TSTP Solution File: LAT296+1 by Beagle---0.9.51

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%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : LAT296+1 : TPTP v8.1.2. Released v3.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s

% Computer : n002.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 Aug 22 10:46:41 EDT 2023

% Result   : Theorem 25.82s 13.11s
% Output   : CNFRefutation 25.93s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   30
%            Number of leaves      :   81
% Syntax   : Number of formulae    :  214 (  65 unt;  69 typ;   0 def)
%            Number of atoms       :  500 (  77 equ)
%            Maximal formula atoms :   19 (   3 avg)
%            Number of connectives :  645 ( 290   ~; 279   |;  44   &)
%                                         (   2 <=>;  30  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   22 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   68 (  47   >;  21   *;   0   +;   0  <<)
%            Number of predicates  :   36 (  34 usr;   1 prp; 0-3 aty)
%            Number of functors    :   35 (  35 usr;  22 con; 0-3 aty)
%            Number of variables   :  155 (; 155   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ v1_partfun1 > v1_funct_2 > r2_lattices > m2_relset_1 > m1_relset_1 > v2_binop_1 > v1_binop_1 > r2_hidden > r1_tarski > m1_subset_1 > v9_lattices > v8_lattices > v7_lattices > v6_lattices > v5_lattices > v4_lattices > v3_struct_0 > v3_lattices > v2_funct_1 > v1_xboole_0 > v1_relat_1 > v1_funct_1 > v17_lattices > v16_lattices > v15_lattices > v14_lattices > v13_lattices > v12_lattices > v11_lattices > v10_lattices > l3_lattices > l2_lattices > l1_struct_0 > l1_lattices > g3_lattices > k7_lattices > k2_zfmisc_1 > #nlpp > u2_lattices > u1_struct_0 > u1_lattices > k1_zfmisc_1 > k1_xboole_0 > #skF_25 > #skF_11 > #skF_18 > #skF_15 > #skF_19 > #skF_7 > #skF_16 > #skF_26 > #skF_14 > #skF_5 > #skF_10 > #skF_6 > #skF_13 > #skF_2 > #skF_3 > #skF_1 > #skF_21 > #skF_8 > #skF_4 > #skF_17 > #skF_22 > #skF_24 > #skF_27 > #skF_23 > #skF_9 > #skF_12 > #skF_20

%Foreground sorts:

%Background operators:

%Foreground operators:
tff(l3_lattices,type,
    l3_lattices: $i > $o ).

tff('#skF_25',type,
    '#skF_25': $i > $i ).

tff('#skF_11',type,
    '#skF_11': ( $i * $i ) > $i ).

tff(v12_lattices,type,
    v12_lattices: $i > $o ).

tff(m2_relset_1,type,
    m2_relset_1: ( $i * $i * $i ) > $o ).

tff(l2_lattices,type,
    l2_lattices: $i > $o ).

tff(v1_funct_1,type,
    v1_funct_1: $i > $o ).

tff(v2_funct_1,type,
    v2_funct_1: $i > $o ).

tff('#skF_18',type,
    '#skF_18': $i ).

tff(r2_hidden,type,
    r2_hidden: ( $i * $i ) > $o ).

tff('#skF_15',type,
    '#skF_15': $i ).

tff(v1_partfun1,type,
    v1_partfun1: ( $i * $i * $i ) > $o ).

tff(k1_xboole_0,type,
    k1_xboole_0: $i ).

tff(l1_lattices,type,
    l1_lattices: $i > $o ).

tff('#skF_19',type,
    '#skF_19': $i ).

tff(r2_lattices,type,
    r2_lattices: ( $i * $i * $i ) > $o ).

tff('#skF_7',type,
    '#skF_7': $i ).

tff(r1_tarski,type,
    r1_tarski: ( $i * $i ) > $o ).

tff(m1_relset_1,type,
    m1_relset_1: ( $i * $i * $i ) > $o ).

tff(v17_lattices,type,
    v17_lattices: $i > $o ).

tff('#skF_16',type,
    '#skF_16': $i ).

tff('#skF_26',type,
    '#skF_26': $i ).

tff('#skF_14',type,
    '#skF_14': $i ).

tff('#skF_5',type,
    '#skF_5': $i ).

tff(v1_funct_2,type,
    v1_funct_2: ( $i * $i * $i ) > $o ).

tff(v4_lattices,type,
    v4_lattices: $i > $o ).

tff('#skF_10',type,
    '#skF_10': $i > $i ).

tff('#skF_6',type,
    '#skF_6': $i ).

tff('#skF_13',type,
    '#skF_13': $i ).

tff(v6_lattices,type,
    v6_lattices: $i > $o ).

tff('#skF_2',type,
    '#skF_2': $i ).

tff(u2_lattices,type,
    u2_lattices: $i > $i ).

tff(v9_lattices,type,
    v9_lattices: $i > $o ).

tff('#skF_3',type,
    '#skF_3': $i ).

tff('#skF_1',type,
    '#skF_1': $i ).

tff(u1_lattices,type,
    u1_lattices: $i > $i ).

tff(g3_lattices,type,
    g3_lattices: ( $i * $i * $i ) > $i ).

tff(v5_lattices,type,
    v5_lattices: $i > $o ).

tff('#skF_21',type,
    '#skF_21': $i ).

tff(v10_lattices,type,
    v10_lattices: $i > $o ).

tff(k1_zfmisc_1,type,
    k1_zfmisc_1: $i > $i ).

tff(l1_struct_0,type,
    l1_struct_0: $i > $o ).

tff('#skF_8',type,
    '#skF_8': $i ).

tff(v1_binop_1,type,
    v1_binop_1: ( $i * $i ) > $o ).

tff(v2_binop_1,type,
    v2_binop_1: ( $i * $i ) > $o ).

tff(v14_lattices,type,
    v14_lattices: $i > $o ).

tff(v1_relat_1,type,
    v1_relat_1: $i > $o ).

tff(k2_zfmisc_1,type,
    k2_zfmisc_1: ( $i * $i ) > $i ).

tff(v13_lattices,type,
    v13_lattices: $i > $o ).

tff('#skF_4',type,
    '#skF_4': $i ).

tff(v11_lattices,type,
    v11_lattices: $i > $o ).

tff('#skF_17',type,
    '#skF_17': $i > $i ).

tff('#skF_22',type,
    '#skF_22': $i ).

tff(v8_lattices,type,
    v8_lattices: $i > $o ).

tff('#skF_24',type,
    '#skF_24': $i ).

tff('#skF_27',type,
    '#skF_27': $i ).

tff('#skF_23',type,
    '#skF_23': $i ).

tff(v3_lattices,type,
    v3_lattices: $i > $o ).

tff(k7_lattices,type,
    k7_lattices: ( $i * $i ) > $i ).

tff(u1_struct_0,type,
    u1_struct_0: $i > $i ).

tff(v16_lattices,type,
    v16_lattices: $i > $o ).

tff(v1_xboole_0,type,
    v1_xboole_0: $i > $o ).

tff('#skF_9',type,
    '#skF_9': ( $i * $i ) > $i ).

tff('#skF_12',type,
    '#skF_12': $i ).

tff(v15_lattices,type,
    v15_lattices: $i > $o ).

tff('#skF_20',type,
    '#skF_20': $i > $i ).

tff(v3_struct_0,type,
    v3_struct_0: $i > $o ).

tff(m1_subset_1,type,
    m1_subset_1: ( $i * $i ) > $o ).

tff(v7_lattices,type,
    v7_lattices: $i > $o ).

tff(f_61,negated_conjecture,
    ~ ! [A] :
        ( ( ~ v3_struct_0(A)
          & v10_lattices(A)
          & v17_lattices(A)
          & l3_lattices(A) )
       => ! [B] :
            ( ( ~ v3_struct_0(B)
              & v10_lattices(B)
              & v17_lattices(B)
              & l3_lattices(B) )
           => ( ( g3_lattices(u1_struct_0(A),u2_lattices(A),u1_lattices(A)) = g3_lattices(u1_struct_0(B),u2_lattices(B),u1_lattices(B)) )
             => ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(B))
                     => ( ( C = D )
                       => ( k7_lattices(A,C) = k7_lattices(B,D) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_filter_2) ).

