    inference(instantiation,[status(thm)],[c_85]) ).

cnf(c_16800,plain,
    ( X0 != sK2
    | X1 != sK3
    | ~ r2_hidden(sK2,sK3)
    | r2_hidden(X0,X1) ),
    inference(instantiation,[status(thm)],[c_13354]) ).

cnf(c_16871,plain,
    ( ~ m1_subset_1(sK2,u1_struct_0(sK1))
    | ~ l3_lattices(sK1)
    | ~ v10_lattices(sK1)
    | k18_filter_2(sK1,sK2) = a_2_0_filter_2(sK1,sK2)
    | v3_struct_0(sK1) ),
    inference(instantiation,[status(thm)],[c_73]) ).

cnf(c_16964,plain,
    ( ~ m1_subset_1(sK2,u1_struct_0(sK1))
    | ~ l3_lattices(sK1)
    | ~ v10_lattices(sK1)
    | k2_filter_2(k1_lattice2(sK1),k5_filter_2(sK1,sK2)) = k18_filter_2(sK1,sK2)
    | v3_struct_0(sK1) ),
    inference(instantiation,[status(thm)],[c_209]) ).

cnf(c_17269,plain,
    ( ~ m1_subset_1(k5_filter_2(sK1,sK2),u1_struct_0(k1_lattice2(sK1)))
    | ~ l3_lattices(k1_lattice2(sK1))
    | ~ v10_lattices(k1_lattice2(sK1))
    | k2_filter_0(k1_lattice2(sK1),k5_filter_2(sK1,sK2)) = k2_filter_2(k1_lattice2(sK1),k5_filter_2(sK1,sK2))
    | v3_struct_0(k1_lattice2(sK1)) ),
    inference(instantiation,[status(thm)],[c_193]) ).

cnf(c_17301,plain,
    ( ~ m1_subset_1(k7_filter_2(sK1,sK3),k1_zfmisc_1(u1_struct_0(k1_lattice2(sK1))))
    | ~ l3_lattices(k1_lattice2(sK1))
    | ~ v10_lattices(k1_lattice2(sK1))
    | k3_filter_0(k1_lattice2(sK1),k7_filter_2(sK1,sK3)) = k3_filter_2(k1_lattice2(sK1),k7_filter_2(sK1,sK3))
    | v1_xboole_0(k7_filter_2(sK1,sK3))
    | v3_struct_0(k1_lattice2(sK1)) ),
    inference(instantiation,[status(thm)],[c_194]) ).

cnf(c_17464,plain,
    k19_filter_2(sK1,sK3) = k19_filter_2(sK1,sK3),
    inference(instantiation,[status(thm)],[c_13348]) ).

cnf(c_17466,plain,
    ( k19_filter_2(sK1,sK3) != X0
    | X1 != X0
    | k19_filter_2(sK1,sK3) = X1 ),
    inference(instantiation,[status(thm)],[c_13350]) ).

cnf(c_17501,plain,
    ( k5_filter_2(sK1,sK2) != sK2
    | X0 != sK3
    | ~ r2_hidden(sK2,sK3)
    | r2_hidden(k5_filter_2(sK1,sK2),X0) ),
    inference(instantiation,[status(thm)],[c_16800]) ).

cnf(c_19101,plain,
    ( ~ v1_xboole_0(k7_filter_2(sK1,sK3))
    | ~ l3_lattices(sK1)
    | ~ v10_lattices(sK1)
    | v1_xboole_0(sK3)
    | v3_struct_0(sK1) ),
    inference(superposition,[status(thm)],[c_51,c_116]) ).

cnf(c_19113,plain,
    ~ v1_xboole_0(k7_filter_2(sK1,sK3)),
    inference(forward_subsumption_resolution,[status(thm)],[c_19101,c_56,c_52,c_55,c_54]) ).

cnf(c_22019,plain,
    ( ~ l3_lattices(sK1)
    | ~ v10_lattices(sK1)
    | k7_filter_2(sK1,sK3) = sK3
    | v3_struct_0(sK1) ),
    inference(superposition,[status(thm)],[c_51,c_71]) ).

cnf(c_22030,plain,
    k7_filter_2(sK1,sK3) = sK3,
    inference(forward_subsumption_resolution,[status(thm)],[c_22019,c_56,c_55,c_54]) ).

cnf(c_22270,plain,
    ( ~ m1_subset_1(sK3,k1_zfmisc_1(u1_struct_0(sK1)))
    | ~ l3_lattices(sK1)
    | ~ v10_lattices(sK1)
    | m1_subset_1(sK3,k1_zfmisc_1(u1_struct_0(k1_lattice2(sK1))))
    | v3_struct_0(sK1) ),
    inference(superposition,[status(thm)],[c_22030,c_85]) ).

