TSTP Solution File: MSC008-1.002 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : MSC008-1.002 : TPTP v8.1.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s

% Computer : n023.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 : Mon May 22 16:35:05 EDT 2023

% Result   : Unsatisfiable 1.06s 1.24s
% Output   : CNFRefutation 1.06s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :   23
% Syntax   : Number of formulae    :  172 (  94 unt;   5 typ;   0 def)
%            Number of atoms       :  990 ( 246 equ;   0 cnn)
%            Maximal formula atoms :    5 (   5 avg)
%            Number of connectives : 1900 ( 229   ~; 331   |;   0   &;1340   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   4 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    8 (   8   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    8 (   5 usr;   4 con; 0-3 aty)
%            Number of variables   :  594 (   0   ^; 594   !;   0   ?; 594   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_eq,type,
    eq: $i > $i > $o ).

thf(tp_greek,type,
    greek: $i > $i > $i > $o ).

thf(tp_latin,type,
    latin: $i > $i > $i > $o ).

thf(tp_p_1,type,
    p_1: $i ).

thf(tp_p_2,type,
    p_2: $i ).

thf(1,axiom,
    ! [Column: $i,Label: $i] :
      ( ( greek @ p_1 @ Column @ Label )
      | ( greek @ p_2 @ Column @ Label ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',greek_row_required) ).

thf(2,axiom,
    ! [Row: $i,Label: $i] :
      ( ( greek @ Row @ p_1 @ Label )
      | ( greek @ Row @ p_2 @ Label ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',greek_column_required) ).

thf(3,axiom,
    ! [Row: $i,Column: $i] :
      ( ( greek @ Row @ Column @ p_1 )
      | ( greek @ Row @ Column @ p_2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',greek_cell_element) ).

thf(4,axiom,
    ! [Column: $i,Label: $i] :
      ( ( latin @ p_1 @ Column @ Label )
      | ( latin @ p_2 @ Column @ Label ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',latin_row_required) ).

thf(5,axiom,
    ! [Row: $i,Label: $i] :
      ( ( latin @ Row @ p_1 @ Label )
      | ( latin @ Row @ p_2 @ Label ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',latin_column_required) ).

thf(6,axiom,
    ! [Row: $i,Column: $i] :
      ( ( latin @ Row @ Column @ p_1 )
      | ( latin @ Row @ Column @ p_2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',latin_cell_element) ).

thf(7,axiom,
    ! [Row1: $i,Column: $i,Label: $i,Row2: $i] :
      ( ~ ( greek @ Row1 @ Column @ Label )
      | ~ ( greek @ Row2 @ Column @ Label )
      | ( eq @ Row1 @ Row2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',greek_row_is_unique) ).

thf(8,axiom,
    ! [Row: $i,Column1: $i,Label: $i,Column2: $i] :
      ( ~ ( greek @ Row @ Column1 @ Label )
      | ~ ( greek @ Row @ Column2 @ Label )
      | ( eq @ Column1 @ Column2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',greek_column_is_unique) ).

thf(9,axiom,
    ! [Row: $i,Column: $i,Label1: $i,Label2: $i] :
      ( ~ ( greek @ Row @ Column @ Label1 )
      | ~ ( greek @ Row @ Column @ Label2 )
      | ( eq @ Label1 @ Label2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',greek_element_is_unique) ).

thf(10,axiom,
    ! [Row1: $i,Column: $i,Label: $i,Row2: $i] :
      ( ~ ( latin @ Row1 @ Column @ Label )
      | ~ ( latin @ Row2 @ Column @ Label )
      | ( eq @ Row1 @ Row2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',latin_row_is_unique) ).

thf(11,axiom,
    ! [Row: $i,Column1: $i,Label: $i,Column2: $i] :
      ( ~ ( latin @ Row @ Column1 @ Label )
      | ~ ( latin @ Row @ Column2 @ Label )
      | ( eq @ Column1 @ Column2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',latin_column_is_unique) ).

thf(12,axiom,
    ! [Row: $i,Column: $i,Label1: $i,Label2: $i] :
      ( ~ ( latin @ Row @ Column @ Label1 )
      | ~ ( latin @ Row @ Column @ Label2 )
      | ( eq @ Label1 @ Label2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',latin_element_is_unique) ).

thf(13,axiom,
    ! [X: $i,Y: $i] :
      ( ~ ( eq @ X @ Y )
      | ( eq @ Y @ X ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry) ).

thf(14,axiom,
    ! [X: $i] : ( eq @ X @ X ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity) ).

thf(15,axiom,
    ~ ( eq @ p_1 @ p_2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p_1_is_not_p_2) ).

thf(16,conjecture,
    $false,
    file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).

thf(17,negated_conjecture,
    $false = $false,
    inference(negate_conjecture,[status(cth)],[16]) ).

thf(18,negated_conjecture,
    ! [Row1: $i,Column1: $i,Label1: $i,Label2: $i,Row2: $i,Column2: $i] :
      ( ~ ( greek @ Row1 @ Column1 @ Label1 )
      | ~ ( latin @ Row1 @ Column1 @ Label2 )
      | ~ ( greek @ Row2 @ Column2 @ Label1 )
      | ~ ( latin @ Row2 @ Column2 @ Label2 )
      | ( eq @ Row1 @ Row2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',no_two_same2) ).

thf(19,negated_conjecture,
    ! [Row1: $i,Column1: $i,Label1: $i,Label2: $i,Row2: $i,Column2: $i] :
      ( ~ ( greek @ Row1 @ Column1 @ Label1 )
      | ~ ( latin @ Row1 @ Column1 @ Label2 )
      | ~ ( greek @ Row2 @ Column2 @ Label1 )
      | ~ ( latin @ Row2 @ Column2 @ Label2 )
      | ( eq @ Column1 @ Column2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',no_two_same1) ).

thf(20,plain,
    $false = $false,
    inference(unfold_def,[status(thm)],[17]) ).

thf(21,plain,
    ( ( ! [Column: $i,Label: $i] :
          ( ( greek @ p_1 @ Column @ Label )
          | ( greek @ p_2 @ Column @ Label ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1]) ).

thf(22,plain,
    ( ( ! [Row: $i,Label: $i] :
          ( ( greek @ Row @ p_1 @ Label )
          | ( greek @ Row @ p_2 @ Label ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(23,plain,
    ( ( ! [Row: $i,Column: $i] :
          ( ( greek @ Row @ Column @ p_1 )
          | ( greek @ Row @ Column @ p_2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3]) ).

thf(24,plain,
    ( ( ! [Column: $i,Label: $i] :
          ( ( latin @ p_1 @ Column @ Label )
          | ( latin @ p_2 @ Column @ Label ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4]) ).

thf(25,plain,
    ( ( ! [Row: $i,Label: $i] :
          ( ( latin @ Row @ p_1 @ Label )
          | ( latin @ Row @ p_2 @ Label ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5]) ).

thf(26,plain,
    ( ( ! [Row: $i,Column: $i] :
          ( ( latin @ Row @ Column @ p_1 )
          | ( latin @ Row @ Column @ p_2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6]) ).

thf(27,plain,
    ( ( ! [Row1: $i,Column: $i,Label: $i,Row2: $i] :
          ( ~ ( greek @ Row1 @ Column @ Label )
          | ~ ( greek @ Row2 @ Column @ Label )
          | ( eq @ Row1 @ Row2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[7]) ).