tff(f_294,axiom,
    ! [A] :
      ( l3_lattices(A)
     => ( l1_lattices(A)
        & l2_lattices(A) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l3_lattices) ).

tff(f_314,axiom,
    ! [A] :
      ( l2_lattices(A)
     => ( v1_funct_1(u2_lattices(A))
        & v1_funct_2(u2_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
        & m2_relset_1(u2_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u2_lattices) ).

tff(f_461,axiom,
    ! [A,B,C] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k2_zfmisc_1(A,A),A)
        & m1_relset_1(B,k2_zfmisc_1(A,A),A)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(A,A),A)
        & m1_relset_1(C,k2_zfmisc_1(A,A),A) )
     => ! [D,E,F] :
          ( ( g3_lattices(A,B,C) = g3_lattices(D,E,F) )
         => ( ( A = D )
            & ( B = E )
            & ( C = F ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',free_g3_lattices) ).

tff(f_306,axiom,
    ! [A] :
      ( l1_lattices(A)
     => ( v1_funct_1(u1_lattices(A))
        & v1_funct_2(u1_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
        & m2_relset_1(u1_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u1_lattices) ).

tff(f_666,axiom,
    ! [A,B,C] :
      ( m2_relset_1(C,A,B)
    <=> m1_relset_1(C,A,B) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).

tff(f_67,axiom,
    ! [A] :
      ( l3_lattices(A)
     => ( v3_lattices(A)
       => ( A = g3_lattices(u1_struct_0(A),u2_lattices(A),u1_lattices(A)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',abstractness_v3_lattices) ).

tff(f_280,axiom,
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l3_lattices(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => m1_subset_1(k7_lattices(A,B),u1_struct_0(A)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_lattices) ).

tff(f_184,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/sandbox/benchmark/theBenchmark.p',cc5_lattices) ).

tff(f_164,axiom,
    ! [A] :
      ( l3_lattices(A)
     => ( ( ~ v3_struct_0(A)
          & v15_lattices(A) )
       => ( ~ v3_struct_0(A)
          & v13_lattices(A)
          & v14_lattices(A) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc4_lattices) ).

tff(f_254,axiom,
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ( ( ~ v3_struct_0(A)
              & v10_lattices(A)
              & v11_lattices(A)
              & v16_lattices(A)
              & l3_lattices(A) )
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ( ( C = k7_lattices(A,B) )
                <=> r2_lattices(A,C,B) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d21_lattices) ).

tff(f_713,axiom,
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v15_lattices(A)
        & v16_lattices(A)
        & l3_lattices(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v10_lattices(B)
            & v15_lattices(B)
            & v16_lattices(B)
            & l3_lattices(B) )
         => ( ( g3_lattices(u1_struct_0(A),u2_lattices(A),u1_lattices(A)) = g3_lattices(u1_struct_0(B),u2_lattices(B),u1_lattices(B)) )
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(B))
                       => ! [F] :
                            ( m1_subset_1(F,u1_struct_0(B))
                           => ( ( ( C = E )
                                & ( D = F )
                                & r2_lattices(A,C,D) )
                             => r2_lattices(B,E,F) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_filter_2) ).

tff(c_4,plain,
    '#skF_3' = '#skF_4',
    inference(cnfTransformation,[status(thm)],[f_61]) ).

tff(c_2,plain,
    k7_lattices('#skF_2','#skF_4') != k7_lattices('#skF_1','#skF_3'),
    inference(cnfTransformation,[status(thm)],[f_61]) ).

tff(c_428,plain,
    k7_lattices('#skF_2','#skF_4') != k7_lattices('#skF_1','#skF_4'),
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_2]) ).

tff(c_8,plain,
    m1_subset_1('#skF_3',u1_struct_0('#skF_1')),
    inference(cnfTransformation,[status(thm)],[f_61]) ).

tff(c_427,plain,
    m1_subset_1('#skF_4',u1_struct_0('#skF_1')),
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_8]) ).

tff(c_18,plain,
    ~ v3_struct_0('#skF_2'),
    inference(cnfTransformation,[status(thm)],[f_61]) ).

tff(c_12,plain,
    l3_lattices('#skF_2'),
    inference(cnfTransformation,[status(thm)],[f_61]) ).

tff(c_20,plain,
    l3_lattices('#skF_1'),
    inference(cnfTransformation,[status(thm)],[f_61]) ).

tff(c_481,plain,
    ! [A_170] :
      ( l2_lattices(A_170)
      | ~ l3_lattices(A_170) ),
    inference(cnfTransformation,[status(thm)],[f_294]) ).

tff(c_518,plain,
    l2_lattices('#skF_1'),
    inference(resolution,[status(thm)],[c_20,c_481]) ).

tff(c_148,plain,
    ! [A_46] :
      ( v1_funct_1(u2_lattices(A_46))
      | ~ l2_lattices(A_46) ),
    inference(cnfTransformation,[status(thm)],[f_314]) ).

tff(c_10,plain,
    g3_lattices(u1_struct_0('#skF_2'),u2_lattices('#skF_2'),u1_lattices('#skF_2')) = g3_lattices(u1_struct_0('#skF_1'),u2_lattices('#skF_1'),u1_lattices('#skF_1')),
    inference(cnfTransformation,[status(thm)],[f_61]) ).

tff(c_2918,plain,
    ! [E_521,B_522,A_519,F_518,C_523,D_520] :
      ( ( E_521 = B_522 )
      | ( g3_lattices(D_520,E_521,F_518) != g3_lattices(A_519,B_522,C_523) )
      | ~ m1_relset_1(C_523,k2_zfmisc_1(A_519,A_519),A_519)
      | ~ v1_funct_2(C_523,k2_zfmisc_1(A_519,A_519),A_519)
      | ~ v1_funct_1(C_523)
      | ~ m1_relset_1(B_522,k2_zfmisc_1(A_519,A_519),A_519)
      | ~ v1_funct_2(B_522,k2_zfmisc_1(A_519,A_519),A_519)
      | ~ v1_funct_1(B_522) ),
    inference(cnfTransformation,[status(thm)],[f_461]) ).

tff(c_2924,plain,
    ! [B_522,A_519,C_523] :
      ( ( u2_lattices('#skF_2') = B_522 )
      | ( g3_lattices(u1_struct_0('#skF_1'),u2_lattices('#skF_1'),u1_lattices('#skF_1')) != g3_lattices(A_519,B_522,C_523) )
      | ~ m1_relset_1(C_523,k2_zfmisc_1(A_519,A_519),A_519)
      | ~ v1_funct_2(C_523,k2_zfmisc_1(A_519,A_519),A_519)
      | ~ v1_funct_1(C_523)
      | ~ m1_relset_1(B_522,k2_zfmisc_1(A_519,A_519),A_519)
      | ~ v1_funct_2(B_522,k2_zfmisc_1(A_519,A_519),A_519)
      | ~ v1_funct_1(B_522) ),
    inference(superposition,[status(thm),theory(equality)],[c_10,c_2918]) ).

tff(c_2991,plain,
    ( ( u2_lattices('#skF_2') = u2_lattices('#skF_1') )
    | ~ m1_relset_1(u1_lattices('#skF_1'),k2_zfmisc_1(u1_struct_0('#skF_1'),u1_struct_0('#skF_1')),u1_struct_0('#skF_1'))
    | ~ v1_funct_2(u1_lattices('#skF_1'),k2_zfmisc_1(u1_struct_0('#skF_1'),u1_struct_0('#skF_1')),u1_struct_0('#skF_1'))
    | ~ v1_funct_1(u1_lattices('#skF_1'))
    | ~ m1_relset_1(u2_lattices('#skF_1'),k2_zfmisc_1(u1_struct_0('#skF_1'),u1_struct_0('#skF_1')),u1_struct_0('#skF_1'))
    | ~ v1_funct_2(u2_lattices('#skF_1'),k2_zfmisc_1(u1_struct_0('#skF_1'),u1_struct_0('#skF_1')),u1_struct_0('#skF_1'))
    | ~ v1_funct_1(u2_lattices('#skF_1')) ),
    inference(reflexivity,[status(thm),theory(equality)],[c_2924]) ).