cnf(c_22279,plain,
    m1_subset_1(sK3,k1_zfmisc_1(u1_struct_0(k1_lattice2(sK1)))),
    inference(forward_subsumption_resolution,[status(thm)],[c_22270,c_56,c_55,c_54,c_51]) ).

cnf(c_22853,plain,
    ( ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK1)))
    | ~ l3_lattices(sK1)
    | ~ v10_lattices(sK1)
    | k3_filter_2(k1_lattice2(sK1),k7_filter_2(sK1,X0)) = k19_filter_2(sK1,X0)
    | v1_xboole_0(X0)
    | v1_xboole_0(sK3)
    | v3_struct_0(sK1) ),
    inference(superposition,[status(thm)],[c_22279,c_213]) ).

cnf(c_22854,plain,
    ( ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK1)))
    | k3_filter_2(k1_lattice2(sK1),k7_filter_2(sK1,X0)) = k19_filter_2(sK1,X0)
    | v1_xboole_0(X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_22853,c_56,c_52,c_55,c_54]) ).

cnf(c_23023,plain,
    ( ~ sP0(sK1)
    | v10_lattices(k1_lattice2(sK1)) ),
    inference(instantiation,[status(thm)],[c_138]) ).

cnf(c_23476,plain,
    ( k18_filter_2(sK1,sK2) != X0
    | X1 != X0
    | X1 = k18_filter_2(sK1,sK2) ),
    inference(instantiation,[status(thm)],[c_13350]) ).

cnf(c_23528,plain,
    ( k3_filter_2(k1_lattice2(sK1),k7_filter_2(sK1,sK3)) = k19_filter_2(sK1,sK3)
    | v1_xboole_0(sK3) ),
    inference(superposition,[status(thm)],[c_51,c_22854]) ).

cnf(c_23540,plain,
    k3_filter_2(k1_lattice2(sK1),k7_filter_2(sK1,sK3)) = k19_filter_2(sK1,sK3),
    inference(forward_subsumption_resolution,[status(thm)],[c_23528,c_52]) ).

cnf(c_24291,plain,
    ( k5_filter_2(sK1,sK2) != sK2
    | k7_filter_2(sK1,sK3) != sK3
    | ~ r2_hidden(sK2,sK3)
    | r2_hidden(k5_filter_2(sK1,sK2),k7_filter_2(sK1,sK3)) ),
    inference(instantiation,[status(thm)],[c_17501]) ).

cnf(c_24435,plain,
    ( ~ l3_lattices(sK1)
    | l3_lattices(k1_lattice2(sK1)) ),
    inference(instantiation,[status(thm)],[c_78]) ).

cnf(c_25044,plain,
    ( k19_filter_2(sK1,sK3) != k19_filter_2(sK1,sK3)
    | X0 != k19_filter_2(sK1,sK3)
    | k19_filter_2(sK1,sK3) = X0 ),
    inference(instantiation,[status(thm)],[c_17466]) ).

cnf(c_35093,plain,
    ( ~ v3_struct_0(k1_lattice2(sK1))
    | ~ sP0(sK1) ),
    inference(instantiation,[status(thm)],[c_146]) ).

cnf(c_38170,plain,
    ( k3_filter_2(k1_lattice2(sK1),k7_filter_2(sK1,sK3)) != k19_filter_2(sK1,sK3)
    | k19_filter_2(sK1,sK3) != k19_filter_2(sK1,sK3)
    | k19_filter_2(sK1,sK3) = k3_filter_2(k1_lattice2(sK1),k7_filter_2(sK1,sK3)) ),
    inference(instantiation,[status(thm)],[c_25044]) ).

cnf(c_39008,plain,
    ( k19_filter_2(sK1,sK3) != k3_filter_2(k1_lattice2(sK1),k7_filter_2(sK1,sK3))
    | X0 != k3_filter_2(k1_lattice2(sK1),k7_filter_2(sK1,sK3))
    | k19_filter_2(sK1,sK3) = X0 ),
    inference(instantiation,[status(thm)],[c_17466]) ).

cnf(c_43163,plain,
    ( k18_filter_2(sK1,sK2) != a_2_0_filter_2(sK1,sK2)
    | X0 != a_2_0_filter_2(sK1,sK2)
    | X0 = k18_filter_2(sK1,sK2) ),
    inference(instantiation,[status(thm)],[c_23476]) ).