thf(28,plain,
    ( ( ! [Row: $i,Column1: $i,Label: $i,Column2: $i] :
          ( ~ ( greek @ Row @ Column1 @ Label )
          | ~ ( greek @ Row @ Column2 @ Label )
          | ( eq @ Column1 @ Column2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8]) ).

thf(29,plain,
    ( ( ! [Row: $i,Column: $i,Label1: $i,Label2: $i] :
          ( ~ ( greek @ Row @ Column @ Label1 )
          | ~ ( greek @ Row @ Column @ Label2 )
          | ( eq @ Label1 @ Label2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9]) ).

thf(30,plain,
    ( ( ! [Row1: $i,Column: $i,Label: $i,Row2: $i] :
          ( ~ ( latin @ Row1 @ Column @ Label )
          | ~ ( latin @ Row2 @ Column @ Label )
          | ( eq @ Row1 @ Row2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10]) ).

thf(31,plain,
    ( ( ! [Row: $i,Column1: $i,Label: $i,Column2: $i] :
          ( ~ ( latin @ Row @ Column1 @ Label )
          | ~ ( latin @ Row @ Column2 @ Label )
          | ( eq @ Column1 @ Column2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[11]) ).

thf(32,plain,
    ( ( ! [Row: $i,Column: $i,Label1: $i,Label2: $i] :
          ( ~ ( latin @ Row @ Column @ Label1 )
          | ~ ( latin @ Row @ Column @ Label2 )
          | ( eq @ Label1 @ Label2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[12]) ).

thf(33,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ~ ( eq @ X @ Y )
          | ( eq @ Y @ X ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[13]) ).

thf(34,plain,
    ( ( ! [X: $i] : ( eq @ X @ X ) )
    = $true ),
    inference(unfold_def,[status(thm)],[14]) ).

thf(35,plain,
    ( ( ~ ( eq @ p_1 @ p_2 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[15]) ).

thf(36,plain,
    ( ( ! [Row1: $i,Column1: $i,Label1: $i,Label2: $i,Row2: $i,Column2: $i] :
          ( ~ ( greek @ Row1 @ Column1 @ Label1 )
          | ~ ( latin @ Row1 @ Column1 @ Label2 )
          | ~ ( greek @ Row2 @ Column2 @ Label1 )
          | ~ ( latin @ Row2 @ Column2 @ Label2 )
          | ( eq @ Row1 @ Row2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[18]) ).

thf(37,plain,
    ( ( ! [Row1: $i,Column1: $i,Label1: $i,Label2: $i,Row2: $i,Column2: $i] :
          ( ~ ( greek @ Row1 @ Column1 @ Label1 )
          | ~ ( latin @ Row1 @ Column1 @ Label2 )
          | ~ ( greek @ Row2 @ Column2 @ Label1 )
          | ~ ( latin @ Row2 @ Column2 @ Label2 )
          | ( eq @ Column1 @ Column2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[19]) ).

thf(38,plain,
    ~ $false = $true,
    inference(polarity_switch,[status(thm)],[20]) ).

thf(39,plain,
    ( ( ! [Row1: $i,Column: $i,Label: $i] :
          ( ~ ( greek @ Row1 @ Column @ Label )
          | ! [Row2: $i] :
              ( ~ ( greek @ Row2 @ Column @ Label )
              | ( eq @ Row1 @ Row2 ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[27]) ).

thf(40,plain,
    ( ( ! [Row: $i,Column1: $i,Label: $i] :
          ( ~ ( greek @ Row @ Column1 @ Label )
          | ! [Column2: $i] :
              ( ~ ( greek @ Row @ Column2 @ Label )
              | ( eq @ Column1 @ Column2 ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[28]) ).

thf(41,plain,
    ( ( ! [Row: $i,Column: $i,Label1: $i] :
          ( ~ ( greek @ Row @ Column @ Label1 )
          | ! [Label2: $i] :
              ( ~ ( greek @ Row @ Column @ Label2 )
              | ( eq @ Label1 @ Label2 ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[29]) ).

thf(42,plain,
    ( ( ! [Row1: $i,Column: $i,Label: $i] :
          ( ~ ( latin @ Row1 @ Column @ Label )
          | ! [Row2: $i] :
              ( ~ ( latin @ Row2 @ Column @ Label )
              | ( eq @ Row1 @ Row2 ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[30]) ).

thf(43,plain,
    ( ( ! [Row: $i,Column1: $i,Label: $i] :
          ( ~ ( latin @ Row @ Column1 @ Label )
          | ! [Column2: $i] :
              ( ~ ( latin @ Row @ Column2 @ Label )
              | ( eq @ Column1 @ Column2 ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[31]) ).

thf(44,plain,
    ( ( ! [Row: $i,Column: $i,Label1: $i] :
          ( ~ ( latin @ Row @ Column @ Label1 )
          | ! [Label2: $i] :
              ( ~ ( latin @ Row @ Column @ Label2 )
              | ( eq @ Label1 @ Label2 ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[32]) ).

thf(45,plain,
    ( ( ! [Row1: $i,Column1: $i,Label1: $i,Label2: $i] :
          ( ~ ( greek @ Row1 @ Column1 @ Label1 )
          | ~ ( latin @ Row1 @ Column1 @ Label2 )
          | ! [Row2: $i,Column2: $i] :
              ( ~ ( greek @ Row2 @ Column2 @ Label1 )
              | ~ ( latin @ Row2 @ Column2 @ Label2 )
              | ( eq @ Row1 @ Row2 ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[36]) ).

thf(46,plain,
    ( ( ! [Row1: $i,Column1: $i,Label1: $i,Label2: $i] :
          ( ~ ( greek @ Row1 @ Column1 @ Label1 )
          | ~ ( latin @ Row1 @ Column1 @ Label2 )
          | ! [Row2: $i,Column2: $i] :
              ( ~ ( greek @ Row2 @ Column2 @ Label1 )
              | ~ ( latin @ Row2 @ Column2 @ Label2 )
              | ( eq @ Column1 @ Column2 ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[37]) ).

thf(47,plain,
    ( ( ! [Row1: $i,Column1: $i,Label1: $i,Label2: $i] :
          ( ~ ( greek @ Row1 @ Column1 @ Label1 )
          | ~ ( latin @ Row1 @ Column1 @ Label2 )
          | ! [Row2: $i,Column2: $i] :
              ( ~ ( greek @ Row2 @ Column2 @ Label1 )
              | ~ ( latin @ Row2 @ Column2 @ Label2 )
              | ( eq @ Column1 @ Column2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[46]) ).

thf(48,plain,
    ( ( ! [Row1: $i,Column1: $i,Label1: $i,Label2: $i] :
          ( ~ ( greek @ Row1 @ Column1 @ Label1 )
          | ~ ( latin @ Row1 @ Column1 @ Label2 )
          | ! [Row2: $i,Column2: $i] :
              ( ~ ( greek @ Row2 @ Column2 @ Label1 )
              | ~ ( latin @ Row2 @ Column2 @ Label2 )
              | ( eq @ Row1 @ Row2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[45]) ).

thf(49,plain,
    ( ( ~ ( eq @ p_1 @ p_2 ) )
    = $true ),
    inference(copy,[status(thm)],[35]) ).