tff(c_3945,plain,
    ~ v1_funct_1(u2_lattices('#skF_1')),
    inference(splitLeft,[status(thm)],[c_2991]) ).

tff(c_3948,plain,
    ~ l2_lattices('#skF_1'),
    inference(resolution,[status(thm)],[c_148,c_3945]) ).

tff(c_3952,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_518,c_3948]) ).

tff(c_3954,plain,
    v1_funct_1(u2_lattices('#skF_1')),
    inference(splitRight,[status(thm)],[c_2991]) ).

tff(c_440,plain,
    ! [A_169] :
      ( l1_lattices(A_169)
      | ~ l3_lattices(A_169) ),
    inference(cnfTransformation,[status(thm)],[f_294]) ).

tff(c_479,plain,
    l1_lattices('#skF_2'),
    inference(resolution,[status(thm)],[c_12,c_440]) ).

tff(c_138,plain,
    ! [A_45] :
      ( v1_funct_2(u1_lattices(A_45),k2_zfmisc_1(u1_struct_0(A_45),u1_struct_0(A_45)),u1_struct_0(A_45))
      | ~ l1_lattices(A_45) ),
    inference(cnfTransformation,[status(thm)],[f_306]) ).

tff(c_140,plain,
    ! [A_45] :
      ( v1_funct_1(u1_lattices(A_45))
      | ~ l1_lattices(A_45) ),
    inference(cnfTransformation,[status(thm)],[f_306]) ).

tff(c_520,plain,
    l2_lattices('#skF_2'),
    inference(resolution,[status(thm)],[c_12,c_481]) ).

tff(c_2004,plain,
    ! [A_358] :
      ( m2_relset_1(u2_lattices(A_358),k2_zfmisc_1(u1_struct_0(A_358),u1_struct_0(A_358)),u1_struct_0(A_358))
      | ~ l2_lattices(A_358) ),
    inference(cnfTransformation,[status(thm)],[f_314]) ).

tff(c_402,plain,
    ! [C_83,A_81,B_82] :
      ( m1_relset_1(C_83,A_81,B_82)
      | ~ m2_relset_1(C_83,A_81,B_82) ),
    inference(cnfTransformation,[status(thm)],[f_666]) ).

tff(c_2012,plain,
    ! [A_358] :
      ( m1_relset_1(u2_lattices(A_358),k2_zfmisc_1(u1_struct_0(A_358),u1_struct_0(A_358)),u1_struct_0(A_358))
      | ~ l2_lattices(A_358) ),
    inference(resolution,[status(thm)],[c_2004,c_402]) ).

tff(c_2687,plain,
    ! [C_471,E_469,B_470,F_466,D_468,A_467] :
      ( ( D_468 = A_467 )
      | ( g3_lattices(D_468,E_469,F_466) != g3_lattices(A_467,B_470,C_471) )
      | ~ m1_relset_1(C_471,k2_zfmisc_1(A_467,A_467),A_467)
      | ~ v1_funct_2(C_471,k2_zfmisc_1(A_467,A_467),A_467)
      | ~ v1_funct_1(C_471)
      | ~ m1_relset_1(B_470,k2_zfmisc_1(A_467,A_467),A_467)
      | ~ v1_funct_2(B_470,k2_zfmisc_1(A_467,A_467),A_467)
      | ~ v1_funct_1(B_470) ),
    inference(cnfTransformation,[status(thm)],[f_461]) ).

tff(c_2695,plain,
    ! [D_468,E_469,F_466] :
      ( ( u1_struct_0('#skF_2') = D_468 )
      | ( g3_lattices(u1_struct_0('#skF_1'),u2_lattices('#skF_1'),u1_lattices('#skF_1')) != g3_lattices(D_468,E_469,F_466) )
      | ~ m1_relset_1(u1_lattices('#skF_2'),k2_zfmisc_1(u1_struct_0('#skF_2'),u1_struct_0('#skF_2')),u1_struct_0('#skF_2'))
      | ~ v1_funct_2(u1_lattices('#skF_2'),k2_zfmisc_1(u1_struct_0('#skF_2'),u1_struct_0('#skF_2')),u1_struct_0('#skF_2'))
      | ~ v1_funct_1(u1_lattices('#skF_2'))
      | ~ m1_relset_1(u2_lattices('#skF_2'),k2_zfmisc_1(u1_struct_0('#skF_2'),u1_struct_0('#skF_2')),u1_struct_0('#skF_2'))
      | ~ v1_funct_2(u2_lattices('#skF_2'),k2_zfmisc_1(u1_struct_0('#skF_2'),u1_struct_0('#skF_2')),u1_struct_0('#skF_2'))
      | ~ v1_funct_1(u2_lattices('#skF_2')) ),
    inference(superposition,[status(thm),theory(equality)],[c_10,c_2687]) ).

tff(c_3142,plain,
    ~ v1_funct_1(u2_lattices('#skF_2')),
    inference(splitLeft,[status(thm)],[c_2695]) ).

tff(c_3145,plain,
    ~ l2_lattices('#skF_2'),
    inference(resolution,[status(thm)],[c_148,c_3142]) ).

tff(c_3149,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_520,c_3145]) ).

tff(c_3151,plain,
    v1_funct_1(u2_lattices('#skF_2')),
    inference(splitRight,[status(thm)],[c_2695]) ).

tff(c_146,plain,
    ! [A_46] :
      ( v1_funct_2(u2_lattices(A_46),k2_zfmisc_1(u1_struct_0(A_46),u1_struct_0(A_46)),u1_struct_0(A_46))
      | ~ l2_lattices(A_46) ),
    inference(cnfTransformation,[status(thm)],[f_314]) ).

tff(c_2841,plain,
    ! [B_491,D_489,E_490,A_488,C_492,F_487] :
      ( ( F_487 = C_492 )
      | ( g3_lattices(D_489,E_490,F_487) != g3_lattices(A_488,B_491,C_492) )
      | ~ m1_relset_1(C_492,k2_zfmisc_1(A_488,A_488),A_488)
      | ~ v1_funct_2(C_492,k2_zfmisc_1(A_488,A_488),A_488)
      | ~ v1_funct_1(C_492)
      | ~ m1_relset_1(B_491,k2_zfmisc_1(A_488,A_488),A_488)
      | ~ v1_funct_2(B_491,k2_zfmisc_1(A_488,A_488),A_488)
      | ~ v1_funct_1(B_491) ),
    inference(cnfTransformation,[status(thm)],[f_461]) ).

tff(c_2849,plain,
    ! [F_487,D_489,E_490] :
      ( ( u1_lattices('#skF_2') = F_487 )
      | ( g3_lattices(u1_struct_0('#skF_1'),u2_lattices('#skF_1'),u1_lattices('#skF_1')) != g3_lattices(D_489,E_490,F_487) )
      | ~ m1_relset_1(u1_lattices('#skF_2'),k2_zfmisc_1(u1_struct_0('#skF_2'),u1_struct_0('#skF_2')),u1_struct_0('#skF_2'))
      | ~ v1_funct_2(u1_lattices('#skF_2'),k2_zfmisc_1(u1_struct_0('#skF_2'),u1_struct_0('#skF_2')),u1_struct_0('#skF_2'))
      | ~ v1_funct_1(u1_lattices('#skF_2'))
      | ~ m1_relset_1(u2_lattices('#skF_2'),k2_zfmisc_1(u1_struct_0('#skF_2'),u1_struct_0('#skF_2')),u1_struct_0('#skF_2'))
      | ~ v1_funct_2(u2_lattices('#skF_2'),k2_zfmisc_1(u1_struct_0('#skF_2'),u1_struct_0('#skF_2')),u1_struct_0('#skF_2'))
      | ~ v1_funct_1(u2_lattices('#skF_2')) ),
    inference(superposition,[status(thm),theory(equality)],[c_10,c_2841]) ).