cnf(c_50585,plain,
    ( k18_filter_2(sK1,sK2) != a_2_0_filter_2(sK1,sK2)
    | k18_filter_2(sK1,sK2) = k18_filter_2(sK1,sK2) ),
    inference(instantiation,[status(thm)],[c_43163]) ).

cnf(c_52734,plain,
    ( k3_filter_0(k1_lattice2(sK1),k7_filter_2(sK1,sK3)) != k3_filter_2(k1_lattice2(sK1),k7_filter_2(sK1,sK3))
    | k19_filter_2(sK1,sK3) != k3_filter_2(k1_lattice2(sK1),k7_filter_2(sK1,sK3))
    | k19_filter_2(sK1,sK3) = k3_filter_0(k1_lattice2(sK1),k7_filter_2(sK1,sK3)) ),
    inference(instantiation,[status(thm)],[c_39008]) ).

cnf(c_81083,plain,
    ( ~ m1_subset_1(k7_filter_2(sK1,sK3),k1_zfmisc_1(u1_struct_0(X0)))
    | ~ r2_hidden(k5_filter_2(sK1,sK2),k7_filter_2(sK1,sK3))
    | ~ l3_lattices(X0)
    | ~ v10_lattices(X0)
    | r1_tarski(k2_filter_0(X0,k5_filter_2(sK1,sK2)),k3_filter_0(X0,k7_filter_2(sK1,sK3)))
    | v3_struct_0(X0) ),
    inference(instantiation,[status(thm)],[c_3816]) ).

cnf(c_121076,plain,
    ( ~ m1_subset_1(k7_filter_2(sK1,sK3),k1_zfmisc_1(u1_struct_0(k1_lattice2(sK1))))
    | ~ r2_hidden(k5_filter_2(sK1,sK2),k7_filter_2(sK1,sK3))
    | ~ l3_lattices(k1_lattice2(sK1))
    | ~ v10_lattices(k1_lattice2(sK1))
    | r1_tarski(k2_filter_0(k1_lattice2(sK1),k5_filter_2(sK1,sK2)),k3_filter_0(k1_lattice2(sK1),k7_filter_2(sK1,sK3)))
    | v3_struct_0(k1_lattice2(sK1)) ),
    inference(instantiation,[status(thm)],[c_81083]) ).

cnf(c_184009,plain,
    ( k18_filter_2(sK1,sK2) != X0
    | k19_filter_2(sK1,sK3) != X1
    | ~ r1_tarski(X0,X1)
    | r1_tarski(k18_filter_2(sK1,sK2),k19_filter_2(sK1,sK3)) ),
    inference(instantiation,[status(thm)],[c_13353]) ).

cnf(c_184876,plain,
    ( k18_filter_2(sK1,sK2) != X0
    | X1 != X0
    | k18_filter_2(sK1,sK2) = X1 ),
    inference(instantiation,[status(thm)],[c_13350]) ).

cnf(c_188325,plain,
    ( k18_filter_2(sK1,sK2) != k18_filter_2(sK1,sK2)
    | X0 != k18_filter_2(sK1,sK2)
    | k18_filter_2(sK1,sK2) = X0 ),
    inference(instantiation,[status(thm)],[c_184876]) ).

cnf(c_193519,plain,
    ( k2_filter_2(k1_lattice2(sK1),k5_filter_2(sK1,sK2)) != k18_filter_2(sK1,sK2)
    | k18_filter_2(sK1,sK2) != k18_filter_2(sK1,sK2)
    | k18_filter_2(sK1,sK2) = k2_filter_2(k1_lattice2(sK1),k5_filter_2(sK1,sK2)) ),
    inference(instantiation,[status(thm)],[c_188325]) ).

cnf(c_193910,plain,
    ( k18_filter_2(sK1,sK2) != k2_filter_2(k1_lattice2(sK1),k5_filter_2(sK1,sK2))
    | X0 != k2_filter_2(k1_lattice2(sK1),k5_filter_2(sK1,sK2))
    | k18_filter_2(sK1,sK2) = X0 ),
    inference(instantiation,[status(thm)],[c_184876]) ).

cnf(c_198118,plain,
    ( k2_filter_0(k1_lattice2(sK1),k5_filter_2(sK1,sK2)) != k2_filter_2(k1_lattice2(sK1),k5_filter_2(sK1,sK2))
    | k18_filter_2(sK1,sK2) != k2_filter_2(k1_lattice2(sK1),k5_filter_2(sK1,sK2))
    | k18_filter_2(sK1,sK2) = k2_filter_0(k1_lattice2(sK1),k5_filter_2(sK1,sK2)) ),
    inference(instantiation,[status(thm)],[c_193910]) ).