thf(50,plain,
    ( ( ! [X: $i] : ( eq @ X @ X ) )
    = $true ),
    inference(copy,[status(thm)],[34]) ).

thf(51,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ~ ( eq @ X @ Y )
          | ( eq @ Y @ X ) ) )
    = $true ),
    inference(copy,[status(thm)],[33]) ).

thf(52,plain,
    ( ( ! [Row: $i,Column: $i,Label1: $i] :
          ( ~ ( latin @ Row @ Column @ Label1 )
          | ! [Label2: $i] :
              ( ~ ( latin @ Row @ Column @ Label2 )
              | ( eq @ Label1 @ Label2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[44]) ).

thf(53,plain,
    ( ( ! [Row: $i,Column1: $i,Label: $i] :
          ( ~ ( latin @ Row @ Column1 @ Label )
          | ! [Column2: $i] :
              ( ~ ( latin @ Row @ Column2 @ Label )
              | ( eq @ Column1 @ Column2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[43]) ).

thf(54,plain,
    ( ( ! [Row1: $i,Column: $i,Label: $i] :
          ( ~ ( latin @ Row1 @ Column @ Label )
          | ! [Row2: $i] :
              ( ~ ( latin @ Row2 @ Column @ Label )
              | ( eq @ Row1 @ Row2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[42]) ).

thf(55,plain,
    ( ( ! [Row: $i,Column: $i,Label1: $i] :
          ( ~ ( greek @ Row @ Column @ Label1 )
          | ! [Label2: $i] :
              ( ~ ( greek @ Row @ Column @ Label2 )
              | ( eq @ Label1 @ Label2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[41]) ).

thf(56,plain,
    ( ( ! [Row: $i,Column1: $i,Label: $i] :
          ( ~ ( greek @ Row @ Column1 @ Label )
          | ! [Column2: $i] :
              ( ~ ( greek @ Row @ Column2 @ Label )
              | ( eq @ Column1 @ Column2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[40]) ).

thf(57,plain,
    ( ( ! [Row1: $i,Column: $i,Label: $i] :
          ( ~ ( greek @ Row1 @ Column @ Label )
          | ! [Row2: $i] :
              ( ~ ( greek @ Row2 @ Column @ Label )
              | ( eq @ Row1 @ Row2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[39]) ).

thf(58,plain,
    ( ( ! [Row: $i,Column: $i] :
          ( ( latin @ Row @ Column @ p_1 )
          | ( latin @ Row @ Column @ p_2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[26]) ).

thf(59,plain,
    ( ( ! [Row: $i,Label: $i] :
          ( ( latin @ Row @ p_1 @ Label )
          | ( latin @ Row @ p_2 @ Label ) ) )
    = $true ),
    inference(copy,[status(thm)],[25]) ).

thf(60,plain,
    ( ( ! [Column: $i,Label: $i] :
          ( ( latin @ p_1 @ Column @ Label )
          | ( latin @ p_2 @ Column @ Label ) ) )
    = $true ),
    inference(copy,[status(thm)],[24]) ).

thf(61,plain,
    ( ( ! [Row: $i,Column: $i] :
          ( ( greek @ Row @ Column @ p_1 )
          | ( greek @ Row @ Column @ p_2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[23]) ).

thf(62,plain,
    ( ( ! [Row: $i,Label: $i] :
          ( ( greek @ Row @ p_1 @ Label )
          | ( greek @ Row @ p_2 @ Label ) ) )
    = $true ),
    inference(copy,[status(thm)],[22]) ).

thf(63,plain,
    ( ( ! [Column: $i,Label: $i] :
          ( ( greek @ p_1 @ Column @ Label )
          | ( greek @ p_2 @ Column @ Label ) ) )
    = $true ),
    inference(copy,[status(thm)],[21]) ).

thf(64,plain,
    ~ $false = $true,
    inference(copy,[status(thm)],[38]) ).

thf(65,plain,
    ! [SV1: $i] :
      ( ( ! [SY51: $i,SY52: $i,SY53: $i] :
            ( ~ ( greek @ SV1 @ SY51 @ SY52 )
            | ~ ( latin @ SV1 @ SY51 @ SY53 )
            | ! [Row2: $i,Column2: $i] :
                ( ~ ( greek @ Row2 @ Column2 @ SY52 )
                | ~ ( latin @ Row2 @ Column2 @ SY53 )
                | ( eq @ SY51 @ Column2 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[47]) ).

thf(66,plain,
    ! [SV2: $i] :
      ( ( ! [SY56: $i,SY57: $i,SY58: $i] :
            ( ~ ( greek @ SV2 @ SY56 @ SY57 )
            | ~ ( latin @ SV2 @ SY56 @ SY58 )
            | ! [SY59: $i,SY60: $i] :
                ( ~ ( greek @ SY59 @ SY60 @ SY57 )
                | ~ ( latin @ SY59 @ SY60 @ SY58 )
                | ( eq @ SV2 @ SY59 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[48]) ).

thf(67,plain,
    ( ( eq @ p_1 @ p_2 )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[49]) ).

thf(68,plain,
    ! [SV3: $i] :
      ( ( eq @ SV3 @ SV3 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[50]) ).

thf(69,plain,
    ! [SV4: $i] :
      ( ( ! [SY61: $i] :
            ( ~ ( eq @ SV4 @ SY61 )
            | ( eq @ SY61 @ SV4 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[51]) ).

thf(70,plain,
    ! [SV5: $i] :
      ( ( ! [SY62: $i,SY63: $i] :
            ( ~ ( latin @ SV5 @ SY62 @ SY63 )
            | ! [SY64: $i] :
                ( ~ ( latin @ SV5 @ SY62 @ SY64 )
                | ( eq @ SY63 @ SY64 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[52]) ).

thf(71,plain,
    ! [SV6: $i] :
      ( ( ! [SY65: $i,SY66: $i] :
            ( ~ ( latin @ SV6 @ SY65 @ SY66 )
            | ! [SY67: $i] :
                ( ~ ( latin @ SV6 @ SY67 @ SY66 )
                | ( eq @ SY65 @ SY67 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[53]) ).

thf(72,plain,
    ! [SV7: $i] :
      ( ( ! [SY68: $i,SY69: $i] :
            ( ~ ( latin @ SV7 @ SY68 @ SY69 )
            | ! [SY70: $i] :
                ( ~ ( latin @ SY70 @ SY68 @ SY69 )
                | ( eq @ SV7 @ SY70 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[54]) ).

thf(73,plain,
    ! [SV8: $i] :
      ( ( ! [SY71: $i,SY72: $i] :
            ( ~ ( greek @ SV8 @ SY71 @ SY72 )
            | ! [SY73: $i] :
                ( ~ ( greek @ SV8 @ SY71 @ SY73 )
                | ( eq @ SY72 @ SY73 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[55]) ).

thf(74,plain,
    ! [SV9: $i] :
      ( ( ! [SY74: $i,SY75: $i] :
            ( ~ ( greek @ SV9 @ SY74 @ SY75 )
            | ! [SY76: $i] :
                ( ~ ( greek @ SV9 @ SY76 @ SY75 )
                | ( eq @ SY74 @ SY76 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[56]) ).