tff(c_3648,plain,
    ! [F_487,D_489,E_490] :
      ( ( u1_lattices('#skF_2') = F_487 )
      | ( g3_lattices(u1_struct_0('#skF_1'),u2_lattices('#skF_1'),u1_lattices('#skF_1')) != g3_lattices(D_489,E_490,F_487) )
      | ~ m1_relset_1(u1_lattices('#skF_2'),k2_zfmisc_1(u1_struct_0('#skF_2'),u1_struct_0('#skF_2')),u1_struct_0('#skF_2'))
      | ~ v1_funct_2(u1_lattices('#skF_2'),k2_zfmisc_1(u1_struct_0('#skF_2'),u1_struct_0('#skF_2')),u1_struct_0('#skF_2'))
      | ~ v1_funct_1(u1_lattices('#skF_2'))
      | ~ m1_relset_1(u2_lattices('#skF_2'),k2_zfmisc_1(u1_struct_0('#skF_2'),u1_struct_0('#skF_2')),u1_struct_0('#skF_2'))
      | ~ v1_funct_2(u2_lattices('#skF_2'),k2_zfmisc_1(u1_struct_0('#skF_2'),u1_struct_0('#skF_2')),u1_struct_0('#skF_2')) ),
    inference(demodulation,[status(thm),theory(equality)],[c_3151,c_2849]) ).

tff(c_3649,plain,
    ~ v1_funct_2(u2_lattices('#skF_2'),k2_zfmisc_1(u1_struct_0('#skF_2'),u1_struct_0('#skF_2')),u1_struct_0('#skF_2')),
    inference(splitLeft,[status(thm)],[c_3648]) ).

tff(c_3652,plain,
    ~ l2_lattices('#skF_2'),
    inference(resolution,[status(thm)],[c_146,c_3649]) ).

tff(c_3656,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_520,c_3652]) ).

tff(c_3658,plain,
    v1_funct_2(u2_lattices('#skF_2'),k2_zfmisc_1(u1_struct_0('#skF_2'),u1_struct_0('#skF_2')),u1_struct_0('#skF_2')),
    inference(splitRight,[status(thm)],[c_3648]) ).

tff(c_2926,plain,
    ! [E_521,D_520,F_518] :
      ( ( u2_lattices('#skF_2') = E_521 )
      | ( g3_lattices(u1_struct_0('#skF_1'),u2_lattices('#skF_1'),u1_lattices('#skF_1')) != g3_lattices(D_520,E_521,F_518) )
      | ~ m1_relset_1(u1_lattices('#skF_2'),k2_zfmisc_1(u1_struct_0('#skF_2'),u1_struct_0('#skF_2')),u1_struct_0('#skF_2'))
      | ~ v1_funct_2(u1_lattices('#skF_2'),k2_zfmisc_1(u1_struct_0('#skF_2'),u1_struct_0('#skF_2')),u1_struct_0('#skF_2'))
      | ~ v1_funct_1(u1_lattices('#skF_2'))
      | ~ m1_relset_1(u2_lattices('#skF_2'),k2_zfmisc_1(u1_struct_0('#skF_2'),u1_struct_0('#skF_2')),u1_struct_0('#skF_2'))
      | ~ v1_funct_2(u2_lattices('#skF_2'),k2_zfmisc_1(u1_struct_0('#skF_2'),u1_struct_0('#skF_2')),u1_struct_0('#skF_2'))
      | ~ v1_funct_1(u2_lattices('#skF_2')) ),
    inference(superposition,[status(thm),theory(equality)],[c_10,c_2918]) ).

tff(c_3865,plain,
    ! [E_521,D_520,F_518] :
      ( ( u2_lattices('#skF_2') = E_521 )
      | ( g3_lattices(u1_struct_0('#skF_1'),u2_lattices('#skF_1'),u1_lattices('#skF_1')) != g3_lattices(D_520,E_521,F_518) )
      | ~ m1_relset_1(u1_lattices('#skF_2'),k2_zfmisc_1(u1_struct_0('#skF_2'),u1_struct_0('#skF_2')),u1_struct_0('#skF_2'))
      | ~ v1_funct_2(u1_lattices('#skF_2'),k2_zfmisc_1(u1_struct_0('#skF_2'),u1_struct_0('#skF_2')),u1_struct_0('#skF_2'))
      | ~ v1_funct_1(u1_lattices('#skF_2'))
      | ~ m1_relset_1(u2_lattices('#skF_2'),k2_zfmisc_1(u1_struct_0('#skF_2'),u1_struct_0('#skF_2')),u1_struct_0('#skF_2')) ),
    inference(demodulation,[status(thm),theory(equality)],[c_3151,c_3658,c_2926]) ).

tff(c_3866,plain,
    ~ m1_relset_1(u2_lattices('#skF_2'),k2_zfmisc_1(u1_struct_0('#skF_2'),u1_struct_0('#skF_2')),u1_struct_0('#skF_2')),
    inference(splitLeft,[status(thm)],[c_3865]) ).

tff(c_3869,plain,
    ~ l2_lattices('#skF_2'),
    inference(resolution,[status(thm)],[c_2012,c_3866]) ).

tff(c_3873,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_520,c_3869]) ).

tff(c_3875,plain,
    m1_relset_1(u2_lattices('#skF_2'),k2_zfmisc_1(u1_struct_0('#skF_2'),u1_struct_0('#skF_2')),u1_struct_0('#skF_2')),
    inference(splitRight,[status(thm)],[c_3865]) ).

tff(c_1808,plain,
    ! [A_334] :
      ( m2_relset_1(u1_lattices(A_334),k2_zfmisc_1(u1_struct_0(A_334),u1_struct_0(A_334)),u1_struct_0(A_334))
      | ~ l1_lattices(A_334) ),
    inference(cnfTransformation,[status(thm)],[f_306]) ).

tff(c_1816,plain,
    ! [A_334] :
      ( m1_relset_1(u1_lattices(A_334),k2_zfmisc_1(u1_struct_0(A_334),u1_struct_0(A_334)),u1_struct_0(A_334))
      | ~ l1_lattices(A_334) ),
    inference(resolution,[status(thm)],[c_1808,c_402]) ).

tff(c_3874,plain,
    ! [E_521,D_520,F_518] :
      ( ~ v1_funct_1(u1_lattices('#skF_2'))
      | ~ v1_funct_2(u1_lattices('#skF_2'),k2_zfmisc_1(u1_struct_0('#skF_2'),u1_struct_0('#skF_2')),u1_struct_0('#skF_2'))
      | ~ m1_relset_1(u1_lattices('#skF_2'),k2_zfmisc_1(u1_struct_0('#skF_2'),u1_struct_0('#skF_2')),u1_struct_0('#skF_2'))
      | ( u2_lattices('#skF_2') = E_521 )
      | ( g3_lattices(u1_struct_0('#skF_1'),u2_lattices('#skF_1'),u1_lattices('#skF_1')) != g3_lattices(D_520,E_521,F_518) ) ),
    inference(splitRight,[status(thm)],[c_3865]) ).

tff(c_3880,plain,
    ~ m1_relset_1(u1_lattices('#skF_2'),k2_zfmisc_1(u1_struct_0('#skF_2'),u1_struct_0('#skF_2')),u1_struct_0('#skF_2')),
    inference(splitLeft,[status(thm)],[c_3874]) ).

tff(c_3883,plain,
    ~ l1_lattices('#skF_2'),
    inference(resolution,[status(thm)],[c_1816,c_3880]) ).

tff(c_3887,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_479,c_3883]) ).

tff(c_3889,plain,
    m1_relset_1(u1_lattices('#skF_2'),k2_zfmisc_1(u1_struct_0('#skF_2'),u1_struct_0('#skF_2')),u1_struct_0('#skF_2')),
    inference(splitRight,[status(thm)],[c_3874]) ).

tff(c_28,plain,
    ! [A_12] :
      ( ( g3_lattices(u1_struct_0(A_12),u2_lattices(A_12),u1_lattices(A_12)) = A_12 )
      | ~ v3_lattices(A_12)
      | ~ l3_lattices(A_12) ),
    inference(cnfTransformation,[status(thm)],[f_67]) ).

tff(c_3686,plain,
    ! [A_566,C_567,A_568,B_569] :
      ( ( u1_lattices(A_566) = C_567 )
      | ( g3_lattices(A_568,B_569,C_567) != A_566 )
      | ~ m1_relset_1(C_567,k2_zfmisc_1(A_568,A_568),A_568)
      | ~ v1_funct_2(C_567,k2_zfmisc_1(A_568,A_568),A_568)
      | ~ v1_funct_1(C_567)
      | ~ m1_relset_1(B_569,k2_zfmisc_1(A_568,A_568),A_568)
      | ~ v1_funct_2(B_569,k2_zfmisc_1(A_568,A_568),A_568)
      | ~ v1_funct_1(B_569)
      | ~ v3_lattices(A_566)
      | ~ l3_lattices(A_566) ),
    inference(superposition,[status(thm),theory(equality)],[c_28,c_2841]) ).