cnf(c_199918,plain,
    ( k18_filter_2(sK1,sK2) != X0
    | k19_filter_2(sK1,sK3) != k3_filter_0(k1_lattice2(sK1),k7_filter_2(sK1,sK3))
    | ~ r1_tarski(X0,k3_filter_0(k1_lattice2(sK1),k7_filter_2(sK1,sK3)))
    | r1_tarski(k18_filter_2(sK1,sK2),k19_filter_2(sK1,sK3)) ),
    inference(instantiation,[status(thm)],[c_184009]) ).

cnf(c_280529,plain,
    ( k18_filter_2(sK1,sK2) != k2_filter_0(k1_lattice2(sK1),k5_filter_2(sK1,sK2))
    | k19_filter_2(sK1,sK3) != k3_filter_0(k1_lattice2(sK1),k7_filter_2(sK1,sK3))
    | ~ r1_tarski(k2_filter_0(k1_lattice2(sK1),k5_filter_2(sK1,sK2)),k3_filter_0(k1_lattice2(sK1),k7_filter_2(sK1,sK3)))
    | r1_tarski(k18_filter_2(sK1,sK2),k19_filter_2(sK1,sK3)) ),
    inference(instantiation,[status(thm)],[c_199918]) ).

cnf(c_280530,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_280529,c_198118,c_193519,c_121076,c_52734,c_50585,c_38170,c_35093,c_24435,c_24291,c_23540,c_23023,c_19113,c_17464,c_17301,c_17269,c_16964,c_16871,c_16670,c_16662,c_16615,c_16610,c_4829,c_49,c_51,c_53,c_50,c_56,c_54,c_55]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem  : LAT311+1 : TPTP v8.1.2. Released v3.4.0.
% 0.10/0.13  % Command  : run_iprover %s %d THM
% 0.14/0.34  % Computer : n009.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.34  % DateTime : Thu May  2 18:07:25 EDT 2024
% 0.14/0.34  % CPUTime  : 
% 0.20/0.47  Running first-order theorem proving
% 0.20/0.47  Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 184.50/25.27  % SZS status Started for theBenchmark.p
% 184.50/25.27  % SZS status Theorem for theBenchmark.p
% 184.50/25.27  
% 184.50/25.27  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 184.50/25.27  
% 184.50/25.27  ------  iProver source info
% 184.50/25.27  
% 184.50/25.27  git: date: 2024-05-02 19:28:25 +0000
% 184.50/25.27  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 184.50/25.27  git: non_committed_changes: false
% 184.50/25.27  
% 184.50/25.27  ------ Parsing...
% 184.50/25.27  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 184.50/25.27  
% 184.50/25.27  ------ Preprocessing... sup_sim: 0  sf_s  rm: 10 0s  sf_e  pe_s  pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe_e  sup_sim: 0  sf_s  rm: 10 0s  sf_e  pe_s  pe_e 
% 184.50/25.27  
% 184.50/25.27  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 184.50/25.27  
% 184.50/25.27  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 184.50/25.27  ------ Proving...
% 184.50/25.27  ------ Problem Properties 
% 184.50/25.27  
% 184.50/25.27  
% 184.50/25.27  clauses                                 154
% 184.50/25.27  conjectures                             8
% 184.50/25.27  EPR                                     45
% 184.50/25.27  Horn                                    98
% 184.50/25.27  unary                                   48
% 184.50/25.27  binary                                  36
% 184.50/25.27  lits                                    484
% 184.50/25.27  lits eq                                 27
% 184.50/25.27  fd_pure                                 0
% 184.50/25.27  fd_pseudo                               0
% 184.50/25.27  fd_cond                                 1
% 184.50/25.27  fd_pseudo_cond                          6
% 184.50/25.27  AC symbols                              0
% 184.50/25.27  
% 184.50/25.27  ------ Input Options Time Limit: Unbounded
% 184.50/25.27  
% 184.50/25.27  
% 184.50/25.27  ------ 
% 184.50/25.27  Current options:
% 184.50/25.27  ------ 
% 184.50/25.27  
% 184.50/25.27  
% 184.50/25.27  
% 184.50/25.27  
% 184.50/25.27  ------ Proving...
% 184.50/25.27  
% 184.50/25.27  
% 184.50/25.27  % SZS status Theorem for theBenchmark.p
% 184.50/25.27  
% 184.50/25.27  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 184.50/25.27  
% 184.50/25.28  
%------------------------------------------------------------------------------