thf(75,plain,
    ! [SV10: $i] :
      ( ( ! [SY77: $i,SY78: $i] :
            ( ~ ( greek @ SV10 @ SY77 @ SY78 )
            | ! [SY79: $i] :
                ( ~ ( greek @ SY79 @ SY77 @ SY78 )
                | ( eq @ SV10 @ SY79 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[57]) ).

thf(76,plain,
    ! [SV11: $i] :
      ( ( ! [SY80: $i] :
            ( ( latin @ SV11 @ SY80 @ p_1 )
            | ( latin @ SV11 @ SY80 @ p_2 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[58]) ).

thf(77,plain,
    ! [SV12: $i] :
      ( ( ! [SY81: $i] :
            ( ( latin @ SV12 @ p_1 @ SY81 )
            | ( latin @ SV12 @ p_2 @ SY81 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[59]) ).

thf(78,plain,
    ! [SV13: $i] :
      ( ( ! [SY82: $i] :
            ( ( latin @ p_1 @ SV13 @ SY82 )
            | ( latin @ p_2 @ SV13 @ SY82 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[60]) ).

thf(79,plain,
    ! [SV14: $i] :
      ( ( ! [SY83: $i] :
            ( ( greek @ SV14 @ SY83 @ p_1 )
            | ( greek @ SV14 @ SY83 @ p_2 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[61]) ).

thf(80,plain,
    ! [SV15: $i] :
      ( ( ! [SY84: $i] :
            ( ( greek @ SV15 @ p_1 @ SY84 )
            | ( greek @ SV15 @ p_2 @ SY84 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[62]) ).

thf(81,plain,
    ! [SV16: $i] :
      ( ( ! [SY85: $i] :
            ( ( greek @ p_1 @ SV16 @ SY85 )
            | ( greek @ p_2 @ SV16 @ SY85 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[63]) ).

thf(82,plain,
    $false = $false,
    inference(extcnf_not_pos,[status(thm)],[64]) ).

thf(83,plain,
    ! [SV17: $i,SV1: $i] :
      ( ( ! [SY86: $i,SY87: $i] :
            ( ~ ( greek @ SV1 @ SV17 @ SY86 )
            | ~ ( latin @ SV1 @ SV17 @ SY87 )
            | ! [SY88: $i,SY89: $i] :
                ( ~ ( greek @ SY88 @ SY89 @ SY86 )
                | ~ ( latin @ SY88 @ SY89 @ SY87 )
                | ( eq @ SV17 @ SY89 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[65]) ).

thf(84,plain,
    ! [SV18: $i,SV2: $i] :
      ( ( ! [SY90: $i,SY91: $i] :
            ( ~ ( greek @ SV2 @ SV18 @ SY90 )
            | ~ ( latin @ SV2 @ SV18 @ SY91 )
            | ! [SY59: $i,SY60: $i] :
                ( ~ ( greek @ SY59 @ SY60 @ SY90 )
                | ~ ( latin @ SY59 @ SY60 @ SY91 )
                | ( eq @ SV2 @ SY59 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[66]) ).

thf(85,plain,
    ! [SV19: $i,SV4: $i] :
      ( ( ~ ( eq @ SV4 @ SV19 )
        | ( eq @ SV19 @ SV4 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[69]) ).

thf(86,plain,
    ! [SV20: $i,SV5: $i] :
      ( ( ! [SY94: $i] :
            ( ~ ( latin @ SV5 @ SV20 @ SY94 )
            | ! [SY95: $i] :
                ( ~ ( latin @ SV5 @ SV20 @ SY95 )
                | ( eq @ SY94 @ SY95 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[70]) ).

thf(87,plain,
    ! [SV21: $i,SV6: $i] :
      ( ( ! [SY96: $i] :
            ( ~ ( latin @ SV6 @ SV21 @ SY96 )
            | ! [SY97: $i] :
                ( ~ ( latin @ SV6 @ SY97 @ SY96 )
                | ( eq @ SV21 @ SY97 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[71]) ).

thf(88,plain,
    ! [SV22: $i,SV7: $i] :
      ( ( ! [SY98: $i] :
            ( ~ ( latin @ SV7 @ SV22 @ SY98 )
            | ! [SY99: $i] :
                ( ~ ( latin @ SY99 @ SV22 @ SY98 )
                | ( eq @ SV7 @ SY99 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[72]) ).

thf(89,plain,
    ! [SV23: $i,SV8: $i] :
      ( ( ! [SY100: $i] :
            ( ~ ( greek @ SV8 @ SV23 @ SY100 )
            | ! [SY101: $i] :
                ( ~ ( greek @ SV8 @ SV23 @ SY101 )
                | ( eq @ SY100 @ SY101 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[73]) ).

thf(90,plain,
    ! [SV24: $i,SV9: $i] :
      ( ( ! [SY102: $i] :
            ( ~ ( greek @ SV9 @ SV24 @ SY102 )
            | ! [SY103: $i] :
                ( ~ ( greek @ SV9 @ SY103 @ SY102 )
                | ( eq @ SV24 @ SY103 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[74]) ).

thf(91,plain,
    ! [SV25: $i,SV10: $i] :
      ( ( ! [SY104: $i] :
            ( ~ ( greek @ SV10 @ SV25 @ SY104 )
            | ! [SY105: $i] :
                ( ~ ( greek @ SY105 @ SV25 @ SY104 )
                | ( eq @ SV10 @ SY105 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[75]) ).

thf(92,plain,
    ! [SV26: $i,SV11: $i] :
      ( ( ( latin @ SV11 @ SV26 @ p_1 )
        | ( latin @ SV11 @ SV26 @ p_2 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[76]) ).

thf(93,plain,
    ! [SV27: $i,SV12: $i] :
      ( ( ( latin @ SV12 @ p_1 @ SV27 )
        | ( latin @ SV12 @ p_2 @ SV27 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[77]) ).

thf(94,plain,
    ! [SV28: $i,SV13: $i] :
      ( ( ( latin @ p_1 @ SV13 @ SV28 )
        | ( latin @ p_2 @ SV13 @ SV28 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[78]) ).

thf(95,plain,
    ! [SV29: $i,SV14: $i] :
      ( ( ( greek @ SV14 @ SV29 @ p_1 )
        | ( greek @ SV14 @ SV29 @ p_2 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[79]) ).

thf(96,plain,
    ! [SV30: $i,SV15: $i] :
      ( ( ( greek @ SV15 @ p_1 @ SV30 )
        | ( greek @ SV15 @ p_2 @ SV30 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[80]) ).

thf(97,plain,
    ! [SV31: $i,SV16: $i] :
      ( ( ( greek @ p_1 @ SV16 @ SV31 )
        | ( greek @ p_2 @ SV16 @ SV31 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[81]) ).

thf(98,plain,
    ! [SV32: $i,SV17: $i,SV1: $i] :
      ( ( ! [SY106: $i] :
            ( ~ ( greek @ SV1 @ SV17 @ SV32 )
            | ~ ( latin @ SV1 @ SV17 @ SY106 )
            | ! [SY107: $i,SY108: $i] :
                ( ~ ( greek @ SY107 @ SY108 @ SV32 )
                | ~ ( latin @ SY107 @ SY108 @ SY106 )
                | ( eq @ SV17 @ SY108 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[83]) ).