tff(c_3690,plain,
    ! [A_566] :
      ( ( u1_lattices(A_566) = u1_lattices('#skF_2') )
      | ( g3_lattices(u1_struct_0('#skF_1'),u2_lattices('#skF_1'),u1_lattices('#skF_1')) != A_566 )
      | ~ m1_relset_1(u1_lattices('#skF_2'),k2_zfmisc_1(u1_struct_0('#skF_2'),u1_struct_0('#skF_2')),u1_struct_0('#skF_2'))
      | ~ v1_funct_2(u1_lattices('#skF_2'),k2_zfmisc_1(u1_struct_0('#skF_2'),u1_struct_0('#skF_2')),u1_struct_0('#skF_2'))
      | ~ v1_funct_1(u1_lattices('#skF_2'))
      | ~ m1_relset_1(u2_lattices('#skF_2'),k2_zfmisc_1(u1_struct_0('#skF_2'),u1_struct_0('#skF_2')),u1_struct_0('#skF_2'))
      | ~ v1_funct_2(u2_lattices('#skF_2'),k2_zfmisc_1(u1_struct_0('#skF_2'),u1_struct_0('#skF_2')),u1_struct_0('#skF_2'))
      | ~ v1_funct_1(u2_lattices('#skF_2'))
      | ~ v3_lattices(A_566)
      | ~ l3_lattices(A_566) ),
    inference(superposition,[status(thm),theory(equality)],[c_10,c_3686]) ).

tff(c_3694,plain,
    ! [A_566] :
      ( ( u1_lattices(A_566) = u1_lattices('#skF_2') )
      | ( g3_lattices(u1_struct_0('#skF_1'),u2_lattices('#skF_1'),u1_lattices('#skF_1')) != A_566 )
      | ~ m1_relset_1(u1_lattices('#skF_2'),k2_zfmisc_1(u1_struct_0('#skF_2'),u1_struct_0('#skF_2')),u1_struct_0('#skF_2'))
      | ~ v1_funct_2(u1_lattices('#skF_2'),k2_zfmisc_1(u1_struct_0('#skF_2'),u1_struct_0('#skF_2')),u1_struct_0('#skF_2'))
      | ~ v1_funct_1(u1_lattices('#skF_2'))
      | ~ m1_relset_1(u2_lattices('#skF_2'),k2_zfmisc_1(u1_struct_0('#skF_2'),u1_struct_0('#skF_2')),u1_struct_0('#skF_2'))
      | ~ v3_lattices(A_566)
      | ~ l3_lattices(A_566) ),
    inference(demodulation,[status(thm),theory(equality)],[c_3151,c_3658,c_3690]) ).

tff(c_3895,plain,
    ! [A_566] :
      ( ( u1_lattices(A_566) = u1_lattices('#skF_2') )
      | ( g3_lattices(u1_struct_0('#skF_1'),u2_lattices('#skF_1'),u1_lattices('#skF_1')) != A_566 )
      | ~ v1_funct_2(u1_lattices('#skF_2'),k2_zfmisc_1(u1_struct_0('#skF_2'),u1_struct_0('#skF_2')),u1_struct_0('#skF_2'))
      | ~ v1_funct_1(u1_lattices('#skF_2'))
      | ~ v3_lattices(A_566)
      | ~ l3_lattices(A_566) ),
    inference(demodulation,[status(thm),theory(equality)],[c_3875,c_3889,c_3694]) ).

tff(c_3896,plain,
    ~ v1_funct_1(u1_lattices('#skF_2')),
    inference(splitLeft,[status(thm)],[c_3895]) ).

tff(c_3899,plain,
    ~ l1_lattices('#skF_2'),
    inference(resolution,[status(thm)],[c_140,c_3896]) ).

tff(c_3903,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_479,c_3899]) ).

tff(c_3905,plain,
    v1_funct_1(u1_lattices('#skF_2')),
    inference(splitRight,[status(thm)],[c_3895]) ).

tff(c_3888,plain,
    ! [E_521,D_520,F_518] :
      ( ~ v1_funct_2(u1_lattices('#skF_2'),k2_zfmisc_1(u1_struct_0('#skF_2'),u1_struct_0('#skF_2')),u1_struct_0('#skF_2'))
      | ~ v1_funct_1(u1_lattices('#skF_2'))
      | ( u2_lattices('#skF_2') = E_521 )
      | ( g3_lattices(u1_struct_0('#skF_1'),u2_lattices('#skF_1'),u1_lattices('#skF_1')) != g3_lattices(D_520,E_521,F_518) ) ),
    inference(splitRight,[status(thm)],[c_3874]) ).

tff(c_3907,plain,
    ! [E_521,D_520,F_518] :
      ( ~ v1_funct_2(u1_lattices('#skF_2'),k2_zfmisc_1(u1_struct_0('#skF_2'),u1_struct_0('#skF_2')),u1_struct_0('#skF_2'))
      | ( u2_lattices('#skF_2') = E_521 )
      | ( g3_lattices(u1_struct_0('#skF_1'),u2_lattices('#skF_1'),u1_lattices('#skF_1')) != g3_lattices(D_520,E_521,F_518) ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_3905,c_3888]) ).

tff(c_3908,plain,
    ~ v1_funct_2(u1_lattices('#skF_2'),k2_zfmisc_1(u1_struct_0('#skF_2'),u1_struct_0('#skF_2')),u1_struct_0('#skF_2')),
    inference(splitLeft,[status(thm)],[c_3907]) ).

tff(c_3911,plain,
    ~ l1_lattices('#skF_2'),
    inference(resolution,[status(thm)],[c_138,c_3908]) ).

tff(c_3915,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_479,c_3911]) ).

tff(c_3916,plain,
    ! [E_521,D_520,F_518] :
      ( ( u2_lattices('#skF_2') = E_521 )
      | ( g3_lattices(u1_struct_0('#skF_1'),u2_lattices('#skF_1'),u1_lattices('#skF_1')) != g3_lattices(D_520,E_521,F_518) ) ),
    inference(splitRight,[status(thm)],[c_3907]) ).

tff(c_3930,plain,
    u2_lattices('#skF_2') = u2_lattices('#skF_1'),
    inference(reflexivity,[status(thm),theory(equality)],[c_3916]) ).

tff(c_3958,plain,
    v1_funct_2(u2_lattices('#skF_1'),k2_zfmisc_1(u1_struct_0('#skF_2'),u1_struct_0('#skF_2')),u1_struct_0('#skF_2')),
    inference(demodulation,[status(thm),theory(equality)],[c_3930,c_3658]) ).

tff(c_3957,plain,
    m1_relset_1(u2_lattices('#skF_1'),k2_zfmisc_1(u1_struct_0('#skF_2'),u1_struct_0('#skF_2')),u1_struct_0('#skF_2')),
    inference(demodulation,[status(thm),theory(equality)],[c_3930,c_3875]) ).

tff(c_3917,plain,
    v1_funct_2(u1_lattices('#skF_2'),k2_zfmisc_1(u1_struct_0('#skF_2'),u1_struct_0('#skF_2')),u1_struct_0('#skF_2')),
    inference(splitRight,[status(thm)],[c_3907]) ).

tff(c_3960,plain,
    g3_lattices(u1_struct_0('#skF_2'),u2_lattices('#skF_1'),u1_lattices('#skF_2')) = g3_lattices(u1_struct_0('#skF_1'),u2_lattices('#skF_1'),u1_lattices('#skF_1')),
    inference(demodulation,[status(thm),theory(equality)],[c_3930,c_10]) ).

tff(c_220,plain,
    ! [F_74,B_67,A_66,E_73,C_68,D_72] :
      ( ( D_72 = A_66 )
      | ( g3_lattices(D_72,E_73,F_74) != g3_lattices(A_66,B_67,C_68) )
      | ~ m1_relset_1(C_68,k2_zfmisc_1(A_66,A_66),A_66)
      | ~ v1_funct_2(C_68,k2_zfmisc_1(A_66,A_66),A_66)
      | ~ v1_funct_1(C_68)
      | ~ m1_relset_1(B_67,k2_zfmisc_1(A_66,A_66),A_66)
      | ~ v1_funct_2(B_67,k2_zfmisc_1(A_66,A_66),A_66)
      | ~ v1_funct_1(B_67) ),
    inference(cnfTransformation,[status(thm)],[f_461]) ).

tff(c_4142,plain,
    ! [D_72,E_73,F_74] :
      ( ( u1_struct_0('#skF_2') = D_72 )
      | ( g3_lattices(u1_struct_0('#skF_1'),u2_lattices('#skF_1'),u1_lattices('#skF_1')) != g3_lattices(D_72,E_73,F_74) )
      | ~ m1_relset_1(u1_lattices('#skF_2'),k2_zfmisc_1(u1_struct_0('#skF_2'),u1_struct_0('#skF_2')),u1_struct_0('#skF_2'))
      | ~ v1_funct_2(u1_lattices('#skF_2'),k2_zfmisc_1(u1_struct_0('#skF_2'),u1_struct_0('#skF_2')),u1_struct_0('#skF_2'))
      | ~ v1_funct_1(u1_lattices('#skF_2'))
      | ~ m1_relset_1(u2_lattices('#skF_1'),k2_zfmisc_1(u1_struct_0('#skF_2'),u1_struct_0('#skF_2')),u1_struct_0('#skF_2'))
      | ~ v1_funct_2(u2_lattices('#skF_1'),k2_zfmisc_1(u1_struct_0('#skF_2'),u1_struct_0('#skF_2')),u1_struct_0('#skF_2'))
      | ~ v1_funct_1(u2_lattices('#skF_1')) ),
    inference(superposition,[status(thm),theory(equality)],[c_3960,c_220]) ).

tff(c_4167,plain,
    ! [D_72,E_73,F_74] :
      ( ( u1_struct_0('#skF_2') = D_72 )
      | ( g3_lattices(u1_struct_0('#skF_1'),u2_lattices('#skF_1'),u1_lattices('#skF_1')) != g3_lattices(D_72,E_73,F_74) ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_3954,c_3958,c_3957,c_3905,c_3917,c_3889,c_4142]) ).

tff(c_4571,plain,
    u1_struct_0('#skF_2') = u1_struct_0('#skF_1'),
    inference(reflexivity,[status(thm),theory(equality)],[c_4167]) ).

tff(c_118,plain,
    ! [A_37,B_38] :
      ( m1_subset_1(k7_lattices(A_37,B_38),u1_struct_0(A_37))
      | ~ m1_subset_1(B_38,u1_struct_0(A_37))
      | ~ l3_lattices(A_37)
      | v3_struct_0(A_37) ),
    inference(cnfTransformation,[status(thm)],[f_280]) ).

tff(c_4696,plain,
    ! [B_38] :
      ( m1_subset_1(k7_lattices('#skF_2',B_38),u1_struct_0('#skF_1'))
      | ~ m1_subset_1(B_38,u1_struct_0('#skF_2'))
      | ~ l3_lattices('#skF_2')
      | v3_struct_0('#skF_2') ),
    inference(superposition,[status(thm),theory(equality)],[c_4571,c_118]) ).

tff(c_4841,plain,
    ! [B_38] :
      ( m1_subset_1(k7_lattices('#skF_2',B_38),u1_struct_0('#skF_1'))
      | ~ m1_subset_1(B_38,u1_struct_0('#skF_1'))
      | v3_struct_0('#skF_2') ),
    inference(demodulation,[status(thm),theory(equality)],[c_12,c_4571,c_4696]) ).

tff(c_4842,plain,
    ! [B_38] :
      ( m1_subset_1(k7_lattices('#skF_2',B_38),u1_struct_0('#skF_1'))
      | ~ m1_subset_1(B_38,u1_struct_0('#skF_1')) ),
    inference(negUnitSimplification,[status(thm)],[c_18,c_4841]) ).

tff(c_26,plain,
    ~ v3_struct_0('#skF_1'),
    inference(cnfTransformation,[status(thm)],[f_61]) ).

tff(c_24,plain,
    v10_lattices('#skF_1'),
    inference(cnfTransformation,[status(thm)],[f_61]) ).

tff(c_22,plain,
    v17_lattices('#skF_1'),
    inference(cnfTransformation,[status(thm)],[f_61]) ).

tff(c_1335,plain,
    ! [A_258] :
      ( v11_lattices(A_258)
      | ~ v17_lattices(A_258)
      | v3_struct_0(A_258)
      | ~ l3_lattices(A_258) ),
    inference(cnfTransformation,[status(thm)],[f_184]) ).

tff(c_1356,plain,
    ( v11_lattices('#skF_1')
    | ~ v17_lattices('#skF_1')
    | ~ l3_lattices('#skF_1') ),
    inference(resolution,[status(thm)],[c_1335,c_26]) ).

tff(c_1381,plain,
    v11_lattices('#skF_1'),
    inference(demodulation,[status(thm),theory(equality)],[c_20,c_22,c_1356]) ).

tff(c_1202,plain,
    ! [A_242] :
      ( v16_lattices(A_242)
      | ~ v17_lattices(A_242)
      | v3_struct_0(A_242)
      | ~ l3_lattices(A_242) ),
    inference(cnfTransformation,[status(thm)],[f_184]) ).

tff(c_1223,plain,
    ( v16_lattices('#skF_1')
    | ~ v17_lattices('#skF_1')
    | ~ l3_lattices('#skF_1') ),
    inference(resolution,[status(thm)],[c_1202,c_26]) ).

tff(c_1248,plain,
    v16_lattices('#skF_1'),
    inference(demodulation,[status(thm),theory(equality)],[c_20,c_22,c_1223]) ).

tff(c_16,plain,
    v10_lattices('#skF_2'),
    inference(cnfTransformation,[status(thm)],[f_61]) ).

tff(c_14,plain,
    v17_lattices('#skF_2'),
    inference(cnfTransformation,[status(thm)],[f_61]) ).

tff(c_1359,plain,
    ( v11_lattices('#skF_2')
    | ~ v17_lattices('#skF_2')
    | ~ l3_lattices('#skF_2') ),
    inference(resolution,[status(thm)],[c_1335,c_18]) ).

tff(c_1384,plain,
    v11_lattices('#skF_2'),
    inference(demodulation,[status(thm),theory(equality)],[c_12,c_14,c_1359]) ).

tff(c_1226,plain,
    ( v16_lattices('#skF_2')
    | ~ v17_lattices('#skF_2')
    | ~ l3_lattices('#skF_2') ),
    inference(resolution,[status(thm)],[c_1202,c_18]) ).

tff(c_1251,plain,
    v16_lattices('#skF_2'),
    inference(demodulation,[status(thm),theory(equality)],[c_12,c_14,c_1226]) ).

tff(c_682,plain,
    ! [A_206] :
      ( v13_lattices(A_206)
      | ~ v15_lattices(A_206)
      | v3_struct_0(A_206)
      | ~ l3_lattices(A_206) ),
    inference(cnfTransformation,[status(thm)],[f_164]) ).

tff(c_706,plain,
    ( v13_lattices('#skF_2')
    | ~ v15_lattices('#skF_2')
    | ~ l3_lattices('#skF_2') ),
    inference(resolution,[status(thm)],[c_682,c_18]) ).

tff(c_731,plain,
    ( v13_lattices('#skF_2')
    | ~ v15_lattices('#skF_2') ),
    inference(demodulation,[status(thm),theory(equality)],[c_12,c_706]) ).

tff(c_1033,plain,
    ~ v15_lattices('#skF_2'),
    inference(splitLeft,[status(thm)],[c_731]) ).

tff(c_1035,plain,
    ! [A_238] :
      ( v15_lattices(A_238)
      | ~ v17_lattices(A_238)
      | v3_struct_0(A_238)
      | ~ l3_lattices(A_238) ),
    inference(cnfTransformation,[status(thm)],[f_184]) ).