thf(99,plain,
    ! [SV33: $i,SV18: $i,SV2: $i] :
      ( ( ! [SY109: $i] :
            ( ~ ( greek @ SV2 @ SV18 @ SV33 )
            | ~ ( latin @ SV2 @ SV18 @ SY109 )
            | ! [SY110: $i,SY111: $i] :
                ( ~ ( greek @ SY110 @ SY111 @ SV33 )
                | ~ ( latin @ SY110 @ SY111 @ SY109 )
                | ( eq @ SV2 @ SY110 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[84]) ).

thf(100,plain,
    ! [SV19: $i,SV4: $i] :
      ( ( ( ~ ( eq @ SV4 @ SV19 ) )
        = $true )
      | ( ( eq @ SV19 @ SV4 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[85]) ).

thf(101,plain,
    ! [SV34: $i,SV20: $i,SV5: $i] :
      ( ( ~ ( latin @ SV5 @ SV20 @ SV34 )
        | ! [SY112: $i] :
            ( ~ ( latin @ SV5 @ SV20 @ SY112 )
            | ( eq @ SV34 @ SY112 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[86]) ).

thf(102,plain,
    ! [SV35: $i,SV21: $i,SV6: $i] :
      ( ( ~ ( latin @ SV6 @ SV21 @ SV35 )
        | ! [SY113: $i] :
            ( ~ ( latin @ SV6 @ SY113 @ SV35 )
            | ( eq @ SV21 @ SY113 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[87]) ).

thf(103,plain,
    ! [SV36: $i,SV22: $i,SV7: $i] :
      ( ( ~ ( latin @ SV7 @ SV22 @ SV36 )
        | ! [SY114: $i] :
            ( ~ ( latin @ SY114 @ SV22 @ SV36 )
            | ( eq @ SV7 @ SY114 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[88]) ).

thf(104,plain,
    ! [SV37: $i,SV23: $i,SV8: $i] :
      ( ( ~ ( greek @ SV8 @ SV23 @ SV37 )
        | ! [SY115: $i] :
            ( ~ ( greek @ SV8 @ SV23 @ SY115 )
            | ( eq @ SV37 @ SY115 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[89]) ).

thf(105,plain,
    ! [SV38: $i,SV24: $i,SV9: $i] :
      ( ( ~ ( greek @ SV9 @ SV24 @ SV38 )
        | ! [SY116: $i] :
            ( ~ ( greek @ SV9 @ SY116 @ SV38 )
            | ( eq @ SV24 @ SY116 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[90]) ).

thf(106,plain,
    ! [SV39: $i,SV25: $i,SV10: $i] :
      ( ( ~ ( greek @ SV10 @ SV25 @ SV39 )
        | ! [SY117: $i] :
            ( ~ ( greek @ SY117 @ SV25 @ SV39 )
            | ( eq @ SV10 @ SY117 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[91]) ).

thf(107,plain,
    ! [SV26: $i,SV11: $i] :
      ( ( ( latin @ SV11 @ SV26 @ p_1 )
        = $true )
      | ( ( latin @ SV11 @ SV26 @ p_2 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[92]) ).

thf(108,plain,
    ! [SV27: $i,SV12: $i] :
      ( ( ( latin @ SV12 @ p_1 @ SV27 )
        = $true )
      | ( ( latin @ SV12 @ p_2 @ SV27 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[93]) ).

thf(109,plain,
    ! [SV28: $i,SV13: $i] :
      ( ( ( latin @ p_1 @ SV13 @ SV28 )
        = $true )
      | ( ( latin @ p_2 @ SV13 @ SV28 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[94]) ).

thf(110,plain,
    ! [SV29: $i,SV14: $i] :
      ( ( ( greek @ SV14 @ SV29 @ p_1 )
        = $true )
      | ( ( greek @ SV14 @ SV29 @ p_2 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[95]) ).

thf(111,plain,
    ! [SV30: $i,SV15: $i] :
      ( ( ( greek @ SV15 @ p_1 @ SV30 )
        = $true )
      | ( ( greek @ SV15 @ p_2 @ SV30 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[96]) ).

thf(112,plain,
    ! [SV31: $i,SV16: $i] :
      ( ( ( greek @ p_1 @ SV16 @ SV31 )
        = $true )
      | ( ( greek @ p_2 @ SV16 @ SV31 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[97]) ).

thf(113,plain,
    ! [SV40: $i,SV32: $i,SV17: $i,SV1: $i] :
      ( ( ~ ( greek @ SV1 @ SV17 @ SV32 )
        | ~ ( latin @ SV1 @ SV17 @ SV40 )
        | ! [SY118: $i,SY119: $i] :
            ( ~ ( greek @ SY118 @ SY119 @ SV32 )
            | ~ ( latin @ SY118 @ SY119 @ SV40 )
            | ( eq @ SV17 @ SY119 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[98]) ).

thf(114,plain,
    ! [SV41: $i,SV33: $i,SV18: $i,SV2: $i] :
      ( ( ~ ( greek @ SV2 @ SV18 @ SV33 )
        | ~ ( latin @ SV2 @ SV18 @ SV41 )
        | ! [SY120: $i,SY121: $i] :
            ( ~ ( greek @ SY120 @ SY121 @ SV33 )
            | ~ ( latin @ SY120 @ SY121 @ SV41 )
            | ( eq @ SV2 @ SY120 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[99]) ).

thf(115,plain,
    ! [SV19: $i,SV4: $i] :
      ( ( ( eq @ SV4 @ SV19 )
        = $false )
      | ( ( eq @ SV19 @ SV4 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[100]) ).

thf(116,plain,
    ! [SV34: $i,SV20: $i,SV5: $i] :
      ( ( ( ~ ( latin @ SV5 @ SV20 @ SV34 ) )
        = $true )
      | ( ( ! [SY112: $i] :
              ( ~ ( latin @ SV5 @ SV20 @ SY112 )
              | ( eq @ SV34 @ SY112 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[101]) ).

thf(117,plain,
    ! [SV35: $i,SV21: $i,SV6: $i] :
      ( ( ( ~ ( latin @ SV6 @ SV21 @ SV35 ) )
        = $true )
      | ( ( ! [SY113: $i] :
              ( ~ ( latin @ SV6 @ SY113 @ SV35 )
              | ( eq @ SV21 @ SY113 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[102]) ).

thf(118,plain,
    ! [SV36: $i,SV22: $i,SV7: $i] :
      ( ( ( ~ ( latin @ SV7 @ SV22 @ SV36 ) )
        = $true )
      | ( ( ! [SY114: $i] :
              ( ~ ( latin @ SY114 @ SV22 @ SV36 )
              | ( eq @ SV7 @ SY114 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[103]) ).

thf(119,plain,
    ! [SV37: $i,SV23: $i,SV8: $i] :
      ( ( ( ~ ( greek @ SV8 @ SV23 @ SV37 ) )
        = $true )
      | ( ( ! [SY115: $i] :
              ( ~ ( greek @ SV8 @ SV23 @ SY115 )
              | ( eq @ SV37 @ SY115 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[104]) ).

thf(120,plain,
    ! [SV38: $i,SV24: $i,SV9: $i] :
      ( ( ( ~ ( greek @ SV9 @ SV24 @ SV38 ) )
        = $true )
      | ( ( ! [SY116: $i] :
              ( ~ ( greek @ SV9 @ SY116 @ SV38 )
              | ( eq @ SV24 @ SY116 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[105]) ).

thf(121,plain,
    ! [SV39: $i,SV25: $i,SV10: $i] :
      ( ( ( ~ ( greek @ SV10 @ SV25 @ SV39 ) )
        = $true )
      | ( ( ! [SY117: $i] :
              ( ~ ( greek @ SY117 @ SV25 @ SV39 )
              | ( eq @ SV10 @ SY117 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[106]) ).

thf(122,plain,
    ! [SV40: $i,SV32: $i,SV17: $i,SV1: $i] :
      ( ( ( ~ ( greek @ SV1 @ SV17 @ SV32 ) )
        = $true )
      | ( ( ~ ( latin @ SV1 @ SV17 @ SV40 )
          | ! [SY118: $i,SY119: $i] :
              ( ~ ( greek @ SY118 @ SY119 @ SV32 )
              | ~ ( latin @ SY118 @ SY119 @ SV40 )
              | ( eq @ SV17 @ SY119 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[113]) ).

thf(123,plain,
    ! [SV41: $i,SV33: $i,SV18: $i,SV2: $i] :
      ( ( ( ~ ( greek @ SV2 @ SV18 @ SV33 ) )
        = $true )
      | ( ( ~ ( latin @ SV2 @ SV18 @ SV41 )
          | ! [SY120: $i,SY121: $i] :
              ( ~ ( greek @ SY120 @ SY121 @ SV33 )
              | ~ ( latin @ SY120 @ SY121 @ SV41 )
              | ( eq @ SV2 @ SY120 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[114]) ).

thf(124,plain,
    ! [SV34: $i,SV20: $i,SV5: $i] :
      ( ( ( latin @ SV5 @ SV20 @ SV34 )
        = $false )
      | ( ( ! [SY112: $i] :
              ( ~ ( latin @ SV5 @ SV20 @ SY112 )
              | ( eq @ SV34 @ SY112 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[116]) ).

thf(125,plain,
    ! [SV35: $i,SV21: $i,SV6: $i] :
      ( ( ( latin @ SV6 @ SV21 @ SV35 )
        = $false )
      | ( ( ! [SY113: $i] :
              ( ~ ( latin @ SV6 @ SY113 @ SV35 )
              | ( eq @ SV21 @ SY113 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[117]) ).

thf(126,plain,
    ! [SV36: $i,SV22: $i,SV7: $i] :
      ( ( ( latin @ SV7 @ SV22 @ SV36 )
        = $false )
      | ( ( ! [SY114: $i] :
              ( ~ ( latin @ SY114 @ SV22 @ SV36 )
              | ( eq @ SV7 @ SY114 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[118]) ).

thf(127,plain,
    ! [SV37: $i,SV23: $i,SV8: $i] :
      ( ( ( greek @ SV8 @ SV23 @ SV37 )
        = $false )
      | ( ( ! [SY115: $i] :
              ( ~ ( greek @ SV8 @ SV23 @ SY115 )
              | ( eq @ SV37 @ SY115 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[119]) ).

thf(128,plain,
    ! [SV38: $i,SV24: $i,SV9: $i] :
      ( ( ( greek @ SV9 @ SV24 @ SV38 )
        = $false )
      | ( ( ! [SY116: $i] :
              ( ~ ( greek @ SV9 @ SY116 @ SV38 )
              | ( eq @ SV24 @ SY116 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[120]) ).

thf(129,plain,
    ! [SV39: $i,SV25: $i,SV10: $i] :
      ( ( ( greek @ SV10 @ SV25 @ SV39 )
        = $false )
      | ( ( ! [SY117: $i] :
              ( ~ ( greek @ SY117 @ SV25 @ SV39 )
              | ( eq @ SV10 @ SY117 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[121]) ).

thf(130,plain,
    ! [SV40: $i,SV32: $i,SV17: $i,SV1: $i] :
      ( ( ( greek @ SV1 @ SV17 @ SV32 )
        = $false )
      | ( ( ~ ( latin @ SV1 @ SV17 @ SV40 )
          | ! [SY118: $i,SY119: $i] :
              ( ~ ( greek @ SY118 @ SY119 @ SV32 )
              | ~ ( latin @ SY118 @ SY119 @ SV40 )
              | ( eq @ SV17 @ SY119 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[122]) ).

thf(131,plain,
    ! [SV41: $i,SV33: $i,SV18: $i,SV2: $i] :
      ( ( ( greek @ SV2 @ SV18 @ SV33 )
        = $false )
      | ( ( ~ ( latin @ SV2 @ SV18 @ SV41 )
          | ! [SY120: $i,SY121: $i] :
              ( ~ ( greek @ SY120 @ SY121 @ SV33 )
              | ~ ( latin @ SY120 @ SY121 @ SV41 )
              | ( eq @ SV2 @ SY120 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[123]) ).

thf(132,plain,
    ! [SV34: $i,SV42: $i,SV20: $i,SV5: $i] :
      ( ( ( ~ ( latin @ SV5 @ SV20 @ SV42 )
          | ( eq @ SV34 @ SV42 ) )
        = $true )
      | ( ( latin @ SV5 @ SV20 @ SV34 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[124]) ).

thf(133,plain,
    ! [SV21: $i,SV35: $i,SV43: $i,SV6: $i] :
      ( ( ( ~ ( latin @ SV6 @ SV43 @ SV35 )
          | ( eq @ SV21 @ SV43 ) )
        = $true )
      | ( ( latin @ SV6 @ SV21 @ SV35 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[125]) ).

thf(134,plain,
    ! [SV7: $i,SV36: $i,SV22: $i,SV44: $i] :
      ( ( ( ~ ( latin @ SV44 @ SV22 @ SV36 )
          | ( eq @ SV7 @ SV44 ) )
        = $true )
      | ( ( latin @ SV7 @ SV22 @ SV36 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[126]) ).

thf(135,plain,
    ! [SV37: $i,SV45: $i,SV23: $i,SV8: $i] :
      ( ( ( ~ ( greek @ SV8 @ SV23 @ SV45 )
          | ( eq @ SV37 @ SV45 ) )
        = $true )
      | ( ( greek @ SV8 @ SV23 @ SV37 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[127]) ).

thf(136,plain,
    ! [SV24: $i,SV38: $i,SV46: $i,SV9: $i] :
      ( ( ( ~ ( greek @ SV9 @ SV46 @ SV38 )
          | ( eq @ SV24 @ SV46 ) )
        = $true )
      | ( ( greek @ SV9 @ SV24 @ SV38 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[128]) ).

thf(137,plain,
    ! [SV10: $i,SV39: $i,SV25: $i,SV47: $i] :
      ( ( ( ~ ( greek @ SV47 @ SV25 @ SV39 )
          | ( eq @ SV10 @ SV47 ) )
        = $true )
      | ( ( greek @ SV10 @ SV25 @ SV39 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[129]) ).

thf(138,plain,
    ! [SV32: $i,SV40: $i,SV17: $i,SV1: $i] :
      ( ( ( ~ ( latin @ SV1 @ SV17 @ SV40 ) )
        = $true )
      | ( ( ! [SY118: $i,SY119: $i] :
              ( ~ ( greek @ SY118 @ SY119 @ SV32 )
              | ~ ( latin @ SY118 @ SY119 @ SV40 )
              | ( eq @ SV17 @ SY119 ) ) )
        = $true )
      | ( ( greek @ SV1 @ SV17 @ SV32 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[130]) ).