tff(c_1059,plain,
    ( v15_lattices('#skF_2')
    | ~ v17_lattices('#skF_2')
    | ~ l3_lattices('#skF_2') ),
    inference(resolution,[status(thm)],[c_1035,c_18]) ).

tff(c_1086,plain,
    v15_lattices('#skF_2'),
    inference(demodulation,[status(thm),theory(equality)],[c_12,c_14,c_1059]) ).

tff(c_1088,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_1033,c_1086]) ).

tff(c_1090,plain,
    v15_lattices('#skF_2'),
    inference(splitRight,[status(thm)],[c_731]) ).

tff(c_703,plain,
    ( v13_lattices('#skF_1')
    | ~ v15_lattices('#skF_1')
    | ~ l3_lattices('#skF_1') ),
    inference(resolution,[status(thm)],[c_682,c_26]) ).

tff(c_728,plain,
    ( v13_lattices('#skF_1')
    | ~ v15_lattices('#skF_1') ),
    inference(demodulation,[status(thm),theory(equality)],[c_20,c_703]) ).

tff(c_737,plain,
    ~ v15_lattices('#skF_1'),
    inference(splitLeft,[status(thm)],[c_728]) ).

tff(c_979,plain,
    ! [A_236] :
      ( v15_lattices(A_236)
      | ~ v17_lattices(A_236)
      | v3_struct_0(A_236)
      | ~ l3_lattices(A_236) ),
    inference(cnfTransformation,[status(thm)],[f_184]) ).

tff(c_1000,plain,
    ( v15_lattices('#skF_1')
    | ~ v17_lattices('#skF_1')
    | ~ l3_lattices('#skF_1') ),
    inference(resolution,[status(thm)],[c_979,c_26]) ).

tff(c_1027,plain,
    v15_lattices('#skF_1'),
    inference(demodulation,[status(thm),theory(equality)],[c_20,c_22,c_1000]) ).

tff(c_1029,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_737,c_1027]) ).

tff(c_1031,plain,
    v15_lattices('#skF_1'),
    inference(splitRight,[status(thm)],[c_728]) ).

tff(c_216,plain,
    ! [F_74,B_67,A_66,E_73,C_68,D_72] :
      ( ( F_74 = C_68 )
      | ( g3_lattices(D_72,E_73,F_74) != g3_lattices(A_66,B_67,C_68) )
      | ~ m1_relset_1(C_68,k2_zfmisc_1(A_66,A_66),A_66)
      | ~ v1_funct_2(C_68,k2_zfmisc_1(A_66,A_66),A_66)
      | ~ v1_funct_1(C_68)
      | ~ m1_relset_1(B_67,k2_zfmisc_1(A_66,A_66),A_66)
      | ~ v1_funct_2(B_67,k2_zfmisc_1(A_66,A_66),A_66)
      | ~ v1_funct_1(B_67) ),
    inference(cnfTransformation,[status(thm)],[f_461]) ).

tff(c_4136,plain,
    ! [F_74,D_72,E_73] :
      ( ( u1_lattices('#skF_2') = F_74 )
      | ( g3_lattices(u1_struct_0('#skF_1'),u2_lattices('#skF_1'),u1_lattices('#skF_1')) != g3_lattices(D_72,E_73,F_74) )
      | ~ m1_relset_1(u1_lattices('#skF_2'),k2_zfmisc_1(u1_struct_0('#skF_2'),u1_struct_0('#skF_2')),u1_struct_0('#skF_2'))
      | ~ v1_funct_2(u1_lattices('#skF_2'),k2_zfmisc_1(u1_struct_0('#skF_2'),u1_struct_0('#skF_2')),u1_struct_0('#skF_2'))
      | ~ v1_funct_1(u1_lattices('#skF_2'))
      | ~ m1_relset_1(u2_lattices('#skF_1'),k2_zfmisc_1(u1_struct_0('#skF_2'),u1_struct_0('#skF_2')),u1_struct_0('#skF_2'))
      | ~ v1_funct_2(u2_lattices('#skF_1'),k2_zfmisc_1(u1_struct_0('#skF_2'),u1_struct_0('#skF_2')),u1_struct_0('#skF_2'))
      | ~ v1_funct_1(u2_lattices('#skF_1')) ),
    inference(superposition,[status(thm),theory(equality)],[c_3960,c_216]) ).

tff(c_4161,plain,
    ! [F_74,D_72,E_73] :
      ( ( u1_lattices('#skF_2') = F_74 )
      | ( g3_lattices(u1_struct_0('#skF_1'),u2_lattices('#skF_1'),u1_lattices('#skF_1')) != g3_lattices(D_72,E_73,F_74) ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_3954,c_3958,c_3957,c_3905,c_3917,c_3889,c_4136]) ).

tff(c_4219,plain,
    u1_lattices('#skF_2') = u1_lattices('#skF_1'),
    inference(reflexivity,[status(thm),theory(equality)],[c_4161]) ).

tff(c_2414,plain,
    ! [A_414,B_415] :
      ( r2_lattices(A_414,k7_lattices(A_414,B_415),B_415)
      | ~ m1_subset_1(k7_lattices(A_414,B_415),u1_struct_0(A_414))
      | ~ v16_lattices(A_414)
      | ~ v11_lattices(A_414)
      | ~ v10_lattices(A_414)
      | ~ m1_subset_1(B_415,u1_struct_0(A_414))
      | ~ l3_lattices(A_414)
      | v3_struct_0(A_414) ),
    inference(cnfTransformation,[status(thm)],[f_254]) ).

tff(c_3330,plain,
    ! [A_544,B_545] :
      ( r2_lattices(A_544,k7_lattices(A_544,B_545),B_545)
      | ~ v16_lattices(A_544)
      | ~ v11_lattices(A_544)
      | ~ v10_lattices(A_544)
      | ~ m1_subset_1(B_545,u1_struct_0(A_544))
      | ~ l3_lattices(A_544)
      | v3_struct_0(A_544) ),
    inference(resolution,[status(thm)],[c_118,c_2414]) ).

tff(c_408,plain,
    ! [B_118,E_146,F_148,A_86] :
      ( r2_lattices(B_118,E_146,F_148)
      | ~ r2_lattices(A_86,E_146,F_148)
      | ~ m1_subset_1(F_148,u1_struct_0(B_118))
      | ~ m1_subset_1(E_146,u1_struct_0(B_118))
      | ~ m1_subset_1(F_148,u1_struct_0(A_86))
      | ~ m1_subset_1(E_146,u1_struct_0(A_86))
      | ( g3_lattices(u1_struct_0(B_118),u2_lattices(B_118),u1_lattices(B_118)) != g3_lattices(u1_struct_0(A_86),u2_lattices(A_86),u1_lattices(A_86)) )
      | ~ l3_lattices(B_118)
      | ~ v16_lattices(B_118)
      | ~ v15_lattices(B_118)
      | ~ v10_lattices(B_118)
      | v3_struct_0(B_118)
      | ~ l3_lattices(A_86)
      | ~ v16_lattices(A_86)
      | ~ v15_lattices(A_86)
      | ~ v10_lattices(A_86)
      | v3_struct_0(A_86) ),
    inference(cnfTransformation,[status(thm)],[f_713]) ).

tff(c_43399,plain,
    ! [B_1763,A_1764,B_1765] :
      ( r2_lattices(B_1763,k7_lattices(A_1764,B_1765),B_1765)
      | ~ m1_subset_1(B_1765,u1_struct_0(B_1763))
      | ~ m1_subset_1(k7_lattices(A_1764,B_1765),u1_struct_0(B_1763))
      | ~ m1_subset_1(k7_lattices(A_1764,B_1765),u1_struct_0(A_1764))
      | ( g3_lattices(u1_struct_0(B_1763),u2_lattices(B_1763),u1_lattices(B_1763)) != g3_lattices(u1_struct_0(A_1764),u2_lattices(A_1764),u1_lattices(A_1764)) )
      | ~ l3_lattices(B_1763)
      | ~ v16_lattices(B_1763)
      | ~ v15_lattices(B_1763)
      | ~ v10_lattices(B_1763)
      | v3_struct_0(B_1763)
      | ~ v15_lattices(A_1764)
      | ~ v16_lattices(A_1764)
      | ~ v11_lattices(A_1764)
      | ~ v10_lattices(A_1764)
      | ~ m1_subset_1(B_1765,u1_struct_0(A_1764))
      | ~ l3_lattices(A_1764)
      | v3_struct_0(A_1764) ),
    inference(resolution,[status(thm)],[c_3330,c_408]) ).