thf(139,plain,
    ! [SV33: $i,SV41: $i,SV18: $i,SV2: $i] :
      ( ( ( ~ ( latin @ SV2 @ SV18 @ SV41 ) )
        = $true )
      | ( ( ! [SY120: $i,SY121: $i] :
              ( ~ ( greek @ SY120 @ SY121 @ SV33 )
              | ~ ( latin @ SY120 @ SY121 @ SV41 )
              | ( eq @ SV2 @ SY120 ) ) )
        = $true )
      | ( ( greek @ SV2 @ SV18 @ SV33 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[131]) ).

thf(140,plain,
    ! [SV34: $i,SV42: $i,SV20: $i,SV5: $i] :
      ( ( ( ~ ( latin @ SV5 @ SV20 @ SV42 ) )
        = $true )
      | ( ( eq @ SV34 @ SV42 )
        = $true )
      | ( ( latin @ SV5 @ SV20 @ SV34 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[132]) ).

thf(141,plain,
    ! [SV21: $i,SV35: $i,SV43: $i,SV6: $i] :
      ( ( ( ~ ( latin @ SV6 @ SV43 @ SV35 ) )
        = $true )
      | ( ( eq @ SV21 @ SV43 )
        = $true )
      | ( ( latin @ SV6 @ SV21 @ SV35 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[133]) ).

thf(142,plain,
    ! [SV7: $i,SV36: $i,SV22: $i,SV44: $i] :
      ( ( ( ~ ( latin @ SV44 @ SV22 @ SV36 ) )
        = $true )
      | ( ( eq @ SV7 @ SV44 )
        = $true )
      | ( ( latin @ SV7 @ SV22 @ SV36 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[134]) ).

thf(143,plain,
    ! [SV37: $i,SV45: $i,SV23: $i,SV8: $i] :
      ( ( ( ~ ( greek @ SV8 @ SV23 @ SV45 ) )
        = $true )
      | ( ( eq @ SV37 @ SV45 )
        = $true )
      | ( ( greek @ SV8 @ SV23 @ SV37 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[135]) ).

thf(144,plain,
    ! [SV24: $i,SV38: $i,SV46: $i,SV9: $i] :
      ( ( ( ~ ( greek @ SV9 @ SV46 @ SV38 ) )
        = $true )
      | ( ( eq @ SV24 @ SV46 )
        = $true )
      | ( ( greek @ SV9 @ SV24 @ SV38 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[136]) ).

thf(145,plain,
    ! [SV10: $i,SV39: $i,SV25: $i,SV47: $i] :
      ( ( ( ~ ( greek @ SV47 @ SV25 @ SV39 ) )
        = $true )
      | ( ( eq @ SV10 @ SV47 )
        = $true )
      | ( ( greek @ SV10 @ SV25 @ SV39 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[137]) ).

thf(146,plain,
    ! [SV32: $i,SV40: $i,SV17: $i,SV1: $i] :
      ( ( ( latin @ SV1 @ SV17 @ SV40 )
        = $false )
      | ( ( ! [SY118: $i,SY119: $i] :
              ( ~ ( greek @ SY118 @ SY119 @ SV32 )
              | ~ ( latin @ SY118 @ SY119 @ SV40 )
              | ( eq @ SV17 @ SY119 ) ) )
        = $true )
      | ( ( greek @ SV1 @ SV17 @ SV32 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[138]) ).

thf(147,plain,
    ! [SV33: $i,SV41: $i,SV18: $i,SV2: $i] :
      ( ( ( latin @ SV2 @ SV18 @ SV41 )
        = $false )
      | ( ( ! [SY120: $i,SY121: $i] :
              ( ~ ( greek @ SY120 @ SY121 @ SV33 )
              | ~ ( latin @ SY120 @ SY121 @ SV41 )
              | ( eq @ SV2 @ SY120 ) ) )
        = $true )
      | ( ( greek @ SV2 @ SV18 @ SV33 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[139]) ).

thf(148,plain,
    ! [SV34: $i,SV42: $i,SV20: $i,SV5: $i] :
      ( ( ( latin @ SV5 @ SV20 @ SV42 )
        = $false )
      | ( ( eq @ SV34 @ SV42 )
        = $true )
      | ( ( latin @ SV5 @ SV20 @ SV34 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[140]) ).

thf(149,plain,
    ! [SV21: $i,SV35: $i,SV43: $i,SV6: $i] :
      ( ( ( latin @ SV6 @ SV43 @ SV35 )
        = $false )
      | ( ( eq @ SV21 @ SV43 )
        = $true )
      | ( ( latin @ SV6 @ SV21 @ SV35 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[141]) ).

thf(150,plain,
    ! [SV7: $i,SV36: $i,SV22: $i,SV44: $i] :
      ( ( ( latin @ SV44 @ SV22 @ SV36 )
        = $false )
      | ( ( eq @ SV7 @ SV44 )
        = $true )
      | ( ( latin @ SV7 @ SV22 @ SV36 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[142]) ).

thf(151,plain,
    ! [SV37: $i,SV45: $i,SV23: $i,SV8: $i] :
      ( ( ( greek @ SV8 @ SV23 @ SV45 )
        = $false )
      | ( ( eq @ SV37 @ SV45 )
        = $true )
      | ( ( greek @ SV8 @ SV23 @ SV37 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[143]) ).

thf(152,plain,
    ! [SV24: $i,SV38: $i,SV46: $i,SV9: $i] :
      ( ( ( greek @ SV9 @ SV46 @ SV38 )
        = $false )
      | ( ( eq @ SV24 @ SV46 )
        = $true )
      | ( ( greek @ SV9 @ SV24 @ SV38 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[144]) ).

thf(153,plain,
    ! [SV10: $i,SV39: $i,SV25: $i,SV47: $i] :
      ( ( ( greek @ SV47 @ SV25 @ SV39 )
        = $false )
      | ( ( eq @ SV10 @ SV47 )
        = $true )
      | ( ( greek @ SV10 @ SV25 @ SV39 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[145]) ).

thf(154,plain,
    ! [SV1: $i,SV17: $i,SV40: $i,SV32: $i,SV48: $i] :
      ( ( ( ! [SY122: $i] :
              ( ~ ( greek @ SV48 @ SY122 @ SV32 )
              | ~ ( latin @ SV48 @ SY122 @ SV40 )
              | ( eq @ SV17 @ SY122 ) ) )
        = $true )
      | ( ( latin @ SV1 @ SV17 @ SV40 )
        = $false )
      | ( ( greek @ SV1 @ SV17 @ SV32 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[146]) ).

thf(155,plain,
    ! [SV18: $i,SV2: $i,SV41: $i,SV33: $i,SV49: $i] :
      ( ( ( ! [SY123: $i] :
              ( ~ ( greek @ SV49 @ SY123 @ SV33 )
              | ~ ( latin @ SV49 @ SY123 @ SV41 )
              | ( eq @ SV2 @ SV49 ) ) )
        = $true )
      | ( ( latin @ SV2 @ SV18 @ SV41 )
        = $false )
      | ( ( greek @ SV2 @ SV18 @ SV33 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[147]) ).

thf(156,plain,
    ! [SV1: $i,SV17: $i,SV40: $i,SV32: $i,SV50: $i,SV48: $i] :
      ( ( ( ~ ( greek @ SV48 @ SV50 @ SV32 )
          | ~ ( latin @ SV48 @ SV50 @ SV40 )
          | ( eq @ SV17 @ SV50 ) )
        = $true )
      | ( ( latin @ SV1 @ SV17 @ SV40 )
        = $false )
      | ( ( greek @ SV1 @ SV17 @ SV32 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[154]) ).

thf(157,plain,
    ! [SV18: $i,SV2: $i,SV41: $i,SV33: $i,SV51: $i,SV49: $i] :
      ( ( ( ~ ( greek @ SV49 @ SV51 @ SV33 )
          | ~ ( latin @ SV49 @ SV51 @ SV41 )
          | ( eq @ SV2 @ SV49 ) )
        = $true )
      | ( ( latin @ SV2 @ SV18 @ SV41 )
        = $false )
      | ( ( greek @ SV2 @ SV18 @ SV33 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[155]) ).

thf(158,plain,
    ! [SV1: $i,SV17: $i,SV40: $i,SV32: $i,SV50: $i,SV48: $i] :
      ( ( ( ~ ( greek @ SV48 @ SV50 @ SV32 ) )
        = $true )
      | ( ( ~ ( latin @ SV48 @ SV50 @ SV40 )
          | ( eq @ SV17 @ SV50 ) )
        = $true )
      | ( ( latin @ SV1 @ SV17 @ SV40 )
        = $false )
      | ( ( greek @ SV1 @ SV17 @ SV32 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[156]) ).

thf(159,plain,
    ! [SV18: $i,SV2: $i,SV41: $i,SV33: $i,SV51: $i,SV49: $i] :
      ( ( ( ~ ( greek @ SV49 @ SV51 @ SV33 ) )
        = $true )
      | ( ( ~ ( latin @ SV49 @ SV51 @ SV41 )
          | ( eq @ SV2 @ SV49 ) )
        = $true )
      | ( ( latin @ SV2 @ SV18 @ SV41 )
        = $false )
      | ( ( greek @ SV2 @ SV18 @ SV33 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[157]) ).

thf(160,plain,
    ! [SV1: $i,SV17: $i,SV40: $i,SV32: $i,SV50: $i,SV48: $i] :
      ( ( ( greek @ SV48 @ SV50 @ SV32 )
        = $false )
      | ( ( ~ ( latin @ SV48 @ SV50 @ SV40 )
          | ( eq @ SV17 @ SV50 ) )
        = $true )
      | ( ( latin @ SV1 @ SV17 @ SV40 )
        = $false )
      | ( ( greek @ SV1 @ SV17 @ SV32 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[158]) ).

thf(161,plain,
    ! [SV18: $i,SV2: $i,SV41: $i,SV33: $i,SV51: $i,SV49: $i] :
      ( ( ( greek @ SV49 @ SV51 @ SV33 )
        = $false )
      | ( ( ~ ( latin @ SV49 @ SV51 @ SV41 )
          | ( eq @ SV2 @ SV49 ) )
        = $true )
      | ( ( latin @ SV2 @ SV18 @ SV41 )
        = $false )
      | ( ( greek @ SV2 @ SV18 @ SV33 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[159]) ).

thf(162,plain,
    ! [SV1: $i,SV32: $i,SV17: $i,SV40: $i,SV50: $i,SV48: $i] :
      ( ( ( ~ ( latin @ SV48 @ SV50 @ SV40 ) )
        = $true )
      | ( ( eq @ SV17 @ SV50 )
        = $true )
      | ( ( greek @ SV48 @ SV50 @ SV32 )
        = $false )
      | ( ( latin @ SV1 @ SV17 @ SV40 )
        = $false )
      | ( ( greek @ SV1 @ SV17 @ SV32 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[160]) ).

thf(163,plain,
    ! [SV18: $i,SV33: $i,SV2: $i,SV41: $i,SV51: $i,SV49: $i] :
      ( ( ( ~ ( latin @ SV49 @ SV51 @ SV41 ) )
        = $true )
      | ( ( eq @ SV2 @ SV49 )
        = $true )
      | ( ( greek @ SV49 @ SV51 @ SV33 )
        = $false )
      | ( ( latin @ SV2 @ SV18 @ SV41 )
        = $false )
      | ( ( greek @ SV2 @ SV18 @ SV33 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[161]) ).

thf(164,plain,
    ! [SV1: $i,SV32: $i,SV17: $i,SV40: $i,SV50: $i,SV48: $i] :
      ( ( ( latin @ SV48 @ SV50 @ SV40 )
        = $false )
      | ( ( eq @ SV17 @ SV50 )
        = $true )
      | ( ( greek @ SV48 @ SV50 @ SV32 )
        = $false )
      | ( ( latin @ SV1 @ SV17 @ SV40 )
        = $false )
      | ( ( greek @ SV1 @ SV17 @ SV32 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[162]) ).

thf(165,plain,
    ! [SV18: $i,SV33: $i,SV2: $i,SV41: $i,SV51: $i,SV49: $i] :
      ( ( ( latin @ SV49 @ SV51 @ SV41 )
        = $false )
      | ( ( eq @ SV2 @ SV49 )
        = $true )
      | ( ( greek @ SV49 @ SV51 @ SV33 )
        = $false )
      | ( ( latin @ SV2 @ SV18 @ SV41 )
        = $false )
      | ( ( greek @ SV2 @ SV18 @ SV33 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[163]) ).

thf(166,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[67,165,164,153,152,151,150,149,148,115,112,111,110,109,108,107,82,68]) ).

thf(167,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[166]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.10  % Problem  : MSC008-1.002 : TPTP v8.1.2. Released v1.0.0.
% 0.03/0.11  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.11/0.32  % Computer : n023.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit : 300
% 0.11/0.32  % WCLimit  : 300
% 0.11/0.33  % DateTime : Mon May 22 17:01:12 EDT 2023
% 0.11/0.33  % CPUTime  : 
% 0.18/0.35  
% 0.18/0.35   No.of.Axioms: 17
% 0.18/0.35  
% 0.18/0.35   Length.of.Defs: 0
% 0.18/0.35  
% 0.18/0.35   Contains.Choice.Funs: false
% 0.18/0.36  (rf:0,axioms:17,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:19,loop_count:0,foatp_calls:0,translation:fof_full)..........
% 1.06/1.24  
% 1.06/1.24  ********************************
% 1.06/1.24  *   All subproblems solved!    *
% 1.06/1.24  ********************************
% 1.06/1.24  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:17,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:166,loop_count:0,foatp_calls:1,translation:fof_full)
% 1.06/1.25  
% 1.06/1.25  %**** Beginning of derivation protocol ****
% 1.06/1.25  % SZS output start CNFRefutation
% See solution above
% 1.06/1.25  
% 1.06/1.25  %**** End of derivation protocol ****
% 1.06/1.25  %**** no. of clauses in derivation: 167 ****
% 1.06/1.25  %**** clause counter: 166 ****
% 1.06/1.25  
% 1.06/1.25  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:17,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:166,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------