tff(c_43404,plain,
    ! [B_38] :
      ( r2_lattices('#skF_1',k7_lattices('#skF_2',B_38),B_38)
      | ~ m1_subset_1(k7_lattices('#skF_2',B_38),u1_struct_0('#skF_2'))
      | ( g3_lattices(u1_struct_0('#skF_2'),u2_lattices('#skF_2'),u1_lattices('#skF_2')) != g3_lattices(u1_struct_0('#skF_1'),u2_lattices('#skF_1'),u1_lattices('#skF_1')) )
      | ~ l3_lattices('#skF_1')
      | ~ v16_lattices('#skF_1')
      | ~ v15_lattices('#skF_1')
      | ~ v10_lattices('#skF_1')
      | v3_struct_0('#skF_1')
      | ~ v15_lattices('#skF_2')
      | ~ v16_lattices('#skF_2')
      | ~ v11_lattices('#skF_2')
      | ~ v10_lattices('#skF_2')
      | ~ m1_subset_1(B_38,u1_struct_0('#skF_2'))
      | ~ l3_lattices('#skF_2')
      | v3_struct_0('#skF_2')
      | ~ m1_subset_1(B_38,u1_struct_0('#skF_1')) ),
    inference(resolution,[status(thm)],[c_4842,c_43399]) ).

tff(c_43418,plain,
    ! [B_38] :
      ( r2_lattices('#skF_1',k7_lattices('#skF_2',B_38),B_38)
      | ~ m1_subset_1(k7_lattices('#skF_2',B_38),u1_struct_0('#skF_1'))
      | v3_struct_0('#skF_1')
      | v3_struct_0('#skF_2')
      | ~ m1_subset_1(B_38,u1_struct_0('#skF_1')) ),
    inference(demodulation,[status(thm),theory(equality)],[c_12,c_4571,c_16,c_1384,c_1251,c_1090,c_24,c_1031,c_1248,c_20,c_3930,c_4219,c_4571,c_4571,c_43404]) ).

tff(c_43425,plain,
    ! [B_1766] :
      ( r2_lattices('#skF_1',k7_lattices('#skF_2',B_1766),B_1766)
      | ~ m1_subset_1(k7_lattices('#skF_2',B_1766),u1_struct_0('#skF_1'))
      | ~ m1_subset_1(B_1766,u1_struct_0('#skF_1')) ),
    inference(negUnitSimplification,[status(thm)],[c_18,c_26,c_43418]) ).

tff(c_43440,plain,
    ! [B_1767] :
      ( r2_lattices('#skF_1',k7_lattices('#skF_2',B_1767),B_1767)
      | ~ m1_subset_1(B_1767,u1_struct_0('#skF_1')) ),
    inference(resolution,[status(thm)],[c_4842,c_43425]) ).

tff(c_104,plain,
    ! [A_27,B_31,C_33] :
      ( ( k7_lattices(A_27,B_31) = C_33 )
      | ~ r2_lattices(A_27,C_33,B_31)
      | ~ m1_subset_1(C_33,u1_struct_0(A_27))
      | ~ v16_lattices(A_27)
      | ~ v11_lattices(A_27)
      | ~ v10_lattices(A_27)
      | ~ m1_subset_1(B_31,u1_struct_0(A_27))
      | ~ l3_lattices(A_27)
      | v3_struct_0(A_27) ),
    inference(cnfTransformation,[status(thm)],[f_254]) ).

tff(c_43444,plain,
    ! [B_1767] :
      ( ( k7_lattices('#skF_2',B_1767) = k7_lattices('#skF_1',B_1767) )
      | ~ m1_subset_1(k7_lattices('#skF_2',B_1767),u1_struct_0('#skF_1'))
      | ~ v16_lattices('#skF_1')
      | ~ v11_lattices('#skF_1')
      | ~ v10_lattices('#skF_1')
      | ~ l3_lattices('#skF_1')
      | v3_struct_0('#skF_1')
      | ~ m1_subset_1(B_1767,u1_struct_0('#skF_1')) ),
    inference(resolution,[status(thm)],[c_43440,c_104]) ).

tff(c_43451,plain,
    ! [B_1767] :
      ( ( k7_lattices('#skF_2',B_1767) = k7_lattices('#skF_1',B_1767) )
      | ~ m1_subset_1(k7_lattices('#skF_2',B_1767),u1_struct_0('#skF_1'))
      | v3_struct_0('#skF_1')
      | ~ m1_subset_1(B_1767,u1_struct_0('#skF_1')) ),
    inference(demodulation,[status(thm),theory(equality)],[c_20,c_24,c_1381,c_1248,c_43444]) ).

tff(c_43453,plain,
    ! [B_1768] :
      ( ( k7_lattices('#skF_2',B_1768) = k7_lattices('#skF_1',B_1768) )
      | ~ m1_subset_1(k7_lattices('#skF_2',B_1768),u1_struct_0('#skF_1'))
      | ~ m1_subset_1(B_1768,u1_struct_0('#skF_1')) ),
    inference(negUnitSimplification,[status(thm)],[c_26,c_43451]) ).

tff(c_43469,plain,
    ! [B_1769] :
      ( ( k7_lattices('#skF_2',B_1769) = k7_lattices('#skF_1',B_1769) )
      | ~ m1_subset_1(B_1769,u1_struct_0('#skF_1')) ),
    inference(resolution,[status(thm)],[c_4842,c_43453]) ).

tff(c_43526,plain,
    k7_lattices('#skF_2','#skF_4') = k7_lattices('#skF_1','#skF_4'),
    inference(resolution,[status(thm)],[c_427,c_43469]) ).

tff(c_43558,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_428,c_43526]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : LAT296+1 : TPTP v8.1.2. Released v3.4.0.
% 0.00/0.14  % Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.14/0.35  % Computer : n002.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Thu Aug  3 12:46:31 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 25.82/13.11  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 25.93/13.13  
% 25.93/13.13  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 25.93/13.17  
% 25.93/13.17  Inference rules
% 25.93/13.17  ----------------------
% 25.93/13.17  #Ref     : 43
% 25.93/13.17  #Sup     : 11077
% 25.93/13.17  #Fact    : 0
% 25.93/13.17  #Define  : 0
% 25.93/13.17  #Split   : 131
% 25.93/13.17  #Chain   : 0
% 25.93/13.17  #Close   : 0
% 25.93/13.17  
% 25.93/13.17  Ordering : KBO
% 25.93/13.17  
% 25.93/13.17  Simplification rules
% 25.93/13.17  ----------------------
% 25.93/13.17  #Subsume      : 8343
% 25.93/13.17  #Demod        : 13486
% 25.93/13.17  #Tautology    : 869
% 25.93/13.17  #SimpNegUnit  : 3114
% 25.93/13.17  #BackRed      : 1458
% 25.93/13.17  
% 25.93/13.17  #Partial instantiations: 0
% 25.93/13.17  #Strategies tried      : 1
% 25.93/13.17  
% 25.93/13.17  Timing (in seconds)
% 25.93/13.17  ----------------------
% 25.93/13.18  Preprocessing        : 0.78
% 25.93/13.18  Parsing              : 0.40
% 25.93/13.18  CNF conversion       : 0.07
% 25.93/13.18  Main loop            : 11.22
% 25.93/13.18  Inferencing          : 2.28
% 25.93/13.18  Reduction            : 6.01
% 25.93/13.18  Demodulation         : 4.93
% 25.93/13.18  BG Simplification    : 0.10
% 25.93/13.18  Subsumption          : 2.43
% 25.93/13.18  Abstraction          : 0.15
% 25.93/13.18  MUC search           : 0.00
% 25.93/13.18  Cooper               : 0.00
% 25.93/13.18  Total                : 12.08
% 25.93/13.18  Index Insertion      : 0.00
% 25.93/13.18  Index Deletion       : 0.00
% 25.93/13.18  Index Matching       : 0.00
% 25.93/13.18  BG Taut test         : 0.00
%------------------------------------------------------------------